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belka [17]
3 years ago
7

Right in equation that will model the proportional relationship given in each real world situation. Jennifer is shopping with he

r mother. They pay two dollars per round for tomatoes at the vegetable stand. Find the constant of proportionality in the situation. Right in equation to re-present the relationship.
Mathematics
2 answers:
Step2247 [10]3 years ago
8 0
Could you take. A picture of the problem
ycow [4]3 years ago
8 0
K=2 (constant of proportionality)
y=2x  (cost = 2 * the cost of tomatoes)
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Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1
Nesterboy [21]

Answer:

x=4

Step-by-step explanation:

Given \displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1, start by squaring both sides to work towards isolating x:

\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2

Recall (a-b)^2=a^2-2ab+b^2 and \sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}:

\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1

Isolate the radical:

\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}

Square both sides:

\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2

Expand using FOIL and (a+b)^2=a^2+2ab+b^2:

\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36

Move everything to one side to get a quadratic:

\displaystyle-\frac{1}{4}x^2+7x-24=0

Solving using the quadratic formula:

A quadratic in ax^2+bx+c has real solutions \displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}. In \displaystyle-\frac{1}{4}x^2+7x-24, assign values:

\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24

Solving yields:

\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}

Only x=4 works when plugged in the original equation. Therefore, x=24 is extraneous and the only solution is \boxed{x=4}

4 0
2 years ago
What is the best estimate for 591.3 divided by 29
Katena32 [7]

Answer:

  about 20

Step-by-step explanation:

The numbers round to 600/30 = 20, which is a reasonable estimate.

You can refine this by doing the next step of long division:

  29×20 = 580

Subtracting this from 591.3 give 11.3, so the fraction is ...

  11.3/29 ≈ 10/30 = 1/3

A better estimate is 20 1/3.

_____

A calculator tells you the quotient is about 20.3897.

4 0
2 years ago
PLEASE HELP HELP ME HELP ME HELP ME ITS MATH EZ STUFF
anyanavicka [17]

Answer:

Bruh your in high school yo know this stuff just make everything a decimal to get your answer. Lol you really forgot this?

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Which of these nonterminating decimals can be converted into a rational number?
ValentinkaMS [17]

A can be converted since it is a repeating decimal


4 0
3 years ago
Last month, 17 people showed up to help a local charity. This month, 55 people volunteered. What is the percentage increase?
astra-53 [7]

Step-by-step explanation:

The formula for percent change is

change/original.

So let's subtract 17 from 55 to find the change. 55-17=38

This is the change. Now we divide it by the original, 17.

38/17=2.235294

We're not done yet! We have to move the decimal point over to the right 2 spaces to make it a percentage. So, the percentage increase is

about 223.53 percent

6 0
3 years ago
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