Answers
Answer: 12
Step-by-step explanation:
By the corresponding angles theorem, [tex]4x-5=97-2x \longrightarrow x=17[/tex].
So, this means that [tex]97-2x=63[/tex].
Now, by the same-side interior angles theorem, we know that [tex]10y-3+63=180 \longrightarrow y=\boxed{12}[/tex]
Related Questions
Find equation of a line with the given slope that passes through the given point. Write the equation in the form Ax + By = C.
M = -5, (-4,-8)
Answers
Answer:
5x + y = -28
Step-by-step explanation:
Hi there!
We're given that a line has a slope of -5 and contains the point (-4, -8)
We want to write the equation of this line in standard form
Standard form is given as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be zero, and a cannot be negative
Before we write the equation in standard form however, we need to write it in slope-intercept form, which is y=mx+b, where m is the slope & b is the y intercept
As we are already given the slope, we can immediately plug that in for m in y=mx+b
y=-5x+b
Now to find b:
As the equation passes through the point (-4, -8), we can use its values to help solve for b
Substitute -4 as x and -8 as y:
-8 = -5(-4) + b
Multiply
-8 = 20 + b
Subtract 20 from both sides
-8 = 20 + b
-20 -20
__________
-28 = b
substitute -28 as b
y = -5x - 28
We found the equation in slope-intercept form, but remember, we want it in standard form
In standard form, both x and y are on the same side; so, let's move 5x to the other side; to do this, we need to add 5x to both sides
y = -5x - 28
+5x +5x
_________
5x + y = -28
Hope this helps!
Find the area of the shaded region. 10 ft 10 ft
Answers
Answer: Its 10 ft
Step-by-step explanation: because if one side is the number the other side is going to be the same number
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PLEASE HELP!!!! A triangle has sides of lengths a=17, b=36, c=45 km.
Find the measures of the 3 angles
Enter your answer as a number; answer should be accurate to 2 decimal places.
Angle A =____?
Angle B = ____?
Angle C = ____?
Explain how you found the 3 angles below. Be sure to show all of your work.
Answers
Answers:
Angle A = 20.64 degreesAngle B = 48.29 degreesAngle C = 111.07 degreesYou may or may not have to type in the word "degrees", and/or use the degree symbol. I would ask your teacher for clarification.
A diagram is shown below.
============================================================
Explanation:
We'll need the law of cosines to solve for angle A.
a^2 = b^2 + c^2 - 2*b*c*cos(A)
17^2 = 36^2 + 45^2 - 2*36*45*cos(A)
289 = 3321 - 3240*cos(A)
289 - 3321 = -3240*cos(A)
-3032 = -3240*cos(A)
-3240*cos(A) = -3032
cos(A) = (-3032)/(-3240)
cos(A) = 0.935802
A = arccos(0.935802)
A = 20.64 degrees
which is approximate to 2 decimal places.
Note: The "arccos" refers to "arccosine" which is the same as inverse cosine (denoted as [tex]\cos^{-1}[/tex] on many calculators).
-----------------------------
Do a similar set of steps for angle B.
b^2 = a^2 + c^2 - 2*a*c*cos(B)
36^2 = 17^2 + 45^2 - 2*17*45*cos(B)
1296 = 2314 - 1530*cos(B)
1296 - 2314 = -1530*cos(B)
-1018 = -1530*cos(B)
-1530*cos(B) = -1018
cos(B) = (-1018)/(-1530)
cos(B) = 0.665359
B = arccos(0.665359)
B = 48.29 degrees
Also approximate to 2 decimal places.
-----------------------------
As you can probably guess by now, we could use the law of cosines to find angle C. But a much quicker shortcut is to use the fact that for any triangle, the interior angles always add to 180 degrees.
This shortcut is only possible since we know the two other angles.
Solve for C.
A+B+C = 180
C = 180-A-B
C = 180 - 20.64 - 48.29
C = 111.07 degrees
Like the others, this is approximate to 2 decimal places.
You can use a graphing tool like GeoGebra to confirm the answers. See below. Due to the SSS (side side side) triangle congruence theorem, only one triangle is possible. This means only one answer is possible per angle.
Where does Pythagorean identities and also how it relates to the right triangles
Answers
Answer:
A pythagorean identity means that for any angle [tex]\theta[/tex], [tex]sin^2\theta+cos^2\theta=1[/tex].
This also means [tex]1+tan^2\theta=sec^2\theta \mbox{ and } 1+cot^2\theta=csc^2\theta.[/tex] The symbol, theta ([tex]\theta[/tex]) represents one of the acute angles in the right triangle. The hypotenuse (familiarly c in the regular pythagorean theorem) is 1. The triangle base is [tex]cos\theta[/tex], and the height (side perpendicular to the base, making a right angle) is [tex]sin\theta[/tex]. The angle theta is opposite the [tex]sin\theta[/tex] side.
Step-by-step explanation:
The pythagorean theorem applies to right triangles, which always have a 90 degree angle. Pythagorean identities are used to simplify trigonometric expressions/evaluate trig functions and to find the trig ratios in a right triangle.
Answer:
The Pythagorean identities are
[tex]sin^{2} x + cos^{2} x = 1\\1+ tan^{2} x = sec^{2} x\\1 + cot^{2} x = csc^{2} x\\where\\csc x = \frac{1}{sinx} \\cot x = \frac{cosx}{sinx} or \frac{1}{tanx} \\tan x = \frac{1}{cotx} or \frac{sinx}{cosx} \\sec x = \frac{1}{cotx}[/tex]
No matter what the value of x (the angle degree amount) is, sin²x+cos²x is equal to 1
When given a side length of a right triangle you will be able to use one of these identities to find the angle amount
Using the diagram below what is the measure of <1
The measure of <1=[m]
Answers
Answer:
The angle measure of 1 is 62 degrees.
Step-by-step explanation:
You need to the exterior angle theorem.
This means that all the exterior angles have to equal up to 360 degrees.
You need to add everything up which should equal 298 degrees.
Then subtract 360 by 298.
The angle measure of 1 is 62 degrees.
Yo math hard. so 25 points, i really need it
Answers
Answer:
10 feet
Step-by-step explanation:
Given,
Volume of right cylinder = 2000 π cubic feet.
Length ( l ) = 20 feet
To find : Radius ( r )
Formula : -
Volume of right cylinder = πr²h
πr²h = 2000 π
Divide π on both sides,
r²h = 2000
r² = 2000 / h
r² = 2000 / 20
r² = 100
= 10 x 10
r²= 10²
r = 10 feet
Hence,
the radius is 10 feet.
Find the linear equations giving brainlest
Answers
Answer:
Step-by-step explanation:
Slope-intercept form of a linear equation: y = mx + b
m is the slopeb is the y-intercept - when x = 0Problem 17: y = -4x + 2
slope: -4y-intercept: (0, 2)Problem 18: y = 1/7x - 5
slope: 1/7y-intercept: (0, -5)Problem 19:
y = 1x + 3
slope: 1y-intercept: (0, 3)Hope this helps!
Clearly, we can tell that the equation is in slope intercept form.
Formula:
Slope intercept form: y = (m)x + (b) [m = Slope; b = y-intercept]
Let us compare the slope intercept form equation with the given equation to determine the slope and the y-intercept.
⇒ y = (m)x + (b) and y = -4x + 2
When comparing both equations, we can observe that:
"-4" takes the place as "m" "2" takes the place as "b"Therefore, the slope and the y-intercept are -4 and 2 respectively.
Determining the coordinates of the y-intercept;
Note: The y-intercept of the line ALWAYS has an x-coordinate of 0.
⇒ Coordinates of y-intercept: (0, y-intercept) ⇒ (0, 2)
Final answers:Slope = -4Coordinates of y-intercept = (0, 2)________________________________________________________
18) y = x/7 - 5Clearly, we can tell that the equation is in slope intercept form.
Formula:
Slope intercept form: y = (m)x + (b) [m = Slope; b = y-intercept]
Let us compare the slope intercept form equation with the given equation to determine the slope and the y-intercept.
⇒ y = (m)x + (b) and y = x/7 - 5
When comparing both equations, we can observe that:
"x/7" takes the place as "m" "-5" takes the place as "b"Therefore, the slope and the y-intercept are x/7 and -5 respectively.
Determining the coordinates of the y-intercept;
Note: The y-intercept of the line ALWAYS has an x-coordinate of 0.
⇒ Coordinates of y-intercept: (0, y-intercept) ⇒ (0, -5)
Final answers:Slope = x/7Coordinates of y-intercept = (0, -5)________________________________________________________
19) y = x + 3Clearly, we can tell that the equation is in slope intercept form.
Formula:
Slope intercept form: y = (m)x + (b) [m = Slope; b = y-intercept]
Let us compare the slope intercept form equation with the given equation to determine the slope and the y-intercept.
⇒ y = (m)x + (b) and y = 1x + 3 [x = 1x]
When comparing both equations, we can observe that:
"1" takes the place as "m" "3" takes the place as "b"Therefore, the slope and the y-intercept are 1 and 3 respectively.
Determining the coordinates of the y-intercept;
Note: The y-intercept of the line ALWAYS has an x-coordinate of 0.
⇒ Coordinates of y-intercept: (0, y-intercept) ⇒ (0, 3)
Final answers:Slope = 1Coordinates of y-intercept = (0, 3)NEED help pls ty. Will mark brainliest
Answers
If the area of a circle is 40 pi square cm, find the radius.
Answers
area equation is pi*r^2. divide by pi then square root. so the answer is the square root of 40
Answer:
√40 centimeters
Step-by-step explanation:
Given :
Area of circle = 40π cm²
===========================================================
Formula for area of a circle :
Area = πr²
===============================================================
Equating the given term and formula to find r :
⇒ 40π = πr²
⇒ r² = 40
⇒ r = √40 centimeters
A cube has an edge length of 10 inches. What is its volume, in cubic in?
Answers
Answer: 1000
Step-by-step explanation: V=a to the 3rd power=10 to the 3rd power=1000
Total points in a board game based on the average number of hours played is predicted using the least-square regression line, 9 = 280.3 + 85.7x, where y
represents the total points scored and x represents the average number of hours spent playing the game. A player plays the game for an average of 3 hours
and has a point total of 550. What is the residual for the player?
O 3.15
03
0-126
0-3.15
O 12.6
Answers
Using the line of best-fit, it is found that the residual for the player is of 12.6.
What is the residual for a line of best-fit?A residual is given by the difference between the observed point and the predicted point.
In this problem, the expected score over x hours is given by:
f(x) = 280.3 + 85.7x.
Hence, for 3 hours, the predicted score is given by:
f(3) = 280.3 + 85.7 x 3 = 537.4.
The observed score was of 550, hence the residual is given by:
R = 550 - 537.4 = 12.6.
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PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL
Answers
Answer:
92 degrees
Step-by-step explanation:
180-88
=92
~rere
4. Add
f(x)= 4x?+5x-1
g(x) = 2x2 + 5x+3
Answers
A. 3x² +6
Explanation:(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions
... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses
... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms
... = 3x² +6
Julieta was offered a job that paid a salary of $49,000 in its first year. The
salary was set to increase by 3% per year every year. If Julieta worked at the
job for 21 years, what was the total amount of money earned over the 21
years, to the nearest whole number?
Answers
Answer:
he will get a total of 41%
Julieta has a job for $49000 which increases at the rate of 3% per year, so the money earned after 21 years is $79870.
What is Simple interest?A quick and simple way to figure out interest on that money is to use the simple interest approach, which adds interest at the same rate for each daily cycle, and it is to the initial principal amount.
A way to figure out how much interest will be charged on an amount of money at a specific rate and for a specific duration of time is by using simple interest.
As per the information received from the question,
Principle amount, P = $49000
Rate, R = 3%
Time, T = 21 years.
SI = ($49000 × 3 × 21)/100
SI = 30870
So, the total amount earned in 21 years is $30870, and the total money he is having after 21 years is $79870.
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It has been observed in one country, that 59 out of every 100 births is a baby with brown eyes. In 640 births how many brown eyed babies would you expect?
Answers
Answer:
377.6
Step-by-step explanation:
You do the ratio of 59/100 and then divide 640 by 100. Then you will get 6.4.
Multiply 59×6.4=377.6
Are EFG and HIJ similar?
Answers
Help!! Which one is it?
Answers
Answer: Choices A and C
Reason:
A) The mode is 134 because the leaf 4 shows up the most for the stem of 13, and for any other stem as well. In other words, stem = 13 and leaf = 4 combine to the value 134 which shows up the most (a total of 5 times) compared to the other numbers. Therefore, we have a true statement.B) In the first row, the leaf 1 shows up three times. This leads to the number 101 (not 111) showing up 3 times. Therefore, statement B is false.C) This is also true. Visually the length of the leaves for the stem 13 is the longest. We have 8 leaves here which is the most of any other row.D) This is false. The leaf counts for the rows from top to bottom are: 6, 4, 0, 8, 2, 3. Those numbers add up to 23. This means there are 23 values (not 20) in the data set.Find the vertex, axis of symmetry, and y-intercept of the quadratic function.
Answers
Answer:
Vertex: (4, 12)Axis of symerty: x = 4y - inrercept: -4Step-by-step explanation:
The vertex form of quadratic function f(x) = ax² + bx + c:
f(x) = a(x - h)² + k
(h, k) - coordinates of a vertex
h = -b/2a
k = f(h)
We have f(x) = -x² + 8x - 4 ⇒ a = -1, b = 8, c = -4.
h = -8/(2 · (-1)) = -8/(-2) = 4
k = f(4) = -4² + 8 · 4 - 4 = -16 + 32 - 4 = 12
Vertex (4, 12)
Axis of symerty = h: x = 4
y - inrercept f(0) = c: -4
Answer:
See below ~
Step-by-step explanation:
Details of Graph
Vertex = (4, 12)Axis of Symmetry : x = 4Y-intercept : -4A bag contains 2 red marbles, 7 blue marbles and 8 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be blue?
Answers
What is the length of the missing side of this triangle?
13
?
9
A
250
В
22
С
15.81
Answers
Answer: C - 15.81
Step-by-step explanation:
pythagorean theorum: a^2 + b^2 = c^2
13^2 + 9^2 = c^2
169 + 81 = c^2
c^2 = 250
root both sides
c = 15.81
Which list of numbers is ordered from greatest to least?
Answers
Answer:
the option b is correct answer
Answer:
c
Step-by-step explanation:
that was arrange from greatest to lowest
Pls help me and show work! Thank you <3
Answers
Answer: 15
Step-by-step explanation:
By the alternate interior angles theorem, [tex]5x+9=84 \longrightarrow x=\boxed{15}[/tex]
Does anyone know the answer ASAP! Please and Thankyou!
Answers
Answer:
m=-2 and b=3
Step-by-step explanation:
One way to find slope is to use rise over run (most useful when there is a graph). First find any two points along the line where it intersects with a point on the grid. (1,1); (2,-1) and (3,-3) are some examples. Then count how many spaces vertically and then horizontally it takes to get to the next point. In this case it is two spaces down (rise) and 1 space right (run). So rise/run = 2/1 =2. That is your slope. Because it is pointing downwards or decreasing we know it is a negative slope.
The y-intercept is just where the line intercepts with the y-axis. In other words, when x=0 what does y equal? Here it is 3.
What is the volume in cubic in, of a rectangular prism with a height of 19in, a width
of 17in, and a length of 18in?
Answers
Answer:
5,814 inches cubed
Step-by-step explanation:
lengthxwidthxheight=volume of a rectangular prism.
19 times 17 times 18 equals 5,814 inches cubed. It is cubed because it is a three-dimensionsal shape. Hope this helps!
Assume the acceleration of the object is a(t) = −9.8 meters per second per second (Neglect air resistance.) A baseball is thrown upward from a height of 3 meters with an initial velocity of 7 meters per second. Determine its maximum height. (Round your answer to two decimal places.)
Answers
Answer:
height = 5.682 meters
Step-by-step explanation:
height = -9.8x^2 + 7x + 3
Find the axis of symmetry: x = -b/(2a)
a = -9.8 b = 7 c = 3
x = -7/(2*-9.8) = -7/-19.6 = .357 = x = +.357 secs is when max height occurs
Find the height, replace x with .561
height = -9.8(.357^2) + 11(.357) + 3
height = -9.8(.127) + 11(.357) + 3
height = -1.245+3.927+3
height = 5.682
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.292302.html
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Find the area of the
parallelogram.
10.7 ft.
5.5 ft.
14 ft.
Answers
Answer: [tex]823.9ft^{2}[/tex]
Step-by-step explanation:
The formula for the area of a parallelogram is : [tex]l * w * h[/tex]
l = length
w = width
h = height
You did not specify which integer was which, but it does not matter as the order in which you multiply them together does not matter.
10.7 * 5.5 * 14 = 823.9
Since you are finding the area, you have to square the units; 823.9 ft^2
If you found this answer helpful, I would greatly appreciate it if you gave me brainliest :D.
please help me get a A
Answers
Answer:
y = 1/2 x.
Step-by-step explanation:
Each value of y is 1/2 of x.
Prove that the bisector of the angle formed by a tangent and a chord drawn from the point of tangency divides the intercepted arc into two congruent arcs.
Answers
Answer:
Step-by-step explanation:
Pls ingore all of the questions below, but help me with the attached image
What is the only number that has the same number of letters as it's meaning? ...
What number doesn't have its own Roman numeral? ...
What is the only even prime number? ...
What is the smallest perfect number? ...
What is our current numerical system based on? ...
Is Pi a rational or irrational number?
Answers
Answer:
A = 51
Step-by-step explanation:
I'm not sure if it is correct but here is my working
180=41+2a+a-14
180=3a+27
153=3a
51=a
Answer:
a=51
Explaination-
ABC + ACB + BAC = 180°
(a-14)° + 2a + 41° = 180°
a=51
Use the graph below to answer the question that:
What are the amplitude, period, and midline of the function? (1 point)
Amplitude: 6; period: 2π; midline: y = −3
Amplitude: 6; period: π; midline: y = −3
Amplitude: 3; period: π; midline: y = −2
Amplitude: 3; period: 2π; midline: y = −2
Answers
The amplitude is equal to 3, the period is π midline y = -1.
For this case the amplitude is given by:
A = (l-5l + 1) / 2
A = 6/2
A = 3
The middle line is given by:
y = -1
What is the formula for period?The period of the function is given by,
T = l x2 - x1 l
T = l 0 - pi l
T = l - pi l
T = pi
Therefore the amplitude: 3; period is π; midline: y = -1.
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