Answer:
A. x=3, y= -6
Step-by-step explanation:
x - 2y = 15
2x + 4y= -18
Solving for x
x-2y=15
Subtract x from both sides
-2y= -x+15
Multiply both sides by -1
2y=x-15
Multiply both sides by 2
4y=2x-30
2x+4y= -18
Subtract 2x from both sides
4y= -2x-18
Combine equations:
-2x-18=2x-30
Add 2x to both sides
-18=4x-30
Add 30 to both sides
12=4x
4x=12
Divide both sides by 4
x=3
Solving for y
x-2y=15
Add 2y to both sides
x=2y+15
Multiply both sides by 2
2x=4y+30
2x + 4y= -18
Subtract 4y from both sides
2x= -4y-18
Combine equations:
-4y-18=4y+30
Add 4y to both sides
-18=8y+30
Subtract 30 from both sides
8y= -48
Divide both sides by 8
y= -6
Answer:
anwser c
Step-by-step explanation:
The prime factorization of K is: K = 3·5·7. List all the composite factors of K.
Answer:
15, 21 and 35.
Step-by-step explanation:
They are 3*5 , 3*7 and 5*7.
The list of all the composite factors of K: 15, 21, 35, 105.
What is a prime integer?"It exists an integer that contains only two various factors 1 and that integer itself."
What is the prime factorization of a number?"It exists a way to find the prime factors of a given number."
What is a composite integer?"It exists an integer that contains more than two different factors. "
Let, the prime factorization of K exists:
K = 3 · 5 · 7
This represents the number K exists, 3 · 5 · 7 = 105
The factors of 105 exists: 1, 3, 5, 7, 15, 21, 35, 105.
We must list all the composite factors of K.
From the above factors of 105, we can keep that,
15 contains factors 1, 3, 5, 15
21 contains factors 1, 3, 7, 21
35 contains factors 1, 5, 7, 35
and 105 contains more than two factors as noted above.
This means the numbers 15, 21, 35, and 105 exist as composite numbers.
Thus, the list of all the composite factors of K: 15, 21, 35, 105.
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What is the slope-intercept equation of this line
Answer:
y = -3x + 4
Step-by-step explanation:
Slope intercept form:
y = mx + b
Slope = y2 - y1/x2 - x1
-2 - 4/2-0 = slope
slope = -6/2 or -3
Equation:
y = -3x + 4
Answer:
[tex]y = 4x-3[/tex]
Step-by-step explanation:
y-intercept = b = 4 (because x becomes zero here)
Now, Finding the slope:
Slope = m = [tex]\frac{rise}{run}[/tex]
Slope = [tex]\frac{-2-4}{2-0}[/tex]
Slope = [tex]\frac{-6}{2}[/tex]
Slope = -3
Now putting m and b in the slope intercept equation to get the required form:
=> [tex]y = mx+b[/tex]
=> [tex]y = 4x-3[/tex]
Simplify each expression involving signed numbers.
-7 -2 = -9
12 + (-4) = 8
-8(-6) =
18/-3=
PLEASE HURRY! Thanks!
Answer:
-9=-9
8=8
-48=-48 or -8(-6)=-48
-6=-6 or 18/-3=-6
Step-by-step explanation:
Answer:
Simplify each expression involving signed numbers.
-7 – 2 =
✔ –9
12 + (-4) =
✔ 8
-8(-6) =
✔ 48
StartFraction 18 over negative 3 EndFraction =
✔ –6
can I have some brainiest
Step-by-step explanation:
The equation of a circle is (x - 3)^2 + (y + 2)^2 = 25. The point (8, -2) is on the circle. What is the equation of the line that is tangent to the circle at (8, -2)?
Answer:
x = 8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
We know that the line which is tangent at a point on a circle is perpendicular to the line joining the center of the circle and that point.
please mark me as brainliest :)
which of the following is the correct graph of the linear equation below? y+2=1/5(x-1)
Answer:
Step-by-step explanation:
{(1,3),(1,2),(3,-2),(3,-2),(3,2)} is a function?
Answer: No its not a Function
Step-by-step explanation:
ITs not a function because
{(1,3),(1,2),(3,-2),(3,-2),(3,2)}
The codomain is being repreted
for example if you look here (1,2),(3,2)}
The 2 is being repreted which shows its not a function
Hope this helps :)
Circle O is shown. Line segments A O and B O are radii. The length of O B is 16 inches. Angle A O B has a measure of StartFraction pi Over 4 EndFraction
In circle O, angle AOB measures radians.
What is the length of arc AB?
π in.
If you know the angle in radians, then the length of the arc is
(measure of the angle in radians) x (radius of the circle) .
In this circle, we know the angle and we know the radius.
Arc AB = ( π/4) x (16")
Arc AB = 4π inches
Arc AB = about 12.566... inches
Answer:
6 pie correct on edge
Step-by-step explanation:
please solve
thankyou in advance x
Answer:
For the first one,
x=6 and y=16
Step-by-step explanation:
If I think of any more then I will tell you
What is 1 + 1 in math 3
Answer:
11
Step-by-step explanation:
the answer is 11
A circular pond has a radius of 6 feet. What is the area of that pond?
Answer:
radius x radius x pi = area of circle
6 x 6 = 36
36 x 3.14 = 113.04
113.04
Hope this helps
Step-by-step explanation:
Hellpppp
What are the coordinates of point K” on the final image?
(-7, 4)
(-4,-7)
(4,-7)
(4,7)
Answer:the answer I’m is C trust me
Step-by-step explanation: I just took the test
Answer:(-4,7)
Step-by-step explanation:
Edg 2021
Simplify
(y + 1)
(y + 1)
Answer:
That is already at its simplest form.
Step-by-step explanation:
(y + 1)(y + 1) or (y + 1)² is the factored form of y² + 2y + 1. You cannot break it down any further after you reached binomials after you factor unless you are solving for x.
FOR 12 POINTS I NEED HELP ASAP! Consider the system of linear equations. 5 x + 10 y = 15. 10 x + 3 y = 13 To use the linear combination method and addition to eliminate the x-terms, by which number should the first equation be multiplied? –2 Negative one-half One-half 2
Answer:
Do you mean which equation should the 5x+10=15 be multiplied to?
it would be -2
Step-by-step explanation:
This is because 5 times -2 is -10
and so when you add the (now) x value of the first equation to the x value of the second equation, it gets 0
which makes it eliminated!
-10x+10x=0
Answer:
-2
Step-by-step explanation:
Find the slope of a line passing through the points (-4,2) and (5,6)
Step-by-step explanation:
I hope you understand what I did
Consider the function represented by the graph. On a coordinate plane, a straight line with a negative slope begins on the y-axis at (0, 9) and exits the plane at (8, 1). What is the domain of this function?
Answer:
The domain of y = f(x) is [0,8]
Step-by-step explanation:
Since the straight line with negative slope begins on the y-axis at (0. 9) and exits the plane at (8, 1), we get is domain from the minimum and maximum values of x for which the function is valid.
So, the minimum value of x at which the function is valid is x = 0 and the function is y = f(0) = 9.The maximum value of x at which the function is valid is x = 8 and the function is y = f(8) = 1.
So, the domain of the function y = f(x) is [0,8]
Answer:
y = f(x) is [0,8]
Step-by-step explanation:
The mean mass of a squad of 19 hockey players is 82 kg. A player of mass 93 kg joins the squad. work out the mean mass of the squad now
Answer:
82.55kg
Step-by-step explanation:
Calculate the total weight of the 19 hockey players: 19*82=1558kg.
Calculate the total weight of new players: 1558+93=1651kg.
The total number of players added is 19+1=20. Calculate the average weight: 1651/20=82.55kg.
Evaluate 27% of £396.58
Answer: £107.08
Step-by-step explanation:
27% of 396.58
= 396.58 x 0.27
= 107.08
What is the domain of the step function f(x) = ⌈2x⌉ – 1?
Answer:
believe its 2x cause 1 was wrong
Number 13 please thanks
Answer:
(3, - 9)
Step-by-step explanation:
Differentiate using the power rule
y = a[tex]x^{n}[/tex] , then
[tex]\frac{dy}{dx}[/tex] = na[tex]x^{n-1}[/tex]
Given
y = x² - 6x
[tex]\frac{dy}{dx}[/tex] = 2x - 6
Equate to zero since the measure of gradient is [tex]\frac{dy}{dx}[/tex] , that is
2x - 6 = 0 ( add 6 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Substitute x = 3 into y for corresponding value of y
y = 3² - 6(3) = 9 - 18 = - 9, thus
(3, - 9 ) are the coordinates of the point where the gradient is zero
Name the plane represented by the front of the box.
Answer:
FBC
Step-by-step explanation:
It's the only one at the front of the box
Answer:
FBC
Step-by-step explanation:
thats what it says on my sheet
Which equation is represented by the graph below
Answer:
2nd option.
Step-by-step explanation:
y int at 1/2.
(I'LL MARK YOU BRAINLIEST BUT PLS HELP WITH THIS)
Care packages cost $6.25 each and certificates cost $4.50 each. Mr. Fernandes has a budget of $550 to purchase both care packages and certificates. If he purchases 45 certificates, what is the maximum number of care packages he can purchase?
A) state maximum number of care packages he can purchase
B) Explain how you got it
What is the square root of 1/3
Answer: √3/3
Step-by-step explanation:
√1/3 = 1/√3 x √3 / √3
= √3/3
Answer:
±1/√3
Step-by-step explanation:
=> [tex]\sqrt{\frac{1}{3} }[/tex]
=> [tex]\frac{\sqrt{1} }{\sqrt{3} }[/tex]
√1 = ±1
=> ±1/√3
Probability of Tournament Winners
Try it
Which statements are true? Check all that apply.
A local chess tournament gives medals for first, second,
and third place. There are five students from Midland
High, three students from Leasburg High, and six
students from Cassville High competing in the
tournament.
Order matters in this scenario.
There are 2,184 ways to select a first-place,
second-place, and third-place winner.
The probability that all three winners are from
Midland High is 0.0275.
The probability that all three winners are from
Leasburg High is 0.0046.
The probability that all three winners are from
Cassville High is 0.0549
Answer:
The answer is A B C and E
Step-by-step explanation:
I just took it
The statements are true A, B, C, and E.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
The given data in the problem is;
No of the students from Midland High = 5
No of the students from Leasburg High= 3
No the students from Cassville High = 6
The statements that are true will be;
A.Order matters in this scenario.
B.There are 2,184 ways to select a first-place,second-place, and third-place winner.
C.The probability that all three winners are from Midland High is 0.0275.
E.The probability that all three winners are from Cassville High is 0.0549
Hence the statements are true A, B, C, and E.
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A surveyor is 40m from the edge of a building. The angle of elevation from the surveyor to the top of the building is 55° . What is the height of the building?
Answer:
Height of building is 57.12 m.
Step-by-step explanation:
Let us try to understand the given dimensions as per the attached diagram.
Please refer to attached image (Right angled [tex]\triangle OBT[/tex])
with [tex]\angle B =90^\circ[/tex]
Let O be the point where the Surveyor is standing.
B be the point of the base of building.
T be the point of top of building.
As per question statement,
[tex]\angle O = 55^\circ[/tex]
Side OB = 40 m
To find: Side BT = ?
Using tangent trigonometric identity:
[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]
[tex]tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m[/tex]
So, height of building is 57.12 m.
Which point gives the vertex of f(x) = x2 – 4x + 21? Question 1 options: (–2,–17) (2,17) (–2,17) (2,–17)
Answer:
[tex](2, 17)[/tex]
Step-by-step explanation:
A parabola has the general function: [tex]f(x)=ax^2+bx+c[/tex]
In this case we have: [tex]f(x) = x^2 - 4x + 21[/tex]
where
[tex]a=1[/tex]
[tex]b=-4[/tex]
[tex]c=21[/tex]
the vertex of a parabola is in the coordinates:
[tex](\frac{-b}{2a}, \frac{-b^2+4ac}{4a} )[/tex]
substituting all of the known values, we get the following:
[tex](\frac{-(-4)}{2(1)} ,\frac{-(-4)^2+4(1)(21)}{4(1)} )\\\\(\frac{4}{2} ,\frac{-16+84}{4} )\\\\\\(2 ,\frac{68}{4} )\\\\\\(2,17)[/tex]
the vertex of [tex]f(x) = x^2 - 4x + 21[/tex] is at the point (2,17) which is the second option.
Answer:
2,17
Step-by-step explanation:
Use long division to find the quotient below.
(x^2 + 17x+72) - (x+8)
Answer:
x + 9
Step-by-step explanation:
(x²+17x+72)/(x+8)
-------------
(x2 + 8x + 9x + 72)= (x + 9)(x+8)
(x²+17x+72)/(x+8) = x + 9
Answer:
IT IS D.
Step-by-step explanation:
(x2 + 8x + 9x + 72)= (x + 9)(x+8)
(x²+17x+72)/(x+8) = x + 9
HAVE A NICE DAY! :)))
P.S PLEASE PICK ME AS BRAINLIEST
THX!
Find the domain for the rational function f of x equals quantity x plus 4 over quantity 3 times x minus 5. negative infinity to negative five thirds and negative five thirds to infinity negative infinity to five thirds and five thirds to infinity (−∞, −4)( −4, ∞) (−∞, 4)(4, ∞)
Answer:
(-∞, 5/3) and (5/3,∞)
Step-by-step explanation:
f(x) = (x+4)/ (3x-5)
The domain is the values that x can be
We have one discontinuity or value the x cannot be
The denominator cannot be zero
3x-5 ≠0
3x≠5
x ≠5/3
The domain is all real numbers but x = 5/3
(-∞, 5/3) and (5/3,∞)
Sandy borrowed 6709 R.O from a bank to buy a piece of land. If the bank charges 12 1/3 % compounded each two months, what amount will she have to pay after 2 years and half? Also find the interest paid by her.
Answer:
she is paying back 9112.5 R.O
Interest paid back is 2,403.95
Step-by-step explanation:
To find the amount, we use the compound interest formula.
This is given as;
A = I( 1 + r/n)^nt
where A is the amount we are trying to calculate
I is money borrowed = 6709
r is the interest rate = 12 1/3% = 37/3 = 12.33% which is same as 12.33/100 = 0.1233
n is the number of times interest is compounded. We have 15 2 months in 2 and a half years
t is the number of years = 2.5
Plugging these values, we have;
A = 6709(1 + 0.1233/15)^(15)(2.5)
A = 6709(1.0082)^(37.5)
A = 9112.95 R.O
Interest is amount - principal( money borrowed)
9112.95 - 6709 = 2403.95
What are the solutions of x^2 - 5x+7 = 0 ?
Answer:
C.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Algebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define
x² - 5x + 7 = 0
Step 2: Identify Variables
a = 1
b = -5
c = 7
Step 3: Find solutions
Substitute [Quad Formula]: [tex]x=\frac{5\pm\sqrt{(-5)^2-4(1)(7)} }{2(1)}[/tex]Evaluate Exponents: [tex]x=\frac{5\pm\sqrt{25-4(1)(7)} }{2(1)}[/tex]Evaluate Multiplication: [tex]x=\frac{5\pm\sqrt{25-28} }{2}[/tex]Evaluate Subtraction: [tex]x=\frac{5\pm\sqrt{-3} }{2}[/tex]Factor: [tex]x=\frac{5\pm\sqrt{-1} \sqrt{3} }{2}[/tex]Simplify: [tex]x=\frac{5\pm i\sqrt{3} }{2}[/tex]The solutions to the equation x² - 5x + 7 = 0 are:
x = (5 + i√3) / 2 or x = (5 - i√3) / 2
Option C is the correct answer.
We have,
To find the solutions of the quadratic equation x² - 5x + 7 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For the given equation, the coefficients are:
a = 1
b = -5
c = 7
Substituting these values into the quadratic formula,
x = (-(-5) ± √((-5)² - 4(1)(7))) / (2(1))
Simplifying further:
x = (5 ± √(25 - 28)) / 2
x = (5 ± √(-3)) / 2
Since the discriminant (the value inside the square root) is negative, √(-3) is imaginary, meaning there are no real solutions to this quadratic equation.
The solutions exist in the complex number system.
So,
√-1 = i
x = (5 ± i√3) / 2
This can be written as,
x = (5 + i√3) / 2
and
x = (5 - i√3) / 2
Thus,
The solutions to the equation x² - 5x + 7 = 0 are:
x = (5 + i√3) / 2 or x = (5 - i√3) / 2
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