Answer:
[tex](x,y,z)=\left(-\dfrac{1}{11},\dfrac{21}{11},\dfrac{21}{11}\right)[/tex]
Step-by-step explanation:
Given:
[tex]-2x+3y-z=-23x+y=4-2y+2z=4[/tex]
Therefore:
[tex]\begin{cases}-2x+3y-z=4\\-23x+y=4\\4-2y+2z=4\end{cases}[/tex]
Rewrite Equation 2 to make x the subject:
[tex]\implies -23x+y=4[/tex]
[tex]\implies -23x+y-y=4-y[/tex]
[tex]\implies -23x=4-y[/tex]
[tex]\implies \dfrac{-23x}{-23}=\dfrac{4}{-23}-\dfrac{y}{-23}[/tex]
[tex]\implies x=-\dfrac{4}{23}+\dfrac{y}{23}[/tex]
Rewrite Equation 3 to make z the subject:
[tex]\implies 4-2y+2z=4[/tex]
[tex]\implies 4-2y+2z-4=4-4[/tex]
[tex]\implies -2y+2z=0[/tex]
[tex]\implies -2y+2z+2y=0+2y[/tex]
[tex]\implies 2z=2y[/tex]
[tex]\implies \dfrac{2z}{2}=\dfrac{2y}{2}[/tex]
[tex]\implies z=y[/tex]
Substitute the found expressions for y and z into Equation 1 and solve for y:
[tex]\implies -2x+3y-z=4[/tex]
[tex]\implies -2\left(-\dfrac{4}{23}+\dfrac{y}{23}\right)+3y-y=4[/tex]
[tex]\implies \dfrac{8}{23}-\dfrac{2}{23}y+2y=4[/tex]
[tex]\implies \dfrac{8}{23}+\dfrac{44}{23}y=4[/tex]
[tex]\implies \dfrac{8}{23}+\dfrac{44}{23}y- \dfrac{8}{23}=4- \dfrac{8}{23}[/tex]
[tex]\implies \dfrac{44}{23}y=\dfrac{84}{23}[/tex]
[tex]\implies \dfrac{44}{23}y \cdot \dfrac{23}{44}=\dfrac{84}{23}\cdot \dfrac{23}{44}[/tex]
[tex]\implies y=\dfrac{84}{44}[/tex]
[tex]\implies y=\dfrac{21}{11}[/tex]
Therefore, as y = z:
[tex]\implies z=\dfrac{21}{11}[/tex]
Substitute the found value of y into the found expression for x and solve for x:
[tex]\implies x=-\dfrac{4}{23}+\dfrac{y}{23}[/tex]
[tex]\implies x=-\dfrac{4}{23}+\dfrac{\frac{21}{11}}{23}[/tex]
[tex]\implies x=-\dfrac{4}{23}+\dfrac{21}{253}[/tex]
[tex]\implies x=-\dfrac{1}{11}[/tex]
Therefore, the final solution is:
[tex](x,y,z)=\left(-\dfrac{1}{11},\dfrac{21}{11},\dfrac{21}{11}\right)[/tex]
On Earth with a gravitational acceleration \text{g} , the potential energy stored in an object varies directly with its mass m and its vertical height h .
a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?
Equation that models the potential energy of a 2 kg skateboard that is sliding down a ramp is :
U = 2gh
What is Gravitational acceleration ?Gravitational acceleration can be defined as the acceleration of any object when the object is in free fall. or we can say that the gravitational acceleration is the quantity which describes the acceleration of free falling object within vacuum. It is denoted by g .
What is Potential Energy ?Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy.
Formula of potential energy :
U = mgh
where, U = gravitational energy
m = mass of object
g = gravitational acceleration
h = vertical height of object
In the question given,
mass = 2kg
as, U = mgh
therefore, U = 2gh
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The complete question is :
On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .
a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?
b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?
4. What is the difference -4 -(-7) =
What are the coordinates of the point P that lies along the directed
segment from L(-6, 5) to M (4, -6) and partitions the segment in
the ratio of 1 to 3?
The coordinates of point P are ( -3.5, 2.25).
Given points L( -6, 5) and M( 4, - 6). We are to determine the coordinate of point P that lies along the directed line segment which partitions the segment in the ratio of 1 to 3.
The coordinates of the point that divides a line segment internally in the ratio m:n are given as follows:
[ (mx₂ + nx₁ ) / (m + n) , (my₂ + ny₁ ) / (m + n) ]
Now, m : n = 1 : 3
( x₁, y₁ ) = L( - 6 , 5 )
( x₂, y₂ ) = M( 4, - 6 )
Therefore,
P( x, y) = [ ( 1 × 4 + 3 × -6 ) / 4 , ( 1 × - 6 + 3 × 5) / 4 ]
P( x, y) = [ ( 4 - 18 ) / 4 , ( - 6 + 15) / 4 ]
P( x, y ) = [ -14/4 , 9/4 ]
P( x, y) = ( - 7/2 , 9/4 )
P( x, y) = ( - 3.5, 2.25 )
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What is the area of a circle if the radius is 19mm
Answer:1133.5 mm²
Step-by-step explanation:
area= πr² where r is the radius
3.14x19²= 1133.5 mm²
What is the equation of the line that passes through the point
(−3,−3) and has a slope of 3?
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-3)}) \implies y +3= 3 (x +3) \\\\\\ y+3=3x+9\implies {\LARGE \begin{array}{llll} y=3x+6 \end{array}}[/tex]
E and f are supplementary. If m e = (9x-38) and m f = (2x+42) find m f
Given that angle E and angle F are supplementary, the numerical measure of angle F is 74°.
What is the numerical measure of angle F?Supplementary angles are angles that sum up to 180 degrees.
Given the data in the question;
E and f are supplementaryMeasure of angle E = ( 9x - 38 )°Measure of angle F = ( 2x + 42 )°Numerical measure of angle F = ?Since E and F are supplementary, it means they sum up to 180 degrees.
Measure of angle E + Measure of angle F = 180°
Plug in the given values and solve for x
( 9x - 38 ) + ( 2x + 42 ) = 180
9x + 2x - 38 + 42 = 180
11x + 4 = 180
11x = 180 - 4
11x = 176
Divide both sides by 11
11x = 176
11x/11 = 176/11
x = 16
Now, the numerical measure of angle F will be;
Measure of angle F = ( 2x + 42 )
Measure of angle F = 2( 16 ) + 42
Measure of angle F = 32 + 42
Measure of angle F = 74°
Given that angle E and angle F are supplementary, the numerical measure of angle F is 74°.
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Describe and correct the error made in solving the equation.
The error is due to different bases of logarithmic value on both sides.
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function or equation
x = expression
Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]In the question,
the error is due to different bases on both the sides.
correct solution is:
[tex]log_2x = 2log_39\\log _2x=log_39^ 2\\log_2x=log_33^4\\log_2x=4log_33\\log_2x=4\\x=16[/tex]
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The complete question is :
Describe and correct the error made in solving the equation.
[tex]log_2x = 2log_39\\log _2x=log_39^ 2\\x=9^2\\x=81[/tex]
Mariana and her children went into a movie theater and she bought $51.25 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.25. She bought a total of 13 candies and pretzels altogether. Write a system of equations that could be used to determine the number of candies and the number of pretzels that Mariana bought. Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
you could use multiplication or addition,
Answer:
Step-by-step explanation:
Hello , this is a question on Geometry and I don’t understand how to do this can someone pls help me ?.
Answer:
m∠COD = 83°(I assumed it was somewhere right in-between 80-89 degrees, so I picked 83 as the most logical in between those integers.)
∠COD is an acute angle since it's less than 90°.
I hope this helps you, let me know if you have concerns related to this question and I will help with that.
Tanya bought 8.05 yards of fleece fabric to make costumes for a school play. She needs 1.25 yards of
fabric for each costume. How many costumes can Tanya make with the fabric she bought ( long division )
Answer: 6 costumes
Step-by-step explanation: 8.05 divided by 1.25 would be 6.44, but how can you make 6.44 costumes? The most costumes Tanya can make are 6 costumes for the school play.
R is between P and T. PR = 3x, RT = 2x + 24 and
PT = 54. Find RT.
P
R
O is the midpoint of EH. Find EH.
Line segments
Based on the information given, the value of line RT is 36
What is a line segment?A line segment can be defined as the part of a straight line bounded by two distinct end point
It also contains every point on the line between its endpoints.
From the information given, we have line PT is a line with segments PR and RT and R is the point between P and T
This can be represented as;
PR + RT = PT
Where;
PR = 3xRT = 2x + 24 PT = 54Substitute into the equation;
3x + 2x + 24 = 54
collect like terms
5x = 54 - 24
5x = 30
Make 'x' the subject of formula
x = 30/ 5
x = 6
But;
RT = 2x + 24
RT = 2(6) + 24
RT = 36
Thus, the value of line RT is 36
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Which of the following is a rational number?
A. [tex]\sqrt{10}[/tex]
B.[tex]\sqrt{100}[/tex]
C.[tex]\sqrt{1000}[/tex]
D.[tex]\sqrt{100000}[/tex]
Can you please explain your answer I want to understand it
The rational numbers are √10, √1000 and √100000 . Options A, C and D
What is a rational number?A rational number can be defined as a number that can be expressed as a fraction.
It also has the numerator and denominators as integers and expressed in decimal forms.
Given the values;
√10√100√1000√100000√10 = 3. 162
√100 = 10
√1000 = 31. 6
√100000 = 316. 22
Thus, the rational numbers are √10, √1000 and √100000 . Options A, C and D
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What is the least common denominator of 3/4 3/8 and 1/4
A=7x
2
−3x+10
B=−4x
2
+6x−4
A-B=A−B=
Answer:
3/4
Step-by-step explanation:
7x +4x = - 3x+10+6x-4
11x=-3x+6x+10-4
11x=3x+6
11x-3x=6
8x=6
X=3/4
what is the common denominator of 3/20 and 9/40 ?
Answer:
The answer is 40.
Step-by-step explanation:
Find the least common multiple (LCM) of the denominators in order to find the least common denominator (LCD).
Which function family does the graphed function belong to? !!!!!70 POINTS!!!!!!
Answer:
Y=x³ is the parent graph I don't know if that helps.
Answer:
Cubic
Step-by-step explanation:
Six friends each use a $2-off coupons to buy themselves a movie tickets. They spend a total of $42. What is the price of one movie ticket without the coupon?
The price of one movie ticket without the coupon is $9.
arithmetic operations
Arithmetic operators are used to perform mathematical operations like addition, subtraction, multiplication and division.
...
There are 7 arithmetic operators in Python :
Addition.
Subtraction.
Multiplication.
Division.
Modulus.
Exponentiation.
Floor division.
since they spend a total of $42.
so the price of one movie ticket without the coupon is
⇒ (42+12)/6
⇒54/6
⇒ 9
so the price of one movie ticket will be $9.
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angle a and angle B are supplementary angles. if M angle a equals 2X +27 and M angle B equals 5X -1 then find the measure of angle a 
The value of the angle A is; ∠A = 74°.
What is meant by the supplementary angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two angles are termed supplements of one another. In other words, because unless Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.Supplementary angles are classified into two types.supplementary angles adjacentNon-adjacent supplementary anglesFrom the stated question;
∠A = 2X +27 and ∠B = 5X -1.
From the property of supplementary angles;
∠A + ∠B = 180
Put the values;
2X +27 + 5X -1 = 180
On simplification;
7X = 154
X = 22
Put the value of X in ∠A = 2X +27.
∠A = 2 x 22 + 27
∠A = 74°.
Therefore, the measure of the angle A is ∠A = 74°.
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What two different stores offer a sale on the same item, but one offers a coupon savings and the other offers a percentage-off discount? How can you tell which offer is better?
Answer:
Personally, I think it depends on the amount of the product you’re buying. If the product is expensive, you should go the store with a percentage-off discount. If the product is not expensive, you should go to the store with coupon savings.
Step-by-step explanation:
For example, if you’re buying a $5 toy with a $1 coupon and 10% off, you should chose the coupon. Because if you chose the discount, it doesn’t change a lot of things. However, if you’re buying a million dollar airplane(just kidding), then you should definitely chose the discount. Because a million dollar minus 1 changes nothing. But a 10% discount can decrease the cost by 1 hundred thousand! Isn’t that surprising? Hope you understand it.
a diver starts at 5 m and changes -16 m?
The depth that the driver is will be -11 meters
How to illustrate the information?From the information, it was stated that diver starts at 5 m and changes -16 m.
Therefore, it should be noted that the depth that he is will be:
= Starting position + Change
= 5 + -16
= -11
Therefore. the depth that he is will be -11 meters.
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A diver starts at 5 m and changes -16 m. What depth is he now?
Find the indicated number of geometrical mens
[tex]-32 and i[/tex]
The geometric mean between -32 and i is given by:
[tex]\sqrt{-32i}[/tex]
What is the geometric mean?The geometric mean between n values is given by the nth root of the multiplication of these values.
For this problem, we have that:
There are 2 values, -32 and i.The multiplication is -32i.Due to the two values, we take the square root, hence, the geometric mean between -32 and i is given by:
[tex]\sqrt{-32i}[/tex]
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g = x - c solve for x
MN¯has an endpoint at M(–2, –2) and an endpoint at N(7, –5).
What is the length of MN to the nearest tenth?
The length of the segment MN is 9.5 units
How to determine the length of the segment MN?The endpoints of the line segment MN are given as
M = (-2, -2)
N = (7, -5)
The length of the segment MN is calculated as:
MN = √(x2 - x1)^2 + (y2 - y1)^2
Substitute the known values in the above equation
So, we have
MN = √(-2 - 7)^2 + (-2 + 5)^2
Evaluate the sum and the difference
So, we have
MN = √-9^2 + 3^2
Evaluate the exponents
So, we have
MN = √81 + 9
Evaluate the sum
So, we have
MN = √90
Evaluate the exponents
So, we have
MN = 9.5
Hence, the length of the segment MN is 9.5 units
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please help please im giving so much
Answer:
D
Step-by-step explanation:
The highest number that divides exactly into two or more numbers. 3 and 9 cannot be divided by anything greater than 3.
Answer: i think its D.
Step-by-step explanation:
Gil traveled 4. 5 miles and continues at a speed of 62. 5 miles per hour. Andy has traveled 29. 5 miles per hour and continues at a speed of 50 miles per hour. If the cars continue at the same speed, how many hours will it take for andy and gill to travel the same number of miles
If Gil traveled 4. 5 miles and continues at a speed of 62.5 miles per hour and Andy has traveled 29.5 miles and continues at a speed of 50 miles per hour, then the number of hours it will take for Andy and Gill to travel the same number of miles is equal to 2.
The number of hours it will take for Andy and Gill to travel the same number of miles can be determined by using an algebraic expression.
An algebraic expression to find the number of hours can be given as,
4.5 + 62.5(x) = 29.5 + 50(x)
Here, x is equal to the number of hours.
Solving to find the value of x,
62.5x - 50x = 29.5 - 4.5
12.5x = 25
x = 25 ÷ 12.5
x = 2
Hence, the number of hours it will take for Andy and Gill to travel the same number of miles is calculated to be 2.
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Evaluate: 50% of 3,000= ?
Answer:
1500
Step-by-step explanation:
imagine 30 / 5 = 15 then add the two zero's after
Answer:
50% of 3,000 is 1500
Step-by-step explanation:
hope this helps!
If AABC = ADEF, AB = 8, BC = 19, AC=14, EF = 4x-1, and DE=y-6, find the values of
x and y.
When given triangles are given then the value of x and y is 5 and 14 respectively.
When BC is similar to EF.
19= 4x-1
19+1=4x
20=4x
x=5
When DE is similar to AB
y-6 =8
y=8+6
y=14
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
A pair of triangles are said to be similar if two pairs of corresponding angles in those triangles are congruent. We can conclude that the third pair must also be equal if the first two angle pairs are. When all three pairs of angles are equal, the sides of the three triangles must also be proportionate.
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11. Harry ordered 9.0 pizzas. Each pizza costs $13.95. How much does he need to pay?
Question:
11. Harry ordered 9.0 pizzas. Each pizza costs $13.95. How much does he need to pay?Answer:
This is pretty simple, just multiply 9.0 by $13.95, which will give you the answer of $125.55.
* I am not responsible if you get this question wrong, for you are the one who asked the question. *
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If this helped, your welcome! Please know that I might be wrong, and if I am, I am truly sorry for that. But If you would, please make me brainliest.
I hope you have a great rest of your day! If there is an issue with this question, be happy to comment. <3
-niaxfandoms
Harry needs to pay $ 125.55 in total for the 9.0 pizzas he ordered at $ 13.95 each.
To calculate how much Harry needs to pay, multiply the number of pizzas (9.0) by the cost of each pizza ($ 13.95).
Total cost = Number of pizzas × Cost per pizza
Total cost = 9.0 × $ 13.95
To find the product, we can treat 9.0 as a whole number and then multiply:
Total cost = 9 × $ 13.95
Now, calculate the product:
Total cost = $ 125.55
Harry needs to pay $ 125.55 in total for the 9.0 pizzas he ordered at $ 13.95 each.
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What value of x makes this equation true?
x -3 = x +3
3 9
The value of x from the given linear equation x/3-3=x/9+3 is 27.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
Given equation
x/3-3=x/9+3
=> x/3-x/9=3+3
=>(3x-x)/9=6
=>2x/9=6
=> x=9*6/2
x=27.
Therefore, the value of x from the given linear equation is 27.
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James has 23 cans, but the people gets 15 cans, What cans left?
A 13
B 8
C 10
D 7
Answer:
B
Step-by-step explanation:
23-15=8