Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.

it is transformed [tex]|x|[/tex] function. moved down by and right by 1 unit,

so $y=|x-1|-1$

Answer:

The answer is 15%.

Step-by-step explanation:

The probability that:

       80% x 90% = 72%

        80% x (1 - 90%) = 8%

        (1 - 80%) x 25% = 5%

        1 - (72% + 8% + 5%) = 15%

Answer:

down 8 units

Step-by-step explanation:

going from +6 to -2 goes down 8 units

Answer:

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

==============================================

We have y = 3/7x + 6. It has been changed to y = 3/7x - 2.

y = 3/7x + 6 → f(x) = 3/7x + 6

f(x) - 8 = (3/7x + 6) - 8 = 3/7x + 6 - 8 = 3/7x - 2

[tex] {3x}^{2} - 4x - 12 = 0[/tex]

[tex]a = 3[/tex]

[tex]b = - 4[/tex]

[tex]c = - 12[/tex]

Formula:

[tex] \boxed{x = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }[/tex]

Replacing:

[tex]x = \dfrac{ -( - 4) \pm \sqrt{ { (- 4)}^{2} - 4(3)( - 12)} }{2(3)} [/tex]

Option: C).

a+b+c=68

b-3=a

c-5=b

now just solve the system of equations, substitue so that there are only b's in the equation:

a+b+c=68

(b-3) + b + (b+5) = 68

3b=66

b=22

Therefore Barbara is 22

The required age of barbar is 22 years.

Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old.  How old is Barbara to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Let the age of Alice, Barbara and Carol are a, b and c.

Age Alice is 3 years younger than Barbara,

a = b - 3     - - - -(1)

Age Barbara is 5 years younger than Carol

b = c - 5

c = b + 5     - - - -(2)

Together the sisters are 68 years old i.e.

a + b +c =68

From equation 1 and 2

b - 3 + b + b +5 = 68

3b + 2 = 68

3b = 66

b  = 33

Thus, the required age of barbar is 22 years.

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Answer:

Hey there!

The two lines in this graph are: y=-1/5x+2, and y=3x-2

Since y=-1/5x+2 is a dotted line, we know that we use the < or > symbols.

Since y=3x-2 is a straight line, we use the ≤ and ≥ symbols.

Thus, for area z, we have y<-1/5x+2, and y≥3x-2

Hope this helps :)

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

[tex]|u|=\sqrt{14^2+9^2}[/tex] which is [tex]\sqrt{277}[/tex]

[tex]|v|=\sqrt{3^2+6^2}[/tex] which is [tex]\sqrt{45}[/tex]

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

[tex]cos\theta=\frac{uv}{|u||v|}[/tex] where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

[tex]cos^{-1}\theta=\frac{96}{111.64676}[/tex] which returns an angle measure of 30.7. Plugging that all into the dot product formula:

[tex]u*v=\sqrt{277}*\sqrt{45}cos(30.7)[/tex] gives you a dot product of 96

Answer:

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

The height of the blimp above the ground is h = 153.884 yard

No,  the fans will not be able to read the advertisement.

The exact angle if the blimp is at 150 feet is 45.74°

Step-by-step explanation:

From the summary of the information given :

The angle of elevation from a point directly under the goal post is 72° and the blimp will be directly above the 50 yard line.

That statement above being illustrated in the attached diagram below for better understanding.

a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line?

The trigonometric ratio that can be used to calculate how high the blimp will be above the 50 yard line is :

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

b. How high above the ground is the blimp?

Using the above derived trigonometric ratio,

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

[tex]tan \ 72^0 = \dfrac{h}{50}[/tex]

[tex]h =tan \ 72^0 \times {50}[/tex]

[tex]h =3.07768 \times {50}[/tex]

h = 153.884 yard

The height of the blimp above the ground is h = 153.884 yard

c. In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet.

Will the fans be able to read the advertisement?

No,  the fans will not be able to read the advertisement.

This is  because, 153.884 yard to feet

=  153.884 × 3

= 461.652 feet which is more than the maximum given 150 feet.

If not, what possible angle of elevation could we use?

The possible angle of elevation can be determined by taking the tangent of the trigonometric ratio.

SO

tan θ = [tex]\dfrac{h}{150}[/tex]

tan θ = [tex]\dfrac{153.884}{150 \ feet}[/tex]

tan θ =  1.026

θ = tan ⁻¹ (1.026)

θ = 45.74°

d. What is the exact angle if the blimp is at 150 feet?

The exact angle if the blimp is at 150 feet is 45.74°

Answer:

125

Step-by-step explanation:

So you can see that the sequence is all of the perfect cubes so knowing that the next perfect cube we have to find is 5's perfect cube which is 125.

Answer:

192

Step-by-step explanation:

Answer:

0.73

Step-by-step explanation:

Data obtained from the question include the following:

Length (L) of square = x

Base (b) of triangle = (3x – 2)

Height (h) of triangle = (2x + 4)

Area of square = L²

Area of square = x²

Area of triangle = ½bh

Area of triangle = ½(3x – 2) (2x + 4)

Expand

½ [3x(2x + 4) –2(2x + 4)]

½[6x² + 12x – 4x – 8]

½[6x² + 8x – 8]

3x² + 4x – 4

Area of triangle = 3x² + 4x – 4

Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:

Area of triangle = area of square

Area of triangle = 3x² + 4x – 4

Area of square = x²

Area of triangle = area of square

3x² + 4x – 4 = x²

Rearrange

3x² – x² + 4x – 4 = 0

2x² + 4x – 4 = 0

Solving by formula method

a = 2, b = 4, c = –4

x = – b ± √(b² – 4ac) / 2a

x = – 4 ± √(4² – 4×2×–4) / 2×2

x = – 4 ± √(16 + 32) / 4

x = – 4 ± √(48) / 4

x = (– 4 ± 6.93)4

x = (– 4 + 6.93)4 or (– 4 – 6.93)4

x = 0.73 or –2.73

Since the measurement can not be negative, the value of x is 0.73.

Answer:

Option D. 9

Step-by-step explanation:

There are two ways to obtain the answer to the question.

Method 1:

Let 2x + 1 = 0

Making x the subject, we have

2x + 1 = 0

Collect like terms

2x = –1

Divide both side by 2

x = –1/2

Now, put the value of x into the expression 4x³ – 6x² – 8x + 7, we have:

4x³ – 6x² – 8x + 7

x = –1/2

4(–1/2)³ – 6(–1/2)² – 8(–1/2) + 7

4(–1/8) – 6(1/4) – 8(–1/2) + 7

–1/2 – 3/2 + 4 +7

– 4/2 + 4 + 7

– 2 + 4 + 7

= 9

Method 2:

Divide 4x³ – 6x² – 8x + 7 by 2x + 1

Please see attached photo for explanation.

Answer:

Her Verticle ramp support was 5.5 ft tall.

Step-by-step explanation:

In this type of question, you would need to use the saying "soh cah toa".

Soh Cah Toa is a saying that people use for Sin, Cosine, and tagent. Each of those mean

Sine: opposite/hypotenuse Cosine: Adjacent/hypotenuse and Tagent: Opposite/Adjacent

In this specific question to figure out how tall or high her support is or needs to be have to 20 degree  angle off the ground, you will need to use Sin which is opposite over Hypotenuse or x/16

To find the answer in your calculator you would do:

Sin(20)=x/16

First thing you do is the get the x on one side by itself so you would multiply 16 on both sides giving you:

16 × Sin(20)= x

You would then follow to put Sin(20) in your calculator giving you 0.34202014332

After that you multiply that number by 16

5.47232229321

Rounding to the nearest tenth you get answer:

5.5

Answer:1 3/7

Step-by-step explanation:When you multiply the nominator and 4you get 20.So it would 20/14 but if you find the simplest form of fraction you would get 1 3/7

Answer:

$430

Step-by-step explanation:

Let the weekly income be x

Money spent on food= $86

% of weekly income spent on food = 20

20% of weekly income in terms = 20/100 * x = x/5

This, income is equal to $86 as given

thus,

x/5 = 86

x = 86*5 = 430

Thus, weekly income is $430.

Answer:

X Intercept (-2,0), (-3,0) and Standard form y = -4x^2 - 20x - 24

Step-by-step explanation:

To write a polynomial in standard form, simplify, and then arrange the terms in descending order.

y = ax^2 + bx + c

y = (−4x−8) (x+3)

Expand (−4x−8) (x+3) using the FOIL Method

y = −4x ⋅ x − 4x ⋅ 3 − 8x−8 ⋅ 3

Simplify and combine like terms.

y = −4x^2 − 20x − 24

Hope this can help

Answer:  13.5 units³

Step-by-step explanation:

[tex]\dfrac{5}{2}\times \dfrac{27}{5}\quad =\dfrac{27}{2}\quad =\large\boxed{13.5\ units^3}[/tex]

Answer:

The angle is determined by dividing 360 by the number of vertexes that it took to complete the circle. The tangent of the 100th triangle would be the same respectively.

Step-by-step explanation:

I remember learning this in kindergarten.

Answer:

B and D

Step-by-step explanation:

I think this is the answer

Answer:

73.2

Step-by-step explanation:

you can find the answer using trigonometry relationship

sin31°=41/x

x=41/sin31°. sin31° is approximately equal to 0.56

x=41/0.56

x=73.2

Answer:

13

Step-by-step explanation:

Put -1 and 12 in the absolute value form and add them together. You'll get 13.

Number of  units separate the points is 13 units.

Given that;

Coordinate of first point = (5 , -1)

Coordinate of second point = (5 , 12)

Find:

Number of  units separate the points

Computation:

Number of  units separate the points = √(x1 - x2)² + (y1 - y2)²

Number of  units separate the points = √(5 - 5)² + (-1 - 12)²

Number of  units separate the points = √(-13)²

Number of  units separate the points = 13 units

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Answer:

a. 5p+3

b. 26p + 6

Step-by-step explanation:

a.

Area = length × width

40p² + 24p = length × 8p

Factorise out 8p from both sides

8p(5p + 3) = length × 8p

Divide both sides by 8p

5p + 3 = length

b.

Perimeter = 2(length + width)

"" = 2(5p+3 + 8p)

"" = 2(13p + 3)

"" = 26p + 6

Answer: C

1/4

Step-by-step explanation:

Given a graph for the transformation of f(x) in the format g(x) = f(kx),

This means that for every value of x, f(x) will take the value it would have had at kx, that is, the graph of f(x) is stretched by a factor of 1/k in the direction of positive x-direction.

Therefore, the value of k will be 1/4.

Answer:

k=4

Step-by-step explanation:

Answer:

Approximately 66.4 Meters

Step-by-step explanation:

So we have a rectangle with a width of 18.8 meters and a diagonal with 23.7 meters. To find the perimeter, we need to find the length first. Since a rectangle has four right angles, we can use the Pythagorean Theorem, where the diagonal is the hypotenuse.

[tex]a^2+b^2=c^2[/tex]

Plug in 18.8 for either a or b. Plug in the diagonal 23.7 for c.

[tex](18.8)^2+b^2=23.7^2\\b^2=23.7^2-18.8^2\\b=\sqrt{23.7^2-18.8^2} \\b\approx14.4 \text{ meters}[/tex]

Therefore, the length is 14.4 meters. Now, find the perimeter:

[tex]P=2l+2w\\P=2(14.4)+2(18.8)\\P=66.4\text{ meters}[/tex]

Answer:

f(-1) = 12

Step-by-step explanation:

Using the graph for f(x)  let x=-1

Find the y value when x= -1

f(-1) = 12

Answer:

x=11 y=6

Step-by-step explanation:

making x the subject in the first equation we get

x=y+5 put that in the second equation we also get

2(y+5)-3y=4

2y+10-3y=4

-y=4-10

-y=-6

y=6 use that to also find x from the equation x=y+5 we get

x=6+5

x=11

therefore x=11 y=6

Answer:

Step-by-step explanation:

(0+2)/(0-10)= 2/-10 = -1/5

y - 0 = -1/5(x - 0)

y = -1/5x

solution is D

Answer:

Step-by-step explanation:

Given the expressions f(x) =  |x| + 9 and g(x) = –6, sine f(x) contains the absolute value of a variable x, this absolute value can be negative and positive. Therefore f(x) can be expressed in two forms as shown;

f(x) = x+9 and f(x) = -x+9

If f(x) = x+ 9 and g(x) =  -6

(f + g)(x) = f(x)+ g(x)

(f + g)(x) = x+9+(-6)

(f + g)(x) = x+9-6

(f + g)(x) = x+3

Similarly, if f(x) = -x+ 9 and g(x) =  -6

(f + g)(x) = f(x)+ g(x)

(f + g)(x) = -x+9+(-6)

(f + g)(x) = -x+9-6

(f + g)(x) = -x+3

(f + g)(x) = 3-x

In  both expresson, we have bith x to be positive and negative, hence we can write the value of resulting x as an absolute value as shown;

(f + g)(x) = |x|+3

This shows that (f + g)(x)≥3 for all values of x

Answer: x = -2 , y = 3

Step-by-step explanation:

4x-y=-11

2x+3y=5

Solve 4x-y=-11 for y

Add -4x to both sides

4x-y+-4x=-11+-4x

-y=-4x-11

Divide both sides by -1

-y/-1=-4x-11/-1

y=4x+11

Substitute 4x+11 for y in 2x +3y=5

2x+3y=5

2x+3(4x+11)=5

Simplify both sides of the equation

14x+33=5

Add -33 to both sides

14x+33+-33=5+-33

14x=-28

Divide both sides by 14

14x/14=-28/14

x=-2

Substitute -2 for x in y= 4x+11

y=4x+11

y=(4)(-2)+11

Simplify both sides of the equation

y=3

Answer:

[tex]44^\circ[/tex]

Step-by-step explanation:

The angle measuring [tex]y^\circ[/tex] is formed by two secants intersecting at an exterior point.

The measure of that angle is half the difference between the big intercepted arc and the little intercepted arc.

y = 1/2 (m arc FKB - m arc CGJ)

Plug in the values you know.

56 = 1/2 (156 - m arc CGJ)

Multiply both sides by 2 to clear the fraction.

112 = 156 - m arc CGJ

Subtract 156.

-44 = - m arc CGJ

44 = m arc CGJ

The measure of the little intercepted arc is [tex]44^\circ[/tex].