[tex]\\ \qquad\quad\sf\longmapsto m=8+n[/tex]
Take n to left[tex]\\ \qquad\quad\sf\longmapsto m-n=8[/tex]
Henceif m=1
[tex]\\ \qquad\quad\sf\longmapsto n=m-8=1-8=-7[/tex]
if n=1
[tex]\\ \qquad\quad\sf\longmapsto m=8+1[/tex]
[tex]\\ \qquad\quad\sf\longmapsto m=9[/tex]
Calculate the volume and surface area of a cone with the base of 20cm, the vertical hieght of 34cm and 35.6cm leaning height.
Answer:
Step-by-step explanation:
Volume = 1/3πr²h
Surface Area = πr(r+√(h²+r²))
V = 1/3π(10)²(34) = 3560 .5 cm³
SA = π(10)(10 + √(34²+10²)) = 1427.5 cm²
sinx =căn 2/3
sinx=5/4
sinx =1
sin3x=can3/2
sin(x-60)=-1/2
sin3x=1/2
Answer:
Correct option is
B
0
D
−1
sinx+sin2x+sin3x
=sin(2x−x)+sin2x+sin(2x+x)
=2sin2xcosx+sin2x [ by using sin(A+B)=sinAcosB+sinBcosA and sin(A−B)=sinAcosB−sinBcosA ]
=sin2x(2cosx+1)........(i)
cosx+cos2x+cos3x
=cos(2x−x)+cos2x+cos(2x+x)
=2cos2xcosx+cos2x [By using cos(a−b)=cosa⋅cosb+sina⋅sinb and cos(a+b)=cosa⋅cosb−sina⋅sinb]
=cos2x(2cosx+1).....(ii)
∴(sinx+sin2x+sin3x)
2
+(cosx+cos2x+cos3x)
2
=1
sin
2
2x(2cosx+1)
2
+cos
2
2x(2cosx+1)
2
=1.......[From(i)(ii)]
⇒(2cosx+1)
2
=1
⇒2cosx+1=±1
∴cosx=0or−1
1/4(8x-4)=
need help please answer
Answer:
2x-1 is the answer (or if you're trying to multiply it, the answer is -8.)
Step-by-step explanation:
Every year the Lee family has a big family dinner, and everyone brings a mug to exchange. The mugs are put on wooden hangers on the wall, and each wooden hanger can hold 12 mugs. Last year the family had 15 mugs to hang up. This year the Lee family filled three wooden hangers. How many more mugs were brought to the Lee family dinner this year compared to the previous year? *
Answer:
21 more mugs were brought this year than last year.
Step-by-step explanation:
We can solve by subtracting the initial amount of mugs from the final amount of mugs.
To find the amount of mugs hung up this year, we will use the equation: m = 12w where m = the number of mugs & w = the number of wooden hangers. The 12 represents the amount of mugs per wooden hanger.
We can plug in 3 for w since 3 wooden hangers were filled up and we would get 12(3) = m = 36 mugs
Now we subtract last year's total mugs hung up from this year's total mugs hung up.
We end up with 36 - 15 = 21
There are 10 students on the basketball team. The coach selects 3 of them to go to the basketball clinic. In how many ways can she choose 3 of the 10 students?
[tex]_{10}C_3=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot 3}=120[/tex]
Question :-
There are 10 students on the basketball team. The coach selects 3 of them to go to the basketball clinic. In how many ways can she choose 3 of the 10 students?Answer :-
The coach can choose 3 of the 10 students in 120 ways.[tex] \rule{200pt}{3pt}[/tex]
Combinations refers to the number of ways of selecting from a set when the order is not important. The number of combinations of n objects taken r at a time is given by [tex]\sf C(n, r) = \dfrac{n!}{(n - r)!r!}, n \geqslant r[/tex].
Solution :-
As per the provided information in the given question, we have been given that the number of combinations of 10 students taken 3 at a time. We have been asked to calculate the ways that she can choose 3 of the 10 students.
To calculate the ways that she can choose 3 of the 10 students, we will apply the formula below :-
[tex] \qquad \bigstar \: \: \: \boxed{ \sf{ \: \: C(n, r) = \dfrac{n!}{(n - r)!r!} \: \: }}[/tex]
Substitute the given values into the above formula and solve for C:
[tex]\sf:\implies{ C(n, r) = \dfrac{n!}{(n - r)!r!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{(10 - 3)!3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{7!3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8 \cdot \cancel{7!}}{ \cancel{7!}3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8}{3 \cdot 2}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{720}{6}}[/tex]
[tex]\sf:\implies \bold{ C(10, 3) = 120 \: ways}[/tex]
Therefore :-
The coach can choose 3 of the 10 students in 120 ways.[tex]\\[/tex]
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Have a great day! <33
10 [25-{8-6 (16-13)}÷5
Answer:
70
Step-by-step explanation:
to solve : start wit the inside brackets first
10 [25-{8-6 (16-13)}÷5 start 16-3
10[25-{8-6(3)}÷5 then multiply 6 and 3
10[25-{8-18}]÷5 then subtract 8-18
10[25-(-10)]÷5
10[25+10)÷5 add numbers inside brackets
10×35÷5=70 multiply and divide
Find the domain for the rational function f of x equals quantity x plus 1 end quantity divided by quantity x minus 2 end quantity.
(−[infinity], 2) (2, [infinity])
(−[infinity], −2) (−2, [infinity])
(−[infinity], 1) (1, [infinity])
(−[infinity], −1) (−1, [infinity])
Answer:
[tex](- \infty, 2), (2, \infty)[/tex]
Step-by-step explanation:
Given the function:
[tex]f(x) = \dfrac{x+1}{x-2}[/tex]
To find:
Domain of the function.
Solution:
First of all, let us learn about definition of domain of a function.
Domain of a function is the valid input values that can be provided to the function for which output is defined.
OR
Domain of a function [tex]f(x)[/tex] are the values of [tex]x[/tex] for which the output [tex]f(x)[/tex] is a valid value.
i.e. The function does not tend to [tex]\infty[/tex] or does not have [tex]\frac{0}0[/tex] form.
So, we will check for the values of [tex]x[/tex] for which [tex]f(x)[/tex] is not defined.
For value to tend to [tex]\infty[/tex], denominator will be 0.
[tex]x-2\neq 0 \\\Rightarrow x \neq 2[/tex]
So, the domain can not have x = 2
Any other value of x does not have any undefined value for the function [tex]f(x)[/tex].
Hence, the answer is:
[tex]\bold{(- \infty, 2), (2, \infty)}[/tex] [2 is not included in the domain].
find the roots of the following equation X + 1 whole square minus x square equal to 2
Answer:
x = 1/2
Step-by-step explanation:
Let's represent this in a mathematical way,
(x+1)^2 - x^2 = 2
Ok now we expand,
x^2 + 2x + 1 -x^2 = 2
rearrange,
x^2 - x^2 + 2x + 1 = 2
subtract,
2x + 1 = 2
subtract 1 from both sides,
2x + 1 - 1 = 2 - 1
2x = 1
Now divide 2 from both sides and get your answer,
x = 1/2
Answer:
[tex](x + 1) { }^{2} - x {}^{2} = 2[/tex]
[tex]x {}^{2} + 2x + 1 - x {}^{2} = 2[/tex]
[tex]2x + 1 = 2[/tex]
[tex]x = 1 \div 2[/tex]
PLEASE HELP
Water flows through a pipe at a rate of 490 milliliters every 6.5 hours. Express this
rate of flow in fluid ounces per minute. Round your answer to the nearest hundredth.
Answer:
[tex]0.042~\dfrac{fl~oz}{min}[/tex]
Step-by-step explanation:
1 gal = 231 in.^3
1 gal = 128 fl oz
1 in. = 2.54 cm
1 ml = 1 cm^3
[tex]\dfrac{490~ml}{6.5~hour} \times \dfrac{1~cm^3}{1~ml} \times \dfrac{1~in.^3}{(2.54~cm)^3} \times \dfrac{1~gal}{231~in.^3} \times \dfrac{128~fl~oz}{1~gal} \times \dfrac{1~hour}{60~min} =[/tex]
[tex]= 0.042~\dfrac{fl~oz}{min}[/tex]
Answer:
On delta math its 0.04
Step-by-step explanation:
daniel thinks of a number and subtracts 2
from it. He divides 32 by the result. If
his answer is 4, what number does he
think of
Answer:
the number is 126
Step-by-step explanation:
1) multiply each side by 32: (n-2) / 32 = 4
2) subtract 2 from each side: n-2 = 128
3) n = 126
Answer:
130
Step-by-step explanation:
So basically this number, minus 2, divided by 32 is 4, so lets write the unknown number as x.
So, (x-2)/32 = 4.
First multiply both sides by 32 to get rid of the denominator.
(32)(x-2)/32 = 4(32) x-2 = 128
Now the -2 remains to figure out x, so you add 2 to both sides to get rid of the -2.
So, x-2+2 = 128+2, -2 +2 is 0, and 128 +2 is 130, so you have x = 130.
James conducted an experiment with 4 possible outcomes. He determined that the experimental probability of event A happening is 10 out of 50. The theoretical probability of event A happening is 1 out of 4. Which action is most likely to cause the experimental probability and theoretical probabilities for each event in the experiment to become closer? removing the last 10 trials from the experimental data completing the experiment many more times and combining the results to the trials already done including a fifth possible outcome performing the experiment again, stopping immediately after each event occurs once
Answer:
Completing the experiment a few more times and combining the results to the trails already done.
Answer:
Completing the experiment a few more times and combining the results to the trails already done.
Step-by-step explanation:
2(x + 4) - 8 = 36-10
Answer:
x=13
Step-by-step explanation:
Find the x-intercept(s) of the equation: y =3x^2-3x-6
a. x-intercepts: (-1,0) and (2,0)
b. x-intercepts:(0,-3) and (0,2)
c. x-intercept: (-6,0)
d. x-intercept: (0,-6)
Answer:
(2,0) ( -1,0)
Step-by-step explanation:
y =3x^2-3x-6
Let y = 0 and solve for x to find the x intercepts
0 =3x^2-3x-6
Factor out a 3
0 =3(x^2-x-2)
Factor inside the parentheses
0 = 3( x-2) (x+1)
Using the zero product property
x-2 =0 x+1 = 0
x=2 x = -1
(2,0) ( -1,0)
Answer:
[tex]\large \boxed{\mathrm{a. \ x-intercepts: (-1,0) \ and \ (2,0)}}[/tex]
Step-by-step explanation:
The x-intercept(s) is when y = 0.
3x² - 3x - 6 = 0
Factor left side of the equation.
3(x + 1)(x - 2) = 0
Set factors equal to 0.
x + 1 = 0
x = -1
x - 2 = 0
x = 2
The x-intercepts are (-1, 0) and (2, 0).
the square of 5 is divided by the cube root of 27. what is the remainder
Step-by-step explanation:
square of 5 is 25 and it divided by the cube root of 27 means 3
Now ,
#25÷3
= 8 [1] (•°• 3×8 = 24)
Here,
we got 1 as a reminder .
Hope it is helpful to you
✌️✌️✌️✌️✌️✌️✌️
The remainder will be 1.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The square of 5 is divided by the cube root of 27.
Now,
Since, The square of 5 is divided by the cube root of 27.
Hence, We get;
⇒ 5² / ∛27
⇒ 25 / 3
After divide we get;
3 ) 25 ( 8
24
--------
1
Thus, The value of remainder = 1
Learn more about the divide visit:
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andy is making floor plans for a tree house using a scale 1in to 2ft he wants to make the floor of the tree house have a length of 8ft. how many inches should he show for this distance on his floor plan
Answer:
Andy should represent the 8 feet long floor on the floor plan with a dimension of 4 inches
Step-by-step explanation:
The scale of the tree house plan is given as 1 in. to 2 ft,
Therefore we have a scale of 1/2 in. of the floor plane is equivalent to 1 ft. in actual dimensions
Given that Andy wants the floor to make the tree house floor to have a length of 8 ft., let the dimension of the floor plan of the house floor be x, we have;
[tex]\dfrac{\frac{1}{2} \ inches \ plan }{1 \ feet \ actual} =\dfrac{x \ inches \ plan}{8 \ feet \ actual}[/tex]
[tex]x \ inches \ plan =\dfrac{\frac{1}{2} \ inches \ plan }{1 \ feet \ actual} \times 8 \ feet \ actual = 4 \ inches[/tex]
Therefore, Andy should represent the 8 feet long floor on the floor plan with a dimension of 4 inches.
Solve for a.
-4a – 2a – 7 = 11
a =
[?]
Answer:
or, -4a - 2a -7 = 11
or, -4a -2a =11 +7
or, - 6a = 18
or, a= 18÷ -6
a= -3
Twice the difference between a number and 4 is twenty. Find the number.
А. 8
B. 9
C. 12
D. 14
Please help!!!
Answer:
D 14
Step-by-step explanation:
Let x be the number
2(x-4) = 20
Divide each side by 2
2/2(x-4) = 20/2
x-4 = 10
Add 4 to each side
x-4+4 = 10+4
x = 14
Answer:
The number is 14
Step-by-step explanation:
Let's call this unknown number of x:
2×(x – 4) = 20
2x – 8 = 20
2x = 20 + 8
2x = 28
x = 28/2
x = 14
Bismah is building 5 raised garden beds in a community garden. Each raised garden bed will need 1 7 8 bags of soil. How many bags of soil will Bismah need for all 5 raised garden beds?
Answer:
890 if it’s 178 bags per garden bed
Step-by-step explanation:
since 1 raised garden bed is supposedly 178 bags, 5 would be 890 since it’s just 5x178. if it’s not 178 bags (which would make sense since 178 is a big number), just multiply 5 by that number and if it’s a decimal round up to the next whole number if it’s about how many bags Bismah needs to buy, since you can’t by 1/2 of a bag
Bismah will need a total of 890 bags of soil for all the 5 raised garden. beds.
What is Multiplication?.Multiplication is one of the basic operations in mathematics where a number is added repeatedly to itself up to the times as the value of the other number.
That is, if a number p is multiplied to another number q, p × q, implies that p is added repeatedly to itself q times or q is added repeatedly to itself up to p times.
Number of garden beds Bismah has raised = 5
Number of bags of soil needed for a garden bed = 178 bags
Number of bags of soil needed for 5 garden bed = 178 × 5 bags
= 890 bags
Hence Bismah would need 890 bags of soil for the 5 raised garden beds in the community garden.
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Find the length of the third side. If necessary, round to the nearest tenth.
20
28
Answer:
Submit Answer
attempt 1 out of 2
PLS HELP ASAP
Answer:
b = 19.6
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
20^2+ b^2 = 28^2
400 + b^2 = 784
b^2 = 784-400
b^2 =384
Taking the square root of each side
sqrt( b^2) = sqrt(384)
b =19.59591794
To the nearest tenth
b = 19.6
Answer:
19.6
Step-by-step explanation:
It is a right triangle so use the pythagorean theorem; a^2 + b^2 = c^2
a=20
b=?
c=28 - c is the hypotenuse because it is across from the right angle
20^2 + b^2 = 28^2
400+ b^2 =784
b^2=384
b= 19.595917... or 19.6 (rounded to nearest tenth)
Is this a function or no?
Function
It is a function
Write the ratio as a fraction in simplest form.
0.65 to 0.15
Answer:
13/3
Step-by-step explanation:
Write as a fraction first,
0.65/0.15
convert decimal to fractions,
13/20/3/20 = 13/3
What is the area?
6 mm
5 mm
3 mm
13 mm
8 mm
9 mm
Answer:
none of above .
Step-by-step explanation:
because the unit of area is always in square forms.
Find the perimeter of this figure. (Image down below)
Answer:
The answer is
44 ftStep-by-step explanation:
The figure above is a rectangle
To find the perimeter of a rectangle we use the formula
Perimeter of a rectangle = 2l + 2w
where
l is the length of the rectangle
w is the width of the rectangle
From the question
length = 14 ft
width = 8ft
Substituting the values into the above formula we have
Perimeter = 2(14) + 2(8)
= 28 + 16
We have the final answer as
Perimeter = 44 ftHope this helps you
Hong buys candy that costs $5 per pound. He will buy at least 7 lbs of candy. What are the possible amounts he will spend on candy? Use c for the amount (in dollars) Hong will spend on candy. Write your answer as an inequality solved for c.
Step-by-step explanation:
if he buys 7 pounds, it will cost 7×5 = $35
he might buy more than that (and it will then also cost more than that) , but not less than that.
so,
c >= $35
132 divide t 12 x 12 - 124 divide 31
Answer:
31
Step-by-step explanation:
what is the volume of a cube with and edge length of 4 cm
Answer:
V = 64 cm^3
Step-by-step explanation:
Volume of a cube is given by
V = s^3 where s is the side length
V = 4^3
V = 64 cm^3
Answer:
64
Step-by-step explanation:
i guess so as the volume is 4×4×4
An office supply store recently sold a black printer ink cartridge for $14.99 and a color printer ink cartridge for $20.99. At start of a recent fall semester, a total of 42 of these cartidges was sold for a total of $695.58. How many of each type were purchased?
Answer:
B = 31, C = 11
Step-by-step explanation:
Let B be the number of Black printer ink cartridges and C be the number of color printer ink cartridges.
42 were sold in total, hence,
B+C= 42 ------------(1)
Also, its given that
14.99 B+20.99C= 695.58 ------(2)
Multiplying (1) by 20.99,
14.99 B+14.99 C= 629.58 ------(3)
Now, subtracting (3) from (2),
14.99 B+20.99C= 695.58
14.99 B+14.99 C= 629.58
------------------------------------
6 C = 66
C= 66/6
C = 11
We know, B+ C= 49
Hence B = 42- 11 = 31
B = 31
Hence, number of Black printer ink cartridges = 31 and color printer ink cartridges = 11 .
7th Grade Math Answer ASAP Please <3
Answer:
Hey there!
Andrew made a mistake in the last step. -11.8+9.8=2, not -21.6.
Let me know if this helps :)
the population of a small city grows by 600 every year. If there were 900 people initially, find the population of the city 60 years after the city was first established
Answer:
36900
Step-by-step explanation:
It's a linear function with equation P(t)=900+600*t. P(60)=900+600*60=36900
Answer:
36,900
Step-by-step explanation:
First do 600 times 60=36,000
Next add 900
36,000+900=36,900
theres your answer :)
ANSWER QUESTIONS QUICKLY PLZZZZZZ
Answer:
See below.
Step-by-step explanation:
Since the two triangles are similar, this means that their corresponding sides are proportional. In other words:
[tex]\frac{PQ}{XY}=\frac{QR}{YZ}=\frac{RP}{ZX}[/tex]
Part A:
We already know PQ, RP, XY, and YZ.
To find XZ, we can use the first and third proportions:
[tex]\frac{PQ}{XY} =\frac{RP}{ZX} \\=\frac{7.2}{18}=\frac{6.5}{ZX}[/tex]
Cross multiply:
[tex]117=7.2(ZX)\\ZX \text{ or } XZ = 16.25[/tex]
Part B:
The same thing as Part A, but with the first and second proportions:
[tex]\frac{PQ}{XY}=\frac{QR}{YZ}\\\frac{7.2}{18}=\frac{QR}{7}\\50.4=18(QR)\\QR=2.8[/tex]