Answers
Related Questions
A student saves $15 per week toward the purchase of a guitar. Her grandmother gives her $50 to help her reach her goal, which function can be used to find the amount in dollars the student has saved after x weeks?
Answers
Answer:
Function: y= 15x + 50
or f(x)=15x+50
Answer:
f(x)=15x+50
Step-by-step explanation:
since her grandmother gave her $50 once you just add it to the problem, and she's collecting $15 every week meaning 15x.
Solve x2 − 24x = −80 by completing the square.
What is the solution set of the equation?
{2, 40}
{4, 20}
{5, 16}
{8, 10}
Answers
Answer:
{4, 20}
Step-by-step explanation:
x2 − 24x = −80
divide -24 by 2 and square result get 144
x^2 - 24x + 144 = -80 + 144
(x - 12)^2 = 64
x - 12 = root (64)
x = 12 + 8 or x = 12 - 8
x = 20 or 4
The solution set of the considered quadratic equation x^2 − 24x = −80 is given by: Option B: {4,20}
What is completing the squares method for solving the quadratic equations in one variable?The method "completing the squares", as per the name suggests, try to make the quadratic equation of the form such that the x variable is totally covered in single squared term, as the square of a linear expression in x.
The quadratic equation would look something like:
(px + q)^2 = s
where p, q and s are some constants.
We do so, so that we can then use square root and some other operations to get the variable 'x' on one side of the equation, and all the constants on the other side, being solution of the considered quadratic equation.
Expressing the quadratic equation in such form converts the form of the equation which contains 'x' with different powers in different term to a form which contains 'x' single time.
What is the expansion of square of sum of two terms?Suppose that two terms are 'a' and 'b'.
Then, their sum's square is expanded as:
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]
For this case, the equation considered is :
[tex]x^2 -24x = -80[/tex]
Comparing the left side with [tex]a^2 + 2ab + b^2[/tex], we see that we can use a = x.
Let we try to make the considered equation look more like the equation [tex]a^2 + 2ab + b^2[/tex] .
[tex]x^2 -24x = -80\\x^2 -2(12)x = -80\\x^2 -2(12)x + 12^2 -12^2 = -80\\x^2 -2(12)x + 12^2 = -80 + 12^2 = 64\\[/tex]
Now, we can use [tex](a+b)^2 = a^2 + 2ab + b^2[/tex] for the left sided expression, as shown below:
[tex]x^2 -2(12)x + 12^2= 64\\\\(x-12)^2 = 64[/tex]
Taking square root, we get:
[tex]\sqrt{(x-12)^2} = \sqrt{64}\\\\(x-12) = \sqrt{(\pm 8)^2} = \pm 8\\or\\\\x = 12 \pm 8\\x = 12+8, x = 12-8\\x = 20, x = 4[/tex]
Thus, the solution set of the considered quadratic equation x^2 − 24x = −80 is given by: Option B: {4,20}
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Suppose y varies inversely with x. Write an equation if y=7 when x=-4
Answers
Answer:
y = -28 ÷ x
Step-by-step explanation:
The standard format of a inversely proportional equation goes by the format of y = k ÷ x. The question asks us to write an equation if y = 7 when x = -4 and y varies inversely with x.
So we substitute the values y = 7 and x = -4 in the equation y = k ÷ x
K = constant, we have to work this out
7 = k ÷ -4
7 × - 4 = k
k = - 4 × 7
k = -28
k = -28 So then we put this back into the original y = k ÷ x to find our final equation which is y = -28 ÷ x
300 mi /20 sec = ? Mi /1 min
Answers
Answer:
900
Step-by-step explanation:
To get your answer, you can just multiply 20 seconds by 3 to get 60 seconds, which is a minute.
Since whatever you do on one side you have to do to the other, multiply 300 mi by 3 as well. That would get you 900.
How do you solve for mass if KE=0.5mv^2
Answers
Answer:
Step-by-step explanation:
We want to isolate m in the formula KE=0.5mv^2. To do this, divide both sides by 0.5v^2:
KE
m = ----------------------
v^2
A region with a 15-mile diameter has a population density of about 5000 people
per square mile. Find the number of people who live in the region.
Answers
Answer:
Approximately 883,572 people
Step-by-step explanation:
I'm assuming the region is a circle.
The formula for finding the area of a circle is A=πr².
Since we know that the diameter of the region is 15 miles, and a diameter is 2 times the radius, the radius must be 7.5 miles. We also know that π is equal to 3.14159265359.
A=πr²
A= 3.14159265359×7.5²
A= 3.14159265359×56.25
A= 176.714586764
The region has an area of 176.714586764 square miles.
176.714586764×5000=883572.933822
We can round this number to the nearest whole, but since we cannot have part of a person, the answer is approximately 883,572 people.
Final answer:
To find the number of people who live in a region with a 15-mile diameter and a population density of 5000 people per square mile, we can calculate the area of the region and then multiply it by the population density.
Explanation:
To find the number of people who live in the region, we need to calculate the area of the region and then multiply it by the population density. The region has a 15-mile diameter, so the radius is half of that, which is 7.5 miles. The formula for the area of a circle is A = πr^2, where π is approximately 3.14. Plugging in the values, the area of the region is A = 3.14 × (7.5)^2 = 176.625 square miles.
Next, we multiply the area by the population density of 5000 people per square mile: 176.625 × 5000 = 883,125 people.
Therefore, there are approximately 883,125 people who live in the region.
If the diagonal of a square is approximately 12.73, what is the length of its sides?
Answers
Answer:
The length of the sides of the square is 9.0015
Step-by-step explanation:
Given
The diagonal of a square = 12.73
Required
The length of its side
Let the length and the diagonal of the square be represented by L and D, respectively.
So that
D = 12.73
The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:
[tex]D^{2} = L^{2} + L^{2}[/tex]
Solving further, we have
[tex]D^{2} = 2L^{2}[/tex]
Divide both sides by 2
[tex]\frac{D^{2}}{2} = \frac{2L^{2}}{2}[/tex]
[tex]\frac{D^{2}}{2} = L^2[/tex]
Take Square root of both sides
[tex]\sqrt{\frac{D^{2}}{2}} = \sqrt{L^2}[/tex]
[tex]\sqrt{\frac{D^{2}}{2}} = L[/tex]
Reorder
[tex]L = \sqrt{\frac{D^{2}}{2}}[/tex]
Now, the value of L can be calculated by substituting 12.73 for D
[tex]L = \sqrt{\frac{12.73^{2}}{2}}[/tex]
[tex]L = \sqrt{\frac{162.0529}{2}}[/tex]
[tex]L = \sqrt{{81.02645}[/tex]
[tex]L = 9.001469325[/tex]
[tex]L = 9.0015[/tex] (Approximated)
Hence, the length of the sides of the square is approximately 9.0015
What is the greatest common factor of 7 21 and 70
Answers
Answer:
1470
Step-by-step explanation:
I am pretty sure that this is the answer.
Tell me if i am wrong.
Can I get brainliest
A jar contains five blue marbles and three red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of the following event.
Both of the selected marbles are red.
Answers
Answer:
The probability that both of the selected marbles are red is [tex]\frac{3}{28}[/tex]
Step-by-step explanation:
Given
Number of red marbles = 3
Number of blue marbles = 5
Required
Probability of selecting two red marbles (without replacement).
First, we need to get the total number of marbles
Total = Red Marbles + Blue Marbles
Total = 3 + 5
Total = 8
Probability is calculated by: Number of required outcome divided by number of possible outcome.
Since there are 3 red marbles out of a total of 8 marbles;
The probability that the first marble you selected is red is 3/8
From the question, you didn't return the marble back to the container.
This means that, there are 2 red marbles and a total of 7 marbles left in the container.
So, the probability that the next marble selected is red is 2/7
Let P(R and R) represent the probability of selecting two red marbles.
This is calculated by multiplying the probability of picking the first red marble and the second red marble.
Hence,
P(R and R) = [tex]\frac{3}{8} * \frac{2}{7}[/tex]
P(R and R) = [tex]\frac{6}{56}[/tex] --- Reduce to lowest term
P(R and R) = [tex]\frac{3}{28}[/tex]
Hence, the probability that both of the selected marbles are red is [tex]\frac{3}{28}[/tex]
Which graph represents the function f (x) = StartFraction 2 x Over x squared minus 1 EndFraction?
Answers
Answer:
Step-by-step explanation:
f(x) = 2 / (x^2 - 1) is better written as
2
f(x) = ------------------
(x - 1)(x + 1)
This is undefined at x = -1 and x = 1; there are vertical asymptotes at x = -1 and x = 1.
The y-intercept is found by letting x = 0; we get
2
f(x) = ------------------ = -2 => (0, -2)
(0 - 1)(0 + 1)
Please, next time, share the answer choices. Thank you.
By analyzing the asymptotes we can find the graph of the rational function. Also a graph is provided below.
Which graph represents the function?We have the rational function:
f(x) = (2x)/(x^2 - 1).
First, you can see that we have two zeros on the denominator. One happens when x = 1 and the other when x = -1.
This means that the graph of this function will have two vertical asymptotes at these values. (four actually as we have one going to each end in each point).
With that description we can find the graph of the function, I will also post it so you can recognize it.
If you want to learn more about rational functions, you can read:
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If the interest rates are the same on a CD, which compounding pays more interest?
annually
semi-annually
monthly
quarterly
Answers
The CD that compounds more frequently will pay more interest; thus, monthly compounding yields more interest than quarterly, which in turn is more than semi-annually, with annual compounding paying the least.
Explanation:When comparing the different compounding frequencies for a Certificate of Deposit (CD) with the same annual interest rate, the compounding option that pays more interest is the one that compounds more frequently. Compounding can occur on an annual, semi-annual, quarterly, or monthly basis. The more frequently the interest is compounded, the greater the amount of interest will be earned because each compounding period, the interest is calculated on the initially invested amount plus the previously earned interest.
For example, if interest is compounded monthly, it will be compounded 12 times a year, and each month's interest will begin to earn interest in subsequent months. Similarly, if interest is compounded quarterly, it will be compounded 4 times a year, and semi-annually compounding will occur twice a year. The least frequent is annually compounding, with only one compound per year.
Therefore, the CD that compounds monthly will pay the most interest, followed by the one that compounds quarterly, then semi-annually, and the least will be the CD that compounds annually, assuming the nominal interest rate is the same for all.
Find area of a circle that has a diameter of 8 m
Answers
8/2 = 4
4^2 = 16
16*pi is about 50.27
Your area is 50.27m^2
Answer:
50.24 m^2
Step-by-step explanation:
Area of a circle = Pi r^2
Pi = 3.14
Diameter = 8 m
Radius r = diameter/2 = 8/2
= 4
Therefore
Area = 3.14 x 4^2
= 3.14 x 4 x 4
= 50.24 m^2
Add the polynomials (4x+11)+(12x+2)
Answers
Answer:
16x + 13
Step-by-step explanation:
(4x + 11) + (12x + 2)
combine like terms (add the x's and add the numbers)
4x + 12x = 16x
11 + 2 = 13
(4x + 11) + (12x + 2) =
16x + 13
In one year, Angelica's height went from 52 inches to 56 inches what was the percent of increase in Angelica's height
Answers
Answer: 7.7%
Step-by-step explanation: First find the increase in height by subtracting 52 from 56. 56-52=4.
To find what percent this is of 52, divide 4 by 52. 4/52=0.0769. Then convert this from a decimal to a percent by multiplying by 100. 0.0769*100=7.69.
I just rounded it to the nearest tenth, you can change it how you need to.
Final answer:
The percent of increase in Angelica's height over one year, from 52 inches to 56 inches, is approximately 7.69%.
Explanation:
The student is asking how to calculate the percent of increase in height over a one year period. We start by finding the initial and final measurements, then calculate the increase and convert it to a percentage.
Angelica's initial height is 52 inches, and her final height after one year is 56 inches. The increase in height is 56 inches - 52 inches, which equals 4 inches. To find the percent increase, use the formula:
Percent increase= (Increase / Original amount) x 100
So, the calculation is
Percent increase= (4 / 52) x 100 = 7.69%
Therefore, the percent increase in Angelica's height is approximately 7.69%.
does a vertical stretch make a graph narrower or wider?
Answers
Answer:
narrower
Step-by-step explanation:
am i correct? will mark brainliest
Answers
Answer:
no, its 11 for the first one and 45 for the second
Step-by-step explanation:
Answer:
No 16 is 11 and 17 is 45%
Could you heart me and mark me ect.
The diagram shows one way to develop the formula for the area of a circle. Pieces of a circle with radius r are rearranged to create a shape that resembles a parallelogram.
A circle is shown. The circle is cut into 8 equal pieces. Pieces of the circle with radius r are rearranged to create a shape that resembles a parallelogram.
Since the circumference of the circle can be represented by 2πr, and the area of a parallelogram is determined using A = bh, which represents the approximate area of the parallelogram-like figure?
A = (2πr)(r)
A = (2πr)(2r)
A =One-half(2πr)(r)
A =One-half(2πr)(r2)
Answers
Answer:
A =One-half(2πr)(r)
Step-by-step explanation:
i got it right!
The approximate representation of the area of a parallelogram like figure is as follows:
A = 1 / 2 (2πr) (r)The circle is cut into 8 equal pieces and used to create a shape that resembles a parallelogram.
Properties of a parallelogramOpposite sides are equal and parallelopposite angles are equaldiagonal bisect each otherCircumference of a circle is the perimeter of the circle.
circumference = 2πrArea of parallelogram = bh
Where
b = base
h = height
Therefore,
A = 1 / 2 (2πr) (r)learn more on area here: https://brainly.com/question/843063
Which number has the least absolute value? A) 30 B) 10 C) −20 D) −40
Answers
Answer:-40
Step-by-step explanation:
Because that means below 0
Answer:
10
Step-by-step explanation:
Need help really bad
Answers
Answer:
10
Step-by-step explanation:
just add
Answer:
When xy are zero multiply by 1.33 and we will find y only if x =70
So the linear function will be
y = 90/0 = 0 = y = x/0
y = 90/2 = 2 = y = x/2
y = 90/4 = 4 = y = x/4
y = 90/8 = 6 = y = x/8
x=90 y = 60 when both = 0
Or we can reverse and do x2+2 and call train f(x) and train = x = 90.
Step-by-step explanation:
70/90 = 0.77 = 70 x 1.33 = 90 as a fraction percentage 77%
60/45= 1.33 = 70 x 1.33 = 90 / 2 = 45 ( and as 22.5 as a fraction percentage 133/3%)
50/22.5=2.22 = 70 x 1.33 = 90/4 = 22.5 as a fraction percentage 222.2%
40/11.25=3.55 = 70 x 1.33 = 90 /8 = 11.25 as a fraction percentage= 355.5%
Number of solutions of quadratic equations
Answers
The number is always 2, the type depends on the discriminant.
How to find the number of solutions of a quadratic equation?For a general quadratic equation:
ax² + bx + c = 0
We can define the discriminant as:
D = b² - 4ac
And we can have 3 cases:
if D > 0, the quadratic equation has 2 real solutions.
if D = 0, the quadratic has two (equal) real solutions.
if D < 0, the quadratic has 2 complex solutions.
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Find the circumference of the circle. Round your answer to the nearest hundredth.
Answers
Answer:
25.13
Step-by-step explanation:
C=2πr
C=2 x 3.14 x 4
C= 25.13
Six students eat 6 apples in 33 seconds. How long will it take nine students to eat 19 apples, if they don't cut apples into parts?
Answers
Answer:
99
Step-by-step explanation:
It takes each student 33 seconds to eat an apple. This is done in parallel.
The time it would take if each person ate the exact same amount of apples is 69.6 repeating (calculated by (19 * 33) / 9). However, the apples cannot be cut into parts, so we need to round up to the next multiple of 33. Therefore 99 is the answer.
which of the following values is between 7 and 8
Answers
7.5 is between 7 and 8
A safe has a 4 digit lock code that does not include zero as a digit and no digit is repeated what is the probability that the lock code consist of all even digits
to find the total number of outcomes for this event find a permutation of ____ things taken 4 at a time
The total number of outcomes is ___
The total number of favorable outcomes is a permutation of ____ things taken 4 at a time
The probability that the lock code consists of all even digits is _____ out of 3,024
Answers
Answer:
3
4
5
Step-by-step explanation:
Answer:
9, 3024, 4 and 24
Step-by-step explanation:
much love
The polynomial x3 + 4x2 - 9x - 36 has 4 terms.
Use factoring by grouping to find the correct
factorization
Answers
Answer:
x2(x+4)-9(x+4)
Step-by-step explanation:
=(x2-9)(x+4)
Answer: D or (x²– 9)(x + 4).
The next one is A (difference-of-squares)
The last one is C (x + 3)(x – 3)(x + 4)
Step-by-step explanation: Edge '21
Helppppppppppp please am struggling
Answers
Answer:
x = 60°
Step-by-step explanation:
The circle is 360°, thus
2y + y = 360
3y = 360 ( divide both sides by 3 )
y = 120°
The tangent- secant angle ABT is one half the measure of the intercepted arc AB, thus
x = 0.5 × 120° = 60°
Select the correct answer. What are the intercepts of y = 4x − 2?
Answers
x-intercept(s): (1/2, 0) or (0.5, 0)
y-intercept(s): (0, −2)
Based on the angle measures in the diagram, what is the value of x?
Answers
Answer:
32°
Step-by-step explanation:
Since the outer angle is 99°, the interior angle must be 180° - 99°. That is 81°. We then do the same for the outer angle 113°. So 180° - 113° is 67°. Since the angles of the interior angles must equal 180°, we add 81° and 67°. That equals 148°. Now to figure out x, 180° - 148° is 32°. I hope this helps! Please mark me brainliest!
Has anyone did the storm tracker portfolio worksheet?
Answers
The 'Storm Tracker Portfolio Worksheet' likely entails exercises related to tracking weather systems, and this can be part of a geography or earth science curriculum in high school. It seeks to enrich students' understanding of weather systems, including Space Weather such as Sun storms.
Explanation:Given that your query refers to a 'Storm Tracker Portfolio Worksheet,' it's presumed that this refers to lessons on tracking weather patterns and phenomena, linking to geography and earth science. In this context, it's important to note that these activities usually entail analyzing and predicting weather system developments, including storms brought about by Space Weather such as those on the Sun.
The 'Storm Tracker Portfolio Worksheet' may include exercises like noting down storm paths, examining storm frequencies, interpreting storm system scenarios, among others. The ultimate goal of this exercise is to deepen students' comprehension of how weather systems and various atmospheric conditions affect our planet.
Each person's worksheet may differ based on their geographical location and the specific details needed to be observed and outlined at a given time. It would be helpful to refer to the instruction set provided along with your worksheet to understand what is required of you and what to look out for when completing the worksheet.
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Find the value of the coefficient a in the equation ax+2y=8, if the solution to the equation is the pair x=2 and y=1.
Answers
Answer:
a = 3
Step-by-step explanation:
Simply substitute 2 for x and y for 1 and solve.
This will get you 2a + 2 = 8
Then simplifying, 2a = 6.
a = 3.
The value of a and the coefficient of x is 3.
What is substitution?
Substitution means putting numbers in place of letters to calculate the value of an expression .
According to the given question.
We have a equation.
ax + 2y = 8.
Also, the solution to the equation is (2, 1).
So, substitute x = 2 and y = 1 in the equation ax + 2y = 8.
⇒ [tex]a(2) + 2(1) = 8[/tex]
⇒ [tex]2a + 2 = 8[/tex]
⇒ [tex]2a = 8-2[/tex] ( subtracting 2 from both the sides)
⇒ [tex]2a = 6[/tex]
⇒ [tex]a = \frac{6}{2}[/tex] (dividing both the sides by 2)
⇒ [tex]a = 3[/tex]
Hence, the value of a and the coefficient of x is 3.
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