Answer:
Let's start first with sin(x+y) :
sin(x+y) sin(x)*cos(y)+cos(x)*sin(y)Now with sin(x)+sin(y) :
sin(x)+sin(y) 2*sin[(x+y)/2] * cos[(x-y)/2]We can see that both expressions are far away from being equal
We can prove the given expression, sin(x + y) ≠ sin x + sin y by taking the value of x and y as 90 respectively.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle. The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
It is given that the expression is"sin(x + y) sin(x+y)
Suppose, x=0 and y=90
We have to prove the following expression,
sin(x + y) ≠ sin x + sin y
Left-hand side,
=sin(x + y)
=sin(90+90)
=sin 180
=0
Right-hand side,
=sin x + sin y
=sin90+sin90
=1+1
=2
As a result,
sin(x + y) ≠ sin x + sin y
Thus, we can prove the given expression, sin(x + y) ≠ sin x + sin y by taking the value of x and y as 90 respectively.
Learn more about trigonometry here:
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Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?
Complete Question:
To create a bulletin board, Maryann is planning to stretch fabric from burlap sacks over cardstock. She collects 6 kg of burlap sacks. The area density of the burlap is 0.4 kg/m².
Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?
Answer:
To complete the bulletin boards for her friends, Maryanne should collect 6 kg of burlap more
Step-by-step explanation:
Mass of burlap sacks that Maryann collects = 6 kg
Area density of burlap = 0.4 kg/m²
Area Density = Mass / Area........(1)
The Area of bulletin board that can be made with the 6 kg of burlap sand can be calculated by using equation (1)
0.4 = 6 / Area
Area = 6/0.4
Area of bulletin board that can be made from 6 kg= 15 m² of bulletin board
The area of bulletin board that Maryann made for herself = 2 * 3 = 6m²
To make similar bulletin boards for her four friends, the total area of bulletin board made for her 4 friends = 6 * 4 = 24m²
To calculate the mass of burlap required to make a 24m² bulletin board, use equation (1)
0.4 = Mass / 24
Mass = 0.4 * 24
Mass = 9.6 kg
The mass of burlap used to make Maryann's bulletin board alone:
0.4 = Mass/6
Mass = 2.4 kg
Out of the 6kg that she got, she has used 2.4 kg for herself
The remaining mass of burlap = 6 - 2.4 = 3.6 kg
Therefore, to complete the bulletin board for her friend, she should collect (9.6 - 3.6) = 6 kg of bulletin more
Which problem could be solved with the expression 4 × (6+3)?
A. Connie has 4 beanbags. She bought 6 additional beanbags. She then played a game with the beanbags and lost 3 of them. How many beanbags does she have now?
B. Issa ate 6 marshmallows on Saturday and 4 marshmallows on Sunday. He follows this pattern for 3 weeks. How many marshmallows did he eat?
C. Mason goes on vacation with her family for 4 days. Each morning, she bikes 6 kilometers to the donut shop and then 3 more kilometers to the swimming hole. She rides home from the swimming hole in her mom's car. How many kilometers does Mason bike on vacation?
Thanks so much :)
Answer:
C. Mason goes on vacation with her family for 4 days. Each morning, she bikes 6 kilometers to the donut shop and then 3 more kilometers to the swimming hole. She rides home from the swimming hole in her mom's car. How many kilometers does Mason bike on vacation?
Step-by-step explanation:
For A., the equation would be 4 + 6 - 3
For B., the equation would be 3 x (6 + 4)
So our only option is C.
For C., the equation would be 4 x (6 + 3)
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▹ Answer
C. Mason goes on vacation with her family for 4 days. Each morning, she bikes 6 kilometers to the donut shop and then 3 more kilometers to the swimming hole. She rides home from the swimming hole in her mom's car. How many kilometers does Mason bike on vacation?
▹ Step-by-Step Explanation
The equation for A would be → 4 + 6 -3
The equation for B would be → 3 × (6 + 4)
The equation for C would be → 4 × (6 + 3)
Therefore, C is the correct answer.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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Peter makes a large amount of pink paint by mixing red and white paint in the ratio 2 : 3. Red paint costs £80 per 10 litres. White paint costs £5 per 10 litres. Peter sells his pink paint in 10-litre tins for £60 per tin. Calculate how much profit he makes for each tin he sells
Answer: £25
Step-by-step explanation:
Given the following :
pink paint production = mixing red and white paint in the ratio 2 : 3
Price of red paint = 80 per 10 Litre
Price of white paint = 5 per 10 Litre
Selling price of pink paint = £60 per 10 litre
Recall the ratio of red to white paint :
2 : 3 ; 2 +3 = 5
Therefore,
Amount of Red paint used:
= (2/5) × 10 ; 20/5 = 4,
Cost per Litre = 80 / 10 = £8
Cost of red paint = 4 × 8 = £32
Amount of white paints used:
= (3/5) × 10 ; 30/5 = 6
Cost per Litre = 5 / 10 = £0.5
Cost of white paint = 6 × 0.5 = £3
Total cost of production = £(32 + 3) = £35
Profit = selling price - product cost
Profit = £(60 - 35) = £25
Find the value of the function f(x) = x2 + 4x - 3, when x = -1.
Answer:
- 6
Step-by-step explanation:
[tex]f(x) = {x}^{2} + 4x - 3 \\ \: plug \: x = - 1 \\ f( - 1) = {( - 1)}^{2} + 4( - 1)- 3 \\ f( - 1) = 1 - 4- 3 \\ f( - 1) = 1 - 7 \\ \huge \red{ \boxed{ f( - 1) = - 6}} \\[/tex]
Please answer it now in two minutes
Answer:
Triangle E, F, G and Triangle T, U, V.
Step-by-step explanation:
They both are congruent because have the same shape, same size, and they both mirror each other.
Answer:
Triangle EFG and triangle TVU
Step-by-step explanation:
You must use congruent segments and keep track of the corresponding sides and vertices.
Triangle EFG and triangle TVU
You can do one or both if u do both I’ll give Brainlynest
Answer:
18) a. X
19) d. 69°
Step-by-step explanation:
18) A reflection is a transformation where an image is flipped over a line. So V will still be in the same place, it will just be flipped over line B. The only answer that makes sense in X.
19) All the angles in the picture are vertical angles. Vertical angles are angles that are across from each other when two lines cross and they are always equal.
The angle opposite the angle that is 78° is also 78°.
The angle opposite the angle that is 33° is also 33°.
The three angles form a straight line so:
78° + 33° + x = 180°
111° + x = 180°
x = 69°
Since the angle is a vertical angle and is opposite angle a, angle a will also be 69°.
Hope this helps. :)
A rectangle with an area of x2 – 4x – 12 square units is represented by the model. What side lengths should be used to model the rectangle? (x + 2) and (x – 6) (x + 6) and (x – 2) (x + 2) and (x – 10) (x + 10) and (x – 2)
Answer: (x+2) and (x-6) represents the side lengths.
Step-by-step explanation:
The area of the rectangle is [tex]x^{2} -4x -12[/tex] so in this case to find the side lengths we need to factor out the area.
To factor [tex]x^{2} -4x-12[/tex] We need to find two numbers that if we multiply together we will have -12 and if we add those two number we will get -4.
-6 and 2 works out
Because -6 * 2 = -12 and -6 +2 = -4
Now we will rewrite the area as
[tex]x^{2}[/tex] +2x - 6x -12 Group them
([tex]x^{2}[/tex] +2x) (-6x -12) factor them
x (x +2) -6(x+2) factor out x+2
(x+2)(x-6) Done!
Answer: The correct answer is A (x+2)(x-6) on Edg 2020;)
What is the range of the function shown on the graph above?
Answer:
A.
Step-by-step explanation:
Since range is y-axis based, we are looking at the y-values. We see that the endpoints of the graphed segment are closed points, so they are included in the range. That eliminates B (exludes values) and C (Not infinity, it's a segment, not a line). Choice A is the best answer because when you identify the y-values, you get -8 to -3 included.
Helppp!!!! please!!!
Answer:
A) 120 ft^2
Step-by-step explanation:
The total surface area is the sum of the areas of the 4 congruent triangular sides and the area of the square base.
TA = 4 * area of triangle + area of square
TA = 4 * bh/2 + s^2
TA = 4 * 6 ft * 7 ft/2 + (6 ft)^2
TA = 84 ft^2 + 36 ft^2
TA = 120 ft^2
Answer:
A) 120 ft^2
Step-by-step explanation:
How do you simplify:
[tex] \sqrt{(125 ^{2} } ) ^{ - \frac{1}{3} } [/tex]
Answer:
[tex]\huge\boxed{\sqrt{(125^2)^{-\frac{1}{3}}}=\dfrac{1}{5}}[/tex]
Step-by-step explanation:
[tex]\sqrt{(125^2)^{-\frac{1}{3}}}\qquad\text{use}\ (a^n)^m=(a^m)^n\\\\=\sqrt{\left(125^{-\frac{1}{3}\right)^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=125^{-\frac{1}{3}}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{125^\frac{1}{3}}\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\dfrac{1}{\sqrt[3]{125}}=\dfrac{1}{5}\qquad\text{because}\ 5^3=125[/tex]
PLS HELP ASAP The following probability distribution table shows information collected from a survey of students regarding their grade level and the transportation they use to arrive at school. What is the probability that a randomly selected eighth grader takes the bus?
Answer:
44%
Step-by-step explanation:
For these types of problems, look at the totals. We know that there are 0.44 out of 1 eighth graders. Since it doesn't specify how the 8th grader is dropped off, we take 0.44 and divide it by 1 (the total). We get 0.44, but since it's most likely asking for percentages, multiply that by 100.
What value of n makes the equation true?
-1/5n + 7=2
n=
Answer:
n = 25
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and is:
Parenthesis
Exponents & roots
Multiplication
Division
Addition
Subtraction
~
First, subtract 7 from both sides:
(-1/5)n + 7 (-7) = 2 (-7)
(-1/5)n = 2 - 7
(-1/5)n = -5
Next, multiply -5 from both sides:
(-1/5)(-5)n = (-5)(-5)
n = -5 * -5
n = 25
25 is your answer for n.
~
Answer: n = 25
Step-by-step explanation: In this equation, our first step is to isolate the n term by subtracting 7 from both sides.
On the left, +7 -7 cancels and we're left with -1/5n.
On the right, 2 - 7 simplifies to -5.
So we have -1/5n = -5.
In order to get n by itself, since it's being multiplied by a fraction,
we multiply both sides of the equation by the reciprocal of that fraction.
The reciprocal of -1/5 is -5/1.
So we multiply both sides of the equation by -5/1.
So we have (-5/1)(-1/5n) = -5(-5/1).
On the left, our 1's cancel and our 1's cancel.
Also, remember that a negative times a negative is a positive.
So on the left we are left with n.
On the right, -5(-5/1) is 25.
So n = 25.
A pyramid arena in Galveston, TX is a rectangular pyramid with a base area of 70,840ft^2 and a height of 12 stories. Each story is approximately 10 feet. Estimate the volume in cubic feet.
Answer:
approximate volume = = 28336 cubic ft.
Step-by-step explanation:
Base area = 70840 sq. ft
Each story is about 10 ft.
approximate height = 12*10 = 120 '
Volume of pyramid
= Base * height /3
= 70840 * 120 / 3
= 28336 cubic ft.
Answer: 2,833,600 [tex]ft^{3}[/tex]
Step-by-step explanation: Please see the image below!
explain the differences between an equation and an equality. how do those differences affect solutions.
Answer:. An equation is a mathematical statement that shows the equal value of two expressions while an inequality is a mathematical statement that shows that an expression is lesser than or more than the other. 2. An equation shows the equality of two variables while an inequality shows the inequality of two variables.
Step-by-step explanation:
2.2 units to the right of 0 horizontal number line
Answer:
2.2
Step-by-step explanation:
2.2 units to the right of zero indicates that the integer is positive on a horizontal number line.
0 + 2.2 = 2.2
Plz write it for me how u got it ❤️On paper then send it to me
Answer:
See below in bold.
Step-by-step explanation:
1. x^2 - 13x - 30
We need 2 numbers whose product is -30 and whose sum = -13.
They are -15 and + 2:
Answer is (x - 15)(x + 2).
2. 2x^2 + 4x - 126
First we can take 2 out to give:
2(x^2 + 2x - 63)
Now we need 2 numbers whose product is - 63 and sum = +2.
These are +9 and - 7 so
Answer is 2(x - 7)(x + 9).
3. -30x^3 + 3x^2 + 9x
First we can take out -3x to give
-3x(10x^2 - x - 3)
Now we want 2 numbers whose product is 10*-3 = -30 and whose sum is -1. They are -6 and +5 so we write the above as:
-3x(10x^2 + 5x - 6x - 3)
Now we factor the parentheses by grouping:
= -3x( 5x(2x + 1) - 3(2x + 1)
= -3x(2x + 1)(5x - 3) Answer.
The answer to the second part is 12x^2 - 13x - 21.
Part 3
1, 18.
2. 6.
3. = 5(2(-3)^2 - 3*3*4 + 4^2) - 3)) - 2(-3)(-3 + 7(4) - 1) - 3*4^2
= 5*(67) - 2(72) - 48
= 143.
4. (11m^2 - 7) - (6m^2 + 3m - 11) + (3m^2 - m - 9)
= 11m^2 - 7 - 6m^2 - 3m + 11 + 3m^2 - m - 9
= 8m^2 - 4m - 5
A = 8, B = 4 and C = 5.
Josh can paint a whole room in m hours while Kevin can paint a whole room in n hours. How many parts of the room can they paint in one hour if both of them worked together? Express in terms of m and n.
Work Shown:
Josh:
1 room = m hours
1/m room = 1 hour
Kevin:
1 room = n hours
1/n room = 1 hour
We see that the rates for Josh and Kevin are 1/m and 1/n respectively. This is the amount of a room they paint in one hour. Combine the fractions
1/m + 1/n = n/(mn) + m/(mn) = (n+m)/(mn) = (m+n)/(mn)
The expression (m+n)/(mn) represents how much of the room they get painted in 1 hour. This is if they work together and it assumes neither worker slows the other one down.
In the image, point A marks the center of the circle. Which two lengths must form a ratio of 1:2?
A.
A F:AE
B.
BC:EF
C.
EF:AI
D.
AI:EF
E.
AI:AD
Answer: AI:EF
Step-by-step explanation:
Answer:
D. ) AI:EF
Step-by-step explanation:
PLATO
As an estimation we are told £3 is €4. Convert £34.50 to euros.
Answer:
46 euros
Step-by-step explanation:
£30 = 40 euros
4.50 = £3 and £1.50
£3 = 4 euros
1.50 = 2 euros because you half the 4 euros because half of 3 is 1.50
hope this helps if not sorry
Answer:
€46
Step-by-step explanation:
→ We know £3 = €4, so we have to work out how many euros in £1
£3 = €4
(÷3) (÷3)
£1 = €1.3
→ Now we multiply £34.50 by €1.3 because we know £1 = €1.3
£34.50 × €1.3 = €46
A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?
Answer:
children take 3 pieces of candy are 6
Step-by-step explanation:
x+y=19-1 x+y=18
3x+5y=85-7 3x+5y=78
eliminate x by multiplying the first equation by 3:
3x+3y=54
3x+5y=85 subtract
(3x+3y)-(3x+6y)=54-78
3x-3y-3x-5y=-24
-2y=-24 y=-24/-2=12
y=12 , substitute for y:
x+y=18
x=18-12
x=6
check: 3x+5y=78
3(6)+5(12)=78
18+60=78 correct
4x - 1
2.
= x + 7
Can someone help please?
Answer:
6[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
4x-12 = x+7
4x-12+12 = x+7+12
4x = x+19
4x-x = x+19-x
3x=19
x = 6[tex]\frac{1}{3}[/tex]
And if we substitute the value of x into the equation 4x-12 = x+7,
we will get 13[tex]\frac{1}{3}[/tex] = 13[tex]\frac{1}{3}[/tex] in the end.
Hope this helps :)
Draw the graphs of y=2x plus 1
Hey there! :)
Answer:
Graphed below.
Step-by-step explanation:
Graphing y = 2x + 1 can be done by finding points on the line. Find the y and x intercepts to make graphing more simple:
Solving for the y-intercept:
y = 2(0) + 1
y = 1, or (0, 1). This is the y-intercept.
Solving for the x-intercept:
0 = 2x + 1
Subtract 1 from both sides:
-1 = 2x
Divide both sides by 2:
x = -1/2, or (-1/2, 0). This is the x-intercept. We can graph the equation given these two points.
The temperature each hour in Elma, Texas on October 1 is modelled by the equation
t(h) = 10 cos(15h - 10)° + 30 where his hour of the day with 0 meaning midnight, and t is the
temperature in degrees Celsius. How hot did it get in Elma on October 1?
Answer:
[tex]39.8^{\circ} C[/tex]
Step-by-step explanation:
We are given that the temperature each hour in Elma Texas on October 1 is modelled by the equation
[tex]t(h)=10cos(15h-10)^{\circ}+30[/tex]
Where h=Hour of the day with 0 meaning midnight
t=Temperature in degree Celsius
We have to find the temperature on October 1.
Substitute h=0
[tex]t(0)=10cos(15(0)-10)+30[/tex]
[tex]t(0)=10cos(-10)+30[/tex]
[tex]t(0)=39.8^{\circ} C[/tex]
Hence, the temperature in Elma on October 1=[tex]39.8^{\circ} C[/tex]
A line is defined by the equation y = two-thirds x minus 6. The line passes through a point whose y-coordinate is 0. What is the x-coordinate of this point? A coordinate plane.
Answer:
9
Step-by-step explanation:
Put the given information into the equation and solve for x.
y = (2/3)x -6
0 = (2/3)x -6 . . . . . substitute for y
0 = x - 9 . . . . . . . . multiply by 3/2
9 = x . . . . . . . . . . . .add 9
The x-coordinate of the x-intercept point is 9.
Answer:
x=9
hope this helps :>
2a + 5a x 4a - a simplify
Answer:
20a² + a
= a(20a + 1)
Step-by-step explanation:
2a + 5a × 4a - a
= 2a + 20a² - a
= 20a² + a
Consider triangle ABC. Triangle A B C. Angle C is 80 degrees and angles B and A are y degrees. What is the value of y in the triangle? Angle y = °
Answer:
y is equal to 50 degrees.
Step-by-step explanation:
The sum of the angles of a triangle is always 180 degrees. To find what y is, subtract 80 from 180 and divide the difference by 2. This will give you 50 degrees.
Answer:
y= 50°
Step-by-step explanation:
∠A =∠B = y. So, ΔABC is an isosceles triangle.
Sum of angles of triangle = 180
∠A + ∠B + ∠C = 180
y + y + 80 = 180 {add like terms}
2y + 80 = 180 {Subtract 80 from both sides}
2y + 80 - 80 = 180 - 80
2y = 100 {divide both sides by 2}
2y/2 = 100/2
y= 50°
An interior angle of a regular convex polygon is 140°. How many sides does the polygon have?
Answer:
hope it will help uh.....
in the function equation ff (xx ) = 1500 (1.43)^xx, is it growth or decay? what is the percent of the growth/decay? what is the initial value?
Answer:
The initial value is 1500
growth
43 % growth
Step-by-step explanation:
Exponential equations are in the form
y = a * b^x
a is the initial value
b is the growth or decay
b>1 is growth b-1 rate of growth
b <1 decay 1-b rate of decay
f(x) = 1500 * 1.43 ^x
The initial value is 1500
1.43 > 1 so it is growth
1- 1.43 = .43
Change to percent
43 % growth
Does anyone know the answer to the table below?
Hey there! :)
Answer:
16 minutes.
Step-by-step explanation:
Create an equation in the form y = mx + b to solve this problem. Begin by solving for the rate of change of the table using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in values from the table into the equation:
[tex]m = \frac{64 - 40}{9 - 5}[/tex]
Simplify:
[tex]m = \frac{24}{4}[/tex]
m = 6.
Plug in the slope and a point from the table into the equation
y = mx + b
40 = 6(5) + b
40 = 30 + b
40 - 30 = b
b = 10.
Rewrite the equation:
y = 6x + 10
To solve for how long it took her to ride 1 km, plug 1 into the equation:
y = 6(1) + 10
y = 6 + 10
y = 16 minutes.
HELP ME PLEASE ~ Thanks :)
Answer:
A
Step-by-step explanation:
99/479
formula: girls in action divided by everyone