Which of the following represents the zeros of f(x) = x3 − 4x2 − 5x + 20?

Answer:

[tex] C.676.01 \: {in}^{3} [/tex]

step-by-step explanation :

The volume of the composite solid = volume of the cuboid + volume of the rectangular pyramid

Volume of the cuboid

[tex] = L \times B \times H[/tex]

where

[tex]L = 9 \: inches \\ B = 9 \: inches \\ H = 5 \: inches[/tex]

By substitution,

[tex] \implies \: V = 5 \times 9 \times 9[/tex]

[tex]\implies \: V = 405 \: {in}^{3} [/tex]

Volume of rectangular pyramid

[tex] = \frac{1}{3} \times base \: area \times height[/tex]

[tex]\implies \: V = \frac{1}{3} \times \:( L \times B ) \times \: H[/tex]

[tex] L = 9 \: inches \\ B = 9 \: inches \\ s= 11 \: inches[/tex]

We use the Pythagoras Theorem, to obtain,

h²+4.5²=11²

h²=11²-4.5²

h=√100.75

h=10.03

By substitution,

[tex]\implies \: V = \frac{1}{3} \times \:( 9 \times 9 ) \times \:10.0374[/tex]

we simplify to obtain

[tex]\implies \: V =271.0098 \: {in}^{3} [/tex]

Hence the volume of the the composite solid

[tex]=676.01\: {in}^{3} [/tex]

Answer:

The correct answer is option C.  676.01 in^3

Step-by-step explanation:

It is given a composite solid.

Total volume = volume of cuboid + volume of pyramid

To find the volume of cuboid

Volume of cuboid = Base area * height

Base area = side * side = 9 * 9

Volume = 9 * 9 * 5 = 405 in^3

To find the volume of pyramid

Before that we have to find the height of pyramid

Height² = Hypotenuse² - base² = 11² - 4.5² = 100.75

Height = √100.75 = 10.03

Volume of pyramid = 1/3(base area * height)

  = 1/3(9 * 9 * 10.03) = 271.01 in^3

To find the volume of solid

Volume of solid =  volume of cuboid + volume of pyramid

 = 405 + 271.01 = 676.01 in^3

Therefore the correct answer is option C.   676.01 in^3

Answer:

Option A. (4,4)

Step-by-step explanation:

step 1

Find the slope of the line k

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

[tex]m1*m2=-1[/tex]

The slope of the given line is [tex]m1=3[/tex]

so

The slope of the line k is

[tex]m2*(3)=-1[/tex]

[tex]m2=-\frac{1}{3}[/tex]

step 2

Find the equation of the line k

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{1}{3}[/tex]

[tex]point(1,5)[/tex]

substitute the values

[tex]y-5=-\frac{1}{3}(x-1)[/tex]

step 3

Verify if the line k pass through the given points

Remember that

If the line passes through a point, then the value of x and the value of y of the point must satisfy the equation of the line

Verify each case

case A) (4,4)

[tex]4-5=-\frac{1}{3}(4-1)[/tex]

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

[tex]-1=-1[/tex] ----> is true

therefore

The line k pass through the point (4,4)

case B) (-2,-5)

[tex]-5-5=-\frac{1}{3}(-2-1)[/tex]

[tex]-10=-1[/tex] -----> is not true

therefore

The line k not pass through the point (-2,-5)

case C) (3,6)

[tex]6-5=-\frac{1}{3}(3-1)[/tex]

[tex]1=-\frac{2}{3}[/tex] -----> is not true

therefore

The line k not pass through the point (3,6)

case D) (9,-1)

[tex]-1-5=-\frac{1}{3}(9-1)[/tex]

[tex]-6=-\frac{8}{3}[/tex] -----> is not true

therefore

The line k not pass through the point (9,-1)

Answer:

If you mean: y =(lnx)

3  

then:  

dy  

/dx = [3(lnx)

Step-by-step explanation:

The value of the function f(3) when, given that differencial function f'(x) = 6lnx and f(2) = -3.682, is 1.7748.

Integration is the operation which is used to find the original function from its darivative form.

The differencial function is given that

[tex]f'(x) = 6\ln x[/tex]

Integrate this function, with respect to the x,

[tex]f(x) =\int { 6\ln x} \, dx\\f(x) =6(\int { \ln x} )\, dx\\f(x) =6(x\ln x-\int { 1} \, dx)+C\\f(x) =6(x\ln x-x)+C\\f(x)=6x(\ln x-1)+C[/tex]

The value of function at 2 is,

[tex]f(2) = -3.682[/tex]

Put this value in the above equation as,

[tex]f(2)=6(2)(\ln (2)-1)+C\\-3.682=12(0.6931-1)+C\\-3.682=-3.682+C\\0=C[/tex]

Hence the value of constat is 0. Thus, the  value of function at 3 is,

[tex]f(3)=6(3)(\ln (3)-1)+0\\f(3)=18(1.0986-1)\\f(3)=1.7748[/tex]

Hence, the value of the function f(3) when, given that differencial function f'(x) = 6lnx and f(2) = -3.682, is 1.7748.

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See attached pic

x = -10 is your answer

Answer:

8 books; 4 from each shelf

Step-by-step explanation:

let x represent equal number of books from each shelf

from shelf A = 40 -x

from shelf B = 16 -x

shelf A has 3 times as many books than shelf B

3(16- x) = 40 -x

48 -3x = 40 -x

48 - 40 = -x + 3x

8 = 2x

x = 4

altogether she borrowed 4 + 4 = 8 books

Answer:

5 students out of each of the 4 homeroom classes (C)

Step-by-step explanation:

Answer:

c 5 students out of each of the 4 homeroom classes

i got it right on edge

Answer:

Circumference of given circle = 10π in

Step-by-step explanation:

Points to remember

Circumference of a circle = 2πr

Where r is the radius of circle

To find the circumference of circle

It is given that diameter of circle d = 10 in

Radius r = d/2 = 10/2 = 5 in

Circumference = 2πr = 2 * π * 5 = 10π in

Therefore the correct answer is circumference = 10π in

Answer:

C.-19

Step-by-step explanation:

add -2 to each interval

6 to 7 =-11-2=-13

7 to 8 =-13-2=-15

8 to 9=-15-2=-17

9 to 10=-17-2=-19

-3+8+9+-7+13 divided by 5 which is 4

The integer represents her average score for 5 rounds will be 4.

Arithmetic mean is the best central measure available for representing the values of a data set.  It is also called average of the values of the considered data set. It serves as one representation of the values of the data set. If for a data set, only its average is given, then we can't say much about the values of the data set. Average provides ill information in case of skewed data.

WE have given that 5 rounds of a game, jill scored -3, 8, 9, -7, and 13.

Then total number of score = - 3+8+9+-7+13

= 20

The total number of round in game = 5

Therefore,

Average =  the total number of score/ number of rounds

Average = - 3+8+9+-7+13 / 5

Average = 20/5

Average = 4

Hence, the integer represents her average score for 5 rounds will be 4.

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Answer:

[tex]2(8x+3y)^2)[/tex]

Step-by-step explanation:

The given expression is [tex]128x^2+96xy+18y^2[/tex].

We factor the GCF to get:

[tex]2(64x^2+48xy+9y^2)[/tex]

This can be rewritten as:

[tex]2[(8x)^2+2(3\times8)xy+(3y)^2][/tex]

We can observe that the quadratic trinomial is a perfect square)

[tex]2(8x+3y)^2)[/tex]

Therefore the completely factored form of the given trinomial is [tex]2(8x+3y)^2)[/tex]

Answer:

the equation is 0 = -3x - 5 + x^2

Answer:  The correct option is

(A) [tex]0=-3x-5+x^2.[/tex]

Step-by-step explanation:  We are given to select the correct quadratic equation that has an a-value of 1, b-value of -3 and c-value of -5.

We know that

a general quadratic equation is of the following form :

[tex]ax^2+bx+c=0,~~a\neq0,[/tex]

where a is the coefficient of x²,

b is the coefficient of x

and

c is the constant term.

For the given equation, we get

the coefficient of x², a = 1,

the coefficient of x, b = -3

and

the constant term, c = -5.

Therefore, the required equation is

[tex]1\times x^2+(-3)\times x+(-5)=0\\\\\Rightarrow 0=-3x-5+x^2.[/tex]

Thus, (A) is the correct option.

[tex]\bf \begin{array}{ccll} books&price\\ \cline{1-2} 8&y\\ 3&x \end{array}\implies \cfrac{8}{3}=\cfrac{y}{x}\implies 8x=3y\implies x=\cfrac{3}{8}y[/tex]

Final answer:

To determine the price of 3 books when given the cost of 8 similar books, you divide the total cost by 8 to find the price per book, then multiply this price by 3.

Explanation:

The student asked: At a bookstore, 8 similar books cost y dollars. What is the price of 3 such books? To find the price of one book, we divide the total cost y by the number of books, which is 8. Let's call the price of one book x. So, x = y/8.

To find the price of 3 books, we multiply the price of one book by 3. Hence, the price of 3 books would be x times 3 or (y/8) times 3, which can be simplified to 3y/8.

Thus, the price of 3 such books is 3y/8 dollars.

From log BNE to BEN

X=2

if you want explaination then ask me

Answer:

4/9

Step-by-step explanation:

since they are independent

p(ab)=p(a/b)=p(a)*p(b)

1/5=p(a)*9/20

p(a)=[tex]\frac{\frac{1}{5} }{\frac{9}{20} }  = 4/9[/tex]

Given that two events are independent, the probability of one event given the other is the same as the probability of the event itself. Therefore, the probability of event A is 1/5.

In probability, the concept of independence plays a crucial role. If two events, A and B, are independent, then the probability of event A occurring, given that event B has already occurred, is the same as the probability of event A.

In your case, P(A|B) = P(A). So, P(A) = P(A|B) = 1/5.

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Answer:

0

Step-by-step explanation:

Plug in -5 for x.

You get [tex]\frac{4}{5}(-5)+4[/tex]

the 5s cancel and you are left with

[tex]-4+4[/tex]

which is equal to 0.

Answer:

4.75

Explanation:

Make a right triangle

It goes right 22 and down 16.5

Those are the two sides

22^2+16.5^2=h^2

484+272.25=h^2

h=27.5

If it were half, it would go right 11, down 8.25

With hypotenuse being=13.75

Being at (7,4.75)

Hope you get it!

$14 is about 10% of $70

14 percent of 70 is about 10%

I think the last one. Sorry if I’m wrong. Minus year 2 and 5

Answer:

Option. A is the correct option.

Step-by-step explanation:

The yearly attendance at a ballpark is shown in the table attached.

We have to describe the average rate of change in attendance from year 2 to year 5.

Since rate of change in the attendance will be described by [tex]\frac{\text{Difference in attendance}}{\text{Difference in years}}[/tex]

Therefore, average change in attendance = [tex]\frac{\text{Attendance in year 5 - attendance in year 2}}{\text{5-2}}[/tex]

= [tex]\frac{333.7-298.3}{5-2}=\frac{35.40}{3}[/tex]

= 11.80 thousands per year

≈ 11800 people per year

Therefore, there is an average rate of change of 11800 people per year from year 2 to year 5.

Option A. is the answer.

Answer:B) (8x5)xb

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the questions are about which numbers are positive or negative and which have the largest magnitude, it is convenient to arrange them in order from least to greatest:

  -3.00 (E), -2.25 (A), -1.50 (C), 1.00 (B), 3.25 (D)

Nearsighted patients are those with negative prescriptions: E, A, C.

Farsighted patients are those with positive prescriptions: B, D.

The most nearsighted patient has the most negative prescription: E

The most farsighted patient has the most positive prescription: D

Answer:

Step-by-step explanation:

38=2(5)+2(x ) find X  

2x5-10

38-10=28

28/2=14  

14/2=7

x =7

so you length is 7

The dimensions of the rectangle are length = 12 cm and width = 7 cm by solving equations of given the width of a rectangle is 5 cm less than the length and the perimeter is 38 cm.

Let's represent the length of the rectangle as "L" and the width as "W".

According to the given information:

The width is 5 cm less than the length, so we can write W = L - 5.

The perimeter of a rectangle is given by the formula P = 2(L + W),

where P is the perimeter, L is the length, and W is the width.

In this case, the perimeter is 38 cm, so we have

38 = 2(L + W).

Now we can use these equations to find the dimensions of the rectangle.

Substitute the value of W from the first equation into the second equation:

38 = 2(L + (L - 5))

Simplify the equation:

38 = 2(2L - 5)

38 = 4L - 10

Add 10 to both sides:

48 = 4L

Divide both sides by 4:

L = 12

Now we can substitute the value of L into the first equation to find the width:

W = L - 5

W = 12 - 5

W = 7

Therefore, the dimensions of the rectangle are length = 12 cm and width = 7 cm by solving equations of given the width of a rectangle is 5 cm less than the length and the perimeter is 38 cm.

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Answer:

Step-by-step explanation:

Put x = -15 to the equation y = 2x - 3:

y = 2(-15) - 3 = -30 - 3 = -33

Answer:

y = 27

Step-by-step explanation:

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

[tex]y=2(15)-3[/tex]

[tex]y=30-3[/tex]

[tex]y=27[/tex]

BC=1/2 AC must be true because B is a mid point so BC=AB=1/2AC

Given that B is the midpoint of AC

AC= AB + BC

Since AB = BC

AC = 2 [tex]\times[/tex] BC

so BC = [tex]\frac{1}{2} \times[/tex]AC

If the Length of BC = Length of BD then they are said to be congruent.

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[tex]\overline{7-18i} = 7+18i[/tex]

Answer:

See below.

Step-by-step explanation:

The graph of ƒ(x) = x² is the red parabola in Figure 1.

Step 1. Vertex of g(x)

g(x) = (x – 1)² + 2

The graph of g(x) will be a parabola like that of ƒ(x) translated one unit to the right and two units up.

The vertex of ƒ(x) is at (0, 0), so the vertex of g(x) is at (1, 2). See Figure 1.

Step 2. Calculate two more points

(a) Try x = 0

g(0) = (0 – 1)² + 2 = 1² + 2 = 1 + 2 = 3

So, there is a point at (0, 3).

(b) Try x = 2

The axis of symmetry is a vertical line passing through the vertex at x = 1. We have calculated a point one unit left of the axis (at x = 0), so let's calculate a point one unit to the right, at x = 2.

g(2) = (2 – 1)² + 2 = 1² + 2 = 1 + 2 = 3

So, there are points at (2, 3) and (1,3). See Figure 2.

Step 3. Sketch the graph of g(x)

Draw a smooth curve through the three points. Extend the arms of the parabola vertically so the graph has the same shape as that of ƒ(x).

Your graph should look like the blue parabola in Figure 3.

Answer:

they are correct, here's proof

Answer:

true

Step-by-step explanation:

took the test

The number of hours in a day is correctly measured in the tens, as a day comprises of 24 hours. This measurement is a human invention rather than a natural observation. Hence true.

The question you've asked is whether the number of hours in a day is measured in the tens. The answer is True. There are 24 hours in a complete day. This measure is not something that naturally exists but rather is a human invention for the purpose of timekeeping. The Babylonians are credited with dividing a circle into 360 degrees, and they chose 24 as it divides neatly into 360, which allows for hours of a reasonable length that can be measured throughout the day. Notably, all days do not have exactly 12 hours of day and 12 hours of night except at the equator, and this occurs every day of the year. Other locations may experience nearly equal amounts of day and night during the equinoxes.

When we say that the number of hours in a day is more than seven hours, we are observing a fact about the number of hours in a day, which is significantly more than seven hours since a full day consists of 24 hours.

Answer:

Right.

Step-by-step explanation:

It is not smaller or larger than a 90% angle, it is exactly at a 90% angle. Therefore, it is a right triangle.

The triangle above is known as a Right Triangle or as the question says it is a Right.

REASON: It is a Right Triangle because it has a Right angle & Right angles always are 90 degrees.

I HOPE U GOT THE ANSWER!....

Answer: the answer is negative 52          (-52 goes in the box)

Answer is -16

Step-by-step explanation:

A. 3x+21

B. 25-5x

C.8x-16

D.x^2+6x+24

a. 3x + 21

b. 25 - 5x

c. 8x - 16

d. x^2 +6x + 8

Answer:

[tex]new\ lenght=24cm\\new\ width=16cm[/tex]

This will scale the drawing up to larger dimensions.

Step-by-step explanation:

You can observe in the figure that the rectangular drawing has these dimensions:

[tex]length=6cm\\width=4cm[/tex]

The new drawing will be obtained by multplying the dimensions of the original drawing by the scale factor 4.

Therefore, the new dimensions will be:

[tex]new\ lenght=(6cm)(4)=24cm\\new\ width=(4cm)(4)=16cm[/tex]

You can observe that this will scale the drawing up to larger dimensions.