By elimination, the solution of the system of equations, x - y + z = -1, x + y + 3z = -3 and 2x - y + 2z = 0, is (4 , 2 , -3).
Given:
x - y + z = -1 (equation 1)
x + y + 3z = -3 (equation 2)
2x - y + 2z = 0 (equation 3)
Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.
Subtracting equations 1 and 3 will eliminate the variable y.
2x - y + 2z = 0 (equation 3)
x - y + z = -1 (equation 1)
x + z = 1 (equation 4)
Adding equations 2 and 3 will eliminate the variable y.
x + y + 3z = -3 (equation 2)
2x - y + 2z = 0 (equation 3)
3x + 5z = -3 (equation 5)
Multiply equation 4 by -5 and add with equation 5.
x + z = 1 (equation 4)
⇒ -5x - 5z = -5
+ 3x + 5z = -3 (equation 5)
-2x = -8
x = 4
Substitute the value of x to either equation 4 or 5 and solve for z.
x + z = 1 (equation 4)
4 + z = 1
z = 1 - 4
z = -3
Finally, substitute the value of x and z to any of the first three equations, and solve for y.
x - y + z = -1 (equation 1)
4 - y + (-3) = -1
-y = -1 - 4 + 3
-y = -2
y = 2
Checking if the values x = 4, y = 2, and z = -3 satisfies all the three equation.
x - y + z = -1 (equation 1)
4 - 2 + (-3) = -1
-1 = -1
x + y + 3z = -3 (equation 2)
4 + 2 + 3(-3) = -3
-3 = -3
2x - y + 2z = 0 (equation 3)
2(4) - 2 + 2(-3) = 0
0 = 0
Hence, the solution of the system of equations is (4 , 2 , -3).
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18. Point B partitions AC in the ratio 1:3. What are the coordinates of C?
Please help I’ll give crown
Using proportions, the coordinates of C are given as follows: (60,41).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Point B partitions AC in the ratio 1:3, hence:
B - A = 1/4(C - A)
The x-coordinate of C is found as follows:
12 + 4 = 1/4(x + 4)
16 = 1/4(x + 4)
x + 4 = 64.
x = 60.
The y-coordinate of C is found as follows:
5 + 7 = 1/4(y + 7)
12 = 1/4(y + 7)
y + 7 = 48
y = 41.
The coordinates of C are given as follows: (60,41).
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Answer:
Step-by-step explanation:
Answers? 100 point btw
Answer:
1. Top left and top right. Middle right
2. 43/24
3. B(42.5%)
4. A(3.25)
Step-by-step explanation:
2. Get the denominators the same(denominator in this case would be 24), and then make an improper fraction.
3. Convert the fraction 17/40 to a percentage(42.5%)
4. 6 hours x 60 minutes= 360 minutes
1170/360 = 3.25 laps per minute
Hope this helps! <3
Use a protractor and ruler to accurately construct a regular pentagon with side length 4cm.
ASAP Please
Step-by-step explanation:
calculate the interior angle of the pentagon then do the rest
Explain how to solve [tex]3^x^-^4=6[/tex] using the change of base formula log base b of y equals log y over log b Include the solution for x in your answer. Round your answer to the nearest thousandth.
The solution of x in the equation 3^(x -4) = 6 is x = 5.63
How to determine the solution of the equation?The equation is given as
3^(x -4) = 6
Apply the law of indices on the expression 3^(x -4) to rewrite it
So, we have
3^x/3^4 = 6
The above equation becomes
3^x = 6 * 3^4
Evaluate the product
So, we have
3^x = 486
Take the logarithm of bot sides
xlog(3) = log(486)
Divide both sides by log(3)
x = log(486)/log(3)
Evaluate
x = 5.63
Hence, the solution of x in the equation 3^(x -4) = 6 is x = 5.63
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Please help me!! Middle school question Integers
Answer:
Step-by-step explanation:
We can do this as a normal problem on the left.
(-7)x2+9 we do the multiplication first, then add. (Multiplication and division always happen before addition and subtraction, unless brackets are being used.)
-> -14+9=-5
Now that we know the left side of the equation is equal to -5, we must find which answer is GREATER than -5, because instead of an equal sign, there is a < meaning greater than.
4+[3x(-2)] for this one we do the multiplication first
4+(-6)=-2. -2> -5
Thus, it is the first answer, because that is the one that is greater than -5.
Solve this and earn 20 points. (Please show work)
Answer:
1 1/2 ÷ 1/2 = 3/2 ÷ 1/2 = 3/2 × 2 = 3
please help i really don’t understand ( ignore the math on top )
Answer: x=2 DS=10 SE=10 DE=20
Step-by-step explanation:
[tex]7x-4=16-3x\\7x-4+3x=16-3x+3x\\10x-6=16\\10x-4+4=16+4\\10x=20\\[/tex]
Divide the equation by 10:
[tex]x=2[/tex]
Hence,
[tex]DS=(7)(2)-4\\DS=14-4\\DS=SE=10\\DE=DS+SE\\DE=10+10\\DE=20[/tex]
hlpppppp!!!!!!!!!!!!!!!!!!!!!!!!
w steps pls
Answer: S=6x²+25x+14
Step-by-step explanation:
[tex]\displaystyle\\S=S_1+2S_2\\S_1=(2x+7)(x+3)\\S_1=(2x)(x)+(7)(x)+(2x)(3)+(7)(3)\\S_1=2x^2+7x+6x+21\\S_1=2x^2+13x+21\\\\S_2=\frac{(\frac{2x+7)}{2})(4x-2) }{2} \\\\S_2=\frac{(2x+7)(4x-2)}{(2)(2)} \\\\S_2=\frac{(2x)(4x)+(7)(4x)+(2x)(-2)+(7)(-2)}{(2)(2)} \\\\S_2=\frac{8x^2+28x-4x-14}{(2)(2)} \\\\S_2=\frac{8x^2+24x-14}{(2)(2)} \\\\S_2=\frac{(2)(4x^2+12x-7)}{(2)(2)} \\\\S_2=\frac{4x^2+12x-7}{2} \\Hence,\\S=2x^2+13x+21+2*\frac{4x^2+12x-7}{2} \\S=2x^2+13x+21+4x^2+12x-7\\S=6x^2+25x+14[/tex]
Help me pls I need help with this or else I won,t pass pls help
Answer:
17
Step-by-step explanation:
put the point on 17 on the number line
Answer:
17
Step-by-step explanation:
12-(-5) = 12+5. Two negatives create a positive. 12+5=17
You scored 88.92+87 on three tests. What score do you need on the fourth test to average 90
The score which is needed on the fourth test so that as average score of 90 is earned as required in the task content is; 93.
What is the score required on the fourth test such that an average of 90 is earned in all four tests as required in the task content?According to the task content, it follows that the score needed so that an average score of 90 is earned on all four tests is to be determined.
Since, The average is the ratio of the sum of all scores to the number of scores; we have;
90 = (88 + 92 + 87 + x)/4
Multiply both sides by 4 so that we have;
360 = 88 + 92 +87 + x
Isolate x on one side of the equation;
x = 360 -88 -92 - 87
x = 93.
Ultimately, The score which is needed on the fourth test so that as average score of 90 is earned as required in the task content is; 93.
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Evaluate 51x³-21 + 7 when x = -2
Answer: Substitute the value of the variable into the equation and simplify.
−
408
v
a
2
l
u
t
e
2
−
14
Step-by-step explanation:
7x - y = 100
Slope:
Y int:
Answer:
slope: 7
Y-int: -100
Step-by-step explanation:
Basically just solve for y
what does SSS stand for ? what does it have to do with similar triangles?
Answer:
Side, Side, Side. The short cut is SSS
find the expression for g(x)
Hello,
[tex]f(x) = 4 {x}^{2} - 9[/tex]
[tex]g(x) = 4 {x}^{2} - 9 + 8 = 4 {x}^{2} - 1[/tex]
Compare the two numbers. Use > or < .
√5, √7
Square root is a factor that, when multiplied by itself, equals the original value.
The values of √5 = 2.236 and √7 = 2.645 then √5 < √7.
What is a square root?In mathematics, a square root is a factor that, when multiplied by itself, equals the original value. Any time the idea of an object's square is mentioned, square roots can be considered more widely. These include square matrices and function spaces, among other mathematical structures.Even though it is only one of the two square roots of a positive number, the term "square root" is occasionally used to describe the major square root of a positive number.Let the values of √5 = 2.236 and √7 = 2.645
then √5 < √7.
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help please i’ll give 10 points
Answer:
The opposite of -3/5 is 3/5 because the opposite of negative is a positive. The absolute value of -3/5 is 3/5 because the absolute value of any number is always positive.
a.) 3/5
b.) 3/5
Hope that Helps! :D
What is the equation of the line that passes through the point (8,2) and has a slope of -3/4 ?
The equation of the line is y = -3/4x + 5
How to determine the equationThe equation of a line is expressed as;
y = mx + c
Where;
m is the slope of the linec is the intercept on the y axisy is the point at the y -axisx is the point at the x - axisTo determine the intercept, we have;
2= -3/ 4(8) + c
2 = -24/8 + c
2 = -3 + c
Make 'c' the subject of formula
c = 2 + 3
c = 5
The equation of the line is y = -3/4x + 5
Thus, the equation of the line is y = -3/4x + 5
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What set of transformations will map the graph of f(x)=x^ 3 onto g(x)=0.5(x-2)^3-2
Answer:
I got 6
Step-by-step explanation:
Hope this is correct :)
Suppose an MP3 player cost 499 in 2003 and 249.99 in 2009 .
c. If the trend continues, what will be the cost of an MP3 player in 2013 ?
The cost of the MP3 player in the year 2013 will be $83.99
If the trend continues, that means the drop in price at the same rate each year
In 2003 it was $499
In 2009 it was $249.99
Price drop each year (from 2003 to 2009) :
= 499 - 249.99 / 2009 - 2003
= 249.01 / 6
Therefore, the price drop each year = $41.50
Similarly, Price drop each year (from 2009 to 2013) :
(2013 - 2009) x 41.5 = $166
Thus, 249.99 - 166 = 83.99
Therefore, cost of the MP3 player in the year 2013 will be $83.99
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Determine the values of y in the equation y2 = 121.
due in 1 hour please help
Answer:
y = 60.5 or 11
Step-by-step explanation:
If this is intended to be 2y = 121 (2 times y), that would mean the answer would be 60.5.
This is because you’d divide both sides by 2, resulting in y = 60.5.
However, should this be intended as [tex]y^{2}[/tex]= 121, the answer would be 11.
What we do to find the pure equivalent of y is square root both sides as y is squared.
[tex]\sqrt{y^{2} } = \sqrt{121}[/tex]
We come to find that the square root of 121 is 11
[tex]y = 11[/tex]
Compare and contrast glide reflections and compositions of transformations.
Compare and contrast the process of graphing a radical function using transformations with graphing a quadratic function using transformations.
What distinguishes glide reflection from reflection?
An interchange of points from one side of a line with points on the other side of the mirror at the same distance from the mirror occurs when a mirror line is fixed in the plane. There is a mirror line in every reflection. A glide reflection is a mirror reflection that is followed by a parallel translation to the mirror.What do the three reflections that make up the glide reflection look like?
Glide reflections and triple line reflections. The combination of the three line reflections Rw Rv Ru constitutes a line reflection if u, v, and w are concurrent or parallel. We'll now show this theorem to be true. If u, v, and w are not parallel or contemporaneous, the arrangement of the three line reflections Rw Rv Ru is a glide reflection.Learn more about glide reflection
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What is the value of 6÷3 X 2/3
Answer:
that would be 4/3 or 1 1/3
Step-by-step explanation:
Hey there!
6 ÷ 3 * 2/3
= 6/3 * 2/3
= 2 * 2/3
= 2/1 * 2/3
= 2 * 2 / 1 * 3
= 4/3
= 1 1/3
Therefore, your answer should be:
4/3 or 1 1/3 (they are both equivalent to each other so any should work)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
please help i need you!
Answer:
38.46
Step-by-step explanation:
using the formula A=πr^2, which is the formula of the area of a circle, you get 38.46, when rounded, ehich the diameter is 2 times the radius, we divide 7 by 2z leaving us with r=3.5, so 38.46=3.14(3.5)^2.
Write two rational expressions that simplify to x+1 / x-5
Two rational expressions that simplify to (x+1) / (x-5) are equals to
(x+1)²/ (x+1) (x-5) and (x+1)(x-5) / (x-5)².
As given in the question,
Simply rational expression is given by (x+1) /(x-5)
Two rational expressions that simplify to given expression are as follow:
Multiply (x+1) to the numerator and denominator of the given rational expression(x+1)²/ (x+1) (x-5).
2. Multiply (x-5) to the numerator and denominator of the given rational
expression
(x+1)(x-5)/ (x-5)².
Therefore, two rational expressions that simplify to (x+1) / (x-5) are equals to (x+1)²/ (x+1) (x-5) and (x+1)(x-5) / (x-5)².
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Solve each system by substitution. Check your answers.
4x+2y=7 , y = 5x
By substitution, the solution of the system of equations, 4x + 2y = 7 and y = 5x, is (1/2 , 5/2).
A system of linear 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 both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
4x + 2y = 7 (equation 1)
y = 5x (equation 2)
Since the second equation is already expressed in y in terms of x, substitute the second equation to the first equation.
4x + 2y = 7 (equation 1)
4x + 2(5x) = 7
4x + 10x = 7
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
4x + 10x = 7
14x = 7
x = 1/2
Substitute the value of x in the second equation and solve for y.
y = 5x
y = 5(1/2)
y = 5/2
Hence, the solution of the given system of equations is (1/2 , 5/2).
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There were 323232 volunteers to donate blood. Unfortunately, nnn of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470470470 milliliters each.
How many milliliters of blood did the volunteers donate?
Write your answer as an expression.
The milliliters of blood the volunteers donate is 470 * (32 - n)
How many milliliters of blood did the volunteers donate?The given parameters are
Total = 32
Unqualified = n
The number of qualified volunteers would be
Qualified = 32 - n
A volunteer donates 470 ml
So, we have
Total = 470 * (32 - n)
Hence, the milliliters of blood the volunteers donate is 470 * (32 - n)
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The graph of the linear function k passes through points (-3,0) and (1.8) what statement is true
Answer: Option A
Step-by-step explanation:
(-3,0) is an x intercept because y is equal 0
1. x intercept of the graph of k is -3
Step-by-step explanation:
2. zeros can be found by setting the function to zero
function is y = 2x + 6
y = 2x + 6 -> 0 = 2x + 6
x would need to be -3 to get the zero of k
3. its not the third option : the slope is 2
4. if you graph it, it doesnt pass thru -1,-8
Which expression is equivalent to 6x+8?
a 2(3x-4)
b 2(3x+4)
c 2(4x+6)
d 2(3x+8
Answer:
b) 2(3x+4)
Step-by-step explanation:
Distributive formula: a(b + c) = ab + ac
Solving steps:
a) 2(3x-4) = 2(3x) + 2(-4) = 6x - 8
b) 2(3x+4) = 2(3x) + 2(4) = 6x + 8
c) 2(4x+6) = 2(4x) + 2(6) = 8x + 12
d) 2(3x+8) = 2(3x) + 2(8) = 6x + 16
Among from all the options, option B is equivalent to 6x + 8.
Find the measures of the angles or sides in each triangle.
The ratios of the measures of the three angles is 4: 5: 11 .
If the ratios of the measures of the three angles is 4: 5: 11 then the measures of the three angles in a triangle is 84°, 30° and 66° respectively.
What is meant by angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The ratios are 4: 5: 11 then
Angle A = 14, Angle B = 5, Angle C = 11
Total ratio = 14 + 5 + 11 = 30
The total angle in a triangle = 180°
Angle A
= 14 / 30 × 180°
= 0.4666666666666 × 180°
= 84°
Angle B
= 5/30 × 180°
= 0.1666666666666 × 180°
= 30°
Angle C
= 11/30 × 180°
= 0.3666666666666 × 180°
= 66°
Therefore, the measures of the three angles in a triangle is 84°, 30° and 66° respectively.
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The measures of the angles in each triangle are 36°, 45°, and 99.°
How do find the measures of the angles in the triangle?Angle A = 4
Angle B = 5
Angle C = 11
Total ratio = 4 + 5 + 11
= 20
The total angle in a triangle = 180°
Angle A = 4 / 20 × 180°
= 36°
Angle B = 5/20 × 180°
= 45°
Angle C = 11/20 × 180°
= 99°
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convert standard form to vertex and explain
H(T)=160+92t-16t^2
