Answer:
x=a²+ab+b²/a+b , y=-ab/a+b
Step-by-step explanation:
The system of the given equation may b written as:
ax+by-a²=0
bx+ay-b²=0
Here,
a1=a,b1=b,c1= -a²
a2=b,b2=a and c2= -b²
By cross multiplication we get
x/b*(-b²)-(-a²)*a = -y/a*(-b²)-(-a²)*b = 1/a*a-b*b
x/-b³+a³ = -y/-ab²+a²b = 1/a²-b²
Now
x/-b³+a³ = 1/a²-b²
x=a³-b³/a²-b²
x=(a-b)(a²+ab+b²)/(a-b)(a+b)
x=a²+ab+b²/a+b
And,
-y/-ab²+a²b = 1/a²-b²
-y=a²b -ab²/a²-b²
y=ab²-a²b/a²-b²
y=ab(b-a)/(a-b)(a+b)
y= -ab(a-b)/(a-b)(a+b)
y= -ab/a+b
Hence x=a²+ab+b²/a+b , y=-ab/a+b....
A triangular flag has an area of 493 square meters and a height of 17 meters. What is the length of the base
Answer:
58 meters
Step-by-step explanation:
We are looking for the length of the base of a triangle, given the height and area. The formula for the area of a triangle
A=1/2 bh
relates A= the area, b= length of the base, and h= the height of a triangle, so this is the formula we should use.
We are given that the area of the triangle is A=493 and the height h=17. Substitute this information into the formula and solve for b to find
A=493
493=1/2⋅b⋅17
493=17/2b
58=b
The length of the base is 58 meters.
The length of the base of the triangle is 58 meters.
Given,
A triangular flag has an area of 493 square meters and a height of 17 meters.
We need to find what is the length of the base.
What is the area of a triangle?The area is given by:
= 1/2 x base x height
Find the area of the triangle.
Area = 493 square meters
Height = 17 meters
Area = 1/2 x base x height
493 square meters = 1/2 x base x 17 meters
Multiply 2 on both sides.
2 x 493 = 2 x 1/2 x base x 17
986 = base x 17
Dividing both sides by 17.
986 / 17 = base
Base = 58 meters.
Thus the length of the base of the triangle is 58 meters.
Learn more about finding the dimensions of triangles here:
https://brainly.com/question/15484541?referrer=searchResults
#SPJ2
Create a dot plot for the data in the table. Hover over each number on the number line. Then click
and drag up to create the dots.
To create a dot plot, you draw a number line from the smallest to the largest value in your dataset. Then, for each number in the dataset, mark a dot above the corresponding number on the line. If a number occurs more than once, stack the dots.
Explanation:Creating a dot plot for a set of data on a number line involves the following steps:
identify the lowest and the highest values in your dataset. These values will define the extents of your number line.Create the number line starting from the smallest value to the largest value.For each number in the dataset, place a dot above the corresponding number on the number line. If a number occurs more than once, you stack the dots vertically.Unfortunately, as this is a text-based platform, it's impossible to hover over the numbers and drag to create a dot plot interactively. This instruction seems to be meant for a specific interactive software or online tool.
Learn more about Dot Plot here:https://brainly.com/question/22746300
#SPJ12
The mean monthly rent of students at Oxnard University is $890 with a standard deviation of $206. John's rent is $1,395. What is his standardized z-score?
Answer:
$299
Step-by-step explanation:
Rent+standard deviation 890+206= $1,096
John's rent: $1,395
Z-score: 1395 - 1096=$299
Answer: 2.4515
Step-by-step explanation:
Given : The mean monthly rent of students at Oxnard University is [tex]\mu=\$890[/tex] with a standard deviation of [tex]\sigma=\$206[/tex]
Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex], we have the standardized z-value for x= 1395 as
[tex]z=\dfrac{1395-890}{206}=2.45145631068\approx2.4515\ \text{ [To the nearest four decimal places.]}[/tex]
Hence, the standardized z-score = 2.4515
Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
[tex]\sqrt{x-2}[/tex] + 8 = x
Answer:
(17+√553)/2
and
(17-√553)/2
Step-by-step explanation:
Subtract 8 from both sides. This leaves you with
sqrt(x-2) = x-8. Square both sides to get rid of the sqrt,
leaving x-2=(x-8)^2
expanding gives x-2=x^2-16x+64
subtract x from both sides leaves
-2=x^2-17x+64
add 2 to both sides
x^2-17x+66=0
this cannot be factored, however, there are other techniques.
Completing the square is a bit annoying, so I will use the quadratic formula, to give the answer.
This gives you:
(17+√553)/2
and
(17-√553)/2
Hope this helps!
Find the product.
(n 3)2 · (n 5)4
For this case we must find the product of the following expression:
[tex](n ^ 3) ^ 2 * (n ^ 5) ^ 4[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Rewriting the expression we have:
[tex]n ^ 6 * n ^ {20} =[/tex]
By definition of multiplication of powers of the same base, we put the same base and add the exponents:
[tex]n^{6 + 20} =\\n^{26}[/tex]
Answer:
[tex]n^{26}[/tex]
Answer:
n^26
Step-by-step explanation:
Let f(x) = x2 − 8x + 5. Find f(−1). (1 point) −3 14 −4 13
Answer:
f(- 1) = 14
Step-by-step explanation:
To evaluate f(- 1) substitute x = - 1 into f(x)
f(- 1) = (- 1)² - 8(- 1) + 5 = 1 + 8 + 5 = 14
Answer:
f(-1)=14
14-4=25
13=70
Step-by-step explanation:
Which statements are true ? Check all that apply ?
Answer: answers 1 and 5 are correct.
Reginald is distributing n boxes of paper to the copy rooms in an office building. If he places 6 boxes of paper in each copy room, there are 7 boxes left over. In order to place 7 boxes of paper in each room, he will need 2 more boxes. How many copy rooms are in the office building?
Answer:
The total number of copy rooms in the building is 9.
Step-by-step explanation:
With the given information we can compute the total number of copy rooms (let's call them r) and the boxes of paper Reginald has to distribute among them (already named n).
From the first arrangement we can see that if reginald gives 6 boxes of paper to each room, he will still have 7 boxes. We can write this as:
[tex]n = 6 \cdot r + 7[/tex]
From the second arrangement we can see that if reginald gives 7 boxes of paper to each room, he would still need 2 boxes. We can write this as:
[tex]n = 7 \cdot r - 2[/tex]
From the above, we have a 2x2 system of equations, which can be solved by any method. In this case, we can use equalization to easily find the number of rooms. From the 2 relations we can write:
[tex]6 \cdot r + 7 = 7 \cdot r - 2[/tex]
Puting known and unknowns on opposite sides, we get:
[tex]7+2 = (7-6) \cdot r [/tex]
Solving we get:
[tex]9 = r[/tex]
Therefor the total number of rooms is 9.
Pluging this solution into any of the 2 equations, we can obtain that the number of boxes of paper is 61.
As a reference, the following link is useful:
https://en.wikipedia.org/wiki/System_of_linear_equations
The number of boxes of paper exists at 61.
How to find the copy rooms in the office building?The whole number of copy rooms as r and the boxes of paper Reginald has to distribute among them (already named [tex]$\mathbf{n}$[/tex] ).
Reginald gives 6 boxes of paper to each room, he will always have 7 boxes. We can write this as:
[tex]$n=6 \cdot r+7$$[/tex]
Reginald shows 7 boxes of paper to each room, he would always require 2 boxes. We can write this as:
[tex]$n=7 \cdot r-2$$[/tex]
From the above equation, we have a [tex]$2 \times 2$[/tex] system of equations, which can be solved in any form. In this issue, we can utilize equalization to easily find the number of rooms.
From the 2 relations we can write:
[tex]$6 \cdot r+7=7 \cdot r-2$[/tex]
Putting known and unknowns on opposite sides, we get:
[tex]$7+2=(7-6) \cdot r$$[/tex]
Solving we get:
[tex]$9=r$$[/tex]
Thus the total number of rooms exists at 9.
Plugging this solution into any of the 2 equations, then we get
The number of boxes of paper exists at 61.
To learn more about the system of linear equations
https://brainly.com/question/960662
#SPJ2
A window is being replaced with tinted glass. The plan below shows the design of the window. Each unit length represents 1 foot. The glass costs $26 per square foot. How much will it cost to replace the glass? Use 3.14 for π.
g790432
The cost to replace the glass of the window is $
Answer:
Step-by-step explanation:
Okay first if each unit length is 1 ft then you need to find out what the total cost would be. Then use 3.14 and find the total area of £
Fractions and decimals order least to greatest 1 3/4, 2.3, 2/5, 1.6
Answer: 2.3, 1 3/4, 1.6, 2/5
Step-by-step explanation: Convert each fraction into a decimal (or vise versa), then order.
1 3/4 = 1.75
2/5 = 0.4
Answer:
Answer is 2/5, 1 3/4, 1.6, 2.3
Step-by-step explanation:
Lets see: 1 3/4 = 7/4
2.3 = 23/10 or 2 3/10
2/5 is 2/5
and
1.6 is 8/5
so the least is 2/5, 1 3/4, 1.6, 2.3
Hope my answer has helped you in any way!
Cylinder A has a radius of 1 m and a height of 4 m. Cylinder B has a radius of 2 m and a height of 4 m. What is the ratio of the volume of cylinder A to the volume of cylinder B?
a: 5:6
b: 1:4
c: 1:2
d: 1:1
Note: The volume of a cylinder is:
radius² × π × height
First lets work out the volume of Cylinder A:
Volume = 1² × π × 4
= 4π m³
Now lets work out the volume of Cylinder B
Volume = 2² × π × 4
= 16π m³
__________________________________________
Now lets compare the volumes ( Cylinder A : Cylinder B) :
4π : 16π
Lets simplify this by dividing both sides by 4π:
4π : 16π ( ÷ 4π)
----> 1 : 4
_____________________________________________________
Answer:
Option b) 1 : 4
Answer:
1:4
Step-by-step explanation:
what is the multiplicative rate of change for the exponential function graphed to the left
Looking at the given points on the right side from (0,2) to (1,6) for 1 increase in X ( 1-0=1) the Y value increases by 3 ( 6/2 = 3)
This same increase happens for th other two points: 18/6 = 3
54 / 18 = 3
The rate of increase is 3.
vertical angles must check all that apply
Answer:
Vertical angles must have the same vertex and be congruent as well.
Step-by-step explanation:
Answer:
Correct answer is B and C.
Step-by-step explanation:
Vertical angles are those angles opposite each other when two lines intersect. So, they have the same vertex.
When two lines intercept form 4 angles. Those that are opposite to each other are vertical angles, these angles are always congruent.
HELP PLEASE!!!!!!!!!!!!!!!!! WILL GIVE BRAINLIEST!!! 6TH GRADE MATH
Which of the sets of ordered pairs represents a function?
A = {(–5, 5), (–2, 2), (2, –2), (5, –5)}
B = {(4, 2), (3, –2), (9, 4), (11, –3)} (4 points)
Only A
Only B
Both A and B
Neither A nor B
Answer:
The answer is both a and b
Answer:
both a and b is correct
How is the equation of this circle written in standard form?
x2 + y2 - 6x + 14y = 142
A)
(x - 3)2 + (y + 7)2 = 200
B)
(x+ 3)2 + (y - 7)2 = 200
(x - 6)2 + (y + 14)2 = 142
D)
(x+6)2 + (y- 14)2 = 142
Answer:
A
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
To obtain this form use the method of completing the square.
Given
x² + y² - 6x + 14y = 142
Collect the x and y terms together
x² - 6x + y² + 14y = 142
add (half the coefficient of both x and y terms )² to both sides
x² + 2(- 3)x + 9 + y² + 2(7)y + 49 = 142 + 9 + 49
(x - 3)² + (y + 7)² = 200 → A
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
Answer:
5/12
Step-by-step explanation:
First find the probability on the first roll
The possible results are 1,2,3,4,5,6
evens: 2,4,6
not 2 = 1,3,4,5,6
P(even)= number of evens/total = 3/6 = 1/2
P (not 2) = number of results not 2/ total = 5/6
Since the rolls are independent (do not depend on each other), we can multiply the probabilities
P(even, then not 2) = 1/2 * 5/6 = 5/12
The graph of which function will have a maximum and a y-intercept of 4?
0 fx) = 4x + 6x-1
f(x) = -4x2 + 8x + 5
f(x) ==x2 + 2x + 4
0 f(x)= x2 + 4x-4
Answer:
f(x) = -x² + 2x + 4Step-by-step explanation:
We have quadratic functions f(x) = ax² + bx + c.
c - y-intercept
If a > 0, then a parabola opens up and has a minimum in a vertex.
If a < 0, then a parabola opens down and has a maximum in a vertex.
The function has maximum and y-intercept of 4:
a < 0 and c = 4
The graph of the function which will have a maximum and a y-intercept of 4 is C. f(x) = x² + 2x + 4.
What is y Intercept?y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.
Given are four functions.
We have to find the function which has a y intercept of 4.
This means that substitute x = 0 and then find the value of f(x).
A. f(x) = 4x² + 6x - 1
When x = 0, f(x) = -1 ≠ 4
B. f(x) = -4x² + 8x - 5
When x = 0, f(x) = -5 ≠ 4
C. f(x) = x² + 2x + 4
When x = 0, f(x) = 4
D. f(x) = x² + 4x - 4
When x = 0, f(x) = -4
Hence the function which has a y intercept of 4 is C. f(x) = x² + 2x + 4.
Learn more about y intercepts here :
https://brainly.com/question/14192363
#SPJ7
The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds, how far is the ball off the ground? 30 meters 40 meters 50 meters 60 meters
Answer:
Answer is 50 meters
Step-by-step explanation:
Solution:
Height of the building (h)= 90 meters.
Time taken by the ball to reach the ground (t) = 3 seconds
According to the statement;
h = kt²
90=k(3)²
90=k(9)
90=9k
Divide both the sides by 9
k=10
h=kt²
Put the value time (t)=2 in the equation
h=10(2)²
h=10(4)
h=40 meters
Distance from the ground = 90 - 40
=50 meters.
Thus the correct option is 50 meters....
Answer:
The answer is A) 50 meters
Step-by-step explanation:
tell whether the graph of the equation is a horizontal or a vertical line. Explain your choice.
y=-1
Answer:
horizontal line
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through.
The equation of a vertical line parallel to the y- axis is
x = c
where c is the value of the x- coordinates the line passes through.
Hence
y = - 1 is a horizontal line passing through all points with a y- coordinate - 1
Ghlj and gstu are both parallelograms why is angle L= angle T
Answer: By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Step-by-step explanation: This is the sample response on Edge.
Both parallelograms are <L ≅ < T
Because, by the parallelogram angle theorem, opposite angles of a parallelogram are congruent.
Given parallelograms, GHLJ and GSTU such the parallelogram GSTU is inscribed inside parallelogram GHLJ with angle G coinciding on the two parallelograms.
Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Therefore, ∠L ≅ ∠T
The parallelogramA parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. The Sum of adjacent angles of a parallelogram is equal to 180 degrees.
Parallelograms are shapes that have four sides with two pairs of sides that are parallel. The four shapes that meet the requirements of a parallelogram are square, rectangle, rhombus, and rhomboid.
Four types of parallelogramsRectangles, rhombus, and squares are parallelograms. A trapezoid has at least one pair of parallel sides. The parallel sides are called the bases and the non-parallel sides are called the legs. There are three types of trapezoid - isosceles, right-angled, and scalene trapezoids.
To learn more about the parallelogram, refer
https://brainly.com/question/970600
#SPJ2
the number line below represents the solution to which inequality?
<--|--|--|--|--|--O--|--|--|--|--|--|--|--|--|-->
__ -6__-4__-2 __0 __2 __4 __6
(Filled circle)
(Arrow pointing left from -2)
F. -2x + 7 > 8
_
G. 7x + 11 < 4
_
H. 6x - 9 < -21
_
J. -3x -15 < -27
_
The number line represents the solution to the inequality -2x + 7 > 8, and the solution is x < -0.5.
Explanation:The filled circle and the arrow pointing left on the number line indicate that the solution to the inequality is to the left of -2.
The inequality that represents this solution is -2x + 7 > 8.
To solve this inequality, we can subtract 7 from both sides to isolate the x variable.
This gives us -2x > 1. Finally, we divide both sides of the inequality by -2, remembering that when we divide by a negative number, the inequality sign flips.
So, the solution to the inequality is x < -0.5.
Thus, Correct option for the given number line is F. -2x + 7 > 8.
Final answer:
The number line indicates the solution to the inequality H. 6x - 9 < -21, where x < -2, including -2 (since the circle is filled). The solution matches the given number line plot.
Explanation:
The number line given indicates the solution to an inequality that includes all numbers to the left of – the filled circle on –2, which means –2 is included in the solution set. This represents an inequality that is of the form x ≤ a where a is –2 in this case. Now let's analyze each of the provided inequalities.
F. -2x + 7 > 8: Solving this we get –x > 1 or x < –1, which does not match the plot.
G. 7x + 11 < 4: Solving this inequality we get x < –1, which also is not a match.
H. 6x - 9 < -21: Resolving this inequality leads to x < –2, which matches the number line.
J. -3x - 15 < -27: Solving this we get x > 4, which is incorrect as per the number line plot.
Therefore, the correct inequality is H. 6x - 9 < -21.
For f (x) = 3x +1 and g(x) = x^2-6, find (g/f)(x)
Answer:
[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]
Step-by-step explanation:
We have the following functions
[tex]f (x) = 3x+1[/tex]
[tex]g (x) = x^2-6[/tex]
To find [tex](g/f)(x)[/tex] we must divide the function g(x) with the function f(x)
Then we perform the following operation
[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]
Finally we have that:
[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]
For [tex]x \neq -\frac{1}{3}[/tex]
The equation 3x2 = 6x - 9 has two real solutions
True
False
Answer: FALSE
Step-by-step explanation:
The first step is to rewrite the equation in the form [tex]ax^2+bx+c=0[/tex], then:
[tex]3x^2 = 6x - 9\\3x^2-6x +9=0[/tex]
Now, we need to calculate the Discriminant with this formula:
[tex]D=b^2-4ac[/tex]
We can identify in the given equation that:
[tex]a=3\\b=-6\\c=9[/tex]
Then, we only need to substitute these values into the formula:
[tex]D=(-6)^2-4(3)(9)[/tex]
[tex]D=-72[/tex]
Since [tex]D<0[/tex] then the equation has no real solutions.
Which graph is the right graph
Answer:
x^2 +8x+16
Step-by-step explanation
Since you didn,t include the picture of the graph, I can still solve the equation for you
f(x+4)=(x+4)^2
=x^2 +8x+16
Find the corresponding graph in your exercise
Answer:
Im not sure what the option chocies are but I graphed both graphs online for you! :)
RACTICL
n set
1. How much interest is earned in 9 months on a deposit of
$7000 at 8 percent simple interest?
Answer:
$420
Step-by-step explanation:
Principal = $7000
Rate = 8%
Time = 9 months
9 months = 3/4 or 0.75 of a year
Simple Interest = Principal * Rate * Time ÷ 100
= $7000 * 8% * 0.75 ÷ 100
= $420
Can someone please help me
Answer:
x < -7Step-by-step explanation:
<, ≤ - line to the left
>, ≥ - line to the right
<, > - open circle
≤, ≥ - closed circle
==================================
We have the line to the left and open circle.
The circle is on -7.
Therefore is x < -7
Following Quotient expression
Answer:
Second choice
and the last 2 choices
Step-by-step explanation:
32m/16m=2 and our constant is 3 not 2 so not choice A
4m^2/2m=2m so possible 6m/2m=3 so choice B
4m/2m=2 and our constant is 3 not 2 so not choice C
10m/5m=2 same reason as A and C
10m^2/5m=2m possible...15m/5m=3 so choice E
32m^2/16m=2m and 48m/16m=3 so this last choice too
Someone please help
Answer:
[tex]\large\boxed{6\sqrt[5]{x^2y}=6x^\frac{2}{5}y^\frac{1}{5}}[/tex]
Step-by-step explanation:
[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\6\sqrt[5]{x^2y}=(6)(\sqrt[5]{x^2})(\sqrt[5]{y})=6x^\frac{2}{5}y^\frac{1}{5}[/tex]
Solve for x
n(17+ x) = 34z - r
Answer:
[tex]x=\frac{34z-r}{n}-17[/tex]
Step-by-step explanation:
Given
[tex]n(17+x)=34z-r[/tex]
We have to isolate x on one side of the equation
Dividing both sides by n
[tex]\frac{n(17+x)}{n} =\frac{34z}{n}-\frac{r}{n}[/tex]
Taking LCM on left side
[tex]17+x = \frac{34z-r}{n}[/tex]
Subtracting 17 from both sides
[tex]17+x-17 = \frac{34z-r}{n}-17[/tex]
So, the value of x will be:
[tex]x=\frac{34z-r}{n}-17[/tex] ..
The answer is:
[tex]x=\frac{34z-r}{n}-17[/tex]
Why?To solve for "x" , we just need to isolate it from the equation.
So, we are given the equation:
[tex]n(17+x)=34z-r[/tex]
Then, isolating we have:
[tex]n(17+x)=34z-r\\\\17+x=\frac{34z-r}{n}\\\\x=\frac{34z-r}{n}-17[/tex]
Hence, the answer is:
[tex]x=\frac{34z-r}{n}-17[/tex]
Have a nice day!
Solve the inequality
| 2x - 4|>-2
[tex]|2x-4|>-2\\x\in\mathbb{R}[/tex]