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ValentinkaMS [17]
3 years ago
15

Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He h

as 72 pencils and 24 calculators and he must use all of the pencils and calculators. If Zayed creates the greatest number of identical packages possible, how many pencils will be in each package?
Mathematics
2 answers:
Yakvenalex [24]3 years ago
6 0

Answer:

3 pencils

Step-by-step explanation:

zmey [24]3 years ago
4 0

Answer:

3 pencils

Step-by-step explanation:

We are given Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators.

Number of pencils=72

Number of calculators=24

If Zayed creates the greatest number of identical packages

Then , we find GCF of 72 and 24

72=2\times 2\times 2\times 3\times 3

24=2\times 2\times 2\times 3

GCF=2\times 2\times 2\times 3

Hence, Zayed creates 24 packages.

Number of pencils in each package=\frac{72}{24}=3

Hence, 3 pencils and one calculator will be in each package .

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Kaitlin earns $16 per hour tutoring students after school. If Kaitlin tutored for 19.5 hours this month, how much money did she
Sidana [21]

Answer: Kaitlin earned $312 this month.

Step-by-step explanation:

since it says $16 per hour and she has tutored for 19.5 hours you just simply multiply the two to get your answer because it wants to know how much she earned this month.

7 0
3 years ago
Find the equation of the lines, that is parallel to the line 9x-8y=1, and tangent to the elipses 9x^2+16y^2=52.
lara31 [8.8K]

Answer:

The equations of the lines that satisfy these conditions are

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

They can be written further as

8y = 9x + 26

and

8y = 9x - 26

Step-by-step explanation:

The line parallel to the line 9x - 8y = 1 has the same slope as 9x - 8y = 1

Writing the equation of the line in the (y = mx + c) form

8y = 9x - 1

y = (9/8)x - 1

So, the line(s) we are looking for has/have slope(s) of (9/8).

Its equation is then

y = (9/8)x + k

This line is then said to be tangent to the ellipses

9x² + 16y² = 52

So, since the line is a tangent to the ellipses, it will have the same coordinates as the ellipses at the point of contact.

9x² + 16y² = 52

y = (9/8)x + k

y² = (81/64)x² + (18k/8)x + k²

y² = (81/64)x² + (9k/4)x + k²

Substituting this into the ellipses equation,

9x² + 16y² = 52

9x² + 16[(81/64)x² + (9k/4)x + k²] = 52

9x² + (81/4)x² + 36kx + 16k² = 52

29.25x² + 36kx + 16k² - 52 = 0

Taking note that the two lines that will be tangent to the ellipses and parallel to the line given, to establish tangency, we make the discriminant of this equation 0. Hence, the roots of that equation will have equal roots.

So, the discriminant, b² - 4ac = 0

29.25x² + 36kx + 16k² - 52 = 0

a = 29.25

b = 36k

c = 16k² - 52

(36k)² - (4)×(29.25)×(16k² - 52) = 0

1296k² - 1872k² + 6084 = 0

576k² = 6084

k = ±(13/4)

So, the equation(s) of the line(s) required is

y = (9/8)x ± (13/4)

So, the equations include

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

Multiplying by 8, we obtain

8y = 9x + 26

8y = 9x - 26

Hope this Helps!!!

6 0
3 years ago
Please Help!! If You Answer First (And It's Good) Then I'll Mark You Brainly! <3
Andrew [12]

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Serga [27]

Answer:

Step-by-step explanation:

2x - y > 4 ⇒ y < 2x - 4

x + y < - 1 ⇒ y < - x - 1

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Dr. Jones is having his Introductory to Criminal Justice students analyze cartoons. He instructs them to identify the number of
ivolga24 [154]

Answer:

The correct option is - content analysis

Step-by-step explanation:

Dr. Jones is having his students use: content analysis.

Content analysis is a type of research technique, where we make similar and valid inferences by coding and interpreting information in text forms.

Here Dr. Jones is asking his students to gather information to identify the violent acts in each cartoon show. So, the students will be gathering content or information and then they will come to some inference.

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