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Korolek [52]
2 years ago
13

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

Mathematics
2 answers:
kotegsom [21]2 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]2 years ago
4 0
As a fraction,
35/42, simplified, 5/6
answer=5/6
hope this helps....
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What is the solution to the system of equations? y=-5+3, y=1
andrew11 [14]

Answer:

x = 2/5 and y =1    (2/5, 1)

Step-by-step explanation:

I will assume that you meant y = -5x + 3.  If that's the case, then we equate

y = -5x + 3 to y = 1, obtaining:

-5x = -2, so that x = 2/5 and y =1.

7 0
2 years ago
Solve for x in the equation x² - 4x - 9 = 29.
alexandr1967 [171]

Answer: First option.


Step-by-step explanation:

 1. To solve this problem you can applly the quadratic formula, which is shown below:

 x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}

2. The quadratic  equation is:

x^{2}-4x-9-29=0\\x^{2}-4x-38=0

3. Then:

a=1

b=-4

c=-38

4. Therefore, when you substitute these values into the quadratic formula, you obtain the following result:

x=\frac{-(-4)+/-\sqrt{(-4)^{2}-4(1)(-38)}}{2(1)}

x=2±√42


7 0
3 years ago
Read 2 more answers
HEY CAN ANYONE HELP ME!
nataly862011 [7]

Answer:

Given: In triangle ABC and triangle DBE where DE is parallel to AC.

In ΔABC and ΔDBE

DE || AC   [Given]

As we know, a line that cuts across two or more parallel lines.  In the given figure, the line AB is a transversal.

Line segment  AB is transversal that intersects two parallel lines.  [Conclusion from statement 1.]

Corresponding angles theorem: two parallel lines are cut by a transversal, then the  corresponding angles are congruent.

then;

\angle BDE \cong \angle BAC  and

\angle BEC \cong \angle BCA

Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.

by Reflexive property of equality:

\angle B \cong \angle B  

By AAA (Angle Angle Angle) similarity postulates states that all three pairs of corresponding angles are the same then, the triangles are similar

therefore, by AAA similarity postulates theorem

\triangle ABC \sim \triangle DBE

Similar triangles are triangles with equal corresponding angles and proportionate side.

then, we have;

\frac{BD}{BA}                  [By definition of similar triangles]

therefore, the missing statement and the reasons are

Statement                                                                   Reason

3.\angle BDE \cong \angle BAC      Corresponding angles theorem

and  \angle BEC \cong \angle BCA        

5. \triangle ABC \sim \triangle DBE   AAA similarity postulates    

6. BD over BA                                                    Definition of similar triangle



7 0
2 years ago
Read 2 more answers
Arun needs to buy 834 pounds of potting soil to fill a large flowerpot. Potting soil costs $0.60 per pound, including tax. What
ivanzaharov [21]

Answer:

$500.4

Step-by-step explanation:

6 0
3 years ago
1) A basket of apples are given to a group of students. If 3 apples are given to each student, there will be 8 apples left. If 5
sattari [20]

Answer:

1) either 5 or 6 students in the group

2) 6 rooms are booked

Step-by-step explanation:

1) x students  

3x + 8 = apples

5 (x-1) + y (the one get less than 5 apples)

3x + 8 = 5 (x - 1) + y

3x + 8 = 5x - 5 + y

2x + y = 13

X       1       2      3      4      5      6

Y       11      9      7      5      3       1

because y < 5 so x = 5 or x = 6

2) x rooms are booked

4x + 20   total students

8 (x-1) + y (the students in room not full))

4x + 20 = 8 (x-1) + y

4x + 20 = 8x - 8 + y

4x + y = 28

X       1       2      3      4      5      6

Y       24    20    16    12     8      4

y < 8 answer is 6 rooms

4 0
3 years ago
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