The solutions to these system of equations are given as follows:
1. x = 1, y = 7.
2. x = 0.5, y = 2.
3. x = 6, y = -2.
4. x = 3, y = 3.
What is a system of equations?A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of a problem.
For item 1, it is already stated that the solution for x is x = 1, hence the solution for y is obtained as follows:
y = 2(1) + 5 = 7.
For item 2, we are given two equations for y, hence the solution for x is obtained as follows:
2x + 1 = 6x - 1
4x = 2
x = 2/4
x = 0.5.
Hence the solution for y is:
y = 2(0.5) + 1 = 1 + 1 = 2.
For item 3, from the second equation, we have that:
y = 4 - x.
Then the solution for x will be of:
2(x - 7) = 4 - x
2x - 14 = 4 - x
3x = 18
x = 18/3
x = 6.
The solution for y is:
y = 4 - 6 = -2.
For item 4, from the first equation, we have that:
y = 3x - 6.
Then, replacing on the second equation, the solution for x is obtained as follows:
x + 3(3x - 6) = 12
x + 9x - 18 = 12
10x = 30
x = 3.
Then the solution for y is:
y = 3x - 6 = 3(3) - 6 = 9 - 6 = 3.
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Can you help me with this problems, thank you.
The probability that student will pass the test is 2/7.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.So, the probability that the student will pass the test:
The total number of questions are 50 and 25 questions need to be correct to pass the test.Out of 25, 15 are correct.Out of the remaining 35 questions, 10 questions need to be right to pass the best.Probability Formula: P(E) = Favourable events/Total events
Now, calculate as follows:
P(E) = Favourable events/Total eventsP(E) =10/35P(E) = 2/7Therefore, the probability that student will pass the test is 2/7.
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Write one quadratic equation that forms a graph through the points (−4,2) and (2,2) and has a
maximum value at the vertex.
Explain please
Quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.
Given,
Quadratic equation passes through the points (-4,2) and (2,2)
(x₁, y₁) =(-4,2)
(x₂ ,y₂) = (2,2)
Here,
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
⇒(y - 2) / (x + 4) = (2 - 2) / (2 + 4)
⇒ (y-2) / (x+4) =0
⇒y -2 =0
⇒y = 2
Quadratic equation formed from the given points (-4,2) and (2,2) is y =2.
Which represents the horizontal line and does not have any vertex.
Therefore, quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.
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According to the general equation for conditional probability, if P(AB) =3/7 and P(B)=7/8,
what is P(AIB)? O A. O B. O c. O D. 16 49 32 24 49
Answer:
(d) 24/49
Step-by-step explanation:
You want to know P(A|B) when P(AB) = 3/7 and P(B) = 7/8.
Conditional probabilityThe general equation for conditional probability tells you ...
P(A|B) = P(AB)/P(B)
P(A|B) = (3/7)/(7/8) = (3/7)·(8/7)
P(A|B) = 24/49
When an object is thrown upward, its height (S), in meters, is given (approximately) by the quadratic equation
S = -5t² + vt + h, where v is the upward initial velocity in meters/second, t is the time of flight in seconds, and h is the
height above level ground from which the object is thrown. Johnny is standing on a platform 16 meters high and
throws a ball straight up as high as he can at a velocity of 16 meters/second. At what time t will the ball hit the
ground?
The ball will strike the ground
seconds after it is thrown.
Check the picture below.
[tex]~~~~~~\textit{initial velocity in meters} \\\\ S = -5t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&16\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&16\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ 0=-5t^2+16t+16\implies 5t^2-16t-16=0 \\\\\\ (5t+4)(t-4)=0\implies t= \begin{cases} -\frac{4}{5}\\\\ 4 ~~ \textit{\LARGE \checkmark} \end{cases}[/tex]
the equation for meters is usually as you see in the picture but for this exercise it got rounded from -4.9 to -5, which is fine.
let's notice that "t" has two values, however the seconds cannot be a negative value, so we dismiss that one.
The ball will strike the ground 4 seconds after it is thrown When an object is thrown upward, its height , in meters, is given by the quadratic equation S = -5t² + vt + h
To find the time at which the ball will hit the ground, we need to determine when the height (S) of the ball becomes zero. At that moment, the ball will be at ground level.
The height (S) of the ball is given by the quadratic equation:
S = -5t² + vt + h
where:
S = height of the ball in meters
t = time of flight in seconds
v = initial velocity in meters/second (upward velocity, so it's positive)
h = height above level ground from which the object is thrown
Given that the initial velocity (v) is 16 meters/second, and the height above the ground (h) is 16 meters, we can substitute these values into the equation:
S = -5t² + 16t + 16
Now, to find the time (t) at which the ball hits the ground, we need to solve for t when S = 0:
0 = -5t² + 16t + 16
This is a quadratic equation in standard form (ax² + bx + c = 0), and we can solve it by factoring or using the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula is given by:
t = (-b ± √(b² - 4ac)) / 2a
In our case, a = -5, b = 16, and c = 16. Plugging these values into the quadratic formula:
t = (-(16) ± √(16² - 4*(-5)16)) / 2(-5)
t = (-16 ± √(256 + 320)) / -10
t = (-16 ± √576) / -10
Now, find the two possible solutions for t:
t₁ = (-16 + √576) / -10
t₁ = (-16 + 24) / -10
t₁ = 8 / -10
t₁ = -0.8 seconds
t₂ = (-16 - √576) / -10
t₂ = (-16 - 24) / -10
t₂ = -40 / -10
t₂ = 4 seconds
We have two solutions for t: t = -0.8 seconds and t = 4 seconds. However, we can disregard the negative value for time, as time cannot be negative in this context.
So, the ball will strike the ground 4 seconds after it is thrown.
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From ratio proportion for the following using
2 different way
45 members of Glee Club to 30 members of Dance
Club
Answer:
see explanation
Step-by-step explanation:
this can be expressed in ratio form and fractional form , that is
45 : 30 ( divide each part by 15 )
= 3 : 2 ← in simplest form
= [tex]\frac{3}{2}[/tex]
Tiffany borrows $8,000 to pay for college. The loan has a 7% interest rate that compounds monthly. She plans to pay off the loan in 15 years. How much will she pay in total?
Tiffany needs to pay $8,084.44 in total.
what is Compound Interest?In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.
Given:
P= 8000
R= 7%= 0.07
Time= 8 years.
Now, Amount = P[tex](1 + r/n)^{nt[/tex]
Amount = 8000 [tex](1 + 0.07/15)^{12 . 15[/tex]
Amount = 8000 x (1 + 5.8333333333333E-5)
amount = $8,084.44
Hence, Tiffany needs to pay $8,084.44 in total
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12 ^-3 wasnt at school the week we did negative integers help pls
1/1728 is the value of negative integers .
What in math is an integer?
A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.Three sorts of integers exist: 0 (zero), positive integers (natural numbers), and negative integers (Additive inverse of Natural Numbers)= 12⁻³
= 1/12³
= 1/1728
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In which quadrant does the point (10, -9) lie?
Answer:Qadrant 4
Step-by-step explanation:
The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles. The measure of the smallest angle is three-
quarters the measure of the middle angle. Find the measure of each angle.
Measure of largest. smallest and middle angle of a triangle under given conditions is 145°, 15° and 20° respectively.
What is angle sum property of a triangle?
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
According to the given question:
Let the measure of middle angle = x
The measure of the smallest angle is three-quarters the measure of the middle angle.
∴ Smallest angle = (3/4)x
The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles.
∴ Largest angle = 110° + x + (3/4)x
Now, by Angle sum property of a triangle
x + (3/4)x + 110° + x + (3/4)x = 180°
On solving for the value of x we get
2x + (3/2)x = 70°
7x = 140°
x = 20°
Therefore,
measure of middle angle x = 20°
measure of smallest angle (3/4)x = 15°
measure of the largest angle 110° + x + (3/4)x = 145°
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Two year ago ernest dorsey purchased a used sports coupe for 8000.00 that is now worth 6000.00 last year he drove it 13569 miles and kept a record od all expenses. His variable costs were gasoline $1589.56 oil changes $245.98 and repairs $548.11 his fix costs were insurance $1105.32 and license $85 find de cost per mile
The cost per mile incurred by Ernest Dorsey for driving the sports coupe for last year was $0.41.
How is the cost per mile derived?The cost per mile is the quotient of the division operation involving the total cost incurred and the driving mileage for the year.
To derive the total cost, add up the value of the car consumed (cost - current value), the annual variable, and fixed costs.
Cost of a used sports coupe last year = $8,000
The current value of the car = $6,000
Used value for the year = $2,000.00 ($8,000 - $2,000)
Yearly variable costs:Gasoline $1,589.56
Oil changes $245.98
Repairs $548.11 $2,383.65
Annual fixed Costs:Insurance $1,105.32
License $85.00 $1,190.32
Total cost for the year = $5,573.97
Driven mileage for the year = 13,569 miles
Cost per mile = $0.41 ($5,573.97/13,569)
Thus, the cost per mile is $0.41.
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Solve the following simultaneous equations using substitution
Answer:
the answer is 18 lol....
if Tn =5n +2 which term will have a value of 52
Answer:
10th term
Step-by-step explanation:
given [tex]T_{n}[/tex] = 5n + 2 and [tex]T_{n}[/tex] = 52 , then equate right sides and solve for n
5n + 2 = 52 ( subtract 2 from both sides )
5n = 50 ( divide both sides by 5 )
n = 10
that is the 10th term has a value of 52
(3^3*6^6)^-3
what is a simplified version of this
The simplified value of the above expression is 5.00248967e-19
we know,'^' this symbol means by times
[tex]3^{3}[/tex] =27
[tex]6^{6}[/tex] =46,656
27 multiplied by 46,656
[tex]27 \times 46,656 = 1,259,712[/tex]
[tex]1,259,712 ^{-3} = 5.00248967e-19[/tex]
if you want you can apply the BODMAS system here.
it is just a fraction try to simplify it.
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Kyle buys $50,000 of company XYZ's shares, at a share price of
$100. A year later, XYZ's share price is $110, and Kyle sells all his
shares. How many dollars did Kyle's investment gain?
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
Given,
The share bought by Kyle of company XYZ = $50,000
The share price = $100
The share price after an year = $110
We have to find the gain amount by Kyle when Kyle sells all his shares.
Here,
We can apply Unitary method;
100 ⇒ 110
50000 ⇒ x
Compute;
100x = 110 x 50000
x = (110 x 50000) / 100
x = 110 x 500
x = $55000
Now,
Kyle gains,
55000 - 50000 = $5000
That is,
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
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The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Find
(a) the co-ordinates of the mid-point of the line PQ,.
The co-ordinates of the mid-point of the line PQ are (6,4).
From the question, we have
The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Mid-point of the line PQ =(10+2)/2 , (12-4)/2
= (6,4).
Midpoint:
A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.
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Please only answer if you know the answer for sure,
URGENT
Carl is making accessories for the soccer team. He uses 773.85 inches of fabric on headbands for 29 players and 4 coaches. He also uses 279.56 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Your answer might be 16.31 inches for each headband and wristband for each player.
---------------------------------------
Hope this helps!
Joke: What has ears but can’t hear a thing?
Answer: A cornfield.
Have a great day and God bless! :D
Solve for y 4(7y+x)=4
Answer:
Step-by-step explanation:
y= 1/7 - x/7
Answer:
y = 1/7 - x/7
Step-by-step explanation:
4(7y + x) = 4 Distribute the 4 to 7y and x
28y + 4x = 4 Subtract the 4x on both sides
28y = 4 - 4x To get 'y' by itself divide 28 on both sides
y = 4/28 - 4x/28 You can simplify the 4/28 since 4 goes into 28 7 times
y = 1/7 - x/7
The cost to produce x units of wire is C= 45x + 450, while the revenue is R= 70x. Find the interval where the product will at least break even.
The interval where the product will be at least break even equals to 18 units.
What is a break even point?In accounting, the break-even point refers to the production level at which total revenues equal total expenses.
Given data
Cost is given as C = 45x + 450
Revenue is given as: R = 70x
In this case, the point of breakeven will be:
Cost = Revenue
45x + 450 = 70x
We will collect like terms:
70x - 45x = 450
25x = 450
We will divide both side by 25:
25x/25 = 450/25
x = 18
Therefore, the interval where the product will be at least break even equals to 18 units.
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Simplify: 3√50+ √24 - 2√72
A. 3√6 +2√2
B. 3√9+2√5
C. 3√2+2√6
D. 10√2+2√6
Answer:
Step-by-step explanation:
13+(-3)^2+4(-3)+1- {-10-(-6)}
_________________________
[4+5}/ [4^2-3^2(4-3)-8]+12
15/3=5
What expression is equivalent to -6(t+9)
-6t -54 is the expression equivalent to-6(t+9)
How determine equivalent expressions?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)
Given: -6(t+9)
First, clear the parenthesis by using -6 to multiply t and 9:
-6(t+9) = (-6 x t) + (-6 x 9)
= -6t + (-54)
= -6t -54
Therefore, the -6t -54 is equivalent to -6(t+9)
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HELP!! which expression is equivalent to the given expression 2X^2 -11 X -6
Answer: C.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
3. Round 134.76821 to the nearest hundredth.
Answer:
134.77
Step-by-step explanation:
Round 134.76821 to the nearest hundredth
by placing each number in reference to what they represent.
1 - hundreds
3 - Tens
4 - units
.7=Tenth
.76=Hundredth
.768=Thousandth
.7682=Ten Thousandth
.76821= Hundred Thousandth
Nearest hundredth will be
134.[76]821
since 2,1 are both round down numbers they will produce approximately 0
since 8 is a round off number it will produce approximately 10
134.77000
or 134.77
you can award the answer as brainliest
A drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green. What is the probability of picking a shirt that is red or striped?
The probability of picking a shirt that is red or striped is 2/3.
Given, that a drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green.
We have to find the probability of picking a shirt that is red or striped,
P(R ∪ S) = P(R) + P(S) - P(R∩S)
where, R be the event that the shirt is red.
and S be the even that the shirt is striped.
P(R) = 5/12 (as, there are 5 red shirts)
P(S) = 5/12 (as, there are 5 striped shirts)
P(R∩S) = 2/12 (as, there are 5 striped red shirts)
P(R ∪ S) = 5/12 + 5/12 - 2/12
P(R ∪ S) = 8/12
P(R ∪ S) = 2/3
The probability of picking a shirt that is red or striped is 2/3.
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In chapters 5-8 of Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm. What causes these feelings
A. A visit from his father
B. A letter from Elizabeth
C. The arrival of Henry Clerval
D. An award for creating the monster
Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm, An award for creating the monster causes these feelings.
How does Victor first react to the monster and what happens to both after the first encounter?Victor is the first to enter and is relieved to see no evidence of the creature. But, exhausted by months of labour and the horror of the creature he has created, he becomes ill with a nervous fever that lasts several months.Victor begins to grasp, for the first time, that what he has made is not only the scientific result of an experiment in animated matter, but a genuine living entity with needs and desires.He informs Victor that all of his horrible deeds stemmed from his desperate loneliness. He offers to take his new friend to South America, where they will hide in the bush away from human interaction. He claims that with the sympathy of a fellow monster, he will no longer be compelled.'Frankenstein,' by Mary Shelley, is the narrative of Victor, who creates a monster with the goal of generating life. He was a genius in college, and he created a monster. His own creation was a failure.To learn more about Frankenstein, refer,
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Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm, An award for creating the monster causes these feelings.
How does Victor first react to the monster and what happens to both after the first encounter?Victor is the first to enter and is relieved to see no evidence of the creature. But, exhausted by months of labor and the horror of the creature he has created, he becomes ill with a nervous fever that lasts several months.Victor begins to grasp, for the first time, that what he has made is not only the scientific result of an experiment in animated matter, but a genuine living entity with needs and desires.He informs Victor that all of his horrible deeds stemmed from his desperate loneliness. He offers to take his new friend to South America, where they will hide in the bush away from human interaction. He claims that with the sympathy of a fellow monster, he will no longer be compelled.'Frankenstein,' by Mary Shelley, is the narrative of Victor, who creates a monster with the goal of generating life. He was a genius in college, and he created a monster. His own creation was a failure.To learn more about Frankenstein, refer,
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The face value of a simple discount note is $17,000. The discount is 4% for 160 days. Calculate the following. a. Amount of interest charged for each note. (Round your answer to the nearest cent.) b. Amount borrower would receive. (Round your answer to the nearest cent.)
The amount of interest to be charged on the note, based on the face value of the note, is $302. 22.
The amount the borrower would receive is $16, 697. 78.
How to find the interest charged?The interest charged on the simple discount note can be found by the formula:
= Face value of note x discount rate x number of days / total days in a year
= 17, 000 x 4% x 160 / 360
= $302. 22
The amount that the borrower would receive is then:
= Face value of note - Interest charged on note
= 17, 000 - 302.22
= $ 16, 697. 78
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Need help please someone
The equation of the linear function is y=8x+(-8).
What do you mean by equation?
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.
According to data in the given question,
We have points (0,-8) and (1,0), thus
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\=\frac{(0-(-8))}{1-0} \\=8[/tex]
Then
y=8x+b
Points (0,-8) means that when x=0, y=-8 and we use this to find b,
y=8x+b
-8=8(0)+b
-8=0+b
b=-8
So, y=8x+(-8)
Therefore, the equation of the linear function is y=8x+(-8).
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Draw the line of reflection that reflects ABC onto A'B'C'.
James shares 5/8 of a cake between 6 people.
What fraction of the cake do they each receive?
Answer:
5/48
Step-by-step explanation:
The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.
As per the given,
James shares 5/8 of a cake between 6 people.
Now, 1/6 of 5/8 will be as,
1/6(5/8) = 5/48
Hence "The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48".
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Load the GSS14SSDS-B data set in SPSS and use the frequency procedure to investigate the variability of the respondent's current age (AGE). Click on Analyze, Descriptive Statistics, Frequencies, and then Statistics. Select the appropriate measures of variability.
The level of measurement for the variable AGE is ---
The variance is ---
The standard deviation is ---
The mean is ---
The number of valid responses (n) is ---
Choices:
55.11
48.18,
50.12
1500
Ordinal
18.058
17.073
1490
Nominal
276.584
Interval
291.495
16.054
301.498