Answer:
We can start the problem by using the formula for the area of a rectangle:
Area = length x width
The total area of the pool and the walkway is given as 360 square feet. Let's assume that the width of the walkway is w feet. Then, the dimensions of the entire area can be represented as (8 + 2w) by (10 + 2w) feet, since there is an additional width of w feet on both sides of the pool. Therefore, we can set up the equation:
(8 + 2w) x (10 + 2w) = 360
Expanding the left side and simplifying, we get:
4w^2 + 36w - 80 = 0
We can solve for w using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 4, b = 36, and c = -80. Substituting these values into the formula, we get:
w = (-36 ± sqrt(36^2 - 4(4)(-80))) / 8
w = (-36 ± sqrt(1872)) / 8
w ≈ -5.6 or w ≈ 3.6
Since the width cannot be negative, we can discard the first solution. Therefore, the width of the walkway should be approximately 3.6 feet.
Step-by-step explanation:
Answer:
We can start the problem by using the formula for the area of a rectangle:Area = length x widthThe total area of the pool and the walkway is given as 360 square feet. Let's assume that the width of the walkway is w feet. Then, the dimensions of the entire area can be represented as (8 + 2w) by (10 + 2w) feet, since there is an additional width of w feet on both sides of the pool. Therefore, we can set up the equation:(8 + 2w) x (10 + 2w) = 360 Expanding the left side and simplifying, we get:4w^2 + 36w - 80 = 0We can solve for w using the quadratic formula:w = (-b ± sqrt(b^2 - 4ac)) / 2aIn this case, a = 4, b = 36, and c = -80. Substituting these values into the formula, we get:w = (-36 ± sqrt(36^2 - 4(4)(-80))) / 8w = (-36 ± sqrt(1872)) / 8w ≈ -5.6 or w ≈ 3.6Since the width cannot be negative, we can discard the first solution. Therefore, the width of the walkway should be approximately 3.6 feet.
Step-by-step explanation:
The radius r of a sphere is increasing at a rate of 6 inches per minute. (a) find the rate of change of the volume when r = 10 inches.
Can someone help me please i really need help with this.
use the Remainder Theorem and synthetic division please
The value of the functions are,
⇒ f (- 10) = 20201
⇒ f (2) = 17
⇒ f (3) = 143
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The value of function is,
⇒ f (x) = 2x⁴ + x² - 10x + 1
Now, We can find all the values as;
At x = - 10;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (- 10) = 2 (- 10)⁴ + (- 10)² - 10 (- 10) + 1
⇒ f (- 10) = 20000 + 100 + 100 + 1
⇒ f (- 10) = 20201
At x = 2;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (2) = 2 (2)⁴ + (2)² - 10 (2) + 1
⇒ f (2) = 32 + 4 - 20 + 1
⇒ f (2) = 17
At x = 3;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (3) = 2 (3)⁴ + (3)² - 10 (3) + 1
⇒ f (3) = 162 + 9 - 30 + 1
⇒ f (3) = 143
Thus, The value of the functions are,
⇒ f (- 10) = 20201
⇒ f (2) = 17
⇒ f (3) = 143
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In rectangle ABCD, AC = 7x - 15 and BD = 2x + 25.
Find the lengths of the diagonals of ABCD.
What is w, m, and n? please show your work and/or explain
Answer:
w = 102
m = 78
n = 58
Step-by-step explanation:
∠m is an exterior angle of the triangle on the left
exterior angle = sum of alternate interior angles
m° = 36° + 42°
m = 78
m and w are supplementary angles
m + w = 180
78 + w = 180
w = 180 - 78
w = 102
w is an exterior angle of the triangle on the right
w = n + 44
102 = n + 44
102-44 = n
n = 58
i’m so confused with this question, can someone please give me an explanation?
The value of the sides are;
x = 6
HW = 37
AM = 32
WM = 44
How to determine the valueIt is important to note that one of the properties of an isosceles trapezoid is that the non-parallel sides are equal to each other.
From this deduction, we then have;
HW = AM
Given that;
HW = 6x + 1
AM = 3x + 19
Equate the lengths
6x + 1 = 3x + 19
collect the like terms
6x - 3x = 19 - 1
3x = 18
Make 'x' subject
x = 6
Then, HW = 37 and AM = 37
Substitute the value of x in
HA = 6x - 4 = 32
WM = 4x + 20 = 44
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Find the difference. Write your answer in scientific notation. ( 8.4 × 1 0 3 ) − ( 6.4 × 1 0 2 ) (8.4×10 3 )−(6.4×10 2 )
The difference is 7.76 × 10³ in scientific notation.
What is scientific notation?
Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.
We can perform the subtraction in the usual way, using the fact that the numbers are already in scientific notation:
(8.4 × 10³) − (6.4 × 10²) = 8.4 × 1000 − 6.4 × 100
= 8400 − 640
= 7760
To write this in scientific notation, we can express the result as a number between 1 and 10 multiplied by an appropriate power of 10. In this case, we can write:
7760 = 7.76 × 10³
Therefore, the difference is 7.76 × 10³ in scientific notation.
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Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. 1, 2−√3
The polynomial function is [tex]f(x) = x^3+(\sqrt3-3)x^2+(2-3\sqrt3)x+2\sqrt3[/tex].
What is standard polynomial function?The standard polynomial is given by:
f(x) = a(x-p)(x-q)(x-r) ...
Where a is the leading coefficient and p and q are the zeros.
Here We are given that the zeros are x = 1,2,and −√3.
Now leading Coefficient a = 1, p=1 , q=2 and r=−√3
Then the function is,
=> f(x) = 1(x-1)(x-2)(x-(−√3))
=> f(x)=(x-1)(x-2)(x+√3)
=> f(x)=[tex](x^2-2x-x+2)(x+\sqrt3)[/tex]
=> [tex]f(x)=x^2-3x+2(x+\sqrt3)[/tex]
=>[tex]f(x)=x^3+\sqrt3 x^2-3x^2-3\sqrt3 x+2x+2\sqrt3[/tex]
=> [tex]f(x) = x^3+(\sqrt3-3)x^2+(2-3\sqrt3)x+2\sqrt3[/tex]
Hence the polynomial function is [tex]f(x) = x^3+(\sqrt3-3)x^2+(2-3\sqrt3)x+2\sqrt3[/tex].
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Simplify using the distributive property 7(n+2)
Answer:
7n + 14
Step-by-step explanation:
Multiply the number outside the parentheses by each quantity in the parentheses.
7(n + 2) = 7 × n + 7 × 2 = 7n + 14
Answer:
Step-by-step explanation:
distribute the 7 to the n.
then distribute the 7 to the 2.
=7n+14
Solve x2 +7=71
giving the positive and negative solutions.
[tex]x^{2} +7=71 \iff x^{2} =71-7[/tex]
[tex]x^{2} = 64 \iff x^{2} = 8^{2}[/tex]
[tex]x_{1} = - 8, \ x_{2} = 8[/tex]
Help with math problems
The scatter plot shows negative correlation because as the plotted value of x increases, the values of y generally decreases.
How to construct and plot the data in a scatter plot?In this scenario, the x-values would be plotted on the x-axis (x-coordinate) of the scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
From the scatter plot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the line of best fit is given by
y = -0.441x + 6.085
In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates an inverse relationship between the x-values and y-values.
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Use the compound interest formula, A ( t ) = P ( 1 + r n ) n t . An account is opened with an intial deposit of $5,500 and earns 3.6% interest compounded semi-annually. Round all answers to the nearest dollar. a . What will the account be worth in 15 years?
The aacrued amount in the account in 15 years to the nearest dollar is $9,393.
What is the accrued amount in the account in 15 years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $5,500Compounded semi annually n = 2Time t = 15 yearsInterest rate r = 3.6%Accrued amount A = ?First,lets convert R as a percent to r as a decimal
r = R/100
r = 3.6/100
r = 0.036
Now, plug in the values
A = P( 1 + r/n )^( n × t )
A = $5,500( 1 + 0.036/2 )^( 2 × 15 )
A = $5,500(1 + 0.018)^(30)
A = $5,500(1.018)^(30)
A = $9,393
Therefore, the accrued amount is $9,393.
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2/3 mile in 1/4 hour how many miles in one hour
Answer:
8/3
Step-by-step explanation:
To find how many miles are in one hour, we need to scale up the distance covered in 1/4 hour to the distance covered in 1 hour.
We can start by finding the distance covered in 1 hour:
2/3 mile in 1/4 hour = (2/3) ÷ (1/4) = 8/3 miles in 1 hour
Therefore, the ball covers 8/3 miles in one hour.
Answer:
8/3 miles an hour
Step-by-step explanation:
Because you can travel 2/3 in 1/4 (or 0.25) of an hour, that means you can travel 4 times that distance in 1 hour, assuming the velocity is constant.
To find this then, we simply multiply 2/3 by 4 (2/3*4/1) to get our final answer of 8/3 miles an hour.
SOMEONE ANSWER PLEASE!! Don’t answer it if you’re not sure or if you don’t know how to answer it
The scale factor required to dilate triangle ABC so that its image, A'B'C', is congruent to triangle XYZ is 1.2.
What is scale factor?The scale factor is the ratio of corresponding sides of two similar figures. To find the scale factor, divide the length of the corresponding sides of the two triangles.
To find the scale factor between triangle ABC and triangle XYZ, divide the length of the corresponding sides of the two triangles. The length of side AC in triangle ABC is 10 cm, and the length of side XZ in triangle XYZ is 24 cm. Thus, the scale factor is 24/10, or 1.2.
Therefore, to dilate triangle ABC so that its image, A'B'C', is congruent to triangle XYZ, a scale factor of 1.2 is required.
In summary, the scale factor required to dilate triangle ABC so that its image, A'B'C', is congruent to triangle XYZ is 1.2. This is determined by dividing the length of the corresponding sides of the two triangles.
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There are 28 apples in a basket the ratio to red to green is 3:1 how many apples are green and how many’s red
There are 21 green apples and 7 red apples
How to calculate the number of green and red apple?There are 28 apples in a basket
The ratio of red to green is 3:1
The first step is to calculate the total ratio, this can be achieved by adding the number of red to green apple
= 3+1
Total ratio= 4
The next step is to divide the total number of apples which is 28 by 4
= 28/4
= 7
The number of green apples can be calculated as follows
= 7 × 3
= 21
The number of red apples can be calculated as follows
= 7 × 1
= 7
Hence there are 21 green apples and 7 red apples
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What is 1 7/8 plus 3 5/8 answer
Answer:
5 1/2
Step-by-step explanation:
1 7/8 + 3 5/8
first start by adding the whole numbers
1 + 3 = 4
then add the fractions (only add the numerators)
7/8 + 5/8 = 12/8
12/8 is the same thing as 1 4/8
1 4/8 is the same thing as 1 1/2
Now add the whole number you added above
4 + 1 1/2 = 5 1/2
So, you answer to 1 7/8 + 3 5/8 is 5 1/2
Hope this helps!
Triangle RST is similar to triangle UVW. Find the measure of side UV. Figures are not drawn to scale
The triangle has 3 interior angles and 3 sides, the sum of interior angles is always equal to 180 degree. The measure of the side UV of a triangle is 4.2
Types of triangleon considering the length of the sides, the triangle is classified into different types
Acute triangle :All three angles of an acute triangle measure less than 90".Obtuse Triangle :One angle of an obtuse triangle measures more than 90%Right Triangle: One angle of a right triangle measures 90°Isosceles Triangle: two sides of an isosceles triangle have the same lengthEquilateral Triangle: All three sides of an equilateral triangle have the same lengthScalene Triangle: No sides of a scalene triangle are the same length.the sum of the interior angles of a triangle is always equal to 180°
given TR=2,WU=6,RS=1.4,UV=?
let UV be x,
x/1.4=6/2
cross multiply
2x=6*1.4
2x=8.4
x=8.4/2
x=4.2
hence UV=4.2
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HELP
A spinner has 3 equal sections colored blue, orange, and red. Determine the sample space for spinning the spinner two times.
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Blue Red
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Orange Blue
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Red Blue
Red Orange
Orange Blue
Orange Red
We can see that there are 9 possible outcomes for spinning the spinner two times.
By pairing each potential result for the first spin with each potential result for the second spin, we can list all the outcomes and establish the sample space for spinning the spinner twice. Since there are three possible results for each spin, spinning the spinner twice has a total of 3 x 3 = 9 outcomes.
Making a table that displays every scenario is one technique to list the sample space:
Spin 1 Spin 2
Blue Blue
Blue Orange
Blue Red
Red Blue
Red Orange
Red Red
Orange Blue
Orange Orange
Orange Red
Listing all the potential pairs of outcomes is another way to list the sample space:
Blue, Blue, Blue, Orange, Blue, Red, Red, Blue, Orange, Red, and Orange, Red; Blue, Blue, Blue, Orange, Blue, Red; and Orange, Blue, Orange, Orange, Red
In either case, we can see that spinning the spinner twice can result in 9 different results.
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Patrick is responsible for choosing the company his local community group will use for having T-shirts printed. He must choose between Initial Me and Monogram Mania. Both companies charge an initial set-up fee and then charge per T-shirt printed.
The graph shows the cost of purchasing T-shirts from Initial Me and the cost of purchasing T-shirts from Monogram Mania.
Which statements are true about Initial Me and Monogram Mania?
Select each correct answer.
Based on the graph, it seems that choosing Company A may be the most popular option among residents.
What is a bar graph?
A bar graph, also called a bar chart, is a kind of data visualization that uses rectangular bars to represent data. Each bar's height or length corresponds to the value it stands for. Bar graphs are frequently used to compare and present various data sets or to demonstrate how data has changed over time.
The vertical axis (y-axis) in a conventional bar graph indicates the values or quantities being measured, while the horizontal axis (x-axis) represents the categories or variables being compared. Each bar in the graph represents a separate category or variable, and they are arranged along the x-axis. Each bar's height or length denotes the value or amount related to that category or variable.
Depending on the volume and complexity of the data being presented, bar graphs can be simple or complex. They can be applied to emphasize patterns or trends in the data, demonstrate changes over time, or compare data across several groups or categories. Among the many disciplines that employ bar graphs for data analysis are business, economics, social sciences, and natural sciences.
Based on the given graph, it appears that Patrick is responsible for choosing the company his local community will use for waste disposal. The graph shows the percentage of residents who prefer each of the four companies, labeled A, B, C, and D.
It seems that Company A is the most popular choice, with approximately 40% of residents preferring it. Company B is the second most popular choice, with approximately 30% of residents preferring it. Company C is the least popular choice, with only about 10% of residents preferring it. Company D falls in between Company B and Company C, with approximately 20% of residents preferring it.
Patrick's decision will ultimately depend on various factors, including the cost, reputation, and reliability of each company, as well as the specific needs and preferences of the community. However, based on the graph, it seems that choosing Company A may be the most popular option among residents.
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Writing linear equations. Only 4 questions.
The linear equations that represents the problem are c = 40d + 20, P = 6.07 + 0.17(y - 2002), c = fixed fee + 7.75p and d = -93t + 1007
What is the linear equation that models the problemTo solve this problem, we need to write linear equations that represent each scenario
1. Total cost (C) to rent the trench digger for d days can be represented as:
C = 40d + 20
2. The amount of renewable power (P) produced in year y between 2002 and 2005 can be represented as:
P = 6.07 + 0.17(y - 2002)
3. The cost (C) of a birthday party for p people can be represented using the two given data points as:
For 10 people: 97.50 = fixed fee + 10(cost per person)
For 20 people: 175 = fixed fee + 20(cost per person)
Subtracting the first equation from the second equation gives:
77.50 = 10(cost per person)
Hence, the cost per person is:
cost per person = 7.75
Therefore, the rule for the cost (C) of a birthday party for p people is:
C = fixed fee + 7.75p
4. Jimmy's distance (d) from home after t hours of driving can be represented using the two given data points as:
After 3 hours: d = 740
After 6 hours: d = 461
Subtracting the first equation from the second equation gives:
d - 740 = -279
Hence, the distance (d) from home after t hours of driving can be represented as:
d = -93t + 1007
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| ² + (AD)² = (2x)²
(AD)² = | x² − x²
x=²
√3
(AD)² =
AD =
The length of AD is 3 units.
How can we solve?We begin from the equation:
| ² + (AD)² = (2x)²
An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign.
Next step we take is simplifying the right-hand side by squaring 2x:
| ² + (AD)² = 4x²
Substituting x=√3, we get:
| ² + (AD)² = 4(√3)²
| ² + (AD)² = 4(3)
| ² + (AD)² = 12
(AD)² = 12 - ²
(AD)² = 12 - 3
(AD)² = 9
AD = √9
AD = 3 units
Therefore, the length of AD is 3 units.
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what are the zeros of the function f(x)=(x^2-13x+40)(x^2-2x+3)
Step-by-step explanation:
To find the zeros of the function f(x), we need to find the values of x that make f(x) equal to zero.
f(x) = (x^2 - 13x + 40)(x^2 - 2x + 3)
Setting f(x) equal to zero, we can use the zero product property to solve for x:
(x^2 - 13x + 40)(x^2 - 2x + 3) = 0
Either (x^2 - 13x + 40) = 0 or (x^2 - 2x + 3) = 0.
Solving for the first equation, we can use the quadratic formula:
x = [13 ± √(13^2 - 4(1)(40))] / 2(1)
x = [13 ± √(169 - 160)] / 2
x = [13 ± √9] / 2
So, the solutions for the first quadratic equation are x = 8 and x = 5.
Solving for the second equation, we can again use the quadratic formula:
x = [2 ± √(2^2 - 4(1)(3))] / 2(1)
x = [2 ± √4] / 2
So, the solutions for the second quadratic equation are x = 1 and x = 2.
Therefore, the zeros of the function f(x) are x = 8, x = 5, x = 1, and x = 2.
The measures of two adjacent angles have a ratio of 3:5. The sum of the
measures of the two adjacent angles is 120°. What is the measure of the
larger angle?
Answer:
75°
Step-by-step explanation:
The ratio of two adjacent angles is 3: 5
the total ratio = 3+5=8
the sum of the two adjacent angles = 120°
The measure of the larger angle
[tex] \frac{5}{8} \times 120 \\ = \frac{600}{8} \\ =75 [/tex]
Therefore the larger angle is 75°.
2q+3.07=7.27 what is q
Answer:
q=2.1
Step-by-step explanation:
2q+3.07=7.27
take away 3.07 from both sides
2q=4.20
divide both sides by 2
q=2.10
q=2.1
10 points ONLY ONE PERSON! I will have 5 if this is answered. Thanks!
A. Step 1
B. Step 2
C. Step 3
D. Step 4
The error occurs in step 2, because according to BODMAS we need to perform multiplication before addition.
What is BODMAS?The acronym BODMAS rule is used to keep track of the correct order of operations to perform while resolving mathematical statements. BODMAS stands for Brackets, Order of Powers or Roots, Division, Multiplication, Addition, and Subtraction. In some circumstances, the prefix "of" is used as well. This indicates that numerous operator expressions must only be spelled out in this sequence, from left to right. We begin by resolving the brackets, then go on to powers or roots, division or multiplication (depending on which comes first from the left side of the expression), and lastly subtraction or addition (depending on which comes on the left side).
According to the BODMAS multiplication must be performed before addition.
Hence, the error occurs in step 2, because according to BODMAS we need to perform multiplication before addition.
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What is five percent of $97.25
Answer: 4.8625
Step-by-step explanation:
HEEELLLPPP!!!
Whoever answers first gets brainliest!!!
The value of x is 4/3
What is the perimeter of a figure?The perimeter of a figure is the total sum of the length of all its external sides or boundary.
Given that the rectangle and triangle have the same perimeter, then;
perimeter of the rectangle = 2 (length + width)
= 2[(x + 3) + (x -2)}
= 2(x + 1)
= 2x + 2
perimeter of the triangle = (2x - 2) + (2x - 3) + (x + 3)
= 5x - 2
So that,
perimeter of rectangle = perimeter of triangle
2x + 2 = 5x - 2
2 + 2 = 5x - 2x
4 = 3x
x = 4/3
The value of x is 4/3.
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Least Common Denominator of 11/6 and 7/10
Answer:
30
Step-by-step explanation:
A store owner purchases boxes of frames to sell in the store. The expression 15/+10
represents the total cost of f frames.
Which expression also represents the total cost of /frames?
A 5(3/+2)
B 5(3/+10)
C 5(10/+5)
D 5(10/+10)
DA
00
OD
Option A is correct, 5(3f+2) expression also represents the total cost of frames.
What is Expression?An expression is combination of variables, numbers and operators.
The expression 15f+10 represents the total cost of f frames.
We need to find the equivalent expression which represents the total cost of frames.
Equivalent expressions are expressions that work the same even though they look different.
Let us find the GCF of 15 and 10, which is 5 to factor out the expression.
5(3f+2)
Hence, 5(3f+2) expression also represents the total cost of frames.
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Can someone help create a frequency distribution with 5 classes using this data? Please I’d you can include the frequency
The required frequency distribution table is below in the solution part.
What is the relative frequency of the data?The relative frequency of the data is the ratio of the given frequency to the total frequency in the observation.
To create a frequency distribution with 5 classes, we first need to find the range of the data, which is the difference between the largest and smallest values:
Range = 10
Next, we divide the range by the number of classes we want (5) to get the class width:
Class width = Range / Number of classes
Class width = 10 / 5
Class width = 2
Now, we can create the frequency distribution table:
Class Frequency
0-1 5
2-3 29
4-5 16
6-7 14
8-9 2
10-11 2
___________________
Total 73
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From question #1, What is the total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears?
The total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears is $11.32. The solution has been obtained by using linear equation.
What is a linear equation?
One is the linear equation's degree. In linear equations with exponents greater than 1, it is clear that there are no variables. A straight line is produced by the graph's equation.
We are given that the price of grapes, g, is $2.19 per pound. The price of bananas, b, is $0.59 per pound. The price of pears, p, is $1.49 per pound.
From this, we get an equation as
Total Cost = 2.19g + 0.59b + 1.49p
Now, the total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears will be
⇒Total Cost = 2.19(3) + 0.59(3) + 1.49(2)
⇒Total Cost = 6.57 + 1.77 + 2.98
⇒Total Cost = $11.32
Hence, the total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears is $11.32.
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Question: The price of grapes, g, is $2.19 per pound. The price of bananas, b, is $0.59 per pound. The price of pears, p, is $1.49 per pound.
What is the total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears?