which of these relations are functions

Answer:

x = -1.59

Step-by-step explanation:

We are here given a equation and we need to solve out for x. The given equation is ,

[tex]\sf\longrightarrow 4^{( x +3)}= 7[/tex]

Take log to the base " e " on both sides , so that we can remove the variable from the exponent .

[tex]\sf\longrightarrow log_e 4^{x+3}= log_e 7[/tex]

Simplify using the property of log , [tex]\sf log a^m = m log a [/tex] , we have ,

[tex]\sf\longrightarrow (x + 3) ln 4 = ln 7 [/tex]

Distribute by opening the brackets ,

[tex]\sf\longrightarrow x ln 4 + 3 ln 4 = ln 7[/tex]

This can be written as ,

[tex]\sf\longrightarrow x ln 4 = ln 7 - 3ln4 [/tex]

Divide both sides by ln 4 ,

[tex]\sf\longrightarrow x = \dfrac{ ln7}{ln 4 } - \dfrac{ 3ln4}{ln4} [/tex]

Simplify ,

[tex]\sf\longrightarrow x = \dfrac{ ln4 }{ln7 } -3[/tex]

On simplifying , we will get ,

[tex]\sf\longrightarrow \boxed{\blue{\sf x = -1.59 }}[/tex]

Answer:

Step-by-step explanation:

If Quan had 15 and Kaden had 3 times as much, then Kaden had 15(3) = 45. If he spent 10 then he had 35 left. The amount of money Quan had after his mom gave him some was 4/5 the amount of Kaden's 35 (let x = the amount of money Quan has after his mom gives him some):

[tex]x=\frac{4}{5}(35)[/tex]  35 divides by the 5 in the denominator 7 times, and 7 times 4 is 28. That's how you get your 28 in part a.

For part b., he started with 15 and ended with 28, so his mom gave him 28-15=13. That's how you get the 13.

Answer:

See answers below

Step-by-step explanation:

For the expression

The sum of two numbers is  25.  The first number is 37 more  than 2 times the second  number

Let the two numbers be x and y

If the sum is 25, then;

x + y = 25 .... 1

37 more  than 2 times the second  the number is expressed as;

37+2y

If the first number is 37 more  than 2 times the second  number, then;

x = 37 + 2y

x - 2y = 37 ...2

This shows that the simultaneous equation that fits the expressions are;

x - 2y = 37

x + y = 25

For the expression

A child has a piggy bank full  of $1 and $2 coins totaling  $37.  There are 25 more $1 coins  than there are $2 coins.

Let x be the $1 coins

Let y be the $2 coins

If a child has a piggy bank full  of $1 and $2 coins totaling  $37, then;

x + 2y = 37 ... 1

Also, if there are 25 more $1 coins  than there are $2 coins, then;

x = 25 + y

x - y = 25 ...2

The equivalent expressions for the statement will be;

x + 2y = 37

x - y = 25

This hence leaves us with the last;

An exam that is worth 37  marks contain 25  questions.  The questions are either  worth 1 mark or 2 marks. The resulting simultaneous equation will be;

x + 2y = 37

x + y = 25

70 days

that is the procedure above

Answer:

D.

Step-by-step explanation:

Find the average rate of change of each given function over the interval [-2, 2]]:

✔️ Average rate of change of m(x) over [-2, 2]:

Average rate of change = [tex] \frac{m(b) - m(a)}{b - a} [/tex]

Where,

a = -2, m(a) = -12

b = 2, m(b) = 4

Plug in the values into the equation

Average rate of change = [tex] \frac{4 - (-12)}{2 - (-2)} [/tex]

= [tex] \frac{16}{4} [/tex]

Average rate of change = 4

✔️ Average rate of change of n(x) over [-2, 2]:

Average rate of change = [tex] \frac{n(b) - n(a)}{b - a} [/tex]

Where,

a = -2, n(a) = -6

b = 2, n(b) = 6

Plug in the values into the equation

Average rate of change = [tex] \frac{6 - (-6)}{2 - (-2)} [/tex]

= [tex] \frac{12}{4} [/tex]

Average rate of change = 3

✔️ Average rate of change of q(x) over [-2, 2]:

Average rate of change = [tex] \frac{q(b) - q(a)}{b - a} [/tex]

Where,

a = -2, q(a) = -4

b = 2, q(b) = -12

Plug in the values into the equation

Average rate of change = [tex] \frac{-12 - (-4)}{2 - (-2)} [/tex]

= [tex] \frac{-8}{4} [/tex]

Average rate of change = -2

✔️ Average rate of change of p(x) over [-2, 2]:

Average rate of change = [tex] \frac{p(b) - p(a)}{b - a} [/tex]

Where,

a = -2, p(a) = 12

b = 2, p(b) = -4

Plug in the values into the equation

Average rate of change = [tex] \frac{-4 - 12}{2 - (-2)} [/tex]

= [tex] \frac{-16}{4} [/tex]

Average rate of change = -4

The answer is D. Only p(x) has an average rate of change of -4 over [-2, 2]

Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Answer:

2.6

Step-by-step explanation:

2.5÷65=2.6

Answer:

24 degrees

Step-by-step explanation:

90-66=24

Answer:

The cost for the snow skis for 4.5 hours is $ 77.5.

Step-by-step explanation:

Since renting snow skis costs $ 15 per hour plus a $ 10 usage fee, to create a step function that models the cost of snow skis in terms of the number of hours the snow skis were rented and determine the cost for the snow skis if you were skiing for 4.5 hours the following calculation must be performed:

10 + (15X) = Cost per hour

10 + 15 x 4.5 = X

10 + 67.5 = X

77.5 = X

Therefore, the cost for the snow skis for 4.5 hours is $ 77.5.

Answer:

$7.47

Step-by-step explanation:

Take the number of pounds and multiply by the price per pound

3 * 2.49

7.47 for 3 pounds of apples

Answer:

7.49

Step-by-step explanation:

Given: 3 pounds, and 2.49 for each pound

Multiply:

2.49 × 3

 ₁   ₂    

 2.49

×      3

----------

 7. 47

Mrs. Ella bought 3 pounds of apples for $7.49

Answer:

 He Saved 18.664%

Step-by-step explanation:

Well first we need to find the total of the original price of the items he got

then we can solve for how much (in percentage) he saved

We know the original price of the pant as € 34.50 because 5+29.50=34.50

Now lets find out the original price of the shirt

The shirt's original price can be found by using this equation

x * .75 = 17

17/ .75  = x

22.67 = x

Now since we know the prices of these two items lets add them together

34.50 + 22.67 = 57.17

He actually spent

29.50 + 17 = 46.5

Now what percentage of 57.17 is 46.5?

We can use 46.5/57.17 = 0.81336

.81336 *100 =  81.336%

100-81.336 = 18.664

18.664% was saved

Answer:

47.12

Step-by-step explanation:

C=2πr=2·π·7.5≈47.12389

Answer:

x = 69

Step-by-step explanation:

since AB is parallel to CD we can find the value of y with the following equation :

2y - 40 = 66 add 40 to both sides

2y = 110 divide both sides by 2

y = 55

from supplementary angles, we know that the exterior angle's measure is 124

since the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle

y + x = 124 we found value of y earlier

55 + x = 124 subtract 55 from both sides

x = 69

Answer:

a. 125 degrees

b. 62 degrees

c. 58 degrees

d. 130 degrees

Step-by-step explanation:

I assume these are the inner angles of the polygons.

remember, for a polygon with n sides we can fully split it into n-2 triangles without overlap.

each of these triangles has an angle sum of 180 degrees.

to get the total inner angle sum of the polygon, we need to multiply 180 by (n-2) (= the number of triangles).

out of that total we can then calculate the size of the missing angle.

a. 6 sides, therefore 4 triangles

4×180 = 720 degrees

the missing angle is

angle = 720 - 88 - 152 - 125 - 105 - 125 = 125

b. 5 sides, 3 triangles

3×180 = 540 degrees

angle = 540 - 109 - 111 - 140 - 118 = 62

c. 4 sides, 2 triangles

2×180 = 360

angle = 360 - 60 - 142 - 100 = 58

d. 7 sides, 5 triangles

5×180 = 900

angle = 900 - 90 - 120 - 140 - 150 - 120 - 150 = 130

9514 1404 393

Answer:

  528

Step-by-step explanation:

The sum can be decomposed into parts that may be easier to figure.

  [tex]\displaystyle\sum_{n=1}^{24}(2n-3)=2\sum_{n=1}^{24}(n)-3\sum_{n=1}^{24}(1)=2\dfrac{24\cdot25}{2}-3\cdot24\\\\=600-72=\boxed{528}[/tex]

Answer:

5 + 20 + 6

Step-by-step explanation:

that's how you get

Answer:

3x^4+8x^3+9x^2+2x

Answer:

The answer is 216

Step-by-step explanation:

Answer:

The answer is 0.6*7=4.2ounces of fish food.

Step-by-step explanation:

If 0.6 ounces of fish food will suffice for Dominic's fish for a month, then for 7 months he would need 7 times the food he requires for 1 month.

7*0.6=4.2 ounces of fish food.

Answer:

8056 mm

Step-by-step explanation:

1 m=1000 mm

(8×1000)mm+56 mm

=8000 mm+56 mm

=8056 mm

Answer:

yes all are right

Step-by-step explanation:

Answer:

Step-by-step explanation:

for question 5 )  

we know that  x-5 = 6   because I'm pretty sure outside of the question we are told that the rectangles  are similar and therefore,  we can say the above

x-5 = 6

add 5 to both side

x = 11

for question 6)

30 is  [tex]\frac{5}{6}[/tex] of 36, so use that on the remaining given side

 [tex]\frac{5}{6}[/tex] * 15 = 12.5

then thats what the other side of the bigger shape is

12.5 = x + 6

minus 6 from both sides

6.5 = x

by the way,  notice that they have used a variable "x" for both 5 & 6 which is named the same but has a different value  in each problem.  X is the name of the variable for each problem, but doesn't have any meaning once outside of each of the problems.  It's just confusing to use the same named variable at times.  something like xy   and xz ,  might have been better names.    anyway  :)

Answer:

y =8x - 64

Step-by-step explanation:

that is the procedure above the

Answer:

a = - 6

Step-by-step explanation:

Given

f(x) = 3x + 5 , then

f(a) = 3a + 5 and f(a) = - 13 , then equating the right sides

3a + 5 = - 13 ( subtract 5 from both sides )

3a = - 18 ( divide both sides by 3 )

a = - 6

Answer:

a = -6

Step-by-step explanation:

see, x has been replaced by a.

so f(a) = 3a + 5 . . . . . . . (i)

a displaces x from it's every position in the equation.

and it's given that f(a) = -13

putting f(a) = -13 in equation (i) :-

3a + 5 = -13

3a = -18

[tex] \blue{ \implies}\mathfrak { \red { \underline{ \: a = - 6 } } } [/tex]

You have the right idea. You'll apply a y-axis reflection to go from above the x axis to below it. This allows us to move the red line into the correct vertical position without having to use a vertical translation.

Afterward, you'll shift the red line 4 units to the right to have it line up perfectly with the blue line.

Going from f(x) to -f(x) is the y-axis reflection part

Going from -f(x) to -f(x-4) will shift the line 4 units to the right.

Answer:

648

Step-by-step explanation:

18√2×18√2= (18√2)²

                  = (18)²×(√2)²

                  = 324×2

                  = 648

Given:- 7x + 1 < 4(x - 2)

7x + 1 < 4(x - 2)

7x + 1 < 4x - 8

7x - 4x < -8 -1

3x < -9

x < -9/3

x < -3

Answer: x=31°

Step-by-step explanation:

To find the missing angle, we need to use SOHCAHTOA. We can eliminate sine and tangent because we aren't given the opposite side. Therefore, we use cosine.

[tex]cos(x)=\frac{48}{56}[/tex]          [use inverse cosine]

[tex]x=cos^{-1}(\frac{48}{56})[/tex]

[tex]x=31[/tex]

Now, we know x=31°.

Answer:

1/6 for white and 1/2 for black

Step-by-step explanation:

My knowledge!

Hope it helps!

Answer:

4/15

Step-by-step explanation:

There are 6 white+4black = 10 marbles in the bag

P (white) = white marbles / total marbles = 6/10 = 3/5

We keep the marble

There are 5 white+4black = 9 marbles in the bag

P (black) = black/total = 4/9

P(white, black no replacement) = 3/5 * 4/9 = 3/9 *4/5 = 1/3*4/5 = 4/15