Answers
Answer:
Step 6: Subtraction Property of =
Step-by-step explanation:
Related Questions
Find the domain and graph, indicate the limits in the graph.
Answers
The domain of a function is the set of all x-values the function can take.
Since we have a radical symbol, (x² - 1) must not be equal to a negative number because it will make the function undefined.
For the function (x² - 1), the value of x must be greater than 1 or less than -1 in order for the function to be defined.
[tex]\begin{gathered} x^2-1>0 \\ x^2>1 \\ \sqrt{x^2}>\sqrt{1} \\ x>1 \\ x<-1 \end{gathered}[/tex]If for instance, the value of x is 0.5, the value of (x² - 1) will be -0.75 and the square root of a negative number is undefined. Therefore, we must not have an x-value that is less than 1 or greater than -1.
Hence, the domain of this function in interval notation is:
[tex](-\infty,-1]\cup[1,\infty)[/tex]In set notation, it is {x|x ≤ -1, x ≥ 1}.
In order to graph the function, let's assume some values of x that are found in the domain.
For the domain, x ≤ -1, we can assume x = -1, x = -2, and x = -3.
At x = -1, y = 1.
[tex]\begin{gathered} y=\sqrt{(-1)^2-1}-(-1) \\ y=\sqrt{1-1}+1 \\ y=\sqrt{0}+1 \\ y=1 \end{gathered}[/tex]At x = -2, y = 3.73
[tex]\begin{gathered} y=\sqrt{(-2)^2-1}-(-2) \\ y=\sqrt{4-1}+2 \\ y=\sqrt{3}+2 \\ y=3.73 \end{gathered}[/tex]At x = -3, y = 5.83.
[tex]\begin{gathered} y=\sqrt{(-3)^2-1}-(-3) \\ y=\sqrt{9-1}+3 \\ y=\sqrt{8}+3 \\ y=5.83 \end{gathered}[/tex]For the domain x ≥ 1, we can assume x = 1, x = 2, and x = 3.
At x = 1, y = -1.
[tex]\begin{gathered} y=\sqrt{1^2-1}-1 \\ y=\sqrt{1-1}-1 \\ y=\sqrt{0}-1 \\ y=-1 \end{gathered}[/tex]At x = 2, y = -0.268
[tex]\begin{gathered} y=\sqrt{2^2-1}-2 \\ y=\sqrt{4-1}-2 \\ y=\sqrt{3}-2 \\ y=-0.268 \end{gathered}[/tex]At x = 3, y = -0.172.
[tex]\begin{gathered} y=\sqrt{3^2-1}-3 \\ y=\sqrt{9-1}-3 \\ y=\sqrt{8}-3 \\ y=-0.172 \end{gathered}[/tex]Let's plot the 6 coordinates. The graph of this function, with limits indicated, is shown below.
Use point-slope form to write the equation of a line that passes through the point (13,-8) with slope 3/2
Answers
Answer: y=3/2x-27.5
Step-by-step explanation:
you use y=3/2x+b
So plug (13,-8) in the equation so,
-8=3/2(13)+b
-8=39/2+b
-27.5=b
So y=3/2x-27.5
Pls give brainliest
Function A is a linear function whose graph contains the points (0, 2) and (8, 0). Function B is represented by the equation y = 4x - 2. Which statement is true? The rate of change for Function A is greater than the rate of change for Function B. The rate of change for Function A is equal to the rate of change for Function B. The initial value for Function A is greater than the initial value of Function B. The initial value of Function A is equal to the initial value of Function B.
Answers
The statement which is true about Function A and Function B is that: C. The initial value for Function A is greater than the initial value of Function B.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope A = (0 - 2)/8 - 0)
Slope A = -2/8
Slope A = -1/4 or -0.25.
Note: The slope of any straight line also represents its rate of change.
Rate of change of Function A = -0.25.
Rate of change of Function B = 4.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (0, 2), we have:
y - 2 = -1/4(x - 0)
y - 2 = -x/4
y = -x/4 + 2.
Therefore, the intercept (initial value) of Function A is greater than the intercept (initial value) of Function B.
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can you please solve this practice problem for me I really need assistance.
Answers
The slope of a straight line is given by the following expression:
[tex]m=\frac{change\text{ in y }}{change\text{ in x}}=\frac{y_1-y_2}{x_1-x_2}[/tex]By looking at the graph we have two locate two pairs of coordinates: Coordinate 1 (2,0) Coordinate 2 (-4,0).
Now we replace on the slope formula, having:
[tex]\begin{gathered} m=\frac{0-0}{2-(-4)} \\ m=0 \end{gathered}[/tex]Pair of coordinates, coordinate 1 (2,0) coordinate 2 (3,2)
[tex]m=\frac{0-2}{2-3}=2[/tex]How many different 3-digit numbers are possible using only the digits 1,2,6,7,8 ? How many different 3-digit numbers are possible using only the digits 1,2,6,7,8, if repetition of digits is not allowed?
Answers
The number of three digit number formed are-
Repetition allowed = 125Repetition not allowed = 60What is defined as the combination?A combination is an algebraic technique for determining the number of distinct arrangements in a set of items in which the sequence of the selection is irrelevant. You can choose the items in either order in combinations. Permutations and combinations are often confused.For the given question;
The three digit number is to be formed.
The digits are given as- 1,2,6,7,8
Case 1: Repetition allowed
The number of combination will be;
= 5×5×5
= 125
Thus, the number of three digit number formed with repetition is 125.
Case 2: Repetition not allowed
The number of combination will be;
= 5×4×3
= 60
Thus, the number of three digit number formed with without repetition is 125.
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A quality control inspector has drawn a sample of 19 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that exactly 4 bulbs from the sample are defective? Round your answer to four decimal places.
Answers
The probability that exactly 4 bulbs from the sample are defective is; 0.2812
How to solve Binomial Probability Distribution problems?
The formula for binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
where;
p = probability of success
n = number of trials, or the sample size
x = the number of successes in the probability
Now, we are given that;
Sample size; n = 19
Number of successes in the probability; x = 4
probability of success; p = 20% = 0.2
Thus;
P(X = 4) = 19C4 * 0.2^(4) * (1 - 0.2)^(19 - 4)
P(X = 4) = 0.2182
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Stacey has a part-time job. She earns $12 an hour. She wants to buy a new smartphone costing $174. How many hours does she need to work to earn enough to buy it?
Answers
Answer:
Step-by-step explanation:
174/12= 14.5 hours of work to earn enough to buy the smartphone.
12x14.5 = 174
the answer could be 14.5 for the minimum amount of time needed but if it asks for full hours then 15 hours.
△TVX is equilateral. Complete the proof that △TUV≅△XWV.
Answers
iven:: △TVX is equilateral.
To prove: △TUV≅△XWV
The given proof is completed and attached below:
he proogf is complete.
What is the value of n?
-6.5(n-5)=18.2
Answers
Answer:
n=2.2
Step-by-step explanation:
1-Combine- [-6.5n(n-5)=18.2
-13(n-5)/2=18.2
2-Distribute-13n-5)/2=18.2
-13n+65/2=18.2
3-Multiply like terms-
-13n+65/2=18.2 [tex]2.-13n+65/2=18.2*2[/tex]
4-Multiply all the numbers=[tex]-13n+65=36.4[/tex]
5-Subtract 65 from both sides- -13n+65-65=36.4-65
6-Simplify= -13n=-28.6
7- Divide both sides by the factor e.g= -13n
8- Simplify= -13n/-13n=-28.6/-13n
QA Answer\Solution amounts to= [tex]2.2[/tex]
The measure of an angle is 70.9°. What is the measure of its supplementary angle?
Answers
Answer:
109.1 and 70.9 are supplementary angles
Step-by-step explanation:
The measure of an angle is 70.9°. What is the measure of its supplementary angle?
Supplementary angles are two angles that sum together to 180 degrees:
180 - 70.9 = 109.1 degrees
Solve similar triangles (advanced). khan academy. solve for x
Answers
Applying the similarity theorem, the value of x is calculated as: x = 3.5.
How to Apply the Similarity Theorem?When two triangles are similar to each other, based on the similarity theorem, the ratio of their corresponding side lengths will be equal because they are proportional to each other.
In the image given, triangle ABC is similar to triangle ADE. Therefore:
AB/AD = BC/DE = AC/AE
Given the following:
AB = 4 units
AD = 4 + 3 = 7 units
BC = 2 units
DE = x
Plug in the values into AB/AD = BC/DE:
4/7 = 2/x
Cross multiply
4(x) = 2(7)
4x = 14
Divide both sides by 4
4x/4 = 14/4 [division property of equality]
x = 3.5
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When looking at a set of ordered pairs. To determine if it makes a function, you must look at the _ _ _
To see if you have any repeated numbers
Answers
Answer: x values make sure they don't repeat if they do its not a function.
randy wants to use the distributive property to rewrite 56-12 which expression can be used
Answers
Consider the given expression,
[tex]56-21[/tex]The expression can be transformed as,
[tex](7\times8)-(7\times3)[/tex]Since 7 is a common factor, take it as common,
[tex]7(8-3)[/tex]Thus, the expression is obtained that,
[tex]56-21=7(8-3)[/tex]Therefore, option (B) is the correct choice.
In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or
spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below.
Answers
The probability of randomly selecting a student who spent the money, given that the student was given four quarters is 0.7. The probability of randomly selecting a student who kept the money is 0.3.
Probability1. Probability of student who spent the money
Probability = 28 / (28 +12)
Probability = 28 / 40
Probability = 0.7
2. Probability of student who kept the money,
Probability = 12 / (28 +12)
Probability = 12 / 40
Probability = 0.3
3. The preceding results suggest : d) A student given four quarters is more likely to have spent the money.
Therefore the probability is 0.7 and 0.3.
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Can anyone help me with this please ??
Answers
The approximate size of Jorge's wrist is 8.5 inches.
What is defined by the term fraction?Fractions represent parts of the whole or group of objects. A fraction is made up of two parts. The number at the start of the line is referred to as the numerator. It specifies the number of equal parts of the whole as well as collection that are taken. The denominator is the number just below line. It displays the total amount of equal parts into which the whole is divided or the total number of identical objects in a collection.For the given question;
For average adults, the size of the wrist is 1/4 of the size of the waist.
The waist size of the Jorge is 34 inches.
Thus, to calculate the wrist size of Jorge, simply multiply the fraction 1/4 with 34.
= 34 × 1/4
= 8.5
Therefore, the wrist size of the Jorge is found as 8.5 inches.
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Consider the equation x 2+ 1 = 7-x
Answers
Since the given equation is
[tex]x^2+1=7-x[/tex]Since (-3, 2) is its solution which means the graphs of each side are intersected at point (-3, 2)
To verify the solution, substitute x by -3 on each side
If the two sides are equal, then the point is the solution to it
[tex]\begin{gathered} L\mathrm{}H\mathrm{}S=x^2+1 \\ x=-3 \\ L\mathrm{}H\mathrm{}S=(-3)^2+1 \\ L\mathrm{}H\mathrm{}S=9+1 \\ L\mathrm{}H\mathrm{}S=10 \end{gathered}[/tex]Let us do the same with the right-hand side
[tex]\begin{gathered} R\mathrm{}H\mathrm{}S=7-x \\ x=-3 \\ R\mathrm{}H\mathrm{}S=7-(-3) \\ R\mathrm{}H\mathrm{}S=7+3 \\ R\mathrm{}H\mathrm{}S=10 \end{gathered}[/tex]L.H.S = R.H.S = 10
This means the value of y = 10, not 2
Then (-3, 2) is not a solution of the given equation
Now we will draw each side, then find the point of intersection between them
From the graph, the solutions are the intersection points between the line and the graph
The two points are (-3, 10) and (2, 5)
Samuel was preparing for the triathlon. He did 3 activities every morning: Ran for 30 minutes, covering 4.5 miles. Swam for 20 minutes, covering 2/3 mi. biked for 45 min, covering 9 miles. What was Samuel's average speed during his morning training?
PLEASE HELP!!!
Answers
If Samuel ran for 30 minutes covering 4.5 miles, swim for 20 minutes covering 2/3 miles and biked for 45 min covering 9 miles, then the Samuel's average speed during his morning training is 0.15 miles per minute
The Morning activities of Samuel
He ran for 30 minutes, covering 4.5 miles,
He swim for 20 minutes covering 2/3 miles
He biked for 45 minutes covering 9 miles
Total distance travelled = 4.5+ 2/3 +9
= 14.17 miles
Total time taken = 30+20+45
= 95 minutes
The average speed = Total distance / Total time taken
= 14.17/95
= 0.15 miles per minutes
Hence, if Samuel ran for 30 minutes covering 4.5 miles, swim for 20 minutes covering 2/3 miles and biked for 45 min covering 9 miles, then the Samuel's average speed during his morning training is 0.15 miles per minute
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The
length of a rectangle is 7 inches longer than it is wide. If the perimeter is 62 inches, what are the dimensions of the rectangle?
The width, or shorter side is
inches.
The length, or longer side is
inches.
Answers
2(x) + 2(x+7)= 62
4x+14=62
4x=58
x=14.5
width= 14.5
length=21.5
All employees of a company work less than 40 hours. Which inequality describes the situation?
Answers
The inequality is represented by x<40
What is inequality?An inequality compares two values and indicates whether one is lower, higher, or just not equal to the other.
A B declares that a B is not equal.
When a and b are equal, an is smaller than b.
If a > b, then an is bigger than b.
The phrase "a b" denotes that an is less than or equal to b.
When a and b are equal, it is said that an exceeds b.
Let the employees of the company be denoted by x.
So, as given the employees work less than 40 hours.
Thus the inequality can be represented as x< 40.
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11. THINKSMARTER Yvonne wrote the numbers sixteen thousand,
nine hundred eighteen and 64,704 on the board. Which of the
numbers has a greater value in the thousands place?
Name
Answers
The number that has a greater value in the thousands place is 16,918.
What is Place Value?A number's place value is the worth of each digit. Depending on its location, such as ones, tens, hundreds, and so forth, each digit in a number has a different value. The position of the digit in the number determines whether two similar digits in the same number have different values.Given numbers are sixteen thousand, nine hundred eighteen,(16,918), and 64,704 on the board.
The thousand places in both numbers contain the digits 6 and 4.
The place value of 6 in 16,918 is expressed as 6 thousand or 6,000.
The place value of 4 in 64,704 is expressed as 4 thousand or 4,000.
As 6000 > 4000, the number that has a greater value in the thousands place is 16,918.
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Mikah invented and patented a new product which sells in local department stores. This is an example of _____ income.
a.
capital gains
b.
earned
c.
hourly
d.
passive
Answers
Since Mikah invented and patented a new product which sells in local department stores, this is an example of: D. passive income.
What is an income?An income simply refers to an amount of money that an individual or business organization (company or firm) earn in return for the sales of its product or for providing a service, to its customers and consumers.
The types of income.In Economics, there are three (3) main types of income and these include the following:
Portfolio incomeEarned incomePassive incomeIn Business management, a passive income generally requires minimal amount of labor from an individual or business organization (company or firm) and as such it is typically earned from rental products or patented products, which is usually on a regular basis.
In this context, we can reasonably infer and logically deduce that Micah's income is an example of passive income.
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A foreman for an injection-molding firm admits that on 29% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 5% to 24%. If a molding is randomly selected from the early morning run of a random day, what is the probability that it is defective?
Answers
When a molding is randomly selected from the early morning run of a random day, what is the probability that it is defective is 0.1051
How to calculate the probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Probabilities can be written as percentages with values between 0 and 1.
From the information, the foreman for an injection-molding firm admits that on 29% of his shifts, he forgets to shut off the injection machine on his line.
The probability that the selected molding is defective will be:
= P(forgets to shut off and defective molding) + P(not fingers to shut off)
= 29% × 24% + (1 - 29%) × 5%
= 0.29 × 0.24 + 0.71 × 0.05
= 0.0696 + 0.0355
= 0.1051
The probability is 0.1051.
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y=-(1/3)x+1 graph it
Answers
Step-by-step explanation:
plug in y=(⅓)x+1 to a graphing calculator and it gives you the answer
One number is 9 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 1068, find the numbers.
The three numbers are
(Use a comma to separate answers as needed.)
Answers
First number (x) = 88
Second number (9x) = 792
Third number (x + 100) = 188
Let x be the first number, so accordingly the second number will be 9 times x i.e., 9x and the third number will be 100 more than the first number i.e., x + 100
Now, put all the numbers into an equation of finding their sum,
First no. + Second no. + Third no. = SUM, i.e.,
x + 9x + (x+100) = 1068
Simplify,
x + 9x + (x+100) = 1068
x + 9x + x +100 = 1068
11x + 100 = 1068
11x = 1068 - 100
11x = 968
x = 968/11
First number (x) = 88
Second number (9x) = 792
Third number (x + 100) = 188
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SOMEONE PLEASE HELP!!
Answers
First angle is 3x° = 3 × 40° = 120°
and, Second Angle is = (x + 20°) = 40° + 20° = 60°
Given,
Lines m and n are parallel (m ll n)
Adjacent Interior Angles are given i.e.,
3x and (x + 20°)
and, To find the value of x
Now, According to the question:
m ll n
So, The two lines are parallel and complementary to the
3x° + (x + 20°) = 180° (Adjacent Interior Angles)
4x°+ 20° = 180°
4x° = 180° - 20°
4x° = 160°
x = 40°
Hence, First angle is 3x° = 3 × 40° = 120°
and, Second Angle is = (x + 20°) = 40° + 20° = 60°
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Which equation applies the associative property of multiplication?
Responses
(−14−53)−35=−14−(53−35)
, open parenthesis fraction negative 1 over 4 end fraction minus fraction 5 over 3 end fraction close parenthesis minus fraction 3 over 5 end fraction equals fraction negative 1 over 4 end fraction minus open parenthesis fraction 5 over 3 end fraction minus fraction 3 over 5 end fraction close parenthesis,
−512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92)
, fraction negative 5 over 12 end fraction times open parenthesis fraction 6 over 5 end fraction times fraction 1 over 3 end fraction close parenthesis times fraction 9 over 2 end fraction equals open parenthesis fraction negative 5 over 12 end fraction times fraction 6 over 5 end fraction close parenthesis times open parenthesis fraction 1 over 3 end fraction times fraction 9 over 2 end fraction close parenthesis,
−67⋅811⋅13=811⋅(−67)⋅13
, fraction negative 6 over 7 end fraction times fraction 8 over 11 end fraction times fraction 1 over 3 end fraction equals fraction 8 over 11 end fraction times open parenthesis fraction negative 6 over 7 end fraction close parenthesis times fraction 1 over 3 end fraction,
(−78⋅25)+(−78⋅35)=−78⋅(25+35)
Answers
The equation applies the associative property of multiplication is −512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92).
What is associative property of multiplication?The associative property of multiplication can be described as the law that is been used in making calculation that involves using the multiplication operation.
When using the associative property of multiplication law, we will need to associate, which means we will join together the given terms which can be done in different ways irrespective of how it is been grouped together and this can be seen in the option B , because the result of the multiplication using the distributive property gives us (−512⋅65)⋅(13⋅92).
Therefore, option B is correct.
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Suppose that the relation S is defined as follows.
S = {(3, 1), (9, d), (1, d)}
Give the domain and range of S.
Write your answers using set notation.
domain =
range =
Answers
Answer:
Domain = {1, 3, 9}Range = {1, d}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
the net decimal equivalent is found by multiplying the complement of the discounts together. what is the net decimal equivalent when a series of discount of 48% , 27%, and 12% is applied?
Answers
The net decimal equivalent is 0.48, 0.27, and 0.12 when a series of discounts of 48%, 27%, and 12% are applied respectively.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
By multiplying the complement of the discounts collectively, one can determine the net decimal equivalent which is given in the question.
To determine the net decimal equivalent when a series of discounts of 48%, 27%, and 12% is applied.
The value of compliment (%) = 1/100
As per the given condition, the required discounts would be as:
discount of 48% = 48/100 = 0.48
discount of 27% = 27/100 = 0.27
discount of 12% = 12/100 = 0.12
Therefore, the net decimal equivalent is 0.48, 0.27, and 0.12 when a series of discounts of 48%, 27%, and 12% are applied respectively.
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Range of a data set
Alan is recording the percentages he earned an each quiz in his math dass. Here are this results for the last 7 quizzes.
79, 91, 76, 87, 93, 79,94
Find the range of the data set.
5
Answers
The range of the given data set is 18.
What is range in statistics?
The difference between the highest and lowest values for a given data collection is the range in statistics. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations. In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations, which is:
Range = Highest Value – Lowest Value = Highest observation – Lowest observation = Maximum value – Minimum Value
Given, the data set is 79, 91, 76, 87, 93, 79,94.
The data in ascending order is : 76, 79, 79, 87, 91, 93, 94.
From the data set, highest value = 94, lowest value = 76
Thus, Range = Highest value - Lowest value = 94 - 76 = 18
Therefore, range of the given data set is 18.
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There are 4 ounces of
lime juice in 52 ounces
of punch. How much
lime juice is needed for
130 ounces of punch?
Answers
There are 4 ounces of lime juice in 52 ounces of punch, let represent the number of ounces of lime juice in 130 ounces of punch, there are 1690 ounces of the lime juice in 130 ounces of punch.
What do you mean by ounces?A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which is almost unmodified.
'Ounce' is also used in the following other contexts:
A unit of the force is the ounce-force (see below).
A unit of the volume is the fluid ounce.
A multitude of distinct ounces measuring mass or volume have been employed historically by various trades at various times and in various countries.
Since,
Ounces of the lime juice=4
Ounces of the punch=52
Ounce needed for 1 punch=52÷4=13
Ounces needed for 130 ounces of the punch=13×130=1690
Therefore, the ounces of the lime juice needed for 130 ounces of punch=1690.
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