Using the graph below graph y = sin(2x + 7) by plotting two points.

The dimensions of the tennis court are 42 feet by 114 feet.

Let the width of the tennis court be x feet.

We can use the formula for perimeter to solve this problem. The perimeter of a rectangle is equal to 2 times the length plus 2 times the width.

2(2x + 30) + 2x = 228

4x + 60 = 228

4x = 168

x = 42

The length of the tennis court is 2x + 30 = 2(42) + 30 = 114 feet.

The dimensions of the tennis court are 42 feet by 114 feet.

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Answer:

Dylan is 10 years old, and Genesis is 11.

Step-by-step explanation:

If Genesis and Dylan's age are consecutive integers, and Genesis is older, we can represent their ages as:

Dylan's age: x

Genesis' age: x+1

This would mean Genesis is a year older than Dylan.

The product of their ages is 110.

We can write an equation:

x×(x+1)=110

x²+x=110 (Distribute x)

x²+x-110=0 (Move 110 to the other side)

You can solve this by the quadratic equation, by factoring or by completing the square

I'll solve it by the quadratic equation:

We must first find the coefficients a, b and c, and then plug it into the formula.

\(x = \frac{ - 1 + - \sqrt{ {1}^{2} - 4 \times 1 \times - 110} }{2 \times 1} \\ x = \frac{ - 1 + - \sqrt{1 + 440} }{2} \\ x = \frac{ - 1 + - 21}{2} \)

Since we have a ± symbol, we get 2 real solutions, x1 and x2.

x=-1±21/2

x1=-1+21/2

x1=20/2

x1=10

x2=-1-21/2

x2=-22/2

x2=-11

Since their age can't be negative, x2 can't be a solution, so Dylan's age must be 10, and Genesis' age must be 11.

Hope this helps, and let me know if you need help with another method to solve this problem!

Answer:

16.94 cm

Step-by-step explanation:

Calculating the value of d and the fixed monthly payments against a $200,000 mortgage that last for 25 years

Given that :

Present value ( PV ) $200,000

Period = 25 years

Total period ( n ) = 25 * 12 = 300

also PMT is done monthly

∴ monthly interest rate = ( 716.67 / 200,000 ) * 100 = 0.358% ( r )

i) Next step : Calculate the value of PMT

using the equation below

\(PMT = [\frac{PV}{\frac{1-(1+r)^{-n} }{r} } ]\)     where :  PV = $200,000, r = 0.358% , n = 300

input values into equation

∴ d = PMT  = $1088.63

ii) Fixed monthly payments

=  d - 716.67

= 1088.63 - 716.67  = $372

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Answer:

b1=$200,000−$372.41=$199,627.59

$199,628

Answer:

(2,1) yes the rest no

Step-by-step explanation:

u got this

Answer:

(-2, 1) is the only solution

Step-by-step explanation:

all other answers are not a solution.

3x - 2y = -8

6x + 7y = -5

substitute

(-2, 1)

3 * -2 - 2 * 1 = ?

-6 - 2 = -8

and

6 * -2 + 7 * 1 = ?

-12 + 7 = -5

all other subitutions do not make it a proper solution:

substitute

(5, -5)

3 * 5 - 2 * -5 = ?

15 - -10 = 25

25\(\neq\)-8

since the values have to be true for both equations this is not a solution, there is no need to do the second equation.

repeat this with the remaining

your answers are

(-2, 1) - yes

(-4, -2) - no

(7, 3) - no

(5, -5) - no

hope this helps:)

Answer:

-10

Step-by-step explanation:

Let the number be x

x - 40 = 5x

⇒ -40 = 5x - x

⇒ 4x = -40

⇒ x = -40/4

⇒ x = -10

Answer:

-10

Step-by-step explanation:

Let the number be x

x - 40 = 5x

4x = -40

x = -10

Answer:

i think the fourth one is equvilent ratio

Step-by-step explanation:

Answer:

\(y =\frac{x}{4}\)

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with \(y=\frac{3}{x} -7\), we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = \(x^\frac{1}{2}\), even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with \(y = \frac{x}{4}\). x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that \(y=\frac{x}{4}\) is linear.

Answer:

GET PHOTOMATH

Step-by-step explanation:

The standard deviation of the given series of ACT scores is approximately 4.90.

To calculate the standard deviation of a series of ACT scores, you need to follow a few steps.

First, find the mean of the scores by adding them up and dividing by the total number of scores.

In this case, the mean is (32 + 20 + 18 + 21 + 24) / 5 = 23. Next, calculate the deviation of each score from the mean by subtracting the mean from each individual score.

The deviations are: 9, -3, -5, -2, 1. Then, square each deviation to eliminate negative values and find the variance. The squared deviations are: 81, 9, 25, 4, 1.

Compute the average of these squared deviations, which gives the variance: (81 + 9 + 25 + 4 + 1) / 5 = 24.

Finally, take the square root of the variance to obtain the standard deviation: √24 ≈ 4.90.

Therefore, the standard deviation of the given series of ACT scores is approximately 4.90.

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Answer:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

46degrees

Step-by-step explanation:

From the question, we are told that both triangles are similar, hence;

<E = <S

<D = <R

<F = <T

From triangle DEF

<D + <F + <E = 180

Since <D = <F = 67

67 + 67 + <E = 180

134 + <E = 180

<E = 180 - 134

<E = 46degrees

Since <E = <S, hence the measure of <S  is 46degrees

Step-by-step explanation:

Lets break this word problem down:

"The difference" means we're going to be finding x - y ("difference" means we're finding how much one value "differs" from the other)

"a number and it's opposite" so we're doing x - y, where y = -x. So already, we can re-write this as x - (-x) or x + x

"is 28" so x + x = 28 ("is" always means "equals")

"Find the number" so we're finding x.

x - (-x) = 28  (I went back a step so I could write everything out more plainly)

simplify

x + x = 28

add

2x = 28

divide both sides by 2 to get x on its own

x = 14

Answer:

14

Which statement best reflects the solution(s) of the equation?

\( \small \sqrt{2x - 1} - x + 2 = 0\)

There is only one solution: x = 5 .

The solution x = 1 is an extraneous solution.

\( \small \sqrt{2x - 1} - x + 2 = 0\)

\( \small \sqrt{2x - 1} = x - 2 \)

\( \small 2x - 1 = {(x - 2 )}^{2} \)

\( \small 2x - 1 = {x}^{2} - 2 \times x \times 2 + {2}^{2} \)

\( \small 2x - 1 = {x}^{2} - 4x + 4\)

\( \small {x}^{2} - 4x - 2x + 4 + 1 = 0\: \)

\( \small {x}^{2} - 6x + 5 = 0\: \)

\( \small {x}^{2} - 5x - x+ 5 = 0\: \)

\( \small x(x- 5) - (x - 5 )= 0\: \)

\( \small (x- 1)(x - 5 )\)

so the root would either be 5 or 1

_____________________________________

putting the value of x as 1,

\( \small \sqrt{2 \times 1 - 1} - 1 + 2 = 0\)

\( \small 1 - 1 + 2 = 0\)

\( \small 3 - 1≠ 0\)

hence , it's not the true solution of the equation

_____________________________________

putting the value of x as 5,

\( \small \sqrt{2 \times 5 - 1} - 5 + 2 = 0\)

\( \small 3 - 5 + 2 = 0\)

\( \small 5 - 5 = 0\)

\( \small 0 = 0\)

hence ,it's the true solution of the equation

Let's solve

\(\\ \rm\rightarrowtail \sqrt{2x-1}-x+2=0\)

\(\\ \rm\rightarrowtail \sqrt{2x-1}=x-2\)

\(\\ \rm\rightarrowtail 2x-1=(x-2)^2\)

\(\\ \rm\rightarrowtail 2x-1=x^2-4x+4\)

\(\\ \rm\rightarrowtail x^2-6x+5=0\)

\(\\ \rm\rightarrowtail (x-1)(x-5)=0\)

Option B is correct

As putting 1 as x

Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

Answer:

(4n-2)+90+(3n+8)=180=>

4n-2+90+3n+8=180=>

7n+96=180=>

7n=84=>

n=12

Answer:

1

Step-by-step explanation:

Because 2 times 1 is 2 plus 1 is equal to 3

Answer:

Step-by-step explanation:

h + (5*u - 10 )

Answer:

9n+18(2n-6)+13

Step-by-step explanation:

First, use distributive property to eliminate the parenthesis:

9n + 18(2n -6) + 13

9n + 36n - 108 + 13

Next, combine like terms:

9n + 36n - 108 + 13

45n - 108 + 13

45n + 121

Hope this helps!!

Alan~

Answer:

The mean of sampling distribution of the proportion of the students who prefer later start times for school

                        μₓ = p = 0.63

Step-by-step explanation:

Explanation:-

Given sample size 'n' =200

given data Of the 200 students surveyed at the local high school, 126 say that they prefer earlier start times for school

sample proportion

                        \(p = \frac{x}{n} = \frac{126}{200} = 0.63\)

The mean of sampling distribution of the proportion of the students who prefer later start times for school

                        μₓ = p = 0.63

Standard deviation of the proportion

                     \(S.D = \sqrt{\frac{p(1-p)}{n} } = \sqrt{\frac{0.63(1-0.63)}{200} } = 0.034\)

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

Answer:

1/2 hour

Step-by-step explanation:

1/6 is closest to 0 hours

3/7 is closest to 1/2 hour

Answer is 1/2 hour

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

The required solution of the given algebraic expression is x = 6.

The algebraic expression consists of constants and variables using mathematical operators. eg x + y + z, or y = x + z etc.

Here,
Given an algebraic expression,
x + 1 +1 +1 +1 +1 +1 +1  = 1 +1 +1 +1 +1 +1 +1 + 1 +1 +1 +1 +1 +1

Combining like terms on each side of the equation, we get,
According to the question

x + 7 = 13
x = 6

Thus, the required solution of the given algebraic expression is x = 6.

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Answer:

x + 7 = 13

Step-by-step explanation:

(in case you also need it) x = 6

A person who has owned a Roth IRA for five years may withdraw money from the account to buy their first home. The individual has to meet certain requirements and can't withdraw more than $10,000 per person.

A Roth IRA is a type of individual retirement account that allows for tax-free withdrawals of contributions at any time, without penalty or taxes. After five years of ownership, a person who has a Roth IRA may withdraw money from the account to buy their first home. This withdrawal is known as a "first-time homebuyer distribution."

However, there are certain rules and limitations to be aware of when withdrawing money from a Roth IRA for a first home purchase. The individual must be a first-time homebuyer, defined as someone who has not owned a home in the past two years. Additionally, the maximum amount that can be withdrawn for a first home purchase is $10,000 per person.

It's important to note that while contributions to a Roth IRA can be withdrawn tax-free and without penalty, earnings on those contributions may be subject to taxes and penalties if withdrawn before age 59 and a half.

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