(SAT Prep) Find the value of x in each of the following exercises:
QUICKLY PLEASE JIMGRANT1 IF YOU WOULD PLEASE HELP.

Answer:

305.12 square inches

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The area of the window is equal to the area of a rectangle, plus the area of two quarter circles plus the area of the smaller square between the two upper corners

so

Find the area of rectangle

[tex]A=(12)(26-4)=264\ in^2[/tex]

Find the area of the two quarter circle

[tex]A=2[\frac{1}{4}(3.14)(4^2)][/tex]

[tex]A=25.12\ in^2[/tex]

Find the area of the smaller square between the two upper corners

[tex]A=(12-8)(4)=4^2=16\ in^2[/tex]

The total area is equal to

[tex]A=264+25.12+16=305.12\ in^2[/tex]

Jaylon's stained-glass window consists of two quarter circles with a radius of 4 inches each and a rectangle with dimensions 4 inches (height) by approximately 25.12 inches (width). The total area of the stained-glass window is approximately 125.6 square inches.

To find the area of the stained-glass window that Jaylon created, we'll break it down into its constituent shapes: two quarter circles and a rectangle.

Quarter Circles:

Each quarter circle has a radius of 4 inches.

The formula for the area of a quarter circle is (1/4) * π * r^2, where r is the radius.

For each quarter circle:

Area = (1/4) * π * (4)^2

≈ (1/4) * 3.14 * 16

≈ 12.56 square inches (rounded to two decimal places).

Since there are two quarter circles, the total area contributed by the quarter circles is:

Total Area of Quarter Circles = 2 * 12.56

≈ 25.12 square inches.

Rectangle:

The rectangle's height is the same as the radius of the quarter circles, which is 4 inches.

The width of the rectangle can be found by calculating the circumference of a circle with a radius of 4 inches (since it will form the other two sides of the rectangle).

The circumference of a circle is given by 2 * π * r.

So, the width of the rectangle is:

Width = 2 * π * 4

≈ 25.12 inches.

Area of the rectangle:

Area = length * width

≈ 4 * 25.12

≈ 100.48 square inches.

Total Area:

The total area of the stained-glass window is the sum of the areas of the quarter circles and the rectangle:

Total Area = Area of Quarter Circles + Area of Rectangle

≈ 25.12 + 100.48

≈ 125.6 square inches.

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Answer:

Explanation:

(a) What is the length of the garden in her model? Show your work, including your proportion

1. Scale:

2. Proportion:

Naming x the model length:

Cross multiply:

Divide both sides by x:

Answer: 3 inches

(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?​

Both the width and the length must use the same scale, thus the corresponding sides of the scale model and the drawing must be proportional.

In the model the ratio of the length to the width is 3 inch / 5 inch

In the paper the ratio of the length to the width is 8.5 inch / 7 inch

Hence, you can see that in the model the length (mumerator of the fraction) is less than the width (denominator) while in the paper it is the opposite. Bieng the two ratios different, they are not proportional, and you conclude that her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches.

Answer:

Y=-5x+32

Step-by-step explanation:

So you would plug in (7,-3) into y=mx+b. Solve the problem and you get -3=-35+b. So b would equal 32 because -35+32 is -3

The value of angle W, written as m∠W is 78

How to obtain m∠W?

First, we shall determine m∠Y. Details below:

m∠XYZ + m∠Y = 180 (straight line angle)

137 + m∠Y = 180

Collect like terms

m∠Y = 180 - 137

m∠Y = 43

Finally, we shall determine the value of m∠W. This is shown below:

m∠X + m∠Y + m∠W = 180

59 + 43 + m∠W = 180

102 + m∠W = 180

Collect like terms

m∠W = 180 - 102

m∠W = 78

Step-by-step explanation:

Equation of line in slope point form is given as:

[tex]y-y_1 =m(x-x_1) \\ \\ \therefore \: y - ( - 4) = - \frac{1}{2} (x - 2) \\ \\ \therefore \: y + 4= - \frac{1}{2} x + \frac{1}{2} \times 2 \\ \\ \therefore \: y + 4= - \frac{1}{2} x + 1 \\ \\ \therefore \: y + 4 - 1= - \frac{1}{2} x \\ \\ \therefore \: y + 3= - \frac{1}{2} x \\ \\ \therefore \: 2y + 6= - x \\ \\ \huge \purple{ \boxed{\therefore \: x + 2y + 6= 0}} \\ is \: the \: required \: equation \: of \: line.[/tex]

Answer:

x=0,3,-6,7

Step-by-step explanation:

set each factor equal to zero and then solve for x.

The zeroes of the polynomial are 0, 3, -6 and 7.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

We have the polynomial in form

x(x-3)(x+6)(x-7)=0

As, we can see the polynomial is of degree 4.

Also, the polynomial is in the form of factors.

Now, to find the zeros of the polynomial we compare each factor to 0.

x= 0

x -3 = 0

x= 3

and, x + 6= 0

x = -6

and, x -7 = 0

x = 7

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Answer:

okay ik the answer

Step-by-step explanation:

up ur butt and to the left

lol jk the answer is

                  the possibly is 15% since their is a bunch

Answer:

8/15

Step-by-step explanation:

there are 75 tickets in both the baskets and she put a total of 40 tickets into both baskets. that makes 40/75 wich reduces down to 8/15

Final answer:

Cole spent 7/12 hours on history homework after spending 5/12 hours on Spanish homework, with the total homework time being 1 hour.

Explanation:

The student asked: Cole spent some time working on his history homework. Then, he spent 5/12 hour working on his Spanish homework. Cole spent 1 hour on homework. What fraction of an hour did Cole spend on history? To find the time Cole spent on history homework, we subtract the time he spent on Spanish homework from the total homework time. Cole's total homework time is 1 hour, which is equivalent to 12/12 hours.

Therefore, the time spent on history homework is: 12/12 hours (total time) - 5/12 hours (Spanish homework) = 7/12 hours on history homework. So, the correct answer is C) 7/12.

Answer:

I believe the answer is 10 - 4m.

Step-by-step explanation:

6m + 10 - 10m

-10m + 6m = -4m

10 - 4m

On simplifying the expression. 6m + 10 - 10m we get, 10 - 4m.

Given : 6m + 10 - 10m

To simplify any linear expression followings are the steps:-

On simplifying we get,

[tex]\rm =6m + 10 - 10m\\-10m + 6m = -4m\\=10 - 4m[/tex]

Therefore, For the expression. 6m + 10 - 10m we get, 10 - 4m.

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Answer:

1

Step-by-step explanation:

The first thing to simplify is the Exponent

If The Exponent is a fraction than the denominator of the fraction will be the power of the root and the numerator will be the power of the expression

It will be in the form

[tex] \sqrt[a]{ {x}^{b} }[/tex]

Where a is the denominator and b is the numerator of the fraction

The first expression 216^1/3 will be

[tex] \sqrt[3]{{216}^{1} } [/tex]

6×6×6=216 so the expression = 6

The second expression 125^1/3 will be

[tex] \sqrt[3]{ {125}^{1} } [/tex]

5×5×5=125 so the expression =5

216^1/3 - 125^1/3

6 - 5

1

Answer:

34 for one ticket

Step-by-step explanation:

374 ÷ 11 = 34

divide by the amount of tickets they bought by the amount of money spent

Answer:

Step-by-step explanation:

-5 means the x coordinate

and 6 means the y coordinate

a) The next three terms are -9, -11, and -13

b) This is an arithmetic sequence

c) An arithmetic sequence is when the difference between one term and the next remains constant

d) We can make the equation y=-2x+1 where x is the term number, then we plug in 27 for x and solve for y

y=-2(27)+1

y=-54+1

y=-53

Hope this helped, and please mark as brainliest!

Answer:

R' (-4,1)

Step-by-step explanation:

Since the current coordinates is (-1, -4) and when rotating clock wise it would put into the second quadrant, which would mean the points would flip and the sign for the Y coordinate would change.

Answer:

i think the answer is A R' (4, -1)

Answer:

slope is -1

Step-by-step explanation:

y1-y2/ x1-x2

= -3 - 7 / 8 - (-2)

= -10/ 10

= -1

Answer:A

N=; 1% = 9.6; PV= -180; PMT 102.5; FV=0; P/Y=12, C/Y=12;PMT ;END

Final answer:

The correct TVM Solver setup for Troy's loan has a monthly interest rate of 0.8% and the rest of the parameters reflect the details of the loan and payment structure, making Option B the right choice.

Explanation:

To calculate the number of monthly payments Troy will have to make to pay off the loan for the television, we can use the Time Value of Money (TVM) formula where certain values will be plugged into the TVM Solver of a graphing calculator. Given the loan amount ($1850) and APR (9.6% annually, compounded monthly), we have to adjust the annual percentage rate to a monthly rate by dividing it by 12 months, resulting in a 0.8% monthly interest rate. Therefore, the values entered should reflect a monthly rate, not an annual rate.

The correct setup for the TVM Solver would be:

Therefore, the correct answer is Option B, where the monthly interest rate is accurately represented.

Cameron should buy 7 cans of wet food to feed his cat for a week.

To calculate the number of cans of wet food Cameron should buy to feed his cat for a week, we need to first determine the amount of dry food and wet food consumed daily. Cameron's cat eats 4 ounces of dry food and 3 ounces of wet food twice a day, so it consumes a total of 8 ounces of dry food and 6 ounces of wet food per day.

Next, we need to calculate the total amount of wet food consumed in a week. Since there are 7 days in a week, the cat would consume 7 times 6 ounces, which is 42 ounces of wet food in a week.

Now, we need to determine how many cans of wet food Cameron should buy. Each can of wet food contains 6 ounces, so to find the number of cans, we divide the total amount of wet food (42 ounces) by the weight of each can (6 ounces). Therefore, Cameron should buy 7 cans of wet food to feed his cat for a week.

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The solutions are [tex]x=15, x=-8[/tex] and [tex]x=9[/tex]

Explanation:

Part a: The equation is [tex]\frac{1}{3} (5x-9)=2(\frac{1}{3} x+6)[/tex]

Let us find the value of x.

Multiply the terms within the bracket, we get,

[tex]\frac{5}{3} x-3=\frac{2}{3} x+12[/tex]

Subtracting both sides by [tex]\frac{2}{3} x[/tex], we have,

[tex]\frac{3}{3} x-3=12[/tex]

Adding both sides by 3,

[tex]x=15[/tex]

Thus, the solution of the equation [tex]\frac{1}{3} (5x-9)=2(\frac{1}{3} x+6)[/tex] is [tex]x=15[/tex]

Part b: The equation is [tex]4(3x+5)-3=9x-7[/tex]

Multiply the terms within the bracket, we get,

[tex]12x+20-3=9x-7[/tex]

Subtracting both sides by 9x, we have,

[tex]3x+17=-7[/tex]

Subtracting both sides by 17,

[tex]3x=-24[/tex]

Dividing both sides by 3, we have,

[tex]x=-8[/tex]

Thus, the solution of the equation [tex]4(3x+5)-3=9x-7[/tex] is [tex]x=-8[/tex]

Part c: The equation is [tex]5(x+7)-3(x-4)=7x+2[/tex]

Multiply the terms within the bracket, we get,

[tex]5x+35-3x+12=7x+2[/tex]

Adding the like terms, we have,

[tex]2x+47=7x+2[/tex]

Subtracting both sides by 2 and 2x, we get,

[tex]45=5x[/tex]

Dividing both sides by 5, we have,

[tex]x=9[/tex]

Thus, the solution of the equation [tex]5(x+7)-3(x-4)=7x+2[/tex] is [tex]x=9[/tex]

This question requires understanding of mathematical equations and their solutions. The answer derives from equations wherein you first simplify inside parentheses, follow with multiplications or other operations, then isolate variables. The solutions to these equations can then be matched with each one.

The task here is drag the tiles to the correct boxes to complete the pairs and match each equation with the correct solution. This is a mathematical practice that requires algebraic methods. Let's solve the equations one by one:

Example 1: 5(3150 - 9) = 2(5x + 6)

First, perform the functions inside the parentheses, then distribute accordingly. Afterwards, isolate the variable to one side of the equation to find its value:

Example 2: 4(35 + 5) - 3 = 9.5 - 7

Follow the same steps as above to match this equation with its solution:

Example 3: 5(5 + 7) - 3(3 - 4) = 7x +:

Again, simplify inside the parentheses first, then distribute and isolate the variable. This process will provide solutions to match with each equation:

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A. There are 33 special characters.

B. The probability of guessing the password under the given circumstances is 1 out of 858 combinations.

Step-by-step explanation:

Step 1; First we need to determine all the possible values that can come in each space of the password.

From 0 to 9, there are a total of 10 values.

For uppercase letters, there are a total of 26 values from A, B, C, D ...Z

For lower case letters, there are also a total of 26 values from a, b, c, d ...z.

So out of these three characters, we have a total of 10 × 26 × 26 = 6,760 different combinations.

If there are 223,080 password combinations we need to divide this by 6,760 to calculate the possible values of the special characters.

6,760 × Number of possible special characters = 223,080,

Number of special characters = [tex]\frac{223,080}{6,760}[/tex] = 33. So there are 33 special characters.

Step 2; If the number and uppercase values are known then the  various lowercase letters and special characters are the unknown values.

The number of possible combinations = number of lowercase letters × number of special characters = 26 × 33 = 858.

So the probability of guessing the password is 1 out of 858 combinations.

(a) There are 216,320 special characters in the password combinations.

(b) The probability of guessing the account password with knowledge of the number and uppercase letter, but not the rest, is [tex]\(\frac{320}{11}\)[/tex].

Let's solve each part of the problem:

(a) Number of Special Characters:

Given that there are 223,080 password combinations and the special character comes last, it means there are 10 possible numbers (0-9), 26 possible uppercase letters, and 26 possible lowercase letters, leaving the remaining positions for special characters. Therefore, the number of special characters is:

[tex]\[ \text{Number of special characters} = 223,080 - (10 \times 26 \times 26) = 223,080 - 6760 = {216,320} \][/tex]word:

If you know the number and uppercase letter but forget the rest, you only need to guess the lowercase letter and special character. The total number of possible lowercase letters is 26, and the total number of possible special characters is 216,320 (calculated in part a).

Therefore, the probability of guessing the account password is:

[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{26 \times 216,320}{223,080} \]\[ \text{Probability} = \frac{6,387,520}{223,080}[/tex]

=320/11

GF = 11, GE = 28, HF = 14, [tex]DG=5\sqrt3[/tex]

Solution:

Given data:

DE = 11, GH = 14

In rectangle, opposite sides are equal.

DE = GF

GF = 11

Property of a rectangle:

The diagonals of a rectangle are equal in length and they bisect each other.

Half of diagonal GE = GH = 14

GE = 2 × GH

     = 2 × 14

GE = 28

HF is also a half of the diagonal DF.

By property of a rectangle, GH = HF

HF = 14

Diagonal of a rectangle formula:

[tex]D=\sqrt{\text{length}^2+\text{breadth}^2}[/tex]

[tex]14=\sqrt{DG^2+11^2}[/tex]

Squaring on both sides, we get

[tex]196={DG^2+121}[/tex]

[tex]{DG^2=196-121}[/tex]

[tex]{DG^2=75}[/tex]

Taking square root on both sides, we get

[tex]DG=5\sqrt3[/tex]

Hence GF = 11, GE = 28, HF = 14, [tex]DG=5\sqrt3[/tex].

Answer:

It will take 3.6 hours to wax a car if they work together.

Step-by-step explanation:

Calvin one hour work = [tex]\frac{1}{3}[/tex]

Alvin one hour work = [tex]\frac{1}{5}[/tex]

To find out how much they can do together per hour,

We have to add [tex]\frac{1}{3}[/tex] and [tex]\frac{1}{5}[/tex]

= [tex]\frac{1}{3} + \frac{1}{5} = \frac{(5 + 3)}{15}[/tex]

= [tex]\frac{8}{15}[/tex]  --------------(1)

They can do [tex]\frac{8}{15}[/tex] of the job per hour.

If "t" is the time taken to finish the  job together, then one hour work

[tex]\frac{1}{t}[/tex] ------------------------(2)

Now we have to find the value of "t" by setting the expression (1) and (2) equal.

[tex]\frac{8}{15} = \frac{1}{t}[/tex]

It can solve by flipping the equation;

[tex]\frac{t}{1} = \frac{18}{5}[/tex]

t = 3.6 hours

It will take 3.6 hours to wax a car if they work together.

Final answer:

The number of factors of 5 times a number depends on the prime factorization of that number. If the second number, 'n', is prime, the product has exactly four factors. However, if 'n' is composite, the number of factors would be the product of the incremented exponents of its prime factors.

Explanation:

The question is asking about the number of factors of a product that involves the number 5 and an unspecified number, let's call it 'n'. So we are looking at the number 5n. The number of factors a product has is related to the prime factorization of that product. The prime factorization of 5 is simple since 5 is a prime number itself. If 'n' is also a prime number, then 5n would have four factors: 1, 5, n, and 5n. However, if 'n' is composite, its prime factorization would need to be considered in finding the total number of factors. To count the factors, you would multiply the exponents of the prime factors, each incremented by one. For example, if n is a prime number, its exponent is 1, and 5's exponent would also be 1, so (1+1)*(1+1) gives us a total of 4 factors.

Answer:

x = 50

Step-by-step explanation:

140 = 85 + 1/2 x + 30

140 = 115 + 1/2x

25 = 1/2 x

x = 50

The minimum value at -1 ⇒ D

Step-by-step explanation:

The completing square form of ax² + bx + c is a(x - h)² + k, where

∵ The expression is x² + 4x + 3

∴ a = 1 , b = 4 , c = 3

- Use the rule above to find h

∵ [tex]h=\frac{-4}{2(1)}[/tex]

∴ h = -2

- To find k substitute x by the value of h

∵ k = (-2)² + 4(-2) + 3 = 4 - 8 + 3

∴ k = -1

- Substitute h and k in the form of the completing square

∵ a(x - h)² + k = 1(x - -2)² + (-1)

∴ a(x - h)² + k = (x + 2)² - 1

∴ x² + 4x + 3 = (x + 2)² - 1

∵ The completing square is (x + 2)² - 1

∵ a = 1 ⇒ greater than zero

∴ The value is minimum

- The minimum value is the value of k

∵ k = -1

∴ The minimum value of the function is -1

The minimum value at -1

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b

Step-by-step explanation:

the pattern goes by 2s so you do 13 times 2 plus 4 which would be your 0th term because six is your first term so you add 4 and 26 you get 30 and it is not 33 because that is the 14th term

Answer:

$72 earned on monday

Step-by-step explanation:

Delta pays Pete Rose $360 per day in the maintenance department at air port. Pete became I'll Monday and went home after 1/5 of a day

Delta works for only 1/5 of the day

To get the amount earn , multiply the work done by the rate

[tex]\frac{1}{5} \cdot 360 =72[/tex]

So $72 earned on monday

Pete Rose earns $360 per full day of work. On Monday, he worked for 1/5 of the day before becoming ill. By calculating 1/5 of his daily rate, we find that Pete earned $72 for that day.

The student's question is about calculating Pete's earnings for the part of the day he worked before he became ill. Since Pete earns $360 for a full day, we want to find out what he earns for 1/5 of that day, as 1/5 of the day is the amount of time he worked before going home.

Therefore, on Monday, Pete earned $72.

Answer:

3x - 4y

Step-by-step explanation:

sum means addition so:

(2x - 5y) + (x + y) =

2x + x = 3x

-5y + y = -4y

put those two answers together and you get 3x - 4y

Answer:

(A) 3x - 4y

Step-by-step explanation:

The unit price per pound is $4.91.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

A 13 ounce box of cereal cost $3.99.

Also, 0.8125 pound of cereal cost $3.99.

So, the unit price

= 3.99 / 0.8125

=  $4.91

Thus, the unit price is $4.91.

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Final answer:

To calculate the unit price per pound of a 13-ounce box of cereal costing $3.99, convert ounces to pounds and divide the cost by the weight in pounds, resulting in approximately $4.91 per pound.

Explanation:

To calculate the unit price per pound of a cereal box that weighs 13 ounces and costs $3.99, first convert the weight from ounces to pounds. Since there are 16 ounces in a pound, we calculate the weight of the cereal in pounds by dividing 13 ounces by 16 ounces/pound, which gives us 0.8125 pounds.

Next, we find the unit price per pound by dividing the total cost by the weight of the cereal in pounds. Therefore, the unit price is $3.99 divided by 0.8125 pounds which equals approximately $4.91 per pound (when rounded to two decimal places).

Answer:

Scientific Notation:

4.2 × 10^-3

E-Notation:

4.2e-3

Engineering Notation:

4.2 × 10^-3

Real Number:

0.0042

______________________________

6120

Step-by-step explanation: