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lozanna [386]
3 years ago
13

Find the value of k if (x-3) is a factor of P(x)=2x3-5x2+3x+k

Mathematics
1 answer:
blsea [12.9K]3 years ago
4 0

Answer:

k = -18

Step-by-step explanation:

If x-3 is a factor, what this means is that if we substitute;

x = 3 into the equation, we should get 0

This is from the factor theorem

Thus ;

P(3) = 0 = 2(3)^3 -5(3)^2 + 3(3) + k

0 = 54 - 45 + 9 + k

k + 18 = 0

k = -18

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Eth enlarged the triangle below by a scale of 5.
levacccp [35]

Answer:

She should have multiplied one half (4)(3.5) by 5 squared.

Step-by-step explanation:

We are given that

Base of triangle=b=4 cm

Height of triangle=h=3.5 cm

Area of triangle=\frac{1}{2}bh=\frac{1}{2}(4)(3.5) cm^2

After enlarged

Scale factor=5

New base of enlarged triangle=b'=4(5) cm

Height of enlarged triangle=h'=3.5(5) cm

Area of enlarged triangle=\frac{1}{2}4(5)(3.5\times 5)=\frac{1}{2}(4)(3.5)(5^2) cm^2

But Beth wrote

Area of enlarged triangle=\frac{1}{2}(4)(3.5)(5)=35 cm^2

She should have multiplied one half (4)(3.5) by 5 squared.

3 0
3 years ago
Jessie borrowed $1800 from the bank at a rate of 7.5% simple interest per year. Over the course of 4 years, how much interest di
cluponka [151]
$540
Explanation:
7.5% of 1800 is 135
135 • 4 = 540
5 0
3 years ago
Which measure of center is the best to use to compare the prices of kid socks and adult socks?
k0ka [10]

Answer:

The answer is mean

Step-by-step explanation:

The mean is the average cost of the socks, so finding the mean of both would give an average price to compare them to. :)

3 0
2 years ago
Read 2 more answers
Elana walked 12 miles. then she walked 1/4 that distance. how far did she walk all together. select all that apply.
Nezavi [6.7K]

Answer:

c., d., f

Step-by-step explanation:

"elana walked 12 miles"

That is 12.

"then she walked 1/4 that distance"

That is 1/4 of 12 miles, so it is 1/4 * 12

She walked altogether

12 + 1/4 * 12 = 12 + 3 = 15

She walked altogether 15 miles.

a.12+1/4  = 12.25 which is not 15

b.12×1/4  = 3 which is not 15

c.12+1/4×12  = 12 + 3 = 15 which is correct

d.12(1+ 1/4)  = 12(1.25) = 15 which is correct

e.12×3/4  = 9 which is not 15

f.12×5/4 = 15 which is correct

Answer: c., d., f

3 0
3 years ago
Benjamín made 3 times more than Alberto and Carlota 2 times more than Benjamín, so how much is it, help me
vichka [17]

Step-by-step explanation:

you are "hiding" some more information (like how much they made together).

without that we cannot calculate the actual values.

all I can do is set up the equations expressing the given relations between the parts of the total :

a = amount Alberto made

b = amount Benjamin made

c = amount Carlota made

b = 3×a

c = 2×b = 2× 3×a = 6×a

that's it.

your see ? now we need something that "ties" all 3 together, an equation of all 3 variables, where we can use the first 2 equations (by substitution) and then solve for the remaining third variable.

and that is missing.

if it is something like "together they made x", then we would have

a + b + c = x

a + 3a + 6a = x

10a = x

a = x/10

b and c we get then from the first 2 equations by simply using the calculated value of a :

b = 3×(x/10) = 3x/10

c = 6×(x/10) = 6x/10 = 3x/5

7 0
2 years ago
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