The value of x of the Quadratic Equation, (x - 7)² = 36 when the right-hand side is positive is 13 and for the negative right-hand side, it is 1. So the value of x could be 13 and 1 both.
Split into two equations:
(x - 7)² = 36
(x- 7) = √36 or (x- 7) = -√36
For equation (x- 7) = √36 value of x:
x - 7 = √(6)²
x - 7 = 6
x = 13
For equation (x- 7) = -√36 value of x:
x - 7 = -√(6)²
x - 7 = - 6
x = 1
∴ value of x could be 13 and 1 both.
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(3/8, - (sqrt(55))/8) Find csc t.
The CSC of the expression [tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)[/tex] is mathematically given as
[tex]\csc (\theta)=-\frac{8 \sqrt{55}}{55}[/tex]
This is further explained below.
What is the CSC ?Generally, the equation for the Problem is mathematically given as
[tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)[/tex]
Therefore
To find the [tex]$\csc (\theta)$[/tex] between the x-axis and the line between the points (0,0) and [tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right),[/tex] draw the triangle between the three points [tex](0,0),\left(\frac{3}{8}, 0\right)$, and $\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)$[/tex]
Opposite [tex]$:-\frac{\sqrt{55}}{8}$[/tex]
Adjacent :[tex]$\frac{3}{8}$[/tex]
Find the hypotenuse using the Pythagorean theorem [tex]$c=\sqrt{a^2+b^2}.[/tex]
[tex]$\csc (\theta)=\frac{\text { Hypotenuse }}{\text { Opposite }}$[/tex]
therefore
[tex]\csc (\theta)=\frac{1}{-\frac{\sqrt{65}}{8}}$.[/tex]
[tex]\frac{1}{-\frac{\sqrt{55}}{8}}[/tex]
Simplify[tex]\csc (\theta)[/tex]
[tex]\csc (\theta)=-\frac{8 \sqrt{55}}{55}[/tex]
Approximate the result.
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Find the value of f (8).
Answer:
4
Step-by-step explanation:
first we go over where 8 is on the x-axis then we move up to the line, and look at the corresponding y value, which is 4
c(x)=(x-5)^3, what is c(3)
Answer:
-8
Step-by-step explanation:
You want the value of c(3) when c(x) = (x -5)^3.
Function valueThe value of a function is found by substituting the argument for the variable and doing the arithmetic.
c(x) = (x -5)^3
c(3) = (3 -5)^3 = (-2)^3
c(3) = -8
Find the equation of a line perpendicular to y=-3x - 4 that contains the point (3, 0). Write the equation in slope-
intercept form.
Answer:
y = 1/3 x + 3
Step-by-step explanation:
1) when finding a perpendicular line, you take the slope and use the reciprocal (you flip it) and change the sign (from negative to positive or positive to negative)
-3 ---> 1/3
2) plug in the slope into a new equation
y=1/3 x + b
3) plug in the points
3= 1/3 (0) + b
b=3
4) rewrite the equation
y=1/3 x + 3
Consider a population that begins growing exponentially at a base rate of 4.3% per year and then follows a logistic growth pattern. If the carrying capacity is 62 million, find the actual fractional growth when the population is at 10 million, 30 million, and 50 million.
The actual fraction of growth-
a) population = 10 million; growth rate = 559/155.
b) population = 30 million; growth rate = 344/155
c) population = 50 million; growth rate = 126/155
What is defined as the exponential population growth?In exponential growth, the per capita (per person) growth rate of a population remains constant regardless of population size, causing the population to grow faster and faster as it grows larger.The logistic growth rate of a population decreases as population size approaches a maximum imposition by limited resources available in the environment, recognised as the carrying capacity (K).The base growth rate = 4.3%.
The current carrying capacity = 62 million.
The actual fractional growth for the given values are-
growth rate = r * (1 - population/carrying capacity)
a) population = 10 million,
Put the values;
growth rate = 4.3 × (1 - 10/62)
growth rate = 559/155 is the actual fraction of growth.
b) population = 30 million,
Put the values;
growth rate = 4.3 × (1 - 30/62)
growth rate = 344/155 is the actual fraction of growth.
c) population = 50 million,
Put the values;
growth rate = 4.3 × (1 - 50/62)
growth rate = 126/155 is the actual fraction of growth.
Thus, the actual fraction of growth is estimated.
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Can you please solve this.
Answer:
x^8
Step-by-step explanation:
You want to simplify x^10/x^2.
Rule of exponentsThe applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
ApplicationUsing this rule on the given expression, we find ...
(x^10)/(x^2) = x^(10-2) = x^8
__
Additional comment
An exponent can be considered to be an indicator of repeated multiplication. That is, it tells how many times the base is a factor in the product. Knowing this, you can use the usual rules of division to cancel common factors:
[tex]\dfrac{x^{10}}{x^2}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x}=x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x=x^8[/tex]
help with the first one ?
The solution of the equation is x = 5.
How to solve equation?The equation is written as follows:
- 94 = -2 (8x + 7)
The variable to be found as variable x.
A variable is a number represented with a letter in an equation.
Hence,
- 94 = -2 (8x + 7)
open the bracket on the right side of the equation
-94 = - 16x - 14
add 14 to both sides of the equation
-94 = - 16x - 14
-94 + 14 = - 16x - 14 + 14
-80 = - 16x
divide both sides by -16
x = -80 / -16
x = 5
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terrance plants a garden that has 8 rows of flowers, with 28 flowers in each row. how many flowers did terance plant
Answer:
224
Step-by-step explanation:
The answer is 224 since 8 x 28 = 224
Answer: Terrence planted 224 flowers in total
Step-by-step explanation: 8x28
75+25x=300 situation
The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the weakest level and 5 is the strongest level.
(a) Find the mean, variance, and standard deviation of the probability distribution.
(b) Interpret the results.
Hurricanes
1
2
3
4
5
0.0
0.1
0.2
0.3
0.4
0.5
Category
Probability
0.419
0.276
0.225
0.068
0.012
The mean = 0.2, variance = 0.03226 and Standard deviation = 0.1796
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
level x
1 0.419
2 0.276
3 0.225
4 0.068
5 0.012
So, mean = (0.419+ 0.276 + 0.225+ 0.068 + 0.012)/5
mean = 0.2
level x (x- mean) (x- mean)²
1 0.419 0.219 0.0479
2 0.276 0.076 0.0057
3 0.225 0.025 0.000625
4 0.068 -0.268 0 .0718
5 0.012 -0.188 0.0353
So, variance = 0.032265
standard deviation = √(variance)
Standard deviation = √(0.032265)
Standard deviation = 0.1796
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Find P(A/B), in S = {10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80), A = 40 or less in S and B = even in S. Use fraction form for the probability
Answer:
P(A|B) = 1/2
Step-by-step explanation:
Sample space for B = {10, 20, 30, 40, 50, 60, 70, 80}
where B is even
Total number of elements in sample space = 8
P(A|B) = Probability of a number being 40 or less from the sample space of 8
Sample space for A|B = {10, 20, 30, 40}
So out of a possible 8 elements in the sample space for B only 4 elements can be chosen for the sample space of A
So P(A|B) = 4/8 = 1/2
Find an irrational number between 1/12 and 1/10
The irrational numbers lying between 1/12 and 1/10 are -
0.456258824......0.32547965.......0.21448663324........What is meant by the irrational number?Irrational numbers are real numbers that can't be represented by a ratio.Irrational numbers are real numbers that can't be expressed as a fraction, p/q, in which p and q are integers. The numerator q does not equal zero (q ≠ 0). Furthermore, an irrational number's decimal expansion is not terminating and neither repeating.For the given question;
The number are given as 1/12 and 1/10
Write both number in its decimal form.
1/12 = 0.8333333
1/10 = 0.1
Thus, write number which lies between these two.
1/12 = 0.8333333
0.456258824......
0.32547965.......
0.21448663324........
1/10 = 0.1
The dotted parts shows that the number is nether terminating nor repeating.
Thus, the irrational numbers lying between 1/12 and 1/10 are found.
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The mark scored in a test by ten pupils are as follows: 15, 14, 15, 13, 16, 16, 17, 13, 16, 17. Find the modal mark?
The modal mark is 16.because as we can see there are two 15, two 13,one 14, two 17 and three 16.
How can you use the Distributive Property to find 11 × 5?
Answer:
You cant use the distributive property because it is when the equation is like this: ax(b+c) so if it was 11x(5+0) you would multiply the 5 by 11 by itself and multiply 0 with 11 then you add them and get 55. I hope that helps :)
Step-by-step explanation:
The graph of a linear function is a horizontal line. When x = -3, y = 4. What is the equation for
this linear function? Explain.
For the graph of a linear function x=-3 and y=4 is horizontal line , the equation for this linear function is y = 0(x) +4.
As given in the question,
Graph of a required linear function is a horizontal line.
Given :
When x=-3 y=4
Two coordinates of the required linear function are :
(x₁ ,y₁) = (-3, 4)
(x₂, y₂) = ( 0,4)
Equation of the linear function :
(y -y₁) /(x-x₁) = (y₂ -y₁) / (x₂- x₁)
⇒( y-4)/(x+3) =(4-4)/(0+3)
⇒ (y-4)/(x+3) = 0/3
⇒ y = 0(x) +4
Therefore, for the graph of a linear function x=-3 and y=4 is horizontal line , the equation for this linear function is y = 0(x) +4.
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Find the mode or modes (if any).5, 9, 96, 3, 2, 8, 79, 1, 4, 16
Given:
5, 9, 96, 3, 2, 8, 79, 1, 4, 16
To determine the mode based on the given data set, we note first that mode is the number in a data set that occurs most frequently. Since each value occurs only once, there is no mode of this data set.
Therefore, the answer is: no mode or none.
Write a polynomial f (x) that satisfies the given conditions.
Polynomial of lowest degree with zeros of -4 (multiplicity 3), 3 (multiplicity 1), and with f (0) =960.
f (x)=
Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1). The polynomial is f(x)=-5(x+4)³(x-3).
Given that,
Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1)
We have to find the polynomial of f(x) which satisfy the conditions.
Here,
We have the zeros of the polynomial are -4 (multiplicity 3), 3(multiplicity 1)
Which we can write as -4,-4,-4,3 are the zeros.
Then we can write the polynomial as
f(x)=ω(x+4)³(x-3)
We have to first find the value of ω.
So,
We have f(0)=960
ω(0+4)³(0-3)=960
ω(4)³(-3)=960
64ω(-3)=960
-192ω=960
ω=960/-192
ω=-5
We got the ω as -5.
The polynomial f(x)=-5(x+4)³(x-3)
Therefore, the polynomial is f(x)=-5(x+4)³(x-3).
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Which of the following questions describes the equation 4 =-20? What number, when multiplied by negative twenty, is equal to four? What number, when divided by four, is equal to negative twenty? What number, when multiplied by four, is equal to negative twenty? What number, when divided by negative four, is equal to twenty?
The option that describes the equation 4x =-20 will be C. What number, when multiplied by four, is equal to negative twenty?
How to illustrate the information?It should be noted that an equation is used to show the relationship between the variables.
In this case, the equation given us illustrated as:
4x = -20
The appropriate question that fits this will be that what number, when multiplied by four, is equal to negative twenty. This can be illustrated as:
4x = -20
Divide through
x = -20 / 4
x = -5
In conclusion, the correct option is C.
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Answer:
Step-by-step explanation:
if researchers are 96% confident that they are correct, what is the probability they are wrong
Based on the fact that the researchers are 96% confident that they are correct, then the probability that they are actually wrong is 4%.
How to find probability?If we are to believe the assertions of the researchers that they are 96% certain of them being correct, then the probability that they are wrong can be found by the formula:
= 1 - Percentage certainty
Solving for that probability of being wrong then gives:
= 1 - 96%
= 4%
It is worthy of note that this probability of being wrong is based on their estimates and so there is a chance that the probability of being wrong is 4%.
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Please help me with this!!!
Answer:
Is this correct??
if yes reply
Use the figure to answer the following question.
If AC||DE, which of the following justifies ΔABC ~ ΔDBE?
A. Definition of Similar Triangles
B. SAS Similarity Theorem
C. SSS Similarity Theorem
D. AA Similarity Postulate
The statement that justifies the triangles' similarity is (c) SSS similarity theorem
How to determine the statement that justifies the triangles?The triangles are given as
Triangle ABC and Triangle DBE
From the figure, we can see that the corresponding vertical lines of either triangle are parallel (but not equal)
This means that, the triangles are similar triangles
This is so because the other two sides of the smaller triangle lie completely on the bigger triangle
As a general rule, the corresponding sides of similar triangles are in proportions
So, we can say that the corresponding side lengths of the triangles are similar
The statement that justifies this is the Side-Side-Side similarity theorem
Hence, the true statement is (c) SSS similarity theorem
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Which figure is a line?
Answer:
Bottom left
Step-by-step explanation:
The figure that looks like <-------------------------> is a line
Top left *------------------------* is a segment
Bottom right is a ray *---------------->
Top right is a * point or dot
I hope this helps!
What are the zeros of the polynomial function f(x) = x3 + 9x2 + 20x? (5 points)
0, −5, −4
0, −5, 4
0, 5, −4
0, 5, 4
The zeros of the function f(x) = x³ + 9x² + 20x is :
0, 5 ,4
Explanation :Steps to solve quadratic equation:
Put all of the terms on one side of the equal sign and zero on the other.Factor.Set each factor to a value of zero.Each of these equations must be solved.Because they are the values of x for which f(x) = 0, the solutions of the quadratic equation ax² + bx + c = 0 correspond to the roots of the function f(x) = ax² + bx + c.Check your answer by plugging it into the original equation.
Given function,
f(x) = x³ + 9x² +20x
take x common from f(x),
=> x(x² + x - 20) = 0
=> x(x² + 5x + 4x + 20) = 0
=> x( x + 5 ) + 4 ( x +5 ) = 0
=> (x + 5) ( x + 4 ) = 0
=> x -5 = 0 or x -4 = 0
=> x = 5 and x = 4 .
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Simplify the fraction
36
84
as much as possible.
36
84
3
7
5
12
Answer:
3/7
Hope this helps!
Have a good day :).
Please help I’ll mark you as brainliest if correct!!
Time can be used to quantify, contrast, or even rank the length of events or the gaps between them. To complete the cooking at 2:00 PM, George needs to start his cooking at 12:30 PM.
What is meant by Time?Time can be defined in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be calculated, compared, or even ordered utilizing time.
Given time needed for each meals are;
Turkey = 70 min
Pumpkin pie = 17 min
Rolls = 30 sec
coffee = 45 sec
Total time = 87 min 75 sec
= 1 hour 27min 75 sec
So in order to complete the cooking at 2:00 PM, George needs to start his cooking at 12:30 PM.
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PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
an equation of the line in point-slope form is
An equation of the line in point-slope form is y = 6x + 50.
Define point slope form.y = y₁ = m(x -x₁) is the equation of a straight line, where m is the slope and (x₁, y₁) are the coordinates at a given point on the line (see slope-intercept form). When you know the slope and another point on the line, the point-slope form of a linear equation is most helpful for locating a point on a line. When two other points are known, it can also be used to locate a point on a line.
Given,
y₂ = 200
y₁ = 230
x₂ = 30
x₁ = 25
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Slope = [tex]\frac{230-200}{30-25}[/tex]
Slope = [tex]\frac{30}{5}[/tex]
Slope = 6
Equation:
y - y₁ = m(x - x₁)
y - 200 = 6(x - 25)
y - 200 = 6x - 150
y = 6x + 50
An equation of the line in point-slope form is y = 6x + 50.
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Find the equation of the line passing through the points (1.-2) and (-2,7). Write the equation in slope-intercept form. A) y = 3x + 13 B) y = 3x - 5 C) y = -3x -2 D) y = -3x + 1
The equation is of the form y=mx+b, where m = slope and b = y-interset. Therefore, find m and b:
For m
[tex]m=\frac{y2-y1}{x2-x1}=\frac{7-(-2)}{-2-1}=\frac{7+2}{-3}=\frac{9}{-3}=-3[/tex]For b
[tex]\begin{gathered} y=mx+b \\ -2=-3(1)+b \\ -2=-3+b \\ -2+3=-3+b+3 \\ b=1 \end{gathered}[/tex]So, the equation is:
[tex]y=-3x+1[/tex]Answer: D.
Mary runs 4 laps around the track inb8 minutes. Paul runs 12 laps in 18 minutes. Who ran faster
Answer:
Step-by-step explanation:
thanks
Parul ran the fastest.
For Mary,
4/8 = x/1
4/8 or 1/2 laps per minute.
x= 0.5
For Paul,
12/18 = y/1
12/18 or 2/3 laps per minute.
y=0.666
Hence, Parul ran faster.
The SI unit of speed is m/s, and speed is defined as the ratio of distance to time.
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2,175/12 what is the answer
Answer: 2,175 divided by 12 will give you 181.25.