The solution of the given system of equations is (3//2, -3/8)
We can solve a system of equations using:
- graphical method
- elimination method
- substitution method
The given system of equations:
(1/2)x + (2/3)y= 1 ......... (1)
(3/4)x - (1/3)y = 2 ..........(2)
Multiply equation (1) by 6
3x + 4y = 6 ..... (3)
Multiply equation (2) by 12
9x - 4y = 24 ...... (4)
Add equation (3) and (4)
3x + 4y = 6
9x - 4y = 24 +
12x = 30
x = 30/12 = 5/2
Substitute x = 5/2 into equation (3)
3x + 4y = 6
3. (5/2) + 4y = 6
15/2 +4y = 6
4y = (12 - 15)/2 = -3/2
y = -3/8
The solution is (3/2, -3/8)
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Select all the expressions that have 2/3 as a product.
A 21/25 × 50/63
B 7/8×9/25
C 1/30×2/3
D 3/25×7/12
E 20/27×27/30
Answer: A and E
Step-by-step explanation:
A. 21/25 × 50/63=
(21*50)/(25*63)=
21/63 * 50/25 =
1/3 * 2 =2/3
B. 7/8×9/25=
(7*9)/(8*25)=
63/200 [tex]\neq[/tex] 2/3
C. 1/30×2/3=
(1*2)/(30*3)=
2/90=
1/45 [tex]\neq[/tex] 2/3
D. 3/25×7/12=
(3*7)/(12*25)=
3/12 * 7/25 =
1/4 * 7/25 =
(1*7)/(4*25)=
7/100 [tex]\neq[/tex] 2/3
E. 20/27×27/30=
(20*27)/(27*30)=
27/27 * 20/30=
1 * 2/3 = 2/3
A and E
Add 3/4+(−2 1/2) using the number line.
Select the location on the number line to plot the sum.
The location on the number line to plot the sum will be between -1 1/2 and -2.
How to illustrate the information?It should be noted that the number line is a straight line that is a visual representation of the numbers. It can be used for addition and subtraction.
In this case, the addition of 3/4 + (-2 1/2) will be:
= 3/4 - 2 1/2
= - 1 3/4
Therefore, the location on the number line to plot the sum will be between -1 1/2 and -2.
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Need help finding the SECOND possible solution!!!
The two possible locations of the point C are (1, 1) and (- 2, - 5).
How to determine the two location of a point within a line based on a given ratio
According to the statement, we find the coordinates of the ends of a line segment and a partition ratio. There are two possible solutions concening the location of the point B:
AC / BC = 4 : 1BC / AC = 4 : 1Thus, we have the corresponding expressions for each case:
Case 1
C(x, y) = A(x, y) + (4 / 5) · [B(x, y) - A(x, y)]
C(x, y) = (- 3, - 7) + (4 / 5) · [(2, 3) - (- 3, - 7)]
C(x, y) = (- 3, - 7) + (4 / 5) · (5, 10)
C(x, y) = (- 3, - 7) + (4, 8)
C(x, y) = (1, 1)
Case 2
C(x, y) = A(x, y) + (1 / 5) · [B(x, y) - A(x, y)]
C(x, y) = (- 3, - 7) + (1 / 5) · [(2, 3) - (- 3, - 7)]
C(x, y) = (- 3, - 7) + (1 / 5) · (5, 10)
C(x, y) = (- 3, - 7) + (1, 2)
C(x, y) = (- 2, - 5)
The two possible locations of the point C are (1, 1) and (- 2, - 5).
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Given g(x) = 3x - 1, find g(2).
The value of the algebraic expression is a 5.
According to the statement
We have to find that the value of the algebraic expression.
So, For this purpose, we know that the
Algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
From the given information:
The function is a
g(x) = 3x - 1
Then
we have to put the value of the x is a 2 to find the value of the g(2) in the expression.
Then
g(x) = 3x - 1
g(2) = 3(2) - 1
g(2) = 5.
The value becomes 5.
So, The value of the algebraic expression is a 5.
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Darius correctly answered 51 questions on his Pre-Algebra 2 class. He received a score of 75%. How many questions were on the quiz?
Answer:
Step-by-step explanation:
The formula for pressure under water is P=rhogh , where \rho is the density of water, g is gravity, and h is the height of the water. Given the water pressure, prove that you can calculate the height of the water using h=P/rhog} .
Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. The proof for calculating water pressure can be given as shown below.
What is Pressure?Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. Gauge pressure is the pressure in relation to the surrounding atmosphere. Pressure is expressed using a variety of units.
The formula given for pressure under water is P=ρgh, where ρ is the density of water, g is gravity, and h is the height of the water.
Now, if the fomula is solved for h it can be written as,
P=ρgh
Divide both the sides of the equation by ρg, therefore, we can write,
P/ρg = ρgh/ρg
h = P/ρg
Now, the value of ρ for water and g is 997 kg/m³ and 9.81 m/sec², respectively. Therefore, we can write,
h = P/(ρg)
h = P/(997kg/m³ × 9.81 m/sec²)
Now, just with the pressure known we can calculate the height of the water column.
Hence, proved.
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The sides of a triangle have lengths x, x+5 , and 25 . If the length of the longest side is 25, what value of x makes the triangle a right triangle?
The value of x makes the triangle a right triangle is 15 .
Pythagoras Theorem states that sum of square of two sides of triangle is equal to the square of longest side of the right angle triangle.
In the given question
the length of longest side = 25.
length of other two side= x and x+5.
By Pythagoras Theorem
[tex]x^{2} +(x+5)^{2} =25^{2}[/tex]
[tex]x^{2} +x^{2} +25+10x=625[/tex]
[tex]2x^{2} +10x-600=0[/tex]
[tex]2x^{2} +40x-30x-600=0[/tex] ( By Splitting the middle term)
[tex]2x(x+20)-30(x+20)=0\\ \\ (2x-30)(x+20)=0\\[/tex]
solving 2x-30=0 and x+20=0
we get x=15 and x= -20 ( not possible as distance can't be negative)
x=15.
Therefore , the value of x makes the triangle a right triangle is 15 .
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An office has recycling barrels that are cylindrical with cardboard sides and plastic lids and bases. Each barrel is 3 feet tall with a diameter of 30 inches. How many square feet of cardboard are used to make each barrel?
Square feet of cardboard are used to make each barrel = 23.4558 sq. ft.
The recycling barrels are cylindrical.
Height of the cylinder, h = 3ft
Diameter of the base circle of the cylinder = 30 inches
So radius, r = 15 inches = 15 x 0.083 ft = 1.245 ft
The total surface area of the cylinder is the sum of its lateral surface area and the area of the base and lid circles.
Here the base and lid of the cylinder is made of plastic and sides made of cardboard. So to find the square feet of cardboard required, we need only to find the lateral surface area of the cylinder.
Lateral surface area of the cylinder = 2πrh
= 2 x 3.14 x 1.245 x 3
= 23.4558 square feet
So 23.4558 square feet of cardboard is used to make each barrel
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PLEASE ANSWER QUICK THANK U SO MUCH
Find the range of the relation.
A. {-4, 4}
B. { -4, -2, 0, 2, 4 }
C. { -7, -4, -2, -1, 0, 2, 4, 5 }
D. { -7, -4, -1, 2, 5 }
Find the sum of each finite arithmetic series. 10+20+30+ . . . . . +110+120
The sum of finite arithmetic series 10+20+30+ . . . . . +110+120 is 780
Suppose we are given an arithmetic series:
a(1) + a(2) + a(3) + ... + a(n)
The sum of the first nth terms is given by:
S(n) = n/2 [a(1) + a(n)]
Where:
a(1) is the first term and a(n) is the nth term.
The given series is:
10+20+30+ . . . . . +110+120
We get, then,
a(1) = 10
a(n) = 120
To find n, recall the formula of the nth term of an arithmetic sequence:
a(n) = a(1) + (n-1) . d
where d is the common difference.
From the given series, we get:
d = 20 - 10 = 10
Substitute a(1) =10, d = 10, and a(n) = 120 into the formula:
120 = 10 + (n-1) . 10
120 = 10 n
n = 12
Substitute n = 12 into the sum formula:
S(n) = n/2 [a(1) + a(n)]
S(12) = 12/2 (10 + 120)
= 6. 130 = 780
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Draw two cards without replacement from a well-shuffled standard deck of 52 cards. find the probability distribution of the number of diamonds drawn. enter exact answers (fractions).
There are 13 diamonds in the deck (as well as other colors). Since there are 52 cards, the probability of getting a diamond on the first draw is 13/52. After the first card is drawn, all that's left are his 12 diamonds. Therefore, the probability of drawing a diamond is 12/51 (note that he has only 51 cards left after pulling/removing the first card since there are no replacement cards). The overall probability is the product of two possibilities. The odds of drawing diamonds from the original deck are 13/52 times the odds of drawing diamonds from his remaining 51 cards. Assuming the first card drawn is a diamond, 12/51.
P=13/52*12/51=1/4*4/17=1/17.
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Landon is driving to a concert and needs to pay for parking. There is an automatic fee
of $5 just to enter the parking lot, and when he leaves the lot, he will have to pay an
additional $2 for every hour he had his car in the lot. How much total money would
Landon have to pay for parking if he left his car in the lot for 4 hours? How much
would Landon have to pay if he left his car in the lot for t hours?
If Landon left his automobile alone for 4 hours, he would be charged $13.
If Landon left his car for t hours, he would be charged 5 + 2t.
It is best to create a phrase for such inquiries.
The set cost of the parking fee is $5.
Additionally, it costs $2 each hour.
In other words, if someone uses the parking lot for t hours, they must pay $2 per hour for those t hours.
Formula = 2 x t = 2 t
Including the set amount, the entire phrase is:
5 + 2t
So, if Landon parked for six hours, he would have to pay:
= 5 + 2 t
= 5 + 2 x 4
= $13
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What is the value of 13x if x = −7?
−20
−71
−91
−137
Solve for x: 2^4x + 2^4+3 = 144
Is the relation y=-3x with inputs x=0, x=1, and x=2 a function?
The relation is a function because it is a one-to-one relation
How to determine if the relation is a function?The relation is given as
y = -3x
The inputs are given as
x = 0, x = 1 and x = 2
Substitute the values of x i.e. x = 0, x = 1 and x = 2 in the equation of the function y = -3x
So, we have
y = -3(0) = 0
y = -3(1) = -3
y = -3(2) = -6
From the above computations, we can see that the y values are different for the inputs
Hence, the relation is a function because it is a one-to-one relation
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Last year, there were 123 pies baked for the bake sale. This year, there were b pies baked. Using b, write an expression for the total number of pies baked in the two years.
Jasmine ran for 98.4 minutes. Throughout her run, she ran at a pace of 8.2 minutes per mile.
Answer: 106.6 is the correct answer
Step-by-step explanation:
24) Samit invests $1800 at a rate of 4.5% per year simple interest.
Work out the value of his investment at the end of 4 years.
Answer: 2124 dollars
Step-by-step explanation:
4.5% of 1800 is 81. As it is simple interest and not compound, it does not change each year. Therefore, 81 x 4 is 324. 1800+324 = 2124 dollars
one half a number is 17 more than one third of that number.what is the number?
Answer:
102
Step-by-step explanation:
Let x equal the unknown number
x/2 = 17 + x/3
3x = 102 + 2x
x = 102
a) Round 98984 to 1 significant figure.
Round 98984 to 1 significant figure.
Answer:100000.
do i set them equal to each other?
Compare and contrast the arithmetic and geometric means of two numbers. When will the two means be equal? Justify your reasoning.
Arithmetic mean and geometric mean of a and b are equal when a = b
Arithmetic mean
Arithmetic mean of two numbers is their sum divided by 2. Generally, arithmetic mean is the sum of the values divided by the total value. It gives the average of two or numbers. It is accurate when the data values are not much skewed.
For two numbers a and b, arithmetic mean = a + b /2
Geometric mean
Geometric mean of two numbers is the square root of its product. It is also used for the calculation of averages. For more than two numbers, the geometric mean is the 1/n th power of the product of the numbers. The skewness of the data values does not affect the accuracy in calculating the geometric mean.
For two numbers a and b, geometric mean = [tex]\sqrt{ab}[/tex]
Always arithmetic mean is larger than the geometric mean.
Arithmetic mean = Geometric mean
⇒ (a+b)/2 = [tex]\sqrt{ab}[/tex]
⇒ a+b = 2 [tex]\sqrt{ab}[/tex]
On squaring,
⇒ [tex]a^2 +2ab+b^2[/tex] = 4ab
⇒ [tex]a^2 -2ab+b^2[/tex] = 0
⇒ [tex](a-b)^2[/tex] = 0
⇒ a -b = 0
⇒ a = b
Arithmetic mean is equal to the geometric mean if the two numbers are equal.
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A local office supply store charges $18 to set up their business card printing machine with the design and $0.15 in materials per business card to print. Select all equations that could represent an expression for the average cost A(x) of printing a batch of x business cards.
a
b
c
d
e
f
The equation [tex]A(x)=\frac{18+0.15x}{x}[/tex] represents the correct expression for the Average cost.
What is a mathematical expression?
In mathematics, an expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. Mathematical symbols can represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to aid in determining the sequence of operations and other features of logical grammar.
The store charges $18 for design setting and $0.15 per print out of business card.
Let the number of cards be [tex]x[/tex]
Then, total cost of printing of [tex]x[/tex] cards = $ [tex]0.15x[/tex]
Thus, the expression for the average cost [tex]A(x)[/tex] is given as,
[tex]A(x)=\frac{18+0.15x}{x}[/tex]
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Solve the equation.
-4/1=x/-2
Answer:
8
Step-by-step explanation:
When all quantum numbers are considered, how many different quantum states are there for a hydrogen atom with n=1 ? with n=2 ? with n=3 ? list the quantum numbers of each state.
Quantum numbers are:
(A) n = 1 ⇒ n -1(B) n = 2 ⇒ n = 2What do we mean by quantum numbers?Quantum numbers are used in quantum physics and chemistry to describe the values of conserved quantities in the dynamics of a quantum system. Quantum numbers are eigenvalues of operators that commute with the Hamiltonian and their corresponding eigenspaces—quantities that can be known with precision at the same time as the system's energy. A specification of all of the quantum numbers of a quantum system, when combined, fully characterizes the system's basis state and can, in theory, be measured together.Quantum numbers:
(A) n = 1
The electron in a hydrogen atom with n=1 is in its ground state; if the electron is in the n=2 orbital, it is in an excited state. For a given n value, the total number of orbitals is n2. Angular Momentum (Secondary, Azimunthal) l = 0,..., n-1 Quantum Number(B) n = 2
The n = 2 states begin to fill up as we move to larger atoms, adding electrons one at a time. Because there are four different values for (l, m), each with two allowed spin states, the n = 2 states can hold up to eight electrons. The n = 2 shell includes all states with a quantum number of n = 2.Therefore, Quantum numbers are:
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Thailand is home to numerous indigenous tribes. The Akha tribe population is about 7×104 people, and the Kariang tribe population is 6 times larger. About how many people are in the Kariang tribe?
The number of people that are in the Kariang tribe is; 420000 people
How to multiply indices?We are given;
Total Population of Akha Tribe in Thailand = 7 * 10⁴ people
Kariang tribe population is a total of 6 times larger than that of Akha Tribe
Thus, for us to be able to get how many people are in the Kariang tribe, we will just multiply both values to get;
6 * 7 * 10⁴ = 42 * 10⁴ = 420000
Therefore, since Thailand is home to numerous indigenous tribes, we can conclude from the calculation above and using the given parameters in the question that the number of people that are in the Kariang tribe is; 420000 people
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What is the y -coordinate of the y -intercept of the line 4 x+3 y=12 ?
The y-coordinate is 4 and the y-intercept is (0,4)
The given equation is 4x + 3y = 12
Comparing the equation with the equation of line ax + by = c
where a = 4, b = 3, c = 12
The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y = f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept. An intercept of a function is a point where the graph of the function cuts the axis.
for y-intercept,
x coordinate is 0
that is x=0
4(0) + 3y = 12
3y = 12
y = 12/3
y = 4
Hence the y-coordinate is 4 and the y-intercept is (0,4)
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Find the coordinates of the circumcenter of the triangle with the given vertices. Explain.
A(0,0), B(0,6), C(10,0)
The triangle with vertices A(0 , 0), B(0 , 6), and C(10 , 0) has its circumcenter located at (5 , 3).
Circumcenter of a triangle refers to the point inside a triangle at which the perpendicular bisectors of the sides of a triangle intersect. This point is also equidistant from the three vertices.
Given the location of the three vertices, there are different methods that can be used to locate the circumcenter of the triangle.
First, try to graph and visualize the triangle formed by the three vertices. (see photo)
From there, we can say that triangle ABC is a right-angled triangle with line BC as the hypotenuse.
One of the properties of the circumcenter of a triangle states that the circumcenter lies in the middle of a hypotenuse if it is a right-angled triangle.
To get the circumcenter, find the midpoint of the line BC.
midpoint = M(xm ,ym) = [(x1 + x2)/2 , (y1 + y2)/2]
M(xm ,ym) = [(0 + 10)/2 , (6 + 0)/2]
M(xm ,ym) = (5 , 3)
Hence, the circumcenter is located at (5 , 3).
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Find the 32 nd term of each sequence. 101,105,109,113, ...........
The arithmetic sequence AP's 32nd term is calculated to be 225.
What is the definition of an AP arithmetic sequence?An arithmetic progression (AP) in mathematics is a list and maybe sequence of numbers with each term is obtained by adding a sequence to the term before it.
With the exception of arithmetic progression, the fixed number is denoted by the letter 'd.'Common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of an AP: an = a + (n - 1) dThe sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l = last term of the AP.Finally, the solution to the question is as follows:
The numbers in the displayed sequence are as follows:
101,105,109,113, ...........
We must explore the 32nd number in the series because it contains 32 terms.
The common difference with both two consecutive terms of an AP which are equal is denoted by 'd.'
Let's assume the first term is'a₁' = 101.
Let's assume 'a₂' = 105 is the second term.
Let's assume the third term is 'a₃' = 109
Substitute the values the preceding equation; the 32nd term is-
d = a₂ - a₁
Obtain the common difference;
d = 105 - 101
d = 4
Put the values in the preceding formula; the 32nd term is
The formula finds the nth term equation;
nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32Initial term is a = 101Common difference d = 4Put the given values in nth term formula;
a₃₂ = a + (n - 1) d
a₃₂ = 101 + (32 - 1)(4)
a₃₂ = 101 + 128 - 4
a₃₂ = 225
Thus, the 32nd term value of the arithmetic sequence is calculated to be 225.
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I dont understand this
