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3 years ago

Find the vertex of the parabola with an equation y=-(-x-2)(x-4)

Mathematics

1 answer:

leonid [27]3 years ago

5 0

Answer:

(3,1)

Step-by-step explanation:

We can have the equation of the parabola re-written

the general form is;

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

where (-h,k) is the vertex

so we have

y = -1(x^2 -6x + 8)

y = -1(x^2 -6x + 9 - 1)

y = -1(x-3)^2 - 1)

y = -1(x-3)^2 + 1

So we have the vertex of the parabola as;

(3,1)

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A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the followi

Vinil7 [7]

Answer:

Step-by-step explanation:

Given that a box contains one yellow, two red, and three green balls.

Two balls are randomly chosen without replacement.

A) one ball is yellow:

This means one is yellow and other can be any other colour

i.e. drawing one yellow and one from 5 remaining.

This can be as (y,r) (y,g) (r,y) or (g,y)

where y for yellow, r for red and g for green.

B) { At least one ball is red }

This means the two balls should not be different from red.

The favorable outcomes are two red, (one red, one yellow) (one green, one red). But should not be (green,yellow)

C) :{ Both balls are green }

Here the balls drawn should be only green, green and not any other combination.

D) { Both balls are of the same col

Since yellow is one, there cannot be two yellows

Hence only possibilities are (red, red) or (green, green)

7 0

3 years ago

Find the annual interest rate.

slega [8]

The annual interest rate is 3.5%.

Solution:

Given Interest (I) = $26.25

Principal (P) = $500

Time (t) = 18 months

Rate of interest (r) = ?

Time must be in years to find the rate per annum.

1 year = 12 months

Divide the time by 12.

Time (t) = $\frac{18}{12}=\frac{3}{2}$ years

Now, find the rate of interest using simple interest formula.

Simple interest formula:

$$I=\frac{Prt}{100}$

$$26.25=\frac{500\times r\times \frac{3}{2} }{100}$

$$26.25\times 100 =500\times r\times \frac{3}{2}$

$$2625 =250\times r\times 3$

$$2625 =750\times r$

$$\Rightarrow r=\frac{2625}{750}$

⇒ r = 3.5%

Hence the annual interest rate is 3.5%.

8 0

3 years ago

Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.

Nataly [62]

Answer: $454.55

Step-by-step explanation:

Tito's weekly salary is always $ 500 per week.

But your weekly commission income depends on the sales you make. Your commissions are 55%.

If we call x the dollar amount of all sales made by Tito in a week, then his income z(x) is given by the following equation:

$z (x) = 0.55x + 500$

We wish that $z (x) = 750$ .

Then we equate the equation to 750 and solve for the variable x.

$0.55x + 500 = 750\\\\0.55x + 500-500 = 750-500\\\\0.55x = 250$

$\frac{0.55}{0.55}x = \frac{250}{0.55}$

$x = \$\ 454.55$

Total sales made by Tito must be $454.55

7 0

3 years ago

Find X. Round to the nearest tenth if necessary.

storchak [24]

Answer:

3.2

Step-by-step explanation:

If there are 2 secont lines intersecting inside a circle like the picture shown, then the theorem tells us that "the product of 2 segments of one secant line is equal to the product of 2 segments of other secant line"

Thus, we can say that:

x * 10 = 8 * 4

10x = 32

x = 32/10

x = 3.2

3 0

3 years ago

Ted pays $35 per hour for scuba class. Identify the constant of proportionality that relates his scuba class charges (y) to the

Naddik [55]

The answer would be D

3 0

3 years ago

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