Answer:
8 more unit of tiles
Step-by-step explanation:
The function is given as;
f(x) = x² - 6x + 1
Now, we want to add more unit tiles to complete the square.
The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.
Now, Let's make a general order 1 expression ax + b to be the side of the square.
From the function forming the square after adding some p unit tiles, we have;
f(x) + p = (side of square)²
Thus;
x² - 6x + 1 + p = (ax + b)²
x² - 6x + 1 + p = a²x² + 2abx + b²
Comparing both sides of the equation, we have;
a² = 1
2ab = 6
b² = 1 + p
From a² = 1, a = 1
From 2ab = 6,putting 1 for a, we have;
2(1)b = 6
b = 6/2
b = 3
From b² = 1 + p
Putting 3 for b, we have;
3² = 1 + p
9 = 1 + p
9 - 1 = p
p = 8
Thus, 8 more unit of tiles are required to complete the square.
What the answer now
Answer:
57°
Step-by-step explanation:
There is a right angle at the point of tangency, so the angle of interest is the complement of the one given:
m∠K = 90° -m∠J = 90° -33°
m∠K = 57°
Please thank you! I will give brainleist to the first correct answer if it lets me
Answer:
x=10 y=12
Step-by-step explanation:
just multiply 15 and 18 by 1/3 because both triangle are similar.
Answer:
x = 10; y = 12
Step-by-step explanation:
find the scale factor ratio using corresponding sides: 9 / 6 = 3/2 so the ratio is 3:2
from large triangle to small triangle you will get:
1. 15 / x
2. 18 / y
to implement the ratio, set the side length ratio equal to the scale factor:
1. [tex]\frac{15}{x}[/tex] = [tex]\frac{3}{2}[/tex]
2. [tex]\frac{18}{y}[/tex] = [tex]\frac{3}{2}[/tex]
cross multiply:
1. 30 = 3x
2. 36 = 3y
divide:
1. x = 10
2. y = 12
Can someone help me with this?
Answer:
9 = k :)
Step-by-step explanation:
1. distribute 3 to the -1/4 k and to the 3 and get -3/4 k + 9 = 1/4 k
2. add 3/4 k to both sides and get 9 = k
What is the surface area of the right cone below?
A. 52 units2
O B. 1047 units2
C. 6870 units2
D. 5471 units2
First find height using Pythagorean theorem.
[tex]h^2+4^2=13^2\implies h=\sqrt{153}\approx12.37[/tex].
Then use cone surface area formula and compute the result:
[tex]A=\pi r(r+\sqrt{h^2+r^2})\approx\boxed{68\pi}\mathrm{units^2}[/tex].
Hope this helps.
Describe the process you would use to explain to your parents (or other significant adults in your life) how you could calculate the sum of the interior angles of a 12-sided object without measuring them
Answer:
Sum of interior angles of 12 sided object = 1800°
Step-by-step explanation:
Formula to calculate the sum of interior angles of a polygon is,
Sum of the interior angles of a polygon = (n - 2) × 180°
Where n = number of sides of the polygon.
If number of sides of a polygon are 12,
For n = 12,
Sum of interior angles = (12 - 2) × 180°
= 10 × 180°
= 1800°
Therefore, sum of interior angles of a 12 sided polygon will be 1800°.
PLSSSSS HELLLLLLP!!!!!
Answer:
[tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex] will be the answer.
Step-by-step explanation:
The given expression is,
[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]
By solving this expression,
[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]
= [tex]\frac{3n(n-4)}{(n+3)(n-4)}+\frac{5(n+3)}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n(n-4)+5(n+3)}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n^2-12n+5n+15}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex]
Therefore, fraction given in option (2) will be the answer.
Suppose I have either a fair coin or a bent coin, and I don’t know which. The bent coin has a 60 % 60\% 60% probability of coming up heads. I throw the coin ten times and it comes up heads 8 times. What is the probability I have the fair coin vs. the probability I have the bent coin? Assume at the outset there is an equal ( . 5 , . 5 ) (.5,.5) (.5,.5) prior probability of either coin.
Answer:
the Probability of Fair coin = 0.2664=26.64 % and
Probability of Bent coin = 0.7336= 73.36 %
Step by step Explanation:
The fair coin has a 60% probability of coming up heads, same thing with the bent coin , when the coin was thrown up ten times,it comes up heads 8 times,
Here we were told to find the probability fair coin vs. probability bent coin
A)THE FAIR COIN::
The probability of getting Head Coin = 1/2
Probability of getting tail Coin = 1/2
Then the Probability of head 8 times out of 10 can be calculated using combination
= ¹⁰C₈ × (1/2)⁸ ×(1/2)²
= 45/1024
= 0.0439
Therefore, the Probability of head 8 times out of 10= 0.0439
B)BENT COIN
the probability of getting Head Coin = 0.6
= 6/10
= 3/5
NOTE: 60%=0.6
The probability of getting tail Coin = 1 - 3/5
= 2/5
Then, the probability of getting head 8 times out of 10 can be calculated using combination;
= ¹⁰C₈ × (3/5)⁸ × (2/5)²
= 45 × 6561 ×( 4 / 5¹⁰)
= 0.1209
Therefore, the probability of getting head 8 times out of 10 = 0.1209
We can now calculate the Probability of Fair coin
(Probability of head 8 times out of 10 in fair coin )/(Probability of head 8 times out of 10 in fair coin )+(the probability of getting head 8 times out of 10 in bent coin)
= (0.0439 )/(0.0439 + 0.1209)
= 0.2664
Probability of bent coin can as well be calculated as 0.1209 /(0.0439 + 0.1209)
= 0.7336
Therefore, the Probability of Fair coin = 0.2664=26.64 % and
Probability of Bent coin = 0.7336= 73.36 %
select the coordinates of two points on the line y = -2
Answer: (0, -2) & (1, -2)
Step-by-step explanation:
There are an infinite number of coordinates on y = -2.
The coordinates can have any x-value, but must have -2 for the y-value.
Given: DF and DE are midsegments of ∆ABC Prove: DE= 1/2 AC (PLEASE HELP)
Answer:
The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.
Answer:
The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.
Step-by-step explanation:
BRAINLIEST!!! MATH HELP ME ASAP PLS!!!
Answer:
-0.0062 and 27.5
Step-by-step explanation:
You can write the equation of the line using the 2-point form:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
The given values of the variables are ...
(h, T) = (10000, -34.5) and (15000, -65.5)
Putting these into the formula, we have ...
T = (-65.5 -(-34.5))/(15000 -10000)(h -10000) +(-34.5)
T = -31/5000(h -10000) -34.5
T = -0.0062h +62 -34.5
T = -0.0062h +27.5
The appropriate choice is ...
-0.0062 and 27.5
Select the correct answer.
Which of the following represents a function?
Answer:
D.
Step-by-step explanation:
A function is when each x-value has only 1 y-value.
A: When x = 5, there are two values for y.
B: When x = -3, there are two values for y.
C: When x = -4, there are two y-values.
D: Each x-value has exactly one y-value.
So, your answer should be D.
Hope this helps!
Option (D) is accurate since the fourth option's x value has exactly one y value.
D. {(₋7,9), (₋4,₋9), (5,15), (7,19)}
What are functions?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that x's value determines what y's value will be. This reliance can be expressed as follows: y = f (x)
Given,
In the first case, y has two different values of 13 and 17, which is not permitted in a function, with the same value of x = 5. The first case is not a function as a result.
For the same value of x = 3 in the second case, y has two different values of 1 and 1, which is not permitted in a function. The second example is therefore not a function.
In the third case, for the same value of x = ₋4, y has two different values of 52 and 16 which is not allowed in a function. Therefore, third case is not a function.
Here, in the fourth situation, no x value is identical and there is only one possible y value.
Hence we get the answer as {(₋7,9), (₋4,₋9), (5,15), (7,19)} which represents the function.
Learn more about "functions" here-
brainly.com/question/10439235
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Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle. Which statements describes how the location of segment EG affects the area of EFGH? A.) the area of EFGH is 1/4 of the area of the rectangle if E and G are not midpoints B.) The area of EFGH is 1/2 of the area of the rectangle only if E and G are midpoints C.) The area of EFGH is always 1/2 of the area of the rectangle. D.) The area of EFGH is always 1/4 of the area of the rectangle.
Answer:
C.) The area of EFGH is always ¹/₂ of the area of the rectangle.Step-by-step explanation:
If EG is parallel to the side of the rectangle then lenght of EG is equal to width of rectangle.
If F and H are midpoints of sides of rectangle then FH is parallel to the side of rectangle {wich is perpendicular to the side parallel to EG}. That means the lenght of FH is equal to lenght of rectangle, and FH is perpendicular to EG.
Then FH is sum of hights of triangles EFG and EHG [tex](FH=H_{_{\Delta EFG}}+H_{_{\Delta EHG}})[/tex], and the area of EFGH is sum of areas of triangles EFG and EHG [tex](A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}})[/tex].
So the area of the rectangle: [tex]\bold{A_{rectangle}=EG\cdot FH}[/tex]
The area of the kite:
[tex]A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}}\\\\A_{kite}=\frac12 EG\cdot H_{_{\Delta EFG}}+\frac12 EG\cdot H_{_{\Delta EHG}}\\\\ A_{kite}=\frac12 EG\cdot (H_{_{\Delta EFG}}+H_{_{\Delta EHG}})\\\\A_{kite}=\frac12 EG\cdot FH\\\\A_{kite}=\frac12 A_{rectangle}[/tex]
No matter the height of the triangles, so no matter the location of the EG
A line has____ rotational symmetry. A. Four-fold B. Six-fold C. Two-fold D. Seven-fold
Answer:
Option C
Step-by-step explanation:
A line has a 2-Fold rotational symmetry because if we rotate the line about 180, The resulting thing will be the same line.
Answer:
[tex]\boxed{\mathrm{C}}[/tex]
Step-by-step explanation:
A line has two-fold rotational symmetry.
The line rotated two times from a central point remains the same.
Or the line rotated 180 degrees from a central point remains the same.
A 5×5×5 wooden cube was painted and then sawed into 1×1×1 cubes. How many 1×1×1 cubes are there? HELPPPPP!!!!!!!!!!!!!!!!!!!!!! QUIKE
Answer:
125
Step-by-step explanation:
1 x 1 x 1 = 1
5 x 5 x 5 = 125
125 / 1 = 125
125 is your answer
Please Help!!! Will get brainiest if answer correctly with an explanation. Name the postulate or theorem you can use to prove wzv=wzy. given:
Answer:
AAS
Step-by-step explanation:
Δwzy=Δwzv
to prove the equality:
1- wz is a common side
angle: wzv=wzy=90 degrees ( height of triangle)
angle v= angle y
Since WZ bisects W, it's good to say that vwz and zwy
prove one side is equal and two angles
so ASA or AAS is the answer
The vertices of triangle ABC are A(5,2), B(-1,-6), and C(1,5). If triangle DEF is similar to triangle ABC and AB/DE = 5, which could be the coordinates of D and E
Answer:
im pretty sure its the third one
Step-by-step explanation:
i guessed but it might be right
What is the solution to the system of linear equations shown in the graph below?
-(3,4)
-(0,-3)
- infinite solutions
-no solutions
The solution is where the two red lines cross. This is the point (3,-4)
If you knew the equation of each red line, you can plug (x,y) = (3,-4) into each equation. You should find the two equations lead to true statements.
Evaluate 8r - r s when r=6 and s=5 pls help!! asap
Answer:
18
Step-by-step explanation:
8r - r s
r=6 and s=5
8*6 - 6*5
48 - 30
18
Answer:
you first take the equation 8r-rs and you substitute r=6 s=5, which will look like this 8(6)-6(5).
after that you distribute 8*6 and 6*5
and then you'll get 48-30
finally you subtract the two numbers which will leave you with = 18
Step-by-step explanation:
Rationalise the denominator and simplify
A) 2sqrt3/sqrt12
B) 5sqrt7/sqrt35
Answer: A) 1 B) [tex]\sqrt5[/tex]
Step-by-step explanation:
[tex]A)\quad \dfrac{2\sqrt3}{\sqrt{12}}=\dfrac{2\sqrt3}{2\sqrt3}=1\\\\\\\\B)\quad \dfrac{5\sqrt7}{\sqrt{35}}=\dfrac{5\sqrt7}{\sqrt5\cdot \sqrt7}=\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\sqrt5[/tex]
The Greenpoint factory produced two-fifths of the Consolidated Brick Company's bricks in 1991. If the Greenpoint factory produced 1,400 tons of bricks in 1991, what was the Consolidated Brick Company's total output that year, in tons?
Answer:
3,500 tons
Step-by-step explanation:
We know that 1,400 tons is 2/5 of the Consolidated Brick Company's output.
This means that 1/5 must be equal to 700 tons if 2/5 is 1,400.
So, we can find the total output by multiplying 700 by 5, since 700 is 1/5 of the total.
700(5) = 3,500 tons
What is 651 minus -13? Please with explanation.
Answer:
664
Step-by-step explanation:
651 - - 13
Negative times negative is positive.
651 + 13
Add.
664
Answer:
664
Step-by-step explanation:
651 - (-13)
Do the keep , change , change method
So , it will be :
651 + 13 = 664
Hope this helps and plsss plss amrl as brianliest and THNXX :)
Plzzzzz Help I really need help
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5
Answer:
(1.5,-3) and (4.5,-3)
Step-by-step explanation:
Which statements are true regarding undefinable terms in geometry?
C. A line has one dimension, length.
E. A plane consists of an infinite set of lines.
Factorize a² +3ab - 5ab - 15b².
Answer:
[tex]a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)[/tex]
Step-by-step explanation:
Work via factoring by groups:
!) re arrange the terms as follows:
[tex]a^2-5ab+3ab-15b^2[/tex]
then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):
[tex]a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)[/tex]
Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:
[tex]a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)[/tex]
which is the final factorization.
Answer:
[tex] \boxed{\sf (a + 3b)(a - 5b)} [/tex]
Step-by-step explanation:
[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)[/tex]
what must be divided to 43659 to get a perfect square
Answer:
11
Step-by-step explanation:
Prime factor: 43659 = 3*3*3*3*7*7*11
Pair: √43659 = √3²×3²×7²×11
11 is odd therefore 11 must be divided by 43659
multiply c^2(c^2-10c+25)
Step-by-step explanation:
c^2( c^2-10c+25)
=c^4 - 10c^3 + 25c^2
simplify the expression without negative exponents
Answer: [tex]-50a^{11}b^{9}[/tex]
Step-by-step explanation:
Any negative exponent can be moved to the other side of the fraction as a positive exponent.[tex]\frac{1}{x^{-3}}=x^3\\ \frac{x^{-3}}{1}=\frac{1}{x^3}[/tex]
Thus, simply move the negative exponents from the bottom into the numerator to get. -10a^2*b^4*5a^9*b^5. Then, use the exponent rule to get [tex]-50a^{11}b^{9}[/tex]
Hope it helps <3
Uma makes a scale drawing of a patio. The drawing below shows the two scales she used to plan two patios of different sizes.
Scale 1: 1 centimeter = 3 meters.
Scale 2: 1 centimeters = 4 meters.
Options
A)Scale 1: 45 m; Scale 2: 60 m
B)Scale 1: 60 m; Scale 2: 45 m
C)Scale 1: 36 m; Scale 2: 27 m
D)Scale 1: 27 m; Scale 2: 36 m
Answer:
Scale 1: 1 centimeter = 3 meters.
Scale 2: 1 centimeters = 4 meters.
Step-by-step explanation:
your answer should be A
15*3=45
15*4=60
Answer:
A.)Scale 1: 45 m; Scale 2: 60 m
Step-by-step explanation:
bcuz......uhhhhhhh, ummmmmm:/
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
2
Step-by-step explanation:
In order to make the equation undefined, you should make the denominator 0. Remember that dividing anything by 0 will become undefined.
[tex]2x-4=0\\\frac{2x=4}{2} \\x=2[/tex]
Answer:
[tex]\boxed{x = 2}[/tex]
Step-by-step explanation:
A rational expression is undefined when Denominator = 0
Here Denominator = 2x-4
So,
=> 2x - 4 = 0
Adding 4 to both sides
=> 2x = 4
Dividing both sides by 2
=> x = 2
help me please i jave 10 min left HELP
Answer:
Option (A).
Step-by-step explanation:
[tex]8\frac{4}{5}[/tex] is a mixed fraction and can be written as,
[tex]8\frac{4}{5}=8+\frac{4}{5}[/tex] [Combination of a whole number and a fraction]
When we multiply this mixed fraction by 7,
[tex]7\times 8\frac{4}{5}=7\times (8+\frac{4}{5})[/tex]
[tex]=(7\times 8)+(7\times \frac{4}{5})[/tex] [Distributive property → a(b + c) = a×b + a×c]
[tex]=56+\frac{28}{5}[/tex]
[tex]=56+5\frac{3}{5}[/tex]
[tex]=56+5+\frac{3}{5}[/tex]
[tex]=61+\frac{3}{5}[/tex]
[tex]=61\frac{3}{5}[/tex]
Therefore, [tex]7\times 8\frac{4}{5}=61\frac{3}{5}[/tex] will be the answer.
Option (A) will be the correct option.