Answers
Using Cramers Rule, X = 10.34, Y = 0.85. See the computations below.
What is Cramers Rule?Cramer's rule is an explicit formula in linear algebra for solving a system of linear expressions with as many equations as unknowns, and it is true whenever the system has a unique solution.
Given:
10x - 4y = 100; ..................1) and
8x - 100y = -2; ...................2)
First things first, let's pick off the variables we will need for Cramer's equation:
Standard equation 1 = ax + by = c and Standard equation 2 = dx + ey = f. Therefore:
a = 10, b = -4, c = 100, d = 8, e = -100, f = -2
Step 1, calculate the denominator Delta (Δ):
Δ = a * e - b * d
Δ = (10 * -100) - (-4 * 8)
Δ = -1000 - -32
Δ = -968
Step 2, calculate the numerator for x
Numerator(x) = c * e - b * f
Numerator(x) = (100 * -100) - (-4 * -2)
Numerator(x) = -10000 - 8
Numerator(x) = -10008
X = Numerator (x) / Δ
x = -10008/-968
x = 10.338842975207
x [tex]\approx[/tex] 10.34
y = Numerator(y)/Δ
y = -820/-968
y = 0.84710743801653
y [tex]\approx[/tex] 0.85
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Related Questions
gwen has £7 a litre of cola costs £1.25 gwen buys as much as literes as she can. how much money does she have left?
Answers
Gwen has £0.75 money left over, as per linear equation if a litre of cola costs £1.25.
"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."
It is given that Gwen has a £5 note and a £2 coin.
Therefore, she has a total of £(5 + 2) = £7
A liter of cola costs £1.25.
Therefore, (7 ÷ 1.25) = 5.6
Therefore, Gwen can buy a total of 5 liters of cola.
Now, Gwen has left money of £[7 - (5 × 1.25)] = £0.75
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Complete question is:
Gwen has a £5 note and a £2 coin
a litre of cola cost £1.25
gwen buys as many liter bottles of cola as she can
how much money will she have left over
a basketball player makes 80% of her free throws. what is the standard deviation of the successes from 100 free throws?
Answers
Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.
Standard deviation is calculated as follows:
p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8
Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.
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What is 2x times 2x in algebra
Answers
Answer: 4x2
Step-by-step explanation:
Answer:
[tex]4x^2[/tex]
Step-by-step explanation:
[tex](2x)(2x)=(2*2)(x*x)=4x^2[/tex]
Select the correct answer.
Which graph shows the solution region of this system of inequalities?
y ≥3(0.8)^x
y ≥ x² - 5
Answers
The solution to the inequality are the region in the shaded area and the graph is attached
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y ≥3(0.8)^x
y ≥ x² - 5
Represent properly
y ≥ 3(0.8)^x
y ≥ x² - 5
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)
None of the options represent the shaded area (see attachment)
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Select all the equations that have 9 as a solution. j + 8 = 72 m × 3 = 27 b + 4 = 13 p – 5 = 4 q ÷ 3 = 27
Answers
m × 3 = 27,
b + 4 = 13
and p – 5 = 4.
Given:
1. j + 8 = 72
j= 72- 8
j= 64
2. m × 3 = 27
m= 37/3
m=9
3. b + 4 = 13
b= 13- 4
b = 9
4. p – 5 = 4
p= 9
6.q ÷ 3 = 27
q= 27 x 3
q= 81
Hence, the equation with solution 9 is m × 3 = 27, b + 4 = 13 and p – 5 = 4.
Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship.
your daily calorie intake and your GPA
Answers
The correlation between your daily calorie intake and your GPA is not likely to be immediately apparent, and it would require further investigation to determine whether there is a positive or negative correlation, or no linear relationship between the two variables.
It is difficult to predict the correlation between your daily calorie intake and your GPA as they are not obviously related variables. However, it is possible that there may be a weak or indirect relationship between the two variables.
If a person is consuming a well-balanced diet with the right amount of nutrients, vitamins, and minerals, they may have the energy and focus necessary to perform well academically. In this case, there may be a positive correlation between calorie intake and GPA. Alternatively, if a person is consuming an excessive amount of calories from unhealthy foods, they may be more likely to experience health problems that could impact their academic performance. In this case, there may be a negative correlation between calorie intake and GPA.
On the other hand, there may be no direct linear relationship between the two variables, and other factors such as sleep, stress, exercise, and overall health may have a greater impact on academic performance than daily calorie intake.
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QUESTION FOR FOR LIH04
Answers
Please help thank you
Answers
The tension forces are 1895 N and 2542 N.
What is the tension in the ropes?
Tension force is a type of force that results from the stretching or pulling of an object, such as a rope, cable, or string. When an object is under tension, it experiences a force that acts along its length, pulling it apart
We know that the third angle in the triangle that is formed is;
180 - [35 + 48]
= 97 degrees
We then have the tension in the ropes as T1 and T2
Using the sine rule;
T1/sin 35 = 3275/sin97
sin97T1 = 3275 sin 35
T1 = 3275 sin 35/sin97
T1 = 1895 N
For T2
T2/sin48 = 3275/sin97
sin97T1 = 3275 sin 48
T1 = 3275 sin 48/sin97
T1 = 2542 N
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Pls help thank you will mark the Brainliest
Answers
The exponential function from the decay function given is y = 30.5(0.7)ˣ
What is an exponential functionAn exponential function is a mathematical function that models the growth of a quantity as a power of another quantity, typically as the exponent of a constant called the base. The general form of an exponential function is given by:
f(x) = a^x
where "a" is the base and "x" is the input. The value of "a" must be positive and greater than zero. When "a" is greater than 1, the exponential function grows very quickly, and when "a" is between 0 and 1, the exponential function decreases very quickly.
In this problem, we can find the exponential function by;
when x = 0
f(0) = 30.5
The function can be written as;
f(x) = 30.5(b)ˣ
To find the value of b,
We can take another point and solve;
f(0) = 30.5
f(1) = (21.35)
Looking at the graph, this is a decay function and we can easily find the value as 0.7.
The function is given as y = 30.5(0.7)ˣ
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Consider the sequence 7, 3, –1, –5, –9, ... a. What kind of sequence is it? Explain how you know. b. Write a rule t(n) for each term in the sequence, where n is the term number.
Answers
The sequence is an arithmetic sequence.
A rule for each term is t(n) = 7 - 4(n - 1).
What is Arithmetic Sequence?Arithmetic sequence is a sequence of numbers where the numbers are arranged in a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Given sequence is 7, 3, –1, –5, –9, ....
First term = 7
Second term = 7 + -4 = 3
Third term = 7 + (-4 × 2) = -1
....................
Here each term is getting by adding -4 to the preceding term.
So -4 is the common difference.
nth term of the sequence is t(n) = 7 - 4(n - 1).
Hence the sequence is arithmetic sequence and any term of the sequence is t(n) = 7 - 4(n - 1).
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which equations for the measures of the unknown angles x and y are correct? check all that apply.(a) x=cos−1(a/c)x=cos−1(a/c)(b) x=sin−1(c/b)x=sin−1(c/b)(c) x=tan−1(c/a)x=tan−1(c/a)(d) y=sin−1(a/c)y=sin−1(a/c)(e)y=cos−1(c/b)y=cos−1(c/b)
Answers
The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Sin θ = Opposite Side to θ/Hypotenuse
Cos θ = Adjacent Side to θ/Hypotenuse
Tan θ = Opposite Side/Adjacent Side
Cot θ = Adjacent Side/Opposite Side
Sec θ = Hypotenuse/Adjacent Side
Cosec θ = Hypotenuse/Opposite Side
where, Hypotenuse (the longest side), Perpendicular (opposite side to the angle), Base (Adjacent side to the angle)
The inverse ratios start with the ratio and then find the angle that produces this ratio.
(a) x=cos−1(a/c)
(b) x=sin−1(c/b)
(c) x=tan−1(c/a)
(d) y=sin−1(a/c)
(e)y=cos−1(c/b)
The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).
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On the windowsill is a plant that is 3 inches tall. It is growing 4 inches per week. A second plant, which is 17 inches tall, is on the coffee table. It is growing 2 inches per week. Eventually the two plants will be the same height. How many weeks will that take? How tall will the plants be?
Answers
The two plants would have the same height in 7 weeks and the height would be 31 inches.
When would the plants have the same height?The form of the expression that represents the length of the plant on the window sill is:
initial length + (length of growth per week x number of weeks)
3 + (4 x w)
3 + 4w
The form of the expression that represents the length of the plant on the coffee table is:
initial length + (length of growth per week x number of weeks)
17 + (2 x w)
17 + 2w
When the two plants have the same height, the two expressions would be equal:
17 + 2w = 3 + 4w
17 - 3 = 4w - 2w
14 = 2w
w = 14/2
w = 7 weeks
Height of the plant = 3 + 4(7)
3 + 28 = 31 inches
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Graph the line that represents this equation:
3x - 4y = 8
Drawing Tools
Select
Point
Line
X
Click on a tool to begin drawing.
-10
-8
-6
-4
-2
10-
4
8
2
S
A
2
2
Delete
++
Answers
Answer:
Step-by-step explanation:
Ryan purchased 3 ties and 4 shirts for $500 Earl purchased 6 ties and 7 shirts at the same store for $920.00. What is the total cost of 1 tie and 1 shirt .? Show working
Answers
Ryan purchased 3 ties and 4 shirts for $500 Earl purchased 6 ties and 7 shirts at the same store for $920.00 then the total cost of 1 tie and 1 shirt is $153.33.
What is system of equations?
A system of equations is a set of two or more equations that are solved simultaneously to find the values of the variables that satisfy all the equations in the system. The solution of the system is the set of values of the variables that satisfy all the equations. There are different methods to solve a system of equations, such as substitution, elimination, and matrix methods.
Let x be the cost of 1 tie and y be the cost of 1 shirt.
From the problem, we can set up a system of equations:
3x + 4y = 500 (equation 1)
6x + 7y = 920 (equation 2)
To solve for x and y, we can use elimination method. Multiply equation 1 by 2 and subtract it from equation 2:
6x + 7y = 920
(6x + 8y = 1000)
-y = -80
Therefore, y = 80. We can substitute y = 80 into equation 1:
3x + 4(80) = 500
Simplifying the equation, we get:
3x = 220
So, x = 220/3 = 73.33 (rounded to two decimal places).
Therefore, the total cost of 1 tie and 1 shirt is $73.33 + $80 = $153.33.
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at most, how many references in this line could be null and might cause the nullpointerexception to be thrown?
Answers
None. There are no references in this line. This line does not contain any references, so no references can be null. Therefore, no NullPointerException can be thrown.
This line does not contain any references, so no references can be null. Therefore, no NullPointerException can be thrown.
This line of code does not contain any references at all. Therefore, it is not possible for any references to be null, and it is impossible for a NullPointerException to be thrown in response to this line. NullPointerExceptions are only thrown when a program attempts to use a reference that is null, but this line does not contain any references, so such an exception is not possible. Consequently, no references can be null in this line and no NullPointerException can be thrown.
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equation of the blue line?
Answers
Answer:
Step-by-step explanation:
y=kx+b
b=3
(1,5)
1*k+3=5
k=2
so, 2x+3=y
Shawn's retirement party will cost $6 if he invitês 3 guests. If there are 8 guests, how much
will Shawn's retirement party cost? Assume the relationship is directly proportional.
Answers
Explanation: If 3 guests costs 6 dollars then each guest is 2 dollars. If there are 8 guests then 8x2 is 16
Step-by-step explanation:
Shawns party will cost $16 if there are 8 guest
The area of a rectangular window is 4234 cm².
If the length of the window is 73 cm, what is its width?
Answers
Answer:
58
Step-by-step explanation:
4234 = 73x divide by 73 on both sides and x=58
PLEASE HELP 20 POINTS
unit 9: transformations homework 1: translations
Answers
The translation of a function and coordinates are given below..
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The following functions:
y = x²
y = 2x
The transformation is:
Translate two units to the left.
So,
y = (x - 2)²
y = 2(x - 2)
Translation 5 units up.
y = x² + 5
y = 2x + 5
The following coordinates:
Translate 2 units to the right.
(1, 4) = (1 + 2, 4) = (3, 4)
(5, 8) = (5 + 2, 8) = (7, 8)
Translation 5 units down.
(1, 4) = (1, 4 - 5) = (1, -1)
(5, 8) = (5, 8 - 5) = (5, 3)
Thus,
The translation of a function and coordinates are given above.
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Lucy thinks of a number.
10 x the number = 10 ÷ the number
Give a possible value of the number.
Answers
Answer: 1
Step-by-step explanation: Knowing the division and multiplication rules, any number times one equals itself and any number divided by one equals itself. Make sure not to put 0 as an answer because any number divided by 0 is undefined.
Howard's pencil is 75 cm long. How many millimeters long is Howard's pencil?
Answers
Answer:
Howard's pencil is 750 millimeters
Step-by-step explanation:
[tex]\begin{array}{|l}\underline{km~}\\~~~~~\underline{|hm~}\\~~~~~~~~~~~\underline{|dam}~~~~~~~~\nwarrow~\div10\\~~~~~~~~~~~~~~~~~\underline{|m~~}\\~~~~~~~~~~\searrow~~~~~~~\underline{|dm~}\\~~~\times10~~~~~~~~~~~~~~~~~~\underline{|cm~}\\\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|mm~}\end{array}\\~~~~~~~~~~~\rm Converting ~Length ~ Unit[/tex][tex]~[/tex]
Step-by-step:
75 cm = 75 × 10 mm
75 cm = 750 mm
Let f(x) = 3x + 5 and g(x) = 4x - 1. Find (f + g)(x), then evaluate when x = 2.
Answers
The resulting sum function if x is equivalent to 2 is 18
Solving composite functionsComposite functions are known as function of a function
Given the following functions
f(x) = 3x + 5 and;
g(x) = 4x - 1.
(f+g)(x) = f(x) + g(x)
(f+g)(x) = 3x + 5 + 4x - 1
(f+g)(x) = 7x + 4
Substitute x = 2 into the result
(f+g)(2) = 7(2) + 4
(f+g)(2) = 18
Hence the value of the sum of the function when x = 2 is 18
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at noon, a ship leaves a harbor and sails south at 20 knots. four hours later, a second ship leaves the harbor and sails east at 15 knots. when will the ships be 100 nautical miles apart? round to the nearest minute. note that 1 knot = 1 nautical mile per hour.
Answers
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in geometry that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:
[tex]a^2 + b^2 = c^2[/tex]
We can use the Pythagorean theorem to find the distance between the two ships at any given time:
d² = (20t)² + (15(t-4))²
Simplifying this equation, we get:
d² = 400t² + 225(t² - 8t + 16)
d² = 625t² - 1800t + 3600
d = √(625t²- 1800t + 3600)
We want to find the value of t when d = 100 nautical miles, so we can set up the following equation:
100 = √(625t² - 1800t + 3600)
Squaring both sides, we get:
10000 = 625t² - 1800t + 3600
Rearranging, we get:
625t² - 1800t - 6400 = 0
Using the quadratic formula, we get:
t = (1800 ± √(1800² + 46256400)) / (2*625)
t = (1800 ± 3900) / 1250
t = 3.84 or t = 8.16
So the time elapsed for the second ship is:
t2 = t + 4
t2 = 7.84 or t2 = 12.16
We can see that the only solution that works is when t = 8.16 and t2 = 12.16. At that time, the first ship will have sailed for 8.16 hours at 20 knots, or 163.2 nautical miles, and the second ship will have sailed for 8.16 - 4 = 4.16 hours at 15 knots, or 62.4 nautical miles. The distance between the two ships will be:
d = √((163.2)² + (62.4)²) = 174.9 nautical miles
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
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Can someone explain and help me through this?
a. Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.
b. Let t = 10 and solve for the distance the cheetah covered in 10 minutes.
Information from the Warm Up:
According to the Travel Almanac, the world’s fastest land animal is the cheetah. It can travel at up to 70 mph. Think of this scenario: A cheetah sitting under a tree sprints toward its prey at 70 mph. It runs back to its initial spot by the tree at a modest 40 mph. The cheetah has embarked on a round-trip. Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.
Can we say that this cheetah’s average rate was 55 mph?
That’s one of the things you’ll determine as you work to complete this task. Make a conjecture. What do you think the answer will be?
Answers
well, let's get the info first.
so going forth the Cheetah goes 70mph and going back it modestly does 40mph.
can we say that on average it did 55mph?
well, what's that? on average means, that in total if we sum all units up and divide them evenly by relevant intervals, that's our average value.
well, let's see both intervals, on is forth and another is back 2 intervals, and the speed values are 70 and 40, so the average will really be (70 + 40) ÷ 2 = 55, that is an average of 55mph, so yes, we can say that.
A)
since an hour is 60 minutes, the Cheetah is really doing 70 miles per 60 minutes, or we can say
[tex]70\cdot \cfrac{miles}{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{60~minutes}\implies \cfrac{70}{60}\cdot \cfrac{miles}{minutes} \implies 1.1\overline{66}\frac{miles}{minutes}[/tex]
[tex]{\Large \begin{array}{llll} \stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t \end{array}}[/tex]
B)
[tex]\stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t\implies \stackrel{t=10}{m(10)=1.1\overline{66}(10)}\implies \stackrel{\textit{miles in 10 minutes}}{m(10)=11.\overline{66}}[/tex]
Please help! I don't understand how my teacher does the work, so therefore, I don't understand how to do these word problems. 100-point jackpot for answering.
Answers
Answer: 1) 4 $3 and 4 $2; 2) 4 candles; 3) 4 adults and 6 students; 4) Small is 11.67 and Large is 83.75
Step-by-step explanation: 1. Total of $20 and needs 9 donuts. One is $3 and one is $2. Start with 3 $3 that 9 and let's do 3 for $2 which is 6. 9+6 is $15. 20-15 is 5. We have $5 left so we can buy in total 4 $3 donuts and 4 $2 donuts.
2. She has to make at least 4 candles. Booth is $40. And $2 per candle. 4*2 is $8. 40+8 = 48 and 48/12 is 4 candles.
3. They have a total of 120 sold. So let's start with adult tickets: $15 each. So let's start with 4 sold. 15*4 = 60. Students: $10 each. 10*4 is $40. 60+40 is 100 sold! So let's do 2 more student tickets to get 120 sold. 4 adults sold and 6 students sold.
4. Let's work with 6 and 8 you set up the equation 6x+8y=670 you get x = 11.67 and y is 83.75. So the large price is $83.75 and the Small is $11.67
Find the sum of (8a + 2b -4) and (3b-5)
Answers
The sum of expression is 8a + 5b - 9.
What is expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
(8a + 2b -4) and (3b-5)
Now, adding the above expression we get
(8a + 2b -4) + (3b-5)
= 8a + 2b - 4 + 3b - 5
= 8a + 2b + 3b -4 - 5
= 8a + b(2+ 3) - 9
= 8a + b(5) -9
= 8a + 5b - 9
Hence, the simplified expression is 8a + 5b - 9.
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The apothem is the perpendicular distance from the _____ of a regular polygon to any one of its sides. center.
Answers
The apothem is perpendicular distance from the center of a regular polygon to any one of it sides.
The Apothem is defined as a term that used in geometry to describe a characteristic feature of a regular polygon.
A Regular Polygon is a polygon that has all sides of equal length and all angles of equal measure.
The Apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to any one of its sides.
The Center of circle is also the center of polygon. So , apothem is the distance from the center of the circle to the midpoint of any side of the polygon .
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The given question is incomplete , the complete question is
The apothem is the perpendicular distance from the _____ of a regular polygon to any one of its sides.
graphing systems of equations
graph equation and state the solution (the point where they intersect)
pls pls pls help i’m ripping my hair off trying to solve this
Answers
The system of linear equations represented in the graph have (b) ne solution at (-3, 1)
How to determine the number of solutionsFrom the question, we have the following parameters that can be used in our computation:
0 = y - x - 4
3y + 9 = -4x
The above system represents two linear functions
The point of intersection of the linear functions represent the solution
In this case, the linear functions intersect at (-3, 1)
See attachment for graph
Hence, it has one solution at (-3, 1)
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a plane ticket to baecelona is £175 the price decreased by 6%
how much is it now?
Answers
The plane ticket to Barcelona is now £164.50. This is because 6% of £175 is £10.50 and if you subtract £10.50 from £175, it equals £164.50.
HELP PLEASE
Which best represents the transformation for the coordinates of the vertices of the given pairs of triangles?
(1, 6), (−1, 3), (5, −2) and
(−1, 6), (−3, 3), (3, −2)
Answers
Step-by-step explanation:
what is the difference between the x- values ?
and what is the difference between the y- values ?
a transformation means a simple shift. so, addition of subtraction. no multiplication or such.
1 to -1 ? -2
-1 to -3 ? -2
5 to 3 ? -2
6 to 6 ? 0
3 to 3 ? 0
-2 to -2 ? 0
so, the transformation is (-2, 0)
