Here is a system of equations: (3x - y = 17 x+4y =10 .Solve the system by graphing the equations (by hand or using technology).
how do you solve it step by step ?
Answers
The graph of the system of equations is shown below, and the solution is: (6, 1).
What is the Solution of a System by Graphing?When a system of equations are plotted on a graph, the lines of the two equations in the system will intersect at a point. The coordinates of that point represents the solution of the system of equations.
In the graph shown below in the attachment, the red line represents the line 3x - y = 17, which has a slope of 3 and intercepts the y-axis at -17.
The green line represents the equation, x + 4y = 10, which has a slope of -1/4 and a y-intercept of 2.5.
Both lines intersect at point (6, 1).
Therefore, the solution is (6, 1)
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Related Questions
What is the formula forfinding the area of a circle using its radius or diameter.
Answers
Answer:
The formula for finding the area of a circle using its radius is:
The formula for finding the area of a circle using its radius is:A = πr²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14
Step-by-step explanation:
Hope it Helps
The formula for finding the area of a circle using its radius is π * r².
The formula for finding the area of a circle using its diameter is (π/4) * d².
The formula for finding the area of a circle using its radius is:
A = π * r²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r represents the radius of the circle.
If you have the diameter of the circle instead of the radius, you can use the following formula:
A = (π/4) * d²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
d is the diameter of the circle.
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Astrid is in charge of
Answers
Astrid is in charge of building a new fleet of ship.
Write the equation 0.3x 2 + 5x - 7 = 0 in general form and then choose the value of "b."
Answers
Answer:
3x^2 + 50x - 70 = 0
b = 50
Step-by-step explanation:
0.3x^2 + 5x - 7 = 0
Multiply both sides by 10 to get rid of the decimal coefficient.
3x^2 + 50x - 70 = 0
b = 50
The monthly rents (in dollars) paid by 8 people are given below. (Note that these are already ordered from least to greatest.) 545, 945, 970, 995, 1015, 1030, 1040, 1124 Suppose that one of the people moves. His rent changes from $545 to $905.
Answer the following. (a) What happens to the median? It decreases by s[ It increases by se It stays the same. It decreases bys] (b) What happens to the mean? It increases by It stays the same.
Answers
Answer:
Step-by-step explanation:
Before: 545, 945, 970, 995 , 1015, 1030 , 1040 , 1124
Now: 905, 945, 970, 995 , 1015, 1030 , 1040 , 1124
a) Median stays same.
As number of data's is 8, median is the average of 4th and 5th term
Median = (995 + 1015)/2 = 2010/2 =
Median = 1005
When rent changes from $545 to $ 905, the 4th and 5th term remains same.
So, median stays same
b) Mean increases 45
Before: 545, 945, 970, 995 , 1015, 1030 , 1040 , 1124
Mean = Sum of rents ÷ 8
= (545 + 945+ 970+ 995 + 1015 +1030 + 1040 + 1124)/8
=7664/8
= 958
Now : 905, 945, 970, 995 , 1015, 1030 , 1040 , 1124
Mean = (905 + 945+ 970+ 995 + 1015 +1030 + 1040 + 1124)/8
= 8024/8
= 1003
Mean increases by 1003 - 958 = 45
If f(x) = 5x+4, which of the following is the inverse of f(x)?
O A. f-1(x) = x-5
4
O B. f-¹(x) = X54
x-4
O C. f¹(x) = 5x-4
OD. f(x)=4-5x
Answers
Answer:
\(f^{-1}(x)=\frac{x-4}{5}\)
Step-by-step explanation:
1. replace f(x) with x, and x with y: x=5y+4
2. solve for y: x=5y+4
⇒ x-4=5y
⇒ (x-4)/5=y
3. replace y with f⁻¹(x)
calculate the difference of 1/5 and 5/8
Answers
Answer: 17/40
Step-by-step explanation: multiply until both are the same and subtract the numerators.
If a triangle has the lengths 7 and 21, find the range of lengths that the
third side could be to form a triangle.
7
14
14
6
Answers
Answer:
0 < x < 28
Step-by-step explanation:
If a triangle has 2 sides, with lengths 7 and 21, the third side must -
have a length longer than zero and less than (7+21) = 28
so if the 3rd side has length x, then
0 < x < 28
Pls answer and show me how you got that answer
Answers
The mass of the radioactive sample at the beginning of the 13th day of the experiment will be around 424.7 grams.
What does one gramme represent?A metric weight measurement unit. A gramme is one thousandth of a kilogramme, or about 30 times smaller than an ounce. Leave a space between the word "gramme" (or the symbol "g") and the number that comes before it when a specific number is provided. In technical and scientific writing, the unit name and the number are either written together in full (for example, ten grammes) or a numeral is used with the sign ( e.g. 10 g ).
When we find the mass of radioactive, we obtain:
m₀=initial mass=1500 grams, r = 13% and n =12 days
⇒m = m₀ x \((1 - \frac{r}{100} )^{n}\)
⇒m =1500×\((1-\frac{13}{100}) ^{12}\)
⇒m=424.7 grams.
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let x and y be i.i.d. unif(0, 1). (a) compute the covariance of x y and x y . (b) are x y and x y independent studysoup
Answers
If x and y be i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero
Here x and y be i.i.d. unif(0, 1)
The i.i.d stands for independent and identically distributed
unif means that the uniformly distributed
Here x and y are i.i.d unif (0,1)
The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable
Here we have to find the covariance of x + y and x - y
According to the properties of covariance
Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0
Because Cov(x, x) = Cov (y, y)
Cov(y, x) = Cov(x, y)
Therefore, the covariance of x+y and x - y is 0
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Given that 150 students were interviewed, 85 signed for mathematics, 70 signed for English, and 50 signed for both. Draw a venn diagram to show.
How many signed for only mathematics
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Answer: 35
Step-by-step explanation:
If 85 students signed up for mathematics but 50 of those students also signed up for both then you need to subtract 85 from 50 to get 35.
How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
Answers
For example, suppose you have the Cartesian equation of a line in the form:
y = mx + b
and the equation of a plane in the form:
ax + by + cz + d = 0
To check if the line belongs to the plane, you can substitute a point (x, y) on the line into the equation of the plane and solve for z. If the resulting value of z satisfies the equation of the plane, then the line belongs to the plane.
Here's an example:
Suppose the Cartesian equation of the line is y = 2x + 1, and the equation of the plane is 2x + 3y + 4z + 5 = 0.
If we substitute a point on the line, such as (1, 3), into the equation of the plane, we get:
2(1) + 3(3) + 4z + 5 = 0
Solving for z, we find that z = -1.5.
Since the resulting value of z satisfies the equation of the plane, the line belongs to the plane.
If the resulting value of z does not satisfy the equation of the plane, then the line does not belong to the plane.
f(x) = x². What is g(x)?
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g(x) is the inverse of f(x)
\(f(x) = {x}^{2} \)
\(g(x) = \sqrt{x} \)
Mai says x is a number that makes Equation A true and also a number that makes Equation B true. Equation A: − 3 ( x + 7 ) = 24 Equation B: x + 7 = − 8 Which statement explains why this is true? Multiple choice question. A) Adding 3 to both sides of Equation A gives x + 7 = − 8 . B) Applying the distributive property to Equation A gives x + 7 = − 8 . C) Subtracting 3 from both sides of Equation A gives x + 7 = − 8 . D) Dividing both sides of Equation A by -3 gives x + 7 = − 8 .
Answers
The statement that explains why this is true is (d) dividing both sides of Equation A by -3 gives x + 7 = − 8 .
How to determine which statement explains why this is true?The equations are given as
Equation A: −3(x + 7) = 24 Equation B: x + 7 = −8In equation A, we have
-3(x + 7) = 24
Divide both sides of this equation by -3
So, we have
-3(x + 7)/-3 = 24/-3
Evaluate the quotient
So, we have
x + 7 = -8
The above equation is the same as equation B
Hence, the statement that explains why this is true is (d) dividing both sides of Equation A by -3 gives x + 7 = − 8 .
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The midpoint of AB is M(-5, -2). If the coordinates of A are (-3, 4), what arethe coordinates of B?
Answers
The midpoint formula to find the midpoint coordintaes of line AB is
\(\begin{gathered} (x,y)=\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2} \\ \text{where (x,y) is the coordinates of midpoint M, (x}_1,y_1)\text{ is coordinates of A} \\ x_2,y_2\text{ are coordinates of B} \end{gathered}\)Substitute
\(\begin{gathered} (-3,4)for(x_1,y_1)\text{ and }(-5,\text{ -2) for }(x,y) \\ -5=\frac{-3+x_2}{2} \\ -5\ast2=-3+x_2 \\ -10+3=x_2 \\ x_2=-7 \\ \text{for y coordinate of }B \\ -2=\frac{4+y_2}{2} \\ -2\ast2=4+y_2 \\ -4=4+y_2 \\ -4-4=y_2 \\ y_2=-8 \end{gathered}\)Thus, the coordinates of B is (x2,y,2)=(-7,-8)
Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.)
F(x, y, z) = \(xyz^3\) i + \(x^2z^3\) j + \(3x^2yz^2\) k
Answers
Answer:its is conservative
Step-by-step explanation:
Anna said that the product of 7/8 ⋅ 1 1/2 =7/2. How can you tell that her answer is wrong/
Answers
Answer:
it's 77/16 and just say Anna's answer is wrong.
Answer:
The answer is 77/16, but you can go much dipper if you want. By just simplify 77/16, in 4×13/16. And the final result will be 4.8125. Please if you find it helpful give me a like and rate me.
Can you please tell me the sum of the question
Answers
Answer:
B) \(4i\sqrt{2}\)
Step-by-step explanation:
\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)
The given figure shows the intersection of plane S with a square pyramid.
Which shape depicts the cross-section?
OA.
D.
E
Answers
The cross section can be of these shapes square and triangle are; A, D
What is cross-segment ?A cross-segment is a plane segment that is a segment of a three-dimensional item that is parallel to one among its planes of symmetry or perpendicular to considered one of its traces of symmetry.
An instance of a go-segment would be a circle. A cross-section is seen whilst a 3-dimensional picture is reduce through a plane.
Then the case of the cone, a circular go-segment emerges while the cone is cut parallel with its base
The go-sectional region is the location of a 3-dimensional shape which is acquired whilst a three-dimensional object - inclusive of a cylinder - is sliced perpendicular to some designated axis at a point.
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4. A bus drives 1 mile west and 4 miles north. Sketch the path of the bus and find the straight line distance and angle from the bus's location to its starting point. (Hint: Use Tan¹ to find the angle whose Tangent is 4/1)
Answers
The distance of the straight line is √17 miles and the angle formed is
75.96°.
We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A bus drives 1 mile west and 4 miles north.
Let, The distance the bus travels along the west be adjacent and the distance traveled in the north be the height.
So, By Pythagoras' theorem,
The straight line distance = √(1² + 4²).
= √(1 + 16) miles.
= √17 miles.
Now, We know tan = opposite/adjacent.
tan = 4/1.
tan⁻¹(4/1) = Ф.
Ф = 75.96°.
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mya stated that a line segment that id 6 inches in length with a scale factor of 3 has a dilated length of 9 inches. is she correct? explain your thinking.
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Mya is not correct, when using a dilation scale factor of 3, you are supposed to multiply the length by 3, it means
\(6\cdot3=18\)The line segment should have dilated to 18 inches not to 9 inches
Answer:
The dilation with center B and scale factor 3 increases the length of \overline{AB} and \overline{AC} by a factor of 3. The point B does not move when we apply the dilation but A and C are mapped to points 3 times as far from B on the same line.
Step-by-step explanation:
A hotel manager is adding a tile border around the hotel's rectangular pool. let n represent the width of the pool, in feet. the length is 5 more than 2 times the width, as shown. Write two expressions that represent the perimeter of the pool.
Answers
Answer:
2(3x+5)
6x+10
Step-by-step explanation:
W= x
L= 2x+5
2(x) + 2(2x+5)
Simplify the following expression. 3 11 5 ÷ 3 − 9 5 A. 12 B. 1 81 C. 81 D.
Answers
Answer:
A
Step-by-step explanation:
To simplify the expression 3 11 5 ÷ 3 − 9 5, let's break it down step by step:
First, let's simplify the division 3 11 5 ÷ 3:
3 11 5 ÷ 3 = (3 × 115) ÷ 3 = 345 ÷ 3 = 115.
Next, let's subtract 9 5 from the result we obtained:
115 - 9 5 = 115 - (9 × 5) = 115 - 45 = 70.
Therefore, the simplified expression is 70.
The correct answer is A. 70.
The probability of choosing a green grape out of the bag that contains red and green grapes without looking is 11/15 . Which term best describes this probability?
Answers
Answer:
Likely
Step-by-step explanation:
Suppose a network has 37 servers of which 8 fail. How many possibilities are there for the 8 that fail?
Answers
The number of possibilities for 8 of 37 servers to fail is 38608020
How to determine the ways of selection?From the question, we have
Total number of servers, n = 37
Numbers to servers that fail, r = 8
The number of ways for 8 serves to fail is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 37 and r = 8
Substitute the known values in the above equation
Total = ³⁷C₈
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 37!/29!8!
Evaluate
Total = 38608020
Hence, the number of ways is 38608020
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7. Find the area of the triangle using trigonometry.
Answers
The area of the triangle shown is 51.96 unit²
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The area of a triangle can be found given two adjacent sides and an angle between the two sides. It is given as:
Area = (1/2) * product of adjacent sides * sin(angle)
Hence:
Area of triangle shown = (1/2) * 10 * 12 * sin(60) = 51.96
The area is 51.96
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ƒ(t) = –1∕2t2 + 2t + 6
Answers
This function represents a downward-opening parabola with a vertical shift of 6 units upward.
How to explain the functionThe given function is Ƒ(t) = –1/(2t²) + 2t + 6.
This is a quadratic function in terms of t. The general form of a quadratic function is f(t) = at² + bt + c, where a, b, and c are constants.
Comparing the given function Ƒ(t) = –1/(2t²) + 2t + 6 with the general form, we can see that a = -1/2, b = 2, and c = 6.
So, the function Ƒ(t) can be written as:
Ƒ(t) = (-1/2)t² + 2t + 6
This function represents a downward-opening parabola with a vertical shift of 6 units upward.
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Patrick is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. He uses the following formula to calculate voltage: voltage=(current) × (resistance) The circuit he tests had a current of 4+j2 amps and a resistance of 2-j3 ohms. What is the voltage of the current?
Answers
Based on the given current and the given resistance, the voltage of the current is 14 + j8
How to determine the voltage of the current?From the question, we have the following parameters
current of 4+j2 amps and a resistance of 2-j3 ohms.
This can be rewritten as:
Current (I) = 4+j2 amps
Resistance (R) = 2-j3 ohms.
The formula to calculate voltage is given as
Voltage=(current) × (resistance)
Rewrite as:
V = I * R
Substitute the known values in the above equation
V = (4 + j2) * (2 - j3)
Expand the brackets
V = 8 - j4 + j12 + 6
Collect the like ters
V = 8 + 6 - j4 + j12
Evaluate the like term
V = 14 + j8
Based on the given current and the given resistance, the voltage of the current is 14 + j8
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Domain:
O-85x<0 or 0
O-85x50or 0≤x≤2
O 1
O 2
Answers
The domain and the range of the piecewise function in this problem are given as follows:
Domain: -6 ≤ x < 0 or 0 < x ≤ 2.Range: 0 ≤ y < 1 or 1 < y ≤ 6.How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:
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PLEASE HELP!!!!
Choose the equation below that is equivalent to 4(x - 7) - 2(x + 1) = -10
2x - 26 = -10
2 ( x - 6) = -10
4x - 28 - 2x - 2 = -10
4x - 28 - 2x +2 = -10
Answers
Step-by-step explanation:
=4(x)+4(-7)-2(x)-2(1) = -10
= 4x-28-2x-2= -10
therefore the third equation is equivalent to the given equation..all you need is to simplify.
Hope this Helps!!!
Which ratio is the simplest form of 68:84? A 2:3 B 17:21 C 34:42 or D 21:17? Please help me!
Answers
Answer:
B
Step-by-step explanation:
That is the answer
Answer:
The answer is B 17:21
Step-by-step explanation:
68:84
68/2=34
84/2=42
34:42 but we can also divide again so 34:42 can't be the simplest form of 68:84
so 34/2=17
42/2=21
17:21