Is the triangle obtuse, acute, equilateral or right?
9514 1404 393
Answer:
obtuse
Step-by-step explanation:
The law of cosines tells you ...
b² = a² +c² -2ac·cos(B)
Substituting for a²+c² using the given equation, we have ...
b² = b²·cos(B)² -2ac·cos(B)
We can subtract b² to get a quadratic in standard form for cos(B).
b²·cos(B)² -2ac·cos(B) -b² = 0
Solving this using the quadratic formula gives ...
[tex]\cos(B)=\dfrac{-(-2ac)\pm\sqrt{(-2ac)^2-4(b^2)(-b^2)}}{2b^2}\\\\\cos(B)=\dfrac{ac}{b^2}\pm\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}[/tex]
The fraction ac/b² is always positive, so the term on the right (the square root) is always greater than 1. The value of cos(B) cannot be greater than 1, so the only viable value for cos(B) is ...
[tex]\cos(B)=\dfrac{ac}{b^2}-\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}[/tex]
The value of the radical is necessarily greater than ac/b², so cos(B) is necessarily negative. When cos(B) < 0, B > 90°. The triangle is obtuse.
Complete a b and c if you do one it would mean alot
Answer: I don't see what your talking about here, so I can't help you.
Step-by-step explanation:
A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space inside so they can also be used to store props.
How much space is inside the steps?
Give an exact answer (do not round).
Give correct answer and I will give you brainlist
Answer:
0.045 m^3
Step-by-step explanation:
0.2 m x 0.15 m x 0.5 m = 0.015 m^3
0.2 m x 0.3 m x 0.5 m = 0.03 m^3
0.045 m^3
Need Help Please with q2 & q4!!
Question 2: ARITHMETIC SEQUENCES AND SERIES
Tamara has decided to start saving for spending money for her first year of college. Her money is currently in a large suitcase under her bed, modeled by the function s(x) = 450. She is able to babysit to earn extra money and that function would be a(x) = 6(x − 2), where x is measured in hours. Explain to Tamara how she can create a function that combines the two and describe any simplification that can be done.
Question 4: GEOMETRIC SEQUENCES
Tommy has $350 of his graduation gift money saved at home, and the amount is modeled by the function h(x) = 350. He reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1.04)^x−1. Explain how Tommy can combine the two functions to model the total amount of money he will have in his bank account as interest accrues after he deposits his $350. Justify your reasoning.
Answer:
Question 2: The first function represents the amount of money she'll have from her 450 under her bed.
s(x) = 450
The second function represents the amount of money she'll earn from babysitting per hour (x):
a(x) = 6(x - 2)
To figure the combined amount, we can add the two functions:
f(x) = s(x) + a(x)
f(x) = 450 + 6(x - 2)
From there, she can simplify the function by distributing, then combining the like terms to simplify:
f(x) = 450 + 6x - 12
f(x) = 438 + 6x
Answer:
f(x) = 438 + 6x
Question 4: His functions are;
h(x)=$350
s(x)=(1.04)^x-1
To find total amount of money in Tommy's account using the functions above, we substitute the first equation x=$350 in the second function.
The blue shape is a dilation of the black shape. What is the scale factor of the dilation? Simplify your answer and write it as a fraction or whole number.
Answer:
3 or 3/1 (the 1 is the denominator)
Step-by-step explanation:
the shape got 3 times bigger. let me know
The sum of twice a number and 13 is 47. Find the number.
Answer: 17
Step-by-step explanation:
In this problem, the phrase "a number" can be interpreted as a variable. In this case, let the variable be "x."
Thus, "twice a number" = "2x"
"and 13" = "+ 13"
"is 47" = "= 47"
Thus, the problem is simply 2x + 13 = 47.
Then, simply subtract 13 from both sides to get 2x = 34.
Then, simply divide both sides by 2 to get x = 17.
Because "the number" is "x," the number is 17.
Hope it helps :) <3 and lmk if you need more help
17
Step-by-step explanation:
you represent the unknown by a variable
for example X
2x +13=47
You are writing a science research paper for your Chemistry class. You can type four pages per hour and you have already typed two pages. Write a function where t represents the number of hours and W(t) is the total pages written.
Answer: W(t) = 4t + 2
Step-by-step explanation:
y = ax + b
Because you have already typed two pages, the y-intercept(b) will be 2
The slope(a) is the number of pages typed per hour, which is 4.
So if you put it together:
W(t) = 4t + 2
(02.02 MC)
Tim mixed 2 parts vinegar and 5 parts water to make a cleaning liquid. How many parts of vinegar did Tim mix with each part of water?
one over ten
one over five
two over seven
two over five
Answer:
2/5 or two over five
Step-by-step explanation:
2:5
Divide each by 5
2/5 : 1
2/5 * 1
2/5
Answer: 2 over 7
Step-by-step explanation:
2/(2+5) = 2/7
Lorenzo’s test scores are shown below.
Lorenzo’s Test Scores
A dot plot titled Lorenzo's Test Scores. A number line going from 80 to 90. 0 dots are above 80, 81, and 82, there is 1 dot above 83, 2 above 84, 2 above 85, 2 above 86, 2 above 87, 0 above 88 and 89, and 1 above 90.
Anika’s test scores are shown below.
Anika’s Test Scores
A dot plot titled Anika's Test Scores. A number line going from 80 to 90. There are 0 dots above 80, 81, 82, and 83, 3 dots above 84, 2 above 85, 2 above 86, 3 above 87, and 0 dots above 88, 89, and 90.
Which statement compares the shape of the two dot plots?
There is a gap in both plots.
There is a gap in Anika’s scores, but not in Lorenzo’s scores.
The data is widely spread across both plots.
The data is more widely spread for Lorenzo’s scores than for Anika’s.
Answer:
The data is more widely spread for Lorenzo’s scores than for Anika’s.
Step-by-step explanation:
Answer:
The data is more widely spread for Lorenzo’s scores than for Anika’s.
Step-by-step explanation:
In other words "D" trust me
I need help please! Not sure on this one.
Answer:
The scale factor is 0.5
Step-by-step explanation:
Figure A is 4 blocks wide and 4 blocks tall, Figure B is 2 blocks tall and 2 blocks wide, to get Figure B from Figure A you would need to scale it down by half (0.5)
plz help me with the attcahment below
Step-by-step explanation:
...............MaRk As BrAiNeSt
Answer:
cos theta = BC/AC
Step-by-step explanation:
The cosine function is the ratio of the length of the adjacent side of one of the angles of a triangle to the length of the hypotenuse:
cos theta = BC/AC
Correct answers only!
After conducting a survey of all her classmates Midge discovers that the amount of money everyone spends buying books each month has a mean of $30. What does the mean say about the amount of classmates spend on books?
Half of her classmates spent exactly $30 per month buying books.
Half of your classmates spent more than $30 per month buying books.
The majority of her classmates spent $30 per month buying books.
If the amount spent on books per month by all her the classmates is leveled, the amount will be $30.
Answer:
C: The majority of her classmates spent $30 per month buying books.
Step-by-step explanation:
The mean is the average of the numbers -> its C
Answer:
C
Step-by-step explanation:
What is the format of this proof? Given: ∠ABC is a right angle, ∠DBC is a straight angle Prove: ∠ABD is a right angle
Answer:
Step-by-step explanation:
abd
lets evaluate (3^6)^1/2
step by step.
Answer:
27Step-by-step explanation:
[tex]\bigg(3^6\bigg)^{\frac{1}{2}}[/tex]
use
[tex](a^n)^m=a^{n\cdot m}[/tex]
[tex]\bigg(3^6\bigg)^{\frac{1}{2}}=3^{6\cdot\frac{1}{2}[/tex]
simplify
[tex]6\!\!\!\!\diagup^3\cdot\dfrac{1}{2\!\!\!\!\diagup_1}=3\cdot\dfrac{1}{1}=3\cdot1=3[/tex]
other
[tex]6\cdot\dfrac{1}{2}=\dfrac{6\cdot1}{2}=\dfrac{6}{2}=3[/tex]
therefore
[tex]\bigg(3^6\bigg)^{\frac{1}{2}}=3^{6\cdot\frac{1}{2}}=3^3=\underbrace{3\cdot3\cdot3}_{3}=27[/tex]
[tex]\displaystyle\bf \boldsymbol{\boxed{(a^n)^m=a^{n\cdot m}}} \\\\(3^6)^{\frac{1}{2}} =3^{\frac{6}{2} }=3^3=\boldsymbol{{\boxed {27}}}[/tex]
HELPPPPP PLEASE
(04.02 MC)
What is the solution to the following system of equations?
4x + 2y = 6
x - y = 3
(2, 1)
(-2, -1)
(2, 4)
(2, -1)
======================================================
Explanation:
Double everything in the second equation to go from x-y = 3 to 2x-2y = 6.
So we have this equivalent system of equations
[tex]\begin{cases}4x+2y = 6\\2x-2y=6\end{cases}[/tex]
We can then add straight down. The x terms add to 6x. The y terms go away because they add to 0. The stuff on the right hand sides add to 12.
After those three sets of addition operations, we have the new equation 6x = 12 which solves to x = 2 after dividing both sides by 6.
Now use x = 2 with any of the equations mentioned that have x,y involved so we can solve for y.
4x+2y = 6
4(2)+2y = 6
8+2y = 6
2y = 6-8
2y = -2
y = -2/2
y = -1
or we could say
x-y = 3
2-y = 3
-y = 3-2
-y = 1
y = -1
Either way, we get the same y value.
Since x = 2 and y = -1 pair up together, we get the ordered pair solution (x,y) = (2, -1). Therefore, the answer is choice D.
If you were to graph the two equations, as shown below, the two lines intersect at (2,-1). This point is on both lines at the same time. This is visual confirmation that the point is a solution to both equations. Though you should still algebraically check each original equation.
Evaluate the expression shown below and write your answer as a fraction in simplest form.
Answer:
9/40
Step-by-step explanation:
[tex]17/20 - 5/8\\[/tex]
-> [tex](34-25)/40[/tex]
-> [tex]9/40[/tex]
What is 27/40 as a decimal? Explain how you got your answer.
Tyrone has a fish tank that measures 36in. long, 24in. high, and 18 in. wide. He wants to fill the fish tank to a height of 14 inches. What will be the volume of water in the tank?
Answer:
Step-by-step explanation:
volume of water=l×w×h
l=length of tank=36 in
w=width of tank=18 in
h=height of water=14 in
volume=36×18×14
=9072 in³
Eva conducted a survey to find out the amount of time high schoolers spend surfing the Internet. From the data collected, the range of time spent was 3 hours. What does this range say about the data?
A. The quotient between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
B. The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
C. All the students surveyed spend exactly 3 hours surfing the Internet.
D. All the students surveyed spend an average of 3 hours surfing the Internet.
Answer
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
Explanation
The meaning of range is the difference between the largest and smallest numbers in a set.
In this case, it's possible that one of the students spends no time surfing the internet, and another student spends 3 hours. The range of the data would be 3. It's also possible that some students spend 20 hours surfing the internet, and other students spends 23 hours surfing the internet (although, that's obviously unreasonable).
Answer:
B. The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
Step-by-step explanation:
I'm going to leave this person anonymous, but they have deleted 2 of my answers and I'm sick of it, so please stop deleting my answers I'm not trying to violate brainly's rules in any way, shape, or form.
please help! :( ive been stuck on this for about 30 minutes
Suppose each cube in this right rectangular prism is a -inch unit cube.
What are the dimensions of the prism?
What is the volume of the prism?
Answer:
dimensions: 4x5x3
volume: 60 cube inches
Step-by-step explanation:
assuming each cube is a one inch cube:
the dimensions of the prism are length 5 -inches, width 4 -inches and height 3 -inches. So, 4x5x3
the volume of a prism is the length x width x height, so the volume is 4x5x3 = 60 inches cubed.
Answer:
length = 5 inches
width = 4 inches
height = 3 inches
So dimensions are 5 x 4 x 3 inches
Volume = l · w · h
V = 5 · 4 · 3 = 60 square inches.
Evaluate the expression shown below and write your answer as a fraction in simplest form.
Answer:
1/42
Step-by-step explanation:
4/7 - 23/42 = 24/42 - 23/42 = 1/42
Help please!! I need help on this question I’m stuck on it this is due like in 10 minutes lol
Answer:
I think the last one.
Step-by-step explanation:
Because whenever you have 5 purple shells you have 3 white shells. So 5p = 3w like how 10p = 6w.
Aryona’s ship is 43 miles west off the dock. Aleena’s yacht is 25 miles north from Aryona. How far is Aleena from the dock?
Answer:
79 miles :p
Step-by-step explanation:
43 + 25
Give correct answer and I will give you branlist
Hello!
Space = 5 cm + 10cm + 10cm + 20cm + 22cm + 30cm => space = 15cm + 10cm + 20cm + 22cm + 30cm => space = 25cm + 20cm + 22cm + 30cm => space = 45cm + 22cm + 30cm => space = 67cm + 30cm => space = 97cm²
Good luck! :)
Answer:
97cm square
Step-by-step explanation:
PLZ HELP 10 POINTS
The slope of a line through the points (-2, 4) and (6, b) is –3/2 . What is the value of b? Explain your method for
calculating b.
Answer:
b = -2
Step-by-step explanation:
Plz help, asap!!
This is a triangular prism
perimeter of the base is:
Height is:
Base area is:
Volume is:
Surface area is:
Answer:
Perimeter of base: 50 cm
Height: 30 cm
Base area: 60 cm
Volume: 21,600 cm
Surface area: I am sorry I forget how to do surface area, but I hope everything else helps.
Step-by-step explanation:
perimeter of base: 50 cm
13+13=26+24=50
Height: 30 cm
already shows height.
Base area: 60 cm
1) 24/2=12 2) 5*12=60
Volume: 21,600 cm
Length*Base*height/2=24*60*30=43,200/2=21,600
surface area:
Sorry I forget how to do surface area.
Answer:
Perimeter of base: 50 cm
Height: 30 cm
Base area: 60 cm
Volume: 21,600 cm
Surface area: I am sorry I forget how to do surface area, but I hope everything else helps.
Step-by-step explanation:
perimeter of base: 50 cm
13+13=26+24=50
Height: 30 cm
already shows height.
Base area: 60 cm
1) 24/2=12 2) 5*12=60
Volume: 21,600 cm
Length*Base*height/2=24*60*30=43,200/2=21,600
Can I have help on the second question only, Thx
Answer:
is this geo?
Step-by-step explanation:
Answer:
measure a = 56
Step-by-step explanation:
Remember all angles on triangles equal up to 180, and it look that measure c is the same as measure b.
62+62=124
180-124=56
Therefore measure a is equal to 56, but I may be wrong, no one is perfect, but I hope this helps!
HELP ASAP I WILL MARK BRAINLIEST AND GIVE POINTS!!!!!! (FAKE ANSWERS REPORTED)
The following figures are not drawn to scale but AB and CD if present) are straight lines. Find x:
Answer:
x=60
Step-by-step explanation:
y=x
90-30=y
60=y
x=60
Evaluate 4 - x, when x = -6
Answer:
10
Step-by-step explanation:
4--6
4+6=10
I need help with this question. Question in image.
Show working out to answer
Answer:
Step-by-step explanation:
38
