Please solve these 2 questions. (Show work and get 70 points)

The length of the given rectangle is 9.

According to the statement

We have to find that the length of the rectangle.

So, For this purpose, we know that the

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel.

From the given information:

The width of a rectangle is 8 units less than the length. The area of the rectangle is 9 units

Then

Let the Length of the rectangle = x

Let the width of the rectangle = x-8

Area of the rectangle = L*B

Then

L*B = 9

x(x-8) = 9

x^2 -8x -9 = 0

x^2 -9x + 1x -9 = 0

x(x-9) +(x-9) = 0

(x+1) (x-9) = 0

here x = -1 and then x = 9.

Here neglect x  = -1 then

Length of the rectangle  is 9

Let the width of the rectangle is 1.

So, The length of the given rectangle is 9.

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39/52 X 13/51 X 38/50 is  the probability of following event.

What in mathematics is a probability?

P(nH) and then P(H) and then P(nH)

“and then” means you Multiply probabilities.

= 39/52 X 13/51 X 38/50

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Answer:

f(2x)=-2x+5

h(5-x)=-2x+10

Answer:

M<DEG + m<GEF = m<DEF

Step-by-step explanation:

Given: Figure

To find: Choose correct option

Solution: In the figure, using angle addition postulate, M<DEG + m<GEF = 180 (sum of < on straight line)

M<DEG + m<GEF = m<DEF

( 1 , 11) , ( 2, 8 ) , ( 3 , 9 ) , ( 4 , 8 ) , ( 5 , 7 ) , ( 6, 6 ) are the Ordered pairs.

What is domain and range?

Definitions of domain and example?

The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} .

Ordered pairs are

( 1 , 11) , ( 2, 8 ) , ( 3 , 9 ) , ( 4 , 8 ) , ( 5 , 7 ) , ( 6, 6 )

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A circle is a curve sketched out by a point moving in a plane. The radius and the circumference of the circle are 13 inches and 81.6814 inches, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that diameter of the circle is 26 inches. Therefore, the radius and the circumference of the circle can be written as,

Diameter of circle = 2 × (Radius of the circle)

Radius of the circle= Diameter of circle / 2

Radius of the circle = 26 inches / 2

Radius of the circle = 13 inches

Circumference of circle = 2 × π × (Radius of the circle)

                                        = 2 × π × 13 inches

                                        = 26π inches

                                        = 81.6814 inches

Hence, the radius and the circumference of the circle are 13 inches and 81.6814 inches, respectively.

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Answer:

all interior angles of a triangle adds up to 180°

therefore,

x°+79°+41°=180°

x°+120°=180°

x°=180°-120°

x°=60°

The nth term of the given quadratic sequence begins 8, 11, 16, 23, 32, = n² + 7.

Quadratic sequences are those that contain a word. They are distinguished by the fact that the first differences between terms really aren't equal, but really the second differences between terms remain equal.

The difference between each term inside a quadratic series is not equal, but the second difference between every term is equal.

A linear sequence is a number pattern that increases or lowers by the same amount each time. The common difference is the amount by which it increases or drops. Quadratic sequence: The difference between every term increases or decreases at a steady rate in quadratic sequence.

Given:

8, 11, 16, 23, 32,

The nth rule is:

n² = 1² , 2², 3², 4² , 5²

n² = 1 , 4 , 9 , 16 , 25

Subtracting the equation:

8 , 11 , 16 , 23,  32

1 , 4, 9 , 16 , 25

we get:

7, 7, 7, 7

So that the nth term of the given quadratic sequence begins

8, 11, 16, 23, 32, = n² + 7.

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We know the formulae:

[tex]\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}[/tex]

Let us solve an example to understand the concept better.

Question: Find the speed of a car which travelled 12 km in 2 hours.

Solution:   We know the following

Substitute the information provided into the speed formula:

[tex]\implies \text{Speed} = \dfrac{\text{Distance}}{\text{Time}}[/tex]

[tex]\implies \text{Speed} = \dfrac{\text{12 km}}{\text{2 hours}} = \boxed{6 \ \text{km/hour}}[/tex]

Therefore, the speed of the car is 6 kilometers per hour.

From the previous concept, we had:

[tex]\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}[/tex]

Finding the distance formula through step-by step work:

Let Speed = S, Distance = D, and Time = T.

[tex]\implies \text{S} = \dfrac{\text{D}}{\text{T}}[/tex]

Multiply "t" on both sides:

[tex]\implies \text{S} \times \text{T}= \dfrac{\text{D}}{\text{T}} \times \text{T}[/tex]

[tex]\implies \text{S} \times \text{T}={\text{D}[/tex]

From the above work, we can say that Distance = Speed × Time.

Let us solve an example to understand the concept better.

Question: A train travelled from point A at a speed of 16 km/h in 2 hours to reach point B. Find the distance (Point A - Point B) travelled by the train.

Solution:   We know the following

Substitute the information provided into the distance formula:

[tex]\implies \text{Distance = Speed} \times \text{Time}[/tex]

[tex]\implies \text{Distance = 16 km/h} \times \text{2 hours}[/tex]

⇒ Distance = 16 km × 2 = 32 km

Therefore, the train travelled 32 km to reach point B.

From the previous concept, we had:

[tex]\text{Distance = Speed} \times \text{Time}[/tex]

Finding the time formula through step-by step work:

Let distance = D, speed = S, and time = T

[tex]\implies \text{D = S} \times \text{T}[/tex]

Dividing "S" both sides:

[tex]\implies \dfrac{\text{D}}{\text{S}} = \dfrac{\text{S} \times \text{T}}{\text{S}}[/tex]

[tex]\implies \dfrac{\text{D}}{\text{S}} = \text{T}[/tex]

From the above work, we can say that Distance/Speed = Time.

Let us solve an example to understand the concept better.

Question: A plane traveled 200 km at a speed of 100 km/h. How much time did it take to travel 200 km?

Solution:   We know the following

Substitute the information provided into the time formula:

[tex]\implies \text{Time} = \dfrac{\text{Distance}}{\text{Speed}}[/tex]

[tex]\implies \text{Time} = \dfrac{\text{200 km}}{\text{100 km/h}} = \dfrac{\text{2 km}}{\text{1 km/h}} = \boxed{\text{2 hours}}[/tex]

Therefore, it took 2 hours to travel 200 km at a speed of 100 km/h.

________________________________________________________

The two incorrect definitions are:

"An algebraic expression is a mathematical sentence connecting one statement to another statement with an equal sign (=)."

"To solve an equation means to isolating the variable on the left hand side of the equal sign."

Here we have some definitions pertaining to solving linear equations, and we need to identify which ones are incorrect.

The first incorrect definition is:

"An algebraic expression is a mathematical sentence connecting one statement to another statement with an equal sign (=)."

The sentences that have an equal sign are called equations,  algebraic expression is more general than that.

The second incorrect definition is:

"To solve an equation means to isolating the variable on the left hand side of the equal sign."

It is true that you need to isolate the variable, but it does not matter in which side of the sign you do that.

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Answer: 70:12?

Step-by-step explanation:

The line segment AB is divided at point P, which has coordinates P(0,-7.5)

A line segment is a section of a line that connects two locations to create a straight line or we can say that is connects two distinct points together to form a single line. It is extendable to either side.

Given are,

A line segment AB with coordinates of A(0,0 ) and B(-15,0) respectively

Two minor line segments, AP and PB, are created from the line segment AB by the provided point P

We must determine the dividing point's coordinates, or P.

We'll apply the formula provided,

The coordinates of the point P are given by  = ([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex] )

Now, x1 = 0, x2 = 0, y1 = -15, y2 = 0

Putting values in the formula, we get

([tex]\frac{0+0}{2}[/tex], [tex]\frac{0-15}{2}[/tex])

(0,-7.5)

Hence, the point P which partitions the line segment AB have coordinates as P(0,-7.5)

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Answer:

3x+1

Step-by-step explanation:

Step-by-step explanation:

that is just to be read from the chart.

a)

we see Kiev has 1° C.

Oslo has 2° C.

what is the difference ? 2 - 1 = 1°

b)

don't get confused.

the chart says temperatures at midday.

6 hours later IS 6pm.

the temperature in Kiev raises during that time from 1° up by 6°.

that means the temperature there is then 1 + 6 = 7° C at 6 pm.

Answer:

a. 9 °C

b. 7°C

Step-by-step explanation:

a. Difference, Rome and Oslo

→Rome: 11°C

→Oslo: 2°C

11°C- 2°C = 9°C

b. Kiev

The chart shows temperatures at midday (12pm). After 6 hours it's 6 pm.

→Kiev 1°C

→Temperature will rise 6°C

1°C + 6 °C = 7°C

At 6pm, the temperature in Kiev will be 7°C.

Answer:

$ 67. 14

Step-by-step explanation:

first you divide 36 miles by $25.20 to find the fare for one mile then multiply the answer with 47 miles

36 ÷ $25.20 = $1.43

$1.43 × 47 = $ 67. 14

hope you understood what I just said

Answer:

the answer is √180>102/8

Answer:

4 out of 9

Step-by-step explanation:

the complement of an event is

1 - probability of event

1 - [tex]\frac{5}{9}[/tex] = [tex]\frac{4}{9}[/tex]

The measures of HI will be 11.8 units under the Corresponding parts of the congruent triangles (CPCT) condition.

So,

The formula sides of the triangle: √(x₂−x₁)²+(y₂−y₁)²

Filling the values in the formula, we obtain:

Then, the side of the triangle will be: 11.8 units

Therefore, the measures of HI will be 11.8 units under the Corresponding parts of the congruent triangles (CPCT) condition.

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To draw a venn diagram for B', we have shade the region that excludes BIf B ⊆ U, where U is a universal set, then U \ B is called the compliment of B with respect to U. If underlying universal set is fixed, then we denote U \ B by B' and it is called compliment of B.

Answer:

Step-by-step explanation:

.

If it costs $855.05 for 342.02 feet of specialized wiring, how much does 1 foot of this wiring cost?

Probability of any point X on line BD is 1/2 , on line BC is 3/10, on line AB is 1/2 and on line AC is 4/5.

A, B, C and D are four points on a line. Length of AB is 5, length of BC is 3, length of AC is 8, length of CD is 2 and length of AD is 10.

Probability of any point X on line BD = ( length of BD / length of AD) = (5/10) = 1/2.

Probability of any point X on line BC = ( length of BC / length of AD) = 3/10.

Probability of any point X on line AB = ( length of AB / length of AD) = 5/10 = 1/2.

Probability of any point X on line AC = ( length of AC / length of AD) = 8/10 = 4/5.

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The Distributive property of real numbers is illustrated by the equation 2(s-t) = 2 s-2 t.

Distributive property of real number is denoted by x(y+z)=x*y+x*z , which means "x" will be multiplied with each term present inside the bracket.

For Example :

3(4+1) =3*4+3*1

         =12+3

         =15

In the given question

LHS   =     2(s-t)

On applying Distributive property we get ,

=2*s-2*t

=2s-2t  =  RHS

Hence distributive property is applied here.

Therefore , the property of real numbers that is illustrated by the equation 2(s-t) = 2 s-2 t  is Distributive property .

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Answer:

y=x

z=110

d=3cm

Answer: T(-4, 0)

Step-by-step explanation:

(x,y) → (x-8, y + 5)

T(4,-5) ==> T(4-8,-5+5) ==> T(-4, 0)

Answer:

4 minutes.

Step-by-step explanation:

45 miles in 60 minutes

3 miles in x minutes

3 x 60 divided by 45 = 4

To check yourself, 45 divided by 3 gives you 15 sets of 3 minute segments. 15 x 4 = 60 minutes or 1 hour.

We can form an endless number of triangles when you are given two sides and no measurement of angle i.e a = 25 , b = 21

For Example -

We can chose the value of angle from 0-360 degrees with side length a = 25 and b =21, how many different triangles are possible to create?

Create one of the triangles with a protractor having the side lengths a = 25 m and b = 21 m and angle 12° and third side can be adjusted to your preferred length. You have built a triangle.

Similarly by changing the length of the third side and measure of the angle we will get an entirely new triangle.

It's important to notice that you choose the side lengths and angle. This suggests that you might make a different decision. By employing the same angles, you were able to make an infinite number of different triangles.

Therefore, with simply the measurements of one angle and a side length, we can create an endless number of triangles.

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