What is the solution to x² - 11x + 24 = 0

To factorize a polynomial you need to find the zeros, and then you can write the polynomial as a product of bynomials.

For a polynomial of the form:

[tex]p(x) = A_n*x^n + A_{n-1}*x^{n-1} + ... + A_1*x + A_0[/tex]

We define the zeros as the values of x such that:

p(x) = 0.

On the above case, the degree of the polynomial is n (the maximum exponent). Then the number of zeros of the polynomial is n (same as the degree).

Once we know the n zeros, we can factorize the polynomial as:

[tex]p(x) = A_n*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]

For example, for the polynomial:

[tex]p(x) = 2x^2 - 8[/tex]

The two zeros are x = 2 and x = -2, then it can be rewriten as:

[tex]p(x) = 2*(x + 2)*(x - 2)[/tex]

If you want to learn more about polynomials:

https://brainly.com/question/4142886

#SPJ1

Problem 1

Triangle ABE is similar to triangle DCE. This is because we have two pairs of congruent corresponding angles.

Refer to the angle angle (AA) similarity theorem for more info.

-------------------

For the other pair of triangles, we don't have enough info to determine if they are similar or not. We have info about one pair of sides, and a pair of angles, but that's about it.

We need to know if JL is proportional to MO, and in the same ratio as KL & NO are, if we wanted to use the side angle side (SAS) similarity theorem.

-------------------

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

Problem 2

Divide the corresponding sides

We see the three ratios are equal to the same value (2) and that proves the triangles LNM and POQ are similar by the SSS (side side side) similarity theorem.

-------------------

Like before, we'll divide the corresponding sides

We don't have a match. Let's try rotating the second rectangle so that the side '8' is horizontal, and the side '3' is vertical

We don't have a match here either. There are other approaches we could take, but basically the two rectangles are not similar.

-------------------

2y=x+10

3y=3x+15

2y-10=x

3y=3(2y-10)+15

2y-10=x

3y=6y-30+15

2y-10=x

0=3y+15

2y-10=x

3y=15

x=2y-10

y=5

2y=x+10

2×5=x+10

x=0

x=0, y=5

Answer:

4x ÷ 7

Step-by-step explanation:

the product of 4 and a number (x)

would be 4x. Then you would divide by 7.

The amount of iced tea left in quartz is  3 quartz

The coach makes 9 quarts of iced tea.

she fills 12 bottles with 2 cups of iced tea each to share with her team.

1 quartz = 4 cups

Therefore, she shared the following amount of tea in cups:

amount shared = 12 × 2 = 24 cups

Then, let's convert to quartz,

4 cups = 1 quartz

24 cups = ?

amount shared in quartz = 24 / 4 = 6 quarts

Therefore,

the amount of ice tea left = 9 - 6 = 3 quartz

learn more on quarts here: https://brainly.com/question/22443564

#SPJ1

(x+8/3)²+y²=1

(x+8/3)²+y²+0²+2×0y=1

(x+8/3)²+(y+0)²=(V1)²

->center: C(8/3,0)

-> radius: V1

The probability that can be chosen by Jake will be 33.5%.

The area of the whole dartboard will be:

= πr²

where r will be:

= 3 + (4 × 4)

= 3 + 16

= 19

Area = π(19)² = 361π²

The area of 30, 40, and 50 points will be:

= π × [3 + (2 × 4)]²

= 121π²

The probability will be:

= (361π - 121π) × 100

= 33.5%

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:

1 / 1024

Step-by-step explanation:

Each flipping has 1/2 chance

In ten flippings:

[tex](\frac{1}{2} )^{10} =\frac{1^{10} }{2^{10} } =\frac{1}{1024}[/tex]

Hope this helps

The area of the triangle DEF is 2 square units

The given parameters are:

D(9,-8), E(8,-3), and F(2,-5),

The area of the triangle is calculated using:

Area = 0.5|x1 * (y2 -y3) + x2 * (y1 -y3) + x3 * (y2 -y1) |

This gives

Area = 0.5|9 * (-3 + 5) + 8 * (-8 + 5) + 2 * (-3 + 8) |

Evaluate

Area = 0.5|4|

Expand

Area = 2

Hence, the area of the triangle DEF is 2 square units

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

Answer:

-66

Step-by-step explanation:

add the numbers

-26 -37 = -66

[tex] - 26 - 37 = - 63[/tex]

Whenever the sign of the numbers is same , add them but don't forget the negative sign.

Please give brainliest

Answer:

10 percent

Step-by-step explanation:

look closl

it's 10 percent ...................... 10%

Answer:

Discount amount = 34

Step-by-step explanation:

Discount amount = 202 - 168 = 34

Answer:

see explanation

Step-by-step explanation:

a translation of 3 squares right means add 3 to the x- coordinate

a translation of 3 squares up means add 3 to the y- coordinate

then

(1, 1 ) → (1 + 3, 1 + 3 ) → (4, 4 )

(3, 1 ) → (3 + 3, 1 + 3 ) → (6, 4 )

(1, 4 ) → (1 + 3, 4 + 3 ) → (4, 7 )

Answer:

[tex]2( \frac{2}{5} x + 2) = \frac{4}{5} x + 4[/tex]

Step-by-step explanation:

Use the distributive property.

Answer:

X=70

Step-by-step explanation:

aw we can for a triangle, where the 2 angles are complementary from the outer ones, so the 2 angles are 50, and 60

so the third one will be 70

Answer:

(-4,1)

Step-by-step explanation:

Factoring, Guess and check.

Answer:

4. x = 9 and y = 18

Step-by-step explanation:

Hello there!

When given such a problem we have to methods to handle this:

On this problem, let's limit ourself to substitution method;

x + y = 27 ..................... eq.1

y = 2x ........................ eq.2

Eq.2 is already manipulated. Substitute it into eq.1

x + y = 27

=> x + 2x = 27

3x = 27

x = 9

Substitute x into eq.2

y = 2 (9)

= 18

In terms of x and y;

(x, y) => (9, 18)

I hope this helps you.

Have a nice time and nice studies.

Considering the given function, we have that:

a) D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.

b) D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.

The distance that the family is from home, after t hours of driving, is given by:

D(t) = 3260 - 55t.

Then, after 12 hours, the distance is given by D(12), that is:

D(12) = 3260 - 55 x 12 = 2600.

D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.

D(t)=2490, hence:

3260 - 55t = 2490

55t = 770

t = 770/55

t = 14

D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.

More can be learned about functions at https://brainly.com/question/25537936

#SPJ1

Answer:

41.34

Step-by-step explanation:

We can use the Pythagorean theorem to solve for the distance. First we will create an imaginary triangle with the leg lengths being the x distance and y distance between the 2 points and the hypotenuse being the distance between the 2 points.

x distance =

[tex]15 - (-20) = 35[/tex]

y distance =

[tex] |-17-5| = | - 22| = 22[/tex]

We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle

xdistance²+ydistance²=distance²

35²+22²=distance²

1709=distance²

[tex] \sqrt{1709} = distance[/tex]

In decimal form the distance would be around 41.34.

That is the answer

- Kan Academy Advance

Step-by-step explanation:

the median is the value, where half of the other values is smaller (or equal), and the other half bigger (or equal).

with an even number of data points that is not directly possible to find.

in this case the 2 middle values are taken and their mean value is the median.

in our case, the 2 middle values are 12 and 14.

their mean value is

(12+14)/2 = 26/2 = 13

so,

13 is the median (even though if is not a data point itself).

Answer:

2/7  ?

Step-by-step explanation:

Because 1/4 divided by 7/8th is 1/4. Hope this works

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the slope of (-4, -7) and (-2, -19).

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's the slope formula:

[tex]\star~\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]

Where

y2 and y1 are y-coordinates

x2 and x1 are x-coordinates

Input the values, which are:

-19: y2

-2: x2

-7: y1

-4: x1

[tex]\star~\mathrm{\cfrac{-19-(-7)}{-2-(-4)}}[/tex]

[tex]\star~\mathrm{\cfrac{-19+7}{-2+4}}[/tex]

Simplify!

[tex]\star~\mathrm{\cfrac{-12}{2}}[/tex]

[tex]\star~\mathrm{-6}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students out :)

The formula for calculating the height is h = 3V/πr²

The formula given is the formula for calculating the volume of a cone

V = 1/3πr²h

where

h is the height

r is the radius

Make h the subject of the formula

Cross multiply

3V = πr²h

Divide both sides by πr²

3V/πr² = πr²h/πr²

h = 3V/πr²

Hence the formula for calculating the height is h = 3V/πr²

Learn more on subject of formula here: https://brainly.com/question/657646
#SPJ1

Answer:

15

Step-by-step explanation:

Let 2n+1 be the first odd integer.

Therefore, the consecutive odd integers will be 2n+3 and 2n+5

If the sum of the consecutive odd integers is 51 then:

⇒ 2n + 1 + 2n + 3 + 2n + 5 = 51

⇒ 6n + 9 = 51

⇒ 6n = 42

⇒ n = 7

To find the values of the integers, substitute the found value of n into the expressions:

Therefore, the three consecutive odd integers that sum to 51 are 15, 17 and 19.  The smallest of which is 15.