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QUIZ:
Foundations - Systems of Equations
Which expression is equivalent
Please help

Answer:

c) [tex]\frac{x-2}{x+6}[/tex]

Step-by-step explanation:

When given that function (f) is the following,

[tex]f(x)=\frac{x+2}{x^2+4x-12}[/tex]

The wisest move to first make is to factor the expression, factoring is the process by which one rewrites a quadratic expression as the product of two linear expressions,

[tex]f(x)=\frac{x+12}{(x+6)(x-2)}[/tex]

If is given that function (g) is the following,

[tex]g(x)=\frac{4x^2-16x+16}{4x+48}[/tex]

Then one should also factor the expression,

[tex]g(x)=\frac{4(x-2)^2}{4(x+12)}[/tex]

One is asked to find the following,

[tex]f(x)*g(x)[/tex]

To do this operation, one must multiply the two functions together. It is easiest to do so when the functions are in factored form,

[tex]f(x)*g(x)[/tex]

Substitute,

[tex](\frac{x+12}{(x+6)(x-2)})(\frac{4(x-2)^2}{4(x+12)})[/tex]

Simplify, cross out like terms in the numerator and denominator,

[tex]\frac{x-2}{x+6}[/tex]

Answer:

70 amps

Step-by-step explanation:

The current I is inversely proportional to the resistance R

I=k/R   (k is the constant of proportionality)

A)   I=210 amperes

     R=4 ohms

I=k/R

k=I×R

k=210×4=840

B)    R=12 ohms

     k=840

    I=k/R

   I=840/12=70 amperes

The current will be 40 mA when the resistance is 15 ohms.​

Ohms law says that the current running through the conductor is directly proportional to the potential difference across its extremities as long as the temperature and other physical conditions are constant.

Ohms law formula is -

V=IR, Where

Voltage is V and is measured in Volts,

The current flowing through the conductor is I and it represented in amperes and the resistance is R and is measured in ohms.

Given that, the voltage, V, in an electric circuit is held constant, If the current is 120mA when resistance is 5 ohms,

120 mA = 0.12 A

Therefore,

V = IR

V = 0.12 × 5

V = 0.6 volts

Now, when the resistance is 15 ohms, the current will be =

0.6 = I × 15

I = 0.6 / 15

I = 0.04 A

I = 40 mA

Hence, the current will be 40 mA when the resistance is 15 ohms.​

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Answer:

m∡ZA = 51°

m∡ZB = 39°

Step-by-step explanation:

∡ZB = 'b'

∡ZA = '12 + b'

b + 12 + b = 90

2b + 12 = 90

2b = 78

b = 39

12 + 39 = 51

Answer:

4

Step-by-step explanation:

Nickels are 5 cents a piece so you will multiple 11 by 5 to find how much Alan has in nickels. Then subtract that from the total of 95 to get your answer.

11 × 5 = 55

95 - 54 = 40

Since dimes are worth 10 cents you divide 40 by 10 and that is how many dimes Alan has.

40/10=4

Answer:

The total number of flowers grown is 163.

Step-by-step explanation:

Since in a flower fertilization experiment, the number of pink flowers grown is twice that of red flowers, and the number of white flowers grown is 3 more than that of red flowers, the number of white flowers grown is 37 fewer than that of pink flowers, to find the total number of flowers grown the following calculation must be performed:

P = 2R

W = R + 3

W = P - 37

W = W

R + 3 = 2R - 37

R + 3 + 37 = 2R

40 = 2R - R

40 = R

P = 2 x 40 = 80

R = 40

W = 40 + 3 = 43

80 + 40 + 43 = X

163 = X

Therefore, the total number of flowers grown is 163.

Answer: b that is too easy

Step-by-step explanation:

9514 1404 393

Answer:

  y = -3x

Step-by-step explanation:

The slope formula gives the slope of the segment between the given points.

  m = (y2 -y1)/(x2 -x1)

  m = (-3 -(-5))/(2 -(-4)) = 2/6 = 1/3

The slope of the perpendicular line is the opposite reciprocal of this, so is ...

  m' = -1/(1/3) = -3

A perpendicular line is ...

  y = -3x

Answer: y= -4 divided by 3 • x (-1)

Step-by-step explanation:

✨photo math✨

Answer:

B ( 6,-6) ..

I think I'm correct

Answer:

The coordinates for the point on a circle of radius at an angle of are At the radius of the unit circle, 1, serves as the hypotenuse of a 30-60-90 degree right triangle, as shown in (Figure).

Step-by-step explanation:

Answer:

sec t = 1/(cos t) = 1/(-3/4) = -4/3

Answer:

A) [tex]\sqrt{8x/3}[/tex]

Step-by-step explanation:

[tex]\sqrt{8x^{2} } /\sqrt{3x}[/tex]

[tex]\sqrt{8x^{2}/{3x}[/tex]

[tex]\sqrt{8x/3}[/tex]

Therefore, A is correct

Answer:

P = 25 + (15)n

Total amount paid by David = $100

Step-by-step explanation:

Given:

Fixed cost of renting chain saw =  $25

Variable cost of renting chain saw =  $15 per hour

Time taken = 5 hour

Find;

Total amount paid by David

Computation:

Assume;

Total amount paid by David = P

Time taken = n

So,

P = 25 + (15)n

P = 25 + (15)(5)

P = 25 + 75

P = 100

Total amount paid by David = $100

By DeMoivre's theorem,

(3 (cos(5π/6) + i sin(5π/6)))⁴ = 3⁴ (cos(4×5π/6) + i sin(4×5π/6))

… = 81 (cos(20π/6) + i sin(20π/6))

… = 81 (cos(10π/3) + i sin(10π/3))

… = 81 (cos(-2π/3) + i sin(-2π/3))

… = 81 (cos(2π/3) - i sin(2π/3))

… = 81 (-1/2 + √3/2 i )

… = -81/2 + 81√3/2 i

Answer:

c

Step-by-step explanation:

10 times 8 = 80

80 times 3 = 240

Answer:

A

Step-by-step explanation:

length times width times height  will give you volume

Answer:

Step-by-step explanation:

Based on the data gathered on that certain day, I would say NO, the store does not need to change its staffing. The data shows that the percentages calculated by the store are extremely close to the actual percentage of people that arrived at those given hours throughout the day. The problem with this solution is that it does not take into account special circumstances, such as specific days, events, holidays, new popular items, etc. All of these can drastically affect the number of people that enter the store at a given time.

1. The retail store should not change its staffing arrangement.

2. Changing the staffing arrangement may not favor the retail store.

Data and Calculations:

                                             8:00 am &   12:00 pm &   4:00 pm &   8:00 pm &

                                              12:00 pm       4:00 pm      8:00 pm      midnight

Expected % of customers        32%             21%              35%                12%

Actual number of customers  214               198              276                  134

Total Number of customers = 822 (214 + 198 + 276 + 134)

Actual % of customers            26%             24%             34%                 16%

Difference between expected percentage of

 customers and actual           6%                3%                1%                  -4%

Variation                                 0.36%           0.09%         0.01%            0.16%

Sum of variation = 0.62%

Standard Deviation = 0.787

Thus, based on the standard deviation, the store should not change its staffing.

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Answer:

0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Distribution of the difference in height between men and woman:

Applying the concept above:

[tex]\mu = 69.3 - 64 = 5.3[/tex]

[tex]\sigma = \sqrt{2.7^2 + 2.8^2} = 3.89[/tex]

What is the probability that the young man is taller than the young woman by more than 5 inches?

Probability of the difference being more than 5 inches, that is, 1 subtracted by the pvalue of Z when X = 5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 5.3}{3.89}[/tex]

[tex]Z = -0.08[/tex]

[tex]Z = -0.08[/tex] has a pvalue of 0.4681

1 - 0.4681 = 0.5319

0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches

Answer: No

Step-by-step explanation: a rectangle can be a parallelogram because it qualifies to be a parallelogram however a parallelogram can’t be a rectangle because a rectangle has all 90 degree angles and that opposite sides can be equal and parallelograms come in different forms

Answer:

[tex]f^{-1} = \frac{ 7(x-4)}{2}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{2x}{7} + 4[/tex]

Required

The inverse function

[tex]f(x) = \frac{2x}{7} + 4[/tex]

Replace f(x) with y

[tex]y = \frac{2x}{7} + 4[/tex]

Swap x and y

[tex]x = \frac{2y}{7} + 4[/tex]

Multiply through by 7

[tex]7x = 2y + 28[/tex]

Solve for 2y

[tex]2y = 7x - 28[/tex]

Solve for y

[tex]y = \frac{ 7x-28}{2}[/tex]

Factorize

[tex]y = \frac{ 7(x-4)}{2}[/tex]

Write as:

[tex]f^{-1} = \frac{ 7(x-4)}{2}[/tex]

Answer:

2b + 10

Step-by-step explanation:

Answer:

15 and -20

Step-by-step explanation:

The zeros/ roots are the x intercepts of the graph

Answer: k^3=1

Step-by-step explanation:

Answer:k^3=1

Step-by-step explanation:

Answer:

multiply the top number by 4 also and what ever answer you get by doing 24×4 place that number over 100 and that number will be your percentage

Answer:

it's

-21

or 12

which one you mean

Answer:

click to see link blahlaldglds.com

JUST KIDNG HERES THE ANSWERS BELOW.

7

15

-5

1

4

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

3(x-9)= 3x-27

3x-27=30

3x=57

x=19

Answer:

$730.08

Step-by-step explanation:

22% = 0.22

1 - 0.22 = 0.78

Value after 2 years

v = 1200(0.78)²

v = 730.08

$730.08