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3 years ago

Given: 5(x-1) = 3(x-4)+1 Prove: x=-3

Mathematics

2 answers:

KonstantinChe [14]3 years ago

7 0

If you need any clarification, just message me.

Nesterboy [21]3 years ago

3 0

Answer:

Step-by-step explanation:5(x-1)=3(x-4)+1

Distribute

5x-5=3x-12+1

Combine like terms

5x-5=3x-11

Begin to try to get the x by itself

5x-5=3x-11

+5. +5

5x=3x-6

-3x. -3x

2x=-6

÷2. ÷2

X=3

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∆ABC is transformed with the center of dilation at the origin.

jonny [76]

Answer:

1/5

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−3, 4), B(−1, 12) and C(4, −2) to the image triangle A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4) and C' (0.8, −0.4).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A (−3, 4) ---> A' (−0.6, 0.8) = $\frac{-0.6}{-3} , \frac{0.8}{4}=(\frac{1}{5} , \frac{1}{5})$

B(−1, 12) ---> B' (−0.2, 2.4) = $\frac{-0.2}{-1} , \frac{2.4}{12} = (\frac{1}{5} , \frac{1}{5})$

C(4, −2) ---> C' (0.8, −0.4) = $\frac{0.8}{4} , \frac{-0.4}{-2} = (\frac{1}{5} , \frac{1}{5})$

Therefore, the scale factor of the dilation is 1/5.

3 0

3 years ago

Problem Solving

Semenov [28]

Answer:

12:30PM

Step-by-step explanation:

Known information:

There are 4 classes.

Each class is 1 hour.

There are 10 minutes between classes, like a break.

Draw a diagram:

start-CLASS1, break, CLASS2, break, CLASS3, break, CLASS4-end

There are 3 breaks because there are no breaks before and after the first and last classes.

Multiply the number of classes by the time length for class.

Multiply the number of breaks by the time length for breaks.

Add the two numbers together to get the total school time:

Classes: 4*1h = 4h

Breaks: 3*10min = 30min

4h + 30min = 4h 30min

Calculate 4h and 30min after 8:00 AM.

Add 4 hours and 30 minutes to 8.

. 8:00

+ 4:30

. 12:30

In the AM/PM clock (not 24 hour clock) there are 12 hours. After 12:59, it becomes 1:00, not 13:00.

Since "12:30" is possible on the AM/PM, we do not need to fix it.

The AM/PM clock changes at 12:00.

This means that after 11:59PM it becomes 12:00AM.

After 11:59AM it becomes 12:00PM. (Usually lunch)

Since 12:30 passed 11:59, the AM/PM sign changes.

The fourth class ends at 12:30PM.

3 0

3 years ago

A student researcher compares the heights of men and women from the student body of a certain college in order to estimate the d

maria [59]

Answer:

(0.6613, 8.3387)

Step-by-step explanation:

Let the heights of men be the first population and the heights of women be the second population. Then

We have $n_{1} = 15$ , $\bar{x}_{1} = 69.4$ , $s_{1} = 3.09$ and

$n_{2} = 7$ , $\bar{x}_{2} = 64.9$ , $s_{2} = 2.58$ . The pooled

estimate is given by

$s_{p}^{2} = \frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(15-1)(3.09)^{2}+(7-1)(2.58)^{2}}{15+7-2} = 8.68$

The 99% confidence interval for the true mean difference between the mean height of the men and the mean height of the women is given by (if the samples are independent)

$(\bar{x}_{1}-\bar{x}_{2})\pm t_{0.01/2}s_{p}\sqrt{\frac{1}{15}+\frac{1}{7}}$ , i.e.,