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3 years ago

5

Thomas earns x dollars each week walking his neighbor’s dog. He also earns $10 allowance each week. Which expression represents

the amount of money Thomas has earned after 4 week select each correct statments

1 answer:

aliya0001 [1]3 years ago

7 0

4(x+10) would be the simplest equation. 4 represent the 4 weeks. X is how much he earns walking his neighbor's dog. 10 represents his allowance.

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Find the two intersection points

bogdanovich [222]

Answer:

Our two intersection points are:

$\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)$

Step-by-step explanation:

We want to find where the two graphs given by the equations:

$\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1$

Intersect.

When they intersect, their <em>x-</em> and <em>y-</em>values are equivalent. So, we can solve one equation for <em>y</em> and substitute it into the other and solve for <em>x</em>.

Since the linear equation is easier to solve, solve it for <em>y: </em>

<em /> $\displaystyle y = -\frac{3}{4} x + \frac{1}{4}$ <em />

<em />

Substitute this into the first equation:

$\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16$

Simplify:

$\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16$

Square. We can use the perfect square trinomial pattern:

$\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16$

Multiply both sides by 16:

$(16x^2+32x+16)+(9x^2-54x+81) = 256$

Combine like terms:

$25x^2+-22x+97=256$

Isolate the equation:

$\displaystyle 25x^2 - 22x -159=0$

We can use the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, <em>a</em> = 25, <em>b</em> = -22, and <em>c</em> = -159. Substitute:

$\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}$

Evaluate:

$\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}$

Hence, our two solutions are:

$\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}$

We have our two <em>x-</em>coordinates.

To find the <em>y-</em>coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

$\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2$

And:

$\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}$

Thus, our two intersection points are:

$\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)$

6 0

2 years ago

A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school coll

Mademuasel [1]

Amount of money collected in the 2-day fundraiser is represented by the following equations:

12x + 4y = 152 .................. (i)
32x + 12y = 420 .................. (ii)

where x is the cost of a chicken lunch and y is the cost of a vegetarian lunch

Multiplying (i) with 3 and subtracting it from (ii)

36x + 12y - (32x + 12y) = 456 - 420

⇒ 4x = 36

⇒ x = 9

Put value of x in (i)

⇒ 12 × 9 + 4y = 152

⇒ 108 + 4y = 152

⇒ 4y = 44

⇒ y = 11

Hence, cost of the vegetarian meal is 11.

7 0

3 years ago

PLEASE HELP MATHS PROBLEM!!!

adoni [48]

Just ask google ot will halp you better but i think its -48

4 0

3 years ago

Read 2 more answers

How do I solve radicals??

Sav [38]

Your question is too general. You might ask instead, "how do I simplify the radical sqrt(48)?"

sqrt(48) can b e simplified by rewriting 48 as the product of the perfect square 16 and the not-a-perfect-square 3:

sqrt(48) = sqrt(16)*sqrt(3) = 4*sqrt(3) (answer)

In #76, rearrange the terms so that you have 3sqrt(7x+4)=15. Then divide both sides by 3, obtaining sqrt(7x+4) =5. Squaring both sides: 7x+4=25.
Solve this linear equation for x.

4 0

3 years ago

Which angles are vertical to each other?

Nutka1998 [239]

The two vertical angles are FDE and JDI

8 0

3 years ago

Read 2 more answers