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Ray Of Light [21]

4 years ago

7

Jasmine and Daniel each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store

. Jasmine spent $145 on 13 square feet of grass and 9 geraniums. Daniel spent $100 on 4 square feet of grass and 12 geraniums. What is the cost of 1 square foot of grass and 1 geranium?

1 answer:

Burka [1]4 years ago

4 0

Answer:

Cost of 1 ft²: $7

Cost of 1 ft² of geranium: $6

Step-by-step explanation:

Let x be the cost of a ft² of grass

Let y be the cost of a ft² of geranium

13x + 9y = 145

4x + 12y = 100

x + 3y = 25

x = 25 - 3y

13(25 - 3y) + 9y = 145

325 - 39y + 9y = 145

180 = 30y

y = 6

x = 25 - 3(6)

x = 7

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Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all tha

vodomira [7]

we have

$\frac{3}{5}x+ \frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x$

Combine like terms in both sides

$(\frac{3}{5}x+ x)+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x$

we know that

$(\frac{3}{5}x+ x)=(\frac{3}{5}x+ \frac{5}{5}x)=\frac{8}{5}x$

substitute in the expression above

$\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x$ -----> equation A

Multiply equation A by $5*3*2=30$ both sides

$30*(\frac{8}{5}x+\frac{2}{3})=30*(\frac{1}{2}-\frac{1}{5}x)$

$48x+20=15-6x$ ---------> equation B

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$48x+6x=15-20$

$54x=-5$ ---------> equation C

Solve for x

$x=-\frac{5}{54} =-0.09$

We are going to proceed to verify each case to determine the solution.

<u>Case a)</u> $\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x$

the case a) is equal to the equation A

so

the case a) have the same solution that the given equation

<u>Case b)</u> $18x+20+30x=15-6x$

Combine like terms in left side

$(18x+30x)+20=15-6x$

$(48x)+20=15-6x$

the case b) is equal to the equation B

so

the case b) have the same solution that the given equation

<u>Case c)</u> $18x+20+x=15-6x$

Combine like terms in left side

$(18x+x)+20=15-6x$

$(19x)+20=15-6x$

$19x+6x=15-20\\25x=-5\\x=-0.20$

$-0.20\neq -0.09$

therefore

the case c) not have the same solution that the given equation

<u>Case d)</u> $24x+30x=-5$

Combine like terms in left side

$54x=-5$

the case d) is equal to the equation C

so

the case d) have the same solution that the given equation

<u>Case e)</u> $12x+30x=-5$

Combine like terms in left side

$42x=-5$

$x=-5/42=-0.12$

$-0.12\neq -0.09$

therefore

the case e) not have the same solution that the given equation

therefore

<u>the answer is</u>

case a) $\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x$

case b) $18x+20+30x=15-6x$

case d) $24x+30x=-5$

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Dennis_Churaev [7]

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Answer:

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Step-by-step explanation:

Ship:

The number f(x) of miles a ship is from its destination x hours after starting a voyage is given by f(x) = 120 - 25x. This means, initially the ship is 120 miles away from its destination.

If the ship traveled 120 miles, then f(x)=0 (the ship will be 0 miles away from its destination) and

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At x = 5 hours, the submarine was 0 miles away.

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Answer:

A.) NM= x

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Step-by-step explanation:

If the legs are both x, then the hypotenuse is equal to $x\sqrt{2$

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4 years ago

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