Consinder this set of expressions.3 -4. -2 + -3. -5 - 4part a: Simplfy each expression.A: 3 =B: -4 =C: -2 + -3 =D: -5 - -4=part b: graph each value on the number line. label the points.
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The absolute value of a negative number is the positive of that same number. Therefore,
Part A
[tex]\lvert3\rvert=3[/tex][tex]-\lvert4\rvert=-4[/tex][tex]\lvert-2\rvert+\lvert-3\rvert=2+3=5[/tex][tex]\lvert-5\rvert-\lvert4\rvert=5-4=1[/tex]part B
Related Questions
Find the slope of the line passing through the points (5,4) and (8,6).
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what is the solution of the system:y = 1/2x + 4-x+2y=8
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Given the following system of equations:
[tex]\begin{cases}y=\frac{1}{2}x+4 \\ -x+2y=8\end{cases}[/tex]notice that we can use the first equation and substitute it on the second equation to get the following:
[tex]-x+2(\frac{1}{2}x+4)=8[/tex]then, solving for 'x', we get:
[tex]\begin{gathered} -x+2(\frac{1}{2}x+4)=8 \\ \Rightarrow-x+x+8=8 \\ \Rightarrow8=8 \end{gathered}[/tex]since the variable x was eliminated in the process of solving for it, we have that both equations represent the same line, therefore, there are infinite solutions for the system
ñTriangle ABC is rotated to create the image A'B'C'.Which rule describes the transformation?yCH4.(x,y) - (x, y)(x, y) - (y,x)(x, y) - (-x, y)(x, y) - (y, -x)SEEBA А2345X5 4 -3 -2 -1AB5Save and ExitNextSubmitUnmark this question
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Assuming that there is an triangle ABC and it is rotated to create a new image, A'B'C', we can check each of the presented rules.
1° - (x,y) - (x,y)
In this rule, every X will stil be the same X after the change. And so will the Y. This rule does not bring any change at all.
2° - (x,y) - (y,x)
In this rule , the coordinates X will become Y, and vice versa. It will mirror the image through an x=y line. This is not a rotation!!!
3° - (x,y) - (-x,y)
In this rule, the value of each X will become -X, and Y will keep unchanged. This rule just mirror the image through Y-axis.
4° - (x,y) - (y,-x)
In this rule, every point will have the X-values becoming the Y-axis value, in the oposite sigh. And for the Y-values, it will just become the X-axis. In this rule, what we got is a clockwise rotation.
solve 67 . Find the equation and also sketch the graph.
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An object enters the solar solar system. Also the sun is at the origin of the path.
The equation of the entering object is given as,
[tex]\begin{gathered} y\text{ = }2x\text{ -2 } \\ y\text{ = 2 ( x - 1)} \end{gathered}[/tex]The equation for departing the solar system is given as,
[tex]\begin{gathered} y\text{ = -2x + 2} \\ y\text{ = -2 ( x - 1 )} \end{gathered}[/tex]The combined equation for the object is given as,
[tex]y\text{ = }\pm2(x-1)[/tex]The equation of the asymptote is given as,
[tex]y\text{ = }\pm\frac{b}{a}(\text{ x -h )+k}[/tex]Comparing the given equation with the asymptote we get,
[tex]\begin{gathered} \frac{b}{a}\text{ = 2} \\ h\text{ = 1} \\ k\text{ = 0} \end{gathered}[/tex]The distance from the sun is 0.5 au .
Therefore,
[tex]\begin{gathered} a\text{ = 0.5} \\ \frac{b}{0.5}\text{ = 2} \\ b\text{ = 2 }\times\text{ 0.5} \\ b\text{ = 1} \end{gathered}[/tex]The general equation for the hyperbola symmetric to x axis is given as,
[tex]\frac{(x-h)^2}{a^2}\text{ + }\frac{(y-k)^2}{b^2}\text{ = 1}[/tex]Substituting the given values in the equation ,
a = 0.5 , b = 1 , h = 1 and k = 0.
[tex]\begin{gathered} \frac{(x-1)^2}{0.5^2}+\frac{(y-0)^2}{1^2}\text{ = 1} \\ \frac{(x-1)^2}{0.25}+\frac{y^2}{1^2}\text{ = 1} \\ 4(x-1)^2+y^2\text{ = 1} \end{gathered}[/tex]Thus the required equation is ,
[tex]4(x-1)^2+y^2\text{ = 1}[/tex]The graph is given as:
What is the value of the least integer?
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The three(3) consecutive odd integers that add up to 9 are;
[tex]1,\text{ 3 and 5}[/tex]Hence, the least among them is 1
5.2. Gene bought a yacht for $320,000. Salestax is 6%. What is the price of the yachtincluding sales tax?OA $192,0001B$320,600OC $339,2001OD $380,000
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the distance between -2 1/2 - (-3)
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The distance between -2 1/2 - (-3)
-2 1/2 + 3
1/2
______________________
Answer
1/2
An electronics manufacturer has 180 capacitors, and the same number of capacitors is needed for eachcircuit board made. The manufacturer uses the capacitors to make 45 circuit boards.Identify and interpret the intercepts, then use the intercepts to graph the line.The y-intercept isThe x-intercept iscapacitors remaining.which means that the manufacturer (select) with capacitors.which means that when boards have been made, there are
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Answer:
The y-intercept is 180 which means that the manufacturer has started with 0 capacitors.
The x-intercept is 45, which means that when 45 boards have been made, there are 0 capacitors remaining.
Explanation:
The electronic manufacturer has 180 capacitors. It means that at the beginning when there are 0 circuit boards made, the electronic manufacturer has 180 capacitors remaining.
It means that the y-intercept is 180 which means that the manufacturer has started with 0 capacitors.
On the other hand, they need 180 capacitors to make 45 circuit boards. So, if they made 45 circuit boards, they will have 0 capacitors remaining.
It means that when y ( capacitors remaining) is 0, x (circuit boards made) is 45.
So, the x-intercept is 45, which means that when 45 boards have been made, there are 0 capacitors remaining.
So, the graph that represents the situation is:
Can someone please tell me the Mad of this question!
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Here we need to find the mean and the median of this data set, so let's do it:
Median:
Is the middle value in the data set. Since the number of data set is even number (26) , the middle value lies between the 13th and 14th data points. The average of the 13th and 14th data points will give us the median value.
Thus, the 13th and 14th values are both 6.
Therefore, median = (6+6) ÷ 2 = 6. Finally we obtain that the median is 6.
Mean: Mean is the sum of all values in the data set divided by the number of data set we have.
Mean= (0+4(3)+5(8)+6(3) +7(1)+8(5)+9(2)+10 (3))/26= (0+12+40+18+7+40+18+30)/26 = 165/26=6.346 ≈ 6.3 (nearest tenth place)
So, the final answers are mean≈6.3 and median=6.
MAD (Mean absolute deviation)
As we alright had the mean, we are going to use it:
The mean is 6.3, now let's calculate the distance between each data point and the mean:
Data Point Distance from mean
0 ||0-6.3=6.3
4 |4-6.3|=2.3 Repatly
|
Complete each proof using properties of equalityPlease do question 3
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Answer:
5x - 2y = x + 14 Given
5x = x + 14 + 2y Addition property
4x - 14 = 2y Subtraction property
2x - 7 = y Division property
y = 2x - 7 Symmetric property
Explanation:
The give expression is
5x - 2y = x + 14
To solve for y, let's use the addition and subtraction propertu of equality as follows
5x - 2y + 2y = x + 14 + 2y
5x = x + 14 + 2y
5x - x - 14 = x + 14 + 2y - x - 14
4x - 14 = 2y
Then, dividing both sides by 2 (division property), we get
4x/2 - 14/2 = 2y/2
2x - 7 = y
Therefore, y = 2x - 7 by the symmetric property.
So, the answer is:
Statement Reason
5x - 2y = x + 14 Given
5x = x + 14 + 2y Addition property
4x - 14 = 2y Subtraction property
2x - 7 = y Division property
y = 2x - 7 Symmetric property
I need help with my homework question please. I’m not good at all with word problems
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Answer:
[tex]A\text{ = \$1,498.38}[/tex]Explanation:
Here, we want to get the total amount in the account
From the given question:
P is the deposited amount which is $800
r is the interest rate which is 8% = 8/100 = 0.08
t is the number of years which is 8 years
n is the number of times interest is compounded yearly which is semi-annually which means twice (2)
Now, we need to get A
Substituting the values above, we have it that:
[tex]\begin{gathered} A\text{ = 800(1 + }\frac{0.08}{2})^{8\times2} \\ \\ A\text{ = \$1,498.38} \end{gathered}[/tex]given Given AB‾∥DC‾AB ∥ DC and BC‾∥AD‾BC ∥ AD , prove △ABC≅△CDA△ABC≅△CDA by filling out the flowchart below.
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Given:
[tex]AB||DC,BC\mleft\Vert AD\mright?[/tex]To show that,
[tex]\Delta ABC\cong\Delta CDA[/tex]First box:
[tex]AB||DC(\text{Given)}[/tex]Below box to the first box:
[tex]\angle BAC=\angle DCA(Parallel\text{ lines cut by the transversal form congruent alternate interior angles)}[/tex]Second box:
[tex]BC\Vert AD(\text{Given)}[/tex]Below box to the second box:
[tex]\angle DAC=\angle BCA(Parallel\text{ lines cut by the transversal form congruent alternate interior angles}[/tex]Third box in the second row:
[tex]AC=AC\text{ (common side)}[/tex]Last box:
So, using ASA congruence axiom,
[tex]\Delta ABC\cong\Delta CDA[/tex]cual letra es correcta\Calculate the following definite integral ∫_2 ^ 4 (2x ^ 3-7) dx, (Hint: use the fundamental theorem of calculus)
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Evaluate the value of definite integral.
[tex]\int ^4_2(2x^3-7)dx=\int ^4_22x^3dx-\int ^4_27dx[/tex][tex]\begin{gathered} \int ^4_22x^3dx-\int ^4_27dx=\lbrack\frac{2x^4}{4}\rbrack^4_2-\lbrack7x\rbrack^4_2 \\ =\frac{1}{2}\lbrack(4)^4-(2)^4\rbrack-7\lbrack4-2\rbrack \\ =\frac{1}{2}\lbrack256-16\rbrack-7\cdot2 \\ =\frac{1}{2}\cdot240-14 \\ =120-14 \\ =106 \end{gathered}[/tex]Answer: 106
Option a is correct.
What is 64,646,480,523x789
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Given: The expression-
[tex]64,646,480,523\times789[/tex]Required: To simplify the expression.
Explanation: The multiplication of two numbers can be performed by making two rows and then multiplying each numbered row-wise. The final rows are then added together for the answer.
Hence, multiplying the numbers as-
[tex]51,006,073,132,647[/tex]Final Answer: The final Answer is 51,006,073,132,647.
Tamie uses2/3of a cup of water with a pound of flour to make a paste for a sculpture she is creating.How many cups of water does she need to mix with 1 pound of flour to create the same paste?
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Given:
Amuount of cup of water used = ⅔ cup
Amount of pound of flour used = ⅙ pound
To find cups of water she needs to mix with 1 pound of flour to create the same paste, we have:
[tex]\begin{gathered} \frac{2}{3}\text{cup}=\frac{1}{6}\text{ pound} \\ \\ x\text{ cup = 1 pound} \end{gathered}[/tex]Let's solve for x:
[tex]\begin{gathered} x=\frac{\frac{2}{3}\ast1}{\frac{1}{6}} \\ \\ x=\frac{\frac{2}{3}}{\frac{1}{6}} \\ \\ x=\frac{2}{3}\div\frac{1}{6} \\ \\ x=\frac{2}{3}\ast\frac{6}{1} \\ \\ x=\frac{2\ast6}{3\ast1} \\ \\ x=\frac{12}{3} \\ \\ x=4 \end{gathered}[/tex]Therefore, she will need to mix 4 cups of water to with 1 pound of floor to create the same paste
determine whether each description of the summary statistic applies to the two data sets shown above. select yes or no for each summary statistic.
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The first statement is NO
The second statement is YES because exercise has more than one trend this makes the first statement false and the second true
the third statement are YES because contains extreme outliers and skewed
Find the root rounded to three significant digits. 77,975
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we have that
cubic root of 77,975=42.722
but remember that
rounded to three significant digits
so
42.7
The tips Karen receives for some of her sales are shown in the table. Which graph best models the data in the table? Items Sold 5 10 15 20 25 Tips Collected (5) 9 25 26 46 51 A C 30 30 20 10 10 5 10 15 20 3 10 3 404 + 5 10 15 20 25 30 35 40 45 B D 90 90 50 5.5.6.3.3.3 50 40 20 19 $
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To determine which graph best models the data without any calculation you have to look at the relationship between the dots and the line to see which one fits better.
The dots represent the observed data, the values that apear in the table.
The line that best fits the observed data will be that one that is closes to the dots. This means that the best of fit line will be the one for which that passes through the middle of all points, and pass through most of them.
The line in graph A passes through the miffle of all points and has two of them over it, the distance between the dots and the lines seem to be the shortest in this graph, so this one is the one that models the data better.
Consider the expression (-3)^-3 divided by 1/-6^2What three choices are equivalent to the expression given
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We can interpret the question as follows:
[tex]\frac{(-3)^{-3}}{\frac{1}{-6^2}}[/tex]Then, we have that:
[tex]\frac{(-3)^{-3}}{\frac{1}{-6^2}}=\frac{\frac{1}{(-3)\cdot(-3)\cdot(-3)}}{-\frac{1}{6^2}}=\frac{\frac{1}{-27}}{-\frac{1}{6^2}}=\frac{-\frac{1}{27}}{-\frac{1}{6^2}}=\frac{\frac{1}{27}}{\frac{1}{6^2}}=\frac{6^2}{27}=\frac{36}{27}[/tex]For the answer above, we use the next exponents' rules:
[tex]a^{-1}=\frac{1}{a},a^{-n}=\frac{1}{a^n}[/tex]We can simplify the fraction as follows:
1. The factors for 36 are 2²* 3².
2. The factors for 27 are 3³.
Then, we have:
[tex]\frac{2^2\cdot3^2}{3^3}=\frac{2^2\cdot3^2}{3^2\cdot3}=\frac{3^2}{3^2}\cdot\frac{2^2}{3}=1\cdot\frac{4}{3}=\frac{4}{3}[/tex]Then, the simplified expression for the fraction is equal to 4/3.
A line is perpendicular to the line given by the equation 9y = x + 13. What is theslope of the perpendicular line?
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the slope of the perpendicular line is -9
Explanation:Given equation: 9y = x + 13
Rewritting in the form of slope-intercept form: y = mx + c
We divide both sides by the coefficient of y:
9y/9 = x/9+ 13/9
y = x/9 + 13/9
where m = 1/9
c = 13/9
For a line to be perpendicular to another line, the slope of one will be the negative reciprocal of the second slope
Since the slope of the first line = 1/9
reciprocal of 1/9 = 9/1 = 9
negative reciprocal = -9
The slope of the second is the negative reciprocal of the 1st line
Hence, the slope of the second (slope of the perpendicular line) is -9
find the measure of Arc vrt
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The first step to calculate the measure of the arc is to determine the angle VR. To do that we need to understand that the angles UV, VQ and QR are suplementary, which means that their sum is equal to 180 degrees. So we have:
[tex]\begin{gathered} \measuredangle UV+\measuredangle VQ+\measuredangle QR=180 \\ 54+95+\measuredangle QR=180 \\ 149+\measuredangle QR=180 \\ \measuredangle QR=180-149 \\ \measuredangle QR=31 \end{gathered}[/tex]The angle QR is equal to 31 degrees, with this we can find the angle VR, because it is the sum of VQ and QR.
[tex]\begin{gathered} \measuredangle VR=\measuredangle VQ+\measuredangle QR \\ \measuredangle VR=95+31=126 \end{gathered}[/tex]The arc measure is equal to 126 degrees.
The radius of a circle is 16 miles. What is the circle's circumference?r = 16 miUse 3.14 for π.
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Given:
a.) The radius of a circle is 16 miles.
b.) Use 3.14 for π
For us to be able to determine the circumference of the circle using the radius, we will be using the following formula:
[tex]\text{ Circumference = 2\pi r}[/tex]Where,
r = radius of the circle
We get,
[tex]\text{ Circumference = 2\lparen3.14\rparen\lparen16\rparen = 100.48 miles}[/tex]Therefore, the circumference of the circle is 100.48 miles.
Explanation:
The circumference of a circle is equal to
π, which is a number ≈3.14, multiplied by the diameter of the circle.
Therefore, C=πd.
We know that the circumference, C, is 16π, so we can say that:
16π=πd
We can divide both sides by π to see that 16=d.
We now know that the diameter of the circle is 16.
We also know that the diameter has twice the length of the radius.
In equation form: 2r=d
2r=16
r=8
Note that since 2r=d, the equation C=2πr holds and can be used in place of C=πd.
Josh calculated the mean absolute deviation of the points he earned throughout the year in four of his classes: science, math, Spanish, and art.science: MAD of 1.14math: MAD of 1.6Spanish: MAD of 1.2art: MAD of 1.93In which class were his scores the closest together?A: scienceB: artC: mathD: Spanish
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Given the mean absolute deviation in four classes
To Determine: In which class were the scores the closest together
Solution:
Explain Mean Absolute Deviation: The Mean Absolute Deviation (MAD) of a set of data is the average distance between each data value and the mean. The mean absolute deviation can also be defined as the "average" of the "positive distances" of each point from the mean.
The larger the MAD, the greater variability there is in the data (the data is more spread out).
The lower the MAD, the lesser variability there is in the data (the data is less spread out). The MAD helps determine whether the set's mean is a useful indicator of the values within the set. The larger the MAD, the less relevant is the mean as an indicator of the values within the set.
From the given question, arranging the MAD in ascending order, we
[tex]\begin{gathered} 1.14,1.2,1.6,1.93 \\ \text{Science, Spanish, Math, and Art} \end{gathered}[/tex]The class with the lowest value of MAD is the class where the scores are the closest together.
Science has the lowest value of MAD. Hence, the class where the scores are closest together is SCIENCE
A tv has an orginal price for $399.Enter the new price after the given percent of chnage.30% increasethe new price is?
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Original price =399
Percentage increase = 30%
Multiply the price by the percentage increase in decimal form ( divided by 100)
399 x (30/100) = 119.7
Add the increase to the original price:
399+119.7 = $518.7
Find the future value for the annuity due with the given rate.Payments of $700 for 9 years at 0.31% compounded annuallyThe future value of the annuity due is $0.(Do not round until the final answer. Then round to the nearest cent as needed.)
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Future value of annuity due is calculated using
[tex]\text{FVA due = }\frac{P\text{ }\times\lbrack(1+r)^n\text{ - 1\rbrack }\times\text{ ( 1 + r)}}{r}[/tex]From the question, we are given
[tex]\begin{gathered} P\text{ =\$700} \\ r\text{ = 0.31\%} \\ n\text{ = 9 years} \end{gathered}[/tex]Hence,
Future Vlaue of annuity due will be
[tex]undefined[/tex]which is a unit rateA. 47 cents for two pensB. 20 gallons for 2 hours C. 15 hours for 3 months D. 18 miles driven in a week
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When rate is expressed as a quantity of 1, is a unit rate. Let's look at the options, A, B and C are expressed per 2 or 3, the only option that is expressed as a quantity of 1 is the option D, that is expressed per week.
The right answer is D. 18 miles driven in a week
I have a question ?
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What is the place value of the underline digit 92007642188
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The given number is
[tex]92,007,642,188[/tex]This number represents billions, where the first digit 2 represents billions and the number 9 represents tens of billions.
Therefore, the right answer is billions.
May I please get help with this. I have tried multiple times but still could not get the right answer
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Answer:
4/1
Explanation:
To calculate the scale factor of the model to the bridge, we need to divide the dimensions of the bridge by the dimensions of the model, so
24 / 6 = 4
32 / 8 = 4
36 / 9 = 4
Therefore, the scale factor is 4. Written as a fraction is 4/1.
So, the answer is 4/1
Calculate the area of the shaded sector given the central angle.
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Hence, the area of the sector is 12.5pie inches squared.