Answer:
[tex](cosA + cos B)^2 + (sin A +sinB)^2 \\\\= cos^2A + cos^2B + 2cosA cosB + sin^2A +Sin^2B +2sinAsinB\\\\=(cos^2A + sin^2 A) + (cos^2B +sin^2B) +2cosAcosB + 2sinAsinB\\\\= 1 + 1 + 2cosAcosB + 2sinAsinB\\\\=2 + cos(A+B)+cos(A-B) + cos(A-B) -cos(A+B)\\\\=2 + 2cos(A-B)\\\\=2(1 + cos(A-B))\\\\=2\times 2 cos^2(\frac{A-B}{2})\\\\=4cos^2(\frac{A-B}{2})[/tex]
Hence proved .
In a 3-digit number, the hundreds digit is one more than the ones digit and the tens digit is twice the hundreds digit. If the sum of the digits is 11, find the number. Plz give equation and answer.
Answer:
362
Step-by-step explanation:
Let the ones digit equal x. If the ones digit is one, then the hundreds digit is one more than it or x + 1. And, since the tens digit is twice the hundreds digit, you can say it is 2(x + 1) or as simplified: 2x + 2. Now, we are given the sum of the digits is 11, so if we add all of them, they should be equal to 11:
x + x + 1 + 2x + 2 = 11
We can combine like terms:
4x + 3 = 11
4x = 8
x = 2
So, the ones digit is 2. Since the hundreds digit is one more, it's 3. And because the tens is twice the hundreds, it's 6. The number is 362.
Answer:
362
Step-by-step explanation:
Hundreds:x
Tens:2x
Ones:x-1
x+2x+x-1=11=equation
3x-1=11
3x=12
x=4-1
x=3
solve the equation
2/3 x (−4/5)
Answer:
below is correct
Step-by-step explanation:
A 15-foot ladder leans against the side of a house with its base 4 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth.
Answer: The ladder reaches 14.46 feet up of the building.
Step-by-step explanation:
According to Pythagorean theorem,
In a right triangle,
(Hypotenuse)²= (Base)²+(perpendicular)^2
Using given information, we have
[tex](15)^2=(4)^2+(height)^2\\\\225=16+(height)^2\\\\(height)^2=209\\\\ (height)^2=\sqrt{209}\approx14.46\ feet[/tex]
Hence, the ladder reaches 14.46 feet up of the building.
To simplify the following expression, which operation would you complete third?
9 + (16 - 2) 42 ÷ 8
simplify the exponent
multiply
add
divide
|x| > - 16 what is the value of x
9514 1404 393
Answer:
x ∈ all real numbers
Step-by-step explanation:
The given inequality is true for any value of x. The absolute value of a quantity is always greater than any negative number.
Jim sells hot dogs for $2.95 each and steak sandwiches for $9.95 each out of his food cart. During a busy outdoor festival, he sold a total of 985 items for $7343.75. How many steak sandwiches did he sell?
Answer:
634 steak sandwiches.
Step-by-step explanation:
Let's say X is the number of hot dogs and Y is the number of steak sandwiches.
2.95x + 9,95y = 7343.75
x + y = 985
y = 985 - x
2.95x + 9.95(985-x) = 7343.75
2.95x + 9800.75 - 9.95x = 7343.75
7x = 2457
x = 351
y = 985 - 351
y = 634
Question 4(Multiple Choice Worth 1 points) (06.07 LC) Which expression is equal to 3x? Ox+ 3 Ox+ x + x O x + x2 0 2x + 1 ting
Answer:
the answer is :.......
x+x+x
Answer:
x+x+x
Step-by-step explanation:
What is the diameter of a circle with a circumference of 11.27pi ft? Use pencil and paper.
The diameter is ... ft
Answer:
[tex]circumference = \pi \: d \\ 11.27\pi = \pi \: d \\ d = 11.27 \: ft[/tex]
NEED HELP ASAP!!!!
3/4 + (1/3 ÷ 1/6) - (-1/2)=?
A:1/4
B:1 1/4
C:3/4
D:2 1/4
⚠️NO LINKS OR I WILL REPORT⚠️
Answer:
anser is 3.24 or 3 and 1/4
Step-by-step explanation:
Answer:
3 1/4
Step-by-step explanation:
3/4+(1/3 ÷1/6)-(-1/2)=
3/4+(2)+1/2
3/4+5/2
3/4+10/4
13/4
3 1/4
Rita can make 8 cakes for a bakery each day. So far she has orders for more than 32 cakes. Right now, Rita needs more than four days to make cakes. Write the inequality for the statement in bold. The other numbers are not needed. Use m.
Answer:
m ≥ 4
Step-by-step explanation:
8m ≥32
m ≥ 4 where m is the number of days needed to make the cakes so it needs 4 or more days to make 32 cakes
A store has a sale with 10% off every item. When you enter the store, you receive a coupon that states that you receive an additional 10% off. Is this equal to a 20% discount
Answer: It's not equal to 20% discount.
Step-by-step explanation:
Let's assume the cost of a good is $100. Since there's 10% off on every item, the cost of the good will be:
= $100 - (10% × $100)
= $100 - $10
= $90
Since the coupon states that one will receive an additional 10% off, therefore the amount that the person will pay will be:
= $90 - (10% × $90)
= $90 - (0.1 × $90)
= $90 - $9
= $81
If the same good is $100 and there's a 20% discount, the amount that'll be paid will be:
= $100 - (20% × $100)
= $100 - (0.2 × $100)
= $100 - $20
= $80
Therefore, it's not equal to 20% discount.
Pls answer ASAP!! If you could give an explanation that would be awesome!!!
Answer:
D, u selected the right one
Step-by-step explanation:
A: asking the teachers who have cafeteria duty won't help you find out why students don't want to buy lunch.
B: the students that are already waiting in line for lunch won't help you find out why student don't want to buy lunch either because they are buying the lunch.
C: Asking all the teachers won't help because you want to know why students don't buy lunch
D: Asking students in the school will help because the students will be able to tell you exactly why THEY don't buy lunch.
How many solutions will the following equation have? 2x - 7 = -3x + 5
a. One Solution
b. Infinite Solutions
c. No Solutions
Answer:
one solution lets see[tex]2x - 7 = 3x + 5 \\ - x = 12 \\ x = - 12[/tex]
If you just want to check then substitute the value
[tex]2x - 7 = 3x + 5 \\ 2 \times ( - 12) - 7 = 3 \times ( - 12) + 5 \\ - 24 - 7 = - 36 + 5 \\ - 31 = - 31[/tex]
Hope it helps
what is the area of the pentagon shown below a.27 square feet b. 58.5 c.85.5 d.117
Explain why.
Answer:
Option B, Area of pentagon = 58.5 Square feet
Step-by-step explanation:
The remaining part of the question is attached as image
Solution
Area of pentagon has a triangle and a trapezoid
Area of triangle = 0.5 *base *height = 0.5*9 *3 = 13.5 square feet
Area of trapezoid = Area of rectangle – 2* area of smaller triangles
= 9 ft * 6ft – ( 2 * 0.5 * 6 ft * (9 ft – 6ft) /2
= 54 – (1*6*1.5)
Area of pentagon = 13.5 + 45 = 58.5 Square feet
Hence, option B is correct
30p+2
can you please answer
Answer:
2(15p+1)
Step-by-step explanation:
hope this helps
Jeanette's Pie Shop recently sold 14 pies, of which 4 were blackberry pies. What is the experimental probability that the next pie sold will be a blackberry pie?
Write your answer as a fraction or whole number.
P(blackberry pie)=
Answer:
2/7
Step-by-step explanation:
All I did was just simplify the fraction 4/14
4/14=2/7
0.009 divided by 0.001
Answer:
9
Step-by-step explanation:
0.001 · 9 = 0.009
Multiply 3 1/3 x 1 1/7
write the answer in simplest form.
What is the median of these numbers 2.4,2.8,2.3,2.9,2.9
Answer:
2.8
Step-by-step explanation:
x2.3, x2.4, 2.8, x2.9, x2.9
A free carnival game offers a prize of $100 If you hit a balloon with a dart and $20 if you at least get the dart to stick on
the board. You win nothing otherwise. You play once. Let X be the amount of money you win. Which of the following
are possible values of X?
$80
$100
$20
$120
$0
Answer:
120 po
thanks again byeeee
A mechanical system has 3 subsystems in series, each has reliabilities 98%, 96% and 94%, respectively. What is the overall reliability of the system
Answer:
The overall reliability of the system is 99.9952%
Step-by-step explanation:
Probability of the system not working:
None working, the first with 2% probability of not working(as it has 98% probability of working), the second with 4% and the third with 6%. So
0.02*0.04*0.06 = 0.000048
Probability of the system working:
1 subtracted by the probability of the systme not working.
1 - 0.000048 = 0.999952
0.999952*100% = 99.9952%
The overall reliability of the system is 99.9952%
)A set of equations is given below:
Equation A: y = x + 1
Equation B: y = 4x + 5
Which of the following steps can be used to find the solution to the set of equations?
x + 1 = 4x + 5
x = 4x + 5
x + 1 = 4x
x + 5 = 4x + 1
Answer:
x + 1 = 4x + 5
Step-by-step explanation:
Simultaneous equations to solve x so equate the equations together.
Answer: x + 1 = 4x + 5 (first option)
A cupcake recipe takes 3 cups of flour for every 2 dozen cupcakes. How many cups of flour does Sally need to make 96 cupcakes? Use the table to help.
Answer: 12 cups of flour
Step-by-step explanation:
12 cups of flour 3 + 3 + 3 + 3 = 12 because I have to make 96 cupcakes for tomorrow.
The amount of flour required will be 8 x 1.5 = 12 cups of flour. Option A is correct.
What is the Ratio?The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
To make 2 dozen cupcakes, the recipe requires 3 cups of flour. Therefore, for 1 dozen cupcakes, the recipe requires 1.5 cups of flour (since 2 dozen cupcakes = 2 x 1.5 = 3 cups of flour).
To make 96 cupcakes, Sally needs 8 dozen cupcakes (since 8 x 12 = 96). Therefore, the amount of flour required will be 8 x 1.5 = 12 cups of flour.
So, the answer is 12 cups of flour, and the explanation should be:
To make 2 dozen cupcakes, the recipe requires 3 cups of flour. Therefore, for 1 dozen cupcakes, the recipe requires 1.5 cups of flour. To make 96 cupcakes, Sally needs 8 dozen cupcakes.
Therefore, the amount of flour required will be 8 x 1.5 = 12 cups of flour.
Learn more about Ratio here:
brainly.com/question/13419413
#SPJ2
Calculate the variance and the standard deviation for the following sample data. Scores: 7, 9, 0, 1, 7, 4, 4, 7, 6
Answer:
Variance = 9
Standard deviation = 3
Step-by-step explanation:
Step 1
Find the Mean
Means = Sum of values/Number of values
= 0 + 1 + 4 + 4 + 6 + 7 + 7 + 7 + 9/9
= 45/9
= 5
Step 2
The formula for Sample variance
= (x - Mean)²/n - 1
Where
n = number of values = 9
Hence:
Sample variance =
( (0 - 5)² + (1 - 5)²+ (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (7 - 5)² + (7 - 5)² + (9 - 5)²)/9 - 1
= (-5² + -4²+ -1² + -1² + 1² + 2² + 2² + 2² + 4²) /8
= (25 + 16 + 1 + 1 + 1 + 4 + 4 + 4 + 16)/8
= 72/8
= 9
Sample Standard deviation = √Sample variance
= √9
= 3
A website has a 24-hour sale offering 12% off all purchases.
Dina buys a sweatshirt in the sale.
She pays £24.20 for the sweatshirt.
Calculate the original price of the sweatshirt.
Answer:
the given 24.20 is not the discount so we have to subtract it by 100%
maths question is here
9+92*12312
Answer:
it would be 101 i believe
Answer:
1,132,713
Step-by-step explanation:
9+ 92 * 12312
= 9 + 1,132,704
= 1,132,713
The area of a square is 58 inches, what is the side length
Answer:
About 7.62
Happy learning!
--Applepi101
Answer:
the side length is ≈7.62 in
Step-by-step explanation:
An alligator if drawn at the scale of 1:84. In the drawing, it is 5.9 cm long. How long is the actual alligator? i am having troubles please help.
Answer: r
Step-by-step explanation:
Answer:
495.6 cm, or 4.956 m
Step-by-step explanation:
1:84 means that a centimeter on the drawing has to be multiplied 84 times in order to find the real length. Therefore, 5.9 x 84 = 495.6
Cathy lives in a state where speeders are fined $15 for each mile per hour over the speed limit. Cathy was given a ticket for $105 for speeding on a road where the speed limit is 60 miles per hour. How fast was Cathy driving?
Given :
Cathy lives in a state where speeders are fined $15 for each mile per hour over the speed limit.
Cathy was given a ticket for $105 for speeding on a road where the speed limit is 60 miles per hour.
To Find :
How fast was Cathy driving.
Solution :
Let, speed of Cathy is v miles per hour.
Number of miles per hour over the speed limit, n = v - 60 miles per hour.
It is given that speeders are fined $15 for each mile per hour over the speed limit.
So, total amount of fine for Cathy is :
105 = 15×( v - 60 )
v-60 = 7
v = 67 miles per hour
Therefore, Cathy was driving with speed of 67 miles per hour.
factorize (2u+3u)(u+v)-2u+3v
Answer:
Step-by-step explanation:
(2u+3u)(u+v)-2u+3v
=2u(u+v)+3u(u+v)-2u+3v
=2u^2+2uv+3u^2+3uv-2u+3v
=5u^2+5uv-2u+3v