9. Rama is using a hand glider to fly directly from the top of one cliff onto another cliff below. The glider is guided by a cable. The cliffs are 740 feet apart and the first cliff is 280 feet taller than the second cliff. How long is the cable between the cliffs?

it is 3+2 = 5 plus a = 5a

Answer:

60

Step-by-step explanation:

3:4:6

Add:

3+4+6=13

3:4:6=13

?:?:?=260

Divide:

260/13=20

Multiply 3 and 20:

60

SO there are 60 small uniforms

Answer:

24 Home games

Step-by-step explanation:

let [tex]x[/tex] denote the number of home games played, and [tex]y[/tex] denote the number of home games played. We are given the total number of games played as 49

and total wins as 26.

The problem can be expressed in equation form as:[tex]\frac{2}{3}x+\frac{2}{5}y=26[/tex]...[tex]eqtn1[/tex]

Total games is expressed as [tex]x+y=49[/tex]...[tex]eqtn2[/tex]

Rewrite equation 1 to remove fractions:

[tex]\frac{2}{3}x+\frac{2}{5}y=26\\=>5x+3y=195\\[/tex]

Solve for x to obtain total home games played.

Making [tex]x[/tex] the subject in eqtn 2:

[tex]x=49-y[/tex]

Substitute for [tex]x[/tex] in eqtn1:

=>

[tex]5(49-y)+3y=195\\-5y+3y=195-245\\-2y=-50\\y=25[/tex]

To obtain [tex]x[/tex], replace y value in eqtn2:

[tex]x+y=49\\y=25\\Therefore\\x=49-25\\x=24[/tex]

Home games played is 24

Answer:

Look at the rise over run

itd be 10/10 or 1

Answer:

David receives £90

Step-by-step explanation:

Let David's share be D

Let Mark's share be M

Let Henry's share be H

From the question, we obtained the following data:

David gets twice as much as Mark i.e

D = 2M

M = D/2

Mark gets three times as much as Henry i.e

M = 3H

H = M/3

H = (D/2) /3

H = D/6

The sum of their shares is £150 i.e

D + M + H = 150

D + D/2 + D/6 = 150

Multiply through by 6 to clear the fraction

6D + 3D + D = 900

10D = 900

Divide both side by the coefficient of D i.e 10

D = 900/10

D = 90

Therefore, David receives £90

Answer:

4x^4 + 6x^3 + 9x^2 − 4x + 3

Step-by-step explanation:

Simplify the expression. 4x^4 + 6x^3 + 9x^2 − 4x + 3

Answer:

4x^4 + 6x^3 + 9x^2 - 4x + 3

Step-by-step explanation:

Distribute (x^2 + 2x + 3)(4x^2 - 2x + 1)​

You will get 4x^4 - 2x^3 + x^2 + 8x^3 - 4x^2 + 2x + 12x^2 -6x + 3

Then you need to combine like terms

And you will get the answer:

4x^4 + 6x^3 + 9x^2 - 4x + 3

Answer: 600 members of the club

Step-by-step explanation:

A sample is a subset of the population that represents the entire population.

Here , we are given that ,

The club surveys  50 of its 600 members.

Clearly , Population = 600 members of the club

Sample = 50 members

Hence, the population of this study is "600 members of the club " .

Answer:

8 quarters

Step-by-step explanation:

You need to break the $20 into smaller bills. The smaller bills value has to be equal to $20. So far you have three $5 bills and three 1$ bills, so the current value is 3*$5 + 3*$1= $18

The value you need to add more will be $20- $18= $2

You need to add $2 more value to the smaller bills and you want to do it using quarters($0.25). The number of the quarter you need will be: $2/ $0.25= 8 quarters

Let's start by calculating the total value of the five-dollar bills and one-dollar bills:
You have 3 five-dollar bills, and each is worth $5, so:
3 five-dollar bills × $5 per bill = $15
You also have 3 one-dollar bills, and each is worth $1, so:
3 one-dollar bills × $1 per bill = $3
Now, let's add the value of the five-dollar bills and one-dollar bills together:
$15 (from five-dollar bills) + $3 (from one-dollar bills) = $18
You started with a twenty-dollar bill, which is worth $20, so we subtract the total value of the bills you have from $20 to find out how much is left to reach $20:
$20 (initial amount) − $18 (value of bills) = $2
You need to make up this remaining $2 with quarters. Since each quarter is worth $0.25 (25 cents), we divide the remaining amount by the value of each quarter to find out how many quarters you need:
$2 ÷ $0.25 per quarter = 8 quarters
Therefore, you need 8 quarters to complete the conversion to $20.

Answer:

Step-by-step explanation:

A

Answer:

Answer A

Step-by-step explanation:

Answer:

165 calories

Step-by-step explanation:

110 cal/28.4 g in Cereal X

How m any cals in 42.6 g of Cereal X

110/x=28.4/42.6

28.4x=4686

x=165

Therefore, 165 calories

The number of calories in 42.6 grams of cereal X will be 165 calories.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

There are 110 calories per 28.4 grams of cereal X. Then the number of calories in each gram is calculated as,

Rate = 110 / 28.4

Rate = 275 / 71  calories per gram

Then the number of calories in 42.6 grams of the cereal X will be given as,

⇒ (275 / 71) x 42.6

⇒ 275 x 0.60

⇒ 165

The number of calories in 42.6 grams of cereal X will be 165 calories.

More about the ratio and the proportion link is given below.

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If it decreases by 80٪, then only 20٪ remains.

15×20٪=15×20/100=15×0.2=3

Answer: 3

Answer:

3 arches

Step-by-step explanation:

Given

15 arches decreased by 80%.

First get 80% of 15 arches

That’s 80%/100% x 15

0.8 x 15

12 arches

Now subtract 12 arches from 15 arches to get the decrease

Decrease = (15 - 12) arches

= 3 arches

Therefore, 80% decrease of 15 inches is equal to 3 arches

Answer:

3/180= 60 seconds = 1m/per cut or 60 sec/per cut.

Step-by-step explanation:

This is 3 cuts executed from a board to get 5 parts.

Answer:

he cuts 1.6 section of a board in one minute

Step-by-step explanation:

They're telling you that it takes 3 minutes for the carpenter to cut one board into 5 qual section. Therfore how many sections he's cutting in one minute divide the 5 by three. With that you will have the rate

The denominator is equal to the numerator.

Step-by-step explanation:

Answer:

[tex]x = - \: 12.55 \: or \: x = 12.55[/tex]

Step-by-step explanation:

We want to solve for x in

[tex] {x}^{2} + 4.7^{2} = 13.4^{2} [/tex]

We group constants on the right to get:

[tex]{x}^{2} = 13.4^{2} - {4.7}^{2} [/tex]

We apply difference of two squares

[tex]{x}^{2} = (13.4 - {4.7})(13.4 + 4.7)[/tex]

[tex] {x}^{2} = 157.47[/tex]

[tex]x = \pm \sqrt{157.47} [/tex]

[tex]x = \pm \: 12.55[/tex]

Step-by-step explanation:

1st term = -n²+6

= -(1)²+6

= -1+6

=5

2nd term = -(2)²+6

= -4+6 = 2

3rd term= -(3)²+6

=-9+6 = -3

4th term= -(4)²+6

= -16+6 = -10

5th term = -(5)²+6 = -25+6 = -19

6th term = -(6)²+6 = -36+6 = -30

5,2, -3,-10,-19, -30

optionB

Answer:

sqrt of 7 goes between 2 and 3

Square root of 20 goes between four and five

Square root of 90 goes between nine and 10

The 101 goes between 4 &5

The 3 90 goes between 4&5

The 3 20 goes between two and three

And 3 800 goes between 9&10

Answer:

Step-by-step explanation:

C=2πr

18=2×3.14×r

18=6.28r

r=2.88

Arc of a circle

A=®/360°πr

6=®/360°×3.14×r

®=239°

6

Answer:

120

Step-by-step explanation:

Answer:

24/35

Step-by-step explanation 3/5 times 8/7 equals 24/35

Answer:

y = 3

x =7

Step-by-step explanation:

to solve this system of equations using substitution method we say, let

5x + 4y = -22 .................... equation 1

2x – 3y = 5...................... equation 2

from equation 2

2x - 3y = 5

2x = 5 + 3y

divide both sides by 2

we have;

2x/2 = (5+3y)/2

x =(5+3y)/2................................ equation 3

put x = (5+3y)/2 in equation 1

5x + 4y = -22 .................... equation 1

5(5+3y)/2 + 4y = -22

(25 + 15y)/2 + 4y = -22

multiply through by 2

25 + 15y + 8y = -44

25 + 23y = -44

collect the like terms

23y = -44 - 25

23y = -69

divide both sides by 23

23y/23 = -69/23

y = 3

put the value of y= 3 into equation 3

x =(5+3y)/2................................ equation 3

x = (5+3(3)]/2

x = 5+9/2

x =14/2

x =7

Answer:

x = (y - 7)/2

Step-by-step explanation:

from the question given  y=2x+7 , so we are to find the value of x now we first make x the subject of the formulae from  y=2x+7

 y=2x+7............. equation 1

y- 7 = 2x

divide both sides by 2

(y-7)/2= 2x/2

x = (y - 7)/2

to check if your answer is correct

put the value of x in to equation 1

y=2x+7............. equation 1

y = 2[ (y-7)/2] + 7

y = y - 7 + 7

y = y.......... proved

Answer:

if there is a right angled square shape at the angle

Answer: MARK BRAINLIEST!!!!!!!!!

Because its the only triangle that has a 90 degree angle

Step-by-step explanation:

Answer:

Expected loss = $342 million.

Step-by-step explanation:

The formula to compute the expected loss is:

[tex]E(Loss)=\sum Loss\ amount\times P (Loss)[/tex]

Given:

P (Loss)      Amount of loss

0.30            $320 million

0.30            $820 million

0.40            $0

Compute the expected loss as follows:

[tex]E(Loss)=\sum Loss\ amount\times P (Loss)\\=(0.30\times320)+(0.30\times820)+(0.4\times0)|_{in\ millions}\\=96 +246+0\\=\$342\ million[/tex]

Thus, the expected loss is $342 million.

Answer:

x = 12

Step-by-step explanation:

⅔x = 8

x = 8 × 3/2

x = 12

Answer:

12

Step-by-step explanation:

8 divided by 2/3 = 12.01 so 12.

Answer:

[tex]4i\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{-80}[/tex]

[tex]\sqrt{80*i^2}[/tex]

i^2 is -1

[tex]i\sqrt{80}[/tex]

[tex]i\sqrt{4^2 * 5}[/tex]

[tex]4i\sqrt{5}[/tex]

Answer:  [tex]4i\sqrt{5}[/tex]

Answer:

[tex]4i\sqrt{5}[/tex]

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

Final answer:

After John ate 1/3 of the pizza and Liz ate 1/4, we convert these fractions to have a common denominator of 12, resulting in 4/12 + 3/12 = 7/12 eaten. Subtracting this from the whole gives us 5/12 of the pizza remaining.

Explanation:

John and Liz are sharing a large pizza. To determine how much of the pizza is left after John has eaten 1/3 and Liz has eaten 1/4, we need to add those fractions together and subtract the sum from the whole pizza, which is 1 (representing the entire pizza).

First, we find a common denominator, which in this case is 12, so we convert 1/3 to 4/12 and 1/4 to 3/12. Adding these fractions, we get 4/12 + 3/12 = 7/12.

Now we subtract the portion eaten from the whole pizza: 1 - 7/12 = 5/12 of the pizza is left.

Answer:

x = -4 and -2x - 8

Step-by-step explanation:

Step 1:  Distribute

-1/3(6x + 15) - 3

-6/3x - 15/3 - 3

-2x - 5 - 3

-2x - 8

Step 2:  IF NEEDED SOLVE FOR X

-2x - 8 + 8 = 0 + 8

-2x / -2 = 8 / -2

x = -4

Answer:  x = -4 and -2x - 8

Answer:

6 .74 seconds

Step-by-step explanation:

The height of the ball is given by the equation:

[tex]R(x) = - 16( {x}^{2} - 5x - 6)[/tex]

When the ball hit the ground, then;

[tex]R(x) = 0 \\ - 16( {x}^{2} - 5x - 6) = 0 \\ {x}^{2} - 5x - 6 = 0 \\ x = -0.74 \: Or \: 6.74[/tex]

We discard x=-0.74 since time is not negative.

Therefore the ball hit the ground after 6.74 seconds.

In an 812-hour day, a cereal company that packages 305.50 lbs of cereal an hour would package approximately 76,331 boxes of cereal, given each box contains 3.25 lbs of cereal. The provided options in the question do not match this result.

The subject of this question is Mathematics, specifically division used in a real-world context regarding a cereal company's packaging process. To find the number of cereal boxes produced in an 812-hour day, we need to divide the total weight of cereal packed in a day by the weight of cereal in each box.

Firstly, we find out the total amount of cereal produced by multiplying the hourly rate by the number of hours. This will give us: 305.50 lbs/hour x 812 hours = 248,071 lbs.

Next, we divide the total amount of cereal by the weight of cereal in each box to find the number of boxes. Therefore, 248,071 lbs ÷ 3.25 lbs/box = 76,331 boxes.

None of the options (A) 752 boxes, (B) 757 boxes, (C) 799 boxes, (D) 858 boxes match our result. There might be an error in the question or the choices provided.

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To solve for x in the equation 4/7 = x-1/12, combine the fractions, cross multiply, and solve to find x=3 and x=-7.

Solve for x: 4/7 = x-1/12

To solve for x, first combine the fractions on the right side: 4/7 = (12x - 1)/12. Then, cross multiply to get 12*4 = 7*(12x - 1). Solve for x to find x=3 and x=-7.

By substituting these values back into the original equation, which is x is equal to (12x-1)/12, you can verify these solutions.