Simplify these:

9-7x     x-4
------- + ---------
x+7       x+7

7x     11x
----- - ------
x-7     x-7

9x       14x
----- - --------
x+9   x+9

3x-4   x-9
------- - ------
x +6    x +6

x-3       x-4
----- + --------
2x        6x

11         3
----- + ------
x+9    x-2

1         1
----- - -------
x²-x       x

Answers

Answer 1

Answer: First one:
Same denominator so ((9-7x)+(x-4))/(x+7)
Final answer:
(5-6x)/(x+7)

Second one:
Again same denominator so ((7x)-(11x))/(x-7)
Final answer:
(-4x)/(x-7)

Third one:
Same denominator again, ((9x)-(14x))/(x+9)
Final answer:
(-5x)/(x+9)

Fourth one:
Same denominator again, ((3x-4)-(x-9))/(x+6)
Final answer:
(2x+5)/(x+6)

Fifth one:
Different denominators here, so we have to make them them same. We do this by multiplying the first fraction by 3/3 to get (3x-9)/(2x), so ((3x-9)+(x-4))/(6x)
Final answer:
(4x-13)/(6x)

Sixth one:
This one is trickier, we have to multiply each by the others denominator, so ((11)*(x-2))/((x+9)*(x-2)) and ((3)*(x+9))/((x-2)*(x+9)) to get
(11x-22)/(x^2+7x-18) and (3x+27)/(x^2+7x-18)
Final answer:
(14x+5)/(x^2+7x-18)

Last one:
You can change the first fraction to 1/(x*(x-1)), then multiple the second fraction by (x-1)/(x-1) to get (x-1)/(x^2-x). Now add them.
Final answer:
(2-x)/(x^2-1)

Hope I helped :)

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The graph of which function has a minimum located at (4, –3)?f(x) = x2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = x2 – 4x + 5
f(x) = 2x2 – 16x + 35

Answers

Answer:

None of the options is the answer to the question

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$f(x)=a(x-h)^(2)+k$

where

(h,k) is the vertex of the parabola

case A) we have

$f(x)=x^(2)+4x-11$

In this case the x-coordinate of the vertex will be negative

therefore

case A is not the solution

case B) we have

$f(x)=-2x^(2)+16x-35$

This case is a vertical parabola open downward (the vertex is a maximum)

The vertex is the point $(4,-3)$ but is not a minimum

see the attached figure

therefore

case B is not the solution

case C) we have

$f(x)=x^(2)-4x+5$

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-5=x^(2)-4x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-5+4=(x^(2)-4x+4)$

$f(x)-1=(x^(2)-4x+4)$

Rewrite as perfect squares

$f(x)-1=(x-2)^(2)$

$f(x)=(x-2)^(2)+1$ --------> vertex form

The vertex is the point $(2,1)$

therefore

case C is not the solution

case D) we have

$f(x)=2x^(2)-16x+35$

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-35=2x^(2)-16x$

Factor the leading coefficient

$f(x)-35=2(x^(2)-8x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-35+32=2(x^(2)-8x+16)$

$f(x)-3=2(x^(2)-8x+16)$

Rewrite as perfect squares

$f(x)-3=2(x-4)^(2)$

$f(x)=2(x-4)^(2)+3$ --------> vertex form

The vertex is the point $(4,3)$

therefore

case D is not the solution

The answer to the question will be the function

$f(x)=2x^(2)-16x+29$

A certain bank offers a car loan with a fixed annual interest rate. Justine applied for the loan and used the entire amount to buy a car worth $43,000. He had to pay the bank for five years for a total amount of $51,600. How much would be the yearly interest if Justine borrowed $50,000 instead? *0 points

Answers

Answer: $10000

Step-by-step explanation:

From the question,

Principal = $43000

Time = 5 years

Rate = Unknown

Simple Interest = $51,600 - $43000 = $8600

We need to calculate the rate of interest which will be:

Interest = PRT/100

8600 = (43000 × 5 × Rate) / 100

Cross multiply

8600 × 100 = 215000 × Rate

Rate = 860000 / 215000

Rate = 4%

Assuming Justine borrowed $50,000 instead, the yearly Interest will be:

= (50000 × 5 × 4%)

= 50000 × 5 × 0.04

= $10000

What is the measure of the central angle of a circle with radius 5 m that intercepts a 2 m arc round your answer to the hundredths place use pie=3.14

Answers

the arc is like the circumference, but only a fraction of it (like the crust of a pizza slice)

ok so find what fraction of the circumference that arc is
C=2pir
r=5
c=2pi5
c=10pi

2 out of 10pi=2/10pi=1/5pi

whole circle=360
1/5pi of 360=360/5pi=72/pi=72/3.14=22.9299
round
22.93 degrees

Answer:

22.93

Step-by-step explanation:

The data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique. {5, 3, 5, 30, 4, 5, 4, 3, 4, 5}

what is the best measure of center for this data set (FQ, mean, median, or range) , and its value is (3, 4, 4.5, or 6.8)

Answers

Answer: The best measure of center for this data set is median , and its value is 4.5 .

Step-by-step explanation:

The given data set : {5, 3, 5, 30, 4, 5, 4, 3, 4, 5}

We can see that it has an outlier (i.e. 30) which is extremely large from all the values.

We know that to measure the center of tendency we measure one of three things arranged in ascending order:

Mode< Median <Mean

But mean gets affected by outlier value.

Then the best measure of center for this data set must be Median.

For this, arrange given data set in order:

{3 ,3 ,4 ,4 ,4 ,5 ,5 ,5 ,5 ,30 }

Since , the number of data values = 10 (even)

Then , Median = Mean of two middle most numbers

$(4+5)/(2)=4.5$

Hence, the best measure of center for this data set is median , and its value is 4.5 .

I need help on these 2

Answers

8)
6(2+2p)=-8(4-p)
12+12p=-32+8p
-8p -8p
12+4p=-32
-12 -12
4p=-44
/4 /4
p=-11

*whatever you do to one side of the equation you have to do to the other

Find the ninth term of the geometric sequence if a1 = 7 and r = 2

Answers

For the geometric sequence:
a n = a 1 * r^(n-1)
a 1 = 7
r = 2
a 9 = a 1 * r^8 =
= 7 * 2^8 = 7 * 256 = 1,792
Answer:
The ninth term of the geometric sequence is 1,792.

Answer:

The ninth term of the geometric sequence is 1,792.

Step-by-step explanation:

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