Answer: the roots are x = 20 and x = -8
Step-by-step explanation:
We have the function
y = (1/4)x^2 - 3x - 40
We want to find the roots, that are the points in where y(x) = 0
For a quadratic equation of the form:
y = a*x^2 + bx + c the roots are:
[tex]x = \frac{-b +-\sqrt{b^2 -4*a*c} }{2*a}[/tex]
in this case we have:
[tex]x = \frac{3 +-\sqrt{3^2 +4*(1/4)*40} }{2*(1/4)}= \frac{3 +-7}{(1/2)}[/tex]
So the two roots are:
x = 2*(3 + 7) = 20
x = 2*(3 - 7) = -8
find the two values that x can have if x2-12=37
Answer:
[tex]x2 - 12 = 37[/tex]
Step-by-step explanation:
Add 12 to both sides:
[tex]x2 - 12 + 12 = 37 + 12[/tex]
Simpilfy:
[tex]x2 = 49[/tex]
Simplify:
[tex]2x^{2} = 49[/tex]
Simplify:
[tex]\frac{2x^{2} }{2} = \frac{49}{2}[/tex]
[tex]x^{2} = \frac{49}{2}[/tex]
For x^2 = f(a) the solutions are x = [tex]\sqrt{f(a)} , - \sqrt{f(a)}[/tex]
x = [tex]\sqrt{\frac{49}{2} } , x = -\sqrt{\frac{49}{2} }[/tex]
-[tex]\sqrt{\frac{49}{2} } = -\frac{7\sqrt{2} }{2}[/tex]
x = [tex]\frac{7\sqrt{2} }{2} , x = -\frac{7\sqrt{2} }{2}[/tex]
Hope I helped, may I get brainliest and a thanks?
Thank you, have a good day! =)
Answer:
[tex]x = 7 \\ x = - 7[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 12 = 37 \\ {x}^{2} = 37 + 12 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7 \\ x = - 7[/tex]
will mark brainliest answer for fastest answer given
Answer:1/8
Step-by-step explanation:
there are 8 slices and its asking for the probability of one number. so its 1 out of 8
Answer: 1/4
Step-by-step explanation:
3 and 6 are multiples of 3. There are 8 possible options, and 2 multiples of 3.
2/8 = 1/4
I need help with this :/ pls help
Answer:
When you divide by 10^3, the decimal point moves three places to the right. When you multiply by 0.001, the decimal point moves three places to the right. So, both equal .0777
Step-by-step explanation:
what is the area of this triangle?
Answer:
1099.589 ft^2
Step-by-step explanation:
idk what happen to my answer but some bozo delete my answer but ehre you go again for any who has the same question:)
if the sides of a triangle and area is given. How to find perimeter
Answer:
add it up to see if it's 180
Answer:
Well since you have the sides you would add up all of the sides to find the perimeter.
Step-by-step explanation:
Anderson's Nursery was choosing between two different greenhouses. 2 greenhouses have a rectangular prism base with a length of 12 meters, width of 12 meters, and height of 10 meters. Greenhouse 1 has a square pyramid top with a base of 12 meters by 12 meters and height of 8 meters. Greenhouse 2 has a triangular prism top. The triangular sides have a base of 12 meters and height of 8 meters. The prism has a height of 12 meters. Which statements are true about the greenhouses? Select two options.
Question:
Anderson’s Nursery was choosing between two different greenhouses.
2 greenhouses have a rectangular prism base with a length of 12 meters, width of 12 meters, and height of 10 meters.
Greenhouse 1 has a square pyramid top with a base of 12 meters by 12 meters and height of 8 meters.
Greenhouse 2 has a triangular prism top. The triangular sides have a base of 12 meters and height of 8 meters. The prism has a height of 12 meters.
Which statements are true about the greenhouses? Select two options.
A) The space inside greenhouse 1 can be found using the equation V = 12 (12) (10) + one-half (12) (12) (8).
B) The space inside greenhouse 1 can be found using the equation V = 12 (12) (10) + one-third (12) (12) (8).
C) The space inside greenhouse 2 can be found using the equation V = 12 (12) (10) + one-half (12) (12) (8).
D) The space inside greenhouse 2 can be found using the equation V = 12 (12) (10) + one-third (12) (12) (8).
E) The space inside greenhouse 1 is 192 meters cubed greater than the space inside greenhouse 2.
Answer:
Options B & C are correct.
Step-by-step explanation:
Given that both greenhouses have a rectangular prism base with a length of 12 meters, width of 12 meters, and height of 10 meters.
L = 12 m
w = 12 m
h = 10 m
To find the volume of this rectangular prism, let's use the formula:
V = w*h*l
V = 12 * 12 * 10
V = 1440 m³
Then, greenhouse 1 has a square pyramid top with a base of 12 meters by 12 meters and height of 8 meters.
b = 12 x 12
h = 8
The volume of a square pyramid formula is:
V = ⅓*a²h
V = ⅓*12²*8
V = 384 m³
To find the total volume of greenhouse 1, let's add the volume of the rectangular prism and the square pyramid.
V = 12*12*10 + ⅓*12²*8
V = 1440 + 384 = 1824m³
Therefore, the space inside greenhouse 1 is 1824m³
Similarly, greenhouse 2 has a triangular prism top. The triangular sides have a base of 12 meters and height of 8 meters. The prism has a height of 12 meters.
b = 12 m
h = 8 m
height of prism = 12 m
To find the volume of a triangular prism, we have:
½*(bh) * h
V = ½(12*8)*12
V = 576 m³
To find the total volume of greenhouse 2, let's add the volume of the rectangular prism and the triangular prism.
V = (12 * 12 * 10) + (½(12*8)*12)
V = 1440 + 576
V = 2016 m³
Therefore, the space inside greenhouse 2 is 2016m³
From the calculations above the correct options would be:
(B) The space inside greenhouse 1 can be found using the equation V = 12 (12) (10) + one-third (12) (12) (8).
(C) The space inside greenhouse 2 can be found using the equation V = 12 (12) (10) + one-half (12) (12) (8).
Options A, D and E are wrong.
Option E is wrong because the space inside greenhouse 1 is (1824-2016 = -192) 192 meters cubed lesser than the space inside greenhouse 2.
Answer:
THE ANSWERS ARE.... B AND C
B: The space inside greenhouse 1 can be found using the equation V = 12 (12) (10) + one-third (12) (12) (8).
C: The space inside greenhouse 2 can be found using the equation V = 12 (12) (10) + one-half (12) (12) (8).
Step-by-step explanation:
i just took it on EDGE 2020. I hope it helps :)
What is the circumference of the circle? Use 3.14 for pi r=6.4 cm circle
So the right answer is of option B.
Look at the attached picture
Hope it will be helpful to you..
Good luck for your test...
what is the solution of this equqtion? 1w= -17
Answer:
-17
Step-by-step explanation:
1w= -17
(1)(-17)=
-17
Answer:
-17
Step-by-step explanation:
in this situations, we normally divide both sides by the number next to the unknown.
1w is the same as saying w
so,
w = -17
Need help ASAP. WILL MARK BRAINLIEST.
Answer:
5pi
Step-by-step explanation:
Thank you for helping me
Answer:
thank you for giving me points ;)
Step-by-step explanation:
Need Help Asap offering 10 Points!!!!
Answer:
13 minutes 30 seconds.
Step-by-step explanation:
You just divide 10.8 by 0.8...
10.8÷0.8=13.5
Solve for the height (h) of this triangular prism if the volume is 1080. The
volume of a triangular prism is V = (B)(h), where B is the area of the
triangle. Remember the area of a triangle is 1/2(b)(h). BE CAREFUL
BECAUSE THERE ARE TWO HEIGHTS, ONE FOR THE TRIANGLE AND ONE
FOR THE TRIANGULAR PRISM. *
h
15
8
Answer: 18
Step-by-step explanation:
Area of triangle = (0.5) × base(b) × height(h)
Base of triangle = 8
Height of triangle = 15
Area of triangle = (0.5) × 8 × 15 = 60
Volume of triangular prism = B × height
Where h = height
B = area of triangle
Volume of triangular prism = 1080
Find the height(h) of the triangular prism
Volume of triangular prism = B × height
1080 = 60 × h
h = 1080 / 60
h = 18
Please answer i'll give brainlist
AD and BE are diameters. What is the measure of arc EDC
A. 125 degrees
B. 145 degrees
C. 235 degrees
D. 215 degrees
Answer:
a
Step-by-step explanation:
a1 = 92 cm
b1 = 66.7 cm
a2 = 38 cm
b2 = 53.42 cm
h = 52 cm
Answer:
area=250.12. perimeter=3380
Step-by-step explanation:
can net worth be negative?
Answer:
our net worth can tell you many things. If the figure is negative, it means you owe more than you own. If the number is positive, you own more than you owe. ... Negative net worth does not necessarily indicate that you are financially irresponsible; it just means that – right now – you have more liabilities than assets
Step-by-step explanation:
hope it help
Yes, of course. A good fraction of the people on earth owe more than they own, so have negative net worth.
In the USA about 14% of the households have negative net worth. I would have guessed that credit card debt was the culprit, but it's mostly student loans that drag folks into this category.
So do i divide by 2 each time?
Find the midpoint of the segment with the following endpoints (6,3) and (10, – 7)
Answer:
-5/2
Step-by-step explanation:
-7-3/10-6 = -10/4 which equals -5/2
What are opposite numbers
Answer:
Opposite numbers are numbers that, when placed on a number line, are the exact same distance away from the 0, but on opposite sides/opposite directions
Answer:
Opposite number or additive inverse of any number (n) is a number which, if added to n, results in 0, the identity element of addition. The opposite number for n is written as −n. For example, −7 is opposite to 7, because with −7+7=0
You can say that the opposite number of a number, is the negative version of the positive number. This is what the opposite of 7 is or the opposite of -7.
A rectangular prism has a length of 12in, a height of 5in, and a width of 8in. What is its volume, in cubic in?
Answer: The volume is 480 in^3
Step-by-step explanation:
v= lwh
v= 12 * 5 * 8
v= 480 in^3
Answer:
Volume of the rectangular prism = [tex]480in.^{3}[/tex]
Step-by-step explanation:
Formula for the volume of a rectangular prism= Ah, where A= base area
& h= height
Base area(A)= Length×Width
= 12in.×8in.
= [tex]96in.^{2}[/tex]
Since height=5in.,
Volume= [tex]96in.^{2}[/tex]×5in.
= [tex]480in.^{3}[/tex]
Hope this helps!!!
Pls mark as brainliest
What is the end behavior of the polynomial function?
Answer:
D) as x approaches neg. infinity, y approaches neg. infinity
Step-by-step explanation:
This is because you get to negative x infinity which is towards the right, you see that the y value is going down sharply as well towards the direction of negative infinity in y direction (x direction is right to left and y direction is up and down)
Answer:
D one Edge 2021 ;))
Step-by-step explanation:
The oblique prism has a rectangular base with a width of 10 units and a length of 13 units.
An oblique prism with a rectangular base is shown. The rectangular base has a width of 10 units and a length of 13 units. The distance between the top and the bottom base is 17 units. The top base extends 8 units to the right of the bottom base.
The top base extends 8 units to the right of the bottom base. What is the volume of the prism?
Answer:
Volume of the prism = 1950unit³ (C)
Step-by-step explanation:
The question is incomplete without the diagram of the oblique prism and its dimension.
Find attached the diagram used in solving the question.
The prism has a rectangular base:
width= 10 units
length = 13 units
The distance between the top and the bottom base = 17 units.
Volume of prism = Area of base × height
Area of base = area of rectangle = Length ×width
= 13× 10
Area of base = 130unit²
To get the height, we would apply Pythagoras theorem
Hypotenuse² = opposite² + adjacent ²
17² = h² + 8²
289 = h² + 64
h² = 289-64 = 225
h = √225
h = 15unit
Volume of the prism = 130 × 15
Volume of the prism = 1950unit³ = 1950 cubic units
Answer:
The answer is C which is 1950 on EDGE
Step-by-step explanation:
Someone help me please
Step-by-step explanation:
Step 1: Convert degrees into radians
[tex]\frac{degrees}{1}*\frac{\pi }{180}[/tex]
[tex]\frac{52}{1}*\frac{\pi}{180}[/tex]
[tex]\frac{52\pi}{180}[/tex]
[tex]\frac{13\pi}{45}[/tex]
Step 2: Find the arc length
[tex]S = r\theta[/tex]
[tex]S=(3)(\frac{13\pi}{45})[/tex]
[tex]S = \frac{39\pi}{45}[/tex]
[tex]S=\frac{13\pi}{15}[/tex]
Answer: Option B
Find the greatest common factor of 24, 40 and 60
Please answer asap ty!!
Answer:
4
Step-by-step explanation:
Answer:
GCF=4
Step-by-step explanation:
It's 4
24/4=6
40/4=10
60/4=15
You can't go any higher because there is no GCF of 6, 10, and 15.
3. Which of the following represents a function?
O (5, 1), (5,2), (5, 3), (5, 4)
O (-1,2), (-2, 1), (-1, -2), (-2,-1)
O (3, 4), (-3, 2), (3, 8), (5,5)
O (2, 3), (4, 3), (-2, -3), (-4,-3)
Answer: D is a function.
Step-by-step explanation:
A function need to have exactly one output to each input.
Answer: D. (2, 3), (4, 3), (-2, -3), (-4,-3)
Step-by-step explanation: This represents a function because they're the opposing of each other. Hope this helps happy holidays! :)
What is the distance between the points (4, 5) and (10, 13) on a coordinate plane?
A. 10 units
B. 14 units
C. 12 units
D. 8 units
Answer:
10
Step-by-step explanation:
Distance = √(x2-x1)² + (y2-y1)²
d = √(10-4)² + (13-5)²
d = √6² + 8²
d = √36+364
d = √100
d = 10
translate (-4,5) up 3 units
then reflect the result over the y-axis
what are the coordinates of the final point?
Answer:
4,8
Step-by-step explanation:
reflecting over y axis is flipping to the other side. and you are going up 3 points so 5+3 is 8. and negative four turns to positive four
3. Nine books are to be bought by a student. Some
cost $6 each and the remainder cost $6.50 each.
If the total amount spent was $56, how many
books at each price are bought?
Answer:grjjrd
Step-by-step explanation:fdfgdjj
Pierce is making a rectangular frame for a photo collage that has a perimeter of 72.2 72.2 inches. The length of the frame is 20.3 20.3 inches. Write an equation to find the width of the frame, x
Answer:
[tex] P = 2x+2y[/tex] (1)
And we know that the lenght is y = 20.3. If we solve for x from equation (1) we got:
[tex] P-2y = 2x[/tex]
[tex] \frac{P-2y}{2} =x[/tex]
And replacing we got:
[tex] x = \frac{72.2 in -2*20.3 in}{2}= 15.8 in[/tex]
And the width for this case would be 15.8 in
Step-by-step explanation:
For this case we know that the photo is rectangular. Let's define:
x = the width, y= the length
And we know that the perimeter is given by:
[tex] P = 2x+2y[/tex] (1)
And we know that the lenght is y = 20.3. If we solve for x from equation (1) we got:
[tex] P-2y = 2x[/tex]
[tex] \frac{P-2y}{2} =x[/tex]
And replacing we got:
[tex] x = \frac{72.2 in -2*20.3 in}{2}= 15.8 in [/tex]
And the width for this case would be 15.8 in
help me plzzzzzzz!!!!
[tex] {y}^{2} + 14 = 3 {y}^{2} \times 5[/tex]
Answer:
[tex]y=1,\:y=-1[/tex]
Step-by-step explanation:
[tex]y^2+14=3y^2\cdot \:5\\\y^2+14-14=3y^2\cdot \:5-14\\y^2=15y^2-14\\y^2-15y^2=15y^2-14-15y^2\\-14y^2=-14\\\frac{-14y^2}{-14}=\frac{-14}{-14}\\y^2=1\\\\y=\sqrt{1},\:y=-\sqrt{1}\\y=1,\:y=-1[/tex]
Answer:
y = ± 1
Step-by-step explanation:
Given
y² + 14 = 3y² × 5, that is
y² + 14 = 15y² ( subtract y² from both sides )
14 = 14y² ( divide both sides by 14 )
1 = y² ( take the square root of both sides )
± [tex]\sqrt{1}[/tex] = y , that is
y = ± 1
Thus y = - 1 or y = 1
what is the y-intercept of the equation y=-x?
Answer:
0,0
Step-by-step explanation:
