The system is inconsistent for values of a equal to √(13) or -√(13).
The correct answer is not listed in the given options.
The determinant of the coefficient matrix to determine whether the system is inconsistent or not.
If the determinant is zero, then the system has no unique solution and is inconsistent.
Otherwise, the system has a unique solution.
The coefficient matrix of the system is:
[1 2 3]
[3 5 4]
[2 3 a²]
The determinant of this matrix is given by:
det = 1 × (5 × a² - 12) - 2 × (3 × a² - 8) + 3 ×(3 × 3 - 2 × 5)
= 5a² - 12 - 6a² + 16 + 9
= -a² + 13
Therefore, the system is inconsistent when the determinant is zero, i.e., when:
-a² + 13 = 0
a² = 13
a = ±√(13)
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The system is inconsistent for a = ±1, and the correct answer is C. a = 1.
To determine the value of a that makes the given system of linear equations inconsistent, we need to check if the system has no solutions or infinitely many solutions. If the system has a unique solution, it is consistent.
To solve the system, we can use Gaussian elimination to transform the system into row echelon form. The augmented matrix for the system is:
[1 2 3 | 1]
[3 5 4 | a]
[2 3 a^2| 0]
First, we can use row operations to eliminate the entries below the first entry in the first column. We can subtract 3 times the first row from the second row and subtract 2 times the first row from the third row to get:
[1 2 3 | 1]
[0 -1 -5 | a-3]
[0 -1 a^2-6| -2]
Next, we can use row operations to eliminate the entry in the second row and third column. We can subtract the second row from the third row to get:
[1 2 3 | 1]
[0 -1 -5 | a-3]
[0 0 a^2-1 | a-1]
Now, we can see that the system will have no solutions if a^2 - 1 = 0 and a - 1 ≠ 0. This simplifies to a = ±1.
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division of 3 fraction
(2/5 ÷ 3/8 ) ÷ -3/5
Answer:
-16/9
Step-by-step explanation:
( [tex]\frac{2}{5}[/tex] ÷ [tex]\frac{3}{8}[/tex] ) ÷ [tex]-\frac{3}{5}[/tex]
= ( [tex]\frac{2}{5} * \frac{8}{3}[/tex] ) ÷ [tex]-\frac{3}{5}[/tex]
= [tex]\frac{16}{15}[/tex] ÷ [tex]-\frac{3}{5}[/tex]
= [tex]\frac{16}{15} * -\frac{5}{3}[/tex]
= -16/9
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answer:
8. yes; 18
9. no
10. no
11. yes; -9
Step-by-step explanation:
The equation for inverse variation is y = k/x. The constant k will be the product of x and y: k = xy.
8.Products are (-3)(-6) = (2)(9) = (4.5)(4) = 18.
Inverse variation with k = 18.
9.Products are ...
(5)(4) ≠ (10)(8).
Not inverse variation.
10.Products are ...
(2)(25) ≠ (2.5)(16).
Not inverse variation.
11.Products are (3)(-3) = (9)(-1) = (12)(-.75) = -9.
Inverse variation with k = -9.
QUICK HELP PLSSSS
which shape is the cross section of a square pyramid
Answer:
B
Step-by-step explanation:
when a square pyramid is cross sectioned the shape that will appear is the same as that of the base
The data below show the hourly wages earned by six employees. The second column shows the number of years of work experience for each employee. The third column is a binary variable indicating whether or not the employee has completed a training program. For the following questions, you may check your work using a calculator but must show how you set up the expression you are using (i.e. show your work).
wage experience training
8 1 0
20 10 0
10 2 0
12 4 0
16 4 1
14 6 1
a) What are the mean, variance, and standard deviation of wages?
b) What is the mean, variance, and standard deviation of experience?
c) Draw a scatter plot with experience on the horizontal axis and wages on the vertical axis. Draw a straight line that best fits the data points. Based on this line, what is the approximate wage of someone with 0 years of experience?
d) What is the covariance of wages and experience? Is this consistent with the line you drew in part c)? Explain.
e) What is the correlation of wages and experience?
The approximate wage of someone with 0 years of experience is -4.64
a) What are the mean, variance, and standard deviation of wages?The dataset of wages is
Wages = 8, 20, 10, 12, 16, 14
The mean is calculated as:
Mean = Sum/Count
This gives
Mean = (8+ 20+ 10+ 12+ 16+ 14)/6
Mean = 13.33
The variance is
Variance = ∑(x- mean)²/n-1
This gives
Variance = [(8 - 13.33)^2 + (20 - 13.33)^2 + (10 - 13.33)^2 + (12 - 13.33)^2 + (16 - 13.33)^2 + (14 - 13.33)^2]/5
Evaluate
Variance = 18.67
The standard deviation is
Standard deviation = √Variance
This gives
Standard deviation = √18.67
Evaluate
Standard deviation = 4.32
b) What is the mean, variance, and standard deviation of experience?The dataset of experience is
Wages = 1, 10, 2, 4, 4, 6
The mean is calculated as:
Mean = Sum/Count
This gives
Mean = (1+ 10+ 2+ 4+ 4+ 6)/6
Mean = 4.5
The variance is
Variance = ∑(x- mean)²/n-1
This gives
Variance = [(1 - 4.5)^2 + (10 - 4.5)^2 + (2 - 4.5)^2 + (4 - 4.5)^2 + (4 - 4.5)^2 + (6 - 4.5)^2]/5
Evaluate
Variance = 10.3
The standard deviation is
Standard deviation = √Variance
This gives
Standard deviation = √10.3
Evaluate
Standard deviation = 3.21
c) Draw a scatter plot with experience on the horizontal axis and wages on the vertical axis.See attachment for the scatter plot and the straight line that best fits the data points.
The equation of the straight line is
y = 0.69x - 4.64
The approximate wage of someone with 0 years of experience is
y = 0.69 * 0 - 4.64
Evaluate
y = -4.64
Hence, the approximate wage of someone with 0 years of experience is -4.64
d) What is the covariance of wages and experience?This is calculated as:
Cov(x,y) = ∑(x - x mean)(y - y mean)/N - 1
So, we have:
Cov(x,y) = [(8 - 13.33) * (1 - 4.5) + (20 - 13.33)*(10 - 4.5) + (10 - 13.33)*(2 - 4.5) + (12 - 13.33)*(4 - 4.5) + (16 - 13.33)*(4 - 4.5) + (14 - 13.33)*(6 - 4.5)]/5
Evaluate
Cov(x,y) = 12.80
Hence, the covariance of wages and experience is 12.80
Is this consistent with the line you drew in part c?
Yes it is
e) What is the correlation of wages and experience?Here, we use a graphing calculator.
From the graphing calculator, we have:
r = 0.9231
Hence, the correlation of wages and experience is 0.9231
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Someone please answer this for me (Algebra 2)
Using division of fractions, the equivalent expression is:
B. [tex]\frac{4}{d - 6}[/tex].
How to divide fractions?To divide two fractions, we multiply the first by the inverse of the second.
In this problem, we have that:
The first fraction is: [tex]\frac{2d - 6}{d^2 + 2d - 48} = \frac{2(d - 3)}{(d + 8)(d - 6)}[/tex].The second fraction is: [tex]\frac{d - 3}{2d + 16} = \frac{d - 3}{2(d + 8)}[/tex].Applying the multiplication, we have that:
[tex]\frac{2(d - 3)}{(d + 8)(d - 6)} \times \frac{2(d + 8)}{d - 3} = \frac{4}{d - 6}[/tex].
Hence option B is correct.
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describe how the graph is transformed from its parent function?
Answer:
It is stretched taller by a factor of 2.
Alan will be traveling out of town for business. during his travel, he is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. his employer will pay him for these meals at the following rate: $20.20 for dinner, $10.70 for lunch, and $6.93 for dinner. what is the total amount alan will be paid for these meals?
money paid by employer to Alan is $ 155.09
word problemA word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.
money paid for dinner by employer=$20.20
money paid for lunch by employer =$10.70
money paid for breakfast by employer =$6.93
according to question,
in this problem we will simply multiply quantity of dinners with amount
to get our answer.
so as given in problem Alan scheduled 4 dinners , 5 lunches and 3 breakfast
(4×$20.20)+(5×$10.70)+(3×$6.93)
80.8+53.5+20.79
=$ 155.09
hence money paid by employer to Alan is $ 155.09
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Tests show that the hydrogen ion concentration of a sample of apple juice is 0.0003 and that of ammonia is . find the approximate ph of each liquid using the formula , where is the hydrogen ion concentration.
The pH value of the apple juice is 3.5, is the correct answer.
The pH value of the ammonia is 8.9, is the correct answer.
The question seems to be incomplete and complete question is shown below
Tests show that the hydrogen ion concentration of a sample of apple juice is 0.0003 and that of ammonia is 1.3 x 10-9. Find the approximate pH of each liquid using the formula pH = -log (H+), where (H+) is the hydrogen ion concentration The pH value of the apple juice is___ The pH value of ammonia is____
1.pH of apple juice
A. 8.11
B. 1.75
C. 3.5
D. 2.1
2. pH of ammonia
A. 1.1
B. 7.0
C. 5.4
D. 8.9
The pH of a solution is defined as the logarithm of the reciprocal of the hydrogen ion concentration [H+] of the given solution.
From the formula;
pH = -log[ H⁺ ]
Given the data in the question.
For the Apple juice
hydrogen ion concentration H⁺ = 0.0003
pH of the apple juice pH = ?
pH = -log[ H⁺ ]
pH = -log[ 0.0003 ]
pH = 3.5
The pH value of the apple juice is 3.5
For the ammonia
hydrogen ion concentration H⁺ = 1.3 × 10⁻⁹
pH of the ammonia pH = ?
pH = -log[ H⁺ ]
pH = -log[ 1.3 × 10⁻⁹]
pH = 8.9
The pH value of the ammonia is 8.9
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WILL GIVE BRAINLIEST!!!!!!!!!
Considering the given proportions, the correct statements are:
A person in the group who is more likely to read is a boy.A person in the group who is more likely to listen to music is a girl.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The table gives these following proportions:
Boys and girls regarding books, boys are likelier to prefer books.Boys and girls regarding music, girls are likelier to prefer music.Hence the correct statements are:
A person in the group who is more likely to read is a boy.A person in the group who is more likely to listen to music is a girl.More can be learned about proportions at https://brainly.com/question/24372153
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help me i kinda stuck
For the given data,
Mean = 2.12
Median = 2
Mode = 2
Range = 3
Statistics
From the question we are to determine the mean
From the given table
Scoops of Ice cream Male Female Other Total frequencies
1 7 3 3 13
2 8 11 2 21
3 10 1 0 11
4 2 1 1 4
∴ [tex]Mean = \frac{(1 \times 13) + (2 \times 21) +(3 \times 11) + (4 \times 4)}{13 +21+11+4}[/tex]
[tex]Mean = \frac{(13) + (42) +(33) + (16)}{49}[/tex]
[tex]Mean = \frac{104}{49}[/tex]
Mean = 2.12
Median = 2
Mode = 2
Range = 4 - 1 = 3
Hence, for the given data
Mean = 2.12
Median = 2
Mode = 2
Range = 3
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Use the base example of two people walking to describe a system of two linear equation has i.) 0 solution 2) 1 solution 3) an infinite solution
The system has:
No solutions for two parallel lines.1 solution for two nonparallel lines.Infinite solutions for two equations that describe the same line.How to identify the number of solutions for the systems?A system of two linear equations is given by:
y = a*x + b
y = c*x + d
1) The system has no solutions when both lines are parallel lines, this happens when both lines have the same slope and different y-intercept.
y = a*x + b
y = a*x + d
2) The system has one solution when the lines have different slopes:
y = a*x + b
y = c*x + d
3) The system has infinite solutions when both equations describe the same line:
y = a*x + b
y = a*x + b
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8 more than 3 times a number is the same as -5 times the number.
a. x = -1
b. x = 1
c. x = -2
Answer:
3x +8 = -5x
3x + 5x = -8
8x = -8x
x = -8 /8
x = -1
Hope it helps...
Please contact me for further explanation....
The height of a certain species of plants is uniformly distributed on the interval of 5-12 cm. a plant was measured by jack. what is the probability that the height of this plant is between 6.3 and 7.8cm?
21 % is the answer.
Problem is that the height of this plant 6.3 and 7.8 cm
P (6.3 <x< 7.8)
12 -5 = 7cm
7.8 - 6.3 = 1.5cm
1.5 / 7 = 0.21
=21%
Probability is a field of mathematics that deals with the numerical description of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the impossibility of the event and 1 indicating certainty.
Probability is a measure of the likelihood that an event will occur. Many events cannot be predicted with absolute certainty. You can only predict the probability that an event will occur.
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Which ordered pair comes from the table?
X Y
3 4
4 4
5 2
6 5
A. (4,3)
B. (2,5)
C. (5,6)
D. (6,5)
The ordered pairs from the options given that is from the table is: D. (6,5).
How to Write an Ordered Pair from a Table?An ordered pair is written in the form, (x, y). The first number in the bracket is the x-value on the table, and the second number is its corresponding y-value form the table.
From the table given, the ordered pairs are: (3, 4), (4, 4), (5, 2), and (6, 5).
The number pair from the table from the given options is: D. (6,5).
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PLSS HELP ASAP
A bag of marbles contains 7 red, 8 orange, 9 purple, 7 white, and 5 yellow. Mark reaches into the bag and randomly picks out 3 marbles all at once.
How many different 3-marble groups are possible?
What is the probability that he will select 2 red and 1 yellow marbles?
based on the number of marbles in the bag, the number of marble groups possible is 7,140 groups.
the probability of selecting 2 red and 1 yellow is 1/68.
what number of 3-marble groups can be made?first, find the number of marbles:
= 7 + 8 + 9 + 7 + 5
= 36
the number of marble groups are:
= 36 ! / (3 ! x 33 !)
= 7,140 groups
the probability of picking 2 red and 1 yellow is:
= (( (7! / (2! x 5!)) x ( ( 5! / (1! x 4!))) / 7,140
= 1 / 68
= 1.47%
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Solve for X
7(8x + 6) = -1
9(5+ x) = 15 (10+ x)
Answer: 7(8x + 6) = -1: Exact form: x = -43/56, decimal form: x = -0.76785714
Thats all i have because you can't solve for x for the second one!
Determine the equation of a line that passes through (-2,5) and is parallel to the line whose equation is 5y +2x = 10.
Answer:
Step-by-step explanation:
Givens
line: 5y + 2x = 10
point (-2 , 5)
Discussion and Solution
You have to rearrange the given line to get the slope. It isn't nice, but it's not impossible.
5y + 2x = 10 Subtract 2x from both sides
5y + 2x - 2x = -2x + 10 Simplify
5y = - 2x + 10 Divide by 5
5y/5 = -2x/5 + 10/5 Simplify
y = -0.4x + 2
So the new equation is going to have a slope of - 0.4
So far what you have is
y = - 0.4x + b
Now use the point to find the y intercept. What you should be thinking about the point is that when x = -2 then y = 5. Substitute that into the new equation.
5 = -0.4*-2 + b
5 = 0.8 + b Subtract 0.8 from both sides
5 - 0.8 = 0.8 - 0.8 + b Simplify
4.2 = b
Answer
y = -0.4x + 4.2
PLEASE HELP ME AS SOON AS POSSIBLE
Answer: [tex]f^{-1}(\text{x}) = (\text{x}-9)^2+4[/tex] when [tex]\text{x} \ge 9[/tex]
=================================================
Work Shown:
[tex]f(\text{x}) = 9 + \sqrt{\text{x} - 4}\\\\\text{y} = 9 + \sqrt{\text{x} - 4}\\\\\text{x} = 9 + \sqrt{\text{y} - 4}\\\\\text{x}-9 = \sqrt{\text{y} - 4}\\\\(\text{x}-9)^2 = (\sqrt{\text{y} - 4})^2\\\\(\text{x}-9)^2 = \text{y}-4\\\\(\text{x}-9)^2+4 = \text{y}\\\\f^{-1}(x) = (\text{x} - 9)^2+4[/tex]
Explanation:
I replaced f(x) with y. After that I swapped x and y, then solved for y to get the inverse.
The smallest that [tex]\sqrt{\text{x}-4}[/tex] can get is 0, which means the smallest f(x) can get is 9+0 = 9. The range for f(x) is [tex]\text{y} \ge 9[/tex]
Since x and y swap to determine the inverse, the domain and range swap roles. Therefore, the domain of the inverse [tex]f^{-1}(\text{x})[/tex] is [tex]\text{x} \ge 9[/tex]
So we will only consider the right half portion of the parabola.
The graph is below. The red curve mirrors over the black dashed line to get the blue curve, and vice versa.
Answer:
[tex]f^-^1(x)=(x-9)^2+4[/tex] OR [tex]x^2-18x+85[/tex] if you simplify it
Step-by-step explanation:
to find the inverse function you have to switch x and y with each other and solve for y.
[tex]y=9+\sqrt{x-4}\\x=9+\sqrt{y-4}[/tex] step 1: switch x and y with each other
[tex]x-9=\sqrt{y-4}[/tex] step 2: subtract 9 from both sides
[tex](x-9)^2=\sqrt{y-4}^2[/tex] step 3: square both sides to get rid of the square root
[tex](x-9)^2=y-4\\(x-9)^2+4=y\\[/tex] step 4: add 4 to both sides
you could leave the answer like this or you can simplify to get [tex]x^2-18x+85[/tex]
The two-way frequency table below shows data on playing a sport and playing a musical instrument for students in a class.
Complete the following two-way table of row relative frequencies.
(If necessary, round your answers to the nearest hundredth.)
Here is the completed table:
Plays a sport Doesn't play a sport
Plays a musical instrument 0.46 0.54
Doesn't play a musical instrument 0.73 0.27
What are the row frequencies?
Relative frequency measures how often a value appears relative to the sum of the total values.
Plays a sport Doesn't play a sport
Plays a musical instrument (6/13) = 0.46 (7/13) = 0.54
Doesn't play a musical instrument (8/11) 0.73 (3/11) =0.27
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A Ferris wheel is boarding platform is 2 meters above the ground, has a diameter of 68 meters, and rotates once every 9 minutes. How many minutes of the ride are spent higher than 37 meters above the ground
4.440 minutes of the ride is spent higher than 37 meters above the ground.
How to find the time spent on the ride?We have to find the amount of time spent by the ride 37 meters above the ground.
We know that 37 meters above the ground is actually one meter above the center.
We can find the angle above the center as shown below:
arcsin(1/34) = 0.0294 radians
Now we have to find the angle of rotation:
The angle of rotation of the Ferris wheel above 37 meters = π - (2*0.0294)
= 3.1 radians
The angular velocity of the Ferris wheel = Angle covered/Time
= 2π/9 rad/min.
Therefore time spent above 37 meters = 3.1*9/2π
= 3.1*9/6.28319
= 4.440 minutes
Therefore, we have found that 4.440 minutes of the ride is spent higher than 37 meters above the ground.
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3.) Solve 5y +1 <36
Answer:
y<7
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer: y < 7
Step-by-step explanation:
We can assume that the less than sign is an equals sign and use algebra to isolate y.
[tex]5y+1-1 < 36-1\\ 5y < 35\\\frac{5y}{5} < \frac{35}{5}\\ y < 7[/tex]
We first subtracted 1 from both sides to get rid of the +1.
Then we divided both sides by 5 to isolate y.
The formula for the area of a triangle is Area=2(base)(height). Write an
expression for the height of a triangle that has an area equal to 10x²+20x and a
base equal to 20x.
Answer:
B
Step-by-step explanation:
area = 10x^2 + 20x
base = 20x
10x^2 + 20x = 0.5(20x)(height)
10x^2 + 20x = 10x(height)
(10x^2 + 20x) / 10x = height
[tex]\frac{10x^2 + 20x}{10x} = \frac{10x + 20}{10} = \frac{x + 2}{1} = x + 2[/tex]
The answer is B
Can someone help me with these problems and show work please !
The domain of g(x)= 3x^2 is Real number and it's range is {y∈R / y≥0}
The domain of h(x)= -3x^2 is Real number and it's range is {y∈R / y ≤0}
The domain of a function f(x) is the set of all values for which the function is defined, and the domain of a function is the set of all values that f takes on. The domain and range are defined for a relation and are the sets of all x-coordinates and all y-coordinates of ordered pairs.
The graph of f(x)= x^2 is given
We need to find the domain and range of g(x)=3x^2 and h(x)= -3x^2
The Graph of 3x^2 is different from x^2 in terms of plotting
When ,
x= -2 g(x)=12
x=-1 g(x)=3
x=0 g(x)=0
x=1 g(x)=3
x=2 g(x)=12
The Graph of -3x^2 is different from x^2 in terms of plotting
When ,
x= -2 g(x)=-12
x=-1 g(x)= -3
x=0 g(x)=0
x=1 g(x)= -3
x=2 g(x)=-12
Domain of g(x) is R and it's range is {y∈R / y≥0}
Domain of h(x) is R and it's range is {y∈R / y ≤0}
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20POINTS
help me please
Answer:
a. 50 students are randomly selected from the school; 11 drive to school
b. 407
Step-by-step explanation:
a. to get an accurate viewing, use random people that share 1 large common denominator (from the same school) that also has to do with the question
b. 11/50 is only between 50 students. make the denominator the same (1850) and multiply the same to the numerator
1850/50 = 37
11/50 x 37 = 407/1850
What is the quotient?
StartFraction t + 3 Over t + 4 EndFraction divided by (t squared + 7 t + 12)
(t + 3) squared
(t + 4) squared
StartFraction 1 Over (t + 4) squared EndFraction
StartFraction 1 Over (t + 3) squared EndFraction
The answer choice which represents the quotient of the expression given is; 1/(t+4)².
Which answer choice represents the quotient?It follows from the task content that the quotient which is to be evaluated is;
(t+3)/t+4) ÷ (t²+7t +12)
The quotient can therefore be evaluated as follows;
= (t+3)/t+4) ÷ (t+3)(t+4)
= (t+3)/t+4) × 1/(t+3)(t+4)
= 1/(t+4) × 1/(t+4)
= 1/(t+4)².
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Answer:
c
Step-by-step explanation:
c
find the equation of the straight line with the following gradient point c) 5, (-1,-3)
Answer:
y = 5x + 2
Step-by-step explanation:
Standard form of Equation of line: y = mx + c
where m = slope or gradient,
c = y-intercept
From the question we know that:
x = - 1
y = - 3
m = 5
We will substitute these values into the equation to find c.
- 3 = (5)(- 1) + c
- 3 = - 5 + c
c = - 3 + 5 = 2
Therefore the equation of this line is: y = 5x + 2
Using the unit circle, determine the value of sin(-240°).
Answer:
See my picture below for the answer.
Step-by-step explanation:
If you look at the unit circle and locate 240 degrees. You will see an ordered pair. The first number -1/2 is the cos of 240 and the second number is the sin.
Answer:
it’s the square root of 3, divided by 2 (sorry, can’t type any special characters at the moment)
Step-by-step explanation:
-240 = 120 because you measure negative angles clockwise starting at 0.
Using unit circle, value of sin for an angle is the 2nd number
Select the correct answer. malik is baking pumpkin bread and banana bread for friends and family. his pumpkin bread recipe calls for 4 eggs and cups of flour, and his banana bread recipe calls for 1 egg and cups of flour. malik has 14 eggs, 16 cups of flour, and plenty of other ingredients to make multiple loaves. what is one combination of breads malik can bake without getting more ingredients? a. 3 loaves of pumpkin bread and 3 loaves of banana bread b. 1 loaf of pumpkin bread and 9 loaves of banana bread c. 2 loaves of pumpkin bread and 6 loaves of banana bread d. 5 loaves of pumpkin bread and 1 loaf of banana bread
The correct answer is
2 loaves of pumpkin bread and 6 loaves of banana bread. Option C.
How to find a possible combination of bread?For the solution for the Pumpkin bread:
4 eggs
3 1/2 cups of flour
Banana bread:
1 egg
1 (0.5) cups of flour
Available ingredients:
14 eggs
16 cups of flour
Assume 2 loaves of pumpkin bread and 6 loaves of banana bread
For the solution for the Pumpkin bread:
PB=4 eggs* 2
PB= 8 eggs
PB=3 *0.5 * 2
PB = 7 cups of flour
For the solution of the Banana bread:
BB =1 *6
BB= 6 eggs
For cups
BB= 1 (0.5) * 6
BB= 9 cups of flour
In conclusion, The solution of the Total used ingredients
I=8 + 6
I= 14 eggs
For cups
IC=7 + 9
IC= 16 cups of flour
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Answer:
C 2 loaves of Pb and 6 loaves of BB
Step-by-step explanation:
please help !!!!!!!!!
Answer:
D. completing the square
Step-by-step explanation:
The process shown rearranges the standard-form quadratic equation to vertex form. It involves factoring out the leading coefficient and distributing the constant so that the variable terms can be written as a perfect square.
What is a perfect square trinomial?A perfect square trinomial is the square of a binomial. It has the form ...
(x +b)² = x² +2bx +b²
Given two variable terms, x² and 2bx, the perfect square trinomial can be formed by adding b², which is the square of half the x-term coefficient.
When b² is added to the sum (x² +2bx), the square is complete. The sum (x² +2bx +b²) can be written as the square (x +b)².
Completing the squareThis process of adding b² to the sum (x² +2bx) will change the polynomial unless a similar quantity is subtracted. That is why the 3rd line of the problem statement show 4 being added and subtracted inside parentheses:
y = 5(x² +4x +4 -4) -17
When we're applying this transformation, we do not want to change the equation. We simply want to rearrange it.
In the next step, the subtracted term is brought outside the parentheses. This lets us write the quantity in parentheses as a perfect square.
y = 5(x² +4x +4) +5(-4) -17
y = 5(x² +4x +4) -20 -17
This process of adding and subtracting a suitable quantity and rearranging the equation so the variable terms make a perfect square is called ...
"completing the square."
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Additional comment
The equation in this form is said to be in "vertex form."
y = a(x -h)² +k
In this form, the constant 'a' is a vertical scale factor; the ordered pair (h, k) identifies the vertex of the quadratic on a graph.
Solve for w, where w is a real number.
Answer:
w= 9
Step-by-step explanation:
[tex] \sqrt{ - 4w + 61} = w - 4[/tex]
Square both sides:
-4w +61= (w -4)²
[tex]\boxed{(a - b)^{2} = a^2 -2ab + b^2 }[/tex]
Expand:
-4w +61= w² -2(w)(4) +4²
-4w +61= w² -8w +16
Simplify:
w² -8w +16 +4w -61= 0
w² -4w -45= 0
Factorize:
(w -9)(w +5)= 0
w -9= 0 or w +5= 0
w= 9 or w= -5 (reject)
Note:
-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.
Why do we use negative square root?
When solving an equation such as x²= 4,
we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.
In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.
However, back to our question, we did not introduce the square root so we should not consider the negative square root value.
Answer: w=9.
Step-by-step explanation:
[tex]\sqrt{-4w+61}=w-4[/tex]
Tolerance range:
[tex]\left \{ {{-4w+61\geq 0} \atop {w-4\geq 0}} \right. \ \ \ \ \left \{ {{4w\leq 61\ |:4} \atop {w\geq 4}} \right. \ \ \ \ \left \{ {{w\leq 15,25} \atop {w\geq 4}} \right. \ \ \ \ \Rightarrow\ \ \ \ \\w\in[4;15,25].[/tex]
Solution:
[tex](\sqrt{-4w+61})^2=(w-4)^2\\-4w+61=w^2-2*w*4+4^2\\-4w+61=w^2-8w+16\\w^2-4w-45=0\\D=(-4)^2-4*1*(-45)\\D=16+4*45\\D=16+180\\D=196.\\\sqrt{D}=\sqrt{196}\\\sqrt{D}=14 \\w_{1,2}=\frac{-(-4)б14}{2} \\w_1=\frac{4-14}{2} \\w_1=\frac{-10}{2} \\w_1=-5\ \notin tolerance\ range.\\w_2=\frac{4+14}{2}\\ w_2=\frac{18}{2} \\w_2=9\ \in tolerance \ range.[/tex]