Are the two expressions equivalent when x = 20?

8(12x + 4)

96x + 32

The combined work rate can be found by using the equation for combined rate.

The time it takes Irina to paint the room alone, t₁ = 9 hours

Time it takes Paulo to paint the room, t₂ = 8 hours

To write the equation for the combined rate of Irina and Paulo

The equation that gives the time, [tex]\mathbf{t_b}[/tex], it will take both Irina and Paulo to paint the room together is given by the combined rate formula, as follows;

The duration it will take them to paint the room when working together.

The time it will take them to paint the room together is found as follows;

[tex]\displaystyle \frac{1}{t_b} = \mathbf{\frac{1}{9} + \frac{1}{8}}[/tex]

Which gives;

[tex]\displaystyle \frac{1}{t_b} = \frac{8 + 9}{9 \times 8} = \mathbf{\frac{17}{72}}[/tex]

Therefore;

[tex]\displaystyle t_b = \frac{72}{17} \approx \mathbf{4.24}[/tex]

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Answer:

Step-by-step explanation:

If this net folds into a cube, then, when we form the cube, side B and side E becomes opposite sides, because side D and side F would be placed next to side B, having side E as opposite.

Therefore, the right answer is the last choice. Sides B and E appear on opposite sides.

Answer: The image faces the same direction as the pre-image.

Step-by-step explanation:

Reflection is a transformation in which a geometric shape (pre- image) is reflected across a line called as axis of reflection, producing a mirror image.

It is a rigid transformation because the image is the same size and shape as the pre-image.

Since it produces the mirror image of the original image therefore, the points on the pre-image are the same distance from the line of reflection as the corresponding points on the image.

So the only statement is not true about reflection is "The image faces the same direction as the pre-image. ".

Answer:the answer is 7290

Step-by-step explanation:

From the given expression

4.9*10^2 =4.9*100=490

and

6.8*10^3=6.8*1000=6800

490+6800=7290

Answer:

The correct option is C .

Step-by-step explanation:

A logarithm function is written in the form of  [tex]y=log_ax[/tex],

Since, y = 0.25x is the type of function y = mx + c,

Which is the general form of a linear function,

⇒ y = 0.25x is not a logarithm function,

[tex]y=x^{0.25}[/tex] is the type of function [tex]y=kx^a[/tex], where k and a are any real number,

Which is the general form of a power function,

⇒ [tex]y=x^{0.25}[/tex] is not a logarithmic function.

[tex]y=(0.25)^x[/tex] is the type of function [tex]y=ab^x[/tex]

Which is the general form of exponential function,

⇒ [tex]y=(0.25)^x[/tex] is not a logarithmic function,

Hence, only the function in option C has written in the form of [tex]y=log_ax[/tex].

Option C is correct.

Answer:

y ≤ 31 students

Step-by-step explanation:

The rental cost is a fixed cost that will be incurred irrespective of the number of students embarking on the class field trip. This cost added to the total ticket cost must be less than or equal to the budget.

the total ticket cost for y number of students

= 9.5y

Hence the total cost = 9.5y + 600 ( measured in $)

In inequality form,

9.5y + 600 ≤ 900 (all in $)

9.5y ≤ 900 - 600

9.5y ≤ 300

y ≤ 300/9.5

y ≤ 31 students

Answer:

A

Step-by-step explanation:

EDU

The credit card feature of "No annual fee" represents the correct alternative of the given ones.

A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.

Given is that you are looking for your first credit card. You plan to use this credit card only for emergencies and to pay the credit card balance in full each month.

The credit card feature of "No annual fee" is suitable for emergencies.

Therefore, the credit card feature of "No annual fee" represents the correct alternative of the given ones.

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The length of the dilated line segment is 2 units. ( option B)

A scale factor is a ratio that describes the proportional change in size between two similar geometric figures.

Scale factor = Dimension of new length /dimension of original length

The dimension of the original length is 4 units

scale factor = 1/2

let the new length be x

Therefore;

1/2 = x/4

2x = 4

x = 4/2 = 2units

Therefore, the length of the dilated segment is 2units

Answer:

The expression gives the distance between the points (4, 6) and (7, -3) is Option (C) .

i.e

[tex]Distance\ formula = \sqrt{(7 - 4)^{2} + (6 +3)^{2}}[/tex]

Step-by-step explanation:

Formula

[tex]Distance\ formula = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]

As the point are  (4, 6) and (7, -3) .

Put points in the formula

[tex]Distance\ formula = \sqrt{(4 -7)^{2} + (6- (-3))^{2}}[/tex]

[tex]Distance\ formula = \sqrt{(7 - 4)^{2} + (6 +3)^{2}}[/tex]

[tex]Distance\ formula = \sqrt{(3)^{2} + (9)^{2}}[/tex]

[tex]Distance\ formula = \sqrt{9 + 81}[/tex]

[tex]Distance\ formula = \sqrt{90}[/tex]

[tex]\sqrt{90} = 9.5\ units\ (Approx)[/tex]

Distance formula = 9.5 Units (Approx)

Therefore Option (C) is correct.

Answer:

Step-by-step explanation:

Let x = the number of hamburgers

Let y = the number of hotdogs

Let us first represent the amount of food:

10x + 5y ≤ 60

This means x packages of $10 hamburgers plus y packages of $5 hotdogs is greater than or equal to $60.

However, we have also been given another important piece of information and that is that he must buy at least three packages of hotdogs.

y ≥ 3

this means that the packages of hotdogs must be no less than 3.

Hence or two inequalities are 10x + 5y ≤ 60 & y ≥ 3.

This also means that the least he can spend on hotdogs is $15. The most he can spend on hamburgers is $45, meaning the most packages of hamburgers he can get is 4

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Answer:

One possible triangle

Step-by-step explanation:

Given that in a triangleABC given one angle A =30 , two sides a and b

We can use sine angle formula for triangles

[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

Substitute to get

[tex]\frac{4}{sin30} =\frac{6}{sin B} =\frac{c}{sinC}[/tex]

[tex]sin B = 0.75\\B=48.6[/tex]

C=[tex]180-30-48.6\\= 101.4[/tex]

[tex]c=8sin 101.4\\c=7.842[/tex]

There can be only one triangle

Answer:constant of variation = 1.2

Step-by-step explanation:

The equation 1/t = 1/5 + 1/3 can be used to find the time it takes for worker A and worker B to assemble a shelving unit together.

To find the time t it takes for worker A and worker B to assemble a shelving unit together, we need to add their work rates.

Worker A's work rate is 1 unit per 5 hours (or 1/5 units per hour), and worker B's work rate is 1 unit per 3 hours (or 1/3 units per hour).

The combined work rate is the sum of their individual work rates:

1/5 + 1/3 = (3 + 5) / 15 = 8 / 15 units per hour

If t is the time they take together to complete one shelving unit, then their combined work rate is 1 unit per t hours. Setting this equal to their combined rate, we get:

1/t = 8/15

Solving for t gives:

t = 15/8 hours

Therefore, the equation 1/t = 1/5 + 1/3 can be used to find the time it takes for worker A and worker B to assemble a shelving unit together.

By solving the equations through linear combination method we are going to get the values of p and q are -6 and three.

It is a bit like elimination method of solving equations within which one variable is eliminated so we'll get the worth of another variable.

We are having two equations:

5p-3q=-39-------------1

-2p-3q=3---------------2

equation1 * 2 and equation 2 *5

10p-6q=-78

-10p-15q=15

Now add both equations

10p-6q-10p-15q=-78+15

-21q=-63

q=3

Put the worth of q in 1

5p-3(-3)=-39

5p+9=-39

5p=-30

p=-6

Hence the system of equations have the worth of p=-6 and q=3.

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Given a parallelogram ABCD, refer to the attached image.

To prove: Opposite angles are congruent.

Proof:

According to the given information,

Step 1: Using a straightedge, extend segment AB and place point P above point B.

Step 2: By the same reasoning, extend segment AD and place point T to the left of point A.

Step 3: Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem.

Step 4: Angles PBC and BAD are congruent by the Corresponding Angles Theorem. ( If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Corresponding angles are the angles which occupy the same relative position at each intersection where a straight line crosses two others.)

Step 5: By the Transitive Property of Equality, angles BCD and BAD are congruent.

Step 6: Angles ABC and BAT are congruent by the Alternate Interior Theorem.(The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Alternate Interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.)

Step 7: Angles BAT and CDA are congruent by the Corresponding Angles Theorem.

Step 8: By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.

The proof requires the use of specific theorems such as the Vertical Angles Theorem and Corresponding Angles Theorem to establish the congruence of angles in a parallelogram.

Theorems that accurately complete the proof:

Angles PBC and BAD are congruent by the Vertical Angles Theorem.

Angles ABC and BAT are congruent by the Corresponding Angles Theorem.

Theorem 12 states that if two angles are congruent, their supplementary angles are also congruent.

The correct answer for APEX is B (2 times the number of pages in the book)