Find the value of c that completes the square.
a2 + 12a + c

Answer:

28 students

Step-by-step explanation:

you get 28.3 if you divide 85 by 3

There will be 133.33% increase of airplane passengers.

Step-by-step explanation:

Present value of passengers = 600

Expected value of passengers by 2020 = 1400

Increase = Expected value - present value

Increase = 1400 - 600 = 800

Increase percentage = [tex]\frac{increase}{present\ value}*100\\[/tex]

[tex]Increase\ percentage=\frac{800}{600}*100\\\\Increase\ percentage=\frac{80000}{600}\\Increase\ percentage=133.33\%[/tex]

There will be 133.33% increase of airplane passengers.

Keywords: percentage, division

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The percent of increase in airplane passengers from 600 to 1400 is 133%, calculated using the formula for percentage increase.

To calculate the percent of increase of airplane passengers from 600 to 1400, we need to use the formula for percentage increase, which is: Percentage Increase = ((New Number - Original Number) / Original Number)  imes 100%.

Following the formula:

Therefore, the percent of increase in airplane passengers from 600 to 1400 is 133%.

Answer:

a) $25,261

b) $25,156

Step-by-step explanation:

I'm sorry but I don't know how to show my work because I just searched up "Car Loan Calulator" :|

So don't put me up for Brainlist

Answer:

Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units

Step-by-step explanation:

Given points:

[tex]P(-12,-2)[/tex]

[tex]Q(3,6)[/tex]

To determine the distance between points P and Q.

Steps to be carried out:

1) Plot the points P and Q on graph.

2) Construct a line from P towards right horizontally and a line from Q downwards vertically such that they meet at point [tex]O(3,-2)[/tex]

3) Join PQ thus forming a right triangle POQ.

4) We can find the distance of sides OP and OQ by counting the units between the points.

OP=[tex]|-12-3|=|-15|=15\ units[/tex]

OQ=[tex]|6-(-2)|=|6+2|=8\ units[/tex]

4)Now, we can apply Pythagorean theorem for triangle POQ.

[tex]PQ^2=OP^2+OQ^2[/tex]   [ [tex]Hypotenuse^2=Leg1^2+Leg 2^2[/tex]]

[tex]PQ^2=15^2+8^2[/tex]

[tex]PQ^2=225+64[/tex]

[tex]PQ^2=289[/tex]

Taking square root both sides:

[tex]\sqrt{PQ^2}=\sqrt{289}[/tex]

[tex]PQ=17\ units[/tex] [We take only the positive value as distance is always positive.

∴ Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units

Answer:

4(7 + 2v).

Step-by-step explanation:

The greatest common factor of 28 and 8v is 4 so we take 4 out:

28 + 8v

= 4(7 + 2v).

Answer:

A

Step-by-step explanation:

(3a^4-2a^2+5a-10)-(2a^4+4a^2+5a-2)

a^4-6a^2-8

The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80

Step-by-step explanation:

Carla is saving money for a trip this summer. She already has some money in her savings account and will add the same amount to her account each week

Write a linear function in the form y = m x + b to represent the amount of money, m, that Carla has saved after w weeks

The linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are 2 points on the line

∵ The slope is the rate of change of y and x

∴ The same amount of money that Carla add every week = m

∵ At the end of 2 weeks, Carla has $130

∴ The first point is (2 , 130)

∵ At the end of 8 weeks, she has $280

∴ The second point is (8 , 280)

∵ [tex]m=\frac{280-130}{8-2}=\frac{150}{6}=25[/tex]

∴ The same amount of money that Carla add every week = $25

∵ The amount of money that Carla saved after w week is m

∴ m = 25 w + b, where b is the initial amount of money that she

   saved in her account

To find b substitute w and m by the coordinates of one of the two

given points, let us use the first point

∵ w = 2 and m = 130

∵ m = 25 w + b

∴ 130 = 25(2) + b

∴ 130 = 50 + b

- Subtract 50 from both sides

∴ 80 = b

∴ m = 25 w + 80

The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80

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Answer:

Step-by-step explanation:

5r + 2b = 14 (5 lbs of oranges and 2 lbs of bananas = $14)

3r + 6b = 18 (3 lbs of oranges and 6 lbs of bananas = $18)

Let's use the elimination method. Multiply the first equation by -3:

-15r - 6b = -42

3r + 6b = 18

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

12r = 24

Divide by 12:

r = 2

Answer:

The price per pound of the oranges is $ 2.

The price per pound of the bananas is $ 2.

Step-by-step explanation:

A system of linear equations is a set of equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all. In these equations the unknowns are related to each other.

In this case a system of equations is applied. For that, you must first define the unknowns (or also called variable):

The price of the 5 pounds of oranges, whose price is "x", and 2 pounds of bananas, whose price is "y", bought by Gail must add $ 14. Then expressed in an equation this represents: 5*x+2*y=14 Equation (A)

The price of the 3 pounds of oranges, whose price is "x", and 6 pounds of bananas, whose price is "y", bought by her husband must add $ 18. Then expressed in an equation this represents: 3*x+6*y=18 Equation (B)

Equation A and equation B form the equation system, where the variables are "x" and "y", which are the price of an orange and a banana:

[tex]\left \{ {{5*x+2*y=14} \atop {3*x+6*y=18}} \right.[/tex]

One of the ways to solve a system of equations is through the substitution method.  This method consists of isolating one of the unknowns (for example, "x") and replacing its expression in the other equation. In this way, a first degree equation is obtained with the other variable, "y".

In this case, x is isolated from the first equation, obtaining:

5*x+2*y=14

5*x=14-2*y

[tex]x=\frac{14-2*y}{5}[/tex]

[tex]x=\frac{14}{5} -\frac{2}{5}*y[/tex] Equation (C)

Replacing this equation (C) in the other equation you get:

[tex]3*[\frac{14}{5} -\frac{2}{5} *y]+6*y=18[/tex]

Isolating the value of "y" you get:

[tex]3*\frac{14}{5} -3*\frac{2}{5} *y+6*y=18[/tex]

[tex]\frac{42}{5} -\frac{6}{5} *y+6*y=18[/tex]

[tex]-\frac{6}{5} *y+6*y=18-\frac{42}{5}[/tex]

[tex]\frac{24}{5} *y=\frac{48}{5} \\[/tex]

[tex]y=\frac{\frac{48}{5} }{\frac{24}{5} }[/tex]

[tex]y=\frac{48}{5} *\frac{5}{24} \\[/tex]

y=2

Remembering that "y" is the price per pounds of the banana, then it is possible to say that the price per pound of the banana is $ 2.

Replacing the value of the variable "y" in equation (c) and isolating the value of the variable "x" gives:

[tex]x=\frac{14}{5} -\frac{2}{5}*2[/tex]

[tex]x=\frac{14}{5} -\frac{4}{5}[/tex]

[tex]x=\frac{14-4}{5}=\frac{10}{5}[/tex]

x=2

Remembering that "x" is the price per pounds of the oranges, then it is possible to say that the price per pound of the oranges is $ 2.

Answer:

0.16

Step-by-step explanation:

Use long division

Answer:

0.16

Step-by-step explanation:

4÷25 = 0.16

Answer:

AB = 9.6 cm

Step-by-step explanation:

ΔAPQ and ΔABC are similar triangles, thus ratio of corresponding sides are equal, that is

[tex]\frac{AP}{AB}[/tex] = [tex]\frac{PQ}{BC}[/tex], substitute values

[tex]\frac{8}{AB}[/tex] = [tex]\frac{10}{12}[/tex] ( cross- multiply )

10AB = 96 ( divide both sides by 10 )

AB = 9.6 cm

Answer:

Therefore, the percent error in 1.   20%

          and the percent error in 2.    6%  

Step-by-step explanation:

Given:

1. In estimation of 30 people only 25 people attended.

2. In estimated length of 150 feet the measurement was 142 feet.

Now, in first case for the percent error we would calculate the difference between the people attended:

[tex]30-25=5[/tex]

And then, we will get the percentage error :

[tex]\frac{5}{25} \times 100[/tex]

[tex]\frac{500}{25}[/tex][tex]=20[/tex].

Therefore, the percentage error is 20%.

Now, in second case for the percent error we would repeat the above process as done in first case:

[tex]150-142=8[/tex]

And then:

[tex]\frac{8}{142}\times 100[/tex]

[tex]\frac{800}{142}[/tex][tex]=5.63[/tex]

Therefore, the percentage error is 6% (approximately).

Therefore, the percent error in 1. is   20%

          and the percent error in 2. is  6%  

Answer:

1. The required slope m, for the context is[tex]m = 1.08[/tex]

2. The y-intercept in the context is [tex]a = y = 1052[/tex]

3. The graph is on Desmos.

Step-by-step explanation:

Given:

[tex]a = 1.08\times t + 1052[/tex]

Where,

a is the speed of sound wave.

t is the air temperature.

This is a linear model type equation.

Can be represented in the slope intercept form  which is equal to

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

Where,

m = Slope of the line.

c = y-intercept.

Now if we compare the given model by slope intercept formula we get

[tex]m = 1.08\\\\c = 1052[/tex]

So ,the slope in the context of the problem is [tex]m = 1.08[/tex].

and the y intercept in the context of the problem [tex]a = c = y = 1052[/tex]

For Sketching the graph we require two point

put t = 0

∴ a = 1052

Let A (1052, 0) be one point.

put a = 0

∴ t = -974.07

Let B (0, -974.07) another point.

So, the x intercept of the linear model is [tex]t = x = -974.07[/tex]

Here in the graph

X axis represent temperature in degree, Fahrenheit.(t)

Y axis represent Speed of sound wave in feet per second.(a)

Scale on both axes:

1 cm = 100 feet per second on y-axis

1 cm = 100 degree Fahrenheit on x-axis

Answer:

12/35 inches are in 1 mile.

Step-by-step explanation:

(3/10)/(7/8)=(3/10)(8/7)=24/70=12/35

1 mile=8/8

(8/8)(12/35)=1(12/35)=12/35

Answer:

The correct answer is s = 27.

Step-by-step explanation:

This problem already gives us an equation so all we need to do is plug in the numbers:

c = 39.95 + 0.15(s + r) becomes 53.45 = 39.95 + 0.15(s + 63). Now to solve:

53.45 = 39.95 + 0.15(s + 63)

13.50 = 0.15(s + 63)                     Subtract 39.95 from both sides

13.50 = 0.15s + 9.45                    Distribute 0.15 to s and 63

4.05 = 0.15s                                 Subtract 9.45 from both sides

27 = s                                           Divide both sides by 0.15

Hope this helps,

❤A.W.E.S.W.A.N.❤

Answer:

n=0

Step-by-step explanation:

6=1-2n+5-4n

Combine like terms

6=-6n+6

now move the +6 to other side

0=-6n

so divide to remove the n from the -6

0=n

No worries I tested it it's right! I hope :/

Answer:

[tex]y=10[/tex]

Step-by-step explanation:

we know that

The y-intercept is the value of y when the value of x is equal to zero

we have

[tex]-7x+3y=30[/tex]

so

For x=0

substitute the value of x in the linear equation and solve for y

[tex]-7(0)+3y=30[/tex]

[tex]3y=30[/tex]

Divide by 3 both sides

[tex]y=10[/tex]

Answer:

We can conclude that Δ ABC ≅ Δ DEF by SSS postulate.

Step-by-step explanation:

Δ ABC and Δ DEF are congruents because:

1. Their sides AB and DE are equal (9 units = 9 units)

2. Their sides BC and EF are equal (5 units = 5 units)

3. Their sides AC and DF are equal (10 units = 10 units)

Now, we can conclude that Δ ABC ≅ Δ DEF by SSS postulate.

A valid reason is :opposite sides of a parallelogram are equal

Step-by-step explanation:

It is possible to notice that RUTS is a parallelogram where RU=TS and RS = UT.

When you introduce a diagonal RT you form triangles RUT and TSR.

∠URT = ∠STR ----alternate angles

∠UTR=∠SRT------alternate angles

RU║ST and RS║UT

RT=TR -----Common

ΔRUT ≡ ΔTSR by AAS theorem

hence RS=UT matching sides of congruent triangles

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Keywords : proof, parallelogram, reason

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Answer:

opposite sides of a parallelogram are equal

Step-by-step explanation:

got it right on odyssey

Final answer:

To express y in terms of x, rearrange the equations to isolate y. The equation expressing y in terms of x is (4x + 20)/3.

Explanation:

To express y in terms of x, we need to isolate y in the given equations.

From the first equation, x = 3t - 8, we can rearrange to solve for t: t = (x + 8)/3.

Substituting this expression for t into the second equation, y = 4 + t, gives us y = 4 + (x + 8)/3. Simplifying further, we have y = (4x + 20)/3.

Answer:

B) 113.1 cm³

Step-by-step explanation:

The cross-section of a sphere is a circle.  The area of a circle is:

A = πr²

The largest cross section passes through the center of the sphere, where the radius of the circle equals the radius of the sphere.

28.27 = πr²

r = 3.00

The volume of the sphere is therefore:

V = 4/3 π r³

V = 4/3 π (3.00)³

V = 113.1

Answer:

B

Step-by-step explanation:

Answer:

3, -3

Step-by-step explanation:

6x^2=54

x^2=54/6

x^2=9

x=sqrt(9)

x=3, -3

The first group of points is not a function due to repetition of elements in domain while second group of points is a function because no element of domain is repeated in any ordered pair.

Step-by-step explanation:

Why {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function?

A relation is said to be a function if there is no repetition in the first elements of each ordered pair. In this group of points, 0 is repeated in two ordered pairs (0, 1), (0, 5) so it is not a function.

Why {(1, 4), (2, 7), (3, 1), (5, 7)} is a function?

The given group of points is a function because there is no repetition in first elements of each ordered pair i.e. there is not repetition in domain so it is a function

Keywords: Functions, Domain

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Answer:

is is 20

Step-by-step explanation:

They both will finish the work in 3.07 hours

Step-by-step explanation:

Time taken by Rachel = 5 hours

Work done by Rachel in one hour = 1/5

Time taken by Carl = 8 hours

Work done by Carl in one hour = 1/8

Let x hours be the time taken by both to do work

Then 1/x will be the work done by both in one hour

So,

[tex]\frac{1}{5} + \frac{1}{8} = \frac{1}{x}[/tex]

Taking LCM

[tex]\frac{8+5}{40} = \frac{1}{x}\\\frac{13}{40} = \frac{1}{x}\\13x = 40\\x = \frac{40}{13}\\x = 3.07\ hours[/tex]

They both will finish the work in 3.07 hours

Keywords: Linear Equation

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Answer:

12 hrs

Step-by-step explanation:

X/30+x/48=1

common denominator

x/1440+x/1440

2x/1440=1

2x=1440

x=720

when you convert to hrs  you get 12

The cafeteria sold 41 corn chips and 80 potato chips.

Step-by-step explanation:

Let,

Corn chips = x

Potato chips = y

Price of corn chips = $0.80

Price of potato chips = $0.60

According to given statement;

x+y= 121   Eqn 1

0.80x+0.60y=80.80   Eqn 2

Multiplying Eqn 1 by 0.80

[tex]0.80(x+y= 121)\\0.80x+0.80y=96.80\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](0.80x+0.80y)-(0.80x+0.60y)=96.80-80.80\\0.80x+0.80y-0.80x-0.60y=16\\0.20y=16[/tex]

Dividing both sides by 0.20

[tex]\frac{0.20y}{0.20}=\frac{16}{0.20}\\y=80[/tex]

Putting y=80 in Eqn 1

[tex]x+80=121\\x=121-80\\x=41[/tex]

The cafeteria sold 41 corn chips and 80 potato chips.

Keywords: linear equation, subtraction

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Answer:

B

Step-by-step explanation:

When we see "square inches" in a statement (or squared centimeters, meters, feet, etc) this refers to an area measure. So we need to find which of the options are areas.

A is not, as it is width, is a longitude measure. I could never be in square inches.

C is volume and it measure should be in cubic inches. So, not.

D is perimeter and is the sum if the lengths of different sides of a figure, so is also in inches, not square inches.

Finally, B is the area,  so is our only chance. B in correct.

Answer:

See below

Step-by-step explanation:

To construct a confidence interval we use the following formula:

ci = (sample mean) +- z*(sd)/[n^(1/2)]

The sample mean is 57, the standard deviation is 2.36, n s 25 and z is the  upper (1-C)/2 critical value for the standard normal distribution. Here, as we want a confidence interval at a 90% we have (1-C)/2=0.05 we have to look at the 1-0.05=0.95 value at the normal distribution table, which is 1.65 approximately. Replacing all these values:

ci = 57 +- 1.65*(2.36)/[25^(1/2)]

ci = 57 +- 3.894*/(5) = 57 +- 0.78

ci => (56.22 , 57.78)

Answer:

6

Step-by-step explanation: