All categories

4 years ago

Complete the statement about parallelogram ABCD.

Mathematics

1 answer:

Crank4 years ago

4 0

Step-by-step explanation:

Opposite angles of parallelograms are congruent

You might be interested in

Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

3 years ago

Read 2 more answers

A frame is marked down by 22 percent from an original price of $14.50. What is the new price?

Valentin [98]

22% = 22/100 22/100 * 14.50 = 3.19 (this is the amount discounted off original price) 14.50 - 3.19 = $11.31

7 0

3 years ago

Read 2 more answers

HELP<br>8 Prove that 8^6+4^11 is divisible by 17. Answer __*17

Marina CMI [18]

Answer:

<u>262,144</u> goes in the blank

Step-by-step explanation:

8^6 = 262,144

4^11 = 4,194,304

4,194,304 + 262,144 = 4,456,448

4,456,448 ÷ 17 = 262,144

8 0

3 years ago

732,178 + 167 - 542,137

klio [65]

Answer:

190,208

Step-by-step explanation:

732,178 + 167 = 732,345

732,345 - 542,137 = 190,208

6 0

3 years ago

Read 2 more answers

At Wallys school 30% of the student are in 8th grade if there are 470 students total find the number of 8th grade students

kiruha [24]

30%*470=141 (So the number of students in 8 grade is 141)

4 0

4 years ago

Read 2 more answers