Answer:
See below.
Step-by-step explanation:
A(x) = x^2 + 5x
A(x) = x^2 + 5x = 14
x^2 + 5x - 14 = 0
(x + 7)(x - 2) = 0
x + 7 = 0 or x - 2 = 7
x = -7 or x = 2
x is the height of a rectangle.
The only viable solution is x = 2 because the height of a rectangle cannot be a negative number such as -7.
The only viable solution for the height is x= 2, because height cannot be a negative value.
What is Rectangle?A rectangle is a quadrilateral with four right angles.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface.
What is Quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2} +bx+c=0[/tex]
Given,
Area of the rectangle = [tex]x^{2} +5x[/tex] = 14
Then,
[tex]x^{2} +5x-14=0\\(x+7)(x-2)=0[/tex]
Therefore x = -7 and 2
But the Height cannot be negative therefore x = 2
Hence, only viable solution for the height is x= 2, because height cannot be a negative value.
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There is a unique positive real number x such that the three numbers
log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
The number x can be written as m/n, where m and n are relatively prime positive integers.
Find m+n.
Step-by-step explanation:
If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
Let a = log82x, b = log4x and c = log2x
If a = log8 2x; 8^a = 2x... (1)
If b = log4 x; 4^b = x ... (2)
If c = log2 x; 2^c = x...(3)
Since a, b c are in GP, then b/a = c/b
Cross multiplying:
b² = ac ...(4)
From eqn 1, x = 8^a/2
x = 2^3a/2
x = 2^(3a-1)
From eqn 2; x = 4^b
x = 2^2b
From eqn 3: x = 2^c
Equating all the values of x, we have;
2^(3a-1) = 2^2b = 2^c
3a-1 = 2b = c
3a-1 = c and 2b = c
a = c+1/3 and b = c/2
Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;
(c/2)² = c+1/3×c
c²/4 = c(c+1)/3
c/4 = c+1/3
Cross multiplying;
3c = 4(c+1)
3c = 4c+4
3c-4c = 4
-c = 4
c = -4
Substituting c = -4 into equation 3 to get the value of x we have;
2^c = x
2^-4 = x
x = 1/2^4
x = 1/16
Since the number x can be written as m/n, then x = 1/16 = m/n
This shows that m = 1, n = 16
m+n = 1+16
m+n = 17
The required answer is 17.
The value of m+n in which m and n are relatively prime positive integers is 17.
What is geometric sequence?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,
[tex]\log_82 x,\log_4x, \log_2x[/tex]
The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,
[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]
Using the base rule of logarithmic function,
[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]
Using the Power rule of logarithmic function,
[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]
The number x can be written as
[tex]\dfrac{m}{n}[/tex]
Here, m and n are relatively prime positive integers. Thus, the value of m+n is,
[tex]m+n=1+16=17[/tex]
Hence, the value of m+n in which m and n are relatively prime positive integers is 17.
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A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games.
A) Design a simulation for this event,
B) what counts as a successful outcome?
C) Estimate the probability using your simulation.
Can anyone help me? I’m kind of confused on this problem
Answer:
C. Estimate the probability using your simulation.
Step-by-step explanation:
A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom.
Answer:
angle of depression = -12 degrees
Step-by-step explanation:
Sin = opposite/hypotenuse
sin = -208/1000
inv sin 0.208 = -12
To solve this problem, we just need to use trigonometric ratio and use the ratio that best fits this problem. The angle of depression is equal to 76.23 degrees.
Trigonometric RatioUsing SOHCAHTOA, we can easily solve this problem, but we need to first know which ratio to use
Data;
opposite (ski run) = 1000 yardsadjacent (vertical drop) = 208 yardssince we have the value of opposite and adjacent, we can solve this using the tangent of the angle
[tex]tan\theta = \frac{opposite}{adjacent} \\tan \theta = \frac{1000}{208} \\tan\theta = 4.807\\\theta = sin^-^1 (4.0807)\\\theta = 76.23^0[/tex]
From the calculation above, the angle of depression is equal to 76.23 degrees.
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pls help it will mean alot!!
due rn!!
Answer:
f(x) = 4^x
f(4) = 4^4 = 256
Hope this helps!
:)
the answer is 256 but i am not sure
hope this helps and be safe :)
PLEASE HELP ASAP A group of 8th and 9th graders were surveyed about whether they use social media to communicate with their friends. The results are shown below in the conditional relative frequency table by row. A 4-column table with 3 rows. The first column has no label with entries 8th grade, 9th grade, total. The second column is labeled do not use with entries 0.06, 0.19, 0.38. The third column is labeled use with entries 0.84, 0.81, 0.62. The fourth column is labeled total with entries 1.00, 1.00, 1.00. Which conclusions can be drawn from the results of the survey? Check all that apply. There is no association between using social media and grade level. The probability a student uses social media, given that he or she is in 9th grade, is 81%. A student who is more likely to not use social media is in 8th grade. An 8th grader is more likely to use social media than not. Knowing a student’s grade level does not help determine if he or she uses social media.
Options A, B, D, and E are correct answers such that the probability of the usage of social media by 8th and 9th-grade students is given.
A. There is no association between using social media and grade level.
B. The probability a student uses social media, given that he or she is in 9th grade, is 81%.
D. An 8th grader is more likely to use social media than not.
E. Knowing a student’s grade level does not help determine if he or she uses social media.
What is Probability?Probability is the ratio of the favorable outcomes to the total outcomes.
Given that, a group of 8th and 9th graders were surveyed about whether they use social media to communicate with their friends.
We can see that, there is no relationship between the usage of social media and grade level so, we can say that there is no association between using social media and grade level.
Probability of using social media by a 9th grader is-
P(9) = 0.81 / 1 x 100 = 81%
Probability of using social media by a 8th grader is-
P(8) = 0.84 / 1 x 100 = 84%
We cannot define the usage of social media depending on the grade level.
Thus, Options A, B, D, and E are correct answers.
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The table is attached
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A. y = 3x
B. y = x
C. y = 2x
D. y = -1/3x
E. y = -3x
F. y = 1/3x
Solve the equation for x, and enter your answer below.
10x - 15x + 5= -45 + 40
Answer: x = 2
Step-by-step explanation:
[tex]10x - 15x + 5= -45 + 40[/tex]
subtract 5
[tex]10x - 15x= -45 + 40-5[/tex]
Combine like terms;
[tex]-5x=-10[/tex]
Divide by -5
[tex]x=\frac{-10}{-5}\\ x=2[/tex]
Answer:
[tex]x = 2[/tex]
Step-by-step explanation:
[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]
5. Jack and Jill use rain gauges that are the same size and shape to measure rain on top of a hill. Jack
uses a rain gauge marked in fourths of an inch. Jill's gauge measures rain in eighths of an inch. On
Thursday, Jack's gauge measured inches of rain. Jill and Jack both had the same amount of water,
so what was the reading on Jill's gauge on Thursday? Draw a number line and write a sentence to
explain your thinking.
Answer:
List the multiples
1/4,2/4,3/4,4/4
1/8,2/8,3/8,4/8,5/8,6/8,7/8,8/8
1/4=2/8
2/4=4/8
4/4=8/8
Those numbers are the common fractions so they would be the only fractions that both Jack and Jill could get.
Step-by-step explanation:
Please can people help??!!
Photo below
i think this is the method for solving it
7. How many Cones will it take to fill a Cylinder with the same height and radius?
O 6 cones
O 3 cones
O 1 cone
O 2 cones
Answer:
3 cones
Step-by-step explanation:
This is why the formula for the volume of a cone is 1/3 (π×r^2)× h, while the volume for a cylinder is (π× r^2)× h, respectively.
Answer:
C) 3 Cones.
Explanation:
Hope this helps! :)
HELP!!! Cumulative Exam!! Which is the simplified form of m Superscript negative 8 p Superscript 0? StartFraction 1 Over m Superscript 8 Baseline p EndFraction StartFraction 1 Over m Superscript 8 EndFraction StartFraction p over m Superscript 8 EndFraction m Superscript 8
Answer:
(B)[tex]\dfrac{1}{m^8}[/tex]
StartFraction 1 Over m Superscript 8 EndFraction
Step-by-step explanation:
We want to find the simplified form of: [tex]m^{-8}p^0[/tex]
[tex]m^{-8}p^0=m^{-8}$ X p^0\\p^0=1\\m^{-8}=\frac{1}{m^8} \\$Therefore:\\m^{-8}$ X p^0=\dfrac{1}{m^8} X 1\\=\dfrac{1}{m^8}[/tex]
The correct option is B.
Answer:
I am 80% sure its 1 if not then its 1/p
Step-by-step explanation:
If (1)=3 and f(n)=f(n-1)-1 then find the value of f(6)
Answer:
f(1) = 3
f(n) = f(n-1) - 1
Otherwise,
f(n) = f(1) - (n-1)
=> f(6) = 3 - 5 = -2
Hope this helps!
:)
Solve for 2.
Write the smaller solution first, and the larger solution second.
(3x – 6)(-x + 3) = 0
smaller x =
larger x =
Answer:
(3x – 6)(-x + 3) = 0
=> 3x - 6 = 0 => x = 6/3 = 2
and
=> -x + 3 = 0 => x = 3
Hope this helps!
:)
Given the fractions 8/15 and 18/35, find the largest number that these fractions can be divided by, so that the quotient will be a whole number.
Answer:
Therefore the largest number that these fractions can be divided by to give them a whole number is
a) 8/15 = The largest number is 8/15
b) 18/35 = The largest number is 18/35
Step-by-step explanation:
A quotient is the result obtained by dividing two numbers.
So that the quotient obtained is a whole number we have to find out, what number they can be divided by to give them that.
Let's assume the whole number is 1
a. 8/15
8/15 ÷ x = 1
8/15 × 1/x = 1
8/15x = 1
We would cross multiply
8 = 15x
We would divide both sides by 15
8/ 15 = x
Hence the largest number that would divide 8/15 and give it a whole number = 8/15
b) 18/35
18/35÷ x = 1
18/35 × 1/x = 1
18/35x = 1
We would cross multiply
18 = 35x
We would divide both sides by 35
18/ 315 = x
Hence the largest number that would divide 18/35 and give it a whole number = 18/35
Answer:
The answer is 2/105
Step-by-step explanation:
first we have to find the LCM of both denominators. IN this case, the LCM of 15 and 35 is 105. Then we have to find the GCF of these numerators. IN this case, the GCF of 8 and 18 is 2.
Now, put the GCF you found over the LCM.
ANSWER: 2/105
This fraction is the largest number you can divide both numbers by to get a whole number.
Find the area of the shaded regions:
The pink is the shaded region.
40π
You dont need paper hw since we're in quarantine
Answer:40
Step-by-step explanation:
Which of the following is true of the values of x and y in the diagram below? A unit circle is shown. A radius with length 1 forms angle theta = StartFraction pi Over 4 EndFraction. The radius intersects point (x, y) on the unit circle. y < x y > x y + x = 1 StartFraction y Over x EndFraction = 1
Answer:
y/x = 1 got it right on edg
Step-by-step explanation:
Answer:
y/x = 1 on E2020
Step-by-step explanation:
Have a Great Day :)
in a certain algebra class of 26 students, 16 of them play basketball and 9 of them play baseball. there are 5 students who play both sports. what is the probability that a student chosen randomly plays basketball or baseball
Answer:
3/26 students or 11%
Step-by-step explanation:
Answer:
8/9
Step-by-step explanation:
24/27 = 8/9
Segment Line segment X Y is dilated using a scale factor of Two-thirds through P. Which segment shows the correct result of the dilation?
Answer:
We need the segments but which ever one has the segment that is 2/3 times the length of segments xy
Step-by-step explanation:
Answer: line c
Step-by-step explanation: I got it correct
Write the equation of a line that passes through the point (4, 2) and is parallel to the line graphed below.
Answer:
Step-by-step explanation:
(-2, 2) (2, -3)
(-3 - 2)/(2 + 2)
-5/4 the slope
y - 2 = -5/4(x + 2)
y - 2 = -5/4x - 5/2
y- 4/2 = -5/4x - 5/2
y = -5/4x - 1/2
i dont know how to do this if someone could show me how and what the answer is
Answer:
It is A because due to the slope it is a parallelogram.
Step-by-step explanation:
Answer:
its a
Step-by-step explanation:
Find two numbers, if their sum is 49 and their difference is 1/2 .
This question is for my little sister who needs help with her Math.
I'm too busy to help.
Answer: 49.5 and -0.5
Step-by-step explanation:
a + b =49
a - b = 0.5
a= 49.5
b= -0.5
The two numbers are approximately 24.25 and 24.75.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
Let's call the two numbers x and y.
According to the problem, we have two equations:
x + y = 49 (since their sum is 49)
x - y = 1/2 (since their difference is 1/2)
We can solve this system of equations using the method of substitution.
First, we can rearrange the second equation to solve for one of the variables in terms of the other:
x - y = 1/2
x = y + 1/2
Now we can substitute this expression for x into the first equation:
(y + 1/2) + y = 49
2y + 1/2 = 49
2y = 48.5
y = 24.25
Now we can use this value of y to solve for x:
x = y + 1/2 = 24.25 + 1/2 = 24.75
Therefore, the two numbers are approximately 24.25 and 24.75.
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Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing!
Answer:
the right answer is : A
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
im smort
At Subway sandwiches, how many different sandwiches can I make from 3 different types of bread, 5 different types of cheese, and 4 different types of meat?
Answer:
60 sandwiches
Step-by-step explanation:
In this case we must know that for each type of bread, it can be combined with each type of cheese and each type of meat, that is to say that the total amount of combinations would be, the amount of types of bread, for the amount of types of cheese for the amount of types of meat, that is to say:
3*5*4 = 60
That means there are a total of 60 ways to make different sandwiches
hi!! <3 i attached a picture of a easy trigonometry question can you please help if you don’t mind <33
Answer:
Side AB has a length of 4, and side BC has a length of 11.7
The parallelogram does not have right angles. Its area is
less than ab.
equal to ab.
greater than ab.
Answer:
equal to ab
Step-by-step explanation:
The area of a parallelogram is Area = ab
therefore, the area is ab
Answer:
Less than ab
Step-by-step explanation:
I don’t understand this question. Can anyone help? I need answers ASAP. Thanks for all the help
There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)
There's no solution to this particular system because the two lines are parallel.
How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.
The line on the left passes through the points (-1, 0) and (0, -2), so it has slope
(-2 - 0)/(0 - (-1)) = -2/1 = -2
The line on the right passes through (0, 2) and (1, 0), so its slope is
(0 - 2)/(1 - 0) = -2/1 = -2
The slopes are equal, so the lines are parallel.
Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.
number 19 very much need the answer please
Answer:
D not possible.........
i think of a number multiply it by 3 and subract 2 . The result is 14
Answer:
5.3
Step-by-step explanation:
Answer:
The answer is 5.3
Step-by-step explanation:
5.3x3-2= 13.9 but when you round its 14
what is 5 + 5 /2 - 4 x 10
Step-by-step explanation:
use bodmas
start with multiplication
-4*10 = -40
5+5/2 - 40
addition next
5 + 5/2 = 7.5
7.5 - 40 = -32.5
what is exponential decay
Answer:
Exponential decay is the decrease in a quantity according to the law. (1) for a parameter and constant (known as the decay constant), where is the exponential function and is the initial value.
Answer:
When a population or group of something is declining, and the amount that decreases is proportional to the size of the population, it's called exponential decay. In exponential decay, the total value decreases but the proportion that leaves remains constant over time.
Step-by-step explanation:
