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3 years ago

14

The vertex of the parabola below is at the point (3,2) and the point (4,6) is on the parabola. What is the equation of the parab

ola?

1 answer:

nata0808 [166]3 years ago

6 0

Answer:

$\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}$

Step-by-step explanation:

The vertex form of a parabola:

$y=a(x-h)^2+k$

(h, k) - vertex

We have the vertex at (3, 2) → h = 3 and k = 2.

Substitute:

$y=a(x-3)^2+2$

The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:

$6=a(4-3)^2+2$ <em>subtract 2 from both sides</em>

$6-2=a(1)^2+2-2$

$4=a\to a=4$

Finally:

$y=4(x-3)^2+2$ <em>vertex form</em>

<em>use (a - b)² = a² - 2ab + b²</em>

$y=4(x^2-6x+9)+2$ <em>use the distributive property</em>

$y=4x^2-24x+36+2$

$y=4x^2-24x+38$ <em>standard form</em>

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Could someone plz help I need the answers by tonight

Maksim231197 [3]

Answer:

7) C) PQR ≈ TSR

8) B) 3

9) D) 102 ft

10) D) 21

11) C) 45

Step-by-step explanation:

7) C) PQR ≈ TSR

8) 2 * 6 = 12

so 4x = 12

x = 3

9)

24/20 = x/85

x = 24 * 85 / 20

x = 202 ft

10)

QT/35 = 24/40

QT/35 = 3/5

QT = 35 * 3 / 5

QT = 21

11)

ΔKLM ≈ΔXYZ

9/4 = 2.25

So

XY = 9 ---> given

YZ = 7 * 2.25 = 15.75

XZ = 9 * 2.25 = 20.25

Perimeter ΔXYZ = 9 + 15.75 + 20.25 = 45

7 0

3 years ago

6 x 10 5 is how many times the value of 3 x 10 (Hint: Write your answer in standard form.)

JulijaS [17]

Answer:

0.000036

Explanation:

When multiplying a number by 10 to the power of a positive exponent (e.g.

10

3

), move the decimal in the number that many spaces to the right (e.g.

4.5

⋅

10

3

=

4500

).

When multiplying a number by 10 to the power of a negative exponent (e.g.

10

−

4

), move the decimal in the number (the absolute value of) that many spaces to the left (e.g.

4.5

⋅

10

−

4

=

0.00045

).

For

3.6

⋅

10

−

5

, move the decimal five spaces to the left:

0.000036

Step-by-step explanation:

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3 years ago

Meredith is saving up to buy a digital camera that costs $490. So far, she saved $175. She would like to buy the camera 4 weeks

MatroZZZ [7]

She would have to get 78.75 dollars every week to get the camera.

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3 years ago

Read 2 more answers

O is the centre of the circle, EF is a tangent, angle BCE = 28°, angle ACD = 31°

andriy [413]

Answer

a. 28˚

b. 76˚

c. 104˚

d. 56˚

Step-by-step explanation

Given,

∠BCE=28° ∠ACD=31° & line AB=AC .

According To the Question,

a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°

b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚

thus , ∠ABC=76° .

c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,

Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°

Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)

∠DAB = 180° - 107° ⇔ 73°

& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°

Now, In Triangle ADC Sum of angles in a triangle is 180°

∠ADC = 180° - (31° + 45°) ⇔ 104˚

d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre

For Diagram, Please Find in Attachment

4 0

3 years ago

The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) for Determine

salantis [7]

The question is incomplete. Here is the complete question.

The probability density function of the time to failure of an electronic component in a copier (in hours) is

$f(x)=\frac{e^{\frac{-x}{1000} }}{1000}$

for x > 0. Determine the probability that

a. A component lasts more than 3000 hours before failure.

b. A componenet fails in the interval from 1000 to 2000 hours.

c. A component fails before 1000 hours.

d. Determine the number of hours at which 10% of all components have failed.

Answer: a. P(x>3000) = 0.5

b. P(1000<x<2000) = 0.2325

c. P(x<1000) = 0.6321

d. 105.4 hours

Step-by-step explanation: <em>Probability Density Function</em> is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

So, probability function is given by:

P(a<x<b) = $\int\limits^b_a {P(x)} \, dx$

Then, for the electronic component, probability will be:

P(a<x<b) = $\int\limits^b_a {\frac{e^{\frac{-x}{1000} }}{1000} } \, dx$

P(a<x<b) = $\frac{1000}{1000}.e^{\frac{-x}{1000} }$

P(a<x<b) = $e^{\frac{-b}{1000} }-e^\frac{-a}{1000}$

a. For a component to last more than 3000 hours:

P(3000<x<∞) = $e^{\frac{-3000}{1000} }-e^\frac{-a}{1000}$

Exponential equation to the infinity tends to zero, so:

P(3000<x<∞) = $e^{-3}$

P(3000<x<∞) = 0.05

There is a probability of 5% of a component to last more than 3000 hours.

b. Probability between 1000 and 2000 hours:

P(1000<x<2000) = $e^{\frac{-2000}{1000} }-e^\frac{-1000}{1000}$

P(1000<x<2000) = $e^{-2}-e^{-1}$

P(1000<x<2000) = 0.2325

There is a probability of 23.25% of failure in that interval.

c. Probability of failing between 0 and 1000 hours:

P(0<x<1000) = $e^{\frac{-1000}{1000} }-e^\frac{-0}{1000}$

P(0<x<1000) = $e^{-1}-1$

P(0<x<1000) = 0.6321

There is a probability of 63.21% of failing before 1000 hours.

d. P(x) = $e^{\frac{-b}{1000} }-e^\frac{-a}{1000}$

0.1 = $1-e^\frac{-x}{1000}$

$-e^{\frac{-x}{1000} }=-0.9$

${\frac{-x}{1000} }=ln0.9$

-x = -1000.ln(0.9)

x = 105.4

10% of the components will have failed at 105.4 hours.

5 0

4 years ago