A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 2 of the recall, the manufacturer fixed 192 cars. In week 4, manufacturer fixed 184 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week at the mechanic.

f(x) = 4x + 200
f(x) = 2x + 192
f(x) = −4x + 200
f(x) = −2x + 192

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow C.\:factor \:\: out \:\: 2x [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 2 {x}^{3} - 18 {x}^{2} + 40x[/tex]

[tex]\qquad \tt \rightarrow \: 2x(x {}^{2} ) - 2x(9x) + 2x(20)[/tex]

[tex]\qquad \tt \rightarrow \: 2x( {x}^{2} - 9x + 20)[/tex]

Henceforth, The most efficient first step in factorising the given trinomial is to factor out 2x

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

(-1,4)

Step-by-step explanation:

Step 1) Change both equations to slope intercept form

3x+y=1 ---> y=-3x+1

5x+y=-1 ---> y=-5x-1

Step 2) Plot lines accordingly on graph

Lines intersect at (-1,4)

Answer:

answer is option C

Step-by-step explanation:

just take 6n as common and divine each value by it

The factored form of expression 6n⁴ - 24n³ + 18n is

6n (n² - 2n + 1) (n² - 2n + 3).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can factor out the greatest common factor of the expression, which is 6n:

6n(n³ - 4n² + 3n)

Next, we can factor the expression inside the parentheses by grouping:

n³ - 4n² + 3n = n²(n-4) + 3(n-4) = (n²+3)(n-4)

Substituting this back into the original expression.

6n (n² + 3) (n - 4)

However, we can further simplify by noticing that the expressions

(n² - 2n + 1) and (n² - 2n + 3) are both equivalent to (n - 1)² + 1 and (n - 1)² + 2, respectively.

Thus,

The factored form can also be written as 6n [ (n - 1)² + 1 ] [ (n - 1)² + 2 ]

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Answer:

no solutions

Step-by-step explanation:

-7 does not equal 7, so there are no solutions.

Infinite solutions would be if it was two equal values, for example, 7 = 7.

Answer:

No solution

Step-by-step explanation:

Answer:

Step-by-step explanation:

Calculate 50% of 684 m.

Give your answer in metres (m).

50% = 1/2

so

684 : 2 = 342 m

Step-by-step explanation:

50% of 684

50/100 × 684

342m ans

Answer:

The slope of the line is -1.

Step-by-step explanation:

SLOPE OF A LINE FORMULA

SLOPE = Y2 - Y1/ x2 - x1

m = Y2 - Y1/ x2 - x1

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

m = -4/4

m = -1

The slope of the line is -1.

Answer:

C

Step-by-step explanation:

(1/4)^x-2 is the answer

"Law of conservation of Mass and Energy", is the reason for which it is important to keep the two sides of an equation balanced when solving.

The other properties that we should consider while rewriting the expressions of an equation is that we should not multiply or divide the expressions by zero on both the sides.

According to the law of conservation of mass, mass is neither generated nor destroyed during a chemical process. For instance, when coal is burnt, the carbon atom in it transforms into carbon dioxide. The carbon atom transforms from a solid to a gas, yet its mass remains constant. Similar to this, according to the law of conservation of energy, energy cannot be generated or destroyed. For instance, kinetic energy is converted to potential energy when a toy vehicle is rolled down a ramp and collides with a wall.

While rewriting expressions of an equation, we should not multiply or divide them by zero, as multiplying or dividing by zero makes two non-equal expressions equal (0 and ∞ respectively.

This is the reason why is it important to keep the two sides of an equation balanced, and that the expressions should not be multiplied or divided by zero.

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Work Shown:

r = 8 = radius

h = 63 = height

V = volume of the cone

[tex]V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*8^2*63\\\\V = \left(\frac{1}{3}*8^2*63\right)\pi\\\\V = \left(\frac{1}{3}*63*8^2\right)\pi\\\\V = \left(21*64\right)\pi\\\\V = 1344\pi\\\\[/tex]

Side note: You could write the symbol π as "pi" without quotes.

Answer:

The next 3 numbers will be 1 3/4, 2, and 2 1/4

Step-by-step explanation:

The numbers in the sequence are increase by 1/4. So to find the next number in the sequence and 1/4 to the previous number. Don't foget to simplify your answers. Ex.) Rather than saying 2 2/4 you would say 2 1/2.

The true statement about the triangle is (a) b^2 + c^2 > a^2

The sides are given as:

a, b and c

The angle opposite of side length a is an acute angle

The above means that:

The side a is the longest side of the triangle.

The Pythagoras theorem states that:

a^2 = b^2 + c^2

Since the triangle is not a right triangle, and the angle opposite a is acute.

Then it means that the square of a is less than the sum of squares of other sides.

This gives

a^2 < b^2 + c^2

Rewrite as:

b^2 + c^2 > a^2

Hence, the true statement about the triangle is (a) b^2 + c^2 > a^2

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Answer:$440, 9

Step-by-step explanation:

The relationship between the number of the times eating out in the total budget represent a linear function.

"A linear functions are those whose graph is a straight line."

Given, I already spent $160 on groceries for the week.

Each time I eat out you will spend another $40.

Let, I eat 'x' times during vacation.

Therefore, the required function will be:

f(x) = 160 + 40x

Hence, the function is a linear function.

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Answer:

3x²y²(1 - 4xy²z)

Step-by-step explanation:

________________________________________
Factor 3 out of 12
Factor x² out of x³
Factor y² out of y⁴

you will get the GCF of 3x²y² and left with (1 - 4xy²z)

3x²y²(1 - 4xy²z)
________________________________________

Hoped this helped

Answer:

63

Step-by-step explanation:

A circle is 360 degrees

So, subtracting 297 from 360, we'd get 63 degrees

Answer:

The function [tex]2(3^x)[/tex] has an initial value of [tex]2[/tex].

Step-by-step explanation:

An exponential function is a mathematical function of the following form: [tex]f(x)=a^x[/tex]where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828. The exponential value can be found by solving the expression to proceed with a solution.

At the initial value,  the exponential function is in the [tex]y[/tex] direction and [tex]x[/tex] is [tex]0[/tex] .

[tex]f(x)=2(3^x)\\f(x)=2(3^0)\\f(x)=2[/tex]

Therefore, the function that has an initial value of [tex]2[/tex] is [tex]2(3^x)[/tex].

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The point on the graph f(x) = 3.4ˣ is (0, 1)

None of the given options is correct.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

To determine which point is on the graph of f(x) = 3.4ˣ, we need to substitute the given x-coordinate into the function and see if we get the given y-coordinate.

Let's try each option:

A. (1, 12): f(1) = 3.4¹ = 3.4, so this point is not on the graph of f(x) = 3.4ˣ.

B. (0, 12): f(0) = 3.4⁰ = 1, so this point is not on the graph of f(x) = 3.4ˣ.

C. (12, 1): f(12) = 3.4¹² ≈ 108089.7, so this point is not on the graph of f(x) = 3.4ˣ.

D. (0, 1): f(0) = 3.4^0 = 1, so this point is on the graph of f(x) = 3.4ˣ.

Therefore, the point (0, 1) is on the graph of f(x) = 3.4ˣ. The answer is option D.

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Answer:

y=-x-7

Step-by-step explanation:

Slope-intercept form is y=mx+b

We have the equation 4x+4y=-28 and must put it into the form above. To do this first subtract 4x from both sides.

4x-4x+4y=-28-4x

This equals 4y=-4x-28. Now, divide 4 from both sides.

4y/4=-4x/4-28/4

y=-x-7

Hope this helps!

If not, I am sorry.

Answer:

$29

Step-by-step explanation:

Substitute x with 8.

3(8) + 5 = 24+5 = 29

Answer: $29

Step-by-step explanation:

x = # toys

if the number of toys is 8

substitute 8 into x

y = 3(8) + 5

y = 24 + 5

y = 29

Answer:

the answer is (3,4) is the solution to line A but not to line b

Answer:

-2

Step-by-step explanation:

15-8+-9

bodmas

15-8=7

7-9

=-2

Answer:

the distance between DE is 2

The distance of EF is 5

The distance of FD is [tex]\sqrt{29}[/tex]

Perimeter is 7+[tex]\sqrt{29}[/tex]

Step-by-step explanation:

Distance of DE

[tex]\sqrt{(-3-(-3))^2+(3-1)^2}[/tex]

sqrt([tex](-3+3)^2+(2)^2[/tex])

sqrt([tex](0)^2+4[/tex])

[tex]\sqrt{4}[/tex]

=2

Distance of EF

[tex]\sqrt{(2-(-3))^2+(3-3)^2}[/tex]

Solve that like DE and it equals 5

Distance of FD

[tex]\sqrt{(2-(-3))^2+(3-1)^2}[/tex]

equals to [tex]\sqrt{29}[/tex]

P=DE+EF+FD

P=2+5+[tex]\sqrt{29}[/tex] = 7+[tex]\sqrt{29}[/tex]

The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A

An equation is an expression that shows the relationship between two or more numbers and variables.

Let k represent the constant of proportionality

3) T = kN

28 = 250k

k = 0.112

i) T = 0.112N

ii) T = 0.112(300) = 33.6

iii) 98 = 0.0112N

N = 875

4) D = kA

270 = 5k

k = 54

i) D = 54A

ii) D = 54(4.5) = 243

iii) 324 = 54A

A = 6

5) T = kA

150 = 2.4k

k = 62.5

i) T = 62.5A

ii) T = 62.5(1.8) = 112.5

iii) 3(60) = 62.5A

A = 2.88

The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A

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Answer:

it should be 319

Step-by-step explanation:

Answer:

639 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

y =  -x + 7.

Step-by-step explanation:

General form:-

y = mx + c where m = slope. So:

y = x + 2 has a slope of 1.

The line perpendicular to it has slope -1/1 = -1

To find the required line we use the point-slope form with m = -1, x1 = 3 and y1 = 4.

y - y1 = m(x - x1)

y - 4 = -1(x - 3)

y - 4 = -x + 3

y =  -x + 7.

Answer:

Using the method of ratio and proportion, we find that the length of the side of Polygon D is 0.8in.

Step-by-step explanation:

Given that Polygon C and Polygon D are similar. This means that the ratio of the length of one side of Polygon C to the length of corresponding side of Polygon D will stay same even if we change the lengths.

Perimeter of polygon C = 60in

Perimeter of polygon D = 12in

Length of side of polygon C = 4in

Let us take the number of sides of both the polygons same. Let the length of the side of polygon D x inches. Let the number of sides be n.

First equation, 4n = 60

Second equation, xn = 12

Dividing second by first

(xn) / (4n) = 12 / 60

x / 4 = 1 / 5

x = 4 / 5 = 0.8in

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The expected length of the arc containing the point (1,0) is; π

First of all, it is pertinent to note that the lengths of the four arcs in which the circle is divided by the three points and (1, 0) have identical distributions.

The problem is same as dividing a circle of length 2π at four points chosen at random, and labelling one of them (1, 0). Now, let us make L₁, L₂, L₃, L₄ to be the lengths of the four arcs determined by those four points.

Thus, we have;

L₁ + L₂ + L₃ + L₄ = 2π

Whereas, the expected value of several random variables is additive as;

E[ L₁ + L₂ + L₃ + L₄] =  [EL₁] + [EL₂] + [EL₃] + [EL₄]

By symmetry the lengths have the same probability distribution and as such; [EL₁] = [EL₂] = [EL₃] = [EL₄] and the sum must be 2π. Thus, we can say that each expected value is 2π/4 = π/4.

Finally, the expected value of the arc containing the point (1, 0) is the sum of the expected values of the two arcs that are adjacent to (1, 0), i.e.,

π/2 + π/2 = π

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Answer:

5 blue marbles

10 Red marbles

3 Green marbles

Step-by-step explanation:

5 times 2 = 10

then 5-2 =3

Add 5+10+3

=18 Marbles in total

The value of angle x is 67 degree.

A right angled Triangle is a triangle with one angle as 90 degree.

It is given that the for the angle x , the base of the triangle is 28 ft.

The hypotenuse = 72ft.

The trigonometric ratios can be used to find the value of x

cos x = 28 /72

x = cos⁻¹ (28/72)

x = 67 degree (Rounded off to nearest tenth)

Therefore the value of angle x is 67 degree.

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