The exterior angle to ∠X is 104.25°
What is the exterior angle theorem?The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.
from the above definition , if ∠Y = 62.45° and ∠Z = 41.8°
It means from exterior angle theorem that
exterior ∠X = ∠Y + ∠Z
exterior ∠X = 62.45° + 41.8°
exterior ∠X = 104.25°
In conclusion the exterior angle X is 104.25°
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what is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?
The answer to this Question based on probability is discussed below
What is probability of a event?
It is just defined as number of favourable outcomes divided by the total number of outcomes.
Solution:
First of all we need total number of events here as we know probability of sample space is 1 only. hence lets assume there are P elements in sample space and Solving more than number of expected puzzles in 5 minutes is 1 favourable case.
Hence probability will be 1/P where P is no of elements of sample space.
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find (9.3x106) + (1.8x104) express your answer in scientific notation
Answer: here is your answer
Step-by-step explanation:
(9.3 × 10^6) + (1.8 × 10^4) is 93.18E+5.
(9.3 × 106) + (1.8 × 10^4)
(9.3 × 106) + (0.018 × 10^6)
(9.3 + 0.018)× 10^6
(9.318)× 10^6
scientific notation
(93.18E+5)
Answers and Explain
The function g(x) is a piecewise function For x 4, 1 g(x) = |x + 1| and for
x 1, 3 g(x) = 2.
What are some rules for the transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
From the graph, we can conclude that g(x) is a piecewise function.
When x is - 4, 1 g(x) = |x + 1|.
And when x is 1, 3 g(x) = 2, A constant function.
Now, g(-2) = | - 2 + 1| = 1.
g(1) = | 1 + 1| = 2.
g(4) = 2.
The value of x when g(x) = 3 is - 4.
The value of x when g(x) = 1 is (0, - 2) as both satisfy g(x).
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3. Marcus Hatfield earns an annual salary of $43,500 working for a natural
history museum. He is single, and his exemptions total $2,000. He pays
$954.50 in state taxes each year. What is the tax rate for his state?
The Rate of Tax for his state is 2.3%.
What is tax rate?
The ratio at which a business or individual is taxed in a tax system is known as the tax rate. Statutory, average, marginal, and effective tax rates are some of the ways that are used to present them. The terms inclusive and exclusive can be used to present these rates when applied to a tax base.
Annual Salary of Marcus Hatfield is = $43500
His Exemption from the tax is = $2000
He pays tax on the remaining amount i.e.
$43500 - $2000 = $41500.
His contribution toward the tax is $ 954.50,
Let the Rate of tax is x, thus
[tex](\frac{X}{100} *41500) = 954.50\\ x = \frac{95450}{41500} \\x = 2.3[/tex]
Thus, the rate of tax is 2.3% of his salary.
Hence, the Rate of Tax for his state is 2.3%.
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Im having trouble..
i keep on getting this question wrong and i need help with the answer, i need to get a high score on this assignment so i can move on
Answer:
The rate of change is also called the slope. The slope is -2
Step-by-step explanation:
Find 2 points on the line. I am going to use the points (0,5) and (4, -3). the rate is the change in y over the change in x. From the two points, my values are -3 and 5. The x values are 4 and 0.
To find the change, I subtract the y values and the x values.
[tex]\frac{-3-5}{4-0}[/tex] = [tex]\frac{-8}{4}[/tex] = -2
Answer: -2
Step-by-step explanation: The rate of change is also known as the slope!
To find the slope, you need to find the rise/run.
Let's pick two points ( 0,5) ( 4, -3)
You see that the y goes down by 8 and the x goes right by 4, so the rate of change is -8/4 = -2
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Please help with this problem!!
Functions f, g, and h are defined as follows: () = − 2, () = 2^2 − 1, and ℎ() =
2^3 + 4.
(a) Find the inverse of function g(x).
(b) Find f(h(-2))
(c) Find g(f(5))
Answer:
Step-by-step explanation:
f −1 (x)= 3x−2
f, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 2, divided by, 3, end fraction.
show steps / why your answer is correct please which equation defines the graph of y=x3 after it is shifted vertically 5 units down and horizontally 4 units left
The equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.
What is a graph?A function is truly equal to its graph in the modern mathematical foundations and typically in set theory. However, it is frequently helpful to think of functions as mappings, which include not just the relationship between input and output but also the sets that make up the domain and codomain. For instance, it is important to consider the codomain while determining whether a function is onto (surjective) or not.
For k=- 5, y=f(x) + k represents a vertical shift down.
For h=4, the horizontal shift left is y=f(x+h).
Therefore, the equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.
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Describe the end behavior, determine whether it’s a graph of an even or odd degree function, determine the sign leading coefficient
Answer:
Right and Left: Negative Infinity
Even Function
Negative Leading Coefficient
Step-by-step explanation:
First of all, both ends of the graph go down to negative infinity. As a result of this, we can determine that the sign of the leading coefficient was also negative. The graph is even because it shifts directions thrice and both ends of the graph go in the same direction.
Pls help 8th grade math
Answer: 27.5, B
Step-by-step explanation:
its a right angled trianalgle,
==> (30)^2= ((12)^2)+(x^2)
==> x^2= 900-144
==> x^2 = 765
==> x=(756)^(0.5)
==> x=27.49
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............ i need help past due
Answer from left to right: 48, 80, 4.5, 160
Step-by-step explanation:
Write y=-3/4x+7 in standard form
-28 is the standard form of the equation.
How do you format a sentence in standard form?Ax+By=C is the formula for a linear equation. You must place the x and y on the same side of the equal sign and the constant on the other side in order to convert an equation in slope-intercept form (y=mx+b) to standard form. Terms can be moved using inverse procedures.
The standard form of a linear equation is
Ax+By=C A x + B y = C .
y=-3/4x+7 in standard form
Multiply both sides by 4 .
4y=4(3.4x+7) 4 y = 4 ( 3 4 x + 7 ).
3x - 4y = -28
-28 is the standard form of the equation.
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18.
Kara solved the following absolute value equation incorrectly. Find and fix her
mistake. Explain what she did wrong.
|- 2x + 6 + 10 = 2
-10 -10
2x+6=-8
-6 -6
-2x = -14
-2
-2
X = 7
|- 2x + 61
{7, - 1}
= -8
2x+6=8
-6 -6
-2x = 2
-2 -2
x = -1
Kara erred when she answered the equation 2x + 6 = -8. Instead, she should have solved the equation 2x + 6 = 8 because it relates to the second situation (where -2x + 6 + 10 is smaller than 0).
Kara made a mistake when solving the equation |- 2x + 6 + 10| = 2. The correct steps to solve this equation are as follows:
First, we need to find the value of -2x + 6 + 10. To do this, we need to remove the absolute value bars by considering two cases:
a. If -2x + 6 + 10 is greater than or equal to 0, then the absolute value is equal to -2x + 6 + 10.
b. If -2x + 6 + 10 is less than 0, then the absolute value is equal to the negative of -2x + 6 + 10.
In the first case, we have -2x + 6 + 10 = 2. Solving this equation gives us x = -1.
In the second case, we have -(-2x + 6 + 10) = 2. Solving this equation gives us x = 7.
Therefore, the solution to the equation |- 2x + 6 + 10| = 2 is x = {7, -1}.
She made a mistake when she solved the equation 2x + 6 = -8. She should have solved the equation 2x + 6 = 8 instead, because this is the equation that corresponds to the second case (where -2x + 6 + 10 is less than 0).
As a result, Kara got the wrong value for x and included the incorrect solution {7, -1} in her final answer.
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Sarah placed 3 identical wooden boards end - to - end. The length is 1.86 m. What is the length of each board?
Answer:
0.62
Step-by-step explanation:
1.86 divided by 3 is 0.62
What is the y-intercept of this line? y=-5x -3 b= [?]
answer:
b=-3
step-by-step explanation:
the equation's format is y=mx+b so b is -3. you can also figure this out if you plug y in as 0. hope that helps!
please help with this nothing hard help is appreciated
The dotted line represents that the region is strictly less than the equation of the line.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The dotted line shown in the graph and the yellow region described by the equation of a line is the region that is strictly less than the given line.
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The table and the graph show the relationship between the edge length, x, of a cube and its surface area, y. Is the relation a function? Edge Length, x Surface Area, y 1 6 2 24 3 54 4 96 A graph of a curve on a coordinate plane that goes up and to the right with edge length in units on the x axis and surface area in square units on the y axis. The curve begins at the origin and passes through the points 1 comma 6 and 2 comma 24 and looks like the right half of a U.
We infer that x and y's relationship is a non-linear function as a result. The relationship between x and y is a non-linear function.
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. Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
Here,
Edge Length, x Surface Area, y
1 6
2 24
3 54
4 96
Because each input value has one and only one output value, the data in the table unmistakably indicate a function. In other words, the x values are not repeated.
Additionally, it is evident from the table numbers and the graph that the function is not linear because the graph is not a straight line. Additionally, the largest power over the x variable(s) in a cubic function is 3. It is not a linear function, therefore.
As a result, we draw the conclusion that x and y's relationship is a non-linear function.
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Pls Help ASAP) Willing to give 25 points) Pls show your work) If you don't know pls don't answer.
To view the representation of graph of check the attached image.
What is called graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
Given that ;
Stewart's overdue assignment = 36
Per day he complete 4 overdue assignments.
To find : In how many days he complete all the overdue assignments
To complete 36 overdue assignments = 36/4
= 9 days
Therefore, In 9 days he complete all the overdue assignments
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0.23 was rounded to 2 significant figures.
What is the upper bound?
Answer: 0.235
Step-by-step explanation:
To round up you need a number = 5 or > 5
So to round to 2 sig fig, the number will have to be 0.235
the dilation of a line segment creates a _[blank]_ line segment, provided the center of dilation is not on the line segment and the scale factor does not equal 1.
The required scale factor for the given line segment is 2.
What is line segment?
In math, a line segment is limited by two unmistakable focuses on a line. Or on the other hand we can say a line portion is essential for the line that interfaces two focuses. A line has no endpoints and broadens endlessly in both the bearing yet a line fragment has two fixed or positive endpoints.
Explain scale factor:Scale factor is the number used to duplicate one item by to get another item that appears to be identical however is an alternate size. It makes a precise duplicate just bigger or more modest than the first. Scale Variable increases the image or item similarly as though you broadened or shrank it on a copier.
According to question:We have,
QS : QS' = 4 : 8 = QU : QU' = 5 : 10 = 1 : 2
Then the scale factor is of the dilation is 2 (magnification)
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In the picture below.
Answer:
∠ GFC = 70°
Step-by-step explanation:
∠ BFE and ∠ CBF are alternate angles and are congruent, that is
∠ BFE = 37°
∠ BFE , ∠ BFC and ∠ GFC lie on a straight line and sum to 180° , then
37° + 73° + ∠ GFC = 180°
110° + ∠ GFC = 180° ( subtract 110° from both sides )
∠ GFC = 70°
To solve the equation t² - t = 12 by factoring, you would use
(t - 4)(t + 3) = 0
t(t - 1) - 12 = 0
t(t - 1) = 12
To solve the given equation, t² - t = 12, by factoring, we will use (t + 3)(t - 4) = 0. The correct option is the first option
Solving an equation by factoringFrom the question, we are to determine how to solve the given equation by factoring
From the given information,
The given equation is
t² - t = 12
First, we will solve the equation by factoring
t² - t = 12
Transfer the constant to the other side
t² - t - 12 = 0
Factorize the expression
t² -4t + 3t - 12 = 0
t(t - 4) +3(t - 4) = 0
(t + 3)(t - 4) = 0
Then,
t + 3 = 0 OR t - 4 = 0
t = -3 OR t = 4
Hence, to solve the equation we will use (t + 3)(t - 4) = 0
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The interior angles in a regular polygon sum to 1620°.
How many sides does the polygon have?
Answer:
the answer to your question is 11
Step-by-step explanation:
1620÷180= 9
9+2=11
Math test!! Please help
1. 12*2/ 3
A. 8
b. 16
c.18
D.24
2. 4/5 *9
a. 9 4/5
b. 8 4/5
c. 8 3/5
d. 7 1/5
3. What is the product of 10 and 3/4? give your answer in lowest terms
a. 7 1/4
b. 7 2/3
c. 7 1/3
d. 7 1/2
4. Andie is making bags of candy to give to her 7 friends. she is putting 2/3 of a pound of candy in each bag. How many pounds of candy will she need in order to fill all 7 bags
a. 4 1/3
b. 4 2/3
c. 4 1/6
d. 4 3/4
5. A recipe calls for 3/4 cup of flour. How many cups of flour will u need to make three batches of the Recipe.
A. 2 3/4 cups
b. 2 1/3 cups
c. 2 1/4 cups
d. 2 1/2 cups
6. Evaluate the expressions, Then select all the expressions that are greater then four.
A. 7 * 5/6
b. 4/5 *10
c. 3/8 *9
d. 1/2 *12
7. Evaluate each expression, then select all the expressions that are whole numbers.
A. 9* 2/3
b. 4/5 *7
c. 7/8 *2
d. 25 * 2/5
Answer:
1. (A.)
2.(D.)
3.(D.)
4.(A.)
5.(A.)
6. (B.) & (D.)
7. (A.), (D.)
Step-by-step explanation:
Trust
Question 9(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the distance between the points (-3, -6) and (5,0).
©22 units
10 units
8 units
05 units
Therefore, the distance between the points (-3, -6) and (5,0) is 10 units. This is option A.
What is the distance formula?A mathematical procedure called the distance formula is used to calculate the separation between two locations on a plane. The Pythagorean theorem, which asserts that the square of a distance between two locations is equal to the sum of the squares of a difference in their coordinates, is where the formula is derived from.
To utilise the distance formula, you must first have the coordinates of the two places. These coordinates are usually expressed as (x1, y1) and (x2, y2), where x1 and y1 stand for the coordinates of the first point and x2 and y2 stand for the coordinates of the second point, respectively.
d = √((x2 - x1)^2 + (y2 - y1)^2)
How to solve?
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((5 - (-3))^2 + (0 - (-6))^2)
= sqrt((8)^2 + (6)^2)
= sqrt(64 + 36)
= sqrt(100)
= 10
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Adrian started a small business making custom t-shirts. His profit the first month was -$20. If this continues for the next 3 months, what would his profit be?
(-20)(3)
(-20)(-3)
(-20) + 3
(-20) - 3
Answer:
His profit would be (-20)*3 or -60 $
Step-by-step explanation:
First month profit = -20 $
if the next three months will be the same, then:
(-20)*3
-60 $
Write a pattern rule that uses algebra to describe each pattern. a) 7, 14, 21, 28, 35, 42,
HELP!!!!
Answer:
as u can see the pattern is going up by 7.
Step-by-step explanation:
Find the interquartile range of the data set shown
5 8 12 12 17 18 20 22 23
what is the interquartile range
Answer:
8
Step-by-step explanation:
12 is quartile 1 and 20 is quartile 3. 20 - 12 = 8
Answer: 8
Step-by-step explanation:
I think this is an elimination problem:
12x-20y=-32
x+20y=10
Answer:
Yup I think so to
Step-by-step explanation:
Answer:
Yes, it is an elimination problem.
x = -1.69230769
Step-by-step explanation:
You can eliminate 20y by adding both equations together.
Then, you will get 13x = -22.
Divide by 13 on both sides to get x= -1.69230769
9.4 Board Game Sales
A small company is selling a new board game, and they need to know how many to
produce in the future.
After 12 months, they sold 4 thousand games; after 18 months, they sold 7 thousand
games; and after 36 months, they sold 15 thousand games.
1. Could this information be reasonably estimated using a single linear model?
2. If so, use the model to estimate the number of games sold after 48 months. If not,
explain your reasoning.
By using slope of a curve, it can be calculated that
This information cannot be estimated by a single linear model
What is slope of a curve?
Slope of a curve at a point is the tangent of the angle that the tangent to the curve at the point makes with the positive direction of x axis.
The sale of the board game is as follows-
After 12 months, they sold 4 thousand games; after 18 months, they sold 7 thousand games; and after 36 months, they sold 15 thousand games.
The curve passes through (12, 4000), (18, 7000) and (36, 15000)
Slope of curve passing through (12, 4000) and (18, 7000) = [tex]\frac{7000 -4000}{18 -12}[/tex] = 500
Slope of curve passing through (18, 7000) and (36, `15000) = [tex]\frac{15000-7000 }{36 -18}[/tex] = [tex]\frac{4000}{9}[/tex]
As the slope is not the same, this information cannot be estimated by a single linear model
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alis teacher plotted the numbers 1/2 and 2/3 on the number line. She asked ali to find and plot a rational number between these two numbers in a number line, Can you help Ali in plotting a rational number between them on a number line?
Yes, there are many rational numbers that can be plotted between 1/2 and 2/3 on the number line. Here are a few examples:
1/2 + 1/6 = 5/6: This rational number is greater than 1/2 and less than 2/3.
2/5: This rational number is also greater than 1/2 and less than 2/3.
1/3: This rational number is halfway between 1/2 and 2/3.
To plot a rational number on a number line, you can start by drawing the number line and marking off the positions of 1/2 and 2/3. Then, you can locate the position of the rational number you are trying to plot by dividing the distance between 1/2 and 2/3 into equal segments and finding the position of the rational number within those segments. For example, if you wanted to plot 5/6, you could divide the distance between 1/2 and 2/3 into six equal segments, and then mark the fifth segment as the position of 5/6 on the number line.