One-eight of class graduated with a A average, 1/2 got a B, and the rest of the class had a C average. In a class of 800, how many had C average?

9514 1404 393

Answer:

  (x, y) = (3, 12)

Step-by-step explanation:

Using the given variable definitions, we can write the equations ...

  y = x + 9

  2(x +y) = 30

__

Solving the second equation for y, we have ...

  y = 15 -x

Substituting this into the first equation gives ...

  15 -x = x +9

  6 = 2x . . . . . . . . . add x-9

  3 = x . . . . . . . . . . divide by 2

  y = 3+9 = 12 . . . . substitute into the first equation

The numbers are (x, y) = (3, 12).

To find the integral we need to divide it according to the intervals that define the piece-wise function, then we have:

Now that we have divide the integral we plug the expressions that define it in the intervals:

Therefore, the integral is 327/10

Answer:6^21

Step-by-step explanation:

The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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The answer would be B a≈9.22

Answer:

x = 5

Step-by-step explanation:

RS  +ST =  RT

2x + 10 + x - 4 = 21

2x + x + 10 - 4 = 21   {Combine like terms}

3x + 6 = 21

Subtract 6 from both sides

3x = 21 - 6

3x = 15

Divide both sides by 3

x = 15/3

x = 5

Answer:

x>-1

Step-by-step explanation:

\( \frac{17}{17}x > - \frac{17}{17} \\x > - 1 \)

The complete factorization of the polynomial is:

h(x) = (x - 3)*(x - 1)*(x + 2)

Here we have the polynomial:

g(x)= x³ - 2x² - 5x + 6

And we know that x = 3 is a zero, then (x - 3) is a factor.

So if f(x) = a*x² + b*x + c

We can write:

h(x) = (x - 3)*f(x)

Let's find f(x).

Expanding that:

x³ - 2x² - 5x + 6 = (x - 3)*(a*x² + b*x + c)

x³ - 2x² - 5x + 6 = ax³ + bx² + cx - 3ax² - 3bx - 3c

x³ - 2x² - 5x + 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c

Comparing like terms, we can see that:

a = 1

b - 3 a = -2

c - 3b = -5

-3c = 6

With the first and last equation we can get:

a = 1

c = 6/-3 = -2

Now with one of these values and the second or third equation we can find the value of b.

b - 3 a = -2

b - 3*1 = -2

b - 3 = -2

b = -2 + 3 = 1

Then:

f(x)  = x² + x - 2

The zeros of this quadratic function are given by:

x = -1±3 / 2

so, we get,

x = (-1 + 3)/2 = 1

x = (-1 - 3)/2 = -2

Then we can factorize this as:

f(x) = (x - 1)*(x + 2)

And then we can write h(x) as:

h(x) = (x - 3)*(x - 1)*(x + 2)

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complete question:

For the polynomial below, 3 is a zero.

g(x)= x³ - 2x² - 5x + 6

Express g (x) as a product of linear factors.

Answer:

Step-by-step explanation:

Answer:

16801.2cm²

Step-by-step explanation:

Cone :

SA = πrl

SA = π · 28 ·  45                     90-45 = 45

SA = 3958.406744

Cylinder :

SA = 2 · π · r · ( r+h)

SA = 2 · π · 28 ( 28 +45 )

SA = 2 · π · 28 (73)

SA = 12842.83077

12842.83077 + 3958.406744 =

16801.2cm²

Answer: y=-9/4x+21

Step-by-step explanation:

To find a line that passes through the given points, we can use them to find the slope. Once we have the slope, we can plug in any point and solve for the y-intercept. The formula to solve for slope is \(m=\frac{y_2-y_1}{x_2-x_1}\).

\(m=\frac{3-12}{7-3} =\frac{-9}{4} =-\frac{9}{4}\)

Now that we have the slope, we can plug in any point.

12=-9/4(4)+b           [multiply]

12=-9+b                   [add both sides by 9]

b=21

Now that we know the y-intercept, the equation is y=-9/4x+21.

Answer:

1- $ 0.25.

2- $ 26.25.

3- $ 1.73.

Step-by-step explanation:

1- Given that a bag of 12 oranges costs $ 2.99, to determine what is the cost per orange, the following calculation must be performed:

2.99 / 12 = X

0.249 = X

Thus, the cost of each orange is $ 0.25.

2- Given that 4 slices of pizza cost $ 10.50, to determine what is the cost of 10 slices of pizza at this rate, the following calculation must be performed:

10.5 / 4 x 10 = X

2.625 x 10 = X

26.25 = X

Thus, the cost of 10 slices of pizza is $ 26.25.

3- Given that 4 pieces of candy cost $ 0.99, to determine what is the cost of 7 pieces of candy at this rate, the following calculation must be performed:

0.99 / 4 x 7 = X

0.2475 x 7 = X

1.7325 = X

Thus, the cost of 7 pieces of candy is $ 1.73.

Answer:

3 1/2 feet

Step-by-step explanation:

10 1/2 / 3 = 7/2 = 3 1/2

Answer:

is correct

x^3 -7x^2+2x +40

multiply the constants of the factors (each factor has opposite sign of the zero)

(x+2)(x-4)(x-5)   2(-4)(-5) = 40,  that eliminates all but c) and d)

(x+2)(x-4)(x-5) = (x^2-2x-8)(x-5)   by using FOIL on the 1st two factors

then (-8)(-5) = +40, eliminating a) and b), leaving only c) and d)

-5 times -2x = 10x,  x times -8 = -8x.   10x-8x = 2x which c) has but d) doesn't.

Step-by-step explanation:

He paid 6.7% in taxes of his annual income.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here: Income = $27000 and paid $1,809 in social security taxes.

Thus percentage of earnings  paid as taxes is

1809/27000 × 100 =6.7%

Hence, He paid 6.7% in taxes of his annual income.

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Answer:

G. 6 months

Step-by-step explanation:

1. 495-165 to remove the one-time payment = 330

2. 330/55 to find the number of months = 6

Barbara receive 6 months of dance lessons from Dance Unlimited

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165.

Let m be the no of months and f(m) is the total cost.

∴ f(m) = 55m + 165.

The equation represents the $495 total cost,

∴ 495 =  55m + 165.

55m = 330.

m = 330/55.

m = 6.

Barbara receives 6 months of dance lessons from Dance Unlimited.

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A scatter plot visually represents the relationship between two variables. It shows a positive correlation between the number of books read per month and SAT Verbal Test scores, with the equation y = 6.4828x + 520.6962.

A scatter plot is a graphical representation of a set of data that allows the observer to observe the relationship between two variables. It is used to graphically display how one variable is affected by the other. It is a chart of data points plotted on a two-dimensional graph with one variable represented on the X-axis and the other variable on the Y-axis.

Scatter Plot of the Data: From the data provided by the Language Arts department, we can create the scatter plot as shown below:
Equation of the line of best fit: The line of best fit is a straight line that is used to model the relationship between the two variables. It is determined by minimizing the sum of the squares of the differences between the observed values and the predicted values.

From the scatter plot, we can see that there is a positive correlation between the number of books read per month and the score on the SAT Verbal Test. This suggests that the more books a student reads per month, the higher their score on the SAT Verbal Test.

The equation of the line of best fit for the given data set is y = 6.4828x + 520.6962. Here, y represents the score on the SAT Verbal Test and x represents the number of books read per month.

To find the equation of the line of best fit, we can use a regression analysis tool such as Excel. The regression analysis will give us the values of the slope and intercept of the line of best fit, which we can use to write the equation of the line.

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The value of the double integration is 7776 after solving and integration. the answer is 7776.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

Double integration (x + y) dA

y = x²

y² = 216x

y = √216 √x

∫∫(√216 √x +  x²)

After solving:

\(\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy\)

=7776

Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.

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Answer:

58

Step-by-step explanation:

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26                   ...1

5x + 7y = 70

(5/7)x + y = 10              ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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Answer:

It Is 186ft

Step-by-step explanation:

Answer:

B(6, 5), C(1, -7)

Step-by-step explanation:

A(2, 5)

From A to B, there is translation x, (4, 0).

Add 4 to A's x-coordinate, and add 0 to A's y-coordinate.

B(2 + 4, 5 + 0) = B(6, 5)

From C to B there is the translation y, (5, 12).

Since we are going from B to C, we undo translation y.

The translation from B to C is (-5, -12).

C(6 - 5, 5 - 12) = C(1, -7)

Answer:

31 degrees

Step-by-step explanation:

90-59

=31

~rere

Answer:

<b = 31 °

Step-by-step explanation:

When the sum of two angles is equal to 90 degrees, they are called complementary angles

So . .

Because the sum is 90 subtract!

<b = 31 °

Answer:

h=2 A/b

h=6.114

The correct expression of 235 * 8 is 200 * 8 + 30 * 8 + 5 * 8

The product expression is given as:

235 * 8

Express 235 as place values

235 * 8 = (200 + 30 + 5) * 8

Expand the bracket

235 * 8 = 200 * 8 + 30 * 8 + 5 * 8

Hence, the correct expression of 235 * 8 is 200 * 8 + 30 * 8 + 5 * 8

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