Is the discriminant of g positive, zero, or negative?
Answer:
Negative
Step-by-step explanation:
Positive discriminant: graph cuts x axis twice
Zero discriminant: graph touches x axis once
Negative discriminant: graph does not cut or touch x axis
ellipse with vertices (-3, 4), (11, 4) and foci (-1, 4), (9.4)?
Answer:
[tex]\frac{(x-4)^2}{49}+\frac{(y-4)^2}{24}=1[/tex]
Step-by-step explanation:
Because the vertices are on the same horizontal line and so are our foci, this is our major axis for a horizontal ellipse.
Horizontal Ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
a>b
Major axis length: 2a
Minor axis length: 2b
Center: (h,k)
Foci: (h±c,k) where a²-b²=c²
We can easily find the center of the ellipse by finding the midpoint of our vertices (-3,4) and (11,4) which works out to be (4,4)
Because our foci must be (-1,4) and (9,4) this means (4±c,4) represents our foci. We can easily see that c=5 since (4-5,4) -> (-1,4) and (4+5,4) -> (9,4).
Knowing that c=5, we need to determine our values for a and b to satisfy the equation a²-b²=5². Our vertices are located on the major axis, which will help us in finding the value of a. The distance between the two vertices will be the length of the major axis, which will be |11-(-3)| = 14. Additionally, because the length of the major axis is equal to 2a, this means 2a=14 where a=7. Now we can solve for b with our equation 7²-b²=5² where b=√24.
In conclusion, our ellipse would be:
[tex]\frac{(x-4)^2}{7^2}+\frac{(y-4)^2}{\sqrt{24}^2}=1[/tex] which works out to be [tex]\frac{(x-4)^2}{49}+\frac{(y-4)^2}{24}=1[/tex]
The equation of ellipse with vertices (-3, 4), (11, 4) and foci (-1, 4), (9.4) is
(x-4)^2/49 + (y-4)^2/24 = 1
What is equation of an ellipse?The standard equation of an ellipse centered at (h, k) with a major axis parallel to the x-axis is given by:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where the coordinates of the vertex are (h±a, 0), coordinates of co-vertex are (h, k ± b) and the coordinates of foci are (h±c, k), where a² = c² + b².
here, we have,
Because the vertices are on the same horizontal line and so are our foci, this is our major axis for a horizontal ellipse.
Horizontal Ellipse:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where,
a>b
Major axis length: 2a
Minor axis length: 2b
Center: (h,k)
Foci: (h±c,k) where a²-b²=c²
We can easily find the center of the ellipse by finding the midpoint of our vertices (-3,4) and (11,4) which works out to be (4,4)
Because our foci must be (-1,4) and (9,4) this means (4±c,4) represents our foci. We can easily see that c=5 since (4-5,4) -> (-1,4) and (4+5,4) -> (9,4).
Knowing that c=5, we need to determine our values for a and b to satisfy the equation a²-b²=5².
Our vertices are located on the major axis, which will help us in finding the value of a.
The distance between the two vertices will be the length of the major axis, which will be |11-(-3)| = 14.
Additionally, because the length of the major axis is equal to 2a, this means 2a=14 where a=7.
Now we can solve for b with our equation 7²-b²=5² where b=√24.
In conclusion, our ellipse would be:
(x-4)^2/49 + (y-4)^2/24 = 1
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a triangle has side lengths 10, 16, and 11. is the triangle actue, obtuse, or right?
Answer:
Obtuse
Step-by-step explanation:
a^2 + b^2 = c^2
10^2 + 11^2 = 16^2
100 + 121 = 256
221 = 256
221 < 256
A triangle has side lengths 10, 16, and 11. is the triangle is obtuse.
Name three types of triangles based on angles?Triangles can be classified into three types with respect to their interior angles which are:
1. Acute-angled
2. Obtuse-angled
3. Right-angled
Acute Triangle
An acute triangle is a triangle whose all the three interior angles are acute. In other words, if all interior angles are less than 90 degrees, then it is an acute-angled triangle.
Obtuse Triangle
Obtuse triangles are those in which one of the three interior angles has a measure greater than 90 degrees. In other words, if one of the angles in a triangle is an obtuse angle, then the triangle is called an obtuse-angled triangle.
Right Triangle
A right triangle is a triangle in which one of the angles is 90 degrees. In a right-angled triangle, the side opposite to the right angle (90-degree angle) will be the longest side and is called the hypotenuse.
Three given sides are 10, 11, 16
Let a = 10, b = 11, c = 16
then, [tex]a^{2} +b^{2} = 10^{2} +11^{2}[/tex]
= 100 + 121
= 221
and [tex]c^{2} = 16^{2} =256[/tex]
Since, [tex]a^{2} +b^{2} < c^{2}[/tex]
Thus, given triangle is obtuse.
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hey guys its my first time using this app, i need help with this question!
b) 3/x + 4/x+2
Answer:
7/x+2
Step-by-step explanation:
2x +7/x
hope this helps
IT IS OVER ALL NOT ONLY 7!!!!!!!
Given the radius is 6 inches, what is the area of the circle?
Area =
inches2 (the 2 is supposed to be an exponent)
Answer:
I wasn't sure how you're supposed to answer, so the answers for each scenario are in the explanation!
Step-by-step explanation:
[tex]A=\pi r^{2}[/tex]
[tex]A=\pi (6^{2})[/tex]
[tex]A=\pi (36)[/tex]
From here, there can be a few different answers:
The exact answer is A=36π inches^2.
If you need to round, round this to wherever you need it: A=113.0973355292326... inches^2
If you're using 3.14 for pi, the answer is A=113.04 inches^2.
Find center and radius of a circle with a diameter that has endpoints of (3,-2) and (-5,-4)
Answer:
Center: (-1,-3)
Radius: 4.12 units
Step-by-step explanation:
Hi there!
1) Find the center of the circle
When given two diameter endpoints, we can find the center of the circle by calculating for the midpoint since the center lies in the middle of the points:
Midpoint: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2})[/tex] where the two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the diameter endpoints (3,-2) and (-5,-4)
[tex](\frac{3+(-5)}{2} ,\frac{-2+(-4)}{2})\\(\frac{3-5}{2} ,\frac{-2-4}{2})\\(\frac{-2}{2} ,\frac{-6}{2})\\(-1,-3)[/tex]
Therefore, the circle is centered at (-1,-3).
2) Find the radius of the circle
The radius of a circle is the distance between the outside edge and the center. We can find the radius by calculating for the distance between the center of the circle and one of the diameter endpoints.
Distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where the two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the center (-1,-3) and a diameter endpoint (3,-2)
[tex]d=\sqrt{(3-(-1))^2+(-2-(-3))^2}\\d=\sqrt{(3+1)^2+(-2+3)^2}\\d=\sqrt{(4)^2+(1)^2}\\d=\sqrt{16+1}\\d=\sqrt{17} \\d=4.12[/tex]
Therefore, the radius of the circle is approximately 4.12 units when rounded to the nearest hundredth.
I hope this helps!
What is the value of X?
Answer:
x = 42-degrees
Step-by-step explanation:
x + 48 = 90 --> *subtract 48 from both sides*
x = 42
Answer:
42
Step-by-step explanation:
Because the entire angle is equal to 90, you have to find 90-48 which is 42.
As a block of ice melts, its weight changes from 1 3/4 lb to 1/4 lb. This change takes 1/4 h. The ice melts at a constant rate. At what rate does the weight of the ice change? Show your work.
pleaseeeeee help =)
As a block of ice melts, its weight changes from 1 3/4 lb to 1/4 lb. This change takes 1/4 h. The ice melts at a constant rate. At what rate does the weight of the ice change?
Answer:-You should have these values backwards like:-
=> 1/34 lb is less than 1/4 lb.
Next:-
We're gonna find a specific common denominator,
Then we get: (17/68 - 2/68)/(1/4) = 60/68 = 15/17 lb/hour
___________________________
[tex]\huge{ \mathfrak{ \underline{ Answer}}} \: \: ✓ [/tex]
____________________________
Change in weight :
[tex]1 \dfrac{3}{4} - \dfrac{1}{4} [/tex][tex] \dfrac{7}{4} - \dfrac{1}{4} [/tex][tex] \dfrac{6}{4} lb[/tex]_____________________________
Time taken to melt :
[tex]\dfrac{1}{4} \: hr[/tex]_____________________________
Rate of change in weight of ice :
[tex] \mathrm{ \dfrac{change \: \: in \: \: weight}{time \: taken} }[/tex][tex] \dfrac{6}{4} \div \dfrac{1}{4} [/tex][tex] \dfrac{6}{4} \times 4[/tex][tex]6[/tex]The rate of change in weight of Ice is 6 lbs per hour ( 6 lb / h )
_____________________________
[tex]\mathrm{ \#TeeNForeveR}[/tex]
What is the measure of x?
Answer:
105+54=x
Step-by-step explanation:
Determine the equation of the circle graphed below
Keith has 7 yards of string. He needs ⅓ yard of string for each of his puppets. How many puppets can Keith make with his string?
Answer:
the no of puppets that could be made with his string is 21
Step-by-step explanation:
Given that
There is 7 yards
And, it needs one -third of string for each of his puppets
= 7 × 3
= 21 puppets
We simply multiply the 7 yards with the 3 so that the no of puppets could come
hence, the no of puppets that could be made with his string is 21
Which expression could be used to find the distance between points (-2,8) and (7,13) on a coordinate plane?
Choose all that apply.
Answer:
A and E.
Step-by-step explanation:
Its square root of [(13-8 and 7 - - 2 ( = 7 + 2)both squared)]
OH I see there are 2 answers.
The other one is A.
Geometry
Find the value of x. The diagram is not to scale.
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
Since lines [tex]\overrightarrow{f}[/tex] and [tex]\overrightarrow{g}[/tex] are parallel, the angles labelled in the diagram must be supplementary (add up to [tex]180^{\circ}[/tex]). Therefore, we have the following equation:
[tex]4x+(7x+26)=180,\\11x+26=180,\\11x=154,\\x=\boxed{14}[/tex]
heyy! i’ll give brainliest please help thanks
Answer:
Aswan, Sudan
Step-by-step explanation:
Answer:
egypt and africa
Step-by-step explanation:
Complete the square for the expression
Answer:
x^2 + 14x + 49 = 0
Step-by-step explanation:
(Translate the sentence into an inequality)
Twice the difference of a number and 2 is at most -30
Answer:
2(x-2) ≤ -30
Step-by-step explanation:
2(twice) (x-2)( the difference of a number and 2) ≤ (is at most )-30
pls can u help me with this
Answer:
A = 1.26
B = 1.22
Store B is better
Step-by-step explanation:
5.04 divided by 4
2.44 divided by 2
help miii plzzzz pretty please wit a cheer on top
Answer:
14 + 5[tex]\sqrt{3}[/tex]
a = 14, b = 5, c = 3
Step-by-step explanation:
Multiply the brackets out:
[tex](2\sqrt{3} )(3\sqrt{3} ) = (2)(3)(\sqrt{3})(\sqrt{3}) = (6)(3) = 18[/tex]
[tex](2\sqrt{3} -1)(4+3\sqrt{3} ) = 8\sqrt{3} +18 - 4 - 3\sqrt{3}[/tex]
[tex]= 14 + 5\sqrt{3}[/tex]
Form 2R Coursework #1
Transformations
1. A is the point (-3,5). What are the coordinates of the image of A after a translation of 5
units to the right and 1 unit down?
Answer: 2,4???
Step-by-step explanation:
Can someone please help me with this, btw don’t mind the white-out
Answer:
x< 10
Step-by-step explanation:
To start the absolute difference between 20 and 5 is 15. Next, write out an equation for the problem:
x * 1.5 < 15,
Then divide by 1.5 on both sides...
Boom! x < 10.
Please help!! I'll give brainlist
Answer:
60°
Step-by-step explanation:
just in case if line AC and BD are straight lines,
angle EGD will be 180-90-30=60
and EGD will equal to x°becoz they are just in opposite
Answer:
The Answer is 60
Step-by-step explanation:
If you look at E B and F those make up a 180-degree angle if you look across from B then you will see that it is a 90-degree angle so you can assume that B is also a 90-Degree angle so if you add up 30 + 90 = 120
You then can subtract 180 - 120 to get the answer 60
So therefor the answer is 60
Tahari is shopping for a new car. She is making her decision based on brand, color, and style. She can choose from 4 brands, 5 colors, and 3 styles. First, Tahari chooses the color. Which explains the number of options that she has left after she chooses the color? Tahari has 60 options left because Tahari has 12 options left because she has options left. Tahari has 12 options left because . Tahari has 7 options left because she has options left.
Answer:After choosing the color she still has the choices of brands and style so:
Tahari has 4*3=12 options left.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
right on edge
what was her overall quiz average of a 90 for the quarter ? pls answer
Answer:
She needs at least a 105 to get a 90 :/
Step-by-step explanation:
If you add all those up and divide it by 5 (the mean) you get an 86.5, then if you add 105 and divide up all those numbers by 6 you get a 90.166667
which expression represents the difference of (5x-3y) and (8x+8y)?
Given:
The expressions are:
[tex](5x-3y)[/tex] and [tex](8x+8y)[/tex]
To find:
The difference of [tex](5x-3y)[/tex] and [tex](8x+8y)[/tex].
Solution:
Difference of [tex](5x-3y)[/tex] and [tex](8x+8y)[/tex] is written as:
[tex]Difference=(5x-3y)-(8x+8y)[/tex]
On simplification, we get
[tex]Difference=5x-3y-8x-8y[/tex]
[tex]Difference=(5x-8x)+(-3y-8y)[/tex]
[tex]Difference=-3x-11y[/tex]
Therefore, the difference of [tex](5x-3y)[/tex] and [tex](8x+8y)[/tex] is [tex]-3x-11y[/tex].
Evaluate the expression when a = -4 and x=4.
4x-a
Answer: 20
Step-by-step explanation: Substitute -4 in for a and 4 in for x. Then, simplify.
4(4) - (-4)
16 + 4
20
Hope this helped. Please mark brainliest if correct!
Answer:
4(4)-(-4)
16+4
20
Step-by-step explanation:
When you put x is 4 in the first term u will get 16 and when you add two negatives u will get a positive, hence positive 4, that is 16+4
20
Write the point-slope form of an equation of the line through the points (-7, 7) and (4, 1).
A. y−4=−611(x−1)
B. y+1=−611(x+4)
C. y+7=−611(x−7)
D. y−7=−611(x+7)
Answer:
D) y-7=-6/11(x+7)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-7)/(4-(-7))
m=-6/(4+7)
m=-6/11
y-y1=m(x-x1)
y-7=-6/11(x-(-7))
y-7=-6/11(x+7)
y=-6/11x-42/11+7
y=-6/11x-42/11+77/11
y=-6/11x+35/11
What is the rule for reflecting across the x-axis?
(x,y)=(x,-Y)
O (x,y)=(-x,y)
O (x,y)=(-x-7)
O (x,y)=(x,y)
Helppppppp what's the answer??????
this is exact and approximate pi
SOMEONE PLS HELP BEFORE I FAIL
Which set of ordered pairs represents y as a function of x? {(2,2), (3,3), (2,4), (5,5)} A. {(2,2), (3,3), (2,4), (5,5)} A. , 2, 2... 3, 3.... 2, 4... 5, 5... , {(−1,−2), (−2,−1), (−2,7), (−4,8)} B. {(−1,−2), (−2,−1), (−2,7), (−4,8)} B. Negative 1, negative 2... Negative 2, negative 1... Negative 2, 7.... Negative 4, 8... , {(−1,6), (4,3), (1,1), (−3,4)} C. {(−1,6), (4,3), (1,1), (−3,4)} C. Negative 1, 6... 4, 3... 1, 1... Negative 3, 4... , {(0,1), (2,1), (3,1), (0,2)} D. {(0,1), (2,1), (3,1), (0,2)}
Answer:
The correct answer is C
Step-by-step explanation:
In a function, no two ordered pair has the same first element. if you check all the Rest, they have one or more two ordered pairs having the same first element. But C has unique first ordered elements, -1, 4, 1 and -3