The solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have three linear equations in three variable:
4x + 3y - z = -6 ..(1)
6x - y+ 3z = 12 ..(2)
8x + 2y + 4z = 6 ...(3)
From the equation (1)
[tex]\rm x=\dfrac{-6-3y+z}{4}[/tex]
Substitute the above value in the equation (2) and (3):
[tex]\rm 6\cdot \dfrac{-6-3y+z}{4}-y+3z=12\\\\ 8\cdot \dfrac{-6-3y+z}{4}+2y+4z=6[/tex]
After simplification:
[tex]\rm -11y+9z-18=24\\ -4y+6z-12=6[/tex]
After solving the above two equations by substitution method:
z = 1
y = -3
Plug the above two values in the equation (1), we get:
x = 1
Thus, the solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.
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Find the area of the triangle.
Answer:
take 1/2 multiply by sin 91°×2×8
Find the length of the side labeled . Round intermediate values
to the nearest tenth. Use the rounded values to calculate the next
value. Round your final answer to the nearest tenth.
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!PLEASE DON'T HESITATE TO ASK WHERE YOU DON'T UNDERSTAND.DJ Erin is making a playlist for work; he is trying to decide what 10 songs to play and in what order they should be played.
Step 2 of 2 : If he has his choices narrowed down to 3 country, 6 pop, 7 disco, and 3 hip-hop songs, and he wants to play all 7 disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.
Using the combination and the arrangements formula, it is found that the number of possible playlists is given by:
[tex]7.98 \times 10^8[/tex]
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
7 disco songs are taken from a set of 7.3 remaining songs are taken from a set of 3 + 6 + 3 = 12 songs.Hence, without considering the order, the number of playlists is given by:
[tex]C_{7,7}C_{12,3} = \frac{7!}{7!0!} \times \frac{12!}{3!9!} = 220[/tex]
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, the 10 musics are arranged, hence the number of playlists, considering the order, is given by:
[tex]n = 10! \times 220 = 798336000 = 7.98 \times 10^8[/tex]
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The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.
A 2-row table with 10 columns. The first row is labeled time (minutes) with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4, 4.5. The second row is labeled temperature (degrees Celsius) with entries 75, 79, 83, 86, 89, 91, 93, 94, 95, 95.5.
According to the line of best fit, at what time will the temperature reach 100°C, the boiling point of water?
5
5.5
6
6.5.
According to the given table the line of best fit is
f(x)=4.54x+77.84
The term "line of best fit" describes a line that passes across a scatter plot of data points and best captures their connection. Statisticians often utilise regression analysis software or manual computations to arrive at the geometric equation for the line using the least squares approach. A straightforward linear regression study of two or more independent variables will provide a straight line.
Hence, as asked by the question we need to find the time at which the tempurature will become 100°C.
To find that let us put f(x)=100 and find out the value of x for which it is satisfied.
4.54x+77.84=100
⇒[tex]x=\frac{100-77.84}{4.54}=4.88[/tex]
⇒x≈5
Therefore the time at which the tempurature is 100°C is 5 minutes.
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Rewrite the expression as a fraction.
I don't even know Brian tanks
Determine whether each set of data can be modeled by an exponential function. If so, find the exponential
function that fits the data.
It can be modeled by an exponential function, f(x) is divided by 3 each time x increases by 1.
This means that the base of the exponential function is 1/3, and since the value of f(x) when x=0 is 81, [tex]f(x)=81\left(\frac{1}{3} \right)^{x}[/tex]
9. What is the exact circumference of a circle that has a radius of 5 cm?
25ncm
5псм
10Kcm
100псм
Answer:
10π cm
Step-by-step explanation:
c = 2πr
c = (2*5) * π
c = 10π
i need help with this geometry question
Answer:
radius ≈ 15.5
Step-by-step explanation:
the radius is RS
the angle between a tangent and the radius at the point of contact is 90°
then Δ RST is a right triangle
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then
RS² + ST² = RT² ( substitute values )
RS² + 7² = 17²
RS² + 49 = 289 ( subtract 49 from both sides )
RS² = 240 ( take square root of both sides )
RS = [tex]\sqrt{240}[/tex] ≈ 15.5 ( to 1 dec. place )
Compute the projection of u on v.
Answer:
[tex]\frac{3}{7}.v[/tex] option (C) is correct
Step-by-step explanation:
projection of vectors: The vector projection of one vector over another vector is the length of the shadow of the given vector over another vector.
projection of vector u on v is given by :
[tex](\frac{u.v}{v.v}).v[/tex]Given,
vector u = <5, 7, 1>
vector v = <2, -1, 3>
substituting these values in the above formula
[tex][\frac{(2,-1,3)(5,7,1)}{(2,-1,3).(2,-1,3)} ].v[/tex] = [tex]\frac{6}{14}.v= \frac{3}{7}.v[/tex]thus the correct answer is option (C)
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Rationalize the denominator. [tex]\frac{9}{\sqrt{x+3} }[/tex] Simplest form
The result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].
What is Rationalization?Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction.
Here, given fraction
[tex]\frac{9}{\sqrt{x+3} }[/tex]
Multiply and divide by [tex]\sqrt{x+3}[/tex], we get
[tex]\frac{9}{\sqrt{x+3} } \frac{\sqrt{x+3} }{\sqrt{x+3} }[/tex] = [tex]\frac{9\sqrt{x+3} }{x+3}[/tex]
Thus, the result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].
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Evaluate using the trigonometric ratios Tan 60° + Cos 30° sin 60° + Cot 30° /CSC 30° Sec 30°
Answer:
(24 + 3√3) / 16.
Step-by-step explanation:
Tan 60° + Cos 30° sin 60° + Cot 30 / csc 30 sec 30
= √3 + √3/2 * √3/2 + √3 / 2 * 2/√3
= 2√3 + 3/4 / 4/√3
= (8√3 + 3)/ 4 / √3
= 24 + 3√3 / 16
Find the next number in the sequence: 2, 2, 5, 12, 62, 749, 46450,
Answer:
34791112
Step-by-step explanation:
Please check the attached for the explanation.
The next number for given sequence is 34791112.
The given sequence is 2,2,5,12,62,749,46450,......
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.
Each number in the sequence is of the form Number3 × Number2 + Number1 = Number4
5×2+2=12
12×5+2=62
62×12+5=749
749×62+12=46450
So, the required number is
46450×749+62=34791112
Therefore, the next number for given sequence is 34791112.
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6x+2y=20 2x-3y=3 solve by substitution
The solution of the system of linear equation by substitution method is (3,1).
What is the method of substitution?The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.
Given here the linear equations are
Equation 1: 6x+2y=20
Equation 2: 2x-3y=3
in equation 1 the value of y will be
6x+2y=20
⇒2y=20-6x
⇒y=(20-6x)/2
⇒y=10-3x
substituting the value of y in the equation 2, we will get
2x-3y=3
⇒2x-3(10-3x)=3
⇒2x-30+9x=3
⇒11x-30=3
⇒11x=30+3
⇒11x=33
⇒x=33/11
⇒x=3
putting the value of x in value of y in equation 1
y=10-3x
⇒y=10-3(3)
⇒y=10-9
⇒y=1
The solution of the system of linear equation by substitution method is (3,1).
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Graph the line with slope 1/4 and y-intercept -8
Solution: Below! ^^
Detailed explanation:
Hii! I'm sorry, I can't graph the line for you, but I'll try to give you the best possible explanation.
First, note that the question provides us with the info that the y intercept is -8. This is a very valuable piece of information!
This means that the line crosses the y axis (since it's the y intercept) at the point (0,-8). Plot it on the co-ordinate plane.
Next, this question also provides us with the fact that the slope of the line is 1/4. This is yet another valuable piece of information!
What this tells us is: from that point (0,-8), you need to go up 1 unit, then over 4, and so forth, until you obtain a line.
_________
Hope I helped, best wishes & happy studies!
Please reach out to me if any queries arise.
_________
Answer:
Image attached below
Step-by-step explanation:
The line should cross y axis as -8 and should have a point of (0,-8)
The line should have a gradient / slope of 1/4
Which equation represents an exponential function with the initial value of 500?
Answer:
A exponential equation is usually of the form f(x)=a (1±r)ˣ.
Our limitation: Initial Vale is 500.
Let's look at our options:
#1- Initial Value of 1000 --- WRONG!
#2- Initial Value of 1000 --- WRONG!
#3- Initial Value of 500 ---- Maybe
#4- Initial Value of 500 ---- Maybe
Let's look at 3 and 4:
#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!
#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!
Hence, #3 Is correct!
Step-by-step explanation:
Well, I hope you understood, and I'd gladly explain anything that didn't make sense. A brainliest would be appreciated, thank you!
-Zylynn Jade Ardenne
which expression is equivalent to....
Answer:
A^32
Step-by-step explanation:
Done
Answer:
Option D: a³²
Step-by-step explanation:
Powers in this case multiply, 8*4=32
therefore answer D a³² is correct
How many kilometers are in 462 meters? How many kilometers are in 462 meters ?
Answer:
0.462
Step-by-step explanation:
1km=1000m
so to get from metres to kilometres you divide by 1000
so 462÷1000=0.462
urgent help needed algebra 2
Answer:
it's 5 degrees celsius I think you must have entered a 4-32 instead of a 41-32 is what threw you off
Step-by-step explanation:
Which graph represents the function f(x)=2·4^x?
Answer:
A (top left)
Step-by-step explanation:
Assuming that the dot is multiplying the numbers, we get the function:
[tex]f(x) = 8^{x}[/tex]
First, lets knock off the obviously wrong answers.
Substitute 0 into the x spot, as anything to the power of zero is one.
[tex]f(0) = 8^{0}=1[/tex]
Automatically, the two answers on the right are incorrect, as y is not equal to 1 when x is 0.
Next, lets substitute 1 into the x spot, as anything to the power of one is itself.
[tex]f(1) = 8^{1} = 8[/tex]
As a result, the top left graph is correct, as y is equal to 8 when x is 1, unlike the bottom left graph.
What is the density of the oak board
Step-by-step explanation:
easy how thick it is we need a picture
Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are spades, your friend will pay you $39 $ 39 . Otherwise, you have to pay your friend $5 $ 5 . Step 2 of 2 : If this same bet is made 623 623 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.
The amount of winning is more than amount of loosing. Then the amount of winning will be $3738.
How to find that a given condition can be modelled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
The expected value will be
E(X) = np
Suppose that you and a friend are playing cards, and you decide to make a friendly wager.
The bet is that you will draw two cards without replacement from a standard deck.
If both cards are spades, your friend will pay you $39.
Otherwise, you have to pay your friend $5.
If this same bet is made 623 times.
The maximum amount of winning will be
E(win) = np
We have
p = 0.25
n = 623
Then we have
E(win) = 0.25 × 623
E(win) = 155.75
Then the winning amount will be
WA = 155.75 × 39
WA = $6074.25
The maximum amount of loosing will be
E(loose) = np
We have
p = 0.75
n = 623
Then we have
E(loose) = 0.75 × 623
E(loose) = 467.25
Then the loosing amount will be
LA = 467.25 × 5
LA = $2336.25
Then the amount of winning will be
⇒ $ 6074.25 - $ 2336.25
⇒ $ 3738
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Pleas hurry!!!!! Which line is perpendicular to a line that has a slope of -5/6
line JK
line LM
line NO
line PQ
Answer:
LM
Step-by-step explanation:
Perpendicular slope would be - 1 / m = - 1/(-5/6) = 6/5
slope m = rise / run line LM rises 6 for a run of 5
The y-intercept of the line whose equation is 2x - 3y = 6 is
-2
3
6
Answer:
y = -2
(first option listed)
Step-by-step explanation:
a y-intercept is a point where the line crosses over the y-axis, which happens when x = 0.
So, the y-intercept is actually pretty each to find.
this is the easier way to find it: {plug directly into equation given}
2x - 3y = 6
(set x equal to 0)
[0] - 3y = 6
(divide both sides by -3)
y = -2
but you might have seen/ learned to solve the equation like this {to actually find the equation of the line and solve from that}
[this method is helpful to know/practice for when equations for functions get more complex]
2x - 3y = 6
+ 3y + 3y {add 3y to both sides}
2x = 3y + 6
-6 -6 {subtract 6 from both sides}
2x - 6 = 3y
÷3 ÷3 {divide both sides by 3 to isolate y}
[tex]\frac{2}{3}x[/tex] [tex]- 2 = y[/tex] [flip sides of the equation]
[tex]y=\frac{2}{3}x-2[/tex]
set x equal to 0 (x = 0)
y = [tex]\frac{2}{3} (0)[/tex] - 2
y = 0 - 2
y = -2
So, the y-intercept is -2.
A retired woman has 70,000toinvestbutneedstomake
9,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. Set up and solve the equation for how much the woman should invest in each option to sustain exactly a $9,000 annual return.
Answer:
$51,250 at 15%$18,750 at 7%Step-by-step explanation:
The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.
__
setupLet x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...
0.15x +0.07(70000-x) = 9000
__
solutionSimplifying the equation gives a 2-step linear equation.
0.08x +4900 = 9000 . . . . simplified
0.08x = 4100 . . . . . . . . . . subtract 4900
x = 51,250 . . . . . . . . . . . .divide by 0.08
70000 -x = 18,750
The woman should invest $51,250 at 15% and $18,750 at 7%.
Richards Corporation uses the FIFO method of process costing. The following
information is available for October in its Fabricating Department:
Units:
Beginning Inventory: 80,000 units, 60% complete as to materials and 20%
complete as to conversion.
Units started and completed: 250,000.
Units completed and transferred out: 330,000.
Ending Inventory: 30,000 units, 40% complete as to materials and 10%
complete as to conversion.
Costs:
Costs in beginning Work in Process - Direct Materials: $37,200.
Costs in beginning Work in Process - Conversion: $79,700.
Costs incurred in October - Direct Materials: $646,800.
Costs incurred in October - Conversion: $919,300.
Calculate the equivalent units of materials.
If Richards Corporation uses the FIFO method of process costing. The equivalent units of materials is 294,000.
Equivalent unit of material (FIFO)
Using this formula
Equivalent unit of material (FIFO) =[(Beginning inventory×Percentage complete)+Units started and complete+ (Ending inventory× Percentage complete as to materials)]
Let plug in the formula
Equivalent unit of material (FIFO) = [80,000×40%+250,000+30,000×40%]
Equivalent unit of material (FIFO) = 32,000+250,000+12,000
Equivalent unit of material (FIFO) = 294,000
Therefore the equivalent units of materials is 294,000.
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What is the solution to the equation 7(a-10)=13-2(2a+3)?
26
O a=11
O a=7
89
O a = 11
O a=621
Answer:
[tex]a = 7[/tex]
Step-by-step explanation:
[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]
can someone please help me solve this question step by step not just give me the answer I want to learn lol
find f(x)•g(x)
if f(x)=8x+1 and g(x)=-5+9.
Answer: 32x+4
Step-by-step explanation:
[tex]f(x) \cdot g(x)=(8x+1)(-5+9)=4(8x+1)=\boxed{32x+4}[/tex]
!!WILL GIVE BRAINLIES PLS HELP!!!
Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex (-6,
12) and includes the point (-9, 15) on the boundary?
Answer:
is B
Step-by-step explanation:
this is the best possible answer
A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures his distance from the tree at 13 meters and the angle of elevation to the tree at 53°. What is the height of the tree to the nearest tenth of a meter
The height of the tree to the nearest tenth of a meter is 73.7m
What is angle of elevation?The angle formed by the line of sight and the horizontal plane for an object above the horizontal.
Given:
base = 13 m
angle of elevation = 53
Using trigonometry
tan 53 = P/B
5.671 = P/ 13
P= 5.671 * 13
P= 73.723
Hence, the height of the tree is 73.7 m.
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A triangle with side lengths a, b, and c is shown below.
Which statement about the side lengths must be true?
A a+b>c
B b+c
C a+b
D a+c
The statement about the sides must respect to represent a triangle is given as follows:
A. a + b > c.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
The smaller sides for the triangle are given as follows:
a and b.
Hence the statement is:
a + b > c.
(as the sum of the lengths of the smaller sides a and b must be greater than the length of the larger side, which is of c).
Hence the correct statement is given by option A.
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