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3 years ago

What is an equation of the line containing the points (-1,5) and (3,9)

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

3 0

Answer:

y = x+6

Step-by-step explanation:

You can find an equation by using the 2-point form of the equation for a line:

y = (y2 -y1)/(x2 -x1)·(x -x1) +y1

Filling in the given values, we have ...

y = (9 -5)/(3 -(-1))·(x -(-1)) +5

y = (4/4)(x +1) +5 . . . . simplifying a bit

y = x +6

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If you deposit $25,000 now at 6.5% compounded quarterly, how much will you have in 30 years?

Mice21 [21]

Answer:

$172,984.44

Step-by-step explanation:

We can use the formula

$A = P(1 + \frac{r}{n})^{nt}$ to compute the final amount

Here P is the principal amount, the original deposit = $25,000

r is the annual interest rate = 6.5% = 0.065 in decimal

n is the number of times the compounding takes place. Here it is quarterly so it is 4 times a year

t is the number of time periods ie 30 years

A is the accrued amount ie principal + interest

Computing different components,

$nt = 4 \times 30 = 120$

$r/n = 0.065/4 = .01625$

$1 + r/n = 1.01625$

$(1 + r/n)^{nt} = 1.01625^{120}$

Therefore

$A = 25000 \times 1.0625^{120} = 172,984.44$

4 0

2 years ago

Can someone plz help me with this!

asambeis [7]

Answer:

(arranged from top to bottom)

System #3, where x=6

System #1, where x=4

System #7, where x=3

System #5, where x=2

System #2, where x=1

Step-by-step explanation:

System #1: x=4

$2x+y=10\\x-3y=-2$

To solve, start by isolating your first equation for y.

$2x+y=10\\y=-2x+10$

Now, plug this value of y into your second equation.

$x-3(-2x+10)=-2\\x+6x-30=-2\\7x=28\\x=4$

System #2: x=1

$x+2y=5\\2x+y=4$

Isolate your second equation for y.

$2x+y=4\\y=-2x+4$

Plug this value of y into your first equation.

$x+2(-2x+4)=5\\x+(-4x)+8=5\\x-4x+8=5\\-3x=-3\\x=1$

System #3: x=6

$5x+y=33\\x=18-4y$

Isolate your first equation for y.

$5x+y=33\\y=-5x+33$

Plug this value of y into your second equation.

$x=18-4(-5x+33)\\x=18+20x-132\\-19x=-114\\x=6$

System #4: all real numbers (not included in your diagram)

$y=13-2x\\8x+4y=52$

Plug your value of y into your second equation.

$8x+4(13-2x)=52\\8x+52-8x=52\\0=0$

<em>all real numbers are solutions</em>

System #5: x=2

$x+3y=5\\6x-y=11$

Isolate your second equation for y.

$6x-y=11\\-y=-6x+11\\y=6x-11$

Plug in your value of y to your first equation.

$x+3(6x-11)=5\\x+18x-33=5\\19x=38\\x=2$

System #6: no solution (not included in your diagram)

$2x+y=10\\-6x-3y=-2$

Isolate your first equation for y.

$2x+y=10\\y=-2x+10$

Plug your value of y into your second equation.

$-6x-3(-2x+10)=-2\\-6x+6x-30=-2\\-30=-2$

<em>no solution</em>

System #7: x=3

$y=10+x\\2x+3y=45$

Plug your value of y into your second equation.

$2x+3(10+x)=45\\2x+30+3x=45\\5x=15\\x=3$

3 0

3 years ago

• A rational number is such that when you multiply it by

Tatiana [17]

Answer:

The number is -1/2.

Step-by-step explanation:

I am assuming they are fractions. So we have the equation:

5/2 x + 2/3 = -7/12

We multiply through by 12 to eliminate the fractions:

5/2 * 12 x + 2/3 * 12 = -7/12 * 12

30x + 8 = -7

30x = -15

x = -15/30

x = -1/2.

7 0

3 years ago

Calculate the length of the circumference of a circle with diameter of 10.4

Kitty [74]

To work out the Circumference of a circle, we must o the calculation
πd
π x d
If we fill in the information we know
π x 10.4
3.14 x 10.4 (to 2 d.p.)
↓
32.656 (units)

7 0

2 years ago

Read 2 more answers

your class is making a rectangular poster for a rally. the posters design is 6 in. high by 10 in. wide. the space allowed for th

Kay [80]

I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.

PLEASE SEE ATTACHED IMAGE.

For this case the area is given by:

A = (22 + x) * (28 + x) = 722

Rewriting we have:

616 + 22x + 28x + x ^ 2 = 722

x ^ 2 + 50x + 616 - 722 = 0

x ^ 2 + 50x - 106 = 0

Solving the polynomial we have:

x1 = 2.04

x2 = -52.04

We take the positive root:

x = 2.04 inches:

Answer:

The width of the border to the nearest inch is:

x = 2inches

3 0

3 years ago

Read 2 more answers

What is an equation of the line containing the points (-1,5) and (3,9)​

What is an equation of the line containing the points (-1,5) and (3,9)