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r-ruslan [8.4K]
2 years ago
12

Write a multiplication expression that can be used to solve 2/3a = 30.

Mathematics
1 answer:
Tresset [83]2 years ago
8 0
<h3>Answer:</h3>

a=45

<h3>Solution:</h3>
  • We need to multiply both sides by 3 in order to get rid of the denominator, 3:
  • 2/3a•3=30•3
  • 2a=90
  • Divide both sides by 2:
  • a=45

Hope it helps.

Do comment if you have any query.

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the wilsons back yard is rectangular plot that has a length of 100 feet and a width of 80 feet .the family planted a garden with
Irina-Kira [14]

the area in square feet is 4400. (because to find the area of the rectangle you multiply the 2 side lengths, 100 and 80 which gives you 8000, then you find the area of the square, multiply 60 by 60 which is 3600, then you subtract the total area of the backyard by the area taken up by the garden, 8000-3600, which gives you your total of 4400.)

8 0
3 years ago
The Johnson twins were born eleven years after their older sister. This​ year, the product of the three​ siblings' ages is exact
vodka [1.7K]
So there are 3 siblings: the first twin, the second twin, and their older sister.

Since the sister is older by 11 years, you can represent their relationship with the following equation;
age of twin = age of older sister - 11
t = s - 11

Representing this next part may be a little hard to show, but i'll do my best :)

Adding the ages together can be represented like this;
total age = t + t + s
If the product of their ages ( t * t * s ) is 1181 more than the sum, you can show it like this:
t * t * s = (t + t + s) + 1181
Now you substitute in (s - 11) for t because s = t - 11.
t * t * s = (t + t + s) + 1181\\&#10;(s-11) * (s-11) * s = ((s-11) + (s-11) + s) + 1181\\&#10;(s^{2}-22x+121)*s=s+s-11-11+1181\\&#10;s^{3}-22s^{2}+121s-2s=1159\\&#10;s^{3}-22s^{2}+118s-1159=0
Factor:
Since it's a third-degree equation, I just entered it into a polynomial solver in my calculator. There was only one factor listed, x = 19. Using (s - 19) = 0 as a factor, the equation becomes the following:
s^{3}-22s^{2}+118s-1159=0\\&#10;(s-19)(s^{2}-3s+61)=0
Using the quadratic formula, you get:
s= \frac{-b(+-)\sqrt{b^{2}-4ac}}{2a}\\&#10;s= \frac{-(-3)(+-)\sqrt{(-3)^{2}-4(1)(61)}}{2*1}\\&#10;s= \frac{3(+-)\sqrt{(9)-244}}{2}\\&#10;s= \frac{3(+-)\sqrt{-235}}{2}

Since you have a square root of a negative number, the answer will be imaginary. You cannot have an age that is imaginary, so the age of the older sister (s) is 19 years.

Because t = s - 11, that means that t = (19) - 11 = 8.
t is the age of the twins, so the twins are 8 years old.
8 0
3 years ago
Given f(x)=-3x+4 , what is f(2) ?
user100 [1]
F(X) means plug in te number within the parenthesis for the given function. It's simply an equation expressed through different notation. In this case it asks you to plug in two, so you do:
-3(2)+4 = f(2)
That means that f(2)=-2.
3 0
3 years ago
At Jefferson Middle School, eighty-two students were asked which sports they plan to participate in for the coming year. Twenty
Keith_Richards [23]

Answer:

Sorry Pinsonjon1129 but you are wrong the question is at the bottom how many people plan to participate in at least two sports? the answer 46

Step-by-step explanation:

20 Cross Country and track 6 cross country and basketball so far 26 8 Track and basketball 34 but 12 plan to participate in all three add them all up and you get 46.

6 0
3 years ago
Read 2 more answers
What is sin(4a) &amp; cos(4a) if tan(a)=3
ratelena [41]

Answer:

  • sin(4a) = -24/25
  • cos(4a) = 7/25

Step-by-step explanation:

Your calculator can tell you these values:

  sin(4a) = sin(4·arctan(3)) = -0.96 = -24/25

  cos(4a) = cos(4·arctan(3)) = 0.28 = 7/25

_____

Some useful trig identities are ...

  sin(2a) = 2tan(a)/(1 +tan(a)^2)

  cos(2a) = (1 -tan(a)^2)/(1 +tan(a)^2)

Filling in the given value for tan(a), we find ...

  sin(2a) = 2(3)/(1+3^2) = 6/10 = 3/5

  cos(2a) = (1 -3^2)/(1 +3^2) = -8/10 = -4/5

Now, double-angle formulas are useful:

  sin(4a) = 2sin(2a)cos(2a) = 2(3/5)(-4/5) = -24/25

  cos(4a) = 1 -2sin(2a)^2 = 1 -2(3/5)^2 = 7/25

The desired trig function values are sin(4a) = -24/25; cos(4a) = 7/25.

6 0
3 years ago
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