The volume of a cone with a height of 6 cm is 8pie cubic centimeters. Which expression can be used to find r, the radius of the base of the cone?

Final answer:

Jack is 64 years old and Jill is 46 years old. These ages satisfy the conditions that the digits of Jack's age reversed are Jill's age, the sum of their ages is 11 times the difference, and Jack is older than Jill.

Explanation:

The puzzle presented by Jack and Jill to their son, Junior, involves figuring out their ages with a given set of clues:

If you reverse the digits in Jack's age, you get Jill's age.

The sum of both Jack's and Jill's ages is equal to 11 times the difference in their ages.

Jack is older than Jill.

Let's denote Jack's age as 10a + b and Jill's age as 10b + a, where a and b are the tens and units digits of Jack's age, respectively. Based on the clues:

10a + b + 10b + a = 11(a - b)

This simplifies to:

Without the third clue, there would be multiple solutions. However, the third clue tells us that Jack is older than Jill, meaning a > b. The possible ages for Jack (from 10-99) that have a digit twice the size of the other would be: 31, 42, 53, 64, 75, 86, and 97. The age of 97 can be discounted as being unrealistic, leaving us with a smaller set of possibilities.

By trial and elimination, we find that Jack is 64 years old and Jill is 46 years old, which fits all the given clues and is a plausible answer.

Answer:

Step-by-step explanation:

if x>−12

add 12 : x+12 >0

but x−(−12) = x+12

so :|x−(−12)| = |x+12| = x+12  .... ( x+12 >0)

note : |a| = a  if a>0

Answer:

The triangles are similar because y=34 and there are three pairs of congruent angles.

Step-by-step explanation:

For triangle ABC, let's start by finding the value of X...

The sum of the interior angles of a triangle sum up to 180 degrees, so...

X = 180 - 34 - 50 = 96 degrees

Angles for ABC are then: 34°, 50° and 96°.

For triangle DEF, let's find y° the same way:

Y = 180 - 50 - 96 = 34 degrees.

Angles for DEF are then: 34°, 50° and 96°

The angles are the same, in the same order... so both triangles are similar.

Answer:

The answer is D

Step-by-step explanation:

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[8-6]^2+[5-(-3)]^2}\implies d=\sqrt{(8-6)^2+(5+3)^2} \\\\\\ d=\sqrt{2^2+8^2}\implies d=\sqrt{68}\implies d\approx 8.24[/tex]

Answer:

B. 8.24 units

Step-by-step explanation:

the distance between two points is given by

√(x₂₋x₁)²+ (y₂-y₁)²

x₂=8, x₁=6

y₂=5, y₁= -3

√(8-6)² + (5- (-3))²

√2²+ (5 + 3)²

√4 + 8²

√4 + 64

√68 = 8.24 units

3Ac?????????????????

Answer:

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

Step-by-step explanation:

Given

kx + 7 = 4 ( isolate the term in x by subtracting 7 from both sides )

kx = - 3 ( divide both sides by k )

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

Answer:

The value of the equation for x is [tex]x=\frac{-3}{k}[/tex]

Step-by-step explanation:

Consider the provided equation.

[tex]kx+7=4[/tex]

We need to solve the equation for x.

Subtract 7 from both the sides.

[tex]kx+7-7=4-7[/tex]

[tex]kx=-3[/tex]

Divide both sides of the equation with k.

[tex]\frac{kx}{k}=\frac{-3}{k}[/tex]

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

Hence, the value of the equation for x is [tex]x=\frac{-3}{k}[/tex]

Answer:

D. Only one

Step-by-step explanation:

Lines are perpendicular if they intersect to form a right angle (90°).

The perpendicular postulate tells you that when you have a line and a point not on the line, then there is only one perpendicular line that can be drawn through the point to the line.

Final answer:

From a point not on a given line, only one perpendicular line to the given line can be drawn, as it is the shortest and unique path between the point and the line.

Explanation:

The question relates to the geometric concept of drawing perpendicular lines to a given line from a point outside of that line. According to geometric principles, through a point not on a given line, you can draw only one perpendicular line to the given line. This is because the perpendicular line is the shortest path between a point and a line, and only one unique shortest distance exists, as any other line from the point to the given line will be longer. Therefore, if you were given a point and a line that the point is not on, you could take a ruler or a straight edge and draw exactly one line that crosses the original line at a 90-degree angle, demonstrating a perpendicular connection.

Answer:

5 + 5 = 10

Step-by-step explanation:

If you know that 5 + 5 = 10, you can solve 5 + 6 = 11.  You are adding one more to the addends (adding 6 instead of adding 5), so you add one more to the sum (11 instead of 10).

Answer:

[tex]x=\frac{4}{3}[/tex]

Step-by-step explanation:

The given logarithmic equation is

[tex]\log_{3x+4}(4096)=4[/tex]

We take antilogarithm to get:

[tex]4096=(3x+4)^4[/tex]

We write the left hand side as a power.

[tex]8^4=(3x+4)^4[/tex]

Since the exponents are the same the bases are also equal.

[tex]8=3x+4[/tex]

[tex]8-4=3x[/tex]

[tex]4=3x[/tex]

Divide both sides by 3;

[tex]x=\frac{4}{3}[/tex]

Answer:

d=5.39 units

Step-by-step explanation:

Given A (-3, -2)  

T= (x+5, y-3)

T= (-3+5, -2-3)

T=(2,-5)

Applying the translation on;

A( -3,-2)

A' (-3+2, -2+ -5)

A'= (-1, -7)

Distance

d= [tex]\sqrt { X2-X1)^2 + (Y2-Y1)^2[/tex]

A = (-3,-2)     and  A'(-1, -7)

d=√ (-1--3)² + (-7--2)²

d=√ (2)²+(-5)²

d=√4+25

d=√29

d=5.39 units

Answer:

The coordinates of point N are (-13 , -20)

Step-by-step explanation:

* Lets revise how to find the mid-point of a segment

- If a line has two endpoints(x1 , y1) and (x2 , y2), then we can find

 the mid-point (x , y) of it by using this rule

 x = (x1 + x2)/2  and y = (y1 + y2)/2

* Now lets solve the problem

∵ The line segment is MN

∵ M is (3 , 4)

∵ The mid-point is (-5 , -8)

- Let M is (x1 , y1) and N is (x2 , y2)

- Let the mid-point is (x , y)

∴ x1 = 3 , y1 = 4

∴ x = -5 , y = -8

∵ x = (x1 + x2)/2

∴ -5 = (3 + x2)/2 ⇒ multiply both sides by 2

∴ -10 = 3 + x2 ⇒ subtract 3 from both sides

∴ x2 = -13

∵ y = (y1 + y2)/2

∴ -8 = (4 + y2)/2 ⇒ multiply both sides by 2

∴ -16 = 4 + y2 ⇒ subtract 4 from both sides

∴ y2 = -20

∴ The coordinates of point N are (-13 , -20)

Answer:

(-13 , -20) TRUST me

Step-by-step explanation:

Answer: 6300 cm 2

Step-by-step explanation: To find the volume of a 3d shape you have to use the formula L x W x H or (Length times Width Times Height).

So now we can see 15 x 15 x 28 = 6300

So you answer is 6300 cm 2

Btw if you did not know the 2 above cm means squared :)

Hope this helped have a nice day :)))))

the assumption here being that both lines JH and FH are tangent lines to the circle, if that's the case the external angle of 34° is the angle made by the equal tangents, meaning the triangle is an isosceles with twin sides.

In an isosceles triangle the twin sides make also twin angles, so the angles at J and F are twins, and they'd be 180° - 34° = 146° total, since they're twins, each one takes half, or 73°.

Answer:

n0

Step-by-step explanation:

Answer: the answer is 12 dollars

Step-by-step explanation: turn the percent 15 into a decimal, then just multiply .15*80 to get your answer

Answer: $12

Step-by-step explanation: 80$ is the cost. you're taking 15% of the cost. 15% of the cost is .15 of 80$. .15 x 80 is 12

Answer:

The diameter of the balloon is [tex]7\ in[/tex]

Step-by-step explanation:

we know that

The volume of a sphere (balloon) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]V=179.5\ in^{3}[/tex]

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]179.5=\frac{4}{3}(3.14)r^{3}[/tex]

[tex]r^{3}=179.5*3/[(4)*(3.14)][/tex]

[tex]r=3.5\ in[/tex]

Find the diameter

The diameter is two times the radius

[tex]D=2(3.5)=7\ in[/tex]

ANSWER

reflection in the x-axis

shift 4 units right

shift 4 units down

EXPLANATION

The given function is

[tex]g(x) = - {2}^{x + 4} - 2[/tex]

The parent function is

[tex]f(x) = {2}^{x} [/tex]

The transformation applied to f(x) to obtain g(x) is of the form

g(x)=-f(x+c)-k

This will shift the graph to the left by c units and shift down by k units and reflected in the x-axis.

For

[tex]g(x) = - {2}^{x + 4} - 2[/tex]

The transformation are:

reflection in the x-axis

shift 4 units right

shift 4 units down

Answer:

54 kilometers

Step-by-step explanation:

87x6 or 522km - 78x6km or 468 = 54

The falcon can fly 54km further than the goose.

How to find the difference between the distance traveled by the falcon and the goose?

Speed of the falcon = 87km/hr

Speed of the goose = 78km/hr

speed = [tex]\frac{distance}{time}[/tex]

distance = speed*time

Distance traveled by falcon in 6 hours = 87*6 km = 522km

Distance traveled by goose in 6 hours = 78*6 km = 468 km

How much further the falcon fly

= Distance traveled by falcon - Distance traveled by goose

= (522 - 468 )km

=54km

To learn more about speed and time, refer:

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Answer:

The answer is x = 5

Step-by-step explanation:

The given equation is

25 - 3x = 10

So when we break down this equation, we will have the value of x. Now breaking down the equation and moving variables to the correct positions.

25 - 3x = 10

Moving -3x and 10 to the other sides

25 - 10 = 3x

3x = 25 - 10

3x = 15

Now dividing both sides with 3, we get the following answer

3x/3 = 15/3

x = 5

Breaking down the equation gives us the value of x, i-e 5

Answer:

24 minutes.

Step-by-step explanation:

This question shows up in a great many places in math or physics, so it is a pretty good question to learn how to do.

First you should note that answer will be under 40 minutes.

1/40 + 1/60 = 1/TimeTotal

The common denominator on the left is 120 minutes

3/40*3 + 2/60*2 = 1/timetotal

3/120 + 2/120      = 1/ timetotal

5/120 = 1/time total  Now to use to the key stop

What you do now is you always turn the left side over. You do the same thing to total time.

120/5 = total time

24 = total time

What this means is that if you let both pipes run for 24 minutes, they will fill the tank working together.

Answer:

Vertex = (-1,4).

Step-by-step explanation:

Given equation is [tex]y=-(x-1)(x+3)[/tex].

Now we need to find the vertex of the graph of given function [tex]y=-(x-1)(x+3)[/tex].

To find that we can rewrite given function into vertex form

[tex]y=-(x-1)(x+3)[/tex]

[tex]y=-(x^2+3x-1x-3)[/tex]

[tex]y=-(x^2+2x-3)[/tex]

[tex]y=-(x^2+2x+1-1-3)[/tex]

[tex]y=-((x+1)^2-1-3)[/tex]

[tex]y=-((x+1)^2-4)[/tex]

[tex]y=-(x+1)^2+4[/tex]

Now compar this equation with [tex]y=a(x-h)^2+k[/tex]

we get: h=-1, k=4

Hence vertex is (h,k) or (-1,4).

Final answer:

The vertex of the graph of the function y = -(x-1)(x+3) is at the point (-1, -2).

Explanation:

The vertex of the graph of the function y = -(x-1)(x+3) can be found by rewriting this function in vertex form or by calculating the axis of symmetry and the value of the function at that point. Since the function is in factored form, we need to find the axis of symmetry which is the average of the x-values of the roots (x-intercepts). In this case, the roots are x = 1 and x = -3.

To find the axis of symmetry, we take the average of 1 and -3, which gives us:

((1) + (-3))/2 = (-2)/2 = -1

Now, we plug x = -1 into the function to find the y-coordinate of the vertex:

y = -((-1)-1)((-1)+3) = -(1)(2) = -2

Therefore, the vertex of the graph of the function is at (-1, -2).

Okay!

The most important part of this problem is knowing which inequality sign to use

Greater than >

Less Than  <

Equal to .. =

Greater or equal to ≥

Less than or equal to  ≤

Charlotte needs AT LEAST 5,000 votes, meaning she has to have 5,000 votes or more

That means we use this sign →  ≤

Now lets set up an equation to find how many more we need

5,000  ≤  3,187 + X

solve for X

1,813 ≤ X

Hope I helped :) Sorry for the long explanation

Answer: 2

Step-by-step explanation:

1 + 1 = 2

the answer equal ：2

+=2

The top left graph is the only one correct. It rises up slowly then faster, and then stays constant for an hour, then decreases.

The temperature starts at 50°, then it slowly increases. Next it increases quickly, then it stays the same temperature for an hour. And finally the temperature slowly decreases.

The 1st graph is your answer(top left)

It is not the 2nd graph (top right) because the temperature stays at 50° for 2 hours, than decreases, which does not match the description.

It is not graph 3 (bottom left) because it increases quickly, than stays the same for 4 hours.

It is not graph 4 (bottom right) because the graph is decreasing most of the time

Answer:

C.) Linear

Step-by-step explanation:

The line of best fit is a straight line.

Linear also make sense because the more nickles minted in a year, the more chance for a nickle to be from that year.

Answer:

The center is (8 , -9)

The vertices are (11 , -9) and (5 , -9)

The foci are (8 , -9 + √58) and (8 , -9 - √58)

The equations of the asymptotes are y = 3/7(x − 8) - 9 , y = -3/7 (x − 8) - 9

Step-by-step explanation:

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the y-axis is

  (y - k)²/a² - (x - h)²/b² = 1

- The length of the transverse axis is 2 a  

- The coordinates of the vertices are ( h ± a , k )  

- The length of the conjugate axis is 2 b  

- The coordinates of the co-vertices are ( h , k ± b )

- The coordinates of the foci are (h , k ± c), where c² = a² + b²

- The equations of the asymptotes are y = ± a/b (x − h) + k

* Now lets solve the problem

∵ (y + 9)²/9 - (x - 8)²/49 = 1

∴ h = 8 and k = -9

∴ a² = 9 ⇒ a = ± 3

∴ b² = 49 ⇒ b = ± 7

∵ c² = a² + b²

∴ c² = 9 + 49 = 58

∴ c = ± √58

∵ The center is (h , k)

∴ The center is (8 , -9)

∵ The coordinates of the vertices are ( h ± a , k )

∴ The vertices are (8 + 3 , -9) and (8 - 3 , -9)

∴ The vertices are (11 , -9) and (5 , -9)

∵ The coordinates of the foci are (h , k ± c)

∴ The foci are (8 , -9 + √58) and (8 , -9 - √58)

∵ The equations of the asymptotes are y = ± a/b (x − h) + k

∴ The equations of the asymptotes are y  = 3/7 (x - 8) - 9 and  

   y  = -3/7 (x − 8) - 9

Answer:

Center = (-9,8)

Foci = (0,±7.6)

Vertices = (0,±3)

Asymptotes y = 8±(3/7)(x+9)

Step-by-step explanation:

We need to find the center, vertices, foci and asymptotes of hyperbola:

[tex]\frac{(y+9)^2}{9} - \frac{(x-8)^2}{49}=1[/tex]

The hyperbola has vertical transverse axis having standard equation:

[tex]\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2}=1[/tex]

The center is (h,k), foci (0,±c) , vertices = (0,±a) and

asymptotes = y= k±(a/b)(x-h)

Solving for the given equation by comparing with standard equation:

a^2 = 9 => a = 3

b^2 = 49 => b =7

h= -9

k= 8

c^2 - a^2 = b^2

c^2 = b^2 + a^2

c^2 = 49+9

c^2 = 58

c = 7.6

Now Center(h,k) = (-9,8)

Vertices (0, ±a) = (0,±3) or (0,+3), (0,-3)

Foci (0,±c) = (0, ±7.6) or (0+7.6), (0,-7.6)

Asymptotes = y= k±(a/b)(x-h)

Putting values:

y= 8±(3/7)(x-(-9)

y = 8±(3/7)(x+9)

or y = 8+(3/7)(x+9) and y= 8-(3/7)(x+9)

Answer:

The first 4 are correct and the last one is incorrect

Step-by-step explanation:

1. The diameter of the circle is 30.8 m ( Correct )

Radius = 15.4 so diameter is 2 times the radius which is 30.8 m

2. The circumference in terms of π is 30.8 π ( Correct )

Circumference = π × Diameter

Circumference = π × 30.8

Circumference = 30.8 π

3 . The circumference of the circle can be found using 2 × π × 15 . 4 ( Correct )

Circumference = π × Diameter

Circumference = π × 30.8

Circumference = 30.8 π

4 . The approximate circumference of the circle rounded to the nearest tenth is 96.7 m ( Correct )

Circumference = 30.8 π = 96.7610537306

5 . A little more than 6 diameters could be wrapped around the circle

( False )

Circumference = 96.7610537306

Diameter = 30 . 8

96.7610537306 ÷ 30 . 8 = 3.14

The fourth vertex of a kite, given the vertices D(0, 3b), E(a, 0), and F(0, -5b), would be located at (-a, 0). This is based on the principles of symmetry inherent to a kite shape in geometry.

To identify the fourth vertex of the kite, we must consider the properties of the kite shape in geometry. A kite is defined by two pairs of adjacent sides that are equal in length. In a coordinate system, this corresponds to certain symmetries in the point coordinates.

Given the vertices D(0, 3b), E(a, 0), and F(0, -5b), we see that vertex D and F are both located on the y-axis, their y-coordinates being mirror images with respect to the x-axis. Thus, we can infer that vertex G is going to be a mirror image of point E with respect to y-axis, as we are dealing with a kite.

Hence, the coordinates for vertex G would be (-a, 0). This is because, the x-coordinate becomes the negative of 'a', while the 'y' coordinate remains the same, reflecting the symmetry of a kite's structure.

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The coordinates of point G in the kite are G(a, 3b)

To find the coordinates of point G, we can use the fact that the kite is a parallelogram.

Since the opposite sides of a parallelogram are congruent, we can find the coordinates of point G by using the coordinates of points D, E, and F.

Point G will have the same x-coordinate as point E and the same y-coordinate as point D.

Therefore, the coordinates of point G are G(a, 3b).

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Answer:

A. 10

Step-by-step explanation:

The two angles are vertical angles, thus they are equal. You solve once you set the two angles equal in an equation. See work for more.

Answer:

The correct answer is option B.  70

Step-by-step explanation:

From the figure we can see that a pair of vertically opposite angles.

Vertical opposite angles are equal.

To find the value of x

From figure we get,

<AEB = <CDE

2x + 50 = 7x

7x - 2x = 50

5x = 50

x = 10

To find m<AEB

m,<AEB =  2x + 50

 = 2*10 + 50

 = 20 + 50

 = 70°

Therefore the correct answer is option B.  70

ten ways(10) i think so

The answer is 21 ways.

Hope this helps!

Answer: mean = 3.6,  standard deviation = 3

Step-by-step explanation:

[tex]\text{Mean: }\dfrac{90\times 4}{100}=\dfrac{360}{100}=3.6\\\\\\\text{Standard Deviation: }\\\bullet n=100\qquad \rightarrow \text{number of students}\\\bullet p=0.9\qquad \rightarrow \text{probability of success}\\\bullet q=0.1\qquad \rightarrow \text{probability of failure}\\\\SD=\sqrt{n\times p\times q}\\.\quad =\sqrt{(100)(0.9)(0.1)}\\.\quad =\sqrt{9}\\.\quad =3[/tex]