The amount of time it will take them when working together is 12/7 hours, or approximately 1.71 hours.
If Harry can paint a room in 3 hours, and Kerry can paint it in 4 hours, then we can use the formula for combined work (work rate) to find how long it will take if they work together. The formula is:
1/t = 1/t₁ + 1/t₂, where t is the time it takes for them to complete the work together, t₁ is the time it takes for Harry to complete the work alone, and t₂ is the time it takes for Kerry to complete the work alone.
Plugging in the values we have, we get:
1/t = 1/3 + 1/4.
Multiplying both sides of the equation by 12t, we get:
12 = 4t + 3t.
Simplifying, we get:
12 = 7t.
Dividing both sides of the equation by 7, we get:
t = 12/7.
Therefore, it will take Harry and Kerry 12/7 hours, or approximately 1.71 hours, to paint the room together.
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The functionh(x)=x−71can be expressed in the formf(g(x))whereg(x)=(x−7)andf(x)is defined as:
The function h(x) can be expressed as f(g(x)) where g(x) = (x-7) and f(x) = x.
The function h(x) = (x-7)1 can be expressed in the form f(g(x)) where g(x) = (x-7) and f(x) is defined as f(x) = x1.
To find f(x), we need to isolate x on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of 1, which is 1.
f(x) = x1 * 11 = x
Therefore, the function h(x) can be expressed as f(g(x)) where g(x) = (x-7) and f(x) = x.
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As khan and jorman practice for college entrance tests, their scores increase. Khan's current score is 750 and is rising 8 points per week.Jormans current score is 650 but is growing by 30 points each week. write and solve a system of equations uising the equal values method to determine when their scores will be the same and what that score will be
Khan and Jorman's scores will be the same in 4.545 weeks, and their score at that time will be 786.36 using the equal values.
What exactly is the equal values approach?With the equal values approach, two expressions are made equal, and the variable that makes them equal is then solved for. When solving systems of equations with two variables, this is often done in order to determine the values of the two variables that will simultaneously make the equations true.
Let us suppose the number of weeks = y.
Let us suppose the score = x.
Given that, Khan's current score is 750 and is rising 8 points per week.
Khan's score: y = 8x + 750
Jormans current score is 650 but is growing by 30 points each week:
Jorman's score: y = 30x + 650
Their scores will be equal at:
8x + 750 = 30x + 650
22x = 100
x = 4.545
Substitute the value of x in the equation to obtain y:
y = 8(4.545) + 750
y = 786.36
Hence, Khan and Jorman's scores will be the same in 4.545 weeks, and their score at that time will be 786.36.
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WXYZ FEDC. Find YZ and DE.
X
10
Y
Z
30
Save answer
WF
27
Write your answers as decimals or whole numbers.
YZ =
DE= =
9
6
C
E
2
D
Answer:
To find YZ and DE in the sequence WXYZ FEDC, we need to understand how the sequence is constructed. The sequence is likely made up of two smaller sequences: WXYZ and FEDC.
To find YZ, we need to look at the WXYZ sequence. Since Y and Z are the last two digits of this sequence, we can conclude that Z is the last digit and Y is the second to last digit. Therefore, YZ = 30.
To find DE, we need to look at the FEDC sequence. Since D and E are the last two digits of this sequence, we can conclude that E is the last digit and D is the second to last digit. Therefore, DE = 96.
So, YZ = 30 and DE = 96
Step-by-step explanation:
brainliest pls
To be on the safe side, three detectors were installed in a factory room to make sure that if there was a fire, at least one of them would signal a warning. The company that manufactured the smoke detectors indicated that, based on their testing, the probability that any one of the smoke detectors will work correctly is 0.75 (meaning that it works 75% of the time in the long run). This also means that there is a 25% chance that if there is smoke or a fire, the detector will not work! What is the probability that if there was smoke in the factory, none of the 3 detectors would work? Does this probability indicate a safety problem for the factory? Explain.
PLEASE HELP MEEEE!!
The probability that none of the 3 detectors would work if there was smoke in the factory is 0.25³, or 0.015625 (1.56%).
What is Probability?Probability is a branch of mathematics that deals with the likelihood of certain outcomes or events occurring. Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1. An event that is certain to occur has a probability of 1, while an event that is impossible to occur has a probability of 0. The probability of an event occurring can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.
This probability indicates that the factory does have a safety problem, as there is a 1.56% chance that none of the smoke detectors would sound an alarm if there was smoke present. This presents a significant risk to the factory, as it could lead to an undetected fire that may cause damage to the facility or put employees in danger.
The company should look into ways to reduce the risk of the smoke detectors not working. One way to do this would be to increase the number of smoke detectors in the factory room, as the more detectors there are, the lower the probability that none of them will work. The company could also consider using more reliable smoke detectors that have a higher probability of working correctly when needed. Ultimately, the company should seek to reduce the risk of none of the detectors working by taking steps to increase the probability that at least one of them will sound an alarm in the event of smoke or a fire.
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Find sin tetha if cos tetha=-5/17 and tetha is in Q III Find cos tetha if sin tetha=1/4 and tan tetha = √3
Find all other trigonometric function values lif sec tetha =-4 and tetha is in Q II
If cos tetha = -5/17 and tetha is in Q III, then sin tetha can be found using the Pythagorean identity: sin^2 tetha + cos^2 tetha = 1.
Substituting the given value for cos tetha and solving for sin tetha gives:
sin^2 tetha + (-5/17)^2 = 1
sin^2 tetha = 1 - 25/289
sin^2 tetha = 264/289
sin tetha = √(264/289)
sin tetha = ±√264/17
Since tetha is in Q III, where sin is negative, the correct answer is:
sin tetha = -√264/17
If sin tetha = 1/4 and tan tetha = √3, then cos tetha can be found using the definition of tan tetha: tan tetha = sin tetha/cos tetha.
Substituting the given values for sin tetha and tan tetha and solving for cos tetha gives:
√3 = (1/4)/cos tetha
cos tetha = (1/4)/√3
cos tetha = √3/12
If sec tetha = -4 and tetha is in Q II, then cos tetha can be found using the definition of sec tetha: sec tetha = 1/cos tetha.
Substituting the given value for sec tetha and solving for cos tetha gives:
-4 = 1/cos tetha
cos tetha = -1/4
Once we have cos tetha, we can find sin tetha using the Pythagorean identity: sin^2 tetha + cos^2 tetha = 1.
Substituting the value for cos tetha and solving for sin tetha gives:
sin^2 tetha + (-1/4)^2 = 1
sin^2 tetha = 1 - 1/16
sin^2 tetha = 15/16
sin tetha = ±√(15/16)
Since tetha is in Q II, where sin is positive, the correct answer is:
sin tetha = √15/4
Once we have sin tetha and cos tetha, we can find the other trigonometric function values using their definitions:
tan tetha = sin tetha/cos tetha = (√15/4)/(-1/4) = -√15
cot tetha = 1/tan tetha = -1/√15 = -√15/15
csc tetha = 1/sin tetha = 4/√15 = 4√15/15
sec tetha = 1/cos tetha = -4 (given)
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(1)/(x-4)-(2)/(x+5)=(2x-1)/(x^(2)+x-20) The restrictions on the variable in the rational equation are x!= and x!
The restrictions on the variable in the rational equation (1)/(x-4)-(2)/(x+5)=(2x-1)/(x^(2)+x-20) are x != 4 and x != -5.
The restrictions on the variable in the rational equation are x != 4 and x != -5. This is because the denominators of the rational expressions (x-4) and (x+5) cannot equal zero, as division by zero is undefined.
To find the restrictions, we can set each denominator equal to zero and solve for x:
x - 4 = 0 => x = 4
x + 5 = 0 => x = -5
So, the restrictions are x != 4 and x != -5.
In summary, the restrictions on the variable in the rational equation (1)/(x-4)-(2)/(x+5)=(2x-1)/(x^(2)+x-20) are x != 4 and x != -5.
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Use the calculator to approximate the trig function of the given angle. Round answer to the fourth decimal place. sin 58°
Based on the provided information The result of rounding to four integer places is sin 58° ≈ 0.8480.
How would you define "rounding"?Making a number easier while maintaining a value that is near to what it was is known as rounding. Although less precise, the outcome is simpler to use. For instance, 73 is 70 when adjusted to the closest ten, since 70 is closer to 73 than 80 is.
Using a calculator, we can approximate sin 58° as follows:
sin 58° ≈ 0.8480
Rounding to four decimal places, we get:
sin 58° ≈ 0.8480
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when the L shape is rotated about the origin (0, 0) by 90° counterclockwise which one of these would it look like?
When the L shape attached is rotated about the origin (0, 0) by 90° counterclockwise it would look like option C.
What is the rationale for the above response?A shows a rotation of 90° clockwise about (0,0)
B shows a rotation of 180° about (0,0)
C shows a rotation of 90° anticlockwise about (0,0)
D shows a rotation of 90° anticlockwise, but the center of rotation is (1,1)
Recall that Rotation in math is a transformation that involves rotating a figure around a fixed point called the center of rotation by a certain angle in a clockwise or counterclockwise direction.
Thus, Option C above is the right answer.
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Question
For which distributions is the median the best measure of center?
Select each correct answer.
Responses
A bar graph that forms the shape of a pyramid on a graph.
Image with alt text: A bar graph that forms the shape of a pyramid on a graph.
A bar graph that forms a gradual incline and a sharp decline of values.
Image with alt text: A bar graph that forms a gradual incline and a sharp decline of values.
A bar graph that forms a sharp incline and a gradual decline of values.
Image with alt text: A bar graph that forms a sharp incline and a gradual decline of values.
A bar graph with values that hover around 10 y.
Answer: The median is the best measure of center for distributions that are skewed or have extreme values, since it is less affected by outliers than the mean. Therefore, the correct answers are:
- A bar graph that forms a gradual incline and a sharp decline of values.
- A bar graph that forms a sharp incline and a gradual decline of values.
Both of these graphs suggest that the data is skewed, and in these cases, the median is a better representation of the "typical" value than the mean.
The other two options do not provide enough information to determine whether the data is skewed or not, so we cannot say for certain whether the median is the best measure of center in those cases. The bar graph with values that hover around 10 y could have a symmetrical distribution with a mean and median that are the same, or it could have a skewed distribution where the median is a better measure of center. Similarly, the pyramid-shaped bar graph could have a symmetrical distribution, or it could be skewed in a way that the median is not a good measure of center.
Step-by-step explanation:
Help as much as you can please!!
Answer:
#7
AB = 4.1
CB = 4.1
#10
AC = 21.21
CB = 15
#11
AC = 2.828
CB =2
#12
AB = 2.616
CB = 2.616
#13
AC = 6
CB = 3√2
#14
AC = 5.94
CB = 4.2
Step-by-step explanation:
The triangle is a right isosceles triangle with AB = AC
This means
AC² = AB² + CB²
= AB² + AB²
= 2AB²
AC = AB√2
and
AC = CB√2 (since CB= AB)
#7
Given AC = 5.8
We know AC = AB√2
[tex]AB= \dfrac{AC}{\sqrt{2}} = \dfrac{5.8}{\sqrt{2}} = 4.1[/tex]
CB = AB is also 4.1
#10
Given AB = 15
AC = AB√2 = 15√2 =
CB= AB = 15
#11
Given CB = 2
AB = CB= 2
AC = CB√2 = 2√2 = 2.828
#12
Given AC = 3.7
We know AC = AB√2
AB= AC/√2 = 3.7 ÷ √2 = 2.616
CB = AB is also 2.616
#13
Given AB = 3√2
AC = AB√2 = 3 x √2 x √2 = 3 x 2 =6 (√2 x √2 = 2)
CB = 3√2
#14
Given AB= 4.2
AC = 4.2 x √2 = 5.94
CB = AB = 4.2
ms. jensen is selling tickets for the prom. the budget was $5000. tickets cost $45 for an individual and $70 for a couple buying 2 tickets. there are only 150 tickets available. write a system of inequalities that represents this situation if x is the number of individual tickets and y is the number of couple tickets.
This distribution of inequities ensures that the total amount of ticket sales revenue stays within the budget, that no more than 150 tickets are sold overall, and that no negative ticket sales occur.
What would be a system of inequalities?Let x represent the quantity of single tickets sold and y represent the quantity of pair tickets sold. The entire revenue from ticket sales, R, is then calculated as follows:
R = 45x + 70y
The entire amount of ticket sales revenue is limited by the budget to $5000:
45x + 70y ≤ 5000
No more than 150 tickets may be sold in total.
x + y ≤ 150
X and Y must both be non-negative since we cannot sell negative tickets:
x ≥ 0\sy ≥ 0
As a result, the system of disparities that best captures this circumstance is:
5000 x + y 45x + 70y 150x 0y 0
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Evaluate the limit { lim_(x rarr 6) } 7(7 x+7)^ 3 Question 13 Evaluate the limit: lim−(x−>9)(7x−63)/(x^2−2x−63)=
Evaluating the limit given by [tex]{ lim_{(x- > 9)} } (7x-63)/(x^2-2x-63)[/tex], we will obtain as a result [tex]7/16[/tex]
How do we evaluate the limit?To evaluate the limit, we need to simplify the expression first. We can do this by factoring the numerator and denominator of the fraction:
[tex]lim_{(x->9)} (7x-63)/(x^2-2x-63) = lim_{(x->9)} (7(x-9))/((x-9)(x+7))[/tex]
Next, we can cancel out the [tex](x-9)[/tex] terms in the numerator and denominator:
[tex]lim_{(x->9)} (7)/(x+7)[/tex]
Now, we can plug in the value of x that the limit is approaching (9) into the expression:
[tex]lim_{(x->9)} (7)/(x+7) = (7)/(9+7) = (7)/(16)[/tex]
Therefore, the limit of the expression as x approaches 9 is 7/16.
Answer: [tex]{ lim_{(x->9)} } (7x-63)/(x^2-2x-63) = 7/16[/tex]
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HELPPPPP PLEASEEEEEEEEEE HURRY
The percentage of races with a finishing time between 64.5 and 65.5 seconds is given as follows:
68%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The measures in this problem are within one standard deviation of the mean, as:
65 - 0.5 = 64.5.65 + 0.5 = 65.5.Hence the percentage is of 68%.
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Add (7x^(8)-6x^(3)+2x^(2)+9) and (9x^(7)+4x^(3)-5x) Give your answer in descending order.
The answer is 7x^(8) + 9x^(7) - 2x^(3) + 2x^(2) - 5x + 9.
To add (7x^(8)-6x^(3)+2x^(2)+9) and (9x^(7)+4x^(3)-5x), we need to combine the like terms in both expressions. Like terms are terms with the same variable and exponent.
Combine the like terms in the first expression:
7x^(8) + 0x^(7) - 6x^(3) + 2x^(2) + 0x + 9
Combine the like terms in the second expression:
0x^(8) + 9x^(7) + 4x^(3) + 0x^(2) - 5x + 0
Add the two expressions together:
(7x^(8) + 0x^(8)) + (0x^(7) + 9x^(7)) + (-6x^(3) + 4x^(3)) + (2x^(2) + 0x^(2)) + (0x - 5x) + (9 + 0)
Simplify the expression:
7x^(8) + 9x^(7) - 2x^(3) + 2x^(2) - 5x + 9
Write the answer in descending order:
7x^(8) + 9x^(7) - 2x^(3) + 2x^(2) - 5x + 9
Therefore, the answer is 7x^(8) + 9x^(7) - 2x^(3) + 2x^(2) - 5x + 9.
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Question 11 Solve the inequality. Write the solution set in interval notation. (5)/(y-4)<9
In interval notation, the the solution set in interval notation. (5)/(y-4)<9 is (41/9, ∞).
What is inequality?Inequality is a mathematical statement that two values or expressions are not equal. It is represented by symbols, like >, <, or ≠, and is used to compare quantities or values.
To solve the inequality (5)/(y-4)<9, we need to isolate the variable on one side of the inequality. We can do this by multiplying both sides of the inequality by (y-4) and then simplifying.
(5)/(y-4)<9
5 < 9(y-4)
5 < 9y - 36
41 < 9y
y > 41/9
This means that any value of y greater than 41/9 will satisfy the inequality.
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Question 9 of 22 Solve the following inequality. Write the solution set using interval notation. 8(2x+3)>8
The solution set for the inequality is (-1, ∞) in interval notation. To solve the inequality, we need to isolate the variable on one side of the inequality sign. We can do this by using the following steps:
Step 1: Divide both sides of the inequality by 8 to simplify the equation.
8(2x+3)>8 → (2x+3)>1
Step 2: Subtract 3 from both sides of the inequality to isolate the variable.
(2x+3)>1 → 2x>-2
Step 3: Divide both sides of the inequality by 2 to find the value of x.
2x>-2 → x>-1
Step 4: Write the solution set using interval notation. Since the inequality sign is ">", we use a parenthesis to indicate that the solution does not include the endpoint -1.
x>-1 → (-1, ∞)
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10 minutes for 2 laps division word problem
examples
The number of minutes to complete 1 lap is found as 5 minutes.
Explain about the division word problem?Multiplication is the reciprocal of division. If 3 groups of 4 add up to 12, then 12 divided into three categories of equal size results in 4 in each group.
Creating equal groups or determining how many people fit into each group after a fair distribution is the basic objective of division. On the bus, there are 9 seats for companions. Divide the total supply of apples by a number of friends to determine how several apples Tom donated to each of his pals. Tom then gives seven apples to every single one of his friends.The stated question:
10 minutes for 2 laps
Applying unitary method:
= 10/2
= 5
Thus, number of minutes to complete 1 lap is found as 5 minutes.
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The complete question -
10 minutes for 2 laps. Then, find number of minutes for 1 lap.
PLEASE HEEEEEEEEEEEEEEEEEEEEEEEEELP ME ONLY TWO QUESTIONS
The product of the two expressions can be set as the one in option 1.
What is product of two expression?The process of multiplying two given expressions with the aid of variables and constants is known as algebraic multiplication. The terms factors and multiplicands refer to the two expressions that make up an algebraic product, which is the combination of two expressions.
The two expressions can be set as follows:
4x³ + 0x² -3x + 4
2x - 5
As the x² term is not present we use the coefficient as 0.
Hence, the product of the two expressions can be set as the one in option 1.
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Use decomposition to find the area of the figure.
A drawing of a composite shape made up of two triangles with a common base and the length of the base equals 10 miles. The heights of the two triangles are 7 miles and 4 miles.
Therefore , the solution of the given problem of triangle comes out to be the shape is 55 square miles.
What precisely is a triangle?Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.
Here.
Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.
The following method can be used to determine a triangle's area:
A = (1/2)bh
where A represents area, B represents foundation, and H represents height.
We can calculate each triangle's area using the following formula:
=> Area of 1st triangle
=> (1/2)(10)(7) = 35 square miles
=> Area of 2nd triangle
=> (1/2)(10)(4) = 20 square miles
The two triangles' combined regions make up the composite shape's surface area.
55 square miles is the combined shape's area
=> (35 + 20).
Consequently, the combined size of the two triangles in the shape is 55 square miles.
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help me please with this math
I need help this is due today
The measurements are shown in the solution
What are Trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Given are right triangles, we need to find the value of x in each,
We will use Trigonometric ratios to find the same,
The sine is the ratio between the length of the opposite leg and the length of the hypotenuse.
The cosine is the ratio between the length of the adjacent leg and the length of the hypotenuse.
The tangent is the ratio between the length of the opposite leg divided by the length of the adjacent leg.
1) sin 21° = 11/x
x = 30.7
2) cos 34° = x/28
x = 23.21
3) tan 49° = 33/x
x = 28.68
4) T = cos⁻¹ (11/23)
= 61.42°
5) T = sin⁻¹(21/44)
= 28.50°
6) T = tan⁻¹(8/12)
= 33.7°
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Solve the following LP problem using Dual SA. Minimize subject to : (x1,x2,x3)=−5x1+x2−2x3
2x1+x3=0
x1−x2≥1
3x1−x2+x3≤3
x1 = 1.3, x2 = 0.3, x3 = 0.7
The solution to the linear programming problem is: x1 = 1.3, x2 = 0.3, x3 = 0.7.
Using the Dual Simplex Algorithm (DSA), we can solve the problem by setting up the initial tableau:
x1 = −5x1 + x2 − 2x3
2x1 + x3 = 0
x1 − x2 ≥ 1
3x1 − x2 + x3 ≤ 3
Once the tableau is set up, we can use DSA to find the optimal solution.
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527 million people speak Spanish out of about 7,530 million people in the world. Find the percent who speak Spanish. Round to the nearest whole percent.
______% of people in the world speak Spanish.
PLEASE BE ACCURATE!!!THANK YOU!!:)
Answer:
To find the percentage of people in the world who speak Spanish, we can use the following formula:
percentage = (part/whole) x 100%
where "part" is the number of people who speak Spanish and "whole" is the total world population.
Substituting the given values, we get:
percentage = (527/7,530) x 100% ≈ 7.00%
Rounding to the nearest whole percent, we get that approximately 7% of people in the world speak Spanish.
Which city should you live in if you want to live in a city with greater variability of temperature?
Answer: If you want to live in a city with greater variability of temperature, you should look for cities with a continental climate. Continental climates are characterized by hot summers and cold winters, with large temperature fluctuations between day and night and between seasons.
Cities located in the interior of large landmasses, far from large bodies of water, are more likely to have a continental climate. Examples of cities with a continental climate include Moscow (Russia), Calgary (Canada), and Chicago (USA). These cities experience wide temperature swings throughout the year, with hot summers and cold winters.
On the other hand, cities located near large bodies of water tend to have a more moderate climate, with smaller temperature fluctuations. Examples of such cities include San Francisco (USA), Sydney (Australia), and London (UK). These cities experience mild summers and winters, with relatively constant temperatures throughout the year.
Step-by-step explanation:
3 Simplify the presion x-1 Answer 5). Simplily the expression 7 14 x2 - 4 - 6x + 8 Answer: 7). Solve the equation: 6 3 - x +1 x +4 Answer:
a) The simplified expression is \frac{(x-4)}{2(x+2)}. b) The solution to the equation is x = -7.
a) To simplify the expression \frac{7}{x^2\ -\ 4}\div\frac{14}{x^2\ -6x\ +8}, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, the reciprocal of \frac{14}{x^2\ -6x\ +8} is \frac{x^2\ -6x\ +8}{14}.
Now, we can multiply the two fractions: \frac{7}{x^2\ -\ 4} \times \frac{x^2\ -6x\ +8}{14} = \frac{7(x^2\ -6x\ +8)}{14(x^2\ -\ 4)}
Next, we can simplify the expression by canceling out any common factors. In this case, both the numerator and denominator have a factor of 7, so we can cancel them out:
\frac{7(x^2\ -6x\ +8)}{14(x^2\ -\ 4)} = \frac{x^2\ -6x\ +8}{2(x^2\ -\ 4)}
Finally, we can factor the numerator and denominator to see if there are any other common factors that can be canceled out:
\frac{x^2\ -6x\ +8}{2(x^2\ -\ 4)} = \frac{(x-4)(x-2)}{2(x+2)(x-2)}
Since both the numerator and denominator have a factor of (x-2), we can cancel them out:
\frac{(x-4)(x-2)}{2(x+2)(x-2)} = \frac{(x-4)}{2(x+2)}
So, the simplified expression is \frac{(x-4)}{2(x+2)}.
b) For the second part of the question, we need to solve the equation \frac{6}{x\ +1}\ =\ \frac{3}{x\ +\ 4}. To do this, we can cross-multiply and then simplify:
6(x+4) = 3(x+1)
6x + 24 = 3x + 3
3x = -21
x = -7
So, the solution to the equation is x = -7.
Note: The question is incomplete. The complete question probably is: a) Simplify the expression \frac{7}{x^2\ -\ 4}\div\frac{14}{x^2\ -6x\ +8} . b) Solve the equation \frac{6}{x\ +1}\ =\ \frac{3}{x\ +\ 4}.
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Find the area of the shaded region.
12 ft
8 ft
6 ft
12 ft
13 ft
The area of the shaded region is 96ft²
What is area of a parallelogram?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².
The area of a parallelogram is expressed as base × height
The area of parallelogram = 12× 12
= 144ft²
The area of the rectangle = l×w
= 8×6
= 48 ft²
The area of the shaded region = area of parallelogram - area of rectangle
area of the shaded region = 144-48
= 96ft².
Therefore the area of the shaded region is 96ft²
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Given the following information, find sin 2x, cos 2x, and tan
2x. (10pts) sinx=1/7, x in QII
sin 2x = -4sqrt(3)/49, cos 2x = 47/49, and tan 2x = -8/15.
Answer:
Given the information sin x = 1/7, x in QII. The second quadrant (QII) lies between 90° and 180°.Therefore, we know the following about the values of the trigonometric functions:cos x is negative because it is in the second quadrant.tan x is negative because it is in the second quadrant.Therefore, cos x = -sqrt(48)/7 and tan x = -1/4.To find sin 2x, cos 2x, and tan 2x, we will use the following trigonometric identities: sin 2x = 2sin x cos x cos 2x = cos² x - sin² x tan 2x = 2tan x / (1 - tan² x)Substituting in the values for sin x and cos x, we get:sin 2x = 2(1/7)(-sqrt(48)/7) = -4sqrt(3)/49cos 2x = (-sqrt(48)/7)² - (1/7)² = 47/49tan 2x = 2(-1/4) / (1 - (-1/4)²) = -8/15Therefore, sin 2x = -4sqrt(3)/49, cos 2x = 47/49, and tan 2x = -8/15.
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2. Decide whether enough information is given to prove that the triangles are congruent using
the HL Congruence Theorem. Explain how you have concluded your answer.
Therefore , the solution of the given problem of triangle comes out to be the HL Congruence Hypothesis cannot be used to demonstrate anything.
What is a triangle exactly?A triangular is a polygon because it has two or maybe more additional sections. It has a straightforward square form. Only the edges A, B, but also C distinguish a triangular from a parallelogram. When the sides are not exactly collinear, Euclidean geometry produces a singular plane instead of a cube. If a shape has three edges and three angles, it is said to be triangular.
Here,
According to the HL Congruence Theorem, a triangle is congruent if its hypotenuse and one of its legs are congruent with the hypotenuse and corresponding limb of another right triangle.
We must assess whether the two right triangles have the following information in order to decide whether the HL Congruence Theorem can be used to prove that the triangles are congruent:
Both of them are right circles.
Each triangle has a limb that is congruent.
Each triangle's hypotenuses are similar to one another.
The HL Congruence Theorem allows us to infer that the triangles are congruent if all three requirements are satisfied.
The HL Congruence Hypothesis cannot be used to demonstrate anything if any one of the prerequisites is not satisfied.
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Which of the following shows an example of two irrational numbers being multiplied to get a rational number?
Responses
3×9
0×5
3√ ×12−−√
2√×3√
Create your own radical inequality that has a solution of x>13. Your equation must have at least 4 terms in it
The answer is true, our inequality has a solution of x > 13. Our final answer is: 4(x^2 - x - 12) > (101 - 2x)^2
To create a radical inequality that has a solution of x > 13 and has at least 4 terms in it, we can start with the basic inequality x > 13 and add terms to both sides to create a more complex equation. For example:
√(x + 3) + 2 > √(x - 4) + 12
Now, we can rearrange the terms and square both sides to get rid of the radicals:
√(x + 3) - √(x - 4) > 10
(√(x + 3) - √(x - 4))^2 > 10^2
x + 3 - 2√(x + 3)(x - 4) + x - 4 > 100
2x - 2√(x + 3)(x - 4) > 101
Now, we can isolate the radical term and square both sides again:
-2√(x + 3)(x - 4) > 101 - 2x
4(x + 3)(x - 4) > (101 - 2x)^2
4(x^2 - x - 12) > 10201 - 404x + 4x^2
0 > 3x^2 - 403x + 10237
Since we want the solution to be x > 13, we can plug in 13 for x and see if the inequality is true:
0 > 3(13^2) - 403(13) + 10237
0 > 507 - 5239 + 10237
0 > 4505
Since this is true, our inequality has a solution of x > 13. Therefore, our final answer is:
4(x^2 - x - 12) > (101 - 2x)^2
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