Answers
9514 1404 393
Answer:
D. Infinitely many solutions
Step-by-step explanation:
To compare two linear equations, it is handy to have them in the same for. It doesn't really matter what that form is. You generally want to reduce the equations as far as possible by removing any common factors from the coefficients.
Here, we can put both equations into standard form: ax +by = c.
First equation:
y = -3x +5 . . . . given
3x +y = 5 . . . . add 3x
Second equation:
6x +2y = 10 . . . . given
3x + y = 5 . . . . divide by 2
These two equations are now identical. That means they describe the same line, so any (x, y) pair that satisfies one of these equation will also satisfy the other one (obviously). That means there are an infinite number of points these lines have in common, an infinite number of solutions.
__
More about number of solutions
Above is one of the possibilities.
Another possibility is that the left side looks the same, but the right side is different. For example, ...
3x +y = 5
3x +y = 4
The ratios of the coefficients of x and y are the same (a:b = 3:1). That means these lines have the same slope and they are the equations of parallel lines. They do not intersect, so this set of equations will have no solutions.
Another suitable form for comparing the slopes is slope-intercept form. The above two equations in that form would be ...
y = mx + b
y = -3x +5
y = -3x +4 . . . . . . same slope, different y-intercept
__
If the equations are different (except as just noted), there is one solution. Lines with different slopes must cross somewhere. They will cross exactly once.
Related Questions
: 1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125
Answers
To simplify this expression, you can first simplify the logarithms by using the properties of logarithms and the simplified expression is -0.00195
What is logarithm?A logarithm is a mathematical function that is used to determine the power to which a number must be raised in order to produce a certain value. The logarithm of a number "b" to base "a" is represented as loga(b) or logb. The logarithm of b to base a is equal to the exponent to which we must raise a to get b.
[tex]1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]
To simplify this expression, you can first simplify the logarithms by using the properties of logarithms.
[tex]1/2 log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]
=[tex]1/2( log10 25 - log10 4) - 2 (log10 4 - log10 5) + (log10 320 - log10 125)[/tex]
= 1/2(1.397940008672037 - 0.6020599913279624) - 2*(-0.6020599913279624 - 0.6989700043360187) + (2.505149978319906 - 2.0969100130080566)
= 0.397940008672037 - 1.204120018655925 - 1.397940008672037 + 0.40825006983185
= -0.2 - 0.2062 + 0.40825
= -0.00195
So the simplified expression is -0.00195
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Complete question is: simplify the given equation: 1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125
Find the missing side round to nearest 10th
Answers
Answer:
x = 73.3
y = 46.2
Step-by-step explanation:
Reference angle (θ) = 39°
Adjacent = 57
Hypotenuse = x
Opposite = y
Recall: SOHCAHTOA
✔️To find x, apply CAH:
Cos θ = Adjacent/Hypotenuse
Plug in the values
Cos 39° = 57/x
x × Cos 39° = 57
x = 57/Cos 39°
x = 73.3 (nearest tenth)
✔️To find x, apply TOA:
Tan θ = Opposite/Adjacent
Plug in the values
Tan 39° = y/57
57 × Tan 39° = y
y = 46.2 (nearest tenth)
find the volume of the figure of each figure
Answers
Answer
1/2
Step-by-step explanation:
what is the missing value , 2/3 and n/12
Answers
If you set 2/3 equal to n/12 then you multiple 3 by 4 to get 12. So you have to multiple 2 by 4 to get N.
what is the value of
sin^-1(0.4182) =
Answers
Answer:
degree 24.7
Radian 0.43
Step-by-step explanation:
please help me this would make my day ^^
Ray YW bisects ∠XYZ such that m∠XYW = (3x−7)° and m∠WYZ=(2x+1)°.
Find the value of x.
Answers
-2x -2x
x-7=1
+7 +7
x=8
In the problem on the previous page, suppose Alex wanted to know how many weeks it would take him to work 51 hours. Alex works 3 hours a day and 4 days a week.
1. What are you asked to find?
2. What is a good plan for solving the problem?
3. Does your answer make sense? Explain.
Answers
1. you are asked to find how many weeks it would take Alex to work 51 hours.
2. Alex works [tex]3\frac{1}{7}[/tex] weeks.
3. It makes sense in fractional from.
What is fraction?In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.
Alex works 3 hours a day and 4 days a week.
Alex works in a week = ( 3×4) hour = 12 hour
Alex works = 51 hours = 48 hours + 3 hours = (48/12) weeks + 1 day
= 3 weeks and 1 day.
= [tex]3\frac{1}{7}[/tex] weeks.
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Jesse had a total of 20 coins, all quarters and nickels. He counted his coins an had a
total of $3.20. How many of each coins does he have?
Answers
Answer: 11 quarters and 9 nickels
Step-by-step explanation:
11 quarters = $2.75 or 275 cents
9 nickels = 45 cents
275 + 45 = $3.20
Which value of x makes the expression equal.
5x, 7x - 6
Answers
Answer: x=3
Step-by-step explanation:
5x=7x-6
6+5x=7x
6=7x-5x
6=2x
solve for x which x=3
Answer:
x = 3
Step-by-step explanation:
Set the equations equal to each other:
5x = 7x - 6
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Division
Addition
Subtraction
~
Subtract 7x from both sides of the equation:
[tex]5x (-7x) = 7x (-7x) - 6\\5x -7x = -6\\-2x = -6[/tex]
Next, divide -2 from both sides of the equation:
[tex]\frac{-2x}{-2} = \frac{-6}{-2}\\ x = \frac{-6}{-2}[/tex]
*Remember that, when you divide two negative numbers, your answer will be positive:
[tex]x = \frac{-6}{-2} = 3[/tex]
3 is your answer for x.
x = 3.
~
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Let f(x) = x ^ 3 - x ^ 2 - 5x - 3 and g(x) = x + 3 3. Find (f/g)(x) . a .) x ^ 2 - 4x + 7R - 24
b .) x ^ 2 - 4x + 7
C.) x ^ 2 - 4x - 7R - 24
d.) x ^ 2 - 4x + 7x
Answers
Answer:
[tex](\frac{f}{g})(x) = \frac{\left(x+1\right)^2\left(x-3\right)}{x + 3}[/tex]
Step-by-step explanation:
The question is not properly formatted.
Given
[tex]f(x) = x^3 - x^2 - 5x - 3[/tex]
[tex]g(x) =x + 3[/tex]
Required
[tex](\frac{f}{g})(x)[/tex]
This is calculated as:
[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]
So, we have:
[tex](\frac{f}{g})(x) = \frac{x^3 - x^2 - 5x - 3}{x + 3}[/tex]
Factorize the numerator: using a calculator
[tex](\frac{f}{g})(x) = \frac{\left(x+1\right)^2\left(x-3\right)}{x + 3}[/tex]
12a-3b squared, when a=9, b=4
Answers
Answer:
60
Step-by-step explanation:
12a - 3b²
12(9) - 3(4)²
108 - 3(16)
108 - 48
60
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{12a - 3b^2}\\\mathsf{= 12(9) - 3(4)^2}\\\mathsf{= 12(9) - 3(4\times4)}\\\mathsf{= 12(9) - 3(16)}\\\mathsf{108 - 3(16)}\\\mathsf{= 108 - 48}\\\mathsf{= 60}\\\\\huge\text{Therefore, your answer should be: }\\\huge\boxed{\mathsf{60}}\huge\chdckmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Gemma's mean speed on her drive home from Chicago is 59mph. If the total trip is 295 miles, how long should she expect the drive to take? Round your answer to two decimal places, if necessary.
Answers
Answer:
5 hours
Step-by-step explanation:
If shes going 59mph and the total trip is 295mph
then you would divid 295 by 59 and get 5
Identify the ratios that correspond to the figure below, where TU = 30, UV = 16, and TV = 34.
Answers
Constant of Variation
Does the function y = 10/x² shown in the graph below have a maximum y=value or a minimum y-value?
Answers
Answer:
No
Step Explanation:
I calculated it logically
A one story home has a total square footage of 1,200. If 900sq ft of the home has a basement, and 300 sq ft has a slab foundation, what percent of the home has a basement foundation?
Answers
Answer:
7
Step-by-step explanation:
What is the sum of 6x+7 and 8x^2+5x-1
Answers
Answer:
8x² + 11x + 6
Step-by-step explanation:
6x + 7 + 8x² + 5x - 1 ← collect like terms
= 8x² + (6x + 5x) + (7 - 1)
= 8x² + 11x + 6
Please help with this math problem if You don’t give me a file link I will mark you brainlist!!
WXYZ is dilated by a scale factor of 3. The length of W'X'Y'Z' is ____
units, and the width is____
units.
Answers
Answer:
18, 12
Step-by-step explanation:
Assuming this is follow-up from the previous question you asked? If not, I apologize for misunderstanding.
Dilation factor by 3 is bigger than 1 = Expansion
Originally 6, 4
6*3 = 18
4*3 = 12
Answer:
18,12
Step-by-step explanation:
W (1, -2), X (7,-2), Y (7,-6), and Z (1, -6).
To dilate the shape, multiply it's coordinates by the scale factor.
W'(3,-6), X'(21,-6), Y'(21,-18), Z(3, -18)
The distance formula: [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
plug W'(3,-6) and X'(21,-6) in to get the length
[tex]\sqrt{(3-21)^2+(-6-(-6))^2}=\sqrt{(-18)^2 +0^2}=\sqrt{324} =18[/tex]
plug X(21,-6) and Y(21,-18) to get the width
[tex]\sqrt{(7-7)^2+(-2-(-6))^2}=\sqrt{0^2 +4^2}=\sqrt{16} =4[/tex]
[tex]\sqrt{(21-21)^2+(-6-(-18))^2}=\sqrt{0^2 +12^2}=\sqrt{144} =12[/tex]
A study of tutoring services at a community college shows a strong positive association between time spent in the math lab (in hours) and math exam average (as a percent). Is the following statement valid or invalid?
a. Students who spend more time in the math lab tend to have higher exam averages.
b. The tutoring services in the math lab are improving student performance on math exams.
c. To improve student performance in math classes, the college should require students to attend the math lab.
Answers
Answer:
A. Invalid
B. Valid
C. Valid.
Step-by-step explanation: A valid statement or argument is one in which the premise correlates with the conclusion.
It means that if all the premises are true then the conclusions from such premises must also be true. In the above statement, the first conclusion is invalid as it's conclusion does not correlates with its premise when considering the argument. Both conclusions B and C are valid as they correlates with their respective premises when considering the argument or statement made.
Graph the quadratic function f(x)= -2x^2-3x+2
Answers
Answer:
it would be the graph with the maximum (opening down) in the first photo with the top on the left side of the y axis
Raj was getting a 5% commission, but now he's getting 6.5%. How much more money will he make on $24,000 of sales than on his old commission?
Answers
If Raj was getting a 5% commission, he would make 24000 * 5% = $<<240005.01=1200>>1200 on $24,000 of sales.
If he is now getting a 6.5% commission, he will make 24000 * 6.5% = $<<240006.5.01=1560>>1560 on $24,000 of sales.
Thus, Raj will make 1560 - 1200 = $<<1560-1200=360>>360 more on $24,000 of sales with his new commission rate of 6.5% than he did with his old commission rate of 5%.
The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have an equal monthly salary of P7200, P7600, P6900, P8200, P7800 and P7400 respectively. What is the mean monthly salary of all the employees of the company?
Answers
The average monthly wage for the entire workforce of the business is $7489.09.
What is Mean?
The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.
Given, The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have equal monthly salaries of $7200, $7600, $6900, $8200, $7800, and $7400 respectively.
First, calculate the total monthly salary
22*7200 + 32*7600 + 18*6900 + 16*8200 + 10*7800 + 12*7200 dollars.
Total monthly salary = $823,800
Then divide this sum by the total number of employees
22 + 32 + 18 + 16 + 10 + 12
Total number of employees = 110
the mean monthly salary of all the employees = [tex]\frac{Total salary}{total number of employee}[/tex]
the mean monthly salary of all the employees = 823800/ 110
the mean monthly salary of all the employees = 7489.0909
Therefore, the mean monthly salary of all the employees of the company is $7489.09.
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Mr.West ate grapes for 11 days. He ate 2 1/11 ounces of grapes each day . How many grapes did he eat ?
Answers
Mr.West ate 23 ounces of grapes in 11 days by eating 2 1/11 ounces of grapes each day.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Mr.West ate grapes for 11 days. He ate 2 1/11 ounces of grapes each day.
Therefore, The total number of grapes Mr.West ate is,
= 11×(2 1/11) grapes.
= 11×(23/11) grapes.
= 23 grapes.
So, He ate 23 ounces of grapes in 11 days.
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find the L.C.M of 10,12,15 by division method
Answers
Answer:
Step-by-step explanation:
The LCM of 10,12,15 is 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 .
Reduce 17/5 to It lowest term
Answers
Answer:
17/5
It is already simplified to lowest terms.
This number, as a mixed fraction, would look like this:
3 2/5.
After a history test with 20 questions, the teacher asks his students to write down the number of the questions that was the most difficult. He then asks a couple of his students to organize this data and inform the class on the results. Here are their results: then the students calculate the median and find it to be 4. Which of the following sentences best describes their teachers response to this report
Answers
Answer:
i think it would be d
Step-by-step explanation:
the median is just the middle of the numbers, it doesnt say which is the hardest question though
hope this helps.
Median does not tell which one was the hardest. That would be mode
A tree that is 30 tall casts a 40 shadow. What is the distance from the top of the tree to the end of the shadow?
Answers
The distance from the top of the tree of height 30 tall to the end of the shadow is 50.
What is distance?Distance is the length between two point.
To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.
Note: The tree and the shadow form a right angle.
Formula:
a = √(b²+c²)................. Equation 1Where:
a = Distance of from the top of the tree to the end of the shadowb = Height of the treec = Length of the shadowFrom the question,
Given:
b = 30 c = 40Susbtitute these values into equation 1
a = √(30²+40²)a = √(900+1600)a = √2500a = 50Hence, the distance from the top of the tree to the end of the shadow is 50.
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Think of two different prime numbers, and write them on your paper. Then write the greatest common factor (GCF) of the two prime numbers.
Answers
Answer:
3, 11
The only common factor of Prime Numbers is 1
If your initial principal is $278 and your principal in 2 years is $1,308.77,
how much interest did you earn?
Answers
Answer:1030.77
Step-by-step explanation:
A strength coach claims that his new regiment will add significant distance to how far his players can hit a baseball. The other coaches decide to test this. They randomly select 33 players to go through his regiment. Before starting, they have each player hit 49 baseballs and record their average distance. The players then go through the strength and conditioning regiment. Afterwards, they again hit 49 baseballs, and record the average distance.
Which of the following would be the most appropriate confidence interval for measuring the average difference in the distance the ball traveled before and after the new regiment?
A. Goodness of Fit interval
B. Two-sample z-interval for proportions
C. Paired t-interval for means
D. Two-sample t-interval for means
E. One-sample z-interval for proportions
Answers
Answer:
C. Paired t-interval for means
Step-by-step explanation:
The answer to this question is the paired t interval for means. The reason is because both of these events are independent. One of the event starts as the other event gets to it's completion. The population standard deviation is not also not known. This makes the paired t interval for means more suitable
Ben has 50 toys. 15 of them are new and 9 are his favorites; 2 are new and favorites.
Ben is giving away all the toys that are neither new nor favorites. How many toys
does Ben give away?
Answers
Answer:
28 toys
Step-by-step explanation:
Ben has 50 toys, of which 15 are new, 9 are favorites, and 2 are new and favorites. You want to know the number that are neither new nor favorite.
GroupingsThe number of new toys includes (new and favorite) and (new and not favorite). That is ...
15 = 2 + new and not favorite
So ...
new and not favorite = 15 -2 = 13
Likewise, the number of favorite toys includes (new and favorite) and (not new and favorite). That is ...
9 = 2 + not new and favorite
not new and favorite = 9 -2 = 7
Donated
The total of 50 toys includes ...
total = (new and favorite) + (new and not favorite) + (not new and favorite) + (not new and not favorite)
50 = 2 + 13 + 7 + (not new and not favorite)
Then the number of (not new and not favorite) is ...
not new and not favorite = 50 -2 -13 -7 = 28
These are the toys that Ben gives away.
Ben gives away 28 toys.
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