Which of the following is an equation of a line that passes through the point
(
−
10
,
2
)
and is perpendicular to the line
4
x
+
5
y
=
15
?

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:4\pm c [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given expression is :

[tex]\qquad \tt \rightarrow \: 5 - |c + 1|[/tex]

[tex]\qquad \tt \rightarrow \: 5 - 1 - |c|[/tex]

[ as 1 is a positive number, it can come out of modulus function as it is ]

[tex]\qquad \tt \rightarrow \:4- |c| [/tex]

Now, there are two cases possible.

Case 1 :

[tex]\qquad \tt \rightarrow \: 4- c[/tex]

[ if c is a positive number, it will come out of modulus as it is ]

Case 2 :

[tex]\qquad \tt \rightarrow \: 4 - (-c)[/tex]

[tex]\qquad \tt \rightarrow \: 4 + c[/tex]

[ if b is a negative number, it will come out of modulus with a negative sign, to make the overall term out of modulus positive ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

For equation f/3-1=1 the value of f is 6

In this question, we have been given an equation f/3-1=1

We need to solve given equation for f.

⇒ f / 3 - 1 = 1                        ................(Given equation)

⇒ f/3 = 1 + 1                            .................(add 1 to each side)

⇒ f/3 = 2                            

⇒ f = 2 × 3                           ....................(Multiply each side by 3)

⇒ f = 6

Therefore, For equation f/3-1=1 the value of f is 6

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ1

Answer:

y=84x

Step-by-step explanation:

The distributive property should be used to rewrite each expression without parenthesis as follows:

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a specific number, the same output (result) would be produced as when each addend is multiplied respectively by the number, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

a(b + c) = ab + ac.

In conclusion, the distributive property of multiplication can be used to evaluate and rewrite a mathematical expression as shown above.

Read more on distributive property here; brainly.com/question/24014491

#SPJ1

On evaluating the value of the expression  [4.2−3(2.1)] + 1 (-0.2)² is -2.06 .

In the question ,

the expression is given as

[4.2−3(2.1)] + 1 (-0.2)²

the value of (-0.2)²= (-0.2)*(-0.2)

                              = 0.04

Substituting the value of (-0.2)² in expression , we get

=[4.2−3(2.1)] + 1*0.04

=[4.2−3(2.1)] + 0.04

Solving the terms inside [ ] , we have

multiplying 3 with 2.1 we get

3*2.1= 6.3

Substituting it in the expression above we get

= [4.2−6.3] + 0.04

Simplifying further , we get

= -2.1 + 0.04

= -2.06

Therefore , on evaluating the value of the expression  [4.2−3(2.1)] + 1 (-0.2)² is -2.06 .

Learn more about Expressions here

https://brainly.com/question/13961297

#SPJ1

Answer:

Step-by-step explanation:

The answer is -2.06.

hope you get a good grade!!!

Simplification the expression in scientific notation 3.6 x 10^(-5)

What is Simplification ?

To implify is to make something simple. In mathematics, simply or simplification means reducing the expression/fraction/problem in a simpler version. Calculations and problem-solving techniques simplify the issue.

We have to multiply the expression

(9x10^-3) (4x10^-3)

We can rewrite this multiplication as

(9 x 4) x (10^-3 x 10^-3)

Now, use the exponent rule,

a^n x a^m = a^(n+m)

(9 x 4) x (10^(-3-3))

(9 x 4) x (10^(-6))

36 x 10^(-6)

Finally, write in scientific notation

3.6 x 10^(-5)

Hence, the scientific notation of the expression is 3.6 x 10^(-5)

To learn more about Simplification click on the link

https://brainly.com/question/723406

#SPJ9

Answer:

6000

Step-by-step explanation:

6000

divide by 12

72000 ÷ 12 = 6000

part 2

often to get the yearly salary if you have an hour salary

quickest math to get that is to multiply by 20

so if someone makes 20 an hour its probably

40000 per year

Answer:

$6,000

Step-by-step explanation:

Because his yearly salary is $72,000 (72k).

You need to divide $72,000 by 12, because there is 12 months in a year.

Hope this helps! If you need further explanation, I’ll be happy to help!

<3

A fter solving system of equations, we can conclude that, you should buy 60 Polo Shirts, 20 T- Shirts, 120 Rugby Shirts.

Let, x be the number of T-shirts, y be the number of polo shirts and z be the number of rugby shirts

A clothing store and budget $6000 to restock 200 shirts.

So, we get an equation,

x + y + z = 200                      ...................(1)

If you want to have twice as many rugby shirts as polo shirts.

So, we get an equation,

z = 2y                                   ......................(2)

You can buy T-shirts for $12 each, polo shirts for $24 each, and rugby shirts for $36 each.

So, we get an equation,

12x + 24y + 36z = 6000

We rewrite above expression as,

x + 2y + 3z = 500                         ..............(3)

Now we substitute z = 2y, into equations (1) and (3)

x + y + 2y = 200

x + 3y = 200                               ..................(4)

and equation (3) becomes,

x + 2y + 3(2y) = 500

x + 8y = 500                               ...............(5)

After solving equations (4) and (5) we get,

y = 60 and x = 20

Now substitute above value of y in equation z = 2y

z = 2(60)

z = 120

Therefore, after solving system of equations, we can conclude that, you should buy 60 Polo Shirts, 20 T- Shirts, 120 Rugby Shirts.

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ1

The mass (in grams of each muffin out of the 100 muffins is 5802 g

given data

number of identical muffins = 100

Total mass of muffins = 5802 g

Deductions from the question

let each muffin have a mass of x such that

100 * x = 5820

100x = 5802

x = 5802 / 100

x = 58.02

Therefore the mass of each muffin is 58.02 g. and this results to mass of 100 muffins being 5802 g

Read more on multiplication and division here: https://brainly.com/question/4721701

#SPJ1

Answer:

Step-by-step explanation:

12/x = x/16

x^2 = 192

x = ± √192 = ± 8√3

Ratio of number of boys to total number of children is 3:4 and number of girls is 8

The comparison of two values using the same unit is called a ratio. Divide the first amount by the second to get it. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0.

Let the number of boys be 3x and girls be x.(As they are in ratio of 3:1)

a) Total number of children = 3x + x = 4x

Ratio of number of boys to total number of children = [tex]\frac{3x}{4x}[/tex]

= 3:4

b) As, number of boys are 24

3x = 24

x = 8

, number of girls = x = 8

To learn more about ratio visit :

brainly.com/question/13419413

#SPJ9

Using multiplication the number of twenty fourths that equal 3/6 is one tenths

let the number of twenty fourths in 3/6 be x

twenty fourths is written mathematically as 20/4

using multiplication the number of twenty fourths in 3/6 is written as

20/4 * x = 3/6

solving the equation gives

20x/4 = 3/6

multiplying both sides by 4 gives

20x = 3/6 * 4

20x = 12/6

20x = 2

dividing both sides by 20 gives

x = 2/20

x = 1/10

Therefore, we can say that the number of twenty fourths in 3/6 is 1/10 or one tenths.

Rad more on fraction multiplication here: https://brainly.com/question/869839

#SPJ1

An expression to represent the weight of an object on Earth is y = 3x.

Let the weight of an object on Mercury be x and the weight of an object on Earth be y.

As given objects weigh 3 times as much on Earth as they do on Mercury.

Expression to represent the weight of an object on Earth is,

y = 3x

To learn more about expressions visit:

https://brainly.com/question/15284271

#SPJ13

Answer:

Local Minimum: (-2.5, -2), (0, -2)

Local Maximum: (1, 2)

Answer:

A is Perpendicular

B is Neither

C is Parallel

In mathematics, an algebraic expression is one that was created using integer constants, variables, and algebraic operations

The amount spent on a new house exists $ 810,000.

Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. In mathematics, an algebraic expression is one that was created using integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).

If n 5, the roots of a degree n polynomial expression, or the solutions of a degree n polynomial equation, may always be expressed as algebraic expressions.

An algebraic solution is what we refer to as a solution to an equation. But if n is greater than five, the Abel-Ruffini theorem asserts that only certain of these equations have algebraic solutions.

Abby spent 1/6 of the lottery on a new car

and 3/4 of the lottery on a new house

Total expenditure = $990,000

a. Let w be the lottery winnings,

then, 1/6 x w + 3/4 x w = $990,000

b. ⇒ w/6 + 3w/4 = $990,000

simplifying the above equation, we get

⇒ (2w + 9w)/12 = $990,000

⇒ 11w = 12 x $990,000

⇒ w = 12 x $990,000/11

⇒ w = 12 x 90,000

⇒ w = $1,080,000

Therefore, the lottery winnings = $1,080,000

Amount spent on a new car = 1/6 x $1,080,000 = $ 180,000

Amount spent on a new house = 3/4 x $1,080,000 = $ 810,000

To learn more about algebraic expressions, refer to:

https://brainly.com/question/953809

#SPJ13

Null hypothesis : [tex]H_{0} : p=0.25[/tex]

Alternative hypothesis : [tex]H_{a};p\neq 0.25[/tex]

Given : A genetic experiment with peas resulted in one sample of offspring that consisted of 429 green peas and 159 yellow peas.

i.e. p=159/429=0.3706

For 95% level of confidence interval , significance level :

Critical value of z =[tex]Z_{a/2}[/tex]=1.96

Confidence interval for population proportion :

p±[tex]Z_{a/2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

=0.37±(1.96)[tex]\sqrt{0.37(1-0.37)/429[/tex]

=0.37±0.045687

=0.37±0.05

(0.32, 0.12)

Since 0.25 is not contained in the confidence interval , it means is not reasonable that the true proportion is 0.25 (25%).

learn more about of percentage here

https://brainly.com/question/13372454

#SPJ4

Answer: 74.5

6 drinks would cost 34.5 dollars
5.75 x 6 = 34.5
8 bags of popcorn would cost 40 dollars
5 x 8 = 40

Now add both numbers
40 + 34.5 = 74.5

74.5 is our answer

hope this helps :)


                                               
                                             

Answer:

Popcorn:40 Drinks:34.5

Step-by-step explanation:

All you gotta do is 5 times 8 for the popcorn and that would equal 40. For the drinks 5.75 times 6 abd you'll get 34.5 Sorry if I'm wrong

y=−0.2x+2.2 is the equation of line  from the given graph .

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, you must first determine the slope and y-intercept. The slope is the ratio of the change in y to the change in x.

(-4 , 3 ) and ( 6 ,1 )

these are two points we will use to find the equation of the line

Slope is -0.2

Intercept is 2.2

y=−0.2x+2.2 is the equation of line

learn more about the equation of line here :
brainly.com/question/21511618

#SPJ13

Antidisestablishmentarianism

For the graph of the function, the new coordinates after the function translation is (D)  (-7,4), (-3,-5), and (6,2).

So, given function is f(x, y) with coordinates: (7,-4), (3, 5), and (-6, -2)

Therefore, for the graph of the function, the new coordinates after the function translation are (D)  (-7,4), (-3,-5), and (6,2).

Know more about the graph of a function here:

https://brainly.com/question/24335034

#SPJ13

Answer:

[tex] - 9 - |9 - 3 - 5 | \\ - 9 - |1| \\ - 9 - 1 \\ - 10[/tex]

Answer:  The correct answer is:  " - 10 ".

___________________
      However, this answer, " -10 ", does not correspond to any of the answer choices given.
___________________

Step-by-step explanation:

Given:  -9 −︱9 + (-3) + (-5)︱ ;

We are to simplify this expression by using the 'order of operations'—as follows:
__________________
BE  MD AS   ;  or:  PE  MD AS
       ⇒   ⇒                      ⇒    ⇒
__________________
  which is a mnemonic device to remember the "order of operations":
       Be Excused, My Dear Aunt Sally (Susan).

or:  Please Excuse My Dear Aunt Sally (Susan).

Note:  the "B" stands for "Brackets" ,
and the  "P" stands for "Parentheses."

Note that "parentheses" can function as "brackets."
The "E" stands for "Exponents".
 → The "Brackets/Parentheses" —if they occur; take priority.

Then:  MD for "Multiplication and Division" are the next priority;
            ⇒
________
 →  and that neither takes priority over the other. Take note of the " ⇒ " symbol" below the "MD".  This means that we perform "multiplication and division"—as they occur, from the far left of ["beginning of"] the expression to the end of the expression.
 Then:  We do the same with "Addition and Subtraction"—from the beginning to the end of the expression, in that order [that is, from "left to right"—as/if they occur]—hence the "⇒" notation.
_____________________
So again, our given expression is:
 " -9 −︱9 + (-3) + (-5)︱ " ;

So; we have an "absolute value" (the positive integer of what is enclosed within the "vertical lines" that indicate "absolute value"—or, if the value of what is enclosed within the "vertical lines" is "0" [zero], then the absolute value would be "0" [zero]; since the absolute value of 0 is 0.
____________
So, let's start simplifying by using the 'order of operations.'
  Do we have brackets or parentheses?  No; except for the absolute value lines — which do take priority. The parentheses within those lines do not count for our purposes—but if they did, then we would use the order of operations within the "absolute value" bars!
       So as a matter of 'semantics', we could say: 'Yes"; that the absolute value bars function as "brackets."

 Do we have any "exponent(s)"?  No.
 Is there any multiplication/division? No.
 Do we have any addition or subtraction?  Yes; only one:
              →   " - 9 −︱9 + (-3) + (-5)︱.
             →   {not including the addition and subtraction within the absolute value bars.}.
____________
Let's start by simplifying the expression within the absolute value bars:
  ︱9 + (-3) + (-5)︱;

Note: The only operations are additional and subtraction; so we just calculate from left to right; as these operations  occur:
 " 9 + (-3) " = 9 − 3 " ;  Note:  Adding a "negative value" is the same as subtracting a "possible value" ;
 to get:  " 6 " ;  
 Then:  the next step is:
     " 6 + (-5) " = 6 − 5 " ;  Note:
Adding a "negative value" is the same as subtracting a "positive value" ;
      to get:  " 1 ".
Now, the absolute of  " 1" is " 1".

 → or; write as: ︱1︱= 1 .  

Now, we can rewrite the entire expression:

 " - 9 − 1 " ;  to calculate and simplify:  
   to get:  " - 10 " .
__________________
Hope this answer is correct and helpful!
__________________
  However, this answer, "-10", does not correspond to any of the given answer choices.
__________________
Best wishes!
__________________

Answer:

P = 2(4+w)

P = 8+2w

P-8 = 2w

[tex] \frac{p - 8}{2w} = \frac{2w}{2} [/tex]

[tex] \frac{p - 8}{2} = w [/tex]

Answer:

7

Step-by-step explanation:

3-7=(-4), -2*(-4)=8, 4+8+16=28, 28/4=7

Answer: YES

Step-by-step explanation:

The length of rectangular yard given its perimeter and width is 300 inches

A rectangle is a 2-dimensional quadrilateral with four right angles that sum up to 360 degrees. A rectangle has two diagonals of equal length that bisect each other .

The perimeter of a rectangle is the distance round the rectangle. It is the sum of the length of the four sides of the rectangle.

Perimeter of a rectangle = 2 x (length + width)

54 = 2(l + 12)

54 / 2 = l + 12

27 = l + 12

l = 27 - 12

l = 25 feet

Now, convert feet to inches

25 x 12 = 300 inches

To learn more about the perimeter of a rectangle, please check: https://brainly.com/question/3205029

#SPJ1

yes Timmy has enough pages to organize all stamps.

Given, we have 810 stamps.

He wants to organize them on pages that hold 16 stamps each.

He has 50 pages.

Therefore, 810 ÷ 16

while dividing we get 50 as the quotient and 10 as the remainder.

Which means 810 stamps are enough for 50 pages, after that 10 more remains.

Hence we get the desired result.

Learn more about Division here:

brainly.com/question/25289437

#SPJ1

Answer: 16 drops

Step-by-step explanation: For every 2 drops is 5 ounces. We can set up an equation such as: 2/5*8/8=16/40. If you divide 40/5 you get 8, and now multiply by 2, you get 16.