The functions q and r are defined as follows
g(x) = -2x-2
r(x) = x² – 2
Find the value of r(q(4)).
r(9 (4)) =

Answer: [tex]3\sqrt{13}[/tex]

Step-by-step explanation:

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

[tex]\sqrt{\left(-4-2\right)^2+\left(3-\left(-6\right)\right)^2}[/tex]

[tex]=3\sqrt{13}[/tex]

Answer:

El valor de x en esta ecuación es -1.

Step-by-step explanation:

4x - 8 + 9 - 6x = 3x + 6

En primer lugar, combinar términos similares en cada lado de la ecuación.

-2x + 1 = 3x + 6

A continuación, resta 3 veces en ambos lados de la ecuación.

-5x + 1 = 6

Ahora, resta 1 de ambos lados de la ecuación.

-5x = 5

Por último, divida por -5 en ambos lados de la ecuación.

x = -1

Answer:

953 902

Step-by-step explanation:

Answer:

953,902

Step-by-step explanation:

nine hundred =900

fifty-three=53

thousand=1000

nine hundred=900

two=2

Answer:

Approximately 439.6 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cone is the following:

[tex]A=\pi r^2+\pi r l[/tex]

Where, r is the radius and l is the slant height.

The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:

[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]

Answer:

292.77

Step-by-step explanation:

πr(r+[tex]\sqrt{h2+r2}[/tex])

13 x 2 = 26

7 x 2 = 14

26 + 14 = 40

[tex]\sqrt{40}[/tex] = 6.32

7 + 6.32 = 13.32

3.14 x 7 = 21.98

21.98 x 13.32 =

292.77

Answer:

[tex]\boxed{x = -5/21}[/tex]

Step-by-step explanation:

Hey there!

To simplify we need to combine like terms and use the communicative property,

34x + 6 = 1 + 13x

-13x to both sides

21x + 6 = 1

-6 to both sides

21x = -5

Divide both sides by 21

x = -5/21

Hope this helps :)

Answer: I'm guessing you need me to solve this for you.

I interpreted the equation this way: 34x + 6 = 1 + 13x

The solution is -5/21.

Step-by-step explanation:

34x + 6 = 1 + 13x

Step 1: Simplify both sides of the equation.

34x + 6 = 13x + 1

Step 2: Subtract 13x from both sides.

34x + 6 − 13x = 13x + 1 − 13x

21x + 6 = 1

Step 3: Subtract 6 from both sides.

21x + 6 − 6 = 1 − 6

21x = − 5

Step 4: Divide both sides by 21.

21x/21 = -5/21

x = -5/21

Hope this helped you!

Answer:

Step-by-step explanation:7.12 meters tall

Answer:

6 more

Step-by-step explanation:

Find 56% of 75 first

75/x=100/56

(75/x)*x=(100/56)*x      

75=1.78571428571*x      

(1.78571428571) to get x

75/1.78571428571=x

42=x

x=42

Then Find 80% of 60

60/x=100/80

(60/x)*x=(100/80)*x    

60=1.25*x      

60/1.25=x

48=x

x=48

Subtract 48 by 42

=6

Answer:Let x km/hr be the speed of train

Let y be the time taken by the train

Distance = speed x time

= x y

To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.

it clearly says that speed is increased by 6 and time is reduced by 4

So , (x + 6) (y - 4) = x y

x y - 4 x + 6 y - 24 = x y

x y - x y - 4 x + 6 y = 24

- 4 x + 6 y = 24

divided by (-2) => 2 x - 3 y = -12 ----- (1)

To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.

it clearly says that speed is reduced by 6 and time is increased by 6

So , (x - 6) (y + 6) = x y

x y + 6 x - 6 y - 36 = x y

x y - x y + 6 x - 6 y = 36

6 x - 6 y = 36

divided by (6) => x - y = 6 ----- (2)

2 x - 3 y = -12

(2) x 2 => 2 x - 2 y = 12

(-) (+) (-)

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

- y = -24

y = 24

Now we have to apply the value of y in the first equation to get value of x

Substitute y = 24 in the first equation we get

2 x - 3 (24) = -12

2 x - 72 = -12

2 x = -12 + 72

2 x = 60

x = 60/2

x = 30

Speed of the train = 30 km/hr

Time taken by the train = 24 hours

Distance covered by the train = x y = 30 x 24 = 720 km

Verification:

2 x – 3 y = -12

2(30) - 3(24) = -12

60 - 72 = -12

-12 = -12

Answer:

Step-by-step explanation:

1- on Monday the number of tricycles: 51/3=17 or 48/3=16 ( can't be 50)

2-the algebraic equation is : t=w/3 ( t=tricycle, w: wheels)

3-On Wednesday: (b for bicycle and t=tricycle)

 2b+3t=61

b+t=24 ⇒ b=24-t

solve by substitution:

2(24-t)+3t=61

48-2t+3t=61

t=61-48 ⇒ t=11

solve for b=24-t

b=24-11=13

4)t: tricycles, b for bicycles, n for tandem

t+b+n=144 ( each has one handlebar)⇒ t=144-b-n

2t+2b+4n ( for the pedales)

3t+2b+2n=320 ( for wheels)

solve by matrix or substitution: substitute t in the equations:

2t+2b+4n =378

3t+2b+2n=320

2(144-b-n)+2b+4n=378 ⇒ 288-2b-2n+2b+4n=378

3(144-b-n)+2b+2n=320 ⇒432-3b-3n+2b+2n=320

288-2b-2n+2b+4n=378

432-3b-3n+2b+2n=320

2n=378-288 ⇒ n=90/2=45

-b-n=320-432

-b-45=-112

-b=-112+45 ⇒ b=67

t=144-45-67= 32

Answer:

3t + 2x + b

Step-by-step explanation:

primera: t

segunda: t + x

tercera: t + x + b

suma: t + t + x + t + x + b = 3t + 2x + b

Answer:

x = -9, 1

Step-by-step explanation:

x (x + 8 )= 9

x^2 + 8x = 9

x^2 + 8x - 9 = 0

(x + 9)(x - 1) = 0

x = -9, 1

Hope this helps!

Answer:

x = 3 and x = 0

Step-by-step explanation:

A way to solve is simplifying the given equation:

X^2 + 8x = 9

So

x = 3 and x = 0

3^2 + 8(0) = 9

9 + 0 = 9

9 = 9

Answer:

New ratio ( white,blue and red) = 6:1:2

Step-by-step explanation:

Given:

Old ratio ( white,blue and red) = 8:3:2

Number of red balls = 10

Removed balls = 10 white , 10 blue

Find:

New ratio ( white,blue and red)

Computation:

Assume total number of balls = x

So,

Number of total balls = 2x / 13 = 10

Number of total balls = 65

Number of white balls = 40

Number of blue balls = 15

So,

Number of new white balls = 40 - 10 = 30

Number of new blue balls = 15 - 10 = 5

New ratio ( white,blue and red) = 30 : 5 : 10

New ratio ( white,blue and red) = 6:1:2

The new ratio of the white, blue, and red balls is 6:1:2.

The balls in the bag are in the ratio 8:3:2, therefore, the balls in the bags are,

white balls = 8x

blue balls = 3x

red balls = 2x =10,

Solving for red balls,

[tex]2x = 10\\x =\dfrac{10}{2}\\x = 5[/tex]

Now, substituting the value of x to know the numbers of balls are,

white balls = 8x

                  [tex]= 8 \times 5\\=40[/tex]

blue balls = 3x

                [tex]= 3\times 5\\=15[/tex]

After removing, 10 white balls and 10 blue balls from the bag,

red balls = 10 balls

white balls = 40 balls - 10 balls = 30 balls

blue balls = 15 balls - 10 balls = 5 balls

Dividing all the number of balls by 5,

red balls = 10 balls

[tex]\dfrac{10\ balls}{5} = 2[/tex]

white balls = 30 balls

[tex]\dfrac{30\ balls}{5} = 6[/tex]

blue balls = 5 balls

[tex]\dfrac{5\ balls}{5} = 1[/tex]

Hence, the new ratio of the white, blue, and red balls is 6:1:2.

Learn more about Ratio:

https://brainly.com/question/1504221

Answer:

D.0.25 inches per months

Step-by-step explanation:

The average rate or speed of human hair growth is about 0.25inches per month.

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          Hi my lil bunny!

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Let's solve your inequality step-by-step.

[tex]2<2x+4<10[/tex]

[tex]2 + -4 < 2x + 4 + -4 < 10 + -4[/tex] (Add -4 to all parts)

[tex]-2 < 2x < 6[/tex]

[tex]\frac{-2}{2} < \frac{2x}{2} < \frac{6}{2}[/tex] (Divide all parts by 2)

[tex]-1 < x < 3[/tex]

So the answer is : [tex]-1 < x < 3[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

[tex]\boxed{ x \geq 0}[/tex]

Step-by-step explanation:

Hey there!

Well we can cross out A. x is all real numbers because,

it’s not it only has all the positive numbers.

B. Is correct because the domain is every number greater than or equal to 0.

x ≥ 0

Hope this helps :)

The domain of the graph of a function is x ∈ [0, ∞) or x ≥ 0 option (B) x ≥ 0 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:

A function is shown in the graph which is plotted on the two-dimensional coordinate plane.

From the graph, we can see the graph of a function exists in the first quadrant only and it is increasing.

The interval in which the graph exists is [0, ∞)

or

The domain of a graph of a function is:

x ≥ 0

Thus, the domain of the graph of a function is x ∈ [0, ∞) or x ≥ 0 option (B) x ≥ 0 is correct.

Learn more about the function here:

brainly.com/question/5245372

#SPJ5

Answer:

V = 300[tex]\pi[/tex] in³ or 942.48 in³

Step-by-step explanation:

Use the cylinder volume formula, V = [tex]\pi[/tex]r²h, where r is the radius and h is the height.

Plug in the values and solve:

V = [tex]\pi[/tex](5²)(12)

V = 300[tex]\pi[/tex] in³ or 942.48 in³

Answer:

11

Step-by-step explanation:

The sum of the shortest two sides must be greater than the longest side.

If n is the longest side:

6 + 8 > n

14 > n

If 8 is the longest side:

6 + n > 8

n > 2

So n must be an integer greater than 2 and less than 14.

n can be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or 13.

There are 11 possible integers.

[tex] \LARGE{ \boxed{ \rm{ \purple{Answer}}}}[/tex]

We know,

Sum of two sides of a triangle > Third side

Then,

⇛ 6 + 8 > n

⇛ 14 > n

Nextly,

Difference of two sides of a triangle < Third side

Then,

⇛ 8 - 6 < n

⇛ 2 < n

Then, Range of third side:

☃️ 2 < n < 14

Possible measures of 3rd sides = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 or 13.

There are 11 possible values of 3rd side. Out of them, any measure is the length of 3rd side.

━━━━━━━━━━━━━━━━━━━━

Answer:

-3

Step-by-step explanation:

When g(0), it means that x=0.

So, if we use 0 instead of x, the answer becomes:

-3

Answer:

-3

Step-by-step explanation:

g(0) = (-2(0)^2) -3

as anything multiplied with 0 is 0,

g(0) = 0 - 3

= - 3

Answer:

14

Step-by-step explanation:

[tex]f(x)=x^2-8x+5[/tex]

now substitute x for -1

[tex]f(-1)=(-1)^2-8(-1)+5[/tex]

now solve

[tex]f(-1)=1+8+5[/tex]

[tex]f(-1)=14[/tex]

there is your answer! hope this helps! :)

Answer:

The vertex is (3,4)

Step-by-step explanation:

f (x) = x^2 - 6 x + 13

Completing the square

-6/2 = -3 and squaring it = 9

    = x^2 -6x +9 +4

   = ( x-3) ^2 +4

The equation is now in vertex form

a( x-h) ^2 +k

where the vertex is ( h,k)

The vertex is (3,4)

Answer:

C on edge

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

correct/total

20/80

1/4

Changing to a decimal

.25

.25*100%

25%

Answer:

1/4 or 25%

Step-by-step explanation:

1). 20 / 80 = 1 / 4 = 25 %

Hope this helps

Answer:

y = -1/4x - 10

Step-by-step explanation:

Hey there!

Well to the slopes of 2 perpendicular lines are reciprocals of each other meaning if the line has a slope of 4 then it’s perpendicular line has a slope of -1/4.

Now to find the y intercept we need to graph,

y = -1/4x and point (4, -11)

Look at the image below.

By looking at the image below we can tell that in order for the perpendicular line to go through point (4,-11) it would be -10.

The equation is y = -1/4x - 10

Hope this helps :)

Step-by-step explanation:

Let the rate of the plane be x

The rate of the wind be y

Against the wind

Resultant velocity = x-y

1650/3 = x - y

550 = x - y

With the wind

Resultant velocity = x + y

3480/4 = x + y

870 = x + y

Solve equation simultaneously

Add both equations

870+550 = x+y+x-y

1420 = 2x

x = 710

x + y = 870

y=870 - 710

y = 160

The rate of jet in still air = 710 mph

The rate of wind = 160 mph

HOPE IT HELPS!

PRETTY PLEASE MARK ME BRAINLIEST :-)

Answer:  0.82

Step-by-step explanation:

Given : P(own skateboard) =0.37

P( own bicycle) =0.81

P(own skateboard and bicycle) = 0.36

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

So, P(own skateboard or  bicycle) = P(own skateboard) + P( own bicycle)-P(own skateboard and bicycle)

= 0.37 + 0.81 -  0.36

= 0.82

Hence, the probability that the teenager owns a skateboard or a bicycle is  0.82.

Answer:

The total duration of the trip is 48 hours.

Step-by-step explanation:

Let suppose that ship travels at constant speed during its travel. Each stage is represented by the following kinematic equation:

[tex]v =\frac{\Delta s}{\Delta t}[/tex]

Where:

[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.

[tex]\Delta t[/tex] - Time, measured in hours.

[tex]v[/tex] - Speed, measured in kilometers per hour.

Now, each stage is represented by the following expressions:

Outbound trip

[tex]v = \frac{700\,km}{\Delta t}[/tex]

Return trip

[tex]v + 10\,\frac{km}{h} = \frac{700\,kh}{\Delta t - 8\,h}[/tex]

By eliminating [tex]v[/tex] and simplifying the resulting expression algebraically:

[tex]\frac{700\,km}{\Delta t} + 10\,\frac{km}{h} = \frac{700\,km}{\Delta t -8\,h}[/tex]

[tex](700\,km)\cdot \left(\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} \right) = 10\,\frac{km}{h}[/tex]

[tex]\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} = \frac{1}{70}\,\frac{1}{h}[/tex]

[tex]\frac{8\,h}{\Delta t \cdot (\Delta t-8\,h)} = \frac{1}{70}\,\frac{1}{h}[/tex]

[tex]560\,h^{2} = \Delta t\cdot (\Delta t - 8\,h)[/tex]

[tex](\Delta t )^{2}-8\cdot \Delta t - 560 = 0[/tex]

This equation can be solved by means of the Quadratic Formula, whose roots are presented below:

[tex]\Delta t_{1} = 28\,h[/tex] and [tex]\Delta t_{2} = -20\,h[/tex]

Only the first roots offers a physically resonable solution. Then, total duration of the trip is:

[tex]t_{T} = 28\,h +20\,h[/tex]

[tex]t_{T} = 48\,h[/tex]

The total duration of the trip is 48 hours.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

Answer:

Step-by-step explanation:

A pyramid has twice as many edges as faces, and 1 more vertex than faces.

Octa- means 8.

Tri- means 3.

a) An octagonal pyramid has 8 faces, 16 edges, and 9 vertices.

b) A triangular pyramid has 3 faces, 6 edges, and 4 vertices.

__

A triangular prism will have 3 additional edges for the second "base", and 2 additional vertices.

c) A triangular prism has 3 faces, 9 edges, and 6 vertices.

__

Additional comments

We have not counted the base as a "face." We have only counted those that meet at the point of the pyramid.

There are as many vertices on the base as there are faces, and there is one more vertex where all the faces meet.

There is one edge at the base for each face, and there is one edge from the base vertex to the point of the pyramid for each face--a total of two edges per face.

__

A triangular pyramid is shown in the attachment.

Answer:

-2

Step-by-step explanation:

slope: (y² - y¹) / (x² - x¹)

(-1 - 1) / (1 - 0) = -2 / 1 = -2

y = -2x + b

plug in an (x, y) value to find b

1 = -2(0) + b

1 = -2 + b

b = 3

y = -2x + 3

rate of change is -2

Answer:

-2

Step-by-step explanation:

Answer:

6.3294✖️10^7

Step-by-step explanation:

To find the statdard form, you place the decimal after the largest unit, int his case 6.

Then you write down all the numbers except for "0".

This becomes:

6.3294

Then, you add the multiplying sign, and count how many digits are there after 6, and in this case, there are 7, so you add the power "7" after 10.

6.3294✖️10^7

Hope this helped!

Have a nice day:)

Answer:

1. Please refer to attached diagram.

2. 135

3. 135

Step-by-step explanation:

Given that

80%examines passed in English, n(E) = 80%

70%In mathematics, n(M) = 70%

and 60% in both subjects, n(E [tex]\cap[/tex] M)  = 60%

45 examines failed in both subject.

1. Venn Diagram is attached in the answer area.

One circle represents the pass examines in Maths and

Other circle represents the pass examines in English.

Rectangle represents the total number of examines that appeared for the exam.

Rectangle minus the area of union of circles represent the number of students who failed in both subjects.

2. To find the number of examines who passed in only one subject.

i.e. n(E) - n(E [tex]\cap[/tex] M) + n(M) - n(E [tex]\cap[/tex] M) = (80 - 60 + 70 - 60)% = 30%

Let us find the number of students who passed in atleast one subject:

[tex]n(E\cup M) = n(E) +n(M)-n(E \cap M)\\\Rightarrow n(E\cup M) = (80 +70-60)\% = \bold{90\%}[/tex]

So, number of students who failed in both subjects = 100 - 90% = 10% of total students = 45

So, total number of students appeared = 450

So, number of examines who passed in only one subject = 450 [tex]\times[/tex] 30% = 135

3. Number of students who failed in mathematics.

100% - Passed in Mathematics = 100% - 70% = 30% of 450 = 135

Answer:

x=30

Step-by-step explanation:

x+2x+3x=180

6x=180

x=180/6=30