A rectangular box has length x and width 3. The volume of the box is given by y = 3x(8 – x). The greatest x-intercept of the graph of this polynomial equals which of the following? Choose all that apply.

Answer:

[tex]{\huge \boxed{x=-2}[/tex]

Step-by-step explanation:

First you do is add and subtracting numbers from left to right.

-5+6=1

-9x+1=19

Then subtract by 1 from both sides of equation.

-9x+1-1=19-1

Simplify.

-9x=18

Divide by -9 from both sides of equation.

-9x/-9=18/-9

Simplify, to find the answer.

18÷-9=-2

x=-2 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

x=-2

Step-by-step explanation:

-9x -5+6=19

Combine like terms

-9x +1 = 19

Subtract 1 from each side

-9x +1-1 = 19-1

-9x = 18

Divide by -9

-9x/-9 = 18/-9

x = -2

Answer:

x^2=5-x

x^2+x-5=0

x=-1± √(1)^2-4(1)(-5)   /2(1)

-1± √21   /2

Step-by-step explanation:

Answer:

The answer will be A.  -1± √21   /2

Step-by-step explanation:

I hope it helps

ANSWER

The system consists of parallel lines. Both lines have the same slope.

EXPLANATION.

The first equation is

[tex]y = \frac{1}{3} x - 4[/tex]

This equation is in the slope-intercept form.

The second equation is

[tex]3y - x = - 7[/tex]

We write this one too in slope-intercept form so that we can make comparison.

[tex] \implies \: y = \frac{1}{3} x - \frac{7}{3} [/tex]

We can see that both equations have slope

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

This means the two lines are parallel.

The two lines have different y-intercepts.

Two parallel lines with different y-intercepts will never meet.

The lines will never intersect.

Answer:

The true statements are:

- The system consists of parallel lines

- Both lines have the same slope

Step-by-step explanation:

* Lets talk about the solution of the linear equations

- There are three types of the solutions of the system of linear equations

# If the two lines intersect each other, then there is one solution

- The equations are ax+ by = c , dx + ey = f

# If the two lines parallel to each other, then there is no solution

- The equations are ax+ by = c , ax + by = d in its simplest form ,

  where a is the coefficient of x , b is the coefficient of y and

  c , d are the numerical terms

# If the two lines coincide (over each other), then there are infinite

   solutions

- The equations are ax+ by = c , ax + by = c in its simplest form, where

  a is the coefficient of x , b is the coefficient of y and c is the

  numerical term

* Lets solve the problem

∵ The system of equation is:

   y = 1/3 x - 4 ⇒ (1)

   3y - x = -7 ⇒ (2)

- Lets put equation (1) in the form of equation (2)

∵ y = 1/3 x - 4 ⇒ multiply both sides by 3

∴ 3y = x - 12 ⇒ subtract x from both sides

∴ 3y - x = -12

∴ Equation (1) is 3y - x = -12

∵ Equation (2) is 3y - x = -7

∵ The coefficients of x and y in the two equation are equal

∵ The numerical terms in the two equations are not equal

∴ The equations have no solution because their lines are parallel

∵ The parallel lines have same slope

* The true statements are

- The system consists of parallel lines

- Both lines have the same slope

Answer:

25 gallons.

Step-by-step explanation:

The container that holds the water for the football team is 1/2 full.

After pouring out 5 gallons of water, it is 3/10 full.

The proportion that was poured out is [tex]\frac{1}{2}[/tex] - [tex]\frac{3}{10}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]

[tex]\frac{1}{5}[/tex] of the water in the container is equal to 5 gallons

The container therefore holds: 1 × 5 ÷ [tex]\frac{1}{5}[/tex] = 5 × 5 = 25 gallons.

Final answer:

The total capacity of the container is calculated to be 25 gallons, found by using the information that 1/2 to 3/10 of the capacity equals a 5 gallon difference.

Explanation:

We have been given that the container is initially 1/2 full and becomes 3/10 full after pouring out 5 gallons of water.

To find out the total capacity of the container, we can set up a proportion where the difference between the two fractions (1/2 and 3/10) represents the 5 gallons removed.

First, we find a common denominator for the two fractions, which is 10. Now we can say:

The difference between 5/10 and 3/10 is 2/10, which equates to the 5 gallons poured out. Thus, 2/10 of the container's capacity is 5 gallons, and we can find the full capacity (10/10) by multiplying the 5 gallons by 5 (since 2 × 5=10).

So, the container's total capacity is 5 gallons × 5 = 25 gallons.

Answer:

6.06 x [tex]10^{9}[/tex]

Step-by-step explanation:

(5.25 x [tex]10^{5}[/tex] ) / (8.7 x [tex]10^{-5}[/tex] )

= (5.25 x [tex]10^{5}[/tex] ) x( [tex]10^{5}[/tex] )/ (8.7 )

= (5.25 x [tex]10^{5 + 5}[/tex] )/ (8.7 )

= 0.606 x [tex]10^{10}[/tex]

= 6.06 x [tex]10^{9}[/tex]

Answer:

$480+$48=$528

Step-by-step explanation:

his friend paid him $480 and 10% so,

=10/100*480

=1/10*480

=480/10

=$48

so,his friend paid him $480+$48=$528.

Answer:

The correct answer option is C. (0, c).

Step-by-step explanation:

We are given an isosceles trapezoid with the coordinates of three of its vertices and we are to find the coordinates of Z.

Z is a point on the middle of one of the sides of the trapezoid.

Since Z lies on the horizontal x axis, therefore its x coordinate is 0 while the y coordinate can be seen from the vertex exactly at its right which is c.

Z (0, c)

==============================================

Explanation:

Note how the point (a,0) mirrors over the y axis to land on (-a,0)

A similar action will happen as we go from te point (b,c) to point W (-b, c), due to this figure being isosoceles.

The x coordinate changes from positive to negative. The y coordinate stays the same.

The point Z is the midpoint of the upper segment which spans from (-b,c) to (b,c)

Apply the midpoint formula to find where Z is located.

Add up the x coordinates and divide by 2: x = (-b+b)/2 = 0/2 = 0

Add up the y coordinates and divide by 2: y = (c+c)/2 = 2c/2 = c

So the midpoint is located at (x,y) = (0, c) which is where point Z is located as well.

Side note: it might help to replace the letters a, b and c with actual values, just so the problem is more concrete.

Answer:

See attachment

Step-by-step explanation:

When the graph of the given function is flipped over the line [tex]y=x[/tex], the coordinates will swap.

The mapping for a reflection in the line [tex]y=x[/tex] is [tex](x,y)\to(y,x)[/tex].

We can observe that one portion of the graph is in the first quadrant [tex](x,y)[/tex]. When we flip this part we will get [tex](y,x)[/tex], which is still in the first quadrant.

Also, when we flip the portion of the graph in the second quadrant (-x,y), we will obtain (y,-x), which is standing for all coordinates in the fourth quadrant.

The image is shown in the attachment.

Answer:C 13/2

Step-by-step explanation: you do 13 x 0.5 equals 6.5, convert to a fratcion equals 13/2

Answer:

[tex]\frac{13}{2}[/tex]

Step-by-step explanation:

When you have a whole number, you gotta add a denominator, so just add 1 underneath:

[tex]\frac{13}{1}[/tex]

Then you have

[tex]\frac{13}{1}[/tex] ×[tex]\frac{1}{2}[/tex]

Multiply straight across and you get

[tex]\frac{13}{2}[/tex]

Answer:

about A+=+2000%281%2B+0.023%2F1%29%5E%281%2A18%29+=+2000%2A1.023%5E18= $3,011.56 thats my math

Step-by-step explanation:

Answer:

$3,698.50

Step-by-step explanation:

When making a compound interest rate this means that the interests generated are taken into consideration when creating new interests in the next period, now there are 4 quarterly periods on a year, this means there are 88 periods in the 22 years that the account will grow, you just have to do the math:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where n is the number of cycles per year and nt is the number of cycles over the years.

We just have to put the values into the formula:

[tex]A=500(1+\frac{.092}{4})^{22*4}[/tex]

[tex]A=500(1+\frac{.092}{4})^{88}[/tex]

[tex]A=$3,698.50[/tex]

Answer:

C

Step-by-step explanation:

tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{24}{10}[/tex] = [tex]\frac{12}{5}[/tex]

Answer:

14, 28, 42, 56, 70, 84, (etc.)

Step-by-step explanation:

14, 28, 42, 56, 70, 84, (etc.) are all multiples of 7. They're also even and have 2 digits.

Answer:     14  28  42  56  70  84

Step-by-step explanation: Hopes this helps

Answer:

if it was 102 when he woke

e up and lowered then it will be 99 degree fahrenheit then

Final answer:

Steve's temperature decreased by 3 degrees from the original 102 degrees F, which means his temperature two hours later was 99 degrees F.

Explanation:

The student's question involves a basic mathematical operation, specifically subtraction, used to determine a change in temperature over time. Steve originally has a temperature of 102 degrees Fahrenheit. After two hours, his temperature has decreased by 3 degrees.

To find the new temperature, we subtract the decrease from the original:
102 degrees F - 3 degrees F = 99 degrees F.

So, Steve's temperature two hours later would be 99 degrees Fahrenheit.

Answer:

umm his friends each got 1/8

Step-by-step explanation:

hernando ate 2/8 meaning 8-2=6= 6/8

6/8 / 6 = 1/8

:D

I guess this what you want

After Hernando ate  [tex]\frac{2}{8}[/tex] of the pizza, the remaining pizza when divided equally among his friend leaves each friend with  [tex]\frac{1}{8}[/tex] of the pizza

Given: Hernando ate [tex]\frac{2}{8}[/tex] of a pizza, number of friends is 6

First, let's find out what fraction of the pizza is left after Hernando ate his portion. Hernando ate  [tex]\frac{2}{8}[/tex], which reduces to [tex]\frac{1}{4}[/tex]. Therefore, the remaining fraction of the pizza is:

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

The remaining [tex]\frac{3}{4}[/tex] of the pizza is to be shared equally among his 6 friends. To find out how much pizza each friend gets, we divide the remaining fraction by the number of friends:

[tex]\frac{3}{4}[/tex] ÷ 6 [tex]=\frac{3}{4} \times \frac{1}{6} = \frac{1}{8}[/tex]

Each of Hernando's 6 friends gets [tex]\frac{1}{8}[/tex] of the pizza.

f(x) is the total number of hours overall that he has worked out.

x would be the number of weeks he works out.

You would multiply x ( number f weeks he works out) by 7 and then add that to the hours he already worked out (15) which will give you the total hours (f(x)).

Answer:

In this case, x represents "week", because they problem says that he exercises 7 hour per week, being week an unknown number because we don't how much time Luke is gonna keep exercising. Si, 7x represents the total amount of hours per week after the first 15 hours.

Similarly, f(x) represents the total amount of hour from the beginning, before the first 15 hours. The difference between x and f(x) is that the first one represents hours after the 15 hours, and the second one represents the total amount of hours, including before the 15 hours.

It's important to notice that 15 is not multiplied by a variable, it's because those 15 hours are already achieve, we don't if those where monthly or weekly, but the fact that they already happened means that they can't change, that's why the don't have a variable.

Answer:

The circumference is:

[tex]C = 43.98\ ft[/tex]

The area is:

[tex]A=153.94\ ft^2[/tex]

Step-by-step explanation:

The circumference of a circle is calculated using the following formula

[tex]C = \pi d[/tex]

Where C is the circumference and d is the diameter of the circle.

In this case we know that

[tex]d = 14\ ft[/tex]

Therefore the circumference is:

[tex]C = \pi *14[/tex]

[tex]C = 43.98\ ft[/tex]

The area of a circle is calculated using the following formula

[tex]A=\pi(\frac{d}{2})^2[/tex]

Where d is the diameter of the circle.

Then

[tex]A=\pi(\frac{14}{2})^2[/tex]

[tex]A=\pi(7)^2[/tex]

[tex]A=49\pi[/tex]

[tex]A=153.94\ ft^2[/tex]

The circumference of the flower bed is approximately 43.96 feet and the area is approximately 153.86 square feet.

The gardener's circular flower bed has a diameter of 14 feet. The formula to calculate the circumference of a circle is C=πd where 'd' represents the diameter. Therefore, by substituting the given diameter, we get C = 3.14 * 14 = 43.96 feet approximately.

The area of the circle can be calculated by using the formula A=πr², where 'r' represents the radius of the circle. The radius is half of the diameter, that is 14/2 = 7 feet. So, A = 3.14 * 7² = 153.86 square feet approximately.

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Answer:

S>6

Step-by-step explanation:

Let us suppose the distance walked by Hanna and swati is represented by H and S.

And total distance travelled is D

D=H+S

D>14

H+S>14

Given H=8

8+S>14

S>6

Hence swati walked more than 6 miles

Answer:

a + 2

Step-by-step explanation:

Given

[tex]\frac{a^2+3a+2}{a+1}[/tex] ← factor the numerator

= [tex]\frac{(a+1)(a+2)}{a+1}[/tex]

Cancel the factor (a + 1) on the numerator/denominator

= a + 2 ← quotient

1.

Cubic Polynomial--

A cubic polynomial is a polynomial of degree three.

2.

End behavior--

The end behavior of a function is it's behavior when x tends to infinity in both the directions i.e. when x tends to minus infinity and when x tends to plus infinity.

3.

Irreducible--

A polynomial is said to be irreducible if it can't be reduced i.e. it cannot be factored.

4.

Leading coefficient--

It is the coefficient of the highest degree term existing in the expression.

5.

Leading term--

It is the term with the highest degree.

6.

quartic polynomial-

A quadratic polynomial is a polynomial of degree 4.

7.

Zeros of polynomial--

The zeros of a polynomial are all the possible values of x at which the polynomial expression is equal to zero.

Answer:

y - 1/3 = 3/4(x - 4)

Step-by-step explanation:

We know that the general equation of a line is the following:

y - yo = m(x-xo), where 'm' represents the slope of the line, and (xo, yo) is any point that belongs to the line.

Then, the equation of the line that passes through (4, 1/3) and has a slope of 3/4 is: y - 1/3 = 3/4(x - 4)

For this case we have that by definition, the slope-intersection equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

They tell us as data that:

[tex]m = \frac {3} {4}[/tex]

Now the equation is:

[tex]y = \frac {3} {4} x + b[/tex]

We substitute the point to find "b":

[tex](4, \frac {1} {3})[/tex]

[tex]\frac {1} {3} = \frac {3} {4} (4) + b[/tex]

[tex]b = \frac {1} {3} -3\\b = - \frac {8} {3}[/tex]

Finally the equation is:

[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]

In point-slope form the equation is:

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

Answer:

[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]

Answer: The percent of students have scored between 60 and 65 points is 34.13%

Step-by-step explanation:

Given : The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points.

i.e. [tex]\mu=60\ \ \ \sigma=5[/tex]

Let x denotes the points obtained by students of a class in a test .

Now , the probability that the students have scored between 60 and 65 points :-

[tex]P(60<x<65)=P(\dfrac{60-60}{5}<\dfrac{x-\mu}{\sigma}<\dfrac{65-60}{5})\\\\= P(0<z<1)\ \ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\= P(z<1)-P(z<0.5)\ \ \ [\because\ P(z_1<Z<z_2)=P(Z<z_2)-P(Z<z_1)]\\\\=0.8413-0.5=0.3413[/tex]

[tex]=34.13\%[/tex]

Hence, the percent of students have scored between 60 and 65 points is 34.13%.

Answer:

The answer would be, both A. and B.

Answer:

both a and b

Step-by-step explanation:

Answer:

(-1, 0)

Step-by-step explanation:

Jim, please use the symbol " ^ " to indicate exponentiation:

y = x^3 + 3x^2 – x – 3.  Thanks.

A "turning point" is a point on the graph of a function at which the derivative changes sign (e. g., from positive to negative or vice versa).  To identify turning points, we differentiate the given function twice, set the second derivative equal to zero and identify the x-values at which the sign of the derivative changes.

Given y = x^3 + 3x^2 – x – 3,

          dy/dx = 3x^2 + 6x - 1

           d²y

          ------ = 6x + 6            and this is zero at x = -1.

           dx²

We can easily show that the 2nd derivative changes sign at x = -1.

Thus, the only turning point here is (-1, [-1]³ + 3[-1]² - [-1] - 3), or (-1, 0).

Answer: (-2,3) and (0,-3)

Step-by-step explanation:

The graph at option 4 represents the given equation y = -4x - 3 correctly. This is obtained by calculating the slope and finding the y-intercept.

The slope of a line given by

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

The ratio of the difference between y-coordinates of two points on the line to the difference of their x coordinates.

The equation is y = -4x - 3

On comparing the equation with the slope-intercept form y = mx + c,

m = -4 and y-intercept c = -3.

Since the y-intercept is -3, the graphs at options 1 and 2 do not represent this equation. So, the remaining graphs may represent the given equation.

The graph at option 3 has a line with two points (2, 5) and (0, -3)

So, the slope is

m = [tex]\frac{-3-5}{0-2}[/tex]

   = 4

Thus, it is not the same as the slope of the given equation.

The graph at option 4 has a line with two points (-2, 5) and (0, -3)

So, the slope is

m = [tex]\frac{-3-5}{0+2}[/tex]

   = -4

Thus, the line shown in the graph at option 4 has a slope of -4 and the y-intercept is -3. These are the same as the given equation. So, option 4 is correct.

Therefore, the graph at option 4 is the correct representation of the given equation.

Learn more about the graph of an equation in a slope-intercept form here:

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Answer:

The correct answer option is D. 5.

Step-by-step explanation:

We are given the following expression where 4 is to be divided by a fraction 1/5:

[tex] 4 [/tex] ÷ [tex]\frac{1}{5}[/tex]

This can also be written as:

[tex]\frac{4}{\frac{1}{5} }[/tex]

Now to find the quotient of this, we will take the reciprocal of the fraction in the denominator to change it into multiplication.

[tex]4 \times \frac{5}{1}[/tex]

Therefore, ignoring the 1 in denominator, we can simply multiply 4 by 5.

Answer:

Hi there!

The answer is last one: 5

Step-by-step explanation:

When ever you are dividing a number by a fraction you always flip the fraction and multiply it, another way of saying it is multiplying by its reciprocal.

Answer:

-4

Step-by-step explanation:

Technically, the negative sign is treated as multiplying by -1, which is then separate from the 2.  This equation can also be rewritten as [tex]-1 * 2^2[/tex], which would be simplified to [tex]-1 * 4[/tex] and then [tex]-4[/tex].

It depends on how the parenthesis is like. -(2)^2 will equal -4 while (-2)^2 equals 4. But the answer will most likely be 4 because they tend to make sure to put parenthesis if they want the answer to be -4. (Calculators are programmed differently which is why you're getting mixed answers.)

Answer:

a=1, b = -3, c=-2

Step-by-step explanation:

The quadratic equation is in the form

a[tex]x^{2}[/tex] + bx +c = 0

Using the given equation

1[tex]x^{2}[/tex] -3x -2 = 0

We can see that

a=1  b=-3  c=-2

Answer:

A

Explanation:

In image A the image becomes smaller but doesn't change shape which is what dilation is supposed to be.

Answer:

Option A

Step-by-step explanation:

The total amount that all three friends have is $84.

Let's assume that Ami, Jan, and Toy have x, y, and z dollars respectively. After the first redistribution, we know that:

x - a = 2(y + z)

y + a = 2(x + z)

z + a = 2(x + y)

where a is the amount of money that Ami gives to Jan and Toy.

Solving these equations, we get:

x = 5z - 4a

y = 5z - 6a

z = z

After the second redistribution, the new amounts are:

x + b = 2(y + c)

y - b + c = 2(x + c)

z + b + c = 2(x + y)

where b is the amount that Jan gives to Ami and Toy, and c is the amount that Toy gives to Ami and Jan.

Solving these equations, we get:

x = 14c

y = 11c

z = 6c

Finally, after the third redistribution, the new amounts are:

x + 2d = 2(y + 2d)

y + 2d = 2(x + 2d)

z - 2d + 2c = 2(x + y)

where d is the amount that Toy gives to Ami and Jan.

Solving these equations, we get:

x = 8d

y = 10d

z = 18d

Since we know that z = $36, we can solve for d and get d = $2. Therefore, the total amount that all three friends have is:

x + y + z = 8d + 10d + 36 = $84.

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