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3 years ago

A line crosses the points 0 comma negative 4 and 5 comma negative 1. Calculate its slope

1 answer:

4 0

Sure, we can use the formula y2-y1/x2-x1 to get the slope. This gives us the points (0, -4) and (5, -1). We can do -1-(-4)/5-0. That gets us -1+4/5 = 3/5. Therefore, 3/5 is the slope.

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Which polynomial function has a leading coefficient of 1 and roots (7 i) and (5 – i) with multiplicity 1? f(x) = (x 7)(x – i)(x

Nuetrik [128]

It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.

The simplest polynomial with these characteristics would be

$f(x) = (x - (7 + i)) (x - (5 - i))$

but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with

$f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))$

which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:

$f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48$

5 0

1 year ago

What does it mean for two fractions to be equivalent? For two ratios to be equivalent?

poizon [28]

Answer:

Equivalent fractions and ratios mean that when simplified, they are the same one fraction or ratio. see examples below.

Step-by-step explanation:

For example, the fraction 1/2 is the same as 2/4 or 15/30 because when you simplify them, they are still 1/2. Therefore they are equivalent.

For example, the ratio 1:2 is the same as 5:10 or 10:20 since when broken down they all come down to 1:2. Hence they are equivalent.

Hope this answers your question.

3 0

2 years ago

A map that has a scale of 3 cm: 18 km. If Riverside and Smithville are 54km apart then they are how far apart on the map?

SVETLANKA909090 [29]

Setting up the ratio, you get 3/18=x/54. Solve the proportion, you get that Riverside and Smithville are 9 cm apart on the map.

8 0

2 years ago

Consider the two functions. Which statement is true?

Nitella [24]

Answer: Function 2 has a greater rate of change by 13/4

Step-by-step explanation:

We must work with linear equations, remember that the general shape is:

y = a*x + b

where a is the slope and b is the y-intercept.

Ok, first we want to find the rate of change (or the slope) of the graphed line:

We know that for a line that passes through the points (x1, y1) and (x2, y2)

The slope is:

a = (y2 - y1)/(x2 - x1)

Then for the graphed function, we can see that it passes through the points:

(0, -2) and (4, 0)

Then the slope is:

a = (0 -(-2))/(4 - 0) = 2/4 = 1/2

Now, the slope of the second line is 15/4.

Let's calculate the difference between the slopes:

15/4 - 1/2 = 15/4 - 2/4 = 13/4

(notice that we are calculating slope2 - slope1)

Then the correct option is:

Function 2 has a greater rate of change by 13/4

8 0

2 years ago

Read 2 more answers

3 ounces of cinnamon cost $2.40. There are 16 ounces in 1 pound how much the cinnamon cost per pound

faltersainse [42]

16 ounces in a pound
2.40 for 3 ounces
16 divided by 3 = 5.333
$2.40 * 5.333 =$
12.8
Approx $12.80 for 1 pound of cinnamon

3 0

2 years ago