To solve this question:
First, we need to know the standard equation of a parabola.Then, with the three points given, we can build a system of three equations.Doing this, we get that the system is, with the 3 equations:
[tex]9a^2 + 3b + c = 8[/tex]
[tex]75a + 15b + 3c = 20[/tex]
[tex]36a + 6b + c = 5[/tex]
Equation of a parabola:
A parabola is a second degree polynomial, having an standard equation of:
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
Point (3,8)
This means that when [tex]x = 3, y = 8[/tex]. So
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]8 = a\times3^2 + 3b + c[/tex]
[tex]9a^2 + 3b + c = 8[/tex]
Thus, [tex]9a^2 + 3b + c = 8[/tex] is the first equation.
(5,20/3)
This means that when [tex]x = 5, y = \frac{20}{3}[/tex]. Thus
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]\frac{20}{3} = a\times5^2 + 5b + c[/tex]
[tex]25a + 5b + c = \frac{20}{3}[/tex]
[tex]75a + 15b + 3c = 20[/tex]
Thus, [tex]75a + 15b + 3c = 20[/tex] is the second equation.
(6,5)
This means that when [tex]x = 6, y = 5[/tex]. Thus
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]5 = a\times6^2 + 6b + c[/tex]
[tex]36a + 6b + c = 5[/tex]
Thus, [tex]36a + 6b + c = 5[/tex] is the third equation.
After all, the system of equations is:
[tex]9a^2 + 3b + c = 8[/tex]
[tex]75a + 15b + 3c = 20[/tex]
[tex]36a + 6b + c = 5[/tex]
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Rochelle is riding a bicycle whose wheels are 26 inches in diameter
A car travels 90 miles in 1.5 hours. How many miles will it travel in 5 hours if its speed remains the same? A) 60 miles B) 180 miles Eliminate C) 222 miles D) 300 miles
HURRY I NEED THE ANSWER.
Which equation represents a line that passes through two points in the table
Answer: C
Step-by-step explanation: A P E X
There are 16 apples in a basket. 9 of these apples are green. the rest of them are red. (a) what is the ratio of all apples in the basket to red apples? (b) what is the ratio of red apples to green apples?
The ratio of (a) the ratio of all apples in the basket to red apples = 16/7 and (b) the ratio of red apples to green apples = 7/9
What is ratio?The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
There are 16 apples in a basket.
9 of these apples are green.
The rest of them are red.
So,
(a) To find the ratio of all apples in the basket to red apples,
Number of apples / number of red apples
= 16/9
(b) To find the ratio of red apples to green apples,
The number of green apples = 16 - 9 = 7
Number of red apples / number of green apples
= 7/9
Therefore, the ratio (a) 16/9 and (b) 7/9
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Jonah has collected 91 coins worth $7.20 in his piggy bank. his collection includes only dimes and nickels. how many dimes are there in jonah's piggy bank?
What is the formula for the sum of interior angles of a regular polygon?
Javier bought a microwave for $150. The cost was 30% off the original price, what was the original price
evaluate the expression 6+[(-24)÷6]/19
Subtract (4x − 3y) from the sum of (12x + 9y) and (−2y).
first step sum means addition so (12x+9y) +(-2y) = 12x +7y
second step subtract (4x -3y) from (12x+7y)
need to use the distributive property:
12x +7y - 4x - -3y =
12x + 7y - 4x +3y
combine like terms
8x+10y
Answer has been edited.
Answer:
Subtract (4x − 3y) from the sum of (12x + 9y) and (−2y) is 8x + 10y .
Step-by-step explanation:
As given the expression
(12x + 9y) , (-2y) and (4x − 3y) .
First add the expression (12x + 9y) and (-2y) .
= (12x + 9y) - (2y)
First open the bracket
= 12x + 9y - 2y
= 12x + 7y
Now subtracted (4x − 3y) from 12x + 7y .
= 12x + 7y - (4x - 3y)
= 12x - 4x + 7y + 3y
= 8x + 10y
Therefore the Subtract (4x − 3y) from the sum of (12x + 9y) and (−2y) is 8x + 10y .
The equation e=1200+11t represents your elevation e in feet for each minute t you hike from a trailhead. If you graphed this equation, what would the slope represent?
If an asset declines in value from $5000 to $3500 over nine years, what is the mean annual growth rate in the asset's value over these nine years? Round your answer to two decimal places.
Mean annual growth rate in the asset’s value over the nine years is -3.8856%.
Given that an asset declines in value from $5000 to 3500 over the nine years.
To determine the mean growth rate over some period of time, compute the geometric mean of the growth factors. A growth factor less than one indicate negative growth.
The formula for the geometric mean over n periods is given by
[tex]y_n =\sqrt[n]{ {y_1 \times y_2 \times y_3 \times ......\times y_n}}[/tex]
Suppose an asset declined over nine years.
[tex]3500 = 5000\times({y_1 \times y_2\times y_3 \times ..\times y_9})[/tex]
[tex]{y_1 \times y_2\times y_3 \times ..\times y_9} = 3500/5000\\\ y_1 \times y_2\times y_3 \times ..\times y_9} = 0.7[/tex]
Then, the mean annual growth factor over these nine years is,
[tex]y_9 = \sqrt[9]{0.7}[/tex]
= 0.961144
Compute the mean annual growth rate in the asset’s value.
= (0.961144 - 1) 100%
= -3.8856%
Therefore, the mean annual growth rate in the asset’s value is -3.8856%.
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To find the mean annual growth rate of an asset declining from $5000 to $3500 over 9 years, you calculate the growth rate 'r' using the formula P(t) = P0 * e^(rt). The result is about -5.13%, indicating a depreciation in the asset's value.
Explanation:To calculate the mean annual growth rate for an asset that declines in value, we can use the formula for the annual growth rate, which is P(t) = P0 * e(rt), where:
P(t) is the future value of the asset.P0 is the initial value of the asset.e is the base of the natural logarithm.r is the growth rate.t is the time in years.In this case, the value of the asset declines from $5000 to $3500 over 9 years. Therefore, we have:
P0 = $5000P(t) = $3500t = 9 yearsFirst, we need to solve for r in the equation:
3500 = 5000 * e(9r)
By dividing both sides by 5000 and taking the natural logarithm, we get:
ln(3500/5000) = ln(e(9r))
ln(0.7) = 9r
r = ln(0.7)/9
Substitute the value of ln(0.7) and divide by 9:
r = -0.0512932942
Since the result is negative, it indicates a decline, and the annual growth rate is about -5.13%, reflecting a decrease in value.
Triangle ABC is an equilateral triangle with side lengths labeled a, b, and c.
Trigonometric area formula: Area =
Which expressions represent the area of triangle ABC? Check all that apply.
Triangle ABC is an equilateral triangle with side lengths labeled a, b, and c.
Trigonometric area formula: Area =
Which expressions represent the area of triangle ABC? Check all that apply.
Answer:
B
C
E
Step-by-step explanation:
One-half bc sin60⁰
One-half a squared sin60⁰ ; if the two opposite sides posses the same parameters.
Start Fraction ab sin60⁰ Over 2 End Fraction
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
A triangle with equal angle and equal sides. The sum of an angle in a triangle is 180⁰ this implies that each angles have 60⁰
The area rule of triangle:
It states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle, multiplied by the sine of the angle.
Therefore, there are three options that defines the expressions to represent the area of triangle ABC:
One-half bc sin60⁰
One-half a squared sin60⁰ ; if the two opposite sides posses the same parameters.
Start Fraction ab sin60⁰ Over 2 End Fraction
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Juan's income y consists of at least $37,500 salary plus 5% commission on all of his sales x. which inequality represents juan's income in one year? answer
Answer:
y < 37,500 + 5x I believe.
PLEASE HELP
What is the equation of the line in slope-intercept form?
1) Divide using synthetic division, and write a summary statement in fraction form.
two x to the fifth minus x to the fourth plus three x squared minus x plus five divided by quantity x minus one
a. 2x4 + x3 + 4x2 + 3x + eight divided by quantity x minus one
b. 2x4 + x3 - x2 + 2x + 1 + six divided by quantity x minus one
c. 2x4 + x3 + x2 + 4x + 3 + eight divided by quantity x minus one
d. 2x4 - 3x3 + x + six divided by quantity x minus one
2) Divide f(x) by d(x), and write a summary statement in the form indicated.
f(x) = x4 - 4x3 + 2x2 - 4x + 1; d(x) = x2 + 1
a. f(x) = (x2 + 1)( x2 + 4x + 1)
b. f(x) = (x2 + 1)( x2 - 4x + 1) + 12x + 3
c. f(x) = (x2 + 1)( x2 + 4x + 1) + 12x + 3
d. f(x) = (x2 + 1)( x2 - 4x + 1)
3) Find the remainder when f(x) is divided by (x - k).
f(x) = 3x3 - 4x2 - 3x + 14; k= 3
a. 50
b. 68
c. -12
d. 112
4) Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f.
k = -1; f(x) = 4x3 - 2x2 + 2x + 4; Lower bound?
a. yes
b. no
5) Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.
f(x) = -2x4 + 4x3 + 3x2 + 18
What is the square root of 500 divided by 2 x pi?
35.124, so rounded it is just 35.124
What is the exact area of the base of a circular swimming pool with diameter 16 ft?
Tim have 46 chocolate bars he eats 34.what does time have now.
A.12
B.8
C.diabetes
D.none of these
Express 2.27272727273... as a rational number, in the form p
Which property is shown? (mn)^5=m^5n^5
A)Product of powers
B) power of a product property
C) power of a power property
D) power of a quotient property
PLEASE ANSWER IMMEDIATELY
Given the function f(x) = x^2 - 9, classify the polynomial.
A. monomial
B. trinomial
C. binomial
Which is the range and interquartile range for the data represented by the box-and-whisker plot?
You flip a coin 5 times. in how many ways could u obtain at least one tail
Be independent uniform random variables on [0, 1], and let u(n) be the maximum find the cdf of u(n) and a standardized u(n), and show that the cdf of the standardized variable tends to a limiting value.
The cumulative distribution function (CDF) of u(n), when u(n) is the maximum of n independent uniformly-distributed random variables, is given by x^n. After standardization, as n approaches infinity, the CDF of the standardized variable converges to a standard normal distribution, as per the central limit theorem.
Explanation:The subject matter relates to the field of statistics, specifically dealing with the concept of uniform distribution and standard normal distribution.
Let's denote the random variables as X1, X2, ..., Xn and they are uniformly distributed over [0, 1].Given that u(n) is the maximum of these random variables, the cumulative distribution function (CDF) of u(n) can be calculated as follows:
P(u(n) < x) = P(X1 < x, X2 < x, ..., Xn < x) = P(X1 < x) * P(X2 < x) * ... * P(Xn < x) = x^n
Given that Z = (u(n) - μ) / σ where μ is the mean and σ is the standard deviation. For the uniform distribution, μ = 0.5 and σ = √ (b - a)² / 12 = √1 / 12. Therefore, the standardized random variable Z can be calculated.
By the central limit theorem, as n increases, the standardized variable tends to a limiting value. Which means as n -> ∞ , the cumulative distribution function of Z = 1, the standardized variable converts to a standard normal distribution, and it poses bell-shaped curve form.
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Gloria collected 28 fantail and comet goldfish. there were 4 fewer fantails than comets. how many comets did gloria have?
The hypotenuse of a 45°-45°-90° triangle measures 18 cm.
What is the length of one leg of the triangle?
9 cm
cm
18 cm
cm
Answer:
9√2
Step-by-step explanation:
18=x√2
18/12=x
√2(18/√2)=x
18√2/2=x
9√2=x
What is the total amount of interest with 12,560 dollar stocks borrowed 2% simple interest for 4 years?
V(t)=t2−3t what is the meaning of the quantity v(4) ?
What is the opposite of -a
the opposite of a negative is a positive
so opposite of - a would be positive a