Given that F( x ) = x 2 + 2, evaluate F(1) + F(5).

Answer:

3^6 = 729

Step-by-step explanation:

3 to the power of 5 equals 243. Explain how to use that fact to quickly evaluate 3 to the power of 6  

Symbolically, we have:

3^5 = 243 (given)

Multiplying both sides by 3, we get:

3^6 = 3(243)

If you want to take this further, multiply 3(243):  3^6 = 729

The value of [tex]3^6[/tex] is 729.

Important information:

We need to find the value of [tex]3^6[/tex].

Using the rules of exponents, we get

[tex]3^6=3^{5+1}[/tex]

[tex]3^6=3^{5}*3^{1}[/tex]          [tex][\because a^{m+n}=a^ma^n][/tex]

[tex]3^6=243*3[/tex]

[tex]3^6=729[/tex]

Therefore, the value of [tex]3^6[/tex] is 729.

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Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

[tex]\sqrt{(x_{2} - x_{1}) ^ {2} + (y_{2} - y_{1}) ^ {2}}[/tex]

[tex]\sqrt{(5-4) ^ {2} + (12 - 9) ^ {2}} = \sqrt{1^{2}+3^{2}} = \sqrt{10}[/tex]

Answer:

So we have a function such that:

Takes elements of Set A, and maps them into Set B.

So Set A is the domain, and Set B is the range.

Where the domain is defined as the set of all the possible inputs of a function, and the range is the set of the possible outputs.

In principle, yes, if f(x) maps Set A into Set B, all the elements of Set A should be used, why?

Because we need to check if there is a problem with Set A, for example the function f(x) = 1/x has a problem when x = 0, so we remove x = 0 from the domain of that function.

So, a function is only a function if it maps ALL the elements of its domain into only one element in the range.

Answer:

-1=-2

4=-7

Step-by-step explanation:

for x=-1

y=(-1^2)+(2*-1)+1

y=-1-2+1

y=-2

for x=1

y= (-1^2)+(2*1)+1

y= -1+2+1

y=2

for x=4

y=(-4^2)+(2*4)+1

y=-16+8+1

y=-7

Answer:

x = 162 degrees.

Step-by-step explanation:

m < RSP = 180 - 72

= 106 degrees (adjacent angles)

m < Q = m < RSP ( Opposite angles in a parallelogram are equal).

So m < Q = 180 degrees.

m < x = 360 - 90 - 108

= 360 - 198

= 162 degrees.

Using the appropriate angle theorems, the value of the angle, x in the parallelogram would be 162°

At angle S :

S + 72 = 180 (sum of straight line angles)

S = 180° - 72°

S = 108°

S = Q (opposite angles of a parallelogram)

Q = 108°

Hence,

108° + x + 90 = 360

x = 360 - (108 + 90)

x = 162°

Hence, the value of x is 162°

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Answer:

18.0

Step-by-step explanation:

Note the tenth place value (underlined and bolded): 18.049

Look at the number to the direct right of the tenth place value (or the hundredth place value in this case). It is a 4.

Note the rules of rounding. If the number:

1) is 5 or greater, round up.

2) is 4 or less, round down.

In this case, it is 4, so you will round down.

18.049 rounded to the nearest tenth is 18.0

~

Answer:

18.0

Step-by-step explanation:

first time i put 18 and it was wrong so

Answer:

-36

Step-by-step explanation:

[tex]-\frac{t}{2} -8 = 10\\-\frac{t}{2} = 18\\\frac{t}{2} = -18\\t = -36[/tex]

Answer:

C

Step-by-step explanation:

Divide 4.5 by 3 = 1.5

1.5 x 3 = 4.5

Answer:

1.5 (c)

Step-by-step explanation:

You have to find the difference:

so you have to divide 4.5 the original and 3 the scaled image to see how much changed.

4.5 / 3 = 1.5  

Answer:

24.2

Step-by-step explanation:

Answer:

Solution: The average rate of change of  represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.

Explanation:

The rate of change shows the change in first variable with respect to change in second variable.

If the rate of chang is given by  it means second variable is decrease by 14 if the first variable increase by 3.

In the context of water slide it shows that the vertical height of slide is decreased by 14 units as we cover the distance of 3 units.

If we cover the distance from x = 0 to x = 15, it means we cover the distance of 15 units.

Let the vertical height of the slide covered from x = 0 to x =15 be y.

It means when distance increased by 15 units the height of slide decreased by y units.

So rate of change = .

It is given that the rate of change is .

Equate both equations.

Therefore, the average rate of change of  represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.

Answer:

$1200

Step-by-step explanation:

Since the value of the car depreciates $325 a year.

After 4 years it would be 1300, becuase $325 × 4 = $1300.

So, $2500 - $1300 = $1200

Answer:

y=¾(4x-20)

y=3x-15

Final answer= y - 3(x+12)

=y - 3x-36

=3x-15-3x-36

= -51

Answer:

The answer is -51

Step-by-step explanation:

Answer:

64 cm^2

Step-by-step explanation:

I assume the side of the base measures 4 cm, and the height of each triangular side (the slant height) is 6 cm.

SA = s^2 + 4 * bh/2

SA = (4 cm)^2 + 2(4 cm)(6 cm)

SA = 16 cm^2 + 48 cm^2

SA = 64 cm^2

Answer:

x = 15

Step-by-step explanation:

9x-30 = 3x (tangent lines are congruent)

- move the variables to one side

9x-3x=30

6x=30

x=5

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

9(5)-30=3(15)

45-30=15

15=15

Done!

Answer:

A. 24+24+120+160+200

Step-by-step explanation:

Surface area of the triangular prism= addition of the area of each shape that forms the prism

There are two triangles

Area of a triangle=1/2*base*height

=1/2*8*6

=1/2*48

=24

Area of two triangles=24+24

There are 3 rectangles with different dimensions

Back rectangle=length×width

=20×6

=120

Bottom rectangle=length ×width

=20x8

=160

Top rectangle=length × width

=20×10

=200

Surface area =Area of two triangles + Back rectangle + Bottom rectangle + Top rectangle

=24+24+120+160+200

Answer:

Below

Step-by-step explanation:

Notice that 81 = 9 * 9

So here is the first expression:

● 9^2

9 is 3^2 so 9^2 is 3^4

That's another expression

● 3^4

81 = 9*9 = 3*3*3*3 = 3^3 *3

That's another expression

● 3*3^3

You can keep manipulating the product and create many expressions like:

● 3^2 * 3^2

● 9 * 3^2

Answer:

DE = 13.4 cm  (to 1 decimal place)

Step-by-step explanation:

Given: ABCD is a square

BC = AC = 12 cm    (opposite sides of a square are congruent)

E is midpoint of BC   (given)

BE = EC  = 12/2 = 6 cm

CD = AB = 12 cm   (opposite sides of a square are congruent)

angle ECD is a right angle (interior angles of a square are 90 deg.)

Consider right triangle ECD

DE = sqrt(EC^2+CD^2)    ............. pythagorean theorem

= sqrt(6^2+12^2)

= sqrt ( 36+144 )

= sqrt (180)

= 2 sqrt(45)

= 13.416 (to three dec. places)

Answer:

A. The students tend to have fewer siblings than the teachers.

Step-by-step explanation:

First we need to draw the dot plots correctly. If you count both sides they have 20 each.

Now, clearly none have fewer nobody here yet has more or less but going on to the next step.

Multiply exactly the number of siblings times how many people chose that many siblings. Ex: 2 (siblings) times 7 (people who has 2 siblings) = 14.  And so on.

On the Student A, we get a total of 41 people having sibling, if you count the 0's then there were a total of 43 people. But now on the Teacher's A Dot Plot, we have a total of 68 people, if you include the 0 then we have a total of 69.

So the answer is A. The students tend to have fewer siblings than the teachers.

Answer:

The sum is A

Step-by-step explanation:

Just ma duty to help the community

Answer:

D, since it horizontal ellipse, a is greater than b

An ellipse has two foci. The correct option is D.

Suppose that the major axis is of the length 2a units and that the minor axis is of 2b units, and let the ellipse is centred on (h,k) with a major ellipse parallel to the x-axis, then the equation of that ellipse would be:

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Coordinates of its foci would be:    (h±c, k) where    c² = a² - b²

If its major axis is parallel to the y-axis, then,

coordinates of its foci would be:  (h, k±c) where   c² = a² - b² and its equation would be:

[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]

Given the foci at (3, 2) and (-9, 2) that pass through the point (-3, 10), therefore, the equation of the ellipse will be,

[tex]\dfrac{\left(x+3\right)^{2}}{100}+\dfrac{\left(y-2\right)^{2}}{64}=1[/tex]

Hence, the correct option is D.

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#SPJ2

Since there is two negative signs in the original equation, you need two negative signs in the equivalent one as well.

Because one of the negatives if before the fraction, it doesn't matter if the second negative is on the 13 or on the 12.

The answer is A.

Answer:

The probability that a 57-year-old was involved in an accident is 0.0656.

Step-by-step explanation:

We are given the data for the drivers involved in an accident of different age groups.

And we have to find the probability that a 57-year-old was involved in an accident.

From the table given to us, it clear that a 57-year-old driver will lie in the age group of 55 - 64.

Now, the number of licensed drivers in the age group of 55 - 64 are 30,355 (in thousands).

The point to be noted here is that the data given of drivers in accidents (thousands) will include the data of drivers in fatal accidents.

So, the number of 57-year-old drivers involved in accidents are 1990 (in thousands).

The probability that a 57-year-old was involved in an accident is given by;

                        = [tex]\frac{1990}{30,355}[/tex]

                        = [tex]\frac{398}{6071}[/tex] = 0.0656 or 6.56%

Answer:

see below

Step-by-step explanation:

Video Game

20% off means you pay 80%

80 dollars * 80% =

80 * .80 = 64

Movie ticket

14 original price

Sale price = 11.40

14* p% = 11.40

Divide each side by 14

p% = 11.40/14

p% =81.4285714

You paid 81 3/7%

The discount is 100 -81 3/7%

18 4/7 % discount

Laptop

1000 original price

Sale price = 750

1000 * p% = 750

p% = 750/1000

p% =75%

You paid 75%

The discount is 100 -75%

25 % discount

Answer:

Below

Step-by-step explanation:

First item)

The original price of the video games is 80$ wich is 100%

This item has a 20% discount.

Let x be the value of the dicount in dollars.

● 80 => 100

● x => 20

● x =(80×20)/100 = 16$

So the amount of the discount is 16$.

● 80-16 = 64 $

So the amount that was paid is 64$

■■■■■■■■■■■■■■■■■■■■■■■■■■

Second item):

The price that was paid is 11.2$out of 14$ initially.

Let x be the percentage of 11.2

● 14$ => 100%

● 11.2$ => x

● x = (11.2×100)/14 = 80%

● 100-80 = 20%

So the percentage of discount was 20%

■■■■■■■■■■■■■■■■■■■■■■■■

Third item):

The laptop was boughr for 750$ out of 1000$ initially

No need to do calculations here.

Notice that: 750/1000 = 3/4 = 0.75 = 75%

● 1000-750 = 250

So 250 is the amount discounted wich is 25% of 1000$

Answer:

B

Step-by-step explanation:

Answer:

I believe it's (4^2)*12

Step-by-step explanation:

To find the correct amount of the window panes there are, we have to find how much window pains are in each of the window's. So we have a 4 by 4 so that's 16. Then we have to do 16*12 to get the total amount of panes since Panes Per Window multiplied by Number Of Windows equals Total Number Of Panes

Hope this helps! ∪ω∪

Answer:

The answer is B

Step-by-step explanation:

A line has Zero slope is when the line is parallel to the x-axis. The slope of the first pair of coordinates will have no slope or zero slopes.

The slope of a line is given by the formula,

[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]

where (x₂,y₂) and (x₁,y₁) are the coordinates of any point on the line of slope.

1. For the first slope, the given coordinates are

(-3,2),(-1,2),(1,2),(3,2)

Now, if we take the first and the last point to calculate the slope of the line, we will get,

[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{2-2}{-3-3}=\dfrac{0}{-6}=0[/tex]

Thus, the slope of the line is 0. And if we plot the points on the graph we will see that the slope of the line is 0.

2. For the second slope, the given coordinates are

(-3,3),(-1,1),(1,-1),(3,-3)

Now, if we take the first and the last point to calculate the slope of the line, we will get,

[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{3-(-3)}{-3-3}=\dfrac{6}{-6}=-1[/tex]

Thus, the slope of the line is -1. And if we plot the points on the graph we will see that the slope of the line is -1.

3. For the third slope, the given coordinates are

(-5,-5), (0,0), (5,5)

Now, if we take the first and the last point to calculate the slope of the line, we will get,

[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{-5-5}{-5-5}=\dfrac{-10}{-10}=1[/tex]

Thus, the slope of the line is 1. And if we plot the points on the graph we will see that the slope of the line is 1.

4. For the fourth slope, the given coordinates are

(-2,5), (-2,0), (-2,5)

Now, if we take the first and the last point to calculate the slope of the line, we will get,

[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{5-0}{-2-(-2)}=\dfrac{5}{0}[/tex]

Thus, the slope of the line is undefined. And if we plot the points on the graph we will see that the slope of the line is undefined or at 90° from the x-axis.

Hence, the slope of the first pair of coordinates will have no slope or zero slopes.

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Answer:

H(2)= 0 , so x = 2 is the correct answer

Step-by-step explanation:

Given:

H(x)= -|x+1| + 3

Computation:

By putting x = 0,1,2

H(x)= -|x+1| + 3

H(0)= -|0+1| + 3

H(0)= -1 + 3

H(0)= 2

H(x)= -|x+1| + 3

H(1)= -|1+1| + 3

H(1)= -2 + 3

H(1)= 1

H(x)= -|x+1| + 3

H(2)= -|2+1| + 3

H(2)= -3 + 3

H(2)= 0

Answer:

27

Step-by-step explanation:

By the theorem of intersecting secant and tangent out side of a circle, we have:

[tex] {60}^{2} = 48 \times (48 + x) \\ 3600 = 48 \times (48 + x) \\ \frac{3600}{48} = 48 + x \\ 75 = 48 + x \\ 75 - 48 = x \\ x = 27 \\ [/tex]

Answer:

5) It was 5/12 of the way full

6) It holds 48 gallons.

Step-by-step explanation:

For #5, you can simply find the lowest common denominator, which was 12, so you would multiply 3/4 by 3/3 and 1/3 by 4/4, giving you 9/12 and 4/12. Next you would subtract 4 from 9 and get the answer 5/12.

For #6 you can set up the problem as a ratio, 5/12 and 20/x, and then cross multiply, getting the equation 5x = 240. Then divide by 5 and you get the answer 48.

Hope this helps!!

Answer:

5/12 When the water leaked out.

48 Gallons when full.

Hope this Helps!

Answer:

Bottom right option

Step-by-step explanation:

To find this, we can calculate:

1/2 * 4.32 * 10⁻⁴

= (1/2 * 4.32) * 10⁻⁴

= 2.16 * 10⁻⁴

The diameter of a new cell is 2.16×10−⁴millimeters

First step is to calculate 4.32×10−⁴ to the original numbers

4.32×10−⁴ =0.000432

Second step is to determine the diameter of a new cell

New cell diameter=0.000432×1/2

New cell diameter=0.000216

New cell diameter=2.16×10−⁴millimeters

Inconclusion The diameter of a new cell is 2.16×10−⁴millimeters

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