If a trench is 102’-6” long by 5’-4” wide and 3’-3” deep, what is the volume of the soil that was removed per cubic feet?

all triangles are similar but B and D may be the answer

say the numbers are "a" and "b", we know that they're in the ratio of 2:3, or namely that

[tex]\stackrel{\textit{in the ratio of 2 to 3}}{a~:~b\qquad \qquad 2:3}\qquad \qquad \implies \qquad \cfrac{a}{b}=\cfrac{2}{3}\implies \cfrac{3a}{2}=b \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their sum is 55}}{a + b = 55}\implies a + \cfrac{3a}{2}=55\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( a + \cfrac{3a}{2} \right)=2(55)} \\\\\\ 2a+3a=110\implies 5a=110\implies a = \cfrac{110}{2}\implies \boxed{a = 22}[/tex]

[tex]\stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(22)}{2}=b\implies \boxed{33=b} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their product is 384}}{ab=384}\implies a\left( \cfrac{3a}{2} \right)=384\implies \cfrac{3a^2}{2}=384\implies 3a^2=768 \\\\\\ a^2=\cfrac{768}{3}\implies a^2=256\implies a=\sqrt{256}\implies \boxed{a=16} \\\\\\ \stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(16)}{2}=b\implies \boxed{24=b}[/tex]

The positive numbers for both the parts are obtained as 22,33 and 16,24 respectively.

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

(a) As per the question, the numbers can be considered as 2x and 3x respectively.

Then, the equation for their sum can be written as follows,

3x + 2x = 55

⇒ 5x = 55

⇒ x = 11

The numbers are obtained as 2 × 11 = 22 and 3 × 11 = 33.

(b) Similarly, the equation for the product of numbers can be written as,

3x × 2x = 384

⇒ 6x² = 384

⇒ x² = 64

⇒ x = 8

The numbers are obtained as 2× 8 = 16 and 3 × 8 = 24.

The required number for both the cases are 22,33 and 16,24 respectively.

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Answer:

x = 35

Step-by-step explanation:

First, set both equations equal to each other because it is the same angle (congruent)

6x - 20 = 4x + 50

-4x and +20 to both sides of the equation and you end up with:

2x = 70

divide both sides by 2 and:

x = 35

Answer:

4/3 or 1 1/3

Step-by-step explanation:

To find slope, we subtract the y-values (9 - 5), then divide the difference we find from that by the difference of the x-values (6 - 3). So, let's go ahead and do that now. First, what's 9 - 5? Well, the answer is 4. Next, we have to divide this value by 6 - 3, which is equivalent to 3. Then, we divide the two numbers - what is 4 ÷ 3? Well, we can represent this as 4/3, or 1 1/3. Hopefully that's helpful - if you have any questions on that, let me know! :)

Answer:

Slope is 4/3

Step-by-step explanation:

Slope or gradient can be found by using several formulas. For this situation, we can use rate of changes between two points also known as rise over run or changes in y over change so in x.

The formula of slope between two points can be expressed as several equations, expressions, etc such as:

[tex]\displaystyle \large{m=\frac{dy}{dx}=\frac{y_2-y_1}{x_2-x_1} =\frac{\Delta y}{\Delta x}[/tex] where m is a variable representing the slope.

Since we are given two points, we are going to use the y2-y1 over x2-x1 formula.

Let (3,5) be (x1,y1,) and (6,9) be (x2,y2) thus the slope is [tex]\displaystyle \large{m=\frac{y_2-y_1}{x_2-x_1} =\frac{9-5}{6-3} =\frac{4}{3}[/tex]

Therefore the slope of two points is 4/3.

__________________

Let me know in comment if you have any questions.

OD Step-by-step explanation:

The median of the of the number of newspapers sold by shopkeeper is 202 .

Given,

A store manager kept track of the number of newspapers sold each week over a seven-week period.

81 71 202 113 269 248 242.

Now,

The median of the dataset is the middle value of the dataset, which means that 50 % of the values are below the mean and 50% of the values are above the mean.

Rearrange the dataset in ascending order as

71, 81, 113, 202, 242, 248, 269.

Thus the median will be the 4th value.

Hence the median will be 202.

Thus the correct option will be 202 Newspapers.

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Answer:

He is correct

Step-by-step explanation:

72 girls and 84 boys

Divide both numbers by 12

6 : 7

He is correct

Jerod says that the ratio of girls to boys is 6:7 is correct.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that in the sixth grade there are 84 boys and 72 girls

Jerod says that the ratio of girls to boys is 6:7

We need to check whether Jerod statement is correct or incorrect

Now the number of boys=84

The number of girls=72

Now divide the number of girls by number of boys

72/84

6/7

So Jerod statement is true

Hence, Jerod says that the ratio of girls to boys is 6:7 is correct.

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Answer:

Option D

Step-by-step explanation:

The expression is a=2b-3

Answer: yes

Step-by-step explanation:

Answer:

B should be the answer because it did rotate and the origin is in the middle 0,0 which it look like to me it is on.

Answer:

x = 33

Step-by-step explanation:

(x-17)°+(5x-1)°=180°

6x-18 = 180

6x = 198

x = 33

Answer:

1 [tex]\frac{3}{8}[/tex]

Step-by-step explanation:

the denominators must be the same so, since 4 goes evenly into 24 we can create an equivalent fraction from 3/4 to 18/24 (multiply numerator and denominator by 6)

now you can add:

[tex]\frac{15}{24}[/tex] + [tex]\frac{18}{24}[/tex] = [tex]\frac{(15+18)}{24}[/tex] = [tex]\frac{33}{24}[/tex]

since the numerator is larger than the denominator this is called an improper fraction and can be changed into a mixed number by dividing 24 into 33

24 goes into 33 one time with a remainder of 9

so 33/24 = 1 [tex]\frac{9}{24}[/tex] wherein 9 and 24 can each have a 3 factored out to make it fully simplified

9÷3 = 3

24÷3 = 8

final answer is 1 [tex]\frac{3}{8}[/tex]

Answer:

11/8 is the correct answer

Step-by-step explanation:

15/24 + 3/4

Reduce the fraction   15/24 ​   to lowest terms by extracting and canceling out 3.

=5/8 +3/4

Least common multiple of 8 and 4 is 8. Convert 5/8 and 3/4 to fractions with denominator 8.

= 5/8 + 6/8

since 5/8 and 6/8 have the same denominator, add them by adding their numerators.

= 5 + 6/8

Add 5 and 6 to get 11.

=11/8

here is why 9/14 is wrong

Answer:

-6 is Y

Step-by-step explanation:

When ever the number is outside of the f(x) it is = y.

Answer:

D 280

Step-by-step explanation:

Pythagoras theorem

Answer:

a

Step-by-step explanation:

LN=√19＾2 - 9＾2

=√361 - 81

=√280

Answer:

mario lost the race and luigi won

Step-by-step explanation:

Step-by-step explanation:

Shop charges =13

Many left for renting bike = 45-13 =$32

If renting for 1hr cost $8

then renting for X Hrs will cost $32

1/X =8/32 cross multiplying

8X= 32

X= 32÷8= 4hrs

Answer:

C

Step-by-step explanation:

[tex]7^{\tfrac 14} = \sqrt[4]{7}[/tex]

The term variable implies that the rate is bound to change over time, in this context variable interest rate may double as an Advantage and also as a disadvantage.

D. increases when the market rate increases

Variable interest rate is advantageous because as the market rate increases, the rate at which the customer will receive his/her interest will increase too

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Answer: a

Step-by-step explanation:

Answer:

4.25 as decimal and 4 1/4 as a fraction

Step-by-step explanation:

The question is cut off.

Answer:

$50.00 is the discount price

Answer:

Step-by-step explanation:

3| -2 =6

4| -5| =20

= -6+20

Simplify -

14

Thank You! I hope I could make your day just a little bit better!

Answer:

(8,-9)

Step-by-step explanation:

using the principle of vectors, you match each number to their coordinates and add them

so we have (7+1,-12+3)

which is equal to (8,-9)

Answer:

5/2

Step-by-step explanation:

Formula: y2-y1/x2-x1

Labeled:

(1,3)

1 = x2

3 = y2

(7,-12)

7= x1

-12 = x1

In order:

3+12 / 1-7

=15/6

which is simplified to 5/2

so when trying to find the slope of two points you want to use a certent formula which is y2 minus y1 over x2 minus x1 and if the x1 or y1 is negative it will be plus.

first you need to label them and then put them in the order you labeled them to the formula. After subtract or add and if you can simplify it then simplified it to get your answer.

this is the best way I can explain it, sorry

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Answer:

x=4

Step-by-step explanation:

x+3=7

subtract 3 from both sides

simplify

Answer:

Solution is given in the photo

Answer: D

Step-by-step explanation:

this is in y=Mx+ b form. M stands for the slope and b stands for the y intercept, or where the line intersects with the y-axis.

Going left to right, the line slopes downwards, therefore it is a negative Slope. This narrows down your answer to either a or d. the slope is -1 because you can only ever write x by itself if it means 1x. In this case it is negative so it would look like this: -x

for the y-intercept, simply look at where the line passes through the y-axis. In this case, it is positive 2.

your finished equation would be: y=-x+2

i hope this is helpful

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I hope this helps you a little ,