Graph the equation. y = 4(x + 6)(x + 4)
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Answer:

He will need a total of 168.8 total gallons of oil.

He will need 34.4 gallons of oil for machine A.

He will need 134.4 gallons of oil for machine B.

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What you need to write in each blank is:

1) positive x-axis.

2) negative x-axis.

3) positive y-axis.

To plot a point (R, θ) on the polar plane. First, if R is positive the angle is measured from the positive x-axis, if R is negative, the angle is measured from the negative x-axis.

Because here R is 4, positive, the point will lie on the x-axis. Then, she needs to move it clockwise by an angle of (3/2)pi (a total of 3 quadrants) This means that the point will end up in the positive y-axis.

So what you need to write in each blank is:

1) positive x-axis.

2) negative x-axis.

3) positive y-axis.

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Answer:

see below

Step-by-step explanation:

Each person payed a specific amount, so you would divide the rental cost by the amount of people and get $38.75 per person

The smallest value of k when the LCM(Lowest common factor) of 14 and

k is 140 is 10.

Factors are numbers or algebraic expressions that divide another number or expression evenly

From the question,

If 14 and k  is 140

⇒ (14×k) = 140

⇒ 14k = 140

⇒ k = 140/14

⇒ k = 10

Hence, the smallest value of k is 10.

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Answer:

Square C is comprised of the areas of squares A and B

It proves that this triangle is a right triangle

By adding the areas of two perfect squares, A and B, square C can only be the sum. This proves the Pythagorean Theorem to be true, as the ratios to the sides, and therefore the equation, will remain fixed in any scalene right triangle.

Step-by-step explanation:

It doesn't really need further explanation

I like this question, though :)

If a point divides any line segment into two equal parts, then the point is the mid-point of that line. The ratio of the whole line segment and the distance from mid-point to any end point of the line segment is always 2:1, hence the scale factor of the dilation is 2.

To find the scale factor of the dilation, we need to find the ratio from initial point of the line segment to the distance from the point that is lie on that line segment.

Following points can be concluded from the given conditions.

The ratio of the whole line segment and the distance from mid-point to any end point of the line segment is always 2:1, hence the scale factor of the dilation is 2.

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Each carton of any flavour costs same

so

Total cartons:-

Total cost

Answer:

97.92 m³ (nearest hundredth)

Step-by-step explanation:

The composite solid is a cube with a cone cut out.

Therefore, to find the volume of the solid, subtract the volume of the cone from the volume of the cube.

[tex]\textsf{Volume of a cube}=\sf s^3 \quad\textsf{(where s is the side length)}[/tex]

Given:

Substitute given value into the formula:

[tex]\begin{aligned}\implies \sf V_{cube} & = \sf 5.1^3\\& = \sf 132.651\: m^3\end{aligned}[/tex]

[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute given values into the formula:

[tex]\begin{aligned}\sf \implies V_{cone} & = \sf \dfrac{1}{3} \pi (2.55^2)(5.1)\\& = \sf 11.05425 \pi \: m^3\end{aligned}[/tex]

[tex]\begin{aligned}\sf V_{solid} & = \sf V_{cube}-V_{cone}\\& = \sf 132.651-11.05425 \pi \\& = \sf 97.92304941...\\& = \sf 97.92 \: m^3 \: (nearest\:hundredth)\end{aligned}[/tex]

Volume of the cube

For the cone

Volume

Total volume of the figure

Answer:

y - 4 = 1/5(x-7)

Step-by-step explanation:

Find slope:

4-3 / 7-2

1 / 5

y - y1 = m(x-x1)

y - 4 = 1/5(x-7)

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Hi Student!

Looking at this problem, it is pretty straight forward and we don't need to do much information gathering to help answer our question.  The main point is that we just need to solve the equation also known as solving for the unknown variable.

Subtract 2 from both sides

Divide both sides by 5

Therefore, our final solution to this problem is that x is equal to 4/5 or we can convert this to a decimal to which we will then get 0.8.

Answer:

45

Step-by-step explanation:

We know that B is 90 because its a right angle, and in that triangle it has to add up to 180

So 180 - 90 = 90

90 ÷ 2 = 45

And thats a right angled triangle so it has a right angle and two equal angles.

Hope it helps :))

Answer:

Part A

To convert degrees to radians, multiply the given value by π/180°.

[tex]\begin{aligned}\implies 20^{\circ} & =20^{\circ} \times \dfrac{\pi}{180^{\circ}} \: \sf rad\\ & =\dfrac{1}{9} \pi \: \sf rad\end{aligned}[/tex]

Part B

Given:

[tex]\begin{aligned}\textsf{Area of a sector of a circle} & =\dfrac12 r^2 \theta\\\\\implies \textsf{Area of slice of cake} & =\dfrac{1}{2} \cdot 10^2 \cdot \dfrac{1}{9} \pi\\\\& = \dfrac{50}{9} \pi \: \sf cm^2\end{aligned}[/tex]

Part C

Given:

[tex]\begin{aligned}\textsf{Perimeter} & = 2r + \textsf{arc length}\\& = 2r + r \theta \\& = 2(10)+10\left(\dfrac{1}{9} \pi \right) \\& = 20 + \dfrac{10}{9} \pi \\& = 23.4906585\\& = 23.5\: \sf cm \:(1 \:dp)\end{aligned}[/tex]

Answer:

I and II

Step-by-step explanation:

In a 'linear function,' the exponents of x and y are both 1.  

This characteristic is found in both I and II but not in III (which is a quadratic function).

Answer:

0.23

Step-by-step explanation:

Was the answer on khan academy

Step-by-step explanation:

first, let's bring them to the same exponent of 10.

8.5 × 10⁸ is already scientific notation

42 × 10⁷ = 4.2 × 10⁸ (this is now scientific notation AND it is using the same exponent of 10)

so, how many times is the first one greater ?

(8.5 × 10⁸) / (4.2 × 10⁸) = 8.5 / 4.2 = 2.023809524...

so, the first number is 2.023809524... times greater than the second number.

maybe you made a typo ?

maybe the second number was actually 42.5 × 10⁷ ?

because then

42.5 × 10⁷ = 4.25 × 10⁸

and

8.5 / 4.25 = 2

so,

8.5 × 10⁸ is 2 times greater than 42.5 × 10⁷ or 4.25 × 10⁸.

Answer:

The answer would be B or 2

Step-by-step explanation:

Answer:

model 2 or B

Step-by-step explanation:

Answer:

We saw in the last video that when you multiply or you divide numbers, or (I guess I should say when you multiply or divide measurements) your result can only have as many significant digits as the thing with the smallest significant digits you ended up multiplying and dividing. So just as a quick example, if I have 2.00 times (I don't know) 3.5 my answer over here can only have 2 significant digits This has 2 significant digits, this has 3. 2 times 3.5 is 7, and we can get

Answer:

1. g(x) = (x - 1)²; translation of 1 unit to the right.

2. g(x) = 3^(x + 1) - 2; translation to the left of 1 unit and translation of 2 units down.

Step-by-step explanation:

1.

f(x) = x²

g(x) = f(x - 1)

g(x) = (x - 1)²

Since x was replaced by x - 1, g(x) is similar to f(x) with a translation of 1 unit to the right.

2.

f(x) = 3^x

g(x) = f(x + 1) - 2

g(x) = 3^(x + 1) - 2

Since x was replaced by x + 1, which is the same as x - (-1), there is a translation to the left of 1 unit. In addition, the -2 causes a translation of 2 units down.

Answer:

Radius = 10

Step-by-step explanation:

Volume of a cylinder=πr^2h

1600πcm^3=πxr^2x16

π cancels out

1600=r^2x16

1600/16=r^2

100=r^2

√100=r

r=10

From the z table the critical value corresponding to the level of significance level for a two-tailed test is z = 1.64.

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test.

The hypothesis which we put against the null hypothesis is an alternate hypothesis.

The null hypothesis is the one that researchers try to disprove.

From the question, we are told that

The number of observations is greater than 50  i.e. n > 50

The  level of significance is  [tex]\alpha = 0.1[/tex]

Generally given that n >  30  then we will make use of the z table

So From the z table the critical value corresponding to the level of significance level for a two-tailed test is z = 1.64.

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Answer:

4 years

Step-by-step explanation:

30 = 25 ( 1.05)^n

1.2 = 1.05^n

log 1.2  / log 1.05   = n years = 3.73    ~ 4 years

The volume of the cube given the dimensions of the side length is [tex]64x^{6} + 144x^{4} + 108x^{2} + 27[/tex]

A cube is a 3-dimensional object that has six faces, twelve edges and eight vertices.

Volume of a cube = a³

Where a = length of a side

(4x² + 3) × (4x² + 3) = 16x^4 + 24x² + 9

(16x^4 + 24x² + 9) × (4x² + 3) = [tex]64x^{6} + 144x^{4} + 108x^{2} + 27[/tex]

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Answer:

3

Step-by-step explanation:

7a+3b=20

3a+7b=10

Substitution:

[tex]\begin{bmatrix}3\cdot \frac{20-3b}{7}+7b=10\end{bmatrix}[/tex]

[tex]a=\frac{20-3\cdot \frac{1}{4}}{7}[/tex]

[tex]a=\frac{11}{4},\:b=\frac{1}{4}[/tex]

11=4 + 1=4 = 12/4

12/4 = 3

Answer:

110687192.78951, 6488.47368421, 4214, 0.0464, 0.03626

SIMPLIFIED WAY OF SAYING IT:

Last One to First Box

3rd One to 2nd Box

1st one to 3rd box

2nd one to 4th box

4th one to 5th box

Step-by-step explanation:

(4.3*10^(6))*(9.8*10^(-4)) = 4,214

(2.9*10^7)*(1.6*10^-9) = 0.0464

(4.7*10^3)*(8.6*10^-7)/(3.8*10^-4)*(6.1*10^2) = 6488.47368421

(4.9*10^3)*(7.4*10^-6) = 0.03626

Last one = 110687192.78951

Answer:

Exponential growth

The answers are 9, 6, 7, 0, 2, 5, 7, 1, 7, and 2 which makes the target value by putting in the blank box.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

The target number is 54

= 9×6 = 54

= 8×7 - 02

= 5×7 + 19

= 27×2 = 54

Thus, the answers are 9, 6, 7, 0, 2, 5, 7, 1, 7, and 2 which makes the target value by putting in the blank box.

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Answer:

Angle B is 155 degrees

Step-by-step explanation:

Vertical angles are congruent; they have the same angle measure.

[tex]m\angle{A} = 155 \cong m\angle{B} = 155[/tex]

Answer:

56 units^2

Step-by-step explanation:

Area of a parallelogram = base length times height length

Base = 7 units
Height = 8 units

A = BH
A = 7x8

A = 56 units^2