Given f (x) = x2 + 3x – 4 and values of the linear function g(x) in the table, what is the range of (f + g)(x)?


x –6 –3 –1 4
g(x) 13 4 –2 –17

ℝ
[–3, 3]
(–∞, –9]
[–9, ∞)

Answer:

1+x it means I plus the rest

Answer:

48 then it would be 32? im not sure that what i caculated

Step-by-step explanation:

Answer:

9. answer: -3, 10. answer: 5

Answer:

m(n) = 60000

Amount = 60000/n

Step-by-step explanation:

Given

Budget = 60000

Solving (a) Represent as a function mn

To do this simple substitute m(n) for Budget.

This gives;

m(n) = 60000

Solving (b) Amount each committee will receive.

Since the amount will be shared evenly.

Amount = m(n)/n

Substitute 60000 for m(n)

Amount = 60000/n

Answer: 1/5

Step-by-step explanation:

Simplify the fraction by dividing both the numerator and denominator by 2

Answer:

y = x - 2

Step-by-step explanation:

1. Find the slope - change in y/change in x

[tex]\frac{0-(-1)}{2-1}[/tex] = 1

Slope is 1

2. Find y-intercept

y = x + b

Substitute a point (2,0)

0 = 2 + b

b = -2

3. Put the equation together

y = x - 2

Answer:

96

Step-by-step explanation:

commom difference = d

a₆ + a₇ = 16

a₅ + a₈ = (a₆ - d) + (a₇ + d) = a₆ + a₇ = 16

a₄ + a₉ = (a₆ - 2d) + (a₇ + 2d) = a₆ + a₇ = 16

Similarly,

a₃ + a₁₀ = 16, a₂ + a₁₁ = 16, a₁ + a₁₂ = 16

so

a₁ + a₂ + ... + a₁₁ + a₁₂ = 6 x 16 = 96

Step-by-step explanation:

The diagonals of a square bisect each other, are perpendicular to each other, bisect opposite angles and are congruent.

Answer:

13.54 years

Step-by-step explanation:

Saw the answer to this before

Hope this helps!

Answer:

5

Step-by-step explanation:

because it is the right answer

Answer:

8 weeks

Step-by-step explanation:

265-30 = 240

240/30(per week)=8

Answer is 8 weeks

Answer:

No. of bags of rice packed = 198

Amount of rice in each bag = 3 kg

Therefore, total kilograms of rice packed=198×3=594 kg

Step-by-step explanation:

Hope this helps you

Do mark me as brainliest

They packed 594 kilograms of rice.

Given:

Number of bags packed by the group of volunteers = 198

Number of kilo a bag contains = 3 kg

Therefore:

Number of kilograms of rice packed by the volunteers = number of bags packed [tex]\times[/tex] number of kilo one bag of rice weighs

Thus:

Number of kilos of rice packed = [tex]198 \times 3 $ kg\\[/tex]

[tex]= 594 $ kg[/tex]

Therefore, the volunteers packed 594 kilograms of rice.

Learn more here:

https://brainly.com/question/21146374

Answer:

No.

Step-by-step explanation:

Translation is a type of rigid transformation. It simply moves the figure around the coordinate plane, so the size doesn't change.

Answer:

B

Step-by-step explanation:

The ice has more thermal energy because it is a solid and the water is a liquid. The water has more thermal energy because the molecules of the water are moving faster than the molecules of the ice. The water and the ice have the same amount of thermal energy because they are different forms of the same substance.

Answer:

its B :)

Step-by-step explanation:

i took the test

Answer:

Here

Step-by-step explanation:

7 = 4x + 7

Cancel out the 7's on each side by adding negative 7 to both sides...

0 = 4x

Now find how much for x alone

4x = 0

divide both sides by 4

x = 0

X = 0

7 = 0 + 7

7 = 7

Answer:

x = 95

Step-by-step explanation:

The total degree of a circle is 360. The twp arcs on each side of the parallel lines are equal.

Subtract 135 and 35 from your total

360 - 135 - 35 = 190

Divide your answer by 2

190 ÷ 2 = 95

Answer:

2(x+2)

Step-by-step explanation:

(2x²+10x+12)/(x+3)=(2(x²+5x+6))/(x+3)=(2(x²+2x+3x+6))/(x+3)=(2(x(x+3)+2(x+3)))/(x+3)=(2(x+3)+(x+2))/(x+3)=2(x+2)

i hope you understand (well it's math)

Answer:

C

Step-by-step explanation:

The weight of the new student is 27 kg.

Average weight

= total weight ÷total number of students

Let the total weight of the 35 students be y kg and the weight of the new student be x kg.

[tex]45 = \frac{y}{35} [/tex]

y= 35(45)

y= 1575 kg

New total number of students

= 35 +1

= 36

Total weight

= total weight of 35 students +weight of new students

= y +x

[tex]44.5 = \frac{y + x}{36} [/tex]

[tex]44.5 = \frac{1575 + x}{36} [/tex]

36(44.5)= 1575 +x

1602= x +1575

Subtract 1575 from both sides:

x= 1602 -1575

x= 27

Thus, the weight of the new student is 27 kg.

Answer:

7,14,21,28,35,42,49,56,63,70

Step-by-step explanation:

just add 7 lol anyways here ya go :)

Answer:

x=8

Step-by-step explanation:

this is a right angle and right angles are 90 degrees. 6*8 equals 48+2 equals 50. 50+40 equals 90!

Answer:

x=8

Step-by-step explanation:

you would subtract 40 from 90 which gives you 50. you would then set 6x+2 equal to 50 and solve from there.

Answer:

above me is maybe a yes or no

Step-by-step explanation:

brainlles to above me

They are both really the same. so they should hold the same. All that happened is one moved a 1/2 inch over to the length from the height.  

Answer:

undefined

Step-by-step explanation:

(y2-y1)/(x2-x1)

replacing x and y with the given value:

(-4-1)/(8-8)

-5/0

the slope is undefined because the run is 0

Answer:

AAS

Step-by-step explanation:

There are two congruent angles, but the congruent side is not included between the two angles.

Answer: -72 I think

Step-by-step explanation:

Hope this helps :)

well, a right-triangle will have one angle that is 90°, and using the pythagorean theorem, we also know that the longest side is really the root of the sum of the square of the other two.  After all that mouthfull let's check

[tex]\stackrel{longest}{16}~~ = ~~\sqrt{\underset{short}{13^2}~~ + ~~\underset{short}{4^2}}\implies 16=\sqrt{169+16} \\\\\\ 16=\sqrt{185}\implies 16^2=185\implies 256~~ \ne ~~185\qquad \leftarrow \textit{nope, it isn't}[/tex]

Answers:

==================================================

Explanation:

Problem 1

This is false because the A and B should swap places. It should be [tex](AB)^{-1} = B^{-1}A^{-1}[/tex].

The short proof is to multiply AB with its inverse [tex](AB)^{-1}[/tex]  and we get: [tex](AB)*(AB)^{-1} = (AB)*(B^{-1}A^{-1}) = A(B*B^{-1})*A^{-1} = A*A^{-1} = I[/tex]

The fact we get the identity matrix proves that we have the proper order at this point. The swap happens so that B matches up its corresponding inverse [tex]B^{-1}[/tex] and the two cancel each other out.

Keep in mind matrix multiplication is not commutative. So AB is not the same as BA.

-------------------------

Problem 2

This statement is true if and only if AB = BA

(A+B)^2 = (A+B)(A+B)

(A+B)^2 = A(A+B) + B(A+B)

(A+B)^2 = A^2 + AB + BA + B^2

(A+B)^2 = A^2 + 2AB + B^2 ... only works if AB = BA

However, in most general settings, matrix multiplication is not commutative. The order is important when multiplying most two matrices. Only for special circumstances is when AB = BA going to happen. In general,  AB = BA is false which is why statement two breaks down and is false in general.

-------------------------

Problem 3

This statement is true.

If A and B are invertible, then so is AB.

This is because both [tex]A^{-1}[/tex] and [tex]B^{-1}[/tex] are known to exist (otherwise A and B wouldn't be invertible) and we can use the rule mentioned in problem 1. Make sure to swap the terms of course.

Or you can use a determinant argument to prove the claim

det(A*B) = det(A)*det(B)

Since A and B are invertible, their determinants det(A) and det(B) are nonzero which makes the right hand side nonzero. Therefore det(A*B) is nonzero and AB has an inverse.

So if we have two invertible matrices, then their product is also invertible. This idea can be scaled up to include things like A^4*B^3 being also invertible.

If you wanted, you can carefully go through it like this:

and so on until you build up to A^4*B^3. Therefore, we can conclude that A^m*B^n is also invertible. Be careful about the order of multiplying the matrices. Something like A*AB is different from AB*A, the first of which is useful while the second is not.

So this is why statement 3 is true.

-------------------------

Problem 4

This is false. Possibly a quick counter-example is to consider these two matrices

[tex]A = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}[/tex]

both of which are invertible since their determinant is nonzero (recall the determinant of a diagonal matrix is simply the product along the diagonal entries). So it's not too hard to show that the determinant of each is 1, and each matrix shown is invertible.

However, adding those two mentioned matrices gets us the 2x2 zero matrix, which is a matrix of nothing but zeros. Clearly the zero matrix has determinant zero and is therefore not invertible.

There are some cases when A+B may be invertible, but it's not true in general.

-------------------------

Problem 5

This is true because each A pairs up with an [tex]A^{-1}[/tex] to cancel out (similar what happened with problem 1). For more info, check out the concept of diagonalization.

Answer:

The Marked Price is 63.75

Step-by-step explanation:

15/100 * 75 = 11.25

75 - 11.25 = 63.75

Hence the Marked Price is 63.75