Answer:
[tex] = { \tt{50 - 2(32 + 1)}}[/tex]
Solve the bracket:
[tex] = { \tt{50 - 2(33)}}[/tex]
Open the bracket:
[tex]{ \tt{ = 50 - 66}}[/tex]
Subtract the expression:
[tex]{ \bf{ = - 16}}[/tex]
Step-by-step explanation:
Multiply 2 by 32 and 1
50-64-2
-14-2
-16 Answer
Evaluate without a calculator:
CSC -120°
Answer:
- [tex]\frac{2\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Using the identity and the exact value
csc x = [tex]\frac{1}{sinx}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
- 120° is in the third quadrant where sin < 0 , then
csc - 120° = - sin60° , then
csc - 120°
= [tex]\frac{1}{-sin60}[/tex]
= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]
= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )
= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= - [tex]\frac{2\sqrt{3} }{3}[/tex]
The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
We know that the cosecant function is defined as the reciprocal of the sine function:
cosec (θ) = 1 / sin(θ)
Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).
We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,
sin(-120°) = -sin(120°)
We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).
Using the same logic as before, we get:
sin(-240°) = -sin(240°)
Now , from the trigonometric relations , we get
Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:
sin(-240°) = -sin(-120°)
Therefore, we have:
sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)
Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:
In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.
Therefore, sin(240°) = O/H = (√3)/2.
Finally, we can use the definition of the cosecant function to find cosec(-120°):
cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.
Hence , cosec(-120°) is equal to (2√3)/3.
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Help me please. Thanks.
Step-by-step explanation:
for your 1008 question:
1008/2
504/2
252/2
126/2
63/3
21/3
7/7
1
1008 = 2x2x2x2x3x3x7
1008 = (2^2)×(2^2)x(3^2)×7, so 7 would be the answer because of this
lmk if you need me to elaborate on anything
Calculate the sum of the integers from 52 to 108
Answer:
4560
Step-by-step explanation:
The combined mass of two children is 75lbs. The first child is four times the mass of the second child. What are the masses of the two children?
A farmer wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $4 a yard, but the farmer needs to use special fencing which cost $5 a yard on the south side of a plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing.
Hello,
Let's assume x the length of the north's wall
and y the length of west side .
Area:x*y=600 ==> y=600/x
Cost: 2*y*4+5*x=8y+5x= 4800/x+5x
Minimize cost: (4800/x+5x)'=0
-4800/x²+5=0
x²=4800/5
x²=960
[tex]x=8\sqrt{15} \\\\y=5\sqrt{15} \\[/tex]
options: (50)^1/2, (65)^1/2, (105)^1/2, (145)^1/2
last sentence options: 55.21, 85.16, 105.26, 114.11
Answer:
Step-by-step explanation:
Vertices of ΔABC are,
A(-3, 6), B(2, 1) and C(9, 5)
Use the formula to get the distance between two points [tex](x_1,y_1)[/tex] and[tex](x_2,y_2)[/tex],
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
By using the formula,
AB = [tex]\sqrt{(1-6)^2+(2+3)^2}[/tex]
= [tex]\sqrt{50}[/tex] units
BC = [tex]\sqrt{(5-1)^2+(9-2)^2}[/tex]
= [tex]\sqrt{65}[/tex] units
AC = [tex]\sqrt{(6-5)^2+(-3-9)^2}[/tex]
= [tex]\sqrt{145}[/tex]
Use cosine rule to find the measure of ∠ABC.
AC² = AB² + BC²- 2(AB)(BC)cos(B)
[tex](\sqrt{145})^2=(\sqrt{50})^2+(\sqrt{65})^2-2(\sqrt{50})(\sqrt{65})\text{cosB}[/tex]
145 = 50 + 65 - 2(√3250)cosB
cos(B) = [tex]-(\frac{145-115}{2\sqrt{3250}})[/tex]
= -0.26312
B = [tex]\text{cos}^{-1}(-0.26312)[/tex]
B = 105.26°
a rectangle consists of two identical squares with a common side. The perimeter of the rectangle is 27 inches. Find its area
Answer:
40.5 square inches
Step-by-step explanation:
Rectangle consists of two identical squares.
So, if the sides of square = x,
Then, Width of rectangle = x &
Length of rectangle = x +x = 2x
Perimeter of rectangle = 27 inches
2*(length + width) = 27
2*( 2x + x) = 27 {Combine like terms]
2* 3x = 27
6x= 27 {Divide both sides by 6}
x = 27/6
x = 4.5
Width = x = 4.5 inches
Length = 2x = 2*4.5 = 9 inches
Area of rectangle = length *width
= 4.5 *9
= 40.5 square inches
Answer:
40.5
Step-by-step explanation:
Express 28 as the sum of three prime numbers
a) 3, 11 and 13
b) 5, 11 and 13
c) 2, 7 and 19
d) 2, 5 and 13
Answer:
a
Step-by-step explanation:
because is a ok yo12222122221112w
Answer:
Option C is correct
Step-by-step explanation:
[tex]3 + 11 + 13 = 27[/tex]
[tex]5 + 11 + 13 = 29[/tex]
[tex]2 + 7 + 19 = 28[/tex]
[tex] 2 + 5 + 13 = 20[/tex]
Hope it is helpful....A company makes steel rod shaped like cylinders. Each rod has a radius of 4 cm and a height of 30 cm. How much steel will the company need to make 113 rods
Answer:
Bob and Charlotte are raising their grandchildren after their daughter dies.The children are moved from California to a farm in Nebraska. The three children are struggling with school, life on a farm and their mother’s death. Sam is having trouble working with his son and new ideas for the farm. Charlotte doesn’t want to make the same mistakes she made with her own children.Their faith and help from friends help. The one thing that stood out was how overworked Charlotte is with no help or time to herself.
What is the answer of this question?
Answer:
2 ( Option A )
Step-by-step explanation:
The given integral to us is ,
[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]
Here 5 is a constant so it can come out . So that,
[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]
Now we can write √x as ,
[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]
Simplify ,
[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]
By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,
[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]
On simplifying we will get ,
[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]
Where do i move the graph (new points)?
Answer:
l
Step-by-step explanation:
15
Which is bigger?
15/20 or 74%
Directions: Graph each equation by using the y-intercept and slope( make sure too show your work)
FIRST QUESTION: y= -2/3x-1
y-intercept=____
Slope:____
Given:
The equation of a linear function is:
[tex]y=-\dfrac{2}{3}x-1[/tex]
To find:
The y-intercept and slope of the given equation, then draw the graph of the equation.
Solution:
Slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept
We have,
[tex]y=-\dfrac{2}{3}x-1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=-\dfrac{2}{3}[/tex]
[tex]b=-1[/tex]
Therefore, the y-intercept is -1 and the slope of the line is [tex]-\dfrac{2}{3}[/tex].
It means the graph intersect the y-axis at point (0,-1) and having slope [tex]-\dfrac{2}{3}[/tex]. So, the graph of the equation is shown below.
If f(x) = x+1 and g(x) =x^2, then gf(2) =
Answer:
g(f(2)) = 9
Step-by-step explanation:
Evaluate f(2) and substitute the value obtained into g(x)
f(2) = 2 + 1 = 3 , then
g(3) = 3² = 9
Answer:
9
Step-by-step explanation:
f(x)=x+1........(i)
g(x)= x^2......( ii ).
gf(2)........(III)
substitute f( 2) to ......(I)
f(2)=2+1
f(2)=3
gx=gf(2)
gf(2)= 3^2
=9
find the greatest number such that x360y is divisible by 24
Answer:
93600
Step-by-step explanation:
The divisibility rule of 24 is that the number has to be divisible by both 3 and 8. So we need to plug in numbers for x and y to find the greatest number. 93600 should be the answer.
Find the value of y...
Answer:
y=0
Step-by-step explanation:
Rewrite Evaluate Powers:
3[tex]3^{2y-1}+3^{-1}+2*3^{y}*3^{-1}=1[/tex]
Calculate:
[tex](3^{y})^{2}*\frac{1}{3} +2*3^{y}*\frac{1}{3}=1[/tex]
Solve using substitution:
[tex](3^{y})^{2}*\frac{1}{3} +\frac{2}{3} *3^{y}=1[/tex] [tex]t=3^{y}[/tex]
Solve the equation for t:
[tex]t^{2}*\frac{1}{3}+\frac{2}{3}t=1[/tex]
t=-3
t=1
Substitute back to t=3^y
3^y=-3
3^y=1
y∉R
[tex]3^{y}=1[/tex]
y=0
On Monday, a localamburger shop said a combined total of 225 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number
of hamburgers sold. How many hamburgers were sold on Monday?
hamburgers
х
?
Answer:
h = hamburgers sold
2h - 72 = 578
2h = 650
2 2
h = 325
There were 72 fewer cheeseburgers sold than hamburgers. That means cheeseburgers = 325 - 72
325 - 72 = 253
253 = cheeseburgers
325 = hamburgers
253 + 325 = 578
Hamburgers = 325
Hope this helps :)
What values of x make this true?
(x^2–3x+2)/(x –1) = x – 2
Answer:
Any value of x makes the equation true. All real numbers Interval Notation: ( − ∞ , ∞ )
Hope This Helps!!!
100 students are interviewed to see which of biology, chemistry or physics they prefer. 42 of the students are girls. 5 of the girls like biology best. 4 of the boys prefer physics. 13 out of the 21 who prefer chemistry are girls. What percentage of the students prefer biology?
Answer:
A total of 51 people prefer biology, 51%
Step-by-step explanation:
Girls: 42
Boys: 58
Biology: 5 girls and 46 boys(100-42=58, 58-[4+8]=46)
Physics: 4 boys and 24 girls(42-[5+13])
Chemistry: 13 girls and 8 boys(21-13=8)
I think this is the answer...
Someone help me please !!!!!
Answer:
a=15 and x=7
Step-by-step explanation:
first we need to plug in the number to the variable than we try to get a and x by themselves.
Someone tell me where everyone is going right please !!
Answer:
Step-by-step explanation:
( 2 , 3 ) , ( 6 , - 5) , ( - 1 , 3 ) - is a function
( 1 , 9 ) , ( -3 , - 2 ) , ( 1 , - 4 ) - is a function
( 7 , - 4 ) , ( 0 , 9 ) , ( 2 , - 2 ) - is a function
( 0 , 3 ) , ( 0 , 7 ) , ( 4 , 0 ) - is a function
( -6 , 5 ) , ( -5 , 6 ) , ( 8 , 2 ) - is a function
A school received 12 boxes of notebooks. Each box had 36 notebooks. How many total notebooks did the school receive?
Answer:
12x36
Step-by-step explanation:
Answer:
36*12 = 432
Step-by-step explanation:
4 + {−5 + [−3 + 4 + 2(−7 + 4) + 4] + 2}
7 + {−2 + [5 + 4(−3) + (−6 + 2) + (−3)]}
(−2) + {3 + [−4 + (3)] + 7} + (−5)
(−10) + {−7 + [−4 + 5(−9) + 5] + 8}
18 + 3{−4 + [−15 + 20 + (−3)] + (−9)}
−(−8 + 5) + {−4 + [−7 + (−9 − 5) + 3]}
− 9 + {−7 − 2[−(4 + 1) + (5 − 9)]} − 3
−1 − 3{6 − [4 + 2(−7 + 8) − 5] − 2}
−(−2) − {−(−7) + [−3 + (−5 − 2) + 6]}
−(−6 − 2) − 2{−4(−5) + 5[−3 + (−2)]}
6 − 2{−4 + 3[3 − 3(−8 − 5) + 14] − 7}
Me pueden ayudar por favor es urgente!!! y Buenas Noches ;)
Answer
it is 5 : )
Step-by-step explanation:
What is the Measure of arc XY?
Answer:
Arc XY = 180- 43
= 137º
answer is C
Step-by-step explanation:
which is grater 0,7_ _ or -6.7
Answer:
There is no way to know to know because we don't have a way to see where 0,7 is on the graph
The amount of time needed to complete a job, t, varies inversely with the number of workers, w. If
9 workers can complete a job in 56 minutes, how many minutes would it take 14 workers?
Do not include the units in your answer.
Answer:
38
Step-by-step explanation:
If 9 workers can complete a job in 56 minutes, then it takes 36 minutes for 14 workers.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that amount of time needed to complete a job, t, varies inversely with the number of workers, w.
t=k/w
k is a constant
9 workers can complete a job in 56 minutes
t=56 and w=9
56=k/9
Apply cross multiplication
k=9×56
k=504
We need to find how many minutes would it take for 14 workers.
t=504/14
t=36
Hence, it takes 36 minutes for 14 workers.
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can someone help me w/ this question plz?
Answer:
16 birds
8 mammals if you need to know.
Step-by-step explanation:
We can set this system of equations up by plugging the 2m from the second equation into where it says r in the first equation. The reason why we do this is because
The 2m is equal to r, so we can replace the r in the first equation with 2m, since they are equal.
Divide both
We can confirm this because
uh
(I like the enter key lol.)
It's the return key on some keyboards in other countries.
Oh yeah.
We can confirm the values.
If there are 16 birds, there is probably going to be a total of 32 legs.
With 8 mammals, it is something like 8 x 4, which is 32
32 + 32 = 64, which is the total.
estimate the answer 210,000 divied by 0.12
ANSWER:-
[tex] 210,000 \: divied \: by \: 0.12 \\ - - > \frac{210000}{0.12} \\ - - > \frac{210000 \times 100}{12} \\ - - > 1,750,000[/tex]
Answer:
1750000
Step-by-step explanation:
when dividing a non decimal number by a decimal number you have to first multiply both the numbers by the number of decimal places of the numbers that has has a decimal,In this case will multiply both numbers by 100 because there are decimal places on 0.12, giving us
21000000/12
=1750000
a. 12.3
b. 8.1
c. 0.1
Answer:
a
Step-by-step explanation:
tan(39⁰)= opposite ÷ adjacent
0.8097= 10 ÷ x
X = 10 ÷ 0.8097
X = 12.3
Lines L and M are parallel.
Answer:
52°
Step-by-step explanation:
The angle 38° and m∠1 equal 90°, so 90-38=52.
Answer:
thats is an obtuse so if 2 is 38 then 1 should be 120 but u add those together u get 158 so it shold be 120 but if not then try looking explamles up
Step-by-step explanation: