7. (3 X 10) X 8 = 3 X (10 X 8)
In this case, we use the associative property of the multiplication (you can group the factors in any way).
8. 16 + 31 = 31 + 16
Commutative property.
9. 0 + 91 = 91
Identity property
10. 21 x 9 = 9 X 21
Commutative property
11. The income is (20 * 18) * 5.
We can multiply the three numbers together, using the associative property.
20 * 18 * 5 = 1800
12. In this case, we have to add each of the groups:
26 + 19 + 34 + 21 = 100
We don't need to apply any properrty in particular. We can add them in any order taking into account the commutative property.
3) Describe what ALL graphs of proportional relationships have in common
SOLUTION
What all graphs of proportional relationships have in common is a straight line.
This line is straight, no curves or bends. This straight line passes through the origin at an intersection of
[tex](0,0)[/tex]Hence, the answer is "A straight line that passes through the origin and goes at a constant rate".
Need help figuring out if the following is Real or Complex Question number 10
Explanation:
We have the expression:
[tex]i^3[/tex]where i represents the complex number i defined as follows:
[tex]i=\sqrt{-1}[/tex]To find if i^3 is real or complex, we represent it as follows:
[tex]i^3=i^2\times i[/tex]And we find the value of i^2 using the definition of i:
[tex]i^2=(\sqrt{-1})^2[/tex]Since the square root and the power of 2 cancel each other
[tex]\imaginaryI^2=-1[/tex]And therefore, using this value for i^2, we can now write i^3 as follows:
[tex]\begin{gathered} \imaginaryI^3=\imaginaryI^2\times\imaginaryI \\ \downarrow \\ \imaginaryI^3=(-1)\times\imaginaryI \end{gathered}[/tex]This simplifies to -i
[tex]\imaginaryI^3=-\imaginaryI^[/tex]Because -i is still a complex number, that means that i^3 is a complex number.
Answer: Complex
Find the value of variable a given the transformation is an isometry.
Answer:
• a =10
,• b = 4
Explanation:
An isometry is a rigid transformation that preserves length and angle measures, as well as perimeter and area.
This means that the two right triangles are congruent.
Thus, we have that:
[tex]\begin{gathered} 3a=30 \\ 10b=40\degree \end{gathered}[/tex]Next, we solve for a and b.
[tex]\begin{gathered} 3a=30 \\ \text{Divide both sides by 3} \\ \frac{3a}{3}=\frac{30}{3} \\ a=10 \end{gathered}[/tex]Likewise:
[tex]\begin{gathered} 10b=40\degree \\ \text{Divide both sides by 10} \\ \frac{10b}{10}=\frac{40\degree}{10} \\ b=4 \end{gathered}[/tex]The values of a and b are 10 and 4 respectively.
Maria jogs 5 laps of a football field that
is 100 m by 50 m. How far does she jog?
Answer:
1500 m
Step-by-step explanation:
given that the field is 100m by 50m we can find that the perimeter of the field is 300m. if she jogged 300m 5 times she would have jogged 1500m
A certain marine engine has cylinders that are 5.25 cm in diameter and 5.64 cm deep.Find the total volume of 4 cylinders (to the nearest hundredth). Use 3.14 as the approximate value of
Given:
A cylinder is given with 5.64 cm deep and 5.25 cm diameter.
Required:
Total volume of 4 cylinders.
Explanation:
Diameter of cylinder d = 5.25 cm
Height of cylinder or deepness of cylinder h = 5.64 cm
Radius r of cylinder is
[tex]r=\frac{d}{2}=\frac{5.25}{2}=2.625\text{ cm}[/tex]volume of cylinder is
[tex]v=\pi r^2h=3.14*2.625^2*5.64=122.03\text{ cm}^3[/tex]here we need volume of 4 cylinder
for this we just multiply v with 4
[tex]V=4v=4*122.03=488.121\text{ cm}^3[/tex]Final Answer:
The volume of 4 cylinder is 488.121 cube cm
What kind of transformation converts the graph of f(x)=(5x+6)^2 into the graph of g(x)=-(5x+6)^2
In order to get from
[tex]f(x)=(5x+6)^2[/tex]To
[tex]f(x)=-(5x+6)^2[/tex]You have to reflect across the x-axis.
Remember that the x-axis is the line with equation
[tex]y=0[/tex]Answer: Option A
Find an equation of the line.Write the equation in the standard form.Through (8,4); parallel to 7x-y= 2.
Answer:
7x-y=53
Explanation:
Given the line
[tex]7x-y=2[/tex]Making y the subject of the equation, we have:
y = 7x-2
Therefore, the slope of the line, m=7
• If two lines are parallel, their slopes are equal.
Therefore, the slope of the parallel line = 7
The equation of the parallel line through (8,4) will then be:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=7(x-8) \\ y-4=7x-57 \\ 7x-y=-4+57 \\ 7x-y=53 \end{gathered}[/tex]Problem solving.When two expressions are not equivalent, you can use an inequality symbol to show their relationship. Do you ever use an inequality symbol when two expressions are equivalent? Use an example in your explanation.
Explanation
When two expressions are not equivalent, you can use an inequality symbol
[tex]\begin{gathered} \leq\Rightarrow less\text{ or equal } \\ \ge\Rightarrow greater\text{ or equal } \\ >\Rightarrow greater\text{ than } \\ <\Rightarrow smaller\text{ than} \end{gathered}[/tex]
now, when comparing two expressions that are equivalent , WE CAN NOT USE an inequality simbol, instead of we need to use The equals sign or equal sign formerly known as the equality sign
[tex]=[/tex]for example
[tex]3x+19x=30x-8x[/tex]the = symbold indicates that both sides have the same value ( rigth and left)
I hope this helps you
what is the slope of any line is perpendicular to the equation y=1/2x-7
The slope = -2
Explanations:The given equation is:
[tex]y\text{ = }\frac{1}{2}x\text{ - 7}[/tex]This is of the form y = mx + c
where the slope, m = 1/2
The equation perpendicular to the equation y = mx + c is:
[tex]y-y_1=\frac{-1}{m}(x-x_1)[/tex][tex]\begin{gathered} \text{The slope = }\frac{-1}{m} \\ \text{The slope = }\frac{-1}{\frac{1}{2}}=\text{ -2} \end{gathered}[/tex]The slope = -2
Find the variance for the set of data: 22, 26, 17, 20, 20.The variance is
The variance of a given data set with size N is given by the formula:
[tex]\begin{gathered} \sigma=\sqrt{\frac{1}{N}\sum_{i=1}^N(x_i-\mu)^2} \\ Var(X)=\sigma^2 \end{gathered}[/tex]Then, for the data set {22, 26, 17, 20, 20} and N = 5, we have:
[tex]\begin{gathered} \mu=\frac{22+26+17+20+20}{5}=21 \\ \sigma=\sqrt{\frac{1^2+5^2+(-4)^2+(-1)^2+(-1)^2}{5}}=\sqrt{\frac{44}{5}}=2\sqrt{\frac{11}{5}} \\ \therefore Var(X)=\frac{44}{5}=8.8 \end{gathered}[/tex]Please show me how to solve this step by step im really confused
Given
[tex]-16t^2+v_0t+h_0[/tex]initial velocity = 60 feet per second
initial height = 95 feet
Find
Maximum height attained by the ball
Explanation
we have given
[tex]\begin{gathered} h(t)=-16t^2+60t+95 \\ h^{\prime}(t)=-32t+60 \end{gathered}[/tex]put h'(t) = 0
[tex]\begin{gathered} -32t+60=0 \\ -32t=-60 \\ t=\frac{60}{32}=1.875sec \end{gathered}[/tex]to find the maximum height find the value of h(1.875)
[tex]\begin{gathered} h(1.875)=-16(1.875)^2+60(1.875)+95 \\ h(1.875)=-56.25+112.5+95 \\ h(1.875)=-56.25+207.5 \\ h(1.875)=151.25 \end{gathered}[/tex]Final Answer
Therefore , the maximum height attained by the ball is 151.25 feet
the equation of line u is y=2x+8/9. line v includes the point (7,9) and is parallel to line u. what is the equation of.line v
The linear equation parallel to line u that passes through (7,9) is y = 2x - 5
How to find the equation of line V?
Two lines are parallel if have the same slope, we know that line V is parallel to:
y = 2x + 8/9
Then line V will be of the form:
y = 2x + c
To find the value of c, we use the fact that the line passes through (7, 9), replacing these values we get:
9 = 2*7 + c
9 = 14 + c
9 - 14 = c
-5 = c
The linear equation is y = 2x - 5
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Select all the true statements about this graph A. The graph is nonlinearB. The function increases at the same rateC. The rate decreases after x = 2.D. The graph is a functionE. The graph is increasing in two intervals.SELECT ALL ANSWER CHOICES THATS RIGHT
In the graph the points are connected by the straight lines, so graph is linear graph. In nonlinear graph the points are connected by the curve. So option A is incorrect.
The slope of the line changes after x=2. The inclination of line with positive x axis is different before and after x=2. So the function not increases at same rate. Then option B is incorrect.
The rate is given by the slope of line. The inclination of line with positive x axis increase after x=2, so rate increases not decreases. Then option C is incorrect.
The graph of a straight line is function or not a function can be inspected by vertical line test.
If we draw a vertical line, then the vertical line intersect the line only once, so the graph is function. Option D is correct.
The value of y increases with increase in value of x but increase in value of y with x is different for two lines. So graph is increasing in two intervals. Option E is also correct.
Thus option D and E is only true for given graph.
quadrilateral WXYZ is reflected across the line y=x to create quadrilateral W’X’Y’Z'. What are the coordinates of quadrilateral W’X’Y’Z'.
Explanation
We are required to determine the coordinates of W’X’Y’Z' when WXYZ is reflected across the line y = x.
This is achieved thus:
From the image, we can deduce the following:
[tex]\begin{gathered} W(-7,3) \\ X(-5,6) \\ Y(-3,7) \\ Z(-2,3) \end{gathered}[/tex]We know that the following reflection rules exist:
Therefore, we have:
[tex]\begin{gathered} (x,y)\to(y,x) \\ W(-7,3)\to W^{\prime}(3,-7) \\ X(-5,6)\to X^{\prime}(6,-5) \\ Y(-3,7)\to Y^{\prime}(7,-3) \\ Z(-2,3)\to Z^{\prime}(3,-2) \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} \begin{equation*} W^{\prime}(3,-7) \end{equation*} \\ \begin{equation*} X^{\prime}(6,-5) \end{equation*} \\ \begin{equation*} Y^{\prime}(7,-3) \end{equation*} \\ \begin{equation*} Z^{\prime}(3,-2) \end{equation*} \end{gathered}[/tex]This is shown in the graph bwlow for further undertanding:
Add and subtract square roots that need simplification Number 186
Hello!
To solve this exercise, we must simplify these square roots until we have the same square root in both numbers (by the factorization process):
[tex]3\sqrt{98}-\sqrt{128}[/tex]First, let's factorize the square root of 98:
So, we know that:
[tex]\begin{gathered} 3\sqrt{98}=3\sqrt{7^2\times2}=3\sqrt[\cancel{2}]{7\cancel{^2}\times2}=3\times7\sqrt{2}=21\sqrt{2} \\ \\ 3\sqrt{98}=21\sqrt{2} \end{gathered}[/tex]Now, let's do the same with the square root of 128:
So:
[tex]\sqrt{128}=\sqrt{2^2\times2^2\times2^2\times2}^1[/tex]Notice that it also could be written as:
[tex]\begin{gathered} \sqrt{128}=\sqrt{2\times2\times2\times2\times2\times2\times2} \\ \text{ or also} \\ \sqrt{128}=\sqrt{2^7} \end{gathered}[/tex]As we are talking about square roots, it will be easier if we group them in pairs of powers of 2, as I did:
[tex]\sqrt[2]{128}=\sqrt[2]{2^2\times2^2\times2^2\times2^1}[/tex]Now, let's analyze it:If the number inside the root has exponent 2, we can cancel this exponent and remove the number inside the root. Then, we can write it outside of the root, look:
[tex]\begin{gathered} \sqrt[2]{128}=\sqrt[2]{2^{\cancel{2}}\times2^{\cancel{2}}\times2^{\cancel{2}}\times2^1} \\ \sqrt[2]{128}=2\times2\times2\sqrt[2]{2^1} \\ \sqrt[2]{128}=8\sqrt[2]{2} \end{gathered}[/tex]Now, let's go back to the exercise:[tex]\begin{gathered} 3\sqrt{98}-\sqrt{128}\text{ is the same as } \\ 21\sqrt{2}-8\sqrt{2} \end{gathered}[/tex]So, we just have to solve it now:
[tex]21\sqrt{2}-8\sqrt{2}=\boxed{13\sqrt{2}}[/tex]Try This question out and I’ll give you brainliest no links or I will report you
Answer: ∠ABD = 19°
Step-by-step explanation:
The angle formed by ABC is a complementary angle. This means the sum of both angles adds up to 90 degrees.
Since angle DBC is 71 degrees, 90 - 71 equals ∠ABD
90 - 71 = 19
Therefore ∠ABD = 19°
Answer:
m∠ABD = 19°
Step-by-step explanation:
Hello!
Recall that all angles of a rectangle are 90° in measure.
Angle B is 90°, and is made up of angles ABD and DBC.
We know the measure of angle DBC, it's given as 71°. We can find the measure of ABD by subtracting 71° from 90°.
Find ABDABC = ABD + DBC90 = ABD + 7119 = ABDSo the measure of angle ABD is 19°.
Amplitude, period, and phase shift of sine and cosine functions
We are given that
[tex]y=-2+2\cos (2x-\frac{\pi}{3})[/tex]Note: Given the cosine function
[tex]y=a\cos (bx-c)+d[/tex]then
[tex]\begin{gathered} Amplitude=a \\ Period=\frac{2\pi}{b} \\ PhaseShift=\frac{c}{b} \\ VerticalShift=d \end{gathered}[/tex]Comparing the question with what is written in the note
We have
[tex]\begin{gathered} a=2 \\ b=2 \\ c=\frac{\pi}{3} \\ d=-2 \end{gathered}[/tex]We want to find
(a). Amplitude
From the given question, the amplitude (a) is
[tex]\begin{gathered} a=2 \\ Amplitude=2 \end{gathered}[/tex](b).Period
From the given question, the period is
[tex]\begin{gathered} Period=\frac{2\pi}{b} \\ Period=\frac{2\pi}{2} \\ Period=\pi \end{gathered}[/tex](c). Phase Shift
From the given question, the phase shift is
[tex]\begin{gathered} PhaseShift=\frac{c}{b} \\ PhaseShift=\frac{\pi}{3}\times\frac{1}{2} \\ PhaseShift=\frac{\pi}{6} \end{gathered}[/tex]I need help to know how to solve graphing a system of inequalities2x - 3y > -12x + y ≥ -2
Answer
2x - 3y > -12 (in red ink)
x + y ≥ -2 (in black ink)
The solution region is the region that the two shaded regions have in common.
Explanation
When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.
If the inequality sign is (< or >), then the line drawn will be a broken line.
If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.
Step 1
For this question, we easily see that the first inequality will have a broken line and the second one will have an unbroken line.
To plot each of the lines, we will use intercepts to obtain the coordinates of two points on each line
Recall, we will first plot the lines like they are equations of a straight line.
To plot the graph
2x - 3y = -12
when x = 0,
2(0) - 3y = -12
-3y = -12
Divide both sides by -3
(-3y/-3) = (-12/-3)
y = 4
First point on the line is (0, 4)
when y = 0
2x - 3(0) = -12
2x = -12
Divide both sides by 2
(2x/2) = (-12/2)
x = -6
Second point on the line is (-6, 0)
For the second line,
To plot the graph,
x + y = -2
when x = 0
0 + y = -2
y = -2
First point on the line is (0, -2)
when y = 0
x + 0 = -2
x = -2
Second point on the line is (-2, 0)
So, for the plotting, we connect the two points for each of the lines.
Step 2
The shaded region now depends on whether the inequality sign is facing y or not.
If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.
If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.
2x - 3y > -12
Can be rewritten as
-3y > -2x - 12
Divide through by -3 (this changes the inequality sign)
y < (2x/3) + 4
Here, we see that the inequality sign is not facing y, hence the numbers below the broken line plotted are the shaded region (in red ink)
x + y ≥ -2
We can rewrite this as
y ≥ -x - 2
Here, we see that the the inequality sign is facing y, hence, the numbers above the unbroken line plotted are the shaded region (in black ink)
The graph of this system of inequalities is presented above under 'Answer'
Hope this Helps!!!
Find the measures of the sine and cosine of the following triangles
Let x be the side opposite to angle 62 degrees
Let y be the adjacent angle.
The sine of the angle is given as follows:
[tex]\begin{gathered} \sin62=\frac{Opposite}{Hypotenuse}=\frac{x}{10} \\ \end{gathered}[/tex]The cosine is given as:
[tex]\cos62=\frac{Adjacent}{Hypotenuse}=\frac{y}{10}[/tex]The period T(In seconds) of a pendulum is given by T=2PI(Square root of L/32) Where L stands for length (in feet) of the pendulum If pi =3.14 and the period is 6.28 what is the length
Let me check your question
[tex]T\text{ = 2}\cdot\text{ 3.14}\cdot\text{ }\sqrt[]{L/\text{ 32}}[/tex][tex]\frac{T}{2\cdot\text{ 3.14}}\text{ = }\sqrt[]{L/\text{ 32}}[/tex]T= the period = 6.28
[tex]\frac{6.28}{6.28}\text{ = }\sqrt[]{L/\text{ 32}}[/tex][tex]L/32=1^2[/tex][tex]L=32[/tex]_________________
Answer
L= 32
A tourist from the U.S. is vacationing in China. One day, he notices that has cost 6.84 yuan per liter. On the same day, 1 yuan is worth 0.14 dollars. How much does the gas cost in dollars per gallon? Fill in the two blanks on the left side of the equation using two of the ratios. THEN WRITE THE ANSWER ROUNDED TO THE NEAREST HUNDREDTH. Will send pic of question.
Solve:
[tex]\frac{6.84\text{ yuan}}{1\text{ L}}\times\frac{0.14\text{ dollars}}{1\text{ yuan}}\times\frac{3.79\text{ L}}{1\text{ gal}}=3.63\frac{dollars}{gal}[/tex]your card gives you a bonus of 0.4%. what is your actual bonus if you charge $3,397.75 on your credit card?
Answer:
$13.591
Explanation:
To know your actual bonus, we need to find what is 0.4% of $3,397.75 as follows
[tex]3,397.75\times\frac{0.4}{100}=13.591[/tex]Therefore, your actual bonus is $13.591
1) There is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. The cost for 6 months is $47.94. The point (6,47.94) is shown on the graph below. 180 160 140 120 100 cost (dollars) 80 60 (6, 47.94) 40 20 16 18 8 20 22 2. 4 6 10 12 14 time (months)
Given:
The point which describes the relationship between the months and total amount is, (6, 47.94).
a) To find the constant proportionality:
6 months =47.94
Then, for 1 month,
[tex]\frac{47.94}{6}=7.99[/tex]Hence, the constant proportionality is $7.99.
b) The constant proportionality tells that, if the month is increased then the cost is also increased by $7.99.
c) To find the three more points and label it:
For the month, m=1, then the cost c=$7.99
For the month, m=2, then the cost c=$15.98
For the month m=3, then the cost c=$23.97
Therefore, the three points are (1, 7.99), (2,15.98) and (3, 23.97).
The graph is,
d) The relationship between the months and the cost is,
C=7.99 m
Identify the word described by the following statement.The type of rule in which you can find any number of term in the sequence without knowing the first or previous term.
Recursive is the type of rule in which you can find any number of term in the sequence without knowing the first or previous term.
Hence, the answer is Recursive.
Casey's Cookie Company opened with 24 cupcakes in the store display case. By noon, therewere only 15 cupcakes left. Was there a percent increase or decrease in the amount ofcupcakes? What was the increase or decrease amount?
Percentage is the proportion between numbers
total initial of cakes for Casey's = 24
final number of cakes = 15
find proportion 15/24 how many represents
15/24 = 5/8
now divide 100/8 = 12.5
then multiply 12.5 x 5
12.5x5= 62.5 %
Professor Ahmad Shaoki please help me! The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square. Help me! From: Jessie
The length of the original square must be equal to 3 inches.
Length of the Original SquareTo find the length of the original square, we have to first assume the unknown length is equal x and then use formula of area of a square to determine it's length.
Since the new length is stretched by 5in, the new length would be.
[tex]l = (x + 5)in[/tex]
The area of a square is given as
[tex]A = l^2[/tex]
But the area is equal 64 squared inches; let's use substitute the value of l into the equation above.
[tex]A = l^2\\l = x + 5\\A = 64\\64 = (x+5)^2\\64 = x^2 + 10x + 25\\x^2 + 10x - 39 = 0\\[/tex]
Solving the quadratic equation above;
[tex]x^2 + 10x - 39 = 0\\x = 3 or x = -13[/tex]
Taking the positive root only, x = 3.
The side length of the original square is equal to 3 inches.
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I need to find the length x of KL
Answer:
3.6Step-by-step explanation:
We're going to use length DC and ML, along with DA and MJ
[tex]\frac{DC}{ML} = \frac{5}{6}[/tex] which is 0.833333333
now for
[tex]\frac{DA}{MJ} =\frac{7}{8.4}[/tex] which is 0.833333333 (again)
as you can see since the shapes ABCD and JKLM are similar, they have a relationship which in this case is 0.833333333
and we can use this 0.833333333 to help us find the length of KL
knowing that any length for ABCD divided by JKLM is 0.833333333
we can do
[tex]\frac{CB}{LK}=0.833333333[/tex]
since we don't know what KL is, we can switch the spots and enlongate it, to become:
[tex]\frac{CB}{0.833333333} =LK[/tex]
put in the value for CB
[tex]\frac{3}{0.833333333} =LK[/tex]
and we get 3.6
The length of x of KL is...
3.6which of the following are the coordinates of point B on the directed line segment AC, such that AB is 1/5 of AC?
Answer:
The coordinates of point B is;
[tex](5,-7)[/tex]Explanation:
Given the attached image;
The coordinate of point A is;
[tex](8,-8)[/tex]The coordinate of point C is;
[tex](-7,-3)[/tex]If AB is 1/5 of AC;
[tex]\Delta x_{AB}=\frac{1}{5}(\Delta x_{AC})_{}_{}_{}_{}_{}_{}[/tex]So; let (x,y) represent the coordinates of B;
[tex]\begin{gathered} (8-x)=\frac{1}{5}(8-(-7)) \\ 8-x=\frac{1}{5}(15) \\ 8-x=3 \\ x=8-3 \\ x=5 \end{gathered}[/tex]The same applies to y coordinate;
[tex]\Delta y_{AB}=\frac{1}{5}(\Delta y_{AC})_{}[/tex]So;
[tex]\begin{gathered} (-8-y)=\frac{1}{5}(-8-(-3)) \\ -8-y=\frac{1}{5}(-8+3) \\ -8-y=\frac{1}{5}(-5) \\ -8-y=-1 \\ y=-8+1 \\ y=-7 \end{gathered}[/tex]Therefore, the coordinates of point B is;
[tex](5,-7)[/tex]If there are 78 questions on a test , how many do you have to get correctly to get an 84 % or better on the exam ?
To answer this question, we have to multiply the number of questions times 0.84 (which is 84% written as a decimal):
[tex]78\cdot0.84=65.52\approx66[/tex]Yo have to get 66 questions correctly to get an 84% or better on the exam.
Referring to the table in question 14, how would you graph the solution set representing students that do not receive a note sent home to parents?Draw points on the integers to the left of, and including, 0.Draw points on the integers to the right of, and including, 0.Draw points on the integers to the left of 0.Draw points on the integers to the right of 0.
According to the table, the statement "note sent to parents" is represented by the following inequality:
[tex]points\text{ < 0}[/tex]this can be represented as all integers less than zero. That is all integers to the left of 0.
We can conclude that the correct answer is:
Answer:Draw points on the integers to the left of 0.
