Composition of functions

Answer:

6

Step-by-step explanation:

The opposite of -3 is 3. Opposite numbers are numbers that when added, sum to 0. The distance between 3 and -3 is |3 - (-3)| = |3 + 3| = |6| = 6.

Answer:

The monthly disability benefit is $2580

Step-by-step explanation:

Given

[tex]Final\ Salary\ (P) = \$43000[/tex]

[tex]Age = 52[/tex]

[tex]Benefit\ Rate (R) = 2\%[/tex]

Worked = 26 years

Expected = 62 years

Required

Determine the monthly disability benefit

First, we need to determine the years (T) left for her to work;

[tex]T = Expected - Worked[/tex]

[tex]T = 62 - 26[/tex]

[tex]T = 36[/tex]

Next, is to calculate the yearly disability benefit as follows;

[tex]Benefit = PRT[/tex]

Substitute 36 for T, 2% for R and 43,000 for P

[tex]Benefit = 43000 * 2\% * 36[/tex]

Convert percentage to decimal

[tex]Benefit = 43000 * 0.02 * 36[/tex]

[tex]Benefit = 30960[/tex]

There are 12 months in a year;

So; Monthly Benefit is as follows;

[tex]Monthly = \frac{30960}{12}[/tex]

[tex]Monthly = \$2580[/tex]

Hence, the monthly disability benefit is $2580

Answer:

-75 meters

Step-by-step explanation:

First, subtract 15 from 50, since it is going up:

50 - 15

= 35

Then, add 40, since it is going back down:

35 + 40

= 75

So, the new position is -75 meters relative to sea level

First condition of submarine=50 m below the sea=-50 m

It goes up 15 m, that means we must add up 15 m.

-50 m+15 m=

15 m-50 m=-35 m (35 m below the sea)

And, then goes down 40 m, so we subtract it with 40 m.

-35 m-40 m=-75 m (75 m below the sea)

So, the right answer is 2. (-75 meters)

Thank you.

Answer:

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

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 3 when x = [tex]\frac{1}{3}[/tex] , then

3 = [tex]\frac{k}{\frac{1}{3} }[/tex] ( multiply both sides by [tex]\frac{1}{3}[/tex] )

3 × [tex]\frac{1}{3}[/tex] = k

1 = k

y = [tex]\frac{1}{x}[/tex] ← equation of variation

|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000

Answer:

Height after 5 seconds is 215 ft

Step-by-step explanation:

Given that:

The initial velocity of object which is projected upwards is 123 ft/sec.

Height of the object, h after time t in seconds,  is given as:

[tex]h=-16t^2+123t[/tex]

Here, t will always be positive, so [tex]123t[/tex] and [tex]16t^2[/tex] will also be positive.

But coefficient of [tex]16t^2[/tex] is negative, that means something is subtracted from the positive term [tex]123t[/tex].

To find:

Height of object after 5 seconds.

Solution:

Given that [tex]t=5[/tex] seconds.

Let us put the value in the given relation of [tex]h[/tex] and [tex]t[/tex]:

[tex]h=-16\times 5^2+123 \times 5\\\Rightarrow h=-400+615\\\Rightarrow \bold{h = 215\ ft}[/tex]

So, height after 5 seconds is 215 ft.

Answer:

1/48 or 0.02083 in decimal form

Step-by-step explanation:

Answer:

1/48

Step-by-step explanation:

1*1=1

6*8=48

Answer:

It will change the x by -1 and the y by +6

Step-by-step explanation:

Translating is sliding a shape up or down, thus coordinates will be changed

Answer:

Option 3

Step-by-step explanation:

AX and XB are congruent because we know that CD is a perpendicular bisector of AB.

The word "bisector" indicates that AB is cut into two equal parts, which allows us to make that claim.

<AXC≅<BXC because they are both equal to 90 degrees. This is because perpendicular means that the two lines are meeting at a 90-degree angle. Since both of them are 90 degrees, they are congruent.

Lastly, we know that XC ≅ XC since they are the same side.

With that in mind, we are able to prove that triangle AXC and BXC are congruent by SAS or side angle side. (The angle is between the two sides)

The correct choice would be option 3.

Answer:

Let x be the number of silver medals.

As there were two more gold medals than silver ones, gold medals are x+2

We also know that the number of bronze medals was 4 less than the sum of gold and silver, so if there are x + 2 of gold and x of silver, there are x+x+2-4 of bronze.

Now, we can do an equation, as we know there were a total of 28 medals:

x + x + 2 + x + x + 2 - 4 = 28

And we isolate x:

4x = 28

x = 28/4 = 7

There were 7 silver medals, so there were 9 gold ones (7-2) and 12 of bronze (9+7-4).

The number of Gold, Silver and Bronze medals are 9, 7 and 12 respectively.

Let the number of silver medals = s

Let the number of good medals = s + 2

Let the number of bronze medals = 2s - 2

Total medals = 28

Therefore, the value for each medal will be:

s + s+2 + 2s-2 = 28

Collect like terms

4s = 28 - 2 + 2

4s = 28

s = 28/4 = 7

Silver medals = 7

Gold medals = s + 2 = 7 + 2 = 9

Bronze medals = 2s - 2 = 2(7) -2 = 14 - 2 = 12

Read related link on:

https://brainly.com/question/16784592

===================================================

Work Shown:

L = length = 2 cm

W = width = 2 cm

H = height = 3 cm

SA = surface area of rectangular prism (aka rectangular block)

SA = 2*(LW + LH + WH)

SA = 2*(2*2 + 2*3 + 2*3)

SA = 2*(4+6+6)

SA = 2*(16)

SA = 32 square cm

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

So there are five candy bars.

Herself and two sisters equals 3 people in total.

This is a graph of 5 candy bars, each line being 1/2.

━ ━

━ ━

━ ━

━ ━

━ ━

If she ate half of one... the graph would become this.

━ ━

━ ━

━ ━

━ ━

━

Now there are 9 halves. You need to split the 9 halves for 3 people. 9 divided by 3 is 3.

Each person gets 3 halves, or 1 and 1 half.

Mai: ━ ━ ━

Sister 1: ━ ━ ━

Sister 2: ━ ━ ━

Altogether that is 9 halves, AKA the number of halves Mai had after she ate 1/2.

The amount Mai ate in the first place: ━

9 halves plus 1 half, equals 10 halves. Each whole has 2 halves. 10 divided by 2 is 5, AKA the number of candy bars she had in the first place.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

Answer:

x⁴-32x³+384x²-2048x+4100

Step-by-step explanation:

f(g(x))= g(x)⁴+4

and simplify it

Answer:

Add 5 to both sides.

Step-by-step explanation:

3.7 = x + (-5)

3.7 + 5 = x + ( -5) + 5

5 cancels on the right

8.7 = x

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 3.7=x+(-5).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 3.7=x-5

Add 5 to both sides of an equation, we get

3.7+5=x-5+5

x=8.7

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

To learn more about the solution of an equation visit:

https://brainly.com/question/14506845.

#SPJ5

Answer:

4x+2=22

4x+2-2=22-2

4x=20

4x/4=20/4

x=5

Answer:

2y+1=0

Step-by-step explanation:

a number one greater than y is y+1

so sum of y and y+1= 2y+1

Answer:

2y+1=0

Step-by-step explanation:

a number one greater than y is y+1

so sum of y and y+1=2y+1

hope its helpful

Answer:

(3x - 5) (x + 3)

Step-by-step explanation:

Multiply the coefficient of the first term by the constant:

3 x -15 = -45

Find two factors of -45 that equals 4:

-5 + 9 = 4

Rewrite the polynomial splitting 4 using -5 and 9:

3x2 - 5x + 9x - 15

Add up the first 2 terms, pulling out like factors:

x • (3x-5)

Add up the last 2 terms, pulling out common factors:

3 • (3x-5)

Add everything up:

Answer

(x+3) (3x-5)

Answer:

14 years

Step-by-step explanation:

To find the answer you have to use the formula to calculate time:

t=(1/r)(A/P-1), where:

t=time

r=rate of interest=4.6%

A=accrued amount=$328.80

P=principal amount=$200

t=(1/0.046)*(328.80/200-1)

t=21.74*(0.644)

t=14

According to this, the answer is that she opened the bank account 14 years ago.

Answer:

See below.

Step-by-step explanation:

So, looking at the graph (and you graphed correctly, so nice job :D ) we can see that the range (the span of y-values) covered by the graph is everything less than or equal to 0. Therefore, our range should be all values less than or equal to 0. And this includes 0.

Therefore, in interval notation, our answer is:

[tex](-\infty,0][/tex]

Your answer of:

[tex](0,-\infty)[/tex]

is incorrect for 2 reasons.

First, we need to use brackets for the 0 since we include it in our solution set. (5,0) is a valid point in the equation (it's also the vertex). Thus, we need to use brackets.

Second, traditionally, the smaller unit comes first. 0 is technically greater than negative infinity. Yes, the graph does go from 0 to negative infinity, but conventionally, we would still write negative infinity first.

And everything else is correct (maybe you forgot to add "flipped over x-axis for the first question," however?) so nice work!

Answer:

5.5

Step-by-step explanation:

The lowest temperature ever recorded on Earth is =-94.7

Before this date, the previous record was at= -89.2

the difference between these two extreme temperatures=-89.2-(-94.7)

                                                                                              =-89.2+94.7

                                                                                              =5.5

The difference between these two extreme temperatures is 5.5

Answer:

1. r+s²=49

2. pq²=24

3. -4xy-6x²+2x²y-6y= -54

Step-by-step explanation:

1. r+s²=0+7²=49

2. pq²=(6)(2)²=6(4)=24

3. -4xy-6x²+2x²y-6y= -4(3)(2)-6(3)²+2(3)²(2)-6(2)

                                = -24-6(9)+2(9)(2)-12

                                = -24-54+36-12

                                = -78+36-12

                                = -42-12

                                = -54

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

So we have:

[tex]-10x+6(x-5)=12x-62[/tex]

Distribute:

[tex]-10x+6x-30=12x-62[/tex]

Combine like terms:

[tex]-4x-30=12x-62[/tex]

Subtract 12x from both sides:

[tex]-16x-30=-62[/tex]

Add 30 to both sides:

[tex]-16x=-32[/tex]

Divide both sides by -16:

[tex]x=2[/tex]

And that's our answer :)

Answer: x=2

Step-by-step explanation:

first you distribute -10x+6x-30=12x-62

then combine all like terms -16x=-32

then divide -16x/-16=-32/-16

answer x=2

Answer:

210 degrees

Step-by-step explanation:

-150 + 360 = 210

The angle between 0° and 360° is 210°

In plane geometry a figure is formed by "two ray or lines and that shares same point is called an angle".

Co terminal are angles in "standard position (angles with initial side along the positive x-axis) they have common terminal side".

According to the question,

The co terminal angle is 150°. The plane is formed by angle between 0° and 360°. In order to find angle is 150° + 360° = 210°.

Hence, the angle between 0° and 360° is 210°.

Learn more about angle here

https://brainly.com/question/16043115

#SPJ2

Answer: [tex]3x^6+x^5-x^4-6x^3+x^2+3x-1[/tex]

Step-by-step explanation:

 (3x^2+x-1)(x^4-2x+1)

=3x^6-6x^3+3x^2+x^5-2x^2+x-x^4+2x-1

=3x^6+x^5-x^4-6x^3+x^2+3x-1

Hope this helps!! :)

Please let me know if you have any question

Answer:

the thing below xd

Step-by-step explanation:

[tex](3x^{2} +x-1)(x^4-2x+1)\\\\=3x^2(x^4-2x+1)\\+x(x^4-2x+1)\\-1(x^4-2x+1)\\\\=3x^6-6x^3+3x^2\\+x^5-2x^2+x\\-x^4+2x-1\\\\=3x^6+x^5-x^4-6x^3+(3-2)x^2+(1+2)x-1\\\\=3x^6+x^5-x^4-6x^3+x^{2} +3x-1[/tex]

Answer:

√2, pi.

Step-by-step explanation:

An irrational number cannot be written as a fraction a/b where a and b are integers ( not = 0)..

Answer:

El costo es:

Primero tenemos un cargo fijo de $140.

Luego tenemos un $25 por cada m^3 consumido.

Entonces, si tenemos x m^3 consumidos en un mes, el cargo de ese mes va a ser:

C(x) = $140 + $25*x.

Esto es una relación linear.

A) En este caso tendríamos x = 140

C(140) = $140 + $25*140 = $3640

B) La formula es, como ya escribimos arriba, C(x) = $140 + $25*x.

C) El grafico estará al final.  En el podemos ver que la linea corta el eje vertical en y = $140, que seria lo minimo que se puede pagar al mes, en el caso de que el consumo sea x = 0.

D) La ordenada al origen es $140, representa el cargo fijo que no depende de la variable x.

Answer:

$54.40

Step-by-step explanation:

First, find the new price after the 20% markdown:

80(0.8)

= 64

Then, find the price with the 15% markdown:

64(0.85)

= 54.4

So, the new price of the coat is $54.40

Answer:

[tex]5x= 15[/tex]

Step-by-step explanation:

Given

[tex]3x - 5 = -2x +10[/tex]

Required

Write the variables and constants on different sides

[tex]3x - 5 = -2x +10[/tex]

Add 2x to both sides

[tex]2x + 3x - 5 =2x -2x +10[/tex]

[tex]5x - 5 =10[/tex]

Add 5 to both sides

[tex]5x - 5 + 5 = 10 + 5[/tex]

[tex]5x= 10 + 5[/tex]

[tex]5x= 15[/tex]

Hence, the equation is

[tex]5x= 15[/tex]

Solving further [divide both sides by 5]

[tex]x = 3[/tex]

I think it is -5=x

Step-by-step explanation:

Answer:

the average cost if you go to ten classes plus the 200 plus 100 it will equal 300

Step-by-step explanation:

200 annual fee then 10+10+10+10+10+10+10+10+10+10 equal 100   so 200+100 equal 300 for the 10 classes plus the annual fee.