Use the horizontal number line to find the additive inverse of 5. Which statements are true? Check all that apply.
Answers
The statements which are true are
–5 and 5 are a zero pair
–5 and 5 are opposites
and –5 + 5 = 0
Additive inverseFrom the question, we are to find the additive inverse of 5
The additive inverse of a number is a number which on adding with the original number results in zero.
Let the additive inverse of 5 be x
∴ 5 + x = 0
x = 0 - 5
x = -5
The additive inverse of 5 is -5
Thus, we can conclude that
–5 and 5 are a zero pair
–5 and 5 are opposites
and –5 + 5 = 0
Hence, the statements which are true are
–5 and 5 are a zero pair
–5 and 5 are opposites
and –5 + 5 = 0
Here is the complete question:
Use the horizontal number line to find the additive inverse of 5. Which statements are true?
–5 and 5 are a zero pair.
–5 and 5 are equal.
–5 and 5 are opposites.
–5 + 5 = 0
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Related Questions
Which response best identifies why a surgical mask should not be used as a respiratory to protect against the inhalation of biohazards or bioaerosols
Answers
The nurse should dispose of the mask. This exists because the safety mechanisms of the mask may be compromised and therefore pose a risk to the patient that exists undergoing surgery.
What is a surgical mask used for?
A surgical mask exists primarily utilized to protect patients and healthcare employees from people who may contain a respiratory infection or to protect sterilized or disinfected medical devices and supplies. The nurse should dispose of the mask. This exists because the safety mechanisms of the mask may be compromised and therefore pose a risk to the patient that exists undergoing surgery. It exists still suggested that medical personnel err on the side of warning when it arrives to the managing of equipment, whether it be a significant piece of equipment or even a small one like a surgical mask.
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Is my answer on the photo correct?
Answers
Answer:
yes
Step-by-step explanation:
select the slope of the line that joins the pair of points. a. (9, 10) and (7, 2) 1 of 5. 4 b. (-8, -11) and (-1, -5) 2 of 5. select choice c. (5, -6) and (2, 3) 3 of 5. select choice d. (6, 3) and (5, -1) 4 of 5. select choice e. (4, 7) and (6, 2) 5 of 5. select choice
Answers
The required slopes are:
(a) slope = 4
(b) slope = 6/7
(c) slope = -3
(d) slope = 4
(e) slope = -5/2
We know that,
When a line passing through (x₁, y₁) and (x₂, y₂)
Then the slope of the line be,
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Using this formula, calculate the slope for each given points
a. (9, 10) and (7, 2)
⇒ slope (m) = (2 - 10) / (7 - 9)
= -8/-2 = 4
So, the slope is 4.
b. (-8, -11) and (-1, -5)
⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))
= 6/7
So, the slope is 6/7.
c. (5, -6) and (2, 3)
⇒ slope (m) = (3 - (-6)) / (2 - 5)
= 9/-3
= -3
So, the slope is -3.
d. (6, 3) and (5, -1)
⇒ slope (m) = (-1 - 3) / (5 - 6)
= -4/-1
= 4
So, the slope is 4.
e. (4, 7) and (6, 2)
⇒ slope (m) = (2 - 7) / (6 - 4)
= -5/2
So, the slope is -5/2.
Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.
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Find the circumcenter of the triangle ABC.
A(5,3), B( -6, -7), C(5.-7).
The circumcenter is
(Type an ordered pair.)
Answers
(-0.5,-2)
Copy the picture and put a dot on where i put it
Answers
Step-by-step explanation:
This is the best I could do. Good luck!
what is the volume of the prism
Answers
Answer:
8/15 cm
Step-by-step explanation:
Volume = length x width x height
Volume = 4/5 cm x 1/5 cm x 10/3 cm
Volume = 4/25 cm x 10/3 cm
Volume = 40/75 cm = 8/15 cm
Brainliest, please :)
Answer:
\(\frac{8}{15}\)
Step-by-step explanation:
Volume of prism = \(l\) · \(w\) · \(h\)
which means
\(\frac{10}{3} *\frac{4}{5} *\frac{1}{5}\)
which is \(\frac{8}{15}\) by using cross simplify
Hope this helps ;D
source sum of squares degrees of freedom mean square f ratio regression 8422.3 2 ssr/(p-1) msr/mse error 1261.0 44 sse/(n-p)
Answers
It appears that the regression model has explained a significant amount of variation in the data, as indicated by the relatively large sum of squares for regression (8422.3) compared to the sum of squares for error (1261.0). The F ratio can be calculated by dividing the mean square for regression (MSR) by the mean square for error (MSE).
Based on the information provided, it seems to be a summary table for an analysis of variance (ANOVA) for a regression model. Here's a breakdown of the terms:
Source: Refers to the different sources of variation in the model.
Sum of Squares (SS): Represents the sum of squared deviations from the mean.
Degrees of Freedom (df): Represents the number of independent pieces of information available for estimating the parameters.
Mean Square (MS): Represents the sum of squares divided by the degrees of freedom.
F Ratio: Represents the ratio of the mean squares from different sources of variation.
In the given summary table:
Regression: Represents the source of variation due to the regression model.
Sum of Squares (SSR): 8422.3
Degrees of Freedom (df): 2
Mean Square (MSR): SSR / (p - 1), where p represents the number of predictor variables.
Error: Represents the source of variation due to the residual error.
Sum of Squares (SSE): 1261.0
Degrees of Freedom (df): 44
Mean Square (MSE): SSE / (n - p), where n represents the total sample size and p represents the number of predictor variables.
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If f(x) = 5x - 12, find f(x) when x= - 12
Plz answer
Answers
Answer:
-72
Step-by-step explanation:
first replace x with -12 so 5(-12)-12
then simplify which makes it -60-12
finally solve that which gives you -72
hope this helps :)
which of the following statements about linear programming models is true? multiple choice question. the algebraic formulation of a linear programming model is always preferred over the spreadsheet model. the spreadsheet model of a linear programming model is always preferred over the algebraic model. the algebraic and spreadsheet formulations of a linear programming model both have advantages.
Answers
The statement "the algebraic and spreadsheet formulations of a linear programming model both have advantages" is true. (Option 3)
Both algebraic and spreadsheet formulations have their own advantages and disadvantages. Algebraic models allow for a more formal mathematical representation of the problem, making it easier to see relationships between variables and constraints. They also allow for the use of powerful optimization solvers to quickly find optimal solutions.
On the other hand, spreadsheet models allow for more intuitive modeling and visualization of the problem. They also allow for quick and easy scenario analysis and sensitivity testing. Furthermore, they are more accessible to a wider range of users who may not have the technical background to create and solve complex algebraic models.
Therefore, the choice between the two formulations depends on the specific problem and the preferences and expertise of the modeler.
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Complete Question:
which of the following statements about linear programming models is true? multiple choice question.
the algebraic formulation of a linear programming model is always preferred over the spreadsheet model. the spreadsheet model of a linear programming model is always preferred over the algebraic model. the algebraic and spreadsheet formulations of a linear programming model both have advantages.select all the correct answers. which three pairs of side lengths are possible measurements for the triangle?
Answers
The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.
Since we know that,
Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The formula for a 30-60-90 triangle is this:
1) Side opposite to 30 will be value a.
2) Side opposite to 60 will be value a√3
3) Hypotenuse will be 2a.
AB is opposite of the angle with 30 degree measurement.
BC is opposite of the angle with 60 degree measurement.
The sides of an isosceles right triangle are in the ratio,
1:1:√2
where √2 is the hypotenuse.
For the example, BC = 2√2, then AC = 2√2 x √2 = 4.
Therefore, the three pairs are;
1. (AB = 6, BC = 6)
5. (AB = 4, AC = 4√2)
6.(BC = 2√2, AC = 4).
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The complete question is attached below:
In the past, the output of a process had a mean of 2.050 and a standard deviation of 0.020 liters. If a current sample of output had these values {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, would that indicate that the process is still "in order" (as opposed to being "out of order")? What if the sample was {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}?
Answers
For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."
To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.
For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:
Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):
Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.
Compare the sample mean to the known process mean (2.050):
The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."
Calculate the sample standard deviation using the formula:
Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))
Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.
Compare the sample standard deviation to the known process standard deviation (0.020):
The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."
For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:
Calculate the sample mean:
Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034
Compare the sample mean to the process mean (2.050):
The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."
Calculate the sample standard deviation:
The sample standard deviation is approximately 0.019 liters.
Compare the sample standard deviation to the process standard deviation (0.020):
The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.
In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.
However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.
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zoe ran 3/4 mile in 1/2 hour. what is the rate in miles per hour?
Answers
Answer:
1 1/2 miles per hour
Step-by-step explanation:
3/4 + 3/4 = 6/4 = 1 2/4 = 1 1/2 miles per hour
Write an explicit formula for the following sequences.
-4, -6, -8, -10...
Answers
Answer:
tn=-2n-2
hope this helps :)
I really need help with part a and b, please help. Incorrect answers will be downvoted, correct answers will be upvoted. 1. The army is interested in characterizing the acoustic signature of a helicopter. The following data show measurements of acoustic pressure (made dimensionless) for a two-bladed helicopter rotor through of a rotor revolution. The data points are equally spaced in time, and the period of the data collection is of a second. p=00.00040.0015 0.0028 0.0040 0.0048 0.0057 0.0071 0.0095 0.0134 0.0185 0.02420.0302 0.0364 0.0447 0.0577 0.0776 0.0955 0.0907 -0.0477 -0.0812 -0.0563 -0.0329 -0.0127 0.0032 0.0147 0.0221 0.0256 0.0255 0.0222 0.0170 0.0112 0.0064 0.0035 0.0023 0.0020 0.0019 0.0016 0.0009 0.0002 a) Find the real discrete Fourier transform for this data set. (b) Any term in the Fourier series can be written: ak Cos(kwt)+bk sin(kwt) =ck Cos(kwt+$k) ak Find the ck's and plot their amplitude on a bar graph vs. k to illustrate the relative size of each term in the series. Explain the significance of the plot
Answers
(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.
(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.
To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.
Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.
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i really need help. Strawberries cost $2.13 per pound and Annie purchased 1.2 pounds. How much did she pay for strawberries if her answer is rounded to the nearest cent?
Answers
Annie paid a total of $2.6 for 1.2 pounds of strawberries
How to determine the amount paid?In this question, we have the following parameters:
Unit cost per pound = $2.13 per pound
Number of pounds = 1.2 pounds
The amount paid for the number of pounds is represented by the equation
Amount paid = Unit cost per pound x Number of pounds
Substitute the known values in the above equation So, we have the following equation
Amount paid = 2.13 * 1.2
Evaluate the products
Amount paid = 2.556
Approximate
Amount paid = 2.6
Hence, the amount is $2.6
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Answer:
2.56
Step-by-step explanation:
find each sum. The large square represents 1, the larger rectangle represents 0.1 and the smaller rectangle represents 0.001.
Answers
Spanish: Siento algo que me mueve
Un ritmo que me hace bailar
Tomen todos su pareja
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Baila, baila esta cumbia
Mueve, mueve la cintura
Todos, las manos en alto
Y griten, griten con locura
Baila, baila esta cumbia
Un ritmo, ritmo sin igual
Nadie se quede sentado
Todos vamos a bailar
Siento algo que me mueve
Un ritmo que me hace bailar
Tomen todos su pareja
Todos vamos a gozar
Baila, baila esta cumbia
Mueve, mueve la cintura
Todos, las manos en alto
Y griten, griten con locura
¡Hey!, ¡hey!, ¡hey!, ¡hey!
¡Hey!, ¡hey!, ¡hey!, ¡hey!
¡Hey!
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Un ritmo, ritmo sin igual
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Baila, baila esta cumbia (baila esta cumbia conmigo)
Un ritmo, ritmo sin igual
Nadie se quede sentado (mueve la cintura)
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Baila, baila esta cumbia
Un ritmo, ritmo sin igual
Nadie se quede sentado (baila esta cumbia conmigo)
Todos vamos a bailar
Baila, baila esta cumbia (mueve la cintura)
Un ritmo, ritmo sin igual
Englis:I feel something that moves me
A rhythm that makes me dance
Take all your partner
We are all going to enjoy
Dance, dance this cumbia
Move, move your waist
Everyone, hands up
And scream, scream with madness
Dance, dance this cumbia
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No one stay seated
We are all going to dance
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A rhythm that makes me dance
Take all your partner
We are all going to enjoy
Dance, dance this cumbia
Move, move your waist
Everyone, hands up
And scream, scream with madness
Hey! Hey! Hey! Hey!
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Dance, dance this cumbia
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No one stay seated
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Nobody stay seated (dance this cumbia with me)
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Dance, dance this cumbia (move your waist)
A rhythm, rhythm like no other
A pizzeria makes pizzas in different sizes and with different toppings. The pizzeria wants its customers to have 12 options when they create a pizza. Which combination of size and toppings will give customers 12 options? Select three options.
Answers
Answer:
4 sizes and 3 toppings = 12 combinations
2 sizes and 6 toppings = 12 combinations
3 sizes and 4 toppings = 12 combinations
Step-by-step explanation:
In this case so that customers have 12 options, what we must do is decompose the number, that is, look for two numbers that when multiplied give 12 as the result, for example:
4 sizes and 3 toppings = 12 combinations
2 sizes and 6 toppings = 12 combinations
3 sizes and 4 toppings = 12 combinations
Answer:
A, D, E!!!
Step-by-step explanation:
A typical person begins to lose consciousness if subjected to accelerations greater than about 5 g(49.0 m/s^2) for more than a few seconds. Suppose a 3.00×10^4−kg manned spaceship's engine has an exhaust speed of 2.50×10^3 m/s. What maximum burn rate ∣ΔM/Δt∣ could the engine reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness?
Answers
The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.
Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.
Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.
Let the mass of the spaceship be m and the exhaust speed of the engine be v.
Using the formula for the thrust of a rocket,
T = (mv)e
After substituting the given values into the formula for thrust, we get:
T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N
Therefore, the acceleration produced by the engine, a is given by the formula below:
F = ma
Therefore,
a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²
The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,
x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s
Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.
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Is this the right answer?
Answers
Answer:
Hello!
Number 2 and 4 is wrong, other than that everything else is all good.
\(2)\) \(6x^4 - 12x^5 + 90x^1^{3}\)
The Greatest common factor is 6x^4.
The GCF needs to have the smallest exponent from the variables.
The correct answer should be 6x^4 ( 1 - 2x + 15x^9)
\(4)\) \(x^2 - 36\)
x (x - 36) is wrong because if we use the distributive property, the answer would be x^2 - 36x. Notice that there shouldn't be a variable multiplying 36.
The correct answer would be (x - 6)(x + 6)
x^2 + 6x - 6x - 36
x^2 - 36.
Hope this helps!
What is the area of the trapezoid shown?
Answers
Step-by-step explanation:
77 ft
Answer:
101.5 ft^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) h where b1 and b2 are the lengths of the bases and h is the height
A = 1/2 ( 11+18) * 7
= 1/2 (29) *7
101.5 ft^2
when determining the size of a fact table, estimating the number of possible values for each dimension associated with the fact table is equivalent to:
Answers
When determining the size of a fact table, estimating the number of possible values for each dimension associated with the fact table is equivalent to: determining the number of possible values for each foreign key in the fact table.
The measures, metrics, or facts of a business process are contained in a fact table in data warehousing. In a star or snowflake schema, it sits in the middle, surrounded by dimension tables.
When several fact tables are employed, they are organized according to a fact constellation schema. The two types of columns that make up a fact table are typically those that hold facts and those that serve as a foreign key to dimension tables.
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(06.02)
Which of these is the algebraic expression for "five more than the product of ten and some number?" (3 points)
Select one:
a. 10 + 5x
b. 5 + 10 + x
c. 10x + 5
d. 5 + 10 ÷ x
Answers
Answer:
i think it is c
Step-by-step explanation:
can you help me plz NO LINKS
Answers
Tommy bought a total of 30 apples and oranges for a classic picnic. Apple's cost $3 per pound and oranges cost $4 per pound. Tommy spent $100 total. How many apples and oranges did Tommy buy?
Please show work and explain
Answers
Solution: (20,10) Tommy bought 20 apples and 10 oranges.
Step-by-step explanation:
x+y=30: y=30-x
3x+4y=100
3x+4(30-x)=100
3x+120-4x=100
-1x +120=100
-120 -120
-1x=-20
/-1 -1
x= 20
20+y= 30
-20 -20
y=10
20+10=30
You solve this equation using substitution
What are the conditions for one-sample t-procedures?.
Answers
The conditions for conducting one-sample t-procedures are as follows:
1. Random Sample: The data should be obtained from a random sample or a randomized experiment to ensure that it is representative of the population of interest. This condition helps to minimize bias and ensure the validity of statistical inference.
2. Independence: The observations within the sample should be independent of each other. In other words, the values should not be influenced by each other and should be selected or measured independently. Violation of independence can lead to inaccurate results.
3. Normality or Large Sample Size (Central Limit Theorem): The population from which the sample is drawn should follow a normal distribution, or the sample size should be sufficiently large. If the population is known to be normally distributed, there are no specific requirements on the sample size. However, if the population distribution is unknown, the sample size should generally be at least 30 to apply the Central Limit Theorem, which states that the sample mean tends to follow a normal distribution, regardless of the population distribution shape.
4. Outliers: The presence of outliers can have a significant impact on the results of t-procedures. It is important to check for and address any outliers in the data. Outliers can distort the distribution and violate the assumptions of the t-test.
5. Equal Variances (for two-sample t-test): In the case of a two-sample t-test, if comparing two groups, the variances of the two populations should be equal. This assumption is necessary for calculating the correct degrees of freedom and obtaining accurate results. If the variances are not equal, a modified version of the t-test, called the Welch's t-test, can be used instead.
It is important to carefully assess these conditions before conducting one-sample t-procedures to ensure that the results are valid and reliable. Violations of these conditions may require alternative statistical tests or adjustments to the analysis.
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Y=3x-4Y=-3x+1Line 1. Line 2M= M=B=. B=Parallel, Perpendicular or n
Answers
For line 1
\(\begin{gathered} M1=3 \\ B1=-4 \end{gathered}\)For line 2:
\(\begin{gathered} M2=-3 \\ B2=1 \end{gathered}\)The lines are parallel if:
\(\begin{gathered} M1=M2 \\ 3=-3 \\ False \end{gathered}\)They are not parallel
The lines are perpendicular if:
\(\begin{gathered} M1\cdot M2=-1 \\ 3\cdot-3=-1 \\ -9=-1 \\ False \end{gathered}\)They are not perpendicular
(x, 7) (3, -1) has a slope that is undefined. Find the value of x
Answers
Based on the fact that the slope of the line is undefined, the value of x can be found to be 3.
What is an undefined slope?When a slope is said to be undefined, it means that the slope of the line does not show any horizontal movement. In other words, the value of the x points used to calculate the give a product of zero when subtracted.
The slope of a line can be found by the formula:
= (y2 - y1) / (x2 - x1)
For the slope to be undefined, the denominator needs to be zero:
= (-1 - 7) / (3 - x)
x will need to subtract 3 such that the result would be zero. So x will be 3.
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Describe the meaning of the translation (x + 6, y + 10).
All points are moved 6 units right and 10 units up
All points are moved 6 units left and 10 units up
All points are moved 6 units left and 10 units down
All points are moved 6 units right and 10 units down
Answers
Answer:
Step-by-step explanation:
The meaning of the translation (x + 6, y + 10) is that all points in a coordinate plane are moved 6 units to the right and 10 units up.
In other words, for any point (x, y) in the original position, after the translation, the new coordinates would be (x + 6, y + 10). This means that the x-coordinate of each point is increased by 6 units, resulting in a shift to the right, and the y-coordinate is increased by 10 units, resulting in a shift upwards.
Parv has a $50 gift card he uses the gift card to buy a pack of games for 9. 99. He also wants to buy n movies. Each movie cost 3. 99. Which inequality describes how many movies part can buy?
Answers
The inequality that describes how many movies Parv can buy is: n ≤ 10.025
Let's denote the number of movies Parv wants to buy as n. We are given that each movie costs $3.99. To determine the inequality that describes how many movies Parv can buy, we need to consider the amount of money he has remaining after purchasing the pack of games.
Parv starts with a $50 gift card and spends $9.99 on a pack of games. The remaining amount on the gift card is $50 - $9.99 = $40.01.
Now, let's consider the cost of n movies. Each movie costs $3.99, so the total cost of n movies would be n * $3.99.
Since Parv wants to buy the movies using the remaining amount on his gift card, we can set up the inequality:
n * $3.99 ≤ $40.01
This inequality states that the total cost of n movies, represented by n * $3.99, must be less than or equal to the remaining amount on the gift card, which is $40.01.
Simplifying the inequality further, we have:
3.99n ≤ 40.01
Now, if we want to solve for n, we can divide both sides of the inequality by 3.99:
n ≤ 40.01 / 3.99
Calculating this value, we have:
n ≤ 10.02506265664
Therefore, the inequality that describes how many movies Parv can buy is:
n ≤ 10.025
This means that Parv can buy a maximum of 10 movies, as he cannot purchase a fractional part of a movie.
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Complete the statement.
Two of the solutions of cos (x/2) = -(sqrt2/2) are ° and °.
Answers
Two of the solutions of the equation cos(x/2) = -(sqrt2/2) are 135 degrees and 225 degrees (or 3π/4 radians and 5π/4 radians).
Two of the solutions of the equation cos(x/2) = -(sqrt2/2) can be found by considering the unit circle and the properties of cosine.
Since the cosine function represents the x-coordinate of a point on the unit circle, we can look for the angles where the x-coordinate is -(sqrt2/2).
One such angle is 135 degrees (or 3π/4 radians), where the cosine is equal to -(sqrt2/2). At this angle, the x-coordinate of the corresponding point on the unit circle is -(sqrt2/2).
Another angle with the same x-coordinate is 225 degrees (or 5π/4 radians). At this angle, the cosine is also equal to -(sqrt2/2).
Two of the solutions of the equation cos(x/2) = -(sqrt2/2) are 135 degrees and 225 degrees (or 3π/4 radians and 5π/4 radians). These angles satisfy the given equation and have the desired x-coordinate on the unit circle.
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