Use completing the square to solve for x in the equation x^2-10x+25=35.

Answer:

D) 3/25

Step-by-step explanation:

(3/5)/5 = .12

3/23 = .12

Hello There!

Your answer would be 3/25. Whenever you have two probabilities together you can multiply them and in this case, multiplying 3/5 by 1/5 will get you a product of 3/25

The equation to calculate the sale price of the skirt, which is 's', given an original price 'p' and a discount of 20% on the original price would be s = p - (0.2 * p). This equation essentially subtracts the discount amount (20% of 'p') from 'p' to get the sale price 's'.

To calculating a sale price, which is a Mathematical exercise commonly carried out in financial and business scenarios. In this context, there's a 20% sale on skirts. Given that the original price of the skirt is 'p', and the discount is 20% of 'p', we can denote that as '0.2p'. If the sale price is represented as 's', the equation to calculate the sale price would be s = p - (0.2 * p). This equation essentially subtracts the discount amount (20% of the original price) from the original price to obtain the price after discount, which is the sale price.

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the equation s = 0.80 * p. This accounts for a 20% reduction from the original price.

We need to determine the sale price using the original price (p) and the discount rate (20%).

Since the discount is 20% off, you can convert this percentage to a decimal
20% = 0.20.

To find the amount discounted, multiply the original price by 0.20,
Discount Amount = 0.20 * p.

Subtract the discount amount from the original price to get the sale price,
Sale Price (s) = p - 0.20 * p.

Alternatively, you can factor out p in the equation: s = p (1 - 0.20),
which simplifies to s = 0.80 * p.

Answer:

The measure of angle x is 12°

Step-by-step explanation:

we know that

(4x+4)°+(5x-22)°=90° ----> by complementary angles

Solve for x

(9x-18)°=90°

9x=90°+18°

9x=108°

x=12°

Step-by-step explanation:

[tex]\text{Use}\ (a+b)^3=a^3+3a^2b+3ab^2+b^3.\\\\\text{We have}\ (2x+y)^3\\\\=(2x)^3+3(2x)^2(y)+3(2x)(y^2)+y^3\\\\\text{The coefficient of}\ y^2\ \text{is}\ (3)(2)=6[/tex]

you need to find the median angle so you take the triangle (A) and solve for the angle using the inverse of sin.(B) take this angle and multiply it by 2 and you should have you arc length I think.

Answer:

89.0

Step-by-step explanation:

Answer:

Spencer will pay off the item 3 months sooner if he pay $260 instead of $170 a month

Step-by-step explanation:

Total Amount = $1880

Down Payment = 20%

Monthly payment = $170

if Monthly payment increased from $170 to $260, How many months sonner Spencer will pay off?

So, First calculate the down payment

Down payment = 20% of 1880

                          = (20/100) * 1880

                         = 376

Amount left to be paid = 1880 - 376

                                     = 1504

Total months to pay off for Spencer if he pay's $170 a month:

1504/170 = 8.8 ≈ 9 months

Total months to pay off for Spencer if he pay's $260 a month:

1504/260 = 5.7 ≈ 6 months

So, 9 -6 = 3 months

So, Spencer will pay off the item 3 months sooner if he pay $260 instead of $170 a month

Answer:

C. 3x + 8

Step-by-step explanation:

A. can be factored; Factor 5 from all terms:

(15x - 10)/5 = 3x - 2

B. can be factored; Factor 4 from all terms:

(4x + 8)/4 = x + 2

D. can be factored; Factor 2 from all terms:

(2x - 2)/2 = x - 1

~

Answer:

It is 17,18 and 19

Step-by-step explanation:

Consecutive numbers are

x, x+1, x+2

x+x+1+x+2=54

3x+3=54

-3       -3

3x=51

x=17

17

17+1=18

17+2=19

17, 18 and 19

Answer:

z = 6

Step-by-step explanation:

Given

6z + 10z = 96 ← collect terms on left side

16z = 96 ( divide both sides by 16 )

z = 6

Answer:

136 un²

Step-by-step explanation:

Rectangles/linear faces: 7 * (5 + 6 + 5) = 7 * 16 = 112

Triangles/bases: 2 * 1/2(6 * 4) = 24

Total: 24 + 112 = 136 un²

The surface area-to-volume ratio is used in Biology to predict cell efficiency in eliminating wastes or procuring nutrients by diffusion.

In Biology, the surface area-to-volume ratio is used to predict which cells might eliminate waste or procure nutrients faster by diffusion. This ratio is calculated by dividing the surface area of a cell by its volume. Cells with a larger surface area-to-volume ratio are more efficient at exchanging materials with their surroundings.

For example, consider a small cell with a high surface area-to-volume ratio. This cell has a relatively larger surface area compared to its volume, which allows for faster diffusion of nutrients into the cell and waste products out of the cell. In contrast, a larger cell with a lower surface area-to-volume ratio has a relatively smaller surface area compared to its volume, resulting in slower diffusion.

By analyzing the surface area-to-volume ratio, we can predict which cells have a greater capacity for diffusion and therefore can eliminate wastes or procure nutrients at a faster rate.

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Answer:

B. Final Exams.

Step-by-step explanation:

The IQR is the difference between the lower and upper quartiles of the data and is a measure of the spread of the data.

Mid Term Exam:

First find the Median

This is (95+92)/2 = 93.5.

The Lower quartile is the median of the bottom 5 values = 88.

The upper quartile is the median of the top 5 values = 100

So the IQR = 100 - 88 = 12.

Final Exam.

We find the IQR of the Final exam data in a similar way:

It comes to 93 - 78 = 15.

Answer:

the equation to find the height is: x = 25 * tan(30°) and the height is x = 14.43 feet

Step-by-step explanation:

Length  of tree = 25 feet

Angle of elevation = 30 degrees

Equation for the height of tree=?

Let x represent the height.

We know that tan Ф = Perpendicular/Base

tan Ф = height of tree/ length of base

tan Ф = x/l

=> x = l*(tanФ)

x = 25 * tan(30°)

Now, putting values:

x= 25 * tan(30°)

x = 25 * 0.577

x = 14.43 feet

So, the equation to find the height is: x = 25 * tan(30°) and the height is x = 14.43 feet

Answer:

X=3.5

Step-by-step explanation:

Answer:

A) x=5 or -11

Step-by-step explanation:

The given equation is:

[tex](x+3)^2=64[/tex]

The most suitable method so solve this quadratic equation is the square root method.

We take square root of both sides to obtain:

[tex]x+3=\pm \sqrt{64}[/tex]

[tex]\implies x+3=\pm8[/tex]

[tex]\implies x=-3\pm8[/tex]

We now split the plus or minus sign to get;

[tex]x=-3-8\:,x=-3+8[/tex]

This simplifies to:

[tex]x=-11\:,x=5[/tex]

The correct choice is A

Given : Radius of cylinder = 8 m

Height = 4 m

Volume of cylinder = πr²h cu. units

= 22/7 × 8 × 8 × 4 m³

= 804.57 m³ (approx.)

Curved surface area = 2πrh sq. units

= 2 × 22/7 × 8 × 4 m²

= 201.14 m² (approx.)

Total surface area = 2πr(r + h) sq. units

= 2 × 22/7 × 8 (8 + 4) m²

= 2 × 22/7 × 8 × 12 m²

= 603.43 (approx.)

Final answer:

The volume of a cylinder with a radius of 8 meters and a height of 4 meters is calculated using the formula V = πr²h, which yields approximately 804.25 cubic meters when using π ≈ 3.14159.

Explanation:

To calculate the volume of a cylinder with a given radius and height, you can use the formula V = πr²h. In the case of a cylinder with a radius of 8 meters and a height of 4 meters, plug these values into the formula to get:

V = π × (8 m)² × 4 m

V = π × 64 m² × 4 m

V = 256π m³

Since π (pi) is approximately 3.14159, you can further calculate the volume as:

V ≈ 256 × 3.14159 m³

V ≈ 804.2477 m³

Thus, the volume of the cylinder is approximately 804.25 cubic meters, when expressed with four significant figures.

For this case we have that by definition, the surface area of a cylinder is given by:

[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

Where:

r: It's the radio

h: It's the height

Substituting according to the data we have:

[tex]SA = 2 \pi * (38) * (51) +2 \pi * (38) ^ 2\\SA = 2 \pi * 1938 + 2 \pi * 1444\\SA = 3876 \pi + 2888 \pi\\SA = 6764 \pi[/tex]

Thus, the surface area of the cylinder is [tex]6764 \pi \ mm ^ 2[/tex]

Answer:

[tex]6764 \pi \ mm ^ 2[/tex]

Answer:

There are 200 $8 tickets

There are 150 $10 tickets

There are 50 $12 tickets

Step-by-step explanation:

Let a = number of $8 tickets

Let b = number of $10 tickets

Let +c = number of $12 tickets

given:

(1) a+b+c = 400

(1) 8a+10b+12c = 3700

(1) a+b = 7c

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

This is 3 equations and 3 unknowns, so

it should be solvable

Substitute (3) into (1)

(1) 7c+c = 400

(1) 8c= 400

(1) c = 50

Plug this value into (2)

(2) 8a+10b+12*50= 3700

(2) 8a+10b+600= 3700

(2) 8a+10b= 3100

(2) 4a+5b= 1550

and

(1) a+b+c= 400

(1) a+b+50= 400

(1) a+b= 350

Multiply both sides of (1) by +4+

(1) 4a+4b= 1400

Subtract (1) from (2)

(2) 4a+5b+=+1550+

(1) -4a-4b= -1400

b= 150

and, since

(3) a+b= 7c

(3) a+150= 7*50

(3) a= 350-150

(3) a= 200

_________________

There are 200 $8 tickets

There are 150 $10 tickets

There are 50 $12 tickets

____________________________

check:

(2) 8*200+10*150+12*50= 3700

(2) 1600+1500+600= 3700

(2) 3700= 3700

Each type was sold are 200 for $8, 150 for $10, and 50 for $12 if the ticket prices were $8, $10, and $12, and the total income from ticket sales was $3700.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

At a college production of A Streetcar Named Desire, 400 tickets were sold. The ticket prices were $8, $10, and $12, and the total income from ticket sales was $3700.

Let x be the number of $8 tickets

Let y be the number of $10 tickets

Let z be the number of $12 tickets

From the data given in the question, we can frame three linear equation in three variables:

x + y + z = 400

8x + 10y + 12z = 3700

x + y = 7z

After solving the above equations by elimination method:

We get:

x = 200

y = 150

z = 50

Thus, each type was sold are 200 for $8, 150 for $10, and 50 for $12 if the ticket prices were $8, $10, and $12, and the total income from ticket sales was $3700.

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Answer:

(a) Rectangle 1 and rectangle 2 are similar

(b) The perimeter of Rectangle 2 is k times the perimeter of Rectangle 1

(c) The area of Rectangle 2 is k² times the area of Rectangle 1

Step-by-step explanation:

* Lets talk about the similarity

- Two rectangles are similar if there is a constant ratio between

  their corresponding sides

- Rectangle 1 has dimensions x and y

- Rectangle 2 has dimensions kx and ky

- The ratio between their dimensions is:

 kx/x = k and ky/y = k, so there is a constant ratio K between their

 corresponding dimensions

(a) Rectangle 1 and rectangle 2 are similar

- The perimeter of any rectangle is 2(the sum of its two dimensions)

∵ Rectangle 1 has dimensions x and y

∴ Its perimeter = 2(x + y) = 2x + 2y ⇒ (1)

∵ Rectangle 2 has dimensions kx and ky

∴ Its perimeter = 2(kx + ky) = 2kx + 2ky

- By taking k as a common factor

∴ Its perimeter = k(2x + 2y) ⇒ (2)

- From (1) and (2)

∵ The perimeter of rectangle 1 = (2x + 2y)

∵ The perimeter of rectangle 2 = k(2x + 2y)

∴ The perimeter of rectangle 2 is k times the perimeter of rectangle 1

(b) The perimeter of Rectangle 2 is k times the perimeter of Rectangle 1

- The area of any rectangle is the product of its two dimensions

∵ Rectangle 1 has dimensions x and y

∴ Its area = x × y = xy ⇒ (1)

∵ Rectangle 2 has dimensions kx and ky

∴ Its area = kx × ky = k²xy ⇒ (2)

- From (1) and (2)

∵ The area of rectangle 1 = xy

∵ The area of rectangle 2 = k²xy

∴ The area of rectangle 2 is k² times the area of rectangle 1

(c) The area of Rectangle 2 is k² times the area of Rectangle 1

(a) Yes, Rectangle 1 and Rectangle 2 are similar. (b) It is proved that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1. (c) It is proved that the area of Rectangle 2 is [tex]k^2[/tex] times the area of Rectangle 1.

(a) Yes, Rectangle 1 and Rectangle 2 are similar. They are similar because each dimension of Rectangle 2 is k times the corresponding dimension of Rectangle 1, which means that all angles remain the same and the sides are in proportion.

(b) To prove that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1, we start by noting that the perimeter of a rectangle is the sum of all its sides. For Rectangle 1, the perimeter [tex]P_1[/tex] is given by :

[tex]P_1 = 2(x + y)[/tex]

For Rectangle 2, each dimension is multiplied by k, so the length becomes kx and the width becomes ky. Therefore, the perimeter [tex]P_2[/tex] of Rectangle 2 is:

[tex]P_2 = 2( kx + ky)[/tex]

[tex]P_2 = 2k(x + y)[/tex]

Since 2(x + y) is the perimeter of Rectangle 1, we can replace it with [tex]P_1[/tex], yielding [tex]P_2 =[/tex] [tex]kP1[/tex] . This shows that the perimeter of Rectangle 2 is indeed k times the perimeter of Rectangle 1.

(c) To prove that the area of Rectangle 2 is [tex]k^2[/tex] times the area of Rectangle 1, we consider the formula for the area of a rectangle, which is the product of its length and width.

The area [tex]A_1[/tex] of Rectangle 1 is:

[tex]A_1 = xy[/tex]

For Rectangle 2, the length and width are both multiplied by k, so the area [tex]A_2[/tex] is:

[tex]A_2 = (kx)(ky)[/tex]

When we multiply these out,

we get:

[tex]A2 =[/tex] [tex]k^2xy[/tex]

Since xy is the area of Rectangle 1, we can replace it with [tex]A_1[/tex], giving us [tex]A_2 =[/tex] [tex]k^2A_1[/tex] . This demonstrates that the area of Rectangle 2 is [tex]k^2[/tex] times the area of Rectangle 1.

The diagram of rectangles:

C is 90°fare and height

Answer:

[tex] \sin(x) = \frac{4}{6 } \\ x = arcsin( \frac{2}{3} ) \\ x = 41.81 \: degrees [/tex]

Step-by-step explanation:

Google search inverse trigonometry geometry for an explanation

answer technically should say

measure of angle A equals 41.81 degrees

there should be the letter m in front of the angle symbol.

Answer:

11 ≤ n

Explanation:

[tex] \frac{66}{6} = 11[/tex]

More than indicates the minimum value, so you use the greater than or equal to.

The above answer is written in reverse, which the exact same result.

I am joyous to assist you anytime.

Answer:

400 seats would be in each section.

Step-by-step explanation:

8,000/20 is equal to 400.

Hope this helps!

Please give brainliest :)

Answer:

p(side effects|child) = 0.44

p(side effects|adult) = 0.14

Conclusion: children have a much greater chance of having side effects than adults.

Step-by-step explanation:

i just did it on apex. good luck!

Answer:

p(side effects/child) = 0.44

p(side effects/adult) = 0.14

Conclusion: Children have a much greater chance of having side effects than adults

~apex

Answer:

The angle of elevation is 60.3°

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problem

∵ The shadow of the tree is 20 feet long

- The shadow of the tree is on the ground

∵ The height of the tree is 35 feet tall

∴ The shadow of the tree and the height of the tree formed the legs of

  a right triangle

- The angle of elevation is opposite to the tree

∴ The shadow of the tree is the adjacent side of the angle of elevation

∴ The height of the tree is the opposite side of the angle of elevation

- let the name of the angle of elevation is Ф

∴ tan Ф = tree height/shadow length

∴ tan Ф = 35/20 = 7/4

∴ Ф = tan^-1(7/4) = 60.3°

* The angle of elevation is 60.3°

Answer:

The measure of these two angles are 80° and 100°

Step-by-step explanation:

Let

x and y ----> the measure of the same side angles

we know that

The sum of of the same side angles of two parallel lines is equal to 180 degrees

x+y=180° -----> equation A

x=y-20° ----> equation B

substitute equation B in equation A and solve for y

(y-20°)+y=180°

2y=180°+20°

y=200°/2

y=100°

Find the value of x

x=100°-20°=80°

Answer:

B) 2 hours 20 minutes

Answer:B 2HRS 20MINS

Step-by-step explanation:

Answer:

 The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. 

so....

About 24 necklaces have more than 28 beads. 

About 48 necklaces have more than 28 beads. 

About 80 necklaces have more than 28 beads. 

About 96 necklaces have more than 28 beads

 About 80 necklaces have more than 28 beads. 

Step-by-step explanation:

About 80 necklaces have more than 28 beads. 

Green thumbs sells lowest price. If you divide the$amount by the amount of roses, you'll get

Flora's : $13.50/3= $4.50 each rose

Green: $15/4= $3.75 each rose

Discount F: $23/6= $3.83 each rose

The correct interpretation for the expression 5(3x - 4)² is The product of 5 and the square of 3x - 4 ( option C)

An expression is a mathematical phrase containing variables, constants, and operators.

It represents a mathematical relationship or computation and does not have a specific value until the variables are assigned values.

Interpreting 5(3x - 4)²

is The product of 5 and the square of 3x - 4

Therefore, the correct interpretation for the expression 5(3x - 4)² is The product of 5 and the square of 3x - 4

Answer:

28 boxes

Step-by-step explanation:

We need to take the total number of cans needed and divide by the number of cans per box to determine the number of boxes

895 / 32 =27  with 31 left over

Making this a fraction

27 31/32 boxes

We cannot normally order part of a box

Rounding up to the next whole box

28 boxes