Given:
The expression is
[tex]2\cos^2(\dfrac{x}{2})-\cos (x)[/tex]
To find:
The expression which is equivalent to the given expression.
Solution:
We have,
[tex]2\cos^2(\dfrac{x}{2})-\cos (x)[/tex]
We know that,
[tex]\cos x=2\cos^2 (\dfrac{x}{2})-1[/tex]
Using this formula, the given expression can be written as
[tex]2\cos^2(\dfrac{x}{2})-\left(2\cos^2(\dfrac{x}{2})-1\right)[/tex]
[tex]=2\cos^2(\dfrac{x}{2})-2\cos^2(\dfrac{x}{2})+1[/tex]
[tex]=1[/tex]
Therefore, the given expression is equivalent to 1.
Answer:
B
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(9, 1) and (5, -7)
Answer:
7;-3
Step-by-step explanation:
9+5/2 ; 1+(-7)/2
14/2 ; -6/2
7 ; -3
Kasey has 8 packages of gelatin. She plans to fill molds that each take 1 1/3 packages of gelatin.
Each mold can be divided into 6 servings. How many servings of gelatin can Kasey make?
Answer:
multiply 1 1/3 by 8x6 and see how many packages
Six 2-foot tall pine tress were planted during the school's observation of Earth Awareness Week in 1990. The trees have grown at an average rate of 3/4 foot per year. What Linear equation in y=mx+b y=mx+b form gives the height of the tree in terms of number of years since they were planted?
Answer:
The linear equation that gives the height of the tree in terms of number of years since they were planted is y = 3/4x + 2 OR y = 0.75x + 2
Step-by-step explanation:
In the linear equation, y =mx + b
This is the equation of a straight line where m is the gradient and b is the intercept on the y-axis.
In the equation, y represents the height of the trees after x years.
m is the gradient, that is, the rate at which the trees are growing.
and b is the height at the time they were planted, that is, at time x = 0.
From the question,
Six 2-foot tall pine trees were planted during the school's observation of Earth Awareness Week in 1990, that is,
b = 2
Also, from the question,
The trees have grown at an average rate of 3/4 foot per year, that is,
m = 3/4
Hence, the equation becomes
y = 3/4x + 2 ([tex]y = \frac{3}{4}x + 2[/tex])
OR
y = 0.75x + 2
Hence, the linear equation that gives the height of the tree in terms of number of years since they were planted is y = 3/4x + 2 OR y = 0.75x + 2.
Equation that represents the height of the tree in terms of number of years since they were planted
[tex]y=\frac{3}{4}x+2[/tex]
Given :
Six 2-foot tall pine tress were planted.
The trees have grown at an average rate of 3/4 foot per year.
We need to frame linear equation that represents the height of the tree in terms of number of years.
Linear equation is y=mx+b
where b is the initial height of the tree
m is the rate of growth of the tree
y is the final height of the tree
and x represents the number of years
Initial height of the tree is 2 foot
rate of growth is 3/4 foot per year
x is the number of years
Replace all the values inside y=mx+b formula
[tex]y=\frac{3}{4}x+2[/tex]
Equation that represents the height of the tree in terms of number of years since they were planted
[tex]y=\frac{3}{4}x+2[/tex]
Learn more : brainly.com/question/20816424
Dracula has 48 pieces of candy. He gave ⅓ of his candy to his friend and 25% of his candy to his cousin. How many pieces of candy does Dracula have left?
Answer:
Dracula will be left with 24 candies
Step-by-step explanation:
The given problem is of fractions and percentages.
Given that
Total pieces of candy = 48
Now as it is mentioned that Dracula gives 1/3 of his candies to his friend, wee have to find the one third of the total pieces of candies first.
[tex]one-third\ of\ candies = \frac{1}{3} * 48\\= 16[/tex]
Dracula will be left with:
[tex]Candies\ left = Total\ candies - one\ third\ of\ candies\\= 48-16 = 32[/tex]
Dracula will be left with 32 candies after giving one third to his friend.
Now he gives 25% of remaining to his cousin
So,
[tex]25\%\ of\ 32\\= \frac{25}{100}*32\\=8[/tex]
Dracula will be left with: 32-8 = 24 candies
Hence,
Dracula will be left with 24 candies
A jar of 26 dimes and quarters has a value of $3.50. How many of each
type of coins are there?
Answer:
6 quarters and 20 dimes
Which are equivalent expressions for root(3, 27 ^ 2) Select all that apply.
Answer:
the second one gives the same answer as the one in the question
Name a multiple of 13 that is between 30 and 100.
Answer:
39
Step-by-step explanation:
just did 13 plus 13 plus 13
What are the zeros of the function? h(t)=(t -4)(t+8)
Answer:
4 and -8
Step-by-step explanation:
Anything multiplied by 0 is 0. So we just need to find values of t which will give you a 0 by setting them equal to 0
[tex]t - 4 = 0\\\\t = 4\\\\t + 8 = 0\\\\t = -8[/tex]
rosy wants a large picture window put in her living room of her new house. the window is to be square with an area of 49 square feet. how long should each side of the window be
I NEED HELP PLEASE !!
Answer:
Step-by-step explanation:
Well looking it up on my link bar if you look up on google there's an answer key which for me its the second link on google!!
(PLZ help)
Which of the following expressions represents the value, in dollars, of a certain number of dimes, d, and pennies, p?
0.01d + 0.10p
0.10d + 0.01p
0.11dp
0.11d + p
Answer: The answer should be 0.10d + 0.01p
Step-by-step explanation: please give brainliest :)
scrieti primi doi mmultipli omuni ai numerelor naturale a) 4 si 6 b)6 si 9
raspunsul repede va rog
Answer:
Step-by-step explanation:
(a).
Multiples of 4 are {4, 8, 12, 16, 20, 24, 28, ..... }
Multiples of 6 are {6, 12, 18, 24, 30, ..... }
12 and 24
(b).
Multiples of 6 are {6, 12, 18, 24, 30, 36, 42, ..... }
Multiples of 9 are {9, 18, 27, 36, 45, ..... }
18 and 36
3
125 men and 150 women are at a wedding. Write this as a ratio of men to
women in its simplest form.
Answer:
The ratio of men to women in this situation is 5/6.
Step-by-step explanation:
If you rewrite this as a percentage, it is 83.33%.
And also the alternative form of the answer is 0.83.
Hope this helps and if you could mark as brainliest. Thanks!
Answer:
125 : 150
25 : 30
5 : 6
Step-by-step explanation:
men ' s ratio is 5 while women' s is 6
Write the missing number to make the fraction equivalent.
Answer:
the number is 30.
Step-by-step explanation:
Look at the denominators, 6 and 36.
6 x 6 = 36, so....
We multiply the 5 on top by 6 as well
5 x 6 = 30
So, the number is 30.
hope this helped!
Answer:
30/36
Step-by-step explanation:
In 8 hours, Raina reads 56 chapters of a book.
What is her rate in chapters per hour?
Answer:
7
Step-by-step explanation:
40x + 44 = 38x + 44
Answer:
x = 0
Step-by-step explanation:
40(0) + 44 = 38(0) + 44
44 = 44
When x = 0 the equation is true
Answer:
x=no solution
Step-by-step explanation:
40x+44=38x+44
-44 -44
40x=38x
The product of two consecutive even integers is 2208. What is their sum?
Answer:
±94
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Standard Form: ax² + bx + c = 0Solving Quadratic EquationsConsecutive IntegersStep-by-step explanation:
Step 1: Define
x (1st consecutive term)
x + 2 (2nd consecutive term)
Step 2: Set up equation
x(x + 2) = 2208
Step 3: Solve for x
Distribute x: x² + 2x = 2208Rewrite in Standard Form: x² + 2x - 2208 = 0Factor quadratic: (x - 46)(x + 48) = 0Find roots: x = -48, 46Step 4: Identify Consecutive Integers
Possibility 1: x = -48
1st Consecutive Even Term: -48
2nd Consecutive Even Term: -48 + 2 = -46
Possibility 2: x = 46
1st Consecutive Even Term: 46
2nd Consecutive Even Term: 46 + 2 = 48
Step 5: Find sums
Possibility 1: x = -48
-48 + -46 = -94
Possibility 2: x = 46
46 + 48 = 94
Every 125 pages that Raul reads during his summer reading challenge, he will collect 5 book points to use at his local library. Which graph models a relationship with the same unit rate?
Answer:
The answer is "[tex]\frac{1}{25}[/tex]"
Step-by-step explanation:
They might claim that perhaps the ratio to Raul would've been:[tex]\frac{y}{x} = \frac{5}{125} = \frac{1}{25}[/tex] per each 125(x) page, which he reviewed throughout a summer competition.
Raul's cost per unit for each paragraph reads is [tex]\frac{1}{25}[/tex] page points, that's why the model a link with the same unit rate. please find the graph in the attached file.
What I Know (Pre-Test)
Click the pin
I am still grade 5
Okay I ned high age so I can get in Brainly ph
Dis is my 3/5 account
Answer:
1. 1/7 x 7/1= 1
2. 5/9 x 9/5= 1
3. 23/11 x 11/23= 1
4. 13/61 x 61/13= 1
5. 8/9 x 9/8= 1
Explanation:
when finding the reciprocal of a fraction, the numerator becomes the denominator, and the denominator becomes the numerator. keep in mind that when you multiply a fraction by its reciprocal, it will always equal 1.
Leo dug up 6 4/5 pounds of
treasure on his first dig. Anne dug
up 4 1/2 pounds of treasure. How
much more treasure did Leo dig
up than Anne?
on the first day of camp, Sara hiked 20 miles in 5 hours. At this rate how long would it take Sara to hike 12 miles?
Answer:
3 hours
Step-by-step explanation:
20 ÷ 5 = 4 mph
12 ÷ 4 = 3 hours
hope this explanation makes sense! :)
Sara took 3 hours to hike 12 miles if, on the first day of camp, Sara hiked 20 miles in 5 hours and the rate is 4 miles per hour.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
On the first day of camp, Sara hiked 20 miles in 5 hours.
The rate = 20/5 = 4 miles per hour
Let x be the time taken by Sara to hike 12 miles
As its rate of speed of Sara is 4 miles per hour
x = 12/4
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.
x = 3 hours
Thus, Sara took 3 hours to hike 12 miles if, on the first day of camp, Sara hiked 20 miles in 5 hours and the rate is 4 miles per hour.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
A rectangle has a height of 4 and a width of x2 + 3x + 2.
Express the area of the entire rectangle.
Expression should be expanded.
Hence, we know that area of rectangle is equals to the product of length and breadth.
Therefore, the area of rectangle is,
[tex] = 4 \times( {x}^{2} +3x + 2 ) \\ = 4({x}^{2} + 3x + 2) \\ = \green{ \boxed{4 {x}^{2} + 12x + 8}}[/tex]
Therefore, the answer is 4x² + 12x + 8.
What's the recursive rule for the arithmetic sequence described in the following list? Use the rule to find the eighth term of the sequence.
5, 9, 13, 17, 21
Answer:
33
Step-by-step explanation:
T8 = A + (8 - 1) d
T8 = 5 + 7d
T8 = 5 + 7(4)
T8 = 5 + 28
T8 = 33
note : d is the common difference gotten from T2 - T1
Answer:
33
Step by step explanation:
Eight term of the sequence = a + 7d
where:
a= first term
d= common difference
first term = 5
common difference = 4
= 5 + 7(4)
= 5 + 28
= 33
80+300????????????????
Answer:
380
Step-by-step explanation:
300+80=380
Hope that helped.
A triangle has sides with lengths 4.15, 7.092 and 12.45. What is the perimeter of the triangle?
Answer:
Perimeter = 23.692 units
Step-by-step explanation:
Perimeter = sum of all his sides
then:
Perimeter = 4.15 + 7.092 + 12.45
Perimeter = 23.692 units
James went to the store and bought a pair of shoes on sale for $40.00. This week they were a regular price of $64.50. What was the percent discount that he bought the shoes for?
I need work shown.
Answer:
A. 62%
Step-by-step explanation:
64.50x = 40
x = 0.62015 or 62%
This means 62% of original price is $40, discount is 38%. From your options seem to be asking for percent of original price paid and not discount.
for what values of x is x2+2x=24 true?
-6 and -4
-4 and 6
4 and -6
6 and 4
Answer:
It is actually choice c
Step-by-step explanation:
I took the test
Answer:
c
Step-by-step explanation:
banlest plzz
Help me with this please
Answer:
101.5m left to use after the big top goes up.
Step-by-step explanation:
18*10=180 [tex]\pi[/tex]r[tex]x^{2}[/tex]= 3.14*5^{2}=3.14*25=78.5
180-78.5= 101.5m
3
Sean scored 48 points in 16 basketball games
last season. Approximately how many points did
Sean average per game?
A. .33
B. 3
C. 64
D. 768
Answer: a
Step-by-step explanation:
least to greatest. 3/20 45% 1/5 7.5% Someone please answer this I need it ASAP
Answer:
3/20, 7.5%, 1/5, 45%