Preparing a glucose solution In a certain medical test
designed to measure carbohydrate tolerance, an adult
drinks 7 ounces of a 30% glucose solution. When the test is
administered to a child, the glucose concentration must be
decreased to 20%. How much 30% glucose solution and
how much water should be used to prepare 7 ounces of
20% glucose solution?

Answer:

[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - \frac{41}{5} [/tex]

Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} + 5x - 2[/tex]

[tex]f(x) = 2( {x}^{2} + \frac{5}{2} x) - 2[/tex]

[tex]f(x) = 2( {x}^{2} + \frac{5}{2} x + \frac{25}{16} ) - 2[/tex]

[tex]f(x) + 2 \times \frac{25}{16} = 2( {x}^{2} + \frac{5}{2} x + \frac{25}{16} ) - 2[/tex]

[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - 2 - \frac{25}{8} [/tex]

[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - \frac{41}{5} [/tex]

Answer:

[tex] \frac{4 + (x + 1)}{x + 1} = \frac{16}{12} \\ \\ \frac{5 + x}{x + 1} = \frac{16}{12} \\ \\ 12(5 + x) = 16(x + 1) \\ 60 + 12x = 16x + 16 \\ 4x = 44 \\ x = 11[/tex]

Answer:

x = 11 cm

Step-by-step explanation:

Segments DE and BC are parallel (that's what the arrows tell you), so there are two similar triangles formed.

[tex]\triangle{ADE} \sim \triangle{ABC}[/tex]

Corresponding sides are in proportion, so

[tex]\frac{AD}{AB}=\frac{12}{16}[/tex]

The length of AB is (x + 1) + 4 = x + 5, and 12/16 simplifies to 3/4, so

[tex]\frac{x+1}{x+5}=\frac{3}{4}[/tex]

"Cross multiply" to get

[tex]4(x+1)=3(x+5)\\4x+4=3x+15\\4x=3x+11\\x=11[/tex]

Answer:

28

Step-by-step explanation:

According to the question,

2 helmets and 1 football cost $80, while 1 helmet and 2 football cost $76

Let x represent cost of football and let y equal cost of helmet.

Write the system of equations,

[tex]x +2 y = 80[/tex]

[tex]2x + y = 76[/tex]

Eliminate the x variable by multiplying the top equation by -2

[tex] - 2x - 4y = - 160[/tex]

[tex]2x + y = 76[/tex]

Add both equations.

[tex] - 3y = - 84[/tex]

[tex]y = 28[/tex]

So one helmet cost $28

Answer:

Step-by-step explanation:

y = k x

Total cost = y

number of pounds = x

constant = 0.59

Equation

y = 0.59 x

Answer:

The mixture for Brand A fruit is 5%.

Answer:

9,700,045,306

Step-by-step explanation:

there you go!

Step-by-step explanation:

nine billion, seven hundred million, forty-five thousand, three hundred six

9,700,045,306

Answer:

The first choice.

Step-by-step explanation:

It pass through the x axis at x = 3, so a factor must be (x - 3).

Answer:

The first option is correct :)

~Hope this helps

Answer:

32 dollar

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Step-by-step explanation:

by deleted user on here.

9514 1404 393

Answer:

  ∠LJM and ∠MJN

Step-by-step explanation:

Ray JL forms a pair of right angles at J on line KN. Ray JM divides one of those right angles into two adjacent angles with a sum of 90°. Those two angles are adjacent complementary angles. They are ...

  ∠LJM and ∠MJN

Answer:

a. ▲▲△

b. ▲▲▲▲▲▲▲▲▲△△△△△△△

c.▲▲▲▲▲▲ △△△

Answer:

D.(CDL)

Step-by-step explanation:

Answer:

CDL

Step-by-step explanation:

C is 100

D is 500

500-100=400

L is 50

400+50=450

Answer:

[tex] \frac{ {6}^{10} }{ {6}^{3} } \\ = \frac{ {6}^{3} \times {6}^{7} }{ {6}^{3} } \\ = {6}^{7} \\ thank \: you[/tex]

Answer:

24.587

Step-by-step explanation:

divide the speed value by 2.237

Answer:

hope this helps you

god bless you

Answer:

[tex]2 \div 3 \\ \frac{2}{3} [/tex]

Answer:

These are the missing numbers

Sec1

A. 12, 29/2, 17 (arithmetic)

C. 3/16, 3/32, 3/64 (geometric)

D. 17, 33, 65 (neither)

Sec2

A. 8, 48 (growth)

B. 16, 32 (growth)

C. 1, 2 (rate)

Step-by-step explanation:

Section 1

A. add by 2.5 or 5/2

C. multiply by 1/2

D. double the value-added

Section2

A & B. multiply by 2

C. add 1/2

Hi ;-)

[tex]3\cdot\boxed9=9\cdot3[/tex]

Answer:

3 × 9 = 9 × 3

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

(x-2)/(x+1)=1/2, we use that a/b = c/d is the same as a*d = c*b

2*(x-2) = 1* (x+1), distribute multiplication over subtraction

2x -4 = x +1 , subtract x and add 4 to both sides

2x -x = 1 +4, combine like terms

x = 5

Answer: x = 5

Solve:

Given

(x - 2) / (x + 1) = 1/2

Cross multiply applied

1 (x + 1) = 2 (x - 2)

Expand parentheses and apply the distributive property

x + 1 = 2x - 4

Add 4 on both sides

x + 1 + 4 = 2x - 4 + 4

x + 5 = 2x

Subtract x on both sides

x + 5 - x = 2x - x

x = 5

Check:

Left-hand side = (x - 2) / (x + 1) = (5 - 2) / (5 + 1) = 3/6 = 1/2

Right-hand side = 1/2

1/2 = 1/2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

4÷ 1 1 /8 =  32 /9 =  3 5 /9

Answer:

This is the formula u can use but the parameters are not complete

Step-by-step explanation:

b=2 A/h

Answer:

8 cm^2.

Step-by-step explanation:

Area = 1/2 * base * height

= 1/2 * 4 * 4

= 8.

Step-by-step explanation:

x + 4 + 3x = 72 Let's agroup all the x

4x + 4 = 72 Subtract 4 on both sides

4x = 68 Divide both sides by 4

x = 17

x + 3 + x – 8 + x = 55 Let's agroup all the x

3x + 3 – 8 = 55 Solve 3 – 8

3x – 5 = 55 Add 5 on both sides

3x = 60 divide both sides by 3

x = 20

Step-by-step explanation:

The x's will simply cancel each other out and you will be left with a 6

hope it makes sense

:)

Answer:

30%=1350

45%=2025

Step-by-step explanation:

30% of 4500 = 0.30 × 4500

=1350

45% of 4500 = 0.45 × 4500

=2025

baiiiiwiedujjjdjdhsb20

Answer:

Step-by-step explanation:

answer B

since for all real positive r,  r^x >0

The unique function who give a negative answer is f(x)=-3* 2^x

congrats? Im not sure what to say.

Answer:

12 workers are required to complete the work in 12 days