If the shared side between angles 1 and 2 has a measure of 2×+9 and the shared side between angles 3 and 4 has a measure of 9x+1, what is the value of X? Round your answer to the nearest hundredth.
Answer:
x = 1.14---------------------------
Given figure is a parallelogram since opposite sides are parallel.
Therefore the sides between angles 1 & 2 and 3 & 4 are of equal length:
2x + 9 = 9x + 19x - 2x = 9 - 17x = 8x = 8/7x = 1.14Write an equation of the line that passes through (1,6) and is parallel to the line shown.
Answer:
[tex]y=2x+4[/tex]
Step-by-step explanation:
The slope of the given line is [tex]\frac{-2-4}{-2-1}=2[/tex].
Parallel lines have the same slope, so the equation is:
[tex]y-6=2(x-1) \\ \\ y-6=2x-2 \\ \\ y=2x+4[/tex]
The mean temperature for the first 4 days in January was 3°C.
The mean temperature for the first 5 days in January was 1°C.
What was the temperature on the 5th day?
The temperature on the fifth day in January is -7°C.
What is mean?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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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 S^-1 = t^2+4t-12/t^2-9t+14
-
Which equation represents the average sales each day for the real estate company?
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 number of computer security breaches is expected to increase at a yearly rate of
86%.
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
Write the number below as a fraction in its simplest form
0.538
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
A tank in the shape of a hemisphere has a radius of 14 feet. If the liquid that fills the tank has a density of 83.1 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
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
Which expression represents "10 subtracted from the quotient of 3 and a number"?
A 3n - 10
B 10 - 3n
C 10 - 3 over n
D 3 over n - 10
The expression that represents "10 subtracted from the quotient of 3 and a number" is D. 3 over n - 10.
What is an expression?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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f(-3) evaluate the function of the graph
The composition f(-3) has a value of 1
How to evaluate the function on the graph?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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f(x) = x + 2
g(x) = 3x
Work out the value of gf (4).
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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Use the given information to prove that x II y
Considering the figure < 4 ≅ < 5 alternate internal angles
What is the alternate internal angle theorem ?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
alternate exterior anglescorresponding angles same side exterior anglesUsing the figure. alternate internal angle theorem proves that
< 4 ≅ < 5< 3 ≅ < 6This helps to complete the required proof that < 4 = < 5
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Someone has the answer?
Find the value of x so that the function has the given value. j(x) = 3-x;j(x) = -5
The input value x in the function j(x) = 3-x as j(x) equals -5 is 8.
What is the value of x in the given function?A function is simply a relationship that maps one input to one output.
Given the function in the question;
j( x ) = 3 - xj( x ) = -5x = ?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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You multiply two integers and the product is -18. List 4 possible pairs of integers
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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if 0.36 x 4=1.4, how would your product be different if the factors were 0.36 and 0.4?
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.
Choose the correct description of the graph of the inequality x − 3 greater than or equal to 5. (5 points)
Open circle on 8, shading to the left.
Closed circle on 8, shading to the left.
Open circle on 8, shading to the right.
Closed circle on 8, shading to the right.
The correct description of the graph of the inequality x - 3 ≥ 5, is: D. Closed circle on 8, shading to the right.
How to Graph an Inequality?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 presense of a midpoint will result in what type of segments?
The presense of a midpoint will result in congruent segments.
What are 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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The product of two fractions is 5/6 .
a) Find three different pairs of fractions that each have a product of 5/6 . Show how you know your answers are correct.
b) Explain why there are more than one pair of fractions that have a product of 5/6
The two fractions which give the product of 5/6 are 1/3 and 5/2.
What is an expression?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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what's the answer to this amthswatxh qu
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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4. (02.08 MC)
Let
f(x) = 2x²5x - 7
and
g(x) = x² - 2.
Find f(g(x)). Show each step of your work. (10 points)
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]
Does the diagram contain enough information to prove that line segment JK is parallel to line segment ML? Explain your answer.
Yes the diagram has enough information to prove that line segment JK is parallel to line segment ML
How to determine of line segment JK is parallel to line segment MLA 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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Square root five as a decimal 
To get the answer go to desmos
Answer:
2.2360679775 or 2.24
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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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How do you find the x for both of these problems?
Considering the figure the required angle is solved using the vertical angle theorem. The values are
14. 42 degrees and 16. 20 degreesHow to determine the required angleThe 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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The slope from problem 7 was 2.
The y-coordinate is 2 when x=0.
What is a slope?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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What is this shape ?
Answer:
Decagon
Step-by-step explanation:
Because it has 10 sides.
Answer:
Its a Decagon
Step-by-step explanation:
Alexa drive a motorcycle 200 kilometers in 3 hours. If she drove at this constant speed, how fat could she travel in 9 hours?
Answer:600
Step-by-step explanation:
i think
Pls help due today!!!!!
Hudson goes to a store an buys an item that costs a dollars. He has a coupon for 20%
off, and then a 5% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hudson paid at the register.
An expression that represents the total amount (a) that Hudson paid is
a-a/10×2+{(a/10×2)/20}.
What do we mean by expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.So, the expression that represents the total amount Hudson paid:
We know that,
Hudson has a coupon for 20% off.A 5% tax is added to the discounted price.Then, the expression can be as follows:
a - (a/100×20) + {(a/100×20)/100 × 5}a - a/10 × 2 + {(a/10×2)/20}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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for a thin piece of 30 inches by 30 inches cardboard, square corners are cut out so that the sides can be folded up to make a box. what dimensions will yield a box of maximum volume? what is the maximum volume?
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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What is -68 as a quotient of integers?
-68 as a quotient of integers is -680/10.
The given integer is -68.
What is a quotient of integers?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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