Rearrange the formula V = 1 3 πr2h for h. A) h = 3V πr2 B) h = V 3πr2 C) h = 3πr2 V D) h = πr2 3V

If α and β are the Roots of a Quadratic Equation ax² + bx + c then :

✿  Sum of the Roots : α + β [tex]\mathsf{= \frac{-b}{a}}[/tex]

✿  Product of the Roots : αβ [tex]\mathsf{= \frac{c}{a}}[/tex]

Let the Quadratic Equation we need to find be : ax² + bx + c = 0

Given : The Roots of a Quadratic Equation are 6 and 3

⇒ α = 6 and β = 3

Given : The Leading Coefficient of the Quadratic Equation is 4

Leading Coefficient is the Coefficient written beside the Variable with Highest Degree. In a Quadratic Equation, Highest Degree is 2

Leading Coefficient of our Quadratic Equation is (a)

⇒ a = 4

⇒ Sum of the Roots [tex]\mathsf{: (6 + 3) = \frac{-b}{4}}[/tex]

⇒ -b = 9(4)

⇒ b = -36

⇒ Product of the Roots [tex]\mathsf{: (6 \times 3) = \frac{c}{4}}[/tex]

⇒ c = 18 × 4

⇒ c = 72

⇒ The Quadratic Equation is 4x² - 36x + 72 = 0

Answer:

y= -2/3x(m) +400(b)

Step-by-step explanation:

1.2x + 3y = 1200

3y = -2x + 1200

y = (-2x/3)x + 1200/3  

the slope is -2/3x the y intercept is 400

2.I would plot the ordered pair (0, 400) on the coordinate plane. Then to find the other ordered pair you would use the slope (-2, 3). You should go two spaces to the right of (0, 400) and then three spaces down. After this your slope look like (-2, 397)

3.the function t(x) gives the number of tablets, given that x smart-phones have been sold/produced  

t(x) = (-2/3)x + 400  

Suppose in the next month, the total profit on smart phone cases and tablet cases is $1,500. The profit amounts are the same, $2 for smart phone case and $3 for the tablet case. In a paragraph of at least three sentences, explain how the graphs of the functions for the two months are the same and how they are different. Be sure to use complete sentences.

They would be similar because the slope would stay the same. The slope would stay the same, because the prices remain the same. They would be different because their y intercept would change

4.F (x) = mx + b

F (x) = mx + 300

F (x) = 6/9x + 300

F (x) = 2/3x + 300

i dont really have clue about how to do next

Answer:

The answer is A (-3,4,6).

Step-by-step explanation:

1 Solve for z in -3x-4y+z=-1

z=3x-1+4y

2 Substitute z=3x-1+4y into 2x+y-z=-8

-x-3y+1=-8

3 Substitute z=3x-1+4y into x+8y-z=23

-2x+4y+1=23

4 Solve for x in -x-3y+1=-8

x=-3y+9

5 Substitute x=-3y+9 into z=3x-1+4y

z=-5y+26

6 Substitute x=-3y+9 into -2x+4y+1=23

10y-17=23

7 Solve for y in 10y-17=23

y=4

8 Substitute y=4 into z=-5y+26

z=6

9 Substitute y=4 into x=-3y+9

x=-3

10 Therefore,

x=-3

y=4

z=6

Calculate your speed per kilometer, by dividing the known time by the distance already ran:

12 minutes /  2 kilometers = 6 minutes per kilometer.

Now multiply the time for 1 by the total distance:

6 minutes per kilometer x 5 kilometers = 30 minutes total.

Answer:

He needs to walk the dog 3 times as 3 times 4 = $12

Step-by-step explanation:

Answer:

Option b is the correct choice.

Step-by-step explanation:

We are asked to find the which of our given expressions has 13y as a term.

Since we know that a term can be a signed number, a variable, or a constant multiplied by a variable or variables as 2a or 5b. In term 2a, 2 is coefficient and a is a variable.

We can see that in 13y, 13 is coefficient and y is variable.

Let us see our given choices one by one.

a. [tex]\frac{13y}{4}-2y[/tex]

Let can write our 1st term as:

[tex]\frac{13}{4}y-2y[/tex]

We can see that both of our terms have y variable, but our 1st term has a coefficient 13/4 and 2nd term has a coefficient of -2. As none of these terms have 13 as a coefficient, therefore, option a is not a correct choice.

b. [tex]8+13y-yz[/tex]

We can see that 8 is a constant, while 13y and -yz are terms. Since our expression has 13y as a term, therefore, option b is the correct choice.

c. [tex]4+13yz[/tex]

We can see that 4 is a constant and 13yz is a term as it has variables yz.  Since our given term has two variables, therefore, option c is not a correct choice as well.

d. [tex]13+y[/tex]

We can see that 13 is a constant and y is term of our given expression. Since our expression don't have 13 as coefficient, therefore, option d is not a correct choice.

b- 8+13y −yz. In the provided options, 13y is a standalone term in expression option b, which is 8+13y−yz. A term is part of an algebraic expression separated by plus or minus signs.

The student is asking to identify in which expression 13y is a term. The correct answer is option b, which is 8+13y−yz. In this expression, 13y is a separate term that is being added to 8 and subtracted by yz.

It's important to recognize that in algebraic expressions a term is a single mathematical expression that can be a number, a variable, or the product of numbers and variables separated by a plus (+) or minus (−) sign. In the case of 13y, it is a term because it is separated by addition or subtraction in the expression. Other options include division or other variables combined with 'y', which do not present '13y' as a standalone term.

Answer:

answer 7.3

13x-7+11x+11=180

Step-by-step explanation:

Answer:

A is a function because if draw a line right down the middle no other dots will intercept

Step-by-step explanation:

A function is where one input has only one out put

As you can tell in the table(c) -3 is repeated that's what makes it not a function.same for B since there are more than one inputs it's not a function

Hope this helps!

Answer:

Step-by-step explanation:

First you need to divide by the amount he needs by the amount he gets, 352 divided by 8. That equals 44, so he will need to work 44 hours to reach his goal.

Answer: 74

Step-by-step explanation:

x = 4:30 - 3:00

  = 1:30

  = 1.5 hours

y = -5.9x² + 39x + 2.2

  = -5.9(1.5)² + 39(1.5) + 2.2

  = -5.9(2.25) + 58.5  + 2.2

  = 13.275 + 60.7

  = 73.975

Answer: 47

Step-by-step explanation:

x = 4:30 - 3:00

  = 1:30

  = 1.5 hours

y = -5.9x² + 39x + 2.2

  = -5.9(1.5)² + 39(1.5) + 2.2

  = -5.9(2.25) + 58.5  + 2.2

  = -13.275 + 60.7

  = 47.425

Answer:

c

Step-by-step explanation:

it is a parabola which has a standard equation of

y = x^2. option a is an exponentially positive curve. option b is a negative parabola. option d is a linear graph which isn't a parabola

Answer:



Step-by-step explanation:

Let x represent the number of buttons on shirts and y represent the number of buttons on jackets.

If 36 shirts and 42 jackets contain 842 buttons. This implies:

36x + 42y = 842 (1)

If 66 shirts and 77 jackets contain 137 buttons. This implies:

66x + 77y = 137 (2)

If you take the first equation: 36x + 42y = 842 and isolate the x, then you will have x = (842 - 42y) / 36

If you substitute x into the second equation:

66((842-42y)/36) + 77y = 137

→ 11(842-42y)/6 + 77y = 137

→ 11(842-42y) + 6(77y) = 137(6)

→ 9262 - 462y + 462y = 822

→ 9262 = 822 which reveals that the equations do not have a solution

To find the length of a rectangle given the diagonal and width, one can utilize the Pythagorean theorem. By treating the diagonal as the hypotenuse of a right triangle formed within the rectangle, we solve for 'x' (length) and get our desired result.

To find the length (x) of the side of a rectangle given the diagonal (17 units) and the width (8 units), you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In the rectangle, the diagonal forms a right triangle with two sides.

In the context of this question, our hypotenuse is the diagonal, which is 17 units long. Let's denote the width as 'w' and the length we're trying to find as 'x'. With 'w' being 8 units, our scenario can be represented by the Pythagorean theorem like this: (17²) = (8²) + (x²)

In determining 'x', we can rearrange the equation to solve for 'x': x = sqrt[(17²) - (8²)]. So, when we subtract the square of 8 from the square of 17 then take the square root, we get the length of 'x'.

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Answer:

After lunch, the family traveled at a speed of 45 mph is the only solution that makes sense when simplifying d(h)=50+45H

Step-by-step explanation:

Answer: After lunch the family drove 45 miles per hr. HOPE THIS HELPS!

It looks like a 90º rotation

Answer:

90 egress

Step-by-step explanation:

Answer: (A) degree of 2; 1 ± i√7

Step-by-step explanation:

Degree of the polynomial designates the number of roots.

x² - 2x + 8

a=1  b=-2 c=8

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

  [tex]=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(8)}}{2(1)}[/tex]

  [tex]=\dfrac{2\pm\sqrt{4-32}}{2}[/tex]

  [tex]=\dfrac{2\pm\sqrt{-28}}{2}[/tex]

  [tex]=\dfrac{2\pm2i\sqrt{7}}{2}[/tex]

  [tex]=\dfrac{2(1\pm\\i\sqrt7)}{2}[/tex]

  = 1 ± i√7

Answer:

After giving 197 cards away, Jenson is left with 361 cards

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(2, 5), B(6, 10) and C(9, −1) to the image triangle A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A(2, 5) ---> A' (0.5, 1.25) = [tex]\frac{0.5}{2} , \frac{1.25}{5}=(\frac{1}{4} , \frac{1}{4})[/tex]

B(6, 10) ---> B' (1.5, 2.5) = [tex]\frac{1.5}{6} , \frac{2.5}{10}=(\frac{1}{4} , \frac{1}{4})[/tex]

C(9, −1) ---> C' (2.25, −0.25) = [tex]\frac{2.25}{9} , \frac{-0.25}{-1}=(\frac{1}{4} , \frac{1}{4})[/tex]

Therefore, the scale factor of the dilation is 1/4.

The scale factor of the dilation that maps triangle ABC to triangle A'B'C' is determined by calculating the ratio of the coordinates of corresponding vertices. The scale factor for this transformation is 0.25.

The student is asking how to find the scale factor of a dilation when given the coordinates of the vertices of a triangle before and after the transformation. To determine the scale factor, you need to compare the corresponding sides or coordinates of the pre-image and the image. Below is the step-by-step explanation:

Therefore, the scale factor for the dilation that maps the pre-image to the image is 0.25.

Answer:

17

Step-by-step explanation:

To find the distance between two points, we use the formula

d =sqrt( (x2-x1)^2 + (y2-y1)^2)

d= sqrt((2--6)^2+(5--10)^2 )

d= sqrt((2+6)^2+(5+10)^2 )

d = sqrt(8^2 + 15^2)

d = sqrt(64+225)

d =sqrt(289)

d =17

Answer: Phillip is correct. The triangles are not congruent.

How do we know this? Because triangle ABC has the 15 inch side between the two angles 50 and 60 degrees. The other triangle must have the same set up (just with different letters XYZ). This isn't the case. The 15 inch side for triangle XYZ is between the 50 and 70 degree angle.

This mismatch means we cannot use the "S" in the ASA or AAS simply because we don't have a proper corresponding pair of sides. If we knew AB, BC, XZ or YZ, then we might be able to use ASA or AAS.

At this point, there isn't enough information. So that means John and Mary are incorrect, leaving Phillip to be correct by default.

Note: Phillip may be wrong and the triangles could be congruent, but again, we don't have enough info. If there was an answer choice simply saying "there isn't enough info to say either if the triangles are congruent or not", then this would be the best answer. Unfortunately, it looks like this answer is missing. So what I bolded above is the next best thing.

Answer:

Phillip states that the triangles are not congruent.

Step-by-step explanation:

Assume for a second the triangles are congruent.

Then the angles are equal

<A =< X

<B= <Y

<C = <Z

Then

Triangle ABC = Triangle XYZ

from this information

AB = XY

and BC = YZ

and CA = ZX

but the only other piece of information we have is CA = 15 and XY = 15

If this is true then CA = ZX = 15  and AB = XY = 15

That would make this an isosceles triangle  (AB = AC)

so angles B  and C would have to be equal,  but they are not.  

So these two triangles cannot be congruent.

Answer:

y=-37

Step-by-step explanation:

A perpendicular line has a negative reciprocal slope to the original line. We will use the slope formula to find the slope of line m, then take the negative reciprocal for the slope of line n which will reveal the value of y.

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

We substitute [tex]x_1=6\\y_1=8[/tex] and [tex]x_2=-1\\y_2=2[/tex]

[tex]m=\frac{2-8}{-1-6}[/tex]

[tex]m=\frac{2-8}{-1-6}=\frac{-6}{-7} =\frac{6}{7}[/tex]

[tex]m\neq \frac{6}{7}[/tex] for line n because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{7}{6}[/tex].

We will substitute [tex]m=-\frac{7}{6}[/tex] into the slope formula to find line n's coordinate value y. We will also substitute [tex]x_1=-1\\y_1=5[/tex] and  [tex]x_2=5\\y_2=y[/tex] .

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

[tex]-\frac{7}{6}=\frac{y-5}{5-(-1)}[/tex]

[tex]-\frac{7}{6}=\frac{y-5}{6)}[/tex]

[tex]6(-\frac{7}{6})=y-5[/tex]

[tex]-42+5=y-5+5[/tex]

[tex]-37=y[/tex]

The value of y that makes Line n perpendicular to Line m is 59/6. This is found by first calculating the slope of Line m and then finding the negative reciprocal (since perpendicular lines have negative reciprocal slopes), and using this new slope to solve for y in Line n.

To solve this problem, we first need to understand that the slopes of two perpendicular lines are negative reciprocals of each other. This means that if Line m has a slope of a, then Line n will have a slope of -1/a.

First, let's find the slope of line m which contains the points (6,8) and (-1,2). The formula for slope is (y2-y1)/(x2-x1). This gives us (2-8)/(-1-6) = -6/-7 = 6/7.

Because line n is perpendicular to line m, its slope will be the negative reciprocal of 6/7, which is -7/6. We can then use this slope and the point (-1,5) to find the value of y when x=5 on line n. We use the equation y-y1 = m(x-x1), and substitute the values in: y - 5 = -7/6 * (5 - (-1)), which simplifies to y = -7 + 5 + 35/6 = 29/6 + 30/6 = 59/6.

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Answer:

1. [tex]x=56^o[/tex]

2. Exterior angle = [tex]116^o[/tex]

Step-by-step explanation:

1.

We can see from our given diagram that (2x+4) degrees is the measure of exterior angle of triangle PQR.

Since the measure of exterior angle of a triangle equals to the sum of the opposite interior angles. So measure of our given triangle's exterior angle will be equal to sum of measure of angle P and angle Q.

We can represent this information as:

[tex](2x+4)^o=60^o+x^o[/tex]

[tex]2x^o+4^o=60^o+x^o[/tex]

Let us subtract [tex]x^o[/tex] from both sides of our equation.

[tex]2x^o+4^o-x^o=60^o+x^o-x^o[/tex]

[tex]x^o+4^o=60^o[/tex]

Let us subtract [tex]4^o[/tex] from both sides of our equation.

[tex]x^o+4^o-4^o=60^o-4^o[/tex]

[tex]x=56^o[/tex]

Therefore, value of x is 56 degrees.

2. Since the measure of exterior angle of our given triangle is 2x+4, let us substitute x=56 in our expression to find the measure of exterior angle.

[tex]\text{Measure of exterior angle}=(2x+4)^o[/tex]

[tex]\text{Measure of exterior angle}=(2*56+4)^o[/tex]

[tex]\text{Measure of exterior angle}=(112+4)^o[/tex]

[tex]\text{Measure of exterior angle}=116^o[/tex]

Therefore, the measure of exterior angle of our given triangle is 116 degrees.

Answer:1/12

Step-by-step explanation:1/3-1/4=1/12

Answer:28934

Step-by-step explanation:

You add 22456 and 6478

After the park workers plant 6478 more trees in the park which currently has 22456 trees, the total number of trees would be 28934.

This is a question of simple addition in mathematics. Currently, the park consists of 22456 pine trees. The park workers are planning to plant another 6478 trees. Therefore, to find out the total number of trees after they plant the new ones, we add together the current number of trees and the number of trees to be planted.

22456 (Current number of trees) + 6478 (Additional number of trees to be planted) = 28934

So, after planting the additional trees, there will be a total of 28934 trees in the park.

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Answer:

Correct answer is option C.

Step-by-step explanation:

Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

Answer:

C. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

Step-by-step explanation:

Given : The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).

To find : Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D'.

Solution : We have given that  trapezoid ABCD.

Parent coordinates of A (2,6), B (5,6), C (7,1), and D (-1,1)

Translated coordinates A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).

By reflection rule :  Reflection across x axis (x , y) →→( x , -y) and  rotating it 90°clockwise  (x , y) →→( -y, x).

Therefore, C. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

Answer:

False

Step-by-step explanation:

The sum of the interior angles of a regular polygon is  (n – 2)180  where n is the number of sides.   Since this is a 10 sided figure,

the sum of the interior angles is (10-2)* 180 =1440

Answer: D.(5, -8)

Step-by-step explanation:

(Multiply by -1)-8x-7y=16

10x+7y=-6

2x=10

X=5

(Subsitite 5 into one) 10(5)+7y=-6

50+7y=-6

7y=-56

Y=-8

Final answer:

To solve the system using elimination, subtract the first equation from the second to find x=5, then substitute x back into one of the original equations to find y=-8. The solution is (5, -8).

Explanation:

To solve the system of equations using elimination, we look at the given pairs:

We can eliminate the y-variable by subtracting the first equation from the second

Divide both sides by 2:

Now that we have x, we can substitute it back into either of the original equations to find y. Let's use the first equation:

Divide both sides by 7:

Therefore, the solution to the system of equations is (5, -8), which corresponds with answer choice D.

Answer:

1. vertical line. slope is undefined.

2. horizontal line. slope of 0

3. vertical line. slope is undefined.

4. horizontal line. slope of 0

Step-by-step explanation:

Answer: 3/10 watts

Step-by-step explanation:

3/5 converts to 6/10

6/10 / 2 = 3/10

Answer:

3/10

Step-by-step explanation:

3/5 converts to 6/10

6/10 / 2 = 3/10

Answer:

Number of ripe mangoes were sold as 132

Step-by-step explanation:

Let's assume number of rip mangoes were sold as 'x'

A store manager ordered 28 crates of mangoes

Number of crates =28

There were 36 mangoes in each crate

Number of mangoes in each crate=36

Total number of mangoes=( Number of crates)*(Number of mangoes in each crate)

Total number of mangoes is

[tex]=28\times 36[/tex]

[tex]=1008[/tex]

WHEN the mangoes were delivered

he sold the ripe mangoes and repacked the rest equally into 73 boxes

There were 12 mangoes in each box

Total number of mangoes is

[tex]=73\times 12+x[/tex]

[tex]=876+x[/tex]

now, we can set them equal

[tex]1008=876+x[/tex]

[tex]x=132[/tex]

To find the number of ripe mangoes sold, multiply the number of crates by the number of mangoes in each crate. Then, multiply the number of boxes by the number of mangoes in each box. Finally, subtract the number of mangoes repacked into boxes from the total number of mangoes delivered.

To find the number of ripe mangoes sold, we need to determine the total number of mangoes delivered and then subtract the number of mangoes repacked into boxes.

First, we find the total number of mangoes delivered by multiplying the number of crates (28) by the number of mangoes in each crate (36): 28 crates * 36 mangoes/crate = 1008 mangoes

Next, we find the number of mangoes repacked into boxes by multiplying the number of boxes (73) by the number of mangoes in each box (12): 73 boxes * 12 mangoes/box = 876 mangoes

Finally, we subtract the number of mangoes repacked into boxes from the total number of mangoes delivered to find the number of ripe mangoes sold: 1008 mangoes - 876 mangoes = 132 ripe mangoes

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