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KengaRu [80]
3 years ago
12

Mrs.Morales wrote a test with 15 questions covering spelling and vocabulary.Spelling questions(x)are worth 5 points and vocabula

ry questions (y) are worth 10 points. The maximum number of points possible on the test is 100.
Mathematics
2 answers:
Cloud [144]3 years ago
7 0
X + y = 15.......x = 15 - y
5x + 10y = 100

5(15 - y) + 10y = 100
75 - 5y + 10y = 100
-5y + 10y = 100 - 75
5y = 25
y = 25/5
y = 5.....there were 5 vocabulary questions

x + y = 15
x + 5 = 15
x = 15 - 5
x = 10......there were 10 spelling questions
leonid [27]3 years ago
3 0
X=10 y=5 would be the answers I'm not sure on the equation
You might be interested in
Calculate the discriminant to determine the number solutions. y = x ^2 + 3x - 10
Nataly_w [17]

1. The first step is to find the discriminant itself. Now, the discriminant of a quadratic equation in the form y = ax^2 + bx + c is given by:

Δ = b^2 - 4ac

Our equation is y = x^2 + 3x - 10. Thus, if we compare this with the general quadratic equation I outlined in the first line, we would find that a = 1, b = 3 and c = -10. It is easy to see this if we put the two equations right on top of one another:

y = ax^2 + bx + c

y = (1)x^2 + 3x - 10

Now that we know that a = 1, b = 3 and c = -10, we can substitute this into the formula for the discriminant we defined before:

Δ = b^2 - 4ac

Δ = (3)^2 - 4(1)(-10) (Substitute a = 1, b = 3 and c = -10)

Δ = 9 + 40 (-4*(-10) = 40)

Δ = 49 (Evaluate 9 + 40 = 49)

Thus, the discriminant is 49.

2. The question itself asks for the number and nature of the solutions so I will break down each of these in relation to the discriminant below, starting with how to figure out the number of solutions:

• There are no solutions if the discriminant is less than 0 (ie. it is negative).

If you are aware of the quadratic formula (x = (-b ± √(b^2 - 4ac) ) / 2a), then this will make sense since we are unable to evaluate √(b^2 - 4ac) if the discriminant is negative (since we cannot take the square root of a negative number) - this would mean that the quadratic equation has no solutions.

• There is one solution if the discriminant equals 0.

If you are again aware of the quadratic formula then this also makes sense since if √(b^2 - 4ac) = 0, then x = -b ± 0 / 2a = -b / 2a, which would result in only one solution for x.

• There are two solutions if the discriminant is more than 0 (ie. it is positive).

Again, you may apply this to the quadratic formula where if b^2 - 4ac is positive, there will be two distinct solutions for x:

-b + √(b^2 - 4ac) / 2a

-b - √(b^2 - 4ac) / 2a

Our discriminant is equal to 49; since this is more than 0, we know that we will have two solutions.

Now, given that a, b and c in y = ax^2 + bx + c are rational numbers, let us look at how to figure out the number and nature of the solutions:

• There are two rational solutions if the discriminant is more than 0 and is a perfect square (a perfect square is given by an integer squared, eg. 4, 9, 16, 25 are perfect squares given by 2^2, 3^2, 4^2, 5^2).

• There are two irrational solutions if the discriminant is more than 0 but is not a perfect square.

49 = 7^2, and is therefor a perfect square. Thus, the quadratic equation has two rational solutions (third answer).

~ To recap:

1. Finding the number of solutions.

If:

• Δ < 0: no solutions

• Δ = 0: one solution

• Δ > 0 = two solutions

2. Finding the number and nature of solutions.

Given that a, b and c are rational numbers for y = ax^2 + bx + c, then if:

• Δ < 0: no solutions

• Δ = 0: one rational solution

• Δ > 0 and is a perfect square: two rational solutions

• Δ > 0 and is not a perfect square: two irrational solutions

6 0
3 years ago
Problem solving with inequalities
anzhelika [568]

Option D:

15c ≤ 200

Solution:

Let c be the number of cases of tea bags.

Cost of each tea bag = 15 gold coins

Total gold coins Mad have = 200

<u>Set up an inequality:</u>

Cost of c tea bags = 15 × c = 15c

Mad can buy tea bags at most 200 gold coins.

(At most 200 means 200 is the greater value)

15 × c ≤ 200

15c ≤ 200

Hence option D is the correct answer.

8 0
3 years ago
How do you answer this question:
Maurinko [17]
66527273848 A. Aaaaaaaaaaaaaaaaa
5 0
2 years ago
Which of the following points is the greatest distance form y -axis a.2,7 b.3,5 c.4,3 d.5,1
ohaa [14]

Answer:

D

Step-by-step explanation:

It's d because it has the highest x value. The higher x value is the farther it is from the y-axis

7 0
3 years ago
Assume adults have IQ scores that are normally distributed with a mean of 102 and standard deviation of 16. Find the probability
Andre45 [30]

Answer:

57.49% probability that a randomly selected individual has an IQ between 81 and 109

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 102, \sigma = 16

Find the probability that a randomly selected individual has an IQ between 81 and 109

This is the pvalue of Z when X = 109 subtracted by the pvalue of Z when X = 81. So

X = 109

Z = \frac{X - \mu}{\sigma}

Z = \frac{109 - 102}{16}

Z = 0.44

Z = 0.44 has a pvalue of 0.67

X = 81

Z = \frac{X - \mu}{\sigma}

Z = \frac{81 - 102}{16}

Z = -1.31

Z = -1.31 has a pvalue of 0.0951

0.67 - 0.0951 = 0.5749

57.49% probability that a randomly selected individual has an IQ between 81 and 109

8 0
3 years ago
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