Fill in the blanks below.
Find the slope of the line passing through the points (-6, 3) and (-6, -8).
slope:
Find the slope of the line passing through the points (-3, -6) and (8,-6).
slope:

The absolute functions |3x - 1| - |2x + 5 - (5 - x)| = 0,  |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|, |(x - 2) / 4| - 1/3 = x and 1/2|x - 3| - 1 = |x - 3| + 2 have solutions of 1/6, 1, 2/15 and no solutions respectively

An absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. Generally, we can represent the absolute value function as, f(x) = a |x - h| + k, where a represents how far the graph stretches vertically, h represents the horizontal shift and k represents the vertical shift from the graph of f(x) = |x|. If the value of 'a' is negative, the graph opens downwards and if it is positive, the graph opens upwards.

In the questions given;

1) |3x - 1| - |2x + 5 - (5 - x)| = 0

x = 1/6

2) |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|

x = 1

3) |(x - 2) / 4| - 1/3 = x

x = 2 / 15

4) 1/2|x - 3| - 1 = |x - 3| + 2

The equation has no solution

Learn more on absolute functions here;

https://brainly.com/question/24368848

#SPJ1

Answer:

1200 dollars

Step-by-step explanation:

1.) Create an equation. If we use x as a variable for the total money, we get [tex]\frac{504}{x}=\frac{42}{100}[/tex] .

2.) By solving this equation, we get 42x = 50400, and x = 1200.

Therefore, their total budget was 1200 dollars.

The point slope form of the equation of the line that passes through the points (6, -9) and (7, 1) is y - 1 = 10(x - 7)

Linear equation can be represented in different form such as point slope form, slope intercept from, standard form and general form.

The line passes through the points (6, -9) and (7, 1). The point slope form can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, let's find the equation of the line that passes through the points (6, -9) and (7, 1).

Let's find the slope.

slope = m = 1 + 9 / 7 - 6

slope = 10 / 1

slope = 10

Therefore,

y - 1 = 10(x - 7)

learn more on point slope form here: https://brainly.com/question/29503162

#SPJ1

Check the picture below.

The present age of Melody is 9 and her sister is 24 .

the two digit number is 39

How to find the ages of a person ?

Consider the difference between the individual's birthdate and the present day: days = current day - birth date. Age = (years 365) + (months 31) + days should be replaced with these variations. The individual's age is expressed in days. To get the age in years, divide the outcome by 365.

Let present age of melody be y and her sister age be x

Four years ago  age of Melody be (y - 4) and her sister age be (x - 4)

After six years age of Melody be (y + 6) and her sister age be (x + 6)

∴ [tex]\frac{(x-4)}{4} = (y - 4)[/tex]

[tex]\frac{(x+6)}{2} = (y + 6)[/tex]

The equation becomes

x + 6 = 2y + 12

x = 2y +6  ⇒ (1)

x - 4 = 4y -16

x = 4y - 12 ⇒(2)

Solving (1) and (2)

x - 2y = 6

x - 4y = -12

  2y = 18

    y = 9

Substituting the value of y in eq(1)

x = 2*9 + 6

x = 18 +6

x = 24

Let xy be the two digit number.  

10x + y

The value of this number is 6 less (-6) than five times the unit digit (5y).  So:

10x + y = 5y - 6

The sum of the digits of the 2-digit number is 12:

x + y = 12

So y = 12 - x

Substitute 12-x for y:

10x + y = 5y - 6

10x + 12 - x = 5(12-x) - 6      [Substituted 12-x in place of y]

9x + 12 = 60 - 5x - 6

14x = 42

x = 3

y = 12 - x

  = 12 - 3

  = 9

The two digit number is 39

To learn more about finding the ages of a person from the given link

https://brainly.com/question/1581212

#SPJ1  

The solution of the given expression will be 9/16.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²

= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²

= 9/16

Hence, The solution of the given expression will be 9/16.

For more references on expression, click;

brainly.com/question/14083225

#SPJ1

Answer:

1 [tex]\frac{19}{20}[/tex] cups

Step-by-step explanation:

[tex]\frac{cookies}{sugar}[/tex] = [tex]\frac{cookies}{sugar}[/tex]

[tex]\frac{5}{\frac{3}{4} }[/tex] = [tex]\frac{13}{x}[/tex]  Cross multiply and solve for x

5x = (13)([tex]\frac{3}{4}[/tex])

5x = [tex]\frac{39}{4}[/tex]  Divide both sides by 5

x = [tex]\frac{39}{4}[/tex]÷5

x = [tex]\frac{39}{4}[/tex] x [tex]\frac{1}{5}[/tex]

x = [tex]\frac{39}{20}[/tex]= 1 [tex]\frac{19}{20}[/tex]

Answer:

Step-by-step explanation:

[tex]l=w+4[/tex]

[tex]A=l*w\\l=w+4\\A=(w+4)w\\A=w^2+4w[/tex]

[tex]P=2l+2w\\A=4p-4\\A=4(2l+2w)-4\\A=8l+8w-4\\l=w+4\\A=8(w+4)+8w-4\\A=8w+32+8w-4\\A=16w+28[/tex]

[tex]16w+28=A=w^2+4w\\16w+28=w^2+4w\\w^2-12w-28=0\\w^2-14w+2w-28=0\\(w^2-14w)+(2w-28)=0\\w(w-14)+2(w-14)=0\\w+2=0=w-14\\w=-2and14[/tex]

Since w represents a measurement of a physical object in inches, it cannot be negative.  So, [tex]w\neq-2[/tex].  The width of the rectangle is 14 inches.

The length is given as 4 inches more than the width, so the length is 18 inches.

This satisfies all the requirements of the question:

[tex]4P-4=A\\P=2(18)+2(14)=64in\\4P=64in(4)=256in\\A=18in*14in=252in^2\\256-4=252\\252=252[/tex]

The equation of the linear relationship in slope-intercept form is: y = 2/3x + 50/3.

The equation in slope-intercept form for a linear relationship can be expressed as y = mx + b, where the slope is m and the y-intercept is b.

Using two points on the graph, (20, 30) and (50, 50), find the slope:

Slope (m) = change in y / change in x = (50 - 30) / (50 - 20)

Slope (m) = 20/30

Slope (m) = 2/3.

Find the y-intercept (b) by substituting m = 2/3 and (x, y) = (20, 30) into y = mx + b:

30 = 2/3(20) + b

30 = 40/3 + b

30 - 40/3 = b

50/3 = b

b = 50/3

Write the equation of the linear equation in slope-intercept form by substituting b = 50/3 and m = 2/3 into y = mx + b:

y = 2/3x + 50/3

Learn more about the slope-intercept form on:

https://brainly.com/question/1884491

#SPJ1

Answer: 36

Step-by-step explanation:

4 sections are 2,000 lbs or 1 ton

To find the pounds Girard has to build, we know we have 9 tons, therefore if each ton is 2,000 lbs, multiply 2,000 by 9 to get 18,000 lbs to use

2,000 lbs per ton x 9 tons= 18,000 lbs to use

now take the 18,000lbs and divide by 500 to find the number of sections we can build

18,000lbs / 500 pounds per section = 36

36 sections is the answer

Answer:

[tex] p(x)= -2x^3-4x^2+6x[/tex]

Step-by-step explanation:

We need to write a polynomial with zeroes -3 , 0 and 1 , with a leading coefficient of 2 . We know that if a polynomial has 3 zeroes say [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the polynomial can we written as ,

[tex]\longrightarrow p(x) = k[ ( x -\alpha)(x-\beta)(x-\gamma)] [/tex]

So , similarly we can write it as;

[tex]\longrightarrow p(x) = -2[ (x -(-3)) (x-0) (x-1)\\[/tex]

Simplify,

[tex]\longrightarrow p(x) = - 2[ (x+3)(x)(x-1) ]\\[/tex]

[tex]\longrightarrow p(x) = -2[ (x^2+3x)(x-1)]\\[/tex]

[tex]\longrightarrow p(x) = -2[ x(x^2+3x)-1(x^2+3x)\\ [/tex]

[tex]\longrightarrow p(x) = -2[ x^3 +3x^2 -x^2-3x ]\\[/tex]

[tex]\longrightarrow p(x)= -2[ x^3 +2x^2 -3x]\\[/tex]

[tex]\longrightarrow\underline{\underline{ p(x)= -2x^3-4x^2+6x }} [/tex]

And we are done!

The surface area of the triangular prism is 1090 metres squared.

A triangular prism  is a polyhedron made up of two triangular bases and three rectangular sides.

Therefore, let's find the surface area of the triangular prism.

Surface area of the triangular prism = bh + l(a + b + c)

where

Therefore,

Surface area of the triangular prism = 16 × 15 + 17(17 + 17 + 16)

Surface area of the triangular prism = 240 + 17(50)

Surface area of the triangular prism =240 + 850

Surface area of the triangular prism = 1090 metres squared

learn more on triangular prism here: https://brainly.com/question/14527059

#SPJ1

If Ibuprofen is given for fever to children 6 months of age up to 2 years.The amount of  much medicine that would be usual dose for a 18 month old weighing 22 pounds is 50kg.

1 pound = 0.45 kg    

Hence,

22 pounds = 22×0.45 Kg

22 pounds = 9.9Kg

Now let find the the amount of medicine that would be the usual dose  

Medicine dose = 5mg × 9.9kg

Medicine dose =49.5 kg

Medicine dose = 50 kg

Therefore the medicine dose is 50kg.

Learn more about medicine dose here:https://brainly.com/question/11185154

#SPJ1

Hence, in option (A) the down payment is what percent of the purchase price is [tex]25[/tex]% and in option (B) the purchase price would be [tex]90000[/tex] $ down payment is [tex]45[/tex] %.

What is the installation amount?

Installation Cost means the total cost payable by the Lessee to the Lessee’s direct contractor under the contract for the carpet installation works.

Payment of the Attendance Fees for the Designated Works may be made by the Lessee progressively in the course of the relevant Designated Works being carried out.

Here given that,

A family buys a studio apartment for $[tex]200,000[/tex]. They pay a down payment of $[tex]50,000[/tex].

(A)

The down payment is the percentage of purchase price is

[tex]\frac{50000}{200000}[/tex] × [tex]100[/tex] [tex]=[/tex] [tex]25[/tex] %

(B)

The percent of the purchase price would be [tex]90000[/tex] $ down payment is

[tex]\frac{90000}{200000}[/tex] ×[tex]100[/tex] [tex]=45[/tex] %

Hence, in option (A) the down payment is what percent of the purchase price is [tex]25[/tex]% and in option (B) the purchase price would be [tex]90000[/tex] $ down payment is [tex]45[/tex] %.

To know more about the price

https://brainly.com/question/9233751

#SPJ1

The proper order from greatest to least is option (C) I, III, IV and II

Convert each term to the decimal form

The first terms is 58/ 67

58 / 67 = 0.87

The second term is 0.58%

Convert the percentage to simple fraction

0.58% = 0.58 / 100

= 0.0058

The third term is 58%

Convert the percentage to simple fraction

58% = 58/100

= 0.58

The fourth term is 5.8%

Convert the percentage to simple fraction

5.8% = 5.8/100

= 0.058

The order from greatest to least is

0.87 > 0.58 > 0.058 > 0.0058

Hence, the proper order from greatest to least is option (C) I, III, IV and II

Learn more about percentage here

brainly.com/question/12715980

#SPJ1

The values of l, ll, lll, lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Therefore, the option (c) is correct.

Answer:

Step-by-step explanation:

If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

A relation is a function if it has only One y-value for each x-value.

Composite functions are when the output of one function is used as the input of another.

If f(x)=x²+4

Then we have to prove f⁻¹of(x)=f⁻¹(f(x)

Let us consider fof⁻¹(x)

f(f⁻¹(x))

x

So (fof⁻¹(x))=x

Now f⁻¹of(x)=f⁻¹(f(x)

=x

Hence, If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ2

The equation y = 8 does not describe a​ function

A function is an equation that has only one output or answer (y) for every input (x) e.g y = 2x

If we plot y =8 on a coordinate plane, you would see that at the point of (0, 8) is a horizontal line.

Also, no matter the value of the input (x), the value of when of the output (y) will always remain 8. This does not fit the description of a function  

Therefore, the equation y =8 does not  describe a​ function

Learn more about function on:

https://brainly.com/question/22340031

#SPJ1

Answer: 1. 50 stops.

Step-by-step explanation:

There is 1,000 meters in a Kilometer. So 20,000/400=50

Answer:

1) 50 stops

2) a: 60 meters

   b: 6,000 centimeters

Step-by-step explanation:

A) we have to convert 20k into meters to solve it

To do that we multiply by 1000

20x1000

20,000 meters now we divide by 400 to see how many stops

20,000/400

50 stops

2)

to find perimeter is meters we add all of the sides together

20+10+5+5+15+5

30+10+20

30+30

60 m is the perimeter

Now in centimeters we multiply by 100

60x100

6,000 centimeters

Hopes this helps please mark brainliest

The correct dividend of 76 is required to yeild a quotient of 25 and a remainder of 1 when divided by 3.

We can know the dividend, the quotient and the remainder of the division using the division formula: (Divisor x Quotient) + Remainder = Dividend

Divisor = 3

Quotient = 25

Remainder = 1

(3 × 25) + 1 = 75 + 1

(3 × 25) + 1 = 76

Thus, the dividend 76 divided by the divisor 3 have the quotient 25 and a remainder when of 1.

Know more about division here: https://brainly.com/question/1622425

#SPJ1

Answer:

78(0.08n)+78

The answer options might not look exactly like this, it may be in different orders but if all these numbers are there like this it should be right

Step-by-step explanation:

When you are increasing by a percent you always turn the percent to a decimal is a formula

8%=0.08

This can be multiplied by n to show how many years

0.08n

And we multiply this by 78 since it’s 8 percent of this

78(0.08n)

And now we add 78 since the tree starts off as 78

78(0.08n)+78

Also to check when n=0 the height will be 78

78(0.08(0)+78

78(0)+78

78

Hopes this helps please mark brainliest

The answer for  8.9395 +1.2973 is 10.2368 for .2.8862 +8.2758=11.162, and for 5.9529 +2.0043 = 7.9572.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

1. 8.9395 +1.2973=10.2368

2.2.8862 +8.2758=11.162

3. 5.9529 +2.0043 = 7.9572

4. 1.223+0.4643=1.6873

5. 3.2292 +9.45 =12.6792

6. 2.421 +6.0473=8.4683

7. 5.2697 + 4.4603=9.73

8. 0.0003 +2.6035 =2.6038

9. 3.7092 +9.2965=13.0057

10. 7.0551 +0.8388=7.8939

Thus, the answer for  8.9395 +1.2973 is 10.2368 for .2.8862 +8.2758=11.162, and for 5.9529 +2.0043 = 7.9572.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ1

From the given parameters of linear equation, we can say that;

The number of $10 bills is; 24

The number of $20 bills is; 13

Let x be the number of the $20 dollars bills.

Then the number of the $10 dollars bills is (x + 11), according to the condition.

The money equation is expressed as;

20x + 10*(x + 11) = 500

Simplify and solve for x.  

20x + 10x + 110 = 500

30x = 500 - 110

30x = 390

x = 390/30

x = 13

Then number of $10 bills is 13 + 11 = 24

Read more about linear equation word problems at; https://brainly.com/question/21405634

#SPJ1

Answer:

5 4/9

Step-by-step explanation:

our equation is 4 2/3+7/9

2/3=6/9.

So we have 4 6/9+7/9

Simplify:

4 13/9

5 4/9

Answer: B. The Total profit made when a person buys a car for $10,000 and sells it for $10,000.

Step-by-step explanation:

Answer A would be wrong since when there is a temperature change from 15 degrees to -15 degrees would lead to an overall change of 30 degrees.

Answer C would be wrong as well since it is decreasing 500 feet in altitude, meaning that there is a negative change in altitude.

Answer D would also be wrong since the train is traveling 35 miles north, then south. That means that even though the train is in the same place that is was before, it traveled a total of 70 miles to return to where it was previously at.

Hope this helps!

Yes, the equation:

y = 8

describes a function.

A function is a relation that maps elements x into elements y, such that each element x is mapped into a single value of y.

In this case, we have the equation:

y = 8

So all our points are of the form (x, 8).

Notice that all the inputs x are mapped into a single output y = 8, then this relation is a function.

Learn more about functions:

https://brainly.com/question/2328150

#SPJ1

Answer:

[tex]Area = 153.938040026m^2[/tex]

[tex]Circumference= 43.9822971503m[/tex]

Step-by-step explanation:

Area

[tex]Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026[/tex]

Circumference

[tex]C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503[/tex]

Step-by-step explanation:

Answer is D.

Breaking it down;

1/3 + 2/6 = 4/6.

4/6 - 5/6 = -1/6

-1/6 × 3/11 = -3/66

y=12/πsin⁻¹(x-35/0.6) is the function which expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters

Two or more expressions with an Equal sign is called as Equation.

Given,

A bird sits on the branch of a tree, then starts to fly.

The height of the bird is described by the function y = 0.6sin(πx/12) + 35

Where y represents the height of the bird measured in meters,

x represents the number of seconds since the bird left the branch

We need to find the function expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters

y=12/πsin⁻¹(x-35/0.6)

Hence, y=12/πsin⁻¹(x-35/0.6) is the function which expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

Answer is A

Step-by-step explanation:

got it right on assignment.

Of the four relationships the ones that have the constant of proportionality of 2 are

The constant of proportionality is the constant that relates the input with output terms

Relationship A

the output, y dies it equal 2 * input

an instance = 2 * 3 = 6 not 2 2/3

Relationship B

y = 2x has the constant written out already

Relationship C

Represents a linear function

Relationship D

y = 6, x = 3

y = 2x

when x = 3 y = 6

when x = 6 y = 12

Learn more about constant of relationship here:

https://brainly.com/question/28909110

#SPJ1

Part (a)

4, read it off the diagram.

Part (b)

(4 in)(1 ft/12 in) = 1/3 ft

Part (c)

(60 ft)(20 ft)(1/3 ft)=400 cu ft

Part (d)

(66 ft)(26 ft)(1/3 ft)=572 cu ft

Part (e)

572 cu ft - 400 cu ft = 172 cu ft