What is the solution to the following system of equations?


2x + 3y = 3

-3x - 2y = 8​

Answer:

1. The input is f

2. The input is g

3. The input is h

Step-by-step explanation:

The value inside the bracket of the function is the input given to the function.

1. g(f) = 2f

The input is f

2. h(g) = -4+g

The input is g

3. f(h) = h - 7

The input is h

Answer:

g(f)=2f⇒  f

h(g)=-4+g ⇒ g

f (h) =h-7 ⇒h

Step-by-step explanation:

Hi, to answer this question we have to understand what is the input of a function.

A function has an input and an output. The input is inside the parentheses, next to the name of the function.

The input is the independent variable.

Now, with this information, we can match each function with its input.

So:

g(f)=2f⇒  f

h(g)=-4+g ⇒ g

f (h) =h-7  ⇒h

Feel free to ask for more if it´s necessary or if you did not understand something

Answer:

The smaller number is 11

Step-by-step explanation:

The question is

One number is 3 less than a second number. Twice the second number is 16 less than 4 times the first. Find the smaller of two numbers

Let

x and y the numbers

x=y-3 ----> equation A

2y=4x-16 ----> equation B

Substitute equation A in equation B and solve for y

2y=4(y-3)-16

2y=4y-12-16

4y-2y=12+16

2y=28

y=14

x=14-3=11

Answer:

y = 1/3 x.

Step-by-step explanation:

The slope of the given line is

(4 - (-2) / 2 - 4)

=   -3.

So the slope of the line perpendicular to it = -1 / (-3) = 1/3.

This line also passes through the point (3, 1) so its equation is ( by the point-slope form):

y - 1 = 1/3(x - 3)

y - 1 = 1/3x - 1

y = 1/3 x (answer).

Answer: The answer is y= x/3

Step-by-step explanation:

Given  points =(2,4)  and (4,-2) whose mid point is (3,1)

Let the points be named  as A(2,4) and B(4,-2) and mid point as C(3,1)

So slope of AB = [tex]\frac{4-(-2)}{2-4}[/tex]

=[tex]\frac{6}{-2}[/tex]

= -3

We know that   Product of Slope of perpendicular lines = -1

Now slope of the line perpendicular to AB × slope of AB = -1

-3 × m2 =-1

i.e. m2 =[tex]\frac{1}{3}[/tex]

Now equation of perpendicular bisector of AB passing through C(3,1)  is

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

[tex]y= 1+\frac{1}{3}x -1[/tex]

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

Hence the equation of line is y =x/3

Answer:

The measure of angle 1 is 115°

Step-by-step explanation:

we know that

If ∠1 and ​ ∠2 ​ are a linear pair

then

∠1 +∠2 =180°​ -----> supplementary angles

If ∠2 and ​ ∠3 ​ are vertical angles

then

∠2 =∠3

step 1

Find the value of y

we know that

∠2 =∠3

substitute values

(5+4y)°=(6y-25)°

6y-4y=(5+25)°

2y=(30)°

y=15°

step 2

Find the measure of angle 2

∠2=(5+4y)°

substitute the value of y

∠2=(5+4(15))°

∠2=65°

step 3

Find the measure of angle 1

we know that

∠1 +∠2 =180°

we have

∠2=65°

substitute

∠1 +65°=180°

∠1 =180°-65°=115°

Answer:

[tex]\large\boxed{(g\cdot h)(5)=-10}[/tex]

Step-by-step explanation:

[tex](g\cdot h)(x)=g(x)\cdot h(x)\\\\g(x)=x^2,\ h(x)=x-7\\\\\text{substitute:}\\\\(g\cdot h)(x)=(x^2)(x-7)\qquad\text{use the distributive property}\\\\(g\cdot h)(x)=(x^2)(x)+(x^2)(-7)=x^2-7x^2\\\\(g\cdot h)(5)-\text{put}\ x=5\ \text{in the expression}\\\\(g\cdot h)(5)=5^2-7(5)=25-35=-10[/tex]

Answer:

25.9

Step-by-step explanation:

That is:

25.9

Hope this helped!

Answer:

The answer is A,C and F

Step-by-step explanation:

A because he said the best price on internet

C because he read some consumer website about review

F. plugged a few payment into his budgets

Ramiro was financially responsible because he has a budget, considers important factors when he shops for a car loan, uses strategies to minimize risks, shops around for car insurance, and spends wisely.

Financially responsible means the careful spending of money after analyzing alternatives and choosing the right path in saving money for the future.

The paragraph is given.

Now we must read and understand the graph and choose the correct answers from the given options.

Option A is true because he has a budget.

Option B is not fully true, as he has no goals for the future yet.

Option C is true as he considers important factors when he shops for a car loan.

Option D is true as he uses strategies to minimize risks.

Option E is true because he has shopped around for car insurance.

Option F is true because he spends wisely.

Therefore, we have found that Ramiro was financially responsible because he has a budget, considers important factors when he shops for a car loan, uses strategies to minimize risks, shops around for car insurance, and spends wisely.

Learn more about being financially responsible here: https://brainly.com/question/1847852

#SPJ2

Answer:

Putting money in a bank and earning interest

Step-by-step explanation:

This problem can be used in real life to describe when you put money in a bank, in this case, it could be two dollars, and leave it there for x amount of years, then taking it out after an amount of years and checking what you have. Since this is a linear equation, your money doesn't go up exponentially. It'll keep going up the same rate for the whole time until you decide to take it out. Here's an example of what it'll look like, if it helps:

Your money keeps going up. Hope this helps!

Final answer:

A real world situation for the function f(x) = 3(1.06x) + 2 could be a situation where a person is investing money in a savings account. The function represents the balance in the account after a certain amount of time (x years) with an interest rate of 6%.

Explanation:

A real world situation for the function f(x) = 3(1.06x) + 2 could be a situation where a person is investing money in a savings account. Let's say the initial amount of money deposited in the account is $2. The function represents the balance in the account after a certain amount of time (x years) with an interest rate of 6%. The key features of the function are:

3: This represents the multiplier of the initial investment, indicating that the account balance increases by three times the amount of the initial investment.

1.06: This represents the growth factor due to the 6% interest rate. It is multiplied by the current balance each year.

2: This represents the $2 initial deposit in the account.

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Since

[tex]6^2 = 36,\quad 7^2 = 49[/tex]

Then we have

[tex]6 = \sqrt{36}<\sqrt{45}<\sqrt{49}=7[/tex]

So, the square root of 45 is somewhere between 6 and 7.

Answer:

C

Step-by-step explanation:

Note that

[tex]\sqrt{36}[/tex] < [tex]\sqrt{45}[/tex] < [tex]\sqrt{49}[/tex], that is

6 < [tex]\sqrt{45}[/tex] < 7

The square root lies between 6 and 7 → point C

Answer:

Look below

Step-by-step explanation:

SOH CAH TOA

We are using sine

sin(75) = x/150

x=sin(75)*150

x=0.9659258263*150

x=144.8888739

Check the picture below.

make sure your calculator is in Degree mode.

Answer: it is B,C, and D

Step-by-step explanation: I got it correct

The statement that best compares the graph of g(x) = -5x³ with the graph of f(x) = x³ is that the graph of g(x) is a reflection of the graph of f(x) across the x-axis and is vertically stretched by a factor of 5."

Option D is the correct answer.

We have,

Reflection across the x-axis:

The negative coefficient of -5 in g(x) reflects the graph across the x-axis compared to f(x).

This means that the points on the graph of g(x) will have the same

x-coordinates as the corresponding points on the graph of f(x) but will have opposite y-coordinates.

Vertical stretching by a factor of 5:

The absolute value of the coefficient (-5) in g(x) indicates that the graph is vertically stretched by a factor of 5 compared to f(x).

This means that for any given x-value, the corresponding y-value on the graph of g(x) will be five times larger (or smaller, depending on the sign) than the corresponding y-value on the graph of f(x).

Thus,

The graph of g(x) is a reflection of the graph of f(x) across the x-axis and is vertically stretched by a factor of 5."

Learn more about reflections here:

https://brainly.com/question/12463306

#SPJ4

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

[tex]x^{2}+y^{2}=4^{2}[/tex]

Is the equation of a circle with center at the origin and radius 4 units

so

the inequality

[tex]x^{2}+y^{2}< 4^{2}[/tex]

[tex]x^{2}+y^{2}< 16[/tex]

The solution is the shaded area inside the dashed line of the circle

using a graphing tool

see the attached figure

Answer:

See below  

Step-by-step explanation:

You order the hundreds digits, then the tens, and finally the ones.

a. 213, 290, 871, 899

b. 213, 291, 871, 899

c.    91, 312, 871, 899

d. 123, 190, 871, 899

Answer:

Step-by-step explanation:

a. 213, 290, 871, 899

b. 213, 291, 871, 899

c.    91, 312, 871, 899

d. 123, 190, 871, 899

i hope this helps u guys

Answer:

See attached file

Step-by-step explanation:

Answer:

D. the last graph

Step-by-step explanation:

Answer:

The solutions are [tex]x=-4(+/-)\sqrt{13}[/tex]

Step-by-step explanation:

we have

[tex]x^{2} +8x=-3[/tex]

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

[tex]x^{2} +8x+16=-3+16[/tex]

[tex]x^{2} +8x+16=13[/tex]

Rewrite as perfect squares

[tex](x+4)^{2}=13[/tex]

square root both sides

[tex]x+4=(+/-)\sqrt{13}[/tex]

[tex]x=-4(+/-)\sqrt{13}[/tex]

Answer: the last one

EXPLAINATION:

The first one follows the rule a+b=c, and when you add all the angles it equals 180

The second one when you add up all of the angles, it is 180

The third one follows a2+b2=c2. 5(5)+12(12)= 169, 13(13)=169

The last one does not follow any of the triangle rules.

Answer:

The length and the width of the garden is equal to [tex]l=8\ ft[/tex]

Step-by-step explanation:

Let

l -----> the length

w----> the width

we have

[tex]l=\frac{64}{w}[/tex] ------> equation A

If the garden is a square

then

l=w

substitute in the equation A

[tex]l=\frac{64}{l}[/tex]

[tex]l^{2}=64[/tex]

square root both sides

[tex]l=8\ ft[/tex]

therefore

The length and the width of the garden is equal to [tex]l=8\ ft[/tex]

Answer:7.C

8.B

9.A

Step-by-step explanation:

Make me the brainliest

Answer:

- 6

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ - 7, - 1 ]

f(b) = f(- 1) = (- 1)² + 2(- 1) - 8 = 1 - 2 - 8 = - 9

f(a) = f(- 7) = (- 7)² + 2(- 7) - 8 = 49 - 14 - 8 = 27

Hence

average rate of change = [tex]\frac{-9-27}{-1-(-7)}[/tex] = [tex]\frac{-36}{6}[/tex] = - 6

Check the picture below.

now, based on the provided information, we know the hexagon and triangle are regular polygons, equal sides and equal angles, we also know the angle in pink there of E and G are twins inside that irregular trapezoid, and you can see the exterior angles labeled there of 220° and 136°.

now, the trapezoid has twin angles at E and G, that means that the sides of DE and JG are equal and that also means that the other two angles inside that trapezoid are also twins, namely D and J.

if you notice the hexagon on the left-hand-side, a hexagon has interior angles of 120° and if we take a peek at the vertex at D, it has two angles then, one interior or 120° and an exterior of 136°, a full revolution will be 360°, so the remaining angle in green there must be 360° - 120° - 136°  = 104°, and her twin at vertex J is also 104°.

Answer:

You are correct my good sir! 7^5/7^2 expanded is (7x7x7x7x7)/(7x7)! another awesome thing to know for future reference is when dividing exponents with the same base you can simply subtract the exponents from each other! for example, 7^5/7^2=7^3! :D Hope This Helps!

Step-by-step explanation:

Answer:

Option D is the answer.

Step-by-step explanation:

The given expression is [tex]\frac{7^{5}}{7^{2}}[/tex]

We know [tex]7^{5}[/tex] = 7×7×7×7×7

and [tex]7^{2}[/tex] = 7×7

Therefore, we can rewrite the expression as [tex]\frac{7\times 7\times 7\times7 \times 7}{7\times 7}[/tex] which maches with option D.

Answer: Jacob ran for half an hour, and walked for the remaining half an hour.  15 km/hr x 0.5 hr = 7.5 km running, and 5km/ hr x 0.5 hr=2.5 km walking

Step-by-step explanation:

Let x hours be the time Jacob ran, and therefore for 1-x hours he walked.

time x speed= distance

we get, 15x + 5*(1-x)=10

15x+5-5x=10,

10x=5,

x=0.5 hours.

Average speed was 10km/h.

HOPE THIS HELPS.

Jacob ran 7.5 km at a speed of 15 km/h. By setting up a system of simultaneous equations, we found the distances for both running and walking that add up to the total distance of 10 km, while also fulfilling the constraint of a 1-hour total journey time.

To solve this problem with simultaneous equations, let's define two variables for the two different parts of the journey: x for the distance Jacob runs at 15 km/h and y for the distance he walks at 5 km/h. We know that Jacob covers a total distance of 10 km and the total time taken for the journey is 1 hour.

Set up the equations:

Equation for the distance: x + y = 10

Equation for the time: (x/15) + (y/5) = 1 (Since time is distance divided by speed)

Solve these equations simultaneously.

Multiply the second equation by 15 to clear the denominators: x + 3y = 15

Subtract the first equation from this new equation to solve for y: 2y = 5, so y = 2.5 km.

Substitute y back into the first equation to find x: x = 10 - 2.5, so x = 7.5 km.

Jacob ran 7.5 km at 15 km/h.

Check the answer:

Is 7.5 km in 1 hour at 15 km/h reasonable? Yes, because 15 km/h means he would run 15 km in 1 hour, so running for less than an hour for 7.5 km is plausible.

ANSWER

[tex]x = 5 \: or \: x = - 5[/tex]

EXPLANATION

The given absolute value equation is

[tex] | - 5x| - 5 = 20[/tex]

We add 5 to both sides of the equation to get:

[tex] | - 5x| - 5 + 5 = 20 + 5[/tex]

[tex] | - 5x| = 25[/tex]

This implies that,

[tex] - 5x = - 25 \: or \: - 5x = 25[/tex]

Divide both sides by -5,

[tex]x = 5 \: or \: x = - 5[/tex]

For this case we must factor the following expression:

[tex]-13m-m ^ 2 = 0[/tex]

We have a common factor "m" because it is the common term, so we have:[tex]m (-13-m) = 0[/tex]

Finally, the factorized expression of [tex]-13m-m ^ 2 = 0[/tex] is:[tex]m (-13-m) = 0[/tex]

ANswer:

[tex]m (-13-m) = 0[/tex]

Option B

Answer:

See explanation

Step-by-step explanation:

Car A: Started at 0 and ended at 300, thus, car A travels 300 miles.

It travels 6 hours, so car A speed is [tex]\frac{300}{6}=50[/tex] mph.

Car B: Started at 100 and ended at 300, thus, car B travels 300-100=200 miles.

It travels 5 hours, so car B speed is [tex]\frac{200}{5}=40[/tex] mph.

Since 50>40, car A traveled faster than car B.

The graph for the car A is steeper than the graph for the car B.

Answer:

Step-by-step explanation:

Answer:

The slope is 5/3. The equation would be, y = 5/3x + 8/-3.

Step-by-step explanation:

Standard form is "Ax  + By = C

5x - 3y = 8

-5x.         -5x

3y  = -5x + 8

now divide both sides by 3

y = 5/3 + 8/-3

Slope is 5/3

Answer: - 2/5

Step-by-step explanation: Isolate the vcariable by divding each side by factors that don't contain the variable.

Exact Form: x = - 2/5

Deciaml form: x = -0.4

Hope this helps! :) ~Zane

Hello there! B. -2/5.

To solve for x, you want to get x alone and isolate all other terms.

2 = -6 – 20x  - Start by adding 6 to both sides of the equation.

2+6 = -6+6 – 20x ⇒ 8 = -20x

8 = -20x - Next, divide both sides of the equation by -20..

8/-20 = -20/-20x ⇒ -8/20 = x

Now, we have -8/20 as our value for x. The last step is to simplify. Since 8 and 20 are both divisible by 4, divide both sides of the fraction by 4.

x = -2/5. This is your final answer. I hope this helps and have a great day! ~ saturns

Edit: Sorry for the typos, i fixed them! You have to press suuuper hard to get the S key on my keyboard to work :)

Answer:

x = 15

Step-by-step explanation:

∠2 and ∠4 are same side interior angles and are supplementary, thus

2x + 10 + 4x + 80 = 180

6x + 90 = 180 ( subtract 90 from both sides )

6x = 90 ( divide both sides by 6 )

x = 15