The graph of y = ax 2 + bx + c is a parabola that opens up and has a vertex at (-2, 5). What is the solution set of the related equation 0 = ax 2 + bx + c?

Hello!

Answer:

[tex]\boxed{-10x+7.5}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

[tex]-2.5*4x-(-2.5)*3[/tex]

[tex]-4*2.5x+3*2.5[/tex]

Simplify.

[tex]4*2.5=10[/tex]

[tex]3*2.5=7.5[/tex]

[tex]=-10x+7.5[/tex]

[tex]\boxed{-10x+7.5}[/tex], which is our final answer.

I hope this helps you!

Have a nice day! :)

Thanks!

Answer:

The answer is -10x+7.5

Step-by-step explanation:

To find the volume of the new sphere, calculate the volume of the original sphere and then multiply it by the scale factor cubed. Convert the volume from cubic centimeters to cubic inches using the conversion factor: 1 cm³ = 0.0610237 in³. The approximate volume of the new sphere in cubic inches is 255.3 in³.

To find the volume of the new sphere, we need to first find the volume of the original sphere and then multiply it by the scale factor cubed. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.

Given that the radius of the original sphere is 5 cm, we can calculate its volume using the formula:

V1 = (4/3)π(5 cm)³ ≈ 523.6 cm³.

Next, we can calculate the volume of the new sphere by multiplying the volume of the original sphere by the scale factor cubed:

V2 = V1 × (2)³ = 523.6 cm³ × 8 ≈ 4188.8 cm³.

Finally, to convert the volume from cubic centimeters to cubic inches, we need to use the conversion factor: 1 cm³ = 0.0610237 in³. Therefore, the approximate volume of the new sphere in cubic inches is:

V2 ≈ 4188.8 cm³ × 0.0610237 in³/cm³ ≈ 255.3 in³.

https://brainly.com/question/21623450

#SPJ11

Answer:

20/6 or 3.33 or 3 1/3 or 3 hours and 20 mins

Step-by-step explanation:

5/6 * 4 = (5*4)/6 = 20/6

Answer:

she will have praticed 3 hours and 20 min

Step-by-step explanation:

Answer:

the square root of thirteen is 3.6

Step-by-step explanation:

if you put the 13 with the square root box and press the = button you will get the square root of 13 is 3.6

Answer:

12x=2pi*r

Step-by-step explanation:

2*22/7*r=12x

r=12x*7/44

r=21x/11

The radius of a circle is calculated by dividing the given circumference by 2π. When given circumferences of 6 inches, 6π inches, 12 inches, and 24π inches, the corresponding radii are approximately 0.955 inches, 3 inches, 1.91 inches, and 12 inches, respectively.

To find the radius of a circle given its circumference, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Since we are given the circumference, we can rearrange this formula to solve for the radius as follows: r = C / (2π).

Given the possible circumferences provided, we can calculate the radius for each.

For 6 inches: r = 6 / (2π) = 6 / (2 * 3.14) = 6 / 6.28 = approximately 0.955 inches

For 6π inches: r = 6π / (2π) = 6 / 2 = 3 inches

For 12 inches: r = 12 / (2π) = 12 / (2 * 3.14) = 12 / 6.28 = approximately 1.91 inches

For 24π inches: r = 24π / (2π) = 24 / 2 = 12 inches

Answer:

No, because they look like they are different sizes. Or you could say the first answer

Hello There!

The answer is "C"

In this problem, you need dilation to map onto each-other.

Dilation is transformation hat changes the size of something

Answer:

The original price of the car can be written in percentage which is 100%. Because the price increased by 6%, therefore, the new price should be represented as:

100% + 6% = 106% = 1.06 (remember: not 0.06, that is how much the price increased, not 0.94 either, because the price increased, not decreased).

So the answer for the first question should be:

(a) new price = 1.06 × original price

from that, we can appy the answer above for the second question:

(b) new price: $33390

[tex]\bf (-5u)(-5u)(-5u)(-5u)\implies (-5u)^1(-5u)^1(-5u)^1(-5u)^1 \\\\\\ (-5u)^{1+1+1+1}\implies (-5u)^4\implies (-5)^4u^4\implies 625u^4[/tex]

Answer:

Step-by-step explanation:

Remember, a sphere is defined as a three-dimensional object where all points on its surface are equidistant form its center.

According to its definition, all point on the boundaries can be called a point on the sphere.

So, among the options, only point B is on the sphere, because J and S are inside.

Therefore, the right answer is Point B.

Answer:

Step-by-step explanation:

[tex]f(x)=0.5|x-4|-3\\\\f(x)=7\Rightarrow0.5|x-4|-3=7\qquad\text{add 3 to both sides}\\\\0.5|x-4|=10\qquad\text{multiply both sides by 2}\\\\|x-4|=20\iff x-4=\pm20\\\\x-4=-20\qquad\text{add 4 to both sides}\\x=-16\\\\x-4=20\qquad\text{add 4 to both sides}\\x=24[/tex]

Answer:

(x-8) (x+5)

Step-by-step explanation:

x^2-3x-40

What 2 numbers multiply to -40 and add to -3

-8 *5 = -40

-8+5 = -3

(x-8) (x+5)

Answer:

22.5 pages

Step-by-step explanation:

First divide the page number by the minutes it takes to read them to find pages per minute-

4.5 / 12 = .375

Then take that number and multiply it by the minutes in an hour-

(.375) (60) = 22.5

22.5 pages in one hour.

Answer:

22 1/2 pages

Step-by-step explanation:

60/12 = 5

5(4.5) = 22 1/2

Answer:

Option B , D and E are correct.

Step-by-step explanation:

We set the denominator equal to zero to find the number to put in division box

So, if 3 is in the division box then the denominator will be

x-3 = 0 => x=3 is the root.

So, Option E is correct

2x^2-2x-12 ÷ x-3 = 2x+4 is correct.

because after division the result given is 2x+4 which is correct.

So, Option B is correct

x-3 is a factor of 2x^2-2x-12 because because when the term is divided we get the remainder 0.

So, Option D is correct

So, Option B,D and E are correct.

Answer:

Δ TUW ≅ ΔVWU ⇒ by AAS case

Step-by-step explanation:

* Lets revise the cases of congruent for triangles

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ  

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

 and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

 leg of the 2nd right angle Δ

* Lets solve the problem

- There are two triangles TUW and VWU

- ∠T and ∠V are right angles

- LINE TW is parallel to line VU

∵ TW // VU and UW is a transversal

∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)

- Now we have in the two triangles two pairs of angle equal each

 other and one common side, so we can use the case AAS

- In Δ TUW and ΔVWU

∵ m∠T = m∠V ⇒ given (right angles)

∵ m∠TWU = m∠VUW ⇒ proved

∵ UW = WU ⇒ (common side in the 2 Δ)

∴ Δ TUW ≅ ΔVWU ⇒ by AAS case

Answer:

Step-by-step explanation:

Given ∠T and ∠V are right angles.

TW ║ UV

To prove ⇒ ΔTUW ≅ ΔVWU

Proof ⇒ In ΔTUW and ΔVUW,

∠T ≅ ∠ V ≅ 90° (given)

Side UW ≅ UW ( Common in both the triangles )

TW ║ UV

and UW is a transverse.

So ∠TWU ≅ ∠WUV [alternate interior angles]

Since Angle = Angle = side are equal

Therefore, ΔTUW ≅ ΔVWU

Answer:

9 cups of milk

Step-by-step explanation:

2 cups of flour - 3 cups of milk

4- cups of flower - 6 cups of milk

6 cups of flower - 9 cups of milk

Please mark brainliest and have a great day!

Answer:

9 cups of milk

Step-by-step explanation:

2 cups of flour need 3 cups of milk

1 cup of milk needs 3/2 cups of milk

:. 6 cups of milk will need

(6 x 3/2) = 18/2

= 9 cups of milk

Answer:

(2.5, - 2)

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

(2.5, - 2 ) ← point of intersection

Answer:

Option D is the correct answer.

Step-by-step explanation:

Refer the given figure showing the graph.

We can see the point of intersection is (2.5, -2).

Option D is the correct answer.

Alternatively:

2x + y = 3  ---------------------eqn 1

2x - 5y = 15  ---------------------eqn 2

eqn1 - eqn 2 gives

  2x + y - ( 2x - 5y) = 3 - 15

           6y = -12

             y = -2

Substituting in eqn 1

         2x - 2 = 3

            x = 2.5

Point of intersection is (2.5, -2).

Option D is the correct answer.

Answer:

Option a: Line slants down.

Step-by-step explanation:

 It is important to remember that the equation of the line in Slope-Intercept form is the following:

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

Where "m" is the slope of the line and "b" is the y-intercept.

The slope of a line can be positive (The line slopes upwards to the right), negative (The line slopes downwards to the right), zero (Horizontal line), or undefined (Vertical line).

Therefore, the statement that best describes a line in a slope-intercept form when the coeficient of the x-term (The slope) is negative is: "Line slants down".

Answer:

A. x = √2

B. x = 1

D. x = -1

E. x = -√2

Step-by-step explanation:

Correct 100%

Without the complete equation, we cannot provide a definitive solution. However, it seems like you are dealing with a quadratic equation where possible solutions can be found using the quadratic formula, '-b ± √ (b² - 4ac) / 2a'. Please provide the full equation for a more precise answer.

The original equation mentioned in your question is missing, but I'll assume you are referring to solutions of the equation x² = √ ( 2x² - 1 ). This equation can be solved by first simplifying the condition as 2(x² - 1)² ≤ 1. Following the standard method for solving quadratic equations, we can use the quadratic formula -b ± √ (b² - 4ac) / 2a. Unfortunately, without a full equation, we cannot provide a comprehensive answer. Please, provide the complete equation for a more accurate solution.

https://brainly.com/question/17595716

#SPJ11

Answer:

The cotangent of 61.6° is .5407.

Step-by-step explanation:

Refer to the sketch attached.

61.6° + 28.4° = 90°. In other words, 61.6° is the complementary angle of 28.4°.

Consider a right triangle OAB with a 61.6° angle [tex]\rm O\hat{A}B[/tex]. The other acute angle [tex]\rm O\hat{B}A[/tex] will be 28.4°.

[tex]\displaystyle \tan{61.6\textdegree{}}=\tan{\rm O\hat{A}B} = \frac{\text{Opposite of }\rm O\hat{A}B}{\text{Adjacent of }\rm O\hat{A}B} = \frac{a}{b}[/tex].

The cotangent of an angle is the reciprocal of its tangent.

[tex]\displaystyle \cot{61.6^{\circ}}=\frac{1}{\tan{\rm O\hat{B}A}} = \frac{\text{Adjacent of }\rm O\hat{B}A}{\text{Opposite of }\rm O\hat{B}A} = \frac{a}{b} = \tan{\rm O\hat{A}B} = \tan{28.4^{\circ}}[/tex].

In other words,

[tex]\cot{61.6^{\circ}} = \tan{28.4^{\circ}} \approx 0.5407[/tex].

Answer:

2 lines meet at a shared point.

Step-by-step explanation:

Hope my answer has helped you!

Answer:

degrees apart in latitude: 91.22

degrees apart in longitude: 147.95

Step-by-step explanation:

Liverpool and Melbourne are two cities that are located very far away from each other. Liverpool is located in the northwestern part of England, while Melbourne is located in the southeastern part of Australia, so understandably their latitudes and longitudes are very different. In order to get to the distance in degrees between these two cities in latitude and longitude, we just simply need to sum the degrees of both of them and we will get to the result. The reason why simple summing will do the job is because they are on separate hemispheres, with Liverpool being on the Northern and Western Hemisphere, while Melbourne being on the Southern and Western Hemisphere.

Latitude distance:

53.41 + 37.81 = 91.22

Longitude distance:

2.99 + 144.96 = 147.95

Answer:

degrees apart in latitude: 91.22

degrees apart in longitude: 147.95

Check the picture below.

let's notice those two corresponding angles of 90° - 2x, and also recall that the sum of all interior angles in a triangle is 180°.

[tex]\bf 60+3x+(90-2x)=180\implies x+150=180\implies x=30[/tex]

Answer:

C

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x) = [tex]4^{x}[/tex] - 8 - (5x + 6)

              = [tex]4^{x}[/tex] - 8 - 5x - 6 ← collect like terms

              = [tex]4^{x}[/tex] - 5x - 14 → C

Answer:

x = 2

Step-by-step explanation:

Given 2 secants intersecting a circle from an external point, then

The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is

(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)

(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides

x² + 13x + 12 = x² + 9x + 20

Subtract x² + 9x from both sides

4x + 12 = 20 ( subtract 12 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

Answer:

14! Hope you ace your test!!

Step-by-step explanation:

The value of the side 'a' will be 14 units.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The value of a is calculated as:-

Sin 30  =  P / H

Sin  30  =  7  /  a

1  /  2  =  7  /  a

a  =  7  x  2

a  =  14 units

Therefore the value of the side 'a' will be 14 units.

To know more about Trigonometry follow

https://brainly.com/question/24349828

#SPJ2

Answer:

Option 1

Step-by-step explanation:

Given expression is:

[tex]\frac{(2mn)^{4}}{6m^{-3}n^{-2}} \\=\frac{2^{4}m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{16m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{8*2*m^{4}*n^{4}}{2*3*m^{-3}*n^{-2}} \\=\frac{8*m^{4+3}n^{4+2}}{3}\\=\frac{8m^{7}n^{6}}{3}[/tex]

So option 1 is the correct answer ..

Answer:  Nick

Step-by-step explanation:

Nick is the one who will go to bed first because he needs the most sleep. Nick needs 10 hours of sleep, then it would be Brad who needs 9 , then Will who needs 8

Nick will be the first to bed on Friday evening out of Will, Brad, and Nick.

On Friday evening, Nick would be the first to bed among Will, Brad, and Nick. Nick needs 10 hours of sleep every night, so to wake up at 6 a.m. on Saturday, he would have to go to bed earlier than Will and Brad who need 8 and 9 hours of sleep, respectively.

Answer:

C

Step-by-step explanation:

The vertical line test is basically just drawing a vertical line and seeing if the line intersects the graph more than once. If it does, then it is not a function, if it doesn't than it is a function.

Answer:

C

Step-by-step explanation: