MATHEMATICS
HIGH SCHOOL

A. Write an expression that shows the distance from Daniel's house to the swimming pool.

B. Write an expression that shows the distance from Daniel's house to his Dr's office

C. if b=3, is the swimming pool or Dr's office closer to Daniel's house? How much closer

Answer:

Answer:

A. ⇒ The expression is b + 3

B. ⇒ The expression is 2b - 4

C. ⇒ The Dr's office is closer by 4 miles

Step-by-step explanation:

A.

∵ The distance between Daniel's house and his school is b miles

∵ The swimming pool is 3 miles farther from his school

∴ The distance between Daniel's house and the swimming pool is b + 3

B.

∵ The distance from Daniel's house to his Dr's office is 4 less than twice the distance from home to Daniel's school

∵ The distance between Daniel's house and his school is b

∴ The expression of distance from Daniel's house to his Dr's office is

2b - 4

C.

∵ b = 3

∴ The distance between his house and swimming pool is:

3 + 3 = 6 miles

∴ The distance between his house and Dr's office is:

2(3) - 4 = 2 miles

∴ The Dr's office is closer to Daniel's house than the swimming pool by:

6 - 2 = 4 miles

HIGH SCHOOL

Julia wrote a linear equation in standard form as –6x – 3y = 10. Arthur noticed that the equation was not written in standard form and wants to tell Julia how to fix it. What advice should he give her?

Multiply both sides of the equation by –1, so that the value for A is positive.

Answer:

A

Step-by-step explanation:

MIDDLE SCHOOL

What is 75 students increased by 80%

5 just simply add in order to get 80

80/100=0.8

75*0.8=60

75+60=135

75*0.8=60

75+60=135

MIDDLE SCHOOL

What's the answer to 3(x-4)=12x

Answer:

x = - 4/3

Step-by-step explanation:

Distribute:

3x - 12 = 12x.

-12 = 9x

x= - 12/9 or - 4/3

3(x-4)=12x

multiply the bracket by 3

(3)(x)=3x

(3)9-4)=-12

3x-12=12x

move 3x to the other side

sign changes from +3x to -3x

3x-3x-12=12x-3x

-12=9x

divide both sides by 9 to get x by itself

-12/9=9x/9

-12/9=x

reduce -12/9 by dividing by 3

-12/3=-4

9/3=3

answer:

-4/3 or - 1 1/3

MIDDLE SCHOOL

(X to the fourth power) squared equals

Answer:

Step-by-step explanation:

Because of the power of a power property, which states that , where m and n are real numbers, the expression you mentioned can be simplified by applying this property like this:

MIDDLE SCHOOL

If the sales tax in your city is 10.8%, and an item costs$191 before tax, how much tax would you pay on that item?

In this question it is important to note down all the information's that are already provided. Then the problem would become easy to solve and the correct answer can be reached in no time at all.

Percentage of sales tax charged = 10.8%

Cost of an item before sales tax = $191

Amount of tax that needs to be paid = (10.8/100) * 191

= 2062.8/100

= 20.628

= 20.63

Then the total amount of sales tax that need to be paid is $20.63. I hope the procedure of doing such problems is clear and you got the answer that you were looking for.

Percentage of sales tax charged = 10.8%

Cost of an item before sales tax = $191

Amount of tax that needs to be paid = (10.8/100) * 191

= 2062.8/100

= 20.628

= 20.63

Then the total amount of sales tax that need to be paid is $20.63. I hope the procedure of doing such problems is clear and you got the answer that you were looking for.

MIDDLE SCHOOL

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula P = 1 /10 x (300 − x) provided that 0 ≤ x ≤ 200. How many ovens must be manufactured in a given week to generate a profit of $1610?

Answer:

Number of ovens must be manufactured in a given week to generate a profit of $1610 is 70

Step-by-step explanation:

We are given

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula

provided that 0 ≤ x ≤ 200

We are given

profit is $1610

so, we can set P=1610

and then we can solve for x

Multiply both sides by 10

now, we can factor it

we can solve for x

and we get

Since, x=230 does not lie on 0 ≤ x ≤ 200

So, we will consider only x=70

So,

Number of ovens must be manufactured in a given week to generate a profit of $1610 is 70

MIDDLE SCHOOL

In triangle ABC, angle ABC is a right angle, AB =3 units. Triangle ABC is dilated by a scale factor of 0.5 with point B as the center of dilation, resulting in the image triangle A’B’C’. Which statement about A’B’ is true?

Answer:

438

Step-by-step explanation:

the answer is

A'B' is 1.5 units long and lies on the same line as AB

because B is the center, so B=B' A B A' B' lie on the same line as AB

COLLEGE

3-3x6+2=what is correct answer This is how I did it:

3 - 1(3x6)+2=

-1x3= -3

-1x6= -6

-3x-6= +18

3+18+2= 23

Is it correct 2 add parentheses around 3x6 and then add an "invisible" 1 in front of the parentheses?

No, because only three is negative when you multiply by six... you could just do

3-3x6+2

3-18+2

-15+2

-13

3-3x6+2

3-18+2

-15+2

-13

HIGH SCHOOL

18. Let z = a + bi represent a general complex number. As noted in the lesson, the conjugate of z, abbreviated conj(z) or conj(a + bi) is the complex number a-bi. Also, the modulus of z, modulus(z) is the "size" of z, or √(a2 + b2). Which of the following is true for all complex numbers? A) All of the following

B) z*conj(z) = [modulus(z)]2

C) z + conj(z) = 2a

D) z - conj(z) = 2bi

E) None of the above

19. Using the definition of "size" of z from problem #18, which of the following is largest?

A) 3i

B) -7

C) 4

D) -2i

E) 4 + 4i

F) None of the above

Question (18):

Answer: (A) All of the following

(I am using in place of conj(z)

Question (19):

Answer: (B) -7

modulus of -7 is sqrt(49)=7

the other choices are all < 7