Answer:
Basic parabola: y = ax2 + bx + c
We have 3 points we can plug in for (x, y) to create 3 simultaneous equations
(-2, 24): 24 = 4a - 2b + c {equation 1}
(3, -1): -1 = 9a + 3b + c {equation 2}
(-1, 15): 15 = a - b + c {equation 3}
Solve this system to find the values of a, b, c
Let's first eliminate variable c:
4a - 2b + c = 24 {equation 1}
a - b + c = 15 {equation 3}
--------------------- subtract
3a - b = 9
9a + 3b + c = -1 {equation 2}
a - b + c = 15 {equation 3}
-------------------- subtract
8a + 4b = -16
We now have two equations with 2 unknowns we can use to find a, b
3a - b = 9 {equation 4}
8a + 4b = -16 {equation 5}
Multiply equation 4 through by 4 and add equations
12a - 4b = 36
8a + 4b = -6
----------------- add
20a = 30
a = 30/20
a = 3/2
8a + 4b = -6
8(3/2) + 4b = -6
12 + 4b = -6
4b = -6- 12
4b = -18
b = -18/4
b = -9/2
Plug these 2 values into one of the original equations and solve for c
15 = a - b + c {equation 3}
15 = 3/2 + 9/2 + c
15 = 12/2 + c
15 = 6 + c
c = 15-6
c = 9
y = (3/2)x2 - (9/2)x+ 9
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Step-by-step explanation:
Jackson earned $327 in November. In December, he makes 3 times less money than he did in November. Write an equation to find the amount of money, m, that Jackson earned in December. Part 2: How much money does Jackson earn in December?
Answer:
Step-by-step explanation:
it is 327x3 3times then take answer and merge it with December and multiply that and you get your answer
Help due soon!
Walker is planning a summer vacation. He wants to visit Petrified National Forest and Meteor Crater, Arizona, the 50,000-year-old impact site of a large meteor. On a map with a scale where 2 inches equals 75 miles, the two areas are about 1 1/2 inches apart. What is the distance between Petrified National Forest and Meteor Crater?
Answer:
56.25 miles
Step-by-step explanation:
2 inches=75 miles
1 inch=37.5
1/2 inch=18.75
37.5+18.75=56.25
please mark me as brainliest!!<3
Find the slope, or rate of change, from the following ordered pairs:
please help me with this :(
Nick and June win some money and share it in the ratio 3:1. Nick gets 30 £60 more than June. How much did they get altogether
Answer:
£120
Step-by-step explanation:
With regards to the above, the difference between the ratio is
3:1 is 2
I.e
(3 - 1) = 2
Nick gets 2 extra, which is equal to £60
Therefore,
1 share = £60/2 = £30
June gets 1 share = 1 × £30 = £30
Nick would get = 3 × £30 = £90
Therefore, the value gotten by both would be;
= £30 + £90
= £120
Please help down below.
Answer:
Maybe the first?
Step-by-step explanation:
If the first choice was 8 yards by 4 yards, then it would be correct.
A reduction means a scale factor of less than 1, while the second, third, and fourth choices have scale factors of 6, 12, and 2 respectively.
is the graph below linear function or non- linear plxxx helppp
Answer:
It is non linear
Step-by-step explanation:
Linear means that it goes at a constant rate (aka a straight line)
This graph does not have a straight line so it is non-linear
how did the Bill of Rights affects us today.
Answer:
As a citizen, the Bill of Rights has a huge effect on us daily. As citizens, we are extremely lucky to have this document to protect and ensure all of our freedoms and rights.
Step-by-step explanation:
Which expression is equivalent to (-4y - x) - (3y - 9x)
Answer: -7y+8x
Step-by-step explanation: I assume you mean to simplify
Step 1: Remove parentheses : -4y - x - (3y - 9x)
Step 2: -(3y - 9x) = -3y + 9x
Step 3: Simplify: -4y - x - 3y +9x
Step 4: Answer: -7y+8x
A number b divided by 7 is less than or equal to 23.
Answer:
b [tex]\leq[/tex] 161
Step-by-step explanation:
Create an inequality:
[tex]\frac{b}{7}[/tex] [tex]\leq[/tex] 23
Multiply each side by 7, to isolate b:
b [tex]\leq[/tex] 161
So, the answer b [tex]\leq[/tex] 161
Answer:
b/7 ≤ 23
Step-by-step explanation:
This is the phrase written as an inequality.
Please help
A 108 square cm
B 63 square cm
C 139.5 square cm
D 171 square cm
so true i fo it all the time
Write a coordinate proof given quadrilateral ABCD with vertices A 3, 2), B (8, 2), C (5, 0), and D (0, 0).
Plot the point and graph the quadrilateral.
Graphing is pretty easy. Think of the x and y axis as a number line, you go to the right of 0 you get positive. You go to the left, you get negative. The x axis is just that, the y axis is just like a number line but flipped. You go up for positive and down for negative on the y axis. The middle point is always (0,0). To graph a shape, you just connect the points. To plot positive points you would go right and up. So to plot (8,2), you would go 8 points right on the x axis, then 2 points up on the y axis. Think of Quadrant I as 2 positive points, if both points are positive, plot them there. If you need to plot a negative point then a positive point you would go to Quadrant II. If both of the points are negative, plot them in Quadrant III. If it is a positive point then negative, go to Quadrant IV. Remember, the x axis always comes first. Always go right or left first, then up or down. You determine how many points to go right or left then up or down by the point given. Lets take another example. If you were told to plot (-1,5), that would go in Quadrant II. You would go left 1 and up 5. I explained the concept of the coordinate plane, although, I'm not sure what you mean by coordinate proof. Hope that helped :)
Find the missing angle.
Answer:
if its 80 on the other side and the are congruent
ITS C.80
Step-by-step explanation:
Answer:
80 Degrees
Step-by-step explanation:
All triangle angle measures must add up to 180 degrees.
You already have 80 and 20, so add them to get 100. The last angle is 80 degrees.
Decrease £16855.21 by 13.5%
Give your answer rounded to 2 DP.
Answer:
£ 14,579.75Step-by-step explanation:
= £16855.21 - ( £16855.21 x 13.5% )
100
= £ 14,579.75
Help me quickly just give the answer
Answer:
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
Divide by 2
32/2 = 16
Therefore-
16 books per box
put them in order from the least to greatest. You can use the number line to help!!
Answer: -1, -0.5, -1/10, 0.6
Step-by-step explanation:
-1/10 is the same thing as -0.1.
-0.5 < -0.1 < 0.6
A can of beans has surface area 337 cm2. It's heights is 11cm. What is the radius of the circular top?
Answer:
3.66 cm
Step-by-step explanation:
r = Radius of cylinder
h = Height of the cylinder = 11 cm
A = Total surface area of the cylinder = [tex]337\ \text{cm}^2[/tex]
Total surface area of a cylinder is given by
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r(r+h)\\\Rightarrow \dfrac{A}{2\pi}=r^2+rh\\\Rightarrow r^2+rh-\dfrac{A}{2\pi}=0\\\Rightarrow r^2+11r-\dfrac{337}{2\pi}=0\\\Rightarrow r^2+11r-53.64=0\\\Rightarrow 100r^2+1100r-5364=0\\\Rightarrow r=\dfrac{-1100\pm \sqrt{1100^2-4\times 100\left(-5364\right)}}{2\times 100}\\\Rightarrow r=3.66,-14.65[/tex]
So, the radius of the circular top is 3.66 cm.
i need help 2021 is bad already
Fraction from or decimal form but has to be rounded
Answer:
x = [tex]\frac{25}{6}[/tex]
Step-by-step explanation:
Given expression is,
[tex]2x-\frac{11}{4}x=-\frac{25}{8}[/tex]
[tex]\frac{8x}{4}-\frac{11}{4}x=-\frac{25}{8}[/tex]
[tex]\frac{8x-11x}{4}=-\frac{25}{8}[/tex]
[tex]-\frac{3x}{4}=-\frac{25}{8}[/tex]
[tex]\frac{3x}{4}\times 4=\frac{25}{8}\times 4[/tex]
[tex]3x=\frac{25}{2}[/tex]
[tex]\frac{3x}{3}=\frac{25}{2}\times \frac{1}{3}[/tex]
x = [tex]\frac{25}{6}[/tex]
Halley’s Comet has an elliptical orbit with the sun at one focus and a major axis of 1,636,484,848 miles. The closest the comet comes to the sun is 54,004,000 miles. What is the maximum distance from the comet to the sun? Round to the nearest whole number.
Answer:
1582480848 miles
Step-by-step explanation:
The maximum distance is another vertex of the major axis
1,636,484,848 miles - 54,004,000 miles = 1582480848 miles
Based on the calculations, the maximum distance from the Comet to the Sun is equal to 1,582,480,848 miles.
How to calculate the maximum distance from the Comet to the Sun?In this scenario, the elliptical orbit of the Comet with respect to the Sun at one focus and a major axis is equal to 1,636,484,848 miles. Also, the closest it came to the Sun is 54,004,000 miles.
Thus, we would divide the length of the major axis by the distance between the Comet and the Sun as follows:
Maximum distance = 1,636,484,848/54,004,000
Maximum distance = 1,582,480,848 miles.
Read more on maximum distance here: https://brainly.com/question/1992509
#SPJ2
2y=x
3x+3y=-18
please help
what is 61,090,000 expressed in scientific notation
Answer: = 6.109 × 107
Answer: 6.109 x 10^7
Step-by-step explanation: I think
The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks, and it will cost an additional $150 for each ton of sugar
transported.
Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this
equation to find the total cost to transport 19 tons of sugar.
Answer:
$2850 is the cost of 19 tons of sugar and $6350 is the cost of trucks and sugar
Step-by-step explanation:
Well if the trucks cost $3500. 19 x 150=$2850 the cost of 19 tons. 3500+2850=$6350 cost of sugar and trucks.
Answer:
Step-by-step explanation:
Now answer me that question because I will search them but I will not find them
Answer:
For which equations does the fraction 23 make the equation true? Select all that apply.
35 × □ = 20; I rewrote 35 as 351 and then multiplied 2 and 35 to get the numerator, and I multiplied 3 and 1 to get the denominator.
26 × □ = 18126; I rewrote 26 as 126 and then multiplied 1 and 2 to get the numerator, and I multiplied 3 and 26 to get the denominator.
48 × □ = 32; I rewrote 48 as 481 and then multiplied 2 and 48 to get the numerator, and I multiplied 3 and 1 to get the denominator.
22 × □ = 1423; I rewrote 22 as 221 and then multiplied 2 and 22 to get the numerator, and I multiplied 3 and 1 to get the denominator.
23 × □ = 15; I rewrote 23 as 123 and then multiplied 2 and 1 to get the numerator, and I multiplied 23 and 3 to get the denominator.
Answer:
27: -5/11
28: 4x^2+12x
29: (2b-7c+5a)(2b-7c-5a)
30: 2/3
Step-by-step explanation:
27 is pretty simple, start by multiplying both sides by 6
so we have 2(6y+1)=y-3
this equal 12y+2=y-3
Subtract 1y and 2 from both sides to get
11y=-5
divide and get y= -5/11
28: this one is a lot to write so if you need me to explain it leave a comment but I got 4x^2+12x
29: Same deal as 28
(2b-7c+5a)(2b-7c-5a)
30: For this one I just distributed then combined like terms to get y=2/3
The bearing of point B from point A is 064°.
Find the bearing of point A from point B.
Answer:
The bearing of A from B is 296 degrees
Step-by-step explanation:
Here, we want to find the bearing of point A from point B
To find the bearing of point A from B, we simply subtract the bearing of B from A from 360
Mathematically, that will be;
360 - 64 = 296 degrees
evaluate 62 in mathematics
Answer:
62
Step-by-step explanation:
62+7000000= 7000062 however when you divide that by its constant of the root of the sqared denominator, you get 4. THENNNN you add 3 to planks constand to get 62.
Please help !!
Solve for x:
-2
-2/3
-3/2
-3
Answer:
x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given 2 intersecting chords, then the product of the parts of one chord is equal to the product of the parts of the other chord, that is
18x = 9 × 3 = 27 ( divide both sides by 18 )
x = [tex]\frac{27}{18}[/tex] = [tex]\frac{3}{2}[/tex]
What is the slope of the line
You can see that for every one grid square to the right, the graph moves two grid squares up. Therefore the slope is 2.
Lions were introduced in the park in 2010. In 2012, the park has a population of 32 lions. A year later, in 2013, the park has 128 lions. Write an exponential function that models this situation. Let x represent the number of years since 2010 and let f(x)represent the number of lions.
Answer:
y = 2(4^(x))
Step-by-step explanation:
In 2012, the park has a population of 32 lions. A year later, in 2013, the park has 128 lions.
This means in 2012, it was 2^(5) lions while after 1 year it was 2^(7) lions
Thus, it increases every year by a ratio of 2^(2)
Thus, in 2011, it was 2^(5) - 2^(2) = 2^(3) lions
In 2010, it was 2^(3) - 2^(2) = 2
Since Lions were introduced in the park in 2010, using f(x), it means;
at x = 0, f(x) = 2
at x = 1, f(x) = 2^(3)
at x = 2, f(x) = 2^(5)
at x = 3, f(x) = 2^(7)
To find an exponential function that models the situation, let's use the generic formula: y = ab^(x)
At x = 0 and y = 2, we have;
2 = a × b^(0)
Thus,a = 2
At x = 1, y = 2^(3)
Thus; 2^(3) = 2 × b^(1)
b = 8/2
b = 4
So the exponential equation is;
y = 2(4^(x))
You can use the fact that the given figures are expressible as 2 raised to some powers.
The exponential function modeling the number of lions to the years passed since 2010 is given as
[tex]f(x) = 2^{1+2x}[/tex]
What is an exponential function?Those functions which are expressed as some constant raised to the power of the argument called exponential function.
How to find which function can model the given condition?Since 2012 - 2010 = 2 and the number of lions = 32 = [tex]2^5[/tex]
and 2013 -2010 = 3 and the number of lions =128 = [tex]2^7[/tex]
Thus, there is increment of 2 exponent as 1 year was changed.
Thus, we have:
[tex]f(x) = 2^{2x + a}[/tex] where a might be some constant( i took this form of exponent just by trial and error. It was already visible that one year was increasing double output, thus 2x and since there was just double increase and no other effect, there might be some non variable thing(a constant) so i thought to try some variable and see if this can work)
Since at x = 2, we get 2 raised to the power 5
thus.
[tex]2(2) + a = 5\\a = 1[/tex]
Thus,
The exponential function modeling the number of lions to the years passed since 2010 is given as
[tex]f(x) = 2^{1+2x}[/tex]
You can see that this will give correct output for x = 2 and x = 3
Learn more about exponential functions here:
https://brainly.com/question/15680851
Please help me.
Please
Answer:
1) x-intercept= (-6,0) y-intercept= (0,-3)
2) x-int= (2,0) y-int= (0,-5)
Step-by-step explanation:
Answer:
1) x = 2 and y = -4
2) x = 4 and y = 5
Step-by-step explanation:
to check if it's correct, simply plug in the numbers to the x and y value.
1) 2 + 2(-4)
2 + -8 = -6
(x + 2y = -6)
2) 5(4) - 2(5)
20 - 10 = 10
(5x - 2y = 10)
Solve for X: -5x - 7<28
Answer:
x < 7
Step-by-step explanation:
Given
5x - 7 < 28 ( add 7 to both sides )
5x < 35 ( divide both sides by 5 )
x < 7
Answer:
x>7
Step-by-step explanation:
Treat this inequality as a regular equation.
-5x<35
-x<7
x>7
(You switch signs if you divide with a negative btw.)