Morgan needs to earn $16.31 more to have $40.00. Four students wrote and solved equations to find m, the amount of money that Morgan has now. Which student wrote and solved the equation correctly?

Answer:

I) B = 20 m², h = 4 m are NOT possible dimensions for the area of the base and the height of the prism.

Step-by-step explanation:

Given that the triangular prism has a volume = 240 m³, we can use the formula for the volume of a triangular prism to check the given answers for possible dimensions.  V = Bh, where B = the area of the base and h = height of the prism.  In this case, we simply need to multiply each of the given dimensions together to see if they equal 240 m³:

F) B = 48 m², h = 5 m:  v = 48 x 5 = 240 m³ (possible)

G) B = 24 m², h = 10 m; v = 24 x 10 = 240 m³ (possible)

H) B = 12 m², h = 20 m: v = 12 x 24 = 240 m³ (possible)

I) B = 20 m², h = 4 m: v = 20 x 4 = 80 m³ (NOT possible)

Answer:

m<1=134

m<2=46

x=13

Step-by-step explanation:

Angle 2 can be set equal to 180 since the angle is supplementary after transferring angle 2 to its alternate interior.

4x-6+10x+4=180

Combine like terms

14x-2=180

Solve for x

14x=182

x=13

Now plug x in for the two angles

10(13)+4

130+4

m<1=134

4(13)-6

52-6

m<2=46

134+46=180, verified

[tex]\log_ab=c\iff a^c=b\\\\4^{x+2}=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^2)^{x+2}=2^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+2)}=2^{-1}\iff2(x+2)=-1\qquad\text{use distributive property}\\\\(2)(x)+(2)(2)=-1\\\\2x+4=-1\qquad\text{subtract 4 from both sides}\\\\2x=-3\qquad\text{divide both sides by 2}\\\\\boxed{x=-1.5}[/tex]

Answer:

y = 2x^2 + 8x + 8

Step-by-step explanation:

The graph touches the x axis at only one point.

so there is only one real solution.

If there is only one real solution then determinant =0

Now we find out the equation that has determinant 0

Determinant is [tex]b^2 - 4ac[/tex]

Let find b^2 - 4ac for each equation

(a) [tex]y = 9x^2 + 6x + 4[/tex]

a= 9 , b = 6 and c=4

[tex]b^2-4ac= 6^2 - 4(9)(4) = -108[/tex]

determinant not equal to 0

(b) [tex]y = 6x^2 – 12x – 6[/tex]

a= 6 , b = -12 and c=-6

[tex]b^2-4ac= (-12)^2 - 4(6)(-6) = 288[/tex]

determinant not equal to 0

(c) [tex]y = 3x^2 + 7x + 5[/tex]

a= 3 , b = 7 and c=5

[tex]b^2-4ac= (7)^2 - 4(3)(5) = -11[/tex]

determinant not equal to 0

(d) [tex]y = 2x^2 + 8x + 8[/tex]

a= 2 , b = 8 and c=8

[tex]b^2-4ac= (8)^2 - 4(2)(8) = 0[/tex]

determinant equal to 0. So there is only one real solution.

Answer:

It's D. on EtDtGtE

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

8x2=16

12 1/2x16=200

Answer:

It takes 2.5 seconds for the ball to reach its  highest point

Maximum height is 196 feet

Step-by-step explanation:

h(t) = -16t^2+80t +96

a=-16, b= 80, c=96

To find the maximum height , we need to find vertex

Let find x coordinate of vertex

[tex]t=\frac{-b}{2a}[/tex]

Plug in the values

[tex]t=\frac{-80}{2(-16)}= 2.5[/tex]

It takes 2.5 seconds for the ball to reach its  highest point

Now plug in 2.5 for t to find maximum height

[tex]h(t) = -16t^2+80t +96[/tex]

[tex]h(2.5) = -16(2.5)^2+80(2.5) +96=196[/tex]

Maximum height is 196 feet

Equation: 300+35x=1700; where x represents the amount of teams participating in the tournament

Answer: 40 teams competed in the lacrosse tournament

How to solve-

300+35x=1700

300-300+35x=1700-300

35x=1400

35/35x=1400/35

x=40

Answer:

none of the solutions

Step-by-step explanation:

if k(x) = 2x-3x

We can substitute x=9 to find k(9)

k(9) = 2(9) -3(9)

      = 18 -27

      = -9

The values of x and y for the Isosceles triangle are 90° and 43° respect.

By observation, the triangle ∆ABC is an Isosceles triangle with the markings on both legs of the triangle so the base angles are equal,

angle C = angle B = 47°.

Since the line AD bisects the angle A, then line AD is perpendicular to the base BC and so angle x is a right angle

x = 90°

Considering the right triangle ∆ADB can evaluate for y as follows;

x + y + angle B = 180° {sum of interior angles of a triangle}

y + 90 + 47 = 180

y + 137 = 180

y = 180 - 137

y = 43°.

Therefore, the values of the x is equal to 90° and that of y is 43° for the Isosceles triangle ∆ABC.

Answer:

No

Yes

Yes

No

Step-by-step explanation:

X's repeat

X's don't repeat

X's don't repeat

X Values repeat

Answer: [tex]398.5750[/tex]

Step-by-step explanation:

It is important to remember that the fourth digit after the decimal point is in the ten-thousandth place.

Then, given the  following number:

[tex]398.574986215[/tex]

You can follow these steps in order ti round it to the nearest ten-thousandth:

1. You can identify that the digit in the ten-thousandth place is:

[tex]9[/tex]

2. Identify the digit to the right of [tex]9[/tex]. This is:

[tex]8[/tex]

3. Since:

 [tex]8>5[/tex]

 You must round up. Increase the digit [tex]9[/tex] by 1. (Notice that [tex]9+1=10[/tex], then the digit to the left of  [tex]9[/tex] increases by 1 too). Then:

[tex]398.5750[/tex]

Answer:

-18  

Step-by-step explanation:

f(x) = x² - 3x -10

f(-10) = (-10)² – 3(-10) – 10

f(-10) = 100 + 30 - 10

f(-10) = 120

f(-5) = (-5)² – 3(-5) – 10

f(-5) = 25 + 15 - 10

f(-5) = 30

=====

The average rate of change is the slope m of the straight line joining the two points.

m = (y₂ - y₁)/(x₂ - x₁)

m = (30 - 120)/(-5 – (-10))

m = -90/(-5+10)

m = -90/5

m = -18

Answer:

(x - 6)(x + 3)

Step-by-step explanation:

Consider the product of the factors of the constant term which sum to give the coefficient of the x-term

product = - 18 and sum = - 3

The factors are - 6 and + 3, hence

x² - 3x - 18 = (x - 6)(x + 3)

Answer:

60,000 i believe :)

Answer:

The length of each side is 12.2 ft

Step-by-step explanation:

First, set the x value to be 0:

2(0) + 4y = 28

4y = 28

y = 28/4 = 7

So when x = 0, y = 28/4

Now set the y value as 0:

2x + 4(0) = 28

2x = 28

x = 14

So when x = 14, y = 0

Simply plot these two values:

(0, 7) and (14 , 0)

And join them up, an attatched image shows this graph.

Answer:

y = -1/2 + 7

Step-by-step explanation:

You have to isolate y so...

2x + 4y = 28 is the original problem. Then subtract 2x on both sides. After you subtract 2x, you have to divide 4 to both sides. Then after you divide 4 to both sides, it'll be y = -2/4 + 7. After that, simplify -2/4, and you'll get y = -1/2 + 7 as your answer.

To estimate the length of each rope, the division sentence 30 ÷ 3 = 10 can be used, suggesting that each jump rope would be approximately 10 feet long using compatible numbers.

The student's question involves dividing a rope into equal lengths to create jump ropes.

To estimate the length of each jump rope using compatible numbers for the division sentence, we can round 29.8 feet to a number that is easier to divide by 3, such as 30 feet.

Therefore, the division sentence would be 30 ÷ 3 = 10. So, each jump rope would be approximately 10 feet long.

This is an estimate that allows us to perform calculations quickly in our head or on paper, and it is very close to the exact answer.

Final answer:

To estimate the length of each rope from a total length of 29.8 feet when the rope is divided into 3 parts, compatible numbers are used, rounding 29.8 to 30, and the division sentence is 30 ÷ 3, resulting in each estimated rope being about 10 feet long.

Explanation:

To estimate the length of each rope when a 29.8-foot long rope is cut into 3 equal parts, we could use compatible numbers for easier division in our head. Compatible numbers are numbers that are close to the actual numbers and make it easy to do mental arithmetic. We could round 29.8 feet to 30 feet because 30 is divisible by 3. Here's the division sentence using compatible numbers:

30 feet ÷ 3 = 10 feet

Thus, each rope would be approximately 10 feet long. This process is similar to converting units where the scale factor may be omitted at the end when it is 1, as in converting 3.55 m to 355 cm.

Answer:

C

Step-by-step explanation:

I am assuming the top and bottom are closed.

Surface are = area of the curved side + 2 * area of the top

=  9* 14 * π + 2 * π * 7^2

= 126π + 98π

= 224π ft^2

Answer:

224

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Answer:

The equation of this line would be y = 3x - 1

Step-by-step explanation:

In order to find this equation we must first find the slope of the original line. The original slope (the coefficient of x) is 3, which means the new slope will also be 3 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.

y - y1 = m(x - x1)

y + 7 = 3(x + 2)

y + 7 = 3x + 6

y = 3x - 1

<, > - opened circle

≤, ≥ - closed circle

<, ≤ - draw line to left

>, ≥ - draw line to right

Answer in the attachment.

<,> - dotted line

≤, ≥ - solid line

<, ≤ - shadow to left

>, ≥ - shadow to right

x = -6 - its a vertical line

Answer: 17.14 ft

Step-by-step explanation:

The area of the flower bed is 60 ft x 80 ft = 4800 ft²

The perimeter of the sidewalk that surrounds the flower bed is:

The area of the sidewalk is:

area of sidewalk = area of flower bed

280w = 4800

[tex]\text{w}=\dfrac{4800}{280}[/tex]

  [tex]=\dfrac{120}{7}[/tex]

  ≈ 17.14

Answer:

{1}

Step-by-step explanation:

We find determinant for the given matrix and set it equal to -1

To find determinant we apply formula

[tex]|A| = a_{11}(a_{22}a_{33} − a_{32}a_{23}) - a_{12}(a_{21}a_{33} − a_{31}a_{23})+a_{13}(a_{21}a_{32} - a_{31}a_{22})[/tex]

[tex]|A| = x(1x - 2) - 0(7-7) + 0(14-7x) [/tex]

|A| = x^2 - 2x

Now we set the determinant = -1

[tex]x^2 - 2x=-1[/tex]

Add 1 on both sides

[tex]x^2 - 2x + 1=0[/tex]

Now factor it

(x-1)(x-1) = 0

Set each factor =0  and solve for x

x- 1=0 so x=1

Answer:

Step-by-step explanation: Thew figures are similar becasue 5/15 equals 3/9. They bothe equal one third. This shows that they are bhoth orportionate to eachoither. The ratios of the lengths of their corresponding sides are equal.

Answer:

15

Step-by-step explanation:

you have to divide 975/65=$15 per person

Answer:

It deducts 1.6 each time so the next one would be 22.5  

Answer:

2 decimal places

Step-by-step explanation:

When you multiply two decimals, the largest possible number of decimal places in the product is the sum of the number of the decimal places of the factors. Here, the product has 2 decimal places. One factor is an integer, so it has no decimal places. The other factor must have at least 2 decimal places.