Solve the following problem. Round to one decimal place if necessary.
Answer:
Sinθ = Opposite/hypotenuse
[tex] \sin(21) = \frac{x}{22} \\ 0.358 = \frac{x}{22} \\ x = 22 \times 0.358 \\ x = 7.88[/tex]
I hope I helped you^_^
Three friends were at a festival together and they won 20 small prizes. They decided to split the prizes as evenly as possible. How many prizes will they each get?
Answer:
they would each get 6 and there would be 2 left over
Step-by-step explanation:
3x6=18
20-18=2
=2 leftovers
Answer:
Each of the friends will get 6 with 2 small prizes remaing
Step-by-step explanation:
20 ÷ 6 = 18 remainder of 2
Ignore the 2 because you cannot split 2 evenly from 3 people.
So each friend gets 6, while there is a 2 remainder
To check our work just do 6 × 3 = 18 and 20 - 18 = 2
So, in conclusion, each friend get 6 while there are 2 small prizes left
Write the equation of the line that passes through the points
(3,-2) and (6, 1).
y=x-5
y = 5x + 1
y = -x + 5
Answer:
It is y = x - 5
Step-by-step explanation:
General equation of a line:
[tex]{ \bf{y = mx + c}}[/tex]
m is the gradient, and c is y-intercept.
For gradient:
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1}} [/tex]
substitute:
[tex]slope = \frac{1 - ( - 2)}{6 - 3} \\ \\ = \frac{3}{3} \\ slope \: = 1[/tex]
m = 1
for y-intercept:
consider point (6, 1):
[tex]y = mx + c \\ 1 = (6 \times 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5[/tex]
therefore:
[tex]{ \sf{equation \: is \: \{y = x - 5 \}}}[/tex]
A square sandbox has an area of 42ft to the power of 2. What is the approximate perimeter of the sandbox to the nearest hundredth?
I need help with 16-25
Solve the following equation for X to find the total number of people who downloaded songs for music site for a certain month.
X= 0.6x + 384
How many people downloaded songs from the site that month?
Answer:
960
Step-by-step explanation:
x=0.6x+384
0.4x=384
960
Answer:
960
Step-by-step explanation:
x = 0.6x + 384
Subtract 0.6x in both sides:
0.4x = 384
Divide both sides by 0.4:
x = 384/0.4
x = 960
9. A doctor charges each patient $75 per consultation. If she works for 6 hours during one day and sees an average of six patients per hour, what was her profit that day? (Her costs per day are $200 for insurance, $200 for leasing the building and $50 for paying the reception desk).
Answer:
She makes $2,250/day
Step-by-step explanation:
$75 x 6 = $450 (amount of patients seen)
$450 x 6 = $2,700 (amount of hours she works)
$2,700 - $450 = $2,250 (the cost of the building, reception desk, & insurance)
We are given that the doctor charges $75 for each patient
In each she sees an average of 6 patients so,
Charge each hr = $75(6) = $450
For each hr she receives $450
So, for 6 hrs she receives = $450(6) = $2700
She pays for all the stuff = $200 + $200 + $50 = $450
Profit = Selling Price - Cost Price
Profit = $2700 - $450
Profit = $2250
Hence, she earns a profit of $2250 that daySimplify (a5b2c5)(ac2). A. a4c10 B. a6b2c10 C. a6b2c7 D. a5b2c7
Answer:
Answer is C.
Step-by-step explanation:
[tex] ( {a}^{5} {b}^{2} {c}^{5} )( {ac}^{2} ) [/tex]
form brackets of common terms:
[tex] = ( {a}^{5} .a)( {b}^{2} )( {c}^{5} . {c}^{2} )[/tex]
from law of indices:
[tex]{ \boxed{ \bf{ {x}^{n} \times {x}^{m} = {x}^{(n + m)} }}}[/tex]
therefore:
[tex] = \{ {a}^{(5 + 1)} \} \{ {b}^{2} \} \{ {c}^{(5 + 2)} \} \\ = {a}^{6} {b}^{2} {c}^{7} [/tex]
Find the surface area of the composite solid below. (2 ft, 2 ft, 2 ft, 3 ft)
Answer:
44 sq. ft
Step-by-step explanation:
5(2^2) = 20
4(3x2) = 24
20+24 = 44
find the value of' m' if (-m 3) is the solution of equation 4x +9y -3=0
[tex]\\ \qquad\quad\sf\longmapsto 4x+9y-3=0[/tex]
[tex]\\ \qquad\quad\sf\longmapsto 4(-m)+9(3)-3=0[/tex]
[tex]\\ \qquad\quad\sf\longmapsto -4m+27-3=0[/tex]
[tex]\\ \qquad\quad\sf\longmapsto -4m+24=0[/tex]
[tex]\\ \qquad\quad\sf\longmapsto -4m=-24[/tex]
[tex]\\ \qquad\quad\sf\longmapsto m=\dfrac{-24}{-4}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto m=6[/tex]
Consider the points (5,0) and (0,3). Plot the points and find the distance between them. Give your answer both in exact form and as a decimal approximation.
Answer:
(5;3)
Step-by-step explanation:
Give your answer both.
The distance between the points (5, 0) and (0, 3) is approximately 5.83095 units.
To find the distance between two points, we can use the distance formula:
Distance = √[tex]((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
Given the points (5, 0) and (0, 3), we have:
[tex]x_1 = 5, y_1 = 0\\\\x_2 = 0, y_2 = 3[/tex]
Substituting these values into the formula:
Distance = √[tex]((0 - 5)^2 + (3 - 0)^2)[/tex]
Distance = √[tex]((-5)^2 + (3)^2)[/tex]
Distance = √(25 + 9)
Distance = √34
The exact distance between the points is √34, which is approximately 5.83095 when rounded to five decimal places.
So, the distance between the points is approximately 5.83095 units.
To know more about distance, refer here:
https://brainly.com/question/24485622
#SPJ3
solve (x+1) (x-11) = -36
x = ?
can someone help pls
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
1. Approach
The most logical steps to solve the given equation are to distribute and simplify the left side of the equation. Then use inverse operations to bring all of the terms to the left side of the equation. After doing so, one can factor the equation again, then use the zero-product property to solve it.
2. Simplify
Distribute the terms on the left side, multiply everything in the first parenthesis by everything in the second,
[tex](x+1)(x-11)=-36[/tex]
[tex](x)(x)+(1)(x)+(-11)(x)+(1)(-11)=-36[/tex]
Simplify this expression by performing the multiplication and then combining like terms,
[tex](x)(x)+(1)(x)+(-11)(x)+(1)(-11)=-36[/tex]
[tex]x^2+x-11x-11=-36[/tex]
[tex]x^2-10x-11=-36[/tex]
Inverse operations,
[tex]x^2-10x-11=-36[/tex]
[tex]x^2-10x+25=0[/tex]
3. Factor and solve,
Now that has the simplified version of the equation, one should factor it. Rewrite the quadratic expression as a product of two linear expressions,
[tex]x^2-10x+25=0[/tex]
[tex](x-5)^2=0[/tex]
Use the zero product property to solve this expression. The zero product property states that any number times zero equals zero. Since ([tex](x-5)^2[/tex]) is just ([tex]x-5[/tex]) multiplied by itself, thus, when solving, one can ignore the square part of the equation:
[tex](x-5)^2=0[/tex]
[tex]x-5=0[/tex]
Inverse operations,
[tex]x-5=0[/tex]
[tex]x=5[/tex]
What is the longest version of pi? Please type the whole thing.
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601
Write the cubes of 5 natural numbers which are of the form 3n + 1 (eg.4,7,10…)and verify the following
"The cube of a natural number of the form 3n + 1 is a natural number of the
Same form
in when divided by 3 it leaves the remainder 1'
Answer:
yes it is true
Step-by-step explanation:
write the first five elements then write their cubes then write the cubes in the same form
for eg:
4³=16= 3×5+1= 3n+1
7³=49=3×16 +1= 3n + 1
and so on till the fifth element...
Giving brainliest, show yo work!
Answer:
done the first 3
Step-by-step explanation:
5×-3=-15
2×4=8
3×-5=-15
(-15+8)²+-15
(-7)²+-15
-49-15
=-74
(2×-3×-6)²-5(4)
(36)²-20
1296-20
=1276
(-3×4×-5)+3(4)³
60+192
=252
Answers;
1. {(5x + 2y)}^{2} + 3z \\ {(5( - 3) + 2(4))}^{2} + 3( - 5) \\ {( - 15 + 8)}^{2} - 15 \\ {( - 7)}^{2} - 15 \\ 49 - 15 \\ 34 \\ \\ 2. \: 2 {(xz)}^{2} - 5y \\ 2 ({( - 3)( - 5)})^{2} - 5(4) \\ 2 {(15)}^{2} - 20 \\ 2(225) - 20 \\ 450 - 20 \\ 430
2(x+1) = -8x +8(x-2)
x=?
4(7+2x)=-2(x+4)+4x
x=?
Hi ;-)
Equation 1°
[tex]2(x+1)=-8x+8(x-2)\\\\2x+2=-8x+8x-16\\\\2x+8x-8x=-16-2\\\\2x=-18 \ \ /:2\\\\\huge\boxed{x=-9}[/tex]
Equation 2°
[tex]4(7+2x)=-2(x+4)+4x\\\\28+8x=-2x-8+4x\\\\8x+2x-4x=-8-28\\\\6x=-36 \ \ /:6\\\\\huge\boxed{x=-6}[/tex]
Simplify 2 root 3 multiply 3 root 6
Answer:
18√2
Step-by-step explanation:
2√3 x 3√6
2 x 3 x (√6 x √3)
=> 6√18
=> 6√(3x3x2)
=> 6 x 3√2
=> 18√2
19. A square is divided into a 100-by-100 grid of smaller squares. If 100
squares are shaded in the top row, 99 in the second row, 98 in the third
row, and so on, what is the ratio of the squares shaded to the squares not
shaded? Write the answer as a fraction in simplest form.
Answer:
13:9 with 9 being unshaded
Step-by-step explanation:
i drew a similar grid, shaded them in in the way you specified, then counted the squares on either side. the i put the numbers in a fraction and simplified
Write the Roman Numeral CLXIV in standard form. Standard Roman Number Numeral 1 1 5 V 10 X 50 100 500 D 1,000 M XJ002 2 A) 169 OB) 166 C) 164
Answer:
C. 164
Step-by-step explanation:
its self explanitory
Round 55,553.65478 to:
a. hundreds
and
b. thousandths
Answer:
a. hundreds
55,600
b. thousandths
55,553.65500
You are six spaces behind your
opponent in a board game. What integer represents your situation?
+ An Integer less than 0 is represented as
Answer:
9,-9
Step-by-step explanation:
Because your opponent is in the positive while you are in the negative
The width of a rectangle with an area of 72 square inches is 6 inches. What is the perimeter of the rectangle, in inches?
b. The sum of three numbers is 51. The second number is three more than the first number, and the third number is
Two times the value of the first number. What are the three numbers?
Answer:
12, 15, 24
Step-by-step explanation:
Let 1st # = x
Let 2nd # = x+3
Let 3rd # = 2x
Your equation is: x + (x+3) + 2x = 51
Add up all the x: x + x +3 +2x =51
Subtract 3 from both sides: 4x + 3 - 3 = 51 - 3
Divide 4 from both sides: 4x / 4 = 48 / 4
Your 1st number is x = 12
For the 2nd # it is 3 more than x so 12 + 3 = 15
For the 3rd # it is 2 times x so 2(12) = 24
Check your answers by adding up the numbers you solved: 12 + 15 +24 = 51
Does it equal to 51 as stated in the question? Yes, answers check out.
Segment addition postulate
Find RT
Answer:
RT = 25.5
Step-by-step explanation:
RT = RS + ST = 17 + 8.5 = 25.5
If y is directly proportional to x and y = 20 when
x = 5,
(i) find an equation connecting x and y,
Answer:
Step-by-step explanation:
y = kx
y = 20
x = 4
20 = k*4 Divide by 4
20/4 = k
k = 5
The equation is y = 5x
help plz i will rate
Perform the operation and reduce the answer fully.
3/20 - 9/16
Answer:
-33/80
Step-by-step explanation:
3/20 - 9/16
(4)(3/20) - (9/16)(5)
12/80 - 45/80
= -33/80
write 3 equivalent rational number of 5/3
Step-by-step explanation:
[tex] \frac{10}{6} \\ \frac{15}{9} \\ \frac{20}{12} [/tex]
What is mZBAC?
60°
(not drawn to scale)
Answer:
<BAC=60°
Step-by-step explanation:
THIS IS THE ANSWER
What is the equation of the line that passes through the point (4, -7) and has a
slope of – } ?
Answer:
Submit Answer
PLS HELP ASAP
Answer:
I think that some information is missing? what is the slope?
If you are trying to say that there is NO SLOPE then the
answer is " x = 4 "
Step-by-step explanation: