All categories

2 years ago

Solve for x. Show your work.

Mathematics

2 answers:

hram777 [196]2 years ago

7 0

5(5+x) = 6(6+4)
25+5x = 60
5x = 35
x = 7

-----------------
3(3+5) = 4(4+x)
24 = 16 + 4x
4x = 24-16
4x = 8
x = 2

sergeinik [125]2 years ago

6 0

Answer:

(i) x=7

(ii) x=2

Step-by-step explanation:

We are given two secant intersect externally at point P.

Theorem: If two secant intersect outside circle, then the product of the lengths of the segments of one secant is equal to the product of the lengths of the other secant.

Please see the attachment for figure and theorem.

According to theorem,

$AP\times BP = CP\times DP$

For first diagram:

AP=x+5, BP=5 , CP=10, DP=6

$(x+5)\times 5=10\times 6$

$x+5=12$

$x=7$

Hence, The value of x is 7

For Second diagram:

AP=8, BP=3 , CP=x+4, DP=4

$8\times 3=4\times (x+4)$

$x+4=6$

$x=2$

Hence, The value of x is 2

You might be interested in

The number of compact discs N purchased each year, in millions, can be

Aleonysh [2.5K]

Answer:

126.5 years

Step-by-step explanation:

N(t) = 384(1.13)^t

2,000,000,000 = 384(1.13)^t

(1.13)^t = 2,000,000,000/384

log [(1.13)^t) = log (2,000,000,000/384)

t × log 1.13 = log (2,000,000,000/384)

t = [log (2,000,000,000/384)]/(log 1.13)

t = 126.5

8 0

1 year ago

Consider the following theorem and proof.Theorem: The number âš2 is not rational number.Proof: Let's suppose âš2 is a rational n

ololo11 [35]

Answer:

The statement "Both of the numbers a and b cannot be even." is justified by the fact that a/b is simplified lowest terms

Step-by-step explanation:

We need to show that the √2 is an irrational number.

And from the given steps of proof stated in the question, we need to find the assumption that justifies the fact : " Both of the number a and b cannot be even".

First take the given options :

Option a : √2 is a rational number

√2 being an rational or irrational has no relation of a and b to be even or odd. So, this option is rejected.

Option B : a/b is simplified lowest terms

This shows that a and b are not even because if a and b are even then a/b can be simplified in other lowest term.

Option c : √2 is a irrational number

Similarly, By using the inverse part of Option A, option c is also rejected.

Option d : The fact that b divides a evenly

This only shows that the a is even. This does not give any idea about b is even or not. So option D is also rejected.

Option E : The fact that a and b are whole numbers

This fact does not imply that the a and b are even or odd. So option E is also rejected.

Hence, The statement "Both of the numbers a and b cannot be even." is justified by the fact that a/b is simplified lowest terms

7 0

3 years ago

Each Saturday the gym holds 45 minute yoga classes. The weekday yoga classes last 30 minutes. The number of weekday classes vari

yanalaym [24]

For this case we have that the total minutes spent in yoga classes last week was 165.

Subtracting the 45 minutes of the Saturday day we have:

$165-45 = 120$

Those 120 minutes were distributed in the weekly yoga classes

where each lasted 30 minutes.

$\frac {120} {30} = 4$

So, 4 week yoga classes were held

ANswer:

4 week yoga classes were held

6 0

3 years ago

Round 6.7086 to the nearest thousandth

Bingel [31]

$\text {Hello! Let's solve this Problem!}$

$\text {To round to the nearest thousandth you must underline the thousandth place}$ $\text {(which is 8), point an arrow to 6 (in the ten-thousandth place)}$

$\text {If the number is 5 or more you raise the score. Meaning you add 1 to the}$ $\text {thousandth place. If the number is 4 or lower you keep the number the same.}$