A system of linear equations includes the line that is created by the equation y=0.5x-1 and the line through the points (3, 1) and (–5, –7), shown below.
What is the solution to the system of equations?
a. (–6, –4)
b. (0, –1)
c. (0, –2)
d. (2, 0)
Answers
Answer: Solution is,
d. (2, 0)
Step-by-step explanation:
Since, the equation of line that passes through points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
[tex](y-y_1)=\frac{x_2-x_1}{y_2-y_1}(y-y_1)[/tex]
Thus, the equation of line through the points (3, 1) and (–5, –7) is,
[tex](y-1)=\frac{-7-1}{-5-3}(x-3)[/tex]
[tex](y-1)=\frac{-8}{-8}(x-3)[/tex]
[tex]y - 1 = x - 3[/tex]
[tex]\implies y = x - 2------(1)[/tex],
Equation of second line is,
[tex]y = 0.5x - 1 -----(2)[/tex],
By equation (1) and (2),
x - 2 = 0.5x - 1 ⇒ 0.5x = 1 ⇒ x = 2,
From equation (1),
We get, y = 0,
Hence, the solution of line (1) and (2) is (2,0).
Related Questions
What is the domain of the relation: (0, 7), (8, -1), (2, 3), (-4, 6)?
A. (-4, 0, 2, 8)
B. (-1, 3, 6, 7)
C. (1, 7, 8, -1)
D. (2, 3, -4, 6)
Answers
When asked for the domain and given a set of ordered pairs, the domain is always all of the x values ordered from least to greatest.
Plato-Match each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion (if any) that proves the relationship.
Answers
The second one on the left is matched with the last one on the right, because it says that two of the angles are equal, and one side is equal, hence, AAS, or ASA.
The last one on the left is matched with the first one on the right, because it says all three sides are equal, therefore, SSS.
The third one on the left is matched with the second one on the left. I'll be honest, I'm not sure why this is, (geometry isn't my best subject either Dx) but by the process of elimination, this is it.
Probability of a lightbulb failing question? If the probability is .001 that a light bulb will fail on any given day, then what is the probability that it will last at least 30 days?
Answers
Mika wrote the table of points below. x y 0 2 3 5 6 8 Which explains whether or not Mika has described a proportional relationship, and why?
Answers
Answer:
B
Step-by-step explanation:
Edg 2020
Answer:
Step-by-step explanation: Answer B
A baby wriggled so much that weighing him at the clinic was a problem. So the doctor held the baby and stood on a scale. Then the nurse held the baby and stood on the scale. Then the doctor held the nurse who held the baby and stood on the scale. the three results were 78 kg, 69 kg and 142 kg respectively. What was the weight of the baby.
Long question but help me out ( it was 69 kg I mean)
Answers
y = weight of the doctor.
z = weight of the nurse.
x + y = 78 so y = 78 - x
x + z = 69 so z = 69 - x
x + y + z = 142
substitute y = 78 - x and z = 69 - x into x + y + z = 142
x + y + z = 142
x +78 - x + 69 - x = 142
-x + 147 = 142
-x = - 5
x = 5
answer
the weight of the baby was 5 kg
weight of the Nurse be N
weight of the Doctor be D
Now if we fit those into equations we have:
1. B+D= 78
2. B+N= 69
3. B+D+N= 142
Now take 1 and 3:
B+D= 78 so substitute 78 in the thrid equation were B+D is
78+N= 142 ( what plus 78 will get you 142)
78+64= 142
The nurse's weight is 64 kg
Now that we have the nurses weight. You take the combined weight of the baby and nurse and subtract 64
The baby weighs 5kg
now take the doctors and babies combine weight and subtract 4
The Doctor weighs 73 kg
ANSWER:
The baby weighs 5kg, the nurse weighs 64, and the doctor weighs 74.
Sorry for the long answer but hope this helps.
When $n$ is divided by 10, the remainder is $a$. when $n$ is divided by 13, the remainder is $b$. what is $n$ modulo 130, in terms of $a$ and $b$?
Answers
If
N = a (mod 10)
N = b (mod 13)
gcd(10,13) = 1
then
N = 10 bx + 13 ay (mod 130)
Where
10x + 13y = 1
-> (10x + 13) (mod 2) = 1 (mod 2)
-> y (mod 2) = 1
y = -3, x = 4
-> N = 40b – 39a (mod 130)
It is given that ra + sb should be non-negative:
N = 40b – 39a (mod 130)
N = 40b + (130 – 39)a (mod 130)
N = 40b + 91a (mod 130)
Therefore, N modulo 130, in terms of a and b is: N = 40b + 91a (mod 130).
Final answer:
To find the value of n modulo 130 in terms of a and b, one must solve two congruences using the Chinese Remainder Theorem. The solution would require computations beyond the scope of this response and would result in n expressed as a linear combination of a and b modulo 130.
Explanation:
To solve for the values of n modulo 130, given that when n is divided by 10, the remainder is a, and when n is divided by 13, the remainder is b, we can express n in the following forms:
n = 10k + a, where k is some integer
n = 13l + b, where l is some integer
Since 10 and 13 are coprime, Chinese Remainder Theorem tells us that there is a unique solution for n modulo 130 that satisfies both of these congruences. To find n in terms of a and b, we must find k and l such that these two equations give the same n for a particular value of n between 0 and 129 inclusive. This can be done through careful calculations or using a method designed for solving simultaneous congruences.
Once the suitable k and l values are found, the value of n modulo 130 can be stated. Since the exact solution requires more context or computational techniques, we can't provide the specific number in this case, but the final answer will be in the form: n ≡ (something involving a and b) (mod 130).
Which expression is equivalent to r^9/r^3
Answers
Answer:
The correct option is B.
Step-by-step explanation:
The given expression is
[tex]\frac{r^9}{r^3}[/tex]
According to the property of exponent,
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this property of exponent, we get
[tex]\frac{r^9}{r^3}=r^{9-3}[/tex]
[tex]\frac{r^9}{r^3}=r^{6}[/tex]
The expression [tex]r^{6}[/tex] is equivalent to the given expression.
Therefore the correct option is B.
What is the initial value of the function represented by this graph?
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5.
0
1
2
5
Answers
The initial value of a function is the value of the function when x = 0
o when x = 0, y = 2 so the initial value is 2
Answer:
2
Step-by-step explanation:
The initial value is what you start off with, so it is 2! :)
One number exceeds another by 11. the sum of the numbers is 3535. what are the numbers?
Answers
2x + 11 = 3535
2x = 3524
x = 1762
1762 and 1773
What is the range of this set of heights in centimeters?
{140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}
38
41
46
50
(If you can help me with this maybe you can help me with my last posted question? It hasn't been answered and I need help!)
Answers
Second, subtract your greatest number from your smallest number: 182-132 = 50
Therefore, your answer is: 50
Final answer:
The range of the given set of heights is 50 cm, which is determined by subtracting the smallest height (132 cm) from the largest height (182 cm) in the set.
Explanation:
The range of a set of numbers is the difference between the largest and the smallest numbers in the set. To find the range of the given heights in centimeters, you first identify the largest and smallest numbers in the set {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}. The smallest height is 132 cm, and the largest is 182 cm.
Now, subtract the smallest value from the largest value to determine the range:
Range = Largest value – Smallest value
Range = 182 cm – 132 cm
Range = 50 cm
Therefore, the range of the given set of heights is 50 cm.
A party rental company has chairs and tables for rent. The total cost to rent 3 chars and 2 tables is $20. The total cost to rent 8 chairs and 4 tables is $45. What is the cost to rent each chair and each table?
Answers
Equations:
8c + 4t = 45
3c + 2t = 20
Modify for elimination: ( multiply 2nd eq by -2)
8c + 4t = 45
-6c + -4t = -40
Subtract and solve for "c":
2c = 5
c = $2.50 (cost of one chair)
Solve for "t":
3c + 2t = 20
3(2.50) + 2t = 20
7.50 + 2t =20
2t=12.50
T= 12.50/2 =6.25
t = $ 6.25 (cost of one table)
Table = 6.25 each
Chair = 2.50 each
Check:
3(2.50) + 2(6.25) =
7.50 +12.50 = 20
8(2.50) + 4(6.25) =
20.00 + 25.00 = 45.00
How can you rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations?
Answers
Make a the subject of the formula
b^2 = 2as + c
subtract c from both sides:-
b^2 - c = 2as
Now divide both sides by 2s ( to isolate a):-
a = (b^2 - c) / 2s
You can rearrange formulas to highlight a specific quantity of interest by identifying it and isolating it using inverse operations.
Explanation:In mathematics, you can rearrange formulas to highlight a specific quantity of interest using the same reasoning as in solving equations. The goal is to isolate the variable or the quantity you want to highlight on one side of the formula. Here are the steps to do it:
Identify the quantity of interest you want to highlight.
Apply inverse operations to isolate that quantity on one side of the equation/formula.
Simplify or solve for the highlighted quantity if needed.
For example, if you have the formula for the area of a rectangle, A = L * W, and you want to solve for the length of the rectangle, you can rearrange the formula as L = A / W, highlighting the length as the quantity of interest.
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What property is illustrated by the equation (8 + 2) + 7 = (2 + 8) + 7? A. Commutative property of addition B. Associative property of Addition C. Distributive property D. Identity Property of Addition
Answers
So, B. Associative property of Addition.
Solve for z: 3z -5 +2z=25 -5z
Answers
To answer this question you will have to combine like terms.
3z-5+2z=25-5z
Combine 3z and 2z first because they have z in common and are on the same side: 3z+2z=5z
Now you have -5+5z=25-5z
Now you will go ahead and distribute since you can't combine anymore on certain sides.
You can add 5 to 25 on the other side: 25+5=30
Then add 5z to 5z on the other side: 5z+5z=10z
So now your equation should look like this: 10z=30
From here you will have to divide both sides by 10: 10/10=1(since it came to 1 it will just stay as z instead of 1z) 30/10=3
So your solution should come to: z=3
How do you find the vertex of this parabola? I just plotted the points down on a graphing calculator, but I figure there's a better way.
Answers
Which of the following shows 2 + (x + 3y) rewritten using the Associative Property of Addition
Answers
(2 + x) + 3y ...>Associative Property of Addition
hope it helps
Answer:
[tex](2+x)+3y[/tex]
Step-by-step explanation:
In associative property , when we add the numbers we can group the numbers in any combination.
for example : [tex]a+(b+c)= (a+b)+c[/tex]
[tex]2 + (x + 3y)[/tex] can be written as [tex](2+x)+3y[/tex] using associative property.
The terms can be grouped in any combination
[tex](2+x)+3y[/tex]
can someone pls help me
Answers
circle=4 <=======
Plug circle value in
diamond+2= 5*(4)
diamond+2=20
diamond=18 <=====
Plug circle and diamond value in
2(4)=18+2*triangle
8=18+2*triangle
-10=2*triangle
-5= triangle <=======
Find x 58 degrees and adjacent 4.0
Answers
For the problem, it might have asked for the opposite side or the hypotenuse. We use the cosine function to find the hypotenuse:
cos 58° = adjacent/hypotenuse = 4/hypotenuse
hypotenuse = 7.55 units
Then, we use the tangent function to find the opposite side.
tan 58° = opposite/adjacent = opposite/4
opposite = 6.4 units
How do you graph y^2=x^3?
Answers
To graph these types of equations, we need to remember our rules about graphing squared values and cubed values. A squared function will create a parabola, while a cubed function will create a curvy line over the y-axis.
A.) How many ways can you select 1 flavor of ice cream, 1 topping and 1 drink if there are 5 flavors of ice cream, 3 toppings and 4 drinks to choose from?
B.) How many ways can you select a 4-digit passcode without repeating any digit?
C.) How many ways can you select 3 toppings for a pizza with 8 toppings to choose from?
D.) What is the probability of rolling a single die and it landing on a prime number? (Remember, the number 1 is not considered prime.)
E.) How many items are in the sample space for rolling a die and spinning a spinner with 4 different colored sections (red, yellow, green and blue)?
F.) What is the probability of rolling the die and spinning the 4-sectioned spinner described in part E, and getting the number 5 and the color red?
G.) If you wanted to purchase a size T-shirt that "most" people could wear, would you purchase the mean size, the median size or the mode size?
Answers
This means a total of 5*3*4=60 ways.
B) assuming that the first digit can be 0, we have 10 choices for the 1. digit, 9 for the 2., 8 for the third and 7 choices for the fourth digit.
In total, there are 10*9*8*7=5040 passwords we can create.
C) Selection of 3 objects out of 8, can be done in
C(8, 3)=8!/(3!5!)=(8*7*6)/3!=8*7=56 many ways.
D.
P(prime)=n(prime)/n{1, 2, 3, 4, 5, 6}=n{2, 3, 5}/6=3/6=1/2=0.5
E.
any of the 6 outcomes of rolling a die, can be combined with any of the 4 colors.
for example (1, red), (1, yellow), (1, green), (1, blue).
so in total, there are 6*4=24 items in the sample space.
F.
(5, red) is just one of the 24 items in the sample space, so its probability is 1/24= 0.0417
G.
the mode, as it is the size which appears the most.
Answers:
A.60
B.5040
C.56
D. 0.5
E.24
F.1/24= 0.0417
G.mode
Write an equation that can be used to find the area A of a rectangular rug whose sides are 5 feet long and x feet long
Answers
What is the solution of the equation 6x - 8 = 4x? X=
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hope this helps you
no idea. please help:)
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A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed?
Answers
180 seconds --- x words
[tex]x= \cfrac{180*120}{100}=18*12=216 \ \text{words}[/tex]
Answer:
216
Step-by-step explanation:
i think
There were 490 people at play. The admission price was $3.00 for adults and $1.00 for children. The admission receipts were $990. How many adults and children attended
Answers
3a + c = 990
3(490 - c) + c = 990
1470 - 3c + c = 990
-3c + c = 990 - 1470
-2c = - 480
c = -480 / -2
c = 240 <=== there were 240 children
a + c = 490
a + 240 = 490
a = 490 - 240
a = 250 <== there were 250 adults
A box contains seven green marbles, six blue marbles and eight orange marbles. Without looking, you choose two marbles out of the bag. What is the probability that the first two picked will both be green if you don’t replace the marble after the first pick?
Answers
The probability is 0.1 (or 10%).
It is required to find the probability.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes.
Given that:
The favorable count is determined as follows: considering Green marbles. There are 7 of them in the box, so 7 possible picks at the first draw.
Since you don't replace the pick, at the next drawing there are only 6 Green ones. So for each of the 7 possible first picks, there are 6 possible second picks: number of possibilities is 7 by 6 = 42.
The total number of possible drawings, irrespective of color is determined as follows: there are 21 marbles in total at first drawing, and 20 at second. So, for each first pick there are 20 possibilities, i.e., total number is 21 by 20 = 420
The probability is P = 42 / 420 = 1 / 10 = 0.1 (or 10%)
So, the probability is 0.1 (or 10%).
Learn more about probability here:
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What is the measure of RST?
Answers
Answer:
∠TSR = 93°
Step-by-step explanation:
In the figure attached as we know ∠S = [tex]\frac{mQR+mPT}{2}[/tex] [ By the theorem of angles of the intersecting secants in a circle]
∠S = [tex]\frac{131+43}{2}[/tex]
= [tex]\frac{174}{2}[/tex]
= 87°
Now we have to find the measure of ∠RST
Since ∠QSR + ∠TSR = 180° [ supplementary angles]
87° + ∠TSR = 180°
∠TSR = 180 - 87 = 93°
Therefore, m∠TSR = 93° is the answer.
Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale.
A. 13
B. 26
C. 77
D. 38.5
Answers
OA = OB = OC = OD [radii]
So, ΔOAB = ΔOCD (SSS)
In congruent triangles all corresponding angles and are congruent, so
∠x = ∠COD = 77°
Jessica plans to purchase a car in one year at a cost of $30,000. how much should be invested in an account paying 10% compounded semiannually to have the funds needed?
Answers
A=p (1+r/k)^kt
A fund needed 30000
p Amount invested?
R interest rate 0.1
K compounded semiannual 2
T time 1 year
Solve the formula for p to get
P=A÷(1+r/k)^kt
P=30,000÷(1+0.1÷2)^(2×1)
P=27,210.88
The mean incubation time for a type of fertilized egg kept at 100.2100.2â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 11 dayday. â(a) what is the probability that a randomly selected fertilized egg hatches in less than 2121 âdays? â(b) what is the probability that a randomly selected fertilized egg hatches between 2222 and 2323 âdays? â(c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?
Answers
To solve this problem, what we have to do is to calculate for the z scores of each condition then find the probability using the standard normal probability tables for z.
The formula for z score is:
z = (x – u) / s
where,
x = sample value
u = sample mean = 23 days
s = standard deviation = 1 day
A. P when x < 21 days
z = (21 – 23) / 1
z = -2
Using the table,
P = 0.0228
Therefore there is a 2.28% probability that the hatching period is less than 21 days.
B. P when 23 ≥ x ≥ 22
z (x=22) = (22 – 23) / 1 = -1
P (z=-1) = 0.1587
z (x=23) = (23 – 23) / 1 = 0
P (z=0) = 0.5
P = 0.5 - 0.1587 = 0.3413
Therefore there is a 34.13% probability that the hatching period is between 22 and 23 days.
C. P when x > 25
z = (25 – 23) / 1
z = 2
P = 0.9772
This is not yet the answer since this probability refers to the left of z. Therefore the correct probability is:
P true = 1 – 0.9772
P true = 0.0228
Therefore there is a 2.28% probability that the hatching period is more than 25 days.