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3 years ago

1. If 4r – 10 = 18, what is the value of 2r + 9?

Mathematics

2 answers:

fgiga [73]3 years ago

8 0

Answer:

Step-by-step explanation:

4r-10=18

4r=28

4r/4=28/4

r=7

2(7)+9=23

Tcecarenko [31]3 years ago

7 0

I’m pretty sure the answer is 23

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Kwamee created a coffee blend for his cafe by mixing Kona beans and Fuji beans. Kona beans cost $11 per pound and Fuji beans cos

yKpoI14uk [10]

Let's use K for Kona and F for Fuji. The system of equations has to be a balanced system. For example, you can't mix the number of pounds of beans with the cost for each because pounds and dollars are different and you can only combine like terms...pounds with pounds and dollars with dollars. So let's start with the number of pounds. Since we don't know how much of each he bought we have the 2 unknowns, F and K, but we DO know that he bought 23 pounds total. So the first equation is
K + F = 23
Now let's see what we can do with the dollars. Again, we don't know how much he bought of each kind of coffee, but we do know that Kona beans cost $11 per pound and that Fuji beans cost $7.50 per pound, and we know that he spent a total of $197. So let's set that up:
11K + 7.50F = 197
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3 years ago

Select all of the proportional relationships

LenKa [72]

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3 years ago

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What is the interest earned on $3000 at a rate of 0.04 for three years? The formula is interest equals (principal) (rate) (time)

bekas [8.4K]

Answer:

The interest after 3 years is $360

Explanation:

Given the principal amount (P) = $3000

Rate of interest (R) = 0.04

Time period (T) is given as 3 years

The Simple Interest is calculated by the formula;

$SI = Principal \times Rate of Interest \times Time$

Substituting the values in the above formula,

$SI = 3000 \times 0.04 \times 3$

SI = $360

Therefore, the interest after 3 years is $360

5 0

3 years ago

Find number a and k so that x-2 is afactor OF F(x)=x4-2ax tax- X+k and F(-1)=3

Slav-nsk [51]

Question:

Find numbers a and k so that x-2 is a factor of

$f(x)=x^4-2ax^3+ax^2- x+k$

and

$f(-1)=3$

Answer:

$k = -2$ and $a=1$

Step-by-step explanation:

Given

$f(x)=x^4-2ax^3+ax^2- x+k$

$Factor:\ x - 4$

$f(-1)=3$

Required

Find a and k

For $f(-1)=3$

Substitute -1 for x

$f(x)=x^4-2ax^3+ax^2- x+k$

$f(-1) = (-1)^4 - 2a *(-1)^3 + a*(-1)^2 - (-1) + k$

$f(-1) = 1 - 2a *-1 + a*1 +1 + k$

$f(-1) = 1 +2a + a +1 + k$

$f(-1) = 2 +3a + k$

Substitute 3 for f(-1)

$3 = 2 +3a + k$

Collect Like Terms

$3 - 2 = 3a + k$

$1 = 3a + k$

Also:

If $x - 2$ is a factor, then

$f(2) = 0$

Substitute 2 for x and 0 for f(x)

$f(x)=x^4-2ax^3+ax^2- x+k$

$0 = 2^4 - 2a * 2^3 + a * 2^2 - 2 + k$

$0 = 16 - 2a * 8 + a * 4 - 2 + k$

$0 = 16 - 16a + 4a - 2 + k$

$0 = 16 - 12a - 2 + k$

Collect Like Terms

$2 - 16 = - 12a + k$

$-14 = k - 12a$

$k = 12a - 14$

Substitute 12a - 14 for k in $1 = 3a + k$

$1 = 3a + 12a - 14$

$1 = 15a - 14$

Collect Like Terms

$15a = 1 + 14$

$15a = 15$

Solve for a

$a = \frac{15}{15}$

$a=1$

Substitute 1 for a in $k = 12a - 14$

$k = 12 * 1 - 14$

$k = 12 - 14$

$k = -2$

3 0

3 years ago

The smallest prime number that is a foctor of 15

GrogVix [38]

The factors of 15 are 1, 3, 5 and 15. Now, as 1 is neither prime and nor a composite number (1 is not Prime because for a number to be a prime, it should have exact 2 factors i.e. 1 and itself, but 1 has only one factor. Therefore 1 is not prime.)

So the smallest prime factor of 15 is 3.

Hope this helped! :)

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3 years ago