What are the factors of9x2 + 42x + 49(3x + 7)O(9x + 7)?O (3x + 7) (3x – 7)(3x – 7)

The linear function of h is h(x) = -2x -13 and the values of h(3) = -19.

Two point form is a method for finding the equation of a function if two of its points are known. If (x1, y1) and (x2, y2) are the two points then equation of the function is given as-

(y - y1) = {(y1 - y2)/ (x1 - x2)} (x - x1)

Here, we are given that h(7) = -10 and h(-2) = 8

This, means that (7, -10) and (-2, 8) will satisfy the given function

Since, we have two points, we will use the two point form to find the equation of function h.

Substituting, x1 = 7, y1 = -10, x2 = -2 and y2 = 8 in the two point form equation we get-

( y - 7) = {(-10 - 8) / (7 + 2)} (x + 10)

y - 7 = (-18/9) (x + 10)

y - 7 = -2(x + 10)

y - 7 = -2x -20

y = -2x -20 + 7

y = -2x -13

Thus, h(x) = -2x -13

Hence, h(3) = -2(3) -13

= -6 -13

= -19

Therefore, h(3) = -19

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Answer:

\(x = \frac{1}{2} \)

The step by step explanation is attached to the answer.

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

A. ¼

Step-by-step explanation:

Rate of change (m) = \( \frac{y_2 - y_1}{x_2 - x_1} \)

Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:

Where,

\( (4, 1) = (x_1, y_1) \)

\( (-4, -1) = (x_2, y_2) \)

Plug in the values

Rate of change (m) = \( \frac{-1 - 1}{-4 - 4} \)

= \( \frac{-2}{-8} \)

= \( \frac{1}{4} \)

Rate of change = ¼

a. The factored form of the expression x² - 3x - 28 is (x - 7)(x + 4).

b. The factored form of the expression x² + 3x - 28 is (x - 4)(x + 7).

c. The factored form of the expression x² + 12x - 28 is (x + 14)(x - 2).

d. The factored form of the expression x² - 28x - 60 is (x - 30)(x + 2).

a. To factorize the expression x² - 3x - 28, we can use the factoring method. We look for two numbers that multiply to give the constant term (-28) and add up to the coefficient of the linear term (-3). In this case, the numbers are -7 and 4.

Split the middle term (-3x) using -7x and 4x:

x² - 7x + 4x - 28

Group the terms and factor by grouping:

(x² - 7x) + (4x - 28)

x(x - 7) + 4(x - 7)

Factor out the common binomial (x - 7):

(x - 7)(x + 4)

b. For the expression x² + 3x - 28, we follow a similar process:

Split the middle term (3x) using 4x and -x:

x² + 4x - x - 28

Group the terms and factor by grouping:

(x² + 4x) + (-x - 28)

x(x + 4) - 1(x + 28)

Factor out the common binomial (x + 4):

(x + 4)(x - 7)

c. Moving on to x² + 12x - 28:

Split the middle term (12x) using 14x and -2x:

x² + 14x - 2x - 28

Group the terms and factor by grouping:

(x² + 14x) + (-2x - 28)

x(x + 14) - 2(x + 14)

Factor out the common binomial (x + 14):

(x + 14)(x - 2)

d. Finally, let's factorize x² - 28x - 60:

Split the middle term (-28x) using -30x and 2x:

x² - 30x + 2x - 60

Group the terms and factor by grouping:

(x² - 30x) + (2x - 60)

x(x - 30) + 2(x - 30)

Factor out the common binomial (x - 30):

(x - 30)(x + 2)

By following these steps, we can factorize the given expressions into their respective factored forms.

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Since $31.65 x 20 = $633, the carpet's total cost includes both installation and delivery.

Describe a yard.

In both the British Imperial and US Customary Systems of Measurement, a yard is a unit of length. It corresponds to 3 feet or 36 inches. Yd is its emblem. Medium-sized object length is frequently measured using it.

How do you convert square yards to area feet?

To get the area value, multiply it by 9. To change the area from square feet to square yards, all you need to do is that. For instance, you must multiply 27 by 9 to convert 27 square feet to square yards.

Floor space is 15 x 12 ft², or 180 ft².

We know that 9ft² is 1 yard

So 180ft2 = 1/9*180 square yard

               = 20 square yard

Cost of 1 square yard = carpet cost + installation cost

                                  = $27.50 + $4.15

                                  = $31.65

Cost of 20 square yard = 20 * 31.65

                                    = $633

As a result, Wendy's room's carpet costs $633.

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The value of the equation that defines the function is f(x) = 3(5/3)ˣ

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

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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4Step-by-step explanation:

Answer:

Step-by-step explanation:

Any solid dot choices are incorrect. The end point is not included in the answer.  I don't see any solid dots, so that eliminates nothing.

4x>-8                       Divide by 4

4x/4 > - 8/4             Simplify

x > - 2

What this tells us is that x must be greater than - 2

You have to be going RIGHT.

So the answer is 3

The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

The first term and the common ratio for this problem is given as follows:

\(a_1 = -32, q = -\frac{1}{4}\)

The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:

\(a_{n + 1} = -\frac{1}{4}a_n\)

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Graph 2

It is the graph with the line on the positive Y-Axis as the equation is ended with +3

Step-by-step explanation:

you can find the answer by vertical opposite angle

if the value of x is computed and it's equal to 78 you will find the answer

78=(12x+18)^

78=(12×5+18)

78=(60+18)

78=78 the problem is solved

may u get branliest please please

Answer: 80cm

Step-by-step explanation:

i know

Answer:

80cm

Step-by-step explanation:

it may be right ......

Answer & Step-by-step explanation:

7). C = 44

8). S = 40

9). S = 40

10). T = 118

You can write in the comments if you want an explanation.

Hope this help ;)

Answer:

Let the required angle be x

7). \(x + 22 = 66 \\ \boxed{x = 44°}\)

8). \(x + 60 = 110 \\ \boxed{x = 50°}\)

9). \(x + 75 = 105 \\ \boxed{ x = 30°}\)

10). \(x = 31 + 87 \\\boxed{ x = 118°}\)

Answer:

48

Step-by-step explanation:

You times 8 by 3 to get 24. Then you multiply 24 by 3 to get 48

Answer:

216

Step-by-step explanation:

8x³

Put x as 3.

8(3)³

Solve for the power first.

8(27)

Multiply both terms.

216

The integral of the rational expression is equal to I = - 1.414 · ㏑ |x + 3.372| + 2.194 · ㏑ |x - 2.372| + 0.219 · ㏑ |x - 1| + C.

In this problem we find the case of a rational expression, whose integral must be determined. This can be done by means of partial fractions method, that is, decompose the rational expression into a sum of fractions. First, write the entire rational expression and use partial fractions method:

(x² - 9) / (x³ - 9 · x + 8)

[(x - 3) · (x + 3)] / [(x + 3.372) · (x - 2.372) · (x - 1)]

A / (x + 3.372) + B / (x - 2.372) + C / (x - 1)

(x - 3) · (x + 3) = A · (x - 2.372) · (x - 1) + B · (x + 3.372) · (x - 1) + C · (x + 3.372) · (x - 2.372)

x² - 9 = A · (x² - 3.372 · x + 2.372) + B · (x² - 2.272 · x - 3.372) + C · (x² + x + 7.998)

x² - 9 = (A + B + C) · x² + (- 3.372 · A - 2.272 · B + C) · x + (2.372 · A - 3.372 · B + 7.998 · C)

Solve the system of linear equations:

A + B + C = 1

- 3.372 · A - 2.272 · B + C = 0

2.372 · A - 3.372 · B + 7.998 · C = - 9

(A, B, C) = (-1.414, 2.194, 0.219)

(x² - 9) / (x³ - 9 · x + 8) = - 1.414 / (x + 3.372) + 2.194 / (x - 2.372) + 0.219 / (x - 1)

Second, integrate the resulting equation:

I = - 1.414 ∫ [1 / (x + 3.372)] dx + 2.194 ∫ [1 / (x - 2.372)] dx + 0.219 ∫ [1 / (x - 1)] dx

I = - 1.414 · ㏑ |x + 3.372| + 2.194 · ㏑ |x - 2.372| + 0.219 · ㏑ |x - 1| + C

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The statement about the linear equation 3a + 1/3(6a −9) = 1/2(10a − 6) that is true is: "The equation has an infinite number of solutions." (Option B)

A linear equation is defined as an equation with a maximum of one degree. A nonlinear equation is one with a degree greater than or equal to two.

On the graph, a linear equation looks like a straight line. On the graph, a nonlinear equation creates a curve.

To justify the above answer, we state the linear equation above:


3a + 1/3(6a −9) = 1/2(10a − 6) ; Simplified by opening the brackets, we have

3a + 2a − 3 = 5a − 3; collecting like terms on the left side, we have

5a -3 = 5a -3

Because 5a -3 = 5a -3, the expression holds true regardless of what integer or value a represents. Hence, it has an infinite number of solutions.

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The area of the circle is approximately 78.5 square meters.

To determine the area of a figure, we need to know what type of figure it is and what its dimensions are. The formulas for finding the areas of different types of figures are as follows:

Rectangles: Area = length x widthSquares: Area = side x sideTriangles: Area = 1/2(base x height)

Circles: Area = πr² (where π is pi and r is the radius)Problem 1:Let's say we have a rectangle with a length of 6 cm and a width of 4 cm.

To find its area, we use the formula Area = length x width. Substituting in our values,

we get:Area = 6 cm x 4 cm = 24 cm²Therefore, the area of the rectangle is 24 square centimeters.Problem 2:Next, let's look at a circle with a radius of 5 meters.

To find its area, we use the formula Area = πr². Substituting in our values, we get:Area = π(5 m)² = π(25 m²) ≈ 78.5 m²

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The surface area of the vase is 168.4 square inches.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.

The surface area of the cylindrical vase can be found using the formula SA = B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the vase. Since the vase has a circular base, the area of the base can be found using the formula for the area of a circle: B = πr², where r is the radius of the base.

The diameter of the vase is 4.3 inches, so the radius is half of that, or 2.15 inches. The area of the base is therefore:

B = πr² = 3.14 * (2.15)² ≈ 14.46 square inches.

The perimeter of the base is the circumference of the circle, which can be found using the formula C = 2πr:

P = 2πr = 2 * 3.14 * 2.15 ≈ 13.53 inches.

Now we can use the formula SA = B + Ph to find the surface area of the vase:

SA = B + Ph = 14.46 + 13.53 * 11 ≈ 168.39 square inches.

Rounding to the nearest tenth of a square inch, the surface area of the vase is approximately 168.4 square inches.

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Answer:Michelle paid $56.15 for her shoes

Step-by-step explanation:

Answer:Michelle paid $56.15 for her shoes

Step-by-step explanation:

Since Michelle paid $3.89 more for her shoes compared to Conrad, who paid $52.26. This means you have to add $3.89 to $52.26.

$3.89+$52.25= $56.15

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Answer:

they were 32 problems because 20/32 is 62.5

By using trigonometry, it can be calculated that

Value of x is \(\frac{2\pi}{3}\)

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

\(sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta\)

Trigonometry is a very important tool in mathematics.

Trigonometry has a very good application in heights and distance.

Trigonometry has also a very good application in calculus and differential equation and also in physics, trigonometry plays a very vital role

Here,

The trigonometric equation is

4cos x + 2 = 0 where 0 ≤ x ≤ π

4cos x = -2

cos x = \(-\frac{2}{4}\)

cos x = \(-\frac{1}{2}\)

cos x = cos \(\frac{2\pi}{3}\)

x = \(\frac{2\pi}{3}\)

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Answer:

A, B, E

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

85-79=6

Answer:

6

Step-by-step explanation:

85-79=6

Answer:

B. y=-x – 7

Step-by-step explanation:

Hope this helps!

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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The future value of the annuity after the end of 5 years is $552.56.

Given that, r =5%= 0.05, 5 years  = 5 yearly payments, so n = 5, and P = $100.

The formula to find the annuity formula \(FV=\frac{P \times ((1+r)^{n}-1 )}{r}\).

Now, \(FV=\frac{100 \times ((1+0.05)^{5}-1 )}{0.05}\)

⇒FV = 100 × 55.256

⇒FV = $552.56

Therefore, the future value of the annuity after the end of 5 years is $552.56.

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The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.

According to the problem, two equations can be set up:

If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:

A + n = 7(B - n)

If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:

A - n = 2(B + n)

We can rearrange these equations to make them easier to solve:

8n = 7B - A

3n = A - 2B

Setting these equal to each other, since they are both equal to 24n, gives:

21B - 3A = 8A - 16B

37B = 11A

A / B = 37 / 11

= 3. 36

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Answers:

There are infinitely many possible ways to answer the third part.

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

Explanation:

The midline is the horizontal line that goes through the center of the sine curve. Visually we can see that is y = 0. Another way we can see this is to note how y = 0 is the midpoint of y = 1.5 and y = -1.5, which are the max and min respectively.

---------

The amplitude is the vertical distance from y = 0 to y = 1.5, and it's also the vertical distance from y = 0 to y = -1.5; in short, it's the vertical distance from center to either the peak or valley.

---------

The general format of a sine curve is

y = A*sin(B(x-C)) + D

where,

In this case, we found so far that

The only thing we're missing is the value of C, which is the phase shift.

Note the point (pi/2, 1.5) is one of the max points on this curve. Also, recall that sin(x) maxes out at 1 when x = pi/2

This must mean that the stuff inside the sine, the B(x-C) portion, must be equal to pi/2 in order to lead sin(B(x-C)) = 1.

So,

B(x-C) = pi/2

0.5(pi/2-C) = pi/2

pi/4 - C/2 = pi/2

4*( pi/4 - C/2 ) = 4*(pi/2)

pi - 2C = 2pi

-2C = 2pi - pi

-2C = pi

C = pi/(-2)

C = -pi/2

This allows us to update the function to get g(x) = 1.5*sin(0.5(x+pi/2)) which is the same as g(x) = 1.5sin(0.5x + pi/4)

This is one possible answer because we could have infinitely many possible values for C, due to sin(x) = 1 having infinitely many solutions.

Also, you could use cosine instead of sine. Cosine is just a phase shifted version and of sine, and vice versa.

If f(x,y,z) is a vector field rather than a scalar function. A vector-valued function is one that has a vector value and a calculable curl. Therefore, if we calculate this value, it will once more be a vector-valued function. The right response in this case is option B.

The following considerations must be made in order to answer this question: It is specified that the divergence of a vector field is a scalar-valued function.

A vector field's specified and actual curl is a vector field. A scalar field's divergence/Curl is not specified. A scalar field's gradient is a vector field that has a definite definition. A vector field's gradient is not known.

Since F is a vector-valued function, we may discover its divergence, which will be a scalar-valued function, and since the gradient of the scalar-valued function will be a vector-valued function, this calculation is attempting to compute the gradient of the divergence of the vector field F.

Complete question:

Let f(x,y,z) be a scalar-valued function, and F(x,y,z) be a vector field. Is the following defined? If it is defined, is it a scalar-valued function or a vector field? (You are only allowed one attempt for each part of this problem.)

(a) V (Vn Defined- it is a scalar-valued function O Defined - it is a vector field O Not defined

(b) VV F) O Defined - it is a scalar-valued function Defined - it is a vector field O Not defined

(c) V (V F) Defined it is a scalar-valued function Defined - it is a vector field Not defined

(d) V (V x F) Defined it is a scalar-valued function Defined it is a vector field Not defined

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