Answers
Answer:
m∠C = 110.9° (1 dp)
Step-by-step explanation:
The largest angle in a triangle is opposite the longest side.
Therefore, from inspection of the diagram, angle C is the largest angle since length AB is the longest side length.
To find angle C, use the cosine rule:
[tex]\sf c^2=a^2+b^2-2ab \cos C[/tex]
(where a, b and c are the sides, and C is the angle opposite side c)
Given:
a = BC = 11cmb = AC = 7 cmc = AB = 15 cmSubstituting the given values into the formula and solving for C:
[tex]\implies \sf c^2=a^2+b^2-2ab \cos C[/tex]
[tex]\implies \sf 15^2=11^2+7^2-2(11)(7) \cos C[/tex]
[tex]\implies \sf 225=170-154 \cos C[/tex]
[tex]\implies \sf \cos C=\dfrac{225-170}{-154}[/tex]
[tex]\implies \sf \cos C=-\dfrac{5}{14}[/tex]
[tex]\implies \sf C=\cos ^{-1}\left(-\dfrac{5}{14}\right)[/tex]
[tex]\implies \sf C=110.9248324...^{\circ}[/tex]
Therefore, m∠C = 110.9° (1 dp)
Answer:
see photo for detailed analysis
Related Questions
Slope
y = 4x + 3
y = -1x -2
y = -6x - 3
y = -1x + 2
=
#1
#2
Х
Х
Answers
Assuming your asking for two sets of systems of equations.
#1: [tex]{y,x}={-1,-1}[/tex]
Steps:
Solve by Substitution :
// Solve equation [2] for the variable x
[2] x = -y - 2
// Plug this in for variable x in equation [1]
[1] y - 4•(-y -2) = 3
[1] 5y = -5
// Solve equation [1] for the variable y
[1] 5y = - 5
[1] y = - 1
// By now we know this much :
y = -1
x = -y-2
// Use the y value to solve for x
x = -(-1)-2 = -1
Solution :
{y,x} = {-1,-1}
2: [tex]{y,x}={3,-1}[/tex]
Steps:
Solve by Substitution :
// Solve equation [2] for the variable x
[2] x = -y + 2
// Plug this in for variable x in equation [1]
[1] y + 6•(-y +2) = -3
[1] -5y = -15
// Solve equation [1] for the variable y
[1] 5y = 15
[1] y = 3
// By now we know this much :
y = 3
x = -y+2
// Use the y value to solve for x
x = -(3)+2 = -1
Solution :
{y,x} = {3,-1}
Can someone help me? :D
Answers
answer: b and a cannot be points on the unit circle so there for the answer is b and a
option A and option D
hope it helps...!!!
To win a lottery, 7 numbers are drawn at random from a pool of 21 numbers. Numbers cannot repeat. If a person has one ticket, what is the probability that they have the winning ticket?
Answers
Answer:
the answer should be 3....this is not right btw
the probability of having a winning raffle ticket is 15%.
Angela needs volume of a sphere. Which formula is correct?
The diameter of the sphere is d=17
A 4/3 pi 17 cubed
B 4/3 pi 17 squared
C 4/3 pi 8.5 cubed
D 4/3 pi 8.5 squared
Answers
Answer:
C-------------------------------------------------
She read a total of 497 pages in 7 days what is the mean number of pages Siriana read each day
Answers
Answer:
71 pages / day
Step-by-step explanation:
You are looking for pages per day so:
497 pages / 7 days = 71 pages/day
Type your answer and then click or tap Done.
The number of seconds is equal to 60 times the
number of minutes. Write the direct variation
equation that represents this situation. Let xbe the
independent variable. Let y be the dependent
variable.
Answers
Answer:
See below
Step-by-step explanation:
x(x-2y)-(y-x)2
Final result :
-y2
Step by step solution :
Step 1 :
Equation at the end of step 1 :
x • (x - 2y) - (y - x)2
Step 2 :
2.1 Evaluate : (y-x)2 = y2-2xy+x2
Final result :
-y2
Answer:
y=60x
Step-by-step explanation:
Let x be the number of minutes, y be the
number of seconds
4=60x
{Direct variation}
please answer question below asap!!
Answers
Answer:
44 boots
Step-by-step explanation:
24/6=4
that means we have to multiply all the numbers by 4 as well
2*4=8
3*4=12
24+8+12=44
A computer and printer cost a total of $1020. The cost of the computer is three times the cost of the printer.
Find the cost of each item.
Answers
Hey Mate ,
Reading the given statement ,
Let the cost of printer be x and the cost of Computer be 3x
ATQ ,
3x + x = $1020
4x = $1020
x = 255
Therefore , the cost of Printer is $255 and the cost of computer is $255× 3 = $765
In a town, 15% of the population is unemployed. what is the
total population, if number of people who are employed is
8381
Answers
Answer:
1479 people
Step-by-step explanation:
If the amount employed is 8381, that means 8381 is 85% of the population. 8381/85 = 98.6
Every 1% of the population is 98.6, so we can just do 15 x 98.6 to get 1479
Answer:
9,860
Step-by-step explanation:
100% - 15% = 85 % = 85/100
85/100 * 8381/x
85x = 838,100
838,100/85 = 9,860
the length of the hypotenuse of a 45°-45°-90° triangle with a leg of 12, what the length
Answers
Answer:
The length of the other two legs are 6√2.
since the hypotenuse is one of the legs multiplied by √2.
dividing the hypotenuse by √2 will get the length of one leg. since it is a 45 45 90 triangle, the length of the two legs are the same.
12/√2= 12√2/2= 6√2
solve the inequility 3x - 3 <9
Answers
Answer:
x<4
Step-by-step explanation:
Here, hope this helped!
A quick tip, just think that the sign is an equal sign, that helps.
Answer: [tex]x < 4[/tex]
Step-by-step explanation:
Our inequality is [tex]3x-3 < 9[/tex]
We will add 3 to both sides. (addition property of equality)
Simplify [tex]9 + 3 9+3 9+3 ~to ~12[/tex].
Then divide both sides by 3. (division property of equality)
[tex]3x[/tex]÷[tex]3 < 12[/tex]÷[tex]3[/tex]
[tex]\frac{3x}{3} < \frac{12}{3}[/tex]
Simplify [tex]312~to~4[/tex].
determine the volume of a sphere if it has a radius of 5 inches
Answers
Answer:
V ≈ 523.6in³
Step-by-step explanation:
Using the second sphere volume equation results in:
4/3 x 3.14159 x 53 = 4.1866 x 125 = 523.6in3
Step-by-Step Explanation:
Radius (r) = 5 in
Volume = 4/3πr^3
Therefore,
=> 4/3πr^3
= 4/3 * π * r * r * r
= 4/3 * 3.14 * 5 * 5 * 5
= 4/3 * 3.14 * 125
= 4.186 * 125
=> 523.25
Volume = 523.25 in^3
Casey is buying snacks for a class trip. She has 16 snacks left over from the last trip. She buys snacks by the case to get a good price. Each case holds 24 snacks. How many cases will she have to buy if she wants to have a total of 160 snacks?
Answers
Answer:
Your answer is 10
Step-by-step explanation:
160 devided by 16 = 10
On Thursday afternoon at camp, Nora played basketball and went swimming before dinner. She started playing basketball at 2:50 P.M. and played for 1 hour and 45 minutes. Then she swam for 50 minutes. Dinner lasted for 1 hour. What time did dinner end?
Answers
Answer:
6:25 PM
Step-by-step explanation:
Start of dinner
2:50 PM + 1:45 + 0:50
convert it to minutes
2:50PM + 60+ 45 + 50
= 2:50Pm + 60 + (50 + 10) + (45 - 10)
= 4:50Pm + 35
= 4:50PM + 10 + 25
= 5:25PM
End of dinner
5:25PM + 1 = 6:25PM
The lines that appear tangent are tangent. What is the value of x, to the nearest tenth.
Answers
Answer:
x ≈ 10.7
Step-by-step explanation:
Is given in the picture that x is the radius of the circle.
The radius of a circle and the tangent line to the circle form a right angle, therefore our triangle is a right triangle.
We can apply the Pythagorean Theorem to find one equation that will have one unknown x.
(x+12)² = x² +20² , use that (a+b)² = a²+b²+2ab
x²+12²+2·x·12 = x² +20², subtract x² from both sides of the equation
12² + 24x = 20², subtract 12² from both sides of the equation
24x = 20²-12², raise to power and combine like terms
24x = 256, divide by 24 both sides of the equation
x = 10.6666666..., round to the nearest tenth
x ≈ 10.7
Given a+b=7 and a-b=3; find the following.
3^a÷3^b
Answers
Steve has overdrawn his checking account by $27. His bank
charged him $15 for an overdraft fee. Then he quickly deposited
$100. What is his current balance?
Answers
He then adds 100 to his account so we would minus 42 from 100 which equals 58 and that’s his current balance
I really need help with this ^-^
Answers
The graph of a function is shown in the picture and the amplitude will be 6
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a trigonometric function:
[tex]\rm y = -6\cos\left(5x\right)-3[/tex]
As we know, the range for the cosx is [-1, 1]
The maximum value of function y = -6cos(5x)—3 is 3 and minimum value is -9.
The amplitude = 6
Thus, the graph of a function is shown in the picture and the amplitude will be 6
Learn more about trigonometry here:
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HELP!!!
Which function increases at a faster rate on 0 to infinity,
f(x) = x2 or g(x) = 2x? Explain your reasoning.
=
Answers
Answer:
f(x) is faster
Step-by-step explanation:
In case it is x^2 then f(x) will be faster.
If you draw these two function in the graph. You can see that
Or you can add any value randomly and see that
Ex:
when x = 5
f(x) = 25, g(x) = 10
when x = 20
f(x) = 400, g(x) = 40
when x is 4 times larger. g(x) is 4 times larger while f(x) is 16 times larger
I need help please I don’t get it
Answers
Answer:
ask your teacher for help. learn more today.
Step-by-step explanation:
A filing cabinet measures 5 feet is 18 inches wide and 2 feet deep what is the volume of the filing cabinet
Answers
Answer:
15 feet
Step-by-step explanation:
From the question above,we are asked to find the volume of a cabinet with the following dimensions:
Height is five feet
Width is eighteen inches
And a depth of two feet.
Here it is quite obvious that we ate dealing with a cuboidal object since its dimensions differ from one another.
So volume of a cuboid as we all know is :
Length multiplied by width and then height
We should head straight away to the calculations, but we need to remember that the width is in inches and needs to be converted to feet
1 inch = 1/12 feet
18 inches = 18× 1/12
= 1.5 feet
L×W×H
= 1.5×5×2
= 15 feet
If a1 = 5 and 5 and an = -3an-1 then find the value of a5. WILL GET BRAINLIEST
Answers
Answer:
405
Step-by-step explanation:
Given
a₁ = 5aₙ = -3aₙ₋₁Solving
a₂ = -3a₁ = -3(5) = -15a₃ = -3a₂ = -3(-15) = 45a₄ = -3a₃ = -3(45) = -135a₅ = -3a₄ = -3(-135) = 405a_1=5
a_2=-3a_1=-3(5)=-15a_3=-3a_2=-3(-15)=45a_4=-3a_3=-3(45)=-135a_5=-3a_4=-3(-135)=405Help with this please i will give brainiest if right
Answers
Answer: 6
Step-by-step explanation:
HELP!!!!!!!! Select an expression that id equivalent to 4squareroot of 2x^2 • 4squareroot of 2x^3
Answers
Answer:
B
Step-by-step explanation:
[tex]\sqrt[4]{2x^2} *\sqrt[4]{2x^3} =(2x^2)^{1/4}*(2x^3)^{1/4}\\= 2^{1/4}*(x^2)^{1/4} *2^{1/4} * (x^3)^{1/4}\\[/tex]
combine like terms
[tex]= 2^{2/4} *x^{2/4}*x^{3/4}\\= 2^{2/4} * x^{5/4}[/tex]
these steps use exponent laws
a few key ones i used:
(x^y^z) = x^(y*z)
x^y * x^z = x^(y+z)
let me know if you have any questions!
Which words mean the same thing as 5/8
Answers
Answer:
c) Five out of 8 equal parts of a whole
Step-by-step explanation:
The statement "Five out of 8 equal parts of a whole" means the fraction of 5/8. Hence, option (c) is the correct answer.
Answer:
"Five out of eight equal parts of a whole"
Step-by-step explanation:
In a fraction, the numerator (top part) is saying "this number out of the number below it."
The denominator (lower part) is the number below it that we are taking the proportion out of.
A denominator is ALWAYS equal parts, so if we match up the phrase: "5 out of eight equal parts of a whole"
You told your friend that you could eat 78 of a large pizza. If you only ate 23 of what you said you could eat, what fraction of a large pizza did you eat?
Answers
Answer:
5/16
Step-by-step explanation:
Fraction of claim is 5/8
But you actually eat 1/2
Fraction of large pizza actually eaten 5/16
Hopefully this is correct and it can help you!
2. If ¡2x+3 = i, where i = V-1, then which of the
following is a solution for x?
(1) x = 16
(3) x = 11
(2) x = 10
(4) x = 14
Answers
I assume you mean the equation
[tex]i^{2x+3} = i[/tex]
Since i = √(-1), we have i⁴ = 1 and so i⁵ = i. Then 2x + 3 must be some multiple of 5.
Now just check for which of the given choices that this holds:
x = 16 ⇒ 2x + 3 = 35 (yes)
x = 11 ⇒ 2x + 3 = 25 (yes)
x = 10 ⇒ 2x + 3 = 23 (no)
x = 14 ⇒ 2x + 3 = 31 (no)
Find the midpoint of the line segment with the given endpoints
(4,-6), (9, 6)
Answers
Answer:
I think it's number 5 or (5,8)
Step-by-step explanation:
The scatter plot with trend line below shows the data comparing wind speed and wind chill. Wind Chill (˚F) Wind Speed (mph) The trend line passes through (10, 9) and (35, 0). Write an equation for the trend line. The equation of the trend line is y = x + .
Answers
The trend line passes through (10, 9) and (35, 0) will be 9x + 25y = 315.
What is the equation of a line passing through two points?Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by
[tex]\rm (y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
The scatter plot with the trend line below shows the data comparing wind speed and wind chill. Wind Chill (˚F) Wind Speed (mph). The trend line passes through (10, 9) and (35, 0).
Write an equation for the trend line.
(x₁, y₁) → (10, 9)
(x₂, y₂) → (35, 0)
Then we have
y - 9 = -9/25(x - 10)
25y - 225 = -9x + 90
9x + 25y = 315
Learn more about straight-line equations here:
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Sarah has private health insurance that costs $575 per month. Her new employer will provide health insurance at no cost to her. What is her health insurance worth as a benefit of employment?
Answers
Based on the above information, it can be inferred that Sarah saves $6,900 per year.
How to calculate how much Sarah saves per year in health service?Taking into account that her new employer is going to give her a free health service and that before she paid $575 for the health service monthly, to calculate her savings per year we must multiply the value of the health service by the number of months of one year (12).
$575 × 12 = $6,900Based on the above, it can be inferred that Sarah is saving $6,900 per year on health care.
Note: This question is incomplete because the is some information missing. The information is missing
How much money is Sarah saving on healthcare each year with her new employer?Learn more about health in: https://brainly.com/question/13179079
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