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2 years ago

What is the area of a trapezoid that has bases measuring 19 centimeters and 23 centimeters, and a height of 14 centimeters?

1 answer:

6 0

Area of a trapezoid, A = 1/2 × (a + b) h, where a = 19 cm, b = 23 cm & h = 14 cm.

By substitution, we have

A = 1/2 × (19 + 23)14

= 1/2 × 14(19 + 23)

= 1/2 × 14(42)

= 7(42)

= 294 sq. cm

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Find the sum of the geometric series 40 + 40(1.005) + 40(1.005)^2 + ⋯ + 40(1.005)^11.

KiRa [710]

Answer:

The sum is 493.4

Step-by-step explanation:

In order to find the value of the sum, you have to apply the geometric series formula, which is:

$\sum_{i=1}^{n} ar^{i-1} = \frac{a(1-r^{n})}{1-r}$

where i is the starting point, n is the number of terms, a is the first term and r is the common ratio.

The finite geometric series converges to the expression in the right side of the equation. Therefore, you don't need to calculate all the terms. You can use the expression directly.

In this case:

a=40

b= 1.005

n=12 (because the first term is 40 and the last term is 40(1.005)^11 )

Replacing in the formula:

$\frac{a(1-r^{n})}{1-r} = \frac{40(1-1.005^{12})}{1-1.005}$

Solving it:

The sum is 493.4

4 0

2 years ago

write a polynomial function of least degree with integral coefficients that has the given zeros. -(1/3), -i

inessss [21]

Answer:

$f(x)=3x^3+x^2+3x+1$

Step-by-step explanation:

If a real number $-\frac{1}{3}$ is a zero of polynomial function, then

$x-\left(-\dfrac{1}{3}\right)=x+\dfrac{1}{3}$

is the factor of this function.

If a complex number $-i$ is a xero of the polynomial function, then the complex number $i$ is also a zero of this function and

$x-(-i)=x+i\ \text{ and }\ x-i$

are two factors of this function.

So, the function of least degree is

$f(x)=\left(x+\dfrac{1}{3}\right)(x+i)(x-i)=\left(x+\dfrac{1}{3}\right)(x^2-i^2)=\\ \\ =\left(x+\dfrac{1}{3}\right)(x^2+1)=\dfrac{1}{3}(3x+1)(x^2+1)=\dfrac{1}{3}(3x^3+x^2+3x+1)$

If the polynomial function must be with integer coefficients, then it has a form

$f(x)=3x^3+x^2+3x+1$

4 0

3 years ago

Find the amount of sap the maple syrup producer would have collected from each tree if the total amount (5 gallons) was redistri

zhuklara [117]

Answer:

Step-by-step explanation:

You cannot solve the problem be cause you dont know how many trees there are.

3 0

3 years ago

I want to know what is 600 minutes to days

Damm [24]

Answer:

Not even a whole day. To be exact, it is .416667 of a day

Step-by-step explanation:

Since 60 minutes are in 1 hour, than 600 minutes would be 10 hours.

24 hours in a day, so you are 14 hours short, about 840 minutes.

6 0

3 years ago

Read 2 more answers

What is the value of -7(x to the second power - 6) +2y when x=2 and y =-6

alexgriva [62]

Answer:

if x equals 2 and y equals negative 6 then the answer is....

A. -1

Step-by-step explanation:

5 0

2 years ago