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Answer:

The average rate of change of f(x) over the interval 1 ≤ x ≤ 4 is -1.

Step-by-step explanation:

We are given the function:

[tex]f(x)=x^2-6x+4[/tex]

And we want to determine its average rate of change over the interval:

[tex]1\leq x\leq 4[/tex]

The average rate of change is synonymous with the slope. So, to find the average rate of change, we simply need to find the slope between the two endpoints.

Evaluate each endpoint:

[tex]f(1)=(1)^2-6(1)+4=-1[/tex]

[tex]f(4)=(4)^2-6(4)+4=-4[/tex]

So, our endpoints are (1, -1) and (4, -4).

The slope between them is:

[tex]\displaystyle m=\frac{(-4)-(-1)}{(4)-(1)}=\frac{-3}{3}=-1[/tex]

So, the average rate of change of f(x) over the interval 1 ≤ x ≤ 4 is -1.

Answer:

y=1/2x-3

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A vertical line will have the steepest slope

Answer:

the first truck

Step-by-step explanation:

the cost difference between the first truck and the second truck = $160,000-$145,000 = $15,000

the difference of gas cost between the first truck and the second truck = $0.31 - $0.26= $0.05 per mile.

so,

I think, this is a very significant number of truck cost compared with gas cost

for the best deal, the first truck is the best choice.

Answer:

6x-4

Step-by-step explanation:

c-the missing length

(2x+5)+(4x-2)+c = 12x-1

2x+5+4x-2+c=12x-1

6x+3+c=12x-1

6x+4+c=12x =>4+c=12x-6x =>4+c=6x => c=6x-4

What is the missing length? 6x-4

Answer:

Step-by-step explanation:

Top/Bottom = 12

Sides = 15

Front/Back = 20

20 + 15 + 12 = 47

47 / 1/2 = 23.5

Answer:

B

Step-by-step explanation:

x² - 4x - 7 = 0

(x - 2)² = 11

Answer:

Option A

Step-by-step explanation:

That is your answer

Answer:

a) 2(a+b)

Step-by-step explanation:

the sum of 2 numbers (or more) is always addition

so the sum of a  and b would be (a+b)

then, 2 times of a and b;

2(a+b)

^the times sign between the bracket and the 2 isnt needed, whenever there is a bracket and a number next to it, it is automatically a multiplication.

Answer:

it is green balls=5

red balls =4

red +green

5+9

=14

Answer:

B is the correct answer

since

a1/a2=b1/b2≠c1/c2

Answer:

56

Step-by-step explanation:

56

hope this helps

¬_¬ :)

Answer:

200.96

Step-by-step explanation:

have a good day:D

Step-by-step explanation:

We know that

[tex]\boxed{\sf a^m\times a^n=a^m+n}[/tex]

[tex] \sf \: {8}^{5} \times {8}^{6} \\ \sf \leadsto \: {8}^{5 + 6} \\ \sf \leadsto {8}^{11} [/tex]

[tex]\sf More\;to\: know{\begin{cases}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{cases}}[/tex]

The answer is 904.8 yd³

Step-by-step explanation:

The formula for a sphere's volume is 4/3πr²

r in this case is 12/2 which is 6. That means that r=6 which gives us 904.78 which is rounded to 904.8.

Answer:

904.32

Step-by-step explanation:

v= [tex]\frac{4}{3\\}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

first cube the radius (6)  (radius is half of the diameter 12)

6x6x6 = 216

multiply by pi

216 x 3.14 = 678.24

multiply by 4/3

[tex]\frac{678.24}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{2712.96}{3\\}[/tex] = 904.32

The best description of a random sample for Kiera's middle school survey to determine the winter dance theme is option D: Fifty randomly selected 7th graders are surveyed.

Random sampling is a technique for picking a sample from a population in such a manner that each possible sample has a preset probability of being chosen.

As per the question, the sample should be representative of the entire student population, so selecting fifty students from each grade (option B) or all the students in Mrs. Jackson's class (option A) may not be representative of the entire student population.

Similarly, selecting fifty randomly selected staff members (option C) may not be representative of the student population.

Therefore, option D is the best choice as it randomly selects students from the population of interest.

Learn more about random sampling here:

https://brainly.com/question/30759604

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We will see that the axis of symmetry is x = 3, so the correct option is c.

The axis of symmetry is a line of the form x = a, such that it divides the parabola in two halves.

Particularly, the axis of symmetry passes through the vertex, so the x-value of the vertex is equal to the value of the axis.

Then we only need to find the x-value of the vertex, remember that for a quadratic:

[tex]y = a*x^2 + b*x + c[/tex]

The vertex is at:

[tex]x = -b/2a[/tex]

Then in our case, the vertex is at:

[tex]x = -12/(2*-2) = -12/-4 = 3[/tex]

So the axis of symmetry is x = 3, then the correct option is C.

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

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Answer:

soi de perú         NO INGLISH IS SPANISH

Step-by-step explanation:

JAJAJAJ

Answer:

I, J

Step-by-step explanation:

Answer:

Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.

Step-by-step explanation:

We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.

Triangle ABC:

Measure of angle A= 60°

Measure of angle C= 40°

Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°

Triangle DEF

Measure of angle E= 80°

Measure of angle F= 40°

Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°

The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.

The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.

Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.

The correct statement is [tex]\frac{a}{b}[/tex] = [tex]\frac{t}{s}[/tex] ,  [tex]\frac{b}{c}[/tex] = [tex]\frac{s}{r}[/tex] ,  [tex]\frac{c}{d}[/tex] = [tex]\frac{r}{q}[/tex].

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Similar figures are those figures whose ratio of the length of sides are proportional.

Similar figures only differ in size, their shape is equal.

The sides a, b, c and d in the larger parallelogram is similar to the sides t, s, r and q respectively in the smaller parallelogram.

So we get the ratio b / c equal to the ratio s / r and the ratio c / d equal to the ratio r / q.

Hence the equation that go with the statement two sides of a parallelogram have the same ratio as the corresponding two sides of a parallelogram is  [tex]\frac{a}{b}[/tex] = [tex]\frac{t}{s}[/tex] ,  [tex]\frac{b}{c}[/tex] = [tex]\frac{s}{r}[/tex] ,  [tex]\frac{c}{d}[/tex] = [tex]\frac{r}{q}[/tex].

Learn more about Parallelogram here :

https://brainly.com/question/29147156

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Answer:The first one is 16 and the second one is 18

Step-by-step explanation:

Answer:

8√2

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

f0llow me if you have time thanks

hope it helps

#carryonlearning

#ownanswer

Answer:

13 pints

Step-by-step explanation:

2 pints per quart

6.5 x 2 = 12 + 1 = 13 pints

If my answer is incorrect, pls correct me!

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-Chetan K