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3 years ago

Find the coordinates of the point where the lines with equations y=x and y=-6 intersect

Mathematics

1 answer:

Kazeer [188]3 years ago

8 0

Answer:

(-6, -6)

Step-by-step explanation:

Find the coordinates of the point where the lines with equations y=x and y=-6 intersect.

The lines intersect at y = y

Equating the right hand side of both expressions we have;

x = -6

Since y = x, hence y = -6

The required coordinate where they intersect is at (-6, -6)

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Provides data on sleep deprivation rates of Californians and Oregonians. The proportion of California residents who reported ins

Bond [772]

Answer:

Step-by-step explanation:

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8 0

3 years ago

A fence is being built around a rectangular garden. The length of the garden is 35 feet, and the total fencing used to enclose t

liraira [26]

The garden's width is 45. We know this because
$35 \times 2$
(length)
$35 \times 2 + 2x = 160 \\$
35x2 is 70 and you need to neutralize that by taking away 70 from both sides.
$160 - 70 = 90$
$2x = 90$
Now divide by 2 on both sides to neutralize the 2 times x.
$90 \div 2 = 45$
meaning that leaves us with
$x = 45$

3 0

3 years ago

Read 2 more answers

Which point below is a solution to the equation y = 2x + 3?

Anastasy [175]

Answer:

C (37, 77)

Step-by-step explanation:

<h3>Option A:</h3>

$291=2(145)+3\\\\291=290+3\\\\\boxed{291\neq 293}$

Option A is not a solution.

<h3>Option B:</h3>

$163=2(78)+3\\\\163=156+3\\\\\boxed{163\neq 159}$

Option B is not a solution.

<h3>Option C:</h3>

$77=2(37)+3\\\\77=74+3\\\\\boxed{77=77}$

Option C is a solution.

Hope this helps.

6 0

3 years ago

Read 2 more answers

Please help me simplify these expressions

Rina8888 [55]

Answer:

4. -2s^9

7. 8b^10

Step-by-step explanation:

First, focus on the number part of the expression. For 4), multiply -2 x -1 x -1 = -2. Then, look at the exponents. When you're multiplying exponents with the same base (in number 4, the base is s), you can add the exponents.

2+3+4 = 9; which makes it s^9. Multiply -2 x s^9, which gives you -2s^9.

Same thing for 7). Multiply all the numbers first. this gives you 8. (Remember two negatives equals a positive). Add all of the exponents of b together, which gives you 10. (when a variable has no exponent, it means that the exponent is 1.) Multiplying 8 and b^10 should give you 8b^10.

It may help to brush up on exponent rules and sign rules.

6 0

4 years ago

A rectangular piece of sheet metal has a length that is 6 in. less than twice the width. a square piece 3 in. on a side is cut f

m_a_m_a [10]

The original width would be 19 and the original length would be 32.

Let w be the width. Then 2w-6 would be the length. However, after cutting a 3-inch square from each corner, both the width and length left over to fold into a box would be 6 inches smaller; thus the dimensions would be w-6 and 2w-6-6 or 2w-12.

Since the section cut out is 3 inches long, 3 will be the height of the box.

Volume is found by multiplying the length, width and height of the box; thus we have:

1014=(w-6)(2w-12)(3)

We multiply the binomials and have:
1014 = [w*2w-12*w-6*2w-6(-12)](3)
1014 = (2w²-12w-12w+72)(3)
1014 = (2w²-24w+72)(3)
1014 = 6w² - 72w + 216

When solving a quadratic equation, we want it set equal to 0. Subtract 1014 from each side:

1014-1014 = 6w² - 72w + 216 - 1014
0 = 6w² - 72w - 798

We will use the quadratic formula to solve this:

$w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}
\\
\\=\frac{--72\pm \sqrt{(-72)^2-4(6)(-798)}}{2(6)}
\\
\\=\frac{72\pm \sqrt{5184--19152}}{12}
\\
\\=\frac{72\pm \sqrt{5184+19152}}{12}
\\
\\=\frac{72\pm \sqrt{24336}}{12}
\\
\\=\frac{72\pm 156}{12}
\\
\\=\frac{72+156}{12} \text{ or } \frac{72-156}{12}
\\
\\=\frac{228}{12} \text{ or } \frac{-84}{12}=19 \text{ or } -7$

Since we cannot have a negative number for a measurement, 19 has to be the width; then 2(19)-6 = 32 would be the length.

4 0

3 years ago