Answer:
6.55 cm
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, acute, scalene, obtuse, right and equilateral triangle.
Cosine rule is used to show the relationship between sides and angles of a triangle. If a, b, and c are sides of a triangle, while A, B, and C are angles opposite to the corresponding sides. Then:
c² = a² + b² - 2ab*cos(C)
Given that PR = 13 cm, PQ = 12 cm and angle QPR = 30°, hence:
QR² = PR² + PQ² - 2(PR)(PQ)cos(∠QPR)
QR² = 13² + 12² - 2(13)(12)cos(30) = 169 + 144 - 270
QR² = 43
QR = 6.55 cm
PLEASE HELP ASAP!!!!
Jackson is testing different types of planting soil to determine which type is most effective for growing strawberry bushes. He purchases two different brands of planting soil from a local store. Jackson applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial sunlight. He waters the area with brand B daily; he waters the area with brand A every other day. At the end of the study, Jackson concludes brand A is more effective in growing strawberry bushes. Is Jackson's conclusion valid? Explain why or why not.
Answer:
It is not valid since there is more than one variable being changed at one.
Step-by-step explanation:
Jackson changed the brand of soil, but he also changes the amount of water, and the amount of sunlight the plants are receiving, so his conclusion that the soil was more effective is not valid.
Answer:
No, Jackson did not take into account alternate theories.
Jackson's findings could have been influenced by the watering schedule and the amount of sunlight. Without adjusting for these variables, the experiment is inconclusive.
The rate of change is
==============================================================
Explanation:
Pick any two rows from the table to plug into the slope formula.
I'll pick the rows where every value is positive (rows 3 and 4)
Using the slope formula, we get the following:
m = (y2-y1)/(x2-x1)
m = (1-5)/(2-1)
m = -4/1
m = -4 is the slope and it's the rate of change
For any linear function, the slope and rate of change are the same thing.
Put these numbers in order from least to greatest.
0.36,7/10, and 0.44
Answer:
0.36,0.44,7/10
Step-by-step explanation:
Answer:
0.36, 0.44, 7/10
Step-by-step explanation:
7/10=0.7=0.70
f(x) = 6r + 2
g(x) = - 5x - 9
Find the product of F and G.
find the equation to the line below *pls help asap* brainliest too the first answer and 30 points
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
If you just plug in the answers, so lets take (1,6) and plug it into y = 6x
You could just solve it so it'd be like
6 = 6(1) and
12 = 6(2)
A rectangular cube of volume 8000cm3 has
length= 4x
width = 2x
Height= 1x
Find it's length, width and height.
Answer:
volumn= l*b*h
4x*2x*1x= 8000 cm3
8x= 8000 cm3
x= 1000cm3
length = 4000
breadth= 2000
height = 1000
Jay has a car worth $36,001. It is depreciating at a rate of 16% per year. How much will
it be worth in 3 years?
Answer:
$18,720.5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Depreciation Formula: A = P(1 - rt)
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 36001
r = 16% = 0.16
t = 3
Step 2: Find Cost
Substitute in variables [Depreciation Formula]: A = 36001(1 - 0.16 · 3)(Parenthesis) Multiply: A = 36001(1 - 0.48)(Parenthesis) Subtract: A = 36001(0.52)Multiply: A = 18720.5PLEASE HELP FAST WILL MARK BRAINLIEST!!!!!!!!
9.
Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green,
four pleces are yellow, two pieces are purple, and three pieces are red. She draws one
piece of candy from the bag at a time and eats it.
a What is the probability that Chelsey will draw out three pieces of candy in this
order: red, green, yellow? (3 points)
b.
What is the probability that Chelsey will draw out three pieces of candy in this
order: green, yellow, red? (3 points)
c.
What is the probability that Chelsey will draw out three pieces of candy in this
order: yellow, red, green? (3 points)
d.
Make a conclusion about how the order in which she draws out the red, green,
and yellow pieces affects the probability. (3 points)
Answer:
The chances of her pulling the candy out in that exact order for all of them is extremley low
Step-by-step explanation:
I cannot figure out D though sorry
Answer:
Your welcome
Step-by-step explanation:
please find the result !
Answer:
[tex] \displaystyle - \frac{1}{2} [/tex]
Step-by-step explanation:
we would like to compute the following limit:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{1}{ \ln(x + \sqrt{ {x}^{2} + 1} ) } - \frac{1}{ \ln(x + 1) } \right) [/tex]
if we substitute 0 directly we would end up with:
[tex] \displaystyle\frac{1}{0} - \frac{1}{0} [/tex]
which is an indeterminate form! therefore we need an alternate way to compute the limit to do so simplify the expression and that yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \ln(x + 1) - \ln(x + \sqrt{ {x}^{2} + 1 } }{ \ln(x + \sqrt{ {x}^{2} + 1} ) \ln(x + 1) } \right) [/tex]
now notice that after simplifying we ended up with a rational expression in that case to compute the limit we can consider using L'hopital rule which states that
[tex] \rm \displaystyle \lim _{x \to c} \left( \frac{f(x)}{g(x)} \right) = \lim _{x \to c} \left( \frac{f'(x)}{g'(x)} \right) [/tex]
thus apply L'hopital rule which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \dfrac{d}{dx} \ln(x + 1) - \ln(x + \sqrt{ {x}^{2} + 1 } }{ \dfrac{d}{dx} \ln(x + \sqrt{ {x}^{2} + 1} ) \ln(x + 1) } \right) [/tex]
use difference and Product derivation rule to differentiate the numerator and the denominator respectively which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \frac{1}{x + 1} - \frac{1}{ \sqrt{x + 1} } }{ \frac{ \ln(x + 1)}{ \sqrt{ {x}^{2} + 1 } } + \frac{ \ln(x + \sqrt{x ^{2} + 1 } }{x + 1} } \right) [/tex]
simplify which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \sqrt{ {x}^{2} + 1 } - x - 1 }{ (x + 1)\ln(x + 1 ) + \sqrt{ {x}^{2} + 1} \ln( x + \sqrt{ {x }^{2} + 1} ) } \right) [/tex]
unfortunately! it's still an indeterminate form if we substitute 0 for x therefore apply L'hopital rule once again which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \dfrac{d}{dx} \sqrt{ {x}^{2} + 1 } - x - 1 }{ \dfrac{d}{dx} (x + 1)\ln(x + 1 ) + \sqrt{ {x}^{2} + 1} \ln( x + \sqrt{ {x }^{2} + 1} ) } \right) [/tex]
use difference and sum derivation rule to differentiate the numerator and the denominator respectively and that is yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \frac{x}{ \sqrt{ {x}^{2} + 1 } } - 1}{ \ln(x + 1) + 2 + \frac{x \ln(x + \sqrt{ {x}^{2} + 1 } ) }{ \sqrt{ {x}^{2} + 1 } } } \right) [/tex]
thank god! now it's not an indeterminate form if we substitute 0 for x thus do so which yields:
[tex] \displaystyle \frac{ \frac{0}{ \sqrt{ {0}^{2} + 1 } } - 1}{ \ln(0 + 1) + 2 + \frac{0 \ln(0 + \sqrt{ {0}^{2} + 1 } ) }{ \sqrt{ {0}^{2} + 1 } } } [/tex]
simplify which yields:
[tex] \displaystyle - \frac{1}{2} [/tex]
finally, we are done!
9514 1404 393
Answer:
-1/2
Step-by-step explanation:
Evaluating the expression directly at x=0 gives ...
[tex]\dfrac{1}{\ln(\sqrt{1})}-\dfrac{1}{\ln(1)}=\dfrac{1}{0}-\dfrac{1}{0}\qquad\text{an indeterminate form}[/tex]
Using the linear approximations of the log and root functions, we can put this in a form that can be evaluated at x=0.
The approximations of interest are ...
[tex]\ln(x+1)\approx x\quad\text{for x near 0}\\\\\sqrt{x+1}\approx \dfrac{x}{2}+1\quad\text{for x near 0}[/tex]
__
Then as x nears zero, the limit we seek is reasonably approximated by the limit ...
[tex]\displaystyle\lim_{x\to0}\left(\dfrac{1}{x+\dfrac{x^2}{2}}-\dfrac{1}{x}\right)=\lim_{x\to0}\left(\dfrac{x-(x+\dfrac{x^2}{2})}{x(x+\dfrac{x^2}{2})}\right)\\\\=\lim_{x\to0}\dfrac{-\dfrac{x^2}{2}}{x^2(1+\dfrac{x}{2})}=\lim_{x\to0}\dfrac{-1}{2+x}=\boxed{-\dfrac{1}{2}}[/tex]
_____
I find a graphing calculator can often give a good clue as to the limit of a function.
Parallel Lines
PLEASE HELP I NEED ASAP!
Answer:
B
Step-by-step explanation:
The triangles do have equal angles and proportional sides, because they are bot right triangles formed on parallel lines.
:)ur welcome
Answer: Choice B
Yes. Right triangles formed on parallel lines have proportional side lengths and congruent angles.
====================================================
Explanation:
Parallel lines always have equal slopes, but different y intercepts.
Recall that slope = rise/run.
The "rise" is the vertical portion of the triangle, while the "run" is the horizontal portion.
So let's say we had a slope of rise/run = 2/3. This means rise = 2 and run = 3.
If we had something like rise/run = 4/6, then that reduces to 2/3, showing that 4/6 = 2/3. They are the same slope.
We can use the SAS similarity theorem to prove the triangles formed in the diagram are congruent based on what is discussed above.
Because the triangles are similar, this means the corresponding angles are congruent. One such pair is the pair of right angles shown.
please hurry i want the answer of this question please
B
Please mark me as a brainlist
Answer:
900
Step-by-step explanation:
3²×5 = 45
3×2²×5² = 300
LCM = 900
Hope this helps... pls vote as brainliest
What is the perimeter of the shape?
4 cm
3 cm
3 cm
4 cm
Answer:
14cm
Step-by-step explanation:
The shape is a rectangle.
The formula for perimeter of a rectangle= 2(lenght + breadth)
lenght = 4cm
width = 3cm
2(4+3)
2 × 7
= 14cm
Which angles are supplementary? You can just give 1 example so I get the idea
Answer
supplementary angles sum to 180
1 & 2
1 & 4
1 & 8
1 & 6
2 & 3
2 & 7
2 & 5
3 & 4
3 & 8
3 & 6
4 & 5
4 & 7
5 & 6
5 & 8
6 & 7
8 & 7
PLEASE HELP WITH THIS GEOMETRY PROJECT IM GIVING ALL MY POINTS (45)
Answer:
YEAH!!!!!! ITS 45
Step-by-step explanation:
MHM!
Answer:
woooooooooooooooohoooooooooo points go brrrrrr
Step-by-step explanation:
!!
find the value of a²+b
if...
a=-2 and b=5
Answer:
9
Step-by-step explanation:
a^2 +b
Let a = -2 and b = 5
(-2)^2 +5
Exponents first
4 +5
Then add
9
Answer:
9
Step-by-step explanation:
Here, we have to observe that a^2 = a×a =-2 × -2 = 4
hence, a^2 + b = 4 + 5 = 9.
What would x be in the image above?
Answer:
x= -7
Step-by-step explanation:
the labeled angles are alternate-interior angles which are congruent
we can solve for 'x' by creating this equation:
x+139 = 132
x = -7
help asap ------------------------------
Answer:
(0,-41)
Step-by-step explanation:
Let see if this table of values are proportional.
All x values decrease by -9.All y values decrease by -19.This mean that the function is proportional. This also gives us the slope which is 19/9.
This tell us that this function will be a linear function since we are trying to find the y intercept we would use this equation
We know the slope and we know a point so let use point slope form to find the intercept.
[tex]y - y _1= m(x - x _1)[/tex]
Let use points (-18,-79) and let m =19/9.
[tex]y + 79 = \frac{19}{9} (x + 18)[/tex]
[tex]y + 79 = \frac{19}{9} x + 38[/tex]
[tex]y = \frac{19}{9} x - 41[/tex]
This is in slope intercept form so the y intercept is
[tex] - 41[/tex]
The answer is -41.
which one is the smallest 4/5 1/6 2/3 1/5
Answer:1/6
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{4}{5}=\boxed{\bf 0.80\ or\ 80\%}}\\\\\\\mathsf{\dfrac{1}{6}=\boxed{\bf 0.166667\ or\ 16.6667\% }}\\\\\\\mathsf{\dfrac{2}{3}=\boxed{\bf 0.666667\ or \ 66.6667\%}}\\\\\\\mathsf{\dfrac{1}{5}=\boxed{\bf 0.20\ or \ 20\%}}[/tex]
[tex]\large\textsf{After converting the fractions to decimals and percentages, we can}\\\large\textsf{now out them from descending (least) to ascending (greatest) order}\\\large\textsf{to determine your result to this question}[/tex]
[tex]\boxed{\mathsf{\dfrac{1}{6}, \ \dfrac{1}{5}, \ \dfrac{2}{3}, \& \ \dfrac{4}{5}}}[/tex]
[tex]\large\textsf{The SMALLEST one out of your set is: }\boxed{\mathsf{\bf \dfrac{1}{6}}}\large\checkmark[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{1}{6}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
angad was thinking of a number. angad halves the number and gets an answer of 78.5. form an equation with x from the information
Answer:
157
Step-by-step explanation:
Let the number Angad was thinking be 'x'
Equation:-
1/2(x) = 78.5
x = 78.5(2)
x = 157
find the value of x in the given right triangle 90 20. please help!
Answer:
X = 3.6
Step-by-step explanation:
tan x = O/A
tan 20° = x/10
x = tan 20°(10)
x = 3.6
Answer:
x = 3.6 cm
Step-by-step explanation:
Using trigonometric ratios :
[tex]sin \theta = \frac{ opposite} {hypotenuse} \\\\cos \theta = \frac{adjacent }{hypotenuse}\\\\tan \theta = \frac{opposite}{adjacent}\\\\[/tex]
[tex]where \ \theta = 20, \ opposite = x \ , hypotenuse = y \ , \ adjacent = 10cm[/tex]
[tex]we \ will \ take \ tan \ 20 , \ because\ we \ have \ to \ find \ opposite \ and \ adjacent \ is\ given.\\\\tan 20 = \frac{x}{10}\\\\x = 10 \times tan 20\\\\x = 10 \times 0.36397\\\\x = 3.6397\\\\x = 3.6 \ cm[/tex]
Bruce Wayne trabaja en un proyecto inmobiliario, éste consiste en un edificio con forma de prisma de base triangular, cuya planta baja se caracteriza por tener una piscina, un gimnasio y una cancha deportiva. Batman tiene este bosquejo de dicho proyecto: Los terrenos destinados para la piscina, el gimnasio y la cancha deportiva son cuadrados, de modo que la superficie de la cancha es de 2.500 m2 y la de la piscina es de 1.600 m2 . ¿Cuál es la superficie destinada al gimnasio?
Answer:
El área del gimnasio sería 2000 metros cuadrados
Step-by-step explanation:
Un lado del gimnasio será igual al lado de la cancha y el otro lado será igual al lado de la piscina.
Dado que tanto la cancha como la piscina tienen forma cuadrada. El lado de la cancha será raíz cuadrada de 2.500 m2 y el de la piscina será raíz cuadrada de 1.600 m2
Por lo tanto, el lado del gimnasio sería 50 y 40.
El área del gimnasio sería 50 * 40 = 2000 metros cuadrados
Which expression is equivalent to ( x^1/4 y^16 )^1/2 ?
Sonya wants to sew ribbon along each side of a square pillow if the pillow has an area of 144 square inches, how much ribbon must she buy to have the exact amount that she needs
Answer:
48 inches
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
144 = s^2
Taking the square root of each side
sqrt(144) = sqrt(s^2)
12 = s
The side length is 12
We want to find the perimeter to determine the amount of ribbon
P =4s
P =4*12
48 inches
Which operation properly transforms matrix I to matrix II?
11
1
2
1
1
5
1
2
1
5
5
5
0
1 2
→ 0 1
2
5
2 7
825
0 36
15
Answer:
D
Step-by-step explanation:
Replace R1 with 1 and R3 with 0 you have -2(1)+0 which equals 0 and that matches matrix II. Repeat the process with the other numbers in R1 and R3 and they all come out equal therefor the answer is D.
ForEASY BRAINLIEST!!!
Answer:
A.
B.
C.
Answer:
A. x-3
B. x-14
C. x-10
Step-by-step explanation:
Answer: THXS FOR MAKIN THIS SO FRIKIN EASY. I think I may done b or c wrong-
Step-by-step explanation:
a) x - 3
b) x - 14
c) x − 10
х
If
5.3
=
12, what is the value of x?
8
0 ООО
18
o 24
Answer:18
Step-by-step explanation:
What is Which expression is equivalent to (8 a minus 3 b + 7) minus (2 a + b minus 4)?
6 a minus 2 b + 11
6 a minus 4 b + 3
6 a minus 2 b + 3
6 a minus 4 b + 11
PLZ PLZ PLZ HELP
Answer:
6 a minus 4 b + 11
Step-by-step explanation:
(8a -3b +7) - (2a + b -4)
= 8a -3b +7 -2a-b +4
= 6a -4b + 11
The weight of three articles is 856 kg. If two of the articles weigh 502kg, what is 1/2 the weight of the third article?
Answer:
177 kg
Step-by-step explanation:
Find the weight of the third article by finding the difference between 502 and 856, since 856 kg is the total weight and 502 kg is the weight of the other 2 articles:
856 - 502
= 354
Now, find 1/2 of the weight, by dividing this by 2:
354/2
= 177
So, 1/2 the weight of the third article is 177 kg
Which statements accurately describe the function f(x) = 3 (squareroot 18) ^x ? Select three options. A. The domain is all real numbers. B. The range is y > 3. C. The initial value is 3. D. The initial value is 9. D. The simplified base is 3 square root 2
Answer:
The domain is all real number
PLEASE HELP WILL MARK BRAINLIEST
Answer:
The second choice is correct
Step-by-step explanation:
Go to a point like 4,3 and 0,1. the difference in x is 4 since 4-0 = 4.
4,3 and 0,1 now we find the change in y, 3-1 which is 2. the formula for slope is change in y over change in x so 2/4 is the slope or 1/2.
The y intercept of the line is 1 since the line touches the y-axis at the y, 1.
therefore the equation is y = 1/2x + 1.