Donna wants to make trail mix made up of almonds, walnuts, raisins. she wants to mix one part almonds, two part walnuts, and three parts raisins. almonds cost $12 per pound,walnuts cost $9 per pound, and raisins cost $5 per pound. Donna has $15 to spend on the trail mix. determine how many pounds of trail mix she can make.[ only an algebraic solution]

Answers

Answer 1

Answer: almons:walnuts:rasins=1:2:3

x=pounds of walnuts
y=pounds of almonds
z=pounds or rasins
2x=y
3x=z
subsitute

12x+9y+5z=15
12x+9(2x)+5(3x)=15
12x+18x+15x=15
45x=15
divide by 45
x=1/3
so
1/3 pound of walnuts
2x=y
2(1/3)=y=2/3
2/3 pounds of almonds
3x=z
3(1/3)=z
1=z
1 pound of rasins

1/3 pound walnuts
2/3 pound almonds
1 pound rasins

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when 12 is added to a certain number and the result is multiplied by 4. the final result is 60.find the number.

Answers

Answer:

The number is 3

Step-by-step explanation:

Let x be the number

Add 12

(x+12)

Then multiply by 4

4(x+12)

This is equal to 60

4(x+12) = 60

Divide each side by 4

4(x+12)/4 = 60/4

x+12 = 15

Subtract 12 from each side

x+12-12 = 15-12

x = 3

Answer is 3

=====================================================

Work Shown:

x = some unknown number

x+12 = adding 12 to the unknown number

4(x+12) = multiplying the previous sum by 4

4(x+12) = 60 .... set this equal to the desired result we want

Now solve for x. We will undo the steps done above to isolate x

----------------

4(x+12) = 60

x+12 = 60/4 .... divide both sides by 4 to undo "multiply by 4"

x+12 = 15

x = 15-12 .... undo "add 12" by subtracting 12 from both sides

x = 3

-----------------

The unknown number is 3

add 12 to it to get 3+12 = 15

multiply that sum by 4 to get 15*4 = 60

Answer is confirmed.

What two numbers multiply to 10 and add to -29 ?

Answers

xy=10
x+y=29

subtract x from both sides for second equation

y=-x-29
subsitute in second equaiton
x(-x-29)=10
-x^2-29x=10
add x^2+29x to both sides
x^2+29x+10=0
quadratic formula
if you have
ax^2+bx+c=0,
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$

so
x^2+29x+10=0
a=1
b=29
c=10
x= $\frac{-29+/- \sqrt{(-29)^(2)-4(1)(10)} }{2(1)}$
x= $(-29+/- √(841-40) )/(2)$
x= $(-29+/- √(801) )/(2)$
x= $(-29+/- 3√(89) )/(2)$

x= $(-29- 3√(89) )/(2)$ or $(-29+ 3√(89) )/(2)$
those are the 2 numbers
aprox=-28.65 and -0.349

There are none.
You can prove this by graphing.
xy = 10
y = 10/x

x + y = -29
y = -x - 29

On the graphing calculator, type in
Y1 = 10/x
Y2 = -x - 29

As you can see the two do not intersect.

The grocery store sells kumquat for $4.50 a pound and Asian pears for $3.75 a pound write an equation in standard form for the weight of kumquat k and Asian pears p that a customer could buy with $16

Answers

Answer:

let k represents the kumquat weight(in pound) and p represents the Asian pears weight respectively.

As per the given conditions,

The grocery store sells kumquat for $ 4.50 a pound

⇒ for 1 pound $\rightarrow$ $4.50

then, in k pound = $4.50 k$

similarly,

The Asian pears for $3.75 a pound

⇒ for 1 pound $\rightarrow$ $3.75

then, in p pound = $3.75 k$

Standard form of the equation is in the form of Ax + By = C:

The weight of kumquat k and Asian pears p that customer could buy with $ 16,

then the standard form of equation is: 4.50k +3.75p = 16

1 pound kumquat = 4.50
1 pound pear = 3.75
4.50k + 3.75p = 16

A topical cream is sold in a 34-gram container. The average amount of topical cream used per application is 2\7 grams. How many applications can be made with the container?

Answers

Since an application is 2/7 grams.

Number of applications = 34 ÷ 2/7

= 34 × 7/2

= 17 × 7

= 119

Number of applications = 119

Final answer:

This is a division problem. You find the number of applications by dividing the total weight of the cream (34 grams) by the amount used per application (2/7 grams), which gives us 119 applications.

Explanation:

This is a problem of simple division under the topic of arithmetic in mathematics. You are given a total quantity of topical cream (34 grams) and you know how much is used per application (2/7 grams). So, the number of applications can be found by dividing the total quantity by the amount used per application.

To calculate, divide 34 (the total weight of the cream) by 2/7 (the amount used per application).

This gives us, 34 ÷ (2/7) = 119,

Therefore, you can make 119 applications with the container of cream.

Learn more about Division here:

brainly.com/question/2273245

#SPJ12

Factor completely and then place the factors in the proper location on the grid.a 2 - a - 20

Answers

Answer:

The correct answer is (a+4)(a-5)

Step-by-step explanation:

We have the polynomial $a^2-a-20$

For the polynomials of the form $ax^2+bx+c$ we have to rewrite the middle term as a sum of two terms whose product is, in this case, a.c=-20 and whose sum is b=(-1).

$a^2-a-20=\na^2+(-5+4)(a)-20=\n=a^2-5a+4a-20$

Because b=(-5)+4=(-1) and a.c=(-5).4=(-20)

Now we have to factor by grouping:

$a^2-5a+4a-20=\n(a^2+4a)-(5a+20)=\na(a+4)-5(a+4)=\n=(a-5)(a+4)$

Then, the correct answer is (a+4)(a-5)

The fully factored form of this expression would be
(A-5)(A+4).

Please solve for a Earn 40 points.
A=16 but I don't how to get that

4(a-1) -5 =3a + 7

Answers

Distributive property says 4 * a and 4 * -1 so 4a - 4 - 5 = 3a + 7
Now do the simple subtraction
-4 - 5 = -9
Then add 9 and subtract 3a Remember: Always do the opposite operation to both
sides. So you have a = 16

$4\cdot(a-1)-5=3a+7\n\n4\cdot a-4\cdot1-5=3a+7\n\n4a-4-5=3a+7\n\n4a-9=3a+7\ \ \ /+9\n\n4a-9+9=3a+7+9\n\n4a=3a+16\ \ \ \ /-3a\n\n4a-3a=3a-3a+16\n\na=16$

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