(6,10)
(a,8)
(4,b)
(2,2)
What are the values of a and b?
a=
b=

Answer:600

Step-by-step explanation:

i think

Yes the diagram has enough information to prove that line segment JK is parallel to line segment ML

A rectangle is a polygon that has four sides. the two opposite sides are parallel to each other.

The given figure is a rectangle and according to the figure line LK is equal to line JM

This defines a parallel line which are lines that are equally spaced apart such that the lines will never meet

hence line segment JK is parallel to line segment ML since they are equally spaced, the spacing is achieved by line segment LK and line segment JM

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Dimensions 5in x 10in x 10in will yield a box with a max. volume of  500 cubic inches.

Volume =  height x length x width

Considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

Square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

Therefore,

V = x  (30-2x) (30-2x)                --------------------------------- (1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative with respect to x:

dV /dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

    dV/dx = 0

⇒  4 (3x² - 60x +225)=0

⇒ 3x² - 60x+225=0   (taking 3 common)

⇒ x² - 20x + 75 =0

Solving this quadratic equation, we get,

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

    x=15

Or,  x-5=0

   x = 5

If we substitute x = 15 in equation (1), volume becomes zero.

Therefore, x cannot be 15

When x= 5, putting in the equation (1)

V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yield a box with a max. volume of  500 cubic inches

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Answer:

Step-by-step explanation:

An expression that represents the total amount (a) that Hudson paid is

a-a/10×2+{(a/10×2)/20}.

So, the expression that represents the total amount Hudson paid:

We know that,

Then, the expression can be as follows:

Therefore, an expression that represents the total amount (a) that Hudson paid is a - a/10 × 2 + {(a/10×2)/20}.

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The composition f(-3) has a value of 1

The definition of the function is represented by the graph

So, we call the graph function f(x)

To find the function f(-3), we set the value of x in the function of the graph f(x) to -3

This is represented by

Calculate f(x), when x = -3

So, we look for the corresponsing points on the graph where x = -3

In this case;

The value of the function is 1 when the value of x is -3

This means that

f(-3) = 1

Hence, the value of the function is 1

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Considering the figure < 4 ≅ < 5 alternate internal angles

Alternate internal angle theorem is a theorem that holds true when in the occurrence of parallel lines and a transversal line.

Some of the theorems occurring at this stage include

Using the figure.  alternate internal angle theorem proves that

This helps to complete the required proof that < 4 = < 5

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The temperature on the fifth day in January is -7°C.

It should be noted that a mean simply means the average of a set of numbers that are given.

Since the mean temperature for the first 4 days in January was 3°C. The rural temperature will be:

= 4 × 3°C

= 12°C

The mean temperature for the first 5 days in January was 1°C. The total temperature will be:

= 5 × 1°C

= 5°C

The temperature of the fifth day will be the difference between the temperature. This will be:

= 5°C - 12°C

= -7°C

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The value of gf(4) is 18

What is Function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given,

f(x) = x + 2

g(x) = 3x

Now we need Function of a function

i.e. g[f(x)]

Then on g(x) we have to replace the x with f(x)

Thus,

g[f(x)] = 3(x + 2)

         = 3x + 6

Now by evaluating at

x = 4 i.e.

gf(4) = 3(4) + 6

gf(4) = 12 + 6

gf(4) = 18

Hence, The value of gf(4) = 18

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The possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)

We need to find the four possible pairs of integers that has product -18

Let x and y be two required integers.

Since the product is negative, one of the integer must be negative integer.

x      y          x*y

9    -2          -18

2     -9         -18

18    -1         -18

-1     18        -18

6      -3        -18

3      -6        -18

Therefore, the possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)

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Answer:

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

Given figure is a parallelogram since opposite sides are parallel.

Therefore the sides between angles 1 & 2 and 3 & 4 are of equal length:

The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

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

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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The input value x in the function j(x) = 3-x as j(x) equals -5 is 8.

A function is simply a relationship that maps one input to one output.

Given the function in the question;

To determine the value x or input value, equate the function to -5 and solve for x.

j( x ) = 3 - x

j( x ) = -5

-5 = 3 - x

Add 5 to both sides

-5 + 5 = 3 + 5 - x

0 = 8 - x

Add x to both sides

0 + x = 8 - x + x

x = 8 - x + x

x = 8

Therefore, the value of x is 8.

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To get the answer go to desmos

Answer:

2.2360679775 or 2.24

The y-coordinate is 2 when x=0.

The slope or gradient of the line is a mathematical term used to describe the direction and steepness of a line. The ratio of the change in the y coordinate to the change in the x coordinate is known as the slope of a line. Δ y and Δx are the net changes in the y and x coordinates, respectively.

The slope of a line is calculated as the proportion of the rise to the run, or the increasing divide by the run. The coordinate plane, it describes the slope of the line. Finding the slope between two different points and calculating the slope of a line are similar tasks.

The slope-intercept form is y= mx +c

Here, given that slope m=2

Let us consider that the above equation is passing through (2,2)

2=2(2)+c

c=2

y=2x+2

Therefore, when x=0,

y=2(0)+2

y=2

Therefore, the y-coordinate is 2 when x=0

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Answer:

Decagon

Step-by-step explanation:

Because it has 10 sides.

Answer:

Its a Decagon

Step-by-step explanation:

The inverse function is given as s⁻¹ = [tex]\frac{t^2+4t-12}{t^2-9t+14}[/tex] and the equation represents the average sales each day for the real estate company would be [tex]s^{-1}=\frac{t+6}{t-7}[/tex].

What is an equivalent expression?

The equivalent is the expression that is in different forms but is equal to the same value.

A real estate company balances the books for its business on the first day of each month.

It hopes to sell houses every other day of the month.

The average number of houses, S, the company sells each day, t is represented by the inverse of the function given below.

               [tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}[/tex]

Then the inverse function can be written as

                   [tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}\\\\s^{-1}=\frac{t^2+6t-2t-12}{t^2-7t-2t+14}\\\\s^{-1}=\frac{(t+6)(t-2)}{(t-7)(t-2)}\\\\s^{-1}=\frac{t+6}{t-7}[/tex]

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Answer:

C. [tex]S=\frac{7t+6}{t-1}[/tex]

Step-by-step explanation:

I got it right on the exam.

First, take the equation and inverse it, replace and t with y and the y with t

[tex]y=\frac{t^{2}+4t-12}{t^{2}-9t+14} \\\\t=\frac{y^{2} +4y-12}{y^{2}-9y+14}[/tex]

Then, factor both the top and bottom

[tex]t=\frac{(y+6)(y-2)}{(y-7)(y-2)}[/tex]

You see that there is a duplicate of the (y-2) in the numerator and denominator, so they cancel out,

[tex]t=\frac{(y+6)}{(y-7)}[/tex]

Now you can start getting the y alone to make an equation,

[tex]t(y-7)=\frac{(y+6)}{(y-7)} (y-7)\\t(y-7)=(y+6)[/tex]

[tex]ty-7t=y+6\\ty-7t-y+7t=y+6-y+7t\\ty-y=7t-6\\y(t-1)=7t-6\\\frac{y(t-1)}{(t-1)} =\frac{7t-6}{t-1} \\y=\frac{7t-6}{t-1}[/tex]

The two fractions which give the product of 5/6 are 1/3 and 5/2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the fraction is 5 / 6. The two fractions will be calculated as,

5 / 6 = ( 1 / 3)  x ( 5 / 2)

The product of the two fractions is,

( 1 / 3)  x ( 5 / 2) = 5 / 6

Therefore, the two fractions which give the product of 5/6 are 1/3 and 5/2.

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The correct description of the graph of the inequality x - 3 ≥ 5, is: D. Closed circle on 8, shading to the right.

An inequality statement compares two unequal quantities. When plotting the graph of an inequality, if the inequality sign involve is "< or >", an open circle is used to mark the value of the variable on the number line, while a closed circle is used when the inequality sign involved is, "≤ or ≥".

Given the inequality, x - 3 ≥ 5, solve for x:

x - 3 ≥ 5

Add 3 to both sides

x - 3 + 3 ≥ 5 + 3 [addition property]

x ≥ 8

This means the possible values of x are greater than or equal to 8. The graph of the inequality would have a closed circle at 8, with the line shaded to the right on the number line.

The correct description is: D. Closed circle on 8, shading to the right.

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The number problems solved by the little Monsters  of Beast Academy in March's meet is 15.

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

let the number of questions solved by little Monsters  of Beast Academy in

In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems = y/5

In March's Math Meet, they solved $\frac23$ of the problems = 2x/3

Hence:

y/5 + 2x/3 = 12

x + y = 30

solving the equation gives

x = y = 15

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The equation of the line is y=3x+1 when the line is on the graph of the given picture.

Given that,

In the picture we have a graph.

We have to find the equation of the line.

We know that,

From the graph we can see the points,

(1,4) and (0,1)

We know that the equation of the line is y=mx +b

The y and x value are from the points and the m is the slope that is rise by run and b is the y intercept.

m is rise/run

m= 1-4/0-1

m=-3/-1

m=3

b is 4=3(1)+b

4=3+b

b=4-3

b=1

The equation of the line is y=3x+1

Therefore, The equation of the line is y=3x+1 when the line is on the graph of the given picture.

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The expression that represents "10 subtracted from the quotient of 3 and a number" is D. 3 over n - 10.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Let the number be n

The expression will be:

= 3/n - 10

Therefore, the correct option is D.

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Considering the figure the required angle is solved using the vertical angle theorem. The values are

The problem is solved considering this theorems

vertical angle theorem

According to this theorem, when two straight lines cross, they create two sets of linear pairs and the vertical opposite angles are equal.

solution for the missing angle

x + 70 + 60 = 180 sum of angles of a triangle

x = 50

Using vertical angle theorem

? + 88 + 50  = 180 sum of angles of a triangle

? = 180 - 88 - 50

? =  42

solution for the missing angle

x + 75 + 30 = 180 sum of angles of a triangle

x = 75

Using vertical angle theorem

? + 88 + 75  = 180 sum of angles of a triangle

? = 180 - 85 - 75

? =  20

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Answer:

0.538 as a fraction in its simplest form is 269/500

Step-by-step explanation:

We all know that 0.538 can be written as 0.538/1

Multiply the numerator and denominator by 1000 which comes out to 538/1000

Divide the numerator and denominator by 2 which comes out to 269/500

Since 269 is a prime number 269/500 is 0.538 in its simplest form

-68 as a quotient of integers is -680/10.

The given integer is -68.

In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Here, -68/1

Multiply 10 to both the numerator and denominator, we get

= -680/10

= -68

Therefore, -68 as a quotient of integers is -680/10.

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The presense of a midpoint will result in congruent segments.

Congruent segments are just equal-length line segments. Congruent means similar. Congruent line segments are typically represented by drawing the same number of little tic lines perpendicular to the segments in the middle of the segments.

A congruent line segment is any line segment with equal measure. Congruent line segments, for example, are the sides of an equilateral triangle since they all have the same length.

When we insert a midpoint to a line segment, it divides the line into two equal portions. Because equal segments are congruent, we can say that congruent segments are generated.

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Answer:

477,577 lb

Step-by-step explanation:

Volume of sphere:

V = (4/3)πr³

V = (1/2)(4/3)(3.14159)(14 ft)³ = 5,747.015 ft³

d = 83.1 lb/ft³

W = Vd

W = 5,747.105 ft³ × 83.1 lb/ft³

W = 477,577 lb

Answer:

Step-by-step explanation:

[tex]f(x) = 2x^{2} + 5x - 7\\\\g(x) = x^{2} -2\\ \\f(g(x)) = 2(x^{2}-2) + 5(x^{2} -2) - 7\\ \\= 2x^{2} - 4 +5x^{2} -10 - 7\\= 2x^{2} + 5x^{2} -4-10-7\\\\\\f(g(x)) = 7x^{2} -21[/tex]

Answer:

0.14 (It would be divided by 10).

Step-by-step explanation:

Originally, our factors were 0.36 and 4. After modifying our problem, our factors are now 0.36 and 0.4. Comparing the original factors with the modified, we can see that there was no change done to 0.36. 4, on the other hand, has been divided by 10 ( [tex]0.4 = \frac4{10}[/tex] ).

We can rewrite [tex]0.36 \times 0.4[/tex] as [tex]0.36 \times 4 \times \frac1{10}[/tex]. Since we know 0.36 x 4 = 1.4, we can replace 0.36 x 4 with 1.4 in our modified problem, giving us [tex]1.4 \times \frac1{10}[/tex], which shows us that the product has now been divided by 10 as one of its factors was divided by 10.

Conclusion: Modifying one of the factors of a product using multiplication/division would also multiply/divide (respectively) the product by the same number.