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leonid [27]
2 years ago
8

a college student needs 11 classes that are worth a total of 40 credits in order to complete her degree. The college offers both

4-credit classes and 3-credit classes. Which system of equations can be used to determine f, the number of 4-credit classes the student can take to complete her degree, and h, the number of 3-credit classes? A) f + h = 40 4h + 3f = 11 B) f + h = 11 4h + 3f = 40 C) f + h = 40 4f + 3h = 11 D) f + h = 11 4f + 3h = 40
Mathematics
1 answer:
Rasek [7]2 years ago
8 0
I’m not entirely sure but I think it’s D
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Divide 81 ft in the ratio 5 :4
Mumz [18]

Answer:

Rr = 51 : 68

Step-by-step explanation:

5 0
2 years ago
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A rectangle is 5 meters longer than its width. If the length is shortened by 2 meters and width is increased by 1 meter, the are
Katarina [22]

Answer: Area = 6m²

              Smaller number = 16

              Hours = 9.6 h

Step-by-step explanation:

A rectangle is 5 meters longer than its width. If the length is shortened by 2 meters and width is increased by 1 meter, the area remains the same. Find the area of the rectangle.

1) w = x m                                2) w = x + 1 m

     l = x + 5  m                               l = x + 5 - 2 = x + 3 m

A₁ = A₂

A = w*l

A₁ = x(x+5) = x² + 5x

A₂ = (x+1)(x+2) = x² + x + 2x + 2 = x² + 3x + 2

A₁ = A₂

x² + 5x = x² + 3x + 2

5x - 3x = 2

2x = 2

x = 1

A₁ = x(x+5) = 1.6 = 6 m²

The ratio of two numbers is 2:5. If the larger number is 40, what is the smaller number.

<u> 2 </u> = <u> x </u>

5     40

5x = 80

x = 80/5 = 16

Sixteen construction workers can finish cementing a floor of a building in 3 hours. On a certain day, only 5 construction workers are available for the job. How long will it take the 5 construction workers to do the cementing job?

workers                      hours

    16                              3

     5                               x

↑                                          ↓              inversely proportional

<u> 5 </u> = <u> 3 </u>

16      x

5x = 16*3

5x = 48

x = 48/5

x = 9.6 h

 

6 0
3 years ago
HURRY PLEASE!<br> (g+2)^5
KengaRu [80]

Step-by-step explanation:

We need to use the binomial theorem/Pascal's triangle here.

(a+b)^5 = (5 choose 0)a^5 + (5 choose 1)a^4*b + (5 choose 2)a^3*b^2 + (5 choose 3)a^2*b^3 + (5 choose 4)a*b^4 + (5 choose 5)b^5.

5 choose 0 = 1

5 choose 1 = 5

5 choose 2 = 10

5 choose 3 = 10

5 choose 4 = 5

5 choose 5 = 1

And 1, 5, 10, 10, 5, 1, is the (5+1) = 6th row of pascal's triangle.

Therefore we get

g^5 + 5g^4*2 + 10g^3*2^2 + 10g^2*2^3 + 5g*2^4 + 2^5

which is

g^4 + 10g^4 + 40g^3 + 80g^2 + 80g + 32

Or, you could do the slow way, by just doing (g+2)(g+2)(g+2)(g+2)(g+2)

3 0
3 years ago
If f(x)=3x−2 and g(x)=x2−5, what is g(f(2))?
Vikki [24]

Answer:

g(f(2)) = 11

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Function Notation

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 3x - 2

g(x) = x² - 5

<u>Step 2: Find g(f(2))</u>

f(2)

  1. Substitute in <em>x</em>:                    f(2) = 3(2) - 2
  2. Multiply:                               f(2) = 6 - 2
  3. Subtract:                              f(2) = 4

g(f(2))

  1. Substitute in <em>x</em>:                    g(4) = 4² - 5
  2. Exponents:                          g(4) = 16 - 5
  3. Subtract:                              g(4) = 11
8 0
3 years ago
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point
kiruha [24]
This is going to be an long answer, so I'm putting the answer first. y=3x-7

First, you have to find the equation of the line given. You can use point slope form for that. You can see that the slope is -1/3, and it goes through (2,2). So, the equation would be
y-2=-1/3(x-2)
Which simplifies to
y=-1/3x+8/3

Now, we can get on to finding the actual answer. The slope of a line perpendicular would be the negative reciprocal of the original slope. That just means you flip it and multiply it by -1. So, the slope of the new line is 3. Now you can use point slope form again and make an equation, which is
y+1=3(x-2)
Which simplifies to
y=3x-7

Please don't ask me why the slope is the negative reciprocal, or how they came up with the formula for the point slope form. I DON'T KNOW. If you want to know so bad you would give up chick-fil-A for the rest of your life, there's always google.
5 0
3 years ago
Read 2 more answers
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