Practice Writing Composite Functions Given: f(x) = x - 7 and h(x) = 2x + 3 Write the rule for h(f(x)).

Answer:

When t= 0

f(t)= 40 degrees

The value of −32(2.718)^−0.06t approach 0 as t increases

If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72

Step-by-step explanation:

The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator.

f(t)=72−32(2.718)^−0.06t

When t= 0

f(t)=72−32(2.718)^−0.06(0)

f(t)=72−32(2.718)^(0)

f(t)=72−32(1)

f(t)=72−32

f(t)= 40 degrees

As t increases −32(2.718)^−0.06t

Let t= 1

=−32(2.718)^−0.06(1)

= −32(2.718)^−0.06

= -30.14

Let t = 2

=−32(2.718)^−0.06(2)

=−32(2.718)^−0.12

=−32(0.8869)

= -28.38

The value of −32(2.718)^−0.06t approach 0 as t increases

If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72

When t = 0, the temperature of the juice is 40°.

                    As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.

                    So, f(t) gets close to 72°

    Function representing the temperature of of the juice at any time 't' is,

[tex]f(t)=72-32(2.718)^{-0.06t}[/tex]

1). If t = 0,

  [tex]f(0)=72-32(2.718)^{-0.06\times 0}[/tex]

          [tex]=72-32(1)[/tex]

          [tex]=40[/tex] degrees

2). If [tex]t\rightarrow \infty[/tex],

    [tex]-\frac{1}{32(2.718)^{0.06t}} \rightarrow 0[/tex]  

[As denominator of the fraction becomes larger and larger with the increase in the value of t, value of fraction gets smaller and smaller]

3). if [tex]t\rightarrow \infty[/tex], [tex]f(t)\rightarrow 72[/tex]

  Therefore, when t = 0, the temperature of the juice is 40°.

                    As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.

                    So, f(t) gets close to 72°.

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Answer:

Hey there!

5. f(4) is 3. f(3) is 2. Thus, f[f(4)]=2

6. g(2) is 3. g(3) is 1. g[g(2)]=1

Hope this helps :)

Answer:

see below

Step-by-step explanation:

4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5

All exponent have to have the same number

42 x 10^5 − 1.2 x 10^5 − 2.5 x 10^5

Subtract the number

42 - 1.2 - 2.5 = 38.3

Add back the exponent

38.3 * 10 ^5

This is not in scientific notation

Move the decimal one place to the left and add one to the exponent

3.83 * 10^6

3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8

All exponent have to have the same number

3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

Add the numbers

3.3+2.6+.77 =6.67

Add back the exponent

6.67*10^9

This is in scientific notation

8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3

All exponent have to have the same number

8.0 x 10^4 − 3.4 x 10^4 − .12 x 10^4

Subtract

8.0 - 3.4 - .12 = 4.48

Add back the exponent

4.48* 10^4

This is in scientific notation

Answer:

NopE, can’t be made into a fraction

Answer:

Yes

Step-by-step explanation:

A number is rational if it can be expressed in the form p/q, where q is not zero.

3.824 can be expressed as 3824/1000.

So, it satisfies the criteria of a rational number.

Answer:

Intersects; intersection point: (-2,3)

Step-by-step explanation:

Substitute -1.5x for y into y=0.5x+4:

-1.5x = 0.5x +4

-1.5x - 4 = 0.5x

-4 = 2x

x = -2

Plug in -2 for x into y=-1.5x

y = -1.5(-2)

y = 3

Organize the x and y values into an ordered pair:

(-2,3)

Answer:

y=0.5x+4 intersects y=-1.5x.

The intersection point is (-2,3)

Step-by-step explanation:

First, note that if two lines are not parallel, then they must intersect eventually in one way or another. Note that since these are two lines, they will only have one intersection points.

So we have the equation:

[tex]y=-1.5x[/tex]

Parallel lines have the same slope. Therefore, a line parallel to this line also has a slope of -1.5

The equation given to us is:

[tex]y=0.5x+4[/tex]

As we can see, this does not have a slope of -1.5. Therefore, the given equation is not parallel to y=-1.5x. However, this does mean that it will intersect y=-1.5x.

To find the x-value of their intersection, simply set the equations equal to each other and solve for x.

[tex]-1.5x=0.5x+4\\-2x=4\\x=-2[/tex]

Now, plug -4 into either of the equations:

[tex]y=-1.5(-2)=3\\y=0.5(-2)+4=-1+4=3[/tex]

Therefore, the point of intersection is (2,3).

Answer:

I have to agree

it's A.

but I'm also thinking it's D.

Answer:

X = 1

Step-by-step explanation:

To solve the system of equation by susbtitution:

3x + y = 9

y = –4x + 10

We can follow the steps thus:

Substitute the value of y in the first equation:

As in the second equation y = -4x + 10 we can substitute in the first equation as follows:

3x + y = 9

3x + -4x + 10 = 9

Combine like terms:

3x + -4x + 10 = 9

Like therms are the therms with X (3x - 4x = -1x):

-1x + 10 = 9

Apply the subtraction property of equality:

-1x + 10 = 9

As 10 is suming, it passes to subtracting the 9:

-1x  = 9 - 10

-1x = -1

Apply the division property of equality:

-1x = -1

Dividing in -1:

x = -1 / -1

Answer:

b

Step-by-step explanation:

The value of x in this system of equations is 1.

3x + y = 9

y = –4x + 10

Substitute the value of y in the first equation:

Combine like terms:

Apply the subtraction property of equality:

Apply the division property of equality:

3x + (–4x + 10) = 9

–x + 10 = 9

–x = –1

x = 1

What is the value of y?

y =  

Analyzing the text, we find that the function is decreasing over the following intervals: (0, 1)

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

Going from maximum to minimum, meaning that between them the function decreases, thus, the first interval it is decreasing is between (0,1).

Going up, increases.

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

Thus, the function decreases over the following interval: (0, 1)

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Hi there!  

»»————-　★　————-««

I believe your answer is:

No.

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

See the graph attached.

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»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

No, (3, -3) is not the solution to the graphed system of inequalities.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

From the graph,

The point of intersection is (2, 3).

This is the solution to the graphed system of inequalities.

But,

(3, -3) is given as the solution which is not true.

Thus,

(3, -3) is not the solution.

Learn more about inequalities here:

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Answer:

2,400,000,000,000

Step-by-step explanation:

2.4 x 10^12 means that the decimal point is moved 12 places to the right (hence the power of 12)

So by moving the decimal point 12 times you get this: 2,400,000,000,000

The reason why there are only 11 zeroes is because the 4 was a decimal place  to the right of 2, thus losing a zero.

Answer:

let R represent red hair

let G represent green eyes

from Baye's theorem:

[tex]P( \frac{R}{G} ) = \frac{P(RnG)}{P(G)} [/tex]

P(RnG) = 5

[tex]P(G) = { \sum}(green \: hair) \\ = (3 + 5 + 5) \\ = 13[/tex]

Therefore:

[tex]P( \frac{R}{G} ) = \frac{5}{13} \\ = 0.385[/tex]

The conditional relative frequency = 0.385

The conditional relative frequency will be  0.385

It is a theorem showing how to compute the conditional probability of each of a set of possible causes for a given observed outcome using knowledge about the probability of each cause and the conditional probability of each cause's outcome.

let R represent red hair

let G represent green eyes

from Baye's theorem:

[tex]P=\dfrac{R}{G}=\dfrac{P(R\cap G)}{P(G)}[/tex]

P(RnG) = 5

P(G) = ∑(Green hairs)

P(G)= 13+5+5 = 13

Therefore:

[tex]P(\dfrac{R}{G})= \dfrac{5}{13}=0.385[/tex]

The conditional relative frequency = 0.385

Hence the conditional relative frequency will be  0.385

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Answer:

180 pages

Step-by-step explanation:

Since her photocopy session is 25 pages per minute, the total number of pages photocopied in 4 hour session can be calculated as;

number of pages = time × speed

                                 = (4 × 60) × 25

                                 = 240 ×25

                                 = 6000 pages

Thus, number of pages photocopied in 4 hours is 6000.

For every 100 pages, 3 would contain some type of printing error. The number of pages she expect with printing error during 4 hour session can be determined as;

           = [tex]\frac{6000}{100}[/tex] × 3

           = 60 × 3

           = 180 pages

The expected number of pages with printing error during 4 hour photocopying session is 180 pages.

Estimate:

2.3 rounds down to 2

So after multiplying by 2, the area is estimated to be 4 cm squared.

Actual Area:

2.3 x 2 = 4.6

The actual area of the shape is 4.6 cm squared.

Hope this helped!

Answer:

4.6

Step-by-step explanation:

Answer:

Sum equation: [tex]d + 0.05d[/tex]

Product equation: [tex]1.05d[/tex]

Step-by-step explanation:

If we have an increase in 5% of d, that means that 5% of d ([tex]0.05\cdot d[/tex]) will be the total amount of money added to it.

However, we need to still count the original price of d, if we increase it by 5%!

So we add d to 0.05d.

[tex]d + 0.05d[/tex] is the sum equation.

Now, we can create the product equation for d by expanding the coefficients for the previous equation,  [tex]d + 0.05d[/tex].

[tex]1d + 0.05d[/tex]

We can add like terms here: [tex]1 + 0.05 = 1.05[/tex]! So we can just multiply this by d for our product equation.

[tex]1.05d[/tex]

Hope this helped!

Answer:

[tex]y=\displaystyle \frac{1}{2}x+1[/tex]

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.

We're given the x-intercept, -2, and the y-intercept, 1. We can directly plug the y-intercept into the equation [tex]y=mx+b[/tex] :

[tex]y=mx+1[/tex]

Now, we must solve for the slope. The x-intercept -2 gives us the point (-2,0), since the x-intercept occurs when y=0. Plug this point into the equation and solve for m:

[tex]0=m(-2)+1\\0=-2m+1\\-1=-2m\\\\\displaystyle m=\frac{-1}{-2} \\\\\displaystyle m=\frac{1}{2}[/tex]

Therefore, the slope of the line is [tex]\displaystyle \frac{1}{2}[/tex]. Plug this back into [tex]y=mx+1[/tex]:

[tex]y=\displaystyle \frac{1}{2}x+1[/tex]

I hope this helps!

Answer:

8

Step-by-step explanation:

total: 28 water attractions

pools: p

game areas: p + 2

water slides: 50% of 28 = 14

14 + p + p + 2 = 28

2p = 12

p = 6

game areas:

p + 2 = 6 + 2 = 8

Answer:

the 8 in the graph

Step-by-step explanation:

the person will travel 40 blocks in 16 minutes

Answer:

10:5 OR 2:1

Step-by-step explanation:

Let x be the parts of 25% dextrose and

y be the parts of 10% dextrose are mixed so that

20% dextrose mixture is obtained.

amount of dextrose in the mixture will be 20% of (x+y).

We have to find the value of [tex]\frac{x}y \ OR\ x:y[/tex]

Now, we can apply the concept that sum of amount of dextrose in the two liquids will be equal to the amount of dextrose in the mixture.

[tex]\Rightarrow x \times 25\% + y \times 10\%=(x+y)\times 20\%\\\Rightarrow x \times\dfrac{25}{100} + y \times \dfrac{10}{100}=(x+y)\times \dfrac{20}{100}\\\Rightarrow x \times25 + y \times 10=(x+y)\times 20\\\Rightarrow 25x + 10y=20x+20y\\\Rightarrow 25x -20x =20y-10y\\\Rightarrow 5x=10y\\\Rightarrow \dfrac{x}{y} = \dfrac{10}{5}\\\Rightarrow \bold{x:y=10:5\ OR\ 2:1}[/tex]

So, the answer is 10:5 or 2:1.

Answer:

4.90% is approximately the new Dextrose concentration.

Explanation:

Volume by Volume percent is given by ;

Volume percentage of dextrose solution = 5%

In 100 mL of solution 5 ml of dextrose is present.

Now, volume sterile water added was equal to the 40% of volume of dextrose volume.

So, volume of the sterile water added =  

Total volume of the solution after addition of water = 100 mL + 1 mL = 102 mL

New concentration of dextrose will be;

4.90% is approximately the new Dextrose concentration.

Step-by-step explanation:

Answer:

That’s ez pz

Step-by-step explanation:

Answer:

The slope is -3 and the y intercept is -44

Step-by-step explanation:

6X+ 2Y= -88

The slope intercept form of a line is y= mx+b where m is the slope and b is the y intercept

Solve for y

6X-6x+ 2Y= -88-6x

2y = -6x-88

Divide by 2

y = -3x -44

The slope is -3 and the y intercept is -44

Answer:

g(x)=3x(superscript)2

Answer:

g(x) = 3x².

Step-by-step explanation:

In the diagram, we see that the vertex has not been shifted from the origin. The only thing that happened to the graph of f(x) was that it was vertically stretched to become g(x).

Where x = 1, f(x) = 1. Where x = 1, g(x) = 3. That means that the graph of f(x) was multiplied by 3.

So, g(x) = 3x².

Hope this helps!

Answer:

y = -x +2

Step-by-step explanation:

y =x  has a slope of 1

Perpendicular lines have slopes that multiply to -1

m* 1 = -1

The slope of the perpendicular line is -1

We have a slope and a point

y = mx+b

y= -1x+b

Substitute the point into the equation

-3 = -1(5) +b

-3 =-5 +b

Add 5 to each side

-3+5 = b

2 =b

y = -x +2

Answer:

10800

Step-by-step explanation:

1 trimesters cost = 1450 + 350  $

2 year -> 6 trimester

1800$ x 6 = 10800 $

Answer:

28

Step-by-step explanation:

[tex]\frac{3}{4}-\frac{5}{7}[/tex]

Least Common Denominator of 4 & 7 is 4 * 7 = 28

[tex]\frac{3}{4}-\frac{5}{7}=\frac{3*7}{4*7}-\frac{5*4}{7*4}\\\\\\=\frac{21}{28}-\frac{20}{28}\\\\\\=\frac{21-20}{28}\\\\\\=\frac{1}{28}[/tex]

Multiplicative inverse of [tex]\frac{1}{28}[/tex] is [tex]\frac{28}{1} = 28[/tex]

Answer:

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Step-by-step explanation:

A. Yes. She solved the problem correctly.

B. No. She multiplied the dividend by the divisor instead of finding the reciprocal.

C. No. She multiplied the denominators instead of finding a common denominator.

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Her workings

7 ÷ 2/ 5

=1/ 7 × 2/ 5

= 2/35

Dividend=7

Divisor=2/5

The correct working

7 ÷ 2/ 5

=7 × 5/2

=35/2

Answer:

D

Step-by-step explanation:

I got an 100% on the quiz I took with this question :)

Hope I could help good luck on passing!!

Answer:

Hey there!

93 ÷ 5 can be written as 93/5.

5 goes into 93, 18 times, so we have [tex]18\frac{3}{5}[/tex]

Let me know if this helps :)

Answer:

x = 24

Step-by-step explanation:

We know that lines s and t are parallel. Then by definition, the two labelled angles, which are same-side angles, are congruent and equal in measure.

Then, we set the expressions equal to each other:

7x - 48 = 5x

Subtract 5x from both sides:

7x - 5x - 48 = 0

2x - 48 = 0

Add 48 to both sides:

2x = 48

Divide by 2:

x = 48/2 = 24

Thus, x = 24.

~ an aesthetics lover

Answer: