Over the closed interval [3, 8], for which function can the extreme value theorem be applied?

Answer:

D

Step-by-step explanation:

x² + 7x + 12

to find the roots equate the expression to zero

x² + 7x + 12 = 0

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)

the factors are + 3 and + 4 , since

3 × 4 = 12 and 3 + 4 = 7 , then

(x + 3)(x + 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 4 = 0 ⇒ x = - 4

Answer:

D -3, -4.

Step-by-step explanation:

x^2 + 7x +12 = 0

12 = 3*4 and 7 = 3 + 4 so we write:

(x + 3)(x + 4) = 0

x + 3 = 0 ,  x + 4 = 0

So x = -3, -4.

Answer: I believe that the answer would be "In an isosceles triangle, two of the angles are congruent."

Step-by-step explanation:

Answer:

In an isosceles triangle, two of the angles are congruent.

hope this helps :)

Answer:

the answer to your question should be 2,068

Step-by-step explanation:

i hope i am right but i think so

Answer:

x = 50

Step-by-step explanation:

∠ BAC and 135° are adjacent angles and sum to 180° , then

∠ BAC = 180° - 135° = 45°

∠ BCA = 180° - 45° - 85° = 180° - 130° = 50° ( sum of angles in triangle )

x and ∠ BCA are alternate angles and are congruent , then

x = 50

Answer:

2.3 cm

Step-by-step explanation:

[tex]\textsf{Area of a trapezium}=\dfrac{1}{2}(a+b)h \quad \textsf{(where a and b are the bases and h is the height)}[/tex]

Given:

Substituting the given values into the formula and solving for x:

[tex]\implies \dfrac{1}{2}(3.8 + 6.1)x=11.385[/tex]

[tex]\implies \dfrac{1}{2}(9.9)x=11.385[/tex]

[tex]\implies 9.9x=22.77[/tex]

[tex]\implies x=2.3[/tex]

Area of trapezoid 1/2(sum of parallel sides)(Height)

These are functions inside another function. The resulting composite function is given as (5x+9)^2 + 3

These are functions inside another function. Given the following functions

m(x) = x^2 +3

n(x) = 5x +9

We are to solve for the function m(n(x))

m(n(x)) = m(5x+9)

Substitute 5x +9 into m(x) to have:

m(n(x)) = (5x+9)^2 + 3

Hence the resulting composite function is given as (5x+9)^2 + 3

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The coordinates of vertex B' are (-1,3)

Reflection is a mathematical transformation in which a image of an object is formed by flipping it over a reflection line a distance equal to the distance of the object from the reflection line.

Analysis:

When an object is reflected along the y-axis, only the the x-coordinate changes , if reflected along the x-axis, only the y-coordinate changes.

So vertex B' is a reflected vertex along the y- axis since it is at x=2

The distance of the x-coordinate of vertex B from the mirror line is 5-2 = 3

so the x-coordinate of vertex B' is going 3 units away from the mirror line which is at -1.

So the coordinates of vertex B' are (-1,3)

In conclusion, the coordinates of vertex B' reflected over the line X= 2 are (-1,3)

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Answer:

16

Step-by-step explanation:

Distance formula = [tex](x_{1}-x_{2})+(y_{1}-y_{2})[/tex]

Depending on which point is A and Which point is B, the answer is one of the two.

However, there is no such thing as negative distance, so your answer is 16 points in a certain direction.

Using the Central Limit Theorem, the state that the sample mean would most likely be within $80 of $2,600 is given by:

c. Equally likely because σ = $800 for both states.

It states that the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, we have that for both states, [tex]\sigma = 800, n = 100[/tex], hence they have the same standard error, being equally as likely to be within $80 of $2,600, meaning that option C is correct.

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Box and whisker plot has shown in the picture which shows different measures of the data set.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have data:

45, 51, 53, 55, 55, 65, 75, 81, 84, 87, 93, 93, 95, 96, 100

Sample size: 15

A  = (c) The Lowest value (45)

B = (e)Lower quartile Median (55)

C = (b) Median (81)

D = (d) Upper quartile (93)

E = (a) The Highest value (100)

Thus,  box and whisker plot has shown in the picture which shows different measures of the data set.

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Answer:

Term-to-term rule: Adding one to the numerator and the denominator

10th term: 10/11

Step-by-step explanation:

Answer:

solution: (x,y)=(-2,8)

Step-by-step explanation:

1) 3x+3y=18

  2x+y=4

2) -x-y=-6

  2x+y=4

3) x=-2

4) 2x(-2)+y=4

5) y=8

6) (x,y)=(2,8)

and that is :D

Explanation:

This is something you could do by trial and error.

The visible numbers are 1,2,3,4,6 which multiply to 144.

Another approach is to notice that 5 is not a factor of 144, so it must be the hidden value not part of the items multiplied.

Every other number 1,2,3,4,6 is a factor of 144.

1*144 = 144

2*72 = 144

3*48 = 144

4*36 = 144

6*24 = 144

Answer:

sorry if this is wrong, I don't take algebra two and I won't have to, but maybe a polynomial with three turns

Answer:

7.4 seconds

Step-by-step explanation:

878 = 16 t^2    divide both sides of the equation by 16

54.875 = t^2    take positive sq rt

7.4 seconds

Answer:

16.06 lbs

Step-by-step explanation:

I believe, I did~ 0.73x22

Answer:

-2 and 1/4

Step-by-step explanation:

1/4 is equal to 0.25

2/5 is equal to 0.40

Because it is negative, 1/4 is considered greater.

Answer:

4.5 %

Step-by-step explanation:

Answer:

4.5%

Explanation:

1)  red = 3
2) green = 4
3) blue = 5

Total bumper cars: (3 + 4 + 5) = 12 cars

Michelle gets red car:

Remaining red cars: 3 - 1 = 2

Remaining total cars: 12 - 1 = 11

Garth get red car:

Probability they both get red cars:

The charge per unit of electricity is #415

The formula for E in terms of N is E = 375 + 40N

Variation is a mathematical term that establishes the relationship between quantities and variables in an equation.

Analysis:

E = K + CN

where K and C are constants

When E = 3655, N = 82 and when E = 2055, N = 42

3655 = K + 82C ---------------1

2055 = K + 42C----------------2

subtract equation 2 from 1

40C = 1600

C = 40

substitute C in equation 1

3655 = K + 82(40)

3655 = K + 3280

K = 3655 - 3280 = 375

charge per unit is N = 1

E = 375 + 40(1) = #415

Formula for E in terms of N is E = 375 + 40N

In conclusion, the charge per unit of electricity is 415 and the equation connecting E and N is E = 375 + 40N

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Answer:

Y = 23

Step-by-step explanation:

In the equation (y = -3x + 11) the X is the input value. When you replace this by -4 you will multiply -4*-3 which will give you 12 and then you will want to add 11 as that is your y intercept. Giving the value of your Y a 23, or the point would be (-4,23)

[tex]\\ \rm\Rrightarrow \dfrac{7513/100\times 5x^3}{3x^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{75.13(5)x^3}{3x^2}[/tex]

[tex]\\ \rm\Rrightarrow {125.22x}[/tex]

Answer:

x < 2

Step-by-step explanation:

the open circle above 2 on the number line indicates that x cannot equal 2

the arrow points left indicating values of x are less than 2 , that is

x < 2

This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:

y = x + 5.5

The possible values are

x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Answer: y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.

Answer:

Step-by-step explanation:

If m and n are both 1 then

Minimum value = 10^(1+1) * 3^(1-1) * 225

= 325.

If m and n have to be different, then m = 2 and n = 1

Minimum value = 10^3 * 3^1 * 15^2

= 675,000.

a) 280 points

b) 80 points

c) 240 points

d) 120 points

The majority of data is between 3.01 to 7.90, when data is represented in dot plot, then the distribution is normal distribution and data set has 5.94 median.

The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.

The data given in the table is-

3.01, 3.26, 3.26, 3.79, 4.26, 4.34, 5.17, 5.94, 5.94, 5.94, 5.94, 7.14, 7.54, 7.90, 8.03, 9.15, 10.25, 11.98, 12.84, 19.86

The majority of data is between 3.01 to 7.90. The percentage of these data values to total data is 70%.

When data is represented in dot plot, then the distribution is a normal distribution. The data set has the value of median and mode equal to 5.94.

Median=5.94

Mode=5.94

Thus, the majority of data is between 3.01 to 7.90, when data is represented in dot plot, then the distribution is normal distribution and data set has 5.94 median.

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Answer:

[tex]\boxed{\sf x = 8.67}[/tex]

Step-by-step explanation:

[tex]\sf 6(6 + x) = 4(4 + 18)[/tex]

Use the distributive property to multiply 6 by (6+x).

[tex]\sf 36+6x=4(4+18)[/tex]

Let's add 4 and 18 = 22.

[tex]\sf 36+6x=4 \times 22[/tex]

Multiply 4 and 22 = 88.

[tex]\sf 36+6x=88[/tex]

Subtract 36 from both sides.

[tex]\sf 6x=88 - 36[/tex]

[tex]\sf 6x=52[/tex]

Divide both sides by 6.

[tex]\sf x = 8.67[/tex]