Given the points A(-5, -6) and B(8, 2), if C is the midpoint of segment AB, find the coordinates of the midpoint of segment CB

The diagonal of a rectangle = sqrt(w^2 + l^2)

w = width

l = length

In this problem,

The diagonal = 20 in

w = x

l = 2x + 8

Let's plug our numbers into the formula above.

20in = sqrt((x)^2 + (2x + 8)^2)

Let's simplify the inside of the sqrt

20 in = sqrt(5x^2 + 32x + 64)

Now, let's square both sides.

400 = 5x^2 + 32x + 64

Subtract 400 from both sides.

0 = 5x^2 + 32x - 336

Factor

0 = (5x - 28)(x + 12)

Set both terms equal to zero and solve.

x + 12 = 0

Subtract 12 from both sides.

x = -12

5x - 28 = 0

Add 28 to both sides.

5x = 28

Divide both sides by 5

x = 28/5

The width cant be a negative number so now we know that the only real solution is 28/5

Let's plug 28/5 into our length equation.

Length = 2(28/5) + 8 = 56/5 + 8 = 96/5

In conclusion,

Length = 96/5 inches

Width = 28/5

Answer:

-16x +[tex]14 4/5

Step-by-step explanation:

Answer:

Given m∠RST = (15x - 10)o

Using angle addition postulate:

m∠RST = m∠RSP + m∠PST (15x - 10)= (x + 25)+ (5x + 10)(15x - 10)=

so your answer would be (6x+35)

Step-by-step explanation:

Answer:

1/16ft²

Step-by-step explanation:

If 26 rolls fits into 1 5/8 ft² pan, then for us to get the number of square feet for each roll, we will fillw the steps;

26rolls = 1 5/8ft²

1 roll = xft²

26 rolls = 13/8 ft²

1roll = xft²

Cross multiply

26×x = 1×13/8

26x = 13/8

Ceoaa multiply

26x×8 = 13

208x = 13

x =13/208

x = 1/16 ft²

Hence the baker uses 1/16ft² for each roll

Answer:

1.2 x 10^-1

Step-by-step explanation:

So you are going to move the decimal to the right once, since it is where the first number is. Since you only moved the decimal once it is 10^-1. It is negative because you moved the the right. If you had moved the decimal to the left it would be positive.

Answer:

Step-by-step explanation:

Density = mass/volume = 20/6.47

Answer:

bias by giving all individuals

Step-by-step explanation:

Answer:

Hey!

I think your answer should definitely be BIAS

Step-by-step explanation:

Picking a choice RANDOMLY removes the likelihood of the person picking BEING BIASED as they have no view / analysis of the options!

I HOPE THIS HELPS!!

Answer:

Answer:

6 1/2 cubic feet

Step-by-step explanation:

A carton has a length of 2 1/6 feet

The width is 1 1/5 feet

The height is 2 1/2 feet

Therefore the volume of the carton can be calculated as follows

= length × width × height

= 2 1/6 × 1 1/5 × 2 1/2

= 13/6 × 6/5 × 5/2

= 390/60

= 13/2

= 6 1/2 cubic feet

Hence the volume of the carton is 6 1/2 cubic feet

Answer:

  45 minutes

Step-by-step explanation:

At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...

  t = d/s

  t = (7.5 mi)/(10 mi/h) = 0.75 h

to catch Peter.

Mitchell will catch Peter in 45 minutes.

__

Alternate Solution

Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:

  3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter

_____

You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.

The equation of a line in slope intercept form with slope (-2/3) and point (10,-5) is y = (-2/3) - 1.

The slope is the rate of change of y-axis with respect to x-axis.

We know that equation of a line in slope intercept form is y = mx + b.

To find the y-intercept b we will substitute the value of m and point (x,y).

∴ The equation of the line in slope intercept form with slope -2/5 and points (10,-5) is,

-5 = -(2/5)×10 + b.

-5 = -4 + b.

b = -1.

So the given equation of the line is y = (-2/3)x - 1.

learn more about slope here :

https://brainly.com/question/3605446

#SPJ5

Answer:

$7075 or 7718

Step-by-step explanation:

91100-6200=84900

84900/11= 7718.18181818 or rounded= 7718

(This is if the december month doesnt count.)

84900/12=7075

(If december is included.)

Answer:

her monthly salary = 84900/12= 7075 dollars

Step-by-step explanation:

total earns= 91100 dollars

actual salary does not include bonus

her actually salary : 91100-6200= 84900

her monthly salary = 84900/12= 7075 dollars

Step-by-step explanation:

∫ 9 arctan(1/x) dx

If u = 9 arctan(1/x), then:

du = 9 / (1 + (1/x)²) (-1/x²) dx

du = -9 dx (1/x²) / (1 + (1/x²))

du = -9 dx / (x² + 1)

If dv = dx, then v = x.

∫ u dv = uv − ∫ v du

= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ln(x² + 1)

Evaluate from x=1 to x=√3.

[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]

[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]

(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)

(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)

(6π√3 − 9π)/4 + 9/2 ln(2)

Answer:

[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]

Step-by-step explanation:

We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].

Now let's say that u = arctan(1/x). The value of 'du' would be as follows:

du = - x / (1 + x²) * dx

If we apply integration by parts, v = 1, and of course u = arctan(1/x):

=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]

Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':

=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx

=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du

=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du

=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )

=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |

So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;

[tex]9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1[/tex]

Now computing the boundaries we have the following answer:

[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]

Looks like the integral should be

[tex]\displaystyle\int\frac{x+2}{\sqrt{x+(2x+3)^2}}\,\mathrm dx[/tex]

Expand the denominator:

[tex]\displaystyle\int\frac{x+2}{\sqrt{4x^2+13x+9}}\,\mathrm dx[/tex]

Notice that

[tex]u=4x^2+13x+9\implies \mathrm du=(8x+13)\,\mathrm dx[/tex]

In order to use this substitution, expand the integral as

[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx+\frac38\int\frac{\mathrm dx}{\sqrt{4x^2+13x+9}}[/tex]

In the first integral, use the previously mentioned substitution:

[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx=\frac18\int\frac{\mathrm du}{\sqrt u}=\frac14\sqrt u[/tex]

[tex]=\dfrac14\sqrt{4x^2+13x+9}[/tex]

In the second integral, complete the square in the denominator:

[tex]4x^2+13x+9=4\left(x+\dfrac{13}8\right)^2-\dfrac{25}{16}[/tex]

Now substitute

[tex]x=\dfrac58\sec t-\dfrac{13}8\implies\mathrm dx=\dfrac58\sec t\tan t\,\mathrm dt[/tex]

so that

[tex]\sec t=\dfrac{8x+13}5[/tex]

Then

[tex]4x^2+13x+9=\dfrac{25}{16}(\sec^2t-1)=\dfrac{25}{16}\tan^2t[/tex]

and the integral becomes

[tex]\displaystyle\frac{\frac{15}{64}}{\frac54}\int\frac{\sec t\tan t}{\sqrt{\tan^2t}}\,\mathrm dt=\frac3{16}\int\sec t\,\mathrm dt[/tex]

[tex]=\dfrac3{16}\ln|\sec t+\tan t|[/tex]

[tex]=\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|[/tex]

So, the integral is

[tex]\dfrac14\sqrt{4x^2+13x+9}+\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|+C[/tex]

A and B is not, because if you were to make the A bigger it'll be the same as B, so I think is C

Answer:

20 miles/hour

Step-by-step explanation:

40 miles in 2 hours,

thus,

         40/2 miles  in 2/2 hours = 20 miles in 1 hour.

Therefore, Tim bikes 20 miles per hour.  

Answer:

357,340

Step-by-step explanation:

Locate the tens place:

357,335

Check the number to the right:

357,335

If the number is greater than or equal to 5, then we round up. If the number is less than or equal to 4, we round down.

The number next to the tens place is a '5'. We round up.

357,335 ≈ 357,340

Hope this helps.

Answer:

357340

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Substitute n into the equation:

-2(3)[5+3-8-3(3)]

-6[-9]

+54

Answer:

It's 3.

Step-by-step explanation:

3x2=6

3x4=12

3x5=15

Answer:

-72

Step-by-step explanation:

-32 + (2-6)(10)

-32 + (-4)(10)

-32 + -40

-72

Answer:

-72

Step-by-step explanation:

Use PEMDAS and solve from left to right.

2 - 6 = -4

Parenthesis means multiplication.

-4 x 10 = -40

Then you add the negatives.

-32 + -40 or

-32 - 40 = -72

Answer:

-3x<12

/-3  /-3

x<-4

Step-by-step explanation:

The original equation: y = |x - 1| + 7

The new equation: y = |-x - 1| + 8

Answer:

10 times as much as 7 hundred is 70 hundreds or 7 thousands.

Step-by-step explanation:

The question given is:

10 times as much as _____ hundreds is 70 hundreds or _____ thousands.

Dividing the question into two fractions, we have:

10 times what is 70 hundreds?

What is 70 hundreds in thousands?

10 x 7 hundred = 10 x 700 = 70 hundreds

Recall that 70 hundreds = 70 00

70 hundreds = 70 00 = 7 thousands = 7 000

Therefore, the question can be written as:

10 times as much as 7 hundreds is 70 hundreds or 7 thousands.

Answer:

17

Step-by-step explanation:

A= 5 B= 3 C=4

Substitute each number to the right letter

4 + (5^2 + 3) -15

Square 5

4 + (25 + 3) -15

Do parentheses first

4 + 28 - 15

32 - 15

Answer = 17

First, let's get the total amount of coins inside the box.

7 quarters + 4 dimes + 4 nickels + 3 pennies = 18 total coins.

(7 quarters / 18 coins) * 100 = 38.89% chance of picking a quarter

(4 dimes / 18 coins) * 100 = 22.22% chance of picking a dime

(4 nickels / 18 coins) * 100 = 22.22% chance of picking a nickel

(3 pennies / 18 coins) * 100 = 16.67% chance of picking a dime

Since the quarters have a higher percentage of being picked, we can expect to draw $0.25 from the box

Answer:

2000

Step-by-step explanation:

(4x5) x 100

Answer:

2000

Step-by-step explanation:

40 x 50 can be easily done by multiplying 4 and 5 which is 20 and adding the remaining 0's which is 2000

Answer:

x-40%-16%

Step-by-step explanation:

Answer:

the order of operations tells us how to solve a problem.

first is P for parentheses. this means you solve all the expressions within the parentheses. this ensures a simplified expression before moving on.

second is E for exponents. this means you solve all the expressions with exponents. by doing this before MDAS, you do not raise the wrong values.

third and fourth is M/D for multiplication/division. the / is between these two because these steps are interchangeable. you can multiply or divide first. the results will be the same.

this also applies to the fifth and sixth, which are A/S for addition/subtraction.

Answer:54

4 1/2times 12

Convert 4 1/2 to an improper fraction.

9/2 times 12

Cancel the common factor of 2

9 times 6

Multiply

9 by 6 the you'll get 54