Write an equivalent expression by applying the distributive property (x + y + 3) x (y + 1) = A: 2y2+xy+4 B: 2y + x + 4 C: y2+xy+4y+x+3 Please help math makes me go insane

Step-by-step explanation:

(6x^3 + 3x² + 3) + (2x^3 - 5x + 1)

6x^3 + 2x^3 = 8x^3

3x^2 + 0 = 3x^2

-5x + 0 = -5x

3 + 1 = 4

8x^3 + 3x^2 - 5x + 4 is the answer because you have to put all the terms that were solved together. This will lead to 8x^3 + 3x^2 - 5x + 4. And, standard form is ax^2 + bx + c. So, 8x^3 + 3x^2 - 5x + 4 is the answer.

8x^3 + 3x^2 - 5x + 4

Hope this helped,

Kavitha

Answer:

= 8x³ + 3x² - 5x + 4

Step-by-step explanation:

(6x³ + 3x² + 3) + (2x³ - 5x + 1)

= 6x³ + 3x² + 3 + 2x³ - 5x + 1    remove parentheses

= 6x³ + 2x³ + 3x² - 5x + 1          group like terms

= 8x³ + 3x² - 5x + 3 + 1              add similar elements

= 8x³ + 3x² - 5x + 4

Answer:

B

Given equation: [tex]x^2 = -8x -7[/tex]

To solve the quadratic equation, we will need to set one side of the equation equal to 0. This can be done by subtracting x² on both sides.

[tex]\implies x^2 - x^2= -8x -7 - x^2[/tex]

[tex]\implies 0= -8x -7 - x^2[/tex]

To further simplify, we can factor -1 from the expression on the R.H.S. Then, we can cancel the -1 since there is a 0 on the other side.

[tex]\implies 0= -1(8x + 7 + x^2)[/tex]

[tex]\implies 0= 8x + 7 + x^2 = x^2 + 8x + 7[/tex]

Finally, factor the expression on the right hand side.

Factoring a quadratic equation can be done in 2 ways.

In this method, we split the middle term into two suitable terms. The suitable terms must follow two conditions.

Then, we factor the first two terms of the expression and the last two terms of the expression. Eventually, we will get a common expression. So, we can further factorize to get a product of two expressions.

In this method, we will compare our equation with the standard form equation to determine the a, b, and c variables. Then, we plug the variables into the formula and simplify to get the roots (solutions).

[tex]\text{Quadratic Formula:} \ \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]

We can use any method to solve for the roots. First, let us check whether the middle term could be split into two suitable terms such that those terms could meet the criteria stated above.

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We can see that 8x is the middle term and it can be split into the sum of 7x and x. The product of the (middle term) coefficients is 7. The product of the coefficients (first and last terms) is also 7. Since both products match, we can use the splitting method to factorize the expression.

[tex]\implies 0= x^2 + 8x+ 7[/tex]

[tex]\implies 0= x^2 + x + 7x+ 7[/tex]

Now, factor the first two terms and the last two terms separately.

[tex]\implies 0= x^2 + x + 7x+ 7[/tex]

[tex]\implies 0= x(x + 1) + 7(x+ 1)[/tex]

We can see a common expression. Finally, let us factor the common expression to get a product of two expressions.

[tex]\implies 0= (x + 7)(x + 1)[/tex]

Since the factorized expression equals to 0, we can set each expression (inside the parentheses) equal to 0.

[tex]\implies x + 7 = 0; x + 1 = 0[/tex]

[tex]\implies x = -7; x = -1[/tex]

Now, let us try to solve using the Quadratic formula.

[tex]0= x^2 + 8x+ 7[/tex]

Tip: Standard form: 0 = ax² + bx + c

Comparing both equations will allow us to determine the a, b, c variables.

⇒ a = 1; b = 8; c = 7

Now, let us plug these values into the quadratic formula and simplify.

[tex]\implies \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{8^{2} - 4(1)(7)} }{2(1)}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{64 - 28} }{2}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{36}}{2} = \dfrac{-8\± 6}{2} = \dfrac{-8 + 6}{2},\ \dfrac{-8 - 6}{2} = \dfrac{-2}{2} ,\ \dfrac{-14}{2} = -1 , -7 \ \text{(B)}[/tex]

Therefore, in both methods, the answer is -1, -7 (B).

Learn more about quadratic formula: brainly.com/question/22364785

Learn more about splitting method: brainly.com/question/13874704

please help me with my homework

Answer: (-5)¹¹ of (-5)^11

Step-by-step explanation:

Since the base of the two exponents are teh same at -5, we can subtract the exponents.

5-(-6)=11

Now, we know that the new exponent will be 11, with the base staying the same.

Answer:

36, 29, 22, 15, 8

Step-by-step explanation:

Step 1: State known information

First difference is -7

Third term of the sequence is 22

Step 2: Find first 5 terms

You just need to add and subtract 7 to 22 and the answer 5 times

1. 36 +7

2. 29 +7

3. 22 <- We know 22 is the 3rd term

4. 15 -7

5. 8 -7

Therefore the first 5 terms of the sequence is 36, 29, 22, 15, 8

Step-by-step explanation:

1. volume = πr²h

= π×(5²)×9

= π×225

= 225π

= 707.1 cubic inches

2. volume = lwh

= 5.2 × 1.8 × 2

= 18.72 square feets

Answer:

i believe the answer is A

Step-by-step explanation:

idek

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(-6,2)

Inbox me on fb for more help with math same name as my brainly

Answer:

(-6,2)

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

you can just plug this into a calculator.

OR you could take -3+1 and get -2 and then subtract that from 2 (-3+1=2) and then you get -4

Answer:

-4

Step-by-step explanation:

-3 + (+1)= -2

2(-3 + (+1)) = -4

Answer:

The expression is missing in the question.

The expression is 4x +450

The variable is x and the coefficient is 4

Step-by-step explanation:

In an expression, a variable is a quantity which is not fixed value and can be of any arbitrary value. A variable is the unknown in the expression. In any expression, the variable are represented by alphabets such as a, b, c, x, y or z etc.

The numeric quantity which lies in the front of a variable is known as a coefficient. It can be any numeric values. For example, 9x --- here 9 is the coefficient of variable x, 4x -- here 4 is the coefficient.

Answer:

0

because -8 powered 2 and -8 powered 2 is same. 64-64=0

Step-by-step explanation:

Greetings from Brasil...

According to the statement, one figure is scaled in relation to another, so we can apply similarity to polygons.....

So

BIG/small = BIG/small

or

small/BIG = small/BIG

27/X = 45/35

OR

35/45 = X/27

27/X = 45/35

45X = 27·35

45X = 945

X = 945/45

Answer:

12

Step-by-step explanation:

We are given the expression:

[tex]\frac{5z+x^2}{x}[/tex]

and asked to evaluate when x= 5 and z=7. Therefore, we must substitute 5 for x and z for 7.

[tex]\frac{(5(7)+(5)^2)}{5}[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

First, evaluate the exponent.

(5)²= 5*5= 25

[tex]\frac{(5(7)+25)}{5}[/tex]

Next, multiply 5 and 7.

5*7=35

[tex]\frac{(35+25)}{5}[/tex]

Next, add 35 and 25.

25+25=60

[tex]\frac{60}{5}[/tex]

Finally, divide 60 by 5.

[tex]12[/tex]

The expression (5z+x²)/x when x=5 and z=7 is 12.

Answer:

r = 5 cm

Step-by-step explanation:

A = πr²

78.53 = (3.14)r²

divide by 3.14

25 = r²

r = ±5

r = 5

She paid $640 for the painting

Step-by-step explanation:

her selling price SP = 800

CP+25%of CP = 800

1.25CP=800

CP=640

Answer:

$640

Step-by-step explanation:

paint sold for $800

profit 25%

the price she paid for the painting = $800 / 1.25 = $640

Answer:

24 1/2

Step-by-step explanation:

Every 1/2 is 2 gallons.

1/2 x 2 gallons = 4 gallons.

The whole number in 6 1/2 is 6.

1 x 6 = 6.

Now, we multiply 6 by 4 because each 1 = 4 gallons.

6 x 4 = 24.

There is still an 1/2 left in 6 1/2.

You add that.

Your answer is 24 1/2.

Hope this helps you!

Answer:

After 6 minutes, the oven temperature will be: [tex]125^o[/tex]

Step-by-step explanation:

If the increase in temperature is [tex]10^o[/tex] per minute, then in 6 minutes, the increase in temperature would be [tex]6\,*\,10^o=60^o[/tex], therefore, since the initial temperature of the oven was [tex]65^o[/tex], its temperature after 6 minutes would be:

[tex]65^o+60^o=125^o[/tex]

Answer:

y = |1/4x|

Step-by-step explanation:

The slope is 1/4

Answer:

Step-by-step explanation:

coordinate of O(2,1),Y(3,-2),T(-3,-3)

let the reflected points are O',Y',T'

distance of O from y=2 is 1 unit.

∴ ordinate of O' =1+2(1)=3

or O' is (2,3)

distance of Y from y=2 is2+2=4

ordinate of Y'=-2+2(4)=6

so coordinate of Y' is (3,6)

distance of T from y=2 is (2+3)=5

so ordinate of T' =-3+2(5)=7

coordinate of T' is(-3,7)

Answer: 9

Step-by-step explanation:

plug in numbers to get 3+6

add them

boom

Answer:

D. 9

Step-by-step explanation:

Plug in 3 as x and -2 as y in the expression:

x - 3y

3 - 3(-2)

3 + 6

= 9

Answer:

11) x=1 or x=3.

12) x=2/3 or x=-7.

Step-by-step explanation:

So we have two equations:

[tex]f(x)=3x(2x-6)\\f(x)=3x(x+7)-2(x+7)[/tex]

And we want to solve them. To do so, make each of them equal 0 and then solve for x:

11)

[tex]f(x)=3x(2x-6)\\0=3x(2x-6)[/tex]

Using the Zero Product Property, either one or both of the factor must be zero for this to be true. Therefore, make each factor equal to zero and solve:

[tex]3x=0 \text{ or } 2x-6=0[/tex]

Divide the left by 3. On the right, add 6 and then divide by 2:

[tex]x=0\text{ or } 2x=6\\x=0 \text{ or } x=3[/tex]

Therefore, the solutions to the first equation is:

x=1 or x=3.

12)

[tex]f(x)=3x(x+7)-2(x+7)[/tex]

First, use the distributive property to group the terms together. The equation is equivalent to:

[tex]f(x)=(3x-2)(x+7)[/tex]

Now, set the function to zero and solve:

[tex]0=(3x-2)(x+7)[/tex]

[tex](3x-2)=0 \text{ or } x+7=0\\3x=2 \text{ or } x=-7\\x=2/3 \text{ or } x=-7.[/tex]

Therefore, the answer is:

x=2/3 or x=-7.

Answer:

[tex]\large \boxed{{\bold{11.} \ x=0, \ x=3}} \\ \\ \large \boxed{{\bold{12.} \ x=-7, \ x=2/3}}[/tex]

Step-by-step explanation:

We will set the outputs of the functions to 0 and solve for x.

0 = 3x(2x - 6)

Set factors equal to 0.

First possibility:

3x = 0

x = 0

Second possibility:

2x - 6 = 0

2x = 6

x = 3

0=3x(x+7)-2(x+7)

Take (x+7) as a common factor.

0 = (3x-2)(x+7)

Set factors equal to 0.

First possibility:

x + 7 = 0

x = -7

Second possibility:

3x - 2 = 0

3x = 2

x = 2/3

Your question has been heard loud and clear.

Slope formula when two points are given= y2-y1/x2-x1

Here y2= 2

X2=2

Y1= -4

X1= -1

= 2-(-4)/2-(-1)= 2

Slope of line= 2

Thank you.

Answer:

[tex]\huge \boxed{\mathrm{B. \ 2}}[/tex]

Step-by-step explanation:

The line crosses two points.

The two points are (-1, -4) and (2, 2).

The slope of a line can be found through two points.

[tex]\displaystyle \sf slope = \frac{rise}{run}[/tex]

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

[tex]y_2=2 \\ y_1 = -4 \\ x_2=2 \\ x_1=-1[/tex]

Plug in the values and evaluate.

[tex]\displaystyle m=\frac{2-(-4)}{2-(-1)}[/tex]

[tex]\displaystyle m=\frac{2+4}{2+1}[/tex]

[tex]\displaystyle m=\frac{6}{3}[/tex]

[tex]m=2[/tex]

The slope of the line is 2.

Answer:

14

Step-by-step explanation:

(multiply 2by7)

2×7

=14

Answer:

120

Step-by-step explanation:

First find the discount

200 * 40%

200 * .40

80

Subtract the discount from the original price

200-80

120

The sale price is 120

Answer:

[tex]\huge \boxed{\mathrm{\$ \ 120}}[/tex]

Step-by-step explanation:

Calculating the discount on the jacket.

[tex]200 \cdot 40\% \\ \\ 200 \cdot 0.4 \\ \\ 80[/tex]

The discount on the jacket is $80.

Let’s find the sale price of the jacket.

[tex]\sf sale \ price = original \ price - discount.[/tex]

[tex]200-80 \\ \\ 120[/tex]

The sale price of the jacket is $120.

Work Shown:

Angle PQR = (far arc - near arc)/2

Angle PQR = ( (major arc PR) - (minor arc PR) )/2

Angle PQR = ( (2x+252) - (2x+108) )/2

Angle PQR = 144/2

Angle PQR = 72

Notice how we didn't need to find the value of x at all.

Answer:

-3

Step-by-step explanation:

3-x if x=6

3-6

-3

Hope this helps ;) ❤❤❤

Answer: -3

Step-by-step explanation: In this case, we are given that x = 6.

So we have 3 - 6 which is -3.

Answer:

The correct answer is h = 3.

Step-by-step explanation:

To solve this problem, we should first use the distributive property on the left side of the equation.  This means that we can multiply each of the terms inside the parentheses by -2 (be careful that you distribute the negative as well).  This is modeled below:

5h - 2(11 - h) = h - 4

5h - 22 + 2h = h - 4

Next, we can combine like terms on the left side of the equation.

7h - 22 = h - 4

Now, we can subtract h from both sides of the equation to move all of the variable terms to the left side of the equation.

6h - 22 = - 4

Next, we can add 22 to both sides of the equation to isolate the variable term on the left side of the equation.

6h = 18

Finally, we can divide both sides by 6 in order to get the variable completely isolated.

h = 3

Therefore, the correct answer is h = 3.

Hope this helps!

Answer:

(A) 139°

Step-by-step explanation:

What we are trying to find here is the distance between -27 and 112.

To do this, we have to think of it as a number line.

The distance from -27 to 0 is 27 units, and the distance from 0 to 112 is 112 units.

So the total distance is [tex]112+27=139[/tex]

Hope this helped!

Answer:

Step-by-step explanation:

Given initial population of animals = 300 animals

If the population increases by 23% annualy, yearly increment will be expressed as:

Yearly increment = 23% of 300

Yearly increment = 0.23*300

Yearly increment for = 69

Let the total number of years of be x

Increment after x years = 69x

Increase in population of animals after x years with an annual rate of 23% = Initial population + Increment after x years

= 300 + 69x

Hence, the equation represents a population of 300 animals at the increase and an annual rate of 23% is expressed as 300 + 69x