Use the functions and the scenario to solve the problem.

f(x)=1/2x+6
g(x)=x−3

Shiloh and Leanne are asked to evaluate f(x)−g(x).

Shiloh suggests f(x)−g(x)=(x−3)−(1/2x+6)=1/2x−9.

Leanne suggests f(x)−g(x)=(12x+6)−(x−3)=−12x+9.

Evaluate each student's answer.

Select two answers. Select the correct evaluation of Shiloh's work and the correct evaluation of Leanne's work.

Answer:

Given a triangle ABC, Pythagoras' Theorem shows that:

[tex]c^2=a^2+b^2[/tex]

Thus,

[tex]c = \sqrt{a^2+b^2}[/tex]

The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.

[tex]d^2 = (x_{2} -x_{1})^2 + (y_{2} -y_{1})^2[/tex]

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

Therefore when given the hypotenuse with endpoints at

[tex](x_{1}, y_{1}) and {(x_{2}, y_{2})[/tex]

We know that the third point of the right triangle will be at

[tex](x_{2}, y_{1})[/tex]

and that the two side lengths will be defined by the absolute values of:

[tex](x_{2} - x_{1}) = a[/tex]

[tex](y_{2} - y_{1}) = b[/tex]

Answer:

17

Step-by-step explanation:

Answer:

x=2+\sqrt{6}, :x=2-\sqrt{6}

Step-by-step explanation:

those are the 2 awnsers

Step-by-step explanation:

[tex](x - |2| ){}^{2} = 2 + {2}^{2} [/tex]

[tex]x - 2 = \sqrt{6} \\ x = + - \sqrt{6} + 2 \\ x = - \sqrt{6} + 2 \\ x = \sqrt{6} + 2[/tex]

Answer:

(x − 2)×(3x+1)

Step-by-step explanation:

We can use this method:

[tex]\begin{aligned}3 x^{2}-5 x-2 &=3 x^{2}-5 x-x+x-2 \\\\&=3 x^{2}-6 x+x-2 \\\\&=3 x \cdot(x-2)+(x-2) \\\\&=(x-2)(3 x+1)\end{aligned}[/tex]

All I did is Subtracting x then adding x which will not affect the result because  -x + x = 0

The values of a and b in the sytem of equation are 12 and 9 respectively.

b = 3 / 4 a

a + b = 21

Therefore, let's substitute b in equation(ii)

a + b = 21

a + 3 / 4 a = 21

4a + 3a / 4 = 21

7a / 4 = 21

cross multiply

7a = 21 × 4

7a = 84

divide both sides by 7

a = 84 / 7

a = 12

b = 3 / 4 a

b = 3 / 4 × 12

b = 36 / 4

b = 9

learn more on system of equation here:  https://brainly.com/question/11837694

Answer:

98 m

Step-by-step explanation:

The formula of the volume is ↓

Length × width × height

= 7 × 7× 2

= 98 m

Answer:

A

Step-by-step explanation:

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps

Hope this helps!

Answer:

180 + 48 = 228 :D

Step-by-step explanation:

We will first find the volume of the brown figure :)

6 x 6 x 5

36 x 5

180

Now we will find the volume of the blue figure :)

6 x 1 x 8

6 x 8

48

Now we add!!

180 + 48 =228

Have an amazing day!!!

Please rate and mark brainliest!!

Answer:

180 +48=228 cubic centimeters

the volume of the first shape=180 (you multipy length width and height)

the volume of second shape=48

add them=180+48=228

Answer:

72.80= 70(x)^1

x^1 is still x, so leave it at 72.8= 70x
divide 70 from both sides to leave x by itself

x= 1.04
4% interest is payed annually.

Hence, the simple percent interest per year is [tex]4[/tex]%.

What is the simple percent interest?

Simple interest is a quick way of calculating interest. Simple interest is worked out by calculating the percentage amount and multiplying it by the number of periods that the money will be invested for.

Here given that,

Sophia invests money in an account paying simple interest. She invests $[tex]70[/tex] and no money is added or removed from the investment. After one year, she has $[tex]72.80[/tex].

So,

[tex]70x=72.80\\\\x=\frac{72.80}{70}\\\\x=1.04[/tex]

which is [tex]4[/tex]% interest is payed annually.

Hence, the simple percent interest per year is [tex]4[/tex]%.

To know more about the simple percent interest

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Answer:

Step-by-step explanation:

Guiding Statement

You must find x before you can find y. If an altitude is dropped from the right angle to the hypotenuse, then the value of the altitude = the two parts of hypotenuse multiplied together = the altitude squared.

Formula

Perhaps, instead of all that language, it is easier just to show you this in terms of what you have been given.

Solution

x^2 = 72                        Factor 72 into prime factors.

x^2 = 8 * 9

x^2 = 2 * 2 * 2 * 3 * 3    Take the square root of both sides.

√x^2 = √(2 * 2 * 2 * 3 * 3)  

Rule

For every pair of equal prime factors, take 1 factor outside the root sign and throw the other one away.

√x^2 = √(2 * 2 * 2 * 3 * 3)

x = √(2 * 2 * 2 * 3 * 3)                 Apply the rule

x = 2 * 3 √2

x = 6√2

Now with y

a = 6√2

b = 12

c = y Use the Pythagorean Theorum

c^2 = a^2 + b^2

c^2 = (6√2)^2 + 12^2

c^2 = 36*2 + 144

c^2 = 72 + 144

c^2 = 216

c = 6 √6

answer

x = 6√2

y = 6√6

Answer:

for because the 3+1 =4

Step-by-step explanation:

thank you

Answer:

Your answer is k< -6

Step-by-step explanation:

Answer:

what was the importance of the meetings of the second continental Congress quizlet answers

Answer: b = 4f

Step-by-step explanation:

     Since every flashlight needs 4 batteries, every flashlight added (f) will be 4 more batteries needed total (b). With this information in mind, we can write the equation:

             b = 4f

Answer:

b = 4f

Step-by-step explanation:

4 batteries per flashlight

Answer:

If we look at this spinner, we first need to find out how many letters there are in total.

There are 12 letters in total.

1.

For this question, they want us to find the probability of getting the letter 'R'.

We need to find how many letter 'R's there are.

There are 2 lettered 'R', out of the 12 letters.

So the probability of getting the letter 'R' is 2/12 which simplifies to 1/6.

2.

For this question, they want us to find the probability of getting the letter 'L'.

We need to find how many letter 'L's there are.

There are 3 lettered 'L's, out of the 12 letters.

So the probability of selecting the letter 'L' is 3/12 which simplifies to 1/4.

3.

For this question, they want us to find the probability of getting the letter 'B'.

We need to find how many letter 'B's there are.

There are 0 lettered 'B's, out of the 12 letters.

Therefore the probability of selecting the letter 'B' is impossible.

4.

For this question, they want us to find out which letter has the most likely chance of getting landed on.

In order to find this, we need to find one letter that is repeated a lot in this spinner, that way it is more likelier of getting that letter.

Let's look at each individual letter keeping the letters we've found so far to the side.

P(Z) = 4/12, which simplifies to 1/3.

P(S) = 1/12, which is already in simplest form.

P(F) = 2/12, which simplifies to 1/6.

Now let's compare all the probabilities for selecting each letter.

P(R) = 1/6

P(L) = 1/4

P(B) = impossible ← immediately eliminate this choice

P(Z) = 1/3

P(S) = 1/12

P(F) = 1/6

Now out of all of these probabilities, we can infer that the chances of getting the letter 'Z' is the most likeliest.

Now

114°

Explanation:

ΔE = mcΔT

ΔE = 5(0.38)(80 - 20)

ΔE = 1.9(60)

ΔE = 114°

Answer:

multiple then dived the numbers together

Based on the previous worth of the stock and the value lost, the new value of the LMNOP stock is $75.14.

The value of $85 lost approximately 11.6% of its value.

The new value can be found as:

= Previous stock price x ( 1 - percentage loss)

Solving gives:

= 85 x (1 - 11.6%

= 85 x 88.4%

= $75.14.

Find out more on stock pricing at https://brainly.com/question/25300299.

Answer:

Area of a triangle = (base x height) / 2

if the base is 3 and height is 4

Area = (3x4)/2 = 6 sq units

if the base is 4 and height is 8

Area = (4x8)/2 = 16 sq units

if base is 3 and height is 8

Area = (3x8)/2 = 12 sq units

Answer:

The third option

Step-by-step explanation:

the lowest point on function 1 is -7

the lowest point on function 2 is -9

Answer:

F(t) = 5t

Step-by-step explanation:

velocity = distance/time

distance = velocity × time

v - velocity

t - time

d - distance

v = 5

Distance as a function of time:

F(t) = 5×t

where F(t) represents distance

A boy hikes a distance of d km in t hours. The formula describes d as a function of t, F(t) = 5t.

velocity = distance/time

v - velocity

t - time

d - distance

v = 5

distance = velocity × time

Distance as a function of time

Therefore, F(t) = 5×t

Where F(t) represents the distance.

To learn more about the distance visit:

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Answer: Choice E

[tex]x \ne -4, -1[/tex]

This is the same as saying [tex]x \ne -4 \text{ and } x \ne -1[/tex]

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

Reason:

If we plugged x = -4 into the function, then the x+4 in the denominator turns to 0.

x+4 = -4+4 = 0

Dividing by zero is not allowed. It leads to a division by zero error. Therefore, we need to exclude -4 from the domain. Similar reasoning will exclude -1 as well because it makes the x+1 in the denominator to be zero.

Any other x value is valid.

Side note: The (x+1) terms cancel, which may appear that x = -1 is valid. However, your calculator will likely not perform such a simplification. It will simply try to directly compute the result using PEMDAS. That means x = -1 is likely to produce a division by zero error.

Answer:

4 layers

128 cm²

0.1 m

Step-by-step explanation:

Layers of chocolate

Volume of box

Length of river on map

Answer:

128

Step-by-step explanation:

Volume of an open box= 2(b x h) + 2(l x b) + 2(l x h)

now here the length and breadth are same, so both are 8, and there is no need to put 2 before (l x b) as it is an open box

(8 x 8) + 2(8 x 2) + (8 x 2)

Answer:

Robert spent $16.54 for the trail mix.

Step-by-step explanation:

Multiply 2.45 with 6.75 to get 16.5375, and round it up to get 16.54

Answer:

[tex] - 3 - 9 = - 3y \\ - 12 = - 3y \\ y = ( - 12) \div ( - 3) \\ y = 4[/tex]

Answer:

35.57 degrees

Step-by-step explanation:

tan x = 108/151

tan x = 0.71523

x = 35.57 degrees

Answer:

-2

Step-by-step explanation:

Given :

Solving :

Answer:

-2

Step-by-step explanation:

Given expression: -k - k

Combine like terms and simplify:

⇒ -k - k

⇒ -(k + k)

⇒ -(2k) = -2k

Determining the constant:

The constant of the term MUST be an integer. It CANNOT be a variable. In this case, the only constant that is a cooeficient of k is -2.

Thus, the cooeficient of -k−k is -2.

Answer:

64.5 in²

Explanation:

[tex]\sf area \ of \ trapezoid = \dfrac{1}{2} * ( a + b) *h[/tex]

Solve for the entire trapezoid:

[tex]\hookrightarrow \sf \dfrac{1}{2} * ( 6.5 +(9.8+5.2+6.5) ) *8.6[/tex]

[tex]\hookrightarrow \sf 120.4 \ in^2[/tex]

Solve for the unshaded rectangle:

Area of the shaded region:

If it didn't have that piece cut out on the bottom, it would be a rectangle that's 9cm wide and 5cm high.  Its area would be 9x5= 45 cm².

But that piece is cut out of the bottom.  The cut-out piece is 3cm wide and 3cm high, so its area is 3x3= 9 cm².

9 cm²  have been cut out of the 45 cm²  of the complete big rectangle.  So the remaining area of the figure is  45 - 9 = 36 cm² .