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3 years ago

5

What is the next number sequence after 459?

1 answer:

Karo-lina-s [1.5K]3 years ago

3 0

4,5,9,16 is the sequence

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A, b, and c are collinear, and B is between a and c. The ratio of AB to AC is 1:2. If A is at (7,-1) and B is at (2,1) what are

Nutka1998 [239]

Answer:

C(-3,3)

Step-by-step explanation:

Given

A = (7,-1)

B = (2,1)

AB:AC = 1:2

Required

Determine the coordinates of C

Since, B is between A and C; we need to determine ratio BC as follows;

$AB:AC = 1:2$

Convert to division

$\frac{AB}{AC} = \frac{1}{2}$

<em>AC = AB + BC;</em>

$\frac{AB}{AB + BC} = \frac{1}{2}$

Cross Multiply

$2 * AB = 1 * (AB + BC)$

$2 AB = AB + BC$

$2AB - AB = BC$

$AB = BC$

Divide both sides by BC

$\frac{AB}{BC} = 1$

Rewrite as

$\frac{AB}{BC} = \frac{1}{1}$

Write as ratio

$AB:BC = 1:1$

Next is to determine the coordinates of C as follows;

Because B is between both points. we have:

$B(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where

$m:n = AB:BC = 1:1$

$B(x,y) = B(2,1)$

$A(x_1,y_1) = A(7,-1)$

So; we're solving for x2 and y2

$B(2,1) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where

Solving for x2;

$x = \frac{mx_2 + nx_1}{m+n}$

$2 = \frac{1 * x_2 + 1 * 7}{1+1}$

$2 = \frac{x_2 + 7}{2}$

Cross Multiply

$2 * 2 = x_2 + 7$

$4 = x_2 + 7$

$x_2 = 4 - 7$

$x_2 = -3$

Solving for y2;

$y = \frac{my_2 + ny_1}{m+n}$

$1 = \frac{1 * y_2 + 1 * -1}{1+1}$

$1 = \frac{y_2- 1}{2}$

Cross Multiply

$2 * 1 = y_2 - 1$

$2 = y_2 - 1$

$y_2 = 2 + 1$

$y_2 = 3$

<em>Hence, the coordinates of C are: C(-3,3)</em>

4 0

3 years ago

Plzzz help I will mark Brainlyest

Katyanochek1 [597]

Answer:

6

Explanation:

the sum of all four angles in a quadrilateral is 360°. thus, to find the angle ∠JML, we need to subtract the values of the other angles from 360° as such:

360° - 66° - 74° - 110° = 110°

the total value of angle ∠JML is 110°.

now, since ∠JML is equal to 17x + 8, we can subtract 8° from 110° to get 102°. following that, we can divide 102° by 17 which yields us the result of 6. hence, we now know that <u>x = 6</u>.

7 0

3 years ago

What three numbers equal 918

Anna35 [415]

330+305+283=918

hope this helps

3 0

3 years ago

The radius of a cylinder is increased by 15% and its height is decreased by 20%. Find the percentage change in the volume of the

Alexxx [7]

First cylinder(V1) = $\pi$ r²h

insert 10 as r&h
⇒V1 = 1000 $\pi$

second cylinder(V2)= $\pi$ ×11.5² × 8 = 1058 $\pi$

V2-V1 = 58 $\pi$

100 × $\frac{58 \pi }{1000 \pi }$ = 5.8% increase

8 0

3 years ago

A sphere of radius 7 in. Is placed inside a rectangular prism with length 15 in., width 18 in., and height 20 in. What is the vo

iragen [17]

Answer:

3964 in³

Step-by-step explanation:

volume of sphere: V = 4/3 πr³

v₁ = 4/3 x 3.14 x 7³ = 1436

volume of prism: v = Bh B = 15 x 18 = 270 h = 20

v₂ = 270 x 20 = 5400

v₂ - v₁ = 5400 - 1436 = 3964 in³

5 0

4 years ago