Find the area of each triangle.

Answer:

$98 a month

Step-by-step explanation:

1,176 divided by 12

The parametric equations graph as a portion of a parabola. The initial point is (5,0), and the terminal point is (3,4). The vertex of the parabola is (2,9). Arrows are drawn along the parabola to indicate motion right to left.

Parametric equations are a way of expressing a set of equations that define the coordinates of a point in terms of a third variable (parameter) that varies over a certain range. In the given problem, the parametric equations:

x(t) = 2 - t

y(t) = (t+3)²

To visualize the graph of these equations, we can substitute different values of t and plot the corresponding points (x(t), y(t)) on a coordinate plane. Since t ranges from -4 to 0, we can choose a few values of t such as t=-4, t=-2, and t=0 to get the corresponding points.

When plotted these points, a portion of a parabola that opens upwards. The vertex of the parabola is at the point (3, 4) where x=2-t and y=(t+3)² intersect. The initial point of the graph is when t=-4, which gives the point (6, 1) and the terminal point is when t=0, which gives the point (2, 9). The arrows are drawn along the parabola to indicate the direction of motion, which is from right to left in this case.

Find out more on  parametric equations here: https://brainly.com/question/30451972

#SPJ1

Answer:

(m-3)^2

Step-by-step explanation:

(m^2-6m+9) is factored by using this formula:
(a-b)^2=a^2-2ab+b^2.

Therefore, we can substitute the values into this equation.

m^2=a^2,

-6m=-2ab,

9=b^2.

Solving for b in the third equation, b is equal to 3 or -3. However, as this equation is negative, then it must be -3.

(m-3)^2

answer:

17%

I hope this helps

The statement that is false, given the table of Ms Stewart's class would be A. 15 % of her students are in biology.

The table shows that out of all he students, Ms. Stewart has 35 % that are doing Biology and not 15 %. But, she does have 15 % of Freshmen doing Biology and not of all her students.

30 % of the students are indeed engaged in doing physical science, and 35 % of her students are in chemistry from the table. 45 % of the total cohort that Ms. Stewart teaches are freshmen.

Find out more on students at https://brainly.com/question/29577073

#SPJ1

You would need to purchase 720 different tickets to guarantee a win.

You must pick the first three finishers in the correct order to win a trifecta race with 10 entries.

Since there are ten participants in the race, there are ten ways to select the winner of the first place prize. In the wake of choosing the primary spot finisher, there are just 9 passages remaining, so the quantity of ways of choosing the second-place finisher is 9.

Finally, since there are only eight entries left after selecting the first two, there are 8 ways to select the third-place finisher.

Therefore, the total number of possible winning trifecta combinations is:

10 x 9 x 8 = 720

This indicates that in order to guarantee a win, you would need to purchase 720 distinct tickets. However, it is essential to keep in mind that betting on a race in this manner may not always be the most profitable or efficient option, and that purchasing each and every possible combination can be very costly. It's vital to painstakingly think about the chances, payouts, and your financial plan prior to putting down any wagers.

know more about combination visit:

https://brainly.com/question/13387529

#SPJ1

Answer:

75=x

Step-by-step explanation:

The constant of proportionality is 2/3

The length of the missing sides of triangle NRF are:

RF = 4.5

NR = 6

From the question, we are to calculate the constant of proportionality in the similar triangles

Constant of proportionality =

Corresponding side length on triangle GTY / Corresponding side length on triangle NRF

Constant of proportionality = GY / NF

Constant of proportionality = 6 / 9

Constant of proportionality = 2/3

We are to find the length of the missing sides of triangle NRF

By the similarity theorem, we can write that

3 / RF = 6 / 9

3 / RF = 2/3

Cross multiply

2 × RF = 3 × 3

2 × RF = 9

RF = 9/2

RF = 4.5

4 / NR= 6 / 9

4 / NR= 2/3

Cross multiply

2 × NR = 4 × 3

2 × NR = 12

NR = 12/2

NR = 6

Hence,

The length of the missing sides are

RF = 4.5

NR = 6

Learn more on Similar triangles here: https://brainly.com/question/31208613

#SPJ1

The geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

It should be noted that to find the geometric mean of two numbers, we multiply them together and then take the square root of the result. So, for each pair of numbers, we can follow these steps:

Multiply the two numbers together.

Take the square root of the product.

Using this formula, we get:

7.16 and 27:

Geometric mean = √(7.16 × 27) ≈ 14.85

5 and 36:

Geometric mean = √(5 × 36) = √180 ≈ 13.42

10.8 and 48:

Geometric mean = √(10.8 × 48) ≈ 22.94

Therefore, the geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

Learn more about mean on;

https://brainly.com/question/1136789

#SPJ1

Step-by-step explanation:

Volume = 20×70×80 = 112000 cm³

Volume of cubes = 20×20×20 ×5 = 8000 ×5 = 40000 cm³

Volume of space in the tank = 112000-40000 = 72000 cm³ = 72000 mL = 72 L

Volume of water from tap = 158 × 1 = 158 L

Volume of water spilt out = 158 - 72 = 86 L

Answer: 30000cm³

Step-by-step explanation:

Capacity of tank-> 30x70x80

                               =168000

Volume of 1 cube->20x20x20

                              =8000

Volume of 5 cubes->8000x5

                                  =40000

Volume of space which can be occupied by water->168000-40000

                                                                                        =128000

Volume of water running for 158 min-> 158x1000

                                                                  =158000

Volume of water spilt out->158000-128000

                                             =30000( Ans)

Answer:

0,-1

Step-by-step explanation:

Hope this helps! =D

Brainliest! =D

Answer:

-1

Remember y=mx+b

m is your slope and b is your y-int
m = -4/3

b = -1

The probability that someone with a credit score of 650 or below defaulted on the loan is 0.14.

The probability that someone with a credit score of 650 or below defaulted on the loan is calculated below:

Probability = number of defaulters/ number of loan recipients

From graph:

The total number of defaulters = 30 + 30 + 30

The total number of defaulters = 90

The total number of loan recipients = 120 + 240 + 270

The total number of loan recipients = 630

Probability to default = 90/630

Probability to default = 0.14

Learn more about probability at: https://brainly.com/question/24756209

#SPJ1

Answer: 135

Step-by-step explanation:

1) The length of the segments BC =√53   FG =√53  JK =√53

2) The statements that are true are;

BC ≅ FG

BC ≅ JK

FG ≅ JK

To find the lengths of the segments, we use the formula d = √((x2 - x1)² + (y2 - y1)²)

For BC, it would be √((1 - (-6))² + (2 - 4)²) = √53.

It would ordinarily be 7.3. However, since approximations are not needed, it has been left in the form of squareroot

For  FG: √((-5 - (-7))² + (-1 - 6)²) = √53.

The answers provided are based on the questions seen in the image

Here are the endpoints of the segment BC, FG and JK.

B (-6, 4)  C (1, 2)        F (-7, 6),  G (-5, -1)        J (1, -8), K (3, -1)

Find the length of each segment. give an exact answer (not a decimal approximate)

BC =     FG =      JK =

Check all the statement that are true below;

BC ≅ FG

BC ≅ JK

FG ≅ JK

None of these are true.

Find more helpful exercises on segments;

https://brainly.com/question/12728072

#SPJ1

Answer:

76°

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°.

p = 360 - 60 - 134 - 90 = 76

Answer:

x = 4√3 y = 8/√2 = 4√2

(4 rad 3) (4 rad 2)

The proof of the three distributions as required as shown in the explanation part.

For x² distribution:

Let's start with the sample variance, which is defined as:

s^2 = ∑(y_i - y_bar)² / (n-1)

where;

We can rewrite this formula as:

s^2 = (∑y_i² - n*y_bar²) / (n-1)

Multiplying both sides by (n-1)/σ², we get:

s^2 / σ² = (∑y_i² - ny_bar²) / (σ²(n-1))

Now, let's define a new variable:

x² = ∑y_i² / σ²

Substituting x² into the above equation, we get:

s^2 / σ² = (x² - n*y_bar²/σ²) / (n-1)

Notice that n*y_bar²/σ² is just the sample mean squared in units of variance. We can rewrite it as:

n*y_bar²/σ² = (y_bar - μ)² / (σ²/n)

where;

Substituting this into the above equation, we get:

s^2 / σ² = (x² - (y_bar - μ)² / (σ²/n)) / (n-1)

Now, let's define a new variable:

ss = ∑(y_i - y_bar)² / σ²

Substituting ss into the above equation, we get:

s^2 / σ² = (x² - ss/(n-1)) / n

This is the desired result. We have shown that s²/σ² follows a x² distribution with n-1 degrees of freedom.

For t distribution:

Let's start with the sample mean, which is defined as:

y_bar = ∑y_i / n

We can rewrite this formula as:

y_bar - μ = (∑y_i - n*μ) / n

Now, let's define a new variable:

t = (y_bar - μ) / (s/√n)

where;

Substituting y_bar - μ and s into the above equation, we get:

t = (∑y_i - nμ) / (s√n)

This is the desired result. We have shown that t follows a t distribution with n-1 degrees of freedom.

For F distribution:

Let's start with the sample variances, which are defined as:

s₁² = ∑(y_i - y₁)² / (n₁-1)

s₂² = ∑(y_i - y₂)² / (n₂-1)

where;

We can rewrite these formulas as:

s₁² = (ss₁ - n₁*(y₁-μ)²) / (n₁-1)

s₂² = (ss₂ - n₂*(y₂-μ)²) / (n₂-1)

where;

ss₁ = ∑(y_i - y₁)²

ss₂ = ∑(y_i - y₂)²

Dividing these equations, we get:

s₁² / s₂² = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))

Now, let's define a new variable:

F = s₁² / s₂

Substituting s₁² / s₂² into the above equation, we get:

F = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))

This is the desired result. We have shown that F follows an F distribution with (n₁-1) and (n₂-1) degrees of freedom.

It's worth noting that the F distribution is only defined for positive values. Therefore, if s₁² / s₂² is less than 1, we need to take the reciprocal of the above equation to ensure that F is positive:

F = (ss₂ / (n₂-1)) / (ss₁ / (n₁-1))

Learn more about proof of distributions here: https://brainly.com/question/29184279

#SPJ1

The above prompts are related to the concepts of Degrees, Radians, Sines and Cosines. See the solutions below.

1)

(a) Cos 150 degrees

To convert 150 degrees to radians, we multiply by π/180:

150 degrees = (150π/180) radians = (5π/6) radians

We can use the unit circle and reference angle of π/6 to find the cosine of 5π/6:

cos(5π/6) = -cos(π/6) = -(√3/2) = -√3/2

Therefore, cos 150 degrees = -√3/2.

(b) Sin 240 degrees

To convert 240 degrees to radians, we multiply by π/180:

240 degrees = (240π/180) radians = (4π/3) radians

We can use the unit circle and reference angle of π/3 to find the sine of 4π/3:

sin(4π/3) = -sin(π/3) = -(√3/2) = -√3/2

Therefore, sin 240 degrees = -√3/2.

2)

To use the law of cosines, we need either a side and the two angles opposite that side, or two sides and the angle between them. In this case, we have two angles and the side opposite one of them, so we can use the law of sines to find the other side and then use the law of cosines to find the remaining side or angle.

Using the law of sines, we have:

sin A / AB = sin B / AC

where AC is the side opposite angle B. Substituting the given values, we get:

sin 52 / 26.7 = sin 70 / AC

Solving for AC, we get:

AC = sin 70 / sin 52 * 26.7 = 30.4

Now we can use the law of cosines to find the remaining side, x:

x^2 = AB^2 + AC^2 - 2ABACcos A

Substituting the given values, we get:

x^2 = 26.7^2 + 30.4^2 - 226.730.4*cos 52

Solving for x, we get:

x ≈ 22.1

Therefore, the missing side is approximately 22.1.

To find the area of the triangle, we can use the formula:

Area = (1/2) * a * b * sin C

where a and b are the lengths of the two sides, and C is the included angle. Substituting the given values, we get:

Area = (1/2) * 7 * 9 * sin 30

Using the fact that sin 30 = 1/2, we can simplify this to:

Area = (1/2) * 7 * 9 * (1/2) = 15.75

Therefore, the area of the triangle is 15.75 square units.

From the law of sines, we have:

sin A / a = sin B / b

Substituting the given values, we get:

sin 45° / (7√2) = sin B / 7

Solving for sin B, we get:

sin B = (7/7√2) * sin 45° = √2/2

Therefore, B = 45° or 135°. We can use the fact that the angles of a triangle sum to 180° to find C:

C = 180° - A - B = 90° or 0°

If C = 0°, then the triangle is degenerate and the sides a and b lie on top of each other. Therefore, we must have C = 90°.

Now we can use the Pythagorean theorem to find the remaining side:

c^2 = a^2 + b^2 - 2ab*cos C

Substituting the given values, we get:

c^2 = (7√2)^2 + 7^2 - 2(7√2)(7)*cos 90°

Solving for c, we get:

c = √(98 + 49) = √147 = 7√3

Therefore, the sides of the triangle are:

a = 7√2

b = 7

c = 7√3

Using the law of cosines to find x:

In triangle ABC with side lengths AB = 18, AC = 15, and angle A = 108 degrees, we want to find the length of side BC (denoted by x). Using the law of cosines:

x^2 = 18^2 + 15^2 - 2(18)(15)cos(108 degrees)

We can evaluate the cosine of 108 degrees using the identity cos(180 - 108) = -cos(108):

cos(108 degrees) = -cos(180 - 108 degrees) = -cos(72 degrees)

Substituting this into the equation above, we get:

x^2 = 18^2 + 15^2 - 2(18)(15)(-cos(72 degrees))

Simplifying:

x^2 = 729

Taking the square root of both sides:

x = ±27

Since x represents a length, we take the positive root:

x = 27

Therefore, the length of BC is 27 units.

Using the law of cosines to find theta:

In triangle ABC with side lengths AB = 20, BC = 12, and AC = 10, we want to find the measure of angle B (denoted by theta). Using the law of cosines:

cos(B) = (12^2 + 10^2 - 20^2) / (2(12)(10)) = -1/2

Since -1/2 is the cosine of an angle in the second quadrant, we have:

B = 180 degrees - arccos(-1/2)

Using a calculator, we find:

B ≈ 150.5 degrees

Therefore, the measure of angle B is approximately 150.5 degrees (or theta = 150.5 degrees).

Learn more about radians at:

https://brainly.com/question/7721249

#SPJ1

Answer:

First, we need to convert 1,200 meters to inches:

1,200 meters * 39.3701 inches/meter = 47,244.12 inches

Next, we need to find the circumference of the wheel:

Circumference = π * Diameter

Circumference = 3.14 * 12 inches

Circumference = 37.68 inches

To find the number of revolutions, we can divide the total distance traveled (47,244.12 inches) by the distance traveled per revolution (37.68 inches):

47,244.12 inches ÷ 37.68 inches/revolution ≈ 1,254 revolutions

Rounding to the nearest whole number, it will take approximately 1,254 revolutions of the wheel to travel 1,200 meters on a child's bicycle.

When the block is cut into smaller pieces, 512 pieces of cheese remain.

A cube is a solid three-dimensional shape with 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedral.

The volume V of a cube  is given by the formula V = a^3, where a = the length of one side of the cube. V = 4 ^ 3 = 64 cubic meters or inches ^ 3. The volume of a cube is 64 cubic meters

The total volume of the cheese block is obtained as follows:

V = edge length³ = 8³ = 512 cubic meters

Since the volume of each piece is 1 cubic inch, the total number of pieces is obtained by dividing the total volume by the volume of each piece:

Number of pieces = V / volume per piece = 512 / 1 = 512 pieces

Therefore, when the block is cut into smaller pieces, 512 pieces of cheese remain.

Learn more about Volume of Cube here

https://brainly.com/question/11168779

#SPJ1

Dimensions of the rectangle are 6 feet and 12 feet.

Rectangle is a quadrilateral whose each pair of opposite sides are equal in length and each two consecutive sides are in right angle to each other. In rectangle one pair of equal opposite sides is called Length and another one is called Width.  

If length of a rectangle is L and width of rectangle is W then the perimeter of that rectangle will be = 2(L+W)

Let W be the rectangle's width.

Here according to question the rectangle is twice as long as it is wide.

So, length of rectangle = 2W

Perimeter will be = 2(W+2W) = 2*(3W) = 6W

So, according to question,

6W = 36

W = 36/6 = 6

Thus the width of the rectangle is = 6 feet.

Then the length = 2*6 = 12 feet.

Hence dimensions of the rectangle are 12 feet and 6 feet respectively.

To know more about Rectangle visit:

https://brainly.com/question/2607596

#SPJ1

The surface area and volume of the tent are 213.5 ft² and 148?75ft³ respectively.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as ;

SA = 2B + ph. Where p is the perimeter and h is the height of the prism. B is the base area

Base area = 1/2 bh

= 1/2 × 7 × 5 = 35/2

= 17.5ft²

perimeter = 7+6+6 = 21ft

SA = 2 × 17.5 + 21 ×8.5

SA = 35+178.5

SA = 213.5 ft²

Volume of prism is expressed as;

V = base area × height

= 17.5 × 8.5

= 148.75 ft³

learn more about area and volume of prism from

https://brainly.com/question/30488690

#SPJ1

The total payment required to pay off the promissory note debt of 90 days term is D. $510.00.

The promissory note issued is for $500.

The interest rate is 8%.

Furthermore, the time frame is 90 days.

So the total payment is

= $500 + ($500 × 8% × 90 days ÷ 360 days)

= $500 + ($500 × 8% × 1/4)

= $500 + 10

= $510

Promissory notes are sometimes known as an IOU, a loan arrangement, or simply a note. It is a legal lending contract in which the borrower pledges to return the lender a specific amount of money within a specific time frame.

This type of document is legally binding and imposes a legal duty to repay the loan. Mortgages, school loans, car loans, company loans, and personal loans between family and friends all use promissory notes.

To know more about promissory note:

https://brainly.com/question/13717659

#SPJ1

Aaron's algebraic expression is:

14 * (18 - 3x)

an algebraic expression is an expression built up from constant algebraic numbers, variables, and the addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number.

This expression represents the product of 14 and the difference of 18 and 3x. The factors of this expression are:

14: This is a constant factor that multiplies the difference of 18 and 3x.

(18 - 3x): This is the distinction of 18 and 3x, which is being duplicated by 14. It is a two-term binomial expression: 18 and -3x. The first term, which has a coefficient of -3, is a variable, while the second term, which has a coefficient of -3, is a constant.

To work on the articulation, we can utilize the distributive property of augmentation to get:

14 * (18 - 3x) = 14*18 - 14*3x = 252 - 42x

In this worked on structure, the elements are as yet 14 and (18 - 3x). However, additional factors of the simplified expression, such as 2 and 21, which are factors of 42 (the coefficient of x), can also be identified.

know more about factors visit:

https://brainly.com/question/14549998

#SPJ1

The calculated line of reflection of the graph is y = -3

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

Read more about transformation at

brainly.com/question/27224272

#SPJ1

Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation:

Step-by-step explanation:

2 1/4 = 9/4

2 × 2 1/4 = 2 × 9/4 = 9/2

There are 24 possible arrangements for the elements in the occurrences where there are no cards in the box with the same letter.

Arrangement of objects in a specific order.

From the information provided:

Using the permutation method, the four cards that are arbitrarily placed in the four boxes can be represented as follows:

No box has a card that begins with the same letter as the box, which suggests that:

There are four different ways to arrange Card A in a box, three different ways to arrange Card B in a box, two methods to arrange Card C in a box, and one way to arrange Card D in a box.

Thus, the Permutation of the four cards can be calculated as:

[tex]4^p_4 = 4! = (4 * 3 * 2 * 1) = 24[/tex]

Learn more about, Permutation here:

brainly.com/question/12468032

#SPJ1

Thus, the length of walk way around the filed is the perimeter of the right triangle which is found as: 206.023 m .

The quickest approach to determine a triangle's perimeter is to sum up all of its sides' lengths, but you must first determine each side's length if you don't already know it.

The walk way around the filed is the perimeter of the right triangle.

walk way = base + height + hypotenuse

walk way = B + P + H

base B = 80 - 10 = 70 m

Altitude P = 70 - 20 = 50 m

For the hypotenuse H , use the Pythagorean theorem:

H² = B² + P²

H² = 70² + 50²

H² = 4900 + 2500

H² = 7400

H = 86.023

So,

walk way = B + P + H

walk way = 70 + 50 + 86.023

walk way = 206.023 m

Thus, the  walk way around the filed is the perimeter of the right triangle which is found as: 206.023 m .

Know more about the perimeter of triangle:

https://brainly.com/question/17394545

#SPJ1