The equation written by Elliot, which was not included in the question, is:
[tex]0.10(7-x)+0.5(x)+0.25(0.5x)=5.90[/tex]
The statements from which you have to identify the errors are:
a) He should have written the expression for the number of dimes as x – 7.
b) He should have written the coin values as 5, 10, and 25 and not as 0.5, 0.10, and 0.25.
c) He should have written the coin value for the nickel as 0.05.
d) He should have translated the scenario as the value of all dimes = value of all nickels and value of all quarters = value of all nickels.
e) He should have written the expression for the number of nickels as 2x.
Answer:
There two errors:
First statement: He should have written the expression for the number of dimes as x - 7.Third statement: He should have written the coin value for the nickel as 0.05Explanation:
I will start by writing the correct expression following the statements step-by-step:
1) He has half as many quarters as nickels
Name x the number of nickels: xThe number of quarters is half the number of nickels: x/22) He has 7 fewer dimes than nickels.
That is: x - 73) Mulitiply each number of coins by its value in dollars:
Dimes: (x - 7) × 0.10 = 0.10 (x - 7)Nickles: x × (0.05) = 0.05xQuarters: x/2 × 0.25 = 0.25× (1/2 × x) = 0.25 (0.5x)4) Add he values of all the coins:
0.10 (x - 7) + 0.05x + 0.25x5) Equal to the total value of $ 5.90:
0.10 (x - 7) + 0.05x + 0.25x = 5.906) Compare with the equation written by Elliot:
0.10 (7 - x) + 0.5(x) + 0.25(0.5x)=5.907) Conclusion:
There are two errors:
He wrote 7 - x, instead of 7 - x. That means that the first error was indicated by the first statement: He should have written the expression for the number of dimes as x - 7.He wrote 0.5x instead of 0.05x. That means that the second error was indicated by the third statement: He should have written the coin value for the nickel as 0.05.Answer:
for the people on edgen the answer is the first and the third options
Step-by-step explanation:
uhhh
Given O below, if XY and YZ are congruent, what is the measure of chord XY
Answer:
B. 10.2
Step-by-step explanation:
Answer : The value of chord XY is, 10.2 units
Step-by-step explanation :
As we are given that, XY and YZ are congruent.
XY and YZ are congruent by SSA.
The ΔXOY and ΔZOY are congruent triangles.
Side OX = Side OZ (side)
Side OY = Side OY (common side)
∠XOY = ∠ZOY (angle)
That means, in this two sides and one angle of a triangle are equal to another triangle then the triangles are congruent.
So, Side XY = Side YZ
As we are given :
Chord YZ = 10.2
So, Chord YZ = Chord XY = 10.2
Hence, the value of chord XY is, 10.2 units
Please answer this correctly
Answer: 12:40
Step-by-step explanation:
Answer:
12:40 PM
Step-by-step explanation:
By the time the plane arrives in Minnesota, the time is already 13:40 or 1:40 PM (eastern time). From eastern time to central time, the time decreases by 1 hour. 1:40 PM - 1 hour is 12:40 PM.
2. The sequence 5, 20, 35, 50….. shows the number of sit ups Margie did each week, starting with her first week of the new year.
(a) What is the recursive rule for the sequence?
(b) What is the explicit rule for the sequence?
(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(b) The explicit rule for the sequence is: [tex]a_{n}=15n-10[/tex]
Step-by-step explanation:
The form of the recursive rule of an arithmetic sequence sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex] , where
[tex]a_{1}[/tex] is the first term in the sequence[tex]a_{n}[/tex] the nth term in the sequence [tex]a_{n-1}[/tex] the term before the nth term n is the term numberd is the common difference between each two consecutive termsThe form of the explicit rule of nth term of an arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
a is the first termd is the common difference between each two consecutive terms∵ The sequence is 5, 20, 35, 50, ….......
∵ 20 - 5 = 15 , 35 - 20 = 15 and 50 - 35 = 15
∴ The sequence is an arithmetic sequence with a common
difference 15
∵ The form of the recursive rule of the arithmetic sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex]
∵ First term = 5
∵ d = 15
∴ [tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
∵ The form of the explicit rule of nth term of an arithmetic
sequence is [tex]a_{n}=a+(n-1)d[/tex]
∵ a = 5 and d = 15
- Substitute these values in the rule
∴ [tex]a_{n}=5+(n-1)15[/tex]
- Simplify the right hand side
∴ [tex]a_{n}=5+15n-15[/tex]
- Add like terms
∴ [tex]a_{n}=15n-10[/tex]
(b) The explicit rule for the sequence is [tex]a_{n}=15n-10[/tex]
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Patsy has cheerleading practice every fourth day. She wants to be in the school play, but they have practice every sixth day. If both start on September 5th, what would be the next date she has to choose between cheerleading and play practice? Show your work and explain.
Answer:
September 17th will be the first date that she has to choose between cheerleading and play practice.
Step-by-step explanation:
Least Common Multiple for 4 and 6 is 12 that is LCM(4, 6) = 12
12 days after September 5th is September 17th
Patsy would need to choose between cheerleading and play practice on September 29th, as this is the next date when both practices fall on the same day, calculated by finding the least common multiple of the practice schedules.
Explanation:To determine when Patsy has to choose between cheerleading and play practice, we need to find the least common multiple (LCM) of the two practice schedules, since she has cheerleading every fourth day and play practice every sixth day.
First, list the multiples of both 4 and 6 until we find a common one:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...Multiples of 6: 6, 12, 18, 24, 30, ...The lowest common multiple of 4 and 6 is 12, but since our sequence started on September 5th and 12 is not a multiple of both 4 and 6, we need to keep going. Continuing our list, 24 is the next common multiple but still not satisfying both conditions. At 24 days, the cycle would repeat itself, and Patsy would again have both practices on the same day.
If these practices both start on September 5th, to find the next date she has both practices, we add 24 days to September 5th. Because September has 30 days, adding 24 days to September 5th results in September 29th. Hence, Patsy would need to choose between cheerleading and play practice on September 29th.
Angelica was at target and saw that a pair of slippers was $15. She also noticed that there is a 30% off sale on all slippers. What is the cost (sale price) of the slippers after the discount?
The cost of slippers is $10.5 after discount.
Step-by-step explanation:
Given,
Price of slippers = $15
Sale = 30%
Amount of discount = 30% of price of slippers
[tex]Amount\ of\ discount=\frac{30}{100}*15\\Amount\ of\ discount=\frac{450}{100}\\Amount\ of\ discount=\$4.5[/tex]
Sale price = Price of slippers - amount of discount
[tex]Sale\ price=15-4.5\\Sale\ price=\$10.5[/tex]
The cost of slippers is $10.5 after discount.
Keywords: percentage, subtraction
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To find the cost of the slippers after the 30% discount, multiply the original price by 30% and subtract the discount from the original price. The cost of the slippers after the discount is $10.50.
Explanation:To find the cost of the slippers after the 30% discount, first calculate the amount of the discount by multiplying the original price by 30% (or 0.30).
Discount = $15 × 0.30 = $4.50
Next, subtract the discount from the original price to find the sale price:
Sale Price = $15 - $4.50 = $10.50
Therefore, the cost of the slippers after the discount is $10.50.
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 150 nails and each large box has 400 nails. The contractor bought 3 times as many large boxes as small boxes, which altogether had 2700 nails. Determine the number of small boxes purchased and the number of large boxes purchased.
The contractor bought 2 small boxes and 6 large boxes of nails. This was determined by setting up and solving a system of equations based on the given conditions.
Explanation:To solve the problem of determining the number of small and large boxes of nails purchased by the contractor, we can set up a system of equations based on the information given:
Each small box contains 150 nails.Each large box contains 400 nails.The contractor bought 3 times as many large boxes as small boxes.Altogether, the nails totaled 2700.Let's denote the number of small boxes as S, and the number of large boxes as L. The equations then are:
L = 3S (3 times as many large boxes as small boxes)150S + 400L = 2700 (total number of nails)Substituting the value of L from equation (1) into equation (2):
150S + 400(3S) = 2700
Solving for S:
150S + 1200S = 2700
1350S = 2700
S = 2
Then, substituting S = 2 into the first equation to find L:
L = 3(2) = 6
Therefore, the contractor bought 2 small boxes and 6 large boxes of nails.
The contractor bought 2 small boxes and 6 large boxes, totaling 2700 nails, with each small box containing 150 nails.
Let's denote:
- x as the number of small boxes purchased.
- y as the number of large boxes purchased.
We're given the following information:
1. Each small box contains 150 nails.
2. Each large box contains 400 nails.
3. The total number of nails purchased is 2700.
4. The contractor bought 3 times as many large boxes as small boxes, so y = 3x.
We can set up two equations to represent the given information:
1. Total number of nails equation:
150x + 400y = 2700
2. Relationship between the number of small and large boxes:
y = 3x
Now, let's substitute the value of y from the second equation into the first equation:
150x + 400(3x) = 2700
150x + 1200x = 2700
1350x = 2700
Now, let's solve for x:
[tex]\[ x = \frac{2700}{1350} \][/tex]
x = 2
So, the number of small boxes purchased [tex](\( x \))[/tex] is 2.
Now, let's find the number of large boxes [tex](\( y \))[/tex]:
y = 3x
y = 3(2)
y = 6
So, the number of large boxes purchased [tex](\( y \))[/tex] is 6.
To summarize:
- The contractor purchased 2 small boxes.
- The contractor purchased 6 large boxes.
I NEED FAST HELP!!!!!!!!!!!!!!!!!!!
Answer:
The student is expected to spend 15.4 hours doing homework
Step-by-step explanation:
The scattered plot shows there is a close correlation between the variables. A line of best fit will go through the 'center' of the points. Since we are not required to find an exact line, we'll draw it in red color as shown below
To know the equation of that line, we must take two clear points of it from the graph. We'll pick (28,4) and (4,25)
The equation of a line, given two points (a,b) and (c,d) is
[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]
Using the selected points
[tex]\displaystyle y-4=\frac{25-4}{4-28}(x-28)[/tex]
Simplifying and computing results, the equation is
[tex]\displaystyle y=-\frac{7}{8}x+\frac{57}{2}[/tex]
Using that equation, we can predict how many hours the students will spend doing homework if they spend 15 hours watching TV
[tex]\displaystyle y=-\frac{7}{8}(15)+\frac{57}{2}[/tex]=15.4 hours
So the student is expected to spend 15.4 hours doing homework
What is the slope of the line of the best fit for this scatter plot?
What is the equation of the line of the best fit?
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 7) and (x₂, y₂ ) = (4, 6) ← 2 points on the line
m = [tex]\frac{6-7}{4-2}[/tex] = - [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, 8) ⇒ c = 8
y = - [tex]\frac{1}{2}[/tex] x + 8 ← equation of line
Answer : The slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex] and [tex]y=\frac{-1}{2}x+8[/tex] respectively.
Step-by-step explanation :
The general form for the formation of a linear equation is:
[tex](y-y_1)=m\times (x-x_1)[/tex] .............(1)
where,
x and y are the coordinates of x-axis and y-axis respectively.
m is slope of line.
First we have to calculate the slope of line.
Formula used :
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Here,
[tex](x_1,y_1)=(2,7)[/tex] and [tex](x_2,y_2)=(4,6)[/tex]
[tex]m=\frac{(6-7)}{4-2)}[/tex]
[tex]m=\frac{-1}{2}[/tex]
Now put the value of slope in equation 1, we get the linear equation.
[tex](y-y_1)=m\times (x-x_1)[/tex]
[tex](y-7)=\frac{-1}{2}\times (x-2)[/tex]
[tex]y-7=\frac{-1}{2}x+1[/tex]
[tex]y=\frac{-1}{2}x+1+7[/tex]
[tex]y=\frac{-1}{2}x+8[/tex]
Thus, the slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex] and [tex]y=\frac{-1}{2}x+8[/tex] respectively.
Will give brainliest plz help
Answer:
[tex]\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]
Step-by-step explanation:
Given:
Center of the ellipse is, [tex](h,k)=(-4,-3)[/tex]
Minor axis length is, [tex]2b=6[/tex]
A vertex of the ellipse is at (1, -3)
Now, distance between the center and the vertex is half of the length of the major axis.
Using distance formula for (-4, -3) and (1, -3), we get:
[tex]a=\sqrt{(1+4)^2+(-3+3)^2}=5[/tex]
Therefore, the value of half of major axis is, [tex]a=5[/tex]. Also,
[tex]2b=6\\b=\frac{6}{2}=3[/tex]
Now, equation of an ellipse with center [tex](h,k)[/tex] is given as:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Plug in [tex]h=-4,k=-3,a=5,b=3[/tex] and determine the equation.
[tex]\frac{(x-(-4))^2}{5^2}+\frac{(y-(-3))^2}{3^2}=1\\\\\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]
Therefore, the equation of the ellipse is:
[tex]\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]
What is the fewest number of transformations needed to take pre-image ABCD to image A'B'C'D'?
(photo attached)
I really need help!
Answer:
2 transformations
Step-by-step explanation:
1)Reflection
2) Rotation 180 degrees clockwise
A number is chosen at random from the first 100 positive integers. Find the probability that the number is either even or
a perfect square
3/5
11/20
1/20
Answer:
[tex]\frac{11}{20}[/tex]
Step-by-step explanation:
Total no. of possible outcome= 100 (from 1 to 100)
total no. of favorable outcome= 60 (50 even and 5 odd perfect square)
Hence PROBABILITY=[tex]\\\frac{55}{100}[/tex]
=[tex]\frac{11}{20}[/tex]
Original price of a hotel: $240.00 per night.
You are staying four nights because then you get a 25% discount.
State and local taxes and 'resort fee' add up to a 29% surcharge.
How much will you pay for four nights?
Answer:
$ 929
Step-by-step explanation:
Given: Original price of stay in hotel= $240 per night
Discount= 25%
Total taxes and fee = 29%
Now, finding the price of stay for four night.
Using unitary method to solve:
As we know original price of hotel stay per night is $240
∴ Price of four night stay at original price is [tex]240\times 4 = \$ 960[/tex]
Next, 25% discount given on the price of four night stay.
∴ [tex]960 - \frac{25}{100} \times 960 = 960 - 240[/tex]
= [tex]\$ 720[/tex]
∴Price of four night hotel stay after discount is [tex]\$ 720[/tex]
Now, 29% taxes and fees been added to the price.
Price of hotel stay after discount + Taxes paid.
[tex]720 + ( \frac{29}{100} \times 720) = 720 + 209[/tex]
= [tex]\$ 929[/tex]
∴ [tex]\$ 929[/tex] is the price to be paid for four night stay at hotel after discount and taxes.
What is the equation of the line that is perpendicular to and
has the same y-intercept as the given line?
y=x+1
y= x+5
y = 5x + 1
y= 5x + 5
can someone please tell me the aswer
Answer:
2x-2+3x
Step-by-step explanation:
2x-2+3x
combine like terms (2x + 3x = 5x)
So 2x-2+3x = 5x-2
Which of the following is approximately equal to the product of the multiplication problem below?
18/4 × 20/17
A.
10
B.
7
C.
5
D.
4
Answer:
5
Step-by-step explanation:
We have: [tex]$ \frac{18}{4} \times \frac{20}{7} $[/tex]
Simplifying we get: [tex]$ 18 \times \frac{5}{7} $[/tex]
⇒ [tex]$ \frac{90}{17} $[/tex]
This is equal to 5.2 ≅ 5.
So, Option C - 5 is the answer.
Maine has one of the lowest sales tax rates in the country. If an item costs $40, you will pay $2 in sales tax. What percent of sales tax will you pay?
You will pay 5% sales tax.
Step-by-step explanation:
Given,
Cost of item = $40
Sales tax = $2
Percent of sales tax = [tex]\frac{Sales\ tax}{Cost\ of\ item}*100[/tex]
[tex]Percent\ of\ sales\ tax=\frac{2}{40}*100\\Percent\ of\ sales\ tax=\frac{200}{40}\\Percent\ of\ sales\ tax=5\%[/tex]
You will pay 5% sales tax.
Keywords: sales tax, division
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Sue invests in a money market account. The balance of the account in dollars after t years can be represented by the function.
5000(1.07)t = B
Answer the questions below:
a) What does the 5000 represent?
b) What is the annual percentage rate?
c) How much money will Sue have after 5 years?
a) 5000 represents the initial amount that Sue invested in a money market account
b) The annual percentage rate is 7%
c) Sue will have $7012.76 after 5 years
Step-by-step explanation:
The exponential growth function is [tex]f(t)=P(1+r)^{t}[/tex] , where
r is the rate of growth in decimalP is the initial amountt is the timeSue invests in a money market account. The balance of the account in dollars after t years can be represented by the function [tex]5000(1.07)^{t}=B[/tex]
∵ The function is [tex]5000(1.07)^{t}=B[/tex]
∵ The form of the exponential growth function is tex]f(t)=P(1+r)^{t}[/tex]
- By comparing the two functions
∴ P = 5000
∵ P is the initial amount
∴ The initial amount is 5000
a) 5000 represents the initial amount that Sue invested in a money market account
∵ [tex](1+r)^{t}=(1.07)^{t}[/tex]
∴ 1 + r = 1.07
- Subtract 1 from both sides
∴ r = 0.07
∵ r is the annual rate in decimal
∵ 0.07 × 100% = 7%
∴ The annual rate is 7%
b) The annual percentage rate is 7%
∵ t = 5
- Substitute the value of t in the function
∴ [tex]5000(1.07)^{5}=B[/tex]
∴ B = 7012.76
c) Sue will have $7012.76 after 5 years
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the quotient of a number and -7, decreased by 2, is 10
Answer:
The number is -84.
Step-by-step explanation:
-x/7-2=10
-x/7=10+2
-x/7=12
-x=12*7
-x=84
x=-84
Which symbol can be used to correctly compare the two fractions? Use > , < , or =. Enter your answer in the box. 75100 34
75100 > 34
75100 is greater than 34
Answer:
its <
Step-by-step explanation:
Simplify: 8x - (14 +4x)
Answer:
4x-14
Step-by-step explanation:
8x-(14+4x)
8x-14-4x
8x-4x-14
4x-14
A textbook store sold a combined total 402 of psychology and math textbooks in a week. The number of psychology textbooks sold was two times the number of math textbooks sold. How many textbooks of each type were sold?
Answer:
The number of textbooks of each type were sold is 134 math and 268 psychology books.
Step-by-step explanation:
Given:
Total number of math and psychology textbooks sold in a week is 402.
Now, let the number of math textbooks sold be [tex]x[/tex].
And, the number of psychology textbooks be [tex]2x[/tex].
According to question:
[tex]x+2x=402[/tex]
[tex]3x=402[/tex]
Dividing both sides by 3 we get:
[tex]x=134[/tex]
So, total number of math textbooks were 134 .
And, total number of psychology textbooks were [tex]2x=2\times 134[/tex]
[tex]=268[/tex].
Therefore, the number of textbooks of each type were sold is 134 math and 268 psychology books.
How to put this promble in standard notation
3.25x10
Answer:
multiply both 3.25 and 10 by 100
or
multiple 3.25 by 10 then multiply by 10
Assume that in October of a particular year about 215 billion text messages were sent or received in the US, and the prediction is that in the next month it will be a 13% increase. About how many will be sent or received in November of the same year? Rounded to the nearest tenth of a billion.
Answer:
There will be [tex]243[/tex] billion messages sent or received in November.
Step-by-step explanation:
Given.
Number of text messages sent or received [tex]=215[/tex] billion.
Increment on the very next month [tex]=13\%=\frac{13}{100}=0.13[/tex]
Lets find what is [tex]13\%\ of\ 215[/tex]
⇒[tex]13\%\ of\ 215[/tex]
⇒[tex]0.13\times 215=27.95[/tex]
So we will add this value to our previous months data.
Now
Number of text messages sent in the month of November [tex]=(27.5+215)=242.95[/tex] billion.
Rounding to the nearest tenth the answer will be [tex]243[/tex] billion.
So [tex]243[/tex] billion text messages were sent or received in November.
Question is in the photo. check all that apply. please help ASAP
Answer:
[tex]x-2x-6=8x+12-x-4\\-x-6=7x+8[/tex]
Step-by-step explanation:
Given:
The equation is;
[tex]x-2(x+3)=4(2x+3)-(x+4)[/tex]
Now we need to simplify this equation we get;
Step 1: We need to simplify all the terms which are in brackets we get,
[tex]x-2x-6=8x+12-x-4[/tex]
Step 2: Now we need to simplify all variable term and non variable term we get:
[tex]-x-6=7x+8[/tex]
Answer:
These two equivalent equations Katrina has used
[tex]x - 2x - 6 = 8x + 12 - x - 4\\-x - 6 = 7x + 8\\[/tex]
Step-by-step explanation:
Given :
[tex]x - 2(x + 3) = 4(2x + 3) - (x + 4)\\[/tex]
Applying distributive property that is [tex]A\times (B +C) = A\times B + A\times C[/tex] we get
[tex]x - 2x + 3\times -2 = 4\times 2x + 4\times 3 - x - 4\\[/tex]
[tex]x - 2x - 6 = 8x + 12 - x - 4\\-x - 6 = 7x + 8\\[/tex]
harry, regan and kelan share £450 in the ratio 2 : 5 : 3 . how much money does kelan get?
Answer:
Kelan gets 135 Euros.
Step-by-step explanation:
First of all you add up the ratio getting 10, with 10 you divide it from 450 getting 45. Then you multiply 3 (Kelan's Part) by 45 getting your answer. Tell me if this helped, i'd appreciate knowing.
This question is based on simple mathematics. Therefore, the answer is £135.
Given:
Harry, regan and kelan share £450 in the ratio 2 : 5 : 3.
We have to determined the money would kelan get.
According to questions,
First of all, adding up the ratios.
We get,
2+5+3 = 10
Regan and kelan share £450. So divided £450 by 10, and solve it further.
We get,
[tex]\dfrac{450}{10} = 45[/tex]
Now, multiplying 45 by 3 (Kelan's part).
We get,
[tex]45\times3= 135[/tex]
Therefore, the money that kelan get is £135.
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Whenever you sign a lease for an apartment, you typically have to pay a security deposit in case you have caused any wear or tear on the apartment that has to be repaired before it can be re-leased. If no repairs need to be made, you get your entire deposit back. One apartment building has apartments that rent for $500 a month and security deposit of $700. The total cost C (in dollars) it costs to rent the apartment for m months is given by the function C=500m+700. Graph the function and identify its domain and range. Identify the domain and range if a renter only leases an apartment for one year and then moves out and doesn't get the security deposit back.
Answer:
what is the question
Step-by-step explanation:
Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.
Answer:
The proof is given below.
Step-by-step explanation:
Given: ( the correct question and ans is as follow )
sin (x + y) = 3sin ( x - y)
To Prove
tan x = 2 tan y
Proof:
[tex]\sin (x+y) = 3\sin (x-y)[/tex]
Using the identities
[tex]\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\[/tex]
we get
[tex]\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y[/tex]
Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get
[tex]3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}[/tex]
A line has a slope of 8 and includes the points (1, z) and (2,8). What is the value of z?
The value of z is zero
Step-by-step explanation:
The slope is the steepness of the line.
The formula for slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\Here\\(x_1,y_1)\ are\ the\ coordinates\ of\ first\ point\ on\ line\\(x_2,y_2)\ are\ the\ coordinates\ of\ second\ point\ on\ line[/tex]
Here
(x1,y1) = (1,z)
(x2,y2) = (2,8)
So,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\8 = \frac{8-z}{2-1}\\8=\frac{8-z}{1}\\8-8 = -z\\z = 0[/tex]
The value of z is zero
Keywords: slope, Line
Learn more about slope at:
brainly.com/question/10879401brainly.com/question/10940255#LearnwithBrainly
please solve much appreciated
Answer:
Two equivalent fractions with whole numbers may be 180/150, or 6/5The height of the tree is 39.6 feet.Explanation:
The diagram provides the proportion of the heights to the shadows:
[tex]\frac{x}{33}=\frac{1.8}{1.5}[/tex]From that you are asked (i) to simplify the fraction of the right side to one with whole numbers.
You can do that in two steps by multiplying both numerator and denominator by 10:
[tex]\frac{1.8\times 10}{1.5\times 10}=\frac{180}{150}[/tex]You can simplify that fraction if you divide by the greatest common factor of 180 and 150, which is 30:
[tex]\frac{180/30}{150/30}=\frac{6}{5}[/tex]The second part (ii) asks to find the height of the tree, that is x. To solve for x you can multiply both sides by the denominator of the fraction on the left and then simplify:
[tex]\frac{x}{33}=\frac{6}{5}\\ \\ x=\frac{6\times 33}{5}\\ \\ x=\frac{198}{5}=39.6[/tex]
Thus, the height of the three is 39.6 feet.
What is the domain of the function f(x)=-4log2(x+3)-6
Enter your answer in the box.
All real numbers greater than
Answer:
-3
Step-by-step explanation:
Given, f(x)=-4log2(x+3)-6
So, for domain of f(x) ,we have to find the domain of log2(x+3) as all other things are just numbers which do not affect the domain.
For domain of f(x), 2(x+3) > 0
Thus, x + 3 > 0
x > -3.
So, all real numbers greater than -3 are in the domain of f(x).