Simplify the expression.
the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15
The correct option is negative 23 over 14 times j plus negative 1 over 15
Given,
The expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
The expression; -1/7j + 2/5 - 3/2j + 7/15
negative one seventh j = - 1/7j
two fifths = 2/5
three halves j = 3/2 j
seven fifteenths = 7/15
Now,
Substitute the values;
- 1/7j + 2/5 - 3/2j - 7/15
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Therefore,
The correct option is negative 23 over 14 times j plus negative 1 over 15
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4. McKenzie wants to determine which ice cream option is the best choice. The chart below gives the description and prices for her options. Use the space below each item to record your findings. Place work below the chart. A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter. A cone has a 2-inch diameter and a height of 4.5 inches. A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches. a. Determine the volume of each choice. Use 3.14 to approximate pi. b. Determine which choice is the best value for her money. Explain your reasoning. (That means some division, you decide which.) $2.00 $3.00 $4.00 One scoop in a сир Two scoops in a cup Three scoops in a cup Half a scoop on a cone filled with ice cream A cup filled with ice cream (level to the top of the cup)
McKenzie wants to determine which ice cream option is the best choice.
Part (a)
Volume of Scoop:
A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter.
The volume of the sphere is given by
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]Where r is the radius.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{2}{2}=1[/tex]So, the volume of a scoop of ice cream is
[tex]V_{\text{scoop}}=\frac{4}{3}\cdot3.14\cdot(1)^3=\frac{4}{3}\cdot3.14\cdot1=4.19\: in^3[/tex]Therefore, the volume of a scoop of ice cream is 4.19 in³
Volume of Cone:
A cone has a 2-inch diameter and a height of 4.5 inches.
The volume of a cone is given by
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the cone.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{2}{2}=1[/tex]So, the volume of a cone of ice cream is
[tex]V_{\text{cone}}=\frac{1}{3}\cdot3.14\cdot(1)^2\cdot4.5=\frac{1}{3}\cdot3.14\cdot1^{}\cdot4.5=4.71\: in^3[/tex]Therefore, the volume of a cone of ice cream is 4.71 in³
Volume of Cup:
A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches.
The volume of a right circular cylinder is given by
[tex]V=\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the right circular cylinder.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{3}{2}=1.5[/tex]So, the volume of a cup of ice cream is
[tex]V_{\text{cup}}=3.14\cdot(1.5)^2\cdot2=3.14\cdot2.25\cdot2=14.13\: in^3[/tex]Therefore, the volume of a cup of ice cream is 14.13 in³
Part (b)
Now let us compare the various given options and decide which option is the best value for money
Option 1:
The price of one scoop in a cup is $2
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{4.19}{\$2}=2.095\: [/tex]Option 2:
The price of two scoops in a cup is $3
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{2\cdot4.19}{\$3}=2.793\: [/tex]Option 3:
The price of three scoops in a cup is $4
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{3\cdot4.19}{\$4}=3.1425[/tex]Option 4:
The price of half a scoop in a cone is $2
The volume of one scoop of ice cream is 4.19 in³
The volume of one cone of ice cream is 4.71 in³
[tex]rate=\frac{\frac{4.19}{2}+4.71}{\$2}=\frac{2.095+4.71}{\$2}=\frac{6.805}{\$2}=3.4025[/tex]Option 5:
The price of a cup filled with ice cream is $4
The volume of a cup is 14.13 in³
[tex]rate=\frac{14.13}{\$4}=3.5325[/tex]As you can see, the option 5 (a cup filled with ice cream) has the highest rate (volume/$)
This means that option 5 provides the best value for money.
Therefore, McKenzie should choose "a cup filled with ice cream level to the top of cup" for the best value for money.
Pure acid is to be added to a 10% acid solution to obtain 90L of 81% solution. What amounts of each should be used?How many liters of 100% pure acid should be used to make the solution? 04
Let's use the variable x to represent the amount of pure acid and y to represent the amount of 10% acid.
Since the total amount wanted is 90 L, we can write the equation:
[tex]x+y=90[/tex]Also, the final solution is 81%, so we can write our second equation:
[tex]100\cdot x+10\cdot y=81\cdot(x+y)[/tex]From the first equation, we can solve for y and we will have y = 90 - x.
Using this value in the second equation, we have:
[tex]100x+10(90-x)=81(x+90-x)[/tex]Solving for x, we have:
[tex]\begin{gathered} 100x+900-10x=81\cdot90 \\ 90x+900=7290 \\ 90x=7290-900 \\ 90x=6390 \\ x=\frac{6390}{90} \\ x=71 \end{gathered}[/tex]Therefore the amount of pure acid to be used is 71 L and the amount of 10% acid is 19 L.
[tex]6x - 9y - 7x + - 6y[/tex]simplify please
6x - 9y - 7x + -6y
To simplify the expression add the like terms
The like terms are the terms which have the same variable and same degree
6x, -7x are like terms
-9y, -6y are like terms
So let us add them
(6x + -7x) + (-9y + -6y)
6 + -7 = -1
6x + -7x = -x
-9 + - 6 = -15
-9y + -6y = -15y
(6x + -7x) + (-9y + -6y) = -x + -15y
Remember (+)
The convex polygon below has 8 sides. Find the value of x.140°11801270153013401561170
Explanation
The formula for calculating the sum of interior angles in a polygon is ( n − 2 ) × 180 ∘ where is the number of sides.
[tex](n-2)\cdot180=\text{ Sum of internal angles}[/tex]Step 1
find the sum of the internal angles in the given polygon
Let
number of sides = 8
Now, replace
[tex]\begin{gathered} (n-2)\cdot180=\text{ Sum of internal angles} \\ (8-2)\cdot180=\text{ Sum of internal angles} \\ 6\cdot180=\text{Sum of internal angles} \\ 1080=\text{Sum of internal angles}\rightarrow equation(1) \end{gathered}[/tex]Step 2
now, we have the other angles, so
sum of internal angles is:
[tex]\text{angle}1+\text{angle}2+\text{angle}3+\text{angle}4+\text{angle}5+\text{angle}6+\text{angle}7+\text{angle}8=\text{ sum of the internal angles}[/tex]replace
[tex]\begin{gathered} 127+140+118+153+156+117+x+132=\text{ Sum of internal angles} \\ x+943=\text{Sum of internal angles}\rightarrow equation\text{ (2)} \end{gathered}[/tex]hence
[tex]x+945=1080[/tex]subtract 945 in both sides to solve for x
[tex]\begin{gathered} x+945=1080 \\ x+945-945=1080-945 \\ x=135 \end{gathered}[/tex]i hope this helps you
What is f(2) - f(0) answer choices:A) 1B) 2C) 3D) 4
The points of the graph of a function f(x) have the form (x,f(x)). This means that the values of f(0) and f(2) are the y-values of the points in the graph that have 0 and 2 as their x-values. If you look at the graph you'll notice that the points (0,1) and (2,4) are part of the graph which implies that:
[tex]\begin{gathered} (0,f(0))=(0,1)\rightarrow f(0)=1 \\ (2,f(2))=(2,4)\rightarrow f(2)=4 \end{gathered}[/tex]Then we get:
[tex]f(2)-f(0)=4-1=3[/tex]AnswerThen the answer is option C.
This is lines, functions and systems. Graph the line with slope 2/3 passing through the point (2, 1).
Note that the slope is expressed as :
[tex]\text{slope}=\frac{\text{rise}}{\text{run}}[/tex]From the given, the slope is 2/3
[tex]\text{slope}=\frac{\text{rise}}{\text{run}}=\frac{2}{3}[/tex]So it means that from the point (2,1)
You need to rise 2 units upward and run 3 units to the right
It will be look like this :
Next step is to connect these two points by drawing a line.
That's it, the line is in blue line.
I need help please and thank you and you have to graph it
From the graph provided we can determine two points which are;
[tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(2,0) \end{gathered}[/tex]For the equation of the line given in slope-intercept form which is;
[tex]y=mx+b[/tex]We would begin by calculating the slope which is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We can now substitute the values shown above and we'll have;
[tex]\begin{gathered} m=\frac{(0-\lbrack-3\rbrack)}{2-0} \\ m=\frac{0+3}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]Now we have the slope of the line as 3/2, we can substitute this into the equation and we'll have;
[tex]\begin{gathered} y=mx+b \\ \text{Where;} \\ x=0,y=-3,m=\frac{3}{2} \end{gathered}[/tex]We now have the equation as;
[tex]\begin{gathered} -3=\frac{3}{2}(0)+b \\ -3=0+b \\ b=-3 \end{gathered}[/tex]We now have the y-intercept as -3. The equation now is;
[tex]\begin{gathered} \text{Substitute m and b into the equation,} \\ y=mx+b \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]The graph of this is now shown below;
We shall now draw lines to indicate the 'rise' and 'run' of this graph.
ANSWER
Observe carefully that the "Rise" is the movement along the y-axis (3 units), while the "Run" is the movement along the x-axis (2 units).
This clearly defines the slope of the equation that is;
[tex]\frac{\Delta y}{\Delta x}=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{3}{2}[/tex]I need help ASAP
Jeannette is participating in a hot-dog-eating contest. She has already eaten 18 hot dogs but needs to eat more than 35 hot dogs to win. Jeannette is eating 2.6 hot dogs per minute. Which of the following inequalities could be used to solve for x, the number of minutes Jeannette needs to continue eating hot dogs to win the contest
A.
2.6x > 35
B.
2.6x - 18 > 35
C.
2.6x > 18
D.
2.6x + 18 > 35
Answer:
I may be wrong but I think it's D.
Step-by-step explanation:
I made an educated guess.
I Need some help on this assignment Also the second half to the problem how much will be spent on the job from the 10 to 20th day
Explanation
[tex]f(x)=4.1x+1.9[/tex]
where x is the number of days since the start of the job
and f(x) is the rate of change
Step 1
a)find the total expenditure if the job takes 12 days
so, as x represents the number of days, just replace and calculate
let x= 12
[tex]\begin{gathered} f(x)=4.1x+1.9 \\ f(12)=4.1(12)+1.9 \\ f(12)=49.2+1.9 \\ f(12)=51.1 \end{gathered}[/tex]so
a) 51.1
Step 2
now, let's find the total spent on the job from the 10 to 20th day
a) find the x value ( number of days since the job started)
x= 20 days-10dys= 10
so
x= 10
Simplify the expression -3n-8-7n + 17
We simplify by combining like terms
therefore
[tex]\begin{gathered} -3n-8-7n+17 \\ =-3n-7n-8+17 \\ =-10n+9 \end{gathered}[/tex]There were 18 students in a class taking a test. 4 students did pass the test. What percent did not pass the test.
Answer
Percent of students who did not pass the test = 77.8%
Explanation
The percent of an event is given as
[tex]\begin{gathered} \text{Percent of an event} \\ =\frac{\text{Number of elements in the event}}{Total\text{ number of elements}}\times100 \end{gathered}[/tex]For this question,
Percent of the event = Percent who did not pass the test = ?
Number of elements in the event
= Number of students who did not pass the test
= (Total number of students) - (Number of students who passed the test)
= 18 - 4
= 14
Total number of elements = Total number of students in the class = 18
Percent of students who did not pass the test
= (14/18) × 100%
= 0.778 × 100%
= 77.8%
Hope this Helps!!!
1. (10 pts) The formula for calculating the distance, d, in miles that one can see to the horizon on aclear day is approximated by d = 1.22√x, where x, is the elevation in feet of a person's eyes.a. Approximate how far in miles can a person whose eyes are 5' 6" from the ground see tothe horizon when they are at sea-level. (Hint: Height is often measured with two units,feet and inches, but this formula does not allow for two units.) Figure out if you need toconvert to feet or inches and then do the conversion out as a multiplication problembefore you answer the question Round to the nearest hundredth if necessary.b. How far does the same person see when they are standing on top of an 8,000 footmountain? (Hint: Consider where are their eyes if the mountain is the given height)Round to the nearest hundredth if necessary.
1) We need to use one single unit to express the elevation of a person's eyes.
a)
[tex]5^{\prime}6"=5\:feet+6\:inches=66"=5.5^{\prime}[/tex]Remember that 1 foot is equal to 12 inches. And dividing 66" by 12 yields 5.5'
Now, let's plug into the formula we've been given:
[tex]d=1.22\sqrt{5.5}\Rightarrow d=2.86\:miles[/tex]b) Now, let's bear in mind that this same person has reached the top of a mountain, and now he's at 8,000 feet high:
[tex]d=1.22\sqrt{8000}\Rightarrow d=109.12\:miles[/tex]Note that x, is always given in feet, as well as, d is in miles.
in exponential growth functions the base of the exponent must be greater than 1.how would the function change if the base of the exponent were1? how would the function change if the base of the exponents were between 0 and 1
A deep-dish pizza is cut into twelve equal slices. If you eat four slices, how manydegrees of pizza do you eat?240°120°45°90°
The shape of the pizza is circular. This means that the total angle possible is 360 degrees.
Since the pizza have 12 equal slices
Then each slice will represent
[tex]\frac{360}{12}=30^0[/tex]Therefore, If you decide to eat 4 four slices, then
you will eat
[tex]4\times30^0=120^0[/tex]Answer = 120 degrees
What is the value of the expression below?2,816 x 714,57214,67219,61219,712
The given expression is
[tex]2,816\times7[/tex]We just have to multiply.
[tex]2,816\times7=19,712[/tex]Hence, the right answer is D.(b) Construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone. Round the answers to at least three decimal places.
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24
who have an Android phone is
SEE PHOTO
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is 0.503 < p < 0.397.
In the given question,
We have to construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone.
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is
..............< p <...............
We have to construct the 90% confidence interval.
From the given question we know that among 240 cell phone owners aged 18 - 24 surveyed, 108 said their phone was an android phone.
So the total number of cell phone owners aged 18 - 24 is 240.
So n=240
From them 108 have an android phone.
So x=108
Estimation of sample proportion([tex]\hat p[/tex]) = x/n
Now putting the value
Estimation of sample proportion([tex]\hat p[/tex]) = 108/240
Estimation of sample proportion([tex]\hat p[/tex]) = 0.45
Now the construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone
C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]
As we know that
[tex]\hat p=0.45[/tex]
Now finding the value of [tex]z_{\alpha /2}[/tex]
We have to find the 90% confidence interval. We can write 90% as 90/100 = 0.90
So [tex]\alpha[/tex] = 1-0.90
So [tex]z_{\alpha /2}=z_{0.10 /2}[/tex]
[tex]z_{\alpha /2}=z_{0.05}[/tex]
From the standard z table
[tex]z_{0.05}[/tex] = 1.645
Now putting the value in the
C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45(1-0.45)}{240}})[/tex]
Simplifying
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45\times0.55}{240}})[/tex]
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.2475}{240}})[/tex]
C.I. = [tex](0.45 \pm 1.645\sqrt{0.001031})[/tex]
C.I. = [tex](0.45 \pm 1.645\times0.0321)[/tex]
C.I. = [tex](0.45 \pm 0.053)[/tex]
We can write it as
C.I. = {(0.45+0.053),(0.45-0.053)}
C.I. = (0.503,0.397)
Hence, a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is
0.503 < p < 0.397.
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fred had a tray of brownies for his birthday. he ate 1/6 of the brownies by himself and his family ate 1/3 of the brownies how many brownies did fred and his family eat altogether
We want to know how many brownmies did Fred and his family eat together.
We will call to the total of the brownies by 1. On this case, after Fred ate 1/3 of the brownies, he will have:
[tex]1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}[/tex]This means that he has left 2/3 of the brownies. After his family ate 1/6 of the brownies:
[tex]\frac{2}{3}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}[/tex]This means they will have left 1/2 of the tray of brownies, and that they ate half of it.
Rationalize the denominator and simplify the expression below. Show all steps and calculations to earn full credit. You may want to do this work by hand and upload an image of that written work rather than try to type it all out. \frac{8}{1- \sqrt[]{17} }
The Solution:
The given expression is
[tex]\frac{8}{1-\sqrt[]{17}}[/tex]Rationalizing the expression with the conjugate of the denominator, we have
[tex]\frac{8}{1-\sqrt[]{17}}\times\frac{1+\sqrt[]{17}}{1+\sqrt[]{17}}[/tex]This becomes
[tex]\frac{8(1+\sqrt[]{17})}{1^2-\sqrt[]{17^2}}[/tex][tex]\frac{8+8\sqrt[]{17}}{1-17}=\frac{8(1+\sqrt[]{17})}{-16}=-\frac{1+\sqrt[]{17}}{2}[/tex]Thus, the correct answer is
[tex]-\frac{1+\sqrt[]{17}}{2}[/tex]Does the following table show a proportional relationship? 8 h 3 9 6 36 9 81 O Yes No
Proportional relationships are relationships between two variables where their ratios are equivalent.
From the table given;
g:h are respectively;
[tex]\begin{gathered} 3\colon9=1\colon3 \\ 6\colon36=1\colon6 \\ 9\colon81=1\colon2 \end{gathered}[/tex]Since the ratios above are not equivalent, their relationship is not proportional.
Hence, the correct option is B
gabrielle opened a savings account and deposited $800.00 . the account earns 2% interest compounded annually.
We need the actual question. I can write the compounded interest accrued value equation for this, but if no question about number of years the deposit is kept, there is no question to be solved. Please continue the formulation of the question. What is it we need to find? what amount of money she needs to collect?
The formula for accrued value with compounded interest would be written as:
[tex]A=P(1+r)^t[/tex]with the information on the account, we can write it as:
[tex]A=800(1+0.02)^t[/tex]but we cannot do anything with it unless you give:
1) the time to keep the account collecting interest,
OR
2) the total amount of money she needs to obtain.
What is the value of that new bicycle she wants?
Well, you have the equation needed. If you don't give me more info on what is needed, I cannot help you solve the equation. We need an extra piece of information.
The information now provided is that the person wants to keep the savings account for 2 years. So we use t = 2 in the equation above to obtain the answer:
[tex]A=800(1.02)^2=832.32[/tex]At the end of the two years she will have a total of $832.32
Find the equation for the line through points (-3,1) and (4,7) use y=Mx+b
A = (-3, 1) and B = (4,7)
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]m=\frac{7-1}{4-(-3)}=\frac{6}{7}[/tex][tex]y=\frac{6}{7}x+b[/tex]Now, for b, using point B
[tex](7)=\frac{6}{7}(4)+b[/tex][tex]b=7-\frac{6}{7}(4)\rightarrow b=\frac{25}{7}[/tex][tex]y=\frac{6}{7}x+\frac{25}{7}[/tex]Solve for x
4x = -5
Put the answer in its simplest form.
Answer:
[tex] \sf x=-1.25 [/tex]
[tex]\sf--------------------------------------------------------------------- [/tex]
Step-by-step explanation:
4x = -5
Divide both sides by 4 to single out the variable
4x/4 = -5/4
x = -1.25
A number from 1-40 is chosen at random. Find each probability.1. Pleven | at least 12)2. P(perfect square | odd)3. P(less than 25 | prime)4. P(multiple of 3 | greater than 15)
Given:
Numbers from 1 - 40
Let's find the probability of:
Pleven | at least 12)
Where:
Even numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 20 numbers
Even numbers that are at least 12 = 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 15 numbers.
Numbers that are at least 12 = 29 numbers
Therefore, to find the probability, we have:
[tex]P(even|atleast12)=\frac{P(even\text{ and at least 12\rparen}}{P(at\text{ least 12\rparen}}[/tex]Where:
[tex]\begin{gathered} P(even\text{ and at least 12\rparen = }\frac{15}{40}=0.375 \\ \\ P(at\text{ least 12\rparen= }\frac{29}{40}=0.725 \end{gathered}[/tex]Therefore, we have:
[tex]\begin{gathered} P(even|atleast12)=\frac{0.375}{0.725} \\ \\ P(even|atleast12)=0.52 \end{gathered}[/tex]Therefore, the probability that a number chosen at random is even given that it is at least 12 is 0.52
ANSWER:
0.52
PLEASE HELP I REALLY NEED AN ANSWER ALSO ONLY ANSWER IF YOUR GOING TO GIVE A STEP BY STEP SOLUTION
The answer of the given expression is 80.
Exponents
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
For example:-
[tex]5^4[/tex] can be written as 5*5*5*5.
Here 4 is the exponent or power and 5 is the base.
There are some laws of exponents which we use while calculating the answer to such expressions.
Given expression:-
[tex]\frac{12^7*30^5}{25^2*8^5*27^4}[/tex]
We have to simplify the given solution using the laws of exponents.
First we will divide them in their prime factors.
We know that,
[tex](x^a)^b=x^{ab}[/tex]
We can write,
[tex]12^7 = (2^2)^7*3^7=2^{14}*3^7[/tex]
[tex]30^5=2^5*3^5*5^5[/tex]
[tex]25^2=(5^2)^2=5^4[/tex]
[tex]8^5=(2^3)^5=2^{15}[/tex]
[tex]27^4=(3^3)^4=3^{12}[/tex]
Hence, we can write the given expression as follows,
[tex]\frac{2^{14}*3^7*2^5*3^5*5^5}{5^4*2^{15}*3^{12}}[/tex]
Also, we know that,
[tex]x^a*x^b=x^{a+b}\\x^a/x^b=x^{a-b}[/tex]
We can write,
[tex]{2^{(14+5-15)}*3^{(7+5-12)}*5^{(5-4)}}[/tex]
[tex]2^4*3^0*5^1[/tex] = 16*1*5 = 80
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In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Find BC.
The length of BC is 29 units (solved using trigonometry and its applications).
What is trigonometry?
Trigonometry (from Ancient Greek v (trgnon) 'triangle' and (métron)'measure') is a field of mathematics that explores the correlations between triangle side lengths and angles. The topic arose in the Hellenistic civilization during the third century BC from geometric applications to astronomical research. The Greeks concentrated on chord computation, whereas Indian mathematicians established the first-known tables of values for trigonometric ratios (also known as trigonometric functions) such as sine. Trigonometry has been used throughout history in geodesy, surveying, celestial mechanics, and navigation. Trigonometry is well-known for its many identities. These trigonometric identities are frequently used to rewrite trigonometrical expressions with the goal of simplifying an expression, finding a more usable form of an expression, or solving an equation.
Let the point where AB is cut through line from C be D
This can be solved using trigonometry and its applications.
In triangle ACD,
tan 45° = CD/AD
or, CD = tan 45° x AD
= 1 x 20
= 20 units
In triangle CDB,
tan Ф = CD/BD
or, Ф = tan⁻¹(CD/BD)
= tan⁻¹(20/21)
= 43.6°
so, sin 43.6° = CD/BC
or, BC = CD/sin 43.6°
= 20/0.689
= 29 units
The length of BC is 29 units.
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#SPJ13
Answer:
29
Step-by-step explanation:
BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/SQRT2
can anyone help me i have a picture of my math question
Answer:
-8, -5, -2, 1, 4
Explanation:
The given sequence is an arithmetic sequence -8, -5, -2 ....
The nth term of the sequence is expressed as;
Tn = a+ (n-1)d
a is the first term = -8
d is the common difference = -5 -(-8) = -2-(-5)
d = -5+8 = -2+5 = 3
Get the 4th term;
n = 4
T4 = -8+(4-1)*(3)
T4 = -8+3(3)
T4 = -8+9
T4 = 1
Get the 5th term:
n = 5
T5 = -8 + (5-1)*3
T5 = -8+4(3)
T5 = -8 + 12
T5 = 4
Hence the next two terms of the sequence are 1 and 4
Perform the indicated operation of multiplication or division on the rational expression and simply.
The rational expression is given as,
[tex]\frac{15x}{2y^3}\cdot\frac{12y^2}{5x}[/tex]Performing the division and multiplication in the given rational expression,
[tex]\frac{15x}{2y^3}\cdot\frac{12y^2}{5x}=\frac{3\times6\times y^3}{y^2}[/tex][tex]\frac{3\times6\times y^3}{y^2}=\frac{18}{y}[/tex]The rational expression after using the indicated operation we get,
[tex]\frac{18}{y}\text{.}[/tex]The ice skating rink charges $5 for a skate rental and $3 for every hour that you skate. What would be the equation you would use to determine how much you would need to pay?
If we use the variable t to represent the number of hours skating, the fixed price is $5 and the variable price is $3 per hour, that is, we have a variable cost of 3t.
So the final cost (variable C) is the sum of the fixed and variable costs:
[tex]C=5+3t[/tex]how many millielters are in 1/5 liters
We know,
1 liter=1000 milliter.
So, millilters in 1/5 liters is,
[tex]\frac{1}{5}liter\times\frac{1000\text{ milliter}}{1\text{ liter}}=200\text{ milliter}[/tex]Therefore, there are 200 milliters in 1/5 liters.