Given f(x) = 3x - 1 and g(x)= -x + 6, find f(-2) + g(5).
-6
6
8

1. You are trying to isolate "F" in the equation

[tex]C=\frac{5}{9}(F-32)[/tex]      Multiply 9/5 on both sides

[tex](\frac{9}{5})C=(\frac{9}{5}) \frac{5}{9} (F-32)[/tex]

[tex]\frac{9}{5}C=F-32[/tex]    Add 32 on both sides

[tex]\frac{9}{5}C+32=F-32+32[/tex]

[tex]\frac{9}{5}C+32=F[/tex]

THIS IS WRONG

2. You are trying to isolate "y" in the equation

[tex]m=\frac{x+y+z}{3}[/tex]   Multiply 3 on both sides

3m = x + y + z        Subtract x and z on both sides

3m - x - z = y

THIS IS CORRECT

3. Isolate "r"

[tex]s=\frac{r}{r-1}[/tex]   Multiply (r - 1) on both sides

s(r - 1) = r    Distribute s into (r - 1)

sr - s = r     Subtract sr on both sides

-s = r - sr    Factor out r from (r - sr)

-s = r(1 - s)    Divide (1 - s) on both sides

[tex]\frac{-s}{1-s}=r[/tex]

THIS IS WRONG

4. Isolate "b"

[tex]A=\frac{1}{2}(a+b)[/tex]    Multiply 2 on both sides

2A = a + b     Subtract a on both sides

2A - a = b

THIS IS CORRECT

5. Isolate "y"

[tex]m=\frac{x+y}{2}[/tex]    Multiply 2 on both sides

2m = x + y    Subtract x on both sides

2m - x = y

THIS IS WRONG

The 2nd and 4th one is right

Answer:

. You are trying to isolate "F" in the equation

     Multiply 9/5 on both sides

   Add 32 on both sides

THIS IS WRONG

2. You are trying to isolate "y" in the equation

  Multiply 3 on both sides

3m = x + y + z        Subtract x and z on both sides

3m - x - z = y

THIS IS CORRECT

3. Isolate "r"

  Multiply (r - 1) on both sides

s(r - 1) = r    Distribute s into (r - 1)

sr - s = r     Subtract sr on both sides

-s = r - sr    Factor out r from (r - sr)

-s = r(1 - s)    Divide (1 - s) on both sides

THIS IS WRONG

4. Isolate "b"

   Multiply 2 on both sides

2A = a + b     Subtract a on both sides

2A - a = b

THIS IS CORRECT

5. Isolate "y"

   Multiply 2 on both sides

2m = x + y    Subtract x on both sides

2m - x = y

THIS IS WRONG

The 2nd and 4th one is right

Step-by-step explanation:

Answer:

$8.40

Step-by-step explanation:

We can write a proportion to find the total amount last year using the information given. A proportion is two equivalent ratios set equal to each other.

[tex]\frac{125}{100}=\frac{10.50}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

125(y)=100(10.50)

125y=1050

y=8.40

Answer:

Expenses for purchasing is $245 ,Revenue $479 and Total profit $ 234

Step-by-step explanation:

Cost of two blouses = 2× 25 = $50

Revenue from blouses = 2× 38 = $76

Profit of blouses = 76- 50 = $26

Similarly cost of 3 skirts = 3×15 = $45

Revenue from Skirts = 3×26 =$78

Profit from skirts = 78-45 =$33

Now cost price of pants = 5×30 =$150

Revenue from Pants = 5×65 =$325

Profit from pants = 325-150 = $175

So Jayla's expenses for purchasing = 50+45+150

                                                           = $245

                                           Revenue = 76+78+325

                                                           = $479

                                        Total Profit = 479 -245

                                                            = $234

Jayla's total expenses were $245, she made $479 in revenue through sales, making her resultant profit $234. This is calculated by subtracting the total expenses from the total revenue.

The subject of this problem deals with the concepts of expenses, revenues, and profit in a small business setting. Jayla spent $50 on the blouses (2 x $25), $45 on the skirts (3 x $15), and $150 on the pants (5 x $30), adding up to a total expense of $245. She sold these items for total revenues of $76 for the blouses (2 x $38), $78 for the skirts (3 x $26), and $325 for the pants (5 x $65), giving her a total revenue of $479. The total profit can be calculated by subtracting the total expenses from the total revenue, and therefore, Jayla made a profit of $234 ($479 - $245).

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Answer:

The focii are 8 feet apart

Step-by-step explanation:

You can use the formula

F = √(a^2 - b^2)   where F is the distance of the focii from the center , a = length of the semi major axis and b = length of the semi minor axis)

So here it is  √(5^2 - 3^2)

= √16 = 4

So the distance is 2*4 = 8

Quadratic relations and comic sections unit test part 1

12. b. 8 feet

1. b ellipse

domain -4<=x<=4

range -3<=y<=3

2. c. x^2/3

3. c. 1/10 x^2

4. b. 5 inches

5. d. x=1/12 (y-4)^2 +2

6. b. (x-4)^2 + (y-5)^2 =49

7. b. (x+8)^2 + (y+4)^2 =25

8. d. (x+3)^2 + (y+2)^2 =9

9. a. center at (7,-6); radius 4

10. b. x^2/25 + y^2/169 =1

11. a. (0, +/- 6)

12. b. 8 ft

13. c. (put equation in graphing calculator to see graph)

14. d. (0, +/-5)

Answer:

The correct answer option is: it is a difference of squares:  (y – 15)(y + 15)

Step-by-step explanation:

We are given a polynomial and we are to determine if it is a difference of squares.

Let us recall the algebraic formulas which include:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex](a+b)(a-b)=a^2-b^2[/tex]

So if we look closely, we can conclude that the given polynomial observes the third formula of the perfect squares.

Hence, we can say that it is a difference of squares:  (y – 15)(y + 15)

[tex]y^2-225 = (y-15)(y+15)[/tex]

Answer:

f(-2)= -8

f(-1) = -1

f(0)= 0

Step-by-step explanation:

f(x) = x^3

if x =-2

f(-2) = (-2) ^3 = -2*-2*-2 = -8

if x =-1

f(-1) = (-1) ^3 = -1*-1*-1 = -1

if x =0

f(0) = (0) ^3 = 0*0*0 = 0

Answer:

Graph 4

Step-by-step explanation:

for part B

Answer:

length of each plan A work out: 1 hour

length of plan B work out: [tex]\frac{1}{2}[/tex] hours

Step-by-step explanation:

Let x represents the time taken to do plan A

y represents the time taken to do plan B

On Monday there were 5 clients who did Plan A and 2 who did Plan B.

Miguel trained his Monday clients for a total of 6 hours

5x + 2y = 6 -----------> equation 1

On Tuesday there were 3 clients who did Plan A and 8 who did Plan B. .He trained his Tuesday clients for a total of 7 hours

3x + 8y = 7  -------------------> equation 2

Now we solve for  x  and y

Let multiply the first equation by -4 to eliminate y

-20x -8y = -24

  3x + 8y = 7

------------------------ (add both equations)

-17x    = -17

Divide both sides by -17

So x= 1

Plug in 1 for x  in first equation and  solve for y

5x + 2y = 6

5(1) + 2y = 6

5 + 2y =6

Subtract 5 on both sides

2y = 1

y = 1/2

length of each plan A work out: 1 hour

length of plan B work out: [tex]\frac{1}{2}[/tex] hours

Answer:

11a^2b^8

Step-by-step explanation:

Rule 1: The coefficient (121 in this case) has it's square root taken to derive the side.

Rule 2: If a variable with a power is part of the area of  a square, then just divide the power by two

The square root of 121 = 11

The square root of a^4 = a^(4/2) = a^2

The square root of b^16 = b^(16/2) = b^8

Answer:

x) =g(x) -1  shifts the graph g(x) down 1 unit

Step-by-step explanation:

g(x) = 3x

When we add  to g(x) and make it g(x) +c, we shift the graph vertically,

+c shifts the graph up

-c shifts the graph down

h(x) =g(x) -1  shifts the graph g(x) down 1 unit

Answer:

Tiffany is 34% closer to the school.

Step-by-step explanation:

Given the statement: Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away.

She lived away from the school = 15 km

as, she moved 9.9 km away.

Now, the distance closer to school from where she lived = 15 -9.9 = 5.1 km

To, find how much percent she is closer to school.

Percent states that a number or ratio expressed as a fraction of 100.

[tex]percent = \frac{5.1}{15} \times 100[/tex] = [tex]\frac{51 \times 100}{150} = \frac{51 \times 10}{15}[/tex]

Simplify:

percent closer to school = 34%

Therefore, she is 34% closer to the school.

Answer: Our function will be

[tex]d=180-9.2t[/tex]

Step-by-step explanation:

Since we have given that

Distance of the entrance = 180 meters

Speed of Nala who is running towards the entrance of the lair = 9.2

As we know the "Distance-Speed formula":

[tex]Time=\frac{Distance}{Speed}\\\\t=\frac{180}{9.2}\\\\t=19.565\\\\t=19.57\ seconds[/tex]

So, our required function will be

[tex]d=180-9.2t[/tex]

As we increase the time distance get reduced from 180 which is the distance of the entrance .

Hence, our function will be

[tex]d=180-9.2t[/tex]

Answer:

No

Step-by-step explanation:

Let us consider two positive radicals first,

[tex]\sqrt{3} , \sqrt{5}[/tex]

We know that [tex]\sqrt{3}[/tex] is an irrational number and [tex]\sqrt{5}[/tex] is also an irrational number.

So the sum of two positive radicals does not always have a rational solution.

There are examples when the some of adding positive radicals can get us a rational solution. For example,

[tex]\sqrt{4}+\sqrt{4}  =4[/tex]

So if the radicand is a perfect square then the solution is rational.

Answer:

1. 24 outcomes

2. 3

3. A= 1/4

   Odd = 1/2 (reduced from 12/24 chances)

   A/Odd = 1/8

4. 50% the letter chosen doesn't affect the outcome of the roll of the dice

5. i believe they are independent

6. 1/8

Hope that helps!

Answer:

3/4

Step-by-step explanation:

Answer:

Length of AC = 48 units.

Step-by-step explanation:

Given in parallelogram ABCD , diagonals AC and B intersects at a point E.

Length of AE = [tex]x^2-16[/tex] units and CE = 6x.

We have to find the length of AC.

According to the property of parallelogram:

Diagonals are intersecting each other at their midpoint.

Since, E is the midpoint AC ;

so, AE = CE

[tex]x^2-16[/tex] =6x

or we can write this as;

[tex]x^2-6x-16[/tex]=0

[tex]x^2-8x+2x-16[/tex]=0

[tex]x(x-8)+2(x-8)[/tex]=0

[tex](x-8)(x+2)[/tex] = 0

Zero product property states that if ab = 0 , then either a=0 or b =0.

By zero product property, we have;

(x-8) = 0 and (x+2) = 0

x = 8 and x = -2

Since, length x cannot be negative so we ignore x = -2.

then;

x = 8

AC = [tex]x^2-16[/tex] = [tex]8^2 -16 = 64- 16 =48[/tex] units.

Therefore, the length of AC = 48 units.

Answer:

I just took the test and got the answer AC=96.

Answer:

B.) 72

Step-by-step explanation:

Because when there is one cup there are 8 fluid ounces, when there are 9 cups there are 9 times more fluid ounces.

Hello :3

To get your answer we would need to multiply.

So, if there's 8 fl. oz. in 1 cup then we need to multiply 8 by 4.

8 x 4 = 32

Your answer would be 32 fl. oz.

Hope This Helps!

Cupkake~

Answer:

Step-by-step explanation:

84-90=90-96=96-102=102-108=-6

its a sequence where A(1)=84 n A(n+1)-A(n)=6

A(n)=84+(n-1)*6; n=1,2,3,4,5

Answer:

f(x) = 84 + 6x where x=0, 1, 2, 3, 4, ...

Step-by-step explanation:

Given 84, 90, 96, 102, 108, ...

the numbers are a sequence with 84 as the initial value and in increment of 6s. So the function can be written as:

f(x) = 84 + 6x where x=0, 1, 2, 3, 4, ...

B - Brandon's age

4B - Michael's age

B + 27 - Michael's age

The equation:

4B = B + 27       subtract B from both sides

3B = 27      divide both sides by 3

B = 9

4B = 4(9) = 36

Answer:

P(1+r) = p(1+0.11)= p+0.11p=1.11p

Step-by-step explanation:

The merchandise is marked up 11%. This means you pay 100% of the price plus 11%. We can represent that as (1+r) where r is the percent marked above. For 11%, this expression would be 1+0.11. We multiply that by the price p. p(1+0.11). This simplifies to p+0.11p. We can further simplify it to 1.11p.

Answer:

p + 0.11p

i did the test

Answer:

$6 Sweet t saved on green-eyed fleas new album .

Step-by-step explanation:

As given

Sweet t saved 20% of the total cost of the green-eyed fleas new album .

.If the regular price is $30.

20% is written in the decimal form.

[tex]= \frac{20}{100}[/tex]

= 0.20

Thus

Sweet t saved on green-eyed fleas new album =  0.20 × 30

                                                                              = $6

Therefore $6 Sweet t saved on green-eyed fleas new album .

Answer:

The object will hit the ground after 10.308 seconds.

Step-by-step explanation:

h(t) = -16t² + 1700

If you graphed this function, the object would be shown hitting the ground when it crosses the x-axis, in other words, when h = 0. So, to find the answer, just set h(t) equal to 0 and solve.

-16t² + 1700 = 0   Plug this into a calculator if you have one.

t = -10.308 and t = 10.308

Since time can't be negative, your answer will be the positive value, 10.308.

The object, described by the equation h(t) = -16t^2 + 1700, will hit the ground after around 10.308 seconds. This is determined by setting h(t) to 0, yielding a valid, positive solution.

The provided equation h(t) = -16t^2 + 1700 describes the height (h) of an object as a function of time (t), taking into account gravitational acceleration. To determine when the object hits the ground, set h(t) to 0 and solve for t:

-16t^2 + 1700 = 0

Solving this equation using the quadratic formula or factoring yields two solutions: t = -10.308 and t = 10.308. However, time cannot be negative in this context, so the only valid solution is t = 10.308.

Consequently, the object will hit the ground after approximately 10.308 seconds. This conclusion is reached by identifying the point where the height function intersects the x-axis, representing ground level. The positive value for t ensures a meaningful interpretation in the temporal context, indicating the time elapsed until the object reaches the ground.

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Answer:

All the fields will be harvested in 6.25 days

Step-by-step explanation:

because 75 ÷ 12 and 62.5 ÷ 12 is 6.25

The measure of the angle 1 cannot be determined

From the question, we have the following parameters that can be used in our computation:

The pentagons ABCDE and FGHIJ

Given that pentagon ABCDE ≅ pentagon FGHIJ

We can see that there is no occurrence of the angle 1 in both figure

This means that the measure of the angle 1 cannot be determined

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Answer:

The function is  1/4x^2  + x - 8

Step-by-step explanation:

In Factor form the function  is

a(x + 8)(x - 4)    where a is a constant to be found.

= a( x^2 + 4x - 32)  Note the coefficient of x is positive because the function has a minimum value.

The line of symmetry is x = (-8+4)/2 = -2.

So the minimum value  will be the  value of f(x) when x = -2, so we have the equation

a(-2+8)(-2-4) = -9

-36a = -9

a = 1/4.

Answer:  10

Step-by-step explanation:

The correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].

The correct option is (a).

To use the distributive property to simplify the expression (9(x+3) + 15x), we need to distribute the terms outside the parentheses to each term inside the parentheses.

The given expression is [tex]\(9(x+3) + 15x\)[/tex].

1. Distribute 9 to (x) and (3):

[tex]\[ 9(x+3) = 9 \times x + 9 \times 3 \][/tex]

2. Distribute 15 to (x):

[tex]\[ 15x \][/tex]

So, after using the distributive property, the expression becomes:

[tex]\[ 9 \cdot x + 9 \cdot 3 + 15x \][/tex]

Now, let's compare this with the options:

a. [tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex] - This matches our result.

b. [tex]\(9(x+3+15)x\)[/tex] - This option seems incorrect as it doesn't distribute 9 to each term inside the parentheses correctly.

c. [tex]\(9:x+3+15x\)[/tex] - This option doesn't seem to use the distributive property correctly.

d. [tex]\(9x+9 \cdot 3+9 \cdot 15x\)[/tex] - This option distributes 9 correctly but includes an extra term (9x) that doesn't appear in the original expression.

Therefore, the correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].

Which expression is equivalent to the given expression after using the distributive property? 9(x+3)+15x

a.9· x+9· 3+15x

b.9(x+3+15)x

c.9: x+3+15x

d.9 x+9· 3+9· 15x

Answer:

24x + 15

Step-by-step explanation:

9(x+3)+15x

Use the distributive property.

9*x +9*3 + 15x

9x + 15 + 15x

Combine the like terms.

24x + 15

You are given the height of the building and the length of the shadow the building gives, so you can set that up as a proportion of Height of building over the length of the shadow so 31/28.

Now you can set the same proportion for Julian, using X for her height, so you would have x/6.

To solve for her height, set the two proportions equal and solve for x:

31/28 = x/6

Cross multiply:

31 * 6 = 28 *x

186 = 28x

Divide both sides by 28:

x = 186 / 28

x = 6.64 feet tall

To find Julian's height using the proportion between the building's height and shadow length and Julian's shadow length, we set up a proportion as follows: 31 feet (building height) / 28 feet (building's shadow) = Julian's height / 6 feet (Julian's shadow). Solving for Julian's height, we determine it is approximately 6.64 feet.

The question pertains to similar triangles and proportionality in shadows cast by objects. Using the concept of similar triangles, we can set up a proportion to find Julian's height. The shadows and the objects (Julian and the building) form two sets of similar triangles because the angles of the sunshine are the same for both objects, and thus their corresponding sides are proportional.

To set up the proportion, we use the building's shadow and height relation and compare it to Julian's shadow and unknown height. So, we write:

Building's height / Building's shadow length = Julian's height / Julian's shadow length
31 feet / 28 feet = Julian's height / 6 feet

To generate an accurate answer, we solve for Julian's height as follows:

Julian's height = (31 feet / 28 feet) \ 6 feet = (31 / 28) \ 6
Julian's height = 6.64 feet (approximately)

This proportional relationship can be used to find unknown heights or lengths of shadows when a reference object is used, provided the angle of light is the same.

Answer:

The length is 25 and the width is 13. (25,13)

Step-by-step explanation:

the formula for perimeter is l+l+w+w=76 or 2l+2w=76

and since we know that the length is 12 more than the width, we can create an equation. w+12=l (-l+w=-12)

solve with elimination method:

2l+2w=76

2(-l+w=-12)

2l+2w=76

-2l+2w=-24

4w=52

w=13

Now that we know w=13, add 12 to the width and you get your width (25)

You can check this with the formula 2l+2w=76

2(25)+2(13)=76

50+26=76

and

w+12=l

13+12=25

Hope this helps!

The dimensions of the field will be 13 ft and 25ft.

The perimeter of a rectangle is given as: = 2l + 2w

Therefore, the perimeter will be:

2(w + 12) + 2w = 76

2w + 24 + 2w = 76

4w = 76 - 24.

4w = 52

w = 52/4.

w = 13

Width = 13 ft

Length will be: = w + 12 = 13 + 12 = 25

Therefore, the dimensions of the field will be 13 ft and 25ft.

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Answer:

Option B is correct.

By ASA rule are these triangles are congruent

Step-by-step explanation:

In triangle JMK and triangle JMN

[tex]\angle KJM \cong \angle NJK[/tex]   [Angle]         [Given]

[tex]JM \cong JM[/tex]   [Common Side]  

[tex]\angle JMK \cong \angle JMN [/tex]   [Angle]

ASA(Angle-Side-Angle) theorem states that if two angles and the included  side of one triangle are congruent to the corresponding parts of another triangle, then these triangles are congruent.

then, by ASA theorem;

[tex]\triangle JMK \cong \triangle JMN[/tex]

Therefore, by ASA rule are these triangles are congruent.

The rules AAS, ASA, SAS, SSS are a set of criteria that can determine if two triangles are congruent. They need accurate measurements of angles and sides of the triangles to be applied. Without these specifics, it's hard to identify which rule applies.

In order to answer which rule makes the triangles congruent, we would need more specific information about these triangles, such as the measures of their angles and sides. However, let me explain what each of these rules represents:

Without specific information about your triangles, it's difficult to conclusively establish which rule applies.

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