Given: Q R ≅ S T
Q T ≅ R S
Prove: Q R S T is a parallelogram

To solve this exercise let's make a sketch of the rectangular field first:

The length, width, and diagonal of the rectangular field form a right triangle, to determine the width of the rectangle you can apply the Pythagorean theorem.

This theorem states that the square of the hypotenuse is equal to the sum of the square of the legs of the triangle.

The diagonal is the hypotenuse of the triangle, the length is one of the legs "a" and the width is the other leg "b".

Write the theorem for b:

Replace the expression with c=157 and a=135

The width of the field is 80.15 meters.

Answer:

1/2 x + 5

Step-by-step explanation:

Haf of x = 1/2 x

then add 5     :     1/2 x + 5

Given,

The area of the front yard is 60x^2 + 12x - 21 .

The grass area of the backyard is 81x^2 - 212x + 68.

The total are is the sum of the front yard and the back yard.

So, to obtain the total area adding the area of the front yard and back yard.

Hence, the total area is 141x^2-200x+47.

Remember that

and

therefore

substitute given values

therefore

The answer is

The answer is the second option

Given that length =8 yards and width = 3 yards of the rectangle bed.

Recall the formula for the area of the rectangle is

We know that one yard=3 feet.

Hence the area of the rectangle flower bed is 216 square feet.

1) To calculate it, we can set a proportion

24--------100%

21---------x

Cross multiply it

x =2100/24

x=87.5

87.5%

Answer: 87.5% did

Step-by-step explanation:

The value of the function f'(g(x)) is -10

What is a function?

an expression or rule or law that describes a relationship between one variable  and another variable. i.e. between independent variable and dependent variable is known as function.

We are given f(-6)=-3, f'(-6)=-5, g(2)=-6, g'(2)=2

We are asked to find F'(2) where F(x)= f(g(x))

We will use the algebra of function to solve the given problem and find the required value

We have

[tex]F(x)=f(g(x))\\F'(x)= f'(g(x))*g'(x)[/tex]

Substituting x=2 in the above equation we get

[tex]F'(2)=f'(g(2))*g'(2)\\F'(2)=f'(-6)*2\\F'(2)=-5*2\\F'(2)=-10[/tex]

Hence the value of F'(2)= -10 as asked

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Answer:

x=31

Step-by-step explanation:

x+87+2x=180(angles on a straight line is equal to 180)

3x+87=180

3x=180-87

3x=93

x=31

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The volume of a cube = Side³

The length of one edge of Julie's Jewelry box is 6 cm.

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges. 

The volume of a cube = Side³

We have,

The volume of the Jewelry box = 216 cm³

The length of one edge of the box = L

The volume of a cube is given as:

V = L³

216 = L³

[ 6 x 6 x 6 = 216 ]

L = ∛216

L = ∛6³

L = 6

Thus,

The length of one edge of Julie's Jewelry box is 6 cm.

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first term a=32805

common ration: r=10935/32805=1/3

11th term:

So the 11th term is 0.555

2 multiply by 700 is 1400

An easier trick to multipy numbers with zeros is;

Remove the zeros first, multiply the numbers, then add back the zeros

That is;

2 x 7 = 14

Then add back the zeros

That is;

1400

Answer:

Linear

Step-by-step explanation:

X values are increasing equally by 1. Y values are decreasing equally by 2. So, the graph is a linear graph.

Answer:

7.5?

Step-by-step explanation:

I'm not sure but i think 60=8x so you would do 60÷8 and it's 7.5

How much hay does each horse and each cow get?

(a)The hay shared by 3 horses =  5 bales

So, the hay shared by 1 horse =  x

Rewriting the statements ,

3 h = 5 b  --(1)

1 h = x    -(2)

By applying cross multiplication method to (1) and (2)

3 (x) = 5

x = 5/3

The hay shared by 1 horse =  5/3

(b)The hay shared by 5 cows =  8 bales

So, the hay shared by 1 cow =  y

Rewriting the statements ,

5 c = 8 b  --(3)

1 c = y    -(4)

By applying cross multiplication method to (3) and (4)

5 (y) = 8

x = 8/5

The hay shared by 1 cow = 8/5

Which animal gets more, a horse of a cow?

Comparing the fractions,

The hay shared by 1 horse =  5/3  = 1.7

The hay shared by 1 cow = 8/5 = 1.6

1.7 > 1.6

So,  a horse gets more than a cow

How much more hay do they get?

Considering the difference of fractions,

Amount of more hay consumed = Hay shared by a horse - hay shared by a cow.

                                                     [tex]=\frac{5}{3} -\frac{8}{5} \\\\=\frac{25-24}{15} \\\\=\frac{1}{15}[/tex]

The horse share [tex]\frac{1}{15}[/tex] more hay than cows

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ΔMNQ ≅ ΔONP are Congruent triangle.

What do you mean by congruent?

1) MN = ON        ⇒ Given

2) ∠1 = 2            ⇒ Angles are equal because sides are equal.

3) MN = ON,MP = OQ  ⇒ Given

4)  ΔNMP and ΔNQO are isosceles trisngle.

5) PN = QN          ⇒  Given

6) PQ = QP          ⇒ Line segment

7) MP + PO = OQ + QM  ⇒ Adding = amount to = line segment

8) ΔMNQ ≅ ΔONP = Congruent

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From the picture, we have the necessary information:

The supplementary angles.

The parallels being intersected by two secant lines. And alternate interior angles are congruent under this condition.

The other angle of the triangle is then:

As a result, the angles vertical angles, therefore

< BAC = 28 (it confirms the alternate interior angle Therefore, we can write all the angles in the following drawing:

Given data:

The given table is shown.

The expression for the probability that the number is multiple of 4.

When 125 times the cards are chosen then expected number card is multiple of 4 is,

Thus, the correct option is (A).

Answer:

5:40 P.M.

Explanation:

From the time map:

• When the time in Denver is 10.00 AM

• The time in Miami is 12:00 Noon

This means that Miami is 2 hours ahead of Denver.

Thus, if it is 3:40 p.m. in Denver:

It is 5:40 P.M. in Miami.

Given data

1. The mean

2. The median

3. The sample standard deviation

Find 75% of 150

First, let's convert 75% to decimal by dividing by 100:

Now, we will multiply 0.75 with 150 to find out answer:

I believe that it would be 112.5.

__________________________________________

Convert 75% to a decimal by dividing it by 100:

[tex]\frac{75}{100} = 0.75[/tex]

Next, multiply 0.75 to 150:

[tex]0.75[/tex] × [tex]150 = 112.5[/tex] ← Final Solution

Hope this helps!

Let price of 1 soup be "x" and 1 stew be "y".

4 soup and 4 stew is $31, thus we can write:

Also, given

2 soup and 1 stew costs $12.25, thus we can write:

Let' solve this for y and substitute it back to Equation 1. Then we will solve for x. The process is shown below:

Substituting,

Finding y:

Thus,

Answer:

Each order of Soup = $4.50

Each order of Stew = $3.25

The side of the right triangle CD is 25.63 units

A right triangle is a triangle that has one of its angles as 90 degrees.

Base on the angles, the side of a right triangle can be named as follows:

Therefore, the side CD of the right triangle can be found as follows:

using Pythagoras theorem,

c² = a² + b²

Hence,

CD = √28.3² - 12²

CD = √800.89 - 144

CD = √656.89

CD = 25.6298653918

Therefore,

CD = 25.63 units

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There are basic six ratios in trigonometry that help in establishing a relationship between the ratio of sides of a right triangle with the angle. If θ is the angle in a right-angled triangle, formed between the base and hypotenuse, then

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

The value of the other three functions: cot, sec, and cosec depend on tan, cos, and sin respectively as given below.

cot θ = 1/tan θ = Base/Perpendicular

sec θ = 1/cos θ = Hypotenuse/Base

cosec θ = 1/sin θ = Hypotenuse/Perpendicular

Given:

cos x/ 1- sin x

Using Trigonometric identities

1-sin²x = cos²x

So, on rationalizing

= (cos x) /(1-sinx) x (1+sinx)/(1+sinx)

= (cos x)  (1+sinx) /(1²-sin²x)

=  (cos x)  (1+sinx) /(1-sin²x)

=  (cos x)(1+sinx)/(cos²x)

= (1+sinx)/(cos x)

=1/ cos x + sin x / cos x

=sec x + tan x

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(a) Daily high temperature

(b) Amount of sleep

(c) Input U

Answer: Hi, the answer would be 150% or in decimal form 1.5 this is an increase. There fore your answere is 1.5 which makes it an increase.

Given data:

The given triangular prism.

The expression for lateral surface area is,

Thus, the lateral surface area is 288 sq-mm.

The given equation is

Square both sides to cancel the square root

Subtract 5 from both sides

Divide both sides by 7

The solution is t = 44/7 OR t = 6 2/7 (mixed number)

The function at its maximum value will be at point (11,4) and its value is 52 which can be derived keeping in mind the constraints that have been given.

The maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.

There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.

Herein we can find the closed region ABC from the three equations or constraints given

and can mark the points as

A = (5,4)

B = (5, 12)

C = (11, 4)

if we put up the values of the points, we get

at (11, 4), Z = 4 x 11 + 2 x 4

=52 that is the maximum value amongst the three.

Thus, the maximum point of the function can be calculated as (11,4)

We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.

If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value

The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.

There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum

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The expression illustrates that C. Yes, Alexandra's work is correct.

The expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The expression is given as:

= (18 + 3²) ÷ 3²

= (18 + 9) ÷ 9

= 27 ÷ 9

= 3

In this case, the work is correct.

Therefore, the correct option is C.

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The line which is passing through the point on the graph (2,7) and with vertex (0,3) having equation is    [tex]x^{2}[/tex] -y +3 = 0

The polynomial equations of degree two in one variable of type f(x) = ax^2 + bx + c = 0 and with a, b, c are R and a [tex]\neq[/tex] 0,  are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).

The general equation of the quadratic equation if (h, k) is the vertex and (x, y) is a point on the curve is given by  

y = [tex]a(x-h)^{2} + k[/tex] ......eqn 1

In the situation where a must be determined at position (h, k) and (x, y)

In the above question, it is given that,

vertex is (h,k) = (0,3) and the point on the graph is (x,y) = (2,7)

Now we'll put the points in the general equation of the quadratic equation to get the desired equation

y = [tex]a(x-h)^{2} + k[/tex]

y = [tex]a(x-0)^{2}[/tex] + 3 .....eqn 1

Now putting the value of (x,y)

7 = [tex]a(2-0)^{2}[/tex] + 3

7 = 4a + 3

4a = 4

a = 1

putting the value of a in the equation 1, we get

y = [tex]1(x-0)^{2}[/tex] + 3

y = [tex]x^{2}[/tex] + 3

[tex]x^{2}[/tex] -y +3 = 0

Hence, the equation of the line passing through a point on the graph (2,7) with the vertex (0,3) is  [tex]x^{2}[/tex]  -y +3 = 0

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