Graph the equation y=−x²−8x−15 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Answers
Answer:
Plot these points
(-3,0)
(-5,0)
(-4,1)
(-2,-3)
(-6,-3)
Step-by-step explanation:
Let find the zeros of the equation.
We can factor this equation.
Factor out the -1.
[tex] - 1( {x}^{2} + 8x + 15)[/tex]
Factor using AC method
[tex] - 1(x + 3)(x + 5)[/tex]
Set all the terms equal to zero.
[tex]x + 3 = 0[/tex]
[tex]x + 5 = 0[/tex]
[tex]x = - 3[/tex]
[tex]x = - 5[/tex]
So our x intercepts are -3,0 and -5,0.
To find our vertex, apply the -b/2a.
[tex] \frac{8}{ - 2} = - 4[/tex]
Then
Substitute-4 for x.
[tex]y = - {4}^{2} - 8( - 4) - 15 = 1[/tex]
So our vertex is at (-4,1).
Find some other points like -2 and -6.
To find -2, substitute-2 into the quadratic.
[tex]y = - ( { - 2}^{2}) - 8( - 2) - 15 = - 3[/tex]
So -2,-3.
Since y=-4 is the axis of symmetry
-6,-3
The 5 points which satisfies the quadratic equation y = −x² − 8x − 15 is
( -5 , 0 ) ( -1 , -8 ) , ( -2 , -3 ) , ( 4 , 1 ) , ( -3 , 0 ) and the vertex point is ( 4 , 1 )
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = −x² − 8x − 15
On simplifying the equation , we get
y = -1 ( x² + 8x + 15 )
On factorizing the equation , we get
y = -1 ( ( x + 5 ) ( x + 3 )
So , the 2 values for x is -5 , -3
So , the two points are ( -5 , 0 ) and ( -3 , 0 )
The vertex will be -b/2a
Substituting the values in the equation , we get
The vertex = -8/2 = -4
So , when x = -4
y = -1 ( ( x + 5 ) ( x + 3 )
y = -1 ( 1 x -1 )
y = 1
So , the vertex is at the point ( 4 , 1 )
Now , when x = -1
y = -1 ( ( x + 5 ) ( x + 3 )
y = -1 ( 4 x 2 )
y = -8
So , the point is ( -1 , -8 )
Now , when x = -2
y = -1 ( ( x + 5 ) ( x + 3 )
y = -1 ( 3 x 1 )
y = -3
So , the point is ( -2 , -3 )
Hence ,
The 5 points which satisfies the quadratic equation y = −x² − 8x − 15 is
( -5 , 0 ) ( -1 , -8 ) , ( -2 , -3 ) , ( 4 , 1 ) , ( -3 , 0 ) and the vertex point is ( 4 , 1 )
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ2
Related Questions
What is 3-(-7)+11-(9)
Answers
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Just had to simplify the expression.
How many times bigger is 3 to the power of 15 compared to 3 to the power of 12?Explain your answer.
Answers
Explanation:
3 to the power of 15 = 14348907
3 to the power of 12 = 531441
14348907 divided by 531441 = 27
Help pleaseeeeeeeeeeeee
Answers
Answer:
option first is the right answer
here's the question
Answers
Answer:
60
Step-by-step explanation:
perimeter (p) = 8 + 17 + 15 = 40
semi-perimeter (s) = p/2 = 20
Area = square root of s(s-a)(s-b)(s-c) where a,b,c are the sides of the triange by Herons formula.
Therefore, area = 20(20-8)(20-15)(20-17) = square root of 3600 = 60
Given X=[b a 4 a], Y=[c d a b], and Z=[a c 16 b]. What is Y if x-2y=z?
Answers
Answer:
A
[2, -4, -6, -2]
Step-by-step explanation:
A 45 foot ladder is set against the side of a house so that it reaches up 27 feet. If Latanya grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 24 ft.) Round to the nearest tenth of a foot.
Answers
Answer:
22.4
Step-by-step explanation:
delta math
Answer:22.4
Step-by-step explanation:
what is (-3, 4) translated by (x,y) → (x – 6, y – 5).
Answers
Answer:
(-9,-1)
Step-by-step explanation:
You plug in the x and y values and solve the algebraic expression.
What is the proper order of organization from simplest to most complex.
A. rib bone, epithelial cell, heart, adipose tissue
B. cardiac muscle tissue, muscle cell, heart, muscular system
C. lung cell, alveoli, lung, respiratory system
D. neuron, nervous tissue, nervous system, brain
HELP ME ASAP
Answers
Answer:
A. 2,4,1,3
B. 2,1,3,4
C. 2,1,3,4
D. 1,2,4,3
Step-by-step explanation:
its always cell the simplest among the choices then tissue which is comprised of cells then organs which comprised of tissues and lastly the systems in our body that is comprised of organs
Subtract the following complex numbers:
(4 + 4i) - (13 + 17i)
Answers
Hope this helped!
plz fast solve it and It should be right
Answers
9514 1404 393
Answer:
(i) ∠CDF = 86°
(ii) ∠BAD = 141°
Step-by-step explanation:
(i) Angles CDF and GFD are "alternate interior" angles, so are congruent.
∠CDF = 86°
__
(ii) Angles BAD and CDA are "alternate interior angles, so are congruent. Angle CDA is the sum of angles CDH and HDA. Angle CDH is supplementary to angle CDF, so is ...
∠CDH = 180° -∠CDF = 180° -86° = 94°
Then ...
∠CDA = ∠CDH +∠HDA = 94° +47°
∠CDA = 141°
For positive acute angles A and B, it is known that cos A= 60/61 and tan B= 45/28. Find the value of sin(A+B) in simplest form
Answers
Answer:
[tex]\displaystyle \sin(A+B)=\frac{3008}{3233}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \cos(A)=\frac{60}{61}\text{ and } \tan(B)=\frac{45}{28}[/tex]
And that the two angles A and B are both in QI (positive acute angles).
Given this, we want to determine the value of sin(A + B).
Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, we can determine the opposite side with respect to A:
[tex]\displaystyle o=\sqrt{61^2-60^2}=\sqrt{121}=11[/tex]
Likewise, for B, tangent gives the ratio of the opposite side to the adjacent. Using this information, we can determine the hypotenuse of B:
[tex]h=\sqrt{45^2+28^2}=\sqrt{2809}=53[/tex]
In conclusion:
With respect to A, the adjacent side is 60, the opposite side is 11, and the hypotenuse is 61.
With respect to B, the adjacent side is 28, the opposite side is 45, and the hypotenuse is 53.
We can rewrite our original expression as:
[tex]\sin(A+B)=\sin(A)\cos(B)+\sin(B)\cos(A)[/tex]
And since A and B are both in QI, all trigonometric ratios will be positive.
Using the above conclusions, substitute:
[tex]\displaystyle \sin(A+B)=\left(\frac{11}{61}\right)\left(\frac{28}{53}\right)+\left(\frac{45}{53}\right)\left(\frac{60}{61}\right)[/tex]
Simplify. Hence:
[tex]\displaystyle \sin(A+B)=\frac{308+2700}{3233} = \frac{3008}{3233}[/tex]
Nina and Luca were told to draw a net for the three-dimensional figure shown below. Which statement about the
students' nets is true?
Answers
Answer:
d
Step-by-step explanation:
Under his cell phone plan, Justin pays a flat cost of $56 per month and $5 per
gigabyte. He wants to keep his bill under $65 per month. Write and solve an
inequality which can be used to determine x, the number of gigabytes Justin can use
while staying within his budget.
>
Inequality:
.
Submit Answer
attempt 1 out of 2
I need this answered as soon as possible it’s worth 100 points
Answers
Answer:
Step-by-step explanation:
The inequality Equation =
42 + 5x < 60
To stay within her budget of less than $60 she must use less than 3.6 Gigabytes
Step-by-step explanation:
Under her cell phone plan, Brooklyn pays a flat cost of $42 per month and $5 per gigabyte. She wants to keep her bill under $60 per month.
Let the number of gigabytes = x
Under $60 means less than $60
The inequality =
$42 + $5×x < $60
42 + 5x < 60
Solving for x
42 + 5x < 60
5x < 60 - 42
5x < 18
x < 18/5
x < 3.6 Giga bytes
Hence, to stay within her budget of less than $60 she must use less than 3.6 Gigabytes
2. The ratio of 7th graders to 8th graders in student council is 2:3.
If there are 51 8th grade students in student council, what is the
total number of students in student council?
Help me please thank you kindly
Answers
Answer:
85 students
Step-by-step explanation:
Given
[tex]7th : 8th =2 : 3[/tex]
[tex]8th = 51[/tex]
Required
Find the total number of students
We have:
[tex]7th : 8th =2 : 3[/tex]
Substitute: [tex]8th = 51[/tex]
[tex]7th: 51 = 2 : 3[/tex]
Express as fraction
[tex]\frac{7th}{51} = \frac{2 }{ 3}[/tex]
Multiply both sides by 51
[tex]51 * \frac{7th}{51} = \frac{2 }{ 3} * 51[/tex]
[tex]7th= \frac{2 }{ 3} * 51[/tex]
[tex]7th= 2 *17[/tex]
[tex]7th= 34[/tex]
So, the total is:
[tex]Total = 7th + 8th[/tex]
[tex]Total = 34 + 51[/tex]
[tex]Total = 85[/tex]
write an expression for b divided by 6
(please only real answers, I am already failing I don't need more bs)
Answers
Answer:
Well divided by is basically he slash between the things so it would be
b/6
Step-by-step explanation:
÷ is basically (divided by) and whatever number comes first jsut write it like for example
10 divided by 4
10 / 4
Answer:
b/6
Step-by-step explanation:
dont you think thats a bit easy? B divided by six, b ÷ 6, b goes in the like box when u do long division and 6 is outside
the vertex of the parabola below is at the point (5,-3). which of the equations below could be the one for this parabola?
Answers
Answer: ty for the points
Step-by-step explanation:
x+-3(y+3)2+5
Plz someone help me on these 2 questions!! I'm desperate :)
Answers
Answer:
Step-by-step explanation:
7. The graph does not touch the x axis and never will
8. Horizontal asymptote is y=-100
Hi help pls no link ty!
Answers
Answer:
84.78
Step-by-step explanation:
The full area of the circle without the cutout is 113.04
The cutout sector is 28.26
So that would make our final answer 84.78
by subtracting 28.26(cutout) from 113.04(full circle)
(In case you are wondering) The way I found the cutout sector's area was this formula: π4²·(angle)/360
4/7(21/8 x + 1/2) = -2(1/7 - 5/28x)
What is x in decimal form?
Answers
Answer:
x=[tex]1.22930[/tex]
Step-by-step explanation:
47(218 x+12 ) =−2(17 −528 x)
Simplify 47(218 x+12 ) : 327(21x+4) 327(21x+4) =−2(17 −528 x)
Multiply both sides by 7(21x+4)
327(21x+4) · 7(21x+4)=−2(17 −528 x)· 7(21x+4)
Simplify, 32=−14(17 −528 x)(21x+4)
Solve 32=−14(17 −528 x)(21x+4): x=32+4√589105 , x=32−4√589105 x=32+4√589105 , x=32−4√589105
Answer:
x = 0.5
Step-by-step explanation:
[tex]\frac{4}{7}(\frac{21}{8}x + \frac{1}{2}) = -2(\frac{1}{7} - \frac{5}{28}x)[/tex]
[tex]1\frac{1}{2}x + \frac{2}{7} = - \frac{2}{7} + \frac{5}{14}x[/tex]
[tex]1\frac{1}{2}x - \frac{5}{14}x + \frac{2}{7} = - \frac{2}{7} + \frac{5}{14}x - \frac{5}{14}x[/tex]
[tex]1\frac{1}{7}x + \frac{2}{7} = - \frac{2}{7}[/tex]
[tex]1\frac{1}{7}x + \frac{2}{7} - \frac{2}{7} = - \frac{2}{7} - \frac{2}{7}[/tex]
[tex]1\frac{1}{7}x = - \frac{4}{7}[/tex]
[tex]\frac{1\frac{1}{7}x}{1\frac{1}{7} } = \frac{- \frac{4}{7}}{1\frac{1}{7} }[/tex]
[tex]x = -\frac{1}{2}[/tex]
Help me please!!!!! I need help with angles
Answers
Answer:
<CFE = 28
<RPQ = 53
Step-by-step explanation:
1)
<CFE + 152 = 180
<CFE = 180 - 152
<CFE = 28
2)
Complementary means the angles add up to 90 so:
<RPQ + 37 = 90
<RPQ = 90 - 37
<RPQ = 53
If f(x) = 3x + 2 and g(x) = -x^2 + 1, which is f(g(x))?
Answers
Answer:
-3x^2+5
Step-by-step explanation:
f(g(x)) = 3(g(x))+2 = 3(-x^2)+3+2 = -3x^2 +5
Mike wants to find the confidence interval for a set of data. He knows the sample size and the sample proportion. Which other piece of information does he need to determine the confidence interval?
A.
the critical value
B.
the number of favorable responses
C.
the standard error of the mean
D.
the standard deviation
Answers
QUESTION 5
One card is selected from a standard deck of playing cards. Find the probability it is an ace or a 9.
Give the answer as a fraction
SHOW ALL WORK!
WILL GIVE U BRAINIEST
Answers
Answer: 2/13
Step-by-step explanation:
4 aces, 4 nines in a deck of 52 cards
so 8/52 chance of getting one of them reduce to 2/13
How many minutes are there between 15 minutes past 10 and 25 minutes to 11am?
Answers
Answer:
20 minutes
Step-by-step explanation:
15 minutes past 10 is 10:15
25 minutes to 11 am is 10:35
(60-25=35)
35-15=20
Rotating the decagon by a multiple of ___ carries the decagon onto itself. Therefore, a rotation of ___ counterclockwise will carry the decagon onto itself. can reflect the decagon ___ different ways , including ____ ways using the lines of symmetry that pass through the midpoints of two opposite sides.
Which of the following the correct sequence to in the blanks above?
Answers
Answer: C
Step-by-step explanation:
i just did this problem and got it right
Decagon is a regular polygon with 10 sides. The correct option that fills up the blanks is given by: Option C: 36°, 72°, 10, 5
What is a decagon?A decagon is a regular polygon with 10 sides.
As shown in the diagram attached below, the angle between two line segments connecting center and two adjacent vertex is of 36°.
Since rotating the decagon by that angle will land it in an unidentifiable way, as it looks alike, thus, rotating the decagon by a multiple of __36°__ carries the decagon onto itself.
Therefore, a rotation of _36 degree or 72 degree or any multiple of 36 degree__ counterclockwise will carry the decagon onto itself.
If we connect one vertex to opposite one, and flip it on that connecting line(this flip is called reflection), then the decagon will look same as before reflection.Thera are 5 such different lines.
Now in addition, we can connect lines from mid point of 1 side to other opposite side too. And this also can be done in 5 ways. On these connecting lines too, the decagon can be reflected onto itself.
Thus, we can reflect the decagon _5+5=10_ different ways. (these are the only ways, and it can be proven mathematically).
And including __5__ ways using the lines of symmetry that pass through the midpoints of two opposite sides
Thus, the correct option that fills up the blanks is given by: Option C: 36°, 72°, 10, 5
Learn more about reflection symmetry here:
https://brainly.com/question/7783612
I need help pls pls pls
Answers
Answer:
e. 55 miles hope that helped
Hope this helps
Evaluate the expression for r = 2.
17 + r =
Answers
Help I would love to give you a thanks
Answers
Answer:
Formula
Step-by-step explanation:
Answer:
formula because it gives you the number and tells you what to do.
Mrs. Rhodes is building the ramp shown below and she wants to paint it blue. How much paint will she need to cover the entire surface?
Answers
Answer:
2/3 of paint I believe because of the amount shown
HELP Math will give 35 brainly points and brainlyest
Answers
9514 1404 393
Answer:
51°
Step-by-step explanation:
The two marked angles are a linear pair, so supplementary.
(3x +15) +(10x +9) = 180
13x = 156 . . . . . . subtract 24
156/13 = x = 12 . . . . divide by 13
The smaller angle is ...
3x +15 = 3(12) +15 = 51
The angle with the basement floor is 51°.
