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3 years ago

Between which two integers does 35 lie?

Mathematics

1 answer:

iren2701 [21]3 years ago

7 0

The answer is the first choice, "5 and 6."

The square root of 35 is equal to 5.92, which is in between the numbers 5 and 6.

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The equation of a circle is x^2 + y^2 -4x + 2y -11 =0 . What are the center and the radius of the circle? Show your work.

stira [4]

Answer:

Center: (2,-1)

Radius: 4 units

Step-by-step explanation:

Equation of the circle in standard form is:

$x^{2}+y^{2}+2gx+2fy+c=0$

The radius of this circle is located at (-g, -f) and its radius is equal to:

$r=\sqrt{g^{2}+f^{2}-c}$

The given equation of circle is:

$x^{2}+y^{2}-4x+2y-11=0$

Re-writing this equation in a form similar to the standard equation:

$x^{2}+y^{2}+2(-2)x+2(1)y-11=0$

Comparing this equation with standard equation we can say:

g= -2

f = 1

c = -11

So, the center of the circle will be located at (-g, -f) = (2, -1)

And the radius will be = $\sqrt{g^{2}+f^{2}-c} =\sqrt{(-2)^{2}+(1)^{2}-(-11)} =\sqrt{16} =4$

Thus the radius of the given circle is 4 units.

7 0

3 years ago

4(3 • 2) + (8 – 3)2 – 62 + 3 • 9 - 23 + 1

Sliva [168]

Answer:

-23

Step-by-step explanation:

6 0

3 years ago

To offer scholarships to children of employees, a company invests $13,000 at the end of every three months in an annuity that pa

Andreyy89

Annuities

Suppose a fixed investment R is done every fixed number of periods m per year for t years at a constant rate r.

The final value of the investments plus the interest is calculated as follows:

$FV=R\cdot\frac{(1+i)^n-1}{i}$

Where:

n = number of total periods of the investment.

n = m*t

$i=\frac{r}{m}$

The company invests R = $13,000 for t = 10 years at the end of every quarter (3 months), thus m = 4. The interest rate is r = 9% = 0.09.

The interest rate compounds quarterly.

Calculate:

n = 4*10 = 40

i = 0.09 / 4 = 0.0225

$\begin{gathered} FV=\$13,000\cdot\frac{(1+0.00225)^{40}-1}{0.0225} \\ FV=\operatorname{\$}13,000\times\frac{(1.00225)^{40}-1}{0.0225} \\ FV=\operatorname{\$}13,000\times\frac{2.435188965-1}{0.0225} \\ FV=\operatorname{\$}13,000\cdot63.786176 \end{gathered}$

Calculating:

FV = $829,220

The company will have $829,220 in scholarship funds

b. The interest can be found by subtracting the final value and the initial value. We have to calculate the latter:

$\begin{gathered} A=FV(1+i)^{-n} \\ A=\$829,220(1.0225)^{-40} \\ A=\$340,516 \end{gathered}$

Thus, the interest is:

welcI = $829,220 - $340,516

I = $488,704

The interest is $488,704

5 0

10 months ago

Find the midpoint of a segment with endpoints A(-3,10) and B(9,2).

lilavasa [31]

Answer:

(3, 6)

Step-by-step explanation:

You add the x points together and divide by two, then you add the y points together and divide by 2.

3 0

3 years ago

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Isaac has a piece of rope that 5 yards long. Into how many 1/2 - yard pieces of rope isaac can cut?

Trava [24]

Answer:

Step-by-step explanation:

So there are 5 pieces of rope, if you cut them all in half then that would double the number.

7 0

3 years ago

Read 2 more answers