Answer:
x = 14,4
Step-by-step explanation:
x = 3,6 * 4
x = 14,4
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. 2x+y+4z=16 5x-2y+2z=-1 x+2y-3z=-9 A(-1, 2, 22) B(-10, 22, 42) C(-1, 2, 4) D(-10, 2, 22) Please select the best answer from the choices provided A B C D
The solution of this system of linear equations is [tex](x,y,z) = (1,2,4)[/tex]. (Correct choice: C)
How to solve a system of equations by augmented matrixThe system of equations is represented by the following augmented matrix:
[tex]\left[\begin{array}{cccc}2&1&4&16\\5&-2&2&-1\\1&2&-3& -9\end{array}\right][/tex] (1)
Where the fourth column represents the vector column of independent coefficients. After making some operations, we find that the reduced row-echelon form of the augmented matrix is:
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&1&0&2\\0&0&1& 4\end{array}\right][/tex]
The solution of this system of linear equations is [tex](x,y,z) = (1,2,4)[/tex]. (Correct choice: C) [tex]\blacksquare[/tex]
To learn more on augmented matrices, we kindly invite to check this verified question: https://brainly.com/question/4945755
Final answer:
To solve the system of equations, we need to find the reduced row-echelon form of the augmented matrix. Applying row operations, we can reduce the matrix to row-echelon form. Then, using backward substitution, we can find the values of x, y, and z. The solution to the system of equations is (-10, 2, 8.5).
Explanation:
To solve the system of equations, we can represent it as an augmented matrix and find its reduced row-echelon form. The augmented matrix for the given system of equations is:
[2 1 4 | 16]
[5 -2 2 | -1]
[1 2 -3 | -9]
Next, we need to apply row operations to reduce the matrix to its row-echelon form. Following the Gaussian elimination method, we perform the row operations:
R2 → R2 - 5R1, and
R3 → R3 - R1
The resulting matrix in row-echelon form is:
[2 1 4 | 16]
[0 -7 -18 | -81]
[0 0 0 | 0]
Now, we can apply backward substitution to find the values of x, y, and z. From the last row of the row-echelon form, we know that 0z=0. We can assign any value to z, such as 1, and then solve for x and y. Plugging in z=1, we get:
2x + 1y + 4(1) = 16
x + 2y - 3(1) = -9
Simplifying these equations, we get:
2x + y + 4 = 16 → 2x + y = 16 - 4 → 2x + y = 12
x + 2y - 3 = -9 → x + 2y = -9 + 3 → x + 2y = -6
Using these equations, we can solve for x and y by setting up a system of linear equations:
2x + y = 12
x + 2y = -6
Solving this system, we can find the values of x and y: x = -10 and y = 2. Finally, substituting these values back into one of the original equations, we can find z:
2(-10) + 1(2) + 4z = 16 → -20 + 2 + 4z = 16 → 4z = 34 → z = 8.5
So, the solution to the system of equations is (-10, 2, 8.5).
What is the cube root of 27x18?
Final answer:
The cube root of 27x18 is 3x6, determined by taking the cube root of each term, with 27 yielding 3 and the x18 exponent reduced by a factor of 3 to x6.
Explanation:
The question posed is, "What is the cube root of 27x18?" To solve this, we need to break down the expression and compute the cube root of both terms separately. The cube root of 27 is 3 because 33 = 27. For the variable x raised to the 18th power, taking the cube root means we divide the exponent by 3, which gives us x6. Therefore, the cube root of 27x18 is 3x6.
10=z+6
How to get answer for integers
Answer:
Step-by-step explanation:
10=z+6
subtract 6 from both sides
4=z
z=4
Answer:
The answer is 4
Step-by-step explanation:
To get the answer for this equation, take 6 and subtract from both sides.. meaning 6-6 and they will cancel and then subtract 6 from 10 and that will give you your answer of 4.
Simplify 10x-5y+2x-3y
Answer:
12x-8y
Step-by-step explanation:
10x+2x=12x
-5y-3y=-8y
Answer: 12x-8y
Step-by-step explanation: add like terms 10x and 2x, and -3-5= 8 so 8y
The Rockwell’s have driven 180 miles, which is 2/3 of the way to their family reunion. How far is the total distance to their family reunion
Answer:
270 miles
Step-by-step explanation:
Let the total distance be d.
Then (2/3)d = 180 miles.
Solve for d by multipying both sides by (3/2):
(3/2)(2/3)d = (3/2)(180 miles) = 270 miles
The total distance is 270 miles.
what is one half of 9
Answer:
Step-by-step explanation:
1/2 of 9
" of " in math means multiply
1/2 * 9 = 9/2 or 4 1/2 or 4.5
An office building has 23 offices. The floor area of each office is 305 square feet. Which shows the equation you can use to find the floor area, , of all the offices and the value of
n?
A.23 + 305 = n, n = 810 square feet
B. 23 x 305 = n, n = 1,405 square feet
C.23 x 305 = n, n = 1,425 square feet
D.23 x 303 = n, n = 7,015 square feet
Answer: 23x305 = n , n = 7,015 square feet
Step-by-step explanation:
1 office = 305 square feet
If we want to calculate the area of 23 offices, we just need to multiply the area of one office, by the number of total offices.
That's 305 square feet * 23 = 7015 square feet
The correct answer is 23x305 = n , n = 7,015 square feet
Hope I helped!
a guy wire for a tree is 20 ft long, making a 21 angle with the ground. How far is the base of the tree from a stake anchoring the wire?
Answer:
18.7 feet far
Step-by-step explanation:
Based on the information given we can conclude that our set up will be a Right triangle (i.e. one angle is 90°), where the hypotenuse will be denoted by the guy wire of [tex]20ft[/tex] and angle of 21° is the angle formed between then hypotenuse and the base (i.e. ground).
Thus we want to find the base length (lets call it [tex]x[/tex] ) of this triangle, so we can use trigonometry as we have one angle and the hypotenuse, as follow:
[tex]cos(21)=\frac{adjacent side}{hypotenuse}=\frac{baselength}{guywire}\\\\ cos(21)=\frac{x}{20} \\x=20cos(21)\\x=18.671\\x=18.7ft[/tex]
So the base is approximately 18.7 feet far from the tree of the anchored wire.
The distance from the base of the tree to the stake anchoring a guy wire that is 20 ft long and makes a 21-degree angle with the ground is approximately 18.8 ft, found using the cosine function of trigonometry.
Explanation:The student asked for help in determining the distance from the base of the tree to the stake anchoring a guy wire that is 20 ft long and makes a 21-degree angle with the ground. To solve this problem, we need to employ trigonometry, specifically the cosine function which relates the adjacent side of a right triangle (the distance we're looking for) to the hypotenuse (the length of the guy wire) and the angle between them.
Using the formula cosine(angle) = adjacent/hypotenuse, we can set up our equation as cos(21°) = distance/20 ft. Rearranging the equation to solve for the distance, we get distance = 20 ft * cos(21°). After calculating, we find that the distance from the base of the tree to the stake is approximately 18.8 ft.
the perimeter of a equilateral triangle is 63 inches. If the length of each side is (4x+3),find the value of x
Answer:
Step-by-step explanation:
each side is 21 inches long.
4x+3=21
subtract 3 from both sides
4x=18
x=4.5
Answer:
4.5
Step-by-step explanation:
Since its an equilateral triangle, all the sides are equal.
SO, you can set up the equation:
3 ( 4x + 3 ) = 63
Start by disributing
12x + 9 =63
Subtract 9 from each side to isolate the variable
12x = 54
Divide both sides by 12
x = 4.5
Write the inequality for the graph.
Answer:
[tex]p\leq 4[/tex]
Step-by-step explanation:
we know that
The solution of the graph shows the interval (-∞,4]
All real numbers less than or equal to 4
In a number line the shaded area is at left of x=4 (closed circle)
The number 4 is included in the solution
therefore
the inequality that represent the graph is
[tex]p\leq 4[/tex]
15. Which one of the following statements is true of parallel lines?
ms &
ources
PROGRAMS
O A. They intersect at one point.
O B. They intersect at more than one point.
O C. They intersect at least twice.
O D. They never intersect.
k(2) = 6x + 100
k(-5) =
Answer:
70
Step-by-step explanation:
To evaluate k( -5), substitute x = - 5 into k(x)
k(−5)=(6×-5)+100=−30+100=70
find nth term of this quadratic sequence:
1,12,29,52,81
The nth term of the quadratic sequence 1, 12, 29, 52, 81 is T(n) = 2n² - n - 2.
1. Check for a Quadratic Sequence:
To determine if a sequence is quadratic, we look at the differences between consecutive terms, and then the differences between those differences (second differences).
First differences: 11, 17, 23, 29
Second differences: 6, 6, 6
The sequence is quadratic since the second differences are constant.
2. General Form of a Quadratic Sequence:
The quadratic sequence formula in general is:
T(n) = an² + bn + c
Where:
T(n) is the nth term
a, b, and c are constants to be determined
3. Forming Equations:
We can use the first three terms of the sequence to create three equations:
For n = 1: a(1)² + b(1) + c = 1
For n = 2: a(2)² + b(2) + c = 12
For n = 3: a(3)² + b(3) + c = 29
Simplifying these equations, we get:
a + b + c = 1
4a + 2b + c = 12
9a + 3b + c = 29
4. Solving the Equations:
By concurrently solving this set of equations, we arrive at:
a = 2
b = -1
c = -2
5. Finding the nth Term:
Substituting the values of a, b, and c into the general formula, we get: T(n) = 2n² - n - 2
How can I show my work for: 120% of what number is 50
120% is "x" is 50, meaning "x" must be the 100%.
if 50 is 120% of "x", and "x" is the 100%, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 50&120 \end{array}\implies \cfrac{x}{50}=\cfrac{100}{120}\implies \cfrac{x}{50}=\cfrac{5}{6}\implies 6x=250 \\\\\\ x = \cfrac{250}{6}\implies x = \cfrac{125}{3}\implies x = 41\frac{2}{3}\implies x = 41.\overline{6}[/tex]
theirs a picture at the top.
17. simplify
18. simplify
Answer:
C, B
Step-by-step explanation:
4x * 1 = 4x
4x * y = 4xy
4x + 4xy
Next
5 * x = 5x
5 * 3 = 15
5x + 15
Answer:
17(c)
18(b)
Step-by-step explanation:
17) (4x*1)+(4x*y)
4x+4xy
18) (x+3)5
(5*x)+(3*5)
5x+15
12.) Western High School is looking for someone to
design and make their senior t-shirt. Stylish Shirts
charges $12 for each shirt and a design fee of $40.
Decatur Clothing sells their shirts for $7 with an $85
design fee. Write and solve a system of to find how
many shirts it will take for the 2 stores to cost the
same.
Answer:
9
Step-by-step explanation:
12x+40 = 7x + 85
12x - 7x = 85 - 40
5x = 45
x=9
so designing 9 shirts will take for the 2 stores to cost the
same.
Final answer:
To find the number of shirts, set up a system of equations and solve for the cost of each store. It will take 9 shirts for the two stores to cost the same.
Explanation:
To find the number of shirts it will take for the two stores to cost the same, we need to set up a system of equations. Let's assume the number of shirts needed is 'x'.
For Stylish Shirts: Total Cost = (Price per shirt * Number of shirts) + Design Fee = ($12 * x) + $40.
For Decatur Clothing: Total Cost = (Price per shirt * Number of shirts) + Design Fee = ($7 * x) + $85.
Setting the two total costs equal to each other, we have: ($12 * x) + $40 = ($7 * x) + $85. Solving this equation gives us x = 9. Therefore, it will take 9 shirts for the two stores to cost the same.
Help trigonometry (angles of evaluation and depression)
Answer:
80.4
Step-by-step explanation:
To remember all of the ratios for trigonometry, using the acronym "SohCahToa". You always divide two sides for trig. ratios.
'S' is sine or sin for short.
'C' is cosine or cos for short.
'T' is tangent, or tan for short.
'h' means hypotenuse, the longest side in the triangle.
'o' means the side that's opposite, or not touching the angle of reference.
'a' means the side that's adjacent, or touching the angle of reference.
The angle of reference means the angle you are talking about (use the symbol θ to mean angle). In this question, the angle of reference is 15°.
We have the adjacent side, 300, and we need to find the opposite side, x.
The trig. ratio that has the side adjacent and opposite is tangent or 'tan'.
tanθ = opposite / adjacent Trig. ratio for tangent
tan15° = x / 300 Substitute what we know. Isolate 'x'.
x = 300tan15° This means 300 times tan15°. Use a calculator.
x = 80.3847..... Exact decimal answer on your calculator
x ≈ 80.4 Answer rounded to nearest tenth (first decimal)
When rounding, you decide to round up or down using the decimal place after where you will cut off.
In 80.3847..... '8' tells us to round up because it is 5 or greater.
If the second decimal place was 4 or less, we round down (the answer would be 80.3).
Urgent please help me!!!!
1) Left 2, down 5
2) Right 2, down 9
3) left, up 9
4) left 2 , down 5
Answer:
right 2, down 9
Step-by-step explanation:
move point A' two places to the right, and down nine to get to point A
The coordinate grid below shows triangle ABC and its image after translation, triangle A'B'C': Triangles ABC and A prime, B prime, C prime are shown. A is located at negative 6, 2. B is located at negative 5, 5. C is locat Which of the following completes the rule for this translation, (x, y) → (x + 6, ___)? (5 points)
y − 6 y + 6 y − 8 y + 8
Answer:
The rule of translation (x,y) → (x+6 , y-8)
Step-by-step explanation:
The rest of the question is the coordinates of the ΔABC and ΔA'B'C'
The coordinates of the ΔABC: A(-6,2) , B(-5,5) , C(-1,3)
The coordinates of the ΔA'B'C': A'(0,-6) , B'(1,-3) , C'(5,-5)
It is required the rule of translation.
By Comparing between any of the points and its image
For example between A and A'
Let A(-6,2) = (x,y) and A'(0,-6) = (x+h , y+k)
So, x = -6 and y = 2
And x+h = 0 , y+k = -6
Substitute with x and y to find h and k
So, -6 + h = 0 ⇒ h = 6
And 2 + k = -6 ⇒ k = -8
So, the rule of translation (x,y) → (x+6 , y-8)
You put $400 in an account. The account earns $18.00 simple interest in 9 months. What is the annual interest rate
Answer:$18.00
Step-by-step explanation:
Subtract 5x+10 from 2x-6 please answer
Answer:
-3x-16
Step-by-step explanation:
(2x-6)-(5x+10)
2x-6-5x-10
2x-5x-6-10
-3x-6-10
-3x-16
convert 24/3 to a mixed number
Answer:
23 over 3 will give you a mixed number / whole number of 8
Step-by-step explanation:
your answer is 8
Answer:
the answer to this is
24/3= 8 ( edited again as I TOOK THE wrong values )
WILL MARK AS BRAINLIEST
Answer:
1246 sq cm
Step-by-step explanation:
you can break this shape into two rectangles, find the area of each, and then add them together
Answer:
First we need to find the area of the whole shape which would be the length times width
Length= 39
Width= 34
39*34=1,326
This is the area if the shape were shaded in
Now we want to find the area of the missing section which is again length times width
Length=10
Width=8
10*8=80
This is the area of the missing section, so to find the area of the shape you would take your total area minus your missing section area
1,326-80= 1,246
Your final answer would be 1,246 sq. cm
Hope this helps ;)
Step-by-step explanation:
A gardener is planting two types of trees:
Type A is 7 feet tall and grows at a rate of 2 inches per year.
Type B is 5 feet tall and grows at a rate of 6 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
It will take 6 years for the trees to be same height.
Step-by-step explanation:
Given,
Initial height of Type A = 7 feet = 7*12 = 84 inches
Growth rate = 2 inches per year
Let,
x be the number of years
Total height = T
T = 2x+84 Eqn 1
Initial height of Type B = 5 feet = 5*12 = 60 inches
Growth rate = 6 inches per year
T = 6x+60 Eqn 2
For same height;
Eqn 1 = Eqn 2
[tex]2x+84=6x+60\\84-60=6x-2x\\24=4x\\4x=24[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{24}{4}\\x=6[/tex]
It will take 6 years for the trees to be same height.
Keywords: linear equation, division
Learn more about division at:
brainly.com/question/899976brainly.com/question/884169#LearnwithBrainly
What is the least number of years until the year rounded to the nearest ten is 2060
Answer:
35
Step-by-step explanation:
Final answer:
To determine the least number of years from 2023 until the year rounds to 2060, subtract 2023 from 2055, the first year that rounds to 2060, resulting in 32 years.
Explanation:
The question is asking for the least number of years it will take for the current year to be rounded to nearest ten to become 2060. To answer this, we consider the year closest to 2060 that when rounded will result in exactly 2060. We are considering that the current year is 2023, optimizing the rounding rule of being closer to or equal to the next multiple of ten (2055-2064 would round to 2060). Following this logic, the first year that rounds to 2060 is 2055, therefore the least number of years from 2023 until we reach a year that rounds to 2060 is 2055 minus 2023, which is 32 years.
What is mZS?
Enter your answer in the box
Next
m∠S = 45°
Solution:
Given ∠R = 3x°, ∠S = 2x°, ∠T = 3x°.
Sum of the angles of a triangle = 180°
⇒ m∠R + m∠T + m∠S = 180°
⇒ 3x° + 3x° + 2x° = 180°
Adding all the angles.
⇒ 8x° = 180°
Divide both sides of the equation by 8, we get
⇒ x° = 22.5°
Substitute x = 22.5° in m∠S.
⇒ m∠S = 2 × 22.5°
⇒ m∠S = 45°
Hence, m∠S = 45°.
What is 7,014,999,999 rounded to the nearest hundred thousand?
I need the help in fast
Answer:
Step-by-step explanation:
7,014,999,999 rounded to the nearest hundred thousand
7,015,000,000 <===
80Points!
will give brainliest, ratings, etc
and after you answer this
if you could be so kind as to aswer my last question that would mean the world!
its has 30points on it!
The information given represents lengths of sides of a right triangle with c the hypotenuse.
Find the correct missing length to the nearest hundredth.
a = ?, b = 11, c = 17
can you please help me find the length of A?
Using Pythagorean theorem
[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \sf\longmapsto P^2=17^2-11^2[/tex]
[tex]\\ \sf\longmapsto P^2=289-121[/tex]
[tex]\\ \sf\longmapsto P^2=168[/tex]
[tex]\\ \sf\longmapsto P\approx 13[/tex]
Answer:
H=17B=11P=?Using Pythagorean theorem
Step-by-step explanation:
the 2619 women students on a campus constitute 54% of the entire student body. what is the total enrollment of the college?
Answer:
4850 students
Step-by-step explanation:
if 2619 women make up 54% of the entire student body, then we know that 0.54x=2619, since 54%=0.54 and we can call x the entire student body. solve:
0.54x=2619
÷0.54 ÷0.54
x=4850
henceforth, the total enrollment is 4850 students.
hope this is helpful!
Answer:
4850 students
Step-by-step explanation:
Let b = total enrollment.
Then 54% of b = 2619. Find b by dividing both sides of
0.54b = 2619 by 0.54:
b = 4850
The total enrollment is 4850.
The ellipse with x-intercepts (2, 0) and (-2, 0); y-intercepts (0, 4) and (0, -4).
Answer:
[tex]\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]
Step-by-step explanation:
If the ellipse has its x-intercepts at points (2, 0) and (-2, 0) and y-intercepts at points (0, 4) and (0, -4), then its symmetric across the y-axis and across the x-axis.
Moreover,
[tex]a=2\\ \\b=4[/tex]
The equation of such ellipse is
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
Hence, the equation of the ellipse is
[tex]\dfrac{x^2}{2^2}+\dfrac{y^2}{4^2}=1\\ \\ \\\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]