Answers
Answer:
(d) y = 3x² +2x -6
Step-by-step explanation:
The equation of a parabola through thee points can be found different ways. One is to use a quadratic regression tool. Another is to write and solve linear equations in the coefficients. (3 equations in 3 unknowns).
__
Here, we can eliminate answer choices that don't work to arrive at the correct answer choice.
The point (0, -6) is the y-intercept of the function. That means the value of the constant term in the quadratic is -6. (Eliminates A and C.)
The y-values of the other two points are both greater than -6, indicating the parabola opens upward. That means the leading coefficient is positive. (Eliminates B.)
The only reasonable choice is D:
y = 3x² +2x -6
__
Additional comment
You get the same answer if you use a regression tool.
Answer:
[tex]y = 3\, x^{2} + 2\, x - 6[/tex].
Step-by-step explanation:
In general, the equation of a parabola is in the form [tex]y = a\, x^{2} + b\, x + c[/tex] for some constants [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex], where [tex]a \ne 0[/tex].
Let [tex]y = a\, x^{2} + b\, x + c\![/tex] denote the equation of this parabola for some constants [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] where [tex]a \ne 0[/tex]. A point [tex](x_{0},\, y_{0})[/tex] is on this parabola if and only if the equation of this parabola holds after substituting in [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex]:
[tex]y_{0} = a\, {x_{0}}^{2} + b\, x_{0} + c[/tex].
Thus, each of the three distinct points on this parabola would give a equation about [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex]:
The equation for [tex](-3,\, 15)[/tex] would be [tex]15 = (-3)^{2}\, a + (-3)\, b + c[/tex].The equation for [tex](0,\, 6)[/tex] would be [tex]6 = 0^{2}\, a + 0\, b + c[/tex].The equation for [tex](2,\, 10)[/tex] would be [tex]10 = 2^{2}\, a + 2\, b + c[/tex].Simplify the equations:
[tex]\left\lbrace\begin{aligned}& 9\, a - 3\, b + c = 15 \\ & c = 6 \\ & 4\, a + 2\, b + c = 10\end{aligned}\right.[/tex].
Solve this linear system of three equations and three unknowns for [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex]:
[tex]\left\lbrace \begin{aligned} & a = 3 \\ & b = 2 \\ & c = (-6) \end{aligned}\right.[/tex].
Therefore, the equation of this parabola would be:
[tex]y = 3\, x^{2} + 2\, x - 6[/tex].
Related Questions
What is the equation of the blue line?
Answers
Answer:
y = 2x + 3
Step-by-step explanation:
Get any two points on the line, say (0, 3) and (2, 7)
Slope = (7 - 3)/(2 - 0) = 4/2 = 2
y = 2x + b
use (0, 3), x = 0, y = 3
3 = b
so the equation is y = 2x + 3
LEVEL:EASY. MATH: WHICH SITUATIONS SHOWS INTERSECTING LINES?
CHOOSE ANSWER:
A. HANDS OF A CLOCK AT 9:00.
B. CORNER OF A BUILDING.
C. HORIZONTAL BARS.
D. CAPITAL LETTER X.
PLEASE HELP ME
Answers
Answer:D) because x had two lines that split through each other.
Step-by-step explanation:
Examine the two boxes.
Box A
Box B
How much greater is the surface area of Box A than Box B?
Answers
Answer:
Box A is greater than Box B by 34.
Step-by-step explanation:
First, you need to start with finding the surface area of every individual side on Box A we have side A, B, and C. After finding the individual area for each side, double each area because there is two of each side. This is the the same method you apply to Box B.
Then subtract the surface area of Box B from Box A.
Find the slope of the line passing through the points (-4,8) and (-8,5)
Answers
Answer:
[tex] \frac{3}{4} [/tex]
Step-by-step explanation:
Slope formula:
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
Slope
[tex] = \frac{8 - 5}{ - 4 - ( - 8)} [/tex]
[tex] = \frac{3}{ - 4 + 8} [/tex]
[tex] = \frac{3}{4} [/tex]
Please give me right answer i mark you brainliest if you answer fast , At a stationery sale, pencils were sold in packets of 4 and erasers were sold in packets of 6. The cost of a packet of pencils was the same as the cost of a packet of erasers. Mrs Tan bought 12 pencils for $6. What was the cost of a packet o erasers?
Answers
Answer:
The answer is $2
I packet has 4 pencils so 12 pencils is 3 packets
if 3 packets cost $6 1 packet costs $2 and since 1 packet of pencils is the same price as one packet of erasers 1 packet of erasers cost $2
Identify the percent of change as an increase or a decrease. 9 points to 4 points
Answers
Answer:
Decrease of 55.6%
Step-by-step explanation:
Because it clearly decreased,
9 - 4 / 9
5 / 9
55.6% decrease
what is the distance between the points C(2,-3) and d(10,-3)
Answers
Kindly help me to solve.
Answers
Answer:
statement : ABCD is a parellogram reason: given
mathematics help ...
no links
Answers
Answer:
Ok ------------------
What is the scale factor in the dilation?
10
y
9
8
image
7
6
5
4
NA
3 pre-image
2
1 -
+
12
3
4
5
B 7
8 9 10 x
Answers
Answer:
the scale factor in the dilation is 1/3
Step-by-step explanation:
image-9
preimage -3
3/9 = 1/3
Answer:1/3 or c
Step-by-step explanation:
just got it right in edgn gimme brain pls
What is the surface area of a cone that has a radius of 5 units and a
height of 10 units? Use 3.14 for i and round your answer to the
nearest whole number.
Answers
Answer:
254 units^2
I took the test and got it correct.
The surface area of a cone that has a radius of 5 units and a
height of 10 units is 508.06 square units.
What is surface area?Surface area is the total area of the exposed surfaces of a three-dimensional object. It is the sum of all the areas of the exposed faces of the object, including any curved surfaces. The formula to find the surface area of a cone is A=πr(r+√(h²+r²)).
Given that, radius of a cone is 5 units and the height of a cone is 10 units.
Surface area = 3.14×10(5+√(10²+5²)
= 508.06 square units
Therefore, the surface area of a cone that has a radius of 5 units and a
height of 10 units is 508.06 square units.
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fill in the equation please
Answers
Answer:
57753.
Step-by-step explanation:
Basta pm na Lang.
Find a polynomial equation with real coefficients that has the given roots.
3 and -9i
x^3-?x^2+?x-?=0
Answers
Answer:
Step-by-step explanation:
(x - 3) (x - 9i) (x + 9i) = 0
(x - 3) (x² + 81) = 0
x³ - 3x² + 81x - 243 = 0
The sum of two numbers is 12 and half of them is twice the other.
What numbers are they?
Answers
Answer:
4+8 I think.. this is poorly worded question so I am not sure it might be something smaller like 10+2
Step-by-step explanation:
Let f(x)=x-2 and g(x) = x^3 . What is (f•g)(2)
Answers
Answer:
f(x)=x2
g(x)=3x+2
(f+g)(x)=x2+3x+2=(x+1)(x+2)
Step-by-step explanation:
Explanation:
a.
A student writes an explicit formula to represent the value of the
computer after n years below. What is the student's error? Explain. (2 points)
an= $1,500 (-15)n-1
Answers
Using exponential function concepts, it is found that the student error is in the subtraction of the day rate, as he forgot to subtract from 100% = 1.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the initial value of the computer is of A(0) = 1500, while it decays at a rate of 15% a year, hence r = 0.15 and the equation is:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 1500(0.85)^t[/tex]
Or equivalently, as a sequence:
[tex]a_n = 1500(0.85)^{n-1}[/tex]
Hence, it is found that the student error is in the subtraction of the day rate, as he forgot to subtract from 100% = 1.
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Noa is thinking of two fractions that a sum of 3/5. Each has a numerator of 1. What are the denominators of the fractions
Answers
Answer:
The denominators of the fractions are 2 and 10.
The fractions with numerators of 1 that have sum of 3 / 5 is calculated below
The sum of the fractions are 3 / 5. Each of the fractions have a numerator of 1. Therefore, let the denominators be x and y
1 / x + 1 / y = 3 / 5
Therefore,
1 / x + 1 / y = 3 / 5
y + x / xy = 3 / 5
cross multiply
5y + 5x = 3xy
Using hit and trial method,
5(2) + 5(10) = 3(10)(2)
10 + 50 = 60
60 = 60
The values are same.
Therefore, the denominators are 2 and 10.
Step-by-step explanation:
Whats the answer for 12.3 x 1.2 =
Answers
14.76
12.3
*
1.2. =14.76
Answer:
14.76
Step-by-step explanation:
12.3 x 1.2=
12.3
x 1.2
--------
24.6
+123.0
---------
14.76
4. Randall's monthly water bill from April to July is listed in the table below. What was the percent
increase in his bill from May to July?
Answers
Answer:
175
Step-by-step explanation:
Divide. 136.50 divided by 78 then times it by 100 and you get it 175
The percent increase is 56.41%.
what is percent increase?We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage. The percentage increase formula is provided by:
percentage increase = (increase in amount /original amount ) x 100
Given:
Bill in may month- 78
Bill in June month = 122
So, change in amount= 122 - 78 = 44
So, percent increase = 44/ 78 x 100
percent increase = 0.5641 x 100
percent increase = 56.41%
Hence, the percent increase is 56.41%.
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can someone pls help me with this
Answers
Answer:
Okay so basically the variables are y and x. Variables in math are just numbers next to a number to represent an unknown number. The coefficient is the number in-front of a variable. The constant would be 5. Think of constants as numbers with variables or negatives or anything. They are pretty much just there. Now as for terms. Terms are just numbers that are part of the equation. Hope this helped!
Step-by-step explanation:
You wish to test the following claim ( Ha) at a significance level of α=0.02
H0:μ1=μ2
Ha:μ1≠μ2
You believe both populations are normally distributed, but you do not know the standard deviations for either. We will assume that the population variances are not equal.
You obtain a sample of size n1=16 with a mean of M1=66.2 and a standard deviation of SD1=10.6 from the first population. You obtain a sample of size n2=26 with a mean of M2=68.8 and a standard deviation of SD2=12.9 from the second population.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? For this calculation, use the conservative under-estimate for the degrees of freedom. The degrees of freedom is the minimum of n1 - 1 and n2 - 1. (Report answer accurate to four decimal places.)
p-value =
Answers
Answer:
Since we assume the variances of the two populations are the same, we can use the pooled variance in the computation of the t-statistic:pooled variance (Sp^2) = (n1-1)s1^2 + (n2-1)*s2^2 / (n1 + n2 - 2) = (13-1)*19.4^2 + (19-1)*12.6^2 / (13 +19- 2) = 245.8Sp = 15.67t-calc = (mean1 - mean2)/ (Sp * sqrt(1/n1 + 1/n2)) = (83.6-72.9)/(15.67 * sqrt(1/13 + 1/19) = 1.897since this is a right tailed test, the p-value = P(t > 1.897) at n1 + n2 - 2 = 30 degrees of freedom = 0.0337so would not reject.
Step-by-step explanation:
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Out of 3500 students of a school, only 36% passed. How many students failed?
Answers
Answer:
2240
Step-by-step explanation:
If 36% out of 100% passed, then
100% - 36% = 64% failed
64% of 3500 = 0.64 × 3500 = 2240
Explanation: using the percentage, move the decimal back two spaces.
36 >>> 3.6 >>> 0.36
Now multiply 0.36 times 3500 to find out how many students PASSED. You get 3500 x 0.36 = 1260.
Finally, to find out how many FAILED, subtract how many PASSED (1260) from the total (3500) to get 3500 - 1260 = 2240
What is the value of x & y? *
1 point
x = 11.25 and y = 18.75
x = 12.25 and y = 18.75
x = 11.25 and y = 16.45
x = 14.28 and y = 17.95
x = 10.25 and y = 20.75
Answers
Answer:
x = 11.25 and y = 18.75
Step-by-step explanation:
ΔABD ≅ ΔBCD
⇒ 20 : 15 = 15 : x
⇒ 20/15 = 15/x
⇒ x = 15 × 15/20
⇒ x = 11.25
⇒ 25 : 20 = y : 15
⇒ 25/20 = y/15
⇒ y = 25/20 × 15
⇒ y = 18.75
WILL GIVE BRAINLIEST
Answers
Answer:
Step-by-step explanation:
Rational Number: -9, 5/8, 30/√25
Irrational Number: √70, π
i neeeeeeeeeeeeeeeeeeddddddddddddddd helpppp
A company sells each product they make for $90.00. They pay $2,300.00 in monthly costs, such as rent and bills, as well as $75.00 in manufacturing costs per unit. If the company sold 495 units last month, what was their total profit?
A.
$34,825.00
B.
$6,610.00
C.
$42,175.00
D.
$5,125.00
Answers
Answer:
Option D
Step-by-step explanation:
Given the following question:
Product costs: $90
Monthly bills: $2,300
Manufacturing costs: $75
How much profit did they make in one month if they sold 495 units?
In order to find the answer, we first need to multiply the cost of the product by the units sold last month, then subtract the bills/manufacturing costs.
One unit = 90 dollars
495 units sold last month
[tex]90\times495=44550[/tex]
[tex]=44550[/tex]
The company made 44,550 from the product last month.
Now apply the fees/costs:
2,300 dollars in monthly costs
75 dollars in manufacturing costs PER UNIT
[tex]44550-2300=42250[/tex]
[tex]75\times495=37125[/tex]
[tex]42250-37125=5125[/tex]
[tex]=5125[/tex]
Which means the company made a total profit of "$5,125 dollars" or option D last month.
Hope this helps.
It takes 5 minutes for an individual to shower. Of each person showers twice per day, approximately how long does each person spend showering in a year?
Answers
Answer:
c
Step-by-step explanation:
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Each person spends 2.53 days showering in a year.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
Given that,
Time taken by one person to shower = 5 minutes.
Also, one person take shower 2 times in a day.
Total time taken to shower twice per day = 5 x 2 = 10 minutes.
Since, in one year total number of days = 365.
Time taken to shower in 365 days = 365 x 10 = 3650 minutes.
In one day total number of minutes = 24 x 60 = 1440 minutes.
Total days = 3650 / 1440 = 2.534722 days = 2.53
Person showers for 2.53 days in a year.
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Naomi's car can go a maximum
of 125 miles on 1 tank of gas.
She has already driven 5 miles
on her current tank. If it takes
her 30 miles roundtrip to get
to work, how many times can
she drive to work before she
has to fill
up
the tank?
Answers
Answer:
89 she drive to work befor she has to fill
Answer:
4 round tripes
Step-by-step explanation:
First, subtract the miles she has already driven
125 - 5 = 120
Then divide the difference of the miles she has already driven
120 ÷ 30 = 4
HELP ME OUT PLS!!!!!!
This is the same triangle you used for Question 2.
Triangle ABC has angle measures as shown below.
Using the information in the diagram, and the value of x that you calculated in Question 2, find the measure of Angle C.
In your answer, give the measure of Angle C and explain how you calculated it.
Answers
here it is the sum of interior angles of a triangle =180
Answer:
35+3 x+2 +52=180
35 +3x+6+52=180
93+3x=180
3x=87
x=87
---
3
x= 29
c=3[x+2]
substituding
c=3[29+2]
c=3x31]
c=93
35+93+52=180
i wrote it down so yall can copy and paste
The scale model of a car is 5% of the size of the actual car. The length of
the model is 9 inches. How many feet long is the actual car? Show your work below.
Answers
Answer:
45 actual car
Step-by-step explanation:
magaceega faatima
select the correct word form for 444,404
Answers
Answer: four hundred forty-four thousand four hundred four.
Step-by-step explanation: Student instructed to give the word form of a given number.
Answer:
four-hundred forty-four thousand four-hundred and four
Step-by-step explanation:
Because i know this