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kiruha [24]
3 years ago
10

Ernie went to the store and bought 33 apples. He bought three times as many red apples as he bought green, and he bought one-hal

f as many yellow as he did red. How many of each type of apple did he buy?
Mathematics
1 answer:
Ray Of Light [21]3 years ago
3 0
(r is red, g is green and y is yellow)
r+g+y=33
r=3g
2y=r

substitution:
y=33-g-r
y=33-(1/3)2y+2y
y=33-8/3y
11/3y=33
y=33÷(11/3)
y=9

Solve for red and green:

r=2y
r=2×9
r=18

3g=r
3g=18
g=18/3
g=6

double check:
6+18+9=33

answer:
6 green apples, 9 yellow apples and 18 red apples.
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Kobotan [32]

Answer:

4

Step-by-step explanation:

1.5 -(-2.5)

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3 years ago
Find the value of 5x and 3x+60
Lerok [7]

Answer:0 and -20

Step-by-step explanation:

5x=0;

x=0/5.

3x+60=0;

3x= -60;

x= -60/3;

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5 0
3 years ago
2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap
telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if \frac{p}{q} is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1  10  35  50  24

  <u>| 0  -1  -9  -26   -24</u>

   <u> 1    9  26  24    0</u>

Hence quotient is x^{3} +9x^{2} +26x+24

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1   9  26   24

   <u>| 0  -2  -14   -24</u>

   <u>  1    7    12     0</u>

Hence quotient is x^{2} +7x+12

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

(-3)^{2}+7(-3)+12=-9-21+12=0

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1  7  12

   <u>| 0 -3  -12</u>

    <u> 1    4    0</u>

Hence quotient is x+4.

So, f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)

Please have a look at the graph attached.

4 0
3 years ago
Figure ABCD is transformed to A′B′C′D′, as shown: A coordinate plane is shown. Figure ABCD has vertices A at 3 comma 1, B at 3 c
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2 years ago
Can someone explain these to me?
s344n2d4d5 [400]

Answer:

Question 2: 4^12

Question 3: (9/64x)^11

Step-by-step explanation:

4 0
3 years ago
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