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Diana has available 280 yards of fencing and wishes to enclose a rectangular area.
(a) Express the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?

Two triangles are congruent if they satisfy SSS or ASA or SAS or AAS or RHS criteria.

What is the meaning of congruent triangles?

If two triangles have both the same shape and the same size then it is said that the two triangles are congruent. In other words, two triangles are congruent if they are copies of each other.

We can prove that two triangles are congruent if they satisfy any one of the following criteria:-

SSS (side side side ):- If three sides of one triangle are equal to the corresponding three sides of the other triangle.

SAS ( side angle side ):- If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle.

ASA ( angle side angle ):- If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle.

AAS ( angle angle side ):- If two angles and a none included side of a triangle are equal to the corresponding angles and side of another triangle.

RHS (right hypotenuse side ):- If the hypotenuse and one side of the right triangle are equal to the corresponding side and the hypotenuse of another triangle.

Hence, two triangles are congruent if they satisfy any one of the criteria of congruence (SSS, ASA, SAS, AAS or RHS).

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Answer:

[tex]f(h(x)) = ( \sqrt{x} - 3)^{2} + 4[/tex]

[tex]f(h(x)) = (x - 9) + 4[/tex]

[tex]f(h(x)) = x - 5[/tex]

Step-by-step explanation:

h(x) became x for function of f(x)

Answer:

compares

Step-by-step explanation:

Answer:

a) 121 feet ; b) 5 seconds

Step-by-step explanation:

maximum height = y coordinare of vertex

x coordinate = -72/2 * -16

-72/-32 = 9/4 = 2.25

y coordinate =

-16(2.25)^2 + 72(2.25) + 40

-81 + 162 + 40

-81 + 202 = 121 feet

The ball hits the ground when y = 0

-16t^2 + 72t + 40 = 0

-2t^2 + 9t + 5 = 0

discriminant = 81 -4 (-2 * 5) = 81 -4(-10) = 81 + 40 = 121

We are searching only positive value

t = (-9 -11)/-4 = -20/-4 = 5 seconds

The equation of Kevin's scenario is 4x + 2y = 45

From the question, we have the following parameters

Represent the buckets of popcorn with x and the number of drinks with y

So, we have the following equation

4x + 2y = total amount

This gives

4x + 2y = 45

See attachment for the graph

An absolute function is represented as

y = a|x - h| + k

Where the vertex is (h, k)

So, we make use of the following function

y = 2|x - 3| + 5

See attachment 2 for the graph

Here, we are to make use of any equation

A linear equation is represented as

y = mx + b

Where

slope = m

y-intercept = b

So, we make use of

m = 2 and b = 3

This gives

y = 2x + 3

When transformed 2 units up and 3 units down, the resulting equation is

y = 2x + 2 - 3

Evaluate

y = 2x - 1

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Answer: i think its 58.9997

Step-by-step explanation:

The graph of f(x)=|x| and m(x)=|x+1| is 1 unit left translation

From the question, we have the following function that can be used in our computation:

f(x) = |x|

m(x) = |x + 1|

First, we have the transformation to be:

From f(x) = |x| to m(x) = |x + 1|

This means the function is translated left by 1 unit

So, we can conclude that

The graph function is translated left by 1 unit

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The player has a total plate of 1985 plate appearances (optionD)

Addition is a way of combining things and counting them together as one large group. Addition is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum. For example if there a 5oranges, 6 bananas and 9 pineapple Ina basket. The total fruit in the basket is 5+6+9= 20 fruits

The baseball player has 746 plate appearances in his first year and 727 plate appearances in the second year and 512 in his third year.

The total plate appearances = 746+727+512=1985 plate appearances

Therefore the plate appearance the player had in three years is 1985 plate appearances.

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This is 224's prime factorization. This is the method of repeated division, and the prime factorization of 224 is 2 2 2 2 7.

Image for number 2. Show that the prime factorization of 220 is the same when 220 is multiplied by 2 times 110 or 10 times 22. What numbers might possibly be in the next form when numbers? Give two or three responses.

Therefore, 22 51 111, where 2, 5, and 11, can be expressed as 220's prime factorization.

220 has three prime factors, which are 22; 51; and 111. Here, the pair does not contain the prime factor 5. Consequently, 220 is not a square perfectly.

Consequently, the first ten multiples of 220 are as follows: 220, 440, 660, 880, 1100, 1320, 1540, 1760, 1980, and 2200.

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Answer:

-3 <-1

-3 is less than -1.

Answer:

see below

Step-by-step explanation:

1. Notice that your inequalities have ≤ and >. So one of the lines on the graph must be dotted, eliminating the bottom two choices.

2. The lines on both of the top choices are graphed identically, so now it's all about shading. The best way to determine correct shading is by testing a point to see if it makes a true statement in BOTH inequalities.

 a) Choose a point in the shaded region of the first option (I highly recommend (0,0)!!). Replace x and y in each inequality with the x and y from the point, and evaluate:

     0 ≤ 2(0) + 1?  ⇒  0 ≤ 1 TRUE

     0 > -2(0) - 3  ⇒  0 > -3 TRUE

 b) Since that point made both true statements, the first option is correct. If EITHER statement had been false, you would need to try a point in the shaded region of the second option. I recommend any where x=0 or y=0.

The cost per message is $0.025.

What is cost?

A cost is the worth of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.

Raw materials, labour expenditures, and other production-related expenses are all considered direct costs. A product, division, or project can simply be linked to the cost. As an illustration, Ford Motor Company (F) produces vehicles and trucks. A automobile is built by a factory employee in eight hours.

Let, Jerry's messaging phone plan is, he paid $0.75 for every 30 messages he send.

So, the cost of each message is,

[tex]\frac{0.75}{30} = 0.025[/tex].

Hence, the per message is, $0.025.

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Danielle Stevenson receives $2600.

What is a total amount?

A total is the sum of several numbers or the number of items in a group, as determined by addition or counting.

Here, we have

Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house.

One-half of the commission goes to the broker and one-half of the remainder to another salesperson.

We have to find out how much amount she receives.

Danielle has a 6.5% × $160,000 = $10400

Then, Danielle half of $10400 to the broker so she remains $10400 × 1/2 = $5200

Now,

Danielle one-half of the $5200 to another salesperson. so she gets $5200 × 1/2 = $2600

Hence, Danielle Stevenson receives $2600.

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The rate of change for the given equation is 4.

The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity. The rate of change from the coordinates of y to coordinates of x can found out as

Δy/ Δx = (y2 - y1 )/ (x2 - x1).

Given an equation, y = 4x + 100

Slope = 4

Hence, The rate of change for the given equation is 4.

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None of the measurement of the sides of the triangle forms a right triangle.

A right triangle is a triangle that has one of its angles as 90 degrees. The measurement of the side of a right triangle can be found using Pythagoras's theorem.

Therefore,

c²= a² + b²

where

Therefore, the measurement of the triangles that forms a right triangle is none of the options

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Answer:

It is common to dilate photos to fit the space that you want it to fit. In police work and crime investigation. Detectives and police dilate photos to see smaller details and evidence. In architecture.

Step-by-step explanation:

Example 1: For Δ ABC, show that AB = AC and Δ ABC is isosceles if the bisector AD of ∠ A is perpendicular to side BC. Also, this condition satisfies the properties of the isosceles triangles.

thus, Δ ABC is an isosceles triangle.

Example 2: Prove that △ACF≅△AEB, if ∠C=∠E and AC=AE.

Solution of the system of linear equation 3a + 6b = 45 , 2a -2b = -12 is equal to a = 1 and b =7.

As given in the question,

System of linear equation are:

3a + 6b = 45 __( 1 )

2a - 2b = -12 __(2 )

Solution of the linear equation by elimination method is given by:

Multiply ( 2 ) by 3 and add it to (1) we get,

3a + 6b = 45

6a - 6b = -36

9a         = 9

⇒ a = 1

Substitute the value of a = 1 in (1) we get,

3( 1 ) + 6b = 45

⇒ 6b = 42

⇒ b = 7

Therefore, the solution of the system of linear equation is a = 1 and

b =7.

The complete question is :

What is the solution (a, b) to this system of linear equations?

3a+6b = 45 ,  2a-2b = -12

a. (-27, 6)

b. (-1, 7)

c. (1, 7)

d. (27, -6)

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Answer:

y=-[tex]\frac{5}{3}[/tex]x-4

Step-by-step explanation:

find the slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m=[tex]\frac{1-6}{-3+6}[/tex]

m=-[tex]\frac{5}{3}[/tex]

Use the slope and one of the points to solve for the y-intercept

y1=mx1+b

6=-[tex]\frac{5}{3}[/tex](-6)+b

6=10+b

b=6-10

b=-4

plug the values for m and b into y=mx+b

y=-[tex]\frac{5}{3}[/tex]x-4

Answer:

First find the slope.

m=y2-y1 / x2-x1

m= 1-6

-3-(-6)

m=-5

-3+6

m=-5

3

m= -1.6

y-y1=m(x-x1)

y-6= -1.6(x-(-6))

y-6= -1.6x+6

Answer:

x ≈ 15.62

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 12² + 10² = 144 + 100 = 244 ( take square root of both sides )

x = [tex]\sqrt{244}[/tex] ≈ 15.62 ( to the nearest hundredth )

We isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.

According to the question,

We have the following information:

Isolating a variable by dividing each side of the equation in which one side does not contain any variable.

Now, in this case, it is clearly stated that the first step to isolate the variable from the equation is to perform division.

Now, this can be done as follows in the given equation:

2x = 14

Now, the variable x can be isolated by dividing both sides of the equation by 2:

x = 14/2

x = 7

Hence, we isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.

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The length of the radius of the given circle with the equation x² + y² = 8 is 2√2 units.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

In the center of a circle, equal chords subtend equal angles.

The chord is divided in half by the radius drawn perpendicular to it.

So, the length of the radius of the circle is:

The formula for the circle's general equation is: (x - h)² + (y - k)² = r²

Where, the center is (h, k) and the radius is represented by r.

The equation we have: x² + y² = 8

Then, r² = 8

Taking square root as follows:
r = √8

r = √2*2*2

r = 2√2

Therefore, the length of the radius of the given circle with the equation x² + y² = 8 is 2√2 units.

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Correct question:
What is the radius of the circle whose equation is x² + y² = 8?

Answer step-by-step explanation:

Step 1: Write out the cross T = tall, t = short Tt x Tt.

Step 2: Draw 2 by 2 Punnett square.

Step 3: Write the alleles for parent 1 on.

the left side of the Punnett square.

Step 4: Write the alleles from parent 2.

above the Punnett square.

The coordinates of the point after the two reflections are (0.3,-7/10).

A reflection is a mapping from an isometric hyperplane with a set of fixed points acting as the reflection's axis or plane from a Euclidean space to itself. A figure's reflection creates its mirror image of that figure in the plane or axis of the reflection.

Given that, the point (-0.3, 7/10) is reflected over the y-axis and then over the x-axis respectively.

The coordinates of the point after the reflection in the y-axis are:
(0.3, 7/10)

Now, the coordinates of the point after the reflection in the x-axis are:
(0.3, -7/10)

Hence, the coordinates of the point after the two reflections are (0.3,-7/10).

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The heights of both trees at the time when they have an equal height are equal to 4 inches and 48 inches respectively.

In order to graphically solve the system of equations, we would first of all write a system of equations that models the situation. Additionally, we would assign variables to the height of Tree A t years after being planted and height of Tree B t years after being planted, and then translate the word problem into algebraic equation as follows:

Therefore, translating the word problem into algebraic equation, we have the following:

A = 32 + 4t

B = 16 + 8t

On a graph, we would plot the height of Tree A on the x-axis while height of Tree B would be plotted on the y-axis of the cartesian coordinate.

By critically observing the graph, the point of intersection which gives a solution to the system of equations include the following:

Height of Tree A, A = 4 inches.

Height of Tree B, B = 48 inches.

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Answer:

.4 times 45

That means it snowed 63 inches

Step-by-step explanation:

Answer:

-5 johu tella no for the best

Step-by-step explanation:

one sfeoo by and the offer and the nd.

A parent graph is the graph of a relatively simple function. By transforming the function in various ways, the graph can be translated, reflected, or otherwise changed.

What is a Parent Function?

A parent function is an equation in the simplest form of a family of functions. A family of functions is a collection of functions that represent similar characteristics and/or transformations of its parent function. A parent function can be represented with different degree values such as degrees 1, 2, or 3.

The most basic parent function is called a constant function. A constant function is one such that y = b, where b is the constant value. A constant function creates a straight horizontal line that will intersect the y -axis.

Hence the answer is A parent graph is the graph of a relatively simple function. By transforming the function in various ways, the graph can be translated, reflected, or otherwise changed.

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The reasons put into the correct order to justify solving the inequality:

-2(x + 6) < 3(x + 1) - Given

-2x - 12 < 3x + 3 - Distributive Property

-2x < 3x + 15 - Addition Property of Order

-5x < 15 - Subtraction Property of Order

x > 3 - Division Property of Order

Check how to solve:

-2(x + 6) < 3(x + 1)

Open the parenthesis

-2x - 12 < 3x + 3

Add 12 to both sides

-2x - 12 + 12 < 3x + 3 + 12

-2x < 3x + 15

Subtract 3x from both sides

-2x - 3x < 3x + 15 - 3x

- 5x < 15

divide both sides by -5

x > 3

Therefore, the solution to the given inequality -2(x + 6) < 3(x + 1) is x > 3.

The properties mentioned above are properties of inequalities and hold for all situations of inequalities as given.

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3/4 add to 5/7 is 1 and 13/28