Answers
Answer:
12.6 units.
Step-by-step explanation:
According to cosine formula:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
Using cosine formula in triangle STU, we get
[tex](SU)^2=(ST)^2+(TU)^2-2(ST)(TU)\cos T[/tex]
[tex]t^2=(5)^2+(15)^2-2(5)(15)\cos (53^{\circ})[/tex]
[tex]t^2=25+225-150(0.60)[/tex]
[tex]t^2=160[/tex]
Taking square root on both sides.
[tex]t=\sqrt{160}[/tex]
[tex]t\approx 12.6[/tex]
Therefore, the value of t is 12.6 units.
Related Questions
Karim sent a chain email to 10 of his friends. The number of people who got the email increases by a factor of 1.4 every week. Write a expression that give the number of people who got the email after 6 weeks?.
Answers
Answer:
10x1.4^6
Step-by-step explanation:
Please help, thanks :) (Question is attached below)
Answers
Answer:
Step-by-step explanation:
the upper left graph is the correct answer
because "... or equal to" always represents a filled dot, while just "greater/less than" represents blank dot
If one- tenth of a number is added to 2, the result is half of that number, find the number. A. 2.5 B. 3.3 C. 4.2 D. 5.0
Answers
Answer:
D. [tex]\boxed{x = 5}[/tex]
Step-by-step explanation:
Let the number be x
Condition:
[tex]\frac{1}{10} x + 2 = \frac{1}{2} x[/tex]
[tex]\frac{x}{10} -\frac{x}{2} = -2\\LCM = 10\\Multiplying \ both \ sides \ by \ 10\\x - 5(x) = -2(10)\\x -5x = -20\\-4x = -20[/tex]
Dividing both sides by -4
x = 5
Answer:
[tex]\boxed{5.0}[/tex]
Step-by-step explanation:
Let the number be [tex]x[/tex].
1/10 of x is added to 2, the result is half of x.
[tex]2+\frac{1}{10} x=\frac{1}{2} x[/tex]
[tex]2=\frac{1}{2} x-\frac{1}{10} x[/tex]
[tex]2=\frac{2x}{5}[/tex]
[tex]10=2x[/tex]
[tex]\frac{10}{2} =x[/tex]
[tex]5=x[/tex]
The number is 5.0
The electromotive force V of an alternating current circuit at time t can be describe by the
following function, where V is volts and t is in seconds. V(t) = 220sin(180πt). How many cycles
will the circuit run through in 1 minute?
Answers
Answer:
5400 cycles
Step-by-step explanation:
You have the following function:
[tex]V(t)=220sin(180\pi t)[/tex]
where t is in seconds.
In order to find the number of cycles in 1 minute, you first calculate the frequency of the function, which is given by:
[tex]f=\frac{180\pi}{2\pi}=90s^{-1}[/tex]
The number of cycles is then given by:
[tex]n=ft=(90s^{-1})(60s)=5400\ cycles[/tex]
There are 5400 cycles in 1 minute
Evaluate the following: 3 to the power 2 ÷ (2 + 1). 2 3 4 5
Answers
Answer:
3
Step-by-step explanation:
A collection of 108 coins containing only quarters and nickels is worth $21. A table titled Coin Collection showing Number of Coins, Value, and Total. The first row shows Nickels, and has n, 0.05, and 0.05 n. The second row shows, Quarters, and has q, 0.25, and 0.25 q. The third row shows total, and has not entries. Which value could replace q on the chart? 21 108 21 – n 108 – n
Answers
Answer:
q = 108-n
Step-by-step explanation:
Given: 108 coins containing only quarters and nickels
q = 108-n
since total number of coins is 108, and n= number of nickels
If you want to know how many of each kind of coin, read on:
First solve the number of quarters and nickels.
If all 108 coins are quarters, the value is 108*0.25 = $27
Since this value exceed the actual by 27-21 = $6,
we replace a number of quarters by nickels.
Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.
So it will take 6/0.2 = 30 replacements.
Therefore there are 108-35 = 78 quarters and 30 nickels.
The solution is : q = 108-n, is the value could replace q on the chart.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Given:
108 coins containing only quarters and nickels
q = 108-n
since total number of coins is 108, and n= number of nickels
If you want to know how many of each kind of coin, read on:
First solve the number of quarters and nickels.
If all 108 coins are quarters, the value is 108*0.25 = $27
Since this value exceed the actual by 27-21 = $6,
we replace a number of quarters by nickels.
Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.
So it will take 6/0.2 = 30 replacements.
Therefore there are 108-35 = 78 quarters and 30 nickels.
The solution is : q = 108-n, is the value could replace q on the chart.
To learn more on multiplication click:
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Write as an algebraic expression and simplify if possible: *150% of 50% of z whoever answers the fastest gets brainliest
Answers
Answer:
3z/4
Step-by-step explanation:
Here, we start by calculating the 50% of z
mathematically, that would be 50/100 * z = 50z/100 = z/2
Now we want to calculate the 150% of this.
That would be 150/100 * z/2 = 150z/200 = 3z/4
If $a$ and $b$ are integers, such that $a\not= 0$ and $b\not= 0$ and $a^2$ and $b^2$ have at most two digits, what is the greatest possible difference between the squares of $a$ and $b?$
Answers
Answer:
80
Step-by-step explanation:
t is important to note that a square of any non-zero integer is positive, and therefore there is no advantage in using negative integers instead of positive integers to attain the greatest difference of squares. So we will not consider negative integers.
The greatest value of a^2 - b^2 occurs when a^2 is at its largest and b^2 is at its smallest.
The larger a, the larger a^2:
8 ^ 2 = 64
9 ^ 2 = 81
10 ^ 2= 100
Since a^2 can have at most two digits, a=10 is too large, and so a=9 is the largest integral value of a we can use.
Now, b^2 is at its smallest when b is closest to zero on the number line (the further b gets from zero, the larger its square becomes):
2 ^ 2 = 4
1 ^ 2 =1
0 ^ 2 = 0
Remember to go back to the original problem sometimes, to make sure you are taking everything into account. It states b doesn't =0, and therefore the b=1 is the closest b can get to zero as an integer. So, the greatest difference between b^2 and a^2 is when b=1 and a=9, giving the result:
a^2-b^2 =9^2-1^2 =81-1= 80.
So, 80 is your answer.
18.2 divided by 18 what’s the answer??
Answers
Answer:1.0111111111
Step-by-step explanation:
18.2 - 18 = .2-18 =1.0111111
area of parallelogramis 30 cm^2. if the length of two adjacent sides are 6 cm and 10 cm respectively. find its diagonal
Answers
Answer:
the long diagonal d=15.49 ( rounded to the nearest hundredth)
the shortest d=√136-120(cos 30)=5.663 ( rounded to the nearest hundredth)
Step-by-step explanation:
Area=height * base
30=h*6
h=30/6=5 cm
height=asinФ
sinФ=5/10=1/2 (Ф=30)
alternate angle=180
180-30=150 degrees
diagonal²=a^2+b^2-2abcos150
d²=10²+6²-2(10)(6)(-√3/2)
d=√136+60(√3)
the long diagonal d=15.49 ( rounded to the nearest hundredth)
the shortest d=√136-120(cos30)=5.663
Does this graph show a function? Explain how you know.
5
-5
-5
A. No; there are y-values that have more than one x-value.
B. No; the graph fails the vertical line test.
C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
Answers
Answer:
Option (C).
Step-by-step explanation:
To check a graph whether it's a function or not we use a vertical line test. In this test first we draw a vertical line on the given graph. If this line intersects the graph at more than one point, the graph is not a function.
In the given parabola, opening upwards passes the vertical line test.
Therefore, this graph shows a function.
Option (C) will be the answer.
Option (c) Yes; the graph passes the vertical line test. And
(d) Yes; there are no y-values that have more than one x-value are correct options. Hence, a given graph is a function.
This is a graph of [tex]y = x^2[/tex]
Which is a graph of parabola.
To determine the given graph is a function or not, we do a vertical line test.
The vertical line test says that if a vertical line intersects a graph more than once, then that graph is not a function. And in this case, y-values have more than one x-values.
Let’s draw a vertical line in the given graph (attached below)
We see that the vertical line touches the graph only at once. That’s why it is a function, and so there are no y-values that have more than one x-value.
Hence, the given graph is a function and option (3) and (4) are correct options.
Learn more about graphs here:
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Please help urgently ❤️❤️❤️
Answers
Greetings from Brasil...
Here we have application of Trigonometry
COS β = adjacent side ÷ hypotenuse (H)
bringing to our problem....
COS A = AC ÷ H
But we dont have AC.... We have to use Pitagoras:
AB² = AC² + BC²
AC² = AB² - BC²
AC = √(AB² - BC²)
AC = √(10² - 8²)
AC = √(100 - 64)
AC = √36
AC = 6So
COS A = AC ÷ H ⇔ COS A = AC ÷ AB
COS A = 6/10
COS A = 3/5Answer: B) 3/5
Step-by-step explanation:
Cos = adjacent/hypotenuse
Thus, the cos is AC/AB.
Because of Pythagorean Theorem, AC^2=AB^2-BC^2. Let AC be x.
[tex]x^2=10^2-8^2\\x^2=100-64\\x^2=36\\x=6[/tex]
Thus, the cos is 6/10, or 3/5
here are members on the board of directors for a certain non-profit institution. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?
Answers
Answer: 1320; 495
Step-by-step explanation:
Explanation is in the attachment file
What is 7/35 converted into a decimal??
Answers
Answer:
0.2
Step-by-step explanation:
it works out to be 0.2 as a decimal and 20% as a percentage.
Answer:
.2
Step-by-step explanation:
Suppose $600 is compounded yearly for 20 years. If no other deposits are made, what rate is needed for the balance to triple in that time? Round your answer to the nearest hundredth of a percent.
Answers
Answer:
5.65%
Step-by-step explanation:
Principal=$600
Time=20 years
FV=600*3=$1800
n=1
r=?
r= n[(A/P)^1/nt - 1]
=1{(1800/600)^ 1/1*20 - 1}
={(3)^1/20-1}
=3^0.05-1
=1.0565-1
=0.0565
rate=0.0565*100
=5.65% to the nearest hundredth percent
HELP FAST PLEASE
Polygon ABCDE is congruent to polygon TVSRK. VSR corresponds to
a,)
b,)
c,)
d,)
Answers
We are given that ABCDE is congruent to TVSRK and want to find what corresponds to VSR.
Look at the ordering of the letters. VSR is the second, third, and fourth letters of TVSRK, respectively.
Thus, we just have to select the second, third, and fourth letters of ABCDE and we get BCD.
Thus, VSR corresponds to BCD. Let me know if you need any clarifications, thanks!
Please help with 4.)
WILL MARK BRAINLIEST X
Answers
Answer:
a) More.
b) Less.
c) More.
Step-by-step explanation:
a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.
b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.
c) The same exact thing as part a.
Hope this helps!
YoIn a sale, the normal price of a book is reduced by 30%. The sale price of the book is £2.80 Work out the normal price of the book.
Answers
Answer: £4
Step-by-step explanation:
From the question, we are informed that when the normal price of a book is reduced by 30%, then the sale price of the book is £2.80.
Since the normal price of a book is reduced by 30%, that means the book is sold at (100% - 30%) = 70% of its normal price.
Let the normal price of the book be y.
70% of y = £2.80
70/100 × y = £2.80
0.7 × y = £2.80
0.7y = £2.80
y = £2.80/0.7
y = £4
The normal price of the book is £4.
please answer this A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bicycle that is sold in the shop. This is called a company’s overhead. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even? A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bicycle that is sold in the shop. This is called a company’s overhead. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even?
Answers
Answer: The store must sell 40 bikes.
Step-by-step explanation:
y=60x+2400
y=120x
120x=60x+2400
-60x on both sides
60x=2400
divide 60 on both sides
2400/60=40
x=40
linear system please help 60 points * please please please help will give brainlist
Answers
Answer:
1. a. b = - 8
b. x = 8
c. x = 11
d. x = 5
2. 12 soccer balls and 8 basketballs can be purchased.
Step by step explanation
a. [tex] - 14 + 6b + 7 - 2b = 1 + 5b[/tex]
Calculate the sum
[tex] - 7 + 6b - 2b = 1 + 5b[/tex]
Collect like terms
[tex] 7 + 4b = 1 + 5b[/tex]
Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S and change its sign
[tex]4b - 5b = 1 + 7[/tex]
Collect like terms
[tex] - b = 8[/tex]
Change the signs on both sides of the equation
[tex]b = - 8[/tex]
-----------------------------------------------------------------
b. [tex] \frac{5x + 10}{ - 6} = - 5[/tex]
Apply cross product property
[tex]5x + 10 = - 5 \times ( - 6)[/tex]
Multiply the numbers
[tex]5x + 10 = 30[/tex]
Move constant to R.H.S and change its sign
[tex]5x = 30 - 10[/tex]
Calculate the difference
[tex]5x = 20[/tex]
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{20}{5} [/tex]
Calculate
[tex]x = 4[/tex]
----------------------------------------------------------------
c. [tex] - 15 = \frac{ - 8x - 17}{7} [/tex]
Apply cross product property
[tex] - 15 \times 7 = - 8x - 17[/tex]
Multiply the numbers
[tex] - 105 = - 8x - 17[/tex]
Swap the sides of the equation
[tex] - 8x - 17 = - 105[/tex]
Move constant to R.H.S and change its sign
[tex] - 8x = - 105 + 17[/tex]
Calculate
[tex] - 8x = - 88[/tex]
Change the signs on both sides of the equation
[tex]8x = 88[/tex]
Divide both sides of the equation by 8
[tex] \frac{8x}{8} = \frac{88}{8} [/tex]
Calculate
[tex]x = 11[/tex]
------------------------------------------------------------------
D. [tex]5 = 6x + 5(x - 10)[/tex]
Distribute 5 through the parentheses
[tex]5 = 6x + 5x - 50[/tex]
Collect like terms
[tex]5 = 11x - 50[/tex]
Swap both sides of the equation
[tex]11x - 50 = 5[/tex]
Move constant to R.H.S and change its sign
[tex]11x = 5 + 50[/tex]
Calculate the sum
[tex]11x = 55[/tex]
Divide both sides of the equation by 11
[tex] \frac{11x}{11} = \frac{55}{11} [/tex]
Calculate
[tex]x = 5[/tex]
------------------------------------------------------------------
2.
Solution,
No.of students in soccer = x
No.of students in basketball = y
Total no.of students = 20
i.e x + y = 20 → equation ( i )
Cost of soccer ball = $ 7
Cost of basketball = $ 10
Total budget = $ 164
i.e 7x + 10 y = 165 → equation ( ii )
In equation ( i ),
x + y = 20
Move 'y' to R.H.S and change its sign
x = 20 - y
Put the value of x in equation ( i )
[tex]7(20 - y) + 10y = 164[/tex]
[tex]140 - 7y + 10y = 164[/tex]
[tex]3y = 164 - 140[/tex]
[tex]3y = 24[/tex]
[tex]y = \frac{24}{3} [/tex]
[tex]y = 8[/tex]
Now, put the value of y in equation ( i ) ,
x + y = 20
[tex]x + 8 = 20[/tex]
[tex]x = 20 - 8[/tex]
[tex]x = 12[/tex]
Hence, 12 soccer balls and 8 basketballs can be purchased.
Hope this helps...
Best regards!!
Answer:
1. b = -8
2. x = 8
3. x = 11
4. x = 5
hope that helpwd
$70 discounted to $63
Answers
Answer:
10% off
Step-by-step explanation:
When $70 is discounted to $63, you can multiply 70 times 0.1 to get 7 which 70-63=7. To make 0.1 to a percentage, multiply by 100 to get 10%.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
work out the shaded area.
plzzzz
Answers
Answer:
Shaded area: 70cm^2
Step-by-step explanation:
Whole=120cm^2
White Square=
10-2.5-2.5=5
12-1-1=10
5✖️10=50cm^2
Whole-white=70cm^2
Help please!! Thanks!!!
Answers
Answer:
your answer is k
Step-by-step explanation:
not all the isosceles triangles are similar
This makes the statement false.
The x-coordinate of the intersection point of Line B D and Line C E is StartFraction 2 (a + c) Over 3 EndFraction. y = (StartFraction b Over a minus c EndFraction)x − (StartFraction 2 b c Over a minus 2 c EndFraction) y = (StartFraction b Over a minus 2 c EndFraction) (StartFraction 2 (a + c) Over 3 EndFraction) minus (StartFraction 2 b c Over a minus 2 c EndFraction) y = (StartFraction b Over a minus 2 c EndFraction) (StartFraction 2 (a + c) Over 3 EndFraction) minus (StartFraction 6 b c Over 3(a minus 2 c) EndFraction) y = StartFraction 2 b (a + c) minus 6 b c Over 3 (a minus 2 c) EndFraction y = StartFraction 2 a b + 2 b c minus 6 b c Over 3 (a minus 2 c) EndFraction What is the y-coordinate? StartFraction b c Over 3 EndFraction StartFraction 2 b Over 3 EndFraction StartFraction 2 b c Over 3 EndFraction StartFraction a b c Over 3 EndFraction
Answers
Answer:
y = 2b/3
Step-by-step explanation:
The x-coordinate of the intersection point of Line B D and Line C E is at [tex]\frac{2(a+c)}{3}[/tex]. Given that:
[tex]y=\frac{b}{a-2c}x -\frac{2bc}{a-2c} \\\\The\ y\ coordinate\ can\ be \ gotten\ by\ substituting\ the \ value\ of\ x\ and\ simplifying.\\ Substituting\ x:\\\\y=\frac{b}{a-2c}(\frac{2(a+c)}{3} ) -\frac{2bc}{a-2c}[/tex]
[tex]Simplyfing\ the\ parenthesis\\y=\frac{2b(a+c)}{3(a-2c)} -\frac{2bc}{a-2c}\\\\y=\frac{2ab+2bc}{3(a-2c)} -\frac{2bc}{a-2c}\\\\Simplyfying\ using\ LCF\\y=\frac{2ab+2bc-6bc}{3(a-2c)}\\\\y=\frac{2ab-4bc}{3(a-2c)}\\\\Factorizing:\\\\y=\frac{2b(a-2c)}{3(a-2c)}\\\\y=\frac{2b}{3}[/tex]
The y-coordinate of the intersection point of Line B D and Line C E is at [tex]\frac{2b}{3}[/tex].
Answer:
b
Step-by-step explanation:
Hurry help plz exam 05 :The following sphere has a diameter of 11 inches.
What is the volume of the sphere? Use 3.14 for it and round your answer to the nearest tenth.
O 5,572.5 in^3
O 696.6 in^3
O 174.1 in^3
O 126.6 in^3
Answers
Answer:
696.6 in³
Step-by-step explanation:
The formula for the volume of a sphere is 4/3πr³
The diameter of 11 in. is given. Therefore, the radius is 5.5 (11/2 = 5.5).
1. Set up the equation
4/3(3.14)(5.5³)
2. Solve
= 696.6 in³
Answer:
[tex]\boxed{Volume = 696.9 \ in.^3}[/tex]
Step-by-step explanation:
Diameter = 11 inches
Radius = 5.5 inches
Volume of sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where r = 5.5 inches
Volume = [tex]\frac{4}{3} (3.14)(5.5)^3[/tex]
Volume = [tex]\frac{4}{3} (3.14)(166.375)[/tex]
Volume = [tex]\frac{2090.7}{3}[/tex]
Volume = 696.9 in.³
Jim's living room is 23 feet wide and 25 feet long. He wants to put a border around the top of the room. The cost of the border is $1.00 per foot. How much will it cost to buy enough of the border to go around the room?
Answers
Answer:
$96.00
Step-by-step explanation:
Perimeter formula, 2w+2l
2(23)+2(25)=96 feet
1$ per foot
96 feet,
so $96
Answer:
I think it 96.00
Step-by-step explanation:
√ (952.695) + √0.00195 – 5.382 please help Thank you to whoever helps
Answers
Answer:
25.52791653032955454422437424679625318128649677442393276098...
Step-by-step explanation:
You can just paste this into wolframalpha.
Answer: 970.72312
Step-by-step explanation:
Straightforward operation.
Help please you need to find the rise in the blue triangle. Thank you!!
Answers
Answer:
12.65
Step-by-step explanation:
In the case of the blue triangle, to calculate the rise, which would be the increase, therefore it would be the hypotenuse formed by the arrow.
We have to Pythagoras is:
h ^ 2 = a ^ 2 + b ^ 2
In this case:
a (x-axis) = 4
b (y-axis) = 12
replacing:
h ^ 2 = 4 ^ 2 + 12 ^ 2
h ^ 2 = 160
h = 12.65
Which means that the rise in the blue triangle is 12.65 units
I need help with solving this problem 4x-c=k
Answers
Answer:
x=1/4c+1/4k
Step-by-step explanation:
4x-c=k
move c over
4x=c+k
then divide by 4
x=1/4c+1/4k
hope this helps
The hypotnuse of a right triangle is three times the length of its first leg. Theblength of the other leg is four feet. Find the lengths of the first leg and the hypotnduse and enter them in the below squares in this order. For non-integer answer(s), round your answer(s) to the nearest tenth.
Answers
Answer:
Length of first leg = 1.4feet
Hypotenuse = 4.2feet
Explanation:
Since we are dealing with a right angled triangle, we will apply the Pythagoras theorem to solve the question. According to Pythagoras theorem, the square of the hypotenuse is equal to the sum if the square of the other two legs.
Mathematically, a² = b²+c² where a is the hypotenuse and b, c are the other two legs.
From the question, since hypotenuse of a right triangle is three times the length of its first leg, then a = 3b.
Also the other leg is four feet i.e c= 4
Substituting this values into the Pythagoras formula;
a²=b²+c²
(3b)² = b²+4²
9b² = b²+16
9b²-b² = 16
8b² = 16
b² = 16/8
b² = 2
b = √2
b = 1.4
Since a = 3b
a = 3(1.4)
a = 4.2
Hence, the length of the first leg is 1.4feet and that of the hypotenuse is 4.2feet both to the nearest tenth.