The graphs of f(x) and g(x) are shown below.

On a coordinate plane, a straight line with a positive slope represents f (x) = x minus 3. The line goes through (0, negative 3) and (3, 0). On a coordinate plane, a straight line with a negative slope represents g (x) = negative 0.5 x. The line goes through (negative 4, 2), (0, 0), and (4, negative 2)

For what interval is the value of (f – g)(x) negative?

9514 1404 393

Answer:

Step-by-step explanation:

We understand this to be two separate problems.

  -3/9 +(-2 9/10) = -(3/9 +2 9/10)

  = -(10/30 +87/30) = -97/30 = -3 7/30

__

  -3√(8 +(-2(9/10))) = -3√(8 -1.8) = -3√6.2 ≈ -7.46994

__

Additional comment

A calculator can help with these, especially if it is able to deal with rational numbers. (Many graphing calculators and some scientific calculators will do that more or less nicely. My favorite Android calculator app makes arithmetic with fractions and mixed numbers very easy.)

Answer:

270

Step-by-step explanation:

by using the proportion rule:

let X be the number of qualified teachers then

1:2=X=540 i.e.

1/2 =  X/540

by cross multiplication,

540x1=2xX

540=2X i.e.

X=540/2

X=270

There are 270 qualified teachers.

To solve this, we would apply the knowledge of proportion.

It is simply a way of stating that two ratios are of equal measure.

For example, [tex]a:b = x:y[/tex] or [tex]\frac{a}{b} = \frac{x}{y}[/tex]

Applying the following proportion rule given that:

Ratio of qualified teachers to unqualified teachers is 1:2.

Number of unqualified teachers = 540

Let number of qualified teachers be represented by x.

Therefore:

[tex]\frac{1}{2} = \frac{x}{540}[/tex]

Cross multiply

[tex]2x = 540(1)[/tex]

Divide both sides by 2

[tex]\frac{2x}{2} = \frac{540}{2} \\x = 270[/tex]

Therefore, the number of qualified teachers is 270.

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We have that Total votes cast in the election is the vote cast for Margie and Rachel summed up

[tex]Total\ vote=\sum Rachel +\sum Margie[/tex]

It is important to note that an election comprise of two or more candidates facing off against each other to decide who a group of people want for a position

From the Question we are told that

There is suppose to be a table of votes cast

Generally the Total votes cast in the election is the vote cast for Margie and Rachel summed up

Therefore

[tex]Total\ vote=\sum Rachel +\sum Margie[/tex]

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[tex]5a + 3 {a}^{2} \\ = 5( - 3) + 3( { - 3}^{2} ) \\ = - 15 + 3(9) \\ = - 15 + 27 \\ = 12[/tex]

I hope I helped you^_^

Answer:

12

Step-by-step explanation:

5a + 3a^2 when a = -3

~Substitute

5(-3) + 3(-3)^2

~Simplify

-15 + 3(9)

-15 + 27

12

Best of Luck!

$81.53 is the cost of nut-raisin mix

Answer:

[tex]3.4 \: apple \: pounds = 5.61 \: dollars \\ 1 \: apple \: pound = \{ \frac{(1 \times 5.61)}{3.4} \} \: dollars \\ \\ = { \boxed{ \boxed{1.65 \: dollars \: per \: pound}}}[/tex]

Answer:

1.65

Step-by-step explanation:

5.61/3.4=1.65

Answer:

LCD = 8

Step-by-step explanation:

All you have to do is times both the denominator and numerator of 1/2 by 4.

So 1 times 4 = 4 and 2 times 4 is 8.

4/8 and 3/8

Answer:

[tex]c(ge + p) = n + j \\ \\ \frac{c(ge + p)}{(ge + p)} = \frac{n + j}{(ge + p)} \\ \\ { \boxed{ \boxed{c = \frac{n + j}{ge + p} }}}[/tex]

Answer:

404.25 dollars

Step-by-step explanation:

First, we do 8.35 times 37, and we get 305.25.

Next, we subtract 37 from 45 and get 8.

Then, we do divide 8.25 in half, and get 4.125.

After that we add 4.125 to 8.25 and get 12.375.

Then we do 12.375 times 8 and get 99

Finally, we add 99 and 305.25 together and get 404.25 dollars.

Answer:

126 cats .................

126 dogs........

Answer:

A= the solution is 27

Step-by-step explanation:

3y+4(y−6)=8y−3(y−10)

3y+4(y−6)=8y−3(y−10) - Simplify

3y+(4)(y)+(4)(−6)=8y+(−3)(y)+(−3)(−10)(Distribute) - Simplify

3y+4y+−24=8y+−3y+30 - Simplify

(3y+4y)+(−24)=(8y+−3y)+(30)(Combine Like Terms)

7y+−24=5y+30

7y−24=5y+30

7y−24−5y=5y+30−5y - Subtract 5y from both sides

2y−24=30

2y−24+24=30+24 - Add 24 to both sides

2y=54

2y/2 = 54/2 - Divide both sides by 2

y=27

Answer:

Step-by-step explanation:

2

Answer:

70

Step-by-step explanation:

The prime factors of 350 are 2,5,7. Therefore, the product of prime factors = 2×5×7=70

Answer:

2 miles and 88 yards.

Step-by-step explanation:

4 has 2*2 as prime factors

5 is prime

10 has 2 and 5 as prime factors

Thus, the lowest common denominator will be 2*2*5

3/4=15/20

3/5=12/20

7/10=14/20

Now that we have three fractions with the same denominator, we can add the numerators

15+12+14=41

So 41/20ths

That’s 2 and 1/20th

So the final answer is 2 miles and 88 yards! :)

Answer:

1

Step-by-step explanation:

-11-(-12) is just -11 plus 12 so 1 is your final answer because 2 negatives make a positive when multiplying.

Answer:

1

Step-by-step explanation:

Answer:

The mean lifetime of a sample of 100 fluorescent light bulbs produced by a company is

The mean lifetime of a sample of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours.

Step-by-step explanation:

https://www.cs.bu.edu/faculty/snyder/cs237/Handouts%20and%20Web%20Documents/Handouts/PracticeProblemsHypothesisTesting.pdf

Have a bless day

Answer:

450

(I can't post the answer if it's less than 20 letters so just ignore this I'm trying to fill up)

Answer:

Three non-collinear points determine a plane.

Step-by-step explanation:

This statement means that if you have three points not on one line, then only one specific plane can go through those points. The plane is determined by the three points because the points show you exactly where the plane is

Cosine is [tex]\frac{hypotenuse}{adjacent}[/tex].

Apply the equation:

[tex]sin(t) = \frac{3}{5} \\3^2 + b^2 = 5^2\\b^2 = 5^2 - 3^2\\\\\sqrt{b^2} = \sqrt{5^2}- \sqrt{3^2}\\\\\\b = 5 - 3 \\\\b = 2[/tex]

B is the adjacent side so

cosine is:

Cos(t) = 5/2

Have a great day,

And I hope this helps you!

Answer:

18e90w002

919293939

jwiwoqo1919

2kw29w9w9ww9

91022929292929 91901

19190193939

19292920202

Answer:

Use the given functions to set up and simplify −by−Step.

f(9)=−55

Re-order terms so constants are on the left

⋅9=−55

f⋅9=−55

9=−55

Divide both sides of the equation by the same term

Simplify

Solution

=−55/9

9514 1404 393

Answer:

Step-by-step explanation:

In order for the total displacement to be zero, the amount of forward displacement must be equal and opposite to the amount of backward displacement. Since the steps are the same length, they must be equal in number.

Half of the 10 steps were forward, and the other half were backward.

  5 steps forward; 5 steps backward.

_____

Additional comment

Math develops from an effort to model the real world. It would probably give you some insight into this problem if you were to physically take some steps to see how many forward and backward you would need to end where you start.

Answers:

D. Dividing by 6

F. Multiplying by 1/6

Step-by-step explanation: Dividing both sides by 6  and Multiplying by 1/6 will isolate the variable on one side because we will get the value of what x is equal too. X is equal to 7.

Answer:

D,E,F,G

Step-by-step explanation:

Answer:

[tex]10x+10y-7[/tex]

Step-by-step explanation:

We just need to add up all of the angles, PQT, TQS, and RQS to find the measure of angle PQR.

[tex]PQT=7x+6\\TQS=-2x+8y-13\\RQS=5x+2y\\PQT+TQS+RQS=PQR\\7x+6+TQS+RQS=PQR\\7x+6+(-2x+8y-13)+RQS=PQR\\7x+6+(-2x+8y-13)+5x+2y=PQR\\7x+6-2x+8y-13+5x+2y=PQR\\7x-2x+5x+8y+2y+6-13=PQR\\5x+5x+8y+2y+6-13=PQR\\10x+8y+2y+6-13=PQR\\10x+10y+6-13=PQR\\10x+10y-7=PQR[/tex]

9514 1404 393

Answer:

  123°

Step-by-step explanation:

Each of the parts of the trisected angle is equal to the others.

  ∠PQT = ∠TQS

  7x +6 = -2x +8y -13

  9x -8y +19 = 0 . . . . . . subtract the right-side expression

  ∠TQS = ∠RQS

  -2x +8y -13 = 5x +2y

  7x -6y +13 = 0 . . . . . . subtract the left-side expression

__

These equations can be solved by any of your favorite methods to give ...

  (x, y) = (5, 8)

Then the angle measures are ...

  ∠PQT = 7x +6 = 7(5) +6 = 41

  ∠TQS = -2x +8y -13 = -2(5) +8(8) -13 = 64 -23 = 41

  ∠RQS = 5x +2y = 5(5) +2(8) = 41

The measure of angle PQR is 3·41° = 123°.

_____

Additional comment

Using Cramer's rule, the solution is ...

  x = (-8(13) -(-6)(19))/(9(-6) -7(-8)) = 10/2 = 5

  y = (19(7) -13(9))/2 = 16/2 = 8

I prefer a method like this, or the graphical solution, when the numbers don't lend themselves to substitution or elimination.

__

Obviously, once we have found angle PQT, we can simply multiply it by 3 to find angle PQR. We chose to compute the values of the other angles as a check on our math.

Answer:

[tex]? \times \frac{?}{?} [/tex]

d

Answer:

2 by 25 feet.

Step-by-step explanation:

Let L and W be the length and the widht of the field

we want W = L + 23 and W x L = 50

So

(L + 23) x L = 50

[tex]L^2 + 23L = 50\\L^2+23L-50 =0\\(L+25)(L-2)=0\\L=-25 \text{ or } L = 2[/tex]

Since L must be positive then L =2 and W = 2 + 23 = 25.

Answer:

The monthly net pay is [tex]\$1555[/tex].

Step-by-step explanation:

Step 1 :

Quintina decided to increase the deduction percentage of her federal income tax rate from [tex]14\%[/tex] to [tex]16\%.[/tex]

Quintina gross pay per month is [tex]\$2,100[/tex]

[tex]16\%[/tex] is written in the decimal form.

[tex]=\frac{16}{100}[/tex]

[tex]=0.16[/tex]

Federal income tax

[tex]=0.16[/tex]  × Gross pay

[tex]=0.156[/tex]  × [tex]2100[/tex]

[tex]=336[/tex]

Step 2:

Monthly net pay = Gross pay- Federal income tax - State Income Tax – social Security- Medicare.

[tex]=2100-336-89-85-35[/tex]

[tex]=2100-545[/tex]

[tex]=\$1555[/tex]

Therefore, the monthly net pay is [tex]\$1555.[/tex]

Learn more about income tax, refer:

Answer$1555

Step-by-step explanation:

Answer:

3.25

Step-by-step explanation:

1 hong kong dollar = 0.13 cents in us dollars

0.13x25=3.25

The value of 25 Hong Kong dollars in U.S dollar is $3.1969

Given that :

$1 = 7.82 Hong Kong dollars

Let the equivalent Number of U.S dollars = p

This means that :

$1 = 7.82 Hong Kong dollars

$1 = 7.82 Hong Kong dollars $p = 25

Cross multiply :

25 × 1 = 7.82 × p

25 = 7.82p

Divide both sides by 7.82

25 / 7.82 = p

p = $3.1969

Hence, 25 Hong Kong dollars is 3.1969 U.S dollars.

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Answer:

x2 + 8

Step-by-step explanation:

The value of the composite function (f - g)(x) is x² + 8.

The correct option is D.

Any function that is created by combining two or more other functions is referred to as a composite function. To put it another way, given two functions, f, and g, the composite function of f and g, denoted as f(g(x)), is a new function that applies g to the input x before applying f to the output of g (x).

Given:

f(x) = 2x² + 1 and g(x) = x² - 7.

To find (f – g)(x), we need to subtract g(x) from f(x):

(f - g)(x) = f(x) - g(x)

where f(x) = 2x² + 1 and g(x) = x² - 7.

Substituting these expressions into the equation, we get:

(f - g)(x) = (2x² + 1) - (x² - 7)

Simplifying the expression on the right-hand side by distributing the negative sign, we get:

(f - g)(x) = 2x² + 1 - x² - 7)

Combining like terms, we get:

(f - g)(x) = x² + 8.

Therefore, (f - g)(x) = x² + 8.

To learn more about the composite function;

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