The system of equations involving 1/3x - 3y = -4 and x - 9y = -12 has infinite number of solutions.
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
1/3x - 3y = -4 (equation 1)
x - 9y = -12 (equation 2)
Using the second equation, find the value of one variable, lets say x, in terms of the other.
x - 9y = -12 (equation 2)
x = 9y - 12
Substitute the equation of x to the first equation.
1/3x - 3y = -4 (equation 1)
1/3(9y - 12) -3y = -4
3y - 4 - 3y = -4
Combining the all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.
3y - 3y = -4 + 4
0 = 0
Since we did not get unique values for x and y, check if one of the equations is a simplified form of the other. Multiply the first equation with 3.
1/3x - 3y = -4 (equation 1)
3(1/3x - 3y) = 3(-4)
x - 9y = -12
Since this new equation is the same with the second equation, this means that the lines of the two equations are the same(overlapping). Hence, the system of equations has infinite number of solutions.
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2. Which graph represents the solution
of 6 + 3y < 9 or 4y > 3y + 2?
Help please!!!!!
Answer: It is likely B
Step-by-step explanation:
1. Subtract 6:
6 -6 + 3y < 9 -6
2. Divide by 3:
3y/3 < 3/3
3. Simplify:
y < 1
--------------------------------------
1. Subtract 3y:
4y -3y < 3y -3y + 2
2. Simplify:
y < 2
(i) So the answer is likely B
Keisha read 8 pages in her book each day for 5 days. Then, she r How many total pages did Keisha read?
Answer:
40
Step-by-step explanation:
suppose electric power is supplied from two independent sources which work with probabilities 0.4, 0.5, respectively. if both sources are providing power enough power will be available with probability 1. if exactly one of them works there will be enough power with probability 0.6. of course, if none of them works the probability that there will be sufficient supply is o.
Answer:
What is the question
Step-by-step explanation:
Venus has switches at the top and bottom of her stairs to control the light for the stairwell. She notices that when the upstairs switch is up and the downstairs switch is down, the light is turned on.
c. If the upstairs switch is in the down position and the downstairs switch is in the up position, will the light be on?
If the upstairs switch is in the down position and the downstairs switch is in the up position, the light will be off
How to determine if the light will be on?The given parameters are
Switches = 2 i.e. top and bottom
Also, we have:
When the upstairs switch is up and the downstairs switch is down, the light is turned on.
This means that the light is only on when the upstairs switch is up and the downstairs switch is down
Any other position of the switches, the light is off
From the question, we have
Upstairs switch is in the down position and the downstairs switch is in the up position
This is different from the required position to on the light
Hence, the light will be off
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what’s the absolute value of the equation
|y-2|=|2y|
what is the range of the function on the graph? i’m
Answer: y∈(-∞,3]
Step-by-step explanation:
[tex]y=-|x+1|+3[/tex]
3. In Mrs. Middleton's math class, there are 7 more boys than girls. If there are 29 total students in the class, how many boys are there?
Convert the word problem into an equation as follows:
Let's use the variable 'x' for girls and 'x+7' for boys.
x + x + 7 = 29
Combine like terms
2x + 7 = 29
Subtract 7 from both sides
2x = 22
Divide 2 into 22 to get x
x=11 girls
x+7 = 18 Boys
three friends ate at restaurant. They ordered nachos for S19 95 and jalapeno poppers. Each friend paid $9.73, not including sales tax or tip, which was 1/3 of the total determine the cost of the jalapeno poppers
The total cost of a Jalapeno is $ 9.24
Three friends ate at a restaurant and ate nachos for $19.95 and jalapeno poppers.
Three of them paid $9.73 each
So the total amount of money paid by three friends = 3×9.73
= 29.19
Now we have to calculate the cost of jalapeno poppers
Therefore we have,
Total amount of money paid = cost of nachos + cost of jalapeno poppers
29.19 = 19.95 + cost of jalapeno poppers
The cost of jalapeno poppers =29.19 - 19.95
= $9.24
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Answer: The cost is $9.24 for the peppers.
Step-by-step explanation: Just do math.
is -24 greater than -24.0
Answer:
yes
Step-by-step explanation:
-24 is. a whole number so it would be greater
A scale drawing of a rectangular park is 6 cm wide and 10 cm long. The actual park is 180 meters wide. What is the area of the actual park in square meters?
The area of the actual park in square meters will be 54000m².
How to calculate the area?The length of the actual park will be:
= 180/6 × 10
= 300m
Width = 180m
Therefore, the area will be:
= Length × Width
= 300 × 180
= 54000 m²
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What did I do wrong ? Question is 7x + 5 = 6x
Answer: Look at the explanation.
Step-by-step explanation: So first you move the 6x to the left side of the equal sign, then u turn it into a negative number. Next, you do 7x-6x=5. Which is 2x=5. And to find x you do 5÷2. Which is 2.5.
Hope this helps!
Answer:
x = -5
Step-by-step explanation:
Let's solve the problem,
→ 7x + 5 = 6x
→ 7x - 6x = -5
→ [ x = -5 ]
Hence, the answer is -5.
your cousin has $156.34 in his bank-
account. He withdraws $15.50 one day
and B 6.75 the next day how much
money is in his bank accout now ?
Answer:
$134.09
Step-by-step explanation:
you take 156.34 and minus 15.50, then you take that and minus it by 6.75
Answer $134.09
why 156.34 - 15.50+6.75=134.09
If y=-1 is a zero of the polynomial q (y) = 4y³+ ky² - y -1, then find the vaLue of k
Answer:
Step-by-step explanation:
Since zero of a polynomial function is a value of the variable at which the function's value is 0, 0=4(-1)^3+k(-1)^2-(-1)-1, for the given polynomial q(y)=4y^3+ky^2-y-1
simplifying the above gives: 0= -4+k+0
k=4
Find the total amount given the original price and tax rate. round to the nearest hundredth if necessary. original price: $123.28 tax rate: 7.5% enter the correct answer in the box.
The Total amount to pay including the tax will be $132.52
In the given question, For the Total amount, we know that we have to add the Tax rate to the Principal amount. It is mentioned that the Principal amount P = $123.28 and the Tax rate is 7.5%. Firstly we have to calculate what amount of interest is to be charged upon the Principal amount. To calculate Interest we have the formula :
=> I = (P * R)/100 , where I = Interest, P = Principal Amt, R = Interest Rate
=> I = (123.28 * 7.5)/100 => I = 9.24
We get Interest amount = $9.24
To calculate the Total amount, We have the formula: T = P + I
where, T = Total Amount, P = Principal Amount, and I = Interest Amount
=> T = 123.28 + 9.24 => T = 132.52
Hence, the Total Amount is $132.52
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8 + 3 (-s + 2 ) -5s - 1 - 4s
Answer:
13 - 12s
Step-by-step explanation:
= 8 - 3s + 6 - 5s - 1 - 4s
= 13 - 12s
Answer:
8+3=11
(-s + 2) - 5s - 1 - 4s = -10s + 1
Tong draws 5 cards from a deck of 52 cards (which has 13 spades) without replacement. what is the probability of getting at most 2 spades?
As per the question, without replacement draw 5 cards from a deck of 52 playing cards. The probability to draw 5 cards can be written as:
[tex]P(getting2 spades) = \frac{P(E)}{n(E)} = \frac{13X12}{52X51} =\frac{1}{17}[/tex]
Therefore, the probability of getting at most two spades is [tex]\frac{1}{17}[/tex].
What is probability?
Probability is the method to measure the occurred events or the occurrence of the events. It is also used to analyze the outcomes of random events. To calculate the probability of a playing card which is [tex]52[/tex] in numbers. And it is divided into fours cards and each are in the count of [tex]13[/tex].These fours cards are heart, spades, diamond and club.
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WILL GIVE BRAINLIEST IF ANSWERED WELL!!!
Answer:
r = S/(2πh)
Step-by-step explanation:
S = 2πrh
divided by (2πh)
r = S/(2πh)
Find the distance between the two points in simplest radical form (0,-7)(-9,5)
Step-by-step explanation:
1111111111111111111111
jaylon created this stained glass window the upper two coners are quater ciecleseach with a radius of 4 inches. find the area of the window
The area of the window is 305.12 square inches.
How to find the area of the window?given that
jaylon created this stained glass window the upper two coners are quater ciecleseach with a radius of 4 inches.
The window's area is equal to the sum of the areas of a rectangle, two quarter circles, and the smaller square between the two upper corners.
The quantity of space occupied by a flat surface with a specific shape is referred to as the area.
now, find the area of rectangle
A = length x breadth
A = 12 x (26-4)
A = 12 x 22
A = 264 square inches
find the area of the two quarter circle
[tex] A= 2( \frac{1}{4} (3.14) \times {4}^{2} ) \\ A = 25.12 {in}^{2} [/tex]
Find the area of the smaller square between the two upper corners
A = (12-8) (4)
A = 4 x 4
A = 16 sq.in
now, find the total area
A = 264 + 25.12 + 16
A = 305.12 square inches
Hence, the area of the window is 305.12 square inches.
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I need to know What is 3/4 x 8 1/2
Answer:
3/4 x 8 1/2 = 6.375
Solve. 4n - 6 (n + 1) > 12 (first blank is the inequality sign, second blank is the value) n
The solution to the inequality is: n < -9.
How to Solve an Inequality?Given the inequality statement, 4n - 6 (n + 1) > 12, to solve for the value of n, we would isolate the n to one side of the inequality as shown below:
4n - 6 (n + 1) > 12
Distribute
4n - 6n - 6 > 12
Combine like terms
-2n - 6 > 12
-2n - 6 + 6 > 12 + 6
-2n > 18
Divide both sides by -2
-2n/-2 < 18/-2
n < -9
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Find the coordinate of the midpoint of the segment with the given endpoints.
-6 and -4
Answer:
-5
Step-by-step explanation:
Let's assume the you are moving horizontally along the number line. If you start at -4 and jump to -6, you have made 2 jumps to the left(-4;-5;-6). So halfway between them (the midpoint) is 1 jump (half of 2 jumps).
1 jump to the left of -4.... You land at -5.
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please help will give brainlist
[tex]\sqrt[3]{} \frac{1}{16} *(-\frac{54}{1} )[/tex]
The simplification of the expression ∛(1/16) × (-54/1) is -27√4/32.
What is defined as the Rationalization?Rationalization is the process of removing a radical as well as imaginary number from of the denominator of an arithmetic fraction. That is, in a fraction, remove the radicals so that the denominator just includes a rational number.
Step 1: Multiply the numerator and denominator by the a radical that removes the radical from the denominator.Step 2: Ensure that all radicals have been simplified.Step 3: If necessary, simplify the fraction.Now the expression is given as;
= ∛(1/16) × (-54/1)
= -54/ ∛16
Taking cube root of 16.
= -54/(4√4)
= -27/2(√4)
By the process of rationalization, multiply the numerator and denominator by the a radical that removes the radical from the denominator which is √4.
= -27×√4/2(√4×√4)
Simplifying the equation;
= -27√4/32
Therefore, the simplification of the expression is -27√4/32.
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AAah! This is my third time aaasking pleeease. Why am I being ignored.
The value of x in the figure is 4
How to determine the value of x in the figure?From the attached figure, we have the following parameters:
DE = x + 1
BC = 4x - 6
The triangles ADX and ABC are similar triangles
Based on the representation of the sides, we have:
BC = 2 * DE
So, we have
2 * (x + 1) = 4x - 6
Expand
2x + 2 = 4x - 6
Evaluate the like terms
2x = 8
Divide by 2
x = 4
Hence, the value of x in the figure is 4
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If a number is "squared" that means it
is raised to the
______ power.
1. 1st
2. 2nd
3. 3rd
4. square root
5. none of the above
Answer:
2nd power
Step-by-step explanation:
3rd is cubed and 1st is: example 3^1 = 3
square root is √
the probability that a carton of eggs taken from the cooler at a store will have at least one cracked egg is 2.5%.2.5%. what are the odds that a carton of eggs will have at least one cracked egg?
The odds that a carton of eggs will have at least one cracked egg is 97.5 %
The question has to do with probability
What is probability?Probability is the likelihood for an event to occur. It is given by P(event) = number of required outcomes/total number of possible outcomes.
How to find the odds that a carton of eggs will have at least one cracked egg?Given that the probability that a carton of eggs taken from the cooler at a store will have at least one cracked egg is 2.5%. Let the probability of at least one cracked egg be P(egg ≤ 1) = 2.5% = 0.025
Now, since we require the probability of that a carton of eggs will have at least one cracked egg, that is the number of cracked is greater than 1.
Let the probability of cracked eggs greater than 1 be P(egg ≥ 1).
From the law of probability
P(egg ≤ 1) + P(egg ≥ 1) = 1
So, P(egg ≥ 1) = 1 - P(egg ≤ 1)
P(egg ≥ 1) = 1 - 0.025
P(egg ≥ 1) = 0.975
P(egg ≥ 1) = 0.975 × 100 %
P(egg ≥ 1) = 97.5 %
So, the odds that a carton of eggs will have at least one cracked egg is 97.5 %
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I don’t know what to do
Answer:
8 - positive
9- no correlation
10- negative
11- positive
12- No correlation
13- negative
14- no correlation
15- no correlation
Step-by-step explanation:
8- Positive because the more hours a person has driven, the more number of miles he/she drives increases.
9- the number of siblings a student has should not affect the grade they have in math class
10- negative because as a car gets older, the value decreases
11- positive because the longer a cd is out the more sales they get
12- In a logical sense, it could be positive, because someone who dropped out of highschool will get paid less than someone who went to school for 18 years and graduated with a hs diploma. it can also mean no correlation. therefore I think it is positive.
13- negative because the more songs someone downloads, the more the ipods space decreases
14- no correlation, the amount of computers in your house does not change how much you message your friends
15- no correlation, your house can be 3 years old and have 5 people living in it
1 3 Given the resting heartrates below, determine the best measure of variability and calculate it. Heartbeats 48 55 60 61 62 63 64 65 66 66 68 70 70 71 71 72 74 74 75 76 77 77 78 79 81 86
The best measure to determine the variability is mean which is equal to 69.48
We are given the data:
48, 55, 60, 61, 62, 63, 64, 65, 66, 66, 68, 70, 70, 71, 71, 72, 74, 74, 75, 76, 77, 77, 78, 79, 81 and 86
The best measure to determine the variability is mean.
Total number of observations = 26
Sum of observations (S) will be:
S = 48 + 55 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 66 + 68 + 70 + 70 + 71 + 71 + 72 + 74 + 74 + 75 + 76 + 77 + 77 + 78 + 79 + 81 + 86
S = 1809
Mean = Sum / total
Mean = 1809 / 26
Mean = 69.58
Therefore, the best measure to determine the variability is mean which is equal to 69.48
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the sum of 2 consecutive intergers is 515 how can i write this as an equation?
We get the consecutive numbers as 257 and 258 from the equation 2 x + 1 = 515.
We are given that,
The sum of 2 consecutive numbers is 515.
Consecutive numbers:
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1 and 2 are consecutive numbers, 34 and 35 are also consecutive numbers.
Here let the first number be x
Second number will be:
x + 1
We need to find their sum:
x + x + 1 = 515
2 x + 1 = 515
2 x = 515 - 1
2 x = 514
x = 514 / 2
x = 257
x + 1 = 257 + 1 = 258
Therefore, we get the consecutive numbers as 257 and 258 from the equation 2 x + 1 = 515.
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