A preschool has a student to teacher ratio of 5:2 The total number of students and teachers was 56 last year and is 70 this year How many students and teachers were there for each of the two years

Step-by-step explanation:

The graph of  linear function is a straight line.

General form of the linear function is -

y = a + bx

where a is the y -intercept and b is the slope.

Both  a and b are constants.

Here,

x is independent variable whereas y is dependent variable.

For example -

y = 2x + 15

Answer:

13.2 miles

Step-by-step explanation:

To solve this, we will need to first solve for the base of the triangle and then use the information we find to solve for the shortest route.

(5.5 + 3.5)² + b² = 15²

9² + b² = 15²

81 + b² = 225

b² = 144

b = 12

Now that we know that the base is 12 miles, we can use that and the 5.5 miles in between Adamsburg and Chenoa to find the shortest route (hypotenuse).

5.5² + 12² = c²

30.25 + 144 = c²

174.25 = c²

13.2 ≈ c

Therefore, the shortest route from Chenoa to Robertsville is about 13.2 miles.

Given:

In triangle ABC, AB=8.2 cm, C=13.5 cm and angle A= 81 degrees.

To find:

The length of AC.

Solution:

According to the Law of Sines:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

Using Law of Sines, we get

[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c}[/tex]

[tex]\dfrac{\sin (81^\circ)}{13.50}=\dfrac{\sin C}{8.2}[/tex]

[tex]\dfrac{\sin (81^\circ)\times 8.2}{13.50}=\sin C[/tex]

[tex]\sin^{-1}\dfrac{\sin (81^\circ)\times 8.2}{13.50}= C[/tex]

[tex]C\approx 36.86^\circ[/tex]

Using angle sum property, we get

[tex]\angle A+\angle B+\angle C=180^\circ[/tex]

[tex]81^\circ+\angle B+36.86^\circ=180^\circ[/tex]

[tex] \angle B =180^\circ-81^\circ-36.86^\circ [/tex]

[tex] \angle B =62.14^\circ [/tex]

Now,

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]

[tex]\dfrac{\sin (81^\circ)}{13.50}=\dfrac{\sin (62.14^\circ)}{b}[/tex]

[tex]b=\dfrac{13.50\times \sin (62.14^\circ)}{\sin (81^\circ)}[/tex]

[tex]b\approx 12.08[/tex]

Therefore, the length of AC is 12.08 cm.

Answer:

????? I am only in first grade

Step-by-step explanation:

???????

Answer: 3 quarts of coffee.

Step-by-step explanation:

A coffee mug can take 16 fluid ounces.

Annie needs to fill up 6 mugs so the total ounces needed for 6 mugs would be:

= 16 * 6

= 96 fluid ounces

As the answer needs to be in quarts, convert the above.

1 quart = 32 fluid ounces

96 fluid ounces = 96/32

= 3 quarts

Answer: 28 degrees

Step-by-step explanation:

Since angle KJL = LJM then that means angle 7x=3x+16

First we need to solve for x

7x=3x+16

4x=16

x=4

now we can input it into either equation to solve for the angle KJL

7(4)= 28 so the angle is 28 degrees

Answer:

6x

6x(x + 4)

Step-by-step explanation:

Both 6x^2 and 24x are divisible by 6x

Casually puts a link to a weird website..

https://theuselessweb.com

*whistles*

Answer:

there is no solution-

Step-by-step explanation:

there's no solution because its impossible for a to have 2 different values; you see that 0.1 and 0.01 are not equal, therefore a can not be equal,, otherwise the equation would be false

Answer:

no

Step-by-step explanation:

x has to be 2 because 4+2=6

Answer:

no, because 4 + 5 = 9 not 6.

Step-by-step explanation:

the only way for this equation to be true is if x = 2.

Answer:

1/6

Step-by-step explanation:

When subtracting or adding fractions, you always want the denominator (aka the bottom number of the fraction) to be the same number. Since both of your denominators are both the same, we can subtract!

                                                 2/6 - 1/6 = 1/6

Remember that you don't subtract the bottom, just the top. Hope this helped :)

Answer:π(2.5)

Step-by-step explanation:

π(2.5)

Answer: BC

Step-by-step explanation:

I know this because i did this one before your welcome

Answer:

200 miles

Step-by-step explanation:

Given data

Rapid Rental Car

charges a $55 rental fee

$20 for gas, and

$0.65 per mile driven

let the number of miles be x, the total charges y

y=55+20+0.65x

y= 75+0.65x----------1

Capital Cars

charges $55 for rental and gas and

$0.75 per mile.

let the number of miles be x, the total charges y

y=55+0.75x

y= 55+0.75x----------2

Required

The number of miles driven before the two Rental companies charge the same amount

equate 1 and 2

75+0.65x= 55+0.75x

collect like terms

75-55= 0.75x-0.65x

20= 0.1x

x= 20/0.1

x= 200miles

Hence the distance will be 200 miles for the charges to be the same

Answer:

4(x−5)=−6x−7+2

first step open bracket and add or subtract no.

4x-20=-6x-5

put common in each side

4x+6x=-5+20

10x=15

x=15/10=3/2

first one is your answer

Answer:

12.23

Step-by-step explanation:

4+5.23 = 9.23

9.23 + 3 = 12.23

Answer:

10/7

Step-by-step explanation:

plug in the numbers to get 10/5--2 or 10/5+2

Answer:

119

Step-by-step explanation:

1/2x5x7x4+7x7

can I have the brainliest ?

Answer:

119 m

Step-by-step explanation:

First find the square 7x7 = 49m

Now the triangle [tex]\frac{5 * 7}{2}[/tex] = 17 .5

17.5 * 4 = 70m

70m + 49m = 119m

Answer: its positive !!!

Step-by-step explanation: got it wrong at first:(

Answer:

[tex]\sqrt{55}[/tex]in.

Step-by-step explanation:

8²=3²+h²(BY P.T)

h=[tex]\sqrt{8^{2}-3^{2} }[/tex]

h=[tex]\sqrt{55}[/tex]

Answer:

31.42 ft.

I dont know if this answer is fully correct because i hate doing circles so sorry if im wrong

Step-by-step explanation:

Answer:

20 is your diameter

Step-by-step explanation:

radius is half of a diameter

Answer and Step-by-step explanation:

Pythagorean theorem

Half of 4 is 2.

2^2 + 9^2 = l^2

4 + 81 = l^2

Square root of 85 = l

#teamtrees #PAW (Plant And Water)

Answer:x + 10 = x2 + 2x + 1 x + 10 = x2 + 1 x + 10 = x2 – 1.

Step-by-step explanation:

The solution is, x+10 = x^2 + 2x + 1 is the equation is related to

√x+10  - 1 = x.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

the equation is,

√x+10  - 1 = x

or, √x+10 = x+1

now, taking square on both side, we get,

x+10 = (x+1)^2

we have,

(a+b)^2 = a^2 + 2ab + b^2

so, applying that, we get,

x+10 = x^2 + 2x + 1

Hence, The solution is, x+10 = x^2 + 2x + 1 is the equation is related to √x+10  - 1 = x.

To learn more on simplification click:

brainly.com/question/28996879

#SPJ7

Answer:

second option

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = x - 9 ( add 9 to both sides

y + 9 = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = x + 9

Answer:

99 inches

Step-by-step explanation:

9*11 =99

Step-by-step explanation:

first you find 60% of 357.50 which is $214.50. Next you would add $357.50+214.50=572

so the awnser is

the sale price of a popular smart phone is $572.

Hope this helps!!

Answer:

395.2

Step-by-step explanation:

380 x 0.04 = 15.2

380 + 15.2 = 395.2

Answer:

The cost of the system including the tax is $395.20.

Step-by-step explanation:

If the tax is 4% that means that the total price will equal...

380 + (380)(0.04) = $395.20

Therefore the cost of the system including the tax will be $395.20.

what question?????????????????

Answer:

x=2.8841≈2.9 feet

Step-by-step explanation: