The solution to the system of equations, in terms of x, considering the augmented matrix, is of:
y = -40x + 81.x = 20x - 40.Augmented matrix of system of equationsThe augmented matrix of a system of equations is built as follows:
Each of the columns before the | represents the coefficients of a variable.The column after the | represents the numeric value of the expression.In this problem, there are three columns before the |, the there are three variables given as follows:
x,y and z.
The expression from the first row is:
x -0.05z = 2.
The expression from the second row is:
y + 2z = 1.
The third row is all zero, meaning that there is a free variable, hence the solution to the system is written as a function of x as follows:
x - 0.05z = 2
0.05z = x - 2.
z = (x - 2)/0.05
z = 20x - 40.
Hence the solution for y is:
y = 1 - 2z
y = 1 - 40x + 80
y = -40x + 81.
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Solve the inequality4x + 13 ≥ 27
Work Shown:
4x + 13 ≥ 27
4x + 13-13 ≥ 27-13
4x ≥ 14
4x/4 ≥ 14/4
x ≥ 7/2
The inequality sign stays the same for each step. The inequality sign only flips if we were to multiply both sides by a negative number (or divide both sides by a negative number).
Note: 7/2 = 3.5
solve the absolute value inequality.
|-3x|-7≥ 11
Answer:
x ≥ 6
Step-by-step explanation:
|-3x| - 7 ≥ 11 The absolute value of -3x is 3x
3x - 7 ≥ 11 Cancel the 7 by adding it on both sides
3x ≥ 18 To get x by itself divide 3 on both sides
x ≥ 6
Can an equation of a line in standard form be written in a way where A, B, or C are either negative or positive? It’s hard to explain… for example
-x+y=-2
Can that be a way to do it? Or would the correct way be like
x-y=2?
Or what about
2x-2y=4? Can I divide by 2 on both sides to rewrite it as
x-y=2? I’m just wondering….
Answer:
2x-2y=4 that is the best way u can write it
round this number to the hundredth 3.6432
Sketch the graph of each line
The straight line y = x -1 is shown figure
Sketching graph of a line:
To plot straight-line graphs we need to take values of x and y values to make a value table and to work out the graph.
Take x values as -1, 0, 1, etc. to make our work easy and clearer, and from that find the values of y.
After calculating the coordinates, use the resultant points to plot the line as a graph.
Here we have a line
y = x -1
To sketch the graph we need to make a value table as given below
First take x values as, -1, 0, 1 from that find the values of y
At x = -1 => y = -1 - 1 = -2
At x = 0 => y = 0 - 1 = -1
At x = 1 => y = 1 - 1 = 0
From the above calculations, the value table is
x -1 0 1
y -2 -1 0
Use the above value and Sketch the graph
[ the resultant graph is shown below ]
The straight line y = x -1 is shown figure
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2y - 3x = 6
Equation of the line is y = 3/2x + 3.
Define slope intercept form.Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The "slope-intercept" form is one of the most popular methods. It is so named because it makes the slope and y-intercept of the equations in the equation more clear. The number that is placed before the x is the slope.
Given,
Slope intercept form:
Formula:
y = mx + b
Where m = slope
2y - 3x = 6
2y = 6 + 3x
Equation:
y = 3 + 3/2x
y = 3/2x + 3
Equation of the line is y = 3/2x + 3.
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A relation is shown: {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)} Which set of information is true about the relation shown?
The set of information that is true about the relation is:
Domain: {3, 4, 5, 6}
Range: {-8, -1, 2, 7}
The relation is not a function.
How to Determine a Relation that is a Function?A relation that represents a function will have each of its domain elements related to exactly one range element.
All the x-values in a relation are referred to as the domain of a function, while all the y-values are called the range of the function,
Therefore, for a relation to be considered a function, a domain element must not correspond to two different range elements or related to two range elements.
Given the relation, {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)}:
The domain of the relation is: {3, 4, 5, 6}
The range of the relation is: {-8, -1, 2, 7}
The relation is not a function because the domain element, 3, corresponds to two different range elements, 2 and -8.
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Mia is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 15 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 18^{\circ}
∘
, and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^{\circ}
∘
. If her eyes are 1.75 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters
How to find the distance between the pointsinformation given in the question
Mia stands at a horizontal distance of 15 meters from the building
The angle of elevation from her eyes to the roof ((point AA)) is 18
the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^
her eyes are 1.75 meters from the ground
The direction of movements describes a right angle triangle of
opposite = height of antenna + height of the building
adjacent = 15 meters
The distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The the height of the antenna is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only
tan 53 = opposite / 15
opposite = 15 * tan 53 = 19.906 meters
opposite = 15 * tan 18 = 14.266 meters
Height of the antenna
= 19.606 - 14.266
= 5.34 meters
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(HELP ASAP) ABC Is Isosceles m
Answer:
m∠A = 55°-----------------------------
A and C are congruent angles opposite to congruent sides of the isosceles triangle.
m∠A = m∠C3x + 40 = x + 503x - x = 50 - 402x = 10x = 5Find the measure of ∠A
m∠A = 3×5 + 40 = 15 + 40 = 55Answer:
The angle A is 55°.
Step-by-step explanation:
We know that,
→ <A = <C
Now the value of x will be,
→ 3x + 40 = x + 50
→ 3x - x = 50 - 40
→ 2x = 10
→ x = 10/2
→ [ x = 5 ]
Then the value of m<A is,
→ A = 3x + 40
→ A = 3(5) + 40
→ A = 15 + 40
→ [ A = 55° ]
Hence, the answer is 55°.
Find the value of k such that the system of linear equations is inconsistent.
6x-12y = -7
2x + ky = 14
For the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.
As given in the question,
Given system of linear equations are as follow:
6x-12y = -7 ____(1)
2x + ky = 14 _____(2)
Form equation (1) we have,
6x -12y = -7
⇒3 ( 2x -4y) = -7
⇒ 2x - 4y = -7 /3 ____(3)
From equation (2) and (3) we have,
2x + ky = 14
2x - 4y = - 7/3
Value of k so that the given system of equations are inconsistent is given by:
k = -4
For inconsistent there is no solution.
Therefore, for the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.
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mr colton needs 4.62 cups of flour to make 3 pound of dough.How many cups does she need to make 2 pounds of dough
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10
Let the number of cups be represented by x.
This will be expressed as:
2/3 = x/4.62
Cross multiply
3x = 2 × 4.62
3x = 9.24
Divide
x = 9.24 / 3
x = 3.08
Therefore, 3.08 cups are needed.
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Answer:
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
Step-by-step explanation:
NEED HELP ASAP!! ( NEED DONE WITHIN THREE MINS OF POSTING)
Answer: i am not positive but i think 2.5 on x and 9, and 27 on y
Step-by-step explanation: just want to help asap
Anna Marie goes to dinner at a restaurant where the sale tax on meals is 9%. she leaves a tip that is 175% of the amount of sales tax. if her total bill is $45 what was the cost of her meal and what percent tip did she leave
Answer: $78.75
Step-by-step explanation:
You have to multiply the price by tax and add
q(x) = -x-2
r(x) = x² + 2
Find the following.
(r∙q)(-5) =
(q∙r)(-5) =
Answer: 5q-5r -5q+5r
A model rocket is launched with an initial upward velocity of 235 feet the Rockets height H in feet after t seconds is given by the following
By assuming that the initial height of the rocket is the ground, we will get the height equation:
H(t) = -16*t^2 + 235*t
How to find the equation for the height?The height equation for any object near the surface of the heart that is not being subject to any other forces than the gravitational one is:
H(t) = -16*t^2 + v*t + h
Where:
t represents the time in seconds.
the first coefficient -16 is half of the gravitational acceleration in feet over squared seconds.
v is the initial velocity, which in this case is 235 ft/s
h is the initial height, in this case we assume is zero (the rocket is launched from the ground)
Replacing all that in the height equation, we will get:
H(t) = -16*t^2 + 235*t
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Can someone help me thank you
The fraction in their simplest form will be:
9. 12/15 = 4/5
10. 6/8 = 3/4
11. 25 / 100 = 1/4
12. 5 / 40 = 1/8
13. 7/77 = 1 / 11
14. 4 / 36 = 1/9
15. 18/20 = 9/10
16. 100/1000 = 1/10
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
It should be noted that in order to divide a fraction in their simplest form, the equivalent numbers must be used.
For example, 100/1000 will be:
(100 ÷ 100) / (1000 ÷ 100)
= 1 / 10
25 / 100 has a common factor of 25 as.this gives 1/4.
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Pls help 3z2-6z for z=5
Answer:
0
Step-by-step explanation:
to me you use the exponent first and then add the variable after, 30-30=0 and if you do the variable first 225-30=195. But my answer would be 0.
Answer: 78
Step-by-step explanation:
3z2-6z for z=5
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be kilograms.
According to the scatter plot provided, the weight for someone who is 1.5 meters tall is predicted to be 45.45 kilograms.
What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical and analytical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the weight (in kilogram) would be plotted on the y-axis of the scatter plot while the height (M) would be plotted on the x-axis of the scatter plot.
From the scatter plot (see attachment) which models the relationship between data points in the table, a linear function for the line of best fit is given by:
Weight, kg = -114.3 + 106.5M
When M = 1.5 meters, we have:
Weight, kg = -114.3 + 106.5(1.5)
Weight, kg = -114.3 + 159.75
Weight, kg = 45.45 kg.
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Complete Question:
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be ____ kilograms.
-1/3v = -7 how do i solve this equation?
Answer: v=2.33333333333333.........
Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......
Screenshot included in this work
The two blanks on the left side of the equation and the solution blank should be completed with the following ratios:
2050 kg/1 m³ × 2.2 lb/1 kg × 1 m³/35.3 ft³ = 127.76 lb/ft³.
What is a conversion factor?In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.
Conversion:
2050 kg/1 m³ × 2.2 lb/1 kg = 4,510 lb/1 m³
4,510 lb/1 m³ × 1 m³/35.3 ft³ = 4,510 lb/35.3 ft³
4,510 lb/35.3 ft³ = 127.76 lb/ft³.
Additionally, take note of the following units of conversion:
kg = kilograms.m³ = cubic meter.lb = pounds.ft³ = cubic foot.In conclusion, we can logically deduce that the crate's density is equal to 127.76 pounds per cubic foot.
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Andrea puts 100 g weight on a pan balance how many 10 g weights does she need to balance the scale?
answer:
10
step-by-step explanation:
easy: 100 ÷ 10 = 10. you need 10
explanation: you need 100 (on the left side) to equal the right side. each weight on the right side weighs 10, but you don't know how many you need. use x for the unknown amount. now, you have:
100 = 10x. solve by dividing each side by 10.
10 = x. verify by doing 10 x 10 = 100
Select the correct answer A developer buys an empty lot to build a small house. What is the area of the lot?
A. 323 yd²
B. 183 yd²
C. 193 yd²
D. 171 yd²
The area of the plot is 193 sq.yd.
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, A developer buys an empty lot to build a small house.
To find the area, we need to be divided the figure into triangles and rectangles
Area of the first triangle = (1/2) * base * height
base = 17 unit and height = 10 unit
= (1/2) * 17 * 10
= 17*5=85 sq. unit
Area of the second triangle = (1/2)* 9* 8
=36 sq. unit
Area of the rectangle = base * height
base = 9 unit and height = 7 unit
Area = 9*7= 63 sq. unit
Area of the last triangle = (1/2) * 2*9
= 9 unit
Adding all the areas to get the area of the plot = 85+36+63+9
Hence, Area of the plot = 193 sq.yd.
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Solve the application problem.
Find the area of a rectangular garden that measures 4 feet by 6/7 feet.
A. 3 3/7 ft
B. 9 5/7 ft^2
C. 9 5/7 ft
D. 3 3/7ft^2
Answer:
D. 3 3/7 ft²
Step-by-step explanation:
A = LW
A = 4 ft × 6/7 ft²
A = 24/7 ft²
A = 3 3/7 ft²
hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?
Answer:
$420
Step-by-step explanation:
multiple 10.50 by 40 to get 420
Find the exact solutions of the given equation in the interval .
sin 4x= –2sin 2x
The exact solutions of the given equation in the interval are;
A: x = 0, π/2, π, ³/₂π
How to find the exact solutions of trigonometric equations?
We are given the equation as;
sin 4x = –2sin 2x
Writing the equation in standard form gives;
sin 4x + 2sin 2x = 0
Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;
2sin 2x cos 2x + 2sin 2x = 0
Factorize to get;
2sin 2x(cos 2x + 1) = 0
A. sin 2x = 0
The unit circle will give us 3 solutions for 2x as follows;
2x = 0
Thus; x = 0
2x = π
Thus; x = π/2
2x = 2π
Thus; x = π
B. cos 2x = - 1
The unit circle gives 2 solutions for 2x as;
2x = π
Thus; x = π/2
2x = 3π
Thus; x = ³/₂π
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Complete question is;
How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
The area of left over wrapping paper is 380 square inches
How to determine the amount left?The given dimensions are:
Box = 8 inches by 9 inches by 10 inchesWrapping paper = 2 feet by 3 feet.The surface area of the box is calculated as
Surface area = 2(lw + lh + wh)
This gives
Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches
The surface area of the wrapping paper is calculated as
Wrapper = lw
This gives
Wrapper = 2 * 3 = 6 square feet
Express the area in square inches
Wrapper = 864 square inches
The area left is the difference between the areas calculated above
i.e. Amount left = Wrapper - Box
So, we have
Amount left = 864 square inches - 484 square inches
= 380 square inches
Hence, the amount left is 380 square inches
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-3x+16+5x+8 x=??????????
The simplified expression of the expression given as -3x+16+5x+8 is 2(x + 12)
How to evaluate the equation?From the question, the equation is given as
-3x+16+5x+8
To start with, we need to rewrite the expression
So, we have the following representation
-3x + 16 + 5x + 8
The above expression is not an equation
Instead, it is an expression
This is so because there is no equality symbol i.e. = in the expression
So, we collect the like terms
-3x + 5x + 8 + 16
Solving further, we need to evaluate the like terms
So, we have the following equation
-3x + 5x + 24
Evaluate the like terms again
So, the equation becomes
2x + 24
The above expression cannot be further simplified, however, it can still be factored
Factor out 2 from the expression
This gives
2(x + 12)
Hence, the solution is 2(x + 12)
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If 5/11 of the class are girls, what is the ratio of girls to boys?
Answer:
5:6
Step-by-step explanation:
The entire class is 11/11.
Girls: 5/11 of the class.
Boys: 11/11 - 5/11 = 6/11
Ratio of girls to boys:
5/11 / 6/11 = 5/11 × 11/6 = 5/6
Answer: 5:6
Thelma and Patrick went to a cafe
for lunch. One of them is a
vegetarian. Thelma ordered a
turkey sandwich with extra
mustard. Who is the vegetarian?
Patrick is vegetarian and Thelma is non vegetarian.
What are vegetarian?
The practice of not eating any meat is known as vegetarianism. It might also mean avoiding eating any leftovers from animal slaughter. There are several reasons to embrace a vegetarian diet. Due to their respect for sentient animal life, many people refrain from eating meat.
Main Body:
As Thelma ordered Turkey sandwich with extra mustard and turkey is an animal , which makes her non vegetarian so it is obvious that Patrick is a vegetarian and Thelma is non vegetarian.
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Need asap! Write the expression as a power and evaluate it. The expression as a power is __. The value is__.
8•2^7 and 16•32
The expression as power is written as 2¹⁰ and 2^9
The values are
2¹⁰= 1024 2^9 = 512How to write expression as a powerpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.
8• 2^7
= 2 * 2 * 2 * 2^7
= 2^10
= 1024
16•32
2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2^9
= 512
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