The first three steps in determining the solution set of the system of equations, y = –x2 – 2x + 8 and y = 2x + 11, algebraically are shown in the table.



Which represents the solution(s) of this system of equations?

(–3, –1)
(–3, 5)
(–3, 5) and (–1, 9)
(1, 13) and (3, 20)

Answer:

Step-by-step explanation:

This is a right triangle because angle V is 90. Draw out a right triangle and put V at the 90 degree angle. It doesn't matter where you put U or T; you get the same cos value for T regardless of how you place your other 2 angles. The things you need to know are that UT is the hypotenuse of the triangle, side VU is across from angle T, and side TV is across from angle U.

The cos ratio is side adjacent to the reference angle over the hypotenuse.

Our reference angle is T, so we are looking for the side next to T that is NOT the hypotenuse. This side measures 33; the hypotenuse measures 65, so the tangent ratio of T is

[tex]tanT=\frac{33}{65}[/tex]

Answer:

x ≈ 7.1

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{6.3}{x}[/tex] ( multiply both sides by x )

x × cos27° = 6.3 ( divide both sides by cos27° )

x = [tex]\frac{6.3}{cos27}[/tex] ≈ 7.1 ( to the nearest tenth )

Answer:

f(f(x)) = 27[tex]x^{4}[/tex] + 18x² + 4

Step-by-step explanation:

To find f(f(x)) substitute x = f(x) into f(x) , that is

f(3x² + 1)

= 3(3x² + 1)² + 1 ← expand parenthesis using FOIL

= 3(9[tex]x^{4}[/tex] + 6x² + 1) + 1 ← distribute parenthesis by 3

= 27[tex]x^{4}[/tex] + 18x² + 3 + 1 ← collect like terms

= 27[tex]x^{4}[/tex] + 18x² + 4

Hello,

[tex](fof)(x)=f(f(x))\\\\=3(3x^2+1)^2+1\\\\=3(9x^4+6x^2+1)+1\\\\\boxed{=27x^4+18x^2+4}[/tex]

Answer:

1. 25

2. 44

3. 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 70

Step-by-step explanation:

We are required to calculate the total distance Cecilia travelled in 5 days

The total distance Cecilia travelled for 5 days is 99 kilometers

Day 1 = 27 kilometers

Day 2 to day 5 = 2/3 of 27

= 2/3 × 27

= 2 × 9

= 18 kilometers each day

Total distance = day 1 + day 2 + day 3 + day 4 + day 5

= (27 + 18 + 18 + 18 + 18) kilometers

= 99 kilometers

Therefore, the total distance Cecilia travelled for 5 days = 99 kilometers

Read more:

https://brainly.com/question/17207658

Step-by-step explanation:

there is something wrong with what your write here as problem description.

either there is something missing in the main expression, or in the answer options.

given your nth-term expression 7n-2, none of the 4 answer options can fit.

so, I thought, maybe there was a typo.

the possible interpretations of the expression could be

7n - 2

7(n-2)

[tex] {7}^{n} - 2[/tex]

[tex] {7}^{n - 2} [/tex]

we know that

a1 = 1

a2 = either

a1 + 2 = 3

a1 - 2 = -1

a1 + 7 = 8

a1 - 7 = -6

so, we can eliminate both negative answer options, because they would cause only negative sequence elements, but the main expression (neither of the 4 possibilities) does not allow that.

but also none of the 4 possibilities of the expression delivers any of the 4 values for a2 as described above.

7×2 - 2 = 14 - 2 = 12

7(2-2) = 7×0 = 0

7² - 2 = 49 - 2 = 47

[tex] {7}^{2 - 2} = {7}^{0} = 1[/tex]

similar not for a3.

so, if I consider your answer options right, we have 4 possible arithmetic sequences:

1. 1, 3, 5, 7, 9, 11, 13, 15, ...

2. 1, -1, -3, -5, -7, -9, -11, -13, ...

3. 1, 8, 15, 22, 29, 36, 43, 50, ...

4. 1, -6, -13, -20, -27, -34, -41, ...

the nth term expression is for

a. an = 2n - 1

b. an = 2×(-n) + 3 = 2×(-n + 1) + 1

c. an = 7n - 6

d. an = 7×(-n) + 8 = 7×(-n + 1) + 1

so, please pick the right expression from this list, and then use the answer option with the same letter.

Answer:

0.50=1.7. They do not equal each other

Step-by-step explanation:

Thats what I got from this question

Answer:

B) 5

Step-by-step explanation:

We are given the function:

[tex]f(x)=x(x+3)[/tex]

We are given that f(a) = 40 and a > 0 and we want to determine the value of a.

Substitute:

[tex]f(a)=40=a(a+3)[/tex]

Distribute:

[tex]a^2+3a=40[/tex]

Subtract 40 from both sides:

[tex]a^2+3a-40=0[/tex]

We can factor using 8 and -5. Hence:

[tex](a+8)(a-5)=0[/tex]

By the Zero Product Property:

[tex]a+8=0\text{ or } a-5=0[/tex]

Solve for each case:

[tex]\displaystyle a=-8\text{ or } a=5[/tex]

Since a > 0, we can eliminate the first solution. Hence:

[tex]a=5[/tex]

Our answer is B.

Answer:

3/10 of a cup

Step-by-step explanation:

Find how many cups of strawberries each student got by dividing 6 by 20:

= 6/20

Simplify this by dividing each number by 2:

= 3/10

So, each student got 3/10 of a cup of strawberries

Answer:

340 ml

Step-by-step explanation:

Answer:

SN

Step-by-step explanation:

The line segment that is adjacent to angle ∠N will be NS and NJ. Then the correct options are A and B.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.

The triangle ΔNSJ is a right angle triangle in which the angle ∠NSJ will be a right angle that is 90°.

The line segment that is adjacent to angle ∠N will be NS and NJ. Then the correct options are A and B.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ2

Answer:

Tom earns $7.00 per hour

Rewrite the fractions as decimals by dividing:

7/8 = 0.7777

3/4 = 0.75

1/2 = 0.5

2/3 = 0.666

0.777 is the largest number so 7/9 is the largest fraction.

Answer: 7/9

Answer:

2/3

Step-by-step explanation:

L.C.M:36

7/9:28/36

3/4:27/36

1/2:1836

2/3:36/36

Answer:

56

Step-by-step explanation:

Step-by-step explanation:

dbdhdhbdbshsjakkakkajnwbsbdbdbdbbdbdbdvdvdvvvddvvdvd

Answer:

290 foils

Step-by-step explanation:

145,000÷500=290

Answer:

measure of angle V + measure angle W = VUF

Answer:

∠ VUF = 94°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles

∠ VUF is an exterior angle of the triangle, then

∠ VUF = 71° + 23° = 94°

Answer: 118°

Step-by-step explanation:

Step-by-step explanation:

C

im not sure of my answer. hope to help

Answer:

3124/999

Step-by-step explanation:

x = 3. 127 127 ....... -------------(I)

127 -----> 3 digits are repeating. so multiply both sides by 1000

(I)*1000             1000x = 3127.127127......

                                 x =       3.127127......        [Now subtract}

                           999x = 3124

x = 3124/999

Answer:

a₂₀ = 77

Step-by-step explanation:

There is a common difference between consecutive terms , that is

5 - 1 = 9 - 5 = 13 - 9 = 4

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 1 and d = 4 , then

a₂₀ = 1 + (19 × 4) = 1 + 76 = 77

Given:

The interval is [2,9].

To find:

The average rate of change in f(x) over the interval [2,9].

Solution:

The average rate of change in f(x) over the interval [a,b] is defined as:

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

In the interval [2,9], the value of a is 2 and the value of b is 9.

Using the above formula, the average rate of change in f(x) over the interval [2,9] is:

[tex]m=\dfrac{f(9)-f(2)}{9-2}[/tex]

[tex]m=\dfrac{f(9)-f(2)}{7}[/tex]

Therefore, the required expression for the average rate of change in f(x) over the interval [2,9] is [tex]\dfrac{f(9)-f(2)}{9-2}[/tex], it is also written is [tex]\dfrac{f(9)-f(2)}{7}[/tex].

Answer:

D

Step-by-step explanation:

right on edge

Step-by-step explanation:

The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,

[tex]\implies 2x -y +6=0\\\\\implies 2x + 3y -6=0[/tex]

On subtracting the given equations we have,

[tex]\implies -y - 3y +6 -(-6) = 0 \\\\\implies -4y = -12 \\\\\implies y = -12/-4\\\\\implies y = 3 [/tex]

Put this value in any equation , we have ,

[tex]\implies 2x -3 +6 =0\\\\\implies 2x = -3 \\\\\implies x =\dfrac{-3}{2} \\\\\implies x =-1.5 [/tex]

Hence the lines will Intersect at ,

[tex]\implies\underline{\underline{ Point=(-1.5, 3)}}[/tex]

for the first one x = 1/2 y-3" and y = 2 x + 6 and for the other one is x =  − 3 /2  y+ 3  and y= − 2 /3  x + 2

how i did this Step 1: Add -3y to both sides.

Step 2: Add 6 to both sides.

Step 3: Divide both sides by 2.

Answer:

y=|x -3| -1

Step-by-step explanation:

Answer:

[tex]x=3\\y=2[/tex]

Step-by-step explanation:

[tex]3x+2y=13\\y=x-1[/tex]

Solve for [tex]y=x-1[/tex] for y:

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

Substitute [tex]x-1[/tex] for y in [tex]3x+2y=13[/tex]:

[tex]3x+2y=13[/tex]

[tex]3x+2(x-1)=13\\[/tex]

[tex]5x-2=13[/tex]

[tex]5x=13+2[/tex]

[tex]5x=15[/tex]

[tex]x=15/5[/tex]

[tex]x=3[/tex]

Substitute 3 for x in [tex]y=x-1[/tex]:

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

[tex]y=(3)-1[/tex]

[tex]y=2[/tex]

[tex]x=3[/tex] and [tex]y=2[/tex]

hope this helps...

Answer:

the correct options are 1, 2, 5, and 6th

1. and 2.

all functions have a dependant variable y and independent variable x, and the set of dependant variables is called its range whereas the set of independent variables is called its domain.

5. and 6.

In a horizontal line 1 input associates itself with exactly one ouput, even tho the output is constant (same) for all values of x, and that's the property of a function

Answer:

all functions have dependent variables

all functions have an independent variable

a horizontal line Is an example of a functional relationship

Answer:

Diameter = 14 units

Step-by-step explanation:

Volume ofa cylinder = πr²h

Volume of the cylinder = 245π cubic units

Height = 5 units

Volume of a cylinder = πr²h

245π = π × r² × 5

245π = 5r²π

Divide both sides by π

245π / π = 5r²π / π

245 = 5r²

r² = 245/5

= 49

r² = 49

r = √49

r = 7 units

Diameter = 2 × radius

= 2 × 7 units

= 14 units

Diameter = 14 units

Answer:

Same side interior angles

Step-by-step explanation:

Same side interior angles are interior angles and on the same side. Sorry don't know how to better explain.