A school communoty had planned to reduce the number of grade 9 students per class room by constructing additional class room however they constructed 4 less rooms than they planned As the result tye number of students per class was 10 more than they planned if there are 1200 grade 9 students in the school determine the current number of class rooms and the number of students per class (I need instant help)​

The zeros of

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

are

x=0,x=-2,x=-5x=0,x=−2,x=−5

EXPLANATION

The given function is

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

To find the zeros of the above function, we just have to equate the function to zero and solve for x.

x(x + 2)(x + 5) = 0x(x+2)(x+5)=0

This implies that,

x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0x=0orx+2=0orx+5=0

x = 0 \: \: or \: x = - 2\:or \: x = - 5x=0orx=−2orx=−5

To graph the above function, we need to consider the multiplicity.

We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.

We also need to consider the position of the graph on the following intervals,

x < - 5x<−5

When

x = - 10x=−10

y = - 10( - 8)( - 5) \: < \: 0y=−10(−8)(−5)<0

The graph is below the x-axis.

- 5 \: < \: x \: < \: - 2−5<x<−2

When

x = - 3x=−3

y = - 3(2)( - 1) \: > 0y=−3(2)(−1)>0

The graph is above the x-axis.

- 2 \: < \: x < \: 0−2<x<0

when

x = - 1x=−1

y = -1(1)(4) \: < \: 0y=−1(1)(4)<0

The graph is below the x-axis.

Finally the interval,

x \: > \: 0x>0

when

x = 1x=1

y = 1(3)(6) \: > \: 0y=1(3)(6)>0

The graph is above the x-axis.

We can now use the above information to sketch graph as shown in the diagram above

Answer: y = 115 and x = 78

Step-by-step explanation:

y = 115 because it is parallel with the angle 115 and parallel are congruent, for x find the angle beside the angle 102 and that angle is parallel with the angle x and that will be 180 - 102 = 78 which is x  

Answer:

a. (10,10)

Step-by-step explanation:

This was by accident the first answer is right

Answer:

Each movie costs 3.99

Step-by-step explanation:

If every month he is paying $7.99 initially for the service, you take $19.96 and subtract the initial cost ($7.99) then your left with $11.97 and since he bought 3 movies then you divide $11.97 by 3 and your left with $3.99 which is your final answer!

Hope this makes sense!

Answer: yes they are perpendicular

Answer:

1,015

Step-by-step explanation:

7 pounds of honey equals 1 pound of wax

So if we have 145 pounds of was, we multiply 145 by 7

145x7= 1,015

Answer:6 . 625 or 6 5/8

Step-by-step explanation

10 + (-3 3/8)         (adding a negative is like subtracting a positive)

10 - 3 3/8

6 5/8

Answer:

\mathrm{X\:Intercepts}:\:\left(-\frac{431}{26},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:43.1\right)

Step-by-step explanation:

Answer:

answer 215 nickels

Step-by-step explanation:

Using the histogram, the mean of the data-set is estimated to be of 31.

In this problem, the intervals and relative frequencies are:

Hence, the mean is:

[tex]E(X) = 23\frac{4}{30} + 28\frac{8}{30} + 33\frac{14}{30} + 38\frac{4}{30} = \frac{23(4) + 28(8) + 33(14) + 38(4)}{30} = 31[/tex]

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Answer:

Step-by-step explanation:

Sum of interior angles is 180

Sum of interior angles is 180

Vertical angles are same, the sum of remaining angles is same for both triangles:

Exterior angle is same as the sum of non-adjacent interior angles:

identicalAnswer:

1) 64, 2) 6, 3) 26, 4) 33

Step-by-step explanation:

#1

Sum of interior angles is 180

70 + 46 + x = 180

116 + x = 180

x = 64

#2

Sum of interior angles is 180

84 + 7x + 1 + 9x - 1 = 84

16x + 84 = 180

16x = 96

x = 6

#3

Vertical angles are identical, the sum of remaining angles is the same for both triangles:

35 + 25 = 34 + x

60 = 34 + x

x = 60 - 34

x = 26

#4

The exterior angle is the same as the sum of non-adjacent interior angles:

5x - 7 + 6x + 3 = 84

11x - 4 = 84

11x = 88

x = 8

m∠G = 5x - 7 = 5*8 - 7 = 40 - 7 = 33

Answer:

A & D

Step-by-step explanation:

Both use SSS to prove triangles congruent.

Therefore, if all three sides of two triangles are the same, then the triangles are said to be congruent. If we have a side, an angle between the sides, and then another side that is congruent, we know they are congruent. In other words, side, angle, side.

"If and only if the following two conditions are met, two triangles are congruent.

Three corresponding sides have the same value.

The measurements of the three related angles are all equal."

given instance,

Think about the triangles PQR and ABC.

If A = P, B = Q, and C = R

AB = PQ, BC = QR, and AC = PR as well.

If ABC and PQR are congruent triangles, then ABC PQR is the way to write it.

As a result, the following are true statements concerning congruent triangles:

The length of each of the three pairs of corresponding sides is the same.

The three pairs of comparable angles in each case are all of the same size.

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Answer:

  (b)  {-8, 2}

Step-by-step explanation:

The given equation

  x³ +6x -16 = 0

cannot be factored in integers. It has one irrational real root near x=1.759, and two complex roots.

__

Perhaps you want to factor ...

  x² +6x -16 = 0

  (x +8)(x -2) = 0

This has solutions x = -8 and x = 2 that make the factors be zero.

_____

Additional comment

"Cubed" refers to an exponent of 3.

Answer:

Option b] (2,-8)

Step-by-step explanation:

⇒ x³ + 6x - 16 = 0

♦ the value of one root is irrational and other two are complex roots.

⇒ x² + 6x - 16 = 0

⇒ (x + 8)(x - 2) = 0

⇒ x = 2 , -8

Answer:

11:18

Step-by-step explanation:

Hope this helped!

Answer:

Answer:

N(h) = 17.5h + 15

Step-by-step explanation:

N(h) = 8.75h + 15              | write original equation

N(h) = 8.75(2) + 15            | multiply the original hourly fee by 2

N(h) = 17.5 + 15                 | solve

Stay healthy and happy <3.

Hope this helped.

The required function represents the new fees is given as N(h) = 17.5h + 15.

Given that,
An administrative assistant works from home and originally charged her clients $8.75 per hour for any clerical work plus a set fee of $15, or C(h) = 8.75h + 15. She decided to double her hourly fee but keeps her set fee the same.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given function,
C(h) = 8.75h + 15.
Now,
According to the question,
N(h) = 2× 8.75h + 15.
N(h) = 17.5h + 15.

Thus, the required function represents the new fees is given as N(h) = 17.5h + 15.

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Answer:

1332.25 yd²

Step-by-step explanation:

To find the area, you do length times width. Since it is a square and each side is 36.5, you do 36.5 * 36.5 to find the area.

36.5 * 36.5=1332.25

Answer:

Step-by-step explanation:

Determine which climbed at a constant rate

A constant rate would produce a straight line.  The slope is the same for all the data for that climber.  We can either calculate the slope between the first and last intervals and see if the slope changes.  Or we can graph the points, which I chose to do.  See the attachment.

Note that Joe's rate is not constant.  It appears as though he's wearing down.  Both Zas and Stephon have constant slopes, so their climbing rates are constant over the period measured.

The slope is the climbing rate:

Joe:           Not Constant

Zas:            2.5 feet/sec

Stephon:     4.0 feet/sec

Time to Reach 30 feet

Joe:           Unknown - he's slowing down at an unpredictable rate.

For Zas and Stephen, use their slopes in the expression:

Use m for slope (ft/sec):  y = m(t) where t is time in seconds

Zas:            2.5 feet/sec:  y = 2.5(t)  Time to reach 30 is 30/2.5 or 12 sec.

Stephon:     4.0 feet/sec:  y = 4.0(t)  Time to reach 30 is 30/4.0 or 7.5 sec.

Answer:

Step-by-step explanation:

Dilation does not affect angles or the direction of lines. The lines of a dilated figure will be parallel to the original, unless they go through the center of dilation.

Line CD does not go through P, so C'D' is distinct and parallel to it (True).

Angles B and B' are congruent. (True)

Answer:

40 i think

Step-by-step explanation:

we have: ∠P + ∠Q + ∠R = 180°

<=> (4x – 14)º + (5x + 6)° + (x - 2)° = 180°

<=> 4x – 14 + 5x + 6 + x - 2 = 180°

<=> 10x - 10 = 180°

<=> 10x = 190

<=> x = 19°

So: ∠R = (x - 2)° = (19 - 2)° = 17°

ok done. Thank to me :>

Answer:

35 dimes and 60 nickels

Step-by-step explanation:

let d = # of dimes and n = # of nickels

We know that Timmy has a total of 95 coins, consisting of dimes and nickels

So d + n = 95

The total value of his bank is $6.50

A dime is worth $0.10 and a nickel is work $0.05

So 0.10d + 0.05n = $6.50

Note that we've just created a system of equations that we can solve

We have the two equations

0.10d + 0.05n = 6.50 and d + n = 95

There are many different methods we can use to solve this system but the easiest way in this situation is probably going to be the substitution method.

First we are going to want to rearrange the terms of the second equations so that one of the variables are defined.

d + n = 95

- subtract d from both sides -

n = 95 - d

We now defined "n"

Now that we have defined one of the variables we can plug in ( or substitute ) the value of it into the other equation. Once we substitute it we can solve for the other variable.

0.10d + 0.05n = 6.50

n = 95 - d

0.10d + 0.05(95 - d) = 6.50

we now solve for d

0.10d + 0.05(95 - d) = 6.50

step 1 distribute the 0.05

0.05 * 95 = 4.75 and 0.05 * -d = -0.05d

0.10d + 4.75 - 0.05d = 6.50

step 2 combine like terms 0.10d  - 0.05d = 0.05d

0.05d + 4.75 = 6.50

step 3 subtract 4.75 from both sides

0.05d = 1.75

step 4 divide both sides by 0.05

0.05d / 0.05 = d and 1.75 / 0.05 = 35

d = 35

Now that we have found the value of one variable we can plug it into one of the equations and solve for the other variable ( note that the equation that we use does not matter, we will acquire the same answer )

d + n = 95

d = 35

35 + n = 95

subtract 35 from both sides

n = 60

We can conclude that he has 35 dimes and 60 nickels

Answer:

A pencil is about 19 centimeters long

Answer:

if 100 inches=254 centimeters

then 10 inches=x

100x=2540

x=2540/100

x=25.4 centimeters

Given that √2 = 1.414

The value of (1/2)√(16200)

16200 can be written as

16200 = 2×8100

16200 = 2×2×4050

16200 = 2×2×2×2025

16200 = 2×2×2×5×405

16200 = 2×2×2×5×5×81

16200 = 2×2×2×5×5×3×27

16200 = 2×2×2×5×5×3×3×9

16200 = 2×2×2×5×5×3×3×3×3

√16200 = √(2×2×2×5×5×3×3×3×3)

√16200 = √2×(2×2)×(5×5)×(3×3)×(3×3)

√16200 = 2×5×3×3√2

√16200 = 90√2

Now,

(1/2)√16200

⇛(1/2)×90√2

⇛90√2/2

⇛45√2

⇛45×1.414

⇛63.63

Answer: Hence, value of (1/2)√(16200) is 63.63

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The value of 1/2√16200 given the value of √2 = 1.414 is 63.63

Prime factorization of √16200

= 3 × 3 × 5 × √2

= 90√2

Given:

1/2√16200

= 1/2 × 90√2

= 90√2 / 2

= 45√2

= 45 × √2

= 45 × 1.414

= 63.63

Therefore, the value of 1/2√16200 is 63.63

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Answer:

x=1+sqr57,1-sqr57

Step-by-step explanation:

Answer:

  x = -6.5, x = 8.5

Step-by-step explanation:

The given equation ...

  x^2 -4x -31 = -2x +25

can be rewritten to a form that facilitates completing the square:

  x^2 -2x = 56 . . . . . add 2x+31

  x^2 -2x +1 = 57 . . . add 1 to complete the square

  (x -1)^2 = 57 . . . . . write the left side as a square

  x -1 = ±√57 . . . . . take the square root

  x = 1 ±√57 ≈ {-6.5, 8.5} . . . . . add 1, evaluate

Solutions are near x = -6.5 and x = 8.5.