answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
FinnZ
3 months ago
15

Jeremy is making a trail mix containing raisins and peanuts. Raisins cost $1.50 per pound. Peanuts cost $2.50 per pound. Jeremy

spends $10.50 to make 5 pounds of trail mix. He uses the table below to organize this information.
Which equation can Jeremy use to determine the amount of raisins in the trail mix?

a.r + 1.50 = 1.5r
b. r + (5 – r) = 5
c. 1.5r + 2.5(5 – r) = 10.50
d. 1.5r + 2.5(5 – r) = 5

Mathematics
2 answers:
tester [12.3K]3 months ago
8 0

Answer:

1.5r + 2.5(5 - r) = 10.50

Step-by-step explanation:

Define 'r' as the quantity of raisins.

The overall mixture weighs 5 pounds.

This means the amount of peanuts is 5 minus r.

The cost for raisins is $1.50 per pound, while peanuts are priced at $2.50 per pound.

Setting up the equation: 1.50(r) + 2.50(5 - r) = 10.50.

Substituting values, we replace raisins with 'r' and peanuts with (5-r).

1.5r + 2.5(5 - r) = 10.50

This forms our necessary equation.

Zina [12.3K]3 months ago
5 0
1.5r + 2.5(5 - r) = 10.50
You might be interested in
D = 5x + 10xf solve literal equation for x
Leona [12618]

Answer:

x=\dfrac{d}{(5+10f)}

Step-by-step explanation:

The equation provided is:

d = 5x + 10xf

We need to isolate x from this equation.

Factoring out x from the right side gives us,

d=x(5+10f)

To find x, divide both sides by (5+10f),

x=\dfrac{d}{(5+10f)}

Thus, this represents the sought value for x.

4 0
3 months ago
Gary has 32 ounces of soda. He shares it with 3 of his friends., splitting the soda evenly into 4 cups. He drinks 8 ounces of so
Svet_ta [12734]

0 ounces remain; since he distributed it evenly among four individuals, each cup contained 8 ounces, meaning he consumed the entire cup.

8 0
2 months ago
Read 2 more answers
Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x?
Zina [12379]

To determine an equivalent for RootIndex 3 StartRoot 8 EndRoot Superscript x, we can proceed with =2^x

Detailed Explanation:

We aim to express RootIndex 3 StartRoot 8 EndRoot Superscript x in a different form.

In mathematical terms:

(\sqrt[3]{8})^x

To solve:

Notably, 8 can be broken down into 2 multiplied by itself three times = 2^3

and \sqrt[3]{x}=x^{\frac{1}{3}}

Using these principles:

=((2^3)^{\frac{1}{3}})^x

=(2^{\frac{3}{3}})^x\\

=2^x

Thus, as we find a solution to RootIndex 3 StartRoot 8 EndRoot Superscript x, it results in =2^x

Terms: Radical Expression

Explore more about Radical Expression at:

8 0
3 months ago
Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o
Svet_ta [12734]

For \fbox{\begin \\\math{x}=6\\\end{minispace}} the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 both yield the same result.

Detailed breakdown:  

The functions involved are

f(x)=-x^{2}+4x+12

g(x)=-x+6

Step 1:  

Insert x=1 in f(x)=-x^{2} +4x+12 to find the value of f(1).

f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15

Insert x=1 in g(x)=-x+6 to find the value of g(1).

g(1)=-1+6\\g(1)=5

Step 2:

Insert x=2 in f(x)=-x^{2} +4x+12 to obtain the value of f(2).

f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16

Substitute x=2 into g(x)=-x+6 to find the value of g(2).

g(2)=-2+6\\g(2)=4

Step 3:

Replace x=3 in f(x)=-x^{2} +4x+12 to find the value of f(3).

f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15

Also, replace x=3 in g(x)=-x+6 to find the value of g(3).

g(3)=-3+6\\g(3)=3

Step 4:

Insert x=4 in f(x)=-x^{2} +4x+12 to find the value of f(4).

f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12

Also, replace x=4 in g(x)=-x+6 to obtain the value of g(4).

g(4)=-4+6\\g(4)=2

Step 5:

Insert x=5 in f(x)=-x^{2} +4x+12 to obtain the value of f(5).

f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7

Replace x=5 in g(x)=-x+6 to find the value of g(5).

g(5)=-5+6\\g(5)=1

Step 6:

Insert x=6 into f(x)=-x^{2} +4x+12 to find the value of f(6).

f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0

Also, substitute x=6 in g(x)=-x+6 to obtain the value of g(6).

g(6)=-6+6\\g(6)=0

Step 7:

According to the provided condition f(x)=g(x).

(a). Insert f(x)=-x^{2} +4x+12 and g(x)=-x+6 into the previously mentioned equation.

-x^{2} +4x+12=-x+6

(b). Multiply through by -1 on both sides.

x^{2} -4x-12=x-6

(c). Move the term x-6 to the left side of the equation.

x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0

(d). Divide the middle term so that its sum equals 5 and the product equals 6.

x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1,6

From the analysis above, it is noted that for x=6 both functions f(x) and g(x) yield the same outcome.

Using a direct approach:

f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1

The table representing function f(x)=-x^{2} +4x+12 and g(x)=-x+6 is included below.

For more information:

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. Which is the graph of f(x) = (x – 1)(x + 4)?

6 0
2 months ago
an apple Orchard sells apples in bags of 10. the orchard sold a total of 2,430 apples one day. how many bags of apples was this
zzz [12365]
243. A division problem
7 0
2 months ago
Read 2 more answers
Other questions:
  • the solution is n = –2 verified as a solution to the equation 1.4n 2 = 2n 3.2. what is the last line of the justification? a.0.8
    15·1 answer
  • Jana earns $25 per week for mowing the lawn and deposits the money into her savings account. The amount of money in Jana’s accou
    6·1 answer
  • Which will result in a difference of squares? (–7x + 4)(–7x + 4) (–7x + 4)(4 – 7x) (–7x + 4)(–7x – 4) (–7x + 4)(7x – 4)
    10·2 answers
  • The are of square frame is 55 square inches. find length of one side frame explain​
    13·1 answer
  • How many 5 1/4 ounce glasses can be completely filled from a 33 1/2 ounce container of juice?
    12·1 answer
  • A company manufactures and sells mini-recorders. A survey of office supply stores indicated that at a price of $82 each, the dem
    14·1 answer
  • One 6 oz juice box has 90 calories. How many calories are there in a 64 oz jug of juice? Round to the nearest calorie
    11·2 answers
  • An equilateral triangle ΔLMQ (see picture to the right) is drawn in the interior of square LMNP so that side LM is common. Find
    5·1 answer
  • Find the equation of the lines, that is parallel to the line 9x-8y=1, and tangent to the elipses 9x^2+16y^2=52.
    7·1 answer
  • Observe the expression below and select the true statement(s).
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!