Given:
In triangle [tex]ABC, AB=9,BC=4,AC=7[/tex].
To find:
The measure of angle C.
Solution:
We have, [tex]AB=9,BC=4,AC=7[/tex]. It means [tex]c=9,a=4,b=7[/tex].
According to the law of cosines:
[tex]cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
[tex]cos C=\dfrac{4^2+7^2-9^2}{2(4)(7)}[/tex]
[tex]cos C=\dfrac{16+49-81}{56}[/tex]
[tex]cos C=\dfrac{-16}{56}[/tex]
Taking cos inverse on both sides, we get
[tex]C=cos^{-1} \dfrac{-16}{56}[/tex]
[tex]C=106.60155[/tex]
[tex]C\approx 106.6[/tex]
Therefore, the correct option is C.
plss help n dont be a B n give me sum gæy link :|
Solve for x
-3x + 6 = 2x - 24
A) -30
B) -6
C) 6
D) 30
Answer:
6
Step-by-step explanation:
ok
Lets start by grouping like terms
we get
-5x=-30
divide -5 from both sides
x=6
Answer:
x = 6 or C) 6
Step-by-step explanation:
Step 1: We will subtract 2x from both sides.
−3x + 6 − 2x = 2x − 24 − 2x
To understand a bit better: -3x - 2x = -5x and 2x - 2x = 0 so it will end up looking like this:
−5x + 6 = −24
Step 2: We will subtract 6 from both sides.
−5x + 6 − 6 = −24 − 6
−5x = −30
Step 3: We will divide both sides by -5.
−5x/−5 = −30/−5
Both will equal to positive 6 so it is your x, I hope this somewhat helped you better understand the equation!
A garden measuring 8 feet by 12 feet will have a walkway around it. The walkway has
a uniform width, and the area covered by the garden and walkway is 192 square feet.
What is the width of the walkway?
O 3.5 feet
O 6 feet
O 2 feet
O 4 feet
Answer:
2 feet
Step-by-step explanation:
By solving a quadratic equation, we will see that the width of the walkway must be 2 ft.
How to get the width of the walkway?
Remember that the area of a rectangle of length L and width W is:
A = L*W
In this case, we know that the dimensions are:
Length = 8ftWidth = 12ftNow, if we add a walkway of width x all around the garden, the new dimensions of the garden are:
Length = 8ft + 2xWidth = 12ft + 2xNow with these dimensions, the area is 192 ft^2, then we can write:
192 ft^2 = (8ft + 2x)*(12ft + 2x)
Now we need to solve that for x:
192 ft^2 = 96ft^2 + 4x^2 + 40ft*x
0 = 96ft^2 - 192ft^2 + 4x^2 + 40ft*x
0 = 4x^2 + 40ft*x - 96ft^2
This is a quadratic equation, the solutions are given by Bhaskara's formula:
[tex]x = \frac{-(40ft) \pm \sqrt{(40ft)^2 - 4*4*(-96ft^2)} }{2*4} \\\\x = \frac{-(40ft) \pm 56ft }{8}[/tex]
Notice that we have two solutions, but we only care for the positive one, so we take:
x = (-40ft + 56ft)/8 = 2ft
So the width of the walkway must be 2ft.
If you want to learn more about quadratic equations, you can read:
https://brainly.com/question/1214333
2x+1=5x-8 Solving Equations with Many or No Solutions
Hello!
[tex]\large\boxed{x = 3}[/tex]
2x + 1 = 5x - 8
Solve by subtracting both sides by 2x:
2x - 2x + 1 = 5x - 2x - 8
1 = 3x - 8
Add 8 to both sides:
1 + 8 = 3x - 8 + 8
9 = 3x
Divide both sides by 3:
9/3 = 3x/3
x = 3
Answer:
x = 3
Step-by-step explanation:
1. Write the equation
2x + 1 + 5x - 8
2. Add 8 on both sides
2x + 9 = 5x
3. Get the variables together
9 = 3x
4. Solve for x and divide both sides by 3
x = 3
Which expression is equivalent to
Answer:
B) x^(5/3)*y^(1/3)
Step-by-step explanation:
Taking the cube root of a number is the same as raising it to the 1/3 power:
∛x=x^1/3
∛(x⁵y) = x^(5(1/3))*y^(1/3)=x^(5/3)*y^(1/3)
Remember to multiply exponents when raising an exponent to an exponent and distribute the 1/3 to each exponent!
PLZ ANSWER THIS I CANT FIGURE OUT THE SECOND ONE
(INSTANTANEOUS ROC)
I will give you brainiest if you answer it right
Answer:
Step-by-step explanation:
The first one is actually 0 I think. The instantaneous ROC at x=1 should also be 0. The last one should be correct.
Basically, the ROC for the first one is 0 because the y value at the start and end of the interval is the same, so the change is the same. However, for the instantaneous ROC at x = 0, you look at the graph and realize that if you find the derivative at that point, it is 0.
Let x and y be inversely related. If x is 5 when y
is 6, find y when x is 3.
Answer:
y=10
Step-by-step explanation:
x=k/y
constant of proportionality
k=xy
k=5*6
k=30
therefore x=30/y
if x=3 y=?
y=30/3
y= 10
What is the solution of 3x + y = 9 and 3x - 5y = 15?
Answer:
(10/3, -1)
Step-by-step explanation:
So there are two different ways.
First you could address for y and fitting it into the number cruncher. one condition for y1 and another for y2. At that point go second follow and press 5 and afterward press enter multiple times to discover the convergence.
the subsequent path is to tackle by hand. I would recommend address the primary condition for y and attachment the condition tackled for y into the other condition. so y = - 3x + 9 and 3x-5y=15. At that point you could do 3x - 5(- 3x+9) = 15. At long last address for x and plug in x into the two conditions to check whether you get a similar y esteem.
The appropriate response ought to be (10/3, - 1)
Answer:
x = 3 1/3, x = -1.
Step-by-step explanation:
3x + y = 9
3x - 5y = 15
Subtract second equation from the first to eliminate the 3x :
3x - 3x + y - (-5y) = 9 - 15
6y = -6
y = -1.
Plug y = -1 in first equation:
3x + -1 = 9
3x = 10
x = 10/3 = 3 1/3.
A triangle has a 90° angle. What type of triangle is it?
A) Acute triangle
B) Right triangle
C) Equilateral triangle
D) Isosceles triangle
Answer:
B) Right triangle
Step-by-step explanation:
Only right triangles have an angle that's 90°.
it is a right triangle...
Tell me the answer please. Give me a short answer and a step-by-step explanation.
PLS HELP ME! . This pattern follows the rule multiply by 3, then subtract 4. What are the next two terms? 5, 11, 29
Answer:
83, 245
Step-by-step explanation:
Using the rule multiply by 3, then subtract 4
a₄ = 3 × a₃ - 4 = 3 × 29 - 4 = 87 - 4 = 83
a₅ = 3 × a₄ - 4 = 3 × 83 - 4 = 249 - 4 = 245
The next 2 terms are 83, 245
what is the difference between 479,310 and 214,991?
Answer:
264,319
Step-by-step explanation:
A difference is a subtraction problem.
Subtract 214,991 from 479,310.
479,310 - 214,991 = 264,319
HELP PLZ BRAINIEST TO WHOEVER RIGHT
Answer:
five-number summary
Step-by-step explanation:
Which equation has the solution x = 2?
A 2x-3=19
B 3x+2=8
C 4x-4=-4
D 5x+1=10
Answer:
The answer is B.
Step-by-step explanation:
You can solve this problem by plugging in 2 for x in the given equations.
2(2) - 3 = 19 is false
3(2) + 2 = 8 is true
4(2) - 4 = -4 is false
5(2) + 1 = 10 is false
.
In the hands of someone with harmful intentions, how can analogies prove to be dangerous tools?
A)Analogies can create long-lasting confusion that prevents people from making decisions.
B)Analogies make significant connections seem far less powerful than they actually are.
C)Analogies meant to persuade or influence people are often disguised as explanations.
D)Analogies, even weak and misleading ones, can be powerful tools of persuasion.
Answer:
I believe, its D.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
In the data set below, what are the lower quartile, the median, and the upper quartile?
15 17 41 15 50 55 55 58 62 66
Answer:
its 55
Step-by-step explanation:
Find the volume of the cone round your answer to the nearest tenth
You invest $500 in an account that pays 6% interest compounded continuously. How
much will be in the account after 6 years?
=====================================================
Explanation:
We'll apply this formula
A = P*e^(r*t)
where,
A = account balance after t yearsP = initial deposit, aka principale = special constant roughly equal to 2.718 but it goes on forever without a pattern; it's better to let the calculator handle this value rather than type the decimal digits in.r = annual interest rate in decimal formt = number of yearsIn this case, we have
P = 500r = 0.06t = 6Again we won't type "2.718..." for 'e', and we'll just type it into the calculator as shown below. That way the calculator can handle the digits instead.
So...
A = P*e^(r*t)
A = 500*e^(0.06*6)
A = 716.66470728026
A = 716.66 dollars is the final answer
14.
Given that sin θ= 1 / √2, we want to find the value of tan θ.
First, find the value of θ.
Answer:
value of tan θ = 1
Step-by-step explanation:
To find θ do the asin of 1/√2
θ = asin (1/√2)
θ = asin (0.707106781)
θ = 45
and then to find tan θ, do tan 45
tan 45 = 1
A triangular prism has a height of 9 meters and a triangular base with the following dimensions.
What is the volume of the prism?
- 420 m^3
- 288 m^3
- 324 m^3
- 432 m^3
Answer:
V = 432 m³
Step-by-step explanation:
The volume (V) of a prism is calculated as
V = Ah ( A is the area of the base and h the height )
A = [tex]\frac{1}{2}[/tex] bh ( area of triangular base, with b the base, h the perpendicular height)
Here b = 16 and h = 6 , then
A = [tex]\frac{1}{2}[/tex] × 16 × 6 = 8 × 6 = 48 m²
Then
V = 48 × 9 = 432 m³
GEOMETRY HELP PLEASE!! WILL MARK BRAINLEIST!
3
Answer:
T(-3,-2)
Step-by-step explanation:
R(x,y)
R(3,2)
P(6,0)
N(0,-4)
The net of a square pyramid and its dimensions are shown in the diagram. What is the total surface area of the pyramid in square meters?
Answer: the general formula for the total surface area of a regular pyramid isbT. S. A. =12pl+B where p represents the perimeter of the base
What speed would a plane average on a trip
of 4000 miles that took 6 hours?
(A) 150.0 miles per hour
(B) 666.6 miles per hour
(C) 366.6 miles per hour
(D) 1500.0 miles per hour
Answer:
B) 666.6 miles per hour
Step-by-step explanation:
To solve this question, divide the 4000 miles with the 6 hours to get an answer in units of X miles per hour.
4000 miles/6 hours = 666.6 miles per hour
Please answer the question below fully will mark brainliest
Answer:
que es eso
Step-by-step explanation:
fuhwiheirj lo siento
Please answer correctly!
answer:
16.24 or 12 square root of 18
The line L passes through the points (0,7) and (3,19). Work out the equation of the line L.
A) y = 4x +7
Or
B) y = 4x + 19
Can you help?
Answer:
A
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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 7 ) and (x₂, y₂ ) = (3, 19 )
m = [tex]\frac{19-7}{3-0}[/tex] = [tex]\frac{12}{3}[/tex] = 4
The line crosses the y- axis at (0, 7 ) ⇒ c = 7
y = 4x + 7 → A
What is -1/2 times 1/4-3/8?
Answer:
The answer is -0.5
Step-by-step explanation:
find the circumference of the pizza nearest to to the nearest whole number if the radius is 7 in
Answer:
69
Step-by-step explanation:
420+911÷360 no scope=69
Each day Gianna practices penalty kicks with her older brother as the goalie. Yesterday she made 18/24 of her penalty kicks. Today she plans on shooting 36 penalty kicks. How many penalty kicks would Gianna have to make to successfully shoot an equivalent fraction as yesterday?
Answer: 27
Step-by-step explanation:
Since we are informed that Gianna practices penalty kicks and that she made 18/24 of her penalty kicks yesterday, this will be converted to its simplest form which will be:
= 18/24 = 3/4 .
If she plans on shooting 36 penalty kicks, the number of penalty kicks that Gianna would have to make to successfully shoot an equivalent fraction as yesterday will be:
= 3/4 × 36
= 3 × 9
= 27 penalty kicks.
Henri puts aside $10 cash every month in a shoebox. He also makes a one-time deposit of $1,500 in a savings
account at 9% annual interest, compounded yearly,
Amount of shoebox savings: f(t) = 120t
Amount of savings account: g(t) = 1,500(1.09)^t
Which function represents the amount of money Henri will have after t years?
Answer:
T(t) = f(t) + g(t)
Step-by-step explanation:
The function which represents the total amount of money Henri will have in t years is the function obtained using an addition operation in the two defied functions, f(t) and g(t) ; total amount saved in shoe box plus the total compounded amount in savings account
Total amount of money in t years, T(t) ;
T(t) = 120t + 1,500(1.09)^t
f(t) = 120t
g(t) = 1,500(1.09)^t
Hence,
T(t) = f(t) + g(t)
if the mean of 12,16,22,X 28 is 19.6 find X
Answer:
20
Step-by-step explanation:
A data is given and the mean of data is 19.6 .The data is ,
12 , 16 , 22 , x , 28 .
We know that the mean is sum of observations divided by Total number of observations . So that ,
⇒ 12 + 16 + 22 + x + 28/ 5 = 19.6
⇒ 78+x/5 = 19.6
⇒ 19.6 × 5 = 78 + x
⇒ 78 + x = 98
⇒ x = 98 - 78
⇒ x = 20
Hence the value of x is 20 .