What is the solution to the system of equations? 2x – y = 7 y = 2x + 3

Answer:

x = - 2 or x = 4

Step-by-step explanation:

To find the x- intercepts let f(x) = 0, that is

(x - 4)(x + 2) = 0

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 2 = 0 ⇒ x = - 2

The x- intercepts are at x = - 2, x = 4

Answer: [tex]\frac{y-4}{6}[/tex]

Step-by-step explanation:

To find the quotient asked, you need to make the division indicated.

You can follow these steps:

1. Find the reciprocal of [tex]\frac{6}{y}[/tex]. You need to turn it upside down. Then you get that the recriprocal is:

[tex]\frac{y}{6}[/tex]

2. Now you must multiply [tex]\frac{y-4}{y}[/tex] by  [tex]\frac{y}{6}[/tex]:

[tex](\frac{y-4}{y})(\frac{y}{6})=\frac{(y-4)(y)}{(y)(6)}[/tex]

3. Simplifying, you get that the quotient is:

[tex]=\frac{y-4}{6}[/tex]

Answer:

Inverse of y=x^3 is f^-1(x) = ∛x

Step-by-step explanation:

We need to find the inverse of y=x^3

Step 1:

Interchange the variables:

x= y^3

Step 2: Now solve to find the value of y

=> y^3 = x

taking cube root on both sides of the equation

∛y^3 = ∛x

y=∛x

Step 3: Replace y with f^-1(x)

f^-1(x) = ∛x

So inverse of y=x^3 is f^-1(x) = ∛x

Answer:

She payed $34.60.

Step-by-step explanation:

It cost $19.60, just to rent the bike.

Then multiply $6 × 2 (hours) = 12

Now 6 ÷ 2 = 3 (half hour)

Add 12 + 3 = 15

Add everything together

19.60 + 15

You then get $34.60.

She paid $34.60.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given

It cost $19.60, just to rent the bike.

Then multiply $6 × 2 (hours) = 12

Now 6 ÷ 2 = 3 (half hour)

Add 12 + 3 = 15

Add everything together

19.60 + 15

You then get $34.60.

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We have been given the following functions:

f(x) = 3x - 9

g(x) = x

(G*f) means to multiply the function of g and f together:

x(3x - 9)

3x^2 - 9x

Now multiply the product of the solution above by 5:

5(3x^2 - 9x)

15x^2 - 45x

So,  (g*f)(5) = 15x^2 - 45x

Answer:

6

Step-by-step explanation:

Substitute x = 5 into f(x) then substitute the value obtained into g(x)

f(5) = (3 × 5) - 9 = 15 - 9 = 6, then

g(6) = 6

Hence (g ￮ f)(5) = 6

Answer:

Option C. 50 square centimeters

Step-by-step explanation:

we know that

The surface area is equal to the area of four triangles plus the area of rectangle

so

[tex]SA=2[\frac{1}{2}(4)(2)]+2[\frac{1}{2}(6)(3)]+(6)(4)[/tex]

[tex]SA=8+18+24[/tex]

[tex]SA=50\ cm^{2}[/tex]

Answer:

C

Step-by-step explanation:

The total area comprises of the rectangle (area is base * height) and the 4 triangles (area = 1/2 * base * height).

Area of rectangle = 6 * 4 = 24

Area of top triangle = 1/2 * 6 * 3 = 9

Area of bottom triangle = 1/2 * 6 * 3 = 9

Area of rightside triangle = 1/2 * 4 * 2 = 4

Area of leftside triangle = 1/2 * 4 * 2 = 4

Let's add them up and find the correct answer:

Area = 24 + 9 + 9 + 4 + 4 = 50

Answer:

Step-by-step explanation:

The vertex form of a parabola:

[tex]y=a(x-h)^2+k[/tex]

(h, k) - vertex

We have the vertex at (-3, -2) → h = -3 and k = -2.

Substitute:

[tex]y=a(x-(-3))^2+(-2)=a(x+3)^2-2[/tex]

The equation of parabola is , [tex]y= -2(x+3)^{2} - 2[/tex]

[tex]y = a(x- h)^{2} + K[/tex].

According to the question:

Applying  value in equation gives.

[tex]y= -2(x-(-3))^{2} -2\\[/tex]

                 [tex]y= -2(x+3)^{2} - 2[/tex]

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Answer:

7 : 8

Step-by-step explanation:

Given 2 similar figures with circumference ratio a : b

Then the ratio of the corresponding areas = a² : b²

Here the ratio of areas = 49 : 64

Taking the square root of both gives ratio of circumference

ratio of circumference = [tex]\sqrt{49}[/tex] : [tex]\sqrt{64}[/tex] = 7 : 8

Let temperature = T

"The temperature stayed above -15 degrees. " means that the temperature is always greater than -15 degrees.

Therefore,

-15 degrees < T

Answer:

Step-by-step explanation:

Mark the given points in the coordinate system (look at the picture).

Find the point D.

Other solutions:

D(-5, 8)

D(7, -2)

Look at the other pictures

If you want calculate it, then:

The vectors AB and DC are congruent and the vectors BC and AD are congruents too.

If a vector ,< a, b > is congruent to a vector < c, d >, then a = c and b = d.

The formula of coordinates of the vetror:

< x₂ - x₁, y₂ - y₁ >

We have A(-2, 4), B(1, 3), C(4, -1) and D(x, y). Substitute:

vector AB = < 1 - (-2), 3 - 4 > = < 3, -1 >

vector DC = < 4 - x, -1 - y >

vector BC = < 4 - 1, -1 - 3 > = < 3, -4 >

vector AD = < x - (-2), y - 4 > = < x + 2, y - 4 >

Therefore we have the equations:

AB = DC ⇒ 4 - x = 3 and -1 - y = -1 ⇒ x = 1 and y = 0

BC = AD ⇒ x + 2 = 3 and y - 4 = -4 ⇒ x = 1 and y = 0

Answer:

[tex]x^\frac{5}{3} y^\frac{1}{3}[/tex]

Step-by-step explanation:

This question is on rules of rational exponential

where the exponential is a fraction, you can re-write it using radicals where the denominator of the fraction becomes the index of the radical;

General expression

[tex]a^\frac{1}{n} =\sqrt[n]{a}[/tex]

Thus    [tex]\sqrt[3]{x} =x^\frac{1}{3}[/tex]

Applying the same in the question

[tex]\sqrt[3]{x^5y} =x^\frac{5}{3} y^\frac{1}{3}[/tex]

=[tex]x^\frac{5}{3} y^\frac{1}{3}[/tex]

Answer: Second option

[tex](x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]

Step-by-step explanation:

By definition we know that:

[tex]a ^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]

In this case we have the following expression

[tex]\sqrt[3]{x^5y}[/tex]

Using the property mentioned above we can write an equivalent expression for [tex]\sqrt[3]{x^5y}[/tex]

[tex]\sqrt[3]{x^5y} = (x^5y)^{\frac{1}{3}}[/tex]

[tex](x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]

Therefore the correct option is the second option

Answer:

= 2a³b - 2ab² + a²b - b³

Step-by-step explanation:

We multiply the each term in the first polynomial by each in the other as follows.

2ab(a² - b²) + b(a² - b²)

We then open the brackets and get the following.

2a³b - 2ab² + a²b - b³

We can not simplify the product further than this since it has no like terms.  

Answer:

First is C

Second is 2

Step-by-step explanation:EDGE 2021

Answer:

[0, -1]

Step-by-step explanation:

According to the Slope-Intercept Formula y = mx + b, b is your y-intercept, and in the above raisin, you have your answer in place of that b.

Answer:

[0, -1], or just -1

Answer:

C. >

Step-by-step explanation:

The answer is C. because 65 is greater than 56!

Answer:

Ste-by-step explanation

400/500 = 0.8 x 35.000 = 28.000

28.000 homes will have wifi access.

Answer:

Estimated .70%2A25000 = 17,500 homes in the city will have wifi access

Step-by-step explanation:

Answer:

2/3 chance (67%)

Step-by-step explanation:

Multiples of 5:

(5)

Multiples of 2:

(2)

(4)

(6)

This is a 4/6 chance or 2/3

[tex]|\Omega|=6\\|A|=3+1=4\\\\P(A)=\dfrac{4}{6}=\dfrac{2}{3}\approx67\%[/tex]

Answer:

a) Current month's interest is: $40

b) The final payment is $7,440

c) Amount saved by paying off loan early is: $600

Step-by-step explanation:

Principal = $6,000

Interest rate = 8% or 0.08

Time = 36 months or 3 years

After 20 payments, the payment is $2,849.08.

a) What is the CURRENT month's interest?

The formula used to find the interest is:

I = P*r*t

Where P= Principal Amount

r = interest rate

and t = time in years

Putting the given values:

I = 6,000 * 0.08 * 3

I = 1440

Total Interest = $1440

Current Month interest = 1440/36

Current Month interest = 40

So, Current month's interest is: $40

b) What is the final payment?

The formula used is:

A = P(1+r*t)

A = 6,000(1+0.08*3)

A = 6000*(1.24)

A = 7,440

So, the final payment is $7,440

c) How much is saved by paying off the loan early?

The current balance paid is $2,849.08

The loan is paid when next payment is due.

So, remaining amount to be paid is:

Remaining Amount = Final Payment - Current balance paid

Remaining Amount = 7,440 - 2,849.08

Remaining Amount = 4,590.92

Remaining months in which amount is to be paid: 36-20 = 16 months

The loan is paid off next month so interest rate of remaining 15 months = 15*40 = 600

The amount paid on next payment = 4590.92 - 600 = $3990.9

So, amount saved by paying off loan early is: $600

Final answer:

Lionel Cooper saved $136.63 by paying off his loan early. The current month's interest on his loan was $19.09, making his final payment $2,868.17 after paying off the remaining balance of $2,849.08.

Explanation:

Lionel Cooper paid for new mechanic's tools with an installment loan of $6,000 at 8% annual interest rate for 36 months, with monthly payments of $187.80. After 20 payments, he decides to pay off the remaining balance of $2,849.08.

a.) What is the CURRENT month's interest?

First, calculate the monthly interest rate, which is 8% annually, or 0.08/12 per month = 0.0067. The current month's interest is the balance multiplied by the monthly interest rate: $2,849.08 * 0.0067 = $19.09.

b.) What is the final payment?

The final payment is the sum of the current month's interest plus the remaining balance: $19.09 (interest) + $2,849.08 (balance) = $2,868.17.

c.) How much is saved by paying off the loan early?

Normally, Lionel would pay $187.80 for 16 more months, totaling $3,004.80. By paying off early, he only paid $2,868.17, so he saved $136.63.

ANSWER

[tex]^8P_4=1680[/tex]

EXPLANATION

The given permutation is

[tex]^8P_4.[/tex]

Recall the formula for permutation

[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

We substitute n=8, and r=4 to obtain:

[tex]^8P_4=\frac{8!}{(8-4)!}[/tex]

[tex]^8P_4=\frac{8!}{4!}[/tex]

Recall the factorial expansion

[tex]n! = n \times (n - 1) \times (n - 2)...3 \times 2 \times 1[/tex]

We apply this expansion to get:

[tex]^8P_4=\frac{8 \times 7 \times 6 \times 5 \times 4!}{4!}[/tex]

[tex]^8P_4=8 \times 7 \times 6 \times 5[/tex]

[tex]^8P_4=1680[/tex]

Answer:

They can be congurent depending on which two figures you are using

Step-by-step explanation:

Answer:

[tex]x^2-10x+2[/tex]

Step-by-step explanation:

Multiply out the two monomials first because of PEMDAS.

[tex](-x + 2) * (2x + 3)=-2x^2+x+6[/tex]

Now add them together.

[tex]3x^2-11x-4-2x^2+x+6=x^2-10x+2[/tex]

Answer:

D. Place the compass on point E and draw a small arc below the line and beneath point R.

Step-by-step explanation:

According, to given construction we need to draw the a perpendicular on a line m from a point R above the line.

According to given figure, we have given a line m and R is a point above the line then they placed the compass on point R and draw the an arc by cutting line m at the points E and F. In next step we need to  

D. Place the compass on point E and draw a small arc below the line and beneath point R.

Answer:  It's 81

Step-by-step explanation:

So, if B= 9 then it's 9^2 which is 9 x 9 = 81

Hope my answer has helped you and if not i'm sorry.

Answer:

x = 44

Step-by-step explanation:

log4(x + 20) = 3

Raise each side to the power of 4

4^ log4(x + 20) = 4^3

x+20 = 4^3

x+20 = 64

Subtract 20 from each side

x+20-20 = 64-20

x = 44

Answer:

The measure of arc AC  is equal to 33°

Step-by-step explanation:

we know that

The inscribed angle measures half that of the arc comprising

so

∠ABC=(1/2) arc AC

substitute the values

(2.5x+4)=(1/2)(7x-2)

solve for x

5x+8=7x-2

7x-5x=8+2

2x=10

x=5

Find the measure of arc AC

arc AC=(7(5)-2)=33°

Final answer:

The measure of arc AC can be calculated by using the inscribed angle theorem and solving the equation 2×(2.5x + 4) = 7x - 2, which represents the relationship between the inscribed angle and its intercepted arc.

Explanation:

To determine the measure of arc AC, we need to consider the relationship between the inscribed angle of a circle (ABC in this case) and the corresponding arc (arc AC).

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. This relationship allows us to set up the equation (2.5x + 4) degrees = 0.5×((7x-2) degrees).

By solving this equation, we can find the value of x, and consequently, the measure of arc AC.

substitute the values

(2.5x+4)=(1/2)(7x-2)

solve for x

5x+8=7x-2

7x-5x=8+2

2x=10

x=5

Find the measure of arc AC

arc AC=(7(5)-2)=33°

[tex]12+0i[/tex]

.....................

Answer:

12+0i

Step-by-step explanation:

Answer:3g+20 on edg

Step-by-step explanation:

Since the guests equals g and 3 cups per guest it would be 3g+ extra 20 so the answer would be 3g+20

Answer:

[tex]110.5\pi \ in^2[/tex]

Step-by-step explanation:

Given

Slant height = l = 17 in

Diameter = d = 13 in

We are given diameter of the circular base. We have to find radius first to calculate lateral area.

Radius = r = d/2

= 13/2

= 6.5 in

The formula for lateral area is:

[tex]LA = \pi rl\\Putting\ the\ values\\\LA = \pi *6.5*17\\= 110.5\pi in^2[/tex]

Hence, second option is correct ..

Answer:

Pls mark me brainliest because other guy is a genius

Step-by-step explanation:

Answer:

[tex]f(x)=(x-5)^{2}+19[/tex]

Step-by-step explanation:

we have

[tex]f(x)=x^{2}-10x+44[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)-44=x^{2}-10x[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]f(x)-44+25=x^{2}-10x+25[/tex]

[tex]f(x)-19=x^{2}-10x+25[/tex]

Rewrite as perfect squares

[tex]f(x)-19=(x-5)^{2}[/tex]

[tex]f(x)=(x-5)^{2}+19[/tex]