Write an equation in slope intercept form of the line that passes through the given points

We have shown that ΔABC ~ ΔDBE because the corresponding angles are congruent and the corresponding sides are proportional.

The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well.

We must demonstrate that the respective angles of the two triangles are congruent and the corresponding sides are proportionate in order to demonstrate that ABC DBE.

To begin with, we can relate the sides of the two triangles using the following equation AB BE = CB BD. Let x, y, and z all be equal to AB. Next, we have:

x · BE = y · z (substituting the given values)

y/x = BE/BD (dividing both sides by BD and then by x)

Now, we can utilise the knowledge that a triangle's angles sum to 180 degrees to get the length of ABC:

ACB - 180° = ABC (from the given triangle ABC)

ABC = 180 degrees - BDE (corresponding angles)

The measure of BDE can then be determined using the connection between the sides that we discovered earlier:

y/x = BE/BD (from above)

BE/DE = y/(x+z) (substituting z = BD)

BDE is equal to tan(y/(x+z)) Inverse tangent is used.

Now, we can use the fact that a triangle's angles sum to 180 degrees to determine the size of the DBE:

DBE = 180°, BDE, and BED

DBE is equal to 180 - tan(y/(x+z)) - ∠BED (substituting the angle measure we just found) (substituting the angle measure we just found)

DBE is equal to 180° - tan(y/(x+z)) - tan(y/z) (using inverse tangent again)

tan(z(y+x)/(xz-yz)) = DBE (using the tangent of the sum formula)

In order to demonstrate that the sides of the two triangles are proportional, we can once more use the relationship between the sides:

BE/BD = AB/CB (from the given equation and simplification)

Y/x = AB/CB (from the relationship between the sides)

As a result, we have demonstrated that ABC DBE since the associated angles and sides are congruent and proportionate, respectively.

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not to sure about that try researching that

depends on ur teacher for me its really hard but the material wouldnt be too bad if you have a good teacher. it contains a lot of logistics and specific wording but memorization is key

Answer:

To find all values of x for which f(x) = 26, we can set up the equation:

8x + 15/x = 26

Multiplying both sides by x, we get:

8x^2 + 15 = 26x

Bringing all the terms to one side, we get:

8x^2 - 26x + 15 = 0

We can factor this quadratic equation using the factoring method or by using the quadratic formula. Here, we will use the factoring method:

8x^2 - 26x + 15 = 0

(4x - 3)(2x - 5) = 0

Setting each factor equal to zero and solving for x, we get:

4x - 3 = 0 OR 2x - 5 = 0

4x = 3 OR 2x = 5

x = 3/4 OR x = 5/2

Therefore, the values of x for which f(x) = 26 are x = 3/4 or x = 5/2.

Answer:

3n + 5n = 8n = 95

n = 11

$95 - $88 = $7

(11 paint brushes, 11 boxes of colored pencils)

Answer:

Step-by-step explanation:

70% of 140 is equal to 0.7 x 140 = 98. Therefore, the answer is 98.

Answer:

98

Step-by-step explanation:

70% can also be written as 0.7, therefore, we can multiply 140 by 0.7.

140 x 0.7 = 98.

Answer:

86.96 inches.

Step-by-step explanation:

C = 2πr

d = 2r

Solving for C

C = πd = π · 28 ≈ 87.96459 inches

Answer:

Step-by-step explanation:

To calculate this, we need to use the formula for future value of an annuity:

FV = PMT x ((1+i)^n - 1)/i

Where:

PMT = the periodic payment (or deposit)

i = the interest rate per period

n = the number of periods

In this case, there are three deposits:

- R3,600 deposited one year ago

- R5,000 deposited today

- R7,500 to be deposited next year

We can calculate the future value of each of these deposits separately, and then add them together to get the total future value:

Future value of R3,600 deposited one year ago:

n = 4 (4 years until the equipment purchase)

i = 7% per year

PMT = R3,600

FV = R3,600 x ((1+0.07)^4 - 1)/0.07 = R4,661.07

Future value of R5,000 deposited today:

n = 3 (3 years until the equipment purchase)

i = 7% per year

PMT = R5,000

FV = R5,000 x ((1+0.07)^3 - 1)/0.07 = R6,885.02

Future value of R7,500 to be deposited next year:

n = 2 (2 years until the equipment purchase)

i = 7% per year

PMT = R7,500

FV = R7,500 x ((1+0.07)^2 - 1)/0.07 = R8,733.63

Total future value = R4,661.07 + R6,885.02 + R8,733.63 = R20,279.72

Therefore, there will be R20,279.72 available when the family is ready to buy the equipment, assuming a 7% rate of return on the investment.

Answer:

28 people

Step-by-step explanation:

21 / 3 = 25

7 = 25%

25 x 4 = 100%

so

7 x 4 = 28

28 people are in the class

Answer:

Step-by-step explanation:

Ici, nous allons réduire la fraction 18/25 aux termes les plus bas et la convertir en un nombre fractionnaire, si nécessaire.

Dans la fraction 18/25, 18 est le numérateur et 25 est le dénominateur.

On commence par trouver le plus grand diviseur commun de 18 et 25, qui est 1. Ensuite, on divise 18 et 25 par le plus grand diviseur commun pour obtenir la plus petite expression, écrite comme suit :

(18 ÷ 1) / (25 ÷ 1)

= 18/25

Answer:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of r=11 m and using π = 3.14, we get:

C = 2πr

C = 2 x 3.14 x 11 m

C = 69.08 m

Therefore, the circumference of the circle is 69.08 meters

Answer:

  (a)  Figure 3

  (b)  66.2 meters per second

Step-by-step explanation:

You want to know the figure that shows the best fit of a curve to the data, and you want to know the value of the curve when x = 8 seconds.

The fit is best when the difference between the data points and the curve is minimized. Often the sum of the squared differences is the metric that is minimized when the fit is best.

The gaps between the data points and the curve shown are greatest in Figures 1 and 2, so Figure 3 has the best fit.

The speed is estimated by the equation of the curve of best fit as ...

  y = 0.6x² +2.1x +11

A slight rearrangement can make this easier to evaluate:

  y = (0.6x +2.1)x +11

For x=8, the value of y is ...

  y = (0.6·8 +2.1)·8 +11 = 6.9·8 +11 = 66.2

The predicted speed at 8 seconds is 66.2 meters per second.

Answer:

D. 1519.8

Step-by-step explanation:

answer: x= 20x

Step-by-step explanation: 2+2 is 4, 4+4 is 8, quick maths

Answer:

(6,3)

(-6,3)

Step-by-step explanation:

The parallelogram ABCD's congruency can be proven using Side-Angle-Side (SAS) congruence theorem.

Prove that ΔABC ≅ ΔDCB using the Side-Angle-Side (SAS) congruence theorem.

Given that ABCD is a parallelogram, AB || CD and BC || AD. Therefore, ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DCA because they are corresponding angles.

AB ≅ CD and BC ≅ AD because opposite sides of a parallelogram are congruent.

Lastly, AC ≅ AC because it is a shared side between the two triangles.

Therefore, the following congruent parts:

∠ABC ≅ ∠DCB (by corresponding angles)

AB ≅ CD (by opposite sides)

BC ≅ AD (by opposite sides)

AC ≅ AC (shared side)

The SAS congruence theorem concludes that ΔABC ≅ ΔDCB.

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Image transcribed:

Prove ΔABC ≅ ΔDCB

Answer:

Vertex: (0,0)

Step-by-step explanation:

Two points on the left: (-10,25), (-20,100)

Two points on the right: (10,25), (20,100)

Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).

Answer:2,160ft

Step-by-step explanation: Volume=length * width * height

30x8x9=2160

Answer:

To find the image of the point (7, 0) under the given translation, we apply the translation rule:

(x, y) → (x + 1, y - 2)

Substituting (7, 0) for (x, y), we get:

(7, 0) → (7 + 1, 0 - 2)

= (8, -2)

Therefore, the image of the point (7, 0) under the given translation is (8, -2).

So, the correct answer is (8, −2).

Step-by-step explanation:

hope its help <:

Using the right cone formula we know that the surface area is 1281.77638m³ respectively.

An axis that is perpendicular to the base plane defines a right circular cone. By rotating a right triangle around one of its legs, we may create a right cone.

The right circular cone in the illustration has an axis that is perpendicular to the base and a circular base with a radius r.

So, the formula for the surface area of the right cone is as follows:

πr(r+√h²+r²)

We have the values: r = 13m and h = 13m

Now, insert values as follows:

= πr(r+√h²+r²)

= π13(r+√13²+13²)

= 1281.77638

Therefore, using the right cone formula we know that the surface area is 1281.77638m³ respectively.

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The answer of the given question based on the graph and the function the answer are,

a) Demi's speed is decreasing over time.

b) Demi's speed decreases  from approximately 8.5 miles per hour to 5 miles per hour and  Demi's speed decreases from approximately 6 miles per hour to 3 miles per hour.

Speed is measure of how fast object is moving, or  rate at which it covers  certain distance over time. Mathematically, speed is calculated as distance traveled divided by time it takes to travel that distance.

a. When the function is decreasing, Demi's speed is decreasing over time. This means that she is running more slowly as time goes on. On the graph, this will be shown as a downward slope or a negative slope. The steeper the slope, the faster her speed is decreasing.

b. From the graph, we can see that the function is decreasing in two intervals. The first interval is from 0 to 5 minutes, where Demi's speed decreases from approximately 8.5 miles per hour to 5 miles per hour. The second interval is from 10 to 15 minutes, where Demi's speed decreases from approximately 6 miles per hour to 3 miles per hour.

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Demi went for a run in the park. The graph shows her speed during the run.

a. Describe the graph when the function is decreasing.

b. In how many intervals is the function decreasing?

Answer:

Yes, ∆PQR is a right triangle.

Step-by-step explanation:

A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.

Answer:

Step-by-step explanation:

If x=8, y = 4(8) - 7 = 25

If x=3, y = 4(3) - 7 = 5

If x=3, y = 2(3^2) = 18

If x=5, y = 2(5^2) = 50

If x=1, y = (2+1)^2 = 9

If x=3.5, y = (2+3.5)^2 = 30.25

2.4 < 2.8

53 > 1.666…

1.43 > .296

92 > 4.500

5.62 > 5.602

0.32 > 0.032

314 < 318

3437 > 3435

Answer:

we will do TanA = perpendicular / Base

A = 35°

Tan 35° = 217 / W

value of Tan 35° is approx = 0.7

0.7 = 217/ W

W = 217 / 0.7

W = 310

The blanks of the number pyramid puzzle can be filled with numbers calculated below.

A number pyramid puzzle is a type of mathematical puzzle where a pyramid-shaped grid of numbers is given, with some of the numbers missing.

Check the attached image for labeling. Since each number is the product of the two numbers directly beneath it. We can say:

m = -4 * 0.5 = -2

k = 0.5 * 1/8 = 1/16

x * (-1/8) = 8

x = 8/(-1/8)

x = -64  

y = x * 1/8

y = -64 * 1/8

y = -8

j = m * k

j =  -2 * 1/16 = -1/8

p = -48 * m

p = -48 * (-2) = 96

n = y * 8

n = -8 * 8 = -64

t = p * j

t = 96 * (-1/8) = -12

w = -1/2 * n

w = -1/2 * (-64) = 32

c = t * 1/16

c = -12 * 1/16 = -3/4

u = 1/16 * w

u = 1/16 * 32 = 2

d = c * u

d = -3/4 * 2 = -3/2

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The answer of the given question based on rational parent function , to identify a correct transformation of the function, The correct answer choice is (c) Left 5.

A function is  mathematical relationship that assigns  unique output value for each input value. It describes relationship between two variables, where  output value is dependent on input value. A function can be represented by  equation, a graph, or  table. In its simplest form,  function takes  input value, performs a specified operation on that value, and produces  corresponding output value.

Functions are used to model real-world phenomena, to solve problems, and to analyze and understand complex systems. They are  fundamental concept in mathematics and are used in  wide variety of fields, like science, engineering, economics, and finance.

The given equation is y = 12/(x + 5), which represents the rational parent function. To identify a correct transformation of the function, we can consider the effect of each transformation on the parent function.

a) Vertical reflection: This transformation would change the sign of the function, resulting in y = -12/(x + 5). This is not the given equation, so it is not a correct transformation.

b) Vertical stretch by 12: This transformation would multiply the function by 12, resulting in y = 12(12/(x + 5)) = 144/(x + 5). This is not the given equation, so it is not a correct transformation.

c) Left 5: This transformation would shift the function to the left by 5 units, resulting in y = 12/(x + 10). This is a correct transformation of the function, as it represents a horizontal shift of 5 units to the left.

d) Down 5: This transformation would shift the function down by 5 units, resulting in y = 12/(x + 5) - 5. This is not the given equation, so it is not a correct transformation.

Therefore, the correct transformation of the rational parent function as described by the given equation is a horizontal shift of 5 units to the left. The answer choice is (c) Left 5.

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The correct transformation of the function on rational parent function as described by the given equation. The correct answer choice is (c) Left 5.

A function is  mathematical relationship that assigns  unique output value for each input value. It describes relationship between two variables, where  output value is dependent on input value. A function can be represented by  equation, a graph, or  table. In its simplest form,  function takes  input value, performs a specified operation on that value, and produces  corresponding output value.

The given equation is y = 12/(x + 5), which represents the rational parent function. To identify a correct transformation of the function, we can consider the effect of each transformation on the parent function.

a) Vertical reflection: This transformation would change the sign of the function, resulting in y = -12/(x + 5). This is not the given equation, so it is not a correct transformation.

b) Vertical stretch by 12: This transformation would multiply the function by 12, resulting in y = 12(12/(x + 5)) = 144/(x + 5). This is not the given equation, so it is not a correct transformation.

c) Left 5: This transformation would shift the function to the left by 5 units, resulting in y = 12/(x + 10). This is a correct transformation of the function, as it represents a horizontal shift of 5 units to the left.

d) Down 5: This transformation would shift the function down by 5 units, resulting in y = 12/(x + 5) - 5. This is not the given equation, so it is not a correct transformation.

Therefore, the correct transformation of the rational parent function as described by the given equation is a horizontal shift of 5 units to the left. The answer choice is (c) Left 5.

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Answer: sorry I can't see it.

Step-by-step explanation:

Therefore , the solution of the given problem of percentage comes out to be the firm expects that each warranty it sells will be worth $1.41.

In statistics, "a%" is used to refer to a figure or number that is expressed as a percentage of 100. Additionally rare are the forms that "pct," "pct," or "pc". It is typically represented by the symbol "%," though. Additionally, there are not any indicators and the proportion of each item to the overall amount is flat. Since percentages typically add up to 100, they are essentially integers. Either the expression "fraction" or the symbol for percentage (%) .

Here,

The price to substitute each item is $200. The anticipated price for each component is thus:

Expected cost per product equals Replacement cost x Failure Probability

=> Cost per product anticipated = 0.008 x $200

=>  Expected price per item is $1.60.

So, the following is the anticipated value of each warranty sold:

Expected worth of the warranty = Failure rate x (Replacement cost - Cost of warranty)

=>   Expected guarantee value = 0.008 * ($200 - $22 - $1.60).

=>  Expected guarantee value = 0.008 * $176.40

=>  Expected warranty worth is $1.41

As a result, the firm expects that each warranty it sells will be worth $1.41.

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Answer:

b=7 & c=7√2

Step-by-step explanation:

b=7 as it is an isosceles triangle

now using Pythagoras theorem,

(c)^2= (7)^2+(7)^2

⇒(c)^2= 49+49

⇒(c)^2= 98

⇒c= √98

⇒c=7√2

Answer:

Step-by-step explanation:

You want the missing side lengths in an isosceles right triangle with one side given as 7.

The two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:

  b = 7

The hypotenuse of an isosceles right triangle is √2 times the side length:

  c = 7√2

__

Additional comment

You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.

  c² = 7² + b²

  c² = 7² +7² = 2·7²

  c = √(2·7²) = 7√2

The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.

The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.