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ANTONII [103]
3 years ago
5

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Mathematics
1 answer:
mamaluj [8]3 years ago
5 0

Answer: The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

Let x represent the number of 3-point questions.

Let y represent the number of 5-point questions.

The maths test consists of 24 questions. This means that

x + y = 24

Each question is worth either 3 points or 5 and the test is worth 100 points. This means that

3x + 5y = 100 - - - - - - - - - - -1

Substituting x = 24 - y into equation 1, it becomes

3(24 - y) + 5y = 100

72 - 3y + 5y = 100

- 3y + 5y = 100 - 72

2y = 28

y = 28/2 = 14

Substituting y = 14 into x = 24 - y , it becomes

x = 24 - 14 = 10

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spin [16.1K]

Answer:

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Step-by-step explanation:

the first thing that will help you solve this question is finding the common ratio between each terms

the first thing that I like to do that usually helps is to take the second term (-24) and divide it by the first term (6) --> this will usually help you spot the common ratio fairly quickly

in your case, the common ratio is -4

- you can also check this by following my note above and then multiplying the second term by the common ratio to see if it matches the third term, which it does!

so now you can go about this two different ways

1. solve directly for the 9th term

2. use the nth term formula for geometric sequences

METHOD 1:

if you continue to multiply by -4 to solve for each term you would end up with:

6, -24, 96, -384, 1536, -6144, 24576, -98304, 393216

and you will recieve 393216 as your answer

METHOD 2:

the nth term formula is An = A1*r^(n-1)

where An = the nth term of the sequence

A1 = first term of the sequence (6)

and r = common ratio

using this formula, you would get:

A9 = 6(-4)^8

A9 = 393216

I hope this helped :)

 

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3 years ago
Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X
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<h3>How to determine angle <XYZ?</h3>

By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the theorem of intersecting secants.

<h3>What is the theorem of intersecting secants?</h3>

The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, angle XYZ will be given by this formula:

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Substituting the given parameters into the formula, we have;

<XYZ = ½ × (175 - 105)

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By applying the theorem of intersecting secants, we can infer and logically deduce that the measure of angle XYZ is equal to 35°.

Read more on intersecting secants here: brainly.com/question/1626547

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Answer:

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Step-by-step explanation:

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