The value of x is 135°
What is Exterior Angle Theorem?
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.
An exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.
Linear pair of angles are,
∠1 + ∠2 = 180°
where, ∠1 is exterior angle
and, ∠2 is interior angle
Given ,
One angle is = 90°
Then other two angle will be = 45° and 45°
Now, According to Exterior angle property,
x + 45 = 180
x = 180 - 45
x = 135°
Hence, the value of x is 135°
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A jar contains three marbles; 1 yellow (y), 1 orange (o), and 1 red (r). Which list shows all the possible outcomes for choosing two marbles at random from the jar if the first marble is replaced after it is drawn?
The list that shows all the possible outcomes for choosing two marbles at random is yy, oo, ro, yo, oy, ry, yr, or, rr
How to determine the list of possible outcomes?From the question, we have the following parameters that can be used in our computation:
Orange = o
Red = r
Yellow = y
From the question, we understand that the selection is with replacement
This means that it is possible to select a marble two times
So, we have the following representation
yy oo ro
yo oy ry
yr or rr
Hence, the list is yy, oo, ro, yo, oy, ry, yr, or, rr
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Determine if each answer choice represents a proportional or not proportional linear relationship. drag each answer choices to the correct column. The order does not matter.
The proportional or not proportional linear relationship of the given options are;
a) y-intercept is not at the origin - non-proportional linear relationship.
b) Direct variation - proportional linear relationship
c) y = -7x - proportional linear relationship.
d) y = 5x + 1 - non-proportional linear relationship.
e) y = x - proportional linear relationship.
f) 4y = 2x - proportional linear relationship.
g) Non linear proportional relationship
h) Proportional linear relationship.
How to Interpret a Proportional Relationship?Proportional relationships are defined as relationships between two variables where their ratios are equivalent.
a) We are told that the y-intercept is not the origin. The equation of a line in slope intercept form is; y = mx + c
If c which is the y-intercept is not equal to zero, the this is a non-proportional linear relationship.
b) Direct variation is a proportional linear relationship because the two variables are directly related to each other.
c) y = -7x can be rewritten as; y/x = -7. Thus, this is a proportional linear relationship.
d) y = 5x + 1. As said in a above, this is also a non-proportional linear relationship.
e) y = x. can be rewritten as; y/x = 1. Thus, this is a proportional linear relationship.
f) 4y = 2x. can be rewritten as; y/x = 2/4. Thus, this is a proportional linear relationship.
g) This is a non linear proportional relationship because the rate is not directly proportional.
h) This is a proportional linear relationship as it is a defined rate.
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Given x>0x>0 and y>0,y>0, select the expression that is equivalent to [tex]\sqrt[4]{256x^6y^10}[/tex]
By simplifying the expression we get [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]
What is square root ?A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol [tex]\sqrt[2]{}[/tex] .The opposite of squaring an integer is finding its square root.
According to the given information
Given x > 0
y > 0
we need to simply the following expression
[tex]\sqrt[4]{256x^{6}y^{10} }[/tex]
By simplifying
we get
= [tex](4^{4}x^{6} Y^{10}) ^{\frac{1}{4} }[/tex]
= [tex]4x^{\frac{6}{4} } y^{\frac{10}{4} }[/tex]
= [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]
Hence
By simplifying the expression we get [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]
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The growth of outpatient surgeries as a percent of total surgeries at hospitals is approximated by
f(x)=1314+303 In x
where x is the number of years since 1900.
(a) What does this function predict for the percent of outpatient surgeries in 1996?
(b) When did outpatient surgeries reach 60%?
(a) What does this function predict for the percent of outpatient surgeries in 1996?
% (Round to the nearest percent as needed.)
(b) When did outpatient surgeries reach 60%?
(Round down to the nearest year.)
The percent of outpatient surgeries in 1996 is 68.99 % and outpatient surgeries reach is 1992.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
total surgeries at hospitals is approximated by
f(x)=1314+303 Inx
A) this function predicts for the percent of outpatient surgeries in 1996 IS
x = 1996-1900 = 96.
So f(96) = -1314 + 303 ln(96) =68.99 %
b) f(x) = 60
60 = -1314 + 303 ln(x)
ln x = (1314+60)/303 = 4.53
x = 92.75.
Hence, the percent of outpatient surgeries in 1996 is 68.99 % and outpatient surgeries reach is 1992.
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What is an equation of the line that passes through the points (-3, -4) and
(-4, -6)?
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-3)}}} \implies \cfrac{-6 +4}{-4 +3} \implies \cfrac{ -2 }{ -1 } \implies 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-3)}) \implies y +4 = 2 ( x +3) \\\\\\ y+4=2x+6\implies {\Large \begin{array}{llll} y=2x+2 \end{array}}[/tex]
i need help with this please!!
There is no horizontal asymptote since n > m.
What is the explanation?Find the place where the phrase x 2 x 2 x 15 x 2 x 12 is undefined.
x = 0
When n is the degree of the numerator and m is the degree of the denominator, the rational function R (x) = an x n b x m is used.
1. The x-axis, with y = 0, is the horizontal asymptote if n m.
2. If n = m, then the line y = a b is the horizontal asymptote.
3. There is no horizontal asymptote if n > m. (there is an oblique asymptote).
Identify n and m.
n= 4 m = 2
There is no horizontal asymptote since n > m.
Domain and Range
Domain: (−∞,0)∪(0,∞),{x|x≠0}
Range: (−∞,∞),{y|y∈R}
Oblique Asymptotes: y = x 2 x 3 x 12.
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Gerald is conducting an experiment with 3 possible outcomes. Kasey is conducting an experiment with 20 possible outcomes. Which statement best relates the possible outcomes to the number of trials needed to produce results similar to their predicted outcomes?
Answer:
Step-by-step explanation:
The number of trials needed to produce results similar to their predicted outcomes is likely to be higher for Kasey's experiment with 20 possible outcomes than for Gerald's experiment with 3 possible outcomes.
Solve each system by elimination: 4x+3y=19 3x-4y=8
Answer: x =4 , y =1
Step-by-step explanation:
Multiply the first equation by 4,and multiply the second equation by 3.
4(4x+3y=19)
3(3x−4y=8)
Becomes:
16x+12y=76
9x−12y=24
Add these equations to eliminate y:
25x=100
Then solve 25x=100 for x:
25x=100
(Divide both sides by 25)
x =4
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
4x+3y=19
Substitute4forxin4x+3y=19:
(4)(4)+3y=19
3y+16=19( Simplify both sides of the equation)
3y+16+−16 = 19+−16 (Add -16 to both sides)
3y=3
(Divide both sides by 3)
y=1
The area of a given triangle is 35 square meters. The height of the triangle is (g-11) meters and the base is (g- 8) meters.
area of triangle = (b × h) ÷ 2
where b is the base so (g - 8)m,
h is the height so (g - 11)m
and area is 35
35 = (g - 11) × (g - 8) /2
35 = g² - 19g + 88 / 2
35 = 1/2g² - 19/2g + 44
1/2g² - 19/2g + 9 = 0
use the quadratic formula to find the two values of g and you will get:
g = 18 and g = 1
if we use g as 1 we will get negative metres for the values for the base and height so we use g = 18 instead!
base = (18) - 8
= 10m
height = (18) - 11
= 7m
To hire an accountant to prepare taxes costs a flat fee and an additional hourly rate. The amount the accountant costs can
be modeled by the function A(x) = 150 + 35x, where x represents the number of hours the accountant works to prepare the
taxes and 150 represents the flat fee. What is the value of A(220) and its interpretation?
OA(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
OA(220) = 7850; If the accountant takes 7,850 hours to prepare the taxes, the cost will be $220.
OA(220) = 2; If the accountant takes 220 hours to prepare the taxes, the cost will be $2.
2
OA(220) = 2; If the account takes 2 hours to prepare the taxes, the cost will be $220.
A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
Hence option (A) is correct.
What is a linear equation in one variable?
The linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
The cost function is A(x) = 150 + 35x
We have to find the value of A(220), so put x = 220 in the given cost function, we get
A(x) = 150 + 35x
A(220)= 150 + 35(220)
= 150 + 7700
= 7850 dollars
Hence, A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
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Two students, Mattie and Pete agreed to display their work.
Their work is shown below.
Pete is correct because the student used multiplication as the correct function operation to simplify the expression.
40-(-16)=
Can someone help me with this please I really am confused
Answer:
56
Step-by-step explanation:
When you subtract a negative number. Just consider it addition.
So, 40+16
It's very simple from there.
Answer:
56!
Step-by-step explanation:
The question is 40 minus negative 16.
When you subtract a negative, it's the same as adding.
So 40 - (-16) is the same as 40 + 16, which equals 56.
Example:
If you have 3 apples, and you remove negative 3 apples from 3, now you have 6.
So, 3 - (-3) = 6.
PLEASE HELP ILL GIVE BRAINLIEST AND STUFF!!!!!
Answer:
The distributions of the income of the 3 states are pretty similar. The highest income in Maine is 50s, in Indiana it is pretty evenly spread out and Connecticut is highest in 60/70 and has multiple stragglers in 170 - 200 and a few near 300. The main place where most of the plot points are is 10 - 150.
Not completely sure if this helps, but I hope it does.
Answer and explain for 10 points!
Answer: 100
Step-by-step explanation:
To solve this expression, we can start by performing the operations inside the parentheses first:
560 divided by 7 + 140 divided by 7
= 80 + 20
= 100
So the result of the expression is 100.
I hope this helps! Let me know if you have any questions.
f(-5)=5, f(0)=10, write a linear function f with the given values
Answer:
F(x)= x +10 (Cus when x is 0, Function is 10)
Answer:
y=x+10
Step-by-step explanation:
You first need to find the y intercept using the coordinates where x equal 0. Then you can figure slope by solving for m when you plug in the other points.
{(8, 2), (4, -1), (0, -1), (-4, 2)}
D=
R =
Function?
Therefore , range of given function is R ={2,-1,2} and Domain is D={8,4,0,-4}
What is a function?A function from a set X to a set Y in mathematics assigns each object of X exactly one element of Y. The domain and codomain of the function are denoted by the sets X and Y, respectively.
Here,
Given:{(8, 2), (4, -1), (0, -1), (-4, 2)}
Thus , to find the domain
D={8,4,0,-4}
And to find the domain we check the last term of every bracket,{(8, 2), (4, -1), (0, -1), (-4, 2)}
R ={2,-1,2}
Therefore , it is many one function and onto function
Therefore ,It is many one - one function because two elements is connected with single element.
It is onto because of all elements of set B is connected with Set A.
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Solve for each variable
x = 2 , y' = 70 , x' = 30 : by using the property of SAS(side angle side) in ΔKMN and ΔKLI as they were similar polygon.
What is SAS property of triangle ?The property of a triangle whose two sides and the angle between these sides are stated is "SAS," which stands for "Side, Angle, Side". The SAS formula can be used to determine the area of a given triangle ABC with two known sides and an included angle between these sides.
Assume that the triangle's three sides are a, b, and c.
A SAS Triangle's perimeter
The following formula can be used to determine a triangle's area using SAS:
When sides "b" and "c" are known, along with angle A, the triangle's area is equal to: 1/2 bc sin(A)
The area of the triangle is equal to 1/2 ab sin(C) when sides 'b' and 'a' as well as included angle B are known
when sides "a" and "c" were added using SAS in triangle 1ΔMKN ~ ΔJKL
So, MN/KN = JL/KL
(x+1)/12 = (3x-2)/32
∴ 5x = 10 ⇒ x = 2
Using same property (SAS) in triangle 2
J = 80
∴ 30 = <x'
∵ in a triangle sum of angles is equal to 180° so, y' + <
J + 30 = 180
∴ <J = 80
then, y' = 70 and x' = 30
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(c) Select all that describe ST.
ST describes the perpendicular bisector of PQ.
What is the perpendicular bisector?
A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.
Here,
We have to find which statement describes the ST.
We concluded that ST describes the perpendicular bisector of PQ.
A perpendicular bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment.
Hence, ST describes the perpendicular bisector of PQ.
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What is a residual for a multiple regression model and the data that is used to create it? select one.
The difference between the actual value of the response variable and the corresponding predicted value(regression error) using the multiple regression model is the correct option.
A residual is a measurement of the vertical distance between a point and the regression line. It is just the discrepancy between an actual value observed and a value that was projected.
To ensure that the requirements for making conclusions about the coefficients in a linear model have been met, one should always perform a residual analysis.
In regression analysis, a residual is the discrepancy between an observed value and a predicted value.
It is determined by,
Residual = Observed value – Predicted value
The residual is the discrepancy between the expected value and the actual value.
Observed value minus predicted value equals residual.
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The x-intercept is -4 and the y-intercept is 5. What is the slope of the line?
Answer:
y = 1.25x + 5
Step-by-step explanation:
I found the answer using linear regression.
What is the value of x?
Enter your answer in the box.
Step-by-step explanation:
angle bisector theorem :
the ratio of the 2 baseline segments is the same as the ratio of the 2 legs of the main triangle.
in our case :
44.8/56 = (x + 4)/35
x + 4 = 44.8×35/56 = 44.8×5/8 = 28 mm
x = 24
FYI : one way of explaining the theorem is : we could see this as 2 projections originating from E at the same angle but onto a tilted projection screen.
the length on the projection screen (HD or GD) is directly related to the distance from the projection point to the end of the tilted projection : ED or EG. and so the ratios of both projections must be equal (due to the equal angle).
so, in our case
35/56 = (x + 4)/44.8
which leads, of course, to the same result
44.8×35/56 = x + 4
............ i need help past due
tim tebow had hit 2 hits in 7 attempts. if he continues this pattern how many hits will he have in 119 attempts?
Answer:
Step-by-step explanation:
it will be 22
2. A loan is amortized over five years with mnthly payments at a nominal interest rate of 9%
compounded monthly. The first payment is ₱10,000 and is to be paid one month from the
date of the loan. Each succeeding monthly payment will be 2% lower than the prior payment.
Calculate the outstanding loan balance immediately after the 40th payment is made.
Answer:
Step-by-step explanation:
hard
What is the highest possible number of positive real zero/s does the polynomial function f(x) = x4 – 3x3 – 4x2 + 6x - 1 have?
a. 3
b. 1
c. 2
d. 4
Answer: The answer to the question is $\boxed{\text{(d)}\ 4}$. This is because a polynomial of degree 4 can have at most 4 zeros, and those zeros can be either real or complex numbers. Since the question asks for the maximum number of positive real zeros, the answer is $\boxed{\text{(d)}\ 4}$.
Step-by-step explanation: The maximum number of positive real zeros that a polynomial function of degree 4 can have is 4. This is because a polynomial of degree 4 can have at most 4 zeros, and those zeros can be either real or complex numbers. Since the question asks for the maximum number of positive real zeros, the answer is $\boxed{\text{(d)}\ 4}$.
solve the system of equations?
7x+10=-4x-23
Answer:
x = -3
Step-by-step explanation:
7x+10 = -4x-23
11x+10 = -23
11x = -33
x = -3
Answer:
x= -33/4
Step-by-step explanation:
If 1.5kg of self raising flour costs 0.60$ find the cost of 1kg
the rate of pay per hour of an employee who gets paid $627 for working 38 hours help
Answer:
16.5
Step-by-step explanation:
627 divided by 38 equals 16.5.
16.5 is the amount earned per hour.
A(n) ____ is formed by two adjacent sides of a triangle. A:Corresponding angles B:Corresponding Sides C:Included Angle D:Congruent triangles E:Included Side
Answer: Corresponding angles
Step-by-step explanation: The answer is corresponding angles or "corresponding internal angles" form when two jointed sides or adjacent sides of a triangle meet. Look in the attachment below to see a picture showing the example of corresponding angles.
Please help me with this
The consequence of the two functions f(x) = (1 / 6) · ∛x and g(x) = 6 · x³ by composition is f[g (x)] = (1 / 6) · ∛3 · x and g[f (x)] = (1 / 6) · x³, respectively.
How to use composition between two functions
In this question we must use the definition of composition between two functions f and g, where the independent variable of the function f is substituted by function g. That is to say:
f ° g (x) = f [g(x)]
If we know that f(x) = (1 / 6) · ∛x and g(x) = 6 · x³, then the result of each composition is:
f [g (x)] = (1 / 6) · ∛(6 · x³)
f[g (x)] = (1 / 6) · ∛3 · x
g[f (x)] = 6 · [(1 / 6) · ∛(6 · x³)]³
g[f (x)] = 6 · (1 / 216) · (6 · x³)
g[f (x)] = (1 / 6) · x³
The results of the compositions of the two functions f(x) = (1 / 6) · ∛x and g(x) = 6 · x³ are f[g (x)] = (1 / 6) · ∛3 · x and g[f (x)] = (1 / 6) · x³, respectively.
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