Y=-x^2-12x-37 find the 1) Roots 2) Factors 3) Vertex (x,y) 4) Interception with 'Y" axis 5) Axis of Symmetry 6)Direction of Opening 7)Max / Min ? Coordinates 8)Sketch 9) Domain 10) Range
Answers
Answer:
1) The roots of the equation Y = -x² - 12·x - 37 are x = -6 - √73 and -6 + √73
2) The factors of the function Y = -x² - 12·x - 37 are (x + (-6 - √73)) and (x - (-6 + √73))
3) The vertex is (-6, -1)
4) The Y-intercept is (0, -37)
5) The axis of symmetry is x = -6
6) The parabola opens downward
7) The maximum point is (-6, -1)
8) The graph of the function created with Microsoft Excel is attached
9) The domain of the function is -∞ < x < ∞
10) The range of the function is -∞ < Y ≤ -1
Step-by-step explanation:
The given function is Y = -x² - 12·x - 37
1) The roots of the equation Y = -x² - 12·x - 37 is given as follows;
0 = -x² - 12·x - 37
∴ -x² - 12·x - 37 = 0
The roots are;
x = (12 ± √((-12)² - 4 × 1 × (-37)))/(-2)
∴ x = -6 - √73 and -6 + √73
2) The factors are (x + (-6 - √73)) and (x - (-6 + √73))
3) The vertex is given by h = -b/(2·a) = 12/(2) = -6
k = c - b²/(4·a) = -37 - 144/(-4) = -1
The vertex = (h, k) = (-6, -1)
4) The intercept with the "Y" axis is given when x = 0, therefore, the y-intercept is (0, -37)
5) The axis of symmetry can be found at the vertex or the line x = -6
6) The sign of the coefficient of x² is negative therefore, the parabola opens downward
7) The maximum point is given as follows;
At the maximum point, dY/dx = d(-x² - 12·x - 37)/dx = -2·x - 12 = 0
x = 12/(-2) = -6, which is the vertex, therefore Y = -(-6)² - 12×(-6) - 37 = -1
The maximum point is the vertex (-6, -1)
8) Please find attached the graph of the function created with Microsoft Excel
9) The domain of the function is -∞ < x < ∞
10) The range of the function is -∞ < Y ≤ -1
Related Questions
Please help ASAP you will get BRAINLIST.
Answers
Answer:
Measure of LKJ is 64
Step-by-step explanation:
Here, we want to find the measure of angle LKJ
mathematically, we know that a bisector line divides an angle into 2
Since one of the divided angle is 32
The other side too will be 32
Thus, the missing value would be;
32 + 32 = 64
Solve the system of equations for x and y.
y = x + 5
y = 2x + 2
Answers
Explanation:
using the
substitution method
y
=
x
−
5
→
(
1
)
y
=
−
2
x
+
4
→
(
2
)
since both equations are expressed in terms of x we
can equate them
⇒
x
−
5
=
−
2
x
+
4
add 2x to both sides
2
x
+
x
−
5
=
−
2
x
+
2
x
+
4
⇒
3
x
−
5
=
4
add 5 from both sides
3
x
+
5
−
5
=
4
+
5
⇒
3
x
=
9
divide both sides by 3
3
x
3
=
9
3
⇒
x
=
3
substitute this value in
(
1
)
y
=
3
−
5
=
−
2
As a check
substitute these values into
(
2
)
right
=
−
6
+
4
=
−
2
=
left
⇒
point of intersection
=
(
3
,
−
2
)
Given that a leg of a 45-45-90 triangle has a length of 5 feet, what is the length of the hypotenuse? (PLEASE HELP im timedd!!!)
Answers
Answer:
5[tex]\sqrt{2\\}[/tex]
Step-by-step explanation:
Use the 45-45-90 triangle property. If the leg is x then the hypotenuse would be [tex]\sqrt{2}x[/tex]. Since x is 5, then the hypotenuse would be 5[tex]\sqrt{2\\}[/tex]
Traveling from City 1 to City 2, a pilot planned a southeast course along the path labeled d. Instead, a storm forced the pilot to travel 32 miles south, then 24 miles east to reach City 2. How many extra miles was the pilot forced to fly?
A. 13 mi.
B. 14 mi.
C. 16 mi.
D. 17 mi.
Answers
The extra miles the pilot was forced to fly, found using Pythagorean Theorem was 16 miles. The correct option is therefore;
C. 16 mi
What does Pythagorean Theorem state?Pythagorean theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the square of the lengths of the other two sides.
The direction the pilot planned initially = A southeast course
The direction the storm forced the pilot to travel = 32 miles south then 24 miles east
The number of extra miles the pilot is forced to fly = Required
Taking the original path as a straight line, and the destination arrived at being that of the new destination, we get by using Pythagoras Theorem
Direct distance, d₁ = √(32² + 24²) = 40The direct distance from City 1 to City 2 = 40 milesThe new distance can be obtained by the scalar addition of the individual distances as follows;
d₂ = 32 + 24 = 56
The new distance traveled, d₂ is 56 milesThe number of extra miles, Δd, is therefore;
Δd = d₂ - d₁Which indicates that we have;
Δd = 56 miles - 40 miles = 16 milesThe number of extra miles the pilot was forced to fly is Δd = 16 milesLearn more about Pythagorean Theorem in mathematics here:
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Answer:
C. 16 mi
Step-by-step explanation:
I wanna make sure this is right pls help
Answers
Answer:
C
Step-by-step explanation:
Set it up like a formula
feet = inches/feet = cm/inches
Solve for y. 10x-3y=2
Answers
Answer:
y = 10/3x - 2/3
Step-by-step explanation:
10x-3y=2
-3y = -10x + 2
-3y/-3 = -10x/-3 + 2/-3
y = 10/3x - 2/3
When x equals 4 what does y equal?
A. 1
B. 3
C. 2
D. 4
Answers
A. 1
B. 3
C. 2
D. 4
Ans is D.4
The table shows the relationship “Dental Assistants make 19 dollars per hour.”
Hours (h)
Dollars (d)
1
19
2
38
3
57
4
76
5
95
Which statements are correct? Check all that apply.
The variable d is the independent variable.
The variable h is the independent variable.
The number of hours worked causes a change in the number of dollars earned.
The variable d is the dependent variable.
The number of dollars earned causes a change in the number of hours worked.
The variable h is the dependent variable.
The more hours that are worked, the fewer dollars that are earned.
Answers
Answer:
The Answers Are:
B. The variable h is the independent variable.
C. The number of hours worked causes a change in the number of dollars earned.
D. The variable d is the dependent variable.
Step-by-step explanation:
As you can see on the picture, the more hours you work, the more dollars you get.
d=19h
The statement,B. The variable h is the independent variable. The number of hours worked causes a change in the number of dollars earned. The variable d is the dependent variable are correct.
We have the given options,
A.The variable d is the independent variable.
B. The variable h is the independent variable.
C. The number of hours worked causes a change in the number of dollars earned.
D. The variable d is the dependent variable.
Here d is dependent on hours,
What is the meaning of the independent variable?In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an independent variable.
As you can see below, the more hours you work, the more dollars you get.
Hours Dollars
1 19
2 38
3 57
4 76
5 95
d=19h.
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Which is the slope of the line that passes through the points (12, -6) and (12, 3)?
Answers
Answer:
use the slope equation: (y2-y1) / (x2-x1)
(3 -(-6) / (12-12) (plug in the values)
9/0 the slope is undefined anytime there's a denominator of 0
Step-by-step explanation:
I hope this helps :)
Answer:
Undefined
Step-by-step explanation:
Slope=y2-y1/x2-x1
3-(-6)=3+6
9
12-12=0
9/0 is undefined
Jason spends $2.35 to buy lunch at school. If he buys a lunch on 9 days, how much total money has he spent? Write and equation and solve.
Answers
Answer:
21.15 $
Step-by-step explanation:
Answer:
$21.15
Step-by-step explanation:
$2.35 x 9= $21.15
Hope this helps
Work out the surface area of this cylinder.
Answers
Answer: A≈2010.62
Step-by-step explanation:
Hope this helps
According to Hinduism, which of the following is the supreme spiritual force?
Answers
Answer:
According to Hinduism, shiva is the supreme spiritual force
but u havent given option
While the correct answer SHOULD be Shiva, if you are doing this for Connexus, then the answer they teach and are seeking is Brahman.
The length of a rectangle is 6 inches the width is 3w inches if the coefficient of the width increases by 2 what could be an expression for the area of the rectangle
Answers
Answer:
Dang it I got it wrong
Step-by-step explanation:
If there are 30 boys and 15 girls in the room fill out all the possible ratios of boys to girls that could be made
Answers
Answer:
All the possible ratios of boys to girls that could be made are:
30:15
10:5
6:3
2:1
Step-by-step explanation:
If there are 30 boys and 15 girls in the room
We have :
Boys : Girls
30 : 15
a) 30 : 15
Dividing through by 3
= 10:5
b) 30 : 15
Dividing through by 5
= 6:3
c) 30 : 15
Dividing through by 15
= 2:1
Hence:
All the possible ratios of boys to girls that could be made are:
30:15
10:5
6:3
2:1
2.
.
X + 3
X + 18
X +4
X=
Answers
x = -1,-16,-2.
TIE FIGHTERS GO ZOOOOOOOM
6. A pencil costs $2 less than a notebook. A pen costs 3 times as much as a pencil. The pen costs
$9. Write and solve an equation to determine the cost of the notebook and the cost of the
pencil.
Answers
Answer:
Step-by-step explanation:
9 x 3 = 27 aka pencil
27 + 2 = 29 = notebook
Solve for x: X -10 = 7
Answers
Answer:
x = 17
Step-by-step explanation:
x - 10 = 7
=> x = 10 + 7
=> x = 17
The question is in the picture
- I really need this !! Thank you !!
Answers
Answer:
y=-1/5x+9
Step-by-step explanation:
-1/5x is the slope and 9 is y intercept
6th grade math !!!!!!!!
Answers
Answer:
Heyy, don't cheat on an online test
Step-by-step explanation:
what fractions are equal to 2
Answers
Answer:
Step-by-step explanation:
Which of the following could be the graph of the equation y = -2x? *
please answer
Answers
The line starts at the origin and goes down by two.
1/4 is 60% of x. Write a proportion that you can use to find x
Answers
Woooooooo
The required value of x is approximately 0.4167 if 1/4 is 60% of x.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
To write a proportion that we can use to find the value of x, we can use the fact that "1/4 is 60% of x" and set up the proportion:
1/4 = (60/100) × x
Here, we have converted 60% to its equivalent decimal form (0.60) and 100% to its equivalent fraction (1).
We can then cross-multiply to solve for x:
1/4 × 1 = 0.60 × x
1/4 = 0.60x
0.25 = 0.60x
x = (0.25) / 0.60
x ≈ 0.4167
Therefore, the value of x is approximately 0.4167.
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please answer all of them
Answers
Answer:
a. x = 5/2
b. y = 16.5
c. z = 12
Step-by-step explanation:
Answer:
1) x = 2.5
b) y = 12.9
c) z = 12
d) 2.75 = w or 2[tex]\frac{3}{4}[/tex] = w
e) t = 4
Step-by-step explanation:
a)
2x = 5
divide both sides of the equation by 2
2x/2 = 5/2
x = 5/2
x = 2.5
b)
y + 1.8 = 14.7
subtract 1.8 from both sides of the equation
y + 1.8 - 1.8 = 14.7 - 1.8
y = 14.7 - 1.8
y = 12.9
c)
6 = 1/2z
divide both sides by 1/2 or multiply both sides by 2
6*2 = 1/2z * 2
6*2 = z
12 = z
d)
3.25 = 0.5 + w
subtract 0.5 from both sides of the equation
3.25 - 0.5 = 0.5 + 2 - 0.5
3.25 - 0.5 = w
2.75 = w
or
2[tex]\frac{3}{4}[/tex] = w
e)
2.5t = 10
t = 10/2.5
t = 4
Use the Zero Product Property to find the x-intercepts for x^2+6x=y
Answers
Answer:
[tex]x=0\ or\ x =-6[/tex]
Step-by-step explanation:
Given
[tex]x^2+6x=y[/tex]
Required
Determine the x intercepts
To get the x intercepts, we simply set y to 0
Substitute 0 for y;
[tex]x^2+6x=0[/tex]
Factorize:
[tex]x(x +6) = 0[/tex]
Apply zero product property
[tex]x=0\ or\ x + 6 =0[/tex]
[tex]x=0\ or\ x =-6[/tex]
Jamie receives 15% commission on magazine subscriptions. One week her sales totaled $860. What was her commission?
Answers
Given:
Jamie receives 15% commission on magazine subscriptions.
One week her sales totaled $860.
To find:
Her commission.
Solution:
We have,
Total sales of one week = $860
Rate of commission = 15%
Now,
[tex]Commission=\dfrac{15}{100}\times 860[/tex]
[tex]Commission=\dfrac{15}{10}\times 86[/tex]
[tex]Commission=\dfrac{1290}{10}[/tex]
[tex]Commission=129[/tex]
Therefore, the amount of commission is $129.
what are the first 100 digits of pi ([tex]\pi[/tex])?
Answers
Answer:
1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
Answer:
3.14...
Step-by-step explanation:
3.14159265358979323846
Find the area and the circumference of a circle with radius 8cm. Use the value 3.14 for π, and do not round your answers. Be sure to include the correct units in your answers.
Answers
Answer:
50.272 cm
Step-by-step explanation:
GIven
radius= 8cm
Pi= 3.142
Required
The circumference C
C= 2πr
substitute
C=2*3.142*8
C=50.272 cm
Hence the circumference is 50.272cm
SOMEBODY PLS HELP ASAPP!!!
A train car is in the shape of a right rectangular prism and has a volume of 540 cubic feet as shown.
feet
12 feet
What is the height of the train car?
A 10 feet
B. 12 feet
C 22.5 feet
D. 24 feet
Answers
Answer:
its c
Step-by-step explanation:
Which one of the following reasons does NOT explain why 2x + 3y ≠ 5xy?
Answers
Answer:
Since 2 and 3 are factors, they should be multiplied to get 6xy.
Step-by-step explanation:
The solution is Option B.
Since 2 and 3 are factors, they should be multiplied to get 6xy and the equation is False
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
2x + 3y ≠ 5xy
a)
If you substitute 4 for x and 5 for y in the expression 2x+3y, it does not equal 5(4)(5)
Substituting the value of x = 4 and y = 5 in the equation , we get
2 ( 4 ) + 3 ( 5 ) ≠ 5 ( 4 ) ( 5 )
8 + 15 ≠ 100
23 ≠ 100
Therefore , the statement is True
b)
Since 2 and 3 are factors, they should be multiplied to get 6xy
2x ( 3y ) = 6xy
But the equation does not equals 6xy
Hence , the statement is False and does not explain the given equation
c)
x and y are not like terms
The statement is true because the variables x and y are not the same
Therefore , the statement is True
d)
Adding x and y is not the same as multiplying x and y
The value of the equation x + y = x + y and on multiplying x and y = xy
And , x + y ≠ xy
Therefore , the statement is True
Hence , the equation 2x ( 3y ) = 6xy is False
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You decide to decrease your average room rate from $160/night to $150/night. What is your rate decrease percentage?
a) 6.25%
b) 6.66%
c) 10%
d) 16%