Write a proportion for the statement.
40 is to 10 as 32 is to 8.

Answer:

c. a[b(b + 6)+7(a²-2)]

Step-by-step explanation:

look at the pic

The equivalent expression of the expression ab² + 6ab + 7a³ - 14a is

C. a [b (b + 6) + 7 (a² - 2)]

Option C is the correct answer.

We have,

To find the expression that is equivalent to ab² + 6ab + 7a³ - 14a, we can factor out common terms from the given expression.

The common terms in the expression are "a" and "(b + 7)".

Step 1:

Factor out "a" from the expression:

ab² + 6ab + 7a³ - 14a = a(b² + 6b + 7a² - 14)

Step 2:

Factor the quadratic expression inside the parenthesis:

b² + 6b can be factored as b(b + 6)

7a² - 14 can be factored as 7(a² - 2)

Step 3:

Putting it all together, the equivalent expression is:

a [b (b + 6) + 7 (a² - 2)]

Now let's check which option matches this expression:

a. (b + 7)(b + 6)(a² - 2) - Not equivalent

b. b(b + 6) + 7(a^2 - 2) - Not equivalent

c. a[b(b + 6) + 7(a² - 2)] - Equivalent

d. a[(b + 6)(b + 7a² - 14)] -Not equivalent

Thus,

The equivalent expression is

C. a [b (b + 6) + 7 (a² - 2)]

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Using the Fundamental Counting Theorem, it is found that there are 10 positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The number of options for each selection are given as follows, considering there are 10 possible digits, and that the last two are fixed at 7 and 1, respectively:

[tex]n_1 = 10, n_2 = n_3 = 1[/tex]

Hence, the number of integers is given by:

N = 10 x 1 x 1 = 10.

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Answer:

slope = -2

Step-by-step explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. Since the given equation is not in the exact slope-intercept form, we need to rearrange it to identify the slope.

y + 2x = 5                         <----- Given equation

y = -2x + 5                       <----- Subtract 2x from both sides

Now, we can see that in the "m" position, there is a value of -2. This makes the slope = -2.

Answer: r - 10 = 51

Step-by-step explanation:

Using the vertex of a quadratic function, she should harvest her honey after 64 days to maximize profit.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

The profit function is given as follows:

P(t) = -16t² + 2050t + 150.

The coefficients are a = -16 < 0, b = 2050, c = 150, hence the t-value of the vertex is:

[tex]t_v = -\frac{b}{2a} = -\frac{2050}{-32} = 64[/tex]

Hence she should harvest her honey after 64 days to maximize profit.

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Answer:

x ≅ 0.477.

Step-by-step explanation:

You probably meant:

[tex]10^x = 3.[/tex]

If that is the case, then let's solve it:

[tex]10^x = 3\\\\log\,10^x=log\,3\\\\x = log\,3\\\\x = (approx.)\,\,0.477.[/tex]

The Domain is (-∞, -2) U (-2, 2) U (2, ∞) and Range is (-∞, -2) U [-1, ∞) and x-intercept = (-1.5, 0), (1.5, 0) and y-intercept = (0, -1).

It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (circle is a special of type of ellipse).

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

From the graph:

a) The domain: all values of x

The range: all values of y

Except: Values at asymptotes are excluded.

Domain = (-∞, -2) U (-2, 2) U (2, ∞)

Range = (-∞, -2) U [-1, ∞)

b)

x-intercept = (-1.5, 0), (1.5, 0)

y-intercept = (0, -1)

c) Horiznotal asymptotes: y = -2

d)Vetical asymptotes: x = -2, x = 2

e) Oblique asymptotes: There is no oblique asymptotes

Thus, the Domain is (-∞, -2) U (-2, 2) U (2, ∞) and Range is (-∞, -2) U [-1, ∞) and x-intercept = (-1.5, 0), (1.5, 0) and y-intercept = (0, -1).

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A function assigns the value of each element of one set to the other specific element of another set. The third, fourth, and fifth terms of the sequence are 5, 8, and 13 respectively

A function assigns the value of each element of one set to the other specific element of another set.

Given the nth term of the sequence is given by the formula,

[tex]a_n = a_{(n-1)}+a_{(n-2)}[/tex]

Also, the first term and the second term of the sequence are 2 and 3 respectively, therefore, the other terms of the sequence are,

[tex]a_3 = a_{(3-1)}+a_{(3-2)}\\\\a_3 = a_2 + a_1\\\\a_3 = 3 + 2\\\\a_3 = 5[/tex]

[tex]a_4 = a_{(4-1)}+a_{(4-2)}\\\\a_4 = a_3 + a_2\\\\a_4 = 5 + 3\\\\a_4 = 8[/tex]

[tex]a_5 = a_{(5-1)}+a_{(5-2)}\\\\a_5 = a_4 + a_3\\\\a_5 = 8 + 5\\\\a_5 = 13[/tex]

Hence, the third, fourth, and fifth terms of the sequence are 5, 8, and 13 respectively.

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There are 6,840 different top 3 finishes.

We need to count the number of options for each position.

The number of different top 3 finishes is given by the product between the numbers of options, so we have:

20*19*18 = 6,840

There are 6,840 different top 3 finishes.

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Answer:

f(g(x)) = 50x² + 140x + 93

Step-by-step explanation:

f(g(x)) means that within the f(x) equation, you want to replace all of the x variables with the g(x) equation.

So,

f(g(x)) = 2 (5x+7)² -5

= 2 ( 25x²+ 70x + 49) - 5

= 50x² + 140x + 93

:)

The amount of pounds of chlorine needed is 62. 5 pounds. Option D

WE have the perimeter of a rectangle to be;

Volume = l × h × w

L = length = 50 meters

w = width = 25 meters

height = 3 meters

Substitute into the formula

Volume = [tex]50[/tex] × [tex]25[/tex] × [tex]3[/tex]

Volume = [tex]3750[/tex] cubic meters

If 0. 25 pounds of chlorine is in 15 cubic meters of water

x pounds would be 3750 cubic meters

Cross multiply

0. 25 × 3750 = 15x

937. 5 = 15x

x = [tex]\frac{937. 5}{15}[/tex]

x = 62. 5 pounds

Thus, the amount of pounds of chlorine needed is 62. 5 pounds. Option D

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Let's take this problem step-by-step:

Note:

'-- (1), -- (2), etc.' are equation markers used to show steps

First step, isolate all the variables to one side and constant to the other

 [tex]3x + 2y = 8--(1)\\3x-y=-3--(2)[/tex]

Second step: (1) - (2)

 [tex](1) - (2)\\3x + 2y-(3x-y)=8-(-3)\\2y + y=11\\3y = 11\\y = \frac{11}{3} --(3)[/tex]

Third step: Plug (3)'s value of y into (2)

[tex](3)_.into_.(2)\\3x -\frac{11}{3} = -3\\3x = \frac{11}{3}-3\\ 3x = \frac{11-9}{3} \\3x = \frac{2}{3} \\x=\frac{2}{9}[/tex]

Answer: x = 2/9, y = 11/3

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Answer:

3x+ 2y=8  ⇒ ( 1 )

  3x+3=y  ⇒ ( 2 )

First, let us take the equation (1).

We can replace y with ( 3x + 3 ).

Solving the below expression let us find the value of x.

[tex]3x + 2y = 8\\3x + 2 ( 3x + 3 ) = 8\\3x + 6x + 6 = 8\\9x + 6 = 8\\9x = 8 - 6\\9x = 2\\x = \frac{2}{9}[/tex]

And now let us take equation ( 2) to find the value of y.

For that let us replace x with 2/9.

Let us find it now.

[tex]3x+3=y\\\\3*\frac{2}{9} +3=y\\ \\\frac{6}{9} +3=y\\ \\\frac{6}{9} +\frac{3}{1} =y\\\\\frac{6}{9} +\frac{3*9}{1*9} =y\\\\\frac{6}{9} +\frac{3*9}{1*9} =y\\\\\frac{6}{9} +\frac{27}{9} =y\\\\\frac{33}{9} =y\\\\\frac{11}{3} = y[/tex]

Answer:

[tex]-6x[/tex]

Step-by-step explanation:

[tex]\sqrt{36x^2} = 6\times\sqrt{x^2}\\\\=6\times-x\\\\=-6x[/tex]

Answer:

1

Step-by-step explanation:

the mode is the number that is repeated more often than any other numbers. the given numbers are 1,2,3,4,5,6,7,8 firstly, the numbers should be counted accordingly.

the number 1 is counted as 1.

the number 2 is counted as 1.

the number 3 is counted as 1.

the number 4 is counted as 1.

the number 5 is counted as 1.

the number 6 is counted as 1.

the number 7 is counted as 1.

the number 8 is counted as 1.

after counting the numbers, the maximum number counted (or) repeated most is 1 as 1 times.

the mode of the given values is 1.

Answer: Options 2, 3, 6

Step-by-step explanation:

Option 2: Correct because both sides are multiplied by 6.

Option 3: Correct because the distributive property is used on the left.

Option 6: Correct because 4 is subtracted from both sides.

Answer:

y=2/3x±3

Step-by-step explanation:

use the formula y=MX+b m being alive b being the y intercept

Hello,

f(x) = ax + b

We know f(0) = 3 = b

a = ∆y/∆x = 3/2

equation that represents the line → y = 3/2x + 3

Answer:

Step-by-step explanation:

given:f(x)=x/x+6

let, f(x)=y

y=x/x+6

interchanging the roles of x and y

or, x=y/y+6

or, xy+6x=y

therefore,inverse of f is xy+6x

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Find the point-slope equation of the line, with the info given

[tex]\Large\maltese\underline{\textsf{This problem has been solved}}[/tex]

Formula used, [tex]\bf y-y1=m(x-x1)[/tex]

[tex]\bf y-5=13(x-0)}[/tex] | result

[tex]\rule{300}{1.7}[/tex]

[tex]\boxed{\bf aesthetic\not101}}[/tex]

The number is 13 / 10

The product of a number and the sum of six and five is equal to the sum of the number and thirteen.

Therefore,

let the number  = x

x(6 + 5) = x + 13

Hence,

x(6 + 5) = x + 13

11x = x + 13

11x - x = 13

10x = 13

x = 13 / 10

Therefore, the number is 13 / 10

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Answer:

160 boxes = 384 pounds

Step-by-step explanation:

sgshshdhdjd

Yes, to some extent President Biden is right in telling them to lower the price rate because due to the war, a lot of gas companies a using it as a yardstick to inflate their prices and sell above the normal rate they bought it and the oil firms needs to consider the times that people are too.

2. The effect of a government price ceiling on gasoline of $2.50 a gallon is shown in the image attached. There is a binding at $2.00.  

3. As  price increases, demand also increases in times of gasoline because due to the war, Russia have refuse selling their oil and as such, this has lead to increase demand on the gasolines on ground.

A binding price ceiling is one that often takes place if the government are known to have set up a  standard price on a good or goods at a specific price that is below equilibrium.

Therefore, to the number one question, we respond Yes, to some extent President Biden is right in telling them to lower the price rate because due to the war, a lot of gas companies a using it as a yardstick to inflate their prices and sell above the normal rate they bought it and the oil firms needs to consider the times that people are too.

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Answer:

the correct answer is 0 54,577.41

Step-by-step explanation:

you needed to take the withdrawal amount divide it by 35 and divide that answer by the 4.5 percentage rate

Answer:

C. $535,528.03

Step-by-step explanation:

Trust me

The payment for the test based on the information about the insurance will be B. $1440.90.

The cost for the payment will be:

= Blood test expenses + Allergy test - MRI expenses

= $345.25 + $175.00 + $920.65

= $1440.90

Therefore, the payment for the test based on the information about the insurance will be $1440.90

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The number of the required towers based on the information given is 3334.

From the information given, it should be noted that the length of power line is 500km

The towers supporting the line are 1.5hm apart. It should be be noted that 1km = 10hm. Therefore, the require towers will be:

= (500 × 10)/1.5

= 3334

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Answer:

742

Step-by-step explanation:

4x203

Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6

A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input.

Here, we have,

Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).

Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).

The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).

Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).

=> f(x) = (x-h)² + k

The outcome of translating a unit to the right with b unit up is

=>f'(x) = (x-h-a)² + k + b

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The member equation which passes through the point (-2,-36) is y = 4 ( x-1)(x+5) .

Parabola is a U shaped figure , whose all points are at a fixed distanced from a point called as focus and a line called as Directrix.

It is given that

The zeroes of the parabola is 1,-5.

The equation of the parabola is given by

y = a( x - x')(x-x'')

y = a( x-1)( x+5)

This is the equation for the parent function for the parabola

The parabola passes through the point ( -2 , -36 )

-36 = a( -2 -1)(-2+5)

-36 = (-3) * (3) a

-36 = -9 a

a = 4

y = 4 ( x-1)(x+5)

The member equation which passes through the point (-2,-36) is y = 4 ( x-1)(x+5) .

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Answer:

You can tell if the sum of the degrees of all the angles adds up to 180.

Step-by-step explanation:

y+4z=0

4x+y-2z=2

-3x-3z=-9

Answer:

Step-by-step explanation:

y + 4z = 0

4x + y - 2z = 2

____________ -

- 4x + 6z = - 2

- 4x + 6z = - 2 → times 3 → - 12x + 18z = - 6

- 3x - 3z = - 9 → times 4 → - 12x - 12z = - 36

- 12x + 18z = - 16

- 12x - 12z = - 36

______________ -

30z = 20

z = 20/30

z = 2/3

y + 4(2/3) = 0

y + 8/3 = 0

y = - 8/3

- 3x - 3z = - 9

- 3x - 3(2/3) = - 9

- 3x - 6/3 = - 9

- 3x - 2 = - 9

- 3x = - 9 + 2

- 3x = - 7

x = - 7/- 3

x = 7/3

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

                     We have the equation [tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x-12=-18}}[/tex].

                     First we should add 12 to both sides of the equation.

                     [tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x=-18+12}}[/tex]. Simplify

                    [tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x=-6}}[/tex].

                   This done, let's multiply the equation by 4. You'll see why

                   [tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{\not4}x\times\not4=-6\times4}}[/tex]

                   Did you see how on the left, the 4's cancelled? That's

                   because dividing by 4 and then multiplying the same

                   number, or the result, by 4, are operations that undo each

                   other.

                   This being said, let's finish solving this equation in terms of x

                   [tex]\large\boldsymbol{\sf{3x=-24}}[/tex]. See how this works?

                  Now, remember that we ought to use inverse operations

                  to solve for x. These are operations that undo each other.

                  So if x is multiplied by 3, we should... divide by 3!

                  Also, please keep in mind that we can only divide the left side

                  by 3 if we divide the right side by 3.

                 [tex]\large\boldsymbol{\sf{\displaystyle\frac{3x}{3}=\displaystyle\frac{-24}{3}}}[/tex]. Once again the 3s on the left cancel, leaving

               x. Wait! Isn't that what we wanted? Yepp, sure!

               The right side is now -8. Thus,

               [tex]\large\boldsymbol{\sf{x=-8}}[/tex]

                 [tex]\orange\hspace{300pt}\above3[/tex]