Part A: The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)

Part B: The area of a rectangle is (81x2 − 4y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Examining the figure the length of the side SU is calculated to be

6

Examining the figure, it can be deduced that

XW = VT = 2 (opposite side of a parallelogram)

XV = WT = 2 (opposite side of a parallelogram)

VT = SV, therefore ST = 2 + 2 = 4

UW = WT, therefore UT = 2 + 2 = 4

The figure form similar triangles and the ratios as written below are equal

SU / VW = ST / XW =  UT / XV

SU / VW = ST / XW

SU / 3 = 4 / 2

SU = 3 * 4 / 2

SU = 6

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Answer:

27

Step-by-step explanation:

45/5=9

9*3=27

Answer: 27

Step-by-step explanation:

45/5=9

9x3=27

Answer:  y=2x-6

Step-by-step explanation:

y=2x-6 is the equation of the linear relationship in slope-intercept form

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let us take any two points from the given table

(1, -4) and (0, -6)

The slope is m=-6+4/-1

=-2/-1

m=2

Now let us find the y intercept

-4=2(1)+b

-4=2+b

-6=b

So the slope intercept form is y=2x-6

Hence,  y=2x-6 is the equation of the linear relationship in slope-intercept form

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The function for the arithmetic sequence (fn) = 8n

The domain is {1,2,3,…10}

An arithmetic sequence is a series of numbers in which each term (save the first) is obtained by adding a constant number to the preceding term. For example, 2, 4, 6, 8,... is an arithmetic sequence because each term is created by adding 2 (a constant integer) to the previous term.

Given that

The arithmetic sequence is 8, 16, 24, 32, 40, 48, 56

Common difference = 16-8 = 8

The sequence is increasing so the common difference is positive 8

fn = 8 + (n-1)d

fn = 8 + (n-1)8

fn = 8 + 8n – 8

fn = 8n

So the function for the arithmetic sequence (fn) = 8n

b. The points to the graph are represented by (nfn). So the points are (1,8);(2,16);(3,24);(4,32);(5,40);(6,48);(7,56)

The domain of the function is the number 10

So, the domain is {1,2,3,…10}

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The answer is 10(t-1) (5t+3).

An algebraic equation of the second degree in x is a quadratic equation. Typically, a quadratic equation is expressed in standard form as,[tex]ax^2 + bx + c = 0[/tex].

And the factor is a number or algebraic expression that divides another number evenly without leaving any remainder.

To factor the given quadratic equation, first, take the common factor of the equation. Therefore,

[tex]50t^2-20t-30=10(5t^2-2t-3)[/tex]

Using the sum-product pattern, we can write 2t as 3t-5t. Therefore,

[tex]50t^2-20t-30=10(5t^2+3t-5t-3)[/tex]

Now, find the common factor between the pairs within the bracket. We get,

[tex]50t^2-20t-30=10(t(5t+3)-1(5t+3))[/tex]

Finally, rewriting the above terms by factoring out the greatest common factor, we get,

[tex]50t^2-20t-30=10(t-1)(5t+3)[/tex]

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Answer: 10 (5t+3) (t-1)

Step-by-step explanation:

Given, 50t²-20t-30

Here we take 10 as the common factor:

⇒ 10(5t²-2t-3)

Then, we use the sum-product pattern to divide the 2t into two parts:

⇒ 10(5t²-5t+3t-3)

Taking the common factor from the two pairs, we get:

⇒ 10 [5t(t-1) + 3(t-1)]

⇒ 10 (5t+3) (t-1)

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11 cups of vinegar would Lorenzo use to make [tex]4\frac{2}{5}[/tex]  recipes.

Given that, Lorenzo uses [tex]2\frac{1}{2}[/tex] cups of vinegar in his salad dressing recipe.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Lorenzo use to make [tex]4\frac{2}{5}[/tex] recipes

Here, [tex]2\frac{1}{2}=\frac{5}{2}[/tex] and [tex]4\frac{2}{5}=\frac{22}{5}[/tex]

Now, 5/2 × 22/5

= 11

Hence, 11 cups of vinegar would Lorenzo use to make [tex]4\frac{2}{5}[/tex]  recipes.

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The number of tires that minimizes the cost is 800., And the cost for that number of tires is, $45.

What is parabola?

When the value of an is less than 0, a 0, the parabola's graph is downward (or opens down). When the value of an is more than zero, a > 0, the parabola's graph is upward (or expands). As a result, the direction of the parabola depends on the sign of the coefficient "a."

Consider, the equation

C = 0.002x^2 - 3.2x + 1325

Here, a = 0.002 > 0

Since, if a > 0 then parabola is open upward and having minimum value at it's vertex.

First, to  find the vertex of the quadratic equation.

Since,

V = (-b/2a, f(-b/2a))

Let, a = 0.002,  b = -3.2,   c = 1325

So,

-b/2a = 3.2/2(0.002) = 800

Therefore, the number of tires that minimizes the cost is 800.

Now to find the cost for that number of tires.

Plug x = 800 into the above quadratic equation

C = 0.002(800)^2 - 3.2(800) + 1325

C = 45

Hence, the cost for that number of tires is $45.

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The dimension of the wood block in centimeter is  40cm by 20cm by 70cm , the volume is  56000 cubic centimeters .

In the question ,

it is given that ,

the dimension of the block of wood is 0.4m by 0.2m by 0.7m ,

that means

the length of the wood block = 0.4 m

we know that 1 m = 100 cm , So 0.4 m = 40 cm

0.2 m = 20 cm

and

0.7 m = 70 cm

So , the length of the wood block = 40 cm

the width of the wood block = 20 cm

the height of the wood block = 70 cm

The Volume of the wooden block = length × width × height

Substituting the values , we get

Volume = 40 × 20 × 70

= 56000 cm³

Therefore , The dimension of the wood block in centimeter is  40cm by 20cm by 70cm , the volume is  56000 cubic centimeters .

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Using equivalent equations to equate both caterer A and B need to serve 10 guests to have equal pay

Equivalent equations are systems of equations that have the same solutions. Equations are said to be equivalent when they have the same solution set. For example, x + 2 = 6 and 2x = 8 are equivalent equations, because when we solve each of them as follows, they have the same solution set: x + 2 = 6. Subtract 2 from both sides. x = 4.

In this case, we can set up two equations and equate them to know how many people they need to serve in order to earn equally.

For caterer A;

y = 15x + 100 ...eq(i)

y = 20x + 50 ...eq(ii)

For the equation to be equivalent, equation(i) and (ii) must be equal

15x + 100 = 20x + 50

x = 10

They both need to serve 10 guests to earn equally.

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The complex number in rectangular form is 17√2 / 2 - i 17√2 / 2. (Correct choice: A)

In this problem we have a complex number in polar form, whose formula is described below:

z = r · (cos θ + i sin θ)

Where:

And the rectangular form of the complex number is represented by:

z = a + i b, where a = r · cos θ and b = r · sin θ.

If we know that r = 17 and θ = 315°, then the rectangular form of the complex number is:

a = 17 · cos 315°

a = 17√2 / 2

b = 17 · sin 315°

b = - 17√2 / 2

The rectangular form of the complex number is 17√2 / 2 - i 17√2 / 2.

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Options B and C are the following conclusions that are true about the transformation of quadrilateral BLUE.

A four-sided polygon having four edges and four corners is referred to as a quadrilateral in geometry. The name is a combination of the Latin words quadri, which is a variation of four, and latus, which means "side." It is sometimes referred to as a tetragon, which is derived from the Greek words "tetra" for "four" and "gon" for "corner" or "angle," in comparison to other polygons (e.g. pentagon). Because "gon" means "angle," it is sometimes referred to as a quadrangle or 4-angle.

Either simple (not self-intersecting) or complicated quadrilaterals exist (self-intersecting, or crossed). Convex or concave surfaces characterize simple quadrilaterals.

From the given figure,

The points in the quadrilateral BLUE are

B(-8,5), L(-5,5), U(-3,4), E(-6,1)

If the quadrilateral BLUE is rotated 270° then,

B(-8,-5), L(-5,-5), U(-3,-4), E(-6,-1)

Now, the image is reflected

So, the points are switched as,

B'(-5,-8), L'(-5,-5), U'(-4,-3), E'(-1,-6)

Distance of BE is,

√(x₂-x₁)²+(y₂-y₁)²

√(-1+5)²+(-6+8)²

=√16+4

=√20

Distance of B'E' is,

√(-6+8)²+(1-5)²

=√4+16

=√20

∴BE=B'E'

And the quadrilateral B'L'U'E' will be located entirely on third quadrant.

Therefore, B and C are the appropriate choices.

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Step-by-step explanation:

1+2+3+4+5=15

180÷15=12

12x1=12

12x2=24

12x3=36

12x4=48

12x5=60

The area of the base and curved surface area is 15400mm²  and 22000 mm² respectively, of the cylindrical surface.

What is the cylindrical surface?

The amount of space that is covered by the curved surface and flat surface of a cylinder's bases is known as the cylinder's surface area. In addition to the area of the curved surface, the cylinder's total surface area also comprises the areas of its two circular bases. Units of surface area are stated as squares, such as square millimeters, square inches, square feet, and so on. Two circular bases joined by a curving face form a 3-D solid object known as a cylinder.

The curved surface area of a cylinder is 2πrh

A = 2 * 22/7*140/2*50

A = 22000 mm²

The base are will be π r²

B= 22/7 * 140/2*140/2

B= 15400mm²

Hence the area of the base and curved surface area is 15400mm²  and 22000 mm² respectively.

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Answer:

[tex] \huge{ \boxed{ \bold{g = - 2}}}[/tex]

Step-by-step explanation:

In order to find g we have to use the formula for finding the slope of the line passing through two points that's

[tex]m = \frac{y_2 -y_ 1}{x_2 -x_1 } \\[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are (g, -1) and (2, 5) and m = 3/2

We substitute it into the equation and find g

That's

[tex] \frac{3}{2} = \frac{5 - - 1}{2 - g} \\ \frac{3}{2} = \frac{5 + 1}{2 - g } \: \: \: \: \: \: \: \frac{3}{2} = \frac{6}{2 - g} \\ \\ 3(2 - g) = 6(2) \\ 6 - 3g = 12 \\ - 3g = 12 - 6 \\ - 3g = 6 \\ \\ \frac{ - 3g}{ - 3} = \frac{6}{ - 3} \\ \\ g = - 2[/tex]

We have the final answer as

Hope this helps you

Answer:

905789 x 9417 = 8529815013

Step-by-step explanation:

I hope this helps, friend :)

If Sharifa's white ball rolled 143 centimeters in 4 seconds and her green ball rolled 112 centimeters in 3 seconds. The ball that rolled at a greater is: B: green ball.

Using this formula to find the fastest speed

White ball :

Speed for white ball = 143 centimeters /4 seconds

Speed for white ball = 34.75

Green ball:

Speed for green ball = 112 centimeters /3 seconds

Speed for green ball= 37.33

37.33 ≥ 34.75 which means that green ball is the fastest.

Therefore the correct option is B.

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Answer:

Four consecutive odd integers are: 2n+1, 2n+3, 2n+5 and 2n+7

Three times the sum of the first and fourth then are 3(2n+1 + 2n+7)

80 less than 4 times the sum of the second and third then are 4(2n+3 + 2n+5) - 80

Since the two are equal:

3(2n+1 + 2n+7) = 4(2n+3 + 2n+5)-80

expanding the brackets:

6n+3 + 6n + 21 = 8n + 12 + 8n + 20 - 80

combining like terms

3 + 21 - 12 -20 + 80 = 8n + 8n - 6n - 6n

72 = 4n

Step-by-step explanation:

Answer:

1) 1 = 120 degrees and 2 = 60 degrees

2) x = 25

3) p = 32

Step-by-step explanation:

1) Angle 1 is 120 degrees, since it is congruent to the corresponding angle below it (because lines a and b are parallel) Angles 1 and 2 are supplementary, meaning they add up to 180, so to find angle 2 we do 180 - 120 to get 60. Angle 1 = 120 degrees and angle 2 = 60 degrees.

I did 2 and 3 on paper, let me know if anything is confusing :))

2) the two lines are parallel, so we know those two angles are congruent since they're corresponding. If they're congruent we can just set them equal to each other to find x. x = 25.

3) the little square mark means a right angle, which is 90 degrees. The two lines are parallel, so we know that the angle below is corresponding and congruent to 90 degrees. So to find p, set 3p - 6 equal to 90. p = 32.

if anythings confusing let me know :-)

Answer:

Step-by-step explanation:

Comment

How many 3 digit numbers are divisible by 4, but do not contain the digit nine?

If you know a computer language, then the main line would be

for x = 100 to 999 do

Answer:

m1 = 33 degrees ; m3 = 33 degrees

Step-by-step explanation:

m8 = m4 = 147 degrees

m4 + m1 = 180

147 + m1 = 180

m1 = 180 - 147

m1 = 33 degrees

m1 = m3 (vertical angles)

Answer:

5.267

Step-by-step explanation:

Let's do long division to figure this out.

Answer: 5.26666666667

Step-by-step explanation:

If your asking for the decimal answer, than it is 5.26666666667, or you can round it to 5.3. :)

Answer:

0.546 is greater than 0.056

Probability of chosen the acre of land as per given conditions are as follow:

a. Probability of chosen the acre of land not forested is 0.62.

b. Probability of chosen the acre of land either forest or agriculture is 0.45.

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

As given in the question,

Given probability are:

Probability of chosen the acre of land is forest is equal to 0.38.

Probability of chosen the acre of land is agriculture is equal to 0.07.

Probability of chosen the acre of land as per given conditions are as follow:

a. Let P(A) represents the probability of chosen the acre of land is forest.

Then P(A') is the probability of not forested.

P(A) + P(A') = 1

⇒0.38 + P(A') = 1

⇒ P(A') = 1 - 0.38

⇒ P(A') = 0.62

b. Let P(G) is the probability of chosen acre of land agricultural.

No common land given for forest or agriculture, they are independent events.

P(A∩G) = 0

Probability of chosen the acre of land either forest or agriculture

= P( A or G)

= P(A) + P(G) - P(A∩G)

= 0.38 + 0.07 -0

= 0.45

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

Therefore, probability of chosen the acre of land as per given conditions are as follow:

a. Probability of chosen the acre of land not forested is 0.62.

b. Probability of chosen the acre of land either forest or agriculture is 0.45.

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

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The amount of paint needed to paint the front of the building knowing that 0.5 kg of paint is needed per m^2 is 20 kg.

We know that,

Area of rectangle = L * W

where L = Length of the rectangle

and W  = Width of the rectangle.

Area of triangle = 1/2 * B * H

where B = Base of the triangle

and H  = Height of the triangle.

From the figure, we are given;

The front of the building has two rectangles that represent the floor and one triangle.

The rectangles are of the same size and it's given;

L = 8 m

W = 4 m

Area of rectangle = L * W = 8 * 4 = 32 m^2

The dimension of the triangle is:

B = 8 m

H = 2 m

Area of triangle = 1/2 * B * H = 1/2 * 8 * 2 = 8 m^2

The total area of the front of the building = 32 + 8 = 40 m^2

Amount of paint required

= total area of the front of the building * paint is needed per m^2

= 40 * 0.5 = 20 kg

So, 20 kg of paint is needed.

Thus, the amount of paint needed to paint the front of the building knowing that 0.5 kg of paint is needed per m^2 is 20 kg.

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Answer:

Yes, it is a direct variation.  The constant of variation is 4

Step-by-step explanation:

As y changes by 20, x changes by 5

[tex]\frac{20}{5}[/tex] = 4

Using the given inequality we can calculate that this is equivalent to

(B) x ≤-1 or x ≥1

The given inequality is |8x| ≥ 2 .

Now we have to solve this inequality to find the range of the value of x.

|8x| ≥ 2

now we will try to remove the modulus function.

either 8x ≥ 2 ⇒ x ≥ 1/4

or, -8x ≥ 2 ⇒ x ≤ -1/4

Therefore the solution of the inequality is x ≤ -1/4 or x ≥ 1/4

Now of the given options the most plausible option or inequality that also satisfies this inequality is given by B)  x ≤-1 or x ≥1

In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On the number line, size comparisons between two numbers are typically conducted.

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Answer: Her mistake is that she would have to make each piece 167.2 inches long to have 5 equal pieces.

Step-by-step explanation:

7 * 5 ≠ 836

836/5 = 167.2

The system of inequalities that models this situation is given as follows:

The variables of the system of inequalities are presented as follows:

Gwen charges $3.50 each time she walks a dog. Julia charges $1.25 each time she waters the flowers, and they need to raise at least $250, hence the first constraint is of:

3.5x + 1.25y ≥ 250.

The number of times Julia plans to water the flowers is no more than six times the number of dogs Gwen plans to walk, hence:

y ≤ 6x.

Gwen plans to walk no less than 12 dogs, hence:

x ≥ 12.

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If the function f (x) = 3 logx and g(x) [tex]=[/tex] x² + 1 , then the value of composite function g[f(x)] is (3logx)² + 1 , the correct option is (a) .

In the question ,

it is given that ,

the function f(x) is

f(x) [tex]=[/tex] 3logx

and the function g(x) is

g(x) [tex]=[/tex] x² + 1 ,

the value of the composite function g[f(x)] will be

g[f(x)] = g(f(x))

Substituting the value of f(x) = 3logx , we get

g(f(x)) = g(3logx)

Substituting the value of 3logx in the place of x in the function  g(x) = x² + 1 ,

we get ,

= (3logx)² [tex]+[/tex] 1

Therefore , If the function f (x) = 3 logx and g(x) = x² + 1 , then the value of composite function g[f(x)] is (3logx)² + 1 , the correct option is (a) .

The given question is incomplete , the complete question is

If f ( x ) = 3 log x and g( x ) = x² + 1 , find the value of composite function g[ f ( x )] .

(a) (3logx)² + 1

(b) 3log(x² + 1)

(c) 3(x² + 1)logx

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The expression n times d times q times in terms of number of nickels is n²(36-3n)/4 .

In the question ,

it is given that ,

there are n nickels , d dimes , q quarters .

Also given that there is  twice as many nickels as dimes ,

that means , n = 2d

So , d = n/2

also that total number of coins = 18 ,

So , n + d + q = 18

n + n/2 + q = 18

q = 18 - 3n/2

we need to find ,  n times d times q in terms of the number of nickels.

that means

= n × d × q

= n × n/2 × 18 - 3n/2

= n × n/2 × (36 - 3n)/2

= (n × n×(36 - 3n))/2×2

= n²(36-3n)/4

Therefore , The expression n times d times q times in terms of number of nickels is n²(36-3n)/4 .

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