The ordered pair (x,y) obtained from the linear equations is: (-2,-12)
What is Linear Equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason. A linear equation is expressed using the linear equation formula. There are several ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form. To discover how a linear equation is stated in its standard form, let's take an example.
The equation is given:
8x-3y=20
5x-y=2
Using the substitution method for solving the linear equations:
From the equation:
5x-y=2;
we can transform this equation as:
⇒-y = 2-5x;
⇒y = 5x-2;
Now substituting the value of y in the other equation: we get;
⇒8x-3(5x-2)=20
⇒8x -15x+6 = 20;
⇒-7x=14;
x = -2;
Now putting the value of x in the equation to get the value of y;
So,
y = 5(-2) -2;
y = -12;
Hence the value of x and y are -2 and -12 respectively;
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Francis mixes 3/8 gal of white paint, 2 7/8 gal of blue paint, and 5/4 gal of red paint.
How much white paint will Francis need to make 7 gallons of the same color paint?
Francis has made _____ gal of paint when he first mixes the three colors.
The constant of proportionality of white paint to gallons of mixed paint is ______
Francis will need __________ gal of white paint to mix together 7 gals of the same color paint.
PLEASE HELP!!!!!
Blank one the options are: thirteen-fourths, thirty-one eights, or nine-halves.
Blank two the options are: one-seventh, one-twelfth, three twenty-sixths, or thirty-six thirds
Blank three the options are one, eighty-four, seven twelfths, or twenty-one twenty-sixths
Please help me with the problem.
The gal in the first mixes is nine-halves, the constant of proportionality is one-twelfth and the white paint required in 7 gals is seven twelfths
How to determine the quantity in mixes and the constant of proportionality?
Given:
White paint = 3/8 gal
Blue paint = 2 7/8 gal
Red paint = 5/4 gal
Gallons of first mixes = White paint + Blue paint + Red paint
Gallons of first mixes = 3/8 + 2 7/8 + 5/4 = 9/2 gal
The constant of proportionality of white paint to gallons of mixed paint:
constant of proportionality = white paint volume/ mixed paint volume
constant of proportionality = (3/8) / (9/2) = 1/12
The constant of proportionality of white paint to gallons of mixed paint gives the fraction of white color in the total volume
In order to make 7 gallons of the same color paint, the quantity of white paint he will need is:
White paint in 7 gallons = 1/12 x 7 = 7/12
Therefore, blank one is nine-halves, blank two is one-twelfth and blank three is seven twelfths
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interval notation for t - 1/3 >= -12/9
Answer: [-1, ∞)
Step-by-step explanation:
First, we will simplify the equation.
Given:
t - 1/3 ≥ -12/9
Add 1/3 to both sides of the equation:
t ≥ -1
Next, we know that a bracket is used when representing greater than or equal to and less than or equal to. Here, it's greater than or equal to so we will use a bracket on the left side.
Then, t can be any value to infinity above -1, so we will use ∞) on the right side.
[-1, ∞)
The function h(t) = -16t² + vt + 10 gives the height of a platform diver above the water, in feet, t seconds
after the diver leaves the platform with an initial velocity, U, in feet per second.
10 feet
On one dive, it takes the diver 1.42 seconds to reach the surface of the water.
• What was the initial velocity, U, in feet per second, of the diver?
. After how much time, in seconds, since leaving the platform did the diver reach the same height as the platform?
• What was the diver's maximum height, in feet, above the water?
Justify your answers. Enter your answers and justifications in the space provided.
The maximum height of the diver as calculated from the function is 14.54 feet.
The function that represents the position of the diver is
h(t) = -16t² + vt + 10
The diver is at a height of 10 feet.
So at t=0 , h=10
Now we will find the rest of the solutions from the graph which follows the path of a parabola .
at t=1.42 , h(t)=0
Therefore 0 = -16(1.42)² + 1.42t + 10
or, V =15.68 ft/s
Again:
For h(t) to be maximum we have to find t for which h'(t)=0 , so we diff
h'(t) = -32t +15.68
or, t = -15.68 / 32
or, t = 0.49 seconds
Now h(0.49) = 16(0.49)² + 1.42 × 0.49 + 10 = 14.54 feet
Hence the maximum height of function is 14.54 feet
Therefore the diver has an initial velocity of 15.68 ft/sec and the diver reached a height of 14.54 feet at the maximum point.
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Nathan ha a $75 budget to rent a car for a day. The daily rental charge i $29. 50 and then he will alo have to pay 0. 55 per mile. How many mile can he drive the car without exceeding hi budget? (All partial mile are counted a full mile. )
Nathan can drive 83 miles without exceeding the budget.
Let us assume the number of miles Nathan can go in $75 budget be x. Now forming the equation based on the mentioned information -
The total budget = daily rental charge + number of miles × cost per mile
Keep the values in formula -
75 = 29.50 + 0.55x
Rewriting the equation according to variable x
0.55x = 75 - 29.50
Performing subtraction on Right Hand Side of the equation
0.55x = 45.5
x = 45.5 ÷ 0.55
Performing division on Right Hand Side of the equation
x = 82.7
As 0.7 will be counted a mile, thus, Nathan can drive 83 miles.
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the value of 1. 35⁷
Give your answer correct to 5 significant figures.
Answer:
1.35⁷ = 8.1722 (to 5sf)
The midpoint of line AB is M(3,−3). If the coordinates of A are (2,−8), what are the coordinates of B?
Answer:
The coordinates of B are (4, 2)
Step-by-step explanation:
The coordinates of B can be calculated as follows ?
The midpoint of line AB is M(3,-3) is derived from the formula
[tex]M=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]
Where [tex]x_1[/tex] and [tex]y_1[/tex] are the coordinates of A and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the coordinates of B
Since the coordinates of A are (2, -8), then the value of [tex]x_1[/tex] is 2 and the value of [tex]y_{1}[/tex] is -8.
Since the [tex]x[/tex]-coordinate of M is 3, then the equation to follow is
[tex]\frac{x_{1}+x_{2}}{2}=3[/tex]
Substitute 2 for [tex]x_{1}[/tex], then it follows that
[tex]\frac{2+x_{2}}{2}=3[/tex]
Multiply both sides of the equation by 2
[tex]\frac{2+x_{2}}{2}\times 2=3\times 2[/tex]
Simplify both sides of the equation
[tex]2+x_{2}=6[/tex]
Substract 2 from both sides of the equation
[tex]2-2+x_{2}=6-2[/tex]
Simplify the equation
[tex]x_{2}=4[/tex]
Since the [tex]y[/tex]-coordinate of M is -3, then the equation to follow is
[tex]\frac{y_{1}+y_{2}}{2}=-3[/tex]
Substitute -8 for [tex]y_{1}[/tex], then it follows that
[tex]\frac{-8+y_{2}}{2}=3[/tex]
Multiply both sides of the equation by 2
[tex]\frac{-8+y_{2}}{2}\times 2=-3\times 2[/tex]
Simplify both sides of the equation
[tex]-8+y_{2}=-6[/tex]
Add 8 to both sides
[tex]-8+8+y_{2}=-6+8[/tex]
Simplify the equation
[tex]y_{2}=2[/tex]
Since the value of [tex]x_{2}[/tex] is 4 and the value of [tex]y_{2}[/tex] is 2, then the coordinates of B are (4,2).
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mmm nnn
333 212121
555 353535
888 565656
Write an equation to describe the relationship between mmm and nnn.
The equation that represents the relationship between m and n is written as: n = 7m.
How to Write a Proportional Relationship Equation?A proportional relationship between two variables have a slope of constant of proportionality, k, which is y/x.
The equation that represents a proportional relationship is expressed in slope-intercept form as y = kx.
In this situation m = x, and n = y.
The constant of proportionality, k = n/m.
Find the constant of proportionality, k, using a pair of values from the given table, say (3, 21):
k = 21/3
k = 7
To write the equation, substitute k = 7 into n = km:
n = 7m.
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Chicken and rabbit are placed in the ame cage. There are 35 head and 94 feet. How many rabbit are there?
Based on heads and feet of chicken and rabbits, there are 12 rabbits in the cage.
Let us represent chicken by x and rabbit by y. So, we all know that chicken and rabbit have 1 head each. We also know that chicken has 2 feet and rabbit has 4 legs. Now forming the equation accordingly.
Equation for head -
x + y = 35 : Equation 1
Equation for feet -
2x + 4y = 94 : Equation 2
Rewriting equation 1 according to x
x = 35 - y : Equation 3
Keep the value of x from equation 3 in equation 2
2(35 - y) + 4y = 94
Preforming multiplication on Left Hand Side
70 - 2y + 4y = 94
Performing subtraction
2y = 94 - 70
2y = 24
y = 24 ÷ 2
Performing division
y = 12
Thus, there are 12 rabbits in the cage.
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someone help step by step
Step-by-step explanation:
we know, the area of a rectangle is
length × width
so, we have here
length × (x - 5) = x² - 7x + 10
therefore,
length = (x² - 7x + 10) / (x - 5)
so, just by looking at it (with experience) I see that length is (x - 2).
but let's do the actual polynomial division, which seems to be the desired exercise here.
x² - 7x + 10 ÷ x - 5 =
it is very similar to actual number divisions.
we go from left to right.
we start with the first term (x²) and see how many times (x - 5) would fit into it. for that we look only at the first term in x - 5 (that is x).
x² / x = x
that is already our first term of the result (quotient) :
x² - 7x + 10 ÷ x - 5 = x
now, we multiply that result with the divisor (x - 5) and subtract that from the dividend.
x² - 7x + 10 ÷ x - 5 = x
- x² - 5x
--------------
0 - 2x
and now we pull down the next term from the dividend :
x² - 7x + 10 ÷ x - 5 = x
- x² - 5x
--------------
0 - 2x + 10
and we repeat the process with that new dividend :
-2x / x = -2
that is our next term of the quotient.
x² - 7x + 10 ÷ x - 5 = x - 2
- x² - 5x
--------------
0 - 2x + 10
we repeat the process of multiplying that term (-2) with the divisor (x - 5) and subtracting that result from the dividend :
x² - 7x + 10 ÷ x - 5 = x - 2
- x² - 5x
--------------
0 - 2x + 10
- -2x + 10
-------------
0 0
there is no remainder, and there is no more term to pull down. we are finished.
the result of the division is (as expected) : x - 2
the expression to describe the length is therefore
x - 2
Solve for x with steps. Will mark brainliest.
x = 1.53347526
Take the log of both sides of the equation.
[tex]ln(2^{3x-1} ) = ln(3^{x-2} )[/tex]
Expand [tex]ln(2^{3x-1} )[/tex] by moving 3x-1 outside the logarithm
[tex](3x-1)ln(2)= ln(3^{x-2} )[/tex]
Move x-2 outside the logarithm [tex]ln(3^{x-2} )[/tex]
[tex](3x-1)ln(2) = (x-2)ln(3)[/tex]
Solve the equation for x
[tex]x = -[\frac{{2ln(3)-ln(2)}}{3ln(2)-ln(3)} ][/tex]
The value of x is 1.53347526(After applying the log values)
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find the product (x+2)(3x+1)(x-3)
(x+2)(3x+1)
x(3x+1)+2(3x+1)
3x²+x+6x+2
3x²+7x+2
(3x²+7x+2)(x-3)
x(3x²+7x+2)-3(3x²+7x+2)
3x³+7x²+2x-9x²-21x-6
3x³+7x²-9x²+2x-21x-6
3x³-2x²-19x-6
What is the area of trapezoid abcd? enter your answer as a decimal or whole number in the box. do not round at any steps. units²
The area of trapezoid ABCD is 37.5 units^2.
Trapezoid is a type of quadrilateral with at least one pair of parallel sides. The area of trapezoid is given by:
Area = ½(a + b)*h
Where a and b are the length of two parallel sides and h is the perpendicular length between the length of two parallel sides.
In the given trapezoid ABCD, which is defined by coordinates of A, B, C, and D, the distance of each side is given by: √((x2 – x1)^2 + (y2 – y1)^2)
The length of a (DA) = √((x2 – x1)^2 + (y2 – y1)^2) = √((-3 – 0)^2 + (2 – (-2))^2) = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5 units
The length of b (BC) = √((x2 – x1)^2 + (y2 – y1)^2) = √((7 – 1)^2 + (-3 – 5)^2) = √((6)^2 + (-8)^2) = √(36 + 64) = √(36 + 64) = √(100) = 10 units
The length of h (AB) = √((x2 – x1)^2 + (y2 – y1)^2) = √((1 – (-3))^2 + (5 – 2)^2) = √((4)^2 + (3)^2) = √(16 + 9) = √(25) = 5 units
Hence, the area of trapezoid:
Area = ½ (5 + 10) * 5 = 7.5 * 5 = 37.5 units^2
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8-9. If AG = 2, GF = 5, FE = 3, GB = 6, CD = 7 and GB || FC || ED, find the lengths of the missing sides?
AB=?
BC=?
FC=?
ED=?
Answer:
AB = 4 2/3BC = 11 2/3FC = 21ED = 30Step-by-step explanation:
In the given triangle AED, segments GB and FC are parallel to base ED. Points G and F are on segment AE in that order. Lengths AG=2, GF=5, FE=3, GB=6, and CD=7 are given. You want the lengths of AB, BC, FC, and ED.
Proportional segmentsSegments of transversals crossed by parallel lines are proportional:
AG : GF : FE = AB : BC : CD
2 : 5 : 3 = AB : BC : 7
Multiplying the first ratios by 2 1/3 will give the second ratios:
2 : 5 : 3 = 4 2/3 : 11 2/3 : 7
This lets us conclude ...
AB = 4 2/3
BC = 11 2/3
Similar trianglesCorresponding segments of similar triangles are proportional:
AG : GB = FA : FC = AE : ED
2 : 6 = (5+2) : FC = (5+2+3) : ED
We notice the second number in the first ratio is 3 times the first number. That means these ratios are ...
2 : 6 = 7 : 21 = 10 : 30
This lets us conclude ...
FC = 21
ED = 30
The lengths of the missing sides are calculated to be
AB = 5BC = 12FC = 21ED = 30How to find the lengths of the missing sidesThe parallel lines in the figure created similarity between the dimensions, this makes the ratio of the dimensions equal
The given dimensions that is used to find the missing sides
Solving for AB
AB / CD = AG / FE
AB / 7 = 2 / 3
cross multiplying
3 * AB = 7 * 2
AB = 14/3 = 4.667
Using AB, GF is calculated
AB / BC = AG / GF
14/3 / BC = 2 / 5
cross multiplying
BC = (5 * 14/3) / 2
BC = 35/3 = 11.667
Solving for FC
GB / FC = AG / A'F
6 / FC = 2 / (2 + 5)
cross multiplying
2 * FC = 6 * 7
FC = 42/2 = 21
Solving for ED
GB / ED = AG / AE
6 / ED = 2 / (2 + 5 + 3)
cross multiplying
2 * ED = 6 * 10
ED = 60/2 = 30
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Eli loads identical crates onto a truck with a load limit of 2000 pounds. Each crate weighs 125 pounds. A function modeling this situation, where y represents the total weight of the crates in pounds, has a range described by which inequality?.
Using the range idea, the following scenario is represented by the inequality 0 ≤ y ≤ 2000. Here option D is the correct answer.
A function's range is the set that contains all of the output values that the function can take. In the context of this problem, the following input and output are provided:
Input the number of crates that have been loaded into the vehicle. Total weight of the crates loaded into the vehicle as output.
Because the weight of an amount can never be negative, and the greatest weight is 2,000 pounds, as stated in the issue, the range in this context is reflected by the following inequality: 0 ≤ y ≤ 2000.
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Complete the statement. Round to the nearest hundredth if necessary.
12 cu ft ≈ gal
Answer:6978
Step-by-step explanation:304585
Solve the equation by graphing on a separate sheet of paper. Check your solution.
2x−3=3
Answer:
See attachment...
Hope this helps! :)
Which of the following graphs represents the solution(s) of the following system?
X^ - y = -2, 4y - 8 = x
The graph that represents the solutions of the given system of equations is attached below.
We are given a system of equations. The first equation is a quadratic polynomial. The second equation is linear in nature. The equations are given below.
x² - y = -2
4y - 8 = x
We need to find the solution to the equations using a graph. The graph of the equations is attached below. The graph of the first equation is represented by an upward parabola. The graph of the second equation is represented by a straight line. The intersection points of the two curves are the solutions to the given system of equations.
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Substitute 6 for the variable, n, using parentheses. Then simplify by multiplying 8 and 6. 8(6) = 48. So you have 56 = 48, which is not a true statement. 6 is not a solution to the equation.
The numeric value of the expression 8n at n = 6 is different of 56, hence n = 6 is not a solution to the expression 8n = 56.
How to verify if a number is a solution to an expression?A number a is a solution to an expression if the numeric value of the expression at input a generates an identity with the expression.
In this problem, the expression is given as follows:
8n = 56.
We want to verify if the number six is a solution to the presented expression.
The numeric value of the expression at n = 6 is found replacing the lone instance of n by 6, hence it is obtained as follows:
8n = 8 x 6 = 48.
(the product of 8 and 6 is 48).
Then the equality would be of:
48 = 56.
Which is a contradiction, hence n = 6 is not a solution to the expression 8n = 56.
Missing InformationThe problem is:
Explain how to determine if the number is a solution to the equation. 56 = 8n for n = 6
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Katalin drove 300 miles on her vacation. she drove an average of 1.9 times faster on the second 150 miles of her trip than she did on the first 150 miles of her trip. which expression represents the time she spent driving?
The expression represents the time she spent driving is [tex]\frac{228.95}{x}[/tex]
The expression represent the time she spent driving can be calculated as follows:
We know that
Time = [tex]\frac{distance}{ speed}[/tex]
Let x be her speed on the first half of the trip.
Then for first half , the tiime she takes is
T1= [tex]\frac{150}{x}[/tex]
while in a second half the time taken by her is
T2= [tex]\frac{150}{1.9x}[/tex]
T2= [tex]\frac{78.95}{x}[/tex]
the total time she spent on driving is
T1 + T2 = [tex]\frac{150}{x}[/tex] + [tex]\frac{78.95}{x}[/tex] = [tex]\frac{228.95}{x}[/tex]
Hence, the expression represents the time she spent driving is [tex]\frac{228.95}{x}[/tex]
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Write a division equation that represents the question: how many 3/8s are in 5/4
The division equation is x * 3/8 = 5/4 and there are (10/3) times 3/8s there in 5/4.
Let's assume that x times 3/8 are in 5/4.
So, calculating a division equation for the value of x.
x * 3/8 = 5/4
=> x = 5/4 * 8/3
=> x = 40/12
Dividing the numerator and denominator by 4.
We get, the value of x equal to
=> x = 10/3
Division equation: A division equation is a mathematical expression containing a division operator. Division equations are useful not only in math class but also in everyday life.
For example, if we want to share a bundle of papers equally with our friends, we can use this solution to find the given question. 100 papers and we have 10 friends. To find out how many papers each person gets, divide 100 by 10. The solution is 10. This means that each friend receives 10 papers.
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i need help on this , Thanks
Answer:
∴ x = 90
Step-by-step explanation:
(180 - x)° = x° (vertically opposite angles)
180 - x = x
-2x = -180
2x = 180
∴ x = 90
Find the slope of the line graphed below.
Answer: -1
Step-by-step explanation:
Answer:
By counting, to go from one point to another, we go down 4, over 4. This means the slope is -4/4. This can then be simplified.
-4/4 = -1
So, the slope is -1
Delaney would like to make a 5 lb but mixture that i 60% peanut and 40% almond. He ha everal kind of peanut and everal kind of a mixture that i 20% peanut and 80% almond. Let p repreent the number of punt of peanut needed to make the mixture, and let m repreent the number of pound of the 80% almond-20% peanut mixture. What i the ytem that model thi ituation
The system that models the equation is m = 2.5 lb.
This is a mixed-up issue. The combination of
80% almonds and 20% peanuts make up combination A.
Completely peanuts in mixture B
both the
As a combination, use 60% peanuts and 40% almonds.
Since mixture C is created by combining mixtures A and B, we may calculate its combined weight in pounds to be 5 pounds.
Hence, we
Let m be the weight in pounds of mixture A (20% peanuts, 80 % almonds).
and
50-m is the quantity of mixture B in pounds.
Consequently, the set of equations that models this circumstance is:
0.20m + 1(50-m) = 0.60(5) (5)
0.80m + 0(50-m) = 0.40(5)
Equation 2's solution for m gives us
m = 2.5 lb.
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What is the approximate value of the square root of 8?
Answer:
64
Step-by-step explanation:
Hope this helps!
Answer:
2nd answer is the right one
Step-by-step explanation:
the square root of 9 is 3. The square root of 8 is a little smaller because 8 is smaller than 9.
A new soup recipe contains 33\%33%33, percent less sodium per serving than the old soup recipe. The old soup recipe contained xxx milligrams of sodium per serving.
Which of the following expressions could represent the amount of sodium per serving, in milligrams, in the new soup recipe?
The expression that could represent the amount of sodium per serving, in milligrams, in the new soup recipe is y = 0.67x
How to get the expression?From the information, the new soup recipe contains 33% less sodium per serving than the old soup recipe.
Let's say Sodium in an old soup recipe per serving = x mg
Let's say Sodium in a new soup recipe per serving = y mg
The new soup recipe contains 33% less sodium per serving than the old soup recipe
y = x - (33/100)x
100y = 100x - 33x
100y = 67x
Divide through by 100
y = 0.67x
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c. What is the slope?
Step-by-step explanation:
the slope is the inclination of a line, or of the tangent (also a line) on a point of a bent curve.
it is expressed as ratio (y coordinate change / x coordinate change) when going from one point on the line or curve to another point on the line.
it tells us how many units y changes when x changes a certain number of units (like 1).
it is positive, if the line goes up (when going from left to right). the larger the value, the steeper the line goes up.
it is negative, if the line is going down (again, going from left to right). the lower the value, the steeper the line goes down.
a horizontal line has a slope of 0/x = 0.
a vertical line has a slope of y/0, which is undefined, or sometimes expressed as infinite.
Kirsty changes $380.80 into pounds (£) when £1 = $1.19. Calculate the amount Kirsty receives.
Answer:
320 pounds sterling
Step-by-step explanation:
All you have to do is $380.80 divided by $1.19 which is equal to one pound sterling. Hope this helps!
If the length of a rectangle is increased by 40% and the width is decreased by 40% then the area:.
The Area of Rectangle would be Decreased by 16% of the original Area. Now the Area of Rectangle is 84%.
Let the Length of rectangle be ‘x’
And width of rectangle be ‘y’
Area of Rectangle = Length X Width
Original Area of rectangle = x X y = xy square units
As the length is increased by 40% then, the new length would be 1+40% i.e 1.4 and,
The width is decreased by 40% then, the new width would be 1-40% i.e 0.6
New Length = 1.4x
New Width = 0.6y
Now , New Area of Rectangle = 1.4x X 0.6y
= 0.84xy square units
The effect is that the New Area of the rectangle is 84% of the original area. There is a decrease of 16% in the area.
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Determine the distance between the points (−6, −3) and (0, 5).
22 units
10 units
8 units
5 units
By using the distance formula, The distance between the points (−6, −3) and (0, 5) is 10 units.
In geometry, we use the distance formula to evaluate the distance between two points whose coordinates are given,
The coordinates of the points are given as [tex](x_{1} ,y_{1})( x_{2} ,y_{2} )[/tex]
Then, the distance (D) between them is given by :
[tex]D = \sqrt{(x_{1} -x_{2} )^{2} -(y_{1} -y_{2} )^{2} }[/tex]
Now, the given points are (−6, −3) and (0, 5).
Putting these values in the distance formula, we have
[tex]D = \sqrt{(-6-0)^{2}+ (-3 -5)^{2} }\\ \\D = \sqrt{36 +64 \\\\ \\D = 10[/tex]
Hence, the distance between the points (−6, −3) and (0, 5) is 10 units.
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Answer: 10 units
Step-by-step explanation: i took the test and got it right
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Answer:
Original equation
distributive property
subtract 5x from both sides
add 12 to both sides
Divide both sides by 14
Step-by-step explanation:
