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Ellen has $75 in her savings account. She deposits $25 every week. Her father also deposits $35 into the account every time Ellen mows the lawn. Her savings account balance can be shown with the following expression:

75 + 25w + 35m

Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)

Part B: If Ellen saves for 8 weeks and mows the lawn 2 times, how much will she have in her account? Show your work to receive full credit. (4 points)

Part C: If Ellen had $95 in her savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)

Answer:

Option 4 is correct .

Step-by-step explanation:

Given : A three dimensional figure

To Find : What is the shape of the cross section?

Solution :

If we intersects the three-dimensional object in the image and divides the object into equal halves by vertical plane then we can see the attached figure what the output will be .

We can see that if we see the cross section from the side then it looks like the fourth one

So, Option 4 is correct .

The required equation of the line passing through the coordinates  (−10, 4), (2, −5) is 4y+3x = -14

The required equation of the line passing through the coordinates (5, 7), (−6, −3) is 11y-10x = -27

The formula for finding the equation of a line is expressed as:

[tex]y-y_0=m(x-x_0)\\[/tex]

Given the coordinates (−10, 4), (2, −5)

Get the slope:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-5-4}{2-(-10)} \\m=\frac{-9}{12}\\m=\frac{-3}{4}[/tex]

Get the required equation

[tex]y-4=-3/4(x+10)\\4(y-4)=3(x+10)\\4y-16=-3x-30\\4y + 3x = -30+16\\4y+3x = -14\\[/tex]

b) For the equation of the line with the coordinates (5,7) and (-6, -3)

Get the slope

m = -3-7/-6-5

m = -10/-11

m = 10/11

The required equation will be:

y - 7 = 10/11(x-5)

11(y-7) = 10(x-5)\

11y - 77 = 10x - 50

11y - 10x = -50 + 77

11y - 10x = -27

Hence the required equation of the line passing through the coordinates (5, 7), (−6, −3) is 11y-10x = -27

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Let

x-------> the time in minutes

y------> the number of laps

we know that

In this problem the linear equation represent a direct variation and the slope is equal to

[tex]m=3\frac{laps}{minute}[/tex]

so

the equation of the line is

[tex]y=3x[/tex]

For [tex]x=1\ minute[/tex]

the value of y is equal to

[tex]y=3*1=3\ laps[/tex]

Plot the point [tex](1,3)[/tex] in the graph

therefore

the answer is

The solution is the line b

see the attached figure to better understand the problem

The total number of possibilities of drawing their names is given by permutation.

4P4 = 24

The total possibility of drawing their names in alphabetical is only 1.

Therefore the probability is:

P = 1 / 24

P = 0.0417

Therefore there is about 4.17% chance that it will be in alphabetical order

Answer:

Step-by-step explanation:

Hal's because there is one age for every height .

Answer:

The answer is A

Step-by-step explanation:

I got it right on edge 2021

To find for the number of fireflies caught in a minute, we simply look at the equation. The equation is linear and takes the form y = slope * x + b

where slope is also equivalent to the fireflies caught each minute.

So the equation of you and your friend is: (where y is the total fireflies caught)

you:

y = 3 m + 13

your friend:

y = 4 m + 6

So the fireflies caught each minute is:

you: 3

your friend: 4

So a total of 7 fireflies each minute combined

Alberto gets [tex]\( \frac{1}{4} \)[/tex] of the inheritance.

To find out the fraction of the money Alberto gets, we first need to find out how much of the total inheritance each part of the ratio represents.

The total parts in the ratio are [tex]\(3 + 4 + 5 = 12\)[/tex].

Alberto's share is [tex]\(3\)[/tex] parts out of [tex]\(12\)[/tex].

So, Alberto's share of the inheritance is [tex]\( \frac{3}{12} \)[/tex] of the total amount.

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is [tex]\(3\)[/tex]:

[tex]\( \frac{3}{12} = \frac{1}{4} \)[/tex]

Therefore, Alberto gets [tex]\( \frac{1}{4} \)[/tex] of the inheritance.

To solve for h and r in the equation bh + hr = 25, isolate one variable, solve for h using division, and solve for r by expanding the equation. There is no unique solution for h and r in terms of each other.

To solve for h and r in the equation bh + hr = 25, we need to isolate one variable on one side of the equation. Let's solve for h first:

bh + hr = 25

Factor out h from the left side of the equation:

h(b + r) = 25

Divide both sides by (b + r) to solve for h:

h = 25 / (b + r)

Now, let's solve for r. Replacing h in the original equation:

bh + hr = 25

b(25 / (b + r)) + r(25 / (b + r)) = 25

Multiply both sides by (b + r) to get rid of the denominators:

25b + 25r = 25(b + r)

Expand the equation:

25b + 25r = 25b + 25r

As we can see, the equation is an identity, meaning any value of r will satisfy it. Therefore, there is no unique solution for r in terms of h, and vice versa.

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Final answer:

Staci can purchase a maximum of 3 T-shirts after buying her festival ticket, given she brings $200.00 and each T-shirt costs $30.00.

Explanation:

To calculate the maximum number of T-shirts Staci can purchase at the music festival, we can follow these steps:

Subtract the cost of the festival ticket from the total amount of money Staci is taking to the festival. This will give us how much money she has left for the T-shirts.

Divide the remaining amount by the cost of one T-shirt to find out the maximum number of T-shirts she can buy.

So for the first step:

Staci has $200.00 and the ticket costs $87.96, leaving her with $200.00 - $87.96 = $112.04.

For the second step:

Each T-shirt costs $30.00, so we divide $112.04 by $30.00, which gives us 3.734.

Since Staci cannot buy a fraction of a T-shirt, we round down to the nearest whole number, which is 3.

Therefore, the maximum number of T-shirts Staci can purchase is 3.

Answer:

The correct option is D

Step-by-step explanation:

Given triangle ABC and triangle DEF so that ∠A≅∠D, ∠B≅∠E, AB = 4, and DE = 8. we have to tell the similarity theorem or postulate that applies to prove above triangles congruent.

In ΔABC and ΔDEF

∠A=∠D    (Given)

∠B=∠E     (given)

Two angles are congruent

Hence, by AA similarity postulate which states that if the two corresponding angles of two triangles are congruent they are similar i.e ΔABC~ΔDEF

Hence, The correct option is D

Answer:

  7/200

Step-by-step explanation:

3.5% = 3.5/100 = (3.5/100)×(2/2) = 7/200

_____

The % symbol is a shorthand way to write "/100", so 3.5% = 3.5/100.

Answer: 8 cm

Step-by-step explanation:

Given : The formula for the area of a triangle is [tex]a=\dfrac{1}{2}bh[/tex]

If a triangle has a base of 7 cm and an area of 28 cm squared.

The substitute the values of b = 7 and a = 28 in the above formula, we get

[tex]28=\dfrac{1}{2}(7)h[/tex]

Divide 7 and multiply 2 on on both sides, we get

[tex]h=\dfrac{28\times2}{7}=4\times2=8\ cm[/tex]

Hence, the height of triangle = 8 cm

Answer:

correct answer is C. Just took the test.

An inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target is [tex]25p+55r\geq225[/tex].

To determine the inequality that represents the number of portable DVD players (p) and DVD recorders (r) that need to be sold to achieve the target profit of at least $225 per day, we can use the information provided about the profits from selling each item.

The store makes a profit of $25 for every portable DVD player sold and $55 for every DVD recorder sold. This can be represented by the following inequality:

[tex]25p+55r\geq225[/tex]

Here, p represents the number of portable DVD players sold.

Here, r represents the number of DVD recorders sold.

This inequality ensures that the total profit from selling portable DVD players and DVD recorders meets or exceeds the manager’s target of $225 per day.