How to solve for 27-30 (X, Y, Z, and W)
27)
Opposite angles are equal.
x° angle is the opposite angle of the 90° angle.
Therefore, x°=90°.
28)
The 90° angle marked in the figure and the y° angles forms a linear pair.
Hence, both angles are supplementary. Supplementary angles sum upto 180°.
Therefore, we can write
[tex]\begin{gathered} y\degree+90\degree=180\degree \\ y\degree=180\degree-90\degree \\ y\degree=90\degree \end{gathered}[/tex]Therefore, y°=90°.
29)
In the figure, let z°+46°=p°.
From figure, we can see that the p° angle is the opposite angle of y° angle.
Since opposite angles are equal, we can write
[tex]\begin{gathered} p\degree=y\degree \\ z\degree+46\degree=y\degree \end{gathered}[/tex]Since from part 28, y°=90°, we get
[tex]\begin{gathered} z\degree+46\degree=90\degree \\ z\degree=90\degree-46\degree \\ z\degree=44\degree \end{gathered}[/tex]Therefore, zh=44e.
30)
From figure,
[tex]\begin{gathered} w\degree=y\degree+90\degree+z\degree \\ \end{gathered}[/tex]Substitute the known values.
[tex]\begin{gathered} w\degree=90\degree+90\degree+44\degree \\ w\degree=224\degree \end{gathered}[/tex]Therefore, w°=224°
-2(-3)+(-2)(-4)-(-2)=
what’s the inverse of Y equals X squared -10 X
The inverse of the function y equals x squared - 10x (y = x² - 10x) is 5 ±√(x + 25).
What is an inverse function?An inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
First of all, we would translate the given word sentence into a function as follows:
y equals x squared - 10x ⇒ y = x² - 10x
In order to determine the inverse of this function f(x) = x² - 10x, we would interchange both the input value (x) and output value (y) as follows:
y = x² - 10x
x = y² - 10y
Next, we would add (half the coefficient of the y-term)² to both sides of the function as follows:
x + (-10/2)² = y² - 10y + (-10/2)²
x + 25 = y² - 10y + 25
x + 25 = (y - 5)²
±√(x + 25) = y - 5
Adding 5 to both sides of the function, we have:
5 ±√(x + 25) = y - 5 + 5
y = f⁻¹(x) = 5 ±√(x + 25)
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one number is six less than a second number. Twice the first is 2 more than 4 times the second. Find the numbers
The two numbers are 11, and 5 if the one number is six less than a second number.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
One number is six less than a second number.
Let the number be x and y:
x - 6 = y
Twice the first is 2 more than 4 times a second.
2x = 2 + 4y
After solving the two linear equations:
2x = 2 + 4(x - 6)
2x = 2 + 4x - 24
2x = 22
x = 11
y = 5
Thus, the two numbers are 11, and 5 if the one number is six less than a second number.
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Please list what the tangent parent function.Can you make graph it scale both axes. With a short table of points+ domain and range. If there are asymptotes please identify and label.
First, use a calculator to create a table of values for the function:
[tex]y=\tan (x)[/tex]A table with inputs for x starting at -6.5 reaching the value of 6.5 with steps of 0.5 would be:
Plotting all the points and joining them with a smooth line, we can see that the graph of y=tan(x) is:
As we can see from the graph, the curve has an asymptote at
[tex]\frac{(2k+1)\pi}{2}+\pi k,k\in\Z[/tex]On the other hand, the graph reaches all the real values over the Y-axis. Then, the range of the function is the set of all real numbers.
herefore, the domain is:
[tex]x\in\R-\lbrace\frac{2k+1}{2}\pi|k\in\Z\rbrace[/tex]he range is:
[tex]y\in\R[/tex]nd the asymptotes are:
[tex]x=\frac{2k+1}{2}\pi,k\in\Z[/tex]-1.4 + {-1.2}
Answer in decimals
Use two unit multipliers to convert 75 square inches to square feet.
In order to use two unit multipliers we will convert from square inches to cm using the following unit multiplier:
[tex]\frac{6.4516}{1^{}}\frac{cm^2}{in^2}\text{.}[/tex]and then we will convert from square cm to square feet, using the following unit multiplier:
[tex]\frac{0.00107639}{1}\frac{ft^2}{cm^2}.[/tex]Answer:
[tex]75in^2=75in^2(\frac{6.4516}{1^{}}\frac{cm^2}{in^2})(\frac{0.00107639}{1}\frac{ft^2}{cm^2})=0.520833ft^2.[/tex]What is 12 2/3 times 19 1/4? Put in your answer as a mixed number.
243.83
Step-by-step explanation:
Multiple: 38/
3
* 77/
4
= 38 · 77/
3 · 4
= 2926/
12
= 1463 · 2/
6 · 2
= 1463/
6
Answer:
[tex]243 \frac{5}{6}[/tex]
Step-by-step explanation:
Given multiplication:
[tex]12 \frac{2}{3} \times 19 \frac{1}{4}[/tex]
Convert the mixed numbers to improper fractions:
[tex]\implies \dfrac{12 \times 3+2}{3} \times \dfrac{19 \times 4+1}{4}[/tex]
[tex]\implies \dfrac{36+2}{3} \times \dfrac{76+1}{4}[/tex]
[tex]\implies \dfrac{38}{3} \times \dfrac{77}{4}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]
[tex]\implies \dfrac{38\times77}{3\times4}[/tex]
[tex]\implies \dfrac{2926}{12}[/tex]
Divide the numerator and denominator by 2:
[tex]\implies \dfrac{2926 \div 2}{12 \div 2}[/tex]
[tex]\implies \dfrac{1463}{6}[/tex]
Convert to a mixed number:
[tex]\implies 243 \frac{5}{6}[/tex]
2 to 4 and 11 to 11/2 are they proportional
Explanation:
In this case we must compare 2 to 4 and 11 to 11/2
1. The first ratio given is 2 to 4
[tex]r_1=\frac{2}{4}=\frac{1}{2}[/tex]So, the first ratio is 1/2
2. The second ratio given is 11 to 11/2
[tex]\begin{gathered} r_2=\frac{11}{\frac{11}{2}}=\frac{2\cdot11}{11} \\ r_2=2 \end{gathered}[/tex]Finally, since r1 ≠ r2 they are not proportional
ANSWER:
they are not proportional
If line a is parallel to line b what is m ∠1?
Explanation
hen a line instersects a pair of paralle lines diverse angles are created
If you copy A of the corresponding angles and you translate it along the transversal, it will coincide with the other corresponding angle (B)
so angles A and B are called
Corresponding angles, those angles are congruents
[tex]m\measuredangle A=m\measuredangle B[/tex]hence, if the lines in the problem are parellel, is must fit
[tex]m\measuredangle1=40\text{ \degree}[/tex]therefore, the answer is
[tex]a)40\text{ \degree}[/tex]I hope this helps you
Logan starts an IRA (Individual Retirement Account) at the age of 24 to save for retirement. He deposits $300 each month. Upon retirement at the age of 65. his
retirement savings is $1,510,293.29. Determine the amount of money Logan deposited over the length of the investment and how much he made in interest upon
retirement.
Total deposited = $147600
Interest earned = $1362693.29
Total no. of years for saving = 65-36-24 = 41
years saving no. of months = 41 x12
= 492 Month
deposit for 1 month = $300 deposit for 492 month = 492 x $300= $147600
Total deposited = $147600
Total saving after retirement = $1,510,293.29 interest = total saving - total deposit= $1,510,293.29 - $147600
= $1362693.29
What is the Interest Rate ?Interest is a periodically paid interest amount related to the amount borrowed, deposited or borrowed (the so-called capital amount). The total interest on the amount borrowed or borrowed depends on the principal amount, the interest rate, the frequency of the interest and the time of loan, deposit or borrowing.
Annual interest is interest for one year. Other interest rates apply to different periods of time, such as a month or a day, but are usually calculated annually.
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In this diagram, angle ABC has been mapped onto angle A'B'C' by a series of rigid motions. Which statement best describes one way to prove that the triangles are congruent?
A) Rigid motions preserve distance and angle measure. This means that AB approximately= A'B', BC approximately=B'C', and angle A approximately= angle A', so the triangles are congruent by SAS.
B) Rigid motions preserve distance and angle measure. This means that AB approximately= A'B', BC approximately=B'C', and angle B approximately= angle B', so the triangles are congruent by SAS.
C) Measure the areas of angle ABC and angle A'B'C' to confirm that their areas are equal. This means that AB approximately= A'B', BC approximately= B'C', and AC approximately= A'C', so the triangles are congruent by SSS.
D) Measure the perimeters of angle ABC and angle A'B'C' to confirm that their perimeters are equal. This means that AB approximately= A'B', BC approximately= B'C', and AC approximately= A'C', so the triangles are congruent by SSS.
The correct answer is Option B.
What is the difference in
|-3| and -3
Answer:
6, because anything inside | | are positive so -3 will now be 3.
3 minus -3 = 6
Step-by-step explanation:
Hope it helps! =D
The airport parking lot charges $2.00 to enter and $3.00 per hour after that. Carmen has N dollars and wants to be able to determine the maximum number of hours she can park. How can Carmen determine the length of time she can afford to park her car in the parking lot?
Carmen can determine the length of time she can afford to park her car in the airport parking lot by first deducting the entrance fixed charge from her N dollars and then dividing the balance by the hourly rate.
What are the mathematical operations?The standard mathematical operations that combine numbers, variables, and operands to arrive at a defined output value are addition, subtraction, division, and multiplication.
In this situation, we can use the mathematical operations of subtraction and division to determine the length of time Carmen can park her car.
The fixed charge for entering the airport parking lot = $2
Hourly charger after the initial entrance = $3
The total amount of dollars possessed by Carmen = N dollars.
Let the length of time she can park there = l.
The maximum number of hours she can park is given by the function, F(l) = (N - 2)/3.
Thus, the best strategy for Carmen to determine her parking time at the airport parking lot based on her N dollars, the fixed entrance fee, and the variable cost per hour, is using the mathematical operations of subtraction and division.
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Trisha's puppy weighs 5 pounds. How many ounces does her puppy weigh?
80 ounces
60 ounces
50 ounces
40 ounces
I NEED TO KNOW NOW PLS HURRY
on the grid, draw 3 triangles with an area of 12 square units.Label the base and height of each triangle
Answer:
Iiiieie I just got off your phone with weee
Step-by-step explanation: why did I get a hold for him or
oh yeah that’s fine I’ll let lol I was thinking of going out to the house for the next few weeks so I’m not good enough for that lol I think it’s so so to do that all day and you can get a hold on you for sure and I can help with your stuff and help me help help you get it
Find a with the given information.
m=-6/7 (-10,0) and (a,-6)
By using the equation to find the slope, we will see that the value of a is -3.
How to find the value of a?
Here we have two points that define a line.
Remember that a linear equation is of the form:
y = m*x + b
Where m is the slope.
And we know that if the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
m = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that the points are:
(-10, 0) and (a, -6), and the slope is m = -6/7, then we can write the equation:
-6/7 = (-6 - 0)/(a + 10) = -6/(a + 10)
The denominator should be the same in both sides, so we must have:
a + 10 = 7
a = 7 - 10 = -3
Then the two points are (-10, 0) and (-3, -6).
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5.The closed figure with 5 straight line segments is called
Answer: Pentagon
Step-by-step explanation:
A closed figure with 5 straight line segments is called a pentagon. See attached for a visual example.
A segment is a straight line with two distinct endpoints.
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10 A large fountain in a city park cycles
69.3 gallons of water every 1.5 hours.
Write an equation to model how to
find the number of gallons of water the
fountain cycles every hour.
The fountain in the city cycles 46.2 gallons of water in every hour if it cycles 69.3 gallons of water every 1.5 hours according to the model equation.
Unitary Method: What is it?The unitary technique in actuality involves first determining the actual value of a single unit, alongside followed by the value of the necessary number of units.
The unitary approach is a kind of a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Total mass = 69.3 gallons
Time taken = 1.5 hrs
For 1 hr = 69.3/1.5
= 46.2 gallons
What is an example of a unitary method?A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.
The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
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four coworkers are discussing their birthdates what is the probability of the months being different?
The probability of four coworkers having different birth months is 0.572 or 55/96
Given there are four coworkers and the condition is they should have different birth months.
As we know probability is the ratio of favorable out comes to the total number of outputs
Favorable outcomes are
For first person 12 months
For second person 11 months
For third person 10 months
For Fourth person 9 months
Total outcomes
For each and every person total outcomes are 12 months which add up to 12 x 12 x 12 x 12 = [tex]12^{4}[/tex]
Now probability will be
Probability = [tex]\frac{(12)(11)(10)(9)}{12^{4} }[/tex]
Probability = 55/96
Hence the probability of four coworkers having different birth months is 55/96
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Find the value of x,y and z
○ x=70,y=58,z=53
○ x=80,y=38,z=63
○ x=85,y=38,z=63
○ x=80,y=48,z=63
Answer:
(b) x=80, y=38, z=63
Step-by-step explanation:
You want to know the values of x, y, and z, given they are angle measures in a diagram showing two triangles.
Linear pairThe angles that form a linear pair are supplementary:
x° +100° = 180°
x = 80 . . . . . . . . . divide by °, subtract 100
Angle sum theoremThe angle sum theorem tells you that the sum of angles in a triangle is 180°.
y° +62° +80° = 180°
y = 38 . . . . . . . . . . . . divide by °, subtract 142
In the other triangle, the same relation holds:
z° +100° +17° = 180°
z = 63 . . . . . . . . . . . . divide by °, subtract 117
The values of x, y, and z are ...
(x, y, z) = (80, 38, 63)
A 4-pint carton of yogurt costs $5.16.
What’s the price per quart
Using mathematical operations we can conclude that the cost per quart of yogurt is $1.29.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).So, the cost per quart:
The 4-pint carton of yogurt costs $5.16.Meaning that in the carton there are 4 quarts of yogurt.Cost per quart:
= 5.16/4= $1.29Therefore, using mathematical operations we can conclude that the cost per quart of yogurt is $1.29.
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8. If a triangle has the given side lengths of
16 and 24, determine the range of
values for the possible length of the 3rd
side.
Answer:
8 < L < 30
Step-by-step explanation:
The third side (L) can't be longer than or equal to the sum of the other two.
So. L < 30.
Also, it must be greater than 24-16 ie > 8
There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 246.5 grams of this cereal.
The amount of calories in 246.5 gm of Cereal 397.5372 calories
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example,
Ram spends 36 Rs. for a dozen (12) bananas. 12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees. As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas. This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
In 177.4 gm of cereal contain 110 calories.
So, 1 gram cereal contain
= 177.4 / 110
= 1.6127
and, 246.5 gm will contain
=246.5 x 1.6127
= 397.5372 calories.
Hence, 397.5372 calories are in 246.5 grams of this cereal.
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helppppppppppppppppppppppppp me
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
PLEASE HELP … Would really appreciate it
The diameter of the outer circle = 12.907 ft
The thickness of the circular pipe = 2.983 ft
The diameter of the inner circle = q = The diameter of the outer circle - The thickness of the circular pipe
⇒ The diameter of the inner circle = 12.907 - 2.983 ft
⇒ The diameter of the inner circle = q = 9.924 ft
What is a Circle?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. The radius of a circle is the separation between any point on the circle and its center.A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.In common parlance, the word "circle" can apply to either the figure's boundary or its entirety, including its inside; in rigorous technical parlance, the circle only refers to the boundary, and the entire shape is referred to as a disc.To learn more about Circles, refer to:
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Solve the problem.
2) The length of the base of an isosceles triangle is 28.35 meters. Each base angle is 29.73°. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.
Answer:
20.99 m
Step-by-step explanation:
Help its due in 5 hours. And I haven’t got the answer right for 2 hours.
Explanation
the volume of a cone is given by:
[tex]\text{Volume}=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]Step 1
find the radius:
let
Circumference= 6n inches
radius= r
[tex]\begin{gathered} \text{Circumference = 2 }\cdot\pi\cdot radius \\ \text{replace} \\ 6n\text{ inches=2}\cdot\pi\cdot\text{ r} \\ \text{divide both sides by 2}\pi \\ \frac{6n\text{ }}{2\pi}\text{=}\frac{\text{2}\cdot\pi\cdot\text{ r}}{2\pi} \\ so \\ r=\frac{6n\text{ }}{2\pi}=\frac{3n}{\pi} \\ r=\frac{3n}{\pi} \end{gathered}[/tex]Step 2
apply the formula for the volume of the cone:
let
h=13 inhces
[tex]\begin{gathered} r=\frac{3n}{\pi} \\ h=13\text{ inches} \end{gathered}[/tex]replace.
[tex]\begin{gathered} \text{Volume}=\frac{1}{3}\pi\cdot r^2\cdot h \\ \text{Volume}=\frac{1}{3}\pi\cdot(\frac{3\text{ n}}{\pi})^2\cdot13 \\ \text{Volume}=\frac{1}{3}\pi\frac{(9n^2)}{\pi^2}\cdot13 \\ \text{Volume}=\frac{3n^2}{\pi}\cdot13 \\ \text{Volume}=\frac{39n^2}{\pi}in^3 \end{gathered}[/tex]so, the answer is
[tex]\begin{gathered} \text{Volume}=\frac{39n^2}{\pi}in^3 \\ \text{Volume}\approx\frac{39n^2}{\pi}in^3 \\ \text{Volume=}12.41n^2inches^3 \end{gathered}[/tex]I hope this helps you
GХLauren has a full box of sugar cubes. The box is a rectangular prism with measurements, in centimeters,as shown. The size of each sugar cube is 1 cubic centimeter.2 cmSugar Cubes3 cm-4 cmFelect the numbers from the drop-down menus to complete each sentence.he volume of the box is measured in Choose...num
To find the volume of the prism we just multiply all the measures
[tex]\begin{gathered} V=2\cdot3\cdot4 \\ \\ V=24\text{ cm}^3 \end{gathered}[/tex]The volume is 24 cm³
If the sugar cubes have 1 cm³ of volume, to find how much sugar cubes fit in the box we must divide the volume of the box by the volume of the sugar cubes
[tex]\frac{V}{V_S}=\frac{24\text{ cm}^3}{1\text{ cm}^3}=24[/tex]Therefore we can fit 24 sugar cubes
Find the circumference of a circle with area
[tex] \frac{1}{ 4} \pi \: d {}^{2} cm {}^{2} [/tex]
The circumference of circle is [tex]\pi[/tex]d
What is a circle ?
A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or center, and the fixed distance between each point and the origin is referred to as the radius.
Given that : the circle with area =[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]
area of circle is =[tex]\pi r^{2}[/tex]
[tex]\pi r^{2}[/tex]=[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]
on comparing we get
r = [tex]\frac{d}{2}[/tex]
circumference of circle is 2[tex]\pi r[/tex]
= 2×[tex]\pi[/tex]×[tex]\frac{d}{2}[/tex]
=[tex]\pi[/tex]d
The circumference of circle is [tex]\pi[/tex]d
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