What decimal is represented by this expanded form?

5×10,000+3×1,000+2×10+8×1+ 6×1/100+4×1/1,000

Answer:

[tex]\frac{19}{12}[/tex] feet

Step-by-step explanation:

First, we need to find the height after one year:

2.25 + 1 1/6 = [tex]\frac{41}{12}[/tex]

Now to find the amount in the second year, we can subtract the above amount from 5:

5 - [tex]\frac{41}{12}[/tex] = [tex]\frac{19}{12}[/tex]

So in the second year it grew [tex]\frac{19}{12}[/tex] feet

Answer:

f(x) = -8 x + 34

Step-by-step explanation:

First, normalize the equation 8y = x-16 into y = ... form (divide by 8):

y = 1/8 x - 2

So the slope of this line is 1/8. The slope of a perpendicular line is the negative reciprocal, which means you swap numerator and denominator and add a minus sign. So the slope of our line is -8 and our function will look like f(x) = -8x + b

Now all we have to do is find b such that f(x) goes through (5,-6).

So f(5) = -8*5 + b = -6, and solve it for b:

-40 + b = -6 =>

b = 34.

So f(x) = -8x + 34

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}.\\\\\text{We have}\ 8y=x-16\qquad\text{divide both sides by 8}\\\\y=\dfrac{1}{8}x-2\to m_1=\dfrac{1}{8}.\\\\\text{Let}\ y=mx+b.\ \text{It's perpendicular to given line. Therefore}\ m=-\dfrac{1}{\frac{1}{8}}=-8.\\\\y=-8x+b.\\\\\text{The line passes through point (5, -6)}.\ \text{Put the coordinates of the point}\\\text{to the equation of a line:}[/tex]

[tex]-6=-8(5)+b\\-6=-40+b\qquad\text{add 40 to both sides}\\34=b\to b=34\\\\Answer:\ \boxed{f(x)=-8x+34}[/tex]

Answer:

angle A and angle D equals 100 degrees, angle B and angle E equals 30 degrees, and angle C and angle F equal 50 degrees.

Step-by-step explanation:

a triangle has to equal 180 degrees, and since they are similar, it should equal the same. Hope this helped you. :))

The angles of triangles △ABC and △DEF, which are similar, are 100°, 30°, and 50°. This is calculated using the properties of similar geometry and the fact that the sum of all angles in a triangle equals 180°.

In Triangle Similarity, the corresponding angles are equal due to the property of similarity in geometry.

Since we know that △ABC and △DEF are similar and we have m∠A=100° and m∠B=30°, we can determine that angles A and B in triangle △DEF are also 100° and 30°, respectively.

The third angle in both triangles can be calculated using the property that the sum of all angles in a triangle equals 180°.

Hence, in △DEF and △ABC we can calculate the measure of the third angle by 180° - (100°+30°) = 50°.

So for triangles △ABC and △DEF, the angles are 100°, 30° and 50° respectively.

Learn more about Triangle Similarity here:

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Answer:

A = 2/5

Step-by-step explanation:

r = sqrt(v) / (pi*h)

10 = sqrt(v) /(pi * h)

Solve for the volume by multiplying by pi * h on each side

10 * pi * h = sqrt(v)

Now square each side

(10*pi* h) ^2 = v

Now we have a second cylinder with a height that is 25 times the height of the other cylinder  but the same volume.  Solving for volume, we will multiply by

r = sqrt(v) / (pi*h)

r = sqrt(v) /(pi *25h)

r* pi * 25h = sqrt(v)

Now square each side

(r*pi*25h) ^2 = (sqrtv) ^2

(r*pi*25h)^2 = v

The problem states the the 2 cylinders have the same volume

(10 * pi * h) ^2 =  ( r * pi * 25h) ^2

Take the square root of each side

10*pi*h = r*pi * 25h

Divide each side by pi and h

10 = 25r

Divide by 25

10/25 =r

2/5 =r

The answer you are looking for is 9/11.

When dividing fractions, you multiply the first value by the inverse of the second value. The inverse is found by simply flipping the numbers of the last fraction. So, the inverse is 9/4. Then, multiply 4/11 and 9/4 to get 36/44. 36/44 simplified (divided by 4/4) is 9/11. Thus making 9/11 the answer.

I hope this helps.

Answer:

9/11

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

Write out the equation

5n-8=n-48

move like terms to the same side

4n=-40

divide 4n and 4 by 4 to get n by itself.

n=-10

The number is -10.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given,

Eight less than 5 times a number is 48 less than the number

Let the number be x

then statement can be written as

5x - 8 = x - 48

5x - x = - 48 + 8

4x = -40

x = 40/4

x = -10

Hence, -10 is the number.

Learn more about equation here:

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Answer:

Option B.

Step-by-step explanation:

Dr. Peterson works about 178 hours each month.

There are 12 months in one year.

So Dr. Peterson works in a year = 178 × 12 = 2,136 hours

We will go through all the options to find which is the closest to the answer.

Option A : 200 × 20 = 4,000 hours

Option B : 180 × 10 = 1,800 hours

Option C : 100 × 12 = 1,200 hours

Option D : 100 × 10 = 1,000 hours

Therefore, Option B is the best estimate of the number of the hours she works in a year.

To find out how much longer the record alligator is than the one Taylor saw, we subtract the length of the alligator Taylor saw from the record length. The record alligator is 6 feet and 3/4 feet longer than the alligator Taylor saw.

To find out how much longer the record alligator is than the one Taylor saw, we need to subtract the length of the alligator Taylor saw from the record length.

To do this, we need to convert the mixed numbers to improper fractions. 12 11/12 is equal to 155/12 and 19 1/6 is equal to 115/6.

Subtracting 155/12 from 115/6 gives us (115/6) - (155/12) = (230/12) - (155/12) = 75/12 = 6 3/4.

Therefore, the record alligator is 6 feet and 3/4 feet longer than the alligator Taylor saw.

Answer:

Solutions are  (3, -8) and (5, -10)

Step-by-step explanation:

From the equation x + y + 5 = 0 :-

x = -y - 5

Substitute for x in the other equation:

y = (-y - 5)^2 - 9(-y-5) + 10

y = (y^2 + 10y + 25) + 9y + 45 + 10

y^2 +  18y + 80 = 0

( y + 8)(y + 10) = 0

y  = -8, -10

Substitute these values of y in the equation x + y + 5 = 0:-

x = -8:-

x - 8 + 5 = 0 so x = 8-5 giving.x = 3

x = -10:-

x - 10 + 5 = 0 sox = 10-5 giving x = 5

Answer:2x−3y=6

Step-by-step explanation:Standard form: Ax + By = C

Just take 2/3x to the other side.

So the answer would be

−23x+y=−2

In standard form

x

can't be negative and A, B and C need to be an integers (whole numbers)

(I multiplied the whole equation by -3)

2x−3y=6

So the final answer would be: 2x−3y=6

Equivalent fractions are fractions that are equal to each other.

So they might have different denominators

and different numerators but they're

going to be equal fractions.

Answer:

First, you have to get all of the variables on one side of the equation.

x15 on both sides

8 + a = 15+15a/6

x6 on both sides

48 + 6a=15+15a

Subtract 15 on both sides and Subtract 6a on both sides

33=11a

a=3

Step-by-step explanation:

[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\dfrac{4}{-3\sqrt{64}}=\dfrac{\not4^1}{-3(\not8_2)}=-\dfrac{1}{6}[/tex]

Answer: Let x=length of the longest side of the smaller triangle.

x/20=3/12

x=60/12

x=5

Final answer:

To find the longest side of the similar triangle, multiply the longest side of the original triangle (20) by the scale factor, which is the ratio of the shortest sides (3/12 = 0.25). This results in a longest side of 5 units for the similar triangle.

Explanation:

The question pertains to finding the longest side of a similar triangle given that the shortest side is 3 and the original triangle has sides 12, 15, and 20. To find the answer, we need to calculate the scale factor between the similar triangles. The scale factor is obtained by dividing the shortest side of the new triangle (3) by the shortest side of the original triangle (12), which is ¼ or 0.25.

We then multiply the longest side of the original triangle (20) by the scale factor (0.25) to get the longest side of the similar triangle. Calculating, 20 * 0.25 = 5. Therefore, the longest side of the triangle with the shortest side 3 is 5 units long.

The volume of a larger cone:

[tex]V_l=\dfrac{1}{3}\pi\cdot4.5^2\cdot(3+6)=\dfrac{1}{\not3_1}\pi\cdot20.25\cdot\not9^3=(20.25)(3)\pi=60.25\pi\ cm^3[/tex]

The volume of a smaller cone:

[tex]V_s=\dfrac{1}{3}\pi\cdot3^2\cdot6=\dfrac{1}{\not3_1}\pi\cdot\not3^1\cdot3\cdot6=18\pi\ cm^3[/tex]

The volume of the frustum:

[tex]V=V_l-V_s\\\\V=60.25\pi-18\pi=42.75\pi\ cm^3[/tex]

Answer:

1/12 of the watermelon in each piece

Step-by-step explanation:

The final answer is 1/12.

I hope this helped!

Answer:

The fraction of the watermelon that corresponds to each piece is [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

Caleb has [tex]\frac{1}{3}[/tex] of a watermelon. To know what fraction each portion of watermelon represents after cutting it into 4 equal parts, just divide the portion that Caleb owns ([tex]\frac{1}{3}[/tex]) by the amount of sliced ​​portions (4):

[tex]\frac{\frac{1}{3} }{4}[/tex]

Given that 4 can also be represented by the fraction [tex]\frac{4}{1}[/tex], then:

[tex]\frac{\frac{1}{3} }{\frac{4}{1} }[/tex]

To divide two fractions, the SECOND FRACTION must be reversed, that is, change the denominator to the numerator and change the numerator to the denominator. Then, the two fractions are multiplied.

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

The fraction of the watermelon that corresponds to each piece is [tex]\frac{1}{12}[/tex]

Answer:

$22.30

Step-by-step explanation:

To determine how much money Chapman saved from purchasing a gift for his mother, calculate 2/5 of $55.75, which equals $22.30.

To find how much money Chapman saved:

Calculate 2/5 of $55.75: (2/5) x $55.75 = $22.30

Therefore, Chapman saved $22.30

Answer:

The pole is 6 ft tall

Step-by-step explanation:

We can solve this using ratio's

4ft tall Mary        x ft tall  pole

-----------        =     -------------------

10 ft shadow      15 ft shadow

Using cross products

4 * 15 = 10 x

60 = 10x

Divide by 10

60/10 = 10x/10

6 =x

The pole is 6 ft tall

Answer:

it is 6 feet

Step-by-step explanation:

i dont have much of an explaination except that you have to draw a diagram inorder not tom get confused.

hope it helps.

Answer:

3/4

Step-by-step explanation:

- He ate 1/4

- 4-1=3

- 3/4 of the pizza is left

Final answer:

The fraction representing the remaining pizza after Jason ate 1/4 of it is 3/4. We calculate this by subtracting the portion Jason ate (1/4) from the whole (4/4).

Explanation:

If Jason ate 1/4 of the whole pizza for dinner, we can easily calculate the fraction that represents the amount of pizza remaining. To find out the remaining portion of the pizza, we subtract the portion Jason ate from the whole. Since the whole is considered to be 1 (or 4/4 in this case, as there are four quarters in a whole), we subtract 1/4 from 4/4:

Remaining pizza = Whole pizza - Portion eaten by Jason

Remaining pizza = 4/4 - 1/4

Remaining pizza = (4 - 1)/4

Remaining pizza = 3/4

Therefore, the fraction that represents the remaining pizza after Jason has eaten is 3/4.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (1, 3) and (3, 1). Substitute:

[tex]d=\sqrt{(3-1)^2+(1-3)^2}=\sqrt{2^2+(-2)^2}=\sqrt{4+4}=\sqrt8\approx2.8[/tex]

Answer:

9/25

Step-by-step explanation:

The answer is 9/25

Answer:

We will need 27/31 of an ounce of red

Step-by-step explanation:

3 /10 red + 11 /15 blue  makes 1 1/30 purple

Get a common denominator of 30

3/10 * 3/3 = 9/30  red

11/15 *2/2 = 22/ 30  blue

1  1/30 = 31/30   purple

So the ratio of red to purple is

9/30

--------  =   9/ 31

31/30

Keeping this ratio, we want 3 ounces purple

9 red                      x red

--------           =  --------------

31 purple             3   purple

Using cross products,

9*3 = 31 *x

27 = 31x

Divide each side by 31

27/31 = x

We will need 27/31 of an ounce of red

Answer:

51,400 thats my answer hope it helps!

Answer:

n=2

Step-by-step explanation:

I am assuming that you want to solve this algebraic equation

4n+3 =11

Subtract 3 from both sides

4n+3-3=11-3

4n =8

Divide each side by 4

4n/4 = 8/4

n =2

Answer:

SA = 201 in^2

Step-by-step explanation:

The formula for surface area of a sphere is

SA = 4pi r^2

We know that the diameter is 8

To find the radius we cut the diameter in half.

r = d/2

r = 8/2 =4

Substitute in what we know.

SA = 4 *pi *4^2

    = 4*pi*16

   = 64*pi

Letting pi = 3.14

  = 200.96 in^2

We want to round to the nearest whole number

SA = 201 in^2

Answer:

72 is 8 times as many as 9

Step-by-step explanation:

72 is the product of 8 groups of nine

72 is 9 times as many as 8 is the answer that completes the statement.

To solve the equation 72 = q × 8, we need to find the value of q.

By dividing both sides by 8, we get:

72/8 = q × 8/8

q = 72/8

q = 9.

This means that 72 is 9 times greater than 8 and to correctly complete the statement, we write: 72 is 9 times as many as 8.