EXPLANATION NEEDED:

In right triangle ABC, ∠ B is a right angle and sin ∠ C = x. cos ∠ A =

a. √x² - 1
b. √1 - x²
c. x
d. √x² + 1
e. x²

The value of (f - g)(x) is x² + 4x + 3 if f(x) =  2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) =  2x² - 5

g(x) = x² - 4x - 8

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

= (2x² - 5) - (x² - 4x - 8)

= 2x² - 5 - x² + 4x + 8

= x² + 4x + 3

(f - g)(x) = x² + 4x + 3

Thus, the value of (f - g)(x) is x² + 4x + 3 if f(x) =  2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.

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Answer:

A

Step-by-step explanation:

Put your information in the the point slope formula y-y1=m(x-x1)

This will give you y+5=3(x+3)

simplify

y+5=3x+9

Now subtract 5

y=3x+4

Temos ai um retangulo. Para usa area, basta multiplicar a medidas - que no caso sao 2,3m e 1,46m

Area Comodo = 2,3 x 1,46

Answer:

1/4

Step-by-step explanation:

The slope of a graph is always the rate of change for every value of x, in this case, days. Since she is adding 1/4 of a mile to her run each day, this means that the slope of this linear relationship is 1/4.

She increases a full mile in 4 days, just a little note.

Answer:

z = 8.5

Step-by-step explanation:

Let O be the center of the circle, and A, B, C are three points on the circle.

Draw OA and OC are shown in the figure. To make the central angle.

In the figure the measure of arc AC is 118 degrees. measure of central angle and subtrahend arc is same. So, central angle is

[tex]\angle AOC=118^{\circ}[/tex]

Subtended angle on arc AC is  

[tex]\angle ABC=(6z+8)^{\circ}[/tex]

According to central angle theorem of circle, central angle is twice of angle subtended by the arc.

[tex]\angle AOC=2\times \angle ABC[/tex]

[tex]118^{\circ}=2\times (6z+8)^{\circ}[/tex]

[tex]118=12z+16[/tex]

[tex]118-16=12z[/tex]

[tex]102=12z[/tex]

[tex]\dfrac{102}{12}=z[/tex]

[tex]8.5=z[/tex]

Therefore, the value of z is 8.5.

Answer:

6 papers

Step-by-step explanation:

5 minutes = 5 * 60 = 300 seconds

He needs to save 30 seconds

300 - 30 = 270 seconds

270 seconds / 42.5 seconds per paper

6.352941176 papers

Rounding down since he want to completely grade the paper

6 papers

Answer:

B

Step-by-step explanation:

The inscribed angle's arc measures 36°, and central angle's arc measures 72°.

Answer:

the answer is B

Step-by-step explanation:

Answer:

[tex]x = 4 - \frac{4}{3}y[/tex]

Step-by-step explanation:

If we have the equation [tex]3x = 12-4y[/tex], we can simplify this equation down.

Divide both sides by 3:

[tex]x = 4 - \frac{4}{3}y[/tex] .

Hope this helped!

Answer:

X = 4 minus four-thirds y

Step-by-step explanation:

Well to solve for x we single it out.

3x = 12 - 4y

Divide 3 by everything,

x = 4 - 4/3y

Thus,

X = 4 minus four-thirds y.

I do hope this helps :)

Answer:

1/3

Step-by-step explanation:

So there are 12 natural numbers in total: (113 - 102) + 1

Then there are the prime numbers: 103, 107, 109, and 113

so there are 4/12 prime numbers or 1/3

Answer:

1/3

Step-by-step explanation:

We can list all the numbers from 102 to 113:

To check if each number is prime, we simply have to check divisibility by 2, 3, 5, and 7 — if any of these numbers are not divisible by those, it will have no factors lower than its square root, and will therefore be prime.

102 - composite, multiple of 2

103 - prime

104 - composite, multiple of 2

105 - composite, multiple of 5

106 - composite, multiple of 2

107 - prime

108 - composite, multiple of 2

109 - prime

110 - composite, multiple of 2

111 - composite, multiple of 3

112 - composite, multiple of

113 - prime

4/12 or 1/3 of the numbers in this list are prime.

Answer:

They using an Algebra calculator on your chromebook :)

Answer:

Slope: -3

y-intercept: 5

  x | y

  0 | 5

5/3 | 0

Answer:

1) $10b

2) 20

3) $5a

Hi,

[tex]y=5x^{2} +12x-2\\y=x(5x+12)-\frac{46}{5} \\y=5(x+\frac{6}{5} )^{2}-\frac{46}{5} \\[/tex]

Have a good day.

Answer:

Please see table completed attached

Yes, there are several patterns, since these two trigonometric functions are periodic with same periodicity, and also satisfy the Pythagorean identity for the same angle.

Step-by-step explanation:

Notice that we are asked about a table of trigonometric functions for the so called "special angles" which render values associated with half of the square root of a counting number between 0 and 4:

[tex]\frac{\sqrt{0} }{2}=0 \\\frac{\sqrt{1} }{2}=\frac{1}{2} \\\frac{\sqrt{2} }{2}\\ \frac{\sqrt{3} }{2}\\ \frac{\sqrt{4} }{2}=\frac{2}{2} =1[/tex]

These two trigonometric functions also satisfy the Pythagorean identity for any angle [tex]\theta[/tex] in the unit circle, so the equality to one will always be true:

[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]

They are also periodic functions of period [tex]2\,\pi[/tex], so their resulting values will be repeated with that periodicity.

Answer:

Range { 1000,1100,1200,1300,1400,1500,1600}

Step-by-step explanation:

The range of the function is the output, so it would be the  values of the pay per month

Range { 1000,1100,1200,1300,1400,1500,1600}

Answer:c

Step-by-step explanation:

Answer:

You need to give more information.

Step-by-step explanation:

Answer: 40x

First, let's find f(2x)

[tex]f(2x)=4(2x)=8x[/tex]

Using this, let's find g(f(2x)):

[tex]g(f(2x))=g(8x)=5(8x)=40x[/tex]

That's the answer. Let me know if you need any clarifications, thanks!

Answer:

80x²

Step-by-step explanation:

f(x) = 4x², g(x) = 5x

f(2x) = 4(2x)² = 16x²

g(f(2x)) = 5(16x²) = 80x²

Answer:

Option A is the correct option.

Step-by-step explanation:

As the graph of ( f + g ) ( x ) is a line. So, ( f + g ) ( x ) is linear which means x² of f ( x ) and x² of g ( x ) get cancelled on adding . They must be equal and opposite in sign.

So, Option A is correct.

Hope this helps..

Best regards!!

Answer: Intercept (b) = - 2.2567

Step-by-step explanation:

(−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6)

Using the online regression calculator :

ŷ = -0.60205X - 2.2567

y is the predictor variable

X - the independent variable

0.60205 = slope or gradient

- 2.2567 = intercept (b) where the line best fit cross the y-axis.

The linear regression line is made using the least-squares method. The value of b is -2.2567.

Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least-squares method.

Given the points of the data(−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6).

Now, Since the question states about using the technology, therefore, if we use the online regression calculator:

ŷ = -0.60205X - 2.2567

y is the predictor variable

X - the independent variable

-0.60205 is the value of m which is the slope or gradient of the regression line, while -2.2567 is the value of the intercept of the regression line.

Hence, the value of b is -2.2567.

Learn more About Linear Regression Line:

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Answer:

The correct answer is D.

Step-by-step explanation:

A function is when an input value has only one output value.

It cannot be A, because -7 produces both 2 and -4.

It cannot be B, because -9 produces both 9 and 7.

It cannot be C, because -4 produces both -6 and -7.

Therefore, it has to be D.

Answer:

C

Step-by-step explanation:

On the horizontal axis, as the discount (%) increases by 1(%), on the vertical axis; the sales increase (%) increases by 3(%).

When the discount is 10%, the sales increase is 32%.

When the discount is 20%, the sales increase is 62%.

20 - 10 = 10

10 × 3 = 30

32 + 30 = 62 (correct)

Answer:

57°

Step-by-step explanation:

∠LOM and ∠MON are complementary angles, so they add up to 90.

This means that:

3x-15 + 5x-23 = 90 =>

8x - 38 = 90 =>

x = 128/8 = 16

So m∠MON = 5*16 - 23 = 57°

Answer:

Step-by-step explanation:

(3x-15)=90

find x

x=35

input it into the equation

42+23 =m<mon

x=45 degrees

Answer:

The equation is true

Step-by-step explanation:

The best way to check if this equate is true is to convert the pi in radians to degree and actually evaluate the trigonometric terms.

Mathematically we know that pi = 180 degrees

So pi/8 = 22.5

and pi/4 = 180/4 = 45

So let’s make our check.

Insert pi = 22.5 and pi = 45

So we have;

tan 22/5 = √(1-cos45)/(1+cos45)

Now let’s evaluate this using a calculator.

tan 22/5 = 0.414213562373

The term in the root; 0.171572875254

The square root of this number is 0.414213562373

This is exactly as what is obtained with the tan 22.5

So we conclude that what we have is true

Answer:

0.0617

Step-by-step explanation:

so the formula is 1.96[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

P is the proportion (.45) and n is the sample size (250). Inserting these into the problem, we get 1.96[tex]\sqrt{\frac{.45(1-.45)}{250} }[/tex]. Solving this out, you should solve the inside of the square root to get .00099. Take the square root of this, and multiply by 1.96 to get your answer!

This method applies to any problems with the same basic format. Good luck!

Answer: x=10

Step-by-step explanation:

We can use the pythagorean theorem here: a^2 + b^2 = c^2, where c is the hypotenuse.

The values for c and one of the legs are already given, so we can plug them into the equation to find the length of the other leg x:

(square root of 200)^2 + x^2 = (square root of 300)^2

200 + x^2 = 300

x^2 = 100

x = 10

Answer:

Step-by-step explanation

square root  300 square - square root 200 square = x square

300 - 200 = x square

100 = x square

square root 100 = x

10= x

Answer:

[tex]c = \frac{2}{5} t[/tex], if the number of texts is 4, then the cost is $1.60.

Step-by-step explanation:

If 2 texts costs $5, then each text costs $[tex]\frac{2}{5}[/tex].

So, we can setup the equation to  [tex]c = \frac{2}{5} t[/tex].

If the number of texts is 4, we can substitute that into our equation.

[tex]c = \frac{2}{5} \cdot 4[/tex]

[tex]c = \frac{8}{5}[/tex]

[tex]c = 1.60[/tex]

Hope this helped!

Answer:

[tex]n^6[/tex].

Step-by-step explanation:

[tex]n^4 * \frac{n^7}{n^5}[/tex]

= [tex]n^4 * n^{7 - 5}[/tex]

= [tex]n^4 * n^2[/tex]

= [tex]n^{4 + 2}[/tex]

= [tex]n^6[/tex].

Hope this helps!

Answer:  (0, 0)

Step-by-step explanation:

ax = by         ay = 6x

[tex]\dfrac{ax}{b}=y\qquad \quad y=\dfrac{6x}{a}[/tex]

Use substitution:

[tex]\dfrac{ax}{b}=\dfrac{6x}{a}\\\\\\\text{Cross Multiply:}\\a^2x=6bx\\\\\\\text{Solve for x:}\\a^2x-6bx=0\\x(a^2-6b)=0\\x=\dfrac{0}{a^2-6b}\\\large\boxed{x=0}[/tex]

Substitute x = 0 to solve for y:

[tex]\dfrac{ax}{b}=y \\\\\dfrac{a(0)}{b}=y\\\\\large\boxed{0=y}[/tex]

Answer:

- 1

Step-by-step explanation:

Given

( [tex]\frac{1+i}{1-i}[/tex] )²

= [tex]\frac{(1+i)^2}{(1-i)^2}[/tex]

= [tex]\frac{(1+i)(1+i)}{(1-i)(1-i)}[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{1+2i+i^2}{1-2i+i^2}[/tex] ← simplify using i² = - 1

= [tex]\frac{1+2i-1}{1-2i-1}[/tex]

= [tex]\frac{2i}{-2i}[/tex]

= - 1