Answer:
Step-by-step explanation:
Given x^2 - 16x + 60 = -12
Using the completing the square method to find x;
subtract 60 from both sides
x2 - 16x + 60-60 = -12-60
x2 - 16x = -72
Add square of the half of the coefficient of x to both sides
x2 - 16x + (1/2(-16))² = -72 + (1/2(-16))²
x^2 - 16x +64 = -72+64
(x-8)² = -8
Take the square root of both sides
√(x-8)² = √-8
x - 8 = ±√8i
x = ±√8i+8
x = ±2√2i+8
The solution of the given equation is: [tex]x = 8+\sqrt{-8}[/tex] and [tex]\\x = 8-\sqrt{-8}[/tex].
Given that:
Equation: [tex]x^2 - 16x + 60 = -12[/tex]
Simplify the above equation as:
x² - 16x + 60 = -12
x² - 16x = -12 - 60
x² - 16x = -72
Add 64 to each side of the equation to complete the square.
x² - 16x + 64 = -72 + 64
x² - 16x + 64 = -8
Write x² - 16x + 64 as (x - 8)² since it is a perfect square trinomial.
(x - 8)² = -8
Take the square root of both sides to get the solutions.
[tex]x - 8 = \±\sqrt{-8}\\x = 8\±\sqrt{-8}\\x = 8+\sqrt{-8}\\x = 8-\sqrt{-8}[/tex]
where i is the imaginary unit.
Hence, the value of x are: [tex]x = 8+\sqrt{-8}[/tex] and [tex]\\x = 8-\sqrt{-8}[/tex].
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What is 17x - (217/19) please answer ASAP
Can someone please Help me. ( picture included)
Answer:
The height of the flagpole is 20 feet.
Can somebody Awnser these for me please
Answer:
The 2nd one is no symmetry the 1st one is (reflection) last one rotational only
Step-by-step explanation:
if a2+b2+c2=ab+bc+ca find a+b/b
Answer:
Step-by-step explanation:
a² + b² + c² = ab + bc + ca
On multiplying both sides by “2”, it becomes
2 ( a² + b² + c² ) = 2 ( ab + bc + ca)
2a² + 2b² + 2c² = 2ab + 2bc + 2ca
a² + a² + b² + b² + c² + c² – 2ab – 2bc – 2ca = 0
a² + b² – 2ab + b² + c² – 2bc + c² + a² – 2ca = 0
(a² + b² – 2ab) + (b² + c² – 2bc) + (c² + a² – 2ca) = 0
(a – b)² + (b – c)² + (c – a)² = 0
=> Since the sum of square is zero then each term should be zero
⇒ (a –b)² = 0, (b – c)² = 0, (c – a)² = 0
⇒ (a –b) = 0, (b – c) = 0, (c – a) = 0
⇒ a = b, b = c, c = a
∴ a = b = c.
hence
a+b/b
a+a/a= (since a=b)
2a/a=
a....
convert 56.6 into radical form
Can anyone do this question?
Answer:
its simple 5.90
Step-by-step explanation:
Which expression is equivalent to 5 (h + 9)?
Answer:
5(m+9) = 5m+25
Answer:
5(m+9) = 5m+25
Step-by-step explanation:
durrrrrrrrrrrrrrr
On January 3rd, the Earth is 147,500,000 kilometers away from the Sun. On July 4th, the Earth is 152,500,000 kilometers away from the Sun. The sun has a radius of about 865,000 kilometers.
Could the Earth’s orbit be a circle with some point in the Sun as its center? Explain your reasoning
Answer:
no
Step-by-step explanation:
yes
Select all polynomials that have (x + 2) as a factor.
Choose all answers that apply:
A A(x) = x^3– 3x^2 – 10x
B B(x)= x^3+ 5x^2 + 4x
C C(x)= x^3 – 2x^2 – 13x – 10
D D(x) = x^3– 6x² + 11x- 6
Answer:
A. (x) = x^3– 3x^2 – 10xx) / (x - 5) x (x + 2) YES
B. (x)= x^3+ 5x^2 + 4x / x (x + 1) (x + 4) NO
C. (x)= x^3 – 2x^2 – 13x – 10 x / (x - 5) (x + 1) (x + 2) Yes
D. (x) = x^3– 6x² + 11x- 6 / x = (x - 3) (x - 2) (x - 1) NO
Step-by-step explanation:
The solution is:;
A. (x) = x^3– 3x^2 – 10xx) / (x - 5) x (x + 2)
C. (x)= x^3 – 2x^2 – 13x – 10 x / (x - 5) (x + 1) (x + 2),
are the polynomials that have (x + 2) as a factor.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
3x+2x-5, for example, is a polynomial.
EXPLANATION
We want to find which of the given polynomials has (x + 2) as a factor.
To do this, we have to equate (x + 2) to 0 and solve for x:
(x + 2) = 0
x = -2
Now, substitute that into each of the polynomials. If (x + 2) is a factor of a polynomial, the polynomial will become 0 after the substitution is made.
A. (x) = x^3– 3x^2 – 10xx) / (x - 5) x (x + 2) YES
B. (x)= x^3+ 5x^2 + 4x / x (x + 1) (x + 4) NO
C. (x)= x^3 – 2x^2 – 13x – 10 x / (x - 5) (x + 1) (x + 2) Yes
D. (x) = x^3– 6x² + 11x- 6 / x = (x - 3) (x - 2) (x - 1) NO
Hence, The solution is:;
A. (x) = x^3– 3x^2 – 10xx) / (x - 5) x (x + 2)
C. (x)= x^3 – 2x^2 – 13x – 10 x / (x - 5) (x + 1) (x + 2),
are the polynomials that have (x + 2) as a factor.
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Steve is turning half of his backyard into a chicken pen. His backyard is a 242424 meter by 454545 meter rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?
Answer:
51 meters
Step-by-step explanation:
The shape of the backyard is rectangular having a length, l=45 meters, and a width, w=24 meters as shown in the figure.
As wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. So,
The length of fencing = The length of the diagonal AC or BD
As the length of both the diagonals of a rectangle are equals, AC=BD.
The length of fencing [tex]=\sqrt{l^2+w^2}[/tex] [length of the diagonal]
[tex]=\sqrt{45^2+24^2}=51[/tex] meters
Hence, Steve needs 51 meters of fencing.
Which sequence of transformations will result in a parallelogram with vertices A(−2, 1), B(−4,−3), C(2,−5), D(4,−1) being carried onto the parallelogram A'B'C'D' shown below?
Answer:
translated 1 unit right and 2 units up followed by a reflection across x axis
Step-by-step explanation:
Parallelogram has vertices A(−2, 1), B(−4,−3), C(2,−5), D(4,−1) while parallelogram A'B'C'D' has vertices A'(-1, -3) B'(-3, 1) C'(3, 3) D'(5, -1)
Transformation is the movement of a point from its initial location to new location. If an object is transformed then all its points are transformed. Types of transformation are rotation, reflection, dilation and translation.
If a point X(x, y) is translated a units right and b unit up , the new point is X'(x + a, y + b).
If a point X(x, y) is reflected across the x axis, the new point is X'(x, -y)
If parallelogram ABCD is translated 1 unit right and 2 units up (i.e. x + 1, y + 2), the new points is A*(-1, 3), B*(-3, -1), C*(3, -3), D*(5, -1). If a reflection across x axis is then done, the new point is A'(-1, -3) B'(-3, 1) C'(3, 3) D'(5, -1)
Answer:
A translation 1 unit right and 2 units up followed by a reflection across the x-axis.
Step-by-step explanation:
Because you slid the shape over.
Hope this helps! Stay safe! :))))Describe the transformation
A) translation 2 units down
B) reflection across y=-1
C) reflection across the x-axis
D) across the y-axis
Answer:
C.
Step-by-step explanation:
Can someone help me please
Answer:
y = 119
x = 29
Step-by-step explanation:
i'm in a math test and i need help what is 1 + 1
Which expression is equivalent to 163?
O 27
O 211
o 212
o 264
Answer:
C
Step-by-step explanation:
For edge
The exponential equation is given by the expression A = 2¹²
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = 16³ be equation (1)
Now , the value of 16 = 2⁴
So , from the laws of exponents , we get
( mᵃ )ᵇ = mᵃᵇ
And , 2⁴⁽³⁾ = 2⁴ˣ³
And , the value of A = 2⁴ˣ³ = 2¹²
Hence , the expression is A = 2¹²
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how do i to find the slope
Answer:
To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
Step-by-step explanation:
Answer:
The equation to find slope is y=mx+b. Find two points in the line that are clear. subtract x1 and x2 and y1 and y2. Plug in the x and y values of one into the equation. b is equal to y when x is 0
Step-by-step explanation:
Help ASAP
Help ASAP
use completing the square to rewrite quadratic function into the form y=a(x+h)²+k
f (x) =4x²+6x-3 (1 point)
Answer:
The second: [tex]\bold{f (x) =4(x+\frac34)^2-\frac{21}4}[/tex]
Step-by-step explanation:
[tex]f (x) =4x^2+6x-3\\\\f (x) =4(x^2+\frac64x]-3\\\\f (x) =4[x^2+2\cdot x\cdot\frac34+(\frac34)^2-(\frac34)^2]-3\\\\f (x) =4[(x+\frac34)^2-(\frac34)^2]-3\\\\f (x) =4(x+\frac34)^2-4(\frac34)^2-3\\\\f (x) =4(x+\frac34)^2-\frac94-\frac{12}4\\\\\underline{f (x) =4(x+\frac34)^2-\frac{21}4}[/tex]
Joe and Carmen are partners in a business. Joe makes $2.00 profit for every $5.00 profit that Carmen makes. If Carmen makes $20 on the first item they sell, how much profit will Joe make?
5x+2y=10
Solve for y
Answer: y=(-5x/2)+5
Step-by-step explanation:
There is no clear cut explanation for this. y cannot directly equal a number. Let me show you.
Subtract 5x from both sides.
5x-5x+2y=10-5x
2y=-5x+10
Then to get to y to being by itself, divide by 2 on both sides
(2y/2)=(-5x+10)/2
y=(-5x+10)/2----> or -5x/2 + 10/2
y=(-5x/2)+5
can you tell me the answer
ANSWER ASAP PLEASE I WILL GIVE BRAINLIEST TO FIRST ANSWER!!!!
Which one would you choose? Explain your reasoning.
1. A 5-pound jug of honey for $15.35
2. Three 1.5-pound jars of honey for $13.05
Answer:
Three 1.5-pound jars of honey for $13.05
Step-by-step explanation:
15.35/5 = 3.07
3x1.5=4.5
13.05/4.5 = 2.90
can someone please help :) i suck at math.
Answer:
c) -11 1/2
Step-by-step explanation:
basically, you work backwards using the inverse operation.
start with -7, subtract 5.25 and you get -12.25, then add .75 (3/4) and you get -11.5 or -11 1/2
which is the choice to the inequality below?
x/6>7
Answer:
[tex]x > 42[/tex]
Step-by-step explanation:
[tex]\frac{x}{6} > 7[/tex]
Multiply 6 on both sides. [tex]6(\frac{x}{6}) > 6(7)[/tex].
Simplify it. [tex]x > 42[/tex]
Therefore, the answer is [tex]x > 42[/tex].
Hope this helped! If not, please let me know! <3
18. The price of a pair of shoes was $65. Then, the price was reduced to $52..
Find the percent decrease in the price of the shoes.
(a) 30%
(b) 13% (c) 5%
(d) 25%
(e) none of these
Please show the work
Answer:
13.
Step-by-step explanation:
65-52=13
I cannot figure out how to solve this, we did not cover it in class today and it is on tonights homework.
Answer:
x = 32.5
y = 65
Step-by-step explanation:
y = 65 degrees
65 and y are the base angles in an isosceles triangle ( single lines) so they are equal
y+z = 180 since they form a straight line
65+z = 180
z = 180-65
z = 115
The second triangle is also an isosceles triangle so the base angles are the same as shown by x
180 = x+x+z
180 =2x+ 115
65 = 2x
Divide by 2
x = 32.5
Your answer should be a polynomial in standard form. ( d^2 +3) (d^2 +2d +1)
Answer:d^4+2d^3+4d^2+6d+3
Step-by-step explanation:
A jewelry artist is selling necklaces at an art fair. It costs $135 to rent a booth at the fair. The cost of materials for each necklace is $4.50. The artist is selling the necklaces at $12 each. The inequality LaTeX: 12n > 135 + 4.50n12n>135+4.50n12n>135+4.50n represents the situation in which the artist makes a profit.
Answer:
The artist makes profits when n>8.18
that is when the number of necklaces exeeds 8.18
Step-by-step explanation:
Given
let the number of necklaces be n
booth rent= $135
The cost of materials for the necklaces = $4.5n
the selling price for all the necklaces =$12n
total expenses= booth rent+cost of material = $135+4.5n
profit = selling price -total expenses
12n > 135 + 4.50n
solving for n we have
12n=135 + 4.50n
12n+4.5n=135
16.5n=135
n=135/16.5
n=8.18
The artist makes profits when n>8.18
WILL MARK BRAINLEST FOR CORRECT ANSWER
STANDARD FORM
4x + 6y = 12
Find the X and Y intercepts
(0, ) ( ,0)
Answer:
Shouldn't it be (4,0) and (0,6)?
Step-by-step explanation:
George is comparing two different phones. The screen of phone A has a width of 5.3 cm. The width of the screen on phone B is 5 and one-third cm. Which statement explains which phone has the wider screen? The screens have the same width. Screen A is wider, because 5.3 is greater than 5 and one-third.. Screen B is wider, because 5.3 is greater than 5 and one-third.. Screen B is wider, because 5 and one-third is greater than 5.3.
Answer:
The answer is "Screen B is wider , because 5.3 is greater than 5 and one-third".
Step-by-step explanation:
The mobile display unit must be made similar. Phone A uses a decimal device, and telephone B uses a fraction in this case.
It's easier for you to use. Attempt using the decimal. The width of the phone B fraction could then be translated to decimal width. The computing is:
= 5 cm + [tex]\frac{1}{3}[/tex] cm
= 5 cm + 0.333cm
= 5.333 cm
It is evident from here that the wider screen of Phone B is than that of Phone A.
Answer:
They are all the same width
Step-by-step explanation:
Can someone please help me
Answer:
z
Step-by-step explanation: