Answer:
x=22.5°
Step-by-step explanation:
(cos²x-sin²x)-sin4x+sin²2x=0
or, (cos2x)²-sin4x+sin²2x=0
or, cos²2x+sin²2x-sin4x=0
or, 1-sin4x=0
or, sin4x=1
or, 4x=90°
or, x=90°/4
or, x=22.5°
answer of a ²-10a+16-6b-b^2
[tex] \quad a^2-10a+16-6b-b^2[/tex]
$=(a^2-10a)-(b^2+6b) +16$
$=[(a^2-2(5)a+25)-25]-[(b^2+2(3)b+9)-9]+16$
$=(a-5)^2-25-(b+3)^2+9+16$
$=(a-5)^2-(b+3)^2$
graph the line that passes through the points (-3,-7) and (-2,-7) and determine the equation of the line
Answer:
y = -7
Step-by-step explanation:
y2 - y1 / x2 - x1
-7 - (-7) / -2 - (-3)
0/1
= 0
y = 0x + b
-7 = 0(-2) + b
-7 = 0 + b
-7 = b
Which two complex numbers when subtracted from each other equal another complex number from the table? A -3 − 4i B -7 − 6i C 13 + i D -9 + 6i E 8 − 8i F -15 + 9i G 2 + 12i H 6 − 10i
Answer:
if you have a ti-84 plus, input ur problem into the calculator
Step-by-step explanation: you may use calculator for answers
Answer:
The difference of A and D equals the complex number in row H in the table (6 − 10i):
A − D
=
-3 − 4i − (-9 + 6i)
=
-3 − 4i + 9 − 6i
=
-3 + 9 − 4i − 6i
=
(-3 + 9) + (-4 − 6)i
= 6 − 10i
Step-by-step explanation:
Part
This table shows the prices of the three TVs in addition to their length and width. Is the price of a TV proportional to the length of its screen? How
do you know
Answer:
No! They are not proportional!
Step-by-step explanation:
Proportional prices to the length means that
(price 1/length 1)=(price 2/length 2)=(price 3/length 3)
Even by plugging in the numbers yourself to double check my numbers, and getting and answer for each ratio, it is clear that they are not proportional.
Answer:
The ratio of screen length to price in the first row is 16/160, which simplifies to 1/10.
The ratio of screen length to price in the second row is 20/180, which simplifies to 1/9.
The ratio of screen length to price in the third row is 24/200, which simplifies to 3/25.
Because 16/160 doesn't = 20/180 doesn't = 24/200, the ratios are not equivalent. This is not a proportional relationship.
PLS ANSWER BRAINLIST AND A THANK YOU WILL BE GIVEN!!!!
Answer:
[tex]\huge\boxed{Option \ D}[/tex]
Step-by-step explanation:
4x + 5x = 180 [They are angles on a "straight" line so they will add up to 180 degrees)
Answer:
D
Step-by-step explanation:
The sum of angles that are formed on a straight line is 180.
4x + 5x = 180
An arc of length 12:57 cm
angle of 60° at the cen me
find the radius or the circle.
subrends an.
or a cordle.
Answer:
r ≈ 12 cm
Step-by-step explanation:
arc length = circumference × fraction of circle, that is
2πr ×[tex]\frac{60}{360}[/tex] = 12.57 ( multiply both sides by 360 to clear the fraction )
2πr × 60 = 4525.2
120πr = 4525.2 ( divide both sides by 120π )
r = [tex]\frac{4525.2}{120\pi }[/tex] ≈ 12 cm
would you Rather geometry
Walk on a line or A line segment
why?
Keith's height and his nephews height was at a ratio of 15:7 then, keith's Height increased by 16% and his nephews height doubled. If Keith is now 34cm taller than his nephew, what is their total current height?
Answer:
314 cm
Step-by-step explanation:
If Keith's height is 15x and his nephew's height is 7x, we can write the following equation:
1.16 * 15x = 34 + 7x * 2 -- (We get the 1.16 from the 16% increase)
17.4x = 34 + 14x
3.4x = 34
x = 10 so Keith's current height is 1.16 * 15 * 10 = 174 cm and his nephew's height is 174 - 34 = 140 cm for a total current height of 174 + 140 = 314 cm.
Write the coefficient of x2 in the following a) 2 + x2 + x b) 2 – 4x2 + x solution pls I will mark as brainliest
Answer:
The coefficient of x²
a) 1
b) -4
the coefficient of x² is the number in front of the x²(variable).
Coefficient= Constanta
I hope this helps
if u have question let me know in comments ^_^
Answer:
a) 1.
b) -4.
Step-by-step explanation:
The coefficient is the number multiplying x2. If it is 1 it is usually omitted.
2x²+3x²+3.(-1) =5x.x+5x .1
[tex]\\ \sf\longmapsto 2x^2+3x^2+3(-1)=5x.x+5x.1[/tex]
[tex]\\ \sf\longmapsto 5x^2-3=5x^2+5x[/tex]
[tex]\\ \sf\longmapsto 5x^2-5x^2-3=5x[/tex]
[tex]\\ \sf\longmapsto 5x=-3[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-3}{5}[/tex]
[tex] \frac{5 + n}{4} = - 1[/tex]
What is n?
Answer:
n= -9
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
5 + n
==== = -1
4
Multiply both sides by 4
5 + n = - 1 * 4
5 + n = - 4
Subtract 5 from both sides
5-5 + n = - 4 - 5
n = - 9
Congratulations on being able to use latex.
round 2.034 to the nearest whole number
Answer:
2
Step-by-step explanation:
2.034
We are rounding to the ones place.
To round, look at the digit to the right of which we are rounding. In this case, it is 0.
0 is less than 5, so we just keep the 2.
I hope this helps!
pls ❤ and mark brainliest pls!
Answer:
2
Step-by-step explanation:
2.034 can be rounded to 2.000, or 2. This is because the digit after the two in the tenths place, 0, is less than 5.
Brainliest, please!
The solution of this equation has an error. Which of the following steps has an error?
Step 1: -2x + 8 - 3x = 7
Step2:–5x+8=7
Step3:-5x = 15
Step4:
x = -3
O Step 2
O Step 1
O Step 3
3rd step
Solution:-
[tex]\\ \sf\longmapsto -2x+8-3x=7[/tex]
[tex]\\ \sf\longmapsto -2x-3x+8=7[/tex]
[tex]\\ \sf\longmapsto -5x+8=7[/tex]
[tex]\\ \sf\longmapsto -5x=7-8[/tex]
[tex]\\ \sf\longmapsto -5x=-1[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-1}{-5}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{1}{5}[/tex]
Rearrange the formulae to make x the subject:
ay/x - dx= wx
Thanks in advance
Answer:
x = ay/(wx+dx)
Step-by-step explanation:
ay/x - dx = wx
ay/x = wx + dx
ay = x(wx+dx)
x = ay/(wx+dx)
Một ôtô đi từ A đến B với vận tốc 60km/h và đi từ B về A với vận tốc 45km/h. Thời gian cả đi và về hết 7giờ. Tính quãng đường AB
Please explain in english
Answer:
Đáp án: 180km
Step-by-step explanation:
Giải thích các bước giải:
Gọi quãng đường AB là x (km)
(x > 0)
Thời gian ô tô đi từ A -> B là x/60 (h)
Thời gian ô tô đi từ B -> A là x/45 (h)
Vì thời gian cả đi và về hết 7h
=> x/60 + x/45 = 7
=> x = 180 (TM)
Vậy quãng đường AB là 180 km
Solve the system using substitution.
X = Y-4
2x + 3y = 12
Answer:
Step-by-step explanation:
If you know that x = y - 4, you can plug that value into the equation 2x + 3y = 12 for x. This would look like:
2(y - 4) + 3y = 12
Simplify:
2y - 8 + 3y = 12
5y - 8 = 12
add 8 to both sides
5y = 20
divide both sides by 5
y = 4
Now, substitute y = 4 back into the equation x = y - 4:
x = 4 - 4
and simplify:
x = 0
This means that the answer is x = 0 and y = 4.
Answer:
(0, 4 )
Step-by-step explanation:
Given the 2 equations
x = y - 4 → (1)
2x + 3y = 12 → (2)
Substitute x = y - 4 into (2)
2(y - 4) + 3y = 12 ← distribute and simplify left side
2y - 8 + 3y = 12
5y - 8 = 12 ( add 8 to both sides )
5y = 20 ( divide both sides by 5 )
y = 4
Substitute y = 4 into (1) for corresponding value of x
x = 4 - 4 = 0
solution is (0, 4 )
The perimeter of an isosceles triangle is 32 inches. If the base is longer than half of the two other equal sides by 2 inches, find the length of all sides of this triangle.
Write as a equation.
Answer:
Step-by-step explanation:
Let equal sides of an isosceles triangle = a inches
Base = [tex]\frac{1}{2}a+2[/tex] inches
Perimeter = 32 inches
a + a + [tex]\frac{1}{2}a+2[/tex] = 32
[tex]2a + \frac{1}{2}a+2 = 32\\\\\frac{2a*2}{1*2}+\frac{1}{2}a+2=32\\\\\frac{4a}{2}+\frac{1}{2}a+2=32\\\\\frac{5}{2}a+2 = 32\\\\[/tex]
Subtract 2 from both sides
[tex]\frac{5}{2}a=32-2\\\\\frac{5}{2}a=30\\\\a=30*\frac{2}{5}\\\\a=6*2[/tex]
a = 12 inches
base = [tex]\frac{1}{2}*12+2[/tex]
= 6 + 2
Base = 8 inches
write as a sentence in words 7.8 > 3.4
Answer:
seven and eight tenths is greater than three and four tenths
Hope it helped youTemperature can be measured in two different common units: degrees Celsius and degrees Fahrenheit. fff represents the temperature in degrees Fahrenheit as a function of the temperature ccc in degrees Celsius. f=32+1.8cf=32+1.8cf, equals, 32, plus, 1, point, 8, c Water freezes at 000 degrees Celsius. What is the freezing temperature of water in degrees Fahrenheit?
Answer:
Water freezes at 32 °F.
How many solutions does the system have?
⎪
⎪
⎨
⎪
⎪
⎧
x+y=3
5x+5y=15
Which of the following graphed systems has no solution?
A. none of these
Last one or third one .
Note down:-
If two lines have intersected each other then the intersection point is the solution.The equations have only If both lines are one and equal then the equations have infinite solutions.If two lines are parallel then the equations have no solutions .If the lines are parallel that means an equal slope but different y-intercepts, then the system has no solution. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The system solutions are as follows:
If the slope of the lines is different, then the system has a unique solution.If the slope of the lines is the same but the y-intercepts are different, then the system has no solution.If the slope and y-intercepts of the lines are the same, then the system has infinitely many solutions.If the lines are parallel that means an equal slope but different y-intercepts, then the system has no solution. Then the correct option is D.
More about the linear equation link is given below.
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Factor this polynomial expression.
x2 + 12x + 36
A. (x + 9)(x + 4)
B. (x - 6)(x - 6)
C. (x + 6)(x + 6)
D. (x - 9)(x - 4)
Answer:
(x+6)(x+6)
Step-by-step explanation:
x^2 + 12x + 36
Factor
What two numbers multiply to 36 and add to 12
6*6 = 36
6+6 =12
(x+6)(x+6)
In a large restaurant, an average of 3 out of every 5 customers ask for water with their meal. A random sample of 10 customers is selected. Find the probability that exactly 6 ask for water with their meal. Let X be the random variable that represents the number of these customers who ask for water.
Answer:
please mark me brainlist
Step-by-step explanation:
a) Let X be the random variable the number of customers asking for water.
X ~B(10,0.6)
= P(X = 6) =( 0.6)6 ( 0.4)4 10!/6 !*4!
= 0.2508
Y ~B(10,0.4)
= P(Y = 4)=( 0.6)6 ( 0.4)4 10!/6 !*4!
= 0.2508
The probability that exactly 6 ask for water with their meal is calculated by binomial distribution and the value is P ( x = 6 ) = 25.08 %
What is a Binomial Distribution?
The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.
The formula for Binomial Distribution is given by
P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
where
n = number of trials
x = number of successes
p = probability of getting a success in one trial
q = probability of getting a failure in one trial
q = 1 - p
Given data ,
Let the probability that exactly 6 ask for water with their meal be P ( x = 6 )
Now , an average of 3 out of every 5 customers ask for water with their meal
So , the probability of getting a success p = 3/5 = 0.6
The probability of getting a failure q = 1 - p = 0.4
The number of trials = 10
The number of successes x = 6
So ,
Probability that exactly 6 ask for water with their meal be P ( x = 6 ) is
P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
Substituting the values in the equation , we get
P ( x = 6 ) = [ 10! / ( 4 )! 6! ] ( 0.6 )⁶( 0.4 )⁴
On simplifying the equation , we get
P ( x = 6 ) = 0.2508
P ( x = 6 ) = 25.08 %
Therefore, the value of P ( x = 6 ) is 25.08 %
Hence , probability that exactly 6 asks for water is 25.08 %
To learn more about binomial distribution click :
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The hypotenuse is 8 inches. The side opposite angle X is 7 inches. Angle X = ?
Step-by-step explanation:
In the picture.
The answer is X = 61°
PLEASE HELP QUICK A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids. The volume of the prism is 234 cubic units. What is the height of the prism? 3 units 4 units 6 units 8 units
==========================================================
Explanation:
Let's find the area of the hexagon. It's composed of two identical (aka congruent) trapezoids.
Each trapezoid has two parallel bases of 4+4 = 8 and 5 units. The height is 3. The area of one trapezoid is
area = height(base1+base2)/2
area = 3*(8+5)/2
area = 19.5
which doubles to 2*19.5 = 39 to represent the area of the entire hexagon
--------------------------------
The volume of any prism is found through this formula
volume = (area of base)*(height of prism)
We just found the area of the base to be 39. The height is unknown, so we'll call it h. The volume is given to be 234.
We end up with this equation
234 = 39h
which solves to h = 6 after dividing both sides by 39. This prism has a height of 6 units.
The height of the prism is 6 units
What is Hexagonal prism?The hexagonal prism is a prism with hexagonal base.
What is isosceles trapezoid?An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.
What is Volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Given,
Each hexagon is made from two congruent isosceles trapezoids
Therefore
Area of one isosceles trapezoids = [tex](a+b).(\frac{h}{2} )[/tex]
where,
a =4+4 = 8 units
b = 5 units
h = 3 units
Area of one isosceles trapezoids =[tex](8+5)(\frac{3}{2} )[/tex] =19.5 unit square
Area of the hexagon = Area of two isosceles trapezoids
Area of hexagon = 2× 19.5 = 39 unit square
We know that,
Volume = Base area × Height
Volume = 234 cubic units
234 = 39 × h
h = [tex]\frac{234}{39}[/tex] = 6 units
Hence, the height of the prism is 6 units
Learn more about Hexagonal prism, Isosceles trapezoids and Volume here
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Factorise each expression 8 - 2v²
Answer:
hello thereee
8 - 2v^2 we are suppose to facotrize...
2 ( 4 - v^2 )
2 ( 2^2 - v^2 )
apply identity a^2 - b^2
2 ( 2 + v ) ( 2- v )
done dana done.....
Do the ratios 9/4 and 18/8 form a proportion?
Yes
Step-by-step explanation:
I believe so. Hope this helps
10. Write a word problem for this equation:
n ($25) = $125
Answer:
The word problem is "How many $25 are there in $125?"
Step-by-step explanation:
Given
[tex]n(\$25) = \$125[/tex]
Required
Write a word problem for the expression
We start by solving the given equation
[tex]n(\$25) = \$125[/tex]
Divide both sides by $25
[tex]\frac{n(\$25)}{\$25} = \frac{\$125}{\$25}[/tex]
[tex]n = \frac{\$125}{\$25}[/tex]
[tex]n = 5[/tex]
This implies that there are 5, $25 in $125
Hence; The word problem is "How many $25 are there in $125?"
Cobalt-60 is used for radiotherapy. It has a half-life of 5.26 years. If 4 g of cobalt-60 is administered, how much remains in 3 years? A. 1.2 g B. 2.7 g C. 3.3 g D. 2.1 g E. 0.2 g
Answer:
B. 2.7 g
Step-by-step explanation:
The half life of a substance is the time taken for the substance to reduce to half of its original amount. It is given by:
[tex]A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\ Where\ A\ is \ the \ amount \ of \ substance\ remaining\ after\ t\ years, \\A_o \ is \ the\ initial\ value\ of \ the\ substance,\ t_{1/2} is\ the\ half\ life\ and\\t\ is\ the\ years\ spent[/tex]
Given that:
Ao = 4 g, t = 3 years, t(1/2) = 5.26 years. Therefore:
[tex]A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\A=4*(\frac{1}{2} )^\frac{3}{5.26}=4*0.6735=2.7\\ A=2.7\ g[/tex]
125 Children get one pen, there are 8
pens in a pack. How many pens are
needed?
Answer:
16 packs
Step-by-step explanation:
Take the number of children and divide by the number of pens in a pack
125/8
15.625
We need to round up to get the number of packs
16 packs
Answer:
125 pens and 16 packs.
Step-by-step explanation:
Given:
Each child gets 1 pen.There are 125 children.Each pack has 8 pens.Each child gets 1 pen, so there needs to be 125 pens.
Since there are 8 pens in a pack, there will need to be:
125 / 8 = 15.62
Estimate:
16 packs
There needs to be 16 packs for the 125 children.