Answer:
(x,y,z) = (1,1,4)
Step-by-step explanation:
[tex]A: -2x + 3y - z = -2\\B: 3x+y=4\\C: -2y+2z=4\\[/tex]
[tex]Solve\ B\ for\ y: y = 4-3x\\Solve\ C\ for\ z: 2z=4+2y\ \ z=2+y\\Substitute\ B_y\ into\ C_z: z = 2+4-3x\ \ z=6-3x\\Substitute\ B_{y\ in\ terms\ of\ x}\ and C_{z\ in\ terms\ of\ x} into A: \\-2x + 3(4-3x) - (6-3x) = -2\\Distribute: -2x + 12-9x-6+3x=-2\\Combine\ Like\ Terms\ on\ either\ side: -2x-9x+3x=-2-12+6\\Factor\ out\ x\ and\ perform\ arithmetic\ on\ right: x(-2-9+3) = -8\\Perform\ Arithmetic: x(-8)=-8\\Divide:x=1[/tex]
[tex]Plug\ x\ into\ B_y: y=4-3(1)\\Perform\ Arithmetic: y=1\\Plug\ y\ into\ C_z: z=2+2(1)\\Perform\ Arithmetic: z=4[/tex]
Vishal came up with an answer of 41 square units for the area of this square.
How long is each side of the tilted square?
_____ units
The length of each side of the given tilted square is √41 units.
What is the length of the side of the square?
The formula to find the area of a square is;
Area = x²
Where x is the side length of the square.
Thus;
x = √41
Now, since all sides of a square are always equal, we can easily say that the length of each side of the given tilted square is √41 units.
Thus, our conclusion is that the length of each side of the given tilted square is √41 units.
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The cost of 5 gallons of gasoline is $20. Write an equation to show the relationship between the cost, c, and the gallons of gasoline, g. Enter your equation AND your work or explanation in the box provided.
An equation to show the relationship between the cost, c, and the gallons of gasoline, g is; c = 4g
How to interpret a Linear Equation?
The general form of a linear equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are told that the cost of 5 gallons of gasoline is $20. Thus, the cost of one gallon of gasoline = 20/5 = $4 per gallons
Therefore if he cost is c, and the gallons of gasoline is denoted by g, then the formula to find the cost with these letters is;
c = 4g
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Which is different? Find “both” answers
Find AC+CB .
Find BC-AC .
Find AB .
Find CA+BC .
The "different" answer is {Blank} The "same" answer is {Blank}.
The different answer is 4 and the same answer is 10.
1. Then a survey of 30 students and it was found that 17 of them have a cat, based on these results, guess how many students out of 300 students in the school have cats?
2. If one out of 12 students in a school shares their locker, how many students share their locker in a school with 456 students?
3. Sabrine runs 2 km in 30 minutes. At this rate, what would you run in 90 minutes? And at what rate did she run each hour?
Answer:
The answer is 47.5 because in my math exam i got 47.5 in 50
Math with a key 6 page 15 task 8 pl. For tomorrow
The value of the expressions will be:
1. -13.
2. 4
3. -9
4. 27
5. 0
How to calculate the value?It should be noted that this is an expression. In this case:
minus × minus = plus
plus × minus = minus
1. (-15) - (-2)
= -15 + 2
= -13
2. (-3( - (-7)
= -3 + 7
= 4
3. 4 - 13
= -9
4. 5 - (-22)
= 5 + 22
= 27
5. (-15) - (-15)
= -15 + 15.
= 0
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Is ✓225 + ✓196 a rational or irrational number?
Answer:
yes
Step-by-step explanation:
√225 + √196
15 + 14
29
29 can be written as 29/1 thus 29 is a rational number
you have 600 feet of fencing to enclose a rectangular plot that borders a river if you do not fence the side along the river
45,000 square feet is the largest area that can be enclosed.
What is rectangle?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.The largest area will always be a square.
600/4=150 feet on each side but one side is not needed
put this 150 feet not needed with the opposite 150 feet to get 300 feet
you have a rectangle 150 by 300 by 150 by the river
= 150 * 300 = 45,000 square feet
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The complete question is -
You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and the width of the plot that will maximize the area. What is the largest area that can be enclosed?
Two ways to group 26 students
There are 26 kids who have either black or red pencils.
15 of them have red
21 of them have black
How many kids have both
Answer:
this doesn't make sense cuz 15 have red 21 have black and that's 36 kids but the title says there is 21 kids in all ?
Step-by-step explanation:
Can someone please help I will be giving Brainliest to whoever can answer :)
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
1. A = {(x, y): y > x^2}
2. B = {(x, y): y ≥ x^2+ 3}
3. C = {(x, y): y ≤ 3x^2 + 2}
4. D = {(x, y): y ≥ 2x^2- 5x + 1}
5. E = {(x, y): 16 ≤ x^2+ y^2 ≤ 25}
6. x^2- 3x ≥ 0
7. x^2- 3x + 2 ≤ 0
8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1}
The questions are matched with the graphs that are labeled A-H. (
1. A = {(x, y): y > x^2} Matching answer D2. B = {(x, y): y ≥ x^2+ 3} Matching answer G3. C = {(x, y): y ≤ 3x^2 + 2} Matching answer C4. D = {(x, y): y ≥ 2x^2- 5x + 1} Matching answer A5. E = {(x, y): 16 ≤ x^2+ y^2 ≤ 25} Matching answer F6. x^2- 3x ≥ 0 Matching answer J (the curve should be solid line)7. x^2- 3x + 2 ≤ 0 Matching answer E8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1} Matching answer BHow to find the matching graphThe graph has some rules for matching them to the equation some of the rules are:
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. The oxygen saturation of a lake is found by dividing the
amount of dissolved oxygen the lake water currently has
per liter by the dissolved oxygen capacity per liter of the
water, and then converting that number into a percent.
If the lake currently has 6.4 milligrams of dissolved oxy-
gen per liter of water and the dissolved oxygen capacity
is 9.5 milligrams per liter, what is the oxygen saturation
level of the lake, to the nearest percent?
A. 64%
B. 67%
C. 70%
D. 89%
E. 95%
Answer:
70% i think
Step-by-step explanation:
Which algebraic expression represents each verbal expression?
a. the product of five and a number, decreased by eleven
b. the sum of a number and five less than eleven
c. five times a number fewer than eleven
d. the quantity of a number minus eleven, multiplied by five
Answer:
A) 5n − 11
B) 11 − (n + 5)
C) 11 − 5n
D) 5(n − 11)
Your Welcome ;)
The required verbal algebraic expressions are given as ,
(a) 5x - 11 (b) (x + 5) - 11
(c) 5x - 11 (d) (x - 11)×5
What is an algebraic expression?The algebraic expression consists of constants and variables. eg x, y, z etc.
Here,
Let the number x,
a. The product of five and a number, decreased by eleven
⇒ 5x - 11
b. The sum of a number and five less than eleven
⇒ (x + 5) - 11
c. Five times a number fewer than eleven
⇒5x - 11
d. The quantity of a number minus eleven, multiplied by five
⇒(x - 11)×5
Thus, the required expression is shown above
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George was solving the equation (2x-1)(x+3)=4 and he got the solution x=1/2 and x=-3. Jeffrey came along and said, "You made a big mistake! You set each factor equal to zero, but it's not equal to zero, it's equal to 4. So you have to set each factor equal to 4 and then solve." Who is correct? Show George and Jeffrey how to solve this equation. To be sure that you are correct, check your solutions.
The solution to the system of equation is -7/2 and 1
Solving linear equationAn algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.
Given the quadratic equation below;
(2x-1)(x+3)=4
Expand
2x^2+6x-x-3 = 4
2x^2+5x-3-4=0
2x^2+5x-7=0
2x^2-2x+7x-7=0
2x(x-1)+7(x-1) = 0
2x+7 = 0 and x - 1 = 0
x = -7/2 and x = 1
Hence the solution to the system of equation is -7/2 and 1
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The inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. Which of the following standard equations represents the parabola in which the base of the bulb is at (1, 5) and top of the bulb is at (1, 1)?
The equation of the parabola that models the situation is given by:
(x - 1)² = -16(y - 5).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
(x - h)² = 4p(y - k).
The focus is located at point (h, k + p).
For this problem, to find the values of the parameters h and k, we have that:
The base is the vertex.The base is at (1,5).Hence:
h = 1, k = 5.
And:
(x - 1)² = 4p(y - 5).
For the focus, and subsequently to find parameter p, we have that:
The top is the focus.The top is at (1,1).Hence:
k + p = 1.
5 + p = 1
p = -4.
Then the equation of the parabola that models this situation is given by:
(x - 1)² = 4p(y - 5).
(x - 1)² = 4(-4)(y - 5).
(x - 1)² = -16(y - 5).
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a sailmaker is designing a mainsail for a newly constructed sailboat. the mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 52° angle at the head with the leach.
So, Part A:
By employing the sines law,
SinA/10 = SinB/13SinA/10 = Sin50/13A = 36.10C = 180-(180-36.10)C = 93.90So,
Sin36.10 / a = Sin50/ b = Sin93.90/cSin36.10 / 10 = Sin50/ 13 = Sin93.90/cc = Sin93.90 × 13 ÷ Sin50c = 16.93 ftNow, Part B:
Area of the mainsail:
= 1/2 × abSinC= 1/2 × 10 × 13 × Sin93.90= 64.85Therefore, the answers to both parts are:
(A) The mainsail foot is 13 feet long, the luff is 10 feet long, the leach is 6.93 feet long, and the mainsail area is 64.85 ft².(B) The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff forms a 50° angle with the leach at the head, requiring the length of the leach and the area of the mainsail.Know more about sines law here:
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The complete question is given below:
A sailmaker is designing a mainsail for a newly constructed sailboat. The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 50° angle at the head with the leach.
Part A: Determine the length of the leach.
Part B: Find the area of the mainsail.
PLS HELP :) 50 POINTS!!!
Say you are given the graph of the line y = -x. Write the equation of the line that is perpendicular to the given line and goes through the point (-8, 2).
Linear equations are often organized in slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptTo find a linear equation, we often first solve for the slope, and then solve for the y-intercept algebraically.
To find the slope of a perpendicular line, we must find the negative reciprocal of the slope of the reference line.
Solving the Question
We're given:
Reference line is [tex]y=-x[/tex]Perpendicular line passes through [tex](-8,2)[/tex]1) Find the slope of the reference line
We can rewrite the reference line to be clearer in slope-intercept form:
[tex]y=-1x+0[/tex]
This means that -1 is the slope.
2) Find the slope of the perpendicular line
The negative reciprocal of -1 is 1. Therefore, the slope of the perpendicular line is 1. Plug this into slope-intercept form:
[tex]y=x+b[/tex]
3) Solve for the y-intercept of the perpendicular line
[tex]y=x+b[/tex]
Plug in the given point (-8,2) and solve for b:
[tex]2=-8+b\\b=2+8\\b=10[/tex]
Therefore, the y-intercept of the perpendicular line is 10. Plug this back into our original equation:
[tex]y=x+10[/tex]
Answer[tex]y=x+10[/tex]
Solve for x and write your answer in simplest form.
x-3(2/3x+3)=3(-3/2x+1)-3/2x
Answer:
x= -6
Step-by-step explanation:
[tex]x-3(\frac{2}{3}x+3)=3(\frac{-3}{2}+1)-\frac{3}{2}\\\\x-2x-9=\frac{-9}{2}+3-\frac{3}{2}\\\\clear fraction\\\\2x-4x-18=-9+6-3\\\\-2x-18=-6\\\\-2x=12\\\\x=-6[/tex]
Find the distance between the two points on the graph.
Answer:
[tex]3 \sqrt{5} [/tex]
Step-by-step explanation:
See attached for details. Basically finding the distance between 2 points requires creating a right angle triangle. And we are looking for the hypotenuse.
The pythagorean theorem is used.
Evaluate.
2/5 exponent 2
Answer: 4/25
Step-by-step explanation:
[tex](\frac{2}{5}) ^2=\frac{2}{5}\times\frac{2}{5}=\large\boxed{\frac{4}{25} }[/tex]
Damian is building a display case to hold
75 model cars. The case will have fewer
than 10 shelves, and each shelf will hold
no more than 15 cars. If Damian wants
each shelf to have the same number of
cars, how many shelves should he put in
the display case?
2. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
The additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
How to state the additional information required?The congruence postulate is given as:
SSS Triangle Congruence Postulate
The above means that the three sides of the triangles are congruent.
From the figure, the following side lengths are said to be congruent
UV and FV
TV and TV
For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent
This is represented as:
UT = T F
Hence, the additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
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find the sum and express it in it's lowest terms 3/11 + 2/3=
Answer:
[tex]\frac{31}{33}[/tex]
Step-by-step explanation:
You need a common denominator to add. The smallest number that is divisible by both 11 and 3 is 33. Rewrite both fractions with a denominator of 33
[tex]\frac{3}{11}[/tex] x [tex]\frac{3}{3}[/tex] [tex]\frac{3}{3}[/tex] is just another name for 1. We are making an equivalent fraction. Multiple 3 x3 for the top and 11 x 3 for the bottom to get:
[tex]\frac{9}{33}[/tex]
Do the same for [tex]\frac{2}{3}[/tex]
[tex]\frac{2}{3}[/tex] x [tex]\frac{11}{11}[/tex] [tex]\frac{11}{11}[/tex] is just another name for 1. We are making an equivalent fraction. Multiple 2 x 11 for the top and 3 x 11 for the bottom to get:
[tex]\frac{22}{33}[/tex]
Now add these two fractions together:
[tex]\frac{9}{33}[/tex] + [tex]\frac{22}{33}[/tex] = [tex]\frac{31}{33}[/tex]
russell runs 9/10 miles in 5 minutes. at this rate how many miles can he run in one mintue?
Answer:
1.8 miles
Step-by-step explanation:
Please answer these two questions!
Answer:
The answer to your first question would be B. The answer to the second is C.
Step-by-step explanation:
Hope it helps! =D
heidi was able to walk 2/3 of a mile in 12 minutes how far could heidi walk in 1 hour
Heidi is able to walk 10/3 miles in 1 hour (60 min).
What is described as unitary method?It is a method for determining the value of a single unit by subtracting the value of multiple units and subtracting the value of multiple units from of the value of a single unit.
The value of many items is given in the unitary method, and we must either determine the worth of more or fewer items. To do so, we must first determine the value of one item by division and then determine the value of more as well as fewer items by multiplication.Now, for the given question;
It takes Heidi 12 minutes to walk 2/3 miles.
Applying the unitary method.
Then, for in 1 minutes Heidi will walk = 2/(3×12).
For walking in 1 hour or 60 min = (2×60)/(3×12).
Further simplifying;
In 1 hour = 10/3 miles.
Therefore, Heidi would be be able to walk 10/3 miles in 1 hour.
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a quarry needs to ship a marble block weighing 10000 pounds. if the cost of shipping is 110 per ton, how much will shipping cost?
The cost of shipping the marble block is 550.
The total weight of the marble block is 10,000 pounds.We need to convert the weight from pounds to tons.Unit conversion is the process of converting various units of measurement for the same amount, often using multiplicative conversion factors that modify the measured quantity value without affecting its effects.1 ton equals 2000 pounds.The total weight of the marble block in tons is 10000/2000.The total weight of the marble block is 5 tons.The cost of shipping is 110 per ton.The total cost of shipping the marble block = 5 * 110.The total cost of shipping the marble block is 550.To learn more about unit conversion, visit :
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You are swimming each 25-yard length of a swimming pool 3 seconds
faster than your personal best. What integer represents your change in
time of your personal best after 200 yards?
24 seconds faster time of your personal best after 200 yards.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Suppose the number of laps = m
According to the question, each lap of 25 yards is covered 3 seconds faster than the previous one, so the series become
x , x-3 , x-6 , x-9, ............................
25 * m = 200
m = 200/25
m = 8
As m is the number of laps, and each lap is 3 second faster.
So 8 laps will be 8*3 = 24 seconds faster.
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Can anyone pleases solve this?
By rationalization and algebra properties, the irrational expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) is equivalent to the integer 1.
How to simplify a subtraction of irrational fractions
In this question we find a composite irrational expression formed by a irrational fraction being subtracted by other two irrational fraction. Eliminating the irrational denominators by transforming it into rational numbers is an important step for this question, this can be done by means of rationalization, along with algebra properties.
The complete procedure of this exercise is shown below:
7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2)
[7√3 · (√10 - √3)] / [(√10 + √3) · (√10 - √3)] - [2√5 · (√6 - √5)] / [(√6 + √5) · (√6 - √5)] - [3√2 · (√15 - 3√2)] / [(√15 + 3√2) · (√15 - 3√2)]
(7√30 - 21) / 7 - (2√30 - 10) - (3√30 - 18) / (- 3)
(7√30 - 21) / 7 + (10 - 2√30) + (3√30 - 18) / 3
(7√30 - 21 + 70 - 14√30) / 7 + (3√30 - 18) / 3
(49 - 7√30) / 7 + (3√30 - 18) / 3
(147 - 21√30 + 21√30 - 126) / 21
21 / 21
1
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Raheem made a down payment of $250.00 at a local store for an HDTV that cost $880.00 with tax included. He arranged to make 8 equal monthly payments to the store to finish paying for the HDTV. Given that he paid no additional fees, how much was Raheem's monthly payment?
Raheem's monthly payment given that he paid no additional fees is $78.75
How to find Raheem's monthly paymentMonthly payment refers to the amount of money paid by a person every month over a period of time.
Total cost of HDTV = $880.00Down payment = $250.00Number of months to make equal payment = 8Amount remaining after down payment = Total cost of HDTV - Down payment
= $880.00 - $250.00
= $630.00
Amount to pay each month = Amount remaining after down payment / Number of months to make equal payment
= $630.00 / 8
= $78.75
In conclusion, the amount Raheem will pay monthly for a period of 8 months if he paid no additional fees is $78.75
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4x100+7x10+6x1+6x(1/10)+3x(1/100)+7x(1/1000)
Please help