A system of linear equations is a collection of two or more linear equations that have two or more variables each. All of these equations are considered at once.
Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations. There could be an unlimited number of solutions for some linear systems, whereas others might not have any. There must be at least as many equations as there are variables for a linear system to have a singular solution. However, this does not ensure an original answer. There is always one answer to a set of equations that makes sense. A consistent system, like the one we just examined, is said to be an independent system if it only has one solution. The two lines cross at one location in the plane and have different slopes. If the equations' slopes and y-intercepts match, the system is said to be consistent and considered a dependent system.
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oops sorry yall theres the stuff
Answer:
42-26
Step-by-step explanation:
it's ok and i think you are correct on your answer
What is this supposed to mean!?!?!?!?
Answer:
h = V/B
Step-by-step explanation:
\(\sf V \div B = h\\Reverse\\h = V \div B\)
Answer:
D. h = V/B
Step-by-step explanation:
"Solve...for h" means get h all by itself on one side of the equation.
V = Bh
Divide both sides by B.
V/B = h
Turn it around and you can see the answer in the choices. D. h = V/B is the correct answer.
Algebraic Method #2: Solving by substitution 2x + 8y = 20 y = 2
if x^2 + 1/x^2 = 7 , find the value of x^3 + 1/x^3 and x^4 + 1/x^4
Answer:
pls show me the question
nvm forget the one i posted look
Answer:
7.5
Step-by-step explanation:
25y-15y=10y
10y=75
y=7.5
5. An apartment complex developer is considering building apartments in College Town, but first wants to do a market study. A sample of monthly rent values (S) for studio apartments in College Town was taken. The data collected from the 70-apartment sample resulted in a sample mean of $490.80. (Based on past experience, the developer assumes a known value of σ: $55 for the population standard deviation.) Develop a 95% confidence interval for the mean monthly rent for all studio apartments in this city monthly rent for all studio
To develop a 95% confidence interval for the mean monthly rent for all studio apartments in College Town, we can use the following formula:
CI = x ± z*(σ/√n)
where:
- CI is the confidence interval
- x is the sample mean ($490.80)
- z* is the z-score for a 95% confidence level (1.96)
- σ is the known population standard deviation ($55)
- n is the sample size (70)
Plugging in the values, we get:
CI = $490.80 ± 1.96*($55/√70)
CI = $490.80 ± $12.15
Therefore, the 95% confidence interval for the mean monthly rent for all studio apartments in College Town is $478.65 to $503.95. We can be 95% confident that the true population mean monthly rent for all studio apartments in College Town falls within this range.
Based on the provided information, we can construct a 95% confidence interval for the mean monthly rent of studio apartments in College Town. Here are the relevant terms and values:
- Sample size (n): 70 apartments
- Sample mean (x): $490.80
- Population standard deviation (σ): $55
To calculate the confidence interval, we will use the formula:
Confidence interval = x ± (z * (σ / √n))
For a 95% confidence interval, the z-value is 1.96. Now, let's plug in the values:
Confidence interval = $490.80 ± (1.96 * ($55 / √70))
Confidence interval = $490.80 ± ($13.61)
So, the 95% confidence interval for the mean monthly rent for all studio apartments in College Town is approximately $477.19 to $504.41. This means that we can be 95% confident that the true mean rent for all studio apartments in this city falls within this range.
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Use the segment addition postulate to write three equations using the diagram below
Answer:
\( PQ + QR = PR \) => equation 1
\( RS + ST = RT \) => equation 2
\( PR + RT = PT \) => equation 3
Step-by-step explanation:
Points P, Q, R, S, and T are collinear therefore, the following equations can be written based on the segment addition postulate:
\( PQ + QR = PR \) => equation 1
\( RS + ST = RT \) => equation 2
\( PR + RT = PT \) => equation 3
More equations can actually be written from the diagram given using the segment addition postulate. Such as:
\( PQ + QR + RS + ST = PT \)
On a piece of paper, graph this system of equations.
y = x-8
y = x2 - 2x - 3
Then determine which answer 'choice matches the graph you drew and
identify the solution(s) to the system.
Plzzzzzz Helpppp
Answer:
Since I don't know what your answer choices are, here's a picture of what it would look like graphed.
Hope this helps, and good luck :)
Pls help me
Explain why this graph is a function?
Answer:
It passes the VLT
Step-by-step explanation:
Draw a vertical line through every point. If it goes through another point, then it is not a function. If it doesn't pass through another point, then it is a function.
This is called the VLT, or vertical line test.
-Chetan K
Which graph represents a linear function?
What is the Domain and Range of the following Graph?
Answer:
This is a square function with its maximum at (-3, 2).
The domain is:
x ∈ [-3, + ∞)The range is:
y ∈ (- ∞, 2]2 and 1/3rd x 5 =? simplest form please and thank you. :)
Answer:
11 and 2/3
Step-by-step explanation:
2 1/3 = 7/3
7/3 x 5 = 35/3
35/3 = 11 and 2/3
Answer:
11 2/3
Step-by-step explanation:
2 1/3 is equal to 7/3 as an improper fraction
7/3 × 5/1 = 35/3 or 11 2/3
Which of the following shows the correct first step to solve x^2-18x=-45
A x^2 - 18x + 18= -45 + 18
B. x^2 - 18x + 9 = -45 + 18
C. x^2 -18x + 81 = -45
D. X^2 -18 + 81 = -45 + 81
Answer:
D, X^2 -18 + 81 = -45 + 81
Step-by-step explanation:
it is complating squer method that used for solving x in a quadratic equetion . in this step you will add
(y/2)^2 if y is the cofitient of x .
Solve the equation in standard form
The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.
To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:
-5/3 x² + 3x + 11 = -9 + 25/3 x²
First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:
-5x² + 9x + 33 = -27 + 25x²
Next, let's combine like terms:
-5x² - 25x² + 9x + 33 = -27
-30x² + 9x + 33 = -27
Now, let's bring all the terms to one side to have a quadratic equation equal to zero:
-30x² + 9x + 33 + 27 = 0
-30x² + 9x + 60 = 0
Finally, we have the quadratic equation in standard form:
-30x² + 9x + 60 = 0
Dividing each term by 3, we get:
-10x² + 3x + 20 = 0
(-2x + 5)(5x + 4) = -10x² + 3x + 20
So, the factored form of the equation -30x² + 9x + 60 = 0 is:
(-2x + 5)(5x + 4) = 0
Now we can set each factor equal to zero and solve for x:
-2x + 5 = 0 --> x = 5/2
5x + 4 = 0 --> x = -4/5
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What is the percent of change in 6 yards to 36 yards - - - 7th-grade math show the work
Answer:
Step-by-step explanation:
Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.
I think sorry if I’m wrong
The equation x²– 8x – 5 = 0 can be transformed into the equation (x - p)² = q, where p and q are real numbers. What are the values of p and q?
The form (x - p)^2 = q is the form that completing the square will leave us with.
---Add 5 to both sides
x^2 - 8x = 5
---Divide the b term by 2, and square it. Then, add that number to both sides.
-8/2 = -4
(-4)^2 = 16
x^2 - 8x + 16 = 5 + 16
x^2 - 8x + 16 = 21
---Factor!
(x - 4)^2 = 21
p = 4
q = 21
Hope this helps!! :)
P and q have values of 4 and 21, respectively.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
The form (x - p)²= q is what we get when we complete the square.
Adding the number 5 on both sides,
x² - 8x = 5
After dividing by two, square the b term. Then divide both sides by that figure.
-8/2 = -4
(-4)² = 16
x² - 8x + 16 = 5 + 16
x² - 8x + 16 = 21
Solve the factors,
(x - 4)² = 21
p = 4
q = 21
As a result, the values of p and q are 4 and 21, respectively.
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Use the Pythagorean theorem to find x, in simplest radical form
Answer:
\(4\sqrt{21}\)
Step-by-step explanation:
Pythagorean theorem is \(a^{2} +b^{2} =c^{2}\).
Which in this case:
'c' is hypotenuse. (hypotenuse = 20)
'a' and 'b' are the other sides. (a = x, b = 8)
\(a^{2} +b^{2}= c^{2}\) \(x^{2} +8^{2} =20^{2}\) \(x^{2} + 64 = 400\) \(x^{2} = 336\)Now we should just take square root from the both sides.
and the answer will be \(\sqrt{336}\) or \(-\sqrt{336}\), but a side of a triangle can not be a negative number! so the answer will be \(\sqrt{336}\).
As you see \(\sqrt{336}\) is not the simplest radical.
We can write \(\sqrt{336}\) as \(\sqrt{16 * 21}\).
And from the laws of radical we can write \(\sqrt{16*21}\) as \(\sqrt{16} * \sqrt{21}\).
\(\sqrt{16} * \sqrt{21} = \sqrt{16}\sqrt{21} = 4\sqrt{21}\)
I hope it helps you. Please choose my answer as the brainliest.
Point A is at (-7, 5) and point C is at (5, -1). Find the coordinates of point B on AC such that AB is 5 times as long as BC
B= (_, _)
Answer:
B= (3, 0)
Step-by-step explanation: I had this question before so I know it
Which one is the right answer
Answer:
The answer is C. Quadrant 3.
Step-by-step explanation:
Looking up a Unit Circle. We can see that 5pi/4 is in quadrant 3.
5pi/4 is also if in degree angle as 225°
Solve for the following equation for the variable below:
-9.6x + 1.8 = -12.3
Answer:
x=1.46875 or x=1.5
Step-by-step explanation:
1st step subtract 1.8 on both sides
-9.6x=-14.1
2nd step divide -9.6 on both sides
x=1.46875
or
x=1.5
Hope this helps!!!
Have a good day!!!
Starting with the graph of f(t) = 34, write the equation of the graph that results from a. reflecting f() about the y-axis. y = b. shifting f(x) 9 units right. y= C. shifting f(x) 8 units upward. y =
a. The equation of the reflected graph is y = -34
b. The equation of the shifted graph is y = 34
c. The equation of the shifted graph is y = 42.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
a. Reflecting f(t) about the y-axis:
When we reflect a function about the y-axis, we change the sign of the x-values while keeping the y-values the same. Therefore, the equation of the reflected graph is:
y = -34
b. Shifting f(x) 9 units to the right:
To shift a function 9 units to the right, we replace t with (t - 9) in the equation. Therefore, the equation of the shifted graph is:
y = 34
c. Shifting f(x) 8 units upward:
To shift a function 8 units upward, we add 8 to the equation. Therefore, the equation of the shifted graph is:
y = 34 + 8
y = 42
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Bob's Gift Shop sold 350 cards for Mother's Day. One salesman, Bentley, sold 2% of the cards sold for Mother's Day. How many cards did Bentley sell?
2% of 350 is 7, so Bentley sold 7 cards on Mother's Day
For what values of c does the quadratic equatrion x^2-2x+c=0 have two roots of the same sign
The roots have positive or same signs when c>0.
Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.
\(b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2\)
Roots of quadrant equation have Samsame sign if product of roots >0.
\(\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0\)
Roots of quadratic equation have positive sign if product of roots<0.
c>0.
Combining results, we get:-
roots have positive signs when:-
c>0.
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rate x time = distance how far will a boat travel moving 20 km per hour for 3.5 hours?
the boat will travel 70 kilometers in 3.5 hours when moving at a rate of 20 kilometers per hour.
To calculate the distance traveled by a boat, we can use the formula: Rate x Time = Distance.
In this case, the rate of the boat is 20 km per hour, and the time is 3.5 hours.
Using the formula, we have:
Distance = Rate x Time
Distance = 20 km/h x 3.5 hours
Calculating the result:
Distance = 70 km
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Consider the points below. P(θ),−4,0),Q(5,1,−2),R(6,4,1) (a) Find a nonzero vector orthogonal to the plane through the points P,Q, and R. (b) Find the area of the triangle PQR.
(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.
(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:
PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)
PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)
Taking the cross product of PQ and PR, we have:
n = PQ x PR = (9, 1, -2) x (10, 4, 1)
Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.
(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:
|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)
Evaluating the magnitude gives |n| = \(\sqrt\)(811).
The area of triangle PQR is then:
Area = |n| / 2 = \(\sqrt\)(811) / 2.
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Help I will be marking brainliest!!!
A. 82°
B. 98°
C. 38°
D. 126°
Show work, if possible. Thanks❤️
Answer:
A. \( 82\degree\)
Step-by-step explanation:
By the theorem of intersecting chords inside a circle.
\( m\angle OVU=\frac{1}{2} (m\widehat {GK} +m \widehat {OU}) \)
\( m\angle OVU = \frac{1}{2} (142\degree + 54\degree) \)
\( m\angle OVU=\frac{1}{2} \times 196\degree \)
\( m\angle OVU = 98\degree \)
\( m\angle OVU + m\angle OVU = 180\degree \)
(Linear pair angles)
\(m\angle OVG + 98\degree = 180\degree \)
\( m\angle OVG =180\degree - 98\degree\)
\( m\angle OVG = 82\degree\)
The graph of g(x) is a transformation of the graph of f(x)=3^x.
Enter the equation for g(x) in the box.
g(x) =
Transformation involves changing the position of a graph
The equation of g(x) is \(\mathbf{g(x) = 8(2)^x}\)
A geometric function is represented as:
\(\mathbf{y =ab^x}\)
The graph of g(x) passes through (-1,4) and (-2,2)
So, we have:
\(\mathbf{2 =ab^{-2}}\)
\(\mathbf{4 =ab^{-1}}\)
Divide both equations
\(\mathbf{\frac{4}{2} =\frac{ab^{-1}}{ab^{-2}}}\)
Divide
\(\mathbf{2 =b}\)
Rewrite as:
\(\mathbf{b =2}\)
Substitute 2 for b in \(\mathbf{4 =ab^{-1}}\)
\(\mathbf{4 = a2^{-1}}\)
Multiply both sides by 2
\(\mathbf{8 = a}\)
Rewrite as:
\(\mathbf{a = 8}\)
Substitute 2 for b and 8 for a in \(\mathbf{y =ab^x}\)
\(\mathbf{y = 8(2)^x}\)
Express as a function
\(\mathbf{g(x) = 8(2)^x}\)
Hence, the equation of g(x) is \(\mathbf{g(x) = 8(2)^x}\)
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Answer:
g(x)=8(2)^x
Step-by-step explanation:
find the perimeter of the regular hexagon
9 ft. 2 in.
please help asap thank u so much
Answer:660 in
Step-by-step explanation: Just add 6 sides, 9 ft= 108 in, + 2 in = 110, 110x6 = 660
What does the quotient 35 over x represent?
Answer:
35 ÷ \(x\)
Step-by-step explanation:
\(\frac{35}{x}=\) 35 ÷ \(x\)
Answer:
Brainliest!
Step-by-step explanation:
the answer of 35/x
the answer to any divison question is going to be called the quotient
PLEASE HELP ASAP
During a lab experiment, the temperature of a liquid changes from 6 2/5°F to 10 3/4°F.
What is the percent of increase in the temperature of the liquid?
Enter your answer in the box as a percent rounded to the nearest hundredth.
Answer: 67.97%
Step-by-step explanation: I took the test. THE ANSWER IS NOT 39.56%.
Answer:
67.97
Step-by-step explanation:
I took the test