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aleksandrvk [35]

3 years ago

8

write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given p

oint. show all work. vertex(4,7)Point(3,6)

1 answer:

Elanso [62]3 years ago

7 0

Vertex form of parabola is

y = a(x - b)^2 + c where a is a constant and the vertex is at the point (b,c)

so here we have

y = a(x - 4)^2 + 7

To find value of a we plug in the point (3,6)

6 = a(3 - 4)^2 + 7
6 = a + 7
a = 6-7 = -1

so equation is y = -(x - 4)^2 + 7

Covert to standard form:-
y = -(x^2 - 8x + 16) + 7
y = -x^2 + 8x - 9

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What is 48 to the square root of 9.5

Leokris [45]

48 divided by sqrt of 9.5 =

48 divided by 3.082207 = 15.57325643605378 is your answer

4 0

3 years ago

I need help quick!!<br><br> you can have brainliest this is algerbra btw

padilas [110]

Answer:

Step-by-step explanation:

Day 1 = 2 birds

day 2 = 3 birds

day 3 = 9 birds

day 4 = 8 birds

day 5 = 1 bird

On day 1 the points are (1,2)

On day 5 the points are (5,1)

(I am picking these for the points because I don't know your options for the selecting area.)

we use this formula y2-y1/x2-x1

2-5/1-1

3/0

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5 0

2 years ago

Read 2 more answers

Find the solution to the inequality<br><br> 23(6x−3)>6?

laiz [17]

Answer:

The answer is x>25/46

Step-by-step explanation:

Distribute 23 through the parentheses

138x-69>6

Move constant to the the right and change the sign. 138x>6+69.

Add the numbers like this: 138x>75

Divide both sides and you'll will get x>25/46 which is your answer. Let me know if this helps

8 0

3 years ago

What two rational expressions sum to 2x+3/x^2-5x+4

Anni [7]

Answer:

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

$x^2 - 5x + 4$

$x^2 - 4x - x + 4$

$(x^2 - 4x) - (x + 4)$

$x(x - 4) - 1(x - 4)$

$(x- 1)(x - 4)$

Thus, we now have: $\frac{2x + 3}{(x- 1)(x - 4)}$

Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

$\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4)$ = $(\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)$

$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(4) + 3 = A(4 - 4) + B(4 - 1)$

$8 + 3 = A(0) + B(3)$

$11 = 3B$

$\frac{11}{3} = B$

$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

$2 + 3 = A(-3) + B(0)$

$5 = -3A$

$\frac{5}{-3} = \frac{-3A}{-3}$

$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}$

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

7 0

3 years ago

a utility worker is 5.5 feet tall and is casting a shadow 4 feet long at the same time a nearby utility pole casts a shadow 20 f

Assoli18 [71]

So this is essentially a proportion problem. They want you to be able to recognize a relationship between the two. The easiest way to go about this is to draw a picture (I have included one). What you want to do is notice that you are given both shadow lengths. This is essentially going to be your first step to creating the proportion.

Understanding that we know the shadow lengths, we can turn these into a fraction such as so:

4ft/20ft.

Now that we know that, we need to look at are unknown. Our unknown is the height of the utility pole. We can solve this by substituting for X since we know the utility worker is 5.5 ft tall.

Your fraction for that would look like:

5.5ft/X

Make sure to always make your top to top match, such as since I put the utility worker's shadow on top, I need to put his height on top.

Now we can solve.

4ft/20ft =5.5ft/X

We need to cross multiply to get an equation we can work with. If we cross multiply, Your equation will look like:

4x = 110ft

This is a simple one step equation. Divide both sides by 4 to get your answer.

x= 27.5ft.

This means your Utility pole's height is 27.5ft.

6 0

3 years ago