Simplify. (3 + 2) + (4 + 3) =

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

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.

Answer:

x = [tex]-\frac{3}{b}[/tex]

x = -1

Step-by-step explanation:

The given equation is,

-2(bx - 5) = 16

Dividing by (-2) on both sides of the equation,

[tex]\frac{-2(bx-5)}{(-2)}=\frac{16}{(-2)}[/tex]

(bx - 5) = -8

By adding 5 on both the sides of the equation,

(bx - 5) + 5 = -8 + 5

bx = -3

Dividing by 'b' on both the sides of the equation,

[tex]\frac{bx}{b}=\frac{-3}{b}[/tex]

x = [tex]-\frac{3}{b}[/tex]

If b = 3,

x = [tex]-\frac{3}{3}[/tex]

x = -1

Answer

6 kg/m

Step-by-step explanation:

The linear density is said to give the way the mass is changing it's position and it's a derivatives of mass m here which is differenciated with respect to x position

Given

mass m = 3x^2.

Density ρ= dm/dx =6x

Then if we substitute x=1 into above expresion we have

ρ(1) =6 Kg/m

ρ= 6Kg/m

Hence this is how fast is the mass changing at that position.

Answer:

Step-by-step explanation:

Given , value of b = -4

To find : ( - b )²

plug the value of b

⇒[tex] \sf{( - {( - 4))}^{2} }[/tex]

we know that ,

[tex] \sf{( - ) \times ( - ) = ( + )}[/tex]

⇒[tex] \sf{ {4}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{16}[/tex]

Hope I helped!

Best regards!!

Answer:

5a + 5b

Step-by-step explanation:

13a - 8a + 9b - 4b =

Combine like terms. 13a and -8a are like terms and can be combined.

9b and -4b are like terms and can be combined.

= 5a + 5b

Answer:

Step-by-step explanation:

[tex]13a-8a+9b-4b\\\mathrm{Add\:similar\:elements:}\:13a-8a=5a\\=5a+9b-4b\\\mathrm{Add\:similar\:elements:}\:9b-4b=5b\\=5a+5b[/tex]

Answer:

i think this is the answer

Answer:

the answer is [tex]\frac{3}{2}[/tex] or 1.5 or 1[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

(-6,2)

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

Answer:

(-6,2)

Step-by-step explanation:

Answer:

Buy stuff and sell them at a higher price

Step-by-step explanation:

Answer:

get a job

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

x - 7 = 18

Adding 7 to both sides (to get rid of the -7 on the left side) gives us:

x - 7 + 7 = 18 + 7

x = 25

Answer:

25 is the correct answer

Step-by-step explanation:

i got it right on the test

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:

Below

Step-by-step explanation:

Let D be the diagonal of this square.

D forms with AB and BC a right triangle where D is the hypotenus.

We will apply then the Pythagorian theorem

●The Pythagorian theorem

● D^2 = AB^2 + BC^2

ABCD is a square, so AB=BC

● D^2 = AB^2 + AB^2

● D^2 = 2AB^2

We khow that is D= 5 cm

● 25 = 2AB^2

● 25/2 = AB^2

● 5/√2 = AB

AB is 5√2 cm

■■■■■■■■■■■■■■■■■■■■■■■■■

The perimeter is:

● P = 4AB

● P = 4×(5/√2)

● P = 20/√2

● P = 10×2/√2

● P = 10√2 cm

■■■■■■■■■■■■■■■■■■■■■■■■■■

The area is

● A = AB^2

● A = (5/√2)^2

● A = 25/2 cm^2

Answer:

Step-by-step explanation:

the sides of a square are equal ( AB=BC=CD=DA)

diagonal of the square creates two right angle triangle

to find the side of the triangle we apply the Pythagorean theorem:

a²+b²=c² ( let AB=a, and BC=b)

2a²=25 ( since AB=BC=a)

a²=25/2

a=(5√2)/2 cm

a=3.54 ( rounded to the nearest 10)

perimeter = 4a

P=4(5√2/2)

P=10√2 cm

Area=a²=(5√2/2)²=25/2=12.5 cm^2

Answer:

$24

Step-by-step explanation:

1/4x + 1/3x + 8 = 22

1/4x + 1/3x = 7/12x

7/12x + 8 = 22

22 - 8 = 14

7/12x = 14

14/ 7/12

x = 24

Answer:

x = ln9

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] = nlogx , lne = 1

Given

[tex]e^{x}[/tex] = 9 ( take the ln of both sides )

ln[tex]e^{x}[/tex] = ln9, thus

xlne = ln9, that is

x = ln9

Answer:

1723

Step-by-step explanation:

10 x 70=700

Answer:

1723

Step-by-step explanation:

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:

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:

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

Answer:

Zero is an integer which is indicated by the symbol 0 in numbers and it is used to indicate that the count of an item when there are non of the item present which is one of the reasons zero along with the fact that it is the number between positive and negative numbers, why it is not associated with a positive or negative sign.

Step-by-step explanation:

A number which is not zero is said to be a non-zero number and the roots of a function is known as the zeros of the function.

Answer:

The multiplicative inverse of -0.7 is -1/0.7

hope it helps

Answer:

y = |1/4x|

Step-by-step explanation:

The slope is 1/4

Answer:

When both the conditions hold true, F is prime.

Step-by-step explanation:

AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.

  AB

+ CD

--------

  EF

1st condition, B and D are consecutive.

Adding B and D gives us F.

Possible values can be (F being the unit value after adding not considering the carry over):

B + D = F

1+2=3

2+3=5

3+4=7

4+5=9

5+6=1

6+7=3

7+8=5

8+9=7

Here F is not prime (because 9 is not prime).

Now, let us consider the 2nd condition as well.

i.e. C = 8

For the following

  AB

+ CD

--------

  EF

C is 8 then A must be 1 because any value other than 1 for A will make the sum of A and C greater than 9 and there will be a carry which is not the case here.

So, E = 8 + 1 = 9

Now, B  and D are consecutive and can not be 1, 8 or 9.

So, possible values are:

B + D = F

2 + 3 = 5

3 + 4 = 7

Here F is prime.

So, when both the conditions hold true, F is prime.

Answer:

The minimum sample size needed for each city  = 922

Step-by-step explanation:

From the information given:

the objective is to find the minimum sample size needed for each city so that the margin of error not to exceed 6%.

If we take a look at the question very well:

we are only given the confidence interval of 99% and the margin of error of 6%

we were not informed or given the value or estimate of any proportions>

so we assume that:

[tex]p_1 =q_ 1= p_2 = q_2 = 0.5[/tex]

At confidence interval of 0.99 , the level of significance = 1 - 0.99 = 0.01

The critical value for [tex]z_{\alpha/2} = z_{0.01 /2}[/tex]

= [tex]z_{0.005}[/tex] = 2.576

The minimum sample size needed can be calculated by using the formula :

[tex]n = \dfrac{z^2_{\alpha/2}}{E^2}(p_1q_1+p_2q_2)[/tex]

[tex]n = \dfrac{2.576^2}{0.06^2}((0.5 \times 0.5)+(0.5 \times 0.5))[/tex]

[tex]n = \dfrac{6.635776}{0.0036}(0.25+0.25)[/tex]

[tex]n =1843.271 \times (0.5)[/tex]

n = 921.63

n [tex]\simeq[/tex] 922

∴ The minimum sample size needed for each city  = 922

Answer:

The pints of each of the two existing types of drinks are 22 and 88 respectively.

Step-by-step explanation:

We are given that the Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure fruit juice.

Let the first type of fruit drink pints in the mixture be 'x' and the second type of fruit drink pints in the mixture be 'y'.

So, according to the question;

                                   x + y = 110

                                   x = 110 - y  ---------------- [equation 1]

                             [tex]0.70x+0.95y=0.90\times 110[/tex]

                              [tex]70x+95y=9900[/tex]

                              [tex]70(110-y)+95y=9900[/tex]

                              [tex]7700-70y+95y=9900[/tex]

                              [tex]25y=9900-7700[/tex]

                                [tex]y=\frac{2200}{25}[/tex]

                                y = 88

Now, putting the value of y in equation 1 we get;

                               x = 110 - y

                               x = 110 - 88 = 22

Hence, the pints of each of the two existing types of drinks are 22 and 88 respectively.

Answer:

-6

Step-by-step explanation:

(-17+4+1-6)=-18

-18/-3=6

6*-1=-6

Answer:

-6

Step-by-step explanation:

(-17+4+1-6)÷(-3)×(-1)

PEMDAS

Parentheses first

(-17+4+1-6)÷(-3)×(-1)

Add and subtract inside the left parentheses

(-18)÷(-3)×(-1)

Multiply and divide from left to right

6 * -1

-6

Answer:

[tex]x = \frac{770}{16}[/tex]

Step-by-step explanation:

Given

[tex]x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60[/tex]

Required

Solve for x

[tex]x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60[/tex]

Start by solving the bracket [Take LCM]

[tex]x + \frac{x}{7} + \frac{1}{11} (\frac{7x + x}{7}) = 60[/tex]

[tex]x + \frac{x}{7} + \frac{1}{11} (\frac{8x}{7}) = 60[/tex]

Open the bracket

[tex]x + \frac{x}{7} + \frac{8x}{77} = 60[/tex]

Take LCM

[tex]\frac{77x + 11x + 8x}{77} = 60[/tex]

[tex]\frac{77x + 11x + 8x}{77} = 60[/tex]

[tex]\frac{96x}{77} = 60[/tex]

Multiply both sides by 77

[tex]77 * \frac{96x}{77} = 60 * 77[/tex]

[tex]96x = 60 * 77[/tex]

Divide both sides by 96

[tex]\frac{96x}{96} = \frac{60 * 77}{96}[/tex]

[tex]x = \frac{60 * 77}{96}[/tex]

Divide the numerator and denominator by 6

[tex]x = \frac{10 * 77}{16}[/tex]

[tex]x = \frac{770}{16}[/tex]

Answer:

48.125

Step-by-step explanation:

Answer:

x = 7.6°, so A = 18.8°

Step-by-step explanation:

What we need to know in order to utilize algebra is the total sum of all triangle's angle. It's 180°. So, we can write

25 + 17x - 1 + 3x - 4 = 180

20x + 28 = 180

20x = 152

x = 7.6°

Now what you need to do is substitute 7.6° into each expression 17x - 1 and 3x - 4.

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:

It would be B

Step-by-step explanation:

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.