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Korolek [52]
3 years ago
13

The ratio for 42 pens : 35 pencils as a fraction is

Mathematics
2 answers:
kotegsom [21]3 years ago
7 0

Answer:

\frac{42 \text{Pens} }{35 \text{Pencils}} or \frac{6 \text{Pens} }{5 \text{Pencils}}

Step-by-step explanation:

Ratio is defined as the comparison between the two sizes.

a:b = a/b

We have to find the ratio for 42 pens : 35 pencils as a fraction:

Given:

42 \text{Pens} : 35 \text{Pencils}

By definition:

⇒\frac{42 \text{Pens} }{35 \text{Pencils}}

Divide numerator and denominator by 7 we get;

\frac{6 \text{Pens} }{5 \text{Pencils}}

Therefore, the ratio for 42 pens : 35 pencils as a fraction is,

\frac{42 \text{Pens} }{35 \text{Pencils}} or \frac{6 \text{Pens} }{5 \text{Pencils}}

Alex73 [517]3 years ago
4 0
As a fraction,
35/42, simplified, 5/6
answer=5/6
hope this helps....
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Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

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6 0
3 years ago
A woman invests a total of $20,000 in two accounts, one paying 2.5% and the other paying 8% simple interest per year. Her annual
djverab [1.8K]
Let's have a variable for each rate
x = account 1 (2.5% rate of interest)
y = account 2 (8% rate of interest) 

The formulas we need are: 
0.025x + 0.08y = 830 (amount of interest paid) 
x + y = 20 000 (combined amount invested) 

To solve we will use substitution (isolate for one variable and plugging into the other formula): 
x + y = 20 000
x = 20 000-y

0.025x + 0.08y = 830
0.025(20 000-y) + 0.08y = 830
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Now that we know y (the 2nd account) = $6000 we need to find x. We do this by using the previous formula.
x = 20 000-y
x=20 000 - 6000
x=14000

She invested $14 000 at a 2.5% interest rate and $6 000  at a 8% interest rate.

*Notes:
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3 years ago
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andrew11 [14]

a=2

b=6

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3 0
3 years ago
Evaluating functions
spayn [35]

(-1/4)x + 2 = 8

Multiply all terms by 4.

(-1)x + 8 = 32

Simplify.

-x + 8 = 32

Subtract 8 from both sides.

-x = 24

Multiply both sides by -1.

x = -24.

<h3>The value of x is equal to -24.</h3>

-1/4(-24) + 2 = 8


5 0
3 years ago
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