Pretest: Manipulating and Interpreting Expressions
Drag each expression to the correct location on the table.
Place each algebraic expressions next to its corresponding verbal description.
5³-²-1 (5-4)³
the difference of 5 times the cube of x cubed and
the quotient of 4 times x and 3
5 times the cube of x divided by 4 times x
the quotient of the difference of 5 times x cubed and 4 and x
the cube of the difference of 5 times x and 4
Submit

The conversion of the following units are done below.

Conversion means to convert the same thing into different units.

We know the following unit's conversion.

1 km = 0.62 miles

6 km = 3.72 miles

    1 L = 0.26 gallons

2.5 L = 0.65 gallons

  1 lb = 0.45 kg

90 lb = 40.5 kg

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Answer:

75

Step-by-step explanation:

you need to divide numbers by 3

3×25=75

Answer:

147

Step-by-step explanation:

Arithmetic sequence:

  a = first term = 3

  d = common difference = second term - first term

     = 9 - 3

  d = 6

  n = 25

  [tex]\sf \boxed{\bf n^{th} \ term = a + (n-1) d}[/tex]

                   = 3 + (25 - 1)*6

                   = 3 + 24*6

                    = 3 + 144

                    = 147

Answer:

Θ = 39°

Step-by-step explanation:

OA = OB ( radii of the circle ) , then

Δ AOB is isosceles with base angles congruent , that is

∠ ABO = ∠ BAO = 52°

the exterior angle of a triangle is equal to the 2 opposite interior angles.

∠ DOB is an exterior angle of the triangle , so

∠ DOB = ∠ ABO + ∠ BAO = 52° + 52° = 114°

the angle between a tangent and the radius at the point of contact is 90°, then

∠ OBC = ∠ ODE = 90°

the sum of the 4 interior angles of quadrilateral OBCD = 360°

∠ OBC + ∠ DOB + ∠ ODC + ∠ BCD = 360°

90° + 114° + (90 + 27)° + Θ = 360°

90° + 114° + 117° + Θ = 360°

321° + Θ = 360° ( subtract 321° from both sides )

Θ = 39°

Answer:

B

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (- 4, 11) ← 2 ordered pairs from the table

m = [tex]\frac{11-(-1)}{-4-2}[/tex] = [tex]\frac{11+1}{-6}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2

Answer:

[tex]\sqrt{69}[/tex]

Step-by-step explanation:

from the pythagorean theorem:

[tex]a^2 + b^2 = c^2\\10^2 + b^2 = 13^2\\100 + b^2 = 169\\b^2 = 69\\b = \sqrt{69}[/tex]

[tex]f(x) = {x}^{2} - 3x + 2 [/tex]

put x = (-1)

[tex] f( - 1) = {( - 1)}^{2} - 3 \times ( - 1) + 2 \\ \\ 1 + 3 + 2 \\ \\ 6.[/tex]

put x = (z)

[tex] f(z) = {z}^{2} - 3 \times z + 2 \\ \\ {z}^{2} - 3z + 2 \\ \\ {z}^{2} - 2z - z + 2 \\ \\ z(z - 2) - 1(z - 2) \\ \\ (z - 1)( z -2 ) \\ \\ (z - 1) = 0 \: \: , \: \: (z - 2) = 0\\ \\ z = 1 \:, \: 2[/tex]

put x = (x+1)

[tex]f(x + 1) = {x}^{2} - 3x + 2 \\ \\ {(x + 1)}^{2} - 3 (x + 1) + 2 \\ \\ {x}^{2} + 1 + 2x - 3x - 3 + 2 \\ \\ {x}^{2} - x \\ \\ x(x - 1) \\ \\ x(x - 1) = 0 \\ \\ x - 1 = \frac{0}{x} \\ \\ x - 1 = 0 \\ \\ x = 1.[/tex]

put x = (√2 + 1 )

[tex]f( \sqrt{2} + 1) = {x}^{2} - 3x + 2 \\ \\ {( \sqrt{2} + 1) }^{2} - 3( \sqrt{2} + 1) + 2 \\ \\ 2 + 1 + 2\sqrt{2} - 3 \sqrt{2} - 3 + 2 \\ \\ 3 - 1 \sqrt{2} - 1 \\ \\ 2 - \sqrt{2} \\ \\ 2 - 1.4 (optional \: \: \: steps)\\ \\ 0.6 \: \: [/tex]

Answer:

-6, 14, -26, 10x -4, -8x + -2x - 6

Step-by-step explanation:

So F(x) is setting that the values before the lines are equal to x and should be applied to the problem. Dont forget PEMDAS with these tho, they'll try to trick u like that.

So for the first one, f(0) you plug 0 where the x's are.

1.) 8(0)^2 +2(0) -6

0 + 0 - 6 = -6

2.) 8(2) +2(2) - 6

16+ 4-6= 20 - 6= 14

3.) 8(-2) + 2(-2) -6

-16 + -4 -6 = -26

On the ones where they leave the x there, you just have to leave the x. But don't forget distribution tho.

4.) 8(x+1) +2(x+1) -6

8x +8 + 2x + 2 -6

10x +10 -6 = 10x -4

5.) 8(-x) + 2(-x) -6

-8x + -2x -6

Step-by-step explanation:

the given function is f(x) = 8x² + 2x -6

f(0) = 8(0)² + 2(0) -6 = -6

f(2) = 8 (2)² + 2 (2) - 6 = 30

f(-2) = 8 (-2)² + 2 (-2) - 6 = 22

f (x+1) = 8(x+1)² + 2 (x+1) -6

= 8(x² +2x +1 ) + 2x -4

8x² + 16x +8 +2x -4 = 8x² + 18x + 4

f(-x) = 8(-x)² + 2 (-x) - 6

= 8x² -2x -6

The measure of angle x will be 88 degrees. Then the correct option is C.

The complete question is attached below.

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

2ab cos θ = a² + b² – c²

The triangle is shown below.

Then the value of the variable x will be

2 · 7 · 10 · cos x = 7² + 10² – 12²

       140 · cos x = 49 + 100 – 144

                cos x = (149 – 144) / 140

                       x = 87.95 ≈ 88°

Then the correct option is C.

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The surface area of the cylinder is 5969.03 cm²

The internal volume is 23156.68 cm³

Given:

A gas tank consists of a cylinder with a hemisphere on top.
The thickness of the metal is 1 cm
The overall height is 90 cm
The external diameter is 20 cm

To Find
a) the surface area of the tank

We will add the area of the bottom circle of radius 10 cm (counting the 1 cm thickness in), the external surface area of cylinder of height (90 - 10) cm =80 cm and radius 10 cm, and the surface area of the hemisphere of radius 10 cm.

So, the surface area of the cylinder is

[tex]\pi\times(10)^2+2\times\pi\times 10\times 80+ 2\times \pi \times (10)^2[/tex]
= π×(100+1600+200)

= π×(1900)

= 5969.03 cm²

b) To find the internal volume of the tank we find the internal volume of the hemisphere with an internal radius (10-1)=9 cm,
the internal volume of the cylinder of radius 9 cm and height (80-1) cm

= [tex]\frac{4}{3}\times \pi \times 9^3[/tex]+[tex]\pi\times 9^2\times 79[/tex]

= 23156.68 cm³

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-1000000 that is the answer

hope this helps!

The appropriate numbers to fill in the magic squares are;

Row 2, Column 2 = 21/133

Row 2, Column 3 = 24/38

Row 3, Column 2 = 70/95

Row 3, Column 3 = 25/95

To solve this magic square, we will follow the procedures below;

When we follow those steps above, we will arrive at the following figures;

Row 2, Column 2 = 21/133

Row 2, Column 3 = 24/38

Row 3, Column 2 = 70/95

Row 3, Column 3 = 25/95

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If the side length is greater than 11.11 cm then it will not overflow.

Otherwise, it will overflow.

If Joe tips the bucket of water in a cuboid container and the water is not overflowing then the cuboid container must be of volume greater than 1370 cm³.

We find the cube root of 1370 cm³.

[tex]\sqrt[3]{1370} \approx11.11[/tex]

Then the cuboid container should have a side of length greater than 11.11 cm.

Here the statement  "If I tip my bucket of water in the cuboid container, it will never overflow" is correct or wrong based on the information that the container has a side length lesser or greater than 11.11 cm.

If the side length is greater than 11.11 cm then it will not overflow.

Otherwise, it will overflow.

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[tex]-3(x^{2} +5x+10)[/tex] is the standard form of the given expression

The given expression is:

[tex]=-3(x+3)^{2} -3+3x\\\\=-3*(x^{2} +2*3*x+3^{2} )-3+3x\\\\=-3x^{2} -3*6x-3*9-3+3x\\\\=-3x^{2} -18x-27-3+3x\\\\=-3x^{2} -15x-30\\\\=-3(x^{2} +5x+10)[/tex]

This is the standard form of the given expression.

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The period of the graphed function is T = 8.

For a sinusoidal function, the period is the horizontal distance between two consecutive peaks.

Here we can see the first peak at x = 1, and the second peak is at x = 9.

The horizontal distance is: 9 - 1= 8.

Then we conclude that the period of the function is T = 8.

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Answer:

^ their right :)

Step-by-step explanation:

Its right on Acellus

have a great day!

The answer is option D which is the range will be ( -∞, ∞ ).

After substituting the domain, the range of a function is the entire set of all possible values for the dependent variable (often y).

Given function is

u(x) = -2x²+3 and v(x) = ( 1 / x ).

The product of the function will give uv(x).

uv(x) = (-2x²+3 ) x  [tex]\dfrac{1}{x}[/tex]

uv(x) = [tex]\dfrac{-2x^2+3}{x}[/tex]

When we plot the graph of the function we found two opposite curved graphs and they are not intersecting at any point so the range will be from negative infinity to positive infinity. The graph of the function is attached with the answer below.

Therefore the answer is option D which is the range will be ( -∞, ∞ ).

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The system of inequalities to represent this situation will be x + y ≤ 15 and 5x + 10y ≤ 95.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Carla babysits and tutors to make extra money.

She babysits for $5 an hour and tutors for $10 an hour.

She can only work at most 15 hours a week.

Likewise, she wants to go on a trip with her friend and needs to make 95 dollars this week to cover the cost of the trip.

Then the system of inequalities to represent this situation will be

Let x be the number of babysits hours and y be the number of tutor's hours.

     x + y ≤ 15

5x + 10y ≤ 95

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Answer:

0 represents the ground level

Answer:

10. Ray ED and Ray EF (two rays)

11. DE and EF (two line segments)

Step-by-step explanation:

hope this helped

Answer:

Ray ED and Ray EF

DE and EF

Step-by-step explanation:

Answer:

54 = 2 × 3 × 3 × 3 = 2 × 3³

[tex] f(x) = 7(\sqrt[3]{54})^x [/tex]

[tex] f(x) = 7(\sqrt[3]{3^3 \times 2})^x [/tex]

[tex] f(x) = 7(3\sqrt[3]{2})^x [/tex]

Initial value: x = 0

[tex] f(0) = 7(3\sqrt[3]{2})^0 [/tex]

[tex] f(0) = 7(1) [/tex]

[tex] f(0) = 7 [/tex]

The initial value is 7.

The domain is all real numbers.

The range is all real numbers greater than zero.

The matchup are:

Reflection is known to be the turning over an object across a line and it is one where we do not need to change its size or shape.

While Translation is said to be sliding a figure into another direction and it is one where we do not need to change its size, shape or make.

The Translation  and reflection matchup are given:

See full question below

Match each function formula with the corresponding transformation of the parent function y = 5-^x Please help ASAP!!

1. y = 5x

Translated left 5 units

2. y = 5–x + 5

Translated right by 5 units

3. y = 5–x – 5

Translated up by 5 units

4. y = 5–x+ 5

Translated down by 5 units

5. y = –5–x

Reflected across the x-axis

6. y = 5–x – 5

Reflected across the y-axis

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Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} + 3x - 3[/tex]

[tex]f( - 1) = 2. {( - 1)}^{2} + 3.( - 1) - 3[/tex]

[tex]f( - 1) = 2 - 3 - 3[/tex]

[tex]f( - 1) = - 4[/tex]

Answer:

this quantity refers to the amount that a container can hold.

The pair of limits that would verify the existence of a vertical asymptote at x = –1 is:

[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

For a vertical asymptote at x = -1, the denominator is zero at -1, hence both lateral limits at x = -1 go to infinity, that is:

[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]

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Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} [/tex]

[tex] \: [/tex]

[tex] = (f \circ f)(x)[/tex]

[tex] = f(f(x))[/tex]

[tex] = 2 {x}^{2} [/tex]

[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]

[tex] = 2(4 {x}^{4} )[/tex]

[tex] = 2.4 {x}^{4} [/tex]

[tex] = 8 {x}^{4} [/tex]

The answer is A.

Answer: The card is 28 cm by 23 cm

Check out the diagram below

Explanation:

I added 4 cm to each dimension of the "24 x 19". Why 4 instead of 2? Because we're effectively adding two copies of "2 cm" to each of the original length and width. Along the horizontal component, we have the left and right boundaries. Along the vertical component, we have the top and bottom boundaries. The diagram hopefully clears up any confusion you may have.

To eliminate the y terms and solve for x in the fewest steps, you can multiply the equations by appropriate constants so that the coefficients of the y terms in Both equations have the same magnitude but opposing signs. So to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x

In this instance, you can do the following steps:

Start with the original equations:

Equation 1: 2x + 3y = 8

Equation 2: 3x - 2y = 4

To eliminate the y terms, multiply Equation 1 by 2 and Equation 2 by 3:

Multiply Equation 1 by 2:

2(2x + 3y) = 2(8)

4x + 6y = 16

Multiply Equation 2 by 3:

3(3x - 2y) = 3(4)

9x - 6y = 12

Now, add the two modified equations together to eliminate the y terms:

(4x + 6y) + (9x - 6y) = 16 + 12

4x + 9x + 6y - 6y = 28

13x = 28

Finally, solve for x by dividing both sides of the equation by 13:

x = 28/13

Therefore, to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x

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The probable question may be:

To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? The first equation should be multiplied by 2 and the second equation by 3. x.

Answer:

Least, Median and Greatest height of boys are all higher then Least, Median and Greatest of girls height

Step-by-step explanation:

Least height of boys: 158cm > 150cm Least height of girls

Median height of boys: 168cm > 165cm Median height of girls

Greatest height of boys: 182cm > 170cm Greatest height of girls

[tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.

It is given that:

Total students are 80

32 pupils use the swimming pool

43 pupils use the gym

19 pupils use neither the swimming pool nor the gym

To know the pupils who use both add 32+43 = 75

75-61= 14 pupils use both

32-14 = 18 pupils use only the swimming pool

43-18= 29 pupils use only the gym

Hence, [tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.

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Answer:

4 days

Step-by-step explanation:

1) Derive a formula.

Let b = bicycle

Let x = the number of days

A set up equation: b = 6x + 15

2) If she pays 39 to hire a bicycle, substitute 39 into b, then solve for x.

39 = 6x + 15

39 - 15 = 6x

24 = 6x

24/6 = x

4 = x

x = 4

Since x is the number of days, she hired the bicycle for 4 days.

Answer:

D

Step-by-step explanation: the larger abs(r value) is, (abs of r closest to 1) the better the correlation. Negative values indicate a negative correlation (negative slope)