Explain how to use a graph of the function f(x) to
find f(3)

Answer:

There are 8 oz of soup per can  :  True

In 8 cans, there are 21 oz of soup  : False

There are 2 oz of soup in 16 cans  : False

In 1/8 of a can, there is 1 oz of soup  : True

Step-by-step explanation:

To start, we know we have 168 oz of soup and 21 cans that are all the same size. To find how much is each can, (We know that they will all have the same amount since it says equally sized cans.) we can simply divide the amount we have of soup in oz by the amount of cans we have.

168 / 21 = 8.

This means that all the cans will be filled with 8 oz of soup. Making the first statement true.

Since there are 8 oz in each can, we can do 8 cans * 8 oz to find how many oz are in 8 cans of soup.

8 * 8 = 64 oz.

There are 64 oz of soup in 8 cans. Making the second statement false.

Now again, since there are 8 oz in each can, we can do 16 cans * 8 oz to find how many oz are in 16 cans of soup.

16 * 8 = 128 oz.

There are 128 oz of soup in 16 cans. Making the third statement false.

For the last question, to find 1/8 of a can of soup, we can take 8 oz (8 oz in one can) and divide it by 8.

8/8 = 1

Meaning 1/8 of a can of soup is 1 oz of soup. Making the fourth statement true.

Answer:

Yes, they intersect at the coordinates (0, 7) and (6, 19)

Step-by-step explanation:

[tex]y = -x^2 + 8x + 7\\y = 2x + 7\\y = y\\-x^2 + 8x + 7 = 2x + 7\\-x^2+ 6x = 0\\x^2 - 6x = 0\\x(x - 6) = 0\\x = 0\ \ \text{or}\ \ x = 6\\[/tex]

[tex]\text{if}\ x = 0\\y = 2x + 7\\y = 2(0) + 7 = 7\\\text{coordinate is:}\ (0, 7)[/tex]

[tex]\text{if}\ x = 6\\y = 2x + 7\\y = 2(6) + 7 = 12 + 7 = 19\\\text{coordinate is:}\ (6, 19)[/tex]

Answer:

B. Yes, they intersect at the coordinates (0, 7) and (6, 19)

Step-by-step explanation:

I took the Algebra exam

Step-by-step explanation:

[tex](x - 2) {?}^{2} + (y + 3) { = 18} [/tex]

An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method.

Simple interest (C) is the amount of money gained and solely related to the initial capital ([tex]C_{o}[/tex]), in monetary units. The money earned by simple interest is determined by the following formula:

[tex]C = \frac{C_{o}\cdot r\cdot t}{100}[/tex]     (1)

Where:

Compound interest (C) takes into account the capital throughout time and its formula is presented below:

[tex]C = C_{o}\cdot \left[\left(1+\frac{r}{100} \right)^{t}-1\right][/tex]

Now we proceed to determine the simple and compound interest: ([tex]C_{o} = 1000[/tex], r = 2, t = 5)

C = [(1000) · (2) · (5)]/100

C = $ 100

C = (1000) · {[1+(2/100)]⁵-1}

C = $ 104.08

An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method. [tex]\blacksquare[/tex]

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Answer:

1 1/2

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

By applying the Newton's law of cooling and performing the neccessary calculations, the time of death of the body is about 4 hours ago.

According to the Newton's law of cooling;

T(t) = T(s) + (To - Ts)e^-kt

T(t) = temperature at time t

T(s) = temperature of the surroundings

To = Initial temperature

k = cooling constant

t = time taken

Substituting the values;

T(t) = 60 + (98.6 - 60)e^- 0.1947t

To find the time taken to attian a temperature of 78°F;

78 = 60  + (98.6 - 60)e^- 0.1947t

78= 60 + 38.6e^- 0.1947t

78 - 60 = 38.6e^- 0.1947t

18/38.6 = e^- 0.1947t

0.466 = e^- 0.1947t

ln0.466 = lne^- 0.1947t

ln0.466 =- 0.1947t

t = ln0.466 /- 0.1947

t = 4 hours

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

First we have to calculate g (-5) :

[tex]\qquad \tt \dashrightarrow \:x - 8[/tex]

[tex]\qquad \tt \dashrightarrow \: - 5 - 8[/tex]

[tex]\qquad \tt \dashrightarrow \: - 13[/tex]

Now, let's find f (g (-5)) :

[tex]\qquad \tt \dashrightarrow \: {x}^{2} + 6x[/tex]

[tex]\qquad \tt \dashrightarrow \:( - 13) {}^{2} + (6 \times - 13)[/tex]

[tex]\qquad \tt \dashrightarrow \:169 + ( - 78)[/tex]

[tex]\qquad \tt \dashrightarrow \:169 - 78[/tex]

[tex]\qquad \tt \dashrightarrow \:91[/tex]

Answer:

-6

Step-by-step explanation:

-2x - 9 = 4/3x+11

-

-6x-27=4x+33

-

-6x-27-4x=33

-

=6x-4x=33+27

-

10x=33+27

-

-10x=60

-

x= -6

Answer:

45.27 miles

Step-by-step explanation:

Pythagorean theorem

23^2 + 39^2 = d ^ 2

d = 45.27 miles

If  a person drives 23 miles south and make a turn to east and drive 39 miles then the distance between starting point and person is 45.27 miles.

Pythagoras theorem applies in a right angled triangle. It says that in a right angled triangle the square of hypotenuse is equal to sum of squares of perpendicular and base of that triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex]

When person drives towards south and then east , it forms a right angled triangle. We have to find the distance of person from the starting point. If we see the figure then we will come to know that we are require to find hypotenuse of triangle.

H=[tex]\sqrt{P^{2} +B^{2} }[/tex]

Distance=[tex]\sqrt{23^{2} +39^{2} }[/tex]

=[tex]\sqrt{1521+529}[/tex]

=[tex]\sqrt{2050}[/tex]

=45.27

Hence the distance of person from starting point is 45.27 miles.

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Answer:

  350 adult tickets

Step-by-step explanation:

If x is the number of adult tickets sold, then x-57 is the number of student tickets sold (57 fewer). The total number sold is ...

  x +(x -57) = 643

  2x = 700 . . . . . . . . collect terms, add 57

  x = 350 . . . . . . . divide by 2

There were 350 adult tickets sold.

Answer:

The value of angle BAC = 75°

Step-by-step explanation:

=> Angle BAC + 105° = 180°

=> Angle BAC = 180° - 105°

=> Angle BAC = 75°

Answer:

6 miles in 66 mins

Step-by-step explanation:

4 miles = 44 mins

simplify to the lowest point

1 mile = 11 mins

? = 66 mins

? = 1 x 6

you can run 6 miles in 66 mins

Answer:

Step-by-step explanation:

4/44= 0.0909090909...*66=6

find the propotunate value by dividing each initial value and multiply it by the listed secondary value

Answer: 40 cm.

Step-by-step explanation: Perimeter involves adding all the sides of a shape to get the perimeter.  So far, two sides of the scrapbook have been given, which are both 37 cm.  37 x 2 = 74, so that leaves us with two sides left, which are the lengths of the scrapbook.  The total perimeter is 154, so if we subtract 74 from 154, we get 80.  However, we have to split the 80 in half because we have two sides left.  Therefore, the scrapbook's length is 40 cm for one side.  I hope this isn't too confusing.

Have a great day! :)

Answer:

x = 6

Step-by-step explanation:

(4x - 3) × 2 = 3(x + 8)

8x - 6 = 3x + 24

8x - 3x = 24 + 6

5x = 30

x = 6

Answer:

-Dilate circle A by scale factor of 2

Got it right on the test (see picture)

Circle A is translated using the rule (x + 1, y - 1). Then the correct option is B.

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Circle A has a center of (2,3) and a radius of 5, and circle B has a center of (1,4) and a radius of 10.

Circle B is translated as 1 unit leftward in the x-direction and 1 unit upward in the y-direction.

Then circle B is dilated by a factor of 2.

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Answer:

B

Step-by-step explanation:

It's 18! Obviously it's not 180 because it's too big. It can't be 36 because 36 doesn't go evenly into 90. 6 is too small, so the answer is 18.

Answer:

Correct ones A and F

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

Correct ones H and K

Answer: 10

Step-by-step explanation:

our number is x

we add seven (+7) to x

x+7

Step-by-step explanation:

The statements that describe the graph are,

The ball travels 24 cm in 1s.

It takes the ball 2s to complete a cycle

The midline is at f(x)=0

I hope it helped you

Answer:

2 is the base, 10 is the base, and x is the base. X is the exponent of 2, x is the exponent of 10, and x is the exponent of x.

Step-by-step explanation:

It will take approximately 169 minutes for a the rocket to travel a distance of  1,260,000,000 feet at 1,540,000 ft/min

Given Data

Applying the relationship between speed, distance and time we have

Speed = Distance/Time

Substituting our given data into the expression we have

1,540,000  = 260,000,000/time

Making time subject of formula

time = 260,000,000/1,540,000

time = 169 miniutes

Learn more about speed, distance and time  here:

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Answer:

x < 4

Step-by-step explanation:

Subtract 10 from both sides.

x + 10 - 10 < 14 - 10

Simplify the arithmetic:

x < 14 - 10

Simplify again..

and then u get x < 4

hope this helps <33

Answer:

55.5 mph

Step-by-step explanation:

Time period of flight

Return trip flight speed

Wind velocity

Answer:

(-10,0)

Step-by-step explanation:

2a =[2(-2) , 2(-3)] = (-4 -6) <--- add them

-3b = [-3(1) . -3(-1)] = (-3 +3) <--- add them

2a - 3b =  

[(-4  -6), (-3  +3)] =

(-10,0)

Answer:

A -- She saves 200₤.

B -- She will have 28₤ after buying presents.

Step-by-step explanation:

If two boxes = 20 then one box will be 10. Now we count all boxes. There are 20 boxes... 20 x 10 = 200, so she saves 200₤. If she spends 172₤ on Christmas presents she will have 28₤. (200 - 172 = 28).

Answer:

4 degrees is the closest thing i could think of while looking at this.

Answer:

15 years old

Step-by-step explanation:

Start by defining the variables that we are going to use throughout our working:

Let the current age of Wei Ling and Wei Xuan be L and X years old respectively.

Next, form equations using the given information.

5 years ago

Wei Ling: (L -5) years old

Wei Xuan: (X -5) years old

Given that the ratio of Wei Ling's age to that of Wei Xuan's is 2: 5,

[tex] \frac{ L - 5}{X - 5} = \frac{2}{5} [/tex]

Cross multiply:

2(X -5)= 5(L -5)

Expand:

2X -10= 5L -25

2X= 5L -25 +10

2X= 5L -15 -----(1)

9 years time

Wei Ling: (L +9) years old

Wei Xuan: (X +9) years old

Given that the ratio of Wei Ling's age to that of Wei Xuan is 3: 4,

[tex] \frac{L + 9}{X + 9} = \frac{3}{4} [/tex]

Cross multiply:

3(X +9)= 4(L +9)

Expand:

3X +27= 4L +36

3X= 4L +36 -27

3X= 4L +9 -----(2)

Let's solve using the elimination method.

(1) ×3:

6X= 15L -45 -----(3)

(2) ×2:

6X= 8L +18 -----(4)

(3) -(4):

6X -6X= 15L -45 -(8L +18)

0= 15L -45 -8L -18

0= 7L -63

7L= 63

L= 63 ÷7

L= 9

Substitute L= 9 into (1):

2X= 5(9) -15

2X= 45 -15

2X= 30

X= 30 ÷2

X= 15

Thus, Wei Xuan is 15 years old now.