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guapka [62]
2 years ago
11

Barbara requires 2 gallons of paint to cover an area of 800 square feet. Identify the graph for the relationship from quantity t

o the area covered, and the parent function that best describes it. Then use the graph to estimate how many gallons of paint Barbara requires to paint an area of 2,400 square feet.
Mathematics
1 answer:
mote1985 [20]2 years ago
4 0

Answer:

6

Step-by-step explanation:

x = area to be painted

y = gallons of paint needed

we know already one point of that function/graph :

x = 800

y = 2

so, for a simple relationship between the 2 variables we can assume

y = ax

2 = a×800

a = 2/800 = 1/400

so, we get

y = (1/400) x

for 2400 ft²

y = 1/400 × 2400 = 1/4 × 24 = 24/4 = 6

she needs 6 gallons of paint for 2400 ft².

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If a circle has a diameter of 91 units how many units is the radius
deff fn [24]

Answer:

r =45.5 units

Step-by-step explanation:

The diameter is twice the radius, or the radius is 1/2 the diameter

r = d/2

r = 91/2

r =45.5 units

7 0
3 years ago
Read 2 more answers
What is the imaginary part of z?
Shkiper50 [21]

Answer:

The imaginary part is the multiple of i. It is common practice to use the letter z to stand for a complex number and write z = a + bi where a is the real part and b is the imaginary part. where a is the real part and b is the imaginary part.

Step-by-step explanation:

You can easily check that a complex number z = x + yi times its conjugate x – yi is the square of its absolute value |z|2. Therefore, 1/z is the conjugate of z divided by the square of its absolute value |z|2.

Complex numbers A complex number z is defined as an ordered pair z = (x, y), where x and y are a pair of real numbers.

8 0
3 years ago
If g(x) = x ² + 2x -8, evaluate f(-2)​
Doss [256]

Answer: -8

Explanation: If g(x) = x² + 2x - 8, then g(-2) = (-2)² + 2(-2) - 8

which simplifies to 4 + (-4) - 8 or 0 - 8 which is -8.

Remember to always use parentheses when

substituting your given value in for <em>x</em>.

4 0
3 years ago
Noah wants to put $1,000 in a savings account with a 1.5% annual interest rate. How much more money will he have after one year
NeX [460]
There are two types of interest: Simple interest and compounding interest:

Simple interest: F = P(1+in)
Compounding interest: F = P(1+i)ⁿ

The compounding interest is always bigger than simple interest for a given amount of n time. The effective interest rate is

Effective interest rate = 1.5%/year * 1 yr/12 months = 0.125% per month

Since there are 12 months in 1 year, n= 12. Then i = 0.125/100 = 0.00125

Difference = Compounded Interest - Simple Interest
Difference = P(1+i)ⁿ - P(1+in) = 1000(1+0.00125)¹² - 1000(1+0.00125*12)
Difference = $0.104

You will only have $0.104 more money than the simple interest.
3 0
3 years ago
a) Suppose f"(z) exists on an interval I and f(s) has a zero at three distinct points a &lt; b&lt; c on I. Show there is a pbint
Fynjy0 [20]

Answer:

We can find a root in the average point (a+b+c)/3

Step-By-Step Explanation:

We can use the Rolle Theorem. Since f is two times deribable on both [a,b] and [b,c], then there exists points x in (a,b) and y in (b,c) such that f'(x) = f'(y) = 0. Now, again by using Rolle Theorem, since f' is derivable in [x,y] (because it is a closed interval in I), then there exists s in [x,y] such that f''(s) = 0. This proves a.

The cube (x-a)(x-b)(x-c) has 3 roots, a, b and c and it is two times derivable because it is a polynomial. Hence we can use (a) to ensure that there is a root on I. Nevertheless, we can try to find the root manually:

f'(x) = (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)

f''(x) = (x-c)+(x-b)+(x-c)+(x-a)+(x-b)+(x-a) = 2(x-a)+2(x-b)+2(x-c) = 2( (x-a) + (x-b) + (x-c) ) = 6x - 2 (a+b+c).

We want x such that

6x - 2(a+b+c) = 0, or, equivalently,

3x - (a+b+c) = 0

Hence

x = (a+b+c)/3

Is a root of f'' in I.

3 0
3 years ago
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