NOTES:
1)⇒ A + B + C = 180°
A + B + C = π
A + B = π - C
2)⇒⇒ sin (A + B) = sin (π - C)
= (sin π)(cos C) - (sin C)(cos π)
= (0)(cos C) - (sin C)(-1)
= 0 - (-sin C)
= sin C
3)⇒⇒⇒cos (A + B) = cos (π - c)
= (cos π)(cos C) + (sin π)(sin C)
= (-1)(cos C) + (0)(sin C)
= - cos C
4)⇒⇒⇒⇒ sin 2A + sin 2B = 2 sin (A + B) cos (A - B)
PROOF (from left side):
sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
2 sin (A + B) cos (A - B) + sin 2C refer to NOTE 4
2 sin (A + B) cos (A - B) + 2 sin C cos C double angle formula
2 sin C cos (A - B) + 2 sin C cos C refer to NOTE 2
2 sin C [cos (A - B) + cos C] factored out 2 sin C
2 sin C [cos (A - B) - (cos(A + B)] refer to NOTE 3
2 sin C [2 sin A sin B] sum/difference formula
4 sin A sin B sin C multiplied 2 sin C by 2 sin A sin B
Proof completed: 4 sin A sin B sin C = 4 sin A sin B sin C
Pygmies do not plant their own , but they will work in them in exchange for food or tools
Answer:
it was a fill in the blank question and the answer is gardens
Step-by-step explanation:
A circle has an area of 5050 square meters. Which answer is closest to the measure of its diameter?
Paws at play made a total of $1,234 grooming 22 dogs. Paws at play charges $43 to groom each small dog and $75 for each large dog. Write a system of equations that can be used to determine the number of small and large dogs that were groomed
Answer:
The system of equation can be used for determine the number of small and the large dogs groomed are
x + y = 22
43x + 75y = 1234
Step-by-step explanation:
Let us assume that the number of small dogs groomed be x.
Let us assume that the number of lagre dogs groomed be y.
As given
Paws at play made a total of $1,234 grooming 22 dogs.
Than the equation becomes
x + y = 22
Paws at play charges $43 to groom each small dog and $75 for each large dog.
Than the equation becomes
43x + 75y = 1234
Therefore the system of equation can be used for determine the number of small and the large dogs groomed are
x + y = 22
43x + 75y = 1234
6 is 24% of a number, what is 40% of the same number?
A. 8
B. 10
C. 15
D. 20
E.25
SHOW ALL WORK
Answer:
B. 10
Step-by-step explanation:
6 = .24 * x
Solve for x
Divide each side by .24
6/.24 = x
25 =x
Now find 40% of 25
25*.4 = 10
"Match the vocabulary word with the correct definition. (altitude of a triangle, base angles, base of an isosceles triangle, centroid, median of a triangle, orthocenter, vertex angle )
1. The two angles that include the base of an isosceles triangle.
2. A point on the interior of a triangle in which the three medians of the triangle intersect.
3. A segment from a vertex perpendicular to the opposite side.
4. A point in which the three altitudes of the triangle intersect. It is possible for the orthocenter to occur on the triangle, on the interior of the triangle or on the exterior of the triangle.
5. The angle formed by the two equal sides of an isosceles triangle.
6. A segment from a vertex to the midpoint of the opposite side.
7. The third, unequal side of an isosceles triangle."
1. base angles
2. centroid
3. altitude of a triangle
4. orthocenter
5. vertex angle
6. median of a triangle
7. base of an isosceles triangle
Answer:
1.Base angles.
2.Centroid.
3.Altitude of a triangle.
4. Orthocenter.
5.Vertex angle.
6.Median of triangle.
7. Base of an isosceles triangle.
Step-by-step explanation:
1. Base angles: The two angles that include the base of an isosceles triangle.
2. Centroid: A point on the interior of a triangle in which the three medians of the triangle intersect.
3.Altitude of a triangle:A segment from a vertex perpendicular to the opposite side.
4.Orthocenter: A point in which the three altitudes of the triangle intersect .It is possible for the orthocentre to occur on the triangle ,on the interior of the triangle or on the exterior of the triangle.
5.Vertex of angle:The angle formed by the two equal sides of an isosceles triangle.
6.Median of triangle:A segment from a vertex to the midpoint of the opposite side .
7.Base of an isosceles triangle: The third , unequal side of an isosceles triangle.
Solve the inequality and enter your solution as an inequality comparing the variable to the solution in the box below. 18 + x > 42Solve the inequality and enter your solution as an inequality comparing the variable to the solution in the box below. 18 + x > 42
Hi there! :)
Answer:
x>24
*The answer must have a positive sign and greater than symbol sign.*
Step-by-step explanation:
First, you switch sides.
[tex]x+18>42[/tex]
Then, you subtract by 18 from both sides of an equation.
[tex]x+18-18>42-18[/tex]
Finally, you subtract by the numbers from left to right.
[tex]42-18=24[/tex]
Final answer is x>24
I hope this helps you!
Have a nice day! :)
-Charlie
:D
A large asteroid crashed into a moon of another planet causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic progression 18,54, 90,126, . Find the distance that the projectile traveled in the eighth second.
Answer:
270 feet
Step-by-step explanation:
From the sequence given, we can see that the asteroid travels 36 feet more with each second. (as seen [tex]54-18=36[/tex] and [tex]90-54=36[/tex] etc.)
So 5th second, it will travel: [tex]126+36=162[/tex]
6th second, it will travel: [tex]162+36=198[/tex]
7th second, it will travel: [tex]198+36=234[/tex]
8th second, it will travel: [tex]234+36=270[/tex]
Hence, in the eighth second, the projectile traveled 270 feet.
The distance the projectile travels in the eighth second is found to be 270 feet.
The question asks for the distance a projectile travels in the eighth second, given that the distances it covers each second form an arithmetic progression with initial distances given as 18, 54, 90, 126, etc. In an arithmetic progression, the difference between any two consecutive terms is constant, known as the common difference.
To find the common difference (d), we subtract the first term from the second term:
d = 54 - 18 = 36
The nth term of an arithmetic sequence can be found using the formula:
T(n) = a + (n - 1)d
Here, a represents the first term, which is 18, and d is the common difference we found to be 36. Substituting the values to find the eighth term:
T(8) = 18 + (8 - 1) x 36T(8)
= 18 + 7 x 36T(8)
= 18 + 252T(8) = 270
Thus, the distance the projectile travels in the eighth second is 270 feet.
Consider the function f(x)=−2/3x+1.
What is f(3)?
f(3)=?
Answer:
Alright well Graph the line using this slope and Y-intercept, or two points
Slope: - 2/3
Y - intercept: 1 Hope this helps have a nice day :)
Step-by-step explanation:
And if you want i can explain the Answer with detail
Answer:
f(3) = [tex]\frac{7}{9}[/tex]
Step-by-step explanation:
The given function is
f(x)= [tex]\frac{-2}{3x}+1[/tex]
To find is the value of f(3)
Now we can find the value of a function by putting the vlaue in the given equation of the function
we can see that we have to find the value of f(3) and or given function is f(x)
so we have to put the value of x to be equal to 3 so that we can get the value of the desired function at a given point
Now
In this
x =3
f(x) = [tex]\frac{-2}{3x}+1[/tex] ................(i)
Put x = 3 in equation (i)
it becomes
f(3) = [tex]\frac{-2}{3*3}+1[/tex]
f(3) = [tex]\frac{-2}{9}+1[/tex]
Taking the LCM and solving it
LCM of 1 and 9 is 9 so it becomes
f(3) = [tex]\frac{-2+9}{9}[/tex]
f(3) = [tex]\frac{7}{9}[/tex]
which is the required value
What is the equation of the line that passes through the points (−2, 1) and (1, 10)?
3x − y = −7
3x − y = −5
3x − y = 5
x + 3y = −5
Answer:
3x - y = -7
Step-by-step explanation:
y = mx + b
m = deltay/deltax
m = (10 - 1)/[( 1 - (-2)]
m = 9/3 = 3
y = 3x + b
From (-2 | 1) we see that when x = -2, y = 1
Placing into the equation, in order to find b (y-intercept)
y = 3x + b
1 = 3(-2) + b
b = 7
y = 3x + 7 or 3x - y = -7
Calculate the slope (m) using the two provided points and use it along with one of the points in the point-slope formula.
Simplify to get the slope-intercept form, and rearrange to find the equation in standard form, which is 3x - y = -7.
Explanation:To find the equation of a line that passes through two given points, first you determine the slope (m) by using the slope formula m = (y2 - y1) / (x2 - x1).
For the points (-2, 1) and (1, 10), we find the slope as (10 - 1) / (1 - (-2)) = 9 / 3 = 3.
Knowing the slope, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), and plug in one of the points, say (-2, 1), to get y - 1 = 3(x + 2).
Better express this equation in slope-intercept form y = mx + b by simplifying it to y = 3x + 7.
To find the standard form, which typically looks like Ax + By = C, rearrange terms to get 3x - y = -7.
This is the standard form equation of the line that passes through (-2, 1) and (1, 10).
Holly and her 2 brst friends go to dinner. Their total bill is 31.84. They use a coupon for 15% off the total. If they split the bill evenly, how much will each person owe, to the nearest tenth?
Xavier downloaded 40 songs last week, including 14 jazz songs. What percent of Xavier's downloads were jazz songs
About 35% of the songs Xavier downloaded were jazz songs. This was calculated by dividing the number of jazz songs (14) by the total number of songs (40) and then multiplying the result by 100.
Explanation:Xavier downloaded a total of 40 songs. Out of these, 14 were jazz songs. To find the percentage of jazz songs out of the total, we need to divide the number of jazz songs by the total number of songs and then multiply the result by 100.
So, the calculation would be (14/40) * 100. When we do the math, we find that about 35% of Xavier's downloads were jazz songs.
Learn more about Percentages here:https://brainly.com/question/32197511
#SPJ3
Joseph needs to find the quotient of 3,216 divided by 8 in what play is the first digit in the quotient
Answer:
3216/8 is = to 402
Step-by-step explanation:
So I am not sure what you are asking sorry
Help!!! #2 Problem Set
Answer:
Independent: time (minutes)
Dependent: Distantce (inches)
Step-by-step explanation:
h(x)=17+ x/6
find x.
i will give brainliest 100 points
Answer:
x = -11
Step-by-step explanation:
h(x) = 17 + x/6
times 6
6 = x + 17
subtract 17
-11 = x
Answer:
H x − x 6 = 17
Step-by-step explanation:
An entertainment firm offers several DJ choices and light shows that range in price based on the rental time period.
The DJ's cost between $219.00 and $369.00 per night and the light shows cost between $159.00 and $309.00 per night.
If you are booking both a DJ and a light show, write a compound inequality that represents the possible total amount you would pay, x.
MUST SHOW VALID WORK :)
Answer:
378 ≤ x ≤ 678
Step-by-step explanation:
If you're looking to book both a DJ and a light show we have to take into account the minimum that you'll pay up to the maximum cost "x". This can be done by adding the lowest cost for both meaning:
$219 + $159 = $378
And the most you'll pay:
$369 + $309 = $678
So you can say that the amount you'll pay is in between $378 and $678. Mathematically speaking you can also say that you'll pay more than or equal to $378 and less than or equal to $678. The previous statement can be written mathematically as a compound inequality as such:
[tex]378\leq x\leq 678[/tex]
20 POINT'S!!!!!!!!!
HELP!!!
Well, the base and height would still be applicable (essentially, base is just width and height is just, uh, height,)
So basically the area of one triangle is 0.5(7*6), which is 21
The area of one triangle is option c., 21.
Answer:
The answer is B or 21
Step-by-step explanation:
I took the assignment
Which expression is equal to 2x/x-2 - x+3/x+5 ?
Following are the complete solution to the given expression:
Given:
[tex]\bold{\frac{2x}{x-2} - \frac{x+3}{x+5}}[/tex]
To find:
Solve expression=?
Solution:
[tex]\to \bold{\frac{2x}{x-2} - \frac{x+3}{x+5} = \frac{2x(x+5) -(x+3)(x-2)}{(x-2)(x+5)}}[/tex]
[tex]\bold{= \frac{2x^2+10x -(x^2+x-6)}{(x-2)(x+5)}}\\\\\bold{= \frac{2x^2+10x -x^2-x+6}{(x-2)(x+5)}}\\\\\bold{= \frac{x^2+9x+6}{(x-2)(x+5)}}\\\\[/tex]
Therefore, the final answer is "4 Option".
Learn more:
brainly.com/question/22052130
The weight of water is 62 and one half lb per cubic foot. What is the weight of 18 and one fourth cubic feet of? water? How much does 18 and one fourth cubic feet of water? weigh?
Answer:
Water - 62.5 pounds per cubic foot
18.25 cubic feet would weigh 18.25 * 62.5 =
1,140.625 pounds.
Step-by-step explanation:
The most popular pizza at pavone's pizza is a 10-inch personal pizza with one topping.What is the area of a pizza with a diameter of 10 inches?Round your answer to the nearest hundredth
a= [tex]\pi[/tex] [tex]r^{2}[/tex]
The area of a pizza with a diameter of 10 inches is 78.5.
Use synthetic division to solve (x^3-x^2-17x-15) / (x-5). What is the quotient?
Answer:
Quotient is [tex]1x^2 + 4x +3[/tex]
Step-by-step explanation:
[tex](x^3-x^2-17x-15)[/tex]
The coefficient of given expression is 1, -1, -17, -15
we divide by x-5, that is x=5
5 1 -1 -17 -15
5 20 15
1 4 3 0 ---> Remainder
Answer 1, 4, 3 is the quotient
We write quotient as 1x^2 + 4x +3
Answer:
A on eden
Step-by-step explanation:
Did the test
5x^2-(3xy-7x^2)+(5xy-12x^2)
When x=-0.25, and y=4
[tex]5x^2-(3xy-7x^2)+(5xy-12x^2)=5x^2-3xy+7x^2+5xy-12x^2=2xy\\\\ 2\cdot(-0.25)\cdot4=-2[/tex]
Answer:
-2
Step-by-step explanation:
5x^2-(3xy-7x^2)+(5xy-12x^2)
5x^2-3xy+7x^2+5xy-12x^2
[(5x^2+7x^2-12x^2)=0]
-3xy+5xy= -3(-.25)(4)+5(-.25)(4)
-3(-.25)(4)+5(-.25)(4)= 3-5= -2
-2
Use the Distributive Property to rewrite each of the expressions -6(r-8)
Answer:
-6r+48
Step-by-step explanation:
(-6)(r)+(-6)(-8)
=-6r+48
Answer:
-6r +48
Step-by-step explanation:
The distributive property has us distribute the number on the outside to the numbers on the inside
-6(r-8)
-6 *r -6 * (-8)
-6r +48
Suppose you deposit $2,500 in a savings account that pays interest at an annual rate of 5%. If no money is added or withdrawn from the account, answer the following questions.
a. How much will be in the account after 3 years?
b. How much will be in the account after 17 years?
c. How many years will it take for the account to contain $3,000?
d. How many years will it take for the account to contain $3,500?
Final answer:
a. The account will have $2,839.25 after 3 years. b. The account will have $5,148.64 after 17 years. c. It will take approximately 4.329 years for the account to contain $3,000. d. It will take approximately 6.646 years for the account to contain $3,500.
Explanation:
a. To calculate the amount in the account after 3 years, we can use the formula: A = P(1 + r)^t, where A is the amount, P is the initial deposit, r is the interest rate, and t is the number of years. In this case, P = $2,500, r = 5% = 0.05, and t = 3. Plugging in these values, we get A = 2500(1 + 0.05)^3. Calculating this, we get A = $2,839.25.
b. Using the same formula, we can calculate the amount in the account after 17 years. P = $2,500, r = 5% = 0.05, and t = 17. Plugging in these values, we get A = 2500(1 + 0.05)^17. Calculating this, we get A = $5,148.64.
c. To find out how many years it will take for the account to contain $3,000, we can rearrange the formula to solve for t. The equation becomes 3000 = 2500(1 + 0.05)^t. Dividing both sides by 2500, we get 1.2 = (1.05)^t. Taking the logarithm of both sides, we have log(1.2) = t * log(1.05). Solving for t, we find t = log(1.2) / log(1.05). Using a calculator, we get t ≈ 4.329 years.
d. Following the same steps, we can find the number of years it will take for the account to contain $3,500. The equation becomes 3500 = 2500(1 + 0.05)^t. Dividing both sides by 2500, we get 1.4 = (1.05)^t. Taking the logarithm of both sides, we have log(1.4) = t * log(1.05). Solving for t, we find t = log(1.4) / log(1.05). Using a calculator, we get t ≈ 6.646 years.
The amount in the account can be calculated using the compound interest formula. After 3 years, the account will have approximately $2,894.07, and after 17 years, it will have approximately $6,003.94. It will take about 3.57 years to reach $3,000 and about 6.57 years to reach $3,500.
To calculate how much money will be in a savings account after a certain number of years with a fixed annual interest rate, we use the compound interest formula:
Compound Interest Formula
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the number of years the money is invested or borrowed for.In this case, the interest is compounded annually, so n = 1.
Question a: How much will be in the account after 3 years?
Given:
P = $2,500r = 5% = 0.05n = 1t = 3Using the formula:
A = 2500 (1 + 0.05/1)¹ˣ³ = 2500 (1.05)³ ≈ $2,894.07
Question b: How much will be in the account after 17 years?
Given:
P = $2,500r = 5% = 0.05n = 1t = 17Using the formula:
A = 2500 (1 + 0.05/1)¹ˣ¹⁷ = 2500 (1.05)¹⁷ ≈ $6,003.94
Question c: How many years will it take for the account to contain $3,000?
Given:
P = $2,500A = $3,000r = 5% = 0.05n = 1Using the formula and solving for t:
3000 = 2500 (1.05)^t
Divide both sides by 2500:(3000/2500) = (1.05)^t1.2 = (1.05)^tTake the natural logarithm of both sides:ln(1.2) = t ln(1.05)Solve for t:t = ln(1.2) / ln(1.05) ≈ 3.57 years
Question d: How many years will it take for the account to contain $3,500?
Given:
P = $2,500A = $3,500r = 5% = 0.05n = 1Using the formula and solving for t:
3500 = 2500 (1.05)^t
Divide both sides by 2500:
(3500/2500) = (1.05)^t1.4 = (1.05)^tTake the natural logarithm of both sides:ln(1.4) = t ln(1.05)Solve for t:
t = ln(1.4) / ln(1.05) ≈ 6.57 years
A cookie recipe calls for 1/4 of a cup of sugar for one batch. How many complete batches can you make if you have 3 cups of sugar?
It costs $23 per hour plus a flat fee of $16 for a plumber to make a house call. What is the equation of the form y = mx + b for this situation? A) y = 16x B) y = 23x C) y = 16x + 23 D) y = 23x + 16
Answer:
It is D 100%
Step-by-step explanation:
Gregory predicts that 310 people will attend the spring play there was an actual total of 220 people who attended the spring play. What is the percent error round to the nearest whole percent
Answer:
41%
Step-by-step explanation:
To calculate the percent error:
We find the difference between the predicted and the actual.We divide the absolute value of the difference by the actual recorded value.Convert to a percent by multiplying by 100 and adding a % sign.Gregory predicted 310 and 220 actually came.
1. 310-220=90
2. 90/220=0.41
3. 0.41(100)=41%
Answer:
the percent error is 41%
Step-by-step explanation:
1. Identify and EXPLAIN the ERROR
2. Show CORRECT WORK
3. What STRATEGY did you use for solving this problem
This might be a trick question. I did the problem and got the exact same answer. I got 31 x + 0.5. If there's anything they did wrong maybe its because they didn't put a zero before 5 so 5 could become a decimal?
What are the zeros of the polynomial function? f(x)=x^3−x^2−4x+4
Select each correct answer.
-3
-2
-1
0
1
2
3
Answer: (B) -2, (E) 1, (F) 2
Step-by-step explanation:
x³ - x² - 4x + 4
= x²(x - 1) - 4(x - 1)
= (x² - 4) (x - 1)
= (x - 2)(x + 2)(x - 1)
Set each factor equal to zero to find the roots:
x - 2 = 0 x + 2 = 0 x - 1 = 0
x = 2 x = -2 x = 1
Answer:
-2,1,2
Step-by-step explanation:
One type of insect is 0.0052 meters long. What is the lenght in scientific notation
Answer:
5.2 × [tex]10^{-3}[/tex]
Step-by-step explanation:
a number in scientific notation is expressed as
a × [tex]10^{n}[/tex]
where 1 ≤ a < 10 and n is an integer
write 0.0052 as a number between 1 and 10, that is 5.2
we have to the move the decimal point 3 places to the left to retain it's value
3 places left means n is - 3
0.0052 = 5.2 × [tex]10^{-3}[/tex]
PLEASE HELP!!
Diagonal AC divides the trapezoid ABCD (with bases AD and BC, AD>BC) into two similar triangles, △ABC and △DCA. Find AC if BC=4 cm and AD=9 cm.
Answer:
6 cm
Step-by-step explanation:
Let k represent the scale factor between ΔABC and ΔDCA. Then ...
... CA = k·BC
... AD = k·CA
So, AD/BC = k·(k·BC)/BC = k² = 9/4
Then k = √(9/4) = 3/2, and ...
... CA = (3/2)·BC = (3/2)·(4 cm)
... CA = 6 cm
Final answer:
To find the length of diagonal AC in trapezoid ABCD, we utilize the properties of similar triangles created by the diagonal. Since triangles △ABC and △DCA are similar, we set up a proportion using the sides BC and AD, and solve for AC to find that AC is 6 cm.
Explanation:
The question asks us to find the diagonal AC of trapezoid ABCD where it's given that BC = 4 cm and AD = 9 cm, and triangles △ABC and △DCA are similar. To find AC, we can use the properties of similar triangles which dictate that corresponding sides are proportional. Let us consider that the trapezoid is split into two triangles by AC. The ratio of the smaller triangle's base to the larger triangle's base (BC:AD) must be the same as the ratio of any other pair of corresponding sides in these two similar triangles. Furthermore, the ratio of the longer leg of △ABC (which is AC) to its base BC is equal to the ratio of the longer leg of △DCA (which is also AC) to its base AD. Using these ratios, we can set up a proportion to solve for AC:
AC/BC = AC/AD
Since the length of AC is the same in both ratios, we can multiply both sides by BC*AD to get:
[tex]AC^2 = BC * AD[/tex]
By substituting the given values for BC and AD into the equation we get:
[tex]AC^2 = 4 cm * 9 cm[/tex]
[tex]AC^2 = 36 cm^2[/tex]
To find AC, we take the square root of both sides:
AC = √36 cm
AC = 6 cm
Hence, the length of diagonal AC is 6 cm.