Complete the point-slope equation of the line through (-5,4) and (1,6). Use exact numbers.
y-6=____

Answer:

[tex]\$16,021[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-k)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

k is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$20,000\\k=0.105\\x=2\ years[/tex]

[tex]V=\$20,000(1-0.105)^{2}=\$16,020.50[/tex]  

round to the nearest dollar

[tex]\$16,020.50=\$16,021[/tex]  

the value of the car after 2 years will be approximately $16,212.

To find the value of the car after 2 years with continuous depreciation, we will use the formula for continuous exponential decay:

[tex]V(t) = V_0 \times e^{-kt}[/tex]

Where V(t) is the value after time t V_0 is the initial value, k is the decay constant and t is time

Plugging in the values:

[tex]V(2) = 20000 \times e^{-0.105 \times 2}[/tex]

Simplifying the exponent:

[tex]V(2) = 20000 \times e^{-0.21}[/tex]

[tex]V(2) = 20000 \times 0.8106 \approx 16212[/tex]

Thus, the value of the car after 2 years will be approximately $16,212.

Answer:

It means meal cost plus the 18% tip

Step-by-step explanation:

Answer:

[tex]0.18m[/tex] represents amount of tip Jake pays to restaurant.

Step-by-step explanation:

We have been given that Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars.

Jake left an 18% tip. The amount Jake pays at the restaurant is represented by the following expression in this expression [tex]m+0.18m[/tex].

We know that Jake's total amount will be equal to cost of his meal plus 18% of the cost of meal.

[tex]\text{Total cost of dinner}=m+(\frac{18}{100}\times m)[/tex]

[tex]\text{Total cost of dinner}=m+0.18m[/tex]

Therefore, the term [tex]0.18m[/tex] represents amount of tip Jake pays to restaurant.

The boat traveled a distance of 80 km during the whole trip.

This question involves determining the distance a boat traveled based on its travel times with and against a current. Let's denote the speed of the boat in still water as b km/h.

Step-by-step solution:

Downstream, distance d = speed × time = (b + 6) × 4

Upstream, distance d = speed × time = (b - 6) × 10

Since the distances are equal:

(b + 6) × 4 = (b - 6) × 10

Expanding and simplifying:

4b + 24 = 10b - 60

84 = 6b

b = 14 km/h

Now, using the downstream speed to find the distance:

Distance, d = (b + 6) × 4 = (14 + 6) × 4 = 20 × 4 = 80 km.

Thus, the boat traveled a distance of 80 km.

The boat traveled 80 kilometers.

To determine how far the boat traveled, let's denote the speed of the boat in still water as B km/h. The current speed is given as 6 km/h.

Using the formula speed = distance/time, we get:

We now have two equations:

Setting the right-hand sides of these equations equal to each other:

4(B + 6) = 10(B - 6)

Simplifying this equation:

4B + 24 = 10B - 60

Bringing like terms together:

84 = 6B

Solving for B:

B = 14

Substituting B back into either distance equation, we use D = 4(B + 6):

D = 4(14 + 6) = 4(20) = 80

Therefore, the boat traveled 80 kilometers.

Answer:

15) f(x) + g(x)  = -x + 8

17) f(x) - g(x) = x + 9

Step-by-step explanation:

15)

f(x) = 3x + 5

g(x)= - 4x + 3

Find f(x) + g(x)

f(x) + g(x)  = 3x + 5  + ( - 4x + 3 )

f(x) + g(x)  = 3x + 5   - 4x + 3

f(x) + g(x)  = -x + 8

17)

f(x) = 2x +4

g(x)= x - 5

Find f(x) - g(x)

f(x) - g(x) = 2x +4  - (x - 5 )

f(x) - g(x) = 2x +4  - x +  5

f(x) - g(x) = x + 9

[tex]

f(x)=3x+5 \\

g(x)=-4x+3 \\

(f+g)(x)=f(x)+g(x)=(3x+5)+(-4x+3) \\

3x+5-4x+3=\boxed{-x+8} \\ \\

f(x)=2x+4 \\

g(x)=x-5 \\

(f-g)(x)=f(x)-g(x)=(2x+4)-(x-5) \\

2x+4-x+5=\boxed{x+9}

[/tex]

Hope this helps.

r3t40

Answer:

A.

⇒The slope of the function f(x) is greater than the slope of the function g(x).

This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5

B.

⇒The function f(x) has a greater y-intercept than the function g(x)

⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4

Step-by-step explanation:

This question is on the standard equation of a linear function using the slope-intercept form

y=m x+c----------where m is the gradient/slope of the line and c is the y-intercept.

Given the values in function f(x) we can identify the points in the line as;

(-1,-7), (0,-1) , (1,5)............plot the points to obtain the graph as indicated in the attachment.

Find the gradient  of the graph ;

m₁=Δy/Δx

m₁= 5--1/1-0 =6/1 =6

Equation of line will be;

y-5/x-1 = 6

y-5=6(x-1)

y-5=6x-6

y=6x-1.........................m₁=6 and c₁= -1

Given that;

g(x)=5x-4.........................m₂=5   c₂= -4

⇒The slope of slope of the function f(x) is greater than the slope of the function g(x).

This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5

B.

⇒The function f(x) has a greater y-intercept than the function g(x)

⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4

In the attached graph;

Red line graph, y=5x-4

Blue line graph, y=6x-1

Answer:

g(x) =   y=5x-4

f(x) =.    y= 6x-1

I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.

I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.  

Step-by-step explanation:

First, I will put both functions into slope-intercept form.

Next, I will use  by picking two points on the table.  and

this equals  or 6.

So, I know the slope is 6.

To find the y-intercept I have to do, -7=6(-1)+b

So, the y-intercept is -1.

From this, I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.

I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.  

Answer:

x=62

Step-by-step explanation:

You set the two angles equal to each other and solve. See work attached for more.

Answer:

A.  38

Step-by-step explanation:

From the diagram, [tex]s=(2x+26)\degree[/tex] because corresponding angles are equal.

[tex]s+(3x-36)\degree=180\degree[/tex]. the sum of interior angles of a triangle.

By substitution, we obtain;

[tex](2x+26)\degree+(3x-36)\degree=180\degree[/tex]

Group similar terms;

[tex]2x+3x=180+36-26[/tex]

[tex]5x=190[/tex]

Divide both sides by 5.

[tex]x=38[/tex]

Answer: 56.25

Step-by-step explanation:

You just need to use common sense.

you just cancel out the x variable first since 4x-4x is 0 then you bring down your y variable and solve for x then you plug x into either equation then solve for x.

Answer:

Step-by-step explanation:

3.14 x 10.6^2= 352.81 pi

Answer is...

Volume = 4988.92

See attached photo

18 is the real part of the complex number

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

18

Step-by-step explanation:

Given a complex number z = a + bi

where a is the real part the imaginary part is b

Given

18 - 6i then 18 is the real part

Answer:

80 Muffins.

Step-by-step explanation:

There are 20 cups of flour in package

It takes [tex]\frac{1}{4}[/tex] cup to make one muffin

From a package of 20 cups of flour, you can make:

20 × 1 ÷ [tex]\frac{1}{4}[/tex] = 20 × 4 = 80 muffins

Answer:

how to find pi you have to add a lot of math and for a volume for the cone is V=πr2h 3

Step-by-step explanation:

i had did this all in my head.

Answer: It has to be A. 8

Step-by-step explanation:

Answer:

315 hamburgers

Step-by-step explanation:

Because 3 times the amount of hamburgers were sold than the cheeseburgers, it is fair to say that 420 burgers is 4 times the amount of cheeseburgers sold.

That means that 420/4 = 105 cheeseburgers were sold.

That means that 105 * 3 = 315 hamburgers were sold.

The total number of hamburgers sold on Friday is 105

Number of Hamburgers sold = h

Number of Cheeseburgers sold = c

h + c = 420

c = 3*h

substitute the value of c in  ( h + c = 420 )

h + 3h = 420

4h = 420

h = [tex]\frac{420}{4}[/tex]

h = 105

The number of hamburgers sold is 105

To learn more about solving an equation using the substitution method, refer to:

https://brainly.com/question/11745624

#SPJ2

Answer:

The solution of the equation are 3 , -11

Step-by-step explanation:

* Lets revise how to make the completing square

- The form of the completing square is a(x - h)² + k, where a , h , k

 are constant

- The general form of the quadratic is ax² + bx + c, where a , b , c

 are constant

- To change the general form to the completing square form equate

  them and find the constant a , h , k

* Now lets solve the problem

∵ x² + 8x = 33 ⇒ subtract 33 from both sides

∴ x² + 8x - 33 = 0

- lets change the general form to the completing square

∴ x² + 8x - 33 = a(x - h)² + k ⇒ solve the bracket of power 2

∴ x² + 8x - 33 = a(x² - 2hx + h²) + k ⇒ multiply the bracket by a

∴ x² + 8x - 33 = ax² - 2ahx + ah² + k ⇒ compare the two sides

∵ x² = ax² ⇒ ÷ x²

∴ a = 1  

∴ -2ah = 8 ⇒ substitute the value of a

∴ -2(1)h = 8 ⇒ -2h = 8 ⇒ ÷ (-2)

∴ h = -4

∵ ah² + k = -33 ⇒ substitute the value of a and h

∴ (1)(-4)² + k = -33

∴ 16 + k = -33 ⇒ subtract 16 from both sides

∴ k = -49

∴ x² + 8x - 33 = (x + 4)² - 49

* Now lets solve the completing square

∵ (x + 4)² - 49 = 0 ⇒ add 49 to both sides

∴ (x + 4)² = 49 ⇒ take square root for both sides

∴ (x + 4) = ± 7

∵ x + 4 = 7 ⇒ subtract 4 from both sides

∴ x = 3

∵ x + 4 = -7 ⇒ subtract 4 from both sides

∴ x = -11

* The solution of the equation are 3 , -11

Answer:

{-11, 3}

Step-by-step explanation:

Answer:

Distance divided by time

I would say that’s correct

OOF yes it's correct...

Answer:

Step-by-step explanation:

D

Answer:

32

Step-by-step explanation:

Number of times a coin is tossed up = 5

Number of possible outcomes in a toss of a coin = 2 ( Head or a Tail)

The sample space can be calculated by calculating total number of possible outcomes in 5 tosses of the coin.

Number of outcomes in 1 toss of a coin = 2

Number of outcomes in 2 tosses of a coin = 2 × 2

Number of outcomes in 3 tosses of a coin = 2 × 2 × 2

Number of outcomes in 4 tosses of a coin = 2 × 2 × 2 × 2

Number of outcomes in 5 tosses of a coin = 2 × 2 × 2 × 2 × 2

⇒ Total number of outcomes = 32

Therefore, Size of the sample space = 32

Answer:

I did the calculations and I also got 32.

Step-by-step explanation:

hope this helps!!

It will take Steve's friend 6.5 hours to catch up to Steve.

The correct answer is:

e) 6.5 hours.

To calculate this, let's first determine the time it takes for Steve's friend to catch up to him after he starts driving.

Steve's speed = 55 mph

Steve's friend's speed = 65 mph

Relative speed = Speed of Steve's friend - Speed of Steve

Relative speed = 65 mph - 55 mph = 10 mph

Now, since Steve's friend starts one hour later, Steve has already traveled for one hour at 55 mph before his friend starts.

Distance traveled by Steve in one hour = Speed × Time

Distance = 55 mph × 1 hour = 55 miles

Now, when Steve's friend starts driving, he needs to catch up this initial distance of 55 miles.

Time = Distance / Relative speed

Time = 55 miles / 10 mph = 5.5 hours

But we must remember that Steve's friend started driving one hour later than Steve. So, we add this one hour to the time calculated above to find the total time it takes for Steve's friend to catch up to Steve.

Total time = 5.5 hours + 1 hour = 6.5 hours

Therefore, it will take Steve's friend 6.5 hours to catch up to Steve.

Steve travels for one hour at 55 mph before his friend starts driving. By then, Steve's friend needs to catch up the initial distance of 55 miles at a relative speed of 10 mph. This gives us a time of 5.5 hours. However, since Steve's friend started one hour later, we add this one hour to the calculated time, resulting in a total time of 6.5 hours. Therefore, the correct answer is 6.5 hours.

Complete question:

Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.

How many hours will it take his friend to catch up to Steve?

a.10 hours

b.5.5 hours

c.8.5 hours

d.55 hours

e. 6.5 hours.

Answer:

P'(7,0)Q'(2,1) R'(12,-6)

Step-by-step explanation:

P(3,5)------>P'(3+4,5-5)

P'(7,0)

Q(-2,6)----->Q'(-2+4,6-5)

Q'(2,1)

R(8,-1)------>R'(8+4,-1-5)

R'(12,-6)

Answer:

i think it is the third one c plz give me brainliest

Step-by-step explanation:

Answer:

Answer is B - 290.

Step-by-step explanation:

The idea here is that we're assuming the frequency each colour is drawn is a reflection of the proportion of marbles in the bag that are that colour. The more of a particular colour you have, the more likely you are to draw it, and vice versa.

Therefore we can assume the proportion of blue, gree, and red marbles is 13%, 29%, and 58% respectively based on the first 100 draws.

These percents should stay relatively similar as more draws are done, approaching the true proportions of each colour better the higher the number of draws. That means 29%, or 290, of the 1000 draws will be green.

Answer: 290

Step-by-step explanation:

QUESTION 1

We have [tex]f(x)=\frac{2x-1}{x+2}[/tex]

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

Interchange x and y.

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

Solve for y.

First, cross multiply;

[tex]x(y+2)=2y-1[/tex]

Expand now:

[tex]xy+2x=2y-1[/tex]

Group the y-terms on the LHS

[tex]xy-2y=-2x-1[/tex]

Factor y on the left hand side;

[tex](x-2)y=-2x-1[/tex]

Divide both sides by (x-2).

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

[tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]

[tex]\boxed{f(x)=\frac{2x-1}{x+2}\to f^{-1}(x)=\frac{-2x-1}{x-2}}[/tex]

QUESTION 2

Given: [tex]f(x)=\frac{x-1}{2x+1}[/tex]

Let  [tex]y=\frac{x-1}{2x+1}[/tex]

Interchange x and y.

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

Solve for y

[tex]x(2y+1)=y-1[/tex]

[tex]2xy+x=y-1[/tex]

[tex]2xy-y=-x-1[/tex]

[tex](2x-1)y=-x-1[/tex]

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

[tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]

[tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]

[tex]\boxed{f(x)=\frac{x-1}{2x+1}\to f^{-1}(x)=\frac{-x-1}{2x-1}}[/tex]

QUESTION 3

Given : [tex]f(x)=\frac{2x+1}{2x-1}[/tex]

We let  [tex]y=\frac{2x+1}{2x-1}[/tex]

Interchange x and y.

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

Solve for y;

[tex]x(2y-1)=2y+1[/tex]

[tex]2xy-x=2y+1[/tex]

[tex]2xy-2y=x+1[/tex]

[tex](2x-2)y=x+1[/tex]

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

[tex]f^{-1}(x)=\frac{x+1}{2(x-1)}[/tex]

[tex]\boxed{f(x)=\frac{2x+1}{2x-1}\to f^{-1}(x)=\frac{x+1}{2(x-1)}}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]g^2+ 3g -10=(x-2)(x+5)[/tex]

Step-by-step explanation:

The trinomial is the following

[tex]g^2+ 3g -10[/tex]

Look for two numbers b and d that when multiplying them get as a result -10 and when you add up these numbers you get 3 as a result.

This is.

[tex]b * d = -10\\\\b + d = 3[/tex]

Then you can write the trinomial as the product of two factors:

[tex](x+b)(x+d)[/tex]

You can check that the numbers that meet this condition are:

[tex]b = -2\\d = 5[/tex]

Then the trinomial is written as

[tex]g^2+ 3g -10=(x-2)(x+5)[/tex]

Answer: 84

Step-by-step explanation:

7 x 3 x 4 = 84

It would be 84.

Hope this helps!

Pls tell me if it is inncorrect and i will revise my answer.

7•3•4=84

Answer:

no because they are parallel

Step-by-step explanation:

The diameter of a circle is the radius times 2.

Diameter = 3 x 2 = 6 meters.

Answer:

6 is the answer.

3 x 2 = 6

Step-by-step explanation:

Answer:

FICA Tax =$8170.2

Step-by-step explanation:

Given

Total income=$165000

Taxable income=$106800

FICA tax includes Social security tax and medicare tax.  

Medicare tax is 1.45% of the taxable wage and social security tax is6.2% of the taxable wage.  

1.45% of medicare is paid by the employer and similarly 6.2% social security tax is paid by the employer.

0.9% of medical surtax is deducted if the employee earns more than $200000

So,

Medicare  Tax=Taxable income*1.45/100

=106800*0.0145

=$1548.6  

Social Security Tax=Taxable Income*6.2/100

=106800*0.062

=$6621.6

As the income of the employee is less than $200000, so there will be no medical surtax.  

Total FICA tax=$1548.6+$6621.6

=$8170.2

36-(4+2a)^2=0

36-16+4a^2=0

4a^2+20=0

a^2+5=0 <— Factored form

Answer:

It's False

Step-by-step explanation:

It does refer to whether the data measures what it claims to measure.

Hope i helped you!

Answer: Second Option

C(8,8)=1

Step-by-step explanation:

We must calculate a combination

The combination [tex]C (n, r) =\frac{n!}{r!(n-r)!}[/tex]

Where n is the number of elements that you can combine and you choose "r" from them.

So

C (8, 8) is the combination of 8 in 8.

Therefore

[tex]n = 8\\r=8[/tex]

[tex]C(8,8)= \frac{8!}{8!(8-8)!}\\\\C(8,8)=\frac{8!}{8!(0)!}\\\\C(8,8)=\frac{1}{1*1}\\\\C(8,8)=1[/tex]

The answer is the second option

The value of  [tex]\( C(8, 8) \)[/tex]  is 1 because choosing all 8 items from 8 yields only 1 combination.

The expression [tex]\( C(8, 8) \)[/tex] represents choosing 8 items from a set of 8 items without regard to order, which is also known as a combination. Here's how we can evaluate it step by step:

Step 1: Recall the formula for combinations.

The formula for combinations is [tex]\( C(n, k) = \frac{n!}{k!(n - k)!} \),[/tex] where [tex]\( n \)[/tex] is the total number of items and [tex]\( k \)[/tex] is the number of items to choose.

Step 2: Substitute the values into the combination formula.

In this case, [tex]\( n = 8 \) and \( k = 8 \),[/tex] so the expression becomes:

[tex]\[ C(8, 8) = \frac{8!}{8!(8 - 8)!} \][/tex]

Step 3:

Simplify the expression.

[tex]\[ C(8, 8) = \frac{8!}{8!0!} \][/tex]

Step 4:

Recall that [tex]\( n! = n \times (n - 1) \times (n - 2) \times \ldots \times 1 \)[/tex] and [tex]\( 0! = 1 \).[/tex]

[tex]\[ C(8, 8) = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 1} \][/tex]

Step 5:

Cancel out the common terms.

[tex]\[ C(8, 8) = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ C(8, 8) = 1 \][/tex]

So, [tex]\( C(8, 8) = 1 \).[/tex]