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zysi [14]
3 years ago
7

Complete the patterns

Mathematics
1 answer:
Rzqust [24]3 years ago
7 0
A. 0.02 0.2 2 20 200 2000
b. 3,400,000 , 34,000 , 340 ,3.4, 0.034
c. 85700 8,570 857 85.7 8.57 0.857
d. 444 4440 44,400 444,000 4,440,000 44,400,000
e. 0.095 9.5 950 95,000 9,500,000 950,000,000
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the coordinates of the vertex of a parabola in the xy-plane are (-4,k). If the y-intercept of the parabola is 12 and the parabol
svp [43]

The value of k is (A) 20/3.

<h3>What is a parabola?</h3>
  • A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics.
  • It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves.
  • A point and a line are two ways to describe a parabola.

To find the value of k:

  • y - b = c (x - a)²

Where (a, b) is the vertex and c is the constant.

  • (a, b) = (-4, k)
  • y - k = c (x - (- 4))²
  • y - k = c (x + 4)²

So,

  • x = 0, y = 12
  • 12 - k = 16c
  • k = 12 - 16c  ...... (1)

Then,

  • (-3, 7) = (x, y)
  • 7 - k = c (1)²
  • k = 7 - c  ...... (2)

Now,

  • 12 - 16c = 7 - c
  • 12 - 7 = 16c - c
  • 5 = 15c
  • c = 5/15 = 1/3

So, the value of k:

  • k = 12 - 16 (1/3) = 12 - 16/3 = 36-16/3 = 20/3

Therefore, the value of k is (A) 20/3.

Know more about a parabola here:

brainly.com/question/4061870

#SPJ4

The complete question is given below:

The coordinates of the vertex of a parabola in the XY plane are (-4,k). If the y-intercept of the parabola is 12 and the parabola passes through the point (-3,7), then what is the value of k?

(A) 20/3

(B) 16/5

(C) 14/3

(D) 12/5

5 0
1 year ago
The measure of ∠BAC is π/3 radians and the measure of ∠CAD is π/2 radians. What is the measure of ∠BAD?
GREYUIT [131]

9514 1404 393

Answer:

  5π/6 radians

Step-by-step explanation:

The whole is the sum of the parts.

  ∠BAD = ∠BAC +∠CAD

  ∠BAD = π/3 + π/2 = π(2/6 + 3/6)

  ∠BAD = 5π/6

6 0
2 years ago
What is 50/45 simplified
icang [17]

Answer:

10/9 is the simplified fraction for 50/45.

Step-by-step explanation:

3 0
3 years ago
At the start of a mission, international spy James withdrew $5,000 in Cairo. In Istanbul, he withdrew half of the remaining mone
lord [1]

Answer:

Initial Amount at the start of the mission=\$20000

Step-by-step explanation:

Let initial amount=x

In Cario James withdrew \$5000.

Remaining Amount=x-5000

In Instanbul he with drew half of the remaining amount so half of the remaining amount will be left.

\frac{1}{2}\times(x-5000)=7500\\\\x-5000=15000\\\\x=20000

8 0
3 years ago
In ΔLMN, the measure of ∠N=90°, the measure of ∠M=17°, and MN = 20 feet. Find the length of LM to the nearest tenth of a foot.
andrey2020 [161]
20.9 ft
This is a right triangle trigonometry question because N is 90 degrees. MN is adjacent to M and LM is the hypotenuse. Adjacent any hypotenuse use the cosine function. 
cos \theta = \frac{adj}{hyp}
plug in known values
cos(17) = \frac{20}{x}
switch cos(20) and x using the products property
x = \frac{20}{cos(17)}
plug into calculator to get 20.9 ft

3 0
2 years ago
Read 2 more answers
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