Darlene is buying a cake for her parent’s anniversary party. She has two to choose from. The cakes are similar prisms.

What is the ratio of the volumes of the smaller cake to the larger cake?

Select the correct response:

A. 8:27
B: 16:81

Answer:

see explanation

Step-by-step explanation:

Using identities

sec²x = tan²x + 1

cosec²x = cot²x + 1

cos²x = [tex]\frac{1}{cos^2x}[/tex]

(1)

sin²θ + [tex]\frac{1}{sec^20}[/tex]

= sin²θ + cos²θ = 1

(2)

9sec²θ - 9tan²θ

= 9sec²θ - 9(sec²θ - 1)

= 9sec²θ - 9sec²θ + 9

= 9

(3)

- 8cot²A + 8cosec²A

= - 8cot²A + 8(cot²A + 1)

= - 8cot²A + 8cot²A + 8

= 8

(4)

- 10cosec²β + 10cot²β

= - 10(cot²β + 1) + 10cot²β

= - 10cot²β - 10 + 10cot²β

= - 10

1. Let the four consecutive numbers be x, x+1, x+2, x+3

The sum of four consecutive number is already given to us = 70

Therefore

⇒(x)+(x+1)+(x+2)+(x+3)=70  

We need to combine x as we have four x terms in the equation. The next step is to get all of the x’s on one side of the equation and all the numbers on the other side. The same rule applies – whatever you do to one side of the equation, you must do to the other side as well!

⇒4x+6=70⇒4x=64⇒x=16

So, the four numbers are 16, 17, 18 and 19.

Hence, the greatest number among them is 19.

Answer: -3

Step-by-step explanation:

plug in -2 for x so that the new problem is:

y=4(-2)+5

then, multiply 4 and -2 so that:

y=-8 +5

finally add -8 to 5 to get:

y=-3

Answer:

11 12 v149

thats what I got......

Answer:

y-1=-4(x-7) is the correct answer

Answer:

Hi im filipino :))

Step-by-step explanation:

Thanks for the points

Answer:

18

Step-by-step explanation:

2 + 1 + 2 + 2 + 3 + 1 + 0 + 0 + 3 + 2 + 0 + 1 + 0 + 1

Get rid of the zeros

2 + 1 + 2 + 2 + 3 + 1 + 3 + 2 + 1 + 1

18

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

Explanation:

Let's add up the positive values only for now. So we get 172+48 = 220 which represents all the money coming into the account.

Do the same for the negative values. We'll simply add the positive versions of each (ignore the negative signs). So -17 and -40 can be thought of as 17 and 40, which add to 17+40 = 57. Ultimately this result is negative leading us to -57.

In other words, -17 + (-40) = -57

So you can see that adding negatives follows the same rule as positives. The only change is that everything turns negative.

The notation -57 means that 57 dollars is going out in terms of expenses, purchases, withdrawals, fees, etc.

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

To summarize everything so far:

We subtract those results to find the final balance

balance = moneyIn - moneyOut = 220-57 = 163 dollars

We subtract positive versions of each number.

Answer:

6 1/2

Step-by-step explanation:

change 1 4/9 into a improper fraction, which is 13/9, and when dividing fractions flip the second number upside down then multiply. 13/9 times -2/9 is -117/18. simplify, which is 13/2, which is also equal to 6 1/2. hope this helped

Answer:

see pics

Step-by-step explanation:

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Answer:

x = (-1 ±[tex]\sqrt{145}[/tex] )/8

Step-by-step explanation:

Quadratic formula: x = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex] )/(2a)  

4x² + x - 9 = 0 ; General form of a quadratic is ax² +bx + c = 0

So a = 4, b = 1, and c = -9

x = -1 ±[tex]\sqrt{1^{2}-4(4)(-9)}[/tex] / 2(4)

x = -1 ± [tex]\sqrt{1 + 144}[/tex] /8

x = -1 ±[tex]\sqrt{145}[/tex] /8

x = (-1 + [tex]\sqrt{145}[/tex])/8    or x = (-1 - [tex]\sqrt{145}[/tex])/8

Answer:

x ≥ 3 and x ≤ -3      See below

Step-by-step explanation:

| x | ≥ 3

 Case I                                     Case II

x ≥ 3                                          -(x) ≥ 3

                                                  -x ≥ 3  multiply by -1 and change the inequality

                                                  x ≤ -3

The graph:

Graph ≤ or ≥ the closed circle at the endpoint.

  x ≥ 3  closed circle at point 3 and shade to the right .

  x  ≤ -3  closed circle at -3 and shade to the left.

Answer:

[tex]a_{n}[/tex] = 0.5n - 2.5

Step-by-step explanation:

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 2 and d = a₂ - a₁ = - 1.5 - (- 2) = - 1.5 + 2 = 0.5 , then

[tex]a_{n}[/tex] = - 2 + 0.5(n - 1) = - 2 + 0.5n - 0.5 = 0.5n - 2.5 ← explicit equation

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

Explanation:

The jump from 4 inches to 5 inches is 5/4 = 1.25

In other words, 4*1.25 = 5

So we need to multiply every dimension by the scale factor 1.25 to enlarge the image. The 5 inch dimension then goes to 5*1.25 = 6.25 inches

----------

Here's another way you can solve

(old width)/(old length) = (new width)/(new length)

4/5 = 5/x

4x = 5*5

4x = 25

x = 25/4

x = 6.25

Answer:

117/50 or 2 17/50 or 2.34

Step-by-step explanation:

i don't know is just simple

You multiply 7 X5+4 is 39, 39/5 and then multiple

#1

[tex]\\ \sf\longmapsto cos75°[/tex]

[tex]\\ \sf\longmapsto cos(45+30)°[/tex]

[tex]\\ \sf\longmapsto cos45cos30+sin45.sin30[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}\times \dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\sqrt{3}+1}{2\sqrt{2}}[/tex]

#2

[tex]\\ \sf\longmapsto tan\left(-\dfrac{\pi}{12}\right)[/tex]

[tex]\\ \sf\longmapsto tan(-15°)[/tex]

[tex]\\ \sf\longmapsto \dfrac{sin(-15)}{cos(-15)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{-sin15}{cos15}[/tex]

[tex]\\ \sf\longmapsto -\dfrac{\dfrac{\sqrt{3}-1}{2\sqrt{2}}}{\dfrac{\sqrt{3}+1}{2\sqrt{2}}}[/tex]

[tex]\\ \sf\longmapsto -\left(\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right)[/tex]

first, make the line into slope-intercept form.

-3x - 5y = 1

-5y = 3x + 1

y = -3/5x - 1/5

a line parallell to this line has to have the same slope, so it could be but doesn't have to be y = -3/5x - 1

a line perpendicular to y = -3/5x - 1/5 has to have the opposite slope of it.

so, y = 5/3x +1

Answer:

x = 4

x = 10

Step-by-step explanation:

x^2 -14x + 40 = 0 ----> factor form

(x - 10)(x - 4) = 0 ---> separate equations

x - 10 = 0 ---> add 10 on both sides

x = 10

x - 4 = 0 ---> add 4 on both sides

x = 4

Answer:

small x= 4

large x= 10

Step-by-step explanation:

hello there!

x^2-14x+40=0

x^2-(10+4)x+40=0

x^2-10x-4x+40=0

pick out the common one!

x(x-10)-4(x-10)=0

(x-10)(x-4)=0

now;

x-10=0

x=10(which is large x)

again:

x-4=0

x=4( which is small x)

hope it helps.. thank u!

hiStep-by-step explanation:

Answer:

x=-2, x=1/2

Step-by-step explanation:

> 2x²-x=2-4x

> 2x²-x+4x-2=0

> 2x²+3x-2=0

> 2x(x+2)-(x+2)=0

> (x+2)(2x-1)=0

> x+2=0; 2x-1=0

> x=-2; x=1/2

Answer:

6:9

Step-by-step explanation:

there are six circle and nine triangle

so the ratio is

6:9

Answer:

Sasha's car moves 13 meters faster than Frank's car

Step-by-step explanation:

I took Sasha's 875 meters and divided it by 7minutes and got 125

Then, I took Frank's 1232 meters and divided it by 11 minutes and got 112

Finally, I subtracted 125 by 112 and got 13 meters

Answer:

125 × 11 = 1375

1375 > 1232

Sashas car goes faster then Frank's

Sashas car goes 143 meters faster then Franks

Answer:

5/6

Step-by-step explanation:

2/3 -> 4/6

4/6+1/6= 5/6

Answer:

5/6

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

3x+7x+2x = 12x

-5+10 = 5

so it's = 12x+5

Answer:

30m or 6m5

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

The simplification of the given expression 6 x m x 5 will be 30m.

Simplification is to make something easier to do or understand and to make something less complicated.

The expression is given below.

6 x m x 5

Then the simplification of the expression will be

30m

Where m can be any number.

Then the expression 6 x m x 5 is written as 30m.

More about the simplification link is given below.

https://brainly.com/question/12616840

#SPJ2

Answer:

Step-by-step explanation:

Given functions:

and

Work out the composite f(g(x)):

Answer:

f(g(x)) = -10x - 13

???? = - 8x - 13

Step-by-step explanation:

f(x) = 5x +7

and

g(x) = -2x - 4

f(g(x)) = f(-2x - 4) = 5(-2x - 4) + 7

f(g(x)) = -10x - 20 + 7

f(g(x)) = -10x - 13

f(g(x)) = -2x - 8x - 13