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3 years ago

What is the distance between (1,-5) and (-3,6)

Mathematics

1 answer:

Wewaii [24]3 years ago

4 0

Answer:

$\large\boxed{\sqrt{137}\approx11.7}$

Step-by-step explanation:

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have two points (1, -5) and (-3, 6). substitute:

$d=\sqrt{(-3-1)^2+(6-(-5))^2}=\sqrt{(-4)^2+11^2}=\sqrt{16+121}=\sqrt{137}$

You might be interested in

The cube of the difference of a number and 4

lbvjy [14]

Answer:

(x - 4)³

Step-by-step explanation:

"The cube of x" would be x³. The difference of a number and 4 would be x - 4.

Therefore, "the cube of the difference of a number and 4" would be

(x - 4)³

6 0

3 years ago

Pratap puri rowed 10 miles down a river in 2 hours, but the return trip took him 2 and one half hours. Find the rate pratap can

N76 [4]

Answer:

Rate of Pratap in still water is 4.5 miles/hour and rate of current is 0.5 miles/hour.

Step-by-step explanation:

Pratap Puri rowed 10 miles down a river in 2 hours, but the return trip took him 2.5 hours.

We know that, $Speed = \frac{Distance}{Time}$

So, the speed of Pratap with the current will be: $(\frac{10}{2})miles/hour = 5$ miles/hour

and the speed of Pratap against the current will be: $(\frac{10}{2.5})miles/hour = 4$ miles/hour.

Suppose, the rate of Pratap in still water is $x$ and the rate of current is $y$ .

So, the equations will be........

$x+y= 5 .............................. (1)\\ \\ x-y=4 .............................. (2)$

Adding equation (1) and (2) , we will get......

$2x=9\\ \\ x=\frac{9}{2}= 4.5$

Now, plugging this $x=4.5$ into equation (1), we will get.....

$4.5+y=5\\ \\ y=5-4.5 =0.5$

Thus, Pratap can row at 4.5 miles per hour in still water and the rate of the current is 0.5 miles/hour.

6 0

3 years ago

( 32.45 - 4.8) - 2.06

Igoryamba

Answer:

25.59

Step-by-step explanation:

The first thing that you will do is solve parenthesis (remember PEMDAS).

(32.45-4.8) - 2.06

(27.65) - 2.06

Then do the subtraction.

(27.65) - 2.06=

25.59

Hope this helps!

5 0

2 years ago

Please help!! Very urgent..thank you!!

erastova [34]

Answer : 4 times

Here it's given that ,

The height and base of the butterfly sitting on the stem (red butterfly) is two times greater than the height and base of the butterfly sitting on the flower .

And we need to find out how many times the area of red winged butterfly is greater than that of sitting on the flower (blue butterfly) .

Let us take ,

base of blue butterfly be b
height of blue butterfly be h
Area be A .

Then ,

base of red butterfly will be 2b .
height of red butterfly will be 2h .
Area be A' .

We know that ,

→ area of the triangle = 1/2 × base × height

So that ,

→ A/A' = (1/2 * b * h) ÷ (1/2 *2b *2h)

→ A/A' = bh/4bh

→ A/A' = 1/4

→ A' = 4A

Henceforth the area of blue butterfly is 4 times greater than that of red winged butterfly .

I hope this helps.

6 0

1 year ago

he owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on w

stellarik [79]

Answer:

90% confidence interval is ( -149.114, -62.666 )

Step-by-step explanation:

Given the data in the question;

Sample 1 Sample 2

x"₁ = 259.23 x"₂ = 365.12

s₁ = 34.713 s₂ = 48.297

n₁ = 5 n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

$S_p^2$ = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

$S_p^2$ = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

$S_p^2$ = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [ 4 + 9 ]

$S_p^2$ = [ 4819.9692 + 20993.4 ] / [ 13 ]

$S_p^2$ = 25813.3692 / 13

$S_p^2$ = 1985.64378

Now the Standard Error will be;

$S_{x1-x2$ = √[ ( $S_p^2$ / n₁ ) + ( $S_p^2$ / n₂ ) ]

we substitute

$S_{x1-x2$ = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

$S_{x1-x2$ = √[ 397.128756 + 198.564378 ]

$S_{x1-x2$ = √595.693134

$S_{x1-x2$ = 24.4068

Critical Value = $t_{\frac{\alpha }{2}, df$ = $t_{0.05, df=13$ = 1.771 { t-table }

So,

Margin of Error E = $t_{\frac{\alpha }{2}, df$ × [ ( $S_p^2$ / n₁ ) + ( $S_p^2$ / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666 )

3 0

3 years ago

What is the distance between (1,-5) and (-3,6)​

What is the distance between (1,-5) and (-3,6)