Answer: The elimination method is a method for solving a system of equations by eliminating one of the variables. One way to do this is to multiply one equation by a constant and then add or subtract it from the other equation to cancel out one of the variables.
We will start by multiplying the first equation by -1:
x + 2y = 4 ----> -x - 2y = -4
Now we will add the second equation to the modified first equation:
-x - 2y = -4
(x + 3y = 10)
0x + 1y = 6
Now we can solve for y:
y = 6
Now that we know y = 6, we can substitute this back into one of the original equations, for example the first one:
x + 2y = 4
x + 2(6) = 4
x = -8
So the solution to the system of equations is x = -8 and y = 6
Therefore, the solution is (-8,6)
Step-by-step explanation:
Need help with questions 12!
Answer:
So the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.
Step-by-step explanation:
We can use algebra to solve for the width and length of the rectangle. Let's call the width of the rectangle "w" and the length "l".We know that the perimeter of the rectangle is the sum of all four sides, so we can use the formula:P = 2l + 2wwhere P is the perimeter and l and w are the length and width of the rectangle. We know that P = 312 feet.Also, we know that the length is seven times the width, so we can express the length as:l = 7wNow we can substitute this value of l into the perimeter equation:312 = 2(7w) + 2w312 = 14w + 2w312 = 16ww = 19.5 feetNow we can use this value of w to find the length:l = 7w = 7(19.5) = 136.5 feetSo the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.
Which are which help asap..
Answer:
H = 20
Step-by-step explanation:
Looks like you got everything correct. Nice!
For your last one, let's get H by itself. Since 1/2 is division, let's multiple it by 2 to turn it into one. Because you multiply by 2 on the left side, you have to on the right side also...
(1/2)(2) = 1
(1)(h) = h
On the other side, 10(2) = 20.
Combining the 2, H = 20
solve it to find the value of X. also find the actual length of each square[tex]perimeter of square 40cm,(x+2)cm[/tex]
The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.
What is the perimeter of the square?The product of the four and the edge length of the square or the sum of all the sides of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,
4(x + 2) = 40
Simplify the equation, then we have
4(x + 2) = 40
(x + 2) = 10
x = 10 - 2
x = 8
The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.
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For a particular company the salaries of five employees are: $45,000 $52,000 $67,000 $42,000 $56,000 A new employee is hired and her salary is $280,000. What word best describes this data set with the new employee included?
4
MP.1 Make Sense and Persevere Alicia
measured 1/4 yard of the Blue Diamonds fabric and5/6
yard of the Yellow Bonnets fabric to make a quilt.
Rename each length of fabric. Use the number of
inches in a yard as a common denominator.
HINT: 1 yard = 3 feet; 1 foot = 12 inches
Alicia made a quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.
Describe the length.The end-to-end measurement or size is called the length. In other words, the larger of the two or three dimensions of a geometric shape or object. For example, the length and width of a rectangle define its dimensions. In the international size system, length is also a dimensional distance quantity.
Blue Diamond fabric is 1/4" x 36" or 9" quarter yards.
5/6 yards of yellow bonnet fabric equals 5/6 x 36 inches or 30 inches.
Alicia made the quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.
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help pls A rational expression has been simplified below.
(x-2)(x+6)/7(x+6) = x-2/7
For what values of x are the two expressions equal?
O A. All real numbers except 2
OB. All real numbers
O C. All real numbers except -6
O D. All real numbers except -6 and 2
The values of x if the two expressions equal are all real numbers.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expression ,
(x-2) (x+6) / 7 (x+6) = x-2/ 7
So, in LHS x+6 can be cancelled
and we get,
=x-2/ 7
which is same as the RHS from the given expression .
So, As the both LHS and RHS are equal , if put any value Both remains same
Hence, The values of x if the two expressions equal are all real numbers.
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find the area of the shaded part given below where the diameter is 14 cm.
Answer:
area of sector = 49π/6 cm² ≈ 25.7 cm²
Step-by-step explanation:
area of sector = (n/360°)πr²
where n = central angle of sector, and r = radius of circle
Here, we have:
n = 60°
r = d/2 = 14 cm / 2 = 7 cm
area of sector = (60°/360°)π(7 cm)²
area of sector = (1/6)π(49 cm²)
area of sector = 49π/6 cm² ≈ 25.7 cm²
Asha pulls five tiles out of a bag that contains only positive and negative x and x² tiles. She simplifies the resulting polynomial and gets x². What are all the possible sets of five tiles that she could have pulled out?
The possible sets of five tiles that she could have pulled out are (2,3),(3,2)
How to find the factors of a quadratic expression?If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:
[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]
Then writing b in terms of alpha and beta would help us getting common factors out.
Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any trial and error.
Given;
Number of tiles asha pulled out=5
Bag contains only positive and negative x and x² tiles
So, the equation will be
-x^2+x=5
x^2-x+5=0
Now,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
x= 1 +[tex]\sqrt{1-4*-1*-5}[/tex])/2
x=2,3
x=3,2
Therefore, the quadratic equation solution will be (2,3),(3,2)
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section 7.5 substitution page 15 pdf answer key 7c i can solve a linear system of equations by substitution.
Yes, substitution can be used to solve a linear system of equations.
Linear System of Equations:
A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution. For example, is a system of three equations in the three variables x, y, z.
The substitution technique involves separating out a single variable from one equation and utilizing that expression to replace the variable in the other equation (s). This will enable you to solve for the remaining variable or variables and discover the system's answer.
Yes, a linear system of equations can be solved via substitution.
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Simplify 3y-(2y-3)÷4
The solution to the algebraic expression 3y - (2y - 3) ÷ 4 is; (10y + 3)/4
How to simplify algebraic expressions?The algebraic expression is given as;
3y - (2y - 3) ÷ 4
With the aid of order of operations named PEMDAS which is an acronym for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction. Thus, we can rewrite the expression as;
3y - (2y - 3)/4
The common denominator is 4 and when we distribute we will have;
(4(3y) - 2y + 3)/4
= (12y - 2y + 3)/4
= (10y + 3)/4
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The longer leg of a right triangle is 3cm longer than the shorter leg. The hypotenuse is 6cm longer than the shorter leg. Find the side lengths of the triangle.
In a case whereby longer leg of a right triangle is 3cm longer than the shorter leg and hypotenuse is 6cm longer than the shorter leg then the side lengths of the triangle is 9 inches.
How can the lenght be calculated?The concept that will be used is pythagoras theorem.
We can make s = the length of the shorter leg.
Where the longer leg can be expressedas (s + 3),
Then the hypotenuse is( s + 6).
From pythagoras theorem, a^2 + b^2 = c^2.
then we have s^2 + (s + 3)^2 = (s + 6)^2
[s^2 + (s + 3)(s + 3)] =[ (s + 6)(s + 6) ]
s^2 + s^2 + 6s + 9 = s^2 + 12s + 36
If we collect like terms we have
s^2 - 6s - 27 = 0
Then if we factorize we have
(x - 9)(x + 3) = 0
then
we can set the whole left side to equal 0.
x - 9 = 0, then x = 9
x + 3 = 0, then x = -3.
But we can only have positive value which sis 9, hence shortest side is 9 inches.
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What type of triangle and are they congruent
Answer: AAS and both triangles are congruent
Step-by-step explanation: Hello! Since you are given two angles and one side that are congruent in both triangles, you know that they are either congruent by ASA (angle side angle congruence postulate) or AAS (angle angle side) congruence postulate. The way you tell the difference between the two is by how the congruent angles and the congruent side is shown. In ASA, the congruent side would be the included side between both congruent angles. Since the congruent side is not in between both angles and both angles do not share the congruent side to the other triangle, the triangles are congruent by AAS. The triangles two given shared angle and given congruent side is in the order of angle angle side, so the triangles are related by AAS. This means that the triangles are congruent.
Fun fact:
By CPCTC, you know that corresponding parts are congruent in congruent triangles. If you know two or more triangles are congruent, then each of their angles and sides are congruent as well.
I hope this helps you!
In the linear equation 4x-3y=6, the slope of the line is
Need help asap, please don’t ignore :(
Answer:c
Step-by-step explanation:
The slope forms a uniform solution in each square box as shown in the drawing
here, s is the value or answer.
SOLUTION -
[tex] \frac{1}{2} = \frac{3}{6} \\ 1 \\ \frac{1}{2} = \frac{1}{2} \\ = \frac{1}{m } = \frac{1}{2} \\ m = 2[/tex]
ANSWER - 2What does the law of demand state?
Answer:
In economics, the LOD or Law of Demand states that as the price increases on a good or service, there are less people that are willing and able to purchase that good or service.
Here is an example
On the image attached there is a Price Quantity Demanded Graph. The Line on the graph represents demand. The furthur right the line of the graph goes, the larger the quantity of demand for a good is, vice versa. The Law Of Demand is demonstrated on the graph and the table, when price (Px) is at 5, then only Quantity Demanded (Dx) equals 100. When Px = 1 then Dx = 500. As price decreases, demand increases.
Hope this helped :)
55oz to ____ lb ____ o
Express the formula v=pie r^2 • H in terms of height, H. Use that formula to find the height when the volume is 45pid and the radius is 3
Option (b) is the correct option i.e. The height is 5 units.
What precisely are volume and height?The height of an object is determined by measuring the distance between its base and its top.
As opposed to length, width, and height for a rectangular shape's area, the basic formula for volume is length, breadth, and height. The calculation is unaffected by how the different dimensions are referred to; for example, "depth" can be used in place of "height."
Given, V = πr².H
V/πr² = H
So, It can be written in terms of height, H as V/πr².
Now, If r = 3 units and V= 45π then,
H = V/πr² = 45π / π(3)²
= 45π/9π
= 5 units.
Hence, height is 5 units.
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Find all non-empty finite sets of integers A and B with the following properties:
i) whenever x is in A, x+1 is in B
ii) whenever x is in B, x^2-4 is in A
Hence, find all positive integers a and b such that there are non-empty finite sets A and B with the property that whenever x is in A, x+a is in B, and whenever x is in B, X^2-b is in A.
Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is represented by a capital letter. The number of elements in the finite set is known as the cardinality (or the cardinal number) of a set. Let us take an example:
A = {1, 2, 3, 4, 5 }
Since a set is usually represented by the capital letter. Thus, A is the set and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but cannot be repeated. All the set elements are represented in small letter in case of alphabets. Also, we can write it as 1 ∈ A, 2 ∈ A etc. The cardinal number of the set is 5. Some commonly used sets are as follows:
N: Set of all natural numbers
Z: Set of all integers
Q: Set of all rational numbers
R: Set of all real numbers
Z+: Set of all positive integers
A non empty is a set that has one or more elements.A “set” is just a well-defined collection of distinct objects, and their union—the set—is an object itself. A set can contain anywhere from 0 to an infinite number of items.
Finite sets are sets having a finite/countable number of members. Finite sets are also known as countable sets, as they can be counted. The process will run out of elements to list if the elements of this set have a finite number of members
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NO SPAM OR LINKS!!! WILL MARK BRAINLEST
Review the Monthly Principal & Interest Factor chart to answer the question:
FICO Score APR 30-Year Term 20-Year Term 15-Year Term
770–789 5.5 $5.68 $6.88 $8.17
750–769 6.0 $6.00 $7.16 $8.44
730-749 6.5 $6.32 $7.46 $8.71
710–729 7.0 $6.65 $7.75 $8.99
690–709 7.5 $6.99 $8.06 $9.27
Calculate the monthly payment, for a 15-year term mortgage, after a 15% down payment on a $315,200.00 purchase price, for a household with a 711 credit score. (2 points)
$1,776.29
$1,984.39
$2,173.56
$2,408.60
Answer: c
Step-by-step explanation:
Find the length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)
The length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0) is; 3√2
How to find the distance between two coordinates?The length of the mid-segment of a trapezoid is half the sum of the lengths of the two parallel sides, AB and CD. T
The vertices are;
A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)
Thus;
Length of sides AB and CD
length = √(x₂ - x₁)² + (y₂ - y₁)²
AB =√(2 - 0)² + (5 - 3)²
AB = 2√2
length = √(x₂ - x₁)² + (y₂ - y₁)²
CD = √(2 - 6)² + (0 - 4)²
CD = 4√2
Formula to use for the mid segment is;
Mid segment = (AB + CD)/2
= (2√2 + 4√2) / 2
= 3√2
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admission to the movies is x dollars, and a bag of popcorn costs $4. write an expression to represent total cost for two people to go to the movies three times and sharing a bag of popcorn each time.
Answer: The total cost for two people to go to the movies three times is 3x2 = 6x dollars.
The cost of a bag of popcorn is $4 and they share one bag of popcorn each time they go to the movie, so the total cost of popcorn is 4*3 = $12 dollars.
So the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12
So an expression to represent the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12.
Step-by-step explanation:
Carter has 10 fewer marbles than April. Nicholas has 3 times as many marbles as April. If April has m marbles, which expression BEST represents how many marbles Carter and Nicholas have altogether?
Which one of these?
4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.
What is Expression?An expression is combination of variables, numbers and operators.
Let m be the number of marbles.
The number of marbles April has be m.
Given that Carter has 10 fewer marbles than April.
If Carter has 10 less than m, that's m - 10.
Nicholas has 3 times as many marbles as April.
3m
marbles Carter and Nicholas have altogether
m-10+3m
4m-10
Hence, 4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.
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each of the following situations, determine whether or not the given random variabas a binomial or geometric distribution. then, find the probability
The probability of 5 heads in 10 flips.
A coin is flipped 10 times and we want to find the probability of getting exactly 5 heads.
This situation is a binomial distribution because it involves a fixed number of trials (10) and each trial has a fixed probability of success (1/2). . The probability of obtaining exactly 6 successes in 10 trials is given by the formula P(x) = nCx * px * (1-p)n-x. In this situation, the probability is P(x) = 10C6 * 0.26 * 0.84 = 0.17496. The probability of getting exactly 5 heads can be calculated using the formula P(X=5) = 10C5 * 0.5^5 * 0.5^5 = 0.246. This is the probability of 5 heads in 10 flips.
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Complete question:What is the probability of getting 5 heads when you toss a fair coin 10 times?
the kappa iota sigma fraternity polled its members on the weekend party theme. the vote was as follows: six for toga, four for hayride, eight for beer bash, and two for masquerade. display the vote count in a pareto chart.
Pareto chart is a type of bar graph which often displays the data in descending order of frequency.
It is made up of vertical bars, with the height of each bar representing the frequency of occurrence for each category. The chart is named after Vilfredo Pareto, who used it to analyze economic data in the late 19th century.
For the given data, we calculate the cumulative frequency of the data by adding the frequencies of each category.
Toga: 6
Hayride: 6 + 4 = 10
Beer Bash: 10 + 8 = 18
Masquerade: 18 + 2 = 20
The Pareto chart is created by plotting the cumulative frequency against the categories. The chart is plotted with the categories on the x-axis and the cumulative frequency on the y-axis.
Toga: 6 (30%)
Hayride: 10 (50%)
Beer Bash: 18 (90%)
Masquerade: 20 (100%)
Hence, the Pareto chart for the given data is as follows:
Toga: 30%
Hayride: 20%
Beer Bash: 40%
Masquerade: 10%
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arrange the following numbers in ascending order: 147, 772,324,256,9199,946,4342,493,891,4
help this is the only question i have left help bsf help
10
Solve for x.
8
6
X
will give brainliest!!!
Answer:
7.5
Step-by-step explanation:
Since the segments are parallel, the side segment lengths are proportional.
8/10 = 6/x
4/5 = 6/x
4x = 30
x = 7.5
PLEASE HELP The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1, where h(t) is their rocket's height in meters.
What was their rocket's height in meters 0.5 seconds after launch? How many sec after launch did their rocket hit the ground? What was their rockets maximum height in meters??
The rocket was at a height of 19.75 meters after 0.5 seconds
The rocket hit the ground after 8.02 seconds
The maximum height is 81 m.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The height (h) of the rocket t seconds after launch is modeled by:
h(t) = -5t² + 40t + 1
a) After 0.5 seconds:
h(0.5) = -5(0.5)² + 40(0.5) + 1 = 19.75 meters
b) The rocket hit the ground when h(t) = 0, hence:
-5t² + 40t + 1 = 0
t = 8.02 s
c) The maximum height is at h'(t) = 0
h'(t) = -10t + 40
-10t + 40 = 0
10t = 40
t = 4 s
h(4) = -5(4)² + 40(4) + 1 = 81 meter
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which of the following properties is true for all normal density curves? 1.) they are symmetric 2.) the curve reaches its peak at the mean 3.) 95% of the area under the curve is within one standard deviation of the mean.
All normal density curves are symmetric and have a peak at the mean. 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.
All normal density curves are symmetric. This means that the curve looks the same to the right and left of the mean (μ). The curve reaches its peak at the mean, which is the highest point on the curve. The area under the curve is equal to 1. The area under the curve that is within one standard deviation (σ) of the mean is equal to 0.68. This means that 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.
The formula for calculating the area under the curve within one standard deviation of the mean is:
Area = 0.68 * 1
The formula for calculating the area under the curve within two standard deviations of the mean is:
Area = 0.95 * 1
These formulas can be used to calculate the area under the curve for any normal density curve.
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y-1=x
Slope intercept for m
Answer:
Slope intercept form = y=mx+b
So
y-1=x
Add 1 to both sides
y=x+1