Answers
A.
Using the points (2,3) and (0,6) to find the slope (m), we have:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{6-3}{0-2}=\frac{3}{-2}[/tex]The slope is m= -3/2
B.
Using the points (-1, 7.5) and (1, 4.5) to find the slope (m), we have:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{4.5-7.5}{1-(-1)}=\frac{-3}{1+1}=\frac{-3}{2}[/tex]The slope is m= -3/2
C.
The slope is the same as we are finding the ratio of the vertical change to the horizontal change between two points. Since the function represents a linear equation the slope is going to be the same despite of the points you choose.
Related Questions
Hello can you please help me with problem number 12
Answers
Turn the 48in to ft
[tex]\begin{gathered} 1ft=12in \\ \\ 48in\times\frac{1ft}{12in}=4ft \end{gathered}[/tex]Then, 48 inches is equal to 4ft.
Comparing the given quatities you get that:
48inches > (greater than) 3ftThe standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds. Round all answers to the nearest hundredth. Conclusion: We estimate with 95% confidence that the mean weight of all elephants is between?
Answers
Confidence interval is written as
point estimate ± margin of error
In this case, the point estimate is the sample mean
the formula for calculating margin of error is expressed as
[tex]\text{margin of error = z }\times\frac{\sigma}{\sqrt[]{n}}[/tex]where
σ = population standard deviation
n = sample size
z is the z score corresponding to a 95% confidence level. From the standard normal distribution table, z = 1.96
From the information given,
σ = 15
n = 50
sample mean = 244
By substituting these values into the formula,
[tex]\text{margin of error = 1.96 }\times\frac{15}{\sqrt[]{50}}\text{ = 4.16}[/tex]Thus,
confidence interval = 244 ± 4.16
Lower limit of conidence interval = 244 - 4.16 = 239.84
Upper limit of conidence interval = 244 + 4.16 = 248.16
Conclusion: We estimate with 95% confidence that the mean weight of all elephants is between 239.84 pounds and 248.16 pounds
Suppose a normal distribution has a mean of 98 and a standard deviation of6. What is P(x < 110)?A. 0.84B. 0.16C. 0.025O D. 0.975
Answers
We know that
• The mean is 98.
,• The standard deviation is 6.
,• The given x-value is 110.
First, we find the z-value using the following formula
[tex]Z=\frac{x-\mu}{\sigma}_{}[/tex]Replacing the given information, we have
[tex]Z=\frac{110-98}{6}=\frac{12}{6}=2_{}[/tex]The z-value or z-score is 2.
Then, we use a z-table to find the probability when P(x<110), or P(z<2).
We obtain a probability of 0.97, which approximates to D.
Hence, the probability would be D.Two figures are similar. The smaller figure has dimensions that are 3:4 the size of the largerfigure. If the area of the larger figure is 100 square units, what is the area of the smallerfigure?
Answers
Answer:
56.25
Explanation:
We are told that the side lengths of the smaller figure are 3/4 the length of the larger figure.
[tex]S_{small}=\frac{3}{4}\times S_{large}[/tex]Now since the area is proportional to the equal of the side lengths, we have
[tex]A_{small}=S_{small}^2^[/tex][tex]A_{small}=(\frac{3}{4})^2\times S_{large}^2[/tex][tex]=A_{small}=(\frac{3}{4})^2\times A_{large}^2[/tex]The last is true since A_large = S^2_large.
Now we are told that A_large = 100 square units; therefore,
[tex]A_{small}=(\frac{3}{4})^2\times100[/tex][tex]\Rightarrow A_{small}=\frac{9}{16}\times100[/tex]which we evaluate to get
[tex]A_{small}=\frac{9}{16}\times100=56.25[/tex][tex]\boxed{A_{small}=56.25.}[/tex]Hence, the area of the smaller figure is 56.25.
Express the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x).
Answers
Answer:
y = 5u², u=x-6
Explanation:
Given the function:
[tex]y=5(x-6)^2[/tex]We want to express f(x) as a composition of two functions.
Let u = x-6
[tex]\implies y=5u^2[/tex]Therefore, the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)
[tex]\begin{gathered} y=5u^2\text{ where:} \\ f(u)=5u^2 \\ u=g(x)=x-6 \end{gathered}[/tex]the four faced of a rectangular pyrimid below are painted yellow. how many square feet will be painted
Answers
The number of square feet to be painted is equal to the surface area of the four face painted yellow.
Total Surface Area (TSA) =
[tex]4(\frac{1}{2}bh)[/tex]By Pythagoras Theorem,
[tex]\begin{gathered} h^2+1.5^2=5^2 \\ h^2=5^2-1.5^2 \\ h=\sqrt[]{25-2.25}\text{ =}\sqrt[]{22.75}=4.7697\text{ fe}et \end{gathered}[/tex]I need help with a math assignment. i linked it below
Answers
Since Edson take t minutes in each exercise set
Since he does 6 push-ups sets
Then he will take time = 6 x t = 6t minutes
Since he does 3 pull-ups sets
Then he will take time = 3 x t = 3t minutes
Since he does 4 sit-ups sets
Then he will take time = 4 x t = 4t minutes
To find the total time add the 3 times above
Total time = 6t + 3t + 4t
Total time = 13t minutes
The time it takes Edison to exercise is 13t minutes
For f(x)=x^2 and g(x)=x^2+9, find the following composite functions and state the domain of each.
(a) f.g (b) g.f (c) f.f (d) g.g
Answers
The composite functions in this problem are given as follows:
a) (f ∘ g)(x) = x^4 + 18x² + 81.
b) (g ∘ f)(x) = x^4 + 9.
c) (f ∘ f)(x) = x^4.
d) (g ∘ g)(x) = x^4 + 18x² + 90.
All these functions have a domain of all real values.
Composite functionsFor composite functions, the outer function is applied as the input to the inner function.
In the context of this problem, the functions are given as follows:
f(x) = x².g(x) = x² + 9.For item a, the composite function is given as follows:
(f ∘ g)(x) = f(x² + 9) = (x² + 9)² = x^4 + 18x² + 81.
For item b, the composite function is given as follows:
(g ∘ f)(x) = g(x²) = (x²)² + 9 = x^4 + 9.
For item c, the composite function is given as follows:
(f ∘ f)(x) = f(x²) = (x²)² = x^4.
For item d, the composite function is given as follows:
(g ∘ g)(x) = g(x² + 9) = (x² + 9)² + 9 = x^4 + 18x² + 90.
None of these functions have any restriction on the domain such as fractions or even roots, hence all of them have all real values as the domain.
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Enter an algebraic inequality for the sentence. Use x as your variable. The quotient of five times a number and 9 is no more than 15. The answer is ____ < ____
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Answer:
[tex]\frac{5x}{9}\leq15[/tex]What is the y-intercept of 4x + 8y = 12?
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Over the next 10 years, town A is expecting to gain 1000 people each year. During the same time period, the population of town B is expected to increase by 5% each year. Both town A and town B currently have populations of 10,000 people. The table below shows the expected population of each town for the next three years.Which number of years is the best approximation of the time until town A and town B once again have the same population?
Answers
From the given figure we can see
The population in town A is increased by a constant rate because
[tex]\begin{gathered} 11000-10000=1000 \\ 12000-11000=1000 \\ 13000-12000=1000 \end{gathered}[/tex]Since the difference between every 2 consecutive terms is the same, then
The rate of increase of population is constant and = 1000 people per year
The form of the linear equation is
[tex]y=mx+b[/tex]m = the rate of change
b is the initial amount
Then from the information given in the table
m = 1000
b = 10,000
Then the equation of town A is
[tex]y=1000t+10000[/tex]Fro town B
[tex]\begin{gathered} R=\frac{10500}{10000}=1.05 \\ R=\frac{11025}{10500}=1.05 \\ R=\frac{11576}{11025}=1.05 \end{gathered}[/tex]Then the rate of increase of town by is exponentially
The form of the exponential equation is
[tex]y=a(R)^t[/tex]a is the initial amount
R is the factor of growth
t is the time
Since R = 1.05
Since a = 10000, then
The equation of the population of town B is
[tex]y=10000(1.05)^t[/tex]We need to find t which makes the population equal in A and B
Then we will equate the right sides of both equations
[tex]10000+1000t=10000(1.05)^t[/tex]Let us use t = 4, 5, 6, .... until the 2 sides become equal
[tex]\begin{gathered} 10000+1000(4)=14000 \\ 10000(1.05)^4=12155 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(5)=15000 \\ 10000(1.05)^5=12763 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(6)=16000 \\ 1000(1.05)^6=13400 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(30)=40000 \\ 10000(1.05)^{30}=43219 \end{gathered}[/tex]Since 43219 approximated to ten thousand will be 40000, then
A and B will have the same amount of population in the year 30
The answer is year 30
Two sides of a triangle have lengths 5 and 4. Which of the following can NOT be the length of the third side?
Answers
SOLUTION
From the triangle inequality theorem, the sum of the lengths any two sides must be greater than the length of the third side
So, looking at the options and looking at 4 and 5, it means that 5 is the longest side. So
[tex]\begin{gathered} 4+2=6>5 \\ 4+4=8>5 \\ 4+1=5=5 \\ 4+3=8>5 \end{gathered}[/tex]So since 4 + 1 = 5 and 5 is not greater than 5, hence 1 cannot be the length of the 3rd side.
The answer is option C
At what rate (%) of simple intrest will $5,000 amount to $6,050 in 3 years?
Answers
Rate of interest for
A = $5000
THEN apply formula
A-P= P•R•T/100
T = 3 years
Then
6050 - 5000= 1050 =
1050= P•R•T/100
Now find R
R= (1050•100)/(P•T) = (105000)/(5000•3) = 7
Then ANSWER IS
ANUAL RATE(%) = 7%
Simplify the expression (3^1/4)^2 to demonstrate the power of a power property. Show any intermittentstepsthat demonstratehow you arrived at the simplified answer.
Answers
(3^1/4)²
= (3^1/4) x (3^1/4)
=(3)^1/4 + 1/4
=(3)^1/2
Which can also be expressed as
= √3
²
value of a machine10(thousands of dollars)01 2 3 4 5 6 7 8 9 10Age of Machine(years)Which equation best represents the relationship between x, the age of the machine in years, and y, thevalue of the machine in dollars over this 10-year period?F.y = -0.002x + 2,500G.y = -500x + 8,000H.y = 500x + 8,000J.y = 0.002x + 2,500
Answers
To find the right answer, first, we find the slope.
Let's use the slope formula, and the points (0,8) and (8,4).
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]Replacing the points, we have.
[tex]m=\frac{4-8}{8-0}=\frac{-4}{8}=-\frac{1}{2}=-0.5[/tex]However, the Value is express in thousands of dollars, which means the slope is -500.
Observe that G is the only equation with the correct slope.
Therefore, G is the right answer.e22. Which expressions have values less than 1 whenx = 47 Select all that apply.(32)xo3x4
Answers
To know the expression that is less than 1 when x=4
we will need to check each expression
As for the first one;
[tex](\frac{3}{x^2})^0[/tex]anything raise to the power of zero will give 1, since the o affects all that is in the bracket, then the expression is 1
Hence it is not less than 1
For the second expression;
[tex]\frac{x^0}{3^2}=\frac{4^0}{9}=\frac{1}{9}[/tex]The value is less than 1
For the third expression;
[tex]\frac{1}{6^{-x}}[/tex]substituting x=4 in the above expression
[tex]\frac{1}{6^{-4}}[/tex]The above is the same as;
[tex]undefined[/tex]One of the legs of a right triangle measures 13 cm and the other leg measures
2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest
tenth.
Answers
Answer:
13.2 cm
Step-by-step explanation:
Use Pythagorean Theorem
Hypotenuse^2 = (leg1)^2 + (leg2)^2
H^2 = 13^2 + 2^2
= 169 + 4
H^2 = 173
H = sqrt (173) = 13.2 cm
the sum of two numbers is 24 . one number is 3 times the other number . find the two numbers
Answers
We are given that the sum of two numbers is 24. If "x" and "y" are the two numbers then we have that:
[tex]x+y=24[/tex]We are also given that one number is three times the other, this is expressed as:
[tex]x=3y[/tex]Now, we substitute the value of "x" from the second equation in the first equation:
[tex]3y+y=24[/tex]Now, we add like terms:
[tex]4y=24[/tex]Now, we divide both sides by 4:
[tex]y=\frac{24}{4}=6[/tex]Therefore, the first number is 6. Now, we substitute the value of "y" in the second equation:
[tex]\begin{gathered} x=3(6) \\ x=18 \end{gathered}[/tex]Therefore, the other number is 18.
If f(x) = ln [ sin2(2x)(e-2x+1) ] , then f’(x) is
I want to solve ?
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Here we will write our function in regular form using an identity.
[tex]log(ab)=loga+logb[/tex][tex]log(a/b)=loga-logb[/tex]Therefore, the rule of our function [tex]f(x)[/tex] will be as follows.
[tex]f(x)=ln(sin^2(2x))+ln(e^{-2x}+1)[/tex]The derivative of the natural logarithm [tex]ln(x)[/tex] function is of the following form.
[tex](ln(x))'=\frac{x'}{x}[/tex]It is found by dividing the derivative of the function in [tex]lnx[/tex] by the function in [tex]lnx[/tex].
For example:
[tex](ln(5x))'=\frac{(5x)'}{5x} =\frac{5}{5x} =\frac{1}{x}[/tex]According to this information, let's take the derivative of our function.
[tex]f'(x)=\frac{2sin(4x)}{sin^2(2x)} +\frac{-\frac{2}{e^{2x}} }{e^{-2x}+1}[/tex][tex]f'(x)=4cot(2x)-\frac{2}{1+e^{2x}}[/tex]Rules:[tex]((sin2x)²)'=2.2sin(2x)cos(2x)=2sin(4x)[/tex][tex](e^x)'=x'.e^x[/tex]Which postulate or theorem proves that ∆ABC and ∆EDC are congruent?
O AAS Congruence Theorem
O HL Congruence Theorem
O SAS Congruence Postulate
O SSS Congruence Postulate B
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what is the expression written in simplified radical form.
question is attached below.
please help
Answers
The expression 6√27 + 11√75 written in simplified radical form is 73√3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
6√27 + 11√75
We will simplify the radicals into the simplest form.
Radical means the numbers under square roots and cube roots.
6√27
= 6 √(9 x 3)
= 6 x √9 x √3
= 6 x √3² x √3
= 6 x 3 x √3
= 18√3
11√75
= 11 x √(25 x 3)
= 11 x √25 x √3
= 11 x √5² x √3
= 11 x 5 x √3
= 55√3
Now,
6√27 + 11√75
= 18√3 + 55√3
= (18 + 55)√3
= 73√3
Thus,
The expression 6√27 + 11√75 written in simplified radical form is 73√3.
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A small toy rocket is launched from a 32-foot pad. The height ( h, in feet) of the rocket t seconds after taking off is given by the formula h=−2t2+0t+32 . How long will it take the rocket to hit the ground?t=______(Separate answers by a comma. Write answers as integers or reduced fractions.)
Answers
Given: A small toy rocket is launched from a 32-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formula
[tex]h=-2t^2+0t+32[/tex]Required: To find out how long will it take the rocket to hit the ground.
Explanation: When the rocket touches the ground its height will be zero i.e.,
[tex]\begin{gathered} -2t^2+0t+32=0 \\ 2t^2=32 \\ t^2=16 \end{gathered}[/tex]Which gives
[tex]t=\pm4[/tex]Neglecting the negative value of t since time cannot be negative. We have
[tex]t=4\text{ seconds}[/tex]Final Answer: Time, t=4 seconds.
write the function below in slope. Show ALL the steps and type the answer.
Answers
This is a simple question to solve. First, let's take a look at a slope-intercept form equation as follows:
Once we know how a slope-intercept form looks like all we need to do is to simplify our equation to find that as follows:
And that is our slope-intercept form:
i have questions on a math problem. i can send when the chats open
Answers
The random sample is determined as the simplest forms of collecting data from the total population.
Under random sampling, each member of the subset carries an equal opportunity of being chosen as a part of the sampling process.
So according to the question given
Assign each person of the population a number. Put all the numbers into bowl and choose ten numbers.
is the random sample because every person carries an equal opportunity of being chosen from the total population.
Hence the correct option is A.
Domain and range from the graph of a quadratic function
Answers
Given the graph of the quadratic function with vertex (-4,-3) as shown below:
The domain of the function is a set of input values. The range of a quadratic function continues in either direction along the x-axis, as shown by the arrows in the above plot. The range is the set of output values. In other words, it is the possible values of y in a quadratic function.
Thus, the domain of the function is:
[tex](-\infty,\text{ }\infty)[/tex]The range of the function is :
[tex]\lbrack-3,\text{ }\infty)[/tex]Translate each sentence into an equation. Then find each number.
The sum of six, and a number divided by two is 0.
the possible answers are:
y/2-6=0;y=12
2y+6=0;y=-3
y/2+6=0;y=12
y/2+6=0;y=-12
Answers
The sum of six and a number divided by two is zero is translating into an equation is y/2+6 = 0, and the number is y = -12
The given sentence is "The sum of six and a number is divided by two is 0"
Consider the number as y
A number is divided by two = y/2
The sum of 6 and a number divided by two = y/2 + 6
The sum of six and a number is divided by two is 0
y/2 + 6 = 0
We have to solve the equation
Move the 6 to the right hand side of the equation
y/2 = -6
Move the 2 to the right hand side of the equation
y = -6×2
Multiply the numbers
y = -12
Hence, the sum of six and a number divided by two is zero is translating into an equation is y/2+6 = 0, and the number is y = -12
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I need help with this math problem
Answers
Answer: [tex]s=4f[/tex]
Step-by-step explanation:
The scaled copy has a side length four times of the original figure, so the equation is [tex]s=4f[/tex].
Use the commutative property of multiplication to write an equivalent expression to 69xuse the distributive property to write an equivalent expression to 8(c+5) that has no grouping symbols.
Answers
Answer
69x = 69 × x = x × 69
8 (c + 5)
= 8c + 40
Explanation
The commutative property of multiplication for two numbers a and b, is given as
a × b = b × a = ab
69x = 69 × x = x × 69 = 69x
Question 2
The distributive property for openingh brackets involving three numbers a, b and c is given as
a (b + c)
= ab + ac
So, for this question
8 (c + 5)
= 8c + 40
Hope this Helps!!!
Gabe made a scale drawing of a neighborhood park. The scale of the drawing was 1 millimeter : 6 meters. If the actual length of the volleyball court is 18 meters, how long is the volleyball court in the drawing?
Answers
The distance d (in inches) that a ladybug travels over time t(in seconds) is given by the function d (1) = t^3 - 2t + 2. Findthe average speed of the ladybug from t1 = 1 second tot2 = 3 seconds.inches/second
Answers
The Solution:
Given that the distance is defined by the function below:
[tex]d(t)=t^3-2t+2[/tex]We are required to find the average speed of the ladybug from t=1 second to t=3 seconds in inches/second.
Step 1:
For t=1 second, the distance in inches is
[tex]d(1)=1^3-2(1)+2=1-2+2=1\text{ inch}[/tex]For t=3 seconds, the distance in inches is
[tex]d(3)=3^3-2(3)+2=27-6+2=21+2=23\text{ inches}[/tex]By formula,
[tex]\text{ Average Speed=}\frac{\text{ distance covered}}{\text{ time taken}}[/tex]In this case,
Distance covered = change in distance, which is
[tex]\text{ change in distance=d(3)-d(1)=23-1=22 inches}[/tex]Time taken = change in time, which is:
[tex]\text{ Change in time=t}_2-t_1=3-1=2\text{ seconds}[/tex]Substituting these values in the formula, we get
[tex]\text{ Average Speed=}\frac{22}{2}=11\text{ inches/second}[/tex]Therefore, the correct answer is 11 inches/second.