Answer:
32/27
Step-by-step explanation:
The fractional division is draculated as follows:
(a/b) / (c/d) = (a*d) / (b*c)
then:
(8/9) / (3/4) = (8*4) / (9*3) = 32/27
Need to know if f(x)=x-4 and g(x)=3x+5, find (f+g) (x)
Answer:
4x+1
Step-by-step explanation:
f(x)=x-4 and g(x)=3x+5,
(f+g) (x) = x-4 +3x+5
Combine like terms
= 4x+1
The system below is consistent and has more unknowns than equations so has an infinite number of solutions. Solve this system by specifying appropriate free variables, solving for the other variables in terms of the free ones then expressing the general solution as a sum of scalar multiples of fixed column vectors. X1 + x3 + 2x4 + X5 + 3x6 = 1 2x1 + x2 + 2x3 + 4x4 +3.25 + 10x6 = 5 3x1 + x2 + 3x3 + 6x4 + 6x5 + 15x6 = 8
The solution of the system is then given by:
x = t[1 -1 1 0.5 0.5 0.33] + s[0 -2 1 1 -2 1]
This is the general solution of the system in the form of a sum of scalar multiples of fixed column vectors.
The system of linear equations can be written in matrix form as:
[1 0 1 2 1 3 | 1]
[2 1 2 4 0 10| 5]
[3 1 3 6 6 15| 8]
where the augmented matrix is [A | B].
To solve the system using the method of specifying appropriate free variables, we first convert the coefficient matrix into reduced row echelon form using Gaussian elimination.
In reduced row echelon form, the first non-zero element of each row (known as the leading entry) is 1, and the leading entries of lower rows are to the right of the leading entries of higher rows.
Applying Gaussian elimination to the coefficient matrix, we get:
[1 0 1 2 1 3 | 1]
[0 1 0 2 -2 7| 0]
[0 0 0 0 0 0| 0]
We can see that there are two non-zero rows, indicating that the system has two independent equations.
We can choose two of the variables to be free variables, and express the other variables in terms of the free ones.
Let's choose x1 and x3 as the free variables.
We can find x2 as follows:
x2 = -x1 - 2x3 + 7
And we can find x4, x5 and x6 as follows:
x4 = (1 - x1 - x3)/2
x5 = 1 - x1 - 2x3 + 2x4
x6 = (1 - x1 - x3 - 2x4)/3
So the general solution of the system can be expressed as a sum of scalar multiples of fixed column vectors:
x1 = t
x2 = -t - 2s + 7
x3 = s
x4 = (1 - t - s)/2
x5 = 1 - t - 2s + (1 - t - s)/2
x6 = (1 - t - s)/3
where t and s are scalars.
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A car traveled 281 miles in 4 hours and 41 minutes. What was the average speed of the car in miles per hour?
The average speed of the car in miles per hour is 60.124 miles per hours.
In the given question,
A car traveled 281 miles in 4 hours and 41 minutes.
We have to find the average speed of the car in miles per hour.
Firstly we know the speed
Speed is the ratio of distance that covered in the certain time.
The formula of speed
Speed = Distance / Time
From the question we know that the speed is 281 miles.
Time = 4 hours and 41 minutes
We have to find the speed of the car in miles per hours.
So we first convert the time in hours
As we know that in 1 hour have 60 minutes.
So in 1 minute have 1/60 hour.
So in 40 minutes have 1/60 × 40 = 2/3 hours.
So Time = 4 + 2/3 hours
Time = 4 × 3/3 + 2/3 hours
Time = 12/3 + 2/3 hours
Time = 12+2/3 hours
Time = 14/3 hours
Now we find the the speed
Speed \(=\frac{281}{14/3}\)
We can write it as
Speed = 281 × 3/14
Speed = 843/14
Speed = 60.214 miles per hours
Hence, the average speed of the car in miles per hour is 60.124 miles per hours.
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Last week Scott ran 43 miles less than James. Scott ran 5 miles. How many miles did James run?
A. 35
B. 44
C. 38
D. 48
Answer:
D) 48
Step-by-step explanation:
Let s = Scott
Let j - James
s = 5
s + 43 = j Substitute 5 for s
5 + 43 = j
48 = j
b) The marks obtained by 40 students in mathematics in examination are given below. Group the data into the class intervals of length 10 and construct a cumulative frequency distribution table.
42, 68, 80, 45, 92, 36, 8, 17, 49, 30
5, 26, 98, 74, 53, 65, 72, 28, 55, 46
86, 70, 62, 27, 16, 44, 85, 59, 51, 73
66, 78, 38, 81, 97, 77, 69, 45, 33, 67
number 5: big ideas 10.1-10.3In the diagram circle B is congruent to circle C. identify all the red arcs that are congruent.
Answer:
HJ, KL, and MN.
Explanation:
Given that circles B and C are congruent, then, the red arcs that are congruent are those that have a measure of 98 degrees from the two circle.
They are arcs:
• HJ
,• KL; and
,• MN
The red arcs that are congruent are HJ, KL, and MN.
If the point C is located at (5, 4) and C' is the image of C after being translated right 2. What are the
coordinates of C'?
Answer:
(7, 4)
Step-by-step explanation:
If point C is being translated to the right 2, the x coordinate will increase by 2. But, the y coordinate will stay the same.
Find the coordinates of C' by adding 2 to the original x coordinate:
5 + 2 = 7
The y coordinate will still be 4.
So, the coordinates of C' will be (7, 4)
Ty bought a new computer for $499. This brand depreciates at a rate of 12% of the original price per year. The value y of Ty's computer, x years after he purchased it, is found using an equation in the form y = mx + b. What is the approximate value of m?
Answer:
the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.
Step-by-step explanation:
o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").
Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:
m = -12% / 100 = -0.12
What input value
corresponds to an output
value of 10?
x f(x)
10. 6
14. 10
18. 15
22. 19
Answer:
14
Step-by-step explanation:
Look for 10 in the f(x) column. This is the output value.
Find the corresponding value in the x-column. This is the input for that output value.
The input that corresponds to an output of 10 is x=14.
The temperature during a winter day was less than 8 degrees Fahrenheit. Digby wants to write an inequality for the temperature during the winter day. What constant should Digby use in the inequality?
Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.
what is inequality ?
An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
To write an inequality for the temperature during a winter day being less than 8 degrees Fahrenheit, we can use the inequality symbol "<" which means "less than."
So, the inequality would be:
Temperature < 8 degrees Fahrenheit
Therefore, Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.
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Multiply the place value of 6 in 37651 by 11
Answer: Hi!
The place value of 6 in 37651 is equal to 600, as it is in the hundreds place.
All we need to do is multiply 600 by 11:
600 * 11 = 6600
Hope this helps!
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So in 37,651, the 6 is in the hundreds place since it's the third digit (from right to left).
6 in the hundreds place is 600.
600 times 11 equals 6600.
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♡ Hope this helps! ♡
❀ 0ranges ❀
An image of lines p and q parallel to each other. Lines m and n are not parallel to each other. Line m, p form an angle of one hundred two degrees and an angle marked y. Lines n, q form an angle marked x and an angle of one hundred fifteen degrees.Parallel lines p and q are cut by two non-parallel lines, m and n, as shown in the figure. The value of x is degrees, and the value of y is degrees.
Answer:
Welcome to Gboard clipboard, any text that you copy will be saved here.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Tap on a clip to paste it in the text box.
Which unit of measure is the most reasonable to measure the length of your pet hamster?
Select one:
A. yards
B. inches
C. feet
D. miles
PLease help, this is due tomorrow by 1 pm.
Note that the parameters of the graph a and graph b are given below.
Graph A - y=2(x-1)²
See graph attached.
Graph B - y = 1/2x² + 3
Vertex: The vertex of the function is (0, 3).
Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.
Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).
Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.
Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.
0 = 1/2 x² + 3
Subtracting 3 from both sides, we get:
-3 = 1/2 x²
Multiplying both sides by -2, we get:
6 = -x²
Taking the square root of both sides, we get:
x = ±√(-6)
Since the square root of a negative number is not a real number, the function has no real roots.
Minimum or maximum value: The minimum value of the function is 3.
Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.
Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.
Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.
See graph attached.
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Find the sum of the following series. Round to the nearest hundredth if necessary. 4 + 24 + 144 +... + 6718464
Answer:
Your answer is 264
Step-by-step explanation:
Simplify the polynomial. Fill in the blanks with the missing numbers.
2x−6+4x2+5x−2x2+10
The Given Polynomial has three different parameters scattered, first we have to rearrange and then solve for the missing numbers the answer is gotten as 2x^2+7x+4
Simplification of PolynomialGiven Data
2x−6+4x^2+5x−2x^2+10
We begin by collecting like terms
4x^2-2x^2+2x+5x-6+10
Carrying out addition and subtraction operation on like terms
2x^2+7x+4
The Simplified polynomial is
2x^2+7x+4
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What does "C" represent and how do you evaluate this?
\(_9C_7=\dfrac{9!}{7!2!}=\dfrac{8\cdot9}{2}=36\)
Mr mole left his burrow that lie below the ground and started digging at a constant rate deeper into the ground. After 5 min. Of descending at a rate of 1.8 meters per min. He was 13.5 meters below ground.
ibrahim drew the graph below.
which of the following statements best describes the graph?
Answer:
B
Step-by-step explanation:
This is a linear function.
:D
If 3/5 of a bag of jelly beans weighs 6 3/4 ounces , how much does one bag of jelly beans weigh?
solve each proportion algebraically. show your work. n/6 = 25/30
The sum of x and 15 is equal to -33. Find x.
Answer:
-48
Step-by-step explanation:
\(x+15=-33 \\ \\ x=-33-15 \\ \\ x=-48\)
If there are 48 boys and 32 girls in a room filled out all of the possible ratios of boys to girls that could be made there are 48boys for every 32 girls
Answer:48 to 32 48:32 48/32
Step-by-step explanation:
Henry's savings account has an APR of 3.65%, calculates interest daily, and
pays interest at the end of the month. If during the month of November, his
balance was $300 for the first 10 days of the month, $1200 for the next 10
days of the month, and $800 for the last 10 days of the month, how much
total interest did Henry earn in November?
Evaluate 26 +2⁶
A) 52
B)90
C)128
D) 481,890,304
Answer:
the answer is B
Step-by-step explanation:
2^6=64
64+26=90
Answer:
B) 90
Step-by-step explanation:
26 + 2⁶
Expand the power.
26 + (2 * 2 * 2 * 2 * 2 * 2)
Combine the twos.
26 + (4 * 4 * 4)
Combine two of the fours.
26 + 16 * 4
Multiply 16 and 4.
26 + 64
Add.
90
Use the formals F=9/5C+32 when c = 25
The value of F in the formula F=9/5C+32 when c = 25 can be written as F = 32.36.
What is the subject of the formula?The variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own. The variable that is stated in terms of the other variables is the subject of a formula. Take into account the cylinder's volume formula.
Given that F=9/5C+32
c = 25
\(F= \frac{9}{5C} + 32\)
\(F= \frac{9}{5*25} + 32\)
\(F= \frac{9}{125} + 32\)
\(F = 32.36\)
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complete question;
Use the formals F=9/5C+32 when c = 25, find the value of x
And please tell me how you did it
The unknown angle in the cyclic quadrilateral is as follows:
m∠CML = 109 degrees
How to find an angle in a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.
The sum of angles in a cyclic quadrilateral is 360 degrees.
Therefore, let's find m∠CML as follows:
Using the arc angle and opposite angle of a quadrilateral theorem,
6x + 25 = 1 / 2 (7x + 14 + 106)
6x + 25 = 1 / 2(7x + 120)
6x + 25 = 7 / 2 x + 60
6x - 7 / 2 x = 60 - 25
6x - 3.5x = 35
2.5x = 35
divide both sides by 2.5
x = 35 / 2.5
x = 14
Therefore,
m∠CML = 6x + 25 = 6(14) + 25 = 84 + 25 = 109 degrees
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help please and thanks
Answer:
Sige los puntos hi llegarás al final
Step-by-step explanation:
Sólo sige
Suppose the function h(x) = 2x - 9 is translated up 5 units to become a new function,
Xx). What's the equation of the new function?
A) x) = 7x-4
B)(x) = 2x - 14
C)(x) = 7x-9
D) (x)=2x-4
According to the given data the equation of the new function is (D) f(x) = 2x - 4.
What is meant by equation?An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign "=" and may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.
According to the given information:If we translate the function h(x) = 2x - 9 up by 5 units, the new function f(x) will have the form:
f(x) = h(x) + 5
Substituting the definition of h(x) into this equation, we get:
f(x) = 2x - 9 + 5
Simplifying, we have:
f(x) = 2x - 4
Therefore, the equation of the new function is (D) f(x) = 2x - 4.
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Los organizadores de la Feria de Alimentos colocan un contenedor de agua que mide 2,76 metros de largo, por 23,5 decímetros de ancho y por 196 centímetros de alto. ¿Cuál es el volumen del contenedor? Expresa la respuesta en metros cúbicos con aproximación a centésimos.
The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.
To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.
The length of the container is 2.76 meters.
The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).
The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).
Now we can calculate the volume of the container:
Volume = Length × Width × Height
Volume = 2.76 meters × 2.35 meters × 1.96 meters
Volume ≈ 12.9516 cubic meters (rounded to four decimal places)
Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.
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