These notes provide a comprehensive guide to solving linear equations using the substitution method, and would be a helpful resource for students studying this topic.
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The notes provide several examples with detailed explanations on how to apply the substitution method to solve linear equations.
The examples include equations with coefficients, constants, and variables, and demonstrate how to rearrange the equations to solve for the variables.
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(1)/(x^(2)-6x)=(x)/(x^(2)-36)+2 Solve for x Please and thank you yall r life savers <3
Answer:
you need an equally
Step-by-step explanation:
Find the value of X tell whether the side links from a pen Taghreed triple number 42
The value of x is given as 9.8
How to solve for xWe have to solve for X using the Pythagorean theorem
The Pythagorean theorem is a mathematical formula that relates to the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other words:
c² = a² + b²
Where:
c is the length of the hypotenuse
a and b are the lengths of the other two sides
14² = x² + 10²
196 = x² + 100
196 - 100 = x²
x = √96
x = 9.8
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if a sample of shoppers showed stating that the supermarket brand was as good as the national brand, what is the p-value (to decimals)?
The p-value is 0.046, or 4.6% if a sample of shoppers showed stating that the supermarket brand was as good as the national brand.
To calculate the p-value, we use null and alternative hypotheses, as well as the test statistic and its distribution under the null hypothesis.
By the null hypothesis, we can say that supermarket brands are as good as national brands, and by the alternative hypothesis, we can say that supermarket brands are not as good as national brands.
This hypothesis can be tested by performing a two-tailed z-test for proportions.
In a sample of n shoppers, say that x shoppers say that supermarket brands are as good as domestic brands. The sample percentage can be calculated as follows:
p hat = x/n
in the null hypothesis, the sample proportion is equal to the hypothesized proportion, that is 0.5
The test statistic for a two-sided z-test for proportions is given by:
z = (p-hat - p0) / sqrt(p0(1-p0)/n)
where p0 is the hypothesized proportion under the null hypothesis.
In this case, we have:
p-hat = 0.5
p0 = 0.5
n = sample size
The null hypothesis states that the supermarket brand is as good as the national brand, so we would expect the proportion of shoppers who state this to be 0.5.
If the test statistic z falls in the rejection region (i.e., if |z| > 1.96 for a significance level of 0.05),
we would reject the null hypothesis and conclude that there is evidence to suggest that the supermarket brand is not as good as the national brand.
If the test statistic falls in the non-rejection region (i.e., if |z| <= 1.96 for a significance level of 0.05),
we would fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that the supermarket brand is not as good as the national brand.
To calculate the p-value, we need to find the probability of getting a test statistic as extreme or more extreme than the one we observed, assuming the null hypothesis is true.
For a two-tailed test, the p-value is twice the observed area of the tails above the absolute value of the test statistic.
Assuming the sample size is large enough, the distribution of the test statistic can be approximated as a standard normal distribution under the null hypothesis.
Suppose in a sample of 100 shoppers, 50 said that supermarket brands are as good as domestic brands. after that:
p hat = 0.5
p0 = 0.5
n=100
The test statistic is:
z = (p hat - p0) / sqrt(p0(1-p0)/n) = 0 / sqrt(0.5 * 0.5 / 100) = 0
The p-value is the probability that the test statistic is extreme or more extreme than 0. This is the probability of getting further away from the 50/100 ratio or 0.5 in either direction.
p-value = P(p hat <= 0.4 or p hat >= 0.6) = 2 * P(p hat <= 0.4) = 2 * P(Z <= ( 0.4 - 0.5) / sqrt (0.5 * 0.5 / 100) ) = 2 * P(Z <= -2) ≈ 0.046
where Z is a standard normal random variable.
Therefore, the p-value is approximately 0.046, or 4.6%.
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The value of a brand new car is $27,000 and the value depreciates 23% every year. Write a function to represent the value of the car after t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent.
[tex]27000(0.77^t)[/tex]and the percentage rate of change per month is 3.13%.
What is the percentage rate?
The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, home loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.
Here, we have
The value of a brand-new car is $27,000 and the value depreciates 23% every year.
we have to write a function to represent the value of the car after t years.
The coefficient of the function is 0.77
To find the rate of change per month, we need to find the rate at which the value of the car is decreasing each month.
we can use the rule of 72
72/r = t where r is the rate of change per month
r = 72/t
[tex]r = 72/23 = 3.13[/tex] (approx)
So the percentage rate of change per month is 3.13%
Hence, The function to represent the value of the car after t years is V(t) = [tex]27000(0.77^t)[/tex] and the percentage rate of change per month is 3.13%.
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For Assessment 2 you are required to conduct a research project where you collect Data, Analysis and Present.
For your Assessment 2 your Presentation must include -
1. What your study of data is on
2. A prediction of what you think the data will reveal.
3. How you collected your data
4. A table of figures – the data you have collected
5. The medium, mean and mode of your data.
6. A graph of your data – you choose the type (pie/line). Preferably created digitally.
7. A written analysis of your graph using graph language
8. What you found in your study; how close you were with your prediction?
PLS HELP!!
The findings of the research project suggest that regular exercise can be an effective tool for managing stress in university students.
What would be the research project?A sample research project is given below:
Study of Data: The impact of exercise on stress levels in university students
Prediction: We predict that there will be a significant decrease in stress levels following a four-week exercise program.
Data Collection: Participants were recruited through flyers and social media. They were asked to complete a pre-test stress survey before beginning the exercise program, and a post-test stress survey after completing the program. The exercise program consisted of a combination of cardiovascular and resistance training, meeting three times a week for four weeks.
Table of Figures:
Participant Pre-Test Stress Score Post-Test Stress Score
1 32 20
2 28 17
3 36 25
... ... ...
30 41 22
Measures of Central Tendency:
Median Pre-Test Stress Score: 34Median Post-Test Stress Score: 21Mean Pre-Test Stress Score: 33.7Mean Post-Test Stress Score: 22.5Mode Pre-Test Stress Score: 32Mode Post-Test Stress Score: 22Graph: Line graph showing the change in stress levels over time, with pre-test scores in blue and post-test scores in red.
Written Analysis: The line graph shows a consistent decrease in stress levels across all participants following the four-week exercise program. The majority of participants showed a decrease in stress levels of 10 or more points, indicating a significant reduction in stress. There is a clear pattern of improvement in stress levels over time, with the post-test scores consistently lower than the pre-test scores.
Findings: Our study found a significant decrease in stress levels following a four-week exercise program in university students. Our prediction was accurate, as we anticipated a decrease in stress levels.
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What is the volume
of a pyramid with
sides of 22 inches and
30 inches, and a
of height of 15 inches?
Answer:
Base length=22
width=30
height=15
volume of pyramid= Lxwxh/3
=22x 30x 15/3 =3300in^3.
For each of the figures write an absolute value equation that has the following solution set.
The absolute value equation that has the solution set with digits -18, 0, and X on a number line is :
|X| = X if X ≥ 0
|X| = -X if X < 0
What do you mean by term Equation?An equation is a mathematical statement that shows the equality of two expressions. It typically includes one or more variables (represented by letters) and may also include constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
If the solution set for the absolute value equation has digits -18, 0, and X on a number line, then the equation must have two separate cases: one where X is positive and one where X is negative. We can write the absolute value equation as:
|X| = X for X ≥ 0
|X| = -X for X < 0
To include the values -18 and 0 in the solution set, we need to check each case separately:
|X| = X if X is greater than 0 or zero. The equation X = a must therefore be resolved, where an is either -18 or 0. As X 0 is satisfied by only one value in the solution set, the case's solution is X = 0.
Example 2: X < 0
When X is negative, |X| equals -X. So, we must find a, where an is either -18 or 0, to solve the equation -X = a. This case's solution is X = 18, as it is the only value in the solution set that satisfies the condition X 0.
As a result, the absolute value equation whose answer is represented by the numbers -18, 0 and X on a number line is:
|X| = X if X ≥ 0
|X| = -X if X < 0
or
|X| = 0 if X = 0
|X| = 18 if X < 0
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according to the text, 69 percent of all 6- to 11-year-olds in the united states: please choose the correct answer from the following choices, and then select the submit answer button. answer choices are harmonious and stable. are chronically poor. live with one parent. live with two parents.
Two parents are present in 69% of all families with children ages six to eleven. Option d is correct.
Option d is the correct choice, which states that 69 percent of all families with children aged six to 11 have two parents. This information is supported by various studies and statistics, which have consistently shown that the majority of families in the United States consist of two-parent households. While single-parent families do exist, they are less common than families with two parents.
This information is important in understanding the dynamics and structure of families in the US, as well as in developing policies and programs that support and strengthen families.
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--The complete question is, According to your text, 69 percent of all families with children aged six to 11:
a) are harmonious and stable.
b) have one parent.
c) are chronically poor.
d) have two parents.
Link to the text is, open.maricopa.edu/devpsych/chapter/chapter-9-early-adulthood/--
Solve for x. Round your answer to the nearest tenth if necessary. Figures are not
necessarily drawn to scale.
R
61°
55
47
52°
P
67⁰
T
67⁰
X
52%
61°
U
S
44
Given the similar triangles, Note that x = 51.2
What is the explanation for the above response?Since both triangles are proportional,
64/60 = x/48
To solve for x in the equation:
64/60 = x/48
We can cross-multiply to get rid of the fractions:
64 * 48 = 60 * x
3072 = 60x
Finally, we isolate x by dividing both sides by 60:
x = 3072/60 = 51.2
Therefore, the solution is:
x = 51.2
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what’s the answer????
Answer:
The vertex of the quadratic function f(x) = -2x^2 + 8x is (2, 8).
Step-by-step explanation:
To find the vertex of the quadratic function f(x) = -2x^2 + 8x, we first need to find the x-coordinate of the vertex using the formula:
x = -b / 2a
where a = -2 and b = 8. Substituting these values, we get:
x = -8 / 2(-2) = 2
Now, to find the y-coordinate of the vertex, we can substitute this value of x back into the equation: f(2) = -2(2)^2 + 8(2) = 8
Verify that the following identity is true. You must show all work to receive credit! (1 - cos a) (1 + cot? a) = 1
Answer:
To verify the given identity:
(1 - cos a) (1 + cot a)
= (1 - cos a) (1 + cos a / sin a) [since cot a = cos a / sin a]
= 1 - cos^2 a / sin a + cos a - cos^2 a / sin a
= 1 - (cos^2 a + cos^2 a) / sin a + cos a
= 1 - 2 cos^2 a / sin a + cos a
= 1 - 2 (1 - sin^2 a) / sin a + cos a [since cos^2 a = 1 - sin^2 a]
= 1 - 2 / sin a + 2 sin a / sin a + cos a
= 1 - 2 / sin a + 2 + cos a
= 1 + 2 (1 - sin a) / sin a
= 1 + 2 cos^2 a / sin a
= 1 + 2 cot^2 a
= (1 + cot^2 a) + 2 cot^2 a
= cosec^2 a + 2 cot^2 a
= 1 + cot^2 a [since cosec^2 a = 1 + cot^2 a]
Therefore, (1 - cos a) (1 + cot a) = 1 is true.
Given: w ∥ x and y is a transversal. prove: ∠3 and ∠5 are supplementary. parallel and diagonal lines w and x are cut by horizontal transversal y. on line w where it intersects with line y, 4 angles are created. labeled clockwise, from uppercase left, the angles are: 1, 3, 4, 2. on line x where it intersects with line y, 4 angles are created. labeled clockwise, from uppercase left, the angles are: 5, 7, 8, 6. use the drop-down menus to complete the proof. given that w ∥ x and y is a transversal, we know that ∠1 ≅∠5 by the . therefore, m∠1 = m ∠5 by the definition of congruent. we also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the . by the , m∠3 m ∠1 = 180. now we can substitute m∠5 for m∠1 to get m∠3 m∠5 = 180. therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary.
we use the definition of supplementary angles again to conclude that ∠3 and ∠5 are supplementary.
To prove that ∠3 and ∠5 are supplementary, we can use the following steps:
Given: w ∥ x and y is a transversal.
∠1 ≅ ∠5 by the corresponding angles postulate.
By definition, ∠3 and ∠1 are a linear pair, so they are supplementary.
Therefore, m∠3 + m∠1 = 180 by the definition of supplementary angles.
Substituting m∠5 for m∠1, we get m∠3 + m∠5 = 180.
Therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary.
In step 1, we use the corresponding angles postulate, which states that when two parallel lines are cut by a transversal, the pairs of corresponding angles are congruent. In step 2, we use the definition of a linear pair, which states that when two angles form a line, they are supplementary. In step 3, we use the definition of supplementary angles, which states that the sum of two supplementary angles is 180 degrees. In step 4, we substitute m∠5 for m∠1, since we know that ∠1 ≅ ∠5. Finally, in step 5, we use the definition of supplementary angles again to conclude that ∠3 and ∠5 are supplementary.
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Need HELP ASAP!!! RIGHT NOW!!!
The value of a brand new car is $27,000 and the value depreciates 23% every year. Write a function to represent the value of the car after t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent.
Answer and Explanation:
The value of a brand new car,
P
=
$
28000
The value depreciates every year,
r
=
19
%
Time,
t
=
1
4
Number of compounding period (Compounded quarterly),
n
=
4
Write a function to represent the value of the car after
t
years:
A
=
P
(
1
−
r
n
)
n
×
t
∴
A
=
28000
(
1
−
19
%
4
)
4
t
Let us evaluate the value of the car after one quarter:
A
=
28000
(
1
−
19
%
4
)
4
t
=
28000
(
1
−
19
100
4
)
4
×
1
4
=
28000
(
1
−
0.19
4
)
4
×
1
4
=
28000
(
1
−
0.19
4
)
1
=
28000
(
1
−
0.19
4
)
=
28000
(
1
−
0.0475
)
=
28000
(
0.9525
)
∴
A
=
26670
Therefore, the value of the car after one quarter is
$
26670
.
To calculate the percentage rate of change per quarter:
Percentage rate
=
P
−
A
P
×
100
%
=
28000
−
26670
28000
×
100
%
=
1330
28000
×
100
%
=
70
⋅
19
70
⋅
400
×
100
%
=
19
400
×
100
%
=
0.0475
×
100
%
∴
Percentage rate of change per quarter
=
4.75
%
Hence, the percentage rate of change per quarter is
4.75
%
.
2[tex]x^{2} =1[/tex]
Answer:
Step-by-step explanation:
x = [tex]+-\sqrt[]{\frac{1}{2} }[/tex]
the shape below is made of two rectangles below 9cm,5cm,8cm
and 5cm
The area of the shape made of two rectangles is 85 square cm.
To find the area of the shape made of two rectangles with dimensions 9cm, 5cm, 8cm, and 5cm, follow these.
As per the given information,
Rectangle 1 has dimensions 9cm and 5cm.
Rectangle 2 has dimensions 8cm and 5cm.
For calculating the area of each rectangle using the formula:
Area = length × width
[tex]{Area\: of\: Rectangle} _1[/tex] = 9cm × 5cm = 45 square cm
[tex]{Area of Rectangle}_ 2[/tex] = 8cm × 5cm = 40 square cm
Add the areas of both rectangles to find the total area of the shape.
Total Area = [tex]{Area\: of\: Rectangle} _1[/tex] + [tex]{Area\: of\: Rectangle} _2[/tex]
Total Area = 45 square cm + 40 square cm
Total Area = 85 square cm.
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Question: The shape below is made of two rectangles joined together. 5 cm 9 cm 8 cm 5 cm Find the total area of the shape.
Write a polynomial f(x) that satisfies the given conditions.
Polynomial of lowest degree with zeros of -4(multiplicity 1) 1( multiplicity 2)and with F(0)=-12
If -4 is a zero with multiplicity 1, then (x + 4) is a factor of the polynomial. Similarly, if 1 is a zero with multiplicity 2, then (x - 1)^2 is a factor of the polynomial. Therefore, we can write the polynomial in factored form as:
f(x) = a(x + 4)(x - 1)^2
where "a" is a constant that we need to determine.
To find "a", we use the fact that f(0) = -12. Substituting x = 0 into the equation above, we get:
f(0) = a(0 + 4)(0 - 1)^2
-12 = -4a
Solving for "a", we get:
a = 3
Therefore, the polynomial is:
f(x) = 3(x + 4)(x - 1)^2
Note that this polynomial has a zero at x = -4 (with multiplicity 1), a zero at x = 1 (with multiplicity 2), and f(0) = -12.
a line segment is divided so that the lesser part is to the greater part as the greater part is to the whole. if is the ratio of the lesser part to the greater part, then the value of
The problem involves a line segment divided into two parts in a specific ratio. The ratio of the length of the lesser part to the length of the greater part is found to be (√2 - 1).
Let the length of the whole line segment be x, and let y be the length of the greater part. Then the length of the lesser part is (x - y).
According to the problem statement, the ratio of the lesser part to the greater part is the same as the ratio of the greater part to the whole. Mathematically, we can write this as:
(x - y)/y = y/x
Simplifying this equation, we get:
x^2 - y^2 = y^2
x^2 = 2y^2
Taking the square root of both sides, we get:
x = y√2
Therefore, the value of the ratio of the lesser part to the greater part is:
(x - y)/y = (√2 - 1)
So, the answer will be (√2 - 1).
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which of the following is not a correct statement about the binomial and poisson distributions? group of answer choices when using the binomial distribution table, the number of trials must be greater than 30. the poisson distribution represents the random arrival of events per unit of time or space. only two outcomes are possible in a binomial situation. to use the poisson distribution tables, mu must be known or be able to be calculated.
The statement which is "The binomial distribution table, the number of trials must be greater than 30." is the not correct statement related to the binomial and Poisson distributions. Hence option a is the right choice.
a. "When using the binomial distribution table, the number of trials must be greater than 30"This is an incorrect statement.
There is no such rule stating that the number of trials must be greater than 30 for the binomial distribution.
b. "The Poisson distribution represents the random arrival of events per unit of time or space" This is the correct statement.
The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space, given a constant average rate of occurrence.
c. "Only two outcomes are possible in a binomial situation" This is correct statement.
A binomial distribution represents the number of successes in a fixed number of trials, each with only two possible outcomes (success or failure).
d. To use the Poisson distribution tables, mu must be known or be able to be calculated: This is correct.
In order to use the Poisson distribution tables, the mean number of events (represented by the symbol µ) must be known or calculable.
So, option a is right choice.
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Question :-
Which of the following is not a correct statement about the binomial and Poisson distributions?
a. When using the binomial distribution table, the number of trials must be greater than 30.
b. The Poisson distribution represents the random arrival of events per unit of time or space.
c. Only two outcomes are possible in a binomial situation.
d. To use the Poisson distribution tables, Mu must be known or be able to be calculated
Pleaseeeee helppp meee
Answer: The missing side e is approximately 21.1 units long. So, the correct answer is E. None of the above
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
the correct answer is: Wide Awake, with a median value of 4.5 gallons. Thus, option A is correct.
What is the medians?Based on the data given, the correct measure of center to determine which shop typically sells the most amount of coffee per hour would be the median.
Calculating the medians for both coffee shops:
For Coffee Ground:
[tex]1.5, 12, 11, 9.5[/tex] (sorted data)
Median [tex]= (11 + 12)/2 = 11.5[/tex]
For Wide Awake:
[tex]2.5, 18, 3, 6[/tex] (sorted data)
Median [tex]= (3 + 6)/2 = 4.5[/tex]
Comparing the medians, we can see that Wide Awake has a median value of 4.5 gallons, which is higher than the median value of 11.5 gallons for Coffee Ground.
Therefore, the correct answer is: Wide Awake, with a median value of [tex]4.5[/tex] gallons.
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Answer: Coffee Ground typically sells more coffee per hour than Wide Awake.
Step-by-step explanation:
Given that:
Coffee ground :
Hour 1: 1.5
Hour 2: 20
Hour 3: 3.5
Hour 4: 12
Hour 5: 2
Hour 6: 5
Hour 7: 11
Hour 8: 7
Hour 9: 2.5
We add up all of these numbers and divide by the total number of hours to find the mean:
(1.5 + 20 + 3.5 + 12 + 2 + 5 + 11 + 7 + 2.5) / 9 = 7.222
therefore mean is 7.2
Median:
Arranging them in Ascending or descending order, we get:
1.5,2,2.5,3.5,5,7,11,12,20
As we know, The median of discrete data is :
((n+1)/2)th element if the number of elements is odd
Average of (n/2) th and ((n+1)/2)th element if the number of elements is even. the value
Here the number of elements is odd, so the median is:
((n+1)/2)th =(9+1)/2 = 5th element
i.e., the median is 5.
Wide Awake:
Given that:
Hour 1: 2.5
Hour 2: 10
Hour 3: 4
Hour 4: 18
Hour 5: 4
Hour 6: 3
Hour 7: 6.5
Hour 8: 5
Hour 9: 15
We add up all of these numbers and divide by the total number of hours to find the mean:
(2.5 + 10 + 4 + 18 + 4 + 3 + 6.5 + 5 + 15) / 9 = 7.056
therefore mean is 7.1
Median:
Arranging them in Ascending or descending order, we get:
3,6.5,5,4,4,2.5,10,18,15
Here the number of elements is odd, so the median is:
((n+1)/2)th =(9+1)/2 = 5th element
i.e., the median is 4.
As we can observe, the mean and median of coffee ground is high.
So we can conclude that the Coffee Ground shop has sold more coffee.
Select all expressions that are equivalent to
0.75x + 0.25(x + 12.4) + (x – 2.1).
a.
x + 3.1 + x + 2.1
b.
x + 3.1 + x – 2.1
c.
2x + 1
d.
x + 1
Answer:
B and C are the answers according to the expression
Please help and show process for any of these questionss
Using equations,
8. The original dimensions of the rectangle are:
Length = 6m and Width = 2m.
9. The meter contains the following:
Value of nickels = 0.63
Value of dime = 2.26
Value of quarters = 0.21
10. Volume of the sphere is V. So, the value of r will be:
r = ∛ (3v/4π)
11. Solving for the linear equation we can get the value of m = -1
Define equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation.
In the question,
1. Let the length of the rectangle be = x.
Let the width of the rectangle be = w.
Given,
l = 3w
When the width is increased by 4 meters, (w + 4) meters is the width now.
Then, the rectangle becomes a square.
That means length and width are equal.
l = w+4
Using l from the 1st equation,
3w = w + 4
Subtracting w from both sides,
⇒ 3w - w = 4
⇒ 2w = 4
Diving both sides by 2,
⇒ w = 2 meters.
We know, l = 3w
l = 3 × 2
l = 6 meters.
2. Here,
Let nickels be n.
Let dimes be d.
Let quarters be q.
Given,
Triple the number of quarters as nickels, so:
3q = n
Solving this for q,
q = n/3
Dimes is one than double the times of nickels, so:
d = 2n + 1
Total value of coins = $3.10
So, n + d + q = 3.10
Substituting the value of q and d,
⇒ n + 2n + 1 + n/3 = 3.10
⇒ 3n + n/3 = 3.10 - 1
⇒ (9n+n)/3 = 2.10
⇒ 10n = 6.3
⇒ n =0.63.
We can now find,
d = 2n + 1
= 2 × 0.63 + 1
= 1.26 + 1
= 2.26
q = n/3
= 0.63/3
= 0.21
3. Given,
Volume of sphere,
V = 4/3 × π × r³
Solving for r,
Multiply 3/4 on both sides,
⇒ 3v/4 = π r³
Divide both sides by π,
⇒ 3v/4π = r³
Now, taking cube root on both sides we get,
r = ∛ (3v/4π)
4. Now given a linear equation,
[tex]y=-2x^{m+2}[/tex]
As the equation is a linear equation,
The value of (x, y) we can take as (0,0)
So, 1 = m +2
⇒ m = -1
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Solve the inequality and graph the solution.
8>
–
3a+2
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
The solution is greater than [tex]-2[/tex]
Define inequalityA mathematical assertion known as an inequality contrasts two values or expressions, demonstrating their relationship in terms of greater than[tex]\geq[/tex], less than (), greater than or equal to [tex]\geq[/tex], or less than or equal to ().
When two quantities are related in a manner other than being equal, it is referred to as an inequality.
[tex]8 > -3a+2[/tex]
Subtracting [tex]2[/tex] from both sides we get:
[tex]6 > -3a[/tex]
Dividing both sides by [tex]-3[/tex] and reverse the inequality sign when dividing by negative number
[tex]a > -2[/tex]
Since a cannot equal [tex]-2[/tex], we can plot an open circle at this value to represent the solution on a number line. We can also depict an arrow pointing up the number line to represent that an is larger than [tex]-2[/tex]
The arrow denotes any value higher than -2, and the open circle at -2 denotes that -2 is not part of the solution.
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Answer:
a>-2
explained:
-3a+2<8
−3+2−2<8−2
−3a<6
−[tex]\frac{3a}{3}[/tex]<[tex]\frac{6}{-3}[/tex]
a>−2
The points
�
(
−
7
,
8
)
,
�
(
−
1
,
9
)
M(−7,8),N(−1,9), and
�
(
0
,
3
)
O(0,3) form a triangle. Find the desired slopes and lengths, then fill in the words that characterize the triangle.
Based on the lengths of the sides, we can see that the triangle is scalene. Based on the slopes of the sides, we can see that the triangle is acute since all the slopes are negative or less than 1.
What is triangle?A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
To find the desired slopes and lengths of the triangle formed by the points M(-7, 8), N(-1, 9), and O(0, 3), we can use the distance formula and the slope formula.
Distance formula:
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Using this formula, we can find the lengths of the sides of the triangle:
Length of MO:
d(MO) = √((0 - (-7))² + (3 - 8)²) = √(7² + 5²) = √(74)
Length of NO:
d(NO) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)
Length of MN:
d(MN) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)
Slope formula:
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Using this formula, we can find the slopes of the sides of the triangle:
Slope of MO:
m(MO) = (3 - 8) / (0 - (-7)) = -5/7
Slope of NO:
m(NO) = (9 - 8) / (-1 - (-7)) = 1/6
Slope of MN:
m(MN) = (9 - 8) / (-1 - (-7)) = 1/6
Characterization of the triangle:
Based on the lengths of the sides, we can see that the triangle is scalene (no two sides have the same length). Based on the slopes of the sides, we can see that the triangle is acute (all angles are less than 90 degrees) since all the slopes are negative or less than 1. Additionally, we can see that the side MO is the longest side of the triangle, and since the slope of MO is negative, we can conclude that the angle opposite side MO is the largest angle in the triangle.
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PLEASE HELP!!!!
Question: Write the equation of a line parallel to y = x -5 that goes through (7,0).
To find the equation of a line parallel to y = x - 5 that goes through (7,0), we need to use the fact that parallel lines have the same slope.
The slope of the line y = x - 5 is 1, since the coefficient of x is 1. Therefore, the slope of the parallel line we want to find is also 1.
Using the point-slope form of a line, we can write the equation of the parallel line as:
y - y1 = m(x - x1)
where (x1, y1) is the point (7,0) and m is the slope of the line, which we know is 1.
Plugging in the values, we get:
y - 0 = 1(x - 7)
Simplifying, we get:
y = x - 7
Therefore, the equation of the line parallel to y = x - 5 that goes through (7,0) is y = x - 7.
Answer:
y = x - 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 5 ← is in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes , then
y = x + c ← is the partial equation
to find c substitute (7, 0 ) into the partial equation
0 = 7 + c ( subtract 7 from both sides )
- 7 = c
y = x - 7 ← equation of parallel line
What is the missing length?
area
A. 8 m
B. 4 m
C. 12 m
D. 18 m
Find w.
12 m
15 m
area = 114 m²
The missing length is 8m which is option A.
Length calculation.
To find the missing length, we need to use the formula for the area of a rectangle:
area = length x width
We are given the area as 114 m² and the width as 15 m. Let's substitute these values into the formula:
114 = length x 15
Solving for length, we get:
length = 114/15
length = 7.6
Therefore, the missing length is approximately 7.6 m.
However, none of the given answer choices match this value exactly. The closest answer is A. 8 m, which is off by only 0.4 m. Therefore, A. 8 m is the best answer choice.
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Solve the following equations. Show your solution.
1.) 1/5x - 2 = -3
2.) 15 = 10 - x/4
3.) x/3 - 12 = -2
4.) x/-2 + (-6) = 6
Answer:
Step-by-step explanation:
1.) 1/5x - 2 = -3
Adding 2 to both sides, we get:
1/5x = -1
Multiplying both sides by 5, we get:
x = -5
Therefore, the solution is x = -5.
2.) 15 = 10 - x/4
Subtracting 10 from both sides, we get:
5 = -x/4
Multiplying both sides by -4, we get:
-20 = x
Therefore, the solution is x = -20.
3.) x/3 - 12 = -2
Adding 12 to both sides, we get:
x/3 = 10
Multiplying both sides by 3, we get:
x = 30
Therefore, the solution is x = 30.
4.) x/-2 + (-6) = 6
Adding 6 to both sides, we get:
x/-2 = 12
Multiplying both sides by -2, we get:
x = -24
Therefore, the solution is x = -24.
The radius of a circle is 4 meters. What is the circle's area? r=4 m
Answer:
Step-by-step explanation:
Write the equation for the line through the given Q-points in slope-intercept form.
8. (5, 21) and (11,3)
9. (4, 8) and (12, 20)
As a result, the slope-intercept form equation for the line through points (5, 21) and (11, 3) is:
y = -3x + 36
Therefore, the equation of the line through (4, 8) and (12, 20) in slope-intercept form is:
y = (3/2)x + 2
The slope of the line must first be determined using the following formula to determine the equation of a line through two points in slope-intercept form:
slope[tex](m) =\frac {(y2 - y1)}{(x2 - x1)}[/tex]
where the coordinates for two points are (x1, y1) and (x2, y2).
The line's slope-intercept form is thus applicable, and it is as follows:
y = mx + b
where b is the y-intercept and m is the slope that we just discovered.
We possess
slope [tex](m) = \frac{(3-21)}{ (11-5)}[/tex],
m = -3
So, using one of our points, we can determine b:
y-21=-3(x-21)
As a result, the slope-intercept form equation for the line through points (5, 21) and (11, 3) is:
y = -3x + 36
9) (4, 8) and (12, 20)
The slope is
[tex]m= \frac{20-8}{12-4}\\m=\frac{12}{8}=\frac{3}{2}[/tex]
equation is (y-8)=1.5(x-4)
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what is the ordered pair of 2x-5y ≥10
Step-by-step explanation:
This is the equation for a AREA greater than or equal to a line
2x-10 >= 5y
y <= 2/5 x -2 there are infinite answers