Answer:
x = 7, -1
Step-by-step explanation:
An ellipse has foci located at (2,4) and (2,16) and vertices located at (2,0) and (2,20) this ellipse is vertical
Answer:
The equation of the ellipse is [tex]\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1[/tex].
Step-by-step explanation:
The statement is incomplete, the most probable outcome may be the equation of the ellipse based on information given.
The equation of an ellipse whose major axis is vertical and is centered at a point different from origin is defined by:
[tex]\frac{(x-h)^{2}}{b^{2}} + \frac{(y-h)^{2}}{a^{2}} = 1[/tex] (1)
Where:
[tex](h,k)[/tex] - Coordinates of the center of the ellipse.
[tex](x,y)[/tex] - Coordinates of a point in the line of the ellipse.
[tex]a[/tex] - Length of the major semiaxis.
[tex]b[/tex] - Length of the minor semiaxis.
The coordinates of the center of the ellipse is midpoint of the segment between vertices, which are collinear with foci:
[tex](h,k) = \frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2}(x,y)[/tex] (1)
Where [tex]V_{1} (x,y)[/tex] and [tex]V_{2} (x,y)[/tex] are the coordinates of the vertices.
If we know that [tex]V_{1} (x,y) = (2,0)[/tex] and [tex]V_{2} (x,y) = (2, 20)[/tex], then the coordinates of the center ellipse are:
[tex](h,k) = (2, 10)[/tex]
The length of the semimajor axis can be determined by using the following vectorial expression, which is equivalent to the Pythagorean Theorem:
[tex]a = \sqrt{[(h,k)-V_{1}(x,y)]\,\bullet\,[(h,k)-V_{1}(x,y)]}[/tex] (2)
If we know that [tex](h,k) = (2, 10)[/tex] and [tex]V_{1} (x,y) = (2,0)[/tex], then the length of the semimajor axis is:
[tex]a = \sqrt{(2-2)^{2}+(10-0)^{2}}[/tex]
[tex]a = 10[/tex]
And the length of the minor semiaxis is found by means of this Pythagorean identity:
[tex]b = \sqrt{a^{2}-c^{2}}[/tex] (3)
Where [tex]c[/tex] is the length between the center and any of the foci. This distance can be found by using this vectorial formula:
[tex]c = \sqrt{[(h,k)-F_{1}(x,y)]\,\bullet\,[(h,k)-F_{1}(x,y)]}[/tex] (4)
If we know that [tex](h,k) = (2, 10)[/tex] and [tex]F_{1} (x,y) = (2,4)[/tex], then the length between the center and any of the foci is:
[tex]c = \sqrt{(2-2)^{2}+(10-4)^{2}}[/tex]
[tex]c = 6[/tex]
And the length of the minor semiaxis is:
[tex]b = \sqrt{10^{2}-6^{2}}[/tex]
[tex]b = 8[/tex]
FInally, the equation of the ellipse is [tex]\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1[/tex].
The center of the circle is G. Below is a student's work to find the
value of x. Explain the error and find the correct value of x.
Answer:
The error are
1) The use of the angle addition postulate, for [tex]m \widehat{ACD}[/tex]
2) The assumption that [tex]m \widehat{BC}[/tex] = 90°
The vertical angle property between [tex]m \widehat{CD}[/tex] and [tex]m \widehat{FA}[/tex] should be used to find 'x'
x = 5
Step-by-step explanation:
From the drawing of the circle, we are given;
AD = A diameter of the circle
∴ [tex]m \widehat{ACD}[/tex] = 180°
By angle addition postulate, we have;
[tex]m \widehat{ACD}[/tex] = [tex]m \widehat{AB}[/tex] + [tex]m \widehat{BC}[/tex] + [tex]m \widehat{CD}[/tex]
By substitution property of equality, we have;
180° = [tex]m \widehat{AB}[/tex] + [tex]m \widehat{BC}[/tex] + [tex]m \widehat{CD}[/tex]
[tex]m \widehat{AB}[/tex] = 5·x°
[tex]m \widehat{BC}[/tex] = Not given
[tex]m \widehat{CD}[/tex] = 15·x°
However;
[tex]m \widehat{CD}[/tex] is the vertically opposite angle to [tex]m \widehat{FA}[/tex]
∴ [tex]m \widehat{CD}[/tex] = [tex]m \widehat{FA}[/tex] = (16·x - 5)°
[tex]m \widehat{CD}[/tex] = 15·x° = (16·x - 5)°
15·x° = (16·x - 5)°
∴ 5 = 16·x° - 15·x° = x
x = 5
[tex]m \widehat{BC}[/tex] = 180° - ([tex]m \widehat{AB}[/tex] + [tex]m \widehat{CD}[/tex]) = 180° - (15·x° + 5·x°) = 180° - (20·x°)
[tex]m \widehat{BC}[/tex] = 180 - (20×5)° = 80°
[tex]m \widehat{BC}[/tex] = 80°
The error are the use of the angle addition postulate, for [tex]m \widehat{ACD}[/tex], and the assumption that [tex]m \widehat{BC}[/tex] = 90° rather than the vertical angle property between [tex]m \widehat{CD}[/tex] and [tex]m \widehat{FA}[/tex] in trying to find 'x', from which x = 5.
i need an answer to this with workings
pls type it if ur answering..cos file links aren't working
Expand (a-b)^7
Answer:
[tex]a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7[/tex]
Step-by-step explanation:
There are multiple ways of expanding a polynomial expression to a high degree. One way of doing it is to write out the problem in the multiplication form, multiply (a - b) by itself (7) times.
[tex](a-b)^7[/tex]
[tex]=(a-b)(a-b)(a-b)(a-b)(a-b)(a-b)(a-b)[/tex]
Now simplify, multiply two terms together,
[tex]=(a^2-2ab+b^2)(a^2-2ab+b^2)(a^2-2ab+b^2)(a-b)[/tex]
Repeat this process,
[tex]=(a^4-4a^3b+6a^2b^2-4ab^3+b^4)(a^3-3a^2b+3ab^2-b^3)[/tex]
Repeat this process one final time,
[tex]a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7[/tex]
15
Decide whether each expression simplifies to a number less than-1, greater than 1, or
Neither
neither. Mark an X in the correct column for each expression.
Greater than 1
Less than -1
Expression
-7+ (-4)
-(3 ÷ 2)
(-5) ÷ (-3)
(-9) - 6
Answer:
less than -1
less than -1
greater than 1
greater than 1
Step-by-step explanation:
[tex] - 7 + - 4 = - 7 - 4 = - (7 + 4) = - 11[/tex]
LESS THAN -1
________________________________
[tex] - ( \frac{3}{2} ) = - (1.5) = - 1.5[/tex]
LESS THAN -1
________________________________
[tex] \frac{( - 5)}{( - 3)} = \frac{5}{3} = 1.66..[/tex]
GREATER THAN 1
________________________________
[tex]( - 9) - 6 = - 9 - 6 = - (9 + 6) = - 15[/tex]
LESS THAN -1
________________________________
Given h(x)=4x-4h(x)=4x−4, find h(-3)h(−3).
Answer:1
Step-by-step explanation:
4x-4x+4=4h(x)
4=4h(x)
h(x)=1
h(-3)h(-3)=(1)(1)=1
if it is exactly 8:00, How long does it take for the hands of the clock to be pointed in the same direction
Answer:
Hey! do not go to brainly for this, sometimes brainly can be no help and people will scam for points, or maybe try to hack you (pt virus) with those links saying the answers there.. I am not saying this for points but go to https://www.varsitytutors.com/basic_geometry-help/how-to-find-the-distance-between-clock-hands for that
Step-by-step explanation:
So don't waste your time on brainly finding answers, you can run out of points fast, some people wont answer at all.
Which term below correctly completes the following sentence?
If a function has a vertical asymptote at a certain x-value, then the function is ______ at that value.
A. zero
B. rational
C. negative
D. undefined
The function has a vertical asymptote at a certain x-value, then the function is undefined at that value.
We have given that,
A function has a vertical asymptote at a certain x-value, then the function------ is at that value.
We have to determine the value and fill in the blank.
What is the vertical asymptotes?
A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.
Therefore option D is correct.
Therefore the function has a vertical asymptote at a certain x-value, then the function is undefined at that value.
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Answer:
D. undefined
Step-by-step explanation:
Which function produces an output of 5 for an input of -6?
A.f(x) = x + 1
B.f(x) = 2x + 4
C.f(x) = x - (-1)
D.f(x) = -x - 1
Answer:
The answer is D
Step-by-step explanation:
Since the input is -6, you input it into the equation. That would make it f(-6)=-(-6)-1 which would be equivalent to f(-6)=6-1 , as the negatives at the beginning of the equation cancel each other out and make it positive. Then you solve and get 5, which is your output. Hope I could help :)
HELP! I NEED THIS QUESTION ANSWERED ASAP!!!!!
HERE!
Angle X measures 53°
What type of angle is angle X?
Answers:
1 ) Obtuse
2) Right
3) Acute
Answer:
3 ) Acute
Step-by-step explanation:
Acute Angle - An angle less than 90 degrees.
Right Angle - An angle that is exactly 90 degrees.
Obtuse Angle - An angle more than 90 degrees and less than 180 degrees.
Straight Angle - An angle that is exactly 180 degrees.
Answer:
3)Acute
Step-by-step explanation:
any angle that is under a 90 degree angle or a right angle, is an acute angle. any angle that is above 90 degrees or a right angle is an obtuse andgle
Write 6431 to the nearest thousand.
the answer is 6430
Answer:
the nearest thousand would be 6000
Step-by-step explanation:
above 6500 would have been 7000
Answer:
6000
Step-by-step explanation:
Look at screen shot below
----------------------------------------------------------
Answer:
1st option is the correct answer
Please help meeeee! I’m stuck
Answer:
x = 12
Step-by-step explanation:
(8x - 1) + (3x + 4) + (3x + 9) = 180 degrees
14x + 12
180 - 12 = 168
14x = 168
/14 | /14
x = 12
Top left angle: (8x - 1)
8*12 - 1
96 - 1
= 95
Sorry! gtg I hope this helps!
Please answer with explanation
Answer:
1. if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = 6/2= 3. Thus, the equation describing this direct variation is y = 3x.
2. Partial Variation, where two variables are related by a formula, such as the formula for a straight line (with a non-zero y-intercept)
example :
in the milk factory Carol makes $10 per hour but gets an extra $20 from another job. since Carol gets a $20 allowance regardless of how much she works, if we want to represent Carol's situation in the form of an equation, it would be
Y=10x + 20
therefore if she worked zero hours
(Y=10(0) + 20),
she would still make $20 unconditionally and for every hour she works, she gets $10 more including the initial $20.
thus Carol's equation would be a partial variation, since her income doesn't entirely depend on how much she works.
3. a relation is non linear because it is has a direct relationship between an independent variable and a dependent variable.
In a relation, changes in the output do not change in direct proportion to changes in any of the inputs.
relations does not create a straight line but instead creates a curve.
I need this answer as soon as possible and also can u explain it
Answer:
56
Step-by-step explanation:
x=5
so x for the gym is 5 and x+3=5+3=8
add 5 and 8 because that is a whole side.
we are trying to find perimeter which us the outside of the shape. you are just going to "walk the fence" . so now, we have two sides of 15 and two sides of 13 (5+8). 13+13=26. 15+15=30
add the 26 and 30
Can someone help me with this. Will mark brainliest.
A meteorologist in Seattle says there is a 75% chance of rain. A meteorologist in Tacoma says there is a 1/4 chance of rain. In which city is it more likely to rain?
A. Seattle
B. Tacoma
C. Batesville
D. Both have the same chance
Angle Measures and segment lengths. Find x.
I hope this helps you
8^2=4.(4+x)
64=4.(4+x)
16=4+x
x=12
What is the products? (2t+1)(t-4)
Step-by-step explanation:
hsusbdjdhssjzssisbzjshzbzbaizussbissbisbsisbsssj
Help please not sure what it can be!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Input(x) Output(y)
32 20
14 2
? −6
-2 -14
-10 ?
Complete the function table and write the function rule.
The function rule is f(x) = x - 12 and the complete table is
Input(x) Output(y)
32 20
14 2
6 −6
-2 -14
-10 -22
Completing the function table and write the function rule.From the question, we have the following parameters that can be used in our computation:
Input(x) Output(y)
32 20
14 2
? −6
-2 -14
-10 ?
The slope is calculated as
m = (2 - 20)/(14 - 32)
m = 1
So, the equation is
y = mx + c
Using the points, we have
1(32) + c = 20
Evaluate
c = -12
So, we have
f(x) = x - 12
Using the above function, we have the following function values
f(-10) = -10 - 12 = -22
x - 12 = -6
x = 6
So, the complete table is
Input(x) Output(y)
32 20
14 2
6 −6
-2 -14
-10 -22
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Jan notes that 6 out of every 18 cars that pass her on the
highway are red. Which of the following is the best prediction of
how many red cars will pass Jan out of the next 54 cars that go
by?
A) 6
B) 18
C) 48
D) 54
Answer:
B) 18
Step-by-step explanation:
6 out of 18 is 6/18 = 1/3
1/3 x 54 = 18
A person paid by the hour works 22 hours a week and makes $459. How much would they make if they work 39 hours?
Answer:
813.681818182
(That's the exact number, but you can circle it to 813.7 )
Step-by-step explanation:
459%22=20.8636363636
20.8636363636 x 39= 813.681818182
Alexis traveled 2.3 km to visit her purchase groceries at the supermarket she travels another 600m to get some vitamin C at the pharmacy how much how many meters did Alex to travel in Total?
Answer:
2.9 km
Step-by-step explanation:
Just add up the two distances: 2.3 km + 600 m = 2.3 km + 0.6 km = 2.9 km total
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Answer:
Yes.
Step-by-step explanation:
If you change nothing but the angle and positioning of the original shape, then it is congruent.
plzzz help square paralellogram
Answer:
1. x=12
2. x=7
Step-by-step explanation:
pls help me with this problem
Answer:
Angle A: 90
Angle B: 48
Angle C: 42
Side length A (Hypotinuse): 23.9
SIde length B (Opposite): 17.8
Side length C (Adjacent): 16
Step-by-step explanation:
https://www.calculator.net/triangle-calculator.html?vc=42&vx=&vy=&va=90&vz=16&vb=&angleunits=d&x=0&y=0
Jon didn’t follow the order of operations. Explain what he did wrong.
What is the length of AD??
Answer:
d
Step-by-step explanation:
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A ringtoss toy is composed of a rectangular prism on top of a cylinder. The rectangular prism is completely filled with water. The dimensions of the rectangular prism are shown in the diagram.
What is the volume of the rectangular prism in cubic centimeters?
165 cm3
270 cm3
348 cm3
26 cm3
Answer:
270 cm3
Step-by-step explanation:
The volume of the given rectangular prism is 270 cm³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.
Volume is defined as the space occupied by an object inside the confines of three-dimensional space. It is also known as the object's capacity.
We have
Length = 9 cm
Width = 2 cm
Height = 15 cm
Using the formula for volume of the rectangular prism
= length x width x height
= 9 x 2 x 15
= 270 cm³
Thus, the volume of the given rectangular prism is 270 cm³.
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.
Mary bought an antique vase to display her flowers like the one pictured below.
The vase has a radius of 1.5 inches and a height of 7 inches. If she wanted to wrap the vase for safe storage, which value best represents the total surface area?
65.97 inches square
14.14 inches square
80.11 inches square
10.5 inches square