Answer:
4.62 units
Step-by-step explanation:
Let's first find the length OR.
OR² = BR² + OB²
OR² = 5² + 12²
OR² = 25 + 144
OR² = 169
OR = 13
Let's find the area of triangle OBR.
Using the formula :
½bh
Where
b = BR
h = OB
Therefore, area of triangle OBR =
½ * BR * OB
= ½ * 5 * 12
= 30
From the diagram, triange OBR and OAR are parallel to each other, and they equal.
Thus, area of OBR = area of OAR
To find the length PA, we have :
Area of OAR = ½ * OR *PA
Let's make PA subject of the formula:
PA = 4.618 ≈ 4.62
PA = 4.62 units
The equivalent expression for (x + 4)^5 is
The expression is given as:
To expand the expression, we make use of Pascal triangle, where:
5:= 1 5 10 10 5 1
So, we have:
Evaluate the exponents
Evaluate the products
Hence, the equivalent expression for (x + 4)^5 is
Read more about binomial expressions at:
Answer:
The systems of equation are .
Vanessa worked for<u> 6 hrs </u>and Geneva worked for <u>15 hrs</u> to earn exactly $240.
Step-by-step explanation:
Let the number of hours worked by Vanessa be 'v'.
Let the number of hours worked by Geneva be 'g'.
Given:
Total number of hours worked = 21 hours
So we can say that;
Total number of hours worked is equal to sum of number of hours worked by Vanessa and number of hours worked by Geneva.
framing in equation form we get;
⇒ equation 1
Also given:
per hour earnings of Vanessa = $10
per hour earning of Geneva = $12
Total they need to earn = $240
So we can say that;
Total they need to earn would be equal to sum of per hour earnings of Vanessa multiplied by number of hours worked by Vanessa and per hour earning of Geneva multiplied by number of hours worked by Geneva.
framing in equation form we get;
⇒ equation 2
Hence The systems of equation are .
On Solving above equations we get;
First we will multiply equation 1 by 10 we get;
⇒ equation 3
Now Subtracting equation 3 from equation 2 we get;
Dividing both side by 2 we get;
Now Substituting the value of g in equation 1 we get;
Hence Vanessa worked for<u> 6 hrs </u>and Geneva worked for <u>15 hrs</u> to earn exactly $240.
Answer:
The number will be -13
Step-by-step explanation:
Let the no. be x
Its twice will be = 2x
According to the question ,