[tex]\fbox{20.25}[/tex]
To find her miles per hour, we need to divide the total miles by the total hours to find how many miles she drives in each hour.
[tex]162\div8[/tex]
[tex]=20.25[/tex]
If f(x) = x2 and g(x) = 3x - 1, find f(g(x))
Given the following functions:
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=3x-1 \end{gathered}[/tex]To compose then, is basically use the inside function as the argument.
[tex]f(g(x))=f(3x-1)[/tex]If we call '3x-1' as 'u'
We know the following
[tex]\begin{gathered} f(u)=u^2 \\ u=3x-1\Rightarrow f(3x-1)=(3x-1)^2 \end{gathered}[/tex]And this is our answer.
[tex]f(x)=(3x-1)^2[/tex]HELP PLEASE HELP PLEASE NEED IT NOW!!
You run m miles on Monday, the same amount on Tuesday, and 3 miles on Wednesday. Write an expression in the simplest form that represents the total amount in each situation.
(please show work)
The expression that represents the given situation is 2x + 3 = T.
What do we mean by expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression to represent the given situation is:
Since the miles run on Monday and Tuesday are the same, then let the miles run be 'x'.
Miles run on Monday is x.Miles run on Tuesday is x.Miles' run on Wednesday is 3.Let, the total mile be T.
Now, the expression will be:
x + x + 3 = T2x + 3 = T
Therefore, the expression that represents the given situation is 2x + 3 = T.
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Use distributive property and combining like terms to simplify.
5x-4y+2(y+x)
The simplified form is 7x - 2y.
Distributive property: What Is It?
This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
According to question,
5x-4y+2(y+x)
5x-4y+2y+2x
7x-2y
Hence, simplified form is 7x - 2y.
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the side length of 11
A perfect square means that the given value is the result of the multiplication of an integer with itself, for example 2*2=4 →√
find the unit rate. round to the nearest hundredth, if necessary $200 for 15 ft
EXPLANATION
The unit rate is given by the following relationship:
Unit rate= $200/15ft = $13.3333.../ft
Then, rounding to the nearest hundreth:
Unit rate = $13.33/ft
Julias frogs are 2/5 of the amount of Remus frogs. If Remus gives a half of his frogs to Julia, what will the ratio of Julia's frogs to Remus frogs be ?
Let:
Rf = Remus frogs
Jf = Julias frogs
[tex]Jf=\frac{2}{5}Rf[/tex]If Remus gives a half of his frogs to Julia, what will the ratio of Julia's frogs to Remus frogs be ? so:
[tex]\begin{gathered} Rf=\frac{5}{2}Jf \\ Jf=\frac{2}{5}Rf+\frac{1}{2}Rf=\frac{9}{10}Rf \end{gathered}[/tex]Therefore, the ratio will be:
[tex]\frac{\frac{9}{10}Rf}{Rf-\frac{1}{2}Rf}=\frac{9}{5}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 5.7 feet, Length = 10.5 feet
Step-by-step explanation:
Let the width be w. Then, the length is 2w-0.9.
[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]
the radius of a semicircle is 5 kilometers. what is the semicircles diameter
The semicircles diameter is 10km
What is diameter?The diameter is defined as twice the length of the radius of a circle.
From the relation diameter of a circle is given as d= 2r
Radius of the semicircle is 5km
Substitute the radius in to d=2r
diameter= 2 x 5= 10km
Therefore, the semicircles diameter is 10km
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12__-15 = -3
divide
multiply
add
subtract
Answer:
multiply 1 is the correct answer
12×1 - 15 = -3
Find the axis of symmetry for the parabola that has the points (-2.5, 3) and (-4.5, 3) Justify your answer
The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
The axis of symmetry always passes through the vertex of the parabola.
The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
A general graph of a vertical parabola is shown below:
Note there are two points x1 and x2 that have the same y-coordinate. These points are equidistant from the axis of symmetry. So, if we are given the coordinates of the points, we can find the axis of symmetry by calculating their average.
We are given the points (-2.5, 3) and (-4.5, 3).
Since they have the same y-coordinate, we calculate the average of the x-coordinates as follows:
[tex]x_s=\frac{-2.5-4.5}{2}=-3.5[/tex]Thus, the axis of symmetry of the parabola is x = -3.5
in a video store,a DVD that usually sells for $15 is marked 10% OFF that price. How much does the DVD cost now that it's on sale?
Answer
The cost of the DVD now that it's on sale will be $13.5
Explanation
DVD actual price = $15
10% off the price will be (10/100 x $15) = $1.5
The selling price of the DVD now will be $(15 - 1.5) = $13.5
∴ The cost of the DVD now that it's on sale will be $13.5
Given MK is a median use the figure below to answer the questions below.
If JM = 23, then JL =
If LJ = 20, then ML =
Answer:
[tex]46, 10[/tex]
Step-by-step explanation:
A median is the segment drawn from the vertex of a triangle that bisects the opposite side.
Solve this equation for N. 3N + 5 = 38
ANSWER
N = 11
EXPLANATION
Given:
3N + 5 = 38
Desired Outcome:
Value of N
Solve for N
[tex]\begin{gathered} 3N+5=38 \\ subtract\text{ 5 from both sides} \\ 3N+5-5=38-5 \\ 3N=33 \\ divide\text{ both sides by 3} \\ \frac{3N}{3}=\frac{33}{3} \\ N=11 \end{gathered}[/tex]Hence, the value of N is 11.
Determine whether the following sequence is geometric. If so, find the common ratio. 1, -4, 16, -64, . . .
Given:
Geometric sequence is:
1,-4,16,-64
Sol:
For geometric sequence is:
[tex]a_n=a_1r^{n-1}[/tex][tex]\begin{gathered} a_1=1 \\ a_2=-4 \end{gathered}[/tex][tex]\begin{gathered} a_n=a_1r^{n-1} \\ -4=1r^{2-1} \\ -4=r \end{gathered}[/tex]Common ratio is -4.
Consider the series. 16+24+36+54+...Does the series converge or diverge?
Explanation
We are asked to determine if the given series converge or diverge
A series is said to be convergent when it approaches a certain value as the series approaches infinity.
To check, we will have this re-written as
[tex]\sum _{n=0}^{\infty \:}16+24+36+54+\ldots \quad :\quad \sum _{n=0}^{\infty \:}-32\left(1-\left(\frac{3}{2}\right)^n\right)[/tex]Every infinite sum of a non-zero constant diverges
Therefore, the series diverges
(8u^2+3u-4)+(8u^2+3u-1)-(3u^2-3u-8)
Simplify the expression
[tex]\mleft(8u^2+3u-4\mright)+\mleft(8u^2+3u-1\mright)-\mleft(3u^2-3u-8\mright)[/tex]Removing all the parentheses, taking special care to change the signs of the last three terms:
[tex]8u^2+3u-4+8u^2+3u-1-3u^2+3u+8[/tex]Now collect like terms:
[tex]8u^2+8u^2-3u^2+3u+3u+3u-4-1+8[/tex][tex]13u^2+9u+3[/tex]Find the length of RS.A.73 unitsB.11 unitsC.About 8.5 unitsD About 3.3 units
Let,
[tex]\begin{gathered} R=(x_1,y_1)=(-4,1) \\ S=(x_2,y_2)=(-1,9) \end{gathered}[/tex]The expression to calculate the distance between two points is,
[tex]\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(-1-(-4))^2+(9-1)^2} \\ D=\sqrt[]{(3)^2+(8)^2} \\ D=\sqrt[]{9+64} \\ D=\sqrt[]{73} \\ D=8.5\text{ units} \end{gathered}[/tex]Thus, the length of the line RS is 8.5 units, and the correct option is option C.
Assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $1000. What percent of day care costs are more than $7100 annually?Click here to view page 1 of the standard normal distribution tableClick here to view page 2 of the standard normal distribution table,% (Round to two decimal places as needed.)
Answer:
81.59%
Explanation:
To find the percentage, we first need to standardize $7100. To standardize, we subtract the mean and then divide by the standard deviation. So, $7100 is equivalent to:
[tex]\begin{gathered} z=\frac{x-\operatorname{mean}}{std\text{ deviation}} \\ z=\frac{7100-8000}{1000}=-0.9 \end{gathered}[/tex]Now, the percentage of day care costs that are more than $7100 is equivalent to the probability that z is greater than -0.9, so:
P(x > $7100) = P(z > -0.9)
Finally, we can use the standard normal distribution table to get:
P(z > -0.9) = 0.8159
So, the answer is 81.59%
what is the sum of the expression 2/12 + 2/4
EXPLANATION:
In the exercise we have to perform the sum of two improper fractions which are heterogeneous because they have different denominators.
The procedure is the next:
[tex]\begin{gathered} \frac{2}{12}\text{ }+\frac{2}{4};=\frac{8+24}{48}=\frac{32}{48};\text{here }we\text{ simplify} \\ \\ \frac{32}{48}=\frac{16}{24}=\frac{8}{12}=\frac{4}{6}=\textcolor{#FF7968}{\frac{2}{3}} \\ \text{the answer is }\frac{2}{3} \end{gathered}[/tex]Write the equation of the line parallel to x+7y=21 that passes through the point (–14, 4).
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First, rearrange x + 7y = 21 into y = mx + c form.
x + 7y = 21
7y = - x + 21
y = -1/7x + 3
Parallel lines have the same gradient so gradient of line is -1/7.
Equation of line is now y = -1/7x + c.
Substitute (-14,4) into the equation to find c.
4 = -1/7(-14) + c
4 = 2 + c
c = 2
Hence, equation of line is y = -1/7x + 2.
10, 15, 24, 24, 25, 30 What is the mode?
Mode means the number that appears most.
The answer is 24 since it appears twice.
8. Draw the graphs described below and answer the question for each.A. Draw the graph of a line with undefined slope. Write the equation of the line youdrew.B. If you wrote the first letter of your LAST NAME (upper-case letter) on a coordinateplane, would it be a function? Make a sketch and provide an explanation as to how youdetermined whether it is a function or not.
Question:
Draw the graphs described below and answer the question for each.
A. Draw the graph of a line with an undefined slope. Write the equation of the line you drew.
B. If you wrote the first letter of your LAST NAME (upper-case letter) on a coordinate plane, would it be a function? Make a sketch and provide an explanation as to how you determined whether it is a function or not.
Solution:
A.
Remember that any line that has an undefined slope is a vertical line, that has no y-intercept. Therefore the equation of a line with an undefined slope is x = a, where a = x-intercept.
we can conclude that the correct answer is:
According to this information, we can take the following equation for a line with an undefined slope:
[tex]x=5[/tex]and its graph would be:
B. Remember that a simple visual way to determine if a particular graph is a function is by imagining vertical lines passing through it. If the vertical line touches more than once, it is not a function.
For example, consider the curve that represents the letter O:
And notice that the above curve is a circle and note also the following fact:
We can conclude that the correct answer is:
The curve of the letter O is not a function, since a line intersects at two points of this line.
How does the allusion to the Pied Piper in “Pan: God of the Wild” contribute to the meaning of the myth?
i need help
The allusion to the pied piper in "Pan: God of the wild" contributes to the meaning of the myth by B. showing that Pan is a god that leads others to destruction.
What's the story of the pied piper about?The story goes that the pied piper went into a town infested with rats and made a deal with the people of the town to drive the rats away for a token. The town agreed and the pied piper drove the rats into the river. When the piped piper asked for his money, they refused to pay up. The pied piper took his revenge on the town by leading children of the town away from the town and they were never discovered.
The myth only shows that Pan is a god that leads others to destruction.
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solve for x……………………..
Answer:
7.5/3
Step-by-step explanation:
7x-7.5 = 4x
-7.5 = -3x
x= 7.5/3
can you guys s show work for graph inequality for
-2<x<5
The graph of the inequality is a straight line on the x-axis
from -2 to 5 also, -2 & 5 are not included in the graph.
Given, an inequality
-2 < x < 5
we have to draw a graph for the given inequality,
as the value of 'x' is from -2 to 5.
So, the graph of the inequality is a straight line on the x-axis
from -2 to 5 also, -2 & 5 are not included in the graph.
Hence, the graph of the inequality is a straight line on the x-axis
from -2 to 5 also, -2 & 5 are not included in the graph.
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Show that the equation is not an identity by finding a value of x for which both sides are defines but not equal.
We are given the expression:
[tex]\cos (x-\pi)=\cos (x)[/tex]We, simply replace the values of solution given and then determine in which it is not a solution, but we can see that when we replace x = 0, we will get:
[tex]\cos (\pi)\ne\cos (0)[/tex]So, this proves that the function is not an identity.
hi, I'm supposed to write a exponential equation for the graph but I'm not sure how to do it
d)
To determine the type of function, we would compare the y values. If the ratio of consecutive y values is the same, then the function is exponential. We have
2/1 = 4/2 = 8/4 = 2
Thus, it is an exponential function. The general formula for an exponential function is
y = ab^x
We would find a and b
Substituting x = 0 and y = 1 into the formula, we have
1 = ab^0
1 = a
Substituting x = 1 and y = 2 into the formula, we have
2 = ab^1
2 = ab
Substituting a = 1 into 2 = ab, then
2 = 1 * b = b
By substituting a = 1 and b = 2 into the original formula, the equation would be
y = 2^x
You have learned about quadratic and linear function in earlier grades. Explain in a variety of ways how you can distinguish the exponential function
f(x)=2^x
from the quadratic function
f(x) = x^2
and linear function
f(x) = 2x
. (Hint: compare the rate of change using finite differences in tables of values, and identify a constant ratio in the table of values).
We can distinguish between the linear, exponential function and quadratic functions graphically. The graph of the functions is as follows:
linear function f(x) = 2x will be straight line,
for exponential function f(x) = 2^x will rise or fall quickly in one direction
and for quadratic function f(x) = x^2 will be a parabola.
What is an exponential function?An exponential function is a type of mathematical function expressed in the form f(x) = a^x. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The most commonly used exponential base is the transcendental number e, which is approximately equal to 2.71828. The exponential function is defined by the formula f(x) = ax. where the input variable x is displayed as an exponent. Exponential curves grow or fall exponentially. A quantity that increases or decreases at a regular rate should exhibit either an exponential increase or an exponential decay.To learn more about exponential function from the given link :
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Could you help me with these two questions? 20 points !
1 ) Create an equation in point-slope form that has a slop of 5 passing through the points (3,5)
2) Create an equation in point slop form that has a slop of 2 and passes through the points (-1, 6)
The equation of line are given as y = 5x - 10 and y = 2x + 8 respectively
Point-Slope FormulaThe point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The equation of a line is an equation that is satisfied by each and every point on the line. This means that a linear equation in two variables represents a line. The equation of a line can be found through various methods depending on the available information.
In this case, we have can proceed to write the equation of a straight line which is given as y = mx + c
m = slopec = y-interceptLet's find the y - intercept and write the equation.
y = mx + c
5 = 5(3) + c; c = 5 - 15 = -10
y = 5x - 10
2) We have the slope as 2 and the points are (-1, 6)
The equation of the line can be written in form of y = mx + c
6 = 2(-1) + c
6 = -2 + c; c = 8
The equation is given as y = 2x + 8
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Point D (8,2) is reflected across the y-axis to form point E.
What are the coordinates of point E?