Let f(x) = 3x + 2 and g(x) =7x + 6. Find f ·g and its domain.

You did not specify the brother's age, so I make a expression, b as the variable.

(3b + 5) - 11

Now do that with the brother age instead of the variable.

(3b + 5) - 11 = 3

you first add 3 and 5 which equals 8 ten you subtract 11 and 8 which equals 3, so jane is 3 years old

Explanation:

15. x = 148°, z = 32°

In a parallelogram, adjacent angles are supplementary, so must add to 180°. That also means opposite angles are congruent.

___

17. x = 8, y = -3

The diagonals bisect each other, so ...

2x -4 = 12

x = (12 +4)/2 = 8

and ...

y +10 = 7

y = 7 -10 = -3

__

21. The diagonals of a parallelogram bisect each other, so their point of intersection is their midpoint. The midpoint of WY can be computed as ...

P = (W+Y)/2 = ((-3, 5) +(3, 1))/2 = (0, 6)/2 = (0, 3)

The diagonals intersect at (0, 3).

Final answer:

The expression to verify that g(x) is the inverse of f(x) is to check if f(g(x)) = x and g(f(x)) = x. When we calculate both expressions for the given functions, they both simplify to x, which confirms that g(x) is the inverse of f(x).

Explanation:

To verify that g(x) is the inverse of f(x), we need to show that composing f with g yields the identity function. In other words, f(g(x)) should equal x, and vice versa, g(f(x)) should also equal x. For the given functions, f(x) = 5x - 25 and g(x) = 1/5x + 5, let's compute f(g(x)) and g(f(x)).

To find f(g(x)), we substitute g(x) into f(x):

f(g(x)) = f(1/5x + 5) = 5(1/5x + 5) - 25 = x + 25 - 25 = x

Next, to find g(f(x)), we substitute f(x) into g(x):

g(f(x)) = g(5x - 25) = 1/5(5x - 25) + 5 = x - 5 + 5 = x

Since both f(g(x)) and g(f(x)) equal x, we can conclude that g(x) is indeed the inverse of f(x).

Answer:

Yep! an open dot is <

A closed dot means ≤

Hope this helps! :)

If you don't mind please mark as brainliest! :)

ANSWER

3 square units

EXPLANATION

The given formula is

[tex]A=12s^2[/tex]

But

[tex] s = \frac{1}{2} [/tex]

We substitute the value of s into the formula to get;

[tex]A=12( \frac{1}{2} )^2[/tex]

[tex]A=12 \times \frac{1}{4}[/tex]

[tex]A=3 {units}^{2} [/tex]

The value of A in square units is

3

Answer:

option A

(1.5,1.2)

Step-by-step explanation:

Given in the question two equations

Equation 1

y = √x

Equation 2

y = x²- 1

Equate both equations

√x = x²- 1

We can see from the graph that both meets when x =  1.5 and y = 1.2

we can plug the options given one by one to see which points satisfy

one thing we know is that x ≠ any negative value since

y = √x and square root of negative value is not possible

so option b and c are rejected

  option A

√1.5 = y = 1.2

1.5²- 1 = y = 1.2

Answer:

29

Step-by-step explanation:

the rule PEMDAS means first use the parentheses, (  ,  )

so order of operation, first you do parentheses, 20/4=5 then 5-5=0

so that is the parentheses now take core of stuff outside of parentheses and    29 x 1=29

P= parentheses

E = Exponents

M= multiply

D = divide

A= addition

S= subtract

also know as order of operation!

hope this helps. please mark brainliest! have a good day

The value of expression 29 • 1 + 2(20 ÷ 4 – 5)= 29

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

To solve the given expression we will use:

The PEMDAS rule means

P= Parentheses

E = Exponents

M= multiply

D = divide

A= addition

S= subtract

first we do parentheses,

29 • 1 + 2(20 ÷ 4 – 5)= 29.1+2(5-5)

                                  = 29.1+2(0)

                                  = 29.1+0

                                 =29

Thus,  29 • 1 + 2(20 ÷ 4 – 5)  =29

Learn more about PEDMAS here:

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ANSWER

[tex]a_{34} = 8[/tex]

EXPLANATION

The given matrix is a 4 by 4 matrix.

The entry in the intersection of the first third row and the fourth column is denoted

[tex]a_{34}[/tex]

This entry is 8.

Check the attachment for how we got the 8.

Therefore

[tex]a_{34} = 8[/tex]

Answer:

So the correct option is X squared -3 X +40

Step-by-step explanation:

If a polynomial has roots x=8 and x=-5, then we know that the factorized form is:

(x-8)(x+5)

So, to find the polynomial we need to expand the polynomials:

(x-8)(x+5) = (x^2 +5x - 8x + 40) = x^2 -3x + 40

Answer:

Never. (Not viable)

Step-by-step explanation:

3% of 500=15

5% of 300=15

Since both of them would get $15 a year, then they would stay the same amount apart. For example, when the first account reached 515 dollars, the second one would be at 315 dollars. Thus, they'd always be 200 dollars apart.

However!

Since it is a compound interest, and if there is the original 7% a year, the formula we'll use for this is the simple interest formula, or:  

I=Pxrxt

Where:

P is the principal amount, $500.00.

r is the interest rate, 3% per year, or in decimal form, 3/100=0.03.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 500 × 0.03 × 5 to get that:  

The interest is: $75.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),  

or 500.00 + 75.00 = 575.00. For example:

If you borrowed the $500.00, you would now owe $575.00

If you loaned someone $500.00, you would now be due $575.00

If owned something, like a $500.00 bond, it would be worth $575.00 now.

You want to calculate the interest on $300 at 5% interest per year after 5 year(s).

The formula we'll use for this is the simple interest formula, or:  

I=Pxrxt

Where:

P is the principal amount, $300.00.

r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 300 × 0.05 × 5 to get that:  

The interest is: $75.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),  

or 300.00 + 75.00 = 375.00. For example:

If you borrowed the $300.00, you would now owe $375.00

If you loaned someone $300.00, you would now be due $375.00

If owned something, like a $300.00 bond, it would be worth $375.00 now.

Answer: there is only one solution and it is viable . ( answer on PLATO)

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

A multiple is a number that can be divided by another number without a remainder. These are all multiples of 12 because they can all be divided by another number without a remainder.

It's subsitution.

-(-10)^2 + (-10) --) -(100) + (-10) --) -100 - 10 --) -110.

g(-10) = -110

Answer:

-110

Step-by-step explanation:

g(x) = -x^2 + x

g(-10) = -(-10)^2 + (-10)

g(-10) = -100 - 10

g(-10) = -110

Answer: I'm pretty sure its 1562

Answer:

The sum of 22 terms of given AP = 1562

Step-by-step explanation:

Formula:-

Sum of n terms of AP,

Sₙ= (n/2)[2a + (n - 1)d]

To find the sum of 22 terms

Here. a = 8, d = 6 and n = 22

Sₙ= (n/2)[2a + (n - 1)d]

S₂₂ = (22/2)[2*8 + (22 - 1)*6]

  = 11[16 + 126] = 11 * 142 = 1562

Answer:

so where the points are on the triangles is where you would go side to side and up and down

Step-by-step explanation:

Find the lengths of the sides:

BA = 4, this would be y1

BC = 6, this would be x1

CD = 2, this would be y2

DE = 3, this would be x2

The slope is the Y over X

Slope of ABC = 4 / 6

Slope of CDE = 2 / 3

Answer A equals both of those:

6-2 / 9-3 = 4/6

8-6 = 12-9 = 2/3

Answer:

9

Step-by-step explanation:

when u add her past five scored together, you get 39. your equation would be

39 + x

-------------         = 8

6

you multiply both sides by 6 and get

39+x = 48

subtract 39 from both sides to get 9

Inscribed angles are pretty easy, they're always half the corresponding central angle.  The arc measure are always of central angles.

1. We're told to arc is 62 degrees so the inscribed angle is half,

WXY = 31 degrees.

2. Here we're told the inscribed angle is 113 degrees so the arc is double,

DGF=226 degrees

3. Angles which subtend a diameter are always right angles.

PQR = 90 degrees

4. If we draw DC we see it's a radius too, so DC=DB and we have an isosceles triangle so DCB=47 degrees so BDC=180-47-47=86.  The central angle is the arc measure so

BC=86 degrees

5. Angle JNK=53 degrees and angles NJK=NKJ because we have an isosceles triangle, two sides radii.  So NKJ=(180-53)/2.

Similarly NKL=(180-65)/2

So angle JKL=NKJ+NKL=180 - (65+53)/2 = 180 - 118/2 = 121 degrees

I better leave the rest for you.

An inscribed angle is formed by two secant lines intersecting on a circle's circumference and is half the measure of the central angle intercepting the same arc. Fundamental theorems like the Pythagorean theorem and mnemonic SOHCAHTOA are important in geometry, especially when dealing with circles and triangles.

An inscribed angle is formed when two secant lines of a circle intersect on the circle's circumference. The value of an inscribed angle is always half the measure of the central angle that intercepts the same arc.

This is a foundational concept in geometry that is often linked to other geometric properties and theorems, such as the relationship between angles and arcs, and the behavior of angles within and outside of circles.

Knowing how to work with inscribed angles is crucial, particularly when dealing with problems involving circles.

For example, if you know the measure of the central angle, you can easily find the inscribed angle by dividing the central angle by 2. Recall other basic geometrical facts, such as the Pythagorean theorem, which states that in a right triangle, a² + b² = c² (where c is the hypotenuse), and the mnemonic SOHCAHTOA which helps remember the relationships of sides and angles in right triangles.

To help visualize these concepts, sketching triangles and remembering that the angles of a triangle sum up to 180 degrees can be helpful. Plane geometry forms the basis for understanding these principles, which is essential in tackling more advanced problems in circles and other geometric figures.

For this case we have that the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have as data that:

[tex]m = \frac {1} {4}\\b = - \frac {3} {4}[/tex]

Substituting:

[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]

Answer:

[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]

Answer:

-6

Step-by-step explanation:

Answer:

3f³/g²

Step-by-step explanation:

√(900f^6/100g^4) =√(9f^6/g^4)=3f³/g²

Answer:

[tex][3f^{3}g^{-2}][/tex]

Step-by-step explanation:

The given expression is [tex]\sqrt{\frac{900f^{6} }{100g^{4}}}[/tex]

We can rewrite the expression as [tex]\sqrt{\frac{(30f^{3})^{2}}{(10g^{2})^{2}}}[/tex]

Now we can remove the radical of the expression =  [tex]\frac{30f^{3} }{10g^{2} }[/tex]

= [tex][\frac{3f^{3} }{g^{2}}][/tex]

= [tex][3f^{3}g^{-2}][/tex]

= [tex][3f^{3}g^{-2}][/tex] is the answer.

Answer:

2,008,747,295,829,492‬

Step-by-step explanation:

2008747295829492= 1000 + 2008747295828492

Answer:

$14

Step-by-step explanation:

20*0.3 0.3 is 30%

20*0.3=6

20-6=14

The answer is 14.

Explanation

Multiply 20 by .3

You get 6

Subtract 20 from 6 and u get 14.

Answer:

the far left table

In Mathematics, a zero slope represents a horizontal line that can be defined by the equation y = C, where C is a constant, showing no relationship between changes in x and y.

In Mathematics, when discussing about slopes, a zero slope signifies that there is no change in y for any change in x. This results in a straight horizontal line when graphed. A real-life example might be that if you were walking on a flat road, the slope of that road is zero because your altitude isn't changing no matter how far you walk horizontally.

The relationship involved in a zero slope scenario can be defined by the equation y = C, where C is a constant. This means that y will remain constant despite any changes in x.

The equation of a line with zero slope can be declared as y = b, where b is the y-intercept. This shows no correlation between x and y as x varies but y remains constant.

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Answer:

Each team recieved $312

Step-by-step explanation:

You will take $5145 - 777 = 4368 which is the balance

4368 of the balance  ÷ 14 teams =312

each team received  $312

After paying the expenses of $777 from the fund-raising total of $5145, $4368 was left. When this amount was divided evenly amongst 14 soccer teams, each team received $312.

To solve the problem, we first need to subtract the expenses from the total fund-raising amount. This gives us $5145 - $777 = $4368.

After the expenses are taken into consideration, the remaining money is divided evenly among the 14 soccer teams. This is calculated by taking the remaining money and dividing it by the number of teams, $4368 ÷ 14 = $312.

So, each team will receive $312 after all the expenses are paid.

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Answer:

The diameter of the rug is [tex]4\ ft[/tex]

Step-by-step explanation:

we know that

The circumference of a circle (circular rug) is equal to

[tex]C=\pi D[/tex]

where

D is the diameter of the circle

In this problem we have

[tex]C=12.56\ ft[/tex]

substitute in the formula and solve for D

[tex]12.56=(3.14)D[/tex]

[tex]D=12.56/(3.14)=4\ ft[/tex]

Answer:

25 meters

Step-by-step explanation:

Answer: 15.9155

is you answer and if it dont include the .9155 just choose 15 or 16 if its there

Step-by-step explanation:

Answer: Alright get ready for a long explanation

he would have 820.00$ in his savings account after the 5 years

Step-by-step explanation:

if he earns 12% interest then you would have to multiply 100 by the 12/100 which is .12 in decimal form.

100 TIMES .12 = $12.00

because we are doing this in months you need to multiply the amount he makes per month by the amount of months that the 100 dollars is in the bank account.

Alright so now that thats over, he makes 12 dollars every month

thers 12 months in a year, so you would have to do 12 (the number of moths) times 5 (the amount of years) that equals 60.  

60 TIMES the amount he makes per month ($12) equals $720.00

LASTLY! add the amount he made to the original amount and you get the answer of $820.00

i hope this helps :)

Answer:

Corresponding angles theorem.

Step-by-step explanation:

The corresponding angles theorem states that corresponding angles are congruent.

Pretty much means that every other angle is congruent if two lines are parallel and a line traverses them.

Answer: angle 2 and angle 6 are both corresponding angles

Step-by-step explanation:

If the two angles are matching corners, they are corresponding to one another. Hope this helps and have a good day:)

Answer:

0.0000135

Step-by-step explanation:

Final answer:

Tipping a fortune teller involves giving them a gratuity as a gesture of appreciation for their service.

Explanation:

When you tip a fortune teller, you are giving them a gratuity or extra money as a gesture of appreciation for their service. Tipping is a common practice in various service industries, including fortune-telling. It is a way to show gratitude for the insights or entertainment provided by the fortune teller.

Answer:

x = 3 is a true solution.

The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.

Step-by-step explanation:

Given in the question an equation,

√(x-2) - 4 = x - 6

√(x-2) = x - 6 + 4

√(x-2) = x -2

Take square on both sides of the equation

√(x-2)² = (x -2)²

x - 2 = x² - 4x + 4

0 = x² - 4x - x + 4 + 2

0  = x² - 5x + 6

a = 1

b = -5

c = 6

x = -b±√(b²-4ac) / 2a

x = -(-5)±√(5²-4(1)(6)) / 2(1)

x = 5 ± √1 / 2

x = 5 + 1 / 2 or  5 - 1 /2

x = 3 or x = 2

Plug value of x in the radical equation:

√(3-2)-4=3-6

√1 -4 = -3

 1 - 4 = -3

    -3 = -3

√(2-2)-4=2-6

0 - 4 = -4

    -4 = -4

Answer:

C. x = 3 is a true solution.

E. The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.

Step-by-step explanation: