The measure of ∠FXD = 44°,
EG = 14 and ∠FZG = 21°.
What are triangles?A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is that the sum of its internal angles to 180 degrees. This quality is referred to as the angle sum property of triangles.
Given a triangle XYZ
and XG, YG, and ZG are angle bisectors,
DG = 14 and ZG = 17
∠DYE = 94°, ∠FXG = 22°
A: to find ∠FXD,
as we know angle bisector divides an angle into two equal parts,
so ∠FXG = ∠GXD = 22°
∠FXD = ∠FXG + ∠GXD
∠FXD = 22 + 22 = 44°
B: to find EG,
since G is the incenter,
Due to the junction point of the central axis being the center of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides.
so DG = EG = FG = 14
C: to find ∠FZG,
we have ∠DYE = 94° and ∠FXD = 44°
from angle sum property,
∠DYE + ∠FXD + ∠FZE = 180°
∠FZE + 94 + 44 = 180
∠FZE = 180 - 94 - 44
∠FZE = 42°
so ∠FZG = ∠GZE = ∠FZE/2 (due to angle bisector)
∠FZG = ∠GZE = 42/2
∠FZG = ∠GZE = 21°
Hence ∠FXD = 44°,
EG = 14,
∠FZG = 21°.
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write the equation of the line passing through the point (-2, 3) with a y-intercept of 6 in slope-intercept form.
Answer:
3 = -2m + 6
-2m = -3, so m = 3/2
y = (3/2)x + 6
Answer: y=6x+15
Step-by-step explanation:
Formula for point-slope (you were given a point and the slope)
\(y-y_{1} =m(x-x_{1} )\)
where m is your slope
\((x_{1} ,y_{1} )\) is your point
y-3=6(x-(-2)) plug in and simplify the negative in the parentheses
y-3=6(x+2) distribute
y-3=6x+12 add 3 to both sides
y=6x+15 this is your answer in slope-intercept form
Given that D( x ) = 2 x , select all of the following that are true statements.
D( x ) is a direct variation.
D( x ) is a function.
D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4)
x is the dependent variable.
D(6) = 3
please help and show work if you can
Answer:
14. x = 6, y = 8
15. x = 5, y = 7
16. x = 7, y = 10
Step-by-step explanation:
For a parallelogram, the length across the point of intersection of its diagonals are equal.
So that;
14. PT = TR
QT = TS
So that,
2x = y + 4
2x - y = 4 ...........1
x + 2 = y
x - y = -2 ............. 2
subtract equation 2 from 1,
x = 6
substitute the value of x in equation 1,
2 x 6 - y = 4
y = 12 - 4
= 8
x = 6, y = 8
15. PT = TR
QT = TS
x + 2 = y
x - y = -2 .......... 1
2x = y + 3
2x - y = 3 ......... 2
Subtract equation 1 from 2
x = 5
substitute the value of x in equation 1
5 - y = -2
5 + 2 = y
y = 7
x = 5, y = 7
16. PT = TR
QT = TS
y = x + 3
x - y = -3 ......... 1
2y = 3x -1
3x - 2y = 1 ......... 2
Multiply equation 1 by 2 to have;
2x - 2y = -6 ....... 3
subtract equation 3 from 2
x = 7
substitute the value of x in equation 1
7 - y = -3
-y = -7 -3
-y = -10
multiply through by minus
y = 10
x = 7, y = 10
what is the area of a circle with a diameter of 15.8 cm? use 3.14 for pi and round your final answer to the nearest hundredth. enter your answer in the box.
Answer:
196.1 cm^2
Step-by-step explanation:
The area of a circle is given by Area = πr^2
R is (15.8 cm)/2 = 7.9 cm
Area = (3.14)*(7.0cm)^2
Area = 196.1 cm^2
Answer:
The formula to calculate the area of a circle is given by: A = π * r^2, where r is the radius of the circle.
Given the diameter of 15.8 cm, we can calculate the radius by dividing the diameter by 2: r = 15.8 cm / 2 = 7.9 cm
Plugging the value of the radius into the formula: A = π * 7.9^2 = 3.14 * 62.41 = 196.0794 cm^2
Rounding the answer to the nearest hundredth, the area of the circle with a diameter of 15.8 cm is approximately 196.08 cm^2.
how many factors does 2000 have
Answer:
20
Step-by-step explanation:
Express as a trinomial.
Answer:
(x+8) (2x - 10)
Answer: the expression (x+8)(2x - 10) can be expressed as the trinomial 2x^2 + 6x - 80
Step-by-step explanation:
To express the expression (x+8)(2x - 10) as a trinomial, we need to simplify the product by multiplying the terms.
Using the distributive property, we can expand the expression as follows:
(x + 8)(2x - 10) = x(2x) + x(-10) + 8(2x) + 8(-10)
Simplifying further:
= 2x^2 - 10x + 16x - 80
Combining like terms:
= 2x^2 + 6x - 80
Explain how to find the surface are of the composite figure. Then find its surface area
If the composite figure consists of of a cube of side length 6cm and a hemisphere of radius 3cm , then the surface area of composite figure is \(236.52 \; cm^{2}\) .
The Composite Figure consists of a Cube and Hemisphere ;
the radius of the hemisphere is given as = 3 cm ;
So, formula for curved surface area of hemisphere is = \(2\pi r ^{2}\) ;
= \(2\pi 3 ^{2}\) = \(56.52cm^{2}\) ;
the side length of the cube is = 6cm ;
only the area of the 5 sides will be calculated because on one side there is a hemisphere ;
Surface Area of Cube = \(5a^{2}\)
= \(5\times 6^{2}\) ;
= \(5 \times 36\) = \(180 \; cm^{2}\) .
So , the surface area of the composite figure = Area of hemisphere + area of 5 sides cube ;
Substituting the areas ,
we get ;
= \(56.52 + 180\) ;
= \(236.52 \; cm^{2}\) .
Therefore, Surface Area of given composite figure is \(236.52 \; cm^{2}\) .
The given question is incomplete , the complete question is
Explain how to find the surface area of the composite figure that consists of a cube of side length 6cm and a hemisphere of radius 3cm .
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Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
(show as much details upon answering)
Answer:
linear equations;15m+10=w
15 pages written for every month for 5 months plus the 10 pages she has already written is equal to the total number of pages written in 5 months m=number months written in this case it is 5 months.
w=number of pages written in 5 months 15(5)+10=w
75+10=w
85 Pages written=w
will have written 85 Pages in 5 months
Jen has 191 inches of ribbon. she used 9 inches per bag. she made as many bags as she could. how much ribbon does she have left?
what is the best estimate for the value of 3/2
Answer:
\(1\frac{1}{2}\) or 1.33%
Step-by-step explanation:
Kelvin found that the least common denominator needed to subtract 22−9 2 x x 2 - 9 – 1+3 1 x + 3 is (x + 3)(x – 3). Which is a correct next step?
The least common denominator for the given fractions is (x+6)(x-2). Therefore, the correct answer is option B.
The given expression is \(\frac{x}{x^2+4x-12}-\frac{3}{x+6}\) and the least common denominator is (x+6)(x-2).
When two or more fractions have the same denominators, they are termed as the common denominators. The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions.
Here, \(\frac{x}{x^2+6x-2x-12}-\frac{3}{x+6}\)
\(=\frac{x}{x(x+6)-2(x+6)}-\frac{3}{x+6}\)
\(=\frac{x}{(x+6)(x-2)}-\frac{3}{x+6}\)
Here, least common denominator is (x+6)(x-2)
\(=\frac{x}{(x+6)(x-2)}-\frac{3(x-2)}{(x+6)(x-2)}\)
Therefore, the correct answer is option B.
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"Your question is incomplete, probably the complete question/missing part is:"
Kelvin found that the least common denominator needed to subtract \(\frac{x}{x^2+4x-12}-\frac{3}{x+6}\) is is (x+6)(x-2). Which is the correct next step?
A) \(\frac{x-3}{x^2+3x-18}\)
B) \(\frac{x}{(x+6)(x-2)} - \frac{3(x-2)}{(x+6)(x-2)}\)
C) \(\frac{x}{(x+6)(x-2)} - \frac{3(x+2)}{(x+6)(x-2)}\)
D) \(\frac{x(x+6)(x-2)}{(x+6)(x-2)} - \frac{3(x+6)(x-2)}{(x+6)(x-2)}\)
Find the distance between (–2, –3) and (–6, –12). Round the answer to the nearest hundredth, if necessary.
a.
9.85 units
c.
13 units
b.
7.26 units
d.
17.49 units
Answer:
A. 9.85 units
Step-by-step explanation:
describe a hypothesis test study that would help your work or conclusions in some way. describe what variable would be tested and what would be your guess of the value of that variable. then include how the result, if the null were rejected or not, might change your conclusions or actions in some way.
If the null hypothesis is rejected, and the proportion of customers willing to pay more is significantly different from 10%, this would support my hypothesis that customers are willing to pay more for eco-friendly packaging.
Let's say you work for a company that has been using a certain type of packaging material for their products. However, there have been concerns raised about the environmental impact of this material, and the company is considering switching to a more eco-friendly option. You believe that customers would be willing to pay more for products that are packaged with the eco-friendly material, but you need to test this hypothesis.
Variable: The variable that would be tested is whether customers are willing to pay more for products that are packaged with the eco-friendly material.
Guess of value: I would guess that customers would be willing to pay more for eco-friendly packaging, but I'm not sure how much more. Let's say my guess is that customers would be willing to pay 10% more for products packaged with the eco-friendly material.
Hypothesis test: To test this hypothesis, I would conduct a survey where I randomly select a sample of customers and ask them if they would be willing to pay more for products packaged with the eco-friendly material. I would then compare the proportion of customers who are willing to pay more to my guess of the value (10%).
Null hypothesis: The null hypothesis would be that the proportion of customers willing to pay more for eco-friendly packaging is not significantly different from 10%.
Alternative hypothesis: The alternative hypothesis would be that the proportion of customers willing to pay more for eco-friendly packaging is significantly different from 10%.
If the null hypothesis is not rejected, this would suggest that customers are not willing to pay more for eco-friendly packaging, and the company may need to reconsider their decision to switch to the more expensive material.
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What is the factored form of y = x2 - 4x + 3?
O y = (x - 4)(x - 1)
O y = (x - 3)(x - 1)
O y = (x - 2)(x - 2)
O y = (x + 1)(x + 3)
Given that TR(x)=20x and TC(x)=120+10x what is the break-even point?
The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).
To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.
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simplify the expression: (4 3i)(2 − 8i).
a. 32 – 26i
b. −16 26 i
c. 32 38i
d. −16 38i
The correct answer should be 32.
To simplify the expression (4 + 3i)(2 - 8i), we can use the distributive property of multiplication.
First, we multiply the real parts of the two complex numbers:
(4)(2) = 8.
Next, we multiply the imaginary parts of the two complex numbers:
(3i)(-8i) = -24i^2.
Remember that i^2 is defined as -1, so we can substitute -1 for i^2:
-24i^2 = -24(-1) = 24.
Now, we combine the real and imaginary parts:
8 + 24 = 32.
Therefore, the simplified expression is 32.
Since none of the given answer choices match the simplified expression, it appears that there may be an error in the options provided. The correct answer should be 32.
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a closed right circular cylinder is to have a volume of 128pi cubic inches. find the radius r and height h of the cylinder with minimal surface area
∛128 is the radius r and height h of the cylinder with minimal surface area .
What is Surface Area?
The term "area" refers to the area occupied by a flat, two-dimensional surface. In square units, it is calculated. A three-dimensional object's surface area is the space it takes up when viewed from the outside.V = πr²n
128π = πr²n
n = 128/r²
s = 2πrn + 2πr²
s = 2πr 128/r² + 2πr²
s = 256π/r + 2πr²
ds/dt = - 256π/r² + 2πr
d²s/dt² = -256/(-2) r³ + 2π
d²s/dt² = 128/r³ + 2π
for maxima or minima
ds/dt = 0
- 256 π/r² + 2πr = 0
256 = 2r³
r = ∛128
d²s/dt² = 128/(∛128)³ + 2π
= 2π + 1
d²s/dt² > 0
so surface area is minimum
a + r = ∛128
n = 128(∛128)²
n = ∛128
r = ∛128 , n= ∛128
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Charlotte owns two entertainment websites. Here are some details about those websites for one entire month:
Website A Website B
Number of writers 555 111111
Number of posts posted 110110110 200200200
Average number of words of post 100100100 170170170
Average likes per post 350035003500 350035003500
Average comments per post 500500500 450450450
Number of new subscribers 900090009000 20{,}00020,00020, comma, 000
Revenue \$30{,}000$30,000dollar sign, 30, comma, 000 \$75{,}000$75,000dollar sign, 75, comma, 000
Expenses \$20{,}000$20,000dollar sign, 20, comma, 000 \$47{,}000$47,000dollar sign, 47, comma, 000
Profit (Revenue-−minusExpenses) \$10{,}000$10,000dollar sign, 10, comma, 000 \$28{,}000$28,000dollar sign, 28, comma, 000
Charlotte wants to know which website generates more revenue per amount of content.
1) Charlotte thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Revenue divided by number of posts
(Choice B)
B
Revenue divided by total number of words
(Choice C)
C
Revenue divided by number of writers
(Choice D)
D
Number of new subscribers divided by total number of words
2) Determine which website generates more revenue per amount of content according to the two definitions. Did you get the same result for both definitions?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes. According to both definitions, website A generates more revenue per amount of content.
(Choice B)
B
Yes. According to both definitions, website B generates more revenue per amount of content.
(Choice C)
C
No. The definitions have opposite results.
Answer:
Part 1:
Revenue divided by number of posts
Revenue divided by total number of words
Part 2:
No. The definitions have opposite results.
Step-by-step explanation:
When you divide revenue by total number of words remember to do words*posts to get total.
Example: $30000/100*110 = 2.72
Helppppppppppppppppppppppppppppppppppppppppp pls
Answer:
Coffee Beans to Go is cheaper, selling coffee at $4.75 per pound.
Step-by-step explanation:
The graph is cruddy and hard to see but! when you go to 2 pounds and then up the the cost, it's $9.50. 9.50/2= 4.75. kapeesh??
what is the sum of all the five digit integers in which each of the digits 1 2 3 4 and 5 appear exactly once
Answer:
3,999,960
Step-by-step explanation:
1)let me take an example, the sum of all the digits numbers can be formed using the 1,2 without repetition.
(12, 21 ) , The sum is 12+21= 33
2)Another one, the sum of all the digits numbers, can be formed using three digits 1,2,3, without repetition.
(123,231,321,213,312,132) Their sum is by adding and is 1332
For the above example, we can find the answer by using the formula.
(n-1)! x sum of the digits x ( 111111111….n times)
For example, 1)
n = 2, the sum of the digits 2+1= 3
(2–1)! x3 (11)
1x 3 x 11= 33
For example 2
n= 3 sums of the numbers 1+2+3 = 6
(3–1)! x 6( 111)
2x1x6x111
12x111= 1332
Both answers verified
For the given question
n= 5 , sum of the digits 1+2+3+4+5=15
(5–1)! x 15 x 11111
4! x 15 x 11111
4 x 3 x x2 x 15 x 11111
24 x 15 x 11111
360 x 11111= 3999960
Answer: 3999960
write the largest open interval on which f is the antiderivative for f.
The largest open interval on which f is the antiderivative for f is called the indefinite integral of f, and it is denoted by ∫f(x)dx. This interval can be determined by finding all the antiderivatives of f and then taking the union of their domains. Note that the antiderivative of f is not unique, as it can differ by a constant, so the indefinite integral of f is only determined up to an arbitrary constant.
To find the largest open interval on which a function f is the antiderivative for f', we'll first need to know the function f' (the derivative of f). However, you didn't provide the function f' in your question.
To give you a general idea of how to approach this problem, follow these steps:
1. Given the function f'(x), find the critical points by setting f'(x) equal to 0 and solving for x.
2. Determine the intervals based on the critical points.
3. Check the behavior of f'(x) in each interval to see where it's continuous and increasing.
4. The largest open interval on which f is the antiderivative for f' will be the interval in which f'(x) is continuous and increasing.
If you provide the function f'(x), I can help you find the largest open interval for the antiderivative.
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What is the quotient of (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1)?
The quotient of (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1) is 2x² + x – 3.
What is Quotient ?A quotient is a quantity produced by the division of two numbers.
The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while the word "quotient" refers to the whole.
For example when 8 is divided by 2, the result obtained is 3. Thus, the quotient is 4.
To determine the quotient when (2x4 – 3x3 – 3x2 + 7x - 3) is divided by (x2 - 2x + 1), we'll apply the long division method as shown below:
2x² + x – 3
x² - 2x + 1|2x⁴ – 3x² – 3x² + 7x - 3
–(2x⁴ – 2x³ + 2x²)
x³ – 5x² + 7x – 3
–(x³ – 2x² + x)
–3x² + 6x – 3
–(3x² + 6x – 3)
0
Thus, the quotient is 2x² + x – 3.
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I had $5.00. My mom gave me $10.00 while my Dad Gave me $30.00. My aunt and uncle gave me $100.00. I had another $5.00. How much did I have? I won against Tada Yazhe
Answer:
Is it $150?
Step-by-step explanation:
Step 1: Add it all together
5 + 10 + 30 + 100 + 5
All adds up to 150.
Probably got it wrong though haha.
Suppose we estimate the following regression: yt = β1 + β2x2t +
β3x3t + ut. Suppose the variance of ut is related to a known
variable zt as follows: Var(ut) = σ^2(zt). How would you transform
the
To transform the regression equation, you would divide both sides of the equation by the square root of Var(ut), which is σ√(zt). This transformation helps in obtaining the transformed regression coefficients and standard errors that account for the heteroscedasticity in the error term.
When the variance of the error term (ut) is related to a known variable (zt), it implies the presence of heteroscedasticity in the regression model. Heteroscedasticity means that the variability of the error term is not constant across different levels of the independent variables.
To address this issue, we can transform the regression equation by dividing both sides by the square root of the variance of the error term, which is σ√(zt). This transformation is known as the weighted least squares (WLS) estimation.
By dividing both sides of the equation, we can obtain the transformed regression equation with the error term divided by its standard deviation. This transformation accounts for the heteroscedasticity by giving different weights to the observations based on the variability of the error term. It allows for a more appropriate estimation of the regression coefficients and standard errors, as it gives more weight to observations with smaller error variances and less weight to observations with larger error variances.
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please view the image and answer the questions.
This is College Algebra.
Step-by-step explanation:
x² - 9
1. There is no common factor other than 1.
2. √x² = x; √9 = 3
3. a = x; b = 3
4. x² - 9 = (x - 3)(x + 3)
PLEASE HELP
WILL GIVE BRAINLIEST AND 5.0 RATING
Answer:
(3,-2)
Step-by-step explanation:
(0,-2)
you move 3 right
you change the x-axis
(3,-2)
Answer:
(3, -2)
There you go!! rlly hope this helps!!
Person who helps will get brainliest comment.
Answer:
Hey,Nothing is there.
Step-by-step explanation:
If you think of the equation as an equation for a line.
=+
y
=
m
x
+
b
where
=5/9(−32)
C
=
5
/
9
(
F
−
32
)
or
=5/9−5/9(32)
C
=
5
/
9
F
−
5
/
9
(
32
)
you can see the slope of the graph is 5/9
5
/
9
, which means that for an increase of 1 degree Fahrenheit, the increase is 5/9
5
/
9
of 1 degree Celsius. Therefore, statement I is true.
This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9/5
9
/
5
degrees Fahrenheit. Since 95
9
5
= 1.8, statement II is true.
On the other hand, statement III is not true, since a temperature increase of 9/5
9
/
5
degrees Fahrenheit, not 5/9
5
/
9
degree Fahrenheit, is equal to a temperature increase of 1 degree Celsius.
The final answer is D.
Answer:
The final answer is D
Step-by-step explanation:
Easy.
So one pls help plzzzz
Find the perimeter of the polygon if
5cm, 4cm, and 3cm
P=
The perimeter of the polygon is found as the 42 cm.
Define the term perimeter of the polygon?The perimeter of an enclosed plane figure is referred to in geometry. The perimeter of an enclosed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides. All sides add up to the perimeter.For the shown polygon:
Points A, B, C and D are tangents on the circle.
Thus, these tangent will subtend equal length from the points.
So,
AB = 3 + 4 = 7 cm
BC = 4 + 5 = 9 cm
As, ∠B ≅ ∠D, sides must also be equal.
CD = 5 + 4 = 9 cm
DA = 4 + 3 = 7 cm
Perimeter = AB + BC + BC + BC
= 7 + 9 + 9 + 7
Perimeter = 42 cm
Thus, the perimeter of the polygon is found as the 42 cm.
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