Which point is an x-intercept of the quadratic function
f(x) = (x + 6)(x – 3)?

Lyla takes 4 quizzes per week. Over 8 weeks, she will have taken a total of 32 quizzes, if the relationship is directly proportional.

Lyla took 16 quizzes over the course of 4 weeks. This indicates that Lyla takes 4 quizzes per week (16 quizzes divided by 4 weeks). We can apply this rate to an 8-week period to find out how many quizzes she will have taken after 8 weeks of school. To do this, you multiply the number of quizzes she takes per week (4) by the number of weeks (8), which results in 32 quizzes. Hence, Lyla will have taken a total of 32 quizzes after 8 weeks. This calculation assumes that the relationship is directly proportional, meaning the number of quizzes she takes each week remains constant.

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The amount invested in the 2% bond is $7,500, and the amount invested in the 6.5% bond is $41,500.

Let's assume that the amount invested in the 2% bond is x dollars. Then, the amount invested in the 6.5% bond is $49,000 - x dollars.

The interest earned from the 2% bond is 0.02x dollars, and the interest earned from the 6.5% bond is 0.065($49,000 - x) dollars.

According to the problem, the sum of these two interests is $2,510. So, we have the equation:

0.02x + 0.065($49,000 - x) = $2,510

Simplifying and solving this equation, we find that x = $7,500. Therefore, $7,500 is invested in the 2% bond, and $41,500 is invested in the 6.5% bond.

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Answer:

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

Let us suppose the sun has angle of elevation x

The triangle formed will be a right triangle, so

[tex]tan x= \frac{opposite}{adjacent}[/tex]

[tex]tanx = \frac{6}{8}[/tex]

taking tan inverse

[tex]x=tan^{-1}(\frac{6}{8} )[/tex]

[tex]x=36.87[/tex]

To the nearest degree, the angle will be 37 degrees.  :   Answer

Hope it will help :)

Answer:
The complement of m∠WXV is m∠UXV

Explanation:

Complementary angles are two (or more) angles with a sum of 90 degrees.

Because line WT is dissected perpendicularly by line UX, two 90° angles are formed in ∠TXU and ∠WXU. We know that they are both 90° because of the box on ∠TXU. ∠TXU and ∠WXU are supplementary angles -- two angles that occupy the same line but are dissected by a perpendicular line forming two angles with a sum of 180 degrees.

If ∠TXU + ∠WXU = 180, and ∠TXU = 90, then ∠WXU must also equal 90:
90 + ∠WXU = 180
90 - 90 + ∠WXU = 180 - 90
0 + ∠WXU = 90
∠WXU = 90°

As we see in the diagram, ∠WXU is dissected by line SV. Because of this, it is broken into the two angles of ∠WXV and ∠UXV. We already established that ∠WXU is 90°. Therefore the sum of these two angles formed must equal 90°, which, in turn, means they are complementary angles. They complement one another.

Therefore, the complement of ∠WXV is ∠UXV

In the next 5 days, 13 renewals must be made.

Given that you made 72% of your goal so far for the month, and you only have 5 days left to reach 100% of your goal, and your target was 45 renewals, to determine how many renewals in the next 5 days you must perform, you must perform the following calculation:

Therefore, in the next 5 days, 13 renewals must be made.

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Final answer:

To find out how much Beau and Belle must markdown the dress for Charlene to stay within her budget of $65, we use the inequality 76.48 - m ≤ 65, which solves to m ≥ 11.48, meaning the dress needs a markdown of at least $11.48.

Explanation:

To determine the markdown Beau and Belle must offer for Charlene to afford the dress within her budget, we can set up an inequality. Let's denote the markdown as m. The original price of the dress is $76.48, and Charlene's budget is $65. Therefore, the dress's price after the markdown should be less than or equal to $65. The inequality that models this scenario is:

76.48 - m ≤ 65

This inequality states that the original price of the dress minus the markdown m should be less than or equal to Charlene's budget of $65. To find out how much of a markdown is needed, we will solve for m.

Subtracting $76.48 from both sides of the inequality:

-m ≤ 65 - 76.48

-m ≤ -11.48 (This indicates that the markdown must be at least $11.48)

To express m as a positive number, we multiply both sides of the inequality by -1, remembering to reverse the inequality symbol:

m ≥ 11.48

Therefore, Beau and Belle must markdown the dress by at least $11.48 for Charlene to stay within her budget constraint.

Set B must contain the elements {b, d}, which are present in its intersection with set A. Besides those, set B can include any other letters from the alphabet.

The question involves finding a possible set B given the information that set A is {a, b, d, f, g} and A ∩ B = {b, d}, where ∩ represents the intersection of two sets. Intersection means the elements that are common to both sets.

Therefore, to solve this, we can conclude that set B must contain at least the elements {b, d}, as these are present in the intersection with set A.

However, set B can also contain other letters of the alphabet since the universe U is the set of all letters in the alphabet.

Hence, the possible set B could be any set containing {b, d} along with any combination of other letters from the alphabet. For example, set B could be {b, d, e, m, n} or {b, d, x, y, z}, or simply {b, d} itself.

Final answer:

Set B must contain the elements {b, d} from the intersection with set A and can include any other letters of the alphabet except for a, f, and g.

Explanation:

The question asks us to determine set B given that the intersection of sets A and B is {b, d}. We know that A = {a, b, d, f, g} and A ∩ B = {b, d}. The intersection of two sets includes only the elements that are present in both sets. Since b and d are the only common elements, they must be in set B. However, set B can also contain any elements from the universal set U that are not in set A. Hence, set B must include {b, d} and can include any of the other letters in the alphabet except for a, f, and g.

The fraction of people running is 7/24. Hence, the correct option is a.

We are asked to find the fraction of people running in a fitness studio, given that 3/8 are lifting weights and 1/3 are doing cross training.

Here's how to calculate it:

First, let's find the fraction of people lifting weights:
3/8 of 36 = 13.5 people (since 36 * 3/8 = 13.5).

Next, we find the fraction of people doing cross training:
1/3 of 36 = 12 people (since 36 * 1/3 = 12).

Now, we can find the total number of people not running by adding those lifting weights and cross training:
13.5 + 12 = 25.5 people.

To find the number of people running, we subtract the number not running from the total:
36 - 25.5 = 10.5 people running.

Finally, we convert this into a fraction of the total number of people in the fitness studio:
10.5 out of 36 is 10.5/36, which can be reduced to 7/24.

The probabilities are:

a) 80%

b) 70%

c) 56%

d) 24%

How to find the probability?

We know that 1 on 5 weels are dry, so 20% are dry, 80% have water.

Out of these 80%, 30% are contaminated, so the percentage of contaminated wells is:

p = 100%*(0.8*0.3) = 24%

Then the ones that are safe to drink are the:

q = 80% - 24% = 56%

Then:

a) Gwen’s well will not be dry. --> 80%

(b) Gwen’s well will be uncontaminated, given that it is not dry.

30% of the non-dry wells are contaminated, so the other 70% aren't.

(c) Gwen will have safe drinking water from her well. 56%

(d) Gwen will not have safe-drinking water from her well. = 24%

To find the total length of 120 watermelon seeds, each 4mm long, we just need to multiply the length of one seed by the total number of seeds. Then, to convert the total length from millimeters to meters, we divide by 1000. So, a line of 120 watermelon seeds would be 0.48 meters long.

This problem involves simple multiplication to solve it. Since each watermelon seed is 4mm long, to find the length of 120 seeds lined up, we just need to multiply 120 by 4. So, 120 seeds * 4mm/seed = 480mm. To convert millimeters to meters, we divide by 1000 (as there are 1000mm in a meter). So, 480mm = 0.48 meters. Therefore, a line of 120 watermelon seeds would stretch 0.48 meters.

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The answer is True :3