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3 years ago

What types of quadrilaterals have congruent diagonals?

Mathematics

1 answer:

labwork [276]3 years ago

8 0

Rectangle and Square

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PLEASE HELP!!

Bezzdna [24]

Answer:

$y=-\dfrac{9}{40}x^2+\dfrac{441}{40}\\ \\y=-\dfrac{9}{160}x^2+\dfrac{1,521}{160}$

Step-by-step explanation:

If a parabola has its vertex on the y-axis, then its equation is

$y=ax^2+b$

This parabola passes through the point R(3,9), then

$9=a\cdot 3^2+b\\ \\9=9a+b$

The area of the right triangle PQR is

$A_{PQR}=\dfrac{1}{2}\cdot PQ\cdot QR$

Find PQ and QR, if $P(x_1,0),\ Q(3,0),\ R(3,9):$

$PQ=\sqrt{(x_1-3)^2+(0-0)^2}=|x_1-3|\\\\QR=\sqrt{(3-3)^2+(0-9)^2}=9$

Now,

$40.5=\dfrac{1}{2}\cdot |x_1-3|\cdot 9\\ \\90=9|x_1-3|\\ \\|x_1-3|=10\\ \\x_1-3=10\ \text{or}\ x_1-3=-10\\ \\x_1=13\ \text{or }x_1=-7$

We get two possible points $P_1(-7,0)$ and $P_2(13,0).$

For point $P_1:\\$

$0=a\cdot (-7)^2+b\\ \\49a+b=0$

So,

$b=-49a\\ \\9=9a-49a\\ \\-40a=9\\ \\a=-\dfrac{9}{40}\\ \\b=\dfrac{441}{40}\\ \\y=-\dfrac{9}{40}x^2+\dfrac{441}{40}$

For point $P_2:\\$

$0=a\cdot (13)^2+b\\ \\169a+b=0$

So,

$b=-169a\\ \\9=9a-169a\\ \\-160a=9\\ \\a=-\dfrac{9}{160}\\ \\b=\dfrac{1,521}{160}\\ \\y=-\dfrac{9}{160}x^2+\dfrac{1,521}{160}$

5 0

3 years ago

two cars start from two towns 400 miles apart and travel towards each other. They pass each other after 4 hours. find the speed

Gemiola [76]

<span>use an expression
s = speed of the slower car
then
(s+20) = speed of the faster car

When they meet is after 400 miles

Write distance equation

slow car d + fast car d = 400 mi
4s + 4(s+20) = 400

8s + 80 = 400

8s = 400 - 80

8s = 320

s = 40 m/H</span>

5 0

3 years ago

Read 2 more answers

Caroline, Krutika and Natasha share some sweets in the ratio 2:5:3. Caroline gets 12 sweets. How many more sweets does Krutika g

bogdanovich [222]

Answer:

12 more sweets

Step-by-step explanation:

6 0

3 years ago

Lines s and t are perpendicular. If the slope of line s is -5, what is the slope of line ?

stiks02 [169]