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3 years ago

What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

1 answer:

7 0

Something funny is that the x value of the vertex lies directl in the middle of the x intercepts
so
we see the x intercepts or 0's at x=8 and 2
the average is x=5
so find f(5) to find the y value of the vertex
f(5)=(5-8)(5-2)
f(5)=(-3)(3)
f(5)=-9

vertex is at (5,-9)

the actual way the teacher wants is to expand then compltete the square to get into the form f(x)=a(x-h)^2+k where the vertex is (h,k)
but whatever

verrtex is at (5,-9)

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A 92 ft path cuts diagonally from Mateo St. to Cove St. It makes an angle of 68° with Cove St. and an angle of 34° with Mateo St

ohaa [14]

Answer:

41.802 feet

Step-by-step explanation:

Given that a 92 ft path cuts diagonally from Mateo St. to Cove St. It makes an angle of 68° with Cove St. and an angle of 34° with Mateo St.

We can visualize a triangle formed by the three streets One side is 92 feet.

Angle opposite 92 feet = $180-68-34 = 78$

Let x be length of Cove st and y length of Mateo st.

Using sine angle for triangles,

$\frac{92}{sin 78} =\frac{x}{sin 34} =\frac{y}{sin 68}$

Simplify to get

x=52.595

y=87.207

Distance saved= $x+y-92\\= 139.802-92\\=41.802$

7 0

3 years ago

Read 2 more answers

Identify the type of function represented by f(x)=1/2•(3)^x

dalvyx [7]

ANSWER

An exponential growth function.

EXPLANATION

The given function is

$f(x) = \frac{1}{2} {(3})^{x}$

This function is of the form,

$f(x) = a {(b})^{kx}$

Since k is positive , the function will grow exponentially and fall asymptote to the negative x-axis.

As x-values becomes bigger and bigger positively, the graph grows exponentially.

6 0

3 years ago

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You invest $15,000 in a savings account with an annual interest rate of 2.5% in

almond37 [142]

Answer:

$\$16,990.62$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=5\ years\\ P=\$15,000\\ r=2.5\%=2.5/100=0.025\\n=4$

substitute in the formula above

$A=15,000(1+\frac{0.025}{4})^{4*5}$

$A=15,000(1.00625)^{20}$

$A=\$16,990.62$

5 0

3 years ago

When servicing a heating boiler and radiators, a plumer knows that the time he will take is given by the formula

Allushta [10]

Answer:

£110

Step-by-step explanation:

We know how much time it takes for a boiler and a radiator, and we need to know how much it will cost for 1 boiler and 4 radiators. We have an initial cost of £30, and since hes doing a boiler - which we know takes an hour - we can already add £20 for a start of £50.

Now, there are 4 radiators, that take 45 minutes each. We need to use this equation:

$(45*4)/60$

We divide by 60 because there are 60 minutes in an hour, and he charges by hour. So:

$180/60=3$

Now, to find out how much to charge, we need to figure out how much to add to the £50. Since it's £20 an hour, and it takes 3 hours to do the 4 radiators, we need to multiply:

$3*20=60$

Now we add our totals for a grand total of...

$50+60=110$

6 0

3 years ago

Which of the following is an arithmetic sequence? A.-2, 4, -6, 8, ... B.2, 4, 8, 16, ... C.-8, -6, -4, -2, ...

castortr0y [4]

Answer:

C. -8, -6, -4, -2, ...

Step-by-step explanation:

An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.

A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.

B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.

C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.

Hope this helps!

3 0

3 years ago