we have the system
y + z = 6 ------> equation P
5y + 9z = 1 -----> equation Q
i will solve by elimination
step 1
Multiply the equation P by -5
so
(y + z = 6) *-5
-5y-5z=-30
adds equation Q
-5y-5z=-30
5y + 9z = 1
------------------
5z+9z=-30+1
therefore
the answer is the option BWrite 2^40 as a power with the following base: 2^10
The equivalent expression as a base of 2¹⁰ is (2¹⁰)⁴
How to rewrite the expression?The mathematical statement in the question implies that
We rewrite 2^40 as a power in the base 2^10
Start by expressing the given number properly
So, we have
2⁴⁰
Express 40 as the product of 10 and 4
So, we have
2⁴⁰ = 2¹⁰ ˣ ⁴
Express as exponents
So, we have the following representation
2⁴⁰ = (2¹⁰)⁴
Hence, the new expression is (2¹⁰)⁴
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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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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]need helpp pls i don't know how to do it.
Answer:
The value of angle QXS is;
[tex]m\measuredangle QXS=40^0[/tex]Explanation:
From the given diagram in question 1:
We can see that angle QXT equals the sum of angle SXT and angle QXS;
[tex]m\measuredangle QXT=m\measuredangle SXT+m\measuredangle QXS[/tex]Given in the question is the value of angle SXT and angle QXS;
[tex]\begin{gathered} m\measuredangle SXT=4x+1 \\ m\measuredangle QXS=2x-2 \end{gathered}[/tex]Substituting the values into the equation above;
[tex]\begin{gathered} m\measuredangle QXT=m\measuredangle SXT+m\measuredangle QXS \\ m\measuredangle QXT=4x+1+2x-2 \\ m\measuredangle QXT=4x+2x+1-2 \\ m\measuredangle QXT=6x-1 \end{gathered}[/tex]Since angle QXT is equal to 125 degree, then;
[tex]\begin{gathered} m\measuredangle QXT=6x-1=125 \\ 6x-1=125 \\ 6x=125+1 \\ 6x=126 \\ \frac{6x}{6}=\frac{126}{6} \\ x=21 \end{gathered}[/tex]We can now substitute the value of x to get the value of angle QXS;
[tex]\begin{gathered} m\measuredangle QXS=2x-2 \\ m\measuredangle QXS=2(21)-2 \\ m\measuredangle QXS=42-2 \\ m\measuredangle QXS=40^0 \end{gathered}[/tex]Therefore, the value of angle QXS is;
[tex]m\measuredangle QXS=40^0[/tex]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
There is a line whose y-intercept is -5 and whose slope is 10 What is its equation in
slope-intercept form?
y=10x-5 is the slope-intercept form
y-intercept= -5,
slope m= 10,
The slope-intercept formula y = mx + b, where m is the slope and b is the intercept.
y = y coordinate
m = slope
x = x coordinate
b = y intercept
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line.
the slope of the line to be examined and the point given is also the y-intercept (0, b)
by putting the given information in the question we get,
y=10x+(-5),
therefore,y=10x-5 is the slope-intercept form
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Can anyone help me find the scale factor?
Answer:
scal factor = 1.5
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{C'D'}{CD}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5
Simplify the expression ✔️72What is the coefficient aWhat is the radicand b
we have the expression
[tex]\sqrt[]{72}[/tex]Remember that
[tex]72=2^3\cdot3^2[/tex]substitute
[tex]\sqrt[]{2^3\cdot3^2}=2\cdot3\sqrt[]{2}=6\sqrt[]{2}[/tex]therefore
a=6
b=2
Which lines are parallel if x=y?
Answer:
the horizontal lines for #9 and those slanted ones for #10
Step-by-step explanation:
parallel lines are lines that never intercept. if these following lines continue infinetly they will never touch
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.
9. Steve claimed he had a slow start and could not keep the pace. Use the data from the rateof change to argue or defined this.10. Explain how a graph can show a rate of change more easily that a data chart.
We can see from Steves rate of change that it was steeper than Peters. That means that it took more minutes per kilometer for each kilometer. It is easier to compare when seeing it on the graph. The steeper the line, the steeper the rate of change.
what is -8(×+2)+2(×-1)=
To find the answer:
1. Remove parenthesis by multiplying the number outside parenthesis
Construct a Venn diagram to determine the validity of the argument (Use Euler's diagram)Some animals are dangerousA car is not an animalTherefore a car is not dangerous
We will have the following:
Here it is the Venn diagram for both; the statement is not valid, since they fall in different categories.
Expand. Your answer should be a polynomial in standard form.
(x - 2)(x - 6) =
(x-2) (x-6)
x(x-6)-2(x-6)
x²-6x-2x-12
X²-4x-12
The length of a rectangle is 3 m longer than its width. If the perimeter of the rectangle is 36 m, find its length and width.
Group of answer choices
width = 7.5 m, length = 10.5 m
width = 16.5 m, length = 13.5 m
width = 16.5 m, length = 19.5 m
width = 7.5 m, length = 4.5 m
The length and width of the rectangle are (a) width = 7.5 m, length = 10.5 m
Let the width (W) = x
Length (L) = x+3
According to question,
Perimeter = 36m
Perimeter = 2(L + W)
36 = 2(x+3+x)
36 / 2 = 2x + 3
18 = 2x + 3
18 - 3 = 2x
15 = 2x
x = 15 / 2
x = 7.5
Length = x+3
= 7.5 + 3
= 10.5
Hence, width = 7.5m and length = 10.5m
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HELO EMEMENEJEJJEJEH
Answer:
E
Step-by-step explanation:
[tex]3 \leq x-2 \\ \\ x-2 \geq 3 \\ \\ x \geq 5[/tex]
Answer:
E
Step-by-step explanation:
if it is supposed to be more or equal to then it has to add 5 or more. It has to add 5 or more because the 2 is negative and 5-2 is 3 so it has to be at least 5
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%
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.
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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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.
Which statements correctly compare two numbers? Select all that apply.
A. 0.1 < 0.125
B. 0.2 < 0.125
C. 0.125 > 0.13
D. 0.125 > 0.12
E. 0.126 < 0.125
A statement like that. An assertion is a single statement or comment. b: an information or idea report, 1 < 0.125= True, 125 > 0.12=True, and 126 < 0.125=True
What is meant by assertion?An assertion is a precise, unequivocal mathematical statement stating that something is true (e.g., that some relation between mathematical objects holds; that some object has some property; etc.). To qualify an assertion, it is not necessary for the statement to be true. An assertion is an emphatic declaration made as part of an argument or as if it is to be understood as a statement of fact. To assert is to make a strong statement. So when someone makes an assertion, they aren't just experimenting with a new idea; they truly believe it. A fundamental assertion is a simple statement that expresses a belief, feeling, opinion, or preference.To learn more about assertion, refer to
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Convert the following fraction to a decimal 3/10
Answer:
Step-by-step explanation: 0.3
Answer:
Step-by-step explanation:
1. The answer is 0.3.
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
the measure of one of the acute angles in a right triangle is (2y) what is the other acute angle
The measure of the other acute angle in the right triangle is 90 - 2y
How to determine the other acute angle?The given parameters in the question are:
Shape = right triangle
Acute angle = 2y
The measures of acute angles in a right triangle add up to 90
This can be represented mathematically as
Acute angle + Other angle = 90
Substitute the known values in the above equation, so, we have the following representation
2y + Other angle = 90
This gives
Other angle = 90 - 2y
Hence, the other angle is 90 - 2y
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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.
PLEASE I NEED HELP ASAP WITH THIS MATH STUFF!!
-download them and draw over them or write over them
The system of equations are y = 50 + 100x and y = 300 + 75x which is linear equations in two variables.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The linear equation can be written in form of:
y = mx + c
From the question:
The equation for Little Learners Pre-School:
y = 50 + 100x
The equation for Growing Place Pre-School:
y = 300 + 75x
Thus, the system of equations are y = 50 + 100x and y = 300 + 75x which is linear equations in two variables.
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1 2 What is the probability of an event that is certain?
The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.
An event that is certain to happen has a probability of 1.
BICPPStatistics: Assignment 2.05Name:We asked 10 randomly selected students in a Speech and Debate class how manycollege courses they had passed prior to taking this class. Their responses areshown below. Find the sample mean and the median.4, 8, 14, 7, 0, 8, 2, 10, 3, 12
The rule of the mean is
[tex]Mean=\frac{Sum}{No.}[/tex]We will find the sum of the given numbers, then divide it by how many numbers
The given numbers are
4, 8, 14, 7, 0, 8, 2, 10, 3, 12
Their sum = 68
There are 10 numbers, then
[tex]Mean=\frac{68}{10}=6.8[/tex]To find the median we have to arrange the numbers from smallest to greatest, then take the middle number
0, 2, 3, 4, 7, 8, 8, 10, 12, 14
Since there are 10 numbers, then there are 2 numbers in the middle
Then we will find their average by adding them and dividing their sum by 2
The 2 middle numbers are the 5th and the 6th positions
The 2 middle numbers are 7 and 8
[tex]Median=\frac{7+8}{2}=7.5[/tex]The answers are:
Sample mean = 6.8
The median = 7.5
help me answer this question please
h ---> Independent Variable
c ---> Dependent variable
h is time, So domain is discrete.
Given,
In the question:
The function c = 15 + 9h represent the amount c (in dollars)
It will cost you for a one - time lawn care service of h hours.
To find the independent and dependent variables .
To check the domain discrete or continuous.
Now, According to the question:
What is domain discrete or continuous?
A discrete domain is a set of input values that consists of only certain numbers in an interval. A continuous domain is a set of input values that consists of all numbers in an interval. Sometimes the set of points that represent the solutions of an equation are distinct, and other times the points are connected.
According to the above statement :
Hence, h ---> Independent Variable
c ---> Dependent variable
h is time, So domain is discrete.
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Which istogram corect shows the one Number of people Number of books
Number of people in the range 0-2 books: 3
Number of people in the range 3-5 books: 6
Number of people in the range 6-8 books: 4
Number of people in the range 9-11 books: 2
Therefore, the correct histogram is option C