the area of the triangle formed by points of intersection of parabola y=a(x-3)(x+2) with the coordinate axes is 10. find a if it is known that parabola opens upward
Answer
1/4 × 6 × (5a) = 12
15a=12
a= 4/5
Step-by-step explanation:
The area of the triangle formed by points of intersection of parabola y=a(x-3)(x+2) with the coordinate axes is 10. The constant (a) of the function is 4.
How to find the if the parabola is open?The triangle formed by the parabola has a base equal to the distance between the points where the graph touches the x-axis and height (h) is the point where the graph touches the y-axis.
The points on the x-axis are the roots of the quadratic equation:
a(x-3)(x+2)=0
(x-3)(x+2)=0
x - 3 = 0
x = 3
or
x + 2 = 0
x = -2
So, the base is the distance between (-2,0) and (3,0).
Since they are in the same coordinate, the distance here;
b = 3 - (-2)
b = 5
The area of the triangle is 10. So
5a = 10 x 2
a = 4
The constant (a) of the function y = a(x-3)(x+2) is 4.
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slove for y . 3x+2y=-6
Answer:
y = -(6+3x)/2
Step-by-step explanation:
♪＼(*＾▽＾*)／＼(*＾▽＾*)／
Please help clarify answer and step by step explanation
Answer:
10
Step-by-step explanation:
When u cross multiply
[tex]5 \div x = 3 \div6[/tex]
= 3x=30(5*6)
= x=30/3
=x=10
The answer the problem
Answer:
The answers 528
put 2 and 5
Answer:
528
Step-by-step explanation:
:)
Help please will mark brainlist!!!
Answer:
radius was given
V=1570 ft cubed
Step-by-step explanation:
Volume of a cylinder= 3.14(r^2)h
=3.14(10^2)5
=15.7(100)
=1570
Consider the sequence 3, 9, 15, 21, ...
Enter numbers in the boxes to represent the second term as an ordered pair.
(
,
)
Answer:
The ordered pair to represent the second term as an ordered pair is:
(2, 9)Step-by-step explanation:
Background knowledge about the sequence function
A sequence is defined as the function whose domain is the set of natural numbers (counting numbers).
1, 2, 3, 4, .... n, ....
↓
a₁, a₂, a₃, a₄, .... aₙ, ....
Here,
1 gets mapped onto a₁,
2 gets mapped onto a₂, and so on
The numbers a₁, a₂, a₃, a₄, .... aₙ, .... are the terms of the sequence.
The number aₙ is the nth term of a sequence.
And the sequence function is denoted by {aₙ}.
Given the sequence
3, 9, 15, 21, ...
Here,
a₁ = 3 is the first term
a₂ = 9 is the second term
Thus, the ordered pair to represent the second term as an ordered pair is:
(2, 9)Is it yes or no ? Because I’m confused on this one
Answer:
Bet the answer is
half way
LOL its yes
Write an equation of the line that passes through the pair of points. (−4, −2), (4, 0)
Answer:
y = 1/4x-1
Step-by-step explanation:
Ok first, you need to find the slope:
0+2 = 2=1
4+4 = 8=4
Slope: 1/4
y=1/4x+b
Now you need to find the y intercept which is b. For that you can take a coordinate pair and substitute it in the equation to find b.
I will use (4,0)
0=1/4 X 4 + b
0=x+b
minus x on both sides. x=1
-1=b
An equation of the line that passes through the pair of points
(- 4, - 2), (4, 0) is y + 2 = (1/4)(x + 4).
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A line that passes through the pair of points. (−4, −2), (4, 0).
We also know slope(m) = (y₂ - y₁)/(x₂ - x₁) = (0 + 2)/(4 + 4) = 1/4.
So, the equation of a line in point-slope form is y - y₁ = m(x - x₁).
∴ y + 2 = (1/4)(x + 4).
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I need help ASAP please
Answer:
18 (-8 squared)
Eight classes from Hillsboro Middle School collected a total of 4,496 books for the library book sale. If each class collected the same number of books, how many did each class collect?
A. 560 books
B. 562 books
C. 570 books
D. 572 books
What is the approximate diameter of a sphere with a volume of 34 cm3?
A. 5 cm
B. 2 cm
C. 4 cm
D. 6 cm
Answer: B
Step-by-step explanation:d≈4.02
V Volume
34
r
d
r
d
d
r
Using the formulas
V=4
3πr3
d=2r
Solving ford
d=(6V
π)⅓=(6·34
π)⅓≈4.01939
What is the volume of the following rectangular prism? Plz help
Answer:
The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height *
Step-by-step explanation:
Find 4% of 1275- I couldn’t seem to figure this one out for some reason I dunno
Answer:
51
Step-by-step explanation:
4% as a decimal is 0.04, so you can just do 0.04 * 1275 = 51.
Answer:
-51
Step-by-step explanation:
ree
Decide whether or not the relation is a function.
[(0,1), (-5,4), (0,2), (5,-4)]
Answer:
The relation {(0,1), (-5,4), (0,2), (5,-4)} does NOT represent the relation.
Step-by-step explanation:
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
Given the relation
{(0,1), (-5,4), (0,2), (5,-4)}
From the given relation is clear that the input value x = 0 is repeated twice.
In other words, the input value x = 0 is duplicated.
As we have already mentioned that we can not have duplicated inputs as there should be only 1 output for each input.
Therefore, the relation {(0,1), (-5,4), (0,2), (5,-4)} does NOT represent the relation.
common difference -34,-44,-54,-64, -74
Answer:
Common difference = -10
Step-by-step explanation:
Given:
Series;
-34,-44,-54,-64, -74
Find:
Common difference
Computation:
Common difference = a2 - a1
Common difference = -44 - (-34)
Common difference = -44 + 34
Common difference = -10
Review the four points shown on the polar coordinate system.
On a polar coordinate plane, point A is at (5, StartFraction pi Over 6 EndFraction), point B is at (5, StartFraction 5 pi Over 6 EndFraction), point C is at (5, StartFraction 7 pi Over 6 EndFraction), point D is at (5, StartFraction 11 pi Over 6 EndFraction)
Which point has coordinates (5, negative StartFraction 7 pi Over 6 EndFraction)?
point A
point B
point C
point D
Answer:
The correct answer is D!!!
Step-by-step explanation:
I used the Desmos Polar graph and got the correct answer!!!
A point C reflected about polar-axis has coordinates [tex](5,-\frac{7\pi}{6} )[/tex]
What is polar coordinate system?"It is a two-dimensional coordinate system in which points are given by an angle and a distance from a central point. ""A point are given as [tex](r,\theta)[/tex], where r is the distance of the point from the pole, and [tex]\theta[/tex] is the measure of the angle."For given question,
We have been given four points.
[tex]A=(5,\frac{\pi}{6} ), B=(5,\frac{5\pi}{6} ),C=(5,\frac{7\pi}{6} ),D=(5,\frac{11\pi}{6} )[/tex]
If we plot the above points on the polar coordinate plane then it would be as shown below.
We need to find the point having coordinates [tex](5,-\frac{7\pi}{6} )[/tex]
If we reflect a point [tex]C(5,\frac{7\pi}{6} )[/tex] about polar-axis then the coordinates of the reflected point would be [tex](5,-\frac{7\pi}{6} )[/tex]
Therefore, point C reflected about polar-axis has coordinates [tex](5,-\frac{7\pi}{6} )[/tex]
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PLEASE HURRY!!!! nora calculated the scale factor to be 6/2.What error did she make? 1)she used the correct ratio of scale drawing dimension to original dimension,but she used the wrong corresponding sides. 2)she only used the dimensions of the scale drawing for her ratio. 3)she only used the dimensions of the original figure for her ratio 4)she should have multiplied the dimensions
Answer:
c
Step-by-step explanation:
Answer:
C is correct
Step-by-step explanation:
Taylor charges $15 for the first hour of dog walking and $10 for each additional hour or fraction of an hour. The rates that Lucy charges for x hours of dog walking are modeled with the function shown.
f(x) = LaTeX: \lbrace{LaTeX: \begin{matrix}\text{20x, 0 ≤ x ≤ 2}\\\text{10x, 2 4}\end{matrix}20x, 0 ≤ x ≤ 2 10x, 2 4
Who will charge more to walk a dog for 2.5 hours, Taylor or Lucy? How much more?
Who?:
How much more?:
Answer:
Taylor will charge more by $15
Step-by-step explanation:
Given
Taylor
First Hour = $15
Hourly Rate = $10
Lucy:
[tex]f(x) = \left \{ {{20x,\ 0 \le \ x \ \le 2} \atop {10x, x>2}} \right.[/tex]
For a dog walk of 2.5 hours.
Taylor's charges is:
[tex]Charges = First\ Hour + Hourly\ Rate * 2.5[/tex]
[tex]Charges = \$15 + \$10 * 2.5[/tex]
[tex]Charges = \$15 + \$25[/tex]
[tex]Charges = \$40[/tex]
Lucy's charges is:
Here, we consider
[tex]f(x) = 10x[/tex] Because [tex]x > 2[/tex]
i.e 2.5 > 2
So, Lucy's charges is:
[tex]Charges = 10 * \$2.5[/tex]
[tex]Charges = \$25[/tex]
By comparison;
Taylor will charge more by $15
The difference is calculated by:
[tex]Difference = \$40 - \$25[/tex]
[tex]Difference = \$15[/tex]
what is the value of the ( x ) in the equation 3x = - 15
Answer:
-5
Step-by-step explanation:
If Bob can run 3 miles in 27 minutes, how many miles
can Bob run in n minutes?
Answer:
e
Step-by-step explanation:
URGENT
Solve for x in the equation x squared minus 12 x + 36 = 90.
x = 6 plus-or-minus 3 StartRoot 10 EndRoot
x = 6 plus-or-minus 2 StartRoot 7 EndRoot
x = 12 plus-or-minus 3 StartRoot 22 EndRoot
x = 12 plus-or-minus 3 StartRoot 10 EndRoot
Answer:
It's A on edge
Step-by-step explanation:
Answer:
A.) x = 6 plus-or-minus 3 StartRoot 10 EndRoot
Step-by-step explanation:
bc im taking test :)
Jim is going to draw an enlargement of his favorite comic strip . In the comic strip , each frame is 2.5 in . long by 2 in . wide . Jim wants to draw each frame on a sheet of paper that is 11 in . long by 8.5 in wide . He wants to draw each frame as large as possible on the new sheet . Which scale should Jim use ?
Answer:
bts
Step-by-step explanation:
Find the area of the isosceles triangle.
13 cm is the side length
10 cm is the base length
what is the hight?
Answer:
23
Step-by-step explanation:
because 10+13 well hope that helps
*WILL MARK BRAINLIEST*
Find the scale factor.
A: 21
B: 10
C: 5.5
D: 3
what is a proportional relationship?
The range of the function RK) = R +26+1 İS {25, 643. What is the function's domain?
A. {5, 8}
B.
{-5, -8}
C.
{3,8}
D. {4,7}
E.
{4, 8}
Answer:
A
Step-by-step explanation:
hope this helped! please let me know if im wrong
The radius of a cone is 10 units and the height is 15 what is the volume?
Answer:
4712.38 - rounded to the nearest tenth- 4712.4
Step-by-step explanation:
r-10
h-15
v-Bh
pie x 10² x 15
Help with this please
Answer:
D. goes down and to the right
Step-by-step explanation:
name the x- and y- intercepts for equation 2x- y=6
Answer:
i dunno this im in third grade
Step-by-step explanation:
24. Paul's car holds a maximum of 19 gallons of gas. About how many
liters of gas does Paul need to fill his gas tank?
no
Answer:
71.915
Step-by-step explanation:
3.785= how many liters that are in a gallon X 19= gallons of gas needed to fill the tank
The number of liters in 1 gallon is 3.78541 therefore,71.92 liters Paul needs to fill in his tank.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
Given that,
The amount of fuel Paul's car holds = 19 gallons.
We know that,
1 gallon = 3.78541 liter
Multiply both sides by 19
19 gallon = 71.92 liter.
Hence "The number of liters in 1 gallon is 3.78541 therefore,71.92 liters Paul needs to fill in his tank".
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