5x+9y=15x+2y=5 solve system of equationsenter exact answer as an ordered pair(x,y
Answers
GIVEN:
We are given the following system of eequations;
\(\begin{gathered} 5x+9y=15---(1) \\ \\ x+2y=5----(2) \end{gathered}\)Required;
To solve the system of equations and enter exact answer as an ordered pair (x,y).
Step-by-step solution;
To solve these equations, we first of all take note that one of the unknowns has a coefficient of 1. That is x in equation (2).
Hence, taking equation (2), make x the subject of the equation and we'll have;
\(x=5-2y\)Now we substitute the value of x into equation (1), as follows;
\(\begin{gathered} 5x+9y=15 \\ \\ Where;\text{ }x=5-2y \\ \\ 5(5-2y)+9y=15 \\ \\ 25-10y+9y=15 \\ \\ 25-y=15 \\ \\ Subtract\text{ }25\text{ }from\text{ }both\text{ }sides; \\ \\ -y=-10 \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }-1; \\ \\ \frac{-y}{-1}=\frac{-10}{-1} \\ \\ y=10 \end{gathered}\)We now have the vaalue of y.
We will substitute this value into either of the equations to get the value of x.
Substitute for y = 10 into equation (2);
\(\begin{gathered} x+2y=5 \\ \\ x+2(10)=5 \\ \\ x+20=5 \\ \\ Subtract\text{ }20\text{ }from\text{ }both\text{ }sides; \\ \\ x=-15 \end{gathered}\)Therefore,
ANSWER:
The answer as an ordered pair will be;
\((-15,10)\)Related Questions
5. Past experience shows that the standard deviation of the distances traveled by consumers to patronize Chinese restaurants is 2 km. How large a sample is needed to estimate the population mean distance traveled to within 0.4 km
Answers
Answer:
96
Step-by-step explanation:
Given that :
Standard deviation (s) = 2km
Error in estimation is within 0.4 km ; Error (E) = 0.4 km
Using the relation :
Sample size = ((Zα/2 * s) /E)^2
Using α = 0.05
The Zcritical at 0.05 = Z0.025 = 1.96
Sample size = ((1.96 * 2) / 0.4)^2
Sample size = (3.92 / 0.4)^2
Sample size = 9.8²
Sample size = 96.04
Required sample size = 96
GIVING BRAINLIST PLEASE HELP!
What is the range?
What is the y-intercept? What does this mean in terms of the snake population?
Answers
Answer:
Range :
\(y \geqslant 5\)
y intercept:
(0,5)
I'm not sure the first point does not have x and y values.
The graph has a direct proportion relationship.
The range and y-intercept of the graph representing snake population in time period n years is equal to y ≥ 5 and y = 5 respectively.
The range is defined as the set of all y values for the which f(x) is defined for the different values of x.
Here in the given graph of snake population and time 'n' years
Snake population represent the y-axis.
Time is on x-axis.
Here y values is greater than or equal to 5 .
Range = y ≥ 5
The y-intercept is the value for which x = 0.
Here for y = 5 we have x = 0.
y-intercept is y = 5.
Therefore, for the given graph range is y ≥ 5 and y-intercept is equal to y = 5 for the snake population in given time period.
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Whats the square root of 225
Answers
Answer:
15
Step-by-step explanation:
√225= 15
Therefore the square root of 225 is equal to 15
If carpet costs $3.25 per square yard, how much would it cost to carpet a rectangular room that is 8 yards wide and 12 yards long?
Answers
Answer: $312.00
Step-by-step explanation:
By multiplying the area of the floor wanted to be carpeted by the price rate, you can conclude that this room would cost $312 dollars to be carpeted.
What is 1 1/12-7/10?
Answers
Answer:
The answer is 23/60
Step-by-step explanation:
First we convert 1 1/12 and 7/10 to a common fraction.
1 1/12 = 13/12 = 65/60
7/10 = 42/60
Next you subtract 65/60 by 42/60.
65/60 - 42/60 = 23/60
Hope this helps! :)
Solve for x round to the nearest hundredth
27=(1/3)^x
Answers
The value of x is x = -3.
What is solving an equation?
Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics. Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.
Consider the given equation,
27 = (1/3)^x
This equation can be written as,
\(27 = \frac{1^x}{3^x}\)
Here 1^x
1\(27 = \frac{1}{3^x}\)
Take 3^x on numerator.
\(27 = 3^-^x\)
Now 27 can be written as, \(27 = (3)(3)(3) = 3^3\)
⇒ \(3^3 = 3^-^x\)
Applying the exponent rule: \(a^b=a^c\) ⇒ b = c
So we get,
3 = -x
Multiply both sides by -1.
-3 = x
x = -3
Hence the value of x is x = 3.
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Please help need urgent
Answers
Convert the cm to feet for the base and the height:
12/2 = 6 x 3 = 18 feet
9/2 = 4.5 x 3 = 13.5 feet
area = 1/2 x base x height
Area = 1/2 x 18 x 13.5
Area = 121.5 square feet
answer: 121.5 square feet
1. Jon waits on tables and is paid $6.75an hour. In a 40-hour period, he earned $310.50 in tips. What were his total earnings?
Answers
Answer:
$617.25
Step-by-step explanation:
$617.25 Because, $310.50(tips) + $306.75(hourly wage)=$617.25
Answer:$580.50
Step-by-step explanation:
:)
A trawler A is 40km west of another trawler B. A set off at 20kmh travel at 25kmh. What course should trawler B take to intercept trawler A
Answers
Trawler B should take a course that is 18 degrees east of north.
How to explain the angleIn order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.
Here are the steps to find the course that Trawler B should take:
Draw a diagram of the situation.
Label the two trawlers A and B.
Draw a line representing the direction that Trawler A is traveling.
Draw a line representing the direction that Trawler B should travel.
Measure the angle between the two lines.
The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.
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The function f(x) = x2 + 6x +7 is graphed below.
Drag the correct word and the the appropriate value to the box with each given interval to indicate whether the function is increasing or decreasing on that interval
Answers
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the function f(x) = x² + 6x + 7. This is a quadratic equation,that is of degree two.
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
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8 less than twice a number is the same as 4 more than that same number
Answers
Answer:
12
Step-by-step explanation:
So: 2x-8=4+x
x-8=4
x=12
Given that a student chose apple wedges, what is the probability that the student is in high school?
Answers
The probability would be 40.0%
John puts $1,500 in a savings account that earns 7% simple interest annually. Find the new
balance in his savings account after three years if John does not deposit or withdraw any
money.
Answers
Answer:
$1,815
Step-by-step explanation:
Use the simple interest formula, I = prt
Plug in the values we know:
I = prt
I = (1,500)(0.07)(3)
I = 315
Add this to the original amount:
1500 + 315
= 1,815
So, John will have $1,815 in his account after 3 years.
Let Q be an orthogonal matrix with an eigenvalue λ1=1. Let x be an eighenvector beloinging to λ1. Show that x is also an eigenvector of QT
Answers
If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).
To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.
Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.
Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.
Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:
QT * (Q * x) = QT * (λ1 * x)
Applying the associative property of matrix multiplication, we have:
(QT * Q) * x = λ1 * (QT * x)
Using the fact that Q * QT = I, we can simplify further:
I * x = λ1 * (QT * x)
Since I * x equals x, we have:
x = λ1 * (QT * x)
Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:
x = λ2 * x
where λ2 = λ1 * (QT * x).
This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).
In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).
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Alejandro kicks a football. The graph below shows the height of the football hh in meters after tt seconds. What is the football’s greatest height?
Answers
Answer:
The answer will be 30.625 m
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At which angle is secant of theta equals radical 2 question mark
7 times pi over 6
5 times pi over 4
7 times pi over 4
11 times pi over 6
Answers
The equation is given to be:
\(\text{sec} \theta=-\sqrt{2}\)
Recall that sec is the inverse of cos. Thus, we have:
\(\frac{1}{\text{cos}\theta}=-\sqrt{2}\)
Rewriting the equation, we have:
\(\text{cos}\theta=-\dfrac{1}{\sqrt{2} }\)
We can find the across of both sides:
\(\theta=\text{across}(-\dfrac{1}{\sqrt{2} } )\)
Since we know that:
\(\text{cos}(-x)=\text{cos}(x)\)
Then, we have:
\(\theta=\text{across}(\dfrac{1}{\sqrt{2} } )\)
Recall the identity:
\(\text{across}(\dfrac{1}{\sqrt{2} } )=\dfrac{3\pi }{4} +2\pi \text{n}=\frac{5\pi }{4} +2\pi \text{n}\)
Therefore, the answer is the SECOND OPTION.
Question 11 sto wants to buy a small wine form worth Re 500.00 he plans to Sell his current home For R3 400 00 which he will use as a deposit for the purchase of the form. He becure toan with a bank with a repayment period of 10 years and a internet roke of 9,5% Compounded monthly. Calcurate bre monthly repayments
Answers
The loan amount is the purchase price of the small wine farm minus the deposit:
Loan amount = 50000 - 3400000 = -3350000 ZAR
Note that the loan amount is negative because the borrower owes the bank money.
The monthly interest rate is the annual interest rate divided by 12:
Monthly interest rate = 9.5% / 12 = 0.007917
The total number of payments over 10 years is 10 x 12 = 120.
Using the formula for monthly loan payments, we get:
Monthly payment = (P x r) / (1 - (1 + r)^-n)
Where P is the loan amount, r is the monthly interest rate, and n is the total number of payments.
Plugging in the values, we get:
Monthly payment = (-3350000 x 0.007917) / (1 - (1 + 0.007917)^-120) = 39779.50 ZAR
Therefore, the monthly repayment is approximately 39,779.50 ZAR.
Dana is making bean soup. The recipe she has makes 10 servings and uses
3/4
of a pound of beans. How many total pounds of beans does she need to make 5 servings of soup?
She has
1/16
of a pound of beans in one container and
1/4
of a pound of beans in another container. How many more pounds of beans does Dana need to make the 5 servings of soup? Show your work or explain your answer.
Answers
6.X + 4 using the algebra
tiles.
What tiles need to be added to both sides to remove the
smaller x-coefficient?
What tiles need to be added to both sides to remove the
constant from the right side of the equation?
What is the solution?
Answers
Answer:
i
Step-by-step explanation:
is
coooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooool
Answer:
What tiles need to be added to both sides to remove the smaller x-coefficient?
✔ 5 negative x-tiles
What tiles need to be added to both sides to remove the constant from the right side of the equation?
✔ 4 negative unit tiles
What is the solution?
✔ x = –6
Step-by-step explanation:
need help pls, here is screenshot.
Answers
Answer:
r = 1/2
Step-by-step explanation:
Each term y is 1/2 of the previous term
A stock lost 8 1/4 points on Monday and then another 2 3/4 points on Tuesday. On Wednesday, it gained 12 points.
What was the net gain or loss of the stock for these three days?
Answers
The net gain of the stock for these three days is 1 points
Net gainMonday = - 8 1/4 pointsTuesday = -2 3/4 pointsWednesday = 12 pointsNet gain / net loss = Monday + Tuesday + Wednesday
= - 8 1/4 + (-2 3/4) + 12
= - 8 1/4 - 2 3/4 + 12
= -11 + 12
Net gain = 1 point
Therefore, the net gain of the stock for these three days is 1 points
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Based on the figure below, what is the value of x?
(5x + 15)
01
09
0 11
15
20°
Answers
Answer:
undefined
Step-by-step explanation:
because
the figure does not appear
indicate below which quantities should be graphed to yield a straight line whose slope could be used to calculate a numerical value for the acceleration due to gravity g. horizontal axis: vertical axis:
Answers
A numerical value for the acceleration due to gravity g on straigh line = 8.665
What is Straight Line?
Simply put, a straight line is a line devoid of bends. A straight line is one that has no curves and continues to infinity on both sides.
we need a table calculation for that see the attachment 1
vertical axis = l cm
horizontal axis = T²(sec²)
slope from the graph
= l/T²
= 0.2197
So, g = 4 T² * l /T²
= 4 * (3.14)² * 0.2147
g = 8.6646
g = 8.665 m/sec²
The acceleration caused by gravity is expressed numerically as g on a straight line = 8.665.
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A circular garden has a diameter of 9 feet. How many feet of trim are
needed to surround the garden?
Answers
C= 28.26
this is how much fence they would need around the garden approximately.
Answer:
29 feet
Step-by-step explanation:
find circumference
(formula diameter times pi)
9*pi=28.2743338823
we have to round up!
29 feet
:>
Jane and johnny are running a race. Jane's speed is 1/4 that of Johnny's.
What is Johnny's speed compared to Jane?
Explain.
25%
50%
150%
400%
Answers
The right response is 400%. In other words, Johnny moves at four times the pace of Jane.
We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.
We may compare the speeds as a fraction to figure out the ratio:
Johnny's speed divided by Jane's speed equals 4/1.
This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.
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Which of the following functions shows the reciprocal parent function,
F(x) = 1, vertically stretched?
LG
F(x) =
6
5
O A. G(X) = 1 + 10
B. G(x) =
X 100
1
OC. G(x) =
X-7
O D. G() =
9x
Answers
Answer:
C
Step-by-step explanation:
but it's also horizontally stretched (see screenshot)
Answer:
The correct answer is G(x)=1/9x
Step-by-step explanation:
seven more than the quotient of a number and 2 is equal to 3 equation
Answers
Answer:
Step-by-step explanation:
seven more than the quotient of a number and 2 is 10
7+n/2=10 n=6 check 7+3=10 ok
Identify the patterns rule for this sequence 2,8,7,13,12,18,17
Answers
Answer:
-1 then +6 thats the pattern
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Please answer the question that is stated in the image below. Thank you. It really means a lot to me.
Answers
Answer:
Below
Step-by-step explanation:
a) they won 120 games out of 369 played = 40/23=.325
b) they lost 248 out of 369 played = 248/369 = .672
c) Home games are 185 out of 369 = .501
d ) at home they won 72 out of (72+112+1) = 72/ 185 = .389
Ms. Hudson runs 6 miles in 2.5 hours. How far does she go in 5 hours?
Answers
Answer:
12 miles
Step-by-step explanation:
2.5 hours= 6 miles
1 hour= 6/2.5 miles
5 hours= 6*5/2.5= 12 miles