What number does x stand for in this equation?
-7x + 6= 27
A
21
B
2
C
-3
D
-7

Based on the intersecting secants theorem:

a. CG*CE = CH*CD

b. length of DH = 10 in.

When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.

a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:

CG*CE = CH*CD

b. Given the following lengths:

CG = 3 in, CH = 2 in, and GE = 5 in

CE = CG + GE = 3 + 5 = 8 in.

CD = CH + DH = 2 + DH

Substitute into CG*CE = CH*CD:

3*8 = 2*(2 + DH)

24 = 4 + 2DH

24 - 4 = 2DH

20 = 2DH

20/2 = DH

DH = 10 in.

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Answer:

\(x = 4\)

Step-by-step explanation:

\(5x + 2 = 22\)

\(5x = 20\)

\(x = 4\)

\(\small\bold{5x + 2 = 22 }\)

Subtract 2 from 22 :

\(\small\bold{ 5x + 2 = 22}\)

\(\small\bold{5x = 22 - 2 }\)

Simplify :

\(\small\bold{5x = 20 }\)

Now , Divide 5x by 20 :

\(\small\bold{ \frac{5x}{20}}\)

\(\small\bold{x = 4 }\)

9514 1404 393

Answer:

  (H)  y = 1/3x + 5

Step-by-step explanation:

When x=0, y=5, so you know G is not a possibility.

Y increases at a lower rate than x does. For example, between the first two table entries, x goes up by 6, but y goes up by 2. The only choice with a rate of change less than 1 is ...

  (H)  y = 1/3x + 5

Answer:

===========================

Twice a number n is no less than 10 units from −1:

The inequality becomes an absolute value and translates as:

Answer:

f(x) + g(x) = 7x² - 4x + 2

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 5x² - 3x - 1

g(x) = 2x² - x + 3

Step 2: Find f(x) + g(x)

Answer:

-1/3

Step-by-step explanation:

because it is a negative number and closer to zero than -3 is making it greater, becuase it is closer to a positive number.

Answer:

-1/3 is greater than -3

-3 < -1/3

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.

Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:

n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

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The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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Answer:

Amount = $3.84

Step-by-step explanation:

Given the following data;

Total bill = $48

Tip = 8%

To find the amount of dollars tipped?

\( Amount = \frac {8}{100} * 48\)

\( Amount = \frac {384}{100} \)

Amount = $3.84

Therefore, the amount of dollars Mr. Cosgrove tipped is $3.84.

Answer: The Gcf Of 4x-7 is equivalent to 1

Step-by-step explanation:

The remainder of the polynomial division \(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\) is 2y²

From the question, we have the following parameters that can be used in our computation:

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\)

When the numerator is expanded, we have

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1) + 2y^2}{y^3 + 1}\)

Split the expanded expression

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1)}{y^3 + 1} + \frac{2y^2}{y^3 + 1}\)

Evaluate

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = y - 1 + \frac{2y^2}{y^3 + 1}\)

From the above, we have

Quotient = y - 1

Remainder = 2y²

Hence, the remainder of the polynomial division is 2y²

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Answer:

(x-2)(x^2+1)

do not exist the answer, so check your question

Step-by-step explanation:

(x^3-2x^2)+(x-2) = x^2(x-2)+(x-2)

= (x-2)(x^2+1)

The vertex form of y = 8 · x² + 32 · x + 17 is the quadratic equation y + 15 = 8 · (x + 2)².

In this problem we find a quadratic equation in standard form, that is, an equation of the form y = a · x² + b · x + c, where a, b, c are real coefficients. By algebra properties we need to find its vertex form, whose definition is shown below:

y - k = C · (x - h)²

Where:

First, write the quadratic equation:

y = 8 · x² + 32 · x + 17

Second, use algebra properties until vertex form is found:

y - 17 = 8 · x² + 32 · x

y - 17 = 8 · (x² + 4 · x)

y - 17 + 32 = 8 · (x² + 4 · x + 4)

y + 15 = 8 · (x + 2)²

The quadratic equation y + 15 = 8 · (x + 2)² is the vertex form of y = 8 · x² + 32 · x + 17.

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Answer:

  x = 42

Step-by-step explanation:

The marked angles are supplementary, so their sum is 180°.

  (2x +8) +(2x +4) = 180

  4x +12 = 180 . . . . . . . . . simplify

  x +3 = 45 . . . . . . . divide by 4 (because we can)

  x = 42 . . . . . . subtract 3

_____

Additional comment

A "two-step" linear equation like this one is usually solved by subtracting the unwanted constant, then dividing by the coefficient of the variable. Here, we have done those steps in reverse order. This makes the numbers smaller and  eliminates the coefficient of the variable. Sometimes I find it easier to solve the equation this way.

The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

In the given question,

We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.

Since we have to find the image after a dilation.

So we learn about it now,

Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.

So the given point is (-9,12).

Scale factor is 1/3.

So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as

=(-9×1/3,12×1/3)

Simplifying

=(-3,4)

Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

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Answer:A

Step-by-step explanation:

To find the rate of decay, we need to use the formula A(t) = P(0.82)^t, where A(t) is the amount after t years, P is the initial amount, and 0.82 is the decay factor.

The decay factor is equal to 1 minus the decay rate, so we can solve for the decay rate as follows:

0.82 = 1 - r

r = 1 - 0.82

r = 0.18

Therefore, the rate of decay is 18%, which corresponds to answer choice A.

Answer:

A

Step-by-step explanation:

The system of equations where the combination of the candies gives you a total of 22 points are:

x + y = 9

2x + 3y = 22

To create the equations, we shall first define the variables:

x = the number of purple candies

y = the number of yellow candies

Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.

Then, we would make sure that the total number of candies selected is 9.

The first equation represents the total number of candies selected:

x + y = 9

The second equation represents the total number of points obtained:

2x + 3y = 22

Therefore, the system of equations is:

x + y = 9

2x + 3y = 22

This is a system of linear equations.

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The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * \(e^{rt}\)

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * \(e^{0.02 * 4}\)

Using a calculator, we can calculate:

A = $16,000 * \(e^{0.08}\)

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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The evaluated value of x from the line geometry given is 36.

An angle is the point where two lines meet. From the given diagram, the sum of the angles on the line is 180 degrees.

Take the sum to have

x + 3x + x = 180

Simplify

4x + x = 180

5x = 180

Divide both sides by 5

5x/5 = 180/5

x = 36

Hence the value of x from the diagram is 36

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The  APR on the loan will be $13. The APR is found by the standard formula. It is calculated annually.

APR is an annualized cost indication for a loan that includes all costs.

Suppose there is an initial amount as P. The interest, or say charge on it, is applied annually as 'C' amount.

The given data in the problem is;

Loan payment = $400

Fees  = $52

APR=?

The value of the APR is found as;

\(APR = \dfrac{C}{P} \times 100 \\\\\ APR = \dfrac{52}{400} \times 100 \\\\\ APR = \$ \ 13\)

Hence, the  APR on the loan will be $13.

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From the problem, there are two running speeds :

In order to graph distance vs time, we need to get the distance function first by taking the integral of both speed functions.

This will be :

Note that the first runner is faster than the second runner, so he will be at distance 0.

and the second runner will be at distance 1.

Set t = 0 and d(t) = 0 for the first runner :

So the distance function of the first runner is :

Set t = 0 and d(t) = 1 for the second runner :

The distance function of the second runner is :

Now graph these functions :

Get atleast 3 points to graph the functions.

With t = 1, 2 and 3

For the first runner :

We have the points (0, 0), (1, 1.5), (2, 1.78) and (3, 1.875)

The graph will be :

where x-axis refers to the time in hours and the y-axis refers to the distance.

For the second runner :

We have the points (0, 1), (1, 1.75), (2, 1.89) and (3, 1.94)

The graph will be :

The blue curve is for the first runner and the orange curve is for the second runner.

To get the point where the two runners will meet. the distance must be equal or the y-coordinate must be the same.

Equating both distance functions :

Since the time is negative, they will not meet each other. and their speed will not be equal to zero.

Looking at the graph, the horizontal asymptote is at y = 2, which they will never reach.

No, the relationship on the table is not proportional

From the question, we have the following parameters that can be used in our computation:

x   y

____ ____

6 -2

7 -1

8 0

9  1

On the table of values, we can see that:

Using the above as a guide, we have the following:

The relationship is not a proportional relationship

This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)

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\(\boxed{A}\\\\ U=5(2n+22)+2\left( n+\cfrac{3}{2} \right) \\\\\\ U=10n+110+2n+3 \implies U=12n+113 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\hspace{5em}\textit{in 2009, that's 9 years after 2000, n = 9}\\\\ U(9)=12(9)+113\implies U(9)=221 ~~ millions\)

Answer:

Y=30

X=40

Step-by-step explanation:

for Y is because 46-16=30

for X is because 180÷3=60

80+60=140

180-140=40

Answer:

it is 0.75

Step-by-step explanation:

Answer:

3 1/3 - 2 7/12 = 3/4

Step-by-step explanation:

Find the improper fractions:

3 1/3 = 10/3

2 7/12 = 31/12

Find the common denominator:

10/3 = 40/12

31/12

Subtract:

40/12 - 31/12 = 9/12

Simply:

9/12 = 3/4

The expression can be rewritten by given term as;  3^15

We need to simplify the expression below:

(3^2 x 3^3)^3

Remember that we can add these exponents, so we get:

(9 x 9)^3 = 81^3

Then we can rewrite this as:

531441

Takin the product between the exponents we will get:

(3^5)^3

Thus, the solution is 3^15

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The solution to the equation 12m + 100 = 700m is given as follows:

m = 0.1453.

The equation in the context of this problem is defined as follows:

12m + 100 = 700m

The variable for which we want to obtain the solution is given as follows:

m.

To obtain the solution, we isolate the variable m, applying inverse operations, as follows:

12m + 100 = 700m

700m - 12m = 100 -> subtraction is the inverse of addition.

688m = 100

m = 100/688 -> division is the inverse of multiplication.

m = 0.1453.

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