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Hello, please consider the following.

When [tex]x_1[/tex] and [tex]x_2[/tex] are two roots, we can factorise as

[tex]ax^2+bx+c=a(x-x_1)(x-x_2)=a(x^2-(x_1+x_2)x+x_1x_2)=0[/tex]

So for the first equation, we can say that the sum of the zeros is

[tex]\dfrac{a^2+b^2}{2}=\dfrac{a^2}{2}+\dfrac{b^2}{2}[/tex]

and the product is

[tex]\dfrac{a^2b^2}{4}=\dfrac{a^2}{2}\dfrac{b^2}{2}[/tex]

So we can factorise as below.

[tex]4x^2-2(a^2+b^2)x+a^2b^2=(2x-a^2)(2x-b^2)=0[/tex]

And the solutions are

[tex]\boxed{\sf \n\bf \ \dfrac{a^2}{2} \ \ and \ \ \dfrac{b^2}{2}}[/tex]

For the second equation, we will complete the square and put the constant on the right side and take the root.

Let's do it!

[tex]9x^2-9(a+b)x+2a^2+5ab+2b^2=0\\\\9(x-\dfrac{a+b}{2})^2-9\dfrac{(a+b)^2}{4}+2a^2+5ab+2b^2=0\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{9(a+b)^2-8a^2-20ab-8b^2}{4}\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{9a^2+18ab+9b^2-8a^2-20ab-8b^2}{4}\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{a^2+b^2-2ab}{4}=\dfrac{(a-b)^2}{4}\\\\(x-\dfrac{a+b}{2})^2=\dfrac{(a-b)^2}{2^2\cdot 3^2}[/tex]

We take the root, and we find the two solutions

[tex]\begin{aligned}x_1&=\dfrac{a+b}{2}-\dfrac{a-b}{6}\\\\&=\dfrac{3a+3b-a+b}{6}\\\\&=\dfrac{2a+4b}{6}\\\\&\boxed{=\dfrac{a+2b}{3}}\end{aligned}[/tex]

[tex]\begin{aligned}x_1&=\dfrac{a+b}{2}+\dfrac{a-b}{6}\\\\&=\dfrac{3a+3b+a-b}{6}\\\\&=\dfrac{4a+2b}{6}\\\\&\boxed{=\dfrac{2a+b}{3}}\end{aligned}[/tex]

Thank you.

Answer:

V is 56

Step-by-step explanation:

V= 20+12(3)

V= 20 + 36

V = 56

Answer:

Step-by-step explanation:

Given P = 6q² + 3, we are to find the derivative of the function with respect to q. Generally if y = axⁿ;

dy/dx = naxⁿ⁻¹

Rewriting the given equation as P =  6q² + 3q⁰

Using the formula to find the derivative;

dP/dq = 2(6)q²⁻¹ + 0(3)q⁰⁻¹

dP/dq = 12q¹ + 0

dP/dq = 12q

Hence the derivative of the function P with respect to q is 12q

Greetings,

I hope you and your family are staying safe and healthy!

Answer: x = -1 and y = 3

Step-by-step explanation:

[tex]10x - 5y = -25 \\10x + 8y = 14[/tex]

Let's start by solving [tex]10x - 5y = -25[/tex] for [tex]x[/tex]

[tex]10x - 5y=-25[/tex]

Add 5y to both sides

[tex]10x - 5y + 5y = -25+5y \\10x = 5y - 25[/tex]

Now we need to divide both sides by 10

[tex]\frac{10x}{10} = \frac{5y-25}{10}[/tex]

[tex]x = \frac{1}{2} y + \frac{-5}{2}[/tex]

That's not the answer for x. We are not done yet :)

Now we need to substitute [tex]\frac{1}{2} y + \frac{-5}{2}[/tex] for [tex]x[/tex]

[tex]10x + 8y = 14\\10(\frac{1}{2} y + \frac{-5}{2} + 8y = 14[/tex]

Now we need to simply both sides

[tex]13y - 25 = 14[/tex]

Now we need to add 25 to both sides

[tex]13y - 25 + 25 = 14 + 25 \\13y = 39 \\y = \frac{39}{13} \\y=3[/tex]

We have the valuee for y! Now we need to find the value for x

To find the value of x, we need to substitute 3 for y in:

[tex]x = \frac{1}{2} y + \frac{-5}{2} \\x = \frac{1}{2} 3 + \frac{-5}{} \\x = -1[/tex]

Therefore,

The answer is x = -1 and y = 3

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Answer:

See answer is Explanation

Step-by-step explanation:

4 divided by 25 is 0.16

6 divided by 25 is 0.24

6 x 4 = 24

4 x 25 = 100

6 x 25 = 150

Answer:

[tex]\Large \boxed{\mathrm{The \ sum \ of \ a \ number \ and \ three \ quarters \ is \ five.}}[/tex]

Step-by-step explanation:

x + 3/4 = 5

x is the unknown number.

3/4 is added to the number.

The result is 5.

The verbal sentence to represent the equation would be:

The sum of a number and three quarters is five.

Answer: B & D

Step-by-step explanation:

In this scenario we want to come out with a situation where both sides are in an even playing field, as the equation solves to zero.

If a diver is 35 feet below water (-35) and he comes up to breathe, he goes up 35ft (35) meaning he is at the surface (0).

If Manuel is in debt for 35$ (-35) and then he pays off the 35$ (+35) then he is even (at 0).

Answer:

A diver is 35 feet below the surface of the water and then comes up to the surface.

Answer:

Hey there!

When z=48, y=6.

z is 8 times as much as y.

11 part 1: z=8y

11 part 2: I'm going to attach a graph I created at the bottom of this answer :)

Let me know if this helps :)

Answer:

[tex]\frac{3}{8}[/tex]

[tex]2\times \frac{3}{8} = \frac{3}{4}[/tex]

Step-by-step explanation:

According to the given scenario given that

if Ali uses [tex]\frac{3}{8}[/tex]  of 2 pounds of clay for a game of 4 bowls

[tex]\frac{3}{8} (2) = \frac{6}{8} = \frac{3}{4}[/tex]

here Ali will use the number of pounds of clay to create a game

[tex]2\times \frac{3}{8} = \frac{3}{4}[/tex]

Now, we need to compute the number of pounds of clay that should be used in every bowl, we need to divide the prior outcome by 4 which is

[tex]\frac{2\times \frac{3}{8}}{4}[/tex]

Answer:

x=-8

Step-by-step explanation:

Step 1.)   0.4x-2.5=1.3x+4.7

Step 2.)  -2.5=1.3x-0.4x+4.7

Step 3.)   -2.5=0.9x+4.7

Step 4.)   -2.5-4.7=0.9x

Step 5.)   -7.2=0.9x

Step 6.)    -7.2/0.9=x

Step 7.)    -8=x

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

Explanation:

T = (0,0) moves to T ' = (3,0) since we shift 3 units to the right. We add 3 to the x coordinate. The y coordinate does not change since we're not shifting up or down.

Q = (-2,0) moves to Q ' = (1,0) after applying the same rule we did to point T.

M = (-3,2) moves to M ' = (0,2)

Y = (-3,3) moves to Y ' = (0,3)

See the diagram below

Answer:

b) −3y2−2x+1

d) −4xy+4y2−y−10

Step-by-step explanation:

b) -4x + y2 - 9 + 10 - x + 3x - 4y2

(i have just underlined, italic and made it bold to show the like terms)

-4x - x + 3x = -2x

y2 - 4y2 = -3y2

-9 + 10 = 1

-2x - 3y2 + 1

d) 0 - 20 - 5xy + 4y2 + 10 - y + xy

(i have just underlined, italic and made it bold to show the like terms, however the '-y' and '4y2' have no like terms)

0 - 20 + 10 = - 10

-5xy + xy = - 4xy

-10-4xy+4y2-y

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

n = -1

Step-by-step explanation:

1 - 8n - 8 = -7n - 6n - 12

Simplify

-8n - 7 = -13n - 12

Add 7 to both sides

-8n = -13n - 5

Add 13n to both sides

5n = -5

Divide both sides by 5

n = -1

Answer:

n = 1

Step-by-step explanation:

1 - 8n - 8 = -7n - 6n - 12

-8n + 7n + 6n = -12 + 8 - 1

5n = -5

n = -5/5

n = -1

probe:

1 - 8*-1 - 8 = -7*-1 - 6*-1 - 12

1 + 8 - 8 = 7 + 6 - 12 = 1

Answer:

(f o g)(x) = [tex]\frac{4x+13}{4x+12}[/tex]

Domain : (-∞, -3) ∪ (-3, ∞)

Step-by-step explanation:

Given : f(x) = [tex]\frac{x-4}{x-5}[/tex]

            g(x) = 4x + 17

We have to find the value of (f o g)(x).

Since (f o g)(x) = f[g(x)]

                        = [tex]\frac{(4x+17)-4}{(4x+17)-5}[/tex]

                        = [tex]\frac{4x+13}{4x+12}[/tex]

For the Domain of the function (f o g)(x),

Given function is defined for (4x + 12) ≠ 0

4x ≠ -12

x ≠ -3

Therefore, Domain of the function will be : (-∞, -3) ∪ (-3, ∞)                    

Answer:

80y-24z

Step-by-step explanation:

Answer:

Blueberry costs 9 dollars

Pumpkin costs 7 dollars

Step-by-step explanation:

Let "b" represent the price of a blueberry pie

Let "p" represent the price of a pumpkin pie

Step 1: Set equation

5b + 12p = 143 ----- 1

10b + 8p = 142 ----- 2

Step 2:  Isolate 1 for "b"

5b = 143 - 12p

[tex]b = \frac{143}{5}-\frac{12}{5}p[/tex]  ------- 3

Step 3: Substitute 3 into 2

[tex]10(\frac{143}{5}-\frac{12}{5} p )+8p=142\\286 - 24p + 8p = 142\\-24p + 8p = 142 - 286\\-16p = -144\\p = -\frac{144}{-16}\\ p = 9[/tex]

Step 4: Subsitute p = 9 into 1 for b

[tex]5p + 12(9) = 143\\5p + 108 = 143\\5p = 143 - 108\\5p = 35\\\frac{5p}{5}=\frac{35}{5}\\p = 7[/tex]

Therefore a pumpkin pie costs 7 dollars while a blueberry pie costs 9 dollars

Answer:

(64x -11)/y

Step-by-step explanation:

Multiply 4x into the parenthesis.

60x + 4xy -11y

Divide by y.

(60x + 4x -11)/y

(64x -11)/y

Steps to solve:

4x + (15x + y) - 11y​

~Remove parenthesis and combine like terms

4x + 15x + y - 11y​

19x - 10y

Best of Luck!

Answer:

x is greater than or equal to -4 but less than or equal to 4

Step-by-step explanation:

The "domain" is all of the x values on the line. But there are an infinite amount of x-values there, so it must be written as that.

Answer:

See below.

Step-by-step explanation:

The domain is simply the range of x-values the graph encompasses. From the given graph, we can see that the graph stretches from x=-4 to x=+4.

However, note that the graph does not include -4 since the point is an open circle. However, it does include +4 since the point is a closed circle. Therefore, the domain of this graph is:

In interval notation:

[tex](-4,4][/tex]

(Parenthesis on the left because -4 is not included. Brackets on the right because +4 is included.)

Answer:

Hey there!

Corresponding angles are in the same position, so 1 and 6 are not corresponding angles.

Let me know if this helps :)

Answer:

A

step by step explanation

1 and 6

Answer:

D) 11x² + 7

Step-by-step explanation:

combine "like" terms

Answer:

original price = $270 new price = $306.99

Step-by-step explanation:

To solve this we first have to find the original price.

13.7 % of the original price is $36.99 from the  question.

We multiply 100 /13.7 * 13.7 /100 to get the 100% value or the original price.

We also multiply 100 /13.7 * 36.99 = $270 to get the original value.

So the original price is $270.

We add $36.99 to the original price to get the new price.

$270 + $36.99 = $306.99

Answer:

4.7 , 6.25 , 16 , 26

Answer:

From least to greatest

4.7

6.25

16

26

Answer:

The correct option is;

A)

Step-by-step explanation:

By the representation of numbers in a figurative for, we have;

1) Th rational numbers that can be expressed in the form a/b, where a and b are real numbers

2) The integers are the direct subset of the set of rational numbers and are displayed in he next larger ellipse in the figure

3) The whole numbers are the direct subset of the set of integers.

Answer:

the correct option is A

Step-by-step explanation:

please mark as brainliest

this is the diagram that is right

Answer:

351.48cm²

Step-by-step explanation:

Heron’s Formula

Find half the perimeter (30+30+26)/2=43

It’s the square root of each side subtracted from 43, multiplied together, times 43.

√(43-30)*(43-30)*(43-26)*43=√13*13*17*43=√=123539=351.481cm²

Area of triangle is, 351. 39 cm²

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

All the sides of triangles are,

⇒ 30 cm, 30 cm, and 26 cm

We know that;

⇒ Area of triangle = √ s (s - a) (s - b) (s - c)

Where, 's' is the semi perimeter of the triangle, and a, b and c are three sides of triangle.

Here, Sides are,

⇒ a = 30

⇒ b = 30

⇒ c = 26

Hence, We get;

⇒ s = (a + b + c) / 2

⇒ s = (30 + 30 + 26) / 2

⇒ s = 86 / 2

⇒ s = 43 cm

So, The area of triangle is,

⇒ Area of triangle = √ s (s - a) (s - b) (s - c)

⇒ Area of triangle = √ 43 (43 - 30) (43 - 30) (43 - 26)

⇒ Area of triangle = √ 43 × 13 × 13 × 17

⇒ Area of triangle = 13 √ 731

⇒ Area of triangle = 13 × 27.03

⇒ Area of triangle = 351. 39 cm²

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ2

Answer:

For example if the three points are A, B and C in your diagram then there are infinitely many planes that contain the points. The final point is that if the three points do not lie on a line then there is exactly one plane that contains the points.

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

We can find the slope using the slope formula

m = (y2-y1)/(x2-x1)

    = ( 8-7)/(9-6)

   = 1/3

Answer:

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

Step-by-step explanation:

Step 1: Use slope formula

[tex]m= \frac{y2 - y1}{x2 - 1} [/tex]

[tex]m = \frac{8 - 7}{9 - 6} [/tex]

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

Therefore the slip of the equation is 1/3

Answer:

m<EBD = 130 degrees

Step-by-step explanation:

We can say that Line EC is bisected by Line AD at point B.  The angle CBD = 50 degrees is a supplement of the bisected line EC.  With this in mind we can say:

EBD + CBD = 180

And we can solve for EBD:

EBD + CBD = 180

EBD + 50 = 180

EBD = 130

So the measure of angle EBD is 130 degrees.

Cheers.

Answer:

130°

Step-by-step explanation:

You need the remaining angle. 50° and the missing angle make up 180°. Therefore, you need to subtract 50 from 180. 180 - 50 = 130. Hence, the missing angle is 130°.

I hope it's ok if I used your photo!

Answer:

  no solution

Step-by-step explanation:

Divide by 4:

  3d -1 = 3d

Subtract 3d:

  -1 = 0 . . . . . . FALSE

There is no value of d that will make this be true. The equation has NO SOLUTION.

Answer:

148

Step-by-step explanation:

a straight line is always 180 degrees. therefore if you subtract 32 from 180 you are left with 148 degrees.

hope this helps

Answer:

D

Step-by-step explanation:

∠ ABD and ∠ ABC are adjacent angles and are supplementary, thus

∠ ABD + 32° = 180° ( subtract 32° from both sides )

∠ ABD = 148° → D