To creat a 4 - digit code, we need to consider that for each digit we have 10 options:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 -----> 10 options for each digit.
Next, we multiply the number of options we have for each digit. In this case, since we need the code to have 4 digits:
[tex]10\times10\times10\times10[/tex]We multiply 4 times 10.
And the result is:
[tex]10\times10\times10\times10=10,000[/tex]He has 10,000 ways to create a 4-digit code.
what is the rate change of the equation?Y=8x+20Remember Y=MX+B
The general equation of the line : y = m * x + b
where m is the slope , b is y -intercept
Given the function :
[tex]y=8x+20[/tex]The rate of change of the equation = the slope of the function
So, by comparing the given equation to the general from
The slope = m = 8
So, the rate of change = 8
Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
Answer: [tex]x\leq 1/3\\[/tex]
Step-by-step explanation:
Please help with this
Answer:
228
Step-by-step explanation:
Top 6x 6 = 36
4 sides 4(6x8)
4(48)
192
192 + 36 = 228
Answer:264
Step-by-step explanation: the surface area is every side added together and you calculate each side by multiplying the width height and length
“ Judy has a bag with 12 DVD’s, 12 marbles, 11 books, and 1 orange. What is the ratio of books to marbles? What is the ratio of DVD’s to the total number of items in the bag? What percentage of the items in the bag are DVD’s? “
First, let's calculate the total number of items:
[tex]12+12+11+1=36[/tex]The ratio of books to marbles is calculated by dividing the number of books by the number of marbles:
[tex]ratio=\frac{books}{\text{marbles}}=\frac{11}{12}[/tex]The ratio of DVD's to the total number of items is:
[tex]\text{ratio}=\frac{\text{dvds}}{\text{total}}=\frac{12}{36}=\frac{1}{3}[/tex]The percentage of dvd's from the total is:
[tex]\frac{1}{3}=0.3333=33.33\text{\%}[/tex]4. Solve the polynomial.
7x³ + 21x² - 63x = 0
After solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}
What is a polynomial?An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² 4x + 7 is an illustration of a polynomial with a single indeterminate x.So, 7x³ + 21x² - 63x = 0:
Now, solve for x as follows:
7x³ + 21x² - 63x = 07x(x² + 3x - 9) = 0Zero factor principal, if ab = 0, then a = 0 and b = 0.
x = 0 and x² + 3x - 9 = 0Now, x² + 3x - 9 = 0:
x = [(-3 ± 3√5)/2]x = 0Therefore, after solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}
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Which of the following sets does the number - 12.12532 ... belong to?Select all correct answers.Select all that apply:Whole NumbersIntegersURational NumbersIrrational NumbersReal NumbersUNone of the Above
Answer:
Explanation:
Let's define each of the given types of numbers;
*Whole numbers are a set of all positive integers including 0. E.g 0, 1, 2,
*Integers
Divide the polynomial by the binomial. (Simplify your answer completely.)
(q² + 5q + 20) / (q + 8)
Answer:
It's already in its simplest form.
Step-by-step explanation:
Factorising QuadraticsI'm writing a book/document on this topic but it's not finished. I suspect there is an error in this question because it's practically impossible to factorise it into integers.
The quadratic polynomial in the numerator has imaginary roots because 5 squared is less than 20 times 4.
ax² + bx + c;
if ( b² < 4ac ) { 'solution is imaginary' }
The quadratic equation will explain the above.
2. Graph the following inequality on the axes provided below: 6x + 2y = 8 -10 8 6 4 2 -101-8-6 1-4-2 -2 2 4_LG_L 8 10 -4 -6 -8 -10 True or False: (1,1) is a solution to the inequality. Explain using evidence from your graph.
We are given the following inequality
[tex]6x+2y<8[/tex]Let us first convert the inequality into slope-intercept form
[tex]\begin{gathered} 6x+2y<8 \\ 2y<-6x+8 \\ y<-\frac{6x}{2}+\frac{8}{2} \\ y<-3x+4 \end{gathered}[/tex]Comparing this inequality with the standard slope-intercept form we see that
Slope = -3 and y-intercept = 4
So the graph of the inequality is
The area left to the red line represents the solution of the inequality.
Now we need to check if the point (1, 1) lies left to the red line.
We can clearly see that point (1, 1) is just left to the red line hence it is a solution.
Therefore, it is true.
I don’t understand how to explain this question
The segments cannot be set equal since the constant terms 15 is greater than two. The variable x remains like a constant term in both sides of the point B. we say that 15x > 2x
What is inequality?In mathematics, the signs used inequality calculations are
greater thanless thangreater than or equal toless than or equal toUsing the picture as evidence the mark represented by B is not the midpoint hence the equality sign will not be used here. The sign to be used is the inequality sign.
In addition, the constants 15 and 2 shows that 15 is greater than 2. and there is no other addition to the variable x to help check the effect of the greatness of 15
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Use the diagram to calculate the measure of angle 5
Answer:
m∠5=22 °
Explanation:
In the diagram:
• Angles 4 and 90 degrees, are ,vertical angles,.
,• Angles 2 and 68 degrees, are ,vertical angles,.
Since the measure of vertical angles is equal:
[tex]\begin{gathered} m\angle4=90\degree \\ m\angle2=68\degree \end{gathered}[/tex]In the triangle:
[tex]m\angle2+m\angle4+m\angle5=180\degree\text{ (sum of angles }in\text{ a triangle)}[/tex]Substitute the measures of angle 2 and 4 obtained earlier:
[tex]\begin{gathered} 90\degree+68\degree+m\angle5=180\degree \\ 158\degree+m\angle5=180\degree \\ Subtract\text{ }158\degree\text{ from both sides of the equation.} \\ m\angle5=180\degree-158\degree \\ m\angle5=22\degree \end{gathered}[/tex]The measure of angle 5 is 22 degrees.
Hey could someone help me out with this thank you
Karen will run more than 28
#8 help with algebra 2 question. That’s the only picture I have. I tried writing it out.
Solution:
Given a cosine function graph;
The general cosine function is
[tex]y=A\cos(Bx-C)+D[/tex]Where
[tex]\begin{gathered} A\text{ is the amplitude} \\ Period=\frac{2\pi}{B} \\ C\text{ is the phase shift} \\ D\text{ is the vertical shift} \end{gathered}[/tex]From the graph,
The midline is y = 1
The amplitude, A, is
[tex]\begin{gathered} A=4-1=3 \\ A=3 \end{gathered}[/tex]The amplitude, A is 3
Where,
[tex]\begin{gathered} Period=12 \\ Period=\frac{2\pi}{B} \\ 12=\frac{2\pi}{B} \\ Crossmultiply \\ 12B=2\pi \\ Duvide\text{ both sides by 12} \\ \frac{12B}{12}=\frac{2\pi}{12} \\ B=\frac{\pi}{6} \end{gathered}[/tex]The phase shift, C = 0, and the vertical, D, is 1
Thus, the equation of the graph is
[tex]\begin{gathered} y=A\cos(Bx-C)+D \\ Where \\ A=3 \\ B=\frac{\pi}{6} \\ C=0 \\ D=1 \\ y=3\cos(\frac{\pi}{6}x)+1 \end{gathered}[/tex]The graph is shown below
Hence, the equation is
[tex]y=3\cos(\frac{\pi}{6}x)+1[/tex]find the value of x so that AB and DC are parallel
According to the properties of a parallelogram, the consecutive interior angles are supplementary, this is that the sum of its measures is 180.
Use the expressions given for 2 of the consecutive angles to find the value of x. Remember, the sum of these expressions must be 180.
[tex]\begin{gathered} (3x+15)+(7x+25)=180 \\ 10x+40=180 \\ 10x=140 \\ x=\frac{140}{10} \\ x=14 \end{gathered}[/tex]x has a value of 14.
Question 19 of 25Which of the following equations is an example of inverse variation betweenthe variables x and y?O A. y -O B. y = 8xO C. y -OD. y=x+8SUBMIT
Where 8 is the constant
The Final answerOption CHi dear how do I get to know you and
Given the picture, we have:
Enclosed area: A = x*y
Fence Length: F= 2x+y
Type your response in the box.Use the information in the table to determine some similarities and differences between linear and exponentialequations. Include observations about the forms of both equations and the placement of the independent variablein the equations.f(3) = 5(3)s() = 2x+55057121192
Ok let's talk about some similarities and differences between linear and exponential equations.
In the linear functions the rate of change is constant. While in the exponential fuctions the rate of change is not constant.
In linear function the graph is a straight line. in the exponential fuctions graph is an exponential curve.
In linear functions the placement of the independent variable is is multiplying a coefficient. In the exponential fuctions the placement of the independent variable is as the power of a coefficient.
I really need help make sure that your answer is 7th grade appropriate
Examples:
1. Five increased by four times a number
[tex]5+4n[/tex]where n is the number
2.The product of 4, and a number decreased by 7
[tex]4(n-7)[/tex]Need help with this question
Given: a quadratic function with vertex (2,3) opening upward .
Find: the given statement is true or false.
Explanation: if parabola has a vertex at (2,3) and opens upward, it has one real solution., (2,3) will be a lowest point. The vertex will be at lowest point, it will be minimum.
that means graph has no one real solution. hence it will never going to intersect. so this statement is false.
Final answer: the given statement is FALSE.
Gina left home, riding her bicycle at a rate of 25 miles per hour. Sean left 1 hour later, riding at a rate of 30 miles per hour. How long will it take Sean to catch up to Gina?
As per the distance formula, it take 1 hour of time for Sean to catch up to Gina.
Distance formula:
The equation that relates the distance, rate, and time is
d = rt
Where d represents the distance traveled, r represents the rate, and t represents the time.
Given,
Gina left home, riding her bicycle at a rate of 25 miles per hour. Sean left 1 hour later, riding at a rate of 30 miles per hour.
Here we need to find the time take by Sean to catch up Gina.
Let us consider x be the time when Gina left the home.
Then, Sean left 1 hour later from her time.
So, it can be written as,
=> x + 1
As the Distance traveled is the same, the ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases.
Therefore, the ratio of Speed in both cases
=> 25 : 30
=> 25/30
=> 5/6
Therefore, it can be written as,
x/x+1 = 5/6
When we cross multiply them, then we get,
5x + 5 = 6x
x = 5.
If Gina left at the time of 5, then Sean left at the time of 6.
So, it take 1 hour for Sean to catch up to Gina.
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The revenue for a small company is given by the quadratic function r(t) = 5tsquared + 5t + 630 where t is the number of years since 1988 and r(t) is in thousands of dollars. If this trend continues, find the year after 1998 in which the company’s revenue will be $730 thousand. Round to the nearest whole year.
for:
[tex]\begin{gathered} r(t)=730 \\ 5t^2+5t+630=730 \\ so\colon \\ 5t^2+5t-100=0 \end{gathered}[/tex]Divide both sides by 5:
[tex]t^2+t-20=0[/tex]Factor:
The factors of -20 which sum to 1, are -4 and 5 so:
[tex](t-4)(t+5)=0[/tex]So:
[tex]\begin{gathered} t=4 \\ or \\ t=-5 \end{gathered}[/tex]Since a negative year wouldn't make any sense:
[tex]t=4[/tex]Therefore, the company revenue will be $730 for the year:
[tex]1998+t=1998+4=2002[/tex]Answer:
2002
Hello, I need help with this practice problem. Thank you so much.
Answer:
5 units
Explanation:
Given the points:
[tex]\begin{gathered} \mleft(x_1,y_1\mright)=K(-2,-1) \\ \mleft(x_2,y_2\mright)=N(2,2) \end{gathered}[/tex]We use the distance formula below:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute the given values:
[tex]\begin{gathered} KN=\sqrt[]{(2-(-2))^2+(2-(-1))^2} \\ =\sqrt[]{(2+2)^2+(2+1)^2} \\ =\sqrt[]{(4)^2+(3)^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5\text{ units} \end{gathered}[/tex]The distance between the two points is 5 units.
Find the measures of the numbered angles in rhombus DEFG. I just need someone to shown me how to find each of the numbered angles
Step 1
Properties of a Rhombus
Below are some important facts about the rhombus angles:
Rhombus has four interior angles.
The sum of interior angles of a rhombus add up to 360 degrees.
The opposite angles of a rhombus are equal to each other.
The adjacent angles are supplementary.
In a rhombus, diagonals bisect each other at right angles.
The diagonals of a rhombus bisect these angles.
Step 2
From the figure
Angle DGF = Angle DEF = 118
Step 3
Since adjacent angles are supplementary, that is add to 180 degrees
[tex]\begin{gathered} \angle\text{DGF + }\angle GFE\text{ = 180} \\ 118\text{ + }\angle GFE\text{ = 180} \\ \angle GFE\text{ = 180 - 118} \\ \angle GFE\text{ = 62} \end{gathered}[/tex]Step 4
The diagonals of a rhombus bisect these angles
[tex]\begin{gathered} \angle3\text{ = }\angle4\text{ = }\frac{62}{2}\text{ = 31} \\ \angle3\text{ = }\angle4\text{ = 31} \end{gathered}[/tex]Step 5
The opposite angles of a rhombus are equal to each other.
[tex]\angle1\text{ = }\angle\text{ 2 = 31}[/tex]Final answer
[tex]\angle\text{1 = }\angle\text{ 2 = }\angle\text{ 3 = }\angle4\text{ = 31}[/tex]A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77. How much was the tip as a percentage of the bill?
Percentage of the bill = 0.185*100=18.5%
what is the curved surface area of a cone on top of a half circle if the cone has a volume and the circle has a 10 area?
Given a cone with base radius, r, and perpendicular height, h,
the volume, V, is given by
[tex]V=\frac{1}{3}\times\pi\times r^2\times h[/tex]In this case,
r = 10ft,
h = 17ft,
Therefore,
[tex]V=\frac{1}{3}\times\pi\times10^2\times17=\frac{1700}{3}\pi[/tex]Hence, V = 1780.24 cubic feet
The volume of the cone is 1780.24 cubic feet
What is the Y intercept of the graph below? A. (0,-2)B. (0,-4) C. (0, 2) D. (0,4)
Recall that the y-intercept of a graph is the point where the graph intersects the y-axis.
From the given graph we get that the line intersects the y-axis at (0,2).
Answer: Option C.
Bill has these expenditures for his utilities: December,
$234.45; January, $281.23; February, $284.33. What is his
average monthly expense for utilities?
The average monthly expenses for Bill's utilities is $266.67.
It is given in the question that:-
Expenditure in December by Bill = $ 234.45
Expenditure in January by Bill = $ 281.23
Expenditure in February by Bill = $ 284.33
We have to find the average monthly expenses for Bill's utilities.
We know that,
Average monthly expense for utilities = (Expenditure in December + Expenditure in January + Expenditure in February)/3
Hence, using the data given in the question, we can write,
Average monthly expense for utilities = (234.45 + 281.23 + 284.33)/3
Average monthly expense for utilities = 800.01/3 = $266.67
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Please help me sketch a graph for this sequence (I've already solved it): 2/3, 1, 3/2, 9/4, 27/8
ANSWER and EXPLANATION
We have that the 1 - 5th terms of the sequence are:
2/3, 1, 3/2, 9/4 and 27/8
To plot the graph of this sequence, we have:
=> on the x axis, the term number (i.e. n = 1, 2, 3, 4, 5)
=> on the y axis, the term(i.e. a(n) 2/3, 1, 3/2, 9/4, 27/8)
We will plot the graph of n versus a(n).
That is:
That is the graph.
57. do not use the answer under the line in the explanation itself, only refer to it to make sure of your work. USE DERIVITIVES NOT GRAPHING
Explanation
Question 57
[tex]\:f\left(x\right)=2x^3-15x^2+24x[/tex]To find the extreme values
[tex]\begin{gathered} \mathrm{Suppose\:that\:}x=c\mathrm{\:is\:a\:critical\:point\:of\:}f\left(x\right)\mathrm{\:then,\:} \\ \mathrm{If\:}f\:'\left(x\right)>0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:maximum.} \\ \mathrm{If\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)>\:0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:minimum.} \\ \mathrm{If\:}f\:'\left(x\right)\mathrm{\:is\:the\:same\:sign\:on\:both\:sides\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:neither\:a\:local\:maximum\:nor\:a\:local\:minimum.} \end{gathered}[/tex]So, we will have the steps below
Step 1:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=0\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=0 \\ \mathrm{Minimum}\left(0,\:0\right) \end{gathered}[/tex]Step2:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=1\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=11 \\ \mathrm{Maximum}\left(1,\:11\right) \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=4\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-16 \\ \mathrm{Minimum}\left(4,\:-16\right) \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=5\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-5 \\ \mathrm{Maximum}\left(5,\:-5\right) \\ \end{gathered}[/tex]Thus, we will have
[tex]\mathrm{Minimum}\left(0,\:0\right),\:\mathrm{Maximum}\left(1,\:11\right),\:\mathrm{Minimum}\left(4,\:-16\right),\:\mathrm{Maximum}\left(5,\:-5\right)[/tex]Hence, our answer is
[tex]\begin{gathered} \begin{equation*} \mathrm{Minimum}\left(4,\:-16\right) \end{equation*} \\ \begin{equation*} \mathrm{Maximum}\left(1,\:11\right) \end{equation*} \end{gathered}[/tex]The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges to rent trucks plus an additional fee of for each ton of sugar. The second company charges to rent trucks plus an additional fee of for each ton of sugar.For what amount of sugar do the two companies charge the same? What is the cost when the two companies charge the same?
step 1
Find the equation of the line First Company
y=100.25x+6,500
where
y is the total charge
x is the number of ton of sugar
Second Company
y=225.75x+4,492
Part a)
Equate both equations
100.25x+6.500=225.75x+4,492
solve for x
225.75x-100.25x=6,500-4,492
125.50x=2,008
x=16
answer part a is 16 tonPart b) For x=16 ton
substitute the value of x in any of the two equations (the result is the same)
y=100.25(16)+6,500
y=$8,104
answer Part b is $8,104What is the quotient of 2.592 x 10^7 and 7.2 x 10^4 expressed in scientific notation?
Answer:
Explanation:
Given the expression:
[tex]\frac{2.592\times10^7}{7.2\times10^4}[/tex]We can rewrite it as:
[tex]\frac{2592\times10^{-3}\times10^7}{72\times10^{-1}\times10^4}[/tex]Combine all powers of 10:
[tex]\begin{gathered} =\frac{2592\times10^{-3+7}}{72\times10^{-1+4}^{}} \\ =\frac{2592\times10^4}{72\times10^3} \\ =\frac{2592}{72^{}}\times\frac{10^4}{10^3} \\ =36\times10 \\ =3.6\times10^1\times10^1 \\ =3.6\times10^{1+1} \\ =3.6\times10^2 \end{gathered}[/tex]The quotient expressed in scientific notation is 3.6 x 10².
