Using Cramer's Rule, what is the value of x in the solution to the system of linear equations below
X+ 3y - 16
3x + y = 8
Answers
Answer:
x = 5
Step-by-step explanation:
Here, we want to use Crammer’s rule to find the value of x
Please check attachment for complete solution
Related Questions
Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes.
The function with the lowest output values as x approaches infinity is _. The function with the greatest output values as x approaches infinity is _.
Answers
The function with the lowest output values as x approaches infinity is A.
The function with the greatest output values as x approaches infinity is B
Two different families pay for entry into a water park.
Family 1 has 2 adults and 3 children and costs a total of £20 to enter the park.
Family 2 has 1 adult and 4 children and costs a total of £15 to enter the park.
Work out the cost of the adult ticket, and the child ticket.
Answers
Answer:
Adult ticket: $7
Child ticket: $2
Step-by-step explanation:
Set up a system of equations where a represents the cost of one adult ticket and c is the cost of one child ticket:
2a + 3c = 20
a + 4c = 15
Solve by elimination by multiplying the bottom equation by -2:
2a + 3c = 20
-2a -8c = -30
Add them together:
-5c = -10
c = 2
Now, we can plug in 2 as c to find the value of a:
2a + 3c = 20
2a + 3(2) = 20
2a + 6 = 20
2a = 14
a = 7
The solution is
The cost of one adult ticket = $ 7
The cost of one child ticket = $ 2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of one adult ticket be = x
Let the cost of one child ticket be = y
Now , for Family 1 :
2 adults and 3 children and costs a total of £20 to enter the park
Substituting the values in the equation , we get
2x + 3y = 20 be equation (1)
Now , for Family 2 :
1 adult and 4 children and costs a total of £15 to enter the park
Substituting the values in the equation , we get
x + 4y = 15 be equation (2)
On simplifying the equations , we get
Multiply equation (2) by 2 , we get
2x + 8y = 30 be equation (3)
Subtracting equation (1) from equation (3) , we get
5y = 30 - 20
5y = 10
Divide by 5 on both sides of the equation , we get
y = 2
So , the cost of one child ticket is $ 2
Now , substituting the value of y in equation (2) , we get
x + 4y = 15
x + 4 ( 2 ) = 15
x + 8 = 15
Subtracting 8 on both sides of the equation , we get
x = 15 - 8
x = 7
So , the cost of one adult ticket is $ 7
Hence , the value of x is $ 7 and value of y is $ 2
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Can someone help me with this question please.
Answers
Answer: The total number of vehicles in the bar graph does not add up to 30.
The spacing between the bars should be equal.
It would be helpful to put the number of each type at the top of its bar.
It may be useful to give the location and time/date of the observation in the title of the graph.
Step-by-step explanation: The total 12 + 8 + 6 = 26.
My other observations would depend on the purpose of the graph. Many people use color to make the graph more visually appealing.
A new hockey stick costs $57.00 at the sporting goods store. If there is a 6%
sales tax, what is the actual cost of the hockey stick?
Answers
Answer:
$60.42
Step-by-step explanation:
0.06 x $57 = $3.42
$57 + $3.42 = $60.42
Hope this helped! :)
Sonya made a graph showing the first ten minutes of her drive to the movies. A graph with time on the x-axis and speed on the y-axis. The graph increases, increases rapidly, and then remains constant. Which description is the best interpretation of the graph? Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway. Sonya backed out of her driveway at a constant speed and then accelerated until she reached the street where the movie was playing. She stopped the car. Sonya drove down her driveway at a constant speed until she reached the street. She turned and drove down the street at a constant speed. Her car went slower as she drove up a hill. At the top of the hill she drove into the parking lot of the movie theater. Sonya accelerated as she drove down her driveway. She accelerated on the street on her way to the highway entrance. She waited for a red light, then accelerated onto the highway.
Answers
Answer:
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
Step by step explanation:
The first scenario is the best match for the increasing slope, (leaving the house and accelerating) rapidly increasing slope (increasing speed on ramp) and level line (constant speed on the highway).
The best interpretation of the graph is,
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
What is Acceleration?When a point or an object moving in a straight line , the acceleration is the rate at which velocity changes with time, in terms of both speed and direction.
Here, we have,
The first scenario is the best match for the increasing slope, (leaving the house and accelerating) rapidly increasing slope (increasing speed on ramp) and level line (constant speed on the highway).
Hence, The best interpretation of the graph is,
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
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1. Bailey withdrew $135 from her checking account. Write an algebraic expression that describes answer asap
Answers
Answer:
x - 135 where x is the money you have in your bank
Step-by-step explanation:
Answer:
X-135
Step-by-step explanation:
$135 from her checking account.=x
PLEASE HELP ASAP FOR ALGEBRA 1 Mr Reder has just robbed a bank and is trying to escape on foot. He is currently 3 miles from the bank and running at 5 miles per hour. Write an equation to model how far from the bank Mr Reder is after a certain amount of time has passed. How far has he gone after 3 hours? Draw an appropriate graph for this equation.
Answers
Answer:
He has ran 15 miles and passed the bank 12 miles from his location where he is at.
Step-by-step explanation:
WHY WAS HE ROBBING A BANK?????????
Answer:
Step-by-step explanation:
His distance from the bank can be modeled using an equation in the form y=mx+b. Since he has already ran 3 miles, the "b" is equal to 3, and can be added to how many miles he runs on from now on. If he can run 5 miles per hour, then that means every hour, he will run 5 miles. We can represent how many hours have passed as x. This would make our equation y=5x+3.
After 3 hours he has gone 5(3)+3 miles, or 18 miles
x+2y=-6
y= -1/2 - 3
name the solution to the system of linear equations
Answers
Answer:
Infinite Amount of Solutions
(1, -3.5) - 2nd Option
Step-by-step explanation:
If your systems of equations is:
x + 2y = -6
y = -1/2x - 3
Then when you put the first equation in slope intercept form, you get the exact same 2 lines. Therefore, our answer is Infinite amount of solutions.
If you systems of equations is:
x+ 2y = -6
y = -1/2 - 3
We find where the 2 graphs intersect. Therefore, our answer is (1, -3.5)
⇒Answer:
(1,-3.5)
⇒Step-by-step explanation:
Well to find the solution we need to do the following
Steps,
_______________________
Substitute y
Combine like terms
Sperearte x
When x is found substitute
Combine like terms
Single out y
_______________________
x + 2(-1/2x - 3) = -6
x - 1 - 6 = -6
x - 7 = -6
x = 1
y = -1/2(1) - 3
y = -1/2 - 3
y = -3.5
____________
Answer:
(1,-3.5)
PLEASE HELP ME Logan has twice as many contacts in his phone as Marcus. Janet has 8 more then 1/3 of the number of contacts that Marcus has. Marcus has 243 contacts in his phone. How many more contacts does Logan have than Janet?
Answers
Which of the sets of ordered pairs represents a function? (1 point)
A = {(2, 7), (1, −5), (7, 2), (2, −9)}
B = {(5, 3), (−2, −9), (−3, 8), (9, 3)}
Answers
Answer:
B = {(5, 3), (−2, −9), (−3, 8), (9, 3)}
Step-by-step explanation:
A function has no repeating inputs (x-values). One input is assigned to exactly one output.
In set 'A', the input of two is repeated.
A = {(2, 7), (1, −5), (7, 2), (2, −9)}
In set 'B', there are no repeating inputs.
Set 'B' is a function.
Brainilest Appreciated.
John who is 5 ft tall is standing 20 feet away from a tree, and you measure the angle of elevation to be 38∘. How tall is the tree? Find your answer to the nearest tenth.Instructions: Find the missing length indicated.
Answers
Answer:
5√17=
20.6
Step-by-step explanation:
[tex]adj \: = 5 \\ opp \: = 20 \\ hyp \: = \: \\ pythagoras \: theorem \: \: = \\ {hyp}^{2} = {opp}^{2} + {adj}^{2} [/tex]
[tex] {hyp \:}^{2} = {20}^{2} + {5}^{2} \\ {hyp }^{2} = 400 + 25 \\ {hyp}^{2} = 425 \\ \sqrt{ {hyp}^{2} } = \sqrt{425} [/tex]
[tex]hypotenuse \: = 5 \sqrt{17} [/tex]
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the tree is 20.6257 feet.
What is Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The digram for the given condition is given below. Now, in ΔABC, the tangent value for ∠A can be written as,
tan(38°) = BC/AB
tan(38°) = 5 feet / AB
AB = 6.3997 feet
Now, in ΔABC and ΔADE for ∠A the value of the tangent can be written as,
tan(38°) = BC/AB = ED/AD
5/6.3997 = ED/(20 + 6.3997)
ED = 20.6257 feet
Hence, the height of the tree is 20.6257 feet.
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Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is . For one performance, advance tickets and same-day tickets were sold. The total amount paid for the tickets was . What was the price of each kind of ticket
Answers
Answer:
Advance tickets=$25
Same-day tickets=$15
Step-by-step explanation:
Complete question below:
Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $ 40. For one performance, 25 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was $1075 . What was the price of each kind of ticket?
Let
advance tickets=x
Same-day tickets=y
Combined cost of advance and same-day tickets=$40
It means,
x+y=40 Equ (1)
25 advance tickets and 30 same-day tickets=$1075
It means,
25x+30y=1075 Equ(2)
From (1)
x+y=40
x=40-y
Substitute x=40-y into (2)
25x+30y=1075
25(40-y)+30y=1075
1000-25y+30y=1075
5y=1075-1000
5y=75
Divide both sides by 5
5y/5=75/5
y=15
Recall,
x+y=40
x+15=40
x=40-15
=25
x=25
Advance tickets=$25
Same-day tickets=$15
Check
25x+30y=1075
25(25)+30(15)=1075
625+450=1075
1075=1075
It is given that and are right angles, and . Since they contain right angles, ΔABR and ΔACR are right triangles. The right triangles share hypotenuse , and reflexive property justifies that . Since and , the transitive property justifies . Now, the hypotenuse and leg of right ΔABR is congruent to the hypotenuse and the leg of right ΔACR, so by the HL congruence postulate. Therefore, ________ by CPCTC, and bisects by the definition of bisector.
Answers
THIS IS THE COMPLETE QUESTION BELOW;
Complete the paragraph proof. Given: ∠ABR and ∠ACR are right angles AB ≅ BC BC ≅ AC Prove: bisects ∠BAC
It is given that ∠ABR and ∠ACR are right angles, AB ≅ BC and BC ≅ AC Since they contain right angles, △ABR and △ACR are right triangles. The right triangles share hypotenuse AR, and reflexive property justifies that AR ≅ AR. Since AB ≅ BC and BC ≅ AC, the transitive property justifies AB ≅ AC. Now, the hypotenuse and leg of right △ABR is congruent to the hypotenuse and the leg of right △ACR, so △ABR ≅ △ACR by the HL congruence postulate. Therefore, by CPCTC, and bisects ∠BAC by the definition of bisector.
Answer:
The answer is ∠BAR=∠CAR
Step-by-step explanation:
From the question, In the ΔABR and ΔACR , AB=AC=X
CHECK THE ATTACHMENT FOR DETAILED STEP BY STEP EXPLANATION:
Answer:
A) <BAR = <CAR
Step-by-step explanation:
Edge
HELP ASAP Linear Relations Question
Answers
Answer:
8.8
Step-by-step explanation:
set up a system
let x be sour keys and y be chocolate bars
2.65=15x+2y
3.35=10x+3y
then solve
X turns out to be 0.05
y turns out to be 0.95
multiply : 24*0.05=1.2
multiply : 0.95*8=7.6
add : 1.2+7.6 = 8.8
Which answers are equivalent to the fraction below? Check all that apply
12/16
A.1/2 B.6/8 C2/3 D.2/6 E.3/4 F.6/4
Answers
Answer: e
Step-by-step explanation: 12/16 6/8 3/4
Answer:
B and E.
Step-by-step Explanation:
B: 6/8
6*2=12
8*2=16
12/16
E: 3/4
3*4=12
4*4=16
12/16
Hope this helps!!!!!
Find the range of the given function y = 5x + 2, where x > -2.
Answers
Answer:
Its -3,2,7
Step-by-step explanation:
Simply put, you plug in all values greater than -2. Which is what thst function tells you.
PLEASE HELP!!!
The model below represents 4x+(-4) -- 2x+8
What is the value of x when solving the equation 4x+(-4) --2x+8 using the algebra tiles?
X-2
Answers
Answer:
x=6
Step-by-step explanation:
4x-4=2x+8
Get all x's to one side. Subtract 2x from both sides.
2x-4=8
Isolate x. Add 4 to both sides.
2x=12
Divide both sides by 2 to get x.
12/2=6
x=6
Answer:
2 A.K.A. C. this answer is really late i think but for people in the future this is the answer lol
This service is NOT important when comparing banks: a: Debit card design. b:Hours of operation. c:Convenience of location. D:Monthly fees and minimum balance required.
Answers
Answer:
A.
Step-by-step explanation:
Debit card design really has nothing to do with banks but has to do with personal preference. If you are comparing banks, you would want to see when they are open, how much you would need to deposit to start an account, that kind of stuff.
Frank is going to an amusement park that costs $36.00 for admission. Treats cost $4.00 each. Frank does not want to spend more than $52.00 in all.
Solve for x, where x equals the number of $4.00 treats Frank can buy.
A. x=3
B. x>4
C. x≤4
D. x<14
Answers
Answer:
B: x>4
Step-by-step explanation:
You want to make an inequality first:
36+4x>52
4x + 36 − 36 > 52−36
4x > 16
4x ÷ 4 > 16 ÷ 4
x > 4
Solve for x -8x+44≥60 and -4x+50<58 Thanks! :)
Answers
Answer:
Step-by-step explanation:
- 8x + 44 ≥ 60
Subtract 44 from both sides
- 8x + 44 - 44 ≥ 60 - 44
- 8x ≥ 16
Divide both sides by -8 and flip the inequality sign
-8x/-8 ≤ 16/-8
x ≤ -2
x = { ......... -4,-3,-2}
2) -4x + 50 < 58
Subtract 50from both sides
-4x + 50 -50 < 58- 50
-4x < 8
Divide both sides by -4 and flip the inequality sign
-4x/-4 > 8/-4
x > -2
x= {-1, 0 , 1 , 2....... }
Answer:
1. [tex]x \leqslant - 2[/tex] 2. [tex]x \: > 2[/tex]Step-by-step explanation:
1. [tex] - 8x + 44 \geqslant 60[/tex]
Move constant to R.H.S and change its sign
[tex] - 8x \geqslant 66 - 44[/tex]
Subtract the numbers
[tex] - 8x \geqslant 16[/tex]
Divide both sides of the inequality by -8 and flip the inequality sign
[tex]x \leqslant - 2[/tex]
2. [tex] - 4x + 50 < 58[/tex]
Move constant to the R.H.S and change its sign
[tex] - 4x < 58 - 50[/tex]
Subtract the numbers
[tex] - 4x < 8[/tex]
Divide both sides of the inequality by - 4 and flip the inequality sign
[tex]x > - 2[/tex]
Hope this helps...
Best regards!!
Please help me to solve this question.
Answers
Answer:
[tex]314 \frac{2}{7} cm^{2} [/tex]
Step-by-step explanation:
Surface area of sphere= 4πr², where r is the radius of the sphere.
Given that the diameter is 10cm,
2(radius)= 10cm
radius= 10 ÷2
radius= 5cm
Surface area of sphere
[tex] = 4( \frac{22}{7} )( {5}^{2} ) \\ = 314 \frac{2}{7} cm^{2} [/tex]
find the solution(s) to x^2-12x+36=0
Answers
Answer:
x = 6
Step-by-step explanation:
x² - 12x + 36 = 0
(x - 6)² = 0
x - 6 = 0
x = 6
Hope this helps! :)
Answer:
x = 6
Step-by-step explanation:
x² - 12x + 36 = 0
Factor left side.
(x - 6)² = 0
Set factor equal to 0.
x - 6 = 0
x = 6
ƒ(x) = -(-x), when x = -3?
Answers
Answer:
-3
Step-by-step explanation:
Substitute negative 3 as x and you get this -(--3). Then the two negatives make a positive and it's -(3) which becomes -3.
From the information given, what is the biggest flaw in the study? A health researcher randomly selected 500 high school students from the city of Oak Grove. In a private interview the researcher asked the students whether they had ever used drugs. She concluded that only 8% of the high school students of Oak Grove have ever used drugs.
Answers
Answer:
The correct answer is - The setting may discourage honest responses.
Step-by-step explanation:
In this particular setting of research and interview regarding this research may not produce hones results as the question is too direct to ask students if they had ever used drugs.
Research should be anonymous and should avoid the questions that can lead to bias results like this case that may lead to dishonest results.
Thus, the correct answer is : The setting may discourage honest responses.
Which statements are true regarding the diagram? Check all that apply.
The side opposite the 60° angle has a length of
The side opposite the 60° angle has a length of .
sin(60°) =
sin(60°) =
The other acute angle of the triangle is 30°.
Answers
Answer:
A. The side opposite the 60° angle has a length of √3/2
C.Sin(60°)=√3/2
E.The other acute angle of the triangle is 30°
Step-by-step explanation:
The diagram has been attached to the answer
A. The side opposite the 60° angle has a length of
B. The side opposite the 60° angle has a length of .
C. sin(60°) =
D. sin(60°) =
E. The other acute angle of the triangle is 30°.
Answer
The side opposite the 60° angle has a length of the square root of 3/2
Opposite side of the 60° angle has a length of √3/2
sin(60°) = the square root of 3/2
Sin(60°)=√3/2
The other acute angle of the triangle is 30°
Proof:
Total angle in a triangle=180°
180°-60°-90°
=30°
Answer:
A, D, E
Step-by-step explanation:
I do is big smart
What is one of the zeros of the function shown in this graph?
Answers
Answer:
-4 or 2Step-by-step explanation:
the x-intercepts of the graph are the zeros of the quadratic function
Gwendolyn shot a coin with a sling shot up into the air from the top of a building. The graph below represents the height of the coin after
x seconds.
Answers
Answer: A
Step-by-step explanation:
A game at the fair involves ping-pong balls numbered 1 to 18. You can win a prize if you correctly choose the 5 numbers that are randomly drawn. What are your chances of winning? The answer is 0.014, but i don't know how to get there.
Answers
Answer: 0.014
Step-by-step explanation: 5 divided by 18!
Please help me answer these two! I’m terrible at maths
Sorry about the screen it’s on my laptop
Answers
Answer:
£54 and 168.75 mins
Step-by-step explanation:
Mrs smith invests £30,000 (some in a 5% account, some in an 8% account). After the year shes earned £2100. How much did she put in each account? PLEASE HELP!!
Answers
Answer:
She deposited £10,000 in the 5% yield account and deposited £20,000 in the 8% yield account
Step-by-step explanation:
Let the amount she put in each account be £x and £y respectively
Total amount deposited is ;
x + y = 30,000 ••••••(i)
Now, let’s look at the earnings:
in the £x , amount earned would be;
5/100 * x = 5x/100
For the £y, amount earned would be;
8/100 * y = 8y/100
Adding both gives the total which is £2,1000
5x/100 + 8y/100 = 2,100
Multiply through by 100
5x + 8y = 210,000 ••••••••(ii)
From the first equation, we know that
x = 30,000 -y
Let’s put this into the second
5(30,000-y) + 8y = 210,000
150,000-5y + 8y = 210,000
3y = 210,000 -150,0000
3y = 60,000
y = 60,000/3
y = £20,000
So mathematically;
x = 30,000-y
x = 30,000 -20,000
x = £10,000