" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a
height of 6 inches.

If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches wnd let
it melt, will the cone hold all of the ice cream?
Use mathematics to explain and justify your answer.

Answer:

MN = 10

Step-by-step explanation:

To find the length of a line segment or the straight distance between two points, use the formula  [tex]L = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex] , where you can substitute two points, which would be (x₁ , y₁) and (x₂ , y₂). "L" stands for length.

Choose point 1 and point 2:

Point 1: M (2, -3)     x₁ = 2  y₁ = -3

Point 2: N (8, 5)     x₂ = 8   y₂ = 5

Substitute the values for the variables:

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

[tex]L = \sqrt{(8-2)^{2}+(5-(-3))^{2}}[/tex]    Solve inside each bracket first by adding

[tex]MN = \sqrt{(6)^{2}+(8)^{2}}[/tex]      Square each number

[tex]MN = \sqrt{36+64}[/tex]        Add the numbers

[tex]MN = \sqrt{100}[/tex]          Find the square root

[tex]MN = 10[/tex]          Length of the line segment

Therefore the length of the line segment MN is 10.

Therefore( [tex]m^3 -6m^2-16m +63[/tex] )÷ (m-7)  [tex]= (m^2 +m-9)[/tex]

Step-by-step explanation:

[tex]m^3 -6m^2-16m +63[/tex]

[tex]=m^3 -7m^2[/tex][tex]+m^2 -7m[/tex][tex]-9m+63[/tex]

[tex]= m^2(m-7)[/tex][tex]+m(m-7)[/tex][tex]-9(m-7)[/tex]

[tex]= (m-7 ) (m^2 +m-9)[/tex]

Therefore( [tex]m^3 -6m^2-16m +63[/tex] )÷ (m-7)  [tex]= (m^2 +m-9)[/tex]

Answer:

answer is 4

Step-by-step explanation:

look at picture

Answer:

x = 1

Step-by-step explanation:

14 x 2x = 28

2 x 1 = 2

14 x 2(1) = 28

14 x 2 = 28

The characteristic of the linear parent function that is not true is that the range is positive real numbers (y > 0).

The correct answer is B. The characteristic of the linear parent function that is not true is that the range is positive real numbers (y > 0).

A linear parent function is represented by the equation y = x and passes through the origin (0,0). Its domain is all real numbers (-∞, ∞) and its range is also all real numbers (-∞, ∞).

A linear function with a slope of 1 is represented by the equation y = x and is a straight line that passes through every point on the graph that has the same x and y value.

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Option B 'The range is positive real numbers (y>0)' is not a characteristic of the linear parent function. The function y=x, known as the linear parent function, has its range as all real numbers, not just positive.

The characteristic of the linear parent function, which is not accurate, is: 'The range is positive real numbers (y>0)'.

The linear parent function is y = x, which indeed meets the criteria of the remaining options. It goes through the origin (0,0), its domain covers all real numbers, as x can be any real number, and it has a slope of 1 throughout. However, its range is not only positive real numbers (y>0). The range of the linear parent function actually includes all real numbers because y (the output) can take any real value, both positive and negative, not just positive.

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Answer:

the 3rd one i believe.

not sure.

hope this helps!

Answer:

Step-by-step explanation:

6t-2=5t

8t+6=7t+6

Answer:

[tex]SA=1.5\ cm^2[/tex]

Step-by-step explanation:

we know that

The surface area of a cube is equal to

[tex]SA=6s^2[/tex]

where

s is the length side of a cube

we have

[tex]s=\frac{1}{2}\ cm[/tex]

substitute

[tex]SA=6(\frac{1}{2})^2[/tex]

[tex]SA=(\frac{6}{4})=1.5\ cm^2[/tex]

Answer:

1,200,000 square miles

Step-by-step explanation:

Given data:

Total land = 3 000 000

40% is covered by sand dunes

Land covered by sand dunes is 40% of the total area therefore

Land covered by sand dunes=(40/100) * 3000000

Land covered by sand dunes= 0.4 * 3000000

Land covered by sand dunes= 1 200 000

Final answer:

Approximately 1,200,000 square miles of Australia are covered by sand dunes, which is 40% of Australia's total area of about 3,000,000 square miles.

Explanation:

The student has asked how much of Australia is covered by sand dunes given that Australia's area is approximately 3,000,000 square miles and sand dunes cover 40% of the land.

To calculate the area covered by sand dunes, we apply the percentage to Australia's total area:

Convert the percentage into decimal form: 40% = 0.40.

Multiply the total area of Australia by the decimal: 3,000,000 square miles × 0.40.

The result gives us the area covered by sand dunes: 1,200,000 square miles.

Therefore, sand dunes cover about 1,200,000 square miles of Australia.

Answer:

2 3/6

Step-by-step explanation:

When reducing the fraction you see how many times the denominator of 6 can fit into to numerator of 15. It is 2 with 3 left over. So you write 2 3/6

Answer:

2 1/2

Step By Step:

15 divided by 6: 2 R3

2 3/6

GCF is 3

Divide both sides by 3, and get 2 1/2

Answer:

16.2

Step-by-step explanation:

45% = 0.45 (as a decimal)

36 × 0.45 = 16.2

Answer:

r=9/2 or 4.5

Step-by-step explanation:

First of all our goal is to get R by itself

by cross multiplying we get,

(r+3)*3=5r

by distributive property we get

3r+9=5r

substracting 3r from both sides we get

9=2r

by dividing by 2 in both sides we get

r=9/2 or 4.5

Answer:

x=-2

Step-by-step explanation:

first u subtract 7 on both sides resulting on 8x=-16. Then to isolate x u divide by 8 on both sides.

Answer:

Step-by-step explanation:

I've already solved this problem.

Answer:

2x+7

Step-by-step explanation:

Answer:

n or the number = 5

Step-by-step explanation:

5 * (-2 + n) = 91 + (-n + 1)

-10 + 5n = 19 - n + 1

6n = 20 + 10

6n/6 = 30/6

n = 5

Answer:

The number is 51.

Step-by-step explanation:

Let the number be x and the opposite of a number is -x.

5(-2+x) = 91 + (-x + 1)

-10 + x = 91-x+1

-10 + 2x = 92

2x = 102

x = 51

Answer:

C) 2x^2+7x-4

Step-by-step explanation:

(2x-1)(x+4)=2x^2-x+8x-4=2x^2+7x-4

Answer:

Saturday

Step-by-step explanation:

Each day of the week is repeated after 7 days

So, after 19 days it would be Saturday

Answer:

y = - 4x - 2 is the required equation of the line.

Step-by-step explanation:

Equation of two parallel lines differ only by a constant.

If the equation of a line is [tex]$ ax + by + l = 0 $[/tex] then the equation of the line parallel to it is given by [tex]$ ax + by + k = 0 $[/tex].

Note that only the constants differ in both the equations.

The given equation is: y = - 4x - 2

This is equivalent to 4x + y + 2 = 0.

Therefore, the equation of the line parallel to the given line will be:

4x + y + k = 0.

We are also given the point which passes through the line. We can substitute it to determine the value of 'k'.

Substituting (- 2, 6), we get:

4(-2) + 6 + k = 0

⇒ - 8 + 6 + k = 0

⇒ k = 2

Hence, the equation of the required line is: y = - 4x - 2

Answer:

2500

Step-by-step explanation:

5^3 is 125/2.5 is 50 and 50^2 is 2500

Answer:

20

Step-by-step explanation:

5x5x5= 125

2.5x2.5=6.25

125÷6.25= 20

Answer:  Unit =2

tens=8

hundred= 3

thousand= 4

Step-by-step explanation:

Answer:94.5pie

Step-by-step explanation:

Final answer:

To calculate the volume of a cylindrical sugar container with a radius of 3 inches and a height of 10.5 inches, use the formula V = πr²h, which yields approximately 296.78 cubic inches.

Explanation:

The question asks for the volume of the container that has the shape of a cylinder. The given dimensions are a radius of 3 inches and a height of 10.5 inches. To find the volume of a cylinder, we use the formula:

V = πr²h

Where V is the volume, π (pi) is a constant approximately equal to 3.14159, r is the radius, and h is the height of the cylinder.

We calculate the volume as follows:

V = π × (3 inches)² × 10.5 inches

V = π × 9 in² × 10.5 in

V = π × 94.5 in³

V ≈ 296.78 in³

Thus, the volume of the cylinder is approximately 296.78 cubic inches

The surface area of prism is 185.815 square inches

Solution:

Given that,

[tex]Length = 2\frac{1}{3}\ inches = \frac{3 \times 2 + 1}{3} = \frac{7}{3}\ inches = 2.33\ inches[/tex]

[tex]Width = 8\frac{1}{2}\ inches = \frac{17}{2}\ inches = 8.5\ inches[/tex]

[tex]Height = 6\frac{3}{4}\ inches = \frac{27}{4}\ inches = 6.75\ inches[/tex]

The surface area of package is given as:

[tex]A=2(wl+hl+hw)[/tex]

Where,

"l" is the length

"w" is the width

"h" is the height

Substituting the values we get,

[tex]A = 2((8.5 \times 2.33) + (6.75 \times 2.33) + (6.75 \times 8.5))\\\\Simplify\ the\ above\ equation\\\\A = 2(19.805+15.7275+57.375)\\\\A = 2 \times 92.9075\\\\A = 185.815[/tex]

Thus the surface area of prism is 185.815 square inches

Answer:

The surface area of the prism is 185.815 square inches.

Hope this helps!

Answer:

6πr/11.

Step-by-step explanation:

The length of the arc = rC where C is the central angle of the sector in radians and r = the radius.

C = (3/11) * 2π

= 6π/11 radians.

So the measure of the arc = 6πr/11.

Answer:

18.75

Step-by-step explanation:

since you are scaling up you do

125/80 which is 1.5625 and multiply that by 12.

Answer: x=2 and y=8

Step-by-step explanation:see attachment

Answer:

B)

Step-by-step explanation:

All three trigonometric functions  are positive in Quadrant I

Sine only is positive in Quadrant II

Tangent only is positive in Quadrant III

Cosine only is positive in Quadrant IV

Now

tan 116°           tan 116° means that the angle 116° lies in the second quadrant.

sin is positive while cos and tan are negative in the second quadrant

tan 116° = -tan(180°-116)

= -tan(64°)

Answer:

You have 6 apples left.

Step-by-step explanation:

You have 10 apple and give away 4.

10 - 4 = 6 apples

You have 6 apples left.