A student attempted to generate an equivalent expression using the distributive property, as shown below:

6(m + 3) = 6m + 3

What was the mistake made?

A. 6 was not multiplied by m
B. Incorrect sign was used for the first term
C. Incorrect sign was used for the second term
D. 6 was not multiplied by 3

A higher density means that lead is heavier than glass for the same volume, signifying that lead particles are both heavier and more numerous in a given volume than the glass particles.

The density of a substance tells us how much mass is in a given volume, and it is expressed in g/cm³. Comparing the densities of glass (2.6 g/cm³) and lead (11.3 g/cm³), we can say that a given volume of lead is much heavier than the same volume of glass. This could mean either there are more lead particles or the lead particles are heavier. But from atomic physics, we know that individual lead atoms are indeed heavier than individual silica atoms (which make up glass). Therefore, the higher density of lead signifies that the lead particles are both more numerous and heavier in a given volume than the glass particles.

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Measure of the Bigger Angle= Measure of Given Angle+Measure of Smaller Angle

Measure of Bigger Angle =Measure of Angle to be Found

Measure of Angle to be Found= Measure of Given Angle + Measure of Smaller Angle

The smaller Angle signifies one quadrant

So, Measure of Smaller Angle = 90°

Measure of Angle to be found=90°+Measure of given Angle

Measure of Angle to be found=90°+55°

Measure of Angle to be found=145°

Answer:145°

The value of  [tex]y[/tex] in the given figure, using the rule of angle sum property  and linear pair will be [tex]65\\[/tex].

According to angle sum property, the sum of all the sides of a triangle will be [tex]180^o[/tex].

A linear pair is defined as two neighboring angles that sum up to 180° or two angles which result in a line or a straight angle when combined, or it can be said that the sum of linear pair is supplementary.

In the given figure,

∠[tex]x + 130^o = 180^o \ \ \ (linear pair)\\\x = 50^o[/tex]

Now, In triangle ABC, using angle sum property:

[tex]A+B+C= 180^o\\50^o + y + y = 180^o\\50^o + 2y = 180^o\\2y = 130^o\\y = 65^o\\[/tex]

Thus, the value of  [tex]y\\[/tex]  in the given triangle is [tex]65^o\\[/tex].

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The figure is added below.

Answer: Tara will have a 2/27 probability of choosing a blue marble from each bag

solution: First, we need to find the probability for the first bag using (p= number of outcomes/ total of outcomes), the number of outcomes is 5, and the total is 15, so our probability for bag 1 is 5/15.

Then, for the second bag, the number of outcomes is 2, and the total is 9, so the probability for the second bag is 2/9

To find the probability for both of the bags, we have to multiply them: 5/15 × 2/9= 10/135=2/27

Answer:

640/(180 - x)

Step-by-step explanation:

The expression for time it takes for the plane to travel the 640 miles is 640/ (180- x).

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let the speed of the wind be x

Speed of the plane is 180 mph

When plane flew with wind , Speed = (180+x)

When plane flew against the wind , Speed=(180-x)

Since we are given that A plane can travel 640 miles against the wind .

So, Time= Distance / speed

Time= 640/ (180 - x)

Hence, time it takes for the plane to travel the 640 miles is 640/ (180- x)

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To find the new volume of the cylinder, multiply the original volume by 9.

To find the new volume of the cylinder, we need to find the new radius first. Since the radius becomes three times as large, the new radius will be 3 times the original radius. Next, we substitute the new radius into the volume formula for a cylinder.

V = πr²h

Let's assume the original radius is 'r' and the original volume is 1,692.46 in³. Therefore:

1,692.46 = πr²h

The new radius will be 3r, so the new volume becomes:

V = π(3r)²h = 9πr²h

So, the new volume of the cylinder will be 9 times the original volume or 9 * 1,692.46 = 15,231.14 in³.

Answer:

8.4

Step-by-step explanation:

Final answer:

Each base angle of the isosceles triangle measures 66.5°, found by subtracting the given angle from 180° and dividing the remainder by 2.

Explanation:

To find the measure of the base angles in an isosceles triangle when one angle measures 47°, we will use the fact that the sum of all angles in any triangle is always 180°.

Additionally, we know from geometry that in an isosceles triangle, the angles opposite the equal sides are equal. Applying these principles, we first subtract the given angle from the total sum of the angles:

180° (total angles in a triangle) - 47° (given angle) = 133°.

Now, since the remaining two angles are equal, we divide 133° by 2 to find the measure of each base angle:

133° ÷ 2 = 66.5°.

Thus, each base angle of the isosceles triangle measures 66.5°.

Answer:

1/3k

Step-by-step explanation:

30kx -6kx=8

We can operate the two terms in left because they are similar

24kx = 8

We divide by 8 both sides

3kx = 1

Finally, we divide by 3k both sides

x = [tex]\frac{1}{3k}[/tex]

Answer: x = 1/3k

Step-by-step explanation:

z

Mila needs at least $8 more to reach her goal of spending $20 on a classified ad. The inequality to represent this problem is x ≥ 8, where x is the amount of additional money she needs.

If Mila wants to spend at least $20 on a classified ad and currently has $12, we need to figure out how much more money she needs. We denote the amount of money she needs with the variable x. An inequality that represents this situation is:

12 + x ≥ 20

Subtracting 12 from both sides of the inequality to isolate x, we get:

x ≥ 20 - 12

x ≥ 8

So, Mila needs at least $8 more to have enough for the classified ad.

It will take the construction company approximately 2 10/21 hours to remove the dirt.

To find the number of hours it will take to remove the dirt, we need to divide the total amount of dirt by the amount of dirt that can be removed each hour. First, we need to convert the mixed number 2 1/6 tons to an improper fraction. 2 1/6 = 13/6 tons. Next, we divide 13/6 by 7/8 to find the number of hours:

13/6 ÷ 7/8 = 13/6 × 8/7 = 104/42 = 2 20/42 = 2 10/21

So, it will take the construction company approximately 2 10/21 hours to remove the dirt.

Final answer:

The equation m∠DEF = m∠D'F'E' must be true following a 90° clockwise rotation of ∆DEF, because rotations preserve angle measures.

Explanation:

When a geometric figure such as ∆DEF is rotated 90° clockwise about a point A, to create ∆D'E'F, corresponding angles in the two triangles will be equal. This is true because a rotation is a type of rigid motion, which preserves angle measures. The equation m∠DEF = m∠D'F'E' must be true because the angle at F in the original triangle ∆DEF becomes the angle at E' in the rotated triangle ∆D'E'F, given the preservation of angle measures through rotation.

Therefore, for such geometric transformations, it's crucial to understand that rotations do not alter the internal angles of the shape being transformed, which is consistent with the rules of plane geometry. This principle is useful in solving many problems that involve the rotation of figures within a plane.

Answer:

Total amount Josiah can expect to pay for postage is:

$ 1.84

Step-by-step explanation:

cost of mailing one letter in the country is:

f(x)=0.42 + 0.20[x-1]

The first weighs 2.9 ounces, and the second weighs 4.1 ounces.

Cost of mailing first letter=0.42+0.20(2.9-1)

                                         =0.42+0.38

                                         =$ 0.8

Cost of mailing second letter=0.42+0.20(4.1-1)

                                               =0.42+0.62

                                               =$ 1.04

total cost=$(0.8+1.04)

              =$ 1.84

Hence, total amount Josiah can expect to pay for postage is:

$ 1.84