Simplify 2(x + y) + 3(x + y).

The graph that represents Margo's coin collection is:

      Graph of line going through (1, 4) and (3, 10).

It is given that:

She was given 1 coin as a gift, and she adds 3 coins per year.

Let a_n denote the amount of Money Margo had in the end of the "nth" year.

According to the given information we have:

[tex]a_1=1+3=4[/tex]

[tex]a_2=4+3=7\\\\a_2=a_1+3[/tex]

[tex]a_3=10\\\\a_3=a_2+3\\\\\\a_3=a_1+3\times 2[/tex]

and so on.

Hence, we get:

[tex]a_n=a_1+3(n-1)[/tex]

Hence, we get a Arithmetic progression.

with first term as 4 and common difference as 3.

Hence, the graph is:

Graph of line going through (1, 4) and (3, 10).

( Since at n=1 we have: [tex]a_n=4[/tex]

and at n=3 we have: [tex]a_3=10[/tex]  )

Answer: 2(C^3) or 2(C to the third power)

Step-by-step explanation: C^3 is the same thing a c+c+c

Hope this helps!

The value of angle θ will be 16 degrees. Then the correct option is D.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

24² + 25² – 2(24)(25) cos θ = 7²

Then the value of angle θ will be

24² + 25² – 2(24)(25) cos θ = 7²

    576 + 625 – 1200 cos θ = 49

                          1200 cos θ = 1152

                                   cos θ = 1152 / 1200

                                          θ = cos⁻¹ (1152 / 1200)

                                           θ = 16°

Then the correct option is D.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

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Answers:

Angle 1 is 40 degrees

Angle 2 is 90 degrees

Angle 3 is 50 degrees

===========================================

Explanations:

Triangle ABC is a reflection of triangle ADC over the line AC. Doing this reflection forms the kite ABCD. Or you can think of it as gluing two congruent triangles together (ABC and ADC). We can prove the two triangles ABC and ADC congruent by the SSS congruence property. Then we use CPCTC (corresponding parts of congruent triangles are congruent) to prove that angle 1 is 40.

Let E be the intersection of the two diagonals. Through similar reasoning as earlier, we can prove that triangle AEB is congruent to triangle AED, so that leads to angle 2 being 90 degrees because this angle adds to its counterpart to get 180. Both unknown angles are x each meaning x+x = 180 leads to x = 90. One property of kites is that the diagonals are perpendicular.

Triangle AED is a right triangle as discussed above. Therefore, the angle 3 and the 40 degree angle are complementary. If angle 3 is y, then y+40 = 90 giving y = 90-40 = 50, which is why angle 3 is 50 degrees.

Using angle theorems, the value of the angles m1 and m3 are 40° and 50° respectively.

Taking the midpoint of DB as O ;

Angle OAD and Angle OAB are equal

OAD = 40° ; OAB = 40°

A right angle is formed at O ;

Hence,

(O + D + A) = 180°

90° + D + 40° = 180° (Sum of interior angles of a triangle)

D = 180 - 130

D = 50°

Hence, m∠3 = 50°.

Therefore, the value of the angles m1 and m3 are 40° and 50° respectively.

Answer:

a.-4

Step-by-step explanation:

I pictured it as a graph and since the slope is negative, the line goes down and to the right. Since the slope is -1/2, for every 2 you move horizontally, you move one vertically. You have to move two up and unless the y intercept is 0, when the line intercepts y, you have 0 as x. You move two up and 4 backwards so the x intercept is -4

Answer:

x = 20

Step-by-step explanation:

In an  equilateral triangle, everything is the same; line length and angles. Each angle in an  equilateral triangle is:

180 ÷ 3 = 60

So 3x = 60

Divide both sides by 3 to get x:

x = 20

The expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.

1. Calculate the sale price after the markdown:

Original price: x dollars

Markdown rate: 20%

Sale price after markdown: x * (1 - 0.20) = 0.8x dollars

2. Calculate the amount of sales tax:

Sales tax rate: 6%

Sales tax amount: 0.06 * 0.8x = 0.048x dollars

3. Calculate the correct total sale price:

Sale price after markdown + Sales tax amount = 0.8x + 0.048x = 0.848x dollars

4. Analyze the given expressions:

x * (1 - 0.20) + 0.06x: This expression correctly calculates the discount and adds the sales tax to the original price, so it represents the total sale price.

x * (1 - 0.20) + 0.06 * 0.8x: This expression also correctly calculates the discount and adds the sales tax to the discounted price, so it represents the total sale price.

x * (1 - 0.20 + 0.06): This expression combines the discount and sales tax into a single percentage (14%), but it applies this percentage to the original price (x) instead of the discounted price (0.8x). This leads to an overestimation of the final sale price, so it does not represent the correct total price.

0.8x + 0.048x: This expression correctly calculates the sum of the discounted price and the sales tax amount, so it represents the total sale price.

Therefore, the expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.

Complete question:

Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?

x * (1 - 0.20) + 0.06x

x * (1 - 0.20) + 0.06 * 0.8x

x * (1 - 0.20 + 0.06)

0.8x + 0.048x

Answer:

C

Step-by-step explanation:

The target area is shown in the attached picture.

We want to figure out probability of hitting red region.

The area of the figure is the area of the red square, which is 196.

Area of red region is area of whole square (196) minus area of blue square (64). So we have:

Area of red region =  196 - 64 = 132

Probability of hitting red region is 132 divided by total, which is 196.

[tex]\frac{132}{196}=0.67[/tex]

Answer choice C is right.

Answer:

2, 240

Step-by-step explanation:

In the table, the values should be

Year 1   725  

Year 2   579

Year 3   696

Since Year 4 sold 112% of the previous 3 years combined, we add 725+579+696=2000. We can find 112% by writing a proportion.

[tex]\frac{112}{100} =\frac{x}{2000}[/tex]

We solve through cross multiplication of numerator and denominator of the opposite fraction.

[tex]112(2000)=100(x)\\224000=100x\\2,240=x[/tex]

Answer:

C = 6 + 7.5 x

Step-by-step explanation:

Given,

The amount is $24.75 for entrance and 2.5 kilograms of strawberries.

⇒ Entrance fee + 2.5 kilograms of strawberries = $24.75

Since, Entrance fee = $ 6,

And,  the price for each kilogram of strawberries is constant.

⇒  $ 6 + 2.5 × 1 kilograms of strawberries = $24.75

⇒ 2.5 × 1 kilograms of strawberries = 18.75

⇒ 1 kilograms of strawberries = $ 7.5.

Thus, the cost of x  strawberries = 7.5 x

Also, the total charge for x strawberries = Entrance fee + the cost of x  strawberries

= 6 + 7.5 x

⇒ C = 6 + 7.5 x

Which is the required function formula.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points E(2, 2), C(0, 3) and G(4, 1), C(0, 3).

Substitute:

[tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}\to\boxed{D}[/tex]

Answer:  The correct option is (D) [tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]

Step-by-step explanation:  Given that ΔCDE and ΔCFG are similar right triangles.

We are to select the correct proportion that can be used to show that the slope of CE is equal to the slope of CG.

We know that the slope of a line passing through two points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

From the given figure, we note that the co-ordinates of the points C, E and G are

C(0, 3), E(2, 2) and G(4, 1).

So, the slope of line CE is given by

[tex]m_1=\dfrac{2-3}{2-0},[/tex]

and the slope of line CG is given by

[tex]m_2=\dfrac{1-3}{4-0}.[/tex]

Since the lines CE and CG are same, they must be parallel and hence they have equal slopes.

Therefore,

[tex]m_1=m_2\\\\\\\Rightarrow\dfrac{2-3}{2-0}=\dfrac{1-3}{4-0}\\\\\\\Rightarrow \dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]

Thus, (D) is the correct option.

Answer:

y+9 =-5(x-2)  point slope form

y = -5x-1  slope intercept form

Step-by-step explanation:

If we have a slope and a point, we can use the point slope form of a line

y-y1 = m(x-x1)

y--9 = -5(x-2)

y+9 =-5(x-2)

If you want to write it in slope intercept form, distribute the -5

y+9 = -5x+10

Subtract 9 from each side

y+9-9 = -5x+10-9

y = -5x-1

Answer:

-.033557047

Step-by-step explanation:

Slope = (y2-y1)/ (x2-x1)

    = (4.2 - 5.6)/(.86- 40.86)

 = -1.4/ (.86 + 40.86)

= -1.4/41.72

-.033557047

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-40.86, 5.6) and (0.86, 4.2). Substitute:

[tex]m=\dfrac{4.2-5.6}{0.86-(-40.86)}=\dfrac{-1.4}{0.86+40.86}=-\dfrac{1.4}{41.72}=-\dfrac{140}{4172}\\\\=-\dfrac{140:4}{4172:4}=-\dfrac{35}{1043}=-\dfrac{35:7}{1043:7}=-\dfrac{5}{149}[/tex]

Answer:

An irrational decimal is a decimal that cannot be written in fraction form

Ex: Pi or any decimal that keeps going and doesn't repeat

Step-by-step explanation:

I would give you more examples but they are all really long numbers and go on forever.

Answer:

Pi!

Step-by-step explanation:

I know it might sound silly but Pi and it's digits are part of the irrational decimal family! It's irrational because the digits of Pi seem like they never end, right? Hope this helped!

Answer:

1.Tom

2.Sally

3.Bob

4.Jills

Answer:

The ratio of dogs to cats is 3 dogs to 5 cats

Step-by-step explanation:

dogs to fish:    1:10

fish to cats :     6:1

dogs to cats:  3:5

FISH:

llllllllll (10)     llllllllll (10)     llllllllll(10)   (30 fish)

DOGS: 1 dog per 10 fish

D D D   3 dogs

CATS: 1 cat per 6 fish

C C C C C

Ratio represents partial data as some multiplies from numerator and denominator are lost due to simplification.  You can assume them to be variables.

The ratio of dogs to cats is 3:5

We actually cannot get real quantities but we can use variables to partially get the information of how much their quantities were.

I said 'partially' since we don't get real values but with variables only.

Since the ratio is a:b, thus let the cancelled multiple during simplification was x.

Then we have:

First quantity = ax

Second quantity = bx

It is given that:

Ratio of dogs to fish = 1:10

Then let number of dogs = 1x = x and number of fishes = 10x

Similarly,

Ratio of fish to cats = 6:1

Then let the multiple was y, then

Number of fishes = 6y,

Number of cats = 1y = y

But we have number of fishes = 10x and 6y both

Since number of fishes is constant, thus, they are equal. Or

[tex]10x = 6y\\\dfrac{x}{y} = \dfrac{6}{10} = \dfrac{3}{5}\\[/tex]

The ratio of dogs to cats = [tex]\dfrac{\text{Numbers of dogs}}{\text{Number of cats}} = \dfrac{x}{y} = \dfrac{3}{5}[/tex]

Thus, the ratio of dogs to cats is 3:5

Learn more about ratio here:

https://brainly.com/question/13513438

Answer: compass and straightedge or ruler

Perpendicular bisector of a line segment

Geometry construction using a compass and straightedge

compass and straightedge or ruler

Step-by-step explanation:

Answer:

You need a straight edge and a compass.

Step-by-step explanation:

The straight edge should not be marked in any way. You are not allowed to put a mark on the straight edge at all. The only property it has is that it has no curvature in any direction.

The compass must be flexible and at the same time it must be able to stay at one radius unless changed by the owner. It's only property is that it can draw a perfect  circle once the radius of the circle has been chosen,

Answer:

the slope is 0.

Step-by-step explanation:

You can use the slope equation

[tex]\frac{y-y}{x-x}[/tex]

and plug in your points

[tex]\frac{10-10}{4-1}[/tex]

[tex]\frac{0}{3}[/tex]

slope = 0

Answer:

A. (-6,18)

Step-by-step explanation:

The point (2,-2) and (-4,13) on the graph

First we frame an equation of the line using two points

y = mx + b where m is the slope and b is y intercept

slope = [tex]\frac{y_2-y_2}{x_2-x_1} =\frac{13+2}{-4-2} = \frac{15}{-6} = -2.5[/tex]

m = -2.5

Lets find out b

y = mx+b

y= -2.5x + b

Plug in (2,-2) and find out b

-2 = -2.5(2) + b

-2 = -5 + b (add 5 on both sides)

b = 3

so equation of line is y = -2.5 x + 3

Now we check with each option

(-6,18)

Plug in the x  and y in our equation and check it

y = -2.5 x + 3

18 = -2.5(-6) + 3

18 = 15+3

18=18  true

So (-6,18) lies on the graph

Answer:

2*(n-6) = 8

Step-by-step explanation:

Twice the difference of a number and 6 equals 8

Equals means =

Difference means subtract

2*(n-6) = 8

a, b, c - sides of a triangle

Therefore:

a + b > c

a + c > b

b + c > a

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

We have a = AB, b = 140mi, c = 100mi.

(1)     a + b > c

AB + 140 > 100    subtract 140 from both sides

AB > -40 → AB > 0

----------

(2)    a + c  > b

AB + 100 > 140      subtract 100 from both sides

AB > 40

-----------

(3)    b + c > a → a < b + c

AB < 140 + 100

AB < 240

Answers:

a) 4/5

b) 1/5

================================================

Let's say you start off with $100. If you spend 3/4 of that, then you spend 75 dollars (because 75/100 = 3/4). Think of it like 75 cents = 3 quarters. If you spend 75 dollars out of 100 total, then you have 100-75 = 25 dollars left after the first round of spending.

If you spend 1/5th of what is left, then you spend $5 on the second round leaving 25-5 = 20 dollars left at the end of the day.

Total up what you spend for both rounds: 75+5 = 80, which divides over the original amount 100 to get 80/100 = 8/10 = 4/5

If you had 20 dollars at he end of the day, out of 100 initially, then 20/100 = 2/10 = 1/5 is the fraction of what you have left.

note how 4/5 and 1/5 add to 5/5 = 1.00 = 100%. This is because the amount you spend and the amount you have left over must add to 100% of all the money you started with

Answer:

The original equation contains 3 multiplications.

When multiplying numbers, the order that they are in doesn't matter so 3 *2 is the same as 2 * 3.

This would make D, the same.

D) (3 × 2)×(5 × 6)

Step-by-step explanation:

Firstly, set the x value as 0:

-0 + 2y = 2

2y = 2

y = 1

So when x = 0, y = 1

Now set y to 0:

-x + 2(0) = 2

-x = 2

x = -2

So when y = 0, x = -2

Simply plot the two following points:

(0 , 1) and (-2 , 0)

And don't forget to join these two points up!

Attatched is an image of this graph.

[tex]4x+3>-9\qquad\text{subtract 3 from both sides}\\\\4x>-12\qquad\text{divide both sides by 4}\\\\\boxed{x>-3}[/tex]

Answer: $7.50

Step-by-step explanation: 1.25(6)

Final answer:

To find the list price of the poster after an 8% discount, subtract 8% of the list price from the list price and set it equal to the sale price.

Explanation:

To find the list price of the poster, we need to first calculate the original price before the discount. Let's assume the list price is 'x' dollars. After an 8% discount, the sale price of the poster is $17.48.

We can set up an equation to solve for the list price: x - 8% of x = $17.48. To calculate 8% of x, we multiply x by 0.08.

So the equation becomes: x - 0.08x = $17.48. Combining like terms, we get 0.92x = $17.48. Dividing both sides by 0.92, we find that x = $19.