By elimination, the system of equations, 4x - 6y = -26 and -2x + 3y = 13, has infinite solutions.
A system of 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 all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
First, simplify the first equation by dividing it by -2.
4x - 6y = -26 ⇒ -2x + 3y = 13 (equation 1)
-2x + 3y = 13 (equation 2)
Since the simplified equation of the first equation is the same as the second equation, then the two lines are exactly the same or overlapping.
Hence, the system of equations has infinite solutions.
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Do 300 MM, 190 MM make a triangle?
The side lengths 300 mm and 190 mm make a valid triangle because of the triangle inequality theorem
How to determine if the side lengths make a triangle?The side lengths are given as
300 mm and 190 mm
To solve this question, we make use of the triangle inequality theorem
The triangle inequality theorem states that
Given that the sides of a triangle are x, y and z.
The sum of any two sides of a triangle is greater than or equal to the third side;
This means that
x + y ≥ z
Using the above as a guide, we have the following inequality expressions
300 + 190 ≥ z
300 + z ≥ 190
z + 190 ≥ 300
Evaluate the inequality expressions
490 ≥ z
z ≥ -110
z ≥ 110
Remove the negative value
490 ≥ z
z ≥ 110
Combine the inequalities
110 ≤ z ≤ 490
The above inequality is a valid inequality expression
Hence, the side lengths 300 mm and 190 mm make a valid triangle
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3(10-8)^2+4
STEP BY STEP PLEASE IT NEED TO BE EVALUATE AND EXPLAIN <33
Answer:
16
Step-by-step explanation:
We use PEMDAS
Parenthesis
Exponents
Multiplication
Division
Addition
Subtracting
1. 3 (10 - 8)^2 + 4: 3 (2)^2 + 4
2. 3 (2)^2 + 4: 3 (4) + 4
3. 3 (4) + 4: 12 + 4
4.12 + 4 = 16
So, our answer is 16.
What else is needed to prove these triangles congruent using the SAA postulate?
The additional information needed to prove that both triangles are congruent by SAA postulate is:
A. <B ≅ <D and <A ≅ <E
What is the SAA Postulate?The SAA postulate is a condition that is used to prove that two triangles are congruent if they have two pairs of corresponding congruent angles and a pair of non-included congruent sides.
From the information we have in the diagram, we can deduce that:
AC ≅ EC (one pair of congruent sides)
ACB ≅ ECB (one pair corresponding congruent angles)
Therefore, the additional information needed to prove that both triangles are congruent by SAA postulate is:
A. <B ≅ <D and <A ≅ <E
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Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
Kirsten thinks 24% of federal tax
dollars should fund education, and
Jackson thinks $0.35 of every tax
dollar should go toward education.
Express each as a rational number.
Who supports more education
funding?
Using rational numbers, Jackson supports more education funding as he 7/20 > 6/20.
What are rational numbers?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers and q 0, can be used to represent a rational number.
According to Kirsten, 24% of federal tax dollars should fund education
⇒ 24% = 24 / 100
⇒ 6/25
According to Jackson, $0.35 of every tax dollar should go toward education
⇒ 0.35 = 35 / 100
⇒ 7/20
As we can infer that 7/20 > 6/20
So Jackson supports more education funding.
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168>=7x+4y
i need help solving for y
btw this is an inequality
For solving y, we can use this inequality: y≤(168-7x)/4
What is an inequality and steps to solve an inequality ?An inequality is an equation which compares two non equal expressions using operators ≤,≥,<,> .
Steps for solving inequalities:
if we add same number to both sides the inequality remains same.If we divide both sides by a positive number the inequality remains same .if we divide both sides by a negative number the inequality , the inequality reverses.For given inequality, 168≥ 7x + 4y
Adding -7x both sides,
168-7x ≥ 7x+4y-7x
168 - 7x ≥ 4y
Dividing both sides by a positive number 4,
(168-7x)/4 ≥ y
we can solve for y using above expression that y will be less than or equal to (168-7x)/4
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If quadrilateral WXYZ is reflected across the y -axis to become quadrilateral W' X' Y' Z' , what are the coordinates of X' ?
When the quadrilateral WXYZ is mirrored across the y axis to form the quadrilateral W' X' Y' Z', the coordinates of X' are (-1,6).
Briefing:When the x value is reflected across the y-axis, it takes on the opposite sign.
What exactly is a coordinate system?A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using one or even more numbers, or coordinates.
Why do we employ a coordinate system?A coordinate system is a framework for specifying the relative locations of objects in a specific area, such as an area here on earth's surface or the entire earth's surface. A geographic coordinate system determines locations on the world by using a three-dimensional spherical surface.
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A die is rolled twice. What is the probability that the first number rolled is a 3 and the second number rolled is a 5 ?
When a die is rolled twice, the probability of getting a 3 and then a 5 is 1/36.
When a die is rolled twice, the following combinations are possible:
1, 1 - 1, 2 - 1, 3 - 1, 4 - 1, 5 - 1, 6
2, 1 - 2, 2 - 2, 3 - 2, 4 - 2, 5 - 2, 6
3, 1 - 3, 2 - 3, 3 - 3, 4 - 3, 5 - 3, 6
4, 1 - 4, 2 - 4, 3 - 4, 4 - 4, 5 - 4, 6
5, 1 - 5, 2 - 5, 3 - 5, 4 - 5, 5 - 5, 6
6, 1 - 6, 2 - 6, 3 - 6, 4 - 6, 5 - 6, 6
Thus, the sample space is 36.
3, 5 only occurs once in the sample space.
∴ P (3 and 5) = 1/36.
Hence, the probability of rolling a 3 and then a 5 is 1/36.
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What are the coordinates of the point on the directed line segment from (1, -3)(1,−3) to (7, 5)(7,5) that partitions the segment into a ratio of 1 to 3?
The coordinates of the point on the directed line segment from (1, -3) to (7, 5) that partitions the segment into a ratio of 1 to 3 is; (x, y) = (2.5, 0.5)
How to partition line segments?
The formula for partitioning a line segment in the ratio m:n is;
(x, y) = (mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)
We are given the ratio as 1:3 with the coordinates as;
(1, -3) and (7, 5). Thus;
m = 1 and n = 3
x1 = 1
x2 = 7
y1 = -1
y2 = 5
Thus;
(x, y) = (1*7 + 3*1)/(1 + 3), (1*5 + 3*-1)/(1 + 3)
(x, y) = (10/4, 2/4)
(x, y) = (2.5, 0.5)
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HELPPPPPP! How many groups of 9/2 are in 1?!?
Task #6
How many buckets do we need?
Abinash wants to fill his pool but his hose is busted! His
friends decided to help him fill the pool with water buckets.
The base of the pool has dimensions 4 m by 2 m and the
height is 1 m, but they decided to fill the pool only
two-thirds way.
Each water bucket has radius
0.13 m and height 0.55 m.
a) How many buckets of water would they need to fill the pool two-thirds way?
b) What assumption did you make to arrive at your answer?
Brandon wants to find the width of his rectangular neighborhood park. How can he
rearrange the formula for perimeter of a rectangle, p = 2( +w), to solve for w?
A. W=(2l+p)/2
B. W=(p-2l)/2
C. W=p-2l
D. W=2l-p
Ricardo went jet skiing while on vacation. The jet ski rental cost a flat rate of $20, plus $16.75 per hour. Ricardo had $132.16. How much did he have left after 3 hours of jet ski riding?
$50.25
$61.91
$81.91
$70.25
By solving a linear equation, we can see that after 3 hours Ricardo has $61.91
How much did he have left after 3 hours of jet ski riding?We know that Ricardo has $132.16, and he rents a jet sky that costs $20 plus $16.75 per hour.
So, the cost of renting the jet sky for x hours is given by the linear equation:
C(x) = $20 + x*$16.75
The cost of renting this for 3 hours is:
C(3) = $20 + 3*$16.75 = $70.25
Subtracting this from what Ricardo had:
$132.16 - $70.25 = $61.91
So the correct option is the second one.
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Please see the attachment. For the sentence part, the choices are associative property of addition/multiplication, communitive property of addition/multiplication, & distributive property.
The expression was rewritten using the commutative property of addition
(7 + 1) + 9 equals 8 + 9 which equals 177 + (1 + 9) equals 7 + 10 which equals 17How to complete the sentences?The expressions are given as
(7 + 1) + 9
7 + (1 + 9)
The commutative property of addition states that
a + b = b + a
This means that the expression was rewritten using the commutative property of addition
Also, we have
(7 + 1) + 9 equals 8 + 9 which equals 177 + (1 + 9) equals 7 + 10 which equals 17Read more about commutative property at
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 21 to 49
Find the 32 nd term of each sequence. 0.1,0.5,0.9,1.3, ...........
The 32nd term of the arithmetic sequence AP is computed to be 12.5.
What is an AP arithmetic sequence?In mathematics, an arithmetic progression (AP) is a list or sequence of numbers in which each term is attained by adding a pattern to the term before it.
With in arithmetic progression's common difference, the fixed number is marked by the letter 'd.'The 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 is the last term of the AP.Finally, here is the answer to the question;
The following are the numbers in the presented sequence:
0.1,0.5,0.9,1.3, ...........
Because the series contains 32 terms, we must find the 32nd number.
Assume the first term is'a₁' = 0.1.
Assume 'a₂' = 0.5 is the second term.
Assume the third term is 'a₃' = 0.9
'd' is the common difference between two consecutive terms of an AP that are equal.
d = a₂ - a₁
Put the values in the preceding formula; the 32nd term is
d = 0.5 - 0.1
d = 0.4
The nth term equation is found by the formula;
nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32Initial term is a = 0.1Common difference d = 0.4Substitute the given values in the formula;
a₃₂ = a + (n - 1) d
a₃₂ = 0.1 + (32 - 1)(0.4)
a₃₂ = 0.1 + 12.8 - 0.4
a₃₂ = 12.5
Therefore, the arithmetic sequence's 32nd term value is estimated to be 12.5.
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Solve each system by elimination.
r + 3s = 7 , 2r - s = 7
By elimination, the solution of the system of equations, r + 3s = 7 and 2r - s = 7, is (r , s) = (4 , 1).
A system of 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 all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in r and s, a variable should be eliminated by adding/subtracting the two equations.
First, multiply the first equation by 2.
r + 3s = 7 ⇒ 2r + 6s = 14 (equation 1)
Subtracting the two equations will eliminate the variable r.
2r + 6s = 14 (equation 1)
2r - s = 7 (equation 2)
7s = 7
s = 1
Substitute the value of s to any of the two equations and solve for r.
2r - s = 7 (equation 2)
2r - 1 = 7
2r = 7 + 1
2r = 8
r = 4
Hence, the solution of the system of equations is (r , s) = (4 , 1).
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Find the 32 nd term of each sequence. 34,37,40,43, ...........
The arithmetic sequence AP's 32nd term is estimated to be 127.
What exactly is an arithmetic sequence AP?An arithmetic progression (AP) in mathematics is a list or sequence of numbers within which each term is acquired by adding a sequence to the term before it.
The fixed number is denoted by the letter 'd' in the arithmetic progression's common difference.nth term of an AP: an = a + (n - 1) dThe common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.The sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the last term of the AP.Finally, the response to the question;
The numbers in the provided sequence are as follows:
34,37,40,43, ...........
There are 32 terms in the series, so we must obtain the 32nd number.
Suppose the first term is 'a₁' = 34.
Suppose 'a₂' = 37 be the second term.
Suppose 'a₃' = 40 be the third term.
The common difference between the two consecutive terms of an AP that are equal is 'd.'
d = a₂ - a₁
Put the values in the preceding formula; the 32nd term is
d = 37 - 34
d = 3
The nth term equation is now used to calculate.
nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32First term is a = 34common difference d = 3Substitute all of the values in the formula now.
a₃₂ = a + (n - 1) d
a₃₂ = 34 + (32 - 1)(3)
a₃₂ = 34 + 96 - 3
a₃₂ = 127
Thus, the arithmetic sequence's 32nd term is evaluated to be 127.
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Simplify by combining like terms. 4 t-(t+3 t)
The simplification by combining like terms of 4t-(t + 3t) is 0.
According to the given question.
We have an expression 4t - (t+3t).
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression 4t-(t+3t).
Here 4t, t and 3t both are the like terms.
So, we add and subtract coeffcients of t to simplify the given expression.
Therefore, the simplification of 4t - (t + 3t) is given by
4t -( t+ 3t)
= 4t - t -3t
= 4t - 4t
= 0
Hence, the simplification by combining like terms of 4t - (t + 3t) is 0.
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HELP WITH THIS MATH PROBLEM PLS PLS
Answer:
MP = 29
Step-by-step explanation:
Given:
The entire line (MP) is equal to 5y + 9MN = 17NP = 3yMN + NP = MP
17 + 3y = 5y + 9
Find what y =____
17 + 3y = 5y + 9
subtract 9 from both sides
17 - 9 + 3y = 5y + 9 - 9
8 + 3y = 5y
subtract 3y from both sides
8 + 3y - 3y = 5y - 3y
8 = 2y
divided both sides by 2 to get y alone
8/2 = 2y/2
4 = y
Now plug in y to MP to find its length
5(4) + 9 = 20 + 9 = 29
MP = 29
To find NP, plug in y as well
3y = 3(4) = 12
NP = 12
Check:
MN + NP = MP
17 + 12 = 29 yes!!!!
determine the length of XY. Round to the nearest hundredth.
X(-9,2)X(−9,2) and Y(5,-4)Y(5,−4)
Answer:
Step-by-step explanation:
15.23 units
mrs. joshi purchase dance shoes for her students to wear to and upcoming festival. The smallest size was 4 1/2 and the largest was 8. Let s respresent the various sizes of shoes the dancers needed. what the answer plssssss
Answer:
C is the correct answer
Step-by-step explanation:
hope you get it right :))
Genesis is going to see a movie and is taking her 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $3 each. How much total money would Genesis have to pay for her family if she were to buy 6 snacks for everybody to share? How much would Genesis have to pay if she bought xx snacks for everybody to share?
Based on the number of people going to see the movie and the price of the snacks, the total that Genesis would pay if she bought 6 snacks is $78.
The amount that Genesis would pay if she bought x snacks is 60 + 3x.
What is the total cost?The total cost to Genesis can be found as:
= (Number of people going to watch movie x Price of ticket) + (Price per snack x number of snacks)
= (4 people including Genesis x 15) + (3 x 6)
= 60 + 18
= $78
The amount that Genesis would pay if she got x snacks is:
= (Number of people going to watch movie x Price of ticket) + (Price per snack x number of snacks)
= (4 x 15) + (3 × x)
= 60 + 3x
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Evaluate each expression for a=3 and b=-5 . -4+2 a b
Evaluating the expression -4 + 2ab for a = 3 and b = -5 is equal to -34.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.
Given the expression -4 + 2ab, substitute the value of the variable a and the value of variable b.
-4 + 2ab
-4 + 2(3)(-5)
Performing the arithmetic operations, we can have the value of the expression.
-4 + 2(3)(-5)
= -4 + (-30)
= -34
Hence, the expression -4 + 2ab when a = 3 and b = -5 is equal to -34.
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Solve for x.
2x-17=51+61
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: 2x - 17 = 51 + 61[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x - 17 = 112[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 112 + 17[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 129[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \dfrac{129}{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 64.5[/tex]
Which quadrilateral is trapezoid?
Answer:
A.
Step-by-step explanation:
A quadrilateral is a trapezoid if two opposite sides are parallel, and the other 2 opposite sides are not parallel.
Answer: A.
Answer:
it's a
Step-by-step explanation:
find the midpoint of the segment that has endpoints (-3,4) and (-6,0)
Answer:
the mid point of (-3,4) and (-6,0) is (4.5,2)
Answer:
[tex]=(-4.5, 2)[/tex]
Step-by-step explanation:
Midpoint formula is:
[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
where
x1=-3, x2=-6
y1=4, y2=0
Now just plug into formula
[tex]=( \frac{-3+-6}{2}, \frac{4+0}{2})[/tex]
[tex]= ( \frac{-9}{2}, \frac{4}{2})[/tex]
[tex]=(-4.5, 2)[/tex]
PLEASE HELP Finding the initial amount and rate of change given a table for a linear function
The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
How to find the initial amount and rate of change given a table for a linear function?The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 467) and (10, 647)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (647 - 467)/(10 - 2)
Evaluate
Rate = 22.5
This means that the rate of change is $22.5
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = 22.5
So, we have
y = 22.5(x - x1) + y1
Using one of the points, we have
y = 22.5(x - 6) + 467
Set x = 0
So, we have
y = 22.5(0 - 6) + 467
Evaluate
y = 332
Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
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Mr. Sanchez’s class sold fruit pies for $1.89 each and Mr. Kelly’s class sold bottles of fruit juice for $1.56 each. Together, the classes sold 82 items and earned $140.13 for their school. Write and solve a system of equations that models this problem. Show all your work!
Mr. Sanchez's class sold fruit pies, and Mr. Kelly's class sold bottles of fruit juice.
Mr. Sanchez's class sold 45 fruit pies, and Mr. Kelly's class sold 37 bottles of fruit juice.
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to write and solve a system of equations that models this problem.To solve this question, we use the following representations:
x represents the fruit pies
y represents the fruit juice
A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
1.89x + 1.56y = 140.13 ---- the total cost
x + y = 82 --- the number of sales
Make x the subject in x + y = 82
So, we have
x = 82 - y
Substitute x = 82 - y in 1.89x + 1.56y = 140.13
1.89(82 - y) + 1.56y = 140.13
Expand
154.98 - 1.89y + 1.56y = 140.13
Evaluate the like terms
-0.33y = -14.85
Divide by -0.33
y = 45
So, we have
x = 82 - y
x = 82 - 45
Evaluate
x = 37
Hence, Mr. Sanchez's class sold 45 fruit pies, and Mr. Kelly's class sold 37 bottles of fruit juice.
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which inequality matches this graph?
Answer:
x>4
Step-by-step explanation:
Since it is pointing right, it must be either
x>4
x≥4
Since it is not a filled circle the answer can't be greater than or equal to. So it must be x>4.
