All categories

3 years ago

Please show work for both problems

Mathematics

1 answer:

sukhopar [10]3 years ago

5 0

(1) The value of x is 25

(2) The measure of ∠CBD is 60°

Explanation:

(1) The given two angles are vertical angles. Since, vertical angles are equal, we can add the two angles to determine the value of x.

Thus, we have,

$5x+15=6x-10$

Subtracting 5x from both sides, we have

$15=x-10$

Adding 10 to both sides , we have,

$25=x$

Thus, the value of x is 25.

(2) It is given that the measure of ∠ABC = (x+7)° and ∠CBD = (2x+14)°

Since, these two angles are supplementary angles and supplementary angles add upto 90°

Thus, we have,

$2x+14+x+7=90$

Simplifying, we get,

$3x+21=90$

$3x=69$

$x=23$

Thus, substituting the value of x in ∠CBD = (2x+14)° to determine its value.

$2x+14=2(23)+14=46+14=60$

Thus, the measure of ∠CBD is 60°

You might be interested in

The Venn diagram displays the number of employees at United Accounting Firm, in hundreds, who travel to work by a given method a

Svetlanka [38]

Answer:

Step-by-step explanation:

if 3500 employees work at the firm, the you minus the total amount of employees taking either a car or the train from 3500 (3500-2300 = 1200)

3 0

3 years ago

We wish to give a 90% confidence interval for the mean value of a normally distributed random variable. We obtain a simple rando

coldgirl [10]

Answer: $(9.27025,\ 11.12975)$

Step-by-step explanation:

Given : Sample size : n= 9

Degree of freedom = df =n-1 =8

Sample mean : $\overline{x}=10.2$

sample standard deviation : $s= 1.5$

Significance level ; $\alpha= 1-0.90=0.10$

Since population standard deviation is not given , so we use t- test.

Using t-distribution table , we have

Critical value = $t_{\alpha/2, df}=t_{0.05 , 8}=1.8595$

Confidence interval for the population mean :

$\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}$

90% confidence interval for the mean value will be :

$10.2\pm (1.8595)\dfrac{1.5}{\sqrt{9}}$

$10.2\pm (1.8595)\dfrac{1.5}{3}$

$10.2\pm (1.8595)(0.5)$

$10.2\pm (0.92975)$

$(10.2-0.92975,\ 10.2+0.92975)$

$(9.27025,\ 11.12975)$

Hence, the 90% confidence interval for the mean value= $(9.27025,\ 11.12975)$

6 0

3 years ago

Ben has a collection of 812 stamps. He gives his brother 345 stamps. About how many stamps does Ben have left

dedylja [7]

It is given in the question that

Ben has a collection of 812 stamps. He gives his brother 345 stamps.

And we have to find how many stamps does Ben have left .

Let x stamps are left.

So we have

$x+345=812$

Subtracting 345 from both sides

$x+345-345 = 812-345$

$x = 467$

Therefore after giving 345 stamps to his brother, 467 stamps are left .

7 0

3 years ago

Send help please!! i want to complete it asap

Nadusha1986 [10]

It’s a little complicated but here’s how it works:
Imagine a table with the intervals
0:4 , 4:6 , 6:7 , 7:10 , 10:13 (10 year intervals)
Then we have different rows
Class width: 4 , 2 , 1 , 3 , 3
Freq density: 0.2 , 0.5 , 1.2 , 0.7 , 0.3
So now calculate frequency where freq = class width * density
Freq: 0.8 , 1 , 3.6 , 2.1 , 0.9
So to find median find cumulative frequency
(Add all freq)
Cfreq = 8.4 now divide by 2 = 4.2
So find the interval where 4.2 lies.
0.8 + 1 = 1.8 + 3.6 = 5.6

So 4.2 (median) will lie in that interval 60-70 years.

7 0

3 years ago

Which of the following relations is NOT a function?

topjm [15]

According to Wikipedia: "<span>In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output."

So based of this we need to look for a set where one of the x values or the y values is the same, and the other number is different.

Answer:
B.
(1,4) and (1,1) both have the same x, but different y!
</span>

5 0

4 years ago