Step by step on how to solve this equation 2 x + 3 = x − 4 because I fogot how to do basic math

What are the coordinates of the point on the directed line segment from (3, 3) to (7,−5) that partitions the segment into a rati

Annette [7]

Answer:

The coordinates of the point is (5.5, -2)

Step-by-step explanation:

Okay, what we want to do here is to get the point that divides the line that joins the points (3,3) to (7,-5) in the ratio 5 to 3

Generally, given the ratio a:b and we want to divide the line joining the points (x1,y1) and (x2,y2) in that ratio, we use the condensed formula below;

Let’s call the point dividing the line in the given ratio z.

The coordinates of Z is;

{(bx1 + ax2)/(a+b), (by1 + ay2)/(a+b)}

In this question (x1,y1) = (3,3)

While (x2,y2) = (7,-5)

while a:b = 5:3

Substituting these values into the coordinate equation for point z, we have ;

{((3(3) + 5(7))/(5+3), ((3)(3) + 5(-5))/(5+3)}

= {44/8 , -16/8} = {5.5, -2}

4 0

3 years ago

A blueprint shows the mater bedroom to be 5 inches long and 3 inches wide. The scale on the blueprint is 2 in : 11 ft. What is t

Anna35 [415]

Answer:

453.75 sq. feet

Step-by-step explanation:

In this question, we are going to calculate the area of a room given the blue print measurement and the actual measurements with the answer being in the actual measurement.

To correctly do this, it is best if the measurements are converted to the actual.

The measurements we’ll be trying to convert is 5 inches by 3 inches with a scale of 2in to 11ft ( same as 1 in to 5.5 ft)

The 5 inches blueprint measurement will be 5 * 5.5 = 27.5 ft

The 3 inches blueprint measurement will be 3 * 5.5 = 16.5 ft

The area in sq. feet will be length * width = 27.5 * 16.5 = 453.75 sq feet

7 0

3 years ago

A researcher surveyed 220 residents of a city about the number of hours they

olga55 [171]

Answer:

Margin of error of 0.0485 hours.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this question:

$\sigma = 0.35, n = 220$

The margin of error is of:

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 1.96\frac{0.35}{\sqrt{200}}$

$M = 0.0485$

Margin of error of 0.0485 hours.

5 0

3 years ago

Does it matter which coordinate is (x1,y1) and (x2,y2) or can I just choose which coordinate I want it to be?

zubka84 [21]

Answer:

Technically not on a graph but on a table yes it matter but here if I were you I would do (2,2) and (-1,-4)

Step-by-step explanation: y=mx+b

(2,2) and (-1,-4) 2=2(2)+b Answer is: y=2x+(-2)

x1 y1 x2 y2 2=4+b

-4-2=-6 -2=b

-1-2=-3 y-intercept

m=2

slope

3 0

2 years ago

Read 2 more answers

On the 1st January 2014 Carol invested some money in a bank account.

Ghella [55]

Answer:

$\large \boxed{\text{\pounds 23 360.00}}$

Step-by-step explanation:

The formula for the accrued amount from compound interest is

$A = P \left(1 + \dfrac{r}{n}\right)^{nt}$

1. Amount in account on 1 Jan 2015

(a) Data:

a = £23 517.60

r = 2.5 %

n = 1

t = 1 yr

(b) Calculations:

r = 0.025

$\begin{array}{rcl}23517.60 & = & P\left (1 + \dfrac{r}{n}\right)^{nt}\\\\& = & P\left (1 + \dfrac{0.025}{1}\right)^{1\times1}\\\\& = & P (1 + 0.025)\\ & = & 1.025 P\\P & = & \dfrac{23517.60 }{1.025} \\\\& = & 22 944.00 \\\end{array}$

The amount that gathered interest was £22 944.00 but, before the interest started accruing, Carol had withdrawn £1000 from the account.

She must have had £23 944 in her account on 1 Jan 2015.

(2) Amount originally invested

(a) Data

A = £23 944.00

$\begin{array}{rcl}23 944.00 & = & 1.025 P\\P & = & \dfrac{23 944.00 }{1.025} \\\\& = & \mathbf{23 360.00} \\\end{array}\\\text{Carol originally invested $\large \boxed{\textbf{\pounds23 360.00}}$ in her account.}$

3. Summary

1 Jan 2014 P = £23 360.00

1 Jan 2015 A = 23 944.00

Withdrawal = <u> -1 000.00 </u>

P = 22 944.00

1 Jan 2016 A = £23 517.60

5 0

3 years ago