What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5)=g(8)=−9. (Do not include "c=" in your answer.)

Answer:

96 in²

36 in²

60 in²

6.51 in

Step-by-step explanation:

Given that :

Dimension of paper = 12 in by 8 in

Dimension of right triangles :

2 in by 9 in ; 3 in by 6 in

Area of sheet of paper = 12 in * 8 in = 96 in²

Area of triangle = 1/2 base * height

Therefore, area of remnant right triangle :

2 * 1/2 * 2 * 9 = 18 in²

2 * 1/2 * 3 * 6 = 18 in²

Combined area of triangle left = 18in + 18in = 36 in²

Area of parallelogram = Area of sheet - Area of triangles left

Area of parallelogram = 96in² - 36in² = 60 in²

Base, b of parallelogram = 9.22 in

Area of parallelogram = base * altitude,h

60in² = 9.22h

h = 60 / 9.22 = 6.51 in

Answer:

151,031

Step-by-step explanation:

If the population of a town is decreasing at 0.8% each year, the new population of the town will be [tex]100\%-0.8\%=99.2\%[/tex] of what it was last year. To find 99.2% of something, multiply it by 0.992. Therefore, we can write the following equation:

[tex]f(x)=157,220\cdot 0.992^x[/tex], where [tex]f(x)[/tex] is the population of the town [tex]x[/tex] years after the town had a population of 157,220.

Substitute [tex]x=5[/tex] into this equation to get the projected population after 5 years:

[tex]f(5)=157,220\cdot 0.992^5, \\f(5)=151031.019048,\\f(5)\approx \boxed{151,031}[/tex]

Therefore, in 5 years, the population should be 151,031.

Answer:

hi?

Step-by-step explanation:

Answer:

See explanation

Question has been corrected

Step-by-step explanation:

Given:

3x² + 11x + 30

To factorise, multiply the coefficient of x² by 30

= 3 * 30

= 90

Find two numbers that have a product of 90 and a sum of 11

** There are no such two numbers, therefore the question can't be solved using factorization

Correcting the error in the question:

x² + 11x + 30

To factorise, multiply the coefficient of x² by 30

= 1 * 30

= 30

Find two numbers that have a product of 30 and a sum of 11

6 and 5

6 + 5 = 11

6 * 5 = 30

x² + 11x + 30

= x² + 6x + 5x + 30

= x(x + 6) + 5(x + 6)

= (x + 6) (x + 5)

Answer:

51

Step-by-step explanation:

1. Approach

One is given the polygon, (ABCDE); the problem asks one to find the area of this polygon. The most logical step to take is to divide this polygon into easier parts, find the area of each part, and then add up the area to find the total area of the figure.

One way to divide this figure up is to draw the line (AC). This will create the triangle (ABC) and rectangle (ACDE).

2. Find the area of (ABC)

The formula to find the area of a triangle is the following:

[tex]A=\frac{b*h}{2}[/tex]

Where (b) is the base of the triangle, and (h) is the height. The base of the triangle (ABC) is (AC), which has a measure of (6) units. The height of the triangle is the distance from the base of the triangle to the vertex opposite the base. This measurement is (3) units. Substitute these values into the formula and solve for the area:

[tex]A=\frac{b*h}{2}[/tex]

Substitute,

[tex]A=\frac{6*3}{2}\\\\A=\frac{18}{2}\\\\A=9[/tex]

3. Find the area of (ACDE)

The formula to find the area of a rectangle is as follows:

[tex]A=b*h[/tex]

The base of the rectangle is the segment (AE), with a measure of (7) units. The height of the rectangle is the segment (AC) with a measurement of (6) units. Substitute these values into the formula and solve for the area:

[tex]A=7*6\\\\A=42[/tex]

4. Find the area of the total figure

To find the area of the total figure, add up the area of the triangle, and the area of the rectangle:

[tex]9+42= 51[/tex]

Answer:

80/3

Step-by-step explanation:

try mathw4y it helps alot.

Answer:

x = 80/3

Step-by-step explanation:

(4x+38) + (2x-18)=180

Combine like terms

6x +20 = 180

Subtract 20 from each side

6x+20 -20 = 180-20

6x = 160

Divide by 6

6x/6 = 160/6

x = 80/3

Answer:

f the mean of this set is equal to 20, we can write down the below equation,

20 = (x1 + x2 +x3 + .... + x10)/10

x1 + x2 + x3 + ... x10 = 200

Then we can also write an equation for the mean of the given numbers as below,

Mean  = [(x1+4) + (x2+8) + (x3+12) + .... + (x10+40)]/10

          = (x1 + x2 + x3 + ... + x10 + 4 + 8 + 12 + ... + 40)/10

Then we can use above equation (1) to replace x1 + x2 + x3 + ... + x10 by 200

Mean = (200 + 4 + 8 +12 + 16 + 20 + 24 + 28 + 32 + 36 + 40)/10

        = 420/10

        = 42

If you remember Arithmetic Progressions you can simply add together the above number set.

If you closely look above, you can find that there is an Arithmetic Progression : 4, 8, 12, ... , 40

Here we want the addition of 10 terms. So we can use,

Sn = n/2(a+l)

S10 = 10/2(4+40)

      = 220

Then you can easily get the answer,

Mean = (200 + 220)/10

         = 42

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

See this attachment

Answer:

D. A straight line segment can be drawn between any two points.

Step-by-step explanation:

Euclid of Alexandria was famously known and regarded as the founder of geometry, as well as the father of geometry. He was born in the Mid-fourth century, BC and he specialized in the field of Mathematics. Some of his popular works in the field of Mathematics were Euclid's Elements, Euclidean algorithm and Euclidean geometry.

One of the basic postulate of Euclidean geometry is that a straight line segment can be drawn between any two points.

Others include;

I. All right angles are congruent.

II. All straight line segment is indefinitely extendable in a straight line.

Answer:

AD=27

Step-by-step explanation:

Answer:    It's "reflexive" because the equation is equal on both sides

Step-by-step explanation:         The reason it isn't symmetric property, is because the variables are mismatched (it's not the same on both sides.)

Hope this helped!!

Answer:

Step-by-step explanation:

{ 2/3 x+y=6

+

{ -2/3x-y=2

= 0=6

Hence,no solution.

Answer:

19 + 1 + 9 + 1

put any of those in the slots

Answer:

19 + 1 + 9 + 1

peace

Answer:

hjjjnnnhjjjjj

Step-by-step explanation:

answer is d

Answer:

Caroline has to pay $8600 taxes

Jennifer has to pay $10320 taxes

Step-by-step explanation:

I guess the question is who has to pay how much taxes, right ?

Caroline earns $49000, and I guess, she belongs to a health fund.

she has to pay $5000 for the first $40000.

and for the remaining $9000 she has to pay $0.40 per dollar.

that means 9000×0.4 = $3600

and no penalties for no health fund.

so altogether $5000 + $3600 = $8600 taxes

Jennifer earns $51000 and did not belong to a health fund.

she has to pay $9000 for the first $50000.

and for the remaining $1000 she had to pay $0.30 part dollar.

that means 1000×0.3 = $300

and 2% of the total income because no health fund

51000×0.02 = $1020

so, altogether $9000+$300+$1020 = $10320 taxes

Answer:

Solution given:

Relationship between base and hypotenuse is given by Cos angle

Cos Angle(?)=base/hypotenuse

Angle{?}=Cos-¹(40/58)

Angle{?}=46°

The indicated angle is 46°

Answer:

Independence and Exclusiveness are two topics which are important to probability and often confused. Discuss the difference between two events being independent and two events being mutually exclusive. Use examples to demonstrate the difference. Remember to explain as if you are talking to someone who knows nothing about the topic.

[my response: talk to them in formal language about the topic.]

Step-by-step explanation:

Answer:

The answer is correct

Step-by-step explanation:

3(x + 4) + 2 = 2 + 5(x – 4)

3x + 12 + 2 = 2 + 5x - 20

3x + 14 = 5x - 18

-2x = -32

x = 16

Answer:

e

Step-by-step explanation:

the graph should look something like this

Recall that 2⁴ = 16. So you have

2⁶⁰ = 2⁴ˣ¹⁵ = (2⁴)¹⁵ = 16¹⁵

Answer:

A. x = 11√3

B. y = 11

Step-by-step explanation:

A. Determination of the value of x.

Angle θ = 60°

Hypothenus = 22

Opposite = x =?

We can obtain the value of x by using sine ratio as illustrated below:

Sine θ = Opposite / Hypothenus

Sine 60 = x / 22

√3/2 = x / 22

Cross multiply

2 * x = 22√3

Divide both side by 2

x = (22√3) / 2

x = 11√3

B. Determination of the value of y.

Angle θ = 60°

Hypothenus = 22

Adjacent = y =?

We can obtain the value of y by using cosine ratio as illustrated below:

Cos θ = Adjacent / Hypothenus

Cos 60 = y / 22

½ = y / 22

Cross multiply

y = ½ × 22

y = 11

Answer:

7/10

Step-by-step explanation:

½ of a cup of cheddar=½ x 1=½

⅕ of a cup of parmesan=⅕ x 1=⅕

all cheese used=½ + ⅕= 7/10

Answer:

Step-by-step explanation:

With some research I found that the medians (QK, RJ, and SI) are broken into 2:1 ratios.

So what this means is that QD is twice as long as DK.

QD = 2DK

QD = 2 * 6.5

QD = 13

Answer:

Following are solutions to the given question:

Step-by-step explanation:

First-test probability: [tex]\frac{3}{4}[/tex]

A person's chances of passing a second test are reduced if he fails the first test: [tex]\frac{1}{3}[/tex]

However, the chance of failing the first test is 1 in 4. As just a result, the probability of these events is low.

[tex]\to \frac{1}{4}\times \frac{1}{3}=\frac{1}{12}\\\\\to \frac{3}{4} + \frac{1}{12} = \frac{9+1}{12} = \frac{10}{12} = \frac{5}{6}[/tex]

One of the other.

Answer:

64 = 2(3x + x)

Step-by-step explanation:

Perimeter of the rectangle = 64 cm

Width of the rectangle = x

Length of the rectangle = 3x

Perimeter of a rectangle = 2(length + width)

The equation is

64 = 2(3x + x)

64 = 6x + 2x

64 = 8x

x = 64/8

x = 8 cm

Width of the rectangle = x = 8 cm

Length of the rectangle = 3x

= 3(8 cm)

= 24 cm

Answer:

m∠ADC = 90°

5x-5 = 90

x = 19

Step-by-step explanation: