please consider giving me a helping hand! I will give you brainliest as a big thanks!!
Answers
Answer:
Step-by-step explanation:
Answer:
1. x = -4, y = -5
Chosen strategy was to substitute for y in the second equation since the first equation gives y in terms of x. This gives an equation in x which can be solved for x, then y can be found by substituting for x in the first equation
2. x = -2, y = -3
Strategy used is to eliminate the x terms by simply adding the equations since the coefficients of x are the same but of opposite signs. Solve for y and use this value to solve for x by substituting in any one equation
3. x = -5, y = 6
Strategy used was to set the RHS of the equations equal to each other since both equations are equations with y on the LHS. Solve for x then use this value to find y value
4. x = 0, y = 1
Strategy used was to get the y coefficients same but of opposite signs, add the two equations to eliminate the y term, solve for x and then solve for y by substituting x in one of the equations - in this case, the second equation
Step-by-step explanation:
Here is how I would answer this question. Remember there are multiple ways of solving a linear equation of two variables but looking at the equations and from experience, I have chosen the most efficient way (my opinion)
Q1.
y = x - 1 [1]
3x - 4y = 8 [2]
Since we are given y = x - 1 in Eq [1], an obvious strategy is to substitute for y in eqn [2]
=> 3x - 4y
=> 3x - 4(x-1)
=> 3x - 4x - 4(-1) =
=> 3x -4x + 4
=> -1x + 4
=> -x + 4
And we know that eqn [2] has 8 on the RHS
∴ -x + 4 = 8
Subtract 4 from both sides
-x + 4 - 4= 8 -4
-x = 4
Multiply by -1 both sides
x = -4
Substitute for x in equation [1] y = x - 1 to get
y = -4 - 1 = -5
Solution: x = -4, y = -5
Q2
3x + 2y = -12 [1}
-3x + 2y = 0 [2]
Here we can see the coefficients of x are the same but with opposite signs
Adding the two equations will eliminate the x terms and allow us to solve for y which can be used then to solve for x
Adding [1] and [2] gives
3x + 2y + (-3x + 2y) = -12 + 0
4y = -12
y = -3
Substitute for y in equation [1]
=> 3x + 2(-3) = -12
=> 3x - 6 = -12
=> 3x = -12 + 6 (adding 6 on both sides
=> 3x = -6
x = -2
Solution x = -2, y = -3
Strategy used: Adding both equations to eliminate x terms since x coefficients are same but of different signs
Q3
y = 3x + 21 [1]
y = 2x + 16 ][2]
Since we have two expressions for y in terms of x, set the RHS of equations [1] and [2] to be equal and solve for x
=> 3x + 21 = 2x + 16
Subtract 2x from both sides
=> 3x - 2x + 21 = 16
=> x + 21 = 16
Subtract 21 from both sides
x = 16 - 21 = -5
Substitute for x in equation [2]
y = 2x + 16
=> y = 2(-5) + 16
y = -10 + 16
y = 6
Solution: x = -5, y = 6
Q4
2x - 7y = -7 [1]
x + y = 1 [2]
We can make the coefficients of one of the variable in both equations the same and either add/subtract as necessary to eliminate one of the variable terms and solve for the other
Multiply [2] by 7 to get
7x + 7 y = 7 [3]
[1] and [3] have y coefficients same but of opposite signs so add [1] and [3] together
2x - 7y + (7x + 7y ) = - 7 + 7
2x + 7x - 7y + 7y = 0
9x = 0
x = 0
Sub for x in [2] x + y = 0 to get
0 + y = 1
or y = 1
Solution: x = 0, y = 1
Strategy used was to get the y coefficients same but of opposite signs, add the two equations to eliminate the y term, solve for x and then solve for y by substituting x in one of the equations - in this case, the second equation
Related Questions
A star shape is made out of 5 congruent triangles. the peak of 1 triange is 25°. what are the sizes of the base angles?
Answers
Answer:
77.5
Step-by-step explanation:
180-25=155
155/2=77.5
How many subsets does the set (1,2,3) have
Answers
Answer:
Answer down below!
Step-by-step explanation:
The set (1, 2, 3) would have 8 sets in total
Refer to Expression 1 and Expression 2.
Expression 1
6-7-3².9+43
r:
Expression 2
5+4+2+6-2-2-1
(a) What is the value of Expression 1?
(b) Insert parentheses in Expression 2 so that it has a value of 19. Then show why your expression has a
value of 19.
Answers
a) Value of Expression 1 is 29.833.
b) After inserting the parentheses the expression is (5+4) * 2 + 6 -2 * 2 - 1.
The order of operations to solve in expression 1 is:
First parenthesis, then multiplication and division, and then addition and subtraction.
So, the expression is:
6 × 7 - 3 ÷ 2 × 9 + 4 ÷ 3
First, solve division and then multiplication:
= 42 - 1.5 × 9 + 1.34
= 42 - 13.5 + 1.34
= 29.84
b) Because the parenthesis is the initial action, so insert it in 5+4 which provides the following result:
(5 + 4) × 2 + 6 - 2 × 2 - 1
First, calculate the parenthesis, then the multiplication and division, and finally perform addition and subtraction:
= (9) × 2 + 6 - 4 - 1
= 18 + 6 - 4 - 1
= 19
The final value is 19.
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Larry plants to invest 275,000 for 30 years at an anticipated rate of 6% per annum compounded yearly what is the approximate difference in his ending balance of the actual rate is 5% instead of six
Answers
Answer:
$390,000
Explanation
To do this, we will use the compound interest formula;
A = P(1+r)^t
P = 275000
rate r = 6%
Time t = 30years
Substitute
A = 275000(1+0.06)^30
A = 275000(1.06)^30
A = 275000(5.7435)
A = 1,579,460.07
For the rate of 5%
A = 275000(1+0.05)^30
A = 275000(1.05)^30
A = 275000(4.3219)
A = 1,188,534.15
Takeing their difference;
Difference = 1,579,460.07-1,188,534.15
Difference =390,925.92
Hence the approximate difference in his ending balance of the actual rate is 5% instead of six is about $390,000
The length of the rectangle is 5 more than twice the width. If the perimeter is 10 times that of the width, what is the width, length, and perimeter of the rectangle?
Answers
The length of the rectangle is 10, the width is 2.5 and the perimeter is 25
Let the width of the rectangle be x
The length of rectangle = 2x + 5
The overall length of the outline determines a rectangle's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter.
Perimeter = 10 times of width
= 10*x
= 10x
The formula for the perimeter of a rectangle is given:
Perimeter = 2(Length+Breadth)
10x = 2(x + 2x+5)
10x = 2(3x+5)
10x = 6x + 10
4x = 10
x=2.5
Length = 10
Width = 2.5
Perimeter = 25
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a certain bacteria doubles every 2 seconds. Starting from a single bacterium, how many bacteria will be there after 20 seconds?
Answers
The answer will de 10 bacterias
Answer: 1024
Step-by-step explanation: Since there's only 1 bacteria at first, we can just do 2^x. x being the amount of time divided by the amount of time between each time it doubles. Since the bacteria doubles every 2 seconds, and 20/2 = 10 we get 2^10 which is 1024.
3.7416573868 to nearest tenth
Answers
Explanation:
The tenths decimal place is right after the decimal point
7 is in the tenths place
The digit just to the right of 7 is 4
Since the 4 is not 5 or larger, this means we erase everything after the 7 and go with 3.7
If we had something like 3.76, then the 7 bumps up to 8 to get 3.8
The team's engagement score was 5.20 this month. the score has been improving at a rate of 8% per month. what was the score 3 months ago? 1.60 3.95 4.13 4.78 5.12
Answers
The score 3 months ago was 4.130.
What is rate of increase?
Rate of increase is defined the change in rate that describes how one quantity changes in relation to another quantity.
Assume the score 3 months ago was x. This means that the above can be expressed as:
Current score = x × ( 1 + rate) ^ number of months
5.20= x(1+8%)^3
5.20 = x(1.259)
x= 5.20/1.259
x= 4.130
therefore, the score was 4.130
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A triangle has been plotted on the coordinate plane.
Which series of transformations will result in Point B” being the greatest distance from the x-axis.
A - reflect over the x-axis then rotate 90° clockwise
B - rotate 80° clockwise then reflect over the line x= -1
C - rotate 90° clockwise then translate following the rule (x+1, y-1)
D - translate (x+1,y-1) then reflect over the y-axis
REALLY NEED THIS
Answers
When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, yreflection )'s across the x-axis is (x, -y). A point's reflection over the y axis is shown. The reflection rule over the y axis is (x,y)(x,y).
What exactly is a coordinate plane?A coordinate plane is a two-dimensional plane formed by two number lines intersecting. One of these number lines is a horizontal number line known as the x-axis, and the other is a vertical number line known as the y-axis.
1) Determine the absolute value of x1(y2-y3) + x2(y3-y1) + x3(y1-y2).
2) The area of the triangle is calculated by dividing this value by two.
3) Use our area of a triangle with coordinates calculator to confirm this result.
The coordinate plane can be used to draw lines and points. This system allows us to visually describe algebraic relationships, as well as create and interpret algebraic concepts.
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Find the value of each variable
Answers
Answer:
x = 58°
y = 74°
z = 106°
w = 42°
Step-by-step explanation:
Finding the value of unknown variables:
x + 32° = 90°
x = 90 - 32
[tex]\sf \boxed{\bf x = 58^\circ}[/tex]
x + y + 48 = 180 {Angle sum property of triangle}
58 + y + 48 = 180
y + 106 = 180
y = 180 - 106
[tex]\sf \boxed{\bf y = 74\°}[/tex]
y + z = 180 {Linear pair}
74 + z = 180
z = 180 - 74
[tex]\sf \boxed{\bf z = 106\°}[/tex]
32 +z + w = 180 {Angle sum property of triangle}
32 + 106 +w = 180
138 + w = 180
w = 180 - 138
[tex]\sf \boxed{\bf w = 42\°}[/tex]
Over the last four months, your investment lost
10%, 20%, 30%, and then 40%. What percent
of the original investment do you have left?
Answers
Answer:
30.24%
Step-by-step explanation:
Each time you lose x%, you end up with 1 - 0.01x.
For example, if you lose 10% of an amount, you end up with 1 - 0.01(10), or 0.9 times the original amount.
Let's say you started with x.
You lost 10%. Now you have 0.9x.
Then you lost 20% of the remaining amount. Now you have 0.8(0.9x).
Then you lost 30% of the remaining amount. Now you have 0.7(0.8)(0.9x).
Finally you lost 40% of the remaining amount. Now you have 0.6(0.7)(0.8)(0.9x).
The final amount you have is
0.6(0.7)(0.8)(0.9x) = 0.3024x = 30.24% of x
Answer: 30.24%
Find the area of the figure below, formed from a triangle and a parallelogram. A figure is formed from a triangle and a parallelogram. The base of the triangle is 8 millimeters and the height is 2 millimeters. The bottom and top of the parallelogram are 6 millimeters and the height is 4 millimeters.
Answers
The total area of the figure is; 32 millimeters sq.
What is the area of a parallelogram?The area of a parallelogram is the product of the base and the height of the figure.
The area of a parallelogram = Base x Height
We have been given that a parallelogram has a base is 6 millimeters and a height is 4 millimeters
The area of a parallelogram = Base x Height
= 6 x 4
Area = 24 millimeters sq.
Similarly, The area of the triangle = 1/2 x b x h
= 1/2 x 8 x 2
= 8 millimeters sq.
The total area of the figure is;
Total = area of the triangle + area of a parallelogram
Total = 24 + 8 = 32
Hence, the total area of the figure is; 32 millimeters sq.
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Find the range, variance & standard deviation of the following sample dataset. Round all answers to the nearest tenth.
The following data represent the number of students from each school that attended a debate tournament: 75, 47, 50, 71, 64, 50, 52, 56, 53, 47, 55
Answers
Answer:
The range is 28
The variance is 90.855
The mean is 56.36
The median is 53
The sample standard deviation is 9.532
Step-by-step explanation:
Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane. Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power plus 4 going through points 0 comma 5 and 1 comma 6. What effect does adding 4 to the parent function have on the transformed function? a Adding 4 to the parent function shifts the function down four units. b Adding 4 to the parent function shifts the function up four units. c Adding 4 to the parent function shifts the function right four units. d Adding 4 to the parent function shifts the function left four units.
Answers
Answer:
b Adding 4 to the parent function shifts the function up four units.
Step-by-step explanation:
The original function is y(x) = 2^x
Adding four is y(x) = 2^x + 4
We've simply told y to take whatever value is generated for x and add four to it.
So the new value for the same x would have 4 added to y: (x,y+4),
Point (1,2) would shift to point (1,6).
Adding four to the parent function will shift the entire graph up by 4. See ate attached graph.
Evaluate compositions of function. Let f(x) = 3x + 2, g(x) = -x2, and h(x) = x-2/5. Find the indicated value. (SHOW WORK PLEASE))
Answers
The indicated numeric values for the composite functions are given as follows:
1. f(g(-3)) = -25.
2. g(f(2)) = -64.
3. h(f(-5)) = -3.
4. g(g(-3)) = -81.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is according to the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function. Hence, to calculate f(g(-3)), for example, we calculate g(-3), then we calculate the numeric value of function f(x) at x = g(-3).
For this problem, the functions are given as follows:
f(x) = 3x + 2.g(x) = -x².h(x) = (x - 2)/5.For item 1, the numeric values are found as follows:
g(-3) = -(-3)² = -9.f(g(-3)) = f(-9) = 3(-9) + 2 = -27 + 2 = -25.For item 2, the numeric values are found as follows:
f(2) = 3(2) + 2 = 6 + 2 = 8.g(f(2)) = g(8) = -(8)² = -64.For item 3, the numeric values are found as follows:
f(-5) = 3(-5) + 2 = -15 + 2 = -13.h(f(-5)) = h(-13) = (-13 - 2)/5 = -3.For item 4, the numeric values are found as follows:
g(-3) = -(-3)² = -9.g(g(-3)) = g(-9) = (-9)² = -81.More can be learned about composite functions at https://brainly.com/question/10687170
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the larger number is 18 more than twice the smaller. If the sum of the two numbers is 93, find
oth numbers.
Answers
Answer:
The larger number is 68 and the small number is 25
Step-by-step explanation:
Large number y
small number is x
y=2x+18
x+y=93
Vinny is serving punch to guests at a party. He has $\frac{3}{4}$ of a gallon of punch, and he pours $\frac{5}{64}$ of a gallon into each guest's cup, filling each to the top. At the most, how many guests' cups can he fill to the top?
Answers
In serving punch to guests at the party, Vinny can fill 9 guests' cups to the top based on this unit rate.
What is a unit rate?The unit rate is the ratio of a variable to another.
The whole number here is the total gallons of punch available to serve the guests.
The unit rate is the volume that each guest's cup can hold or contain.
This implies that the ratio is 5/64: 3/4
The total number of gallons of punch = 3/4 or 0.75 gallons.
The volume or capacity of each guest's cup = 5/64 gallons or 0.078125.
The number of guests' cups to fill to the brim = 9.6 cups (0.75/0.078125)
= 9 guests' cups.
Thus, Vinny can fill 9 guests' cups to the brim, using the given ratio or unit rate.
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The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election. What percentage of the members voted?
Answers
The percentage of members that voted is 70%.
How to find the percentage of members that voted?The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election.
Therefore, the percentage of the members that voted can be calculated as follows;
percentage that voted = number of people that voted / total number members × 100
Therefore,
number of people that voted = 42
total number members = 60
Hence,
percentage that voted = 42 / 60 ×100
percentage that voted = 4200 / 60
Therefore,
percentage that voted = 70%
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Please I need help right now
Answers
A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.
What is meant by mathematical function?A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.
The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A mathematical phrase, rule, or law that establishes the relationship between two variables, one of which is independent and the other dependent (the dependent variable)
The complete question is:
What is a mathematical function? After studying the vending machine examples, write a definition that communicates precisely what it means for a mathematical relationship to be a function.
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i'll give you brainliest
Answers
2. Incorrect
What is the slope of this image?? I NEED HELP
Answers
Answer:
Positive, so the answer would be y=4/2 or 2. y=2x-4
Step-by-step explanation:
Slope formula y=mx+b
The mx is the rise/ over run
The b is the y-intercept
You can check in the end by checking so to see if the rise over the run is correct
Also, you can check the b by looking at the y-intercept, which is -4
Hope this helps!
13 gallon of water in a 3-gallon container. What fraction of the container is filled?
Answers
Answer:
1/9
Step-by-step explanation:
There is 1/3 gallon of water in a 3 gallon container. The fraction of the container that is filled is 1/9
(1/3 of a gallon divided by 3 gallons equals 1/9)
-53 = 8y + 4y - 17 solve for y and simplify as much as possible
Answers
Answer:
y = -3
Step-by-step explanation:
-53 = 8y + 4y - 17
combine y terms on right side:
-53 = 12y - 17
add 17 to both sides:
-53 + 17 = 12y - 17 + 17
-36 = 12y
divide both sides by 12:
-36/12 = 12y/12
y = -3
how long would it take to drive 1km at a speed of 1.71km/h (with working)
Answers
It would take 35 minutes to drive 1 km at a speed of 1.71 km/h.
How do distance and speed compare?Speed is the ratio of distance traveled in a given time. Speed is given by distance/time.
The time can be computed by dividing distance by speed.
This implies that time is the quotient of distance and speed.
The total distance drove = 1 km
The driving speed = 1.71 km/h
Time = Distance/Speed
= 1/1.71
= 0.58 hours
= 0.58 x 60 seconds
= 35 minutes 5 seconds
Thus, to travel 1 kilometer at the speed of 1/71 kilometers per hour would take 35 minutes.
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Please help me with this. Show the solution as well. Thank you
Answers
Step-by-step explanation:
any ordered pair is a solution, if we can use its coordinates in the equation, and the equation stays true.
for x - 3y = 6
1. (3, -1)
3 - 3×-1 = 6
3 + 3 = 6
6 = 6
true, this is a solution.
2. (0, 2)
0 - 3×2 = 6
-6 = 6
false, this is not a solution.
3. (3, 1)
3 - 3×1 = 6
3 - 3 = 6
0 = 6
false, this is not a solution.
Which of the following values are in the range of the function graphed below?
Check all that apply.
Answers
The range of the function is 1
As seen by the graph in the following figure
As can be seen, x's value falls between
nonetheless, y is equal to 1 for all values of x.
This holds true regardless of x's value.
Consequently, the function's range is 1.
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Jai is 1.45 meters tall. At 11 a.m., he measures the length of a tree's shadow to be
39.55 meters. He stands 34.1 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
오ㅜ
39.55 m-
(Diagram is not to scale.)
1.45 m
34.1 m-
Answers
By using triangles laws, we know that the height of the tree is 8.42 meters.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.So, 1.45 m is Joshua's height.
Tree shadow length: L=31.65 mJoshua's distance from the tree is 26.2 meters.We must ascertain the tree's height.
BC = 26.2 mBD = 31.65mCD = BD-BCCD = 31.65-26.2=5.45 mEC = 1.45 mThe right triangles are all alike.
The ratio of the corresponding sides is equal when two triangles are comparable.
△ABD ≈ △ECDAB/EC = BD/CDNow, put values as follows:
AB/1.45 = 31.65/5.45AB = 31.65 × 1.45/5.45AB = 8.42mTherefore, by using triangles laws, we know that the height of the tree is 8.42 meters.
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The correct form of the question is given below:
Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away from the tree so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
What is 39,400,000 in scientific notation?
Answers
Answer:
3.94*10^7
Step-by-step explanation:
Answer:
3.94 * 10^7
Step-by-step explanation:
:]
5(1-1)+10=
5(2-1)+10=
5 (3-1) +10=
5(4-1)+10=
Answers
Step-by-step explanation:
First is
5(1-1)+10= 5×0+10= 0+10 = 10
2nd is
5(2-1)+10=5× 1+10= 5+10=15
3rd= 5(3-1)+10= 5×2+10=10+10=20
4th=5(4-1)+10=5×3+10=15+10=25
I hope it will be helpful for you.
The quadratic 3x^2+4x-9 has two real roots. What is the sum of the squares of these roots? Express your answer as a common fraction in lowest terms.
Answers
If the quadratic [tex]3x^2[/tex]+4x-9 =0 has two real roots, then the sum of the square of the these roots is 7.77
The polynomial is [tex]3x^2[/tex]+4x-9 =0
Here,
a = 3
b = 4
c = -9
Here the quadratic equation
= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values in the quadratic equation
= [tex]\frac{-4+/-\sqrt{4^2-4(3)(-9)} }{2(3)}[/tex]
The result will be
= [tex]\frac{-2+/-\sqrt{31} }{3}[/tex]
Therefore, the roots are
[tex]\frac{-2+\sqrt{31} }{3}[/tex] and [tex]\frac{-2-\sqrt{31} }{3}[/tex]
Square of the first root = [tex](\frac{-2+\sqrt{31} }{3} )^{2}[/tex]
= 1.414
Square of the second root = [tex](\frac{-2-\sqrt{31} }{3} )^2[/tex]
= 6.363
The sum of the square of the roots = 1.414+6.363
= 7.77
Hence, if the quadratic [tex]3x^2[/tex]+4x-9 =0 has two real roots, then the sum of the square of the these roots is 7.77
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