The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Check all that apply. a x2 + 2x – 24 = 0 b x(x + 2) = 24 c x2 + (x + 2)2 = 100 d 0.5(x)(x + 2) = 24 e x2 + 2x – 48 = 0 f x2 + (x + 2)2 = 24

The answer is:

The total fall in 30 feet will be 7.5 inches.

To calculate the total fall in 30 feet, given the slope (decreasing rate for this case), we need to use the following equation:

[tex]TotalFall=\frac{\frac{1}{4} inch}{foot}*FeetAmount[/tex]

We are asked to calculate the total fall in 30 feet, so, substituting it into the equation, we have:

[tex]TotalFall=\frac{\frac{1}{4} inch}{foot}*30feet[/tex]

[tex]TotalFall=7.5inch[/tex]

Hence, we have that the total fall in 30 feet will be 7.5 inches.

Have a nice day!

Final answer:

To calculate the total fall in elevation for a sewer line with a 1/4" per foot grade over 30 feet, simply multiply 1/4" by 30, resulting in a total fall of 7.5 inches.

Explanation:

The student is asking how to calculate the total fall in elevation for a sewer line that has a consistent slope over a given distance. The slope given is 1/4" per foot of sewer line. To find the total fall over 30 feet, you need to multiply the slope per foot with the total distance.

Calculation:

Determine the slope per foot, which is 1/4".

Multiply this slope by the total distance, which is 30 feet.

1/4" x 30 = 7.5". This is the total fall in elevation over 30 feet.

The total fall in elevation for a sewer line over 30 feet, with a slope of 1/4" per foot, is 7.5 inches.

Answer:

D

Step-by-step explanation:

well you see I just guessed :D

Answer:

Down below

Step-by-step explanation:

Well, the company can predict that most of the 8 dentists recommend the ProTooth toothbrush about 88 percent of the dentists recommend it 88 percent =0.88 as a decimal.  

They can also predict that the one person that didn't recommend it beacause maybe there was a downside to the Protooth brush that the person didn't like

In a survey of 64 dentists, 56 of them will recommend a ProTooth toothbrush is the predicted option.

This involves gathering of information through relevant questions from a sample of people to better understand them.

7/8 was the initial recommendation

We can get the final one by multiplying both sides by same value.

7 × 8  = 56

8 × 8      64

Therefore, in a survey of 64 dentists, 56 of them will recommend a ProTooth toothbrush.

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Answer:

[tex]3m^3-7m^2n+3mn^2-n^3[/tex]

Step-by-step explanation:

[tex](5m^3 + 3mn^2) + (-7m^2n + mn^2 - n^3) - (mn^2 + 2m^3)\\Solving:\\5m^3 + 3mn^2 -7m^2n + mn^2 - n^3 - mn^2 - 2m^3\\Adding\,\,like\,\,terms\,\,\\5m^3 -2m^3+ 3mn^2 -mn^2+mn^2-7m^2n-n^3\\3m^3 +3mn^2-7m^2n-n^3\\Arranging\,\,in\,\,desecnding\,\,order\,\,in\,\,power\,\,of\,\,m\\3m^3-7m^2n+3mn^2-n^3[/tex]

Answer:

80 just did it in a lesson

Step-by-step explanation:

Answer:

Yeah the other dude is right it is 80

Step-by-step explanation:

it would be y = −1/2x + 5

Answer:

a. 1.75

Step-by-step explanation:

r values, or the correlation coefficient  must be between -1 and 1, inclusive

-1 is a perfect negative correlation

0 is no correlation

+1 is a perfect positive correlation

1.75 is not between -1 and 1

Answer:

C

Step-by-step explanation:

49x² + 28xy + 4y² ← is a perfect square of the form

(ax + by)² = a²x² + 2abxy + b²y²

49 = 7² ⇒ a = 7 and 4 = 2² ⇒ b = 2

2ab = 2 × 7 × 2 = 28

Hence

49x² + 28xy + 4y² = (7x + 2y)²

with factor 7x + 2y ⇒ C

Answer:

118.3 m²

Step-by-step explanation:

The area (A) of a triangle is

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Note the legs 13 and 18.2 are at right angles to each other, hence

A = 0.5 × 13 × 18.2 = 118.3

Answer:

y = 57, PQ = 60, RS = 28

Last option is the answer

Step-by-step explanation:

3 * y = 9 * 19

3y = 171

y = 57

PQ = 3 + 57 = 60

RS = 9 + 19 = 28

Answer:

y = 57; PQ = 60; RS = 28

Step-by-step explanation:

The product of lengths of parts of a chord is a constant, so ...

PT·TQ = RT·TS

TQ = y = RT·TS/PT = 9·19/3 = 57

Of course the total chord length is the sum of its parts, so ...

PQ = PT +TQ = 3 +57 = 60

RS = RT +TS = 9 +19 = 28

Then your answer choice is ...

y = 57; PQ = 60; RS = 28.

Answer: Third Option

[tex]y = -10x + 110[/tex]

Step-by-step explanation:

The equation of a line in the pending intersection form has the following form:

[tex]y=mx +b[/tex]

Where m is the slope of the line and b is the intersection with the y axis.

Observe in the graph that the data form a decreasing line. Then the adjustment line must have a negative slope [tex]m <0[/tex].

The first and the second option have positive slopes, therefore we discard them.

Notice in the scatter diagram that the intersection of the line with the y-axis (x = 0) is above 90.

The line of the fourth option has a value of [tex]b = -110 <90[/tex].

Therefore the line that best fits the data is the third option

[tex]y = -10x + 110[/tex]

Note that the line has a slope [tex]m = -10[/tex] and a value of [tex]b> 90[/tex]

Answer 13;

because sqrt148~12.16

Answer:

The smallest integer greater than √148 is 13

Step-by-step explanation:

√169 = 13

√144 = 12

so √148 is between 12 and 13

12 < √148 < 13

On those option choices

11 and 12 are smaller than √148

13, 14 and 15 are greater than √148

The smallest integer greater than √148 is 13

Answer:

A. x < 6 and x > - 28

Step-by-step explanation:

We have been given the following inequality;

| x+11 | < 17

We can replace the absolute value function by re-writing the inequality as;

-17< x+11<17

subtract 11 from both sides;

-17-11<x+11-11<17-11

-28<x<6

splitting this we have;

x<6

x>-28

Answer:

A. x < 6 and x > - 28

Step-by-step explanation:

| x+11 |< 17

x + 11 < 17

x < 6

-(x + 11) < 17

-x - 11 < 17

-x < 28

x > - 28

Answer

6 > x > -28 (x < 6 and x > - 28)

Answer:

The slant height of the pyramid is 3√2 ft, or to the nearest tenth ft,

4.2 ft

Step-by-step explanation:

The equation for the volume of a pyramid of base area B and height h is

V = (1/3)·B·h.  Here, V = 432 ft³, B = (12 ft)² and h (height of the pyramid) is unknown.  First we find the height of this pyramid, and then the slant height.

V = 432 ft³ = (144 ft²)·h, so h = (432 ft³) / (144 ft²) = 3 ft.

Now to find the slant height of this pyramid:  That height is the length of the hypotenuse of a right triangle whose base length is half of 12 ft, that is, the base length is 6 ft, and the height is 3 ft (as found above).

Then hyp² = (3 ft)(6 ft) = 18 ft², and the hyp (which is also the desired slant height) is hyp = √18, or √9√2, or 3√2 ft.

The slant height of the pyramid is 3√2 ft, or to the nearest tenth ft,

4.2 ft

Answer:

B

Step-by-step explanation:

The interquartile range is the difference between the upper quartile ( the right side of the box plot ) and the lower quartile ( the left side of the box plot )

For cars this is 29 - 22 = 7 and

For minivans is 21 - 18 = 3

Answer:

The second one, cars 7mpg, minivans 3mpg

Step-by-step explanation:

This is because if you subtrect the upper quartile from the lower quartile you get a range this range is the answer to the queestion.

Answer:

Richard, at 2/3, versus Cooper, at 5/8

Step-by-step explanation:                              12 min

Richard's ratio of cardio to resistance is  R = ------------ = 2/3

                                                                            18 min

                            10 min

Cooper's is  C = ------------ = 5/8

                            16 min

The LCD here is 24.  Rewrite 2/3 and 5/8 with denominator 24 for greater ease in comparing the two fractions/ratios:

R = 16/24 and C = 15/24

So it becomes obvious that Richard does a higher ratio of carido to resistance.

That is because the English language is three child languages standing on each other's shoulders in long trenchcoat pretending to be an adult language.

Also, your answer is 32,000in^3

Answer:

B. {-5, 12}

Step-by-step explanation:

the quadratic equation is given by the formula

x = -b± √b² - 4ac

           2a

where a is the coefficient of x², b is the coefficient of x, and c is the constant

in the equation; x² - 7x -60 = 0

a = 1, b = -7, c = -60

x = -(-7)± √(-7)² - 4*1*-60            (negative sign multiplied by negative sign will                

                    2*1                                a positive sign)

x = 7 ± √49 + 240

               2

x = 7 ± √289

            2

x = 7 ± 17

        2

x= 7 + 17   or    7 - 17

       2                  2

x = 24/2   or    -10/2

x =  12      or     -5

Answer:

1.48

Step-by-step explanation:

4 times 2 = 8

4 minus 3 = 1

The three-digit no. is 2a a a - 3 whose hundredth digit is twice the size of the tenth digit. The unit's digit is 3 less than the tenth digit.

The standard decimal form of numbers is written in base 10 as there are 10 different numbers from 0 to 9.

Each digit has a face value and a place value.

Let, The tens digit be 'a'.

Given, The hundredth's digit is twice the size of the tenth's digit.

∴ The hundredth digit be '2a' and the unit digit is (a - 3).

So, The 3-digit no. is 2a a a - 3, where a is, {2, 3, 4}.

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Answer:

x=4

Step-by-step explanation:

Simplifying

4x + 16 + -1x = 22 + 6

Reorder the terms:

16 + 4x + -1x = 22 + 6

Combine like terms: 4x + -1x = 3x

16 + 3x = 22 + 6

Combine like terms: 22 + 6 = 28

16 + 3x = 28

Solving

16 + 3x = 28

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-16' to each side of the equation.

16 + -16 + 3x = 28 + -16

Combine like terms: 16 + -16 = 0

0 + 3x = 28 + -16

3x = 28 + -16

Combine like terms: 28 + -16 = 12

3x = 12

Divide each side by '3'.

x = 4

Simplifying

x = 4

Hope this helps! And please correct me if I'm wrong so others can have the correct answer.

For this case we must solve the following equation:

[tex]4x + 16-x = 22 +6[/tex]

We add similar terms on both sides of equality:

[tex]3x + 16 = 28[/tex]

We subtract 16 from both sides of the equation:

[tex]3x = 28-16\\3x = 12[/tex]

We divide between 3 on both sides of the equation:

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

ANswer:

[tex]x = 4[/tex]

Answer:

c is the answer

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

4, 3, 1, -2, -5

Hope this helps.

The following integers from the greatest to least are as follows:

+4, +3, +1, -2, -5

Answer:

  A.)  285

Step-by-step explanation:

The sum of an arithmetic series is the sum of the first and last terms multiplied by half the number of terms.

  (10 +85)·6/2 = 285 . . . sum of 6 terms

The following integers from the greatest to least are as follows:

+3, 0, -3, -2, -8

The answer is +3,0,-2,-3,-8

Answer:

  10.8 ft

Step-by-step explanation:

The height from the base can be found from the formula for the volume. Fill in the given information and solve for the height.

  V = (1/3)Bh = (1/3)s²·h

  432 ft³ = (1/3)(12 ft)²·h . . . . . fill in side length and volume

  h = 432 ft³/(48 ft²) = 9 ft . . . divide by the coefficient of h

The slant height is the hypotenuse of a right triangle with this height as one leg and half the side length as the other leg.

  slant height = √((9 ft)² +(12 ft/2)²) = √(117 ft²) = 3√13 ft

  slant height ≈ 18.817 ft ≈ 18.8 ft

Answer:

A.-7

Step-by-step explanation:

If [tex]2x-3y=11[/tex] and [tex]3x+15=0[/tex]

To know the value of y we need to clear x in the equation [tex]3x+15=0[/tex] and the result replace it in [tex]2x-3y=11[/tex].

Then, let's clear x in the equation [tex]3x+15=0[/tex]

[tex]3x=-15\\x=-\frac{15}{3} =-5[/tex]

Substituting the value of x in the equation [tex]2x-3y=11[/tex]

[tex]2(-5)-3y=11\\-10-3y=11\\-3y=11+10\\y=\frac{11+10}{-3} \\y=\frac{21}{-3}\\ y=-7[/tex]

Answer:

a) y = -7.

Step-by-step explanation:

2x − 3y = 11

3x + 15 = 0

From the second equation:

3x = -15

x =  -5.

Substitute this value in the first equation:

2(-5) - 3y = 11

-10 - 11 = 3y

3y = -21

y = -7.

Answer:

select -3 and 2

Step-by-step explanation:

f(x)=g(x) means set them equal and solve for x

x^2+2x-8=-x^2+4

Add x^2 on both sides and subtract 4 on both sides.

2x^2+2x-12=0

Divide both sides by 2

x^2+x-6=0

Think of two numbers that multiply to be -6 and add up to be 1

that is 3 and -2

so The factored form is (x+3)(x-2)=0

So x=-3 or x=2

Answer:

6/25

Step-by-step explanation:

6/10 chance for grey.

4/10 chance for blue.

And = Multiplication

Or = Addition

6/10 times 4/10 = 24/100

24% chance or 6/25 chance it will land on grey and blue.

(Theoretical Probability)

The probability that the first spin lands on blue and the second spin lands on gray is 6/25.

The probability of the first spin landing on blue and the second spin landing on gray can be calculated as follows:

Probability of landing on blue on the first spin = 4/10 = 2/5

Probability of landing on gray on the second spin = 6/10 = 3/5

Multiply the probabilities of each spin: (2/5) * (3/5) = 6/25

Therefore, the probability that the first spin lands on blue and the second spin lands on gray is 6/25.