Mathematics High School

## Answers

**Answer 1**

**Answer:**

k = 20

**Step-by-step explanation:**

Expressing 18, 36 and 54 as a product of their prime factors

18 = 2 × 3 × 3 = 2 × 3²

36 = 2 × 2 × 3 × 3 = 2² × 3²

54 = 2 × 3 × 3 × 3 = 2 × 3³

The common prime factors are 2 and 3²

HCF = 2 × 3² = 2 × 9 = 18

Thus

k - 2 = 18 ( add 2 to both sides )

k = 20

## Related Questions

Classify the number (choose all that apply): -20 *

Whole Number

Integer

Rational Number

Irrational Number

### Answers

**Answer:**

Whole Number

Integer x

Rational Number

Irrational Number x

**Step-by-step explanation:**

How to solve 1.25 x 10^-4

### Answers

**Answer:**

0.000125x

**Step-by-step explanation:**

Simplify 9 - {x-(7 + x)}

16

-2x + 16

2x+2

0 - 22+2

### Answers

answer **: **

**16**

explanation **:**

**9 - (x - (7 + x))**

**9 - (x - 7 - x)**

**9 - (-7)**

**9 + 7**

**= 16**

8x + 1 = -8 - X

Answer? Please

### Answers

**Answer:**

[tex]x = -1[/tex]

**Step-by-step explanation:**

-Solve for [tex]x[/tex] :

[tex]8x + 1 = -8 - x[/tex]

-Add both side by [tex]x[/tex] :

[tex]8x + 1 + x = -8 - x + x[/tex]

[tex]9x + 1 = -8[/tex]

-Subtract both sides by [tex]1[/tex] :

[tex]9x + 1 - 1 = -8 - 1[/tex]

[tex]9x = -9[/tex]

-Divide both sides by [tex]9[/tex] :

[tex]\frac{9x}{9} = \frac{-9}{9}[/tex]

[tex]x = -1[/tex]

So, the value of [tex]x[/tex] is [tex]-1[/tex].

**Answer:**

[tex] \boxed{\sf x = - 1} [/tex]

**Step-by-step explanation:**

[tex] \sf Solve \: for \: x: \\ \sf \implies 8x + 1 = - 8 - x \\ \\ \sf Add \: x \: to \: both \: sides: \\ \sf \implies 8x + x + 1 = - 8 + (x - x ) \\ \\ \sf x - x = 0 : \\ \sf \implies 8x +x + 1 = - 8 \\ \\ \sf 8x + x = 9x : \\ \sf \implies 9x + 1 = - 8 \\ \\ \sf Subtract \: 1 \: from \: both \: sides: \\ \sf \implies 9x + (1 - 1 )= - 8 - 1 \\ \\ \sf 1 - 1 = 0 : \\ \sf \implies 9x = - 8 - 1 \\ \\ \sf - 8 - 1 : \\ \sf \implies 9x = - 9 \\ \\ \sf Divide \: both \: sides \: of \: 9 x = 9 \: by \: 9: \\ \sf \implies \frac{9x}{9} = - \frac{9}{9} \\ \\ \sf \frac{9}{9} = 1 : \\ \sf \implies x = - 1[/tex]

half of a number,increased by 4,is 18, what is that number

### Answers

**Answer:28**

**Step-by-step explanation:**

**28/2=14**

**14+4=18**

Answer: 14

28/2=14

14+4 = 18

use vieta's formulas to find the sum and the product of the roots of the equation: x^2-210x=0

### Answers

**Answer:**

sum of the roots: [tex]x_1+x_2=0[/tex] product of the roots: [tex]x_1x_2=-210[/tex] **Step-by-step explanation:**

[tex]x^2-210=0\quad\implies\quad a=1\,,\ b=0\,,\ c=-210\\\\b^2-4ac=0-(-810)=810>0[/tex]

From Vieta's formulas applied to quadratic polynomial we have:

if [tex]b^2-4ac\geqslant0[/tex] then

sum of roots: [tex]x_1+x_2=-\dfrac ba=-\dfrac{0}2=0[/tex]

product of the roots: [tex]x_1x_2=\dfrac ca=\dfrac{-210}1=-210[/tex]

Find the zeros of the function g(x) = 4x^2 - 484

### Answers

**Answer:**

**Step-by-step explanation:**

There are two **zeros of the function **g(x) that is 11 , -11

What are zeros of the function?

The **zero of a function** is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

According to the question

g(x) = [tex]4x^{2}[/tex] - 484

To find the **zeros of a function**, find the values of x where g(x) = 0.

Therefore,

0 = [tex]4x^{2}[/tex] - 484

0 = [tex]x^{2} - 121[/tex]

0= [tex](x-11)(x+11)[/tex]

i.e ,

[tex]x = 11 ,-11[/tex]

Hence , there are 2 **zeros of the function **g(x) that is 11 , -11 .

To know more about **zeros of the function **here :

https://brainly.com/question/22101211

# SPJ2

I

Eugenia quiere comprar un departamento de interés social

que cuesta $320,520.00. En la inmobiliaria, le ofrecen: la

mitad al contado y el resto en 12 cuotas fijas iguales. ¿Cuál

es el valor de la cuota?

### Answers

**Answer:**

The answer is "**13355 pesos per installment**"

**Step-by-step explanation:**

The social representation division spends $320,520, But it offers half money, which means we'll pay for half at $320,520, which is equal to $160,260. It divided into equal-sized fixed installment payments but we said, that we took half at $32,520, which would be equal to $13,355 pesos, which would be equal to $1,355 per installment.

Suppose that x = 2+2t and y = t - 21. If x = 8, what is y?

### Answers

**Answer:**

[tex]y=-18[/tex]

**Step-by-step explanation:**

So we know that:

[tex]x=2+2t\text{ and}\\y=t-21[/tex]

And we want to figure out the value of y when x is 8.

So first, substitute 8 into the first equation:

[tex]8=2+2t[/tex]

Solve for t. Subtract 2 from both sides:

[tex]6=2t[/tex]

Divide both sides by 2:

[tex]t=3[/tex]

Now, substitute this into the second equation for t:

[tex]y=(3)-21[/tex]

Subtract:

[tex]y=-18[/tex]

So, the value of y is -18.

And we're done!

What would be the area of a piece of metal that is 50 cm wide by 7 cm long?

-Science

### Answers

**Answer:**

50*7

**Step-by-step explanation:**

bcoz the formula is L*b

15.24 x 1.64 the answer needs to be converted from us dollars to British pounds and can i have steps to plz

### Answers

**Answer:**

**19.334**

**Step-by-step explanation:**

**First I multiplied.**

15.24 x 1.64 = 24.9936

**Then I convert my answer to British pounds.**

**24.9936 = 19.334 British Pound Sterling**

**Have a blessed day and hope this helps.**

A cab charges customers a one time fee plus a fee per mile driven. If the cab drove someone for 7 miles and charged them $42 and also drove someone else for 10 miles and charged them $57. What is the rate of change in this scenario?

### Answers

Answer:

7

Step-by-step explanation:

Simplify 29-4.37+(-5.68)

### Answers

**Answer:**

18.95

**Step-by-step explanation:**

I hope this is correct!

Eva wants to buy a bicycle.The bicycle costs $240.Eva already has $42 saved.She babysits for $12 per hour.Eva needs to babysit for h hours to earn enough money to buy the bicycle.

### Answers

**Hi, **

**She lacks 240-42 = 198 **

**She earns 12 usd per hours so : 198 /12 = 16.5**

The required hour **Eva **needs to **babysit **is given as 16.5 hours.

Given that,

Eva wants to buy a bicycle. The **bicycle costs **$240.Eva already has $42 saved. She babysits for $12 per hour. Eva needs to babysit for h hours to earn enough money to buy the bicycle is to be determined.

What is arithmetic?

In **mathematics**, it deals with numbers of **operations **according to the **statements**. There are four major **arithmetic operators**, addition, subtraction, multiplication and division,

Here,

Eva had $42

Remaining money = 240 - 42 = $198

She babysits for $12 per hour,

For hours she needs to babysit to earn $198 = 198 / 12 = 16.5 hours,

Thus, the required **hour **Eva needs to **babysit **is given as 16.5 hours.

Learn more about **arithmetic **here:

https://brainly.com/question/11424589

#SPJ5

In a geometric series, the sum of the first three terms is 14.25 and the sum of the first four terms is

24.375. Find the first term and the common ratio.

First term =

Common ratio =

### Answers

**Answer:**

Ratio: 3/2

First Term: 3

**Step-by-step explanation:**

The** first term **of the geometric sequence **is 3 **and the** common ratio is 3/2**

Geometric series are is defined as the **sum** of the** sequence of numbers. **

The sum of the **nth term** of a **geometric sequence** is expressed as:

[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]

If the **sum **of the** first three terms **is** 14.25**, then;

n = 3

S₃ = 14.25

Substitute into the formula

[tex]S_3=\frac{a(r^3-1)}{r-1}\\14.25=\frac{a(r^3-1)}{r-1} ................. 1[/tex]

Also, if the sum of the first four terms is 24.375, then:

[tex]S_4=\frac{a(r^4-1)}{r-1}\\24.375=\frac{a(r^4-1)}{r-1} ................. 2[/tex]

Divide equations 1 and 2

[tex]\frac{14.25}{24.375}=\frac{r^3-1}{r^4-1} \\\\14.25r^4-14.25=24.3745r^3-24.375\\14.25r^4-24.3745r^3 =-24.375 + 14.25\\ 14.25r^4-24.3745r^3 =-10.125\\ 14.25r^4-24.3745r^3+10.125=0[/tex]

On factorizing:

r = 3/2

substitute r - 3/2 into equation 1

From 1:

[tex]14.25=\frac{a((3/2)^3-1)}{3/2-1} \\14.25=\frac{a(27/8-1)}{3/2-1} \\14.25=\frac{a(19/8)}{0.5} \\\frac{19a}{8} = 14.25 * 0.5\\ \frac{19a}{8} = 7.125\\19a=57\\a=\frac{57}{19}\\a= 3\\[/tex]

This shows that the** first term is 3 **and the** common ratio is 3/2**

Learn more here: https://brainly.com/question/9300199

Point Q is the midpoint between points P and R on a number line. If the coordinate of point Q is 6 and the coordinate of point P is -5, what is the coordinate of point R? Group of answer choices

### Answers

**Answer:**

[tex]R = 17[/tex]

**Step-by-step explanation:**

**Given**

[tex]P = -5[/tex]

[tex]Q = 6[/tex]

**Midpoint: Q**

**Required**

**Determine R**

**Since Q is the midpoint, then**

[tex]Q = \frac{1}{2}(P + R)[/tex]

**Substitute values for P and Q**

[tex]6 = \frac{1}{2}(-5 + R)[/tex]

**Multiply both sides by 2**

[tex]12 = -5 + R[/tex]

**Add 5 to both sides**

[tex]12 + 5 = -5 + 5 + R[/tex]

[tex]17 = R[/tex]

[tex]R = 17[/tex]

Drew soda lemonade and apples at the school Fair he's sold a total of $64 if he sold $21 in lemonade how many dollars worth of apples did he sell

### Answers

$43 because 64-21 is 43

**Answer:**

$43

**Step-by-step explanation:**

We know the total amount of money Drew earned from selling = $64. Since he is only selling two items, lemonade and apples, we can turn the info into an equation: lemonade + apples = $64 (or L + A = 64)

We also know that he sold $21 in lemonade. If we plug that into our new equation, it looks like this:

21 + A = 64

From there we just need to find A (the amount of money he earned from selling apples). We can do this by subtracting 21 from 64:

A = 64 - 21

**A = $43**

How many solutions does the following equation have?

-4(x+ 5) = -4x – 20

### Answers

**Answer:**

infinite solutions

**Step-by-step explanation:**

-4(x+ 5) = -4x – 20

Distribute

-4x-20 = -4x-20

Add 4x to each side

-20 = -20

This is always true so there are infinite solutions

**Answer: Infinite number of solutions; **if you need the answer, it will be** all real number**

**Step-by-step explanation:**

To find out how many solutions a equation has, you need to first simplify it.

Given

-4(x+5)=-4x-20

Distributive property

-4x-20=-4x-20

Add -4x on both sides

-20=-20

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

As seen above, both sides have the same expression. This means any number that is substitute as x will give the same result on both sides so there are infinite number of solution.

All real number (ARN) will be the answer for this equation.

I need help with this (simplify 8^3)

### Answers

**Answer:**

512

**Step-by-step explanation:**

8 = 2^3

Therefore,

8^3

= (2^3)^3

= 2^(3*3)

= 2^9

= 512

Thus, 8^3 = 512

Please mark my answer as Brainliest!!!

**Answer:**

so you just need to do 8x8x8 do the number by itself 3 times so the awnser would be 512 :)

**Step-by-step explanation:**

what is the decimal equivalent of 16/3

### Answers

Answer:

5.33333

How to:

16/3

**Answer:**

5.3333

**Step-by-step explanation:**

2. Given: RS and ST share endpoint S. Critique the reasoning of others. Based on this information, Michaela says that the Segment Addition Postulate justifies the statement that RS + ST = RT. Is there a flaw in Michaela's reasoning, or is she correct? Explain. TAL

### Answers

**There is a slight flaw. She is only correct if all three points are on the same line. **

If S is on segment RT, then segment RT can be broken up into RS and ST. Through the segment addition postulate, we can then say

RS+ST = RT

So put another way, Michaela's claim is only true if angle RST is 180 degrees.

However, if angle RST is some other angle, then saying RS+ST = RT is not correct. So Michaela needs to clarify that point S is on segment RT. Or she could say that all three points are on the same straight line.

**A diagram is provided below.**

Side note: in the figure on the right, RS+ST adds up to something larger than RT. This is due to the triangle inequality theorem. That theorem states that adding any two sides of a triangle adds to something larger than the third remaining side.

(4/5 -7/5) + 1/5= Please hurry

### Answers

it is = -0.4, negative zero point four

Finding the inverse of linear functions

### Answers

**Answer:**

y = -1/2x - 4

**Step-by-step explanation:**

To find the inverse of a linear function, simply switch the x and y positions. Solve for y.

y = -2x - 8

x = -2y - 8

x + 8 = (-2y - 8) + 8

x + 8 = -2y

(x + 8)/-2 = (-2y)/-2

-1/2x - 4 = y

y = -1/2x - 4

Which statement is true about the ratios of squares to circles in the tables? O The ratios in Table A are greater than the ratios in Table B. O The ratios in Table B are greater than the ratios in Table A. o Only some of the ratios in Table A are greater than the ratios in Table B. O The ratios in Table A are equal to the ratios in Table B.

### Answers

[B] The ratios in Table B are greater than the ratios in Table A.

**Step-by-step explanation:**

Can i get brainlist

**Answer: Answer is b **

**Step-by-step explanation: I took the test and got 100%**

If f(x) = 2x+5 and the

domain off is { 2,8,1:4},

what is the range of

f (x)?

### Answers

**Answer:**

work is shown and pictured

How many pairs of consecutive natural numbers have a product of less than 40000? I am in 5th grade. This is supposed to be easy for me, but it's not. I would greatly appreciate any help at all. Thank you, Anonymous

### Answers

**Answer:**

There are 199 pairs of consecutive natural numbers whose product is less than 40000.

**Step-by-step explanation:**

We notice that such statement can be translated into this inequation:

[tex]n \cdot (n+1) < 40000[/tex]

Now we solve this inequation to the highest value of [tex]n[/tex] that satisfy the inequation:

[tex]n^{2}+n < 40000[/tex]

[tex]n^{2}+n -40000<0[/tex]

The Quadratic Formula shows that roots are:

[tex]n_{1,2} = \frac{-1\pm\sqrt{1^{2}-4\cdot (1)\cdot (-40000)}}{2\cdot (1)}[/tex]

[tex]n_{1,2} = -\frac{1}{2}\pm \frac{1}{2} \cdot \sqrt{160001}[/tex]

[tex]n_{1} = -\frac{1}{2}+\frac{1}{2}\cdot \sqrt{160001}[/tex]

[tex]n_{1} \approx 199.501[/tex]

[tex]n_{2} = -\frac{1}{2}-\frac{1}{2}\cdot \sqrt{160001}[/tex]

[tex]n_{2} \approx -200.501[/tex]

Only the first root is valid source to determine the highest possible value of [tex]n[/tex], which is [tex]n_{max} = 199[/tex]. Each natural number represents an element itself and each pair represents an element as a function of the lowest consecutive natural number. Hence, there are 199 pairs of consecutive natural numbers whose product is less than 40000.

Find the nth term of these sequences.

1 2 3 4 ...... n

3 6 9 12

### Answers

1st answer is n and 2nd is 3n.

**Step-by-step explanation:**

1st one....

first term (a) = 1

common difference (d) = 2-1 =1

no. of term (n) = n

Now,

nth term = a + ( n-1 ) d

= 1 + ( n-1 ) 1

= 1 + n - 1

= n

2nd one...

first term (a) = 3

common difference (d) = 6-3 =3

no. of term (n) = n

Now,

nth term = a + ( n-1 ) d

= 3 + ( n-1 ) 3

= 3 + 3n - 3

= 3n

a=3

d =u2 -u1=6-3=3

un=n/2(2a+(n-1)d)

=n/2 (6+3n+3)

=n/2 (3n+9)

ihope i was help ful

hey answer these 3 questions 1/2 of 18 equals ? and my second question is 12/ times 18 equal what? and last 18 multiplied by 1/2 is less,equal or greater than 18

### Answers

Twelve times 18 is 216

10. | 23 | + | 19 | = I 19 I =

### Answers

|23| + |19| = 42 if that’s what you meant

James uses the Distributive Property to find how many cans of paint are in the art supply closet. There are 5 boxes in the closet. Each box holds 14 cans.

### Answers

Answer:

70 cans of paint

Step-by-step explanation:

We are told in the question that:

1 box holds = 14 cans of paint

5 boxes =

Cross Multiplying

5 boxes will hold = 5 × 14

= 70 cans of paint

This question, requires that we use Distributive property

Distributive property states that: when 2 factors or numbers are multiplied together the result will be the same as splitting on of the numbers(factors) into two distinct numbers, multiplying both number by the other factor, and adding together both products.

Applying the definition above to solve the question, we would be splitting the number of boxes which is 5 into 2 distinct number = 2 and 3

As , 2 + 3 = 5

Hence, we have:

14 × 5 = 14( 2 + 3)

70 = 28 + 42

70 cans of paint = 70 cans of paint.

The numbers of cans of paint that are in the art supply closet is 70 cans of paint