Let f(x) = -4x + 7 and g(x) = 2x - 6. Find (gof) (1)

Answer:

A

Step-by-step explanation:

Given

cx - 4 = 7 ( isolate the term in x by adding 4 to both sides )

cx = 11 ( divide both sides by c )

x = [tex]\frac{11}{c}[/tex] → A

Answer:

P(A or B) = 0.65

Step-by-step explanation:

Given that P(A) = 0.60, P(B) = 0.20, and P(A and B) = 0.15

We have to find P(A or B)

Apply the formula:

P(A or B) = P(A)+P(B)- P(A and B)

Now substitute the values in the formula:

P(A or B) = 0.60 + 0.20 - 0.15

P(A or B) = 0.80 - 0.15

P(A or B) = 0.65

Thus P(A or B) = 0.65  ....

Answer:

0.65 ~apex

Step-by-step explanation:

Answer:

r = 3

Step-by-step explanation:

x^2 + 6x + y^2 - 8y = - 16

Take half the linear term and square it.

x^2 + 6x + (3)^2 + y^2 - 8y + (-4)^2 = - 16

Add the squared amounts to the right.

x^2 + 6x + 9 + y^2 - 8y + 16 = - 16 + 9 + 16  

Combine on the right.

x^2 + 6x + 9 + y^2 - 8y + 16 = 9

Represent the 2 quadratics as perfect squares.

(x + 3)^2 + y - 4)^2 = 9

The radius is the square root of 9 which is 3

Answer:

radius=3

Step-by-step explanation:

Given:

x^2 +6x +y^2 - 8y=-16

completing the squares

: x^2 +6x +9 = (x+3)^2

:y^2-8y+16 = (y-4)^2

(x+3)^2 + (y-4)^2 -9-16=-16

(x+3)^2 + (y-4)^2=-16+9+16

(x+3)^2 + (y-4)^2=9

Now comparing with standard equation of circle i.e. (x-h)^2 + (y-k)^2=r^2, we get

origin(h,k)= (-3,4)

r=3 !

Answer:

No intersection

Zero intersections

Step-by-step explanation:

Let's determine the slope first.

If the slopes are different, then there is one solution.

If the slopes are the same, there are 2 possibilities.  The first possibility is that there is no solutions because the lines are parallel.  The second possibility is that there is infinitely many solutions because they are the same line. When I say solution, I'm also referring to intersection.

So I'm going to find the slope by lining up the points and subtracting vertically then putting 2nd difference over 1st difference.

Let's do that for line A:

 (  2  ,   8)

- (  -2 , -4)

---------------

  4        12

So the slope is 12/4 or just 3.

Let's do this for line B now:

  (  4  ,  10)

-  ( -3  ,  -11)

-------------------

    7     21

So the slope is 21/7 or just 3.

So we have more work now. The lines either are the same or parallel.

We are going to use this to determine if they same or parallel, we are going to find the slope-intercept form of the equation for both lines.

That is y=mx+b where m is slope and b is y-intercept.

Let's look at line A:

y=mx+b with m=3 and a point (x,y)=(2,8)

8=3(2)+b

8=6+b

2=b

So the line is y=3x+2

Let's look at line B.

y=mx+b with m=3 and a point (x,y)=(4,10)

10=3(4)+b

10=12+b

-2=b

The equation of this line is y=3x-2

So the lines y=3x+2 and y=3x-2 are not the same, they are parallel which means they intersect zero times.

Answer:

Zero

Step-by-step explanation:

How many points of intersection are there between line A and line B if they contain the points listed?

Line A: (2, 8) and (–2, –4)

Line B: (4, 10) and (–3, –11)

Answer:

(−29, 7)  CORRECT

(19, 7)  CORRECT

(−21, 7)

(13, 7)

(−5, −17)

(−5, 31)

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

Just got it right

Answer:

(D) 4m/2

Step-by-step explanation:

took test

Answer:

8x + 24

Step-by-step explanation:

Given photograph length L = 7" and width W = 5"

Also that the frame is 2x" longer and 2x" wider

hence,

new length = ( 7 + 2x) inches

new width= ( 5 + 2x) inches

Hence perimeter of frame,

= 2 x ( new length + new width)

= 2 [( 7 + 2x)  + ( 5 + 2x)]

= 2 (4x + 12)

= 8x + 24 (Answer)

Answer:

V = 1017.88

Step-by-step explanation:

The volume of a right circular cylinder with a radius of 6 and a height of 9 is 1017.88.

V=πr2h=π·62·9≈1017.87602

The sample space encompasses all of the potential outcomes of an event.  The correct option is D, 5H.

The sample space encompasses all of the potential outcomes of an event. Sometimes determining the sample space is simple. For example, if you roll a die, six different outcomes are possible. You may get a 1, 2, 3, 4, 5, or 6 on the dice.

Since the sample space for rolling dice is 1, 2,3, 4, 5, and 6. While the sample space for tossing coins is H and T. Thus, the sample space for first rolling a die and then tossing a coin is,

As it can be seen that the only option that is in the sample space is 5H.

The correct option is 5H.

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Answer:

4 x + 5 = 2 x + 2 x + 5

Step-by-step explanation:

If we simplify the following equation it will be 4 x + 5 = 4 x + 5. This equation has infinitely many solutions because every value for x we substitute in, it will be the same on both sides, for example

Substitute x = 7 into 4 x + 5 = 4 x + 5

4 × ( 7 ) + 5 = 4 × ( 7 ) + 5

28 + 5 = 28 + 5

33 = 33

Every x value that we substitute in will result in the equation having the same result on both sides

Answer:

Here's what I get    

Step-by-step explanation:

∆PQR is a right triangle.

PR² = PQ² + QR² = 48² + 64² = 2304 + 4096 = 6400

PR = √6400 = 80  

PQ:QR:PR = 48:64:80 = 3:4:5

We can consider ∆PQR as a 3:4:5 triangle.

[tex]\sin \theta = \dfrac{4}{5} \\\\\cos \theta = \dfrac{3}{5}\\\\\tan \theta = \dfrac{4}{3}\\\\\cot \theta = \dfrac{3}{4} \\\\\csc \theta = \dfrac{5}{4}\\\\\sec \theta = \dfrac{5}{3}[/tex]

Answer:

The formula used for Pythagoras Theorem.

(Hypotenuse)² = (Base)² + (Perpendicular)²

We have

PQ = 48, QR = 64 and PR = ?

⇒ (PR)² = (PQ)² + (QR)²

⇒ (PR)² = (48)² + (64)²

⇒ (PR)² = 2304 - 4096 = 64 00

⇒ PR = 80

The six trigonometric functions we have are:

The equation 11r + 4 = 55 is equivalent to the equation 11r = 55 – 4. Then the correct option is B.

The equivalent is the expressions that are in different forms but are equal to the same value.

The equation is given below.

11r + 4 = 55

Then the equation can be written as

11r = 55 – 4

Then the correct option is B.

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Answer:

are perpendicular

Step-by-step explanation:

Two lines that intersect and make a right angles are by definition perpendicular

Answer:

C) are perpendicular

Step-by-step explanation:

Perpendicular: a straight line at an angle of 90° to a given line, plane, or surface.

Answer:

The correct option is 24 square units.

Step-by-step explanation:

Given data:

Base= 4units

height = 6 units

Area = ?

Now substitute the values in the formula:

Area= base * height

Area= 4*6

Area= 24 square units

Thus the correct option is 24 square units....

Answer:

I am a little late but its 24

Step-by-step explanation:

4*6 = 24

Answer:

D

Step-by-step explanation:

The area (A) of a triangle is calculated using

A = 0.5 absinC

Here a = 13 and ∠C = 65°, hence

A = 0.5 × 13 × b × sin65° = 95, that is

6.5b × sin65° = 95 ( divide both sides by 6.5sin65° )

b = [tex]\frac{95}{6.5sin65}[/tex] ≈ 16 ft ( to the nearest foot )

Given the area of 95 square feet and side AC of 13 feet, the value of side b, opposite the 65° angle, is 7 feet rounded to the nearest foot. Thus, the correct option is A.

From the image, we see that triangle ABC is a right triangle with a right angle at C. We are given that the area of the triangle is 95 square feet and that the length of side AC is 13 feet. We want to find the length of side b, which is opposite the 65° angle.

To find the area of a right triangle, we use the formula:

Area = (1/2) * base * height

In this case, the base is side b and the height is side AC. We are given that the area is 95 square feet and that AC is 13 feet, so we can plug these values into the formula to solve for b:

95 = (1/2) * b * 13

b = 95 * 2 / 13

b = 7.3 feet

Since we are asked to round the answer to the nearest foot, we round 7.3 feet up to 7 feet.

Therefore, the value of b, to the nearest foot, is 7 ft.

Answer:

D: x = -2, x = 5

Step-by-step explanation:

To solve for a variable, you first have to isolate it on one side of the equation. Remember that whatever you do to one side, you also have to do to the other.

2x² + 2x + 12 = 3x² - x + 2   Subtract 2x² from both sides

2x + 12 = x² - x + 2   Subtract 2x from both sides

12 = x² - 3x + 2   Subtract 12 from both sides

0 = x² - 3x - 10   Using factoring, split this into two expressions

0 = (x - 5) (x + 2)   Set each expression equal to 0

x - 5 = 0 and x + 2 = 0   Solve each expression

x = 5 and x = -2

Now, you can plug in both answers to check your work

2x² + 2x + 12 = 3x² - x + 2   Plug in 5

2(5)² + 2(5) + 12 = 3(5)² - 5 + 2   Simplify

2(25) + 10 + 12 = 3(25) - 5 + 2   Simplify some more

50 + 10 + 12 = 75 - 5 + 2   Simplify one more time

72 = 72   It works!

2x² + 2x + 12 = 3x² - x + 2   Plug in -2

2(-2)² +2(-2) + 12 = 3(-2)² -(-2) + 2   Simplify

2(4) - 4 + 12 = 3(4) + 2 + 2   Simplify again

8 - 4 + 12 = 12 + 2 + 2   Simplify one more time

16 = 16   It also works!

In the polygon QRST, the angle that is formed between sides SR and SQ is known as the angle RSQ.

In the polygon QRST, the angle included between sides SR and SQ is named as the angle RSQ. In polygons, the included angle between two sides is the angle that both sides share. Here, sides SR and SQ share vertex S, so the included angle is at S, formed by extending from R through S to Q. Hence, we denote this angle as RSQ.

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Answer:

(see attached)

Step-by-step explanation:

Rearrange the equation in the form y (≥ or ≤) mx + c , so that you get:

y ≥ (-1/2)x - (9/20)

Graph this equation.

Test a random point on either side of the line to see which side is valid (and shade)

we try the origin (0,0)

This makes the equation :

(0) ≥ (-1/2)(0) - (9/20)

0 ≥ - (9/20)  (this inequality is valid, so that means the point we picked (0,0) falls on the valid side. Shade that side. (in this case the region above the line)

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

If the slope m = 0, then an equation in form y = 0x + b → y = b it's a horizontal line with a slope equal to 0.

Answer:

y = [tex]\frac{1}{4}[/tex] x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 3 ← is in slope- intercept form

with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (8, 1 ) into the partial equation

1 = 2 + c ⇒ c = 1 - 2 = - 1

y = [tex]\frac{1}{4}[/tex] x - 1 ← equation of perpendicular line

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have:

[tex]leg=7\ mm,\ leg=a,\ hypotenuse=\sqrt{85}\ mm[/tex]

Substiute:

[tex]7^2+a^2=(\sqrt{85})^2[/tex]       use (√a)² = a for a ≥ 0

[tex]49+a^2=85[/tex]           subtract 49 from both sides

[tex]a^2=36\to a=\sqrt{36}\\\\a=6\ mm[/tex]

Answer:

A. 6mm

Step-by-step explanation:

Using the Pythagorean Theorem, which is a^2 + b^2 = c^2, the c is always the hypotenuse so the problem would be: a^2 + 7^2 = square root of 85 squared. square root of 85 squared is just 85. 7^2 is 49. 85 - 49=36. square root of 36 is 6... If you liked this answer then mark me as brainliest.

Answer:

Step-by-step explanation:

First, we know that the sin function is odd which means:

sin(-x) = -sin(x).

Secondly evaluating an inverse trigonometric function with a normal trigonometric function as the argument can be rewritten as an algebraic expression.

Let [tex]t = \sin(-\frac{11\pi}{4}) = - \sin(\frac{11\pi}{4})[/tex]

We know the certain identity.

[tex]\sin(\theta) = \sin(2\pi + \theta)[/tex]

We use it to evaluate sin(11 pi / 4).

[tex]\sin(\frac{11 \pi}{4}) = \sin({\frac{8\pi}{4} + \frac{3 \pi}{4}}) = \sin(2\pi + \frac{3 \pi}{4}) = \sin(\frac{3\pi}{4})[/tex]

Another helping identity is the following:

[tex]\sin(\theta) = \sin(\pi - \theta)[/tex]

[tex]\sin(\frac{3\pi}{4}) = \sin(\pi - \frac{3\pi}{4}) = \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}[/tex]

But let's not forget that t = -sin(11 pi/4) = - sqrt(2) / 2

Now we end up with the following equation.

[tex]\cos^{-1}(-\frac{\sqrt{2}}{2}) = x\\\cos(x) = -\frac{\sqrt{2}}{2} => x = \frac{3\pi}{4}[/tex]

Answer:

0.095

Step-by-step explanation:

the probability of getting the word riddle is 0.095.

I'm sorry if the answer is wrong.... I'm not that good at maths either but I wanted to help :)

Answer:

D.

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

The slope of y=4x+2 is 4.

Let's look at the choices:

A) The slope of y=-2x+3 is -2.

B) The slope of y=2x-3 is 2.

C) The slope of y=-4x+2 is -4.

D) The slope of y=4x-2 is 4.

So we are looking for a line that has the same slope as the given line which is 4.

The answer is D.

Answer:

D.

Y = mx + b is the equation for a straight line. "B" is called the y intercept. "M" is the value of the slope of the line. "X" is the value where the line intercepts the x axis.

so the reason the awnser is D is because the M=4 in both equations, meaning that they have the same slope

Answer:

4

Step-by-step explanation:

The equation is in the form

y= mx+b

where m is the slope and b is the y intercept

y = -3x +4

-3 is the slope and 4 is the y intercept

Answer:

y intercept is 4

Step-by-step explanation:

When you are finding the Y intercept, you need to pretend that x=0. Cover up the x and you would find the y-intercept which is 4

if it is wrong, let me know and I will fix it

hope this helps!

Answer:

the line is horizontal

Step-by-step explanation:

Note the y- coordinates of the 2 points the line passes through are equal.

This indicates that the line is horizontal and parallel to the x- axis

The equation of a horizontal line is y = c

where c is the value of the y- coordinates the line passes through.

Here the y- coordinates are 30, hence

Equation of horizontal line is y = 30

Answer:

It has a slope of zero because the change in the y-values is 0.

Step-by-step explanation:

Answer:

$8.40

Step-by-step explanation:

You multiply $12 by 0.7 and get $8.40

Answer:

$8.40

Step-by-step explanation:

Since 1 Liter costs $12, you can multiply 12 by 0.7 (L) to get the answer.

Answer is 8.4, so it's $8.40

Answer:

no

Step-by-step explanation:

it asks if the given value is a solution of the inequality, but I'm pretty sure it's not

Answer:

5/32.

Step-by-step explanation:

                     1

                  1      1

              1       2      1

           1       3      3       1

      1       4       6      4       1

  1      5      10      10     5       1

As there are 5 lights we need the last row in the above Pascals triangle.

And  there is 1 red and 4 green  ( = 5) and it can happen in 5 ways, so that gives us the second term in the last row . The total  in that last row = 1+5+10+10+5+1 = 32.

so the probability is 5/32.

Answer:

B. 5 units

Step-by-step explanation:

[tex]\tt |AB|=\sqrt{(3-7)^2+(12-9)^2}=\sqrt{16+9}=\sqrt{25}=5 \ \ units[/tex]

The length of AB is 5 units.

Length is defined as the measurement or extent of something from end to end.

In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects.

Given that there are two points A = (7,9) and B = (3, 12),

So, we need to find the distance between them,

We know that the distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by,

D = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

D = [tex]\sqrt{(3-7)^2 + (9-12)^2}[/tex]

D = [tex]\sqrt{4^2+3^2}[/tex]

D = 5

Hence the length of AB is 5 units.

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