An equilateral triangle has a side length of $12 \sqrt{3}.$ The triangle is rotated about one of its altitudes as an axis, sweeping out a cone in space. Find the volume of the cone.

Answer:

Each geometry book costs $6, each algebra book costs $8.

Let a=cost of one algebra book and g=cost of one geometry book. We have:

2a + 3g = 34-------->6a + 9g = 102

3a + 2g = 36-------->6a + 4g = 72

-------------------

5g = 30

g = 6

2a + 3(6) = 34

2a + 18 = 34

2a = 16--->a = 8

Question: John paid $34 for two algebra and three geometry books. He paid $36 for three algebra and two geometry books. What is the cost of each book?

Answer: The cost of each algebra book is $8 and the cost of each geometry book is $6.

Step-by-step explanation:

a= algebra book cost

g= geometry book cost

Here's what we know:

2a + 3g = 34 (the 2 alg and 3 geo comes to $34)

3a + 2g = 36 (the 3 alg and 2 geo comes to $36)

This is a classic elimination method problem. I suggest that we multiply the first equation by -2 and the second by 3. This way, we can eliminate the variable g and still keep the other parts of the problem in the positive range:

-4a - 6g = -68

9a + 6g = 108

-------------------

5a = 40

Divide by 5:

a = 8

Now to solve for g:

2 * 8 + 3g = 34

16 + 3g = 34

3g = 18

g = 6

check (by using the second equation):

3 * 8 + 2 * 6 = 36

24 + 12 = 36

Answer:

x < 1

Step-by-step explanation:

an open circle means it contains no equal signs.....everything to the left is shaded....means it is less then

x <  1 (thats a less then sign only) ....no equal sign in there

Answer:

x < 1

Step-by-step explanation:

Open circle:  < or >

Closed circle:  ≤ or ≥

Shading to the left: < or ≤

Shading to the right: > or ≥

Therefore, as there is an open circle and shading to the left:

x < 1

(x is smaller than 1)

Answer:

Step-by-step explanation:

-40

−20−8-12

−28−12

-40

====================================

[tex]\large \sf \underline{Problem:}[/tex]

The weight of the rectangle is 80 grams.

The weight of the triangle is double the weight of the

circle.

Determine the weight of the circle.

====================================

[tex]\large \sf \underline{Answer:}[/tex]

Rectangle has four sides. The total weight of the circle is 20 grams.

====================================

[tex]\large \sf \underline{Explanation:}[/tex]

What is a rectangle?

A rectangle is a 2D shape that has four sides, and the pair of opposite sides are equal and parallel to each other.

As it is given that the weight of the rectangle is 80 grams, and a rectangle is made up of two triangles. Therefore, the weight of each triangle can be written as,

[tex]Weight \: of \: the \: reactangle \: = \frac{80}{2} = 40 grams[/tex]

It is given that the total weight of the triangle is double the weight of the circle. therefore, the relationship can be written as,

[tex]Weight \: of \: the \: triangle = 2x \\ Weight \: of \: the \: circle \: \\ 40 = 2 \times Weight \: of \: the \: circle

[/tex]

[tex]Weight \: of \: the \: circle = 20 grams[/tex]

Hence, the total weight of the circle is 20 grams.

Learn more about Rectangle:

https://brainly.com/question/994316

====================================

Hence the weight of the circle is 20 grams.

Answer:

Solution Given:

Weight of rectangle =80grams

we know that

twice the weight of triangle =weight of rectangle

2*weight of triangle =80 grams

weight of the triangle = 80/2=40 grams

again

The weight of the triangle is double the weight of the

circle.

weight of the circle=½*weight of triangle

=½*40=20grams

Answer:

It's A

Step-by-step explanation:

y/x

it's starting point is 5 and it goes up 1 and over 2

1 is on the y-axis and 2 is on the x-axis and it is y over x so the answer is 1/2x+5

NOTE:I MAY NOT BE ACCURATE BUT IM PROBABLY IT COULD BE WRONG BUT IF U REALLY ARE STUCK ON A QUESTION THEN CHOOSE A

Answer:

x=40,y=22

Step-by-step explanation:

62/2=31

31+9=40

31-9=22

40+22=62

Answer:

15cm

Step-by-step explanation:

150 meters are too long since 1 meter is about one big step.

15 meters would also be too long.

150 centimeters is the same as 1.5 meters, which is also too long.

Step-by-step explanation:

some might be wrong..if u can..try to cross check it..

Reason:

The tree is already 48 inches tall. We add on 3x to represent the idea the tree is growing 3 inches per month. Therefore, the total height is 48+3x or 3x+48 inches.

Let's say x = 5 months have elapsed as an example.

The tree would have grown 3*x = 3*5 = 15 inches to get 48+15 = 63 inches tall. In other words, y = 3x+48 will have y = 63 when x = 5.

Answer:

e

Step-by-step explanation:

e

[tex]\\~~~~~3x^2 +4x +7 = -1\\\\\implies 3x^2 +4x +7 +1 = 0\\\\\implies 3x^2 +4x +8 = 0\\\\\text{It is now in the standard form of quadratic equation}~( ax^2 +bx +c = 0)\\[/tex]

Answer:

s=55°

Step-by-step explanation:

sum of angles of the inside pentagon is 540°

2s+2s+1s+130°+135° =540°

5s+265°=540°

5s=540°-265°

5s=275°

5s/5=275°/5

s=55°

Answer:

exponential

Step-by-step explanation:

The function follows the rule :

Let's check

Common ratio

Its a geometric sequence

Hence exponential

Let's see

[tex]\\ \rm\Rrightarrow 1\dfrac{1}{5}\times2\dfrac{1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6}{5}\times \dfrac{7}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6(7)}{5(3)}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{42}{15}[/tex]

[tex]\\ \rm\Rrightarrow2 \dfrac{12}{15}[/tex]

Answer:

9y(c=7) witch means the answer is 8,6

Step-by-step explanation:

I took it and got 5 out of 5 right ✅

Answer:

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

[tex]20x - 20 = -60\\20x = -40\\x = -2[/tex]

hope this helped!!

Answer:

x = -2

Step-by-step explanation:

Divide both sides by 5 :

Add 4 to both sides :

Divide both sides by 4 :

Answer: see my work

Step-by-step explanation:

volume is lwh

volume is 3*3*10

volume is 9*10

volume is cubic cm

volume is 90

volume is 90 cubic cm

Answer:

90cm^2

Step-by-step explanation:

3x3=9

9x10=90

Answer:

B

Step-by-step explanation:

We know that AB has endpoints at A(4, -3) and B(3, 7).

To find Line D, which is the perpendicular bisector of AB, we first need to find the slope of AB and its midpoint.

So, let's find the slope of AB using the slope formula:

Let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the slope formula:

So, the slope of AB is -10.

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

Therefore, the slope of our Line D is the negative reciprocal of -10. Which is -10 flipped and multiplied by a negative.

So, Line D has a slope of 1/10.

Now, since Line D is also the perpendicular bisector of AB, we need to find the midpoint of AB since Line D must pass through this point.

To find the midpoint, we can use the midpoint formula:

We can again let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the midpoint formula to obtain:

Evaluate. So, the midpoint is:

Now, we can find the equation of our Line D. We know that its slope is 1/10, and that it must pass through (3.5, 2). So, we can use the point-slope form:

Where m is the slope. Let's let (3.5, 2) be (x₁, y₁) and substitute 1/10 for m. This yields:

This is the same as choice C. So, choice C is indeed an equation of Line D.

We can distribute the right to obtain:

Add 2 to both sides to acquire:

This is the same as choice D. So, choice D is indeed an equation of Line D.

Moreover, we can put this into standard form by multiply everything by 10, which gives:

Subtracting x from both sides yields:

This is the same as A. So, choice A is also an equation of Line D.

There is no way to acquire choice B. So, B is not an equation of Line D.

Therefore, our answer is B.

And we're done!

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Since, the Area of smaller rectangle is 35,

Let's calculate it's length ~

[tex]\qquad \sf  \dashrightarrow \:a = l \cdot w[/tex]

[tex]\qquad \sf  \dashrightarrow \:35 = l \cdot5[/tex]

[tex]\qquad \sf  \dashrightarrow \:l = 35 \div 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:l = 7 \: ft[/tex]

And the two rectangles are similar ~ so the ratio of their sides are equal as well ~

Assume length of greater rectangle be x

[tex]\qquad \sf  \dashrightarrow \: \dfrac{25}{5} = \dfrac{x}{7} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 5 \times 7[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 35[/tex]

Now, since the length and width of the greater rectangle is known, let's find it's Area ~

[tex]\qquad \sf  \dashrightarrow \:a = l \cdot w[/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 35 \sdot25[/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 875 \: \: ft {}^{2} [/tex]

So, Area of the greater rectangle is 875 ft²

Answer:

Step-by-step explanation:

Answer:

the stripe chip design has

the greatest probability of selection

Step-by-step explanation:

p(draw a dot chip) = 1/10

p(draw a star chip) = 2/10

p(draw a heart chip) = 3/10

p(draw a stripe chip) = 4/10

4/10 > 3/10 > 2/10 > 1/10

Therefore , the stripe chip design has

the greatest probability of selection.

Answer:

She left at 7:55

Step-by-step explanation:

She travels 150 miles at 50 miles an hour, it takes her 3 hours to get to stoke but she stopped for 20 minutes. Subtract 20 minutes from 11:15, and you get 10:55, then subtract 3 hours. You get 7:55. This means she left the house at 7:55.

Answer:

96 days. Divide 3072 by 32 and you get 96.

Hi Student!

Looking at the question we can see that we are given a number which is 120 days.  The question is asking for us to convert the amount of days it took to break the code into hours.  We can do this by multiplying the amount of days that we have by 24 because there are 24 hours in a day.  The days would cancel and that would result us with just hours left.

[tex]120\ days*\frac{24\ hours}{1\ day}[/tex]

[tex]\frac{120\ days\ *\ 24\ hours}{1\ day}[/tex]

[tex]\frac{2880\ hours}{1}[/tex]

[tex]2880\ hours[/tex]

Therefore, our final answer is that it took the computer 2880 hours to break the code after we converted the days to hours.

Answer:

x < 0

( x is less than 0 )

Explaination:

That open circle point means the answer will not be equal to, which would be options including <(less than) or >(greater than).

If the circle was closed you would use these symbols, ≤(less than or equal to) and ≥(greater than or equal to)

The open circle lands on 0 and the arrow points to the left into the negative numbers. The answer should be x<0 or x is less than 0.

A way to help remember less than vs greater than on a line like this is that the arrow points in the same direction as the symbol! For example, your question shows an arrow going to the left, and the symbol used for it is less than (<) which also looks like a left pointing arrow.

Hope this helps out! :D