20 points!! Solve this system of lineal equations.separate the x- and y- values with a comma
12x=54-6y
-17x=-62-6y
Answers
Express the system in standard form:{12 x + 6 y = 54 | (equation 1)-(17 x) + 6 y = -62 | (equation 2)
Swap equation 1 with equation 2:{-(17 x) + 6 y = -62 | (equation 1)12 x + 6 y = 54 | (equation 2)
Add 12/17 × (equation 1) to equation 2:{-(17 x) + 6 y = -62 | (equation 1)0 x+(174 y)/17 = 174/17 | (equation 2)
Multiply equation 2 by 17/174:{-(17 x) + 6 y = -62 | (equation 1)0 x+y = 1 | (equation 2)
Subtract 6 × (equation 2) from equation 1:{-(17 x)+0 y = -68 | (equation 1)0 x+y = 1 | (equation 2)
Divide equation 1 by -17:{x+0 y = 4 | (equation 1)0 x+y = 1 | (equation 2)
Collect results:Answer: {x = 4 {y = 1
Please note the { are supposed to span over both equations but it interfaces doesn't allow it. Please see attachment for clarification.
Related Questions
if R and S are two points in a plane, the perpendicular bisector of line RS is the set of all points equidistant from R and S. True or false?
Answers
Answer: True
Step-by-step explanation:
A student got 34 pencils for school. If she sharpen 16 of the pencils before school what is her ratio of unsharpened pencils to sharpened pencils
Answers
34-16 = 18
so 18 are unsharpened
ratio is 18/16 reduced to 9/8
so the ratio of unsharpened pencils to sharpened pencils is :
18:16 which reduces to 9:8 or 9/8 or 9 to 8 <==
Which of the following terms, when added to the given polynomial, will change the end behavior?
y = –2x7 + 5x6 – 24
a)–x8
b)–3x5
c)5x7
d)1,000
e)–300
Answers
Answer:
1.A
2.C
Step-by-step explanation:
The end behaviour of the polynomial function y = -2x⁷ + 56x⁶ - 24 will change for a) - x⁸ and c) 5x⁷.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
Given, a polynomial function y = -2x⁷ + 56x⁶ - 24.
So, the given polynomial function has a degree of 7 and its end behavior will be changed by adding or subtracting terms that are of degree 7 and higher.
learn more about the end behavior of a polynomial here :
https://brainly.com/question/18076811
#SPJ2
Suzanne bought 50 apples at the apple orchard she bought four times as many red apples has green apples how many more red apples and green apples that Suzanne buy
Answers
Four students are playing the same video game. Their scores for the first three level are added together to see if the student has enough points to move on to round 2
Answers
This question is a high school-level mathematics problem involving statistics and data interpretation related to video game scores and soccer game performance.
Explanation:The question involves analyzing and interpreting different sets of data related to video game scores, hours played, and goals scored in soccer games. This requires an understanding of statistics and mathematical data interpretation techniques. Problems similar to these are often encountered in high school mathematics classes, especially those focusing on statistics and probability.
For example, when dealing with video game scores, a student may need to sumup numbers, compare totals, or calculate averages. In the case of the hours of video games played, one may need to aggregate data and analyze distributions. With soccer goals per game, the student might have to compute means and assess performance across different groups. Furthermore, the mention of a 'communist model' of grading ties into mathematical concepts of averaging and distribution of data.
These types of problems help students appreciate the practical applications of mathematics in understanding and interpreting real-world scenarios such as video game scoring systems and sports team performance analysis.
Jesse and three friends buy snacks for a hike. They buy trail mix for $5.42, apples for $2.55, and granola bars for $3.39. If the four friends split the cost of the snacks equally, how much should each friend pay?
Answers
Add $5.42, $2.55, and $3.39 together then divide by 4 (how many people in total there are) and you will get $2.84
Answer:
$2.84 is your answer
Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. are the given families of curves orthogonal trajectories of each other? that is, is every curve in one family orthogonal to every curve in the other family? x2 + y2 = ax x2 + y2 = by
Answers
[tex]P(x,y)=x^2+y^2-ax=0\\\\ \dfrac{\partial{P}}{\partial{x}}=2x-a\\\\ \dfrac{\partial{P}}{\partial{y}}=2y\\\\ Q(x,y)=x^2+y^2-by=0\\\\ \dfrac{\partial{Q}}{\partial{x}}=2x\\\\ \dfrac{\partial{Q}}{\partial{y}}=2y-b\\\\ \dfrac{\partial{P}}{\partial{x}}*\dfrac{\partial{Q}}{\partial{x}}+\dfrac{\partial{P}}{\partial{y}}*\dfrac{\partial{Q}}{\partial{y}}=(2x-a)*2x+2y(2y-b)\\ =4x^2+4y^2-2ax-2by\\ =2(2x^2+2y^2-ax-by)\\ =2*P(x,y)+Q(x,y))\\ =2*(0+0)=0\\\\ Answer YES [/tex]
Yes, the given curves are orthogonal. A further explanation is below.
Given equation is:
[tex]x^2+y^2=ax[/tex]By differentiating both sides, we get
→ [tex]2x+2yy'=a[/tex]
→ [tex]y'=\frac{a-2x}{2y} = m_1[/tex]
again,
[tex]x^2+y^2=by[/tex]By differentiating both sides, we get
→ [tex]2x+2yy' =by'[/tex]
→ [tex]y' = \frac{-2x}{2y-b}[/tex]
For both curves are orthogonal, we get
→ [tex]m_1 \ m_2 = -1[/tex]
By substituting the values, we get
→ [tex]\frac{(a-2x)}{2y} \ \frac{(-2x)}{2y-b} = -1[/tex]
→ [tex]-2ax +4x^2=-4y^2+2yb[/tex]
→ [tex]4(x^2+y^2)=2ax+2yb[/tex]
Since,
[tex]ax=x^2+y^2[/tex][tex]by=x^2+y^2[/tex]then,
→ [tex]4(x^2+y^2) =2(x^2+y^2)+2(x^2+y^2)[/tex]
→ [tex]4x^2+4y^2=4x^2+4y^2[/tex] (true)
Thus the above response is appropriate.
Learn more about orthogonal here:
https://brainly.com/question/20308962
What is the image of E for a dilation with center (0, 0) and a scale factor of 6?
(30, 6)
(-30, 6)
(30, -1)
(-30, 1)
Answers
Answer:
-30, 6
Step-by-step explanation:
6x-5= =30
1x6=6
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3427 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 65.75 feet per second and Plane B is gaining altitude at 35.5 feet per second.
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when they're at the same altitude.
Answers
65.75s - 35.5s = 5000 - 3427
30.25s = 1573
s = 1573 / 30.25
s = 52 seconds <== they are the same at 52 seconds
3427 + 65.75(52) = 6846
5000 + 35.5(52) = 6846
and their altitude is 6846 <===
Plane B, 4467+50.75x
x is number of seconds of time.
When altitudes equal?
5000+40+1/2x=4467+50+.75x
5000-4467=10.25x
x=53.3 seconds.
Use either formula for altitude of a plane to find what the altitude would be.
Value of the expression
Answers
Note: 5/7 ÷ 5/7 = 1
This brings us to
1/4 ÷ 4/10 + 1
1/4 * 10/4 + 1
10/16 + 1
5/8 + 1
Answer: 13/8
Catherine walks her dog 3/4 mile everyday how far does she walk each week
Answers
3/4 x 7 = 21/28
Catherine alks her dog 21/28 in a week.
I hope this helped!
52 companies; 25% increase
Answers
it increased to 65 companies.
I think thats wat u meant... if not then sry
distributive property of the product of 127 and 32
Answers
That comes out to 3900 + 260 - 90 - 6. Combine the positive terms. Then combine the negative terms. Last, combine the single positive term with the single negative one: 4160 - 96 = ?
In how many ways can you arrange 3 out of 5 books (a, b, c, d, and
e.on a shelf, if the order of each arrangement matters (so abc is different from cba)?
Answers
There are 60 different ways to arrange 3 out of 5 books on a shelf with the order mattering. So option (c) is correct.
To calculate the number of ways to arrange 3 out of 5 books with order mattering, we'll use the permutation formula [tex]\( P(n, k) = \frac{{n!}}{{(n-k)!}} \)[/tex], where ( n ) is the total number of items and ( k ) is the number of items to arrange.
In this case, we have ( n = 5 ) books and we want to arrange ( k = 3 ) of
them. So, [tex]\( P(5, 3) = \frac{{5!}}{{(5-3)!}} \)[/tex].
Let's break down the calculation step by step:
Calculate ( 5! ):
[tex]\( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \).[/tex]
Calculate [tex]\( (5-3)! = 2! \)[/tex]:
[tex]\( (5-3)! = 2! = 2 \times 1 = 2 \).[/tex]
Divide [tex]\( 5! \) by \( (5-3)! \)[/tex]:
[tex]\( \frac{{5!}}{{(5-3)!}} = \frac{{120}}{{2}} = 60 \).[/tex]
So, there are 60 different ways to arrange 3 out of 5 books on a shelf with the order mattering.
The correct answer is: c. 60
Complete Question:
In how many ways can you arrange 3 out of 5 books (A, B, C, D, and E) on a shelf, if the order of each arrangement matters (so ABC is different from CBA)?
a. 5
b. 120
c. 60
d. 10
What are the steps for using a compass and straightedge to construct a square ?
Answers
1. Using your straightedge, draw a reference line, if one is not provided.
2. Copy the side of the square onto the reference line, starting at a point labeled A'.
3. Construct a perpendicular at point B' to the line through .
4. Place your compass point at B', and copy the side of the square onto the perpendicular . Label the end of the segment copy as point C.
5. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.
6. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.
7. Connect points A' to D, D to C, and C to B' to form a square.
Hope this Helps
need this solved (3x+2y)(5x-6y)
Answers
A variable times itself gets you a square.
then just multiply the numbers.
Find the measure of angle y. Round your answer to the nearest hundreth.
Answers
You toss a coin a randomly selecte a number from 0 to 9. What is the probability of getting tails and selecting a 9?
A.0.05
B.0.95
C.0.25
D.0
Answers
Now, lets find the probability of selecting a 9. Since this includes 0, there are 10 possible outcomes and 1 way to get a 9, so the probability is 1/10.
To find them combined, multiply:
1/2 * 1/10
1/20
0.05
Hope this helps!
What is the average rate of change of f(x), represented by the graph, over the interval [0,2]?
A: 2
B: 1
C: 0.5
D: -0.5
Answers
The school cafeteria is baking cookies for lunch. each student gets 3 cookies with their lunch. if there are 231 children buying lunch, how many cookies do they have to make?
Answers
Multiply students x cookies per student
231 students x 3 cookies= 693 cookies
Josh rented a truck for one day. There was a base fee of$14.99,and there was an additional charge of81cent for each mile driven. Josh had to pay$117.05 when he returned the truck. For how many miles did he drive the truck
Answers
- $ 14.99
-------------
$102.46 left
Divide 102.46 by 0.81, and you get 126, which makes it 126 miles.
Hope this helps!
the area of a square is 225 square inches. find the length of a side of the square.
Answers
Let x represent the length.
x^2 = 225
You would have to square root both sides.
x = 15
The length is 15 inches.
Complete the square
Answers
Gwen has a £5 note and a £2 coin
A liter of cola costs £1.25
Gwen buys as many liter bottles as she can
How much money will she have left over
Answers
7/1.25=5.6
1.25*5=6.25
7-6.25=.75
$0.75 is your answer.
She will have £0.75 left over after the purchases.
First, we calculate the total amount of money Gwen has:
£5 (note) + £2 (coin) = £7
Next, we determine how many liter bottles of cola Gwen can buy:
Each bottle costs £1.25
Number of bottles she can buy = £7 ÷ £1.25
= 5 bottles
Now, we compute the total cost of 5 bottles:
5 bottles × £1.25/bottle
= £6.25
Finally, we find out how much money Gwen will have left over:
Total money - Total cost = £7 - £6.25
= £0.75
Gwen will have £0.75 left over after buying as many liter bottles of cola as she can.
Why do computer manufacturers typically make their new processors backward compatible with earlier processors?
Answers
Backward compatible typically means that the new invention would be compatible with previous inventions. So in this case, the new processor is compatible with the older processors. This is intended so that programs made for older processors can be used on the new one without the need for further modification.
"given a population in which the probability of success is p = 0.20, if a sample of 500 items is taken, then calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23 if the sample size is 200."
Answers
To find the probability that the proportion of successes in a sample is between 0.18 and 0.23, we approximate the binomial distribution with a normal distribution and calculate the z-scores for the specified values using the distribution N(0.2, sqrt((0.2)(0.8)/200)).
Explanation:To calculate the probability of the proportion of successes being between 0.18 and 0.23 for a population with a success probability of p = 0.20 and a sample size of n = 200, we use the sampling distribution of the sample proportion.
Firstly, to ensure the use of the normal approximation, we check the conditions: np = 40 and nq = 160, both greater than 5, allowing us to approximate the binomial distribution with a normal distribution where μ = p and σ = sqrt(pq/n).
For n = 200 and p = 0.20, the sampling distribution of the sample proportion p' is approximately N(0.2, sqrt((0.2)(0.8)/200)). Using this distribution, we can calculate the z-scores for 0.18 and 0.23 and then use standard normal distribution tables or software to find the probability that p' falls between these two values.
Learn more about Sampling Distribution here:https://brainly.com/question/39609355
#SPJ2
Darcy plants some flowers in her back yard. She plants 5 zinnias and 7 verbenas in each of her 3 flower beds. What is the total number of flowers she planted?
Answers
The circumference of circle p is 800 mm, the circumference of circle q is 200 cm, and the circumference of circle r is 4 m. What is the sum of the distance around each circle
Answers
Let us use the following conversions:
1 cm = 10 mm
1 meter = 100 cm = 1000 mm
Given:
p = 800 mm
q = 200 cm = 2000 mm
r= 4 m = 4000
X = sum of the distance around each circle
X = p+q+r
X = 800+2000+4000
X = 6800 mm or 680 cm or 6.80 m
a patient is to take 4 1/4 tablespoons of medicine per day in 5 equally divided doses. how much medicine is to be taken in each dose?
Answers
Follow below steps:
A patient is to take 4 1/4 tablespoons of medicine per day in 5 equally divided doses. How much medicine is to be taken in each dose?
Convert 4 1/4 tablespoons to a proper fraction, which is 17/4 tablespoons.
Divide 17/4 by 5 to find out how much medicine is to be taken in each dose. This equals 17/4 ÷ 5 = 17/4 × 1/5 = 17/20 tablespoons.
Melanie connected a brown garden hose, a green garden hose, and a black garden hose to make one long hose. The brown hose is 10.75 feet long, the green hose is 16.4 feet long, and the black hose is 8.5 feet long. What is the farthest distance the one long hose can reach?
Answers
Hope this helps!
Answer:
35.65 feet.
Step-by-step explanation:
We have been given that the brown hose is 10.75 feet long, the green hose is 16.4 feet long, and the black hose is 8.5 feet long. We are asked to find the distance that one long hose can reach.
The length of one long hose will be equal to sum of distances of each hose.
[tex]\text{The length of one long hose}=10.75\text{ ft}+16.4\text{ ft}+8.5\text{ ft}[/tex]
[tex]\text{The length of one long hose}=35.65\text{ ft}[/tex]
Therefore, the one long hose can reach 35.65 feet.