Please find the slope of line ST

The perimeter of right isosceles ΔABC with midsegment DE is 16 + 8√2.

If right isosceles ΔABC has hypotenuse length h, then the two other sides are congruent.

side a = side b

Using Pythagorean theorem, c^2 = a^2 + b^2

h^2 = a^2 + b^2      a = b

h^2 = 2a^2

a = h/√2

If DE is a midsegment not parallel to the hypotenuse, then it is a segment that connects the midpoints of one side of a triangle and the hypotenuse. See photo for reference.

ΔABC and ΔADE are similar triangles.

a : b : h = a/2 : 4 : h/2

If a/2 = a/2, then b/2 = 4.

b/2 = 4

b = 8

If a = b, then a = 8.

If a = h/√2, then

8 = h/√2

h = 8√2

Solving for the perimeter,

P = a + b + h

P = 8 + 8 + 8√2

P = 16 + 8√2

P = 27.3137085

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Answer:

Well, (2,3) is transformed into (-3,2)

(-3,-1) changes into (1,-3)

and (2,-1) changes into (1,2)

Step-by-step explanation:

Smort

Answer: 2000

12.5÷100=0.125

1600×0.125×10=2000

The simplified expression for (10-22 / 8-17) is 4/3 .

The given expression is,

( 10-22 / 8-17 )

First we need to solve the numerator which is (10-22) and on simplifying the numerator we can write,

Numerator = ( 10 - 22 ) = -12                         equation 1

Similarly, now we can proceed to solve the denominator which is (8 - 17) and on simplifying the denominator we write,

Denominator  = (8 - 17) = -9                       equation 2

Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression ( 10-22 / 8-17 ) as,

(Numerator / Denominator) = (10-22 / 8-17) = ((-12)/(-9)) = 4/3

The simplified expression for (16-12 / 15-11) is 4/3 .

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The amount A has in terms of d is 5d + 32.

The amount A has in terms of B is calculated as follows;

If a has 32 more than b, our equation becomes;

A = b + 32

The amount B has in terms of C is calculated as follows;

If  B has five times as much money as C and C has d dollars, our equation becomes;

B = 5C = 5d

The amount A has in terms of d is calculated as follows;

A = b + 32

A = 5d + 32

Thus, the amount A has in terms of d is 5d + 32.

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Answer:

14.   [tex]-3(x+2)+4[/tex]

12.   [tex]4[/tex]

15.   [tex]0[/tex]

Step-by-step explanation:

Question 14

To find the function in terms of "x+2", simply replace "x" in the original equation with "x+2":

[tex]f(x+2)=-3(x+2)+4[/tex]

Now simplify by distributing the 3:

[tex]f(x+2)=-3x-6+4[/tex]

Finish by adding the constants:

[tex]f(x+2)=-3x-2[/tex]

Question 12

This one follows the same concept! Replace "x" in the original equation with 1/2:

[tex]F(\frac{1}{2})=-2(\frac{1}{2} )+5[/tex]

Simplify:

[tex]f(\frac{1}{2})=-1+5\\f(\frac{1}{2})=4[/tex]

Question 15

For this question, it looks like you are given a set of coordinate pairs in the function. You are asked to find "f(4)". Essentially, you are being asked to find the value of y given 4 as the value of x.

The given coordinate pair (4,0) has 4 as the x value, so the y value when x=4 is 0!

Using a function to express the number of pieces of the two lengths, Evie should have 3 pieces of ribbon of length 12.5 cm and 5 pieces of ribbon of length 8.5 cm.

In mathematics, a function is the representation of the relationship of a set of input(X) and its corresponding output(Y).

If Evie has a price of ribbon that is 80cm long that she wants to cut into lengths of exactly 8.5cm or 12.5cm and that no ribbon left over, then the function for this statement is:

12.5x + 8.5y = 80     ⇒     y = (80 - 12.5x)/8.5

where x is the number of pieces of length 12.5 cm and y is the number of pieces of length 8.5 cm, and x and y must be whole numbers(pieces of ribbon)

Listing down the possible integers for the value of x and solving for the corresponding y value.

x = 1 , y = 135/17

x = 2 , y = 110/17

x = 3 ,  y = 5

x = 4 , y = 60/17

x = 5 , y = 35/17

x = 6 , y = 10/17

Since when x = 3, y = 5 is the only ordered pair that is both integers, then it is the answer.

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The statement which represents the expression one over seven raised to the third power is Option (C) one over three hundred forty-three is the correct option.

We are given the expression:

one over seven raised to the third power

This can be written as:

(1 / 7) ³

Simplifying and solving the expression by finding the cube of 1 and 7.

1³ = 1

7³ = 343

So, the expression will now become:

(1 / 7) ³ = 1 / 343

which can also be written as:

one over three hundred forty - three

Therefore, option (C) one over three hundred forty-three is the correct option which represents the expression one over seven raised to the third power.

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33.80 was deducted from the original price costing 84.50.

84.50 × 40% = 33.80

That's it, the answer is H. 33.80

The full cost of purchasing an asset is known as the original price. When calculating an asset's original cost, all of the costs associated with buying and using the asset are taken into account.

Included in these expenses are the purchase price as well as things like commissions, shipping, appraisals, warranties, installation, and testing. Equipment, real estate, and security instruments are all examples of asset types that can be valued using original cost.

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The volume of sphere and hemisphere is 7×10⁵ inches and 3.5×10⁵ inches respectively.

We are given the area of circle. From this given information, we will be calculating radius of the circle, which will be further required to calculate volume of sphere and hemisphere.

Area of circle = πr²

Keep the value in formula -

55π = πr²

Cancelling  π and taking square root to find the value of radius

r = √55

r = 7.4 inches

Now, volume of sphere is calculated by the formula -

Volume of sphere = 4/3 πr³

Volume of sphere = 4/3 π (55)³

Volume of sphere = 6.97×10⁵ inches

Now, volume of hemisphere is calculated by the formula -

Volume of hemisphere = 2/3 πr³

Volume of hemisphere = 2/3 π (55)³

Volume of hemisphere = 3.48×10⁵ inches

On rounding off, we get volume of sphere and hemisphere as 7×10⁵ inches and 3.5×10⁵ inches

Hence, the volume of sphere and hemisphere is 7×10⁵ inches and 3.5×10⁵ inches respectively.

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The area of the quadrilateral ABCD is 26 square units

The quadrilateral ABCD is a trapezoid, and it  has the following parameters:

The lengths of these sides can be calculated using

d = √[(x2 - x1)^2 +(y2 - y1)^2]

So, we have

BC = √[(0 - 4)^2 +(3 + 1)^2] = 4√2

AD = √[(-5 - 4)^2 +(4 + 5)^2] = 9√2

CE = √[(2 - 4)^2 +(-3 + 1)^2] = 2√2

The area of the quadrilateral ABCD is then calculated as

Area = 0.5 * (BC + AD) * CE

This gives

Area = 0.5 * (4√2 + 9√2) * 2√2

Evaluate

Area = 26

Hence, the area of the quadrilateral ABCD is 26 square units

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The area of the trapezoid is 169.6 cm² for the dimensions as 8 cm, 5.7 cm and 15.5 cm.

We are given that:

The dimensions of the trapezoid are:

Height = 8 cm

Shorter side = 5.7 cm

longer side = 15.5 cm

Area of the trapezoid will be:

A = (a + b) / 2 × h

Substituting the values in the formula, we get that:

A = (5.7 + 15.5) / 2 × 8 cm²

A = 21.2 × 8 cm²

A = 169.6 cm²

Therefore, we get that, the area of the trapezoid is 169.6 cm² for the dimensions as 8 cm, 5.7 cm and 15.5 cm.

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The perfect square equation is f(x) = (x + 7/2)^2 - 9/4

The equation of the function is given as

f(x) = x^2 + 7x + 10

Rewrite the equation as

x^2 + 7x + 10 = 0

Subtract 10 from both sides of the equation

So, we have

x^2 + 7x = -10

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

Take the coefficient of x

k = 7

Divide by 2

k/2 = 7/2

Square both sides

(k/2) = 49/4

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

Add 49/4 to both sides of the equation

So, we have

x^2 + 7x + 49/4 = -10 + 49/4

Express as a perfect square

So, we have

(x + 7/2)^2 = -10 + 49/4

Evaluate the sum

So, we have

(x + 7/2)^2 = 9/4

This gives

(x + 7/2)^2 - 9/4 = 0

So, we have

f(x) = (x + 7/2)^2 - 9/4

Hence, the perfect square equation is f(x) = (x + 7/2)^2 - 9/4

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Answer:

Step-by-step explanation:

p= AB+BC+AC

AB=[tex]\sqrt{(-5-(-5))^2+(4-(-2))^2} =6[/tex]

BC=[tex]\sqrt{(-5-6)^2+(4-(-2))^2} =\sqrt{157}[/tex]

AC=[tex]\sqrt{(6-(-5))^2+(-2-(-2))^2} =11[/tex]

p= 17+[tex]\sqrt{157\\[/tex]

Answer:

1056 feet

Step-by-step explanation:

5280/5=1056

The missing 2nd term of the given arithmetic sequence 25, _, 53,...(a₂ = 39).

The difference between the two different numerical orders is a fixed number in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd come along through a few specific words in AP that were labeled as:

The AP can also be understood in terms of common differences, as shown below.

Now, for the given AP;   25, _, 53....

Let the initial term be 'a₁' = 25

Let the second term be 'a₂' = ?

Let the third term be 'a₃' = 53.

The AP must have the same common difference. So,

d =  a₂ - a₁ or d = a₃ - a₂

Equating the common difference to find the 2nd missing term.

a₃ - a₂ = a₂ - a₁

Substitute the given values;

53 - a₂ = a₂ - 25

Bring the variable part on one side.

2a₂ = 53 + 25

a₂ = 78/2

a₂ = 39

Therefore, the 2nd missing value of an AP is found to be 39.

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Answer:

I believe the correct answer would be C.

Step-by-step explanation:

Have a great day! :)

Answer:

Use the given functions to set up and simplify

[

3

,

4

]

Step-by-step explanation:

Answer:

67 is the answer

Answer:

67 would be the nearest whole number.

The probability that a nut selected from the jar at random will be a cashew = 0.29

The correct answer is option (B) 0.29

In this question,

A jar contains 150 peanuts and 60 cashews.

So, the total number of nuts = 150 + 60

                                               = 210

We need to find the probability that a nut selected from the jar at random will be a cashew.

To find the probability we use the formula,

P = number of possible outcomes / total number of outcomes

Let event A: a nut selected from the jar at random is a cashew

n(A) = 60

total number of nuts n(S) = 210

So, the probability that a nut selected from the jar at random will be a cashew,

P(A) = 60/210

P(A) = 0.29

Therefore, the probability that a nut selected from the jar at random will be a cashew = 0.29

The correct answer is option (B) 0.29

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Answer:

r<2

Step-by-step explanation:

r + (-5) < -3

r -5 < -3

r<-3+5

= r<2

Answer:

Step-by-step explanation:

2w = 2w + 1

2w - 2w = 1

w(2 - 2) = 1

0w = 1

w = 1/0

w is undefined

Answer:

1.15 is 115%

Step-by-step explanation:

7/8 is 0.875 so it makes it 87.5%

The percentage form of the given number is:

1.15 as a percent is 115%

7/8 as a percent is 187.5%

To convert a decimal to a percent,

we need to multiply it by 100.

So for 1.15,

Multiply it by 100 to get 115%.

To convert a mixed number to a percent,

We have to convert it to an improper fraction first.

To do that, we multiply the denominator by the whole number and add the numerator.

Then we put that answer over the original denominator.

For 7/8, the improper fraction would be,

(8 x 1) + 7 = 15/8.

To convert this to a percentage,

We need to divide the numerator by the denominator and multiply by 100.

So 15/8 as a decimal is 1.875, and when we multiply that by 100 we get 187.5%.

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The radius that can he use for the garden is H. 8

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

Length of fence = 50 feet

⇒ Circumference of  vegetable garden = 50 feet

Since, Circumference = 2πr

⇒ 2πr = 50

⇒ r = 50/2π

⇒ r = 50/6.28

⇒ r = 7.96

⇒ r ≈ 8 feet

Thus, the radius that can he use for the garden is H. 8

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Answer: 25%

Step-by-step explanation:

0.25

25%

Step-by-step explanation:

Pythagoras :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle).a and b are the legs of the right-angled triangle.

so,

x² + 12² = (x + 8)² = x² + 16x + 64

144 = 16x + 64

16x = 80

x = 5

Answer:

Step-by-step explanation:

The expression for the given condition is: 8n + 3 = 9

Number is a mathematical word that is used to measure various attributes or count items. In essence, it is arithmetic values. Natural numbers, whole numbers, rational or irrational numbers are among the several types of counting numbers.

The supplied condition is three greater than the product of a number, and eight equals nine, according to the query.

So let's suppose that n is the number.

Three is more than the result of a number and eight, according to the question:

The necessary formula will be: 8n + 3 = 9.

Now, n has been computed to be worth: n = 6/8 = 3/4.

As a result, 3/4 is the value of the supposed integer "n."

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A typical golf ball having a diameter of approximately 1.5 inches has a volume of 1.8 cubic inches.

Volume refers to the amount of space occupied by a three-dimensional object.

From the problem, the golf ball resembles the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida which is a sphere.

If a typical golf ball has a diameter of approximately 1.5 inches, and radius is half of the diameter, then the radius of the golf ball is approximately 0.75 inches.

The volume of the golf ball can be calculated using the formula for the volume of a sphere given by:

V = 4/3 π r^3

V = 4/3 π (0.75 inches)^3

V = 4/3 π (0.421875 cubic inches)

V = 1.767145868 cubic inches

Rounding off to the nearest tenth,

V = 1.8 cubic inches

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