The total number of hockey cards is 200
The number of cards on a page is 20.
The number of pages in a section is 2.
Let there are x number of sections in a book. So number of cards on the x sections should be equal to total number of cards.
Determine the number of cards on the sections.
[tex]20\times2\times x[/tex]
The total number of hocker card is equal to 200. So equation is,
[tex]200=20\times2\times x[/tex]Net force = ?Net force = ?16 NThe net force for example A isNAThe net force for example B is NA
Part A
The net force is 4 N up
Part B
The net force is 3 N to the left
what is 3(x+5) 12 please help I’ve been stuck on it
Given data:
The given inequality is 3(x+5) >12.
The given inequality can be written as,
[tex]\begin{gathered} 3\mleft(x+5\mright)>12 \\ 3x+15>12 \\ 3x>-3 \\ x>-1 \\ x\in(-1,\text{ }\infty) \end{gathered}[/tex]The graph of the above solution is,
Thus, the solution of the given inequality is (-1, ∞).
A team digs 12 holes every 20 hours, what is the unit rate?
The unit rate = 0.6 holes per hour
Explanation:Number of holes dug by the team = 12
Total time taken = 20 hours
The unit rate = (Number of holes) / (Time)
The unit rate = 12/20
The unit rate = 0.6 holes per hour
what is an equation of the line that passes through the point (-2,-3) and is parallel to the line x+3y=24
Solve first for the slope intercept form for the equation x + 3y = 24.
[tex]\begin{gathered} \text{The slope intercept form is }y=mx+b \\ \text{Convert }x+3y=24\text{ to slope intercept form} \\ x+3y=24 \\ 3y=-x+24 \\ \frac{3y}{3}=\frac{-x}{3}+\frac{24}{3} \\ y=-\frac{1}{3}x+8 \\ \\ \text{In the slope intercept form }y=mx+b,\text{ m is the slope. Therefore, the slope of} \\ y=-\frac{1}{3}x+8,\text{ is }-\frac{1}{3}\text{ or } \\ m=-\frac{1}{3} \end{gathered}[/tex]Since they are parallel, then they should have the same slope m. We now solve for b using the point (-2,-3)
[tex]\begin{gathered} (-2,-3)\rightarrow(x,y) \\ \text{Therefore} \\ x=-2 \\ y=-3 \\ \text{and as solved earlier, }m=-\frac{1}{3} \\ \\ \text{Substitute the values to the slope intercept form} \\ y=mx+b \\ -3=(-\frac{1}{3})(-2)+b \\ -3=\frac{2}{3}+b \\ -3-\frac{2}{3}=b \\ \frac{-9-2}{3}=b \\ b=-\frac{11}{3} \end{gathered}[/tex]After solving for b, complete the equation.
[tex]y=-\frac{1}{3}x-\frac{11}{3}\text{ (final answer)}[/tex]Patios Plus sold an outdoor lighting set for $119.95. The Markup on the set was $25.99. Find the selling price as a percent of cost. Round to the nearest percent
The selling price as a percent of the cost is given by the ratio between the selling price and the the cost. The selling price is given, which is $119.95 the cost is given by the difference between the selling price and the Markup($25.99). Combining all those informations in an equation, we have
[tex]\frac{119.95}{119.95-25.99}=1.27660706684\ldots[/tex]To write this as a percentage, we just multiply the ratio by 100.
[tex]1.27660706684\ldots\times100=127.660706684\ldots\approx128[/tex]The selling price is 128% of the cost.
solve the system of equations by graphing. y = -5x + 4 andy = 3x + 4
1) To solve this System of Solutions graphically, we'll need to plot those lines described by those respective equations.
2) Let's set two tables
y=-5x +4
x | y
1 -1 ( 1,-1)
2 -6 ( 2,-6)
3 -11
y=3x + 4
x | y
1 | 7 ( 1,7)
2 |10 ( 2,10)
3 | 13
2.2 Let's plot those equations and interpret the results:
3) As these lines have point (0,4) as their common point. Therefore we can state that the solution for this consistent system is S=(0,4)
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is nine times the measure of the first angle. The third angle is 26 more than the second let x,y, and z represent the measures of the first second and third angles, find the measures of the three angles
Answer:
x = 18, y = 68, z = 94.---------------------------------
Set equations as per given details.The sum of the measures of the angles of a triangle is 180:
x + y + z = 180 (1)The sum of the measures of the second and third angles is nine times the measure of the first angle:
y + z = 9x (2)The third angle is 26 more than the second:
z = y + 26 (3)SolutionSubstitute the second equation into first:
x + y + z = 180,y + z = 9x.Solve for x:
x + 9x = 180,10x = 180,x = 18.Substitute the value of x into second and solve for y:
y + z = 9x,y + z = 9*18,y + z = 162,y = 162 - z.Solve the third equation for y:
z = y + 26,y = z - 26.Compare the last two equations and find the value of z:
162 - z = z - 26,z + z = 162 + 26,2z = 188,z = 94.Find the value of y:
y = 94 - 26,y = 68.Answer:
x = 18°
y = 68°
z = 94°
Step-by-step explanation:
Define the variables:
Let x represent the first angle.Let y represent the second angle.Let z represent the third angle.Given information:
The sum of the measures of the angles of a triangle is 180°. The sum of the measures of the second and third angles is nine times the measure of the first angle. The third angle is 26 more than the second.Create three equations from the given information:
[tex]\begin{cases}x+y+z=180\\\;\;\;\;\;\:\: y+z=9x\\\;\;\;\;\;\;\;\;\;\;\;\;\: z=26+y\end{cases}[/tex]
Substitute the third equation into the second equation and solve for x:
[tex]\implies y+(26+y)=9x[/tex]
[tex]\implies 2y+26=9x[/tex]
[tex]\implies x=\dfrac{2y+26}{9}[/tex]
Substitute the expression for x and the third equation into the first equation and solve for y:
[tex]\implies \dfrac{2y+26}{9}+y+26+y=180[/tex]
[tex]\implies \dfrac{2y+26}{9}+2y=154[/tex]
[tex]\implies \dfrac{2y+26}{9}+\dfrac{18y}{9}=154[/tex]
[tex]\implies \dfrac{2y+26+18y}{9}=154[/tex]
[tex]\implies \dfrac{20y+26}{9}=154[/tex]
[tex]\implies 20y+26=1386[/tex]
[tex]\implies 20y=1360[/tex]
[tex]\implies y=68[/tex]
Substitute the found value of y into the third equation and solve for z:
[tex]\implies z=26+68[/tex]
[tex]\implies z=94[/tex]
Substitute the found values of y and z into the first equation and solve for x:
[tex]\implies x+68+94=180[/tex]
[tex]\implies x=18[/tex]
Find cosθ, cotθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.cosθ=cotθ=secθ=
First let's find the missing value of the hypotenuse:
[tex]\begin{gathered} c^2=a^2+b^2 \\ a=4 \\ b=5 \\ \Rightarrow c^2=(4)^2+(5)^2=16+25=41 \\ \Rightarrow c=\sqrt[]{41} \\ \end{gathered}[/tex]we have that the hypotenuse equals sqrt(41). Now we can find the values of the trigonometric functions:
[tex]\begin{gathered} \cos (\theta)=\frac{adjacent\text{ side}}{hypotenuse} \\ \Rightarrow\cos (\theta)=\frac{4}{\sqrt[]{41}} \\ \sec (\theta)=\frac{1}{\cos (\theta)} \\ \Rightarrow\sec (\theta)=\frac{1}{\frac{4}{\sqrt[]{41}}}=\frac{\sqrt[]{41}}{4} \\ \tan (\theta)=\frac{opposite\text{ side}}{adjacent\text{ side}} \\ \Rightarrow\tan (\theta)=\frac{5}{4} \\ \cot (\theta)=\frac{1}{\tan (\theta)} \\ \Rightarrow\cot (\theta)=\frac{1}{\frac{5}{4}}=\frac{4}{5} \end{gathered}[/tex]80 students scores recorded 68 84 75 82 68 90 62 88 76 93 73 88 73 58 93 71 59 58 5161 65 75 87 74 62 95 78 63 72 66 96 79 65 74 77 95 85 78 8671 78 78 62 80 67 69 83 76 62 71 75 82 89 67 58 73 74 73 6581 76 72 75 92 97 57 63 83 81 82 53 85 94 52 78 88 77 71mean exam score
Solution
We have the following values:
68,84,75,82,68,90,62,88,76,93,73,79,88,73,58,93,71,59,
58,51,61,65,75,87,74,62,95,78,63,72,66,96,79,65,74,77,95,
85,78,86,71,78,78,62,80,67,69,83,76,62,71,75,82,89,67,58,
73,74,73,65,81,76,72,75,92,97,57,63,68,83,81,82,53,85,94,
52,78,88,77,71
Part a
Range = Max- Min= 97-51= 46
Part b
The mean is given by:
[tex]\text{Mean}=\frac{\sum ^n_{i\mathop=1}x_i}{n}=75[/tex]Part c
The median is given by:
Position 40 ordered= 75 and Position 41 ordered= 75
Then the median is:
[tex]\text{Median}=\frac{75+75}{2}=75[/tex]Part d
The most is the most frequent value and for this case is:
Repeated 5 times
Mode = 78
Part e
The data within the interval 50-54 is:
51 52 53
The variance is given by:
[tex]s^2=\frac{\sum ^n_{i\mathop=1}(x_i-Mean)^2}{n-1}=1[/tex]And the deviation si:
[tex]s=\sqrt[]{1}=1[/tex]
14. What is the volume of a box with these dimensions? 4 cm 5 cm 10 cm.
The volume of a rectangular prism is given by the product of its three dimensions.
Since the box dimensions are 4 cm, 5 cm and 10 cm, its volume is:
[tex]\begin{gathered} V=4\cdot5\cdot10 \\ V=200\text{ cm}^3 \end{gathered}[/tex]So the volume of the box is equal to 200 cm³.
factoring quadratics h^2+12h+11
i really need help writting the slope intercept form
Equation in slope intercept form is written as
y = mx + b
If slope m = 1/3 and y-intecept b = 3
Equation form using the information above is
[tex]y\text{ =}\frac{1}{3}x\text{ + 3}[/tex]Point slope form using the point (3, 4)
simply use the formula
y - y₁ = m( x- x₁ )
[tex]y\text{ -4=}\frac{1}{3}(x-3)[/tex]
-16 = m - 3 solve m
m = -13
Explanations:-16 = m - 3
Add 3 to both sides of the equation
-16 + 3 = m - 3 + 3
-13 = m
m = -13
The sum of three numbers is 106. The second number is 2 times the third. The first number is 6 more than the third. What are the numbers?First numberSecond number Third number
Let's call the numbers a, b and c.
The first statement tells us that the sum of the three numbers is 106, so:
[tex]a+b+c=106.[/tex]The second statement tells us that the second number is two times the third so:
[tex]b=2c\text{.}[/tex]The final statement tells us that the first number is 6 more than the third, so:
[tex]a=c+6.[/tex]This gives us a system of three equations with three variables. Let's take the value of a given by the third equation, use it in the first one and isolate another variable:
[tex](c+6)+b+c=106,[/tex][tex]2c+b+6=106,[/tex][tex]2c+b=100,[/tex][tex]b=100-2c\text{.}[/tex]Let's take this value of b and use it in the second equation:
[tex]100-2c=2c,[/tex][tex]100=4c,[/tex][tex]c=25.[/tex]Now we know the exact value of c, so let's go back to the third equation:
[tex]a=25+6=31,[/tex]and now we also know the exact value of a, so let's go back to the second equation:
[tex]b=2(25)=50.[/tex]So, the first number (a) is 31, the second (b) is 50 and the third (c) is 25.
31+50+25=106.
Identify any congruent figures in the coordinate plane. Explain. This is a fill in the blank question based off of the options that are listed down below!
Solution
For this case we can conclude the following:
triangle HJK ≅ triangle QRS because one is rotation of 90º about the origin of the other
Rectangle DEFG ≅ rectangle MNLP because one is a translation of the other
triangle ABC ≅ no given figure because one is not related by rigid motions of the other
If y=kx, where k is a constant, and y=24 when x=6, what is the value of y when x=5?A. 6B. 15C. 20D. 23
First, we will find the value of k
We can do this by sybstituting y=24, x=6 in;
y=kx and then solve for k
24= k(6)
divide both-side of the equation by 6
24/6 = k
4 = k
k=4
Then when x = 5, we will substitute x=5 and k=4 in; y=kx and then solve for y
y= (4)(5)
y = 20
A surveyor wants to find the height of a tower used to transmit cellular phone calls. He stands 125 feet away from the tower and meandered the angle of elevation to be 40 degrees. How tall is the tower?
Given
Answer
[tex]\begin{gathered} \tan 40=\frac{h}{125} \\ 0,84\times125=h \\ h=105\text{ ft} \end{gathered}[/tex]height of tower is 105 ft
what is the smallest angle of rotational symmetry of a pentagon
Answer:
72°
Step-by-step explanation:
Origin is completely 360° and its divided into 5 sides. So,360÷5=72°
Solve the following system of equations using the elimination method. Note that the method of elimination may be referred to as the addition method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY.)20x − 5y = 208x − 2y = 8(x, y) =
Given
The system of equations,
20x − 5y = 20
8x − 2y = 8
To find: The solution.
Explanation:
It is given that,
20x − 5y = 20 _____(1)
8x − 2y = 8 _____(2)
That implies,
Divide (1) by 5 and (2) by 2.
Then, (1) and (2) becomes,
4x - y = 4.
Hence, there is infinitely many solution.
I am having a tough time solving this problem from my prep guide, can you explain it to me step by step?
The range in the average rate of change in temperature of the substance is from a low temperature of -[tex]22^{0}[/tex]F to a high of [tex]16^{0}[/tex]F
The domain of the function f(x) = sin x includes all real numbers, but its range is −1 ≤ sin x ≤ 1. The sine function has different values depending on whether the angle is measured in degrees or radians. The function has a periodicity of 360 degrees or 2π radians.
Given f(x) = -19sin(7/3x + 1/6) – 3
We have to the range in the average rate of change in temperature of the substance is from a low temperature of ___F to a high of ___F
We know that the range of sin x is [-1, 1]
f(x) = -19 sin(7/3x + 1/6) – 3
We know
-1 ≤ sin(7/3x + 1/6) ≤ 1
Now multiply with -19 on both sides
19 ≥ -19sin(7/3x + 1/6) ≤ -19
-19 ≤ -19sin(7/3x + 1/6) ≤ 19
Now subtract 3 from both sides
-19 - 3 ≤ -19sin(7/3x + 1/6) - 3 ≤ 19 - 3
-22 ≤ -19sin(7/3x + 1/6) ≤ 16
-22 ≤ f(x) ≤ 16
Therefore the range in the average rate of change in temperature of the substance is from a low temperature of -220F to a high of 160F
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If f(x) = 6x + 8(x + 2), find f-1(x).f-1(x) = (x - 16)/14f-1(x) = x +16/14f-1(x) = -x - 16/14f-1(x) = -x + 16/14
SOLUTION:
We want to find the inverse of f(x);
[tex]f(x)=6x+8(x+2)[/tex]We solve for x;
[tex]\begin{gathered} y=6x+8(x+2) \\ y=6x+8x+16 \\ y=14x+16 \\ y-16=14x \\ x=\frac{y-16}{14} \\ interchange\text{ }y\text{ }and\text{ }x \\ f^{-1}(x)=\frac{x-16}{14} \end{gathered}[/tex]Thus the answer is OPTION A
Multiply.
7.
-2 7
-5 -6
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Write your answer in simplest form solve this
The simplest form of 7 × (-2/-5) × (7/-6) is - 49/15.
Multiplication of fractions:A whole number or another fraction is produced when one fraction is multiplied by another fraction. We all know that a fraction has two components: a numerator and a denominator. In order to multiply any two fractions, we must multiply the numerators and denominators, respectively.
Here we have
=> [tex]7. \frac{-2}{-5} .\frac{7}{-6}[/tex]
Can be multiplied as given below
=> [tex]7 \times\frac{-2}{-5} \times\frac{7}{-6}[/tex]
=> [tex]7 \times\frac{1}{5} \times\frac{7}{-3}[/tex]
=> [tex]-\frac{49}{15}[/tex]
Therefore,
The simplest form of 7 × (-2/-5) × (7/-6) = -49/15
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The standard form of the equation of a parabola isy=x²-4x+21. What is the vertex form of the equation?O A. y = ¹/(x-4)² +13OB. y=(x-4)² +21C. y = 1/(x+4)² +1+13O D. y = 1/(x+4)² +21
Answer:
[tex]y=\frac{1}{2}(x-4)^2+13\text{ }\operatorname{\Rightarrow}(A)[/tex]Explanation: We have to find the vertex form of the parabola equation from the given standard form of it:
[tex]y=\frac{1}{2}x^2-4x+21\rightarrow(1)[/tex]The general form of the vertex parabola equation is as follows:
[tex]\begin{gathered} y=A(x-h)^2+k\rightarrow(2) \\ \\ \text{ Where:} \\ \\ (h,k)\rightarrow(x,y)\Rightarrow\text{ The Vertex} \end{gathered}[/tex]Comparing the equation (2) with the original equation (1) by looking at the graph of (1) gives the following:
[tex](h,k)=(x,y)=(-4,13)[/tex]
Therefore the vertex form of the equation is as follows:
[tex]y=\frac{1}{2}(x-4)^2+13\Rightarrow(A)[/tex]Therefore the answer is Option(A).
PerioAlgebra 2NameUsing Linear Equations to Solve Problems Date1) The chess club is selling popcorn balls for $1.00 and jumbo candy bars for$1.50 each. This week they have made a total of $229 and have sold 79popcorn balls. How many candy bars have they also sold?
The popcorn balls cost $1.00 each
Jumbo candy bars cost $1.50 each
This week they have made a total of $229 and have sold 79
popcorn balls.
First, let's make a function with includes this information.
Let's say that popcorn balls are x and Jumbo candy bars are y.
So the function would be
1.00x+ 1.50y = 229
We already have the x value which represents the total of popcorn balls sold this week, so replace this value in the function:
1.00x+ 1.50y = 229
1.00(79)+ 1.50y = 229
79.00 + 1.50y = 229
Solve the equation for y to find the total of candy bars sold.
79 + 1.50y = 229
1.50y = 229 - 79
1.50y = 150
y = 150/1.50
y = 100
So the have sold 100 candy bars this week
2x + 2/3y= -2 x, y intercept
We need to find the points at which the expression below intercept the axis of the coordinate plane:
[tex]2x+\frac{2}{3}y=-2[/tex]To find the "x" intercept we need to find the value of "x" that results in a value of "y" equal to 0. We have:
[tex]\begin{gathered} 2x+\frac{2}{3}\cdot0=-2 \\ 2x+0=-2 \\ 2x=-2 \\ x=\frac{-2}{2}=-1 \end{gathered}[/tex]To find the "y" intercept we need to find which value of "y" the function outputs when we make x equal to 0.
[tex]\begin{gathered} 2\cdot0+\frac{2}{3}y=-2 \\ \frac{2}{3}y=-2 \\ 2y=-6 \\ y=\frac{-6}{2}=-3 \end{gathered}[/tex]The x intercept is -1 and the y intercept is -3.
The circle below has center S. Suppose that m QR = 84°. Find the following.
Given:
[tex]\text{m}\hat{\text{QR}}=84^{\circ}[/tex]b) To find:
[tex]\angle QSR[/tex]We know that,
[tex]\hat{QR}=\angle QSR=84^{\circ}[/tex]Thus, the answer is,
[tex]\angle QSR=84^{\circ}[/tex]a) To find:
[tex]\angle QPR[/tex]We know that,
[tex]\begin{gathered} \angle QPR=\frac{1}{2}\angle QSR \\ \angle QPR=\frac{1}{2}(84^{\circ}) \\ \angle QPR=42^{\circ} \end{gathered}[/tex]Thus, the answer is,
[tex]\angle QPR=42^{\circ}[/tex]Graph the linear function using the slope and the y-intercept.y = 2x + 3CORTUse the graphing tool to graph the linear equatium. Use the slope and y-intercept when drawing the line.Click toenlargegraph
Answer:
Explanation:
If we have a linear equation of the form
[tex]y=mx+b[/tex]then m = slope and b = y-intercept.
Now in our case, we have
[tex]y=2x+3[/tex]which means that slope = 2 and y-intercept = 3
Therefore, we graph a line that has a slope of 2 and a y-intercept of 3.
A slope of 2 means that for every step you take to the right on a graph, you move 2 steps up to get to a point on the line.
The y-intercept of 3 means that the line passes through the point (0, 3).
Using these two facts about the line, we draw the following line.
From the above plot, we can clearly see that the line has a slope of 2 and a y-intercept of 3 - the same line described by y = 2x + 3.
verizon charges $200 to start up a cell phone plan. then there is a $50 charge each month. what is the total cost (start up fee and monthly charge) to use the cel phone plan for 1 month?
write the total costs a linear function in the form
[tex]y=mx+b[/tex]in which:
y= total cost
x= number of months
m= charge per month
b= fixed start up fee
replace all data in the equation
[tex]\begin{gathered} y=50\cdot x+200 \\ y=50x+200 \end{gathered}[/tex]Since the question is the cost for 1 month, x=1
[tex]\begin{gathered} y=50(1)+200 \\ y=250 \end{gathered}[/tex]The cost for the use of the cellphone is $250
Anthony has already taken 1 quiz during past quarters, and he expects to have 5 quizzes during each week of this quarter. How many weeks of school will Anthony have to attend this quarter before he w have taken a total of 31 quizzes?
The first step to solve the problem is to create a function that relates the number of quizzes he attends by the number of weeks that elapses. Since he alread took one quizz, then the function must start from that and must grow at a rate of 5 quizzes per week. We have:
[tex]\text{quizzes(w)}=5\cdot w+1[/tex]We want to know how many weeks until he takes 31 quizzes, then we need to make the expression equal to 31 and solve for the value of w. We have:
[tex]\begin{gathered} 5\cdot w+1=31 \\ \end{gathered}[/tex]Then we subtract both sides by 1.
[tex]\begin{gathered} 5\cdot w+1-1=31-1 \\ 5\cdot w=30 \end{gathered}[/tex]Then we divide both sides by 5.
[tex]\begin{gathered} \frac{5\cdot w}{5}=\frac{30}{5} \\ w=6 \end{gathered}[/tex]It'll take 6 weekes before he have taken a total of 31 quizzes.
Find at least three solutions to the equation y = 3x - 1, and graph the solutions as points on the coordinate plane.Connect the points to make a line. Find the slope of the line.
To find a solution to the equation y = 3x - 1, we have to replace a variable by a number and compute the other variable.
Assuming x = 0, then
y = 3(0) - 1
y = 0 - 1
y = -1
Then, the point (0, -1) is a solution
Assuming x = 1, then
y = 3(1) - 1
y = 3 - 1
y = 2
Then, the point (1, 2) is a solution
Assuming x = 2, then
y = 3(2) - 1
y = 6 - 1
y = 5
Then, the point (2, 5) is a solution
In the next graph, the solutions and the line are shown
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with points (0, -1) and (1,2) we can compute the slope, as follows:
[tex]m=\frac{2-(-1)}{1-0}=3[/tex]