Someone deleted the previous answer. Can someone please help with this equation:

Solve the equation p2 + 14p = 32 by completing the square method (and need to show work)

It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

The total amount to each person end up paying $20.54.

To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.

To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.

The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.

Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.

To split this evenly among the five people, we divide by 5:

$102.72 ÷ 5 = $20.54

So each person will end up paying $20.54.

20% of $85.60 is ($85.60 * 0.20) = $17.12

Add the tip to the total bill:

$85.60 + $17.12 = $102.72

Divide the total amount by the number of people (5): $102.72 / 5 = $20.54

Therefore, the answer is B. $20.54.

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Answer:

the digit 3 (or 30,000,000,000) is in the ten billions place.

Answer:

andrew

Step-by-step explanation:

Answer:

192 feet of fabric

Step-by-step explanation:

Since each curtain needs to be 36 inches long, or 3 feet long, the total length of fabric needed for one curtain is 3 feet. To make 64 curtains, Ivania's curtain company will need a total of:

3 feet/curtain x 64 curtains = 192 feet of fabric

The number of feet of fabric that Ivania needs to make the curtains is 192 feet.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Ivania's curtain company is making curtains for a local hotel.

Length of each curtain needed = 36 inches

                                                    = 36/12 feet

                                                    = 3 feet

At the fabric store, fabric is sold by the foot.

Number of curtains needed to make = 64

We have to multiply the length of each curtain with the total number of curtains to find the total length of the curtain needed.

Feet needed = 64 × 3 feet = 192 feet

Hence the feet of curtains needed is 192 feet.

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The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

x = (-2)(-3/2) = 3

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

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The exact solutions of the Quadratic equation x^2 - 3x - 5 = 0 are:

x = (3 + √29) / 2 ,x = (3 - √29) / 2. The correct answer choice is:

x = the quantity of 3 plus or minus the square root of 29 all over 2.

The exact solutions of the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula, we can identify the values of a, b, and c, and substitute them into the formula:

a = 1

b = -3

c = -5

Now, we can apply the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values into the formula:

x = (-(−3) ± √((−3)^2 - 4(1)(−5))) / (2(1))

x = (3 ± √(9 + 20)) / 2

x = (3 ± √29) / 2

Therefore, the exact solutions of the quadratic equation x^2 - 3x - 5 = 0 are:

x = (3 + √29) / 2

x = (3 - √29) / 2

The correct answer choice is:

x = the quantity of 3 plus or minus the square root of 29 all over 2.

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Answer: 512

Step-by-step explanation:

Hello, I hope the answer is correct if not let me know and i will work step by step on it with you. Your welcome and Happy to help.

The surface area of the design is 384 inches².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

The given design is a cube.

All the sides are of the length 8 inches.

The formula to find the surface area of a cube is,

Surface area = 6a², where "a" is the length of a side of the cube.

Given, a = 8 inches

Surface area of the design = 6 × 8²

                                             = 6 × 64

                                             = 384 inches²

Hence the given design has the surface area of 384 inches².

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Answer:

y = 4\(\sqrt{5}\) , ? = 10

Step-by-step explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100

Take square root of both sides

? = \(\sqrt{100}\) = 10

Answer: The McGee family would pay $52 either way if they rented the truck for 2 additional days.

Step-by-step explanation:

Luther's Moving Company:

38 is how much they'll pay on the first day plus 7 per every additional day

This is represented by 7x+38

Springdale Rent-a-Truck

44 is how much they'll pay on the first day plus 4 per every additional day

This is represented by 4x+44

Set the equations equal to each other

7x+38=4x+44

Move the 38 to the other side by subtracting

7x=4x+44-38

7x=4x+6

Move 4x to the other side by subtracting

7x-4x=6

3x=6

Divide 3 to get x alone

3x/3=6/3

x=2

They'll be equal after 2 additional days

Plug in 2 to each equation

Luther: 7(2)+38

14+38=52

Springdale: 44+4(2)

44+8=52

Answer:

yes, by SAS similarity theorem.

Step-by-step explanation:

"The SAS similarity theorem stands for side angle side. When you've got two triangles and the ratio of two of their sides are the same, plus one of their angles are equal, you can prove that the two triangles are similar." - Study pug

Here, we can see that one of the angles is equal. Check!

Then, the adjacent sides of that angle can both be divided by 5 to get the corresponding sides in the other triangle. Therefore, they have the same ratio of those sides. Check!

The triangles are similar by the SAS similarity theorem.

Hope this helps!

Answer:

Step-by-step explanation:

is solved with an equation between the corresponding sides

10 : 2 = 15 : 3

5 = 5

your answer is yes

Answer:

Triangle= 24x

Rectangle= 8x+7

Step-by-step explanation:

10x+8x+6x=24x

7x+4+x+3=8x+7

Combine Like Terms

The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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The expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

From the question, we have the following polynomial that can be used in our computation:

P(x) = 2x² (x + 3) − (7x − 10)

Q(x) = 8(x − 1) (x² + x + 1) − 3x² + 4

R(x) = (2x + 1)² - (2x² + 7)

S(x) = 2(5x³+6) + x(x - 11)

Add the expressions P(x) and Q(x)

So, we have

P(x)  + Q(x) = 2x² (x + 3) − (7x − 10) + 8(x − 1) (x² + x + 1) − 3x² + 4

Evaluate

P(x)  + Q(x) = 10x³ + 3x² - 7x + 6

Add the expressions R(x) and S(x)

So, we have

R(x) + S(x) = (2x + 1)² - (2x² + 7) + 2(5x³+6) + x(x - 11)

R(x) + S(x) = 10x³ + 3x² - 7x + 6

So, we have

P(x) + Q(x)} − {R(x) + S(x)} = 10x³ + 3x² - 7x + 6 - (10x³ + 3x² - 7x + 6)

Evaluate

P(x) + Q(x)} − {R(x) + S(x)} = 0

Hence, the expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

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To stop a deep cut from bleeding, apply pressure on, gauze or cloth while elevating Clean the wound.

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Answer:

It is permutation without repetition. I just took the quiz. This is a permutation because different orderings of the pieces produce different pictures. Repetition is not allowed because there are a limited number of puzzle pieces.

Step-by-step explanation:

Answer:

Permutation without repetition

Step-by-step explanation:

This is a permutation because different orderings of the pieces produce different pictures. Repetition is not allowed because there are a limited number of puzzle pieces.

Rectangular coordinates are x = -3.5 , y = 7\(\sqrt{3}\)/2 by using the relation between rectangular and polar coordinates

What do you mean by rectangular coordinates?

Rectangular coordinates, commonly known as cartesian coordinates, are a way to represent graphs and show where points are located on a two-dimensional surface or in three-dimensional space.

The origin is the intersection of the two perpendicular axes that make up the Cartesian plane.

The xy plane is another name for the Cartesian plane.

Given polar coordinates are (-7,5π/3)

To change polar coordinates to recatngular coordinate use

x = rcosθ , y = rsinθ

here r = -7 and θ = 5π/3

x = -7cos5π/3 = -7 × 1/2 = -7/2 = -3.5

y = -7sin5π/3 = -7 × -\(\sqrt{3}\)/2 = 7\(\sqrt{3}\)/2

Therefore, rectangular coordinates are x = -3.5 , y = 7\(\sqrt{3}\)/2

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The word that describes the slope of the line representing the data in the table is "negative."

To determine the slope of the line representing the data in the table, we need to examine the relationship between the number of cards sold and the remaining amount of money needed.

Looking at the given data, we observe that as the number of cards sold increases, the remaining amount of money needed decreases. This indicates an inverse relationship between the two variables.

The slope of a line represents the rate of change between two variables. In this case, the slope is negative because the line decreases as we move from left to right.

Therefore, the word that describes the slope of the line representing the data in the table is "negative."

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Answer:

16. 12√5

17. 3 2/2 as it actually equal 4!

Answer:

Each person has 1/4 of a peice of paper

Step-by-step explanation:  Tyler cut the peices of paper in 4 equal pieces and if he gave himself and another person one peice then they would each of 1/4 of a peice of paper

Answer:

y = 5x + 25

Step-by-step explanation:

She starts out with 25 dollar.  That does not get increased each day, but what does get increased every day is $5

Answer: 30%

Step-by-step explanation:

Answer: 12

add 12 to the left side to cancel out the -12 then add 12 to 24 to get 36, then divide 3x from 36 to get 12 (x=12)

The ratio of a:b in 5a-3b=7b is 4:5.

We know that,

A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are equal to each other. For example, if there are 2 boys and 6 girls, you can write the ratio as: 1 : 3 (for every boy there are 3 girls).

Ratios compare two numbers obtained by dividing. If one data point (A) is compared to another data point (B), it is expressed as A/B. It means that we are partitioning information A from information B. For example, if A is five and B is 10, your ratio would be 5/10, or 1/2.

For above information,

5a - 3b =  7b

5a = 7b- 3b

5a= 4b

So, a/b= 4/5

a:b  is 4:5

Thus, the ratio of a:b in 5a-3b=7b is 4:5.

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Answer: 17

Step-by-step explanation:

The mean number of cookie boxes sold this week is 17

From the question, we have the following parameters that can be used in our computation:

Cookies by a Girl Scout troop: 12 9 15 14 29 17 20 25 12

The mean is calculated as

Mean = Sum/Count

So, we have

Mean = (12 + 9 + 15 + 14 + 29 + 17 + 20 + 25 + 12)/9

Evaluate

Mean = 17

Hence, the mean is 17

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Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.