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 )
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Related Questions
Mr. Jones has $410,000 in a retirement account that earns 3.85% simple interest each year. Find the amount of interest earned by this investment if it is in there for 5 years. *
Answers
Answer:
Amount of interest earned = $78,925
Step-by-step explanation:
Given:
Amount deposit = $410,000
Rate of interest = 3.85% = 0.0385
Number of year = 5 year
Find:
Amount of interest earned
Computation:
Using simple interest formula
Amount of interest earned = Amount deposit x Rate of interest x Number of year
Amount of interest earned = 410,000 x 0.0385 x 5
Amount of interest earned = $78,925
In triangle ABC, AC = 6, AB = 7, and BC = 5. Which is true?
A) The measure of Angle C is the greatest of the three angles.
B) The measure of Angle C is the least of the three angles.
C) The measure of Angle B is the least of the three angles.
D) The measure of Angle B is the greatest of the three angles.
Answers
hope this helps
giving brainliest!! *easy*
Answers
Surface area is 1256.64
If each small cube has a volume of 1 cm,
what is the volume of this rectangular prism? HELP A.S.A.P. ILL GIVE BRAINLIST
Answers
Answer:
The answer is 40 Centimeters.
Step-by-step explanation:
This answer is correct since there are 4 rows of 10, creating the Rectangular prism. i hope this helped!
CAN ANYONE HELP ME ASAP AND THANKS:)
Answers
Answer:
true, true, false
Step-by-step explanation:
the sales do not decrease between week 4 and 5
Answer:
The answer is True, True, False
Step-by-step explanation:
For the first one, it is true because if you look on the graph, on the bottom or the x-axis, it is labeled "weeks". If you pay attention to when the line on the graph is, you will se that it is a straight line through weeks 1 and 2, so number one is true.
For the second one, it is also true because on the graph, you can see the the line starts to go upwards or increase. While the line is doing that, you can look right under it and see that it is passing through weeks 3 and 4, so that is True.
For the last one, it is false because on the graph, the line keeps going upwards for weeks 5 and 6, and the statement says that it is decreasing or going down, which is incorrect, so finally, the last question is false.
Hope this helps!
RENAME 11/12 / 8/9 AS A MIXED NUMBER
Answers
Answer: 1(29)/(36)
Step-by-step explanation:
Help pls............. Will choose brainliest
Answers
Answer:Its D enjoy =)
According to a candy company, packages of a certain candy contain 21% orange candies.
Find the approximate probability that the random sample of 500 candies will contain 22% or more orange candies.
Using a normal approximation, what is the probability that at least 22% of 500 randomly sampled candies will be orange?
Answers
Answer:
vvvvvvvvvvvvvvvvvvvvvvv v v v v
Which statements must be true to model a data set using a normal distribution?
The sample mean must equal the population mean.
The standard deviation of the population must be less than 30.
The sample must be randomly selected.
The sample size, n, must be at least 30.
The population mean must be greater than the sample mean.
Answers
Answer:
The sample must be randomly selected.
The sample size, n, must be at least 30.
Step-by-step explanation:
Plato
Answer:
The sample must be randomly selected.
The sample size, n, must be at least 30.
Step-by-step explanation:
Plato/Edmentum
nick is baking fudge. what is the minimum amount of plastic wrap needed to cover this piece of fudge?
Answers
Answer:
4 inches
Step-by-step explanation:
Answer:
where is the picture?
Step-by-step explanation:
You toss a coin in the air and it lands on the table. What is the probability that it lands on heads? *
Answers
Answer:
Hi! The answer to your question is D. 0.5
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!!
Stay Safe!!!
- Brooklynn Deka
20 points! Please help
A population has a standard deviation of 7.89. What is the approximate standard error of the mean for a sample size of 300?
A.
0.026
B.
0.46
C.
17.32
D.
2.20
Answers
Using the Central Limit Theorem, it is found that the approximate standard error of the mean for a sample size of 300 is given by:
B. 0.46
What does the Central Limit Theorem State?It states that the sampling distribution of sample means of size n from a population with standard deviation [tex]\sigma[/tex] has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that the parameters are [tex]\sigma = 7.89, n = 300[/tex], hence the standard error is given by:
[tex]s = \frac{7.89}{\sqrt{300}} = 0.46[/tex]
Hence option B is correct.
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What volume of 1M HCI would be needed
to neutralize 50mL of 1M Ca(OH)2?
Answers
Answer: 100
Step-by-step explanation: BRAINLIEST
Find the volume..
Pleaseeeee helppp being timed
Answers
Answer:
The right answer is 125.6
Answer:
A. 502.4
Step-by-step explanation
Please help me! Please! I am so lost! Pythagorean Theorem!
(The prism said to have an equilateral triangle base has the measurements shown)
Part A
Are the bases of the prism equilateral triangle‘s? Why or why not? Note: the bases of a triangular prism are triangles.
Part B
For this prism to be a right prism, all the lateral faces must be rectangles. Is enough information given to prove the lateral faces are rectangles? Why or why not?
Part C
Without using a protractor, you can determine whether the angles are right angles by measuring the length of the diagonal and applying the converse of the Pythagorean theorem.
The length of both diagonals for each lateral side is 13 cm. From this can you prove that the lateral sides are rectangles? Why or why not?
Part D
Some of the measurements of the triangular prism with a right angle base are shown. What is the length of the hypotenuse of the base?
Part E
Which lateral face has the largest area, the bottom one, left one, or diagonal one? What is the area?
Answers
Answer:
Part A- yes, because all 3 sides are Equal (each side is 5)
Part B- yes, each rectangle has the dimensions 12*5
Part C- yes- since the sides are 5 and 12 you can determine that the diagonal is 13, using they Pythagorean theorem [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]5^{2} +12^{2} =13^{2} \\25+144=169[/tex]- true statement, so the lateral sides are rectangles, because the corners are 90
Part D- [tex]4\sqrt{2}[/tex] (it is a 45-45-90 triangle- so the hypotenuse is the side length times [tex]\sqrt{2}[/tex]
Part E- the diagonal face as the largest area- dimensions are [tex]4\sqrt{2} * 12\\[/tex]
the area would be [tex]48\sqrt{2}[/tex]
Step-by-step explanation:
Kurt is running for student senate. He designed the t-shirt logo for his campaign. The logo is made up of a square with 14 cm sides and four half circles. Use 3.14 for pi to approximate the area of the logo.
Answers
Answer:
......
Step-by-step explanation:
I need them all in about five minutes, please help me no BS I’m giving you 50 points.
Answers
Answer: 1 is 5.7
2 is 21.75
3 is 8.8
Step-by-step explanation:
here ya go
Sally is building a fence. She needs 234 inches of fencing material. How many yards of fencing material does she need?
Answers
Answer:
6.5 yards
Step-by-step explanation:
1 yard = 36 inches
234/36 = 6.5
What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?
Answers
Answer:
[tex]d = 1.2973\pi r^3[/tex]
Step-by-step explanation:
Given
[tex]R_1 = r[/tex]
[tex]R_2 = 0.3[/tex]
Required
The difference in their volumes
The volume of a sphere is:
[tex]V = \frac{4}{3}\pi r^3[/tex]
So, the difference d is:
[tex]d = \frac{4}{3}\pi [R_1^3 - R_2^3][/tex]
[tex]d = \frac{4}{3}\pi [r^3 - (0.3r)^3][/tex]
[tex]d = \frac{4}{3}\pi [r^3 - 0.027r^3][/tex]
[tex]d = \frac{4}{3}\pi *0.973r^3[/tex]
[tex]d = \frac{3.892}{3}\pi r^3[/tex]
[tex]d = 1.2973\pi r^3[/tex]
Volume is a three-dimensional scalar quantity. The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is 4.0757r³ unit³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the sphere with radius(r) is,
Volume = (4/3)×π×r³
The volume of the sphere with radius (0.3r) is,
Volume = (4/3)×π×(0.3r)³
The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is,
Difference = [(4/3)×π×r³] - [(4/3)×π×(0.3r)³]
= (4/3)πr³[1-0.027]
= (4/3)πr³(0.973)
= 4.0757r³ unit³
Hence, The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is 4.0757r³ unit³.
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For each equality decide whether the solution is represented by X less than 2 .5 or X greater than 2.5 -4x+5>-5 -25>-5(x+2.5)
Answers
Answer:
[tex]x<2.5[/tex] and [tex]x > 2.5[/tex] are the solutions
Step-by-step explanation:
Given
[tex]-4x + 5 > -5[/tex]
[tex]-25 > -5(x + 2.5)[/tex]
Required
Determine if their solution is x < 2.5 or x > 2.5
[tex]-4x + 5 > -5[/tex]
Collect like terms
[tex]-4x>-5-5[/tex]
[tex]-4x>-10[/tex]
Divide by -4
[tex]x<\frac{-10}{-4}[/tex]
[tex]x<2.5[/tex]
[tex]-25 > -5(x + 2.5)[/tex]
Open bracket
[tex]-25 > -5x - 12.5[/tex]
Collect like terms
[tex]5x > 25- 12.5[/tex]
[tex]5x > 12.5[/tex]
Divide by 5
[tex]x > \frac{12.5}{5}[/tex]
[tex]x > 2.5[/tex]
The nutrition facts label on a container of dry roasted cashews indicates there are 161 calories in 28 grams. You eat 9 cashews totaling 12 grams.
A) How many calories do you consume
B) How many cashews are in one serving?
(PLEASE HELP)
Answers
Answer:
A) I consumed 69 calories.
B) There are 21 cashews in one serving.
Step-by-step explanation:
Given that the nutrition facts label on a container of dry roasted cashews indicates there are 161 calories in 28 grams, and I eat 9 cashews totaling 12 grams, to determine how many calories do I consume and how many cashews are in one serving should be performed the following calculations:
A)
28 = 161
12 = X
12 x 161/28 = X
1932/28 = X
69 = X
So, I consumed 69 calories.
B)
12 = 9
28 = X
28 x 9/12 = X
252/12 = X
21 = X
Therefore, there are 21 cashews in one serving.
Which expression is a perfect cube?
224
m 28
Answers
Answer:
alan walker dead girl
Step-by-step explanation:
Find the Value when 2 is added to 11.
Answers
Step-by-step explanation:
Gravity, also called gravitation, in mechanics, the universal force of attraction acting between all matter. ... On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth's mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects
13 is the value when 2 is added to 11
Emile went out for dinner and received a bill for $32.45. He left an 18% tip How much
did Emile pay for dinner including his tip?
Answers
Answer:
$38.29
Step-by-step explanation:
which of the following is equivalent to 2:1
Answers
Answer:
use m a t h w a y
Step-by-step explanation:
put it all together and they will give you opitions
n2−8=7n solve by factoring
Answers
2
−
8
=
7
n
2
−
8
=
7
n
n2−8=7n
2
−
8
−
(
7
)
=
0
find the median of the data 74,78,86,67,80, the mean is... the median is... find the modes of the data 67,74,77,78 or there is no mode
Answers
Answer:
data set one (74, 78, 86, 67, 80):
the mean is 77.
The median is 78
data set two (67, 74, 77, 78):
there is no mode
Step-by-step explanation:
i hope this helped<33
PLEASE HELP! DUE SOON (also include the check if you can) *I’ll give brainiest*
Answers
Answer:
x=24
Step-by-step explanation:
0.22(x+6)=0.2x+1.8
simplify the given equation
0.22x+1.32=0.2x+1.8
shift same kind of variables on one side
0.22x-0.2x=1.8-1.32
0.02x=0.48
For x
x=0.48/0.02
x=24
Check:
For checking subsitute the calculated value x if both sides of x are equal then its true...
0.22(24+6)=0.2(24)+1.8
5.28+1.32=4.8+1.8
6.6=6.6
Swapna gathered data on the number of page views for each of her blog posts. For her 40 latest posts, she found a sample mean of 358 with a population standard deviation of 54.3. What is the approximate 95% confidence interval for her page views? HINT: It's not D.
A. 344 and 372
B. 356 and 360
C. 341 and 375
D. 336 and 380
Answers
Answer: for plato users
D. 341 and 375
Step-by-step explanation:
I just took the test
The approximate 95% confidence interval for Swapna's page views is [341, 375].
What is confidence interval?It is a range of values that's likely to include a population value with a certain degree of confidence. It is expressed as a percent (%) where a population mean lies between an upper and lower interval.A confidence interval is how much uncertainty is with any particular statistic.When it is a 95% confidence interval, it means a range of values that you can be 95% certain contains the true mean of the population.A confidence interval is obtained from the observed data that holds the actual value of the unknown parameter.Formula of confidence interval:Confidence interval = mean ± Z * (standard deviation/ √sample size)
For given question,
Sample size = 40
Sample mean = 358
Standard deviation = 54.3
Critical value at 95% confidence level= 1.96
Confidence interval = 358 ± 1.96 * (54.3/ √40)
= [358 - 1.96 * (54.3/ √40) ,358 + 1.96 * (54.3/ √40)]
= [341, 375] (approximately)
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The length of a rectangle is 1 ft less than twice its
width. If the area of the rectangle is 78 ft^2 ,what
are the dimensions of the rectangle?
Answers
Answer:
Width: 13/2 ft.
Length: 12 ft.
Step-by-step explanation:
Let's assume the width is x
This means that the length is 2x-1, because it it one less than double the width.
The formula for the area of a rectangle is length*width, so
(2x-1)*x=78
Now let's solve for x
2x^2-x=78
2x^2-x-78=0
Use the quadratic formula
x=13/2 and x=-6
x cannot be negative, so we can rule out x=-6 and are left with x=13/2.
Substituting x back into our original assumptions, we now know that
The width is x=13/2 and
The length is 2x-1=2(13/2)-1=12
Final answer: The width is 13/2 ft. and the length is 12 ft.