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3 years ago

Help or u will not get brainlest

Mathematics

1 answer:

klemol [59]3 years ago

7 0

Answer:

1st Equation: 0.95 x 15 answer if needed: 14.25

2nd Equation: 15 - 0.25 answer if needed: 14.25

Step-by-step explanation:

1st: 100% would be 1, so subtract 0.05 (5%) from that to get 0.95 (95%), then multiply that by the total amount of money (undiscounted)

2nd: Find the original price. Get the the discount percentage. Calculate the savings. Subtract the savings from the original price to get the sale price

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Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.

jok3333 [9.3K]

Answer:

$\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1$

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

$\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}$

And, the distance from P to (0, -2) will be:

$\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}$

So sum of the two distances must be 6. Therefore:

$d_1+d_2=6$

Now, by substitution:

$(\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6$

Simplify. We can subtract the second term from the left:

$\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}$

Square both sides:

$(x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)$

We can cancel the x² terms and continue squaring:

$y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4$

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

$-8y=36-12\sqrt{x^2+(y+2)^2}$

We can divide both sides by -4:

$2y=-9+3\sqrt{x^2+(y+2)^2}$

Adding 9 to both sides yields:

$2y+9=3\sqrt{x^2+(y+2)^2}$

And, we will square both sides one final time.

$4y^2+36y+81=9(x^2+(y^2+4y+4))$

Distribute:

$4y^2+36y+81=9x^2+9y^2+36y+36$

The 36y will cancel. So:

$4y^2+81=9x^2+9y^2+36$

Subtracting 4y² and 36 from both sides yields:

$9x^2+5y^2=45$

And dividing both sides by 45 produces:

$\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1$

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

5 0

3 years ago

Read 2 more answers

What is the length of side TS?

-Dominant- [34]

We know that

in the triangle TQS
applying the Pythagorean theorem
QS²=TS²+TQ²---------> TQ²=QS²-TS²--------> TQ²=18²-9x²-----> equation 1

in the triangle TRS
TS²=TR²+RS²--------------> TR²=TS²-RS²-------> TR²=9x²-144----> equation 2

in the triangle QTR
TQ²=TR²+36-----------> equation 3

I substitute 1 and 2 in 3
18²-9x²=9x²-144+36--------> 18x²-432=0------> x²=24-------> x=√24
x=2√6
TS=3*x------> 3*2√6-----> 6√6
TS=6√6 units

the answer is
TS=6√6 units
6 is the square root of 6 units

6 0

3 years ago

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Solve each inequality. Then compare the solutions. 3x +4> 16 - 2x + 19< 11

Makovka662 [10]

Answer:

$3x + 4 > 16 \\ 3x > 16 - 4 \\ \frac{3x}{3} > \frac{12}{3} \\ x > 4 \\ \\ - 2x + 19 < 11 \\ - 2x < 11 - 19 \\ - 2x < - 8 \\ \frac{ - 2x}{ - 2} > \frac{ - 8}{ - 2} \\ x > 4 \\ \\ comparing \\ 4 < x > 4$

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3 years ago

7 watermelons cost $8.96.Which equation would help determine the cost of the 5 watermelons?

postnew [5]

Answer: ($8.96 / 7) * 5 or $6.40

Step-by-step explanation: You need to find the price for one watermelon then multiply it by 5 to find the price of 5.

4 0

4 years ago

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Prove that the diagonals of a parallelogram bisect each other. The midpoint of AC is

iren2701 [21]

Answer:

Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Step-by-step explanation:

3 0

3 years ago