Answer:
54
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] and [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a , then
[tex]\sqrt{6}[/tex] × 3[tex]\sqrt{54}[/tex]
= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9(6)}[/tex]
= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{6}[/tex] × [tex]\sqrt{6}[/tex] × 3 × 3
= 6 × 9
= 54
[tex]{ \qquad\qquad\huge\underline{\boxed{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{6} \times 3 \sqrt{54} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{2 \times 3} \times \sqrt{2 \times {3}^{3} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {2}^{2} \times {3}^{4} } [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \times {3}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \times 9[/tex]
[tex]\qquad \sf \dashrightarrow \:18[/tex]
What is the simple interest paid if $900 principal 6% interest rate for 2 year
Simple Interest is the method of finding the interest amount for a particular principal amount of money at a particular rate of interest.
The simple interest for $900 at an interest rate of 6% is $108.
What is simple interest?Simple Interest is the method of finding the interest amount for a particular principal amount of money at a particular rate of interest.
We have,
Principal = $900
Rate of interest = 6%
Time = 2 years.
Remember that time should always be in years.
The formula for simple interest is given by:
SI = PRT / 100
Where,
P = principal
R = rate of interest
T = Number of years
So,
SI = 900 x 6 x 2 / 100
SI = $108
Thus the simple interest for $900 at an interest rate of 6% is $108.
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Which angle is supplementary to LSM?
A.OSN
B.SLM
C.LSM
D.MSN
Answer:
D.MSN
Step-by-step explanation:
Supplementary angles complete each other to 180° and they are on a straight line.
We are asked to find the supplementary angle to angle LSM on figure 2.
Amongst given options we see angle LSM and angle MSN make a straight line therefore they are supplementary angles.
25 points plus brainliest
Answer:
[tex]|4x+3|+7 < 10[/tex]
Step-by-step explanation:
When you evaluate the expression, you get [tex]-\frac{3}{2} < x < 0[/tex]
In the figure, m∠AOD=105. If m∠AOB=8x, m∠BOC=7x and m∠COD=6x, what is the value of x?
Answer:
x = 5
Step-by-step explanation:
from the diagram
∠ AOB + ∠ BOC + ∠ COD = ∠ AOD ( substitute values )
8x + 7x + 6x = 105
21x = 105 ( divide both sides by 21 )
x = 5
Answer:
5
Step-by-step explanation:
AOB+BOC+COD=AOD
6x+8x+7x=105
21x=105
x=105÷21
x=5
a rectangle has a perimeter of 10 meters. choose ,begin emphasis,all,end emphasis, the possible dimensions of the rectangle.
The possible dimensions of the rectangle having a perimeter 10 are
1)length= 4 and bredth= 1
2)length= 3 and bredth= 2
The perimeter of rectangle=2( length of rectangle + breadth of rectangle)
Given that the perimeter of rectangle=10
10=2( length of rectangle + breadth of rectangle)
5=length of rectangle + breadth of rectangle
For a rectangle, length must be always greater than the breadth
The possible values of length of rectangle= 4 and 3
As a result,the Breadth of the rectangle will be 1 if length =4
As a result,the Breadth of rectangle will be 3 if length =2
Therefore, The possible dimensions of the rectangle having a perimeter 10 are
1)length= 4 and bredth= 1
2)length= 3 and bredth= 2
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mcgraw hill determine whether each relation is a function
2 is subtracted from the product of 5 and a number
Answer:
2 - 5 = -3.
Step-by-step explanation:
I subtracted two from five and got negative three lol
Caroline is driving to a concert and needs to pay for parking. there is an automatic fee of $5 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. how much total money would caroline have to pay for parking if she left her car in the lot for 3 hours? how much would caroline have to pay if she left her car in the lot for t hours?
The total money Caroline would have to pay for parking if she left her car in the lot for 3 hours is $11
For t hours the Caroline would pay 5+2t
What is algebraic expression?
Algebraic expression is a mathematical statement which points to when operations such as addition, subtraction, multiplication as well as division, are used for variables and constants, in essence, using algebraic expression, we can derive the equation that gives the total cost of Caroline driving and using the parking lot at the concert
There is a fixed charge of $5, there is also an additional $2 for every spent, if represent hours spent by t, then she would pay 2t in total for using the parking lot.
Total cost=5+2t
when t=3 hours
total cost=5+(2*3)
total cost=$11
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A, B, C and D are junctions on a motorway.
A B C D
distance CD= 3 x distance AB
distance BC= 25 miles
Salma drives from A to C.
She drives for 30 minutes at an average speed of 62 miles per hour.
Work out the distance AD.
Not drawn
accurately
The distance AD is 49 miles.
As per the given values of speed and time, we will calculate the distance AC. Firstly equalising the units.
As per the known fact, 60 minutes = 1 hour
30 minutes = (1/60)×30
30 minutes = 0.5 hour
Now, speed, distance and time are related as -
Speed = distance ÷ time
Distance = speed × time
Distance = 62 × 0.5
Distance = 31 miles
So, AC = 31 miles and BC = 25 miles.
Therefore, AB = AC - BC
AB = 31 - 25
AB = 6 miles
The distance AD = AC + CD
AD = 31 + 3 × AB
AD = 31 + 3 × 6
AD = 31 + 18
AD = 49 miles
Therefore, the distance between AD is 49 miles.
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The complete question is attached.
21. a. What four factors were used to create this Product Game board?
9 15 18
21 ? 30 35 Factors:
36 42 49
b. What product is missing from the grid?
What is the missing number from the grip I need help
The four factors were used to create this Product Game board are {2, 3, 5, 7} and the product missing from the grid is 25
To see what are factors are used in the given list, we just need to write each of the numbers, as a product of prime factors such as 2, 3, 5, 7 .
9 = 3* 3
15 = 3 *5
18 = 3 *2*3
21 = 7*3
30 = 5*3*2
35 = 7*5
36 = 3*3*2*2
42 = 2*3*7
49 = 7*7
As we can see, the 4 factors used to product the numbers in the given list are {2, 3, 5, 7}
for the second part that is to find the missing number between 21 and thirty we first need to write all the numbers between 21 and thirty and check which number is having the only factors of at least one of (2,3,5,7)
the numbers are 22 , 23 ,24, 25 ,26 ,27 ,28, 29
After checking the missing number is 25(5*5) because there has to be at least 4 products who have same factor and 5 is the factor who has appeared only three times
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consider measurements of the width w and length l of a piece of paper used to calculated the area of the paper using a
The area of the piece of paper is;
Area = length x width
⇒ a = l w unit square.
Here,
Given that;
The width of piece of paper = w
The length of piece of paper = l
We have to find the area of piece of paper by using a.
What is Area of rectangle?
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
Now,
Consider the shape of piece of paper is rectangular.
The width of piece of paper = w
The length of piece of paper = l
Since, we know that;
Area of rectangle = length x width
Then, The Area of piece of paper 'a' = length x width
⇒ a = l * w
Where, a = Area of rectangle, l = length of piece of paper and
w = width of rectangle.
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2p=47−17 please help with explinations
We calculate the right side of the equation : 47 - 17 = 30
2p = 30
Divide both side by 2, we have : p/2 = 30/2 -> p = 15.
Answer:
P=15
Step-by-step explanation:
2p = 47-17
2p = 30
Divide both sides by the coefficient of p which is 30
[tex]\frac{2p}{2} =\frac{30}{2}[/tex]
P= 15
How many two-ninths are in eight-ninths?
Answer:
4
Step-by-step explanation:
2/9 + 2/9 + 2/9 + 2/9 = 8/9
a boy throws a baseball across a field. the ball reaches its maximum height, 18 meters, after 1 second. after approximately 2.3 seconds, the ball lands on the ground. the ball’s motion can be modeled using the function f(x)
The height of the ball after 1.5 seconds is 15.5 meters so option (C) will be correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
Given the function as the height of ball f(x) and time x
f(x) = -10x² + 20x + 8
At x = 1.5
f(1.5) = -10(1.5)² + 20(1.5) + 8
f(1.5) = 15.5
Hence "The height of the ball after 1.5 seconds is 15.5 meters".
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Given question is incomplete complete question is attached below image ;
On a coordinate plane, 2 straight lines are shown. The first solid line is horizontal at y = negative 1. Everything above the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 1) and (0, 0). Everything below the line is shaded.
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?
Using a linear function, one constraint on the inequality is given by:
y < -0.5x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Given two points, the slope is given by change in y divided by change in x.
For the line in the inequality, the points are:
(-2,1) and (0,0).
Hence the slope is given by:
m = (0 - 1)/(0 - (-2)) = -1/2 = -0.5.
Hence:
y = -0.5x + b.
When x = 0, y = 0, meaning that the y-intercept is of b = 0, and:
y = -0.5x.
Everything below the line is shaded, meaning that the values of y that are less than the line are shaded, and the inequality is:
y < -0.5x.
The inequality is only less, not less or equal, because the line is dashed and not solid.
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Compare square root of one hundred seventy and one hundred six eighths using <, >, or =.
square root of one hundred seventy is greater than one hundred six eighths
square root of one hundred seventy is equal to one hundred six eighths
one hundred six eighths is less than square root of one hundred seventy
one hundred six eighths is greater than square root of one hundred seventy
Square root of one hundred and seventy is greater than square root of one hundred and sixty eight.
What is a perfect square number ?A perfect square number is a number which when taken square root comes out as an integer.Every number which is not a perfect square when taken square root of it is irrational number.We can obtain square root of a perfect square number by prime factorisation method.
Given we have to compare [tex]\sqrt{170}[/tex] and [tex]\sqrt{168}[/tex].
We know that if the square roots are not given then we have easily concluded that 170 > 168.Same in the case of square root:
[tex]\sqrt{170} > \sqrt{168}[/tex].
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They spent $150 to rent a bounce house for 4 hours. How much is the hourly rate for the rental?
Show your work using the long division algorithm.
Answer:
$37.50
Step-by-step explanation:
In the rectangle shown below, the length is longer than its width w. List all the possible
whole number dimensions for the rectangle, and name the dimensions that give the smallest
perimeter.
Area is 40 m2
Answer: w can be 1,2,4,5
Step-by-step explanation:
Let's recap the formula of Area:
Area = width x length = w x l
Area = 40 = w x l
The definition of a whole number: is a number without fractions; an integer such as 0, 1, 2, 3, 4, 5, 6,...
Let's start with 0. 0 times anything is equal to 0, so we cannot make 40 out of zero. Cross this out.
Next, let's try with 1:
a. 1x40 = 40
Then, applying the same concept to the rest we have these multiplications:
b. 2x20 = 40
c. 4x10 = 40
d. 5x8 = 40
e. 8x5 = 40
f. 10x4 = 40
g. 20x2 = 40
h. 40x1 = 40
Let's recap the formula of Perimeter:
P = 2 x (w + l)
So, we have the calculated perimeters (according to the above finding):
a. P= 2x(1+40)=82
b. P= 2x(2+20)=44
c. P= 2x(4+10)=28
d. P= 2x(5+8)=26
The below answers do not fit the [width < length]
e. P= 2x(8+5)=26 [not an answer]
f. P= 2x(10+4)=28 [not an answer]
g. P= 2x(20+2)=44 [not an answer]
h. P= 2x(40+1)=82 [not an answer]
in mrs. middleton's math class, there are 7 more boys than girls. if there are 29 total students in the class, how many boys are there?
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
18 boys + 11 girls = 29 students
18-11=7
Rationalize the denominator
-x5
√12x - 9
Answer:
Step-by-step explanation:
-2x^6-9
please give me the brainliest
help it due in 4 mins please
Answer:
Step-by-step explanation:
draw an open circle on point -11 and a line going towards the left. Because it is less than -11 and not equal.
Point ( open circle ) on 0 going to the right because it is greater and does not including 0.
Sep 16, 1:21:38 AM
(3x-26)°, then find the measure of
The measurement or the value of x in the given equation [tex](3x-26)degrees = 180degrees[/tex] is [tex]x=68.67[/tex]°
As per the question statement, we are supposed to find the measure of angle x in the given equation, [tex](3x-26)= 180[/tex]
Before solving this question, we should know that this question is an example of solving a linear equation in one variable.
[tex](3x-26)= 180\\3x=206\\x=\frac{206}{3} \\x=68.67[/tex]
Hence the measure of the angle x is x=68.67°
This question is a good example of solving a linear equation in one variable.
Linear Equation: It is an equation which when plotted on a graph forms a straight line and we solve for an unknown number called as variable.
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A 3.5 ft child casts a 60 inch shadow, the child is next to a telephone pole that casts a 50 ft shadow how tall is the telephone pole
The telephone pole is 35ft tall .
What is height?The height of any object is define as the distance measurement of that object from the top to its base. In geometry it is also called as altitude.
Height can be measured in various quantities such as feet, inches, centimeters etc.
Some of measurements are as below.
feet to inches1 feet = 12 inches
feet to centimeters1 feet = 30.48 cm
inches to centimeters1 inch = 2.54 cm
meters to feet1 feet = 3.28 feet
In the given question,
Convert 60 inches to feet ,
60 inches = 60/12 feet = 5 feet
Given, pole shadow = 50ft
child height =3.5ft
now, Set up proportion between the ratios of the child and his shadow and the telephone pole and its shadow.
[tex]\frac{child \ height}{child \ shadow \ length} =\frac{pole \ height}{pole \ shadow \ length}[/tex]
Let, x be pole height
=> [tex]\frac{3.5}{5} =\frac{x}{50}[/tex]
now solve the equation,
3.5 ×50 = x × 5
x = 35
Thus, the pole is 35 feet tall.
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Can anyone answer these for me?
Answer:
x=12 y=10 z=-12
Step-by-step explanation:
Ax-5=19
I need help solving this problem?
CAN SOMEONE PLS HELP ME W THIS ONE PROBLEM ASAPPPP I RLLY NEED HELP
segment XY has a midpoint at M. The coordinates of X are (3,4) and the coordinates of M are (5,0). what are the coordinates of endpoint y?
endpoint y would be
(7,-4)
because when you graph all 3 points
(7,-4) adds nicely to the line that the other 2 make
X
-3
1
O
y =
= 2x+2
q
-2
b
2
C
व
use the table to work out!
a, b, c,d when
Y=2x+2
Answer:
y and x = 4 if wanted a dinner equation in one hand over least common multiple
is 7.69 x 24^8 in scientific notation
Reason:
The 24 needs to be changed to a 10 for it to be in scientific notation.
The template for scientific notation is [tex]a * 10^b[/tex] where [tex]0 \le |a| < 10[/tex]
So for example, [tex]1.23 \times 10^4[/tex] is in scientific notation.
10. A line passes through points (4, 18) and (6x,2k). What is the slope of the line?
8k-9
12x-4
A
B
2k-9
6x-4
C
D
k-9
3x-2
2k-9
3x-4
The slope of the line which passes through the points (4, 18) and (6x, 2k) is (k - 9)/(3x - 2).
According to the given question.
A line passes through points (4, 18) and (6x,2k).
Which means we have two points (4, 18) and (6x,2k).
As we know that, the slope of a line is the ratio of the amount that y increases as x increases some amount.And the slope formula is m=(y2-y1)/(x2-x1) if a lines passes through the point (x2, y2) and (x1, y1).
Therefore, the slope of the line which passes through the points (4, 18) and (6x,2k)
= 2k - 18/ 6x - 4
= 2[k - 9]/2[3x - 2]
= (k-9)/(3x - 2)
Hence, the slope of the line which passes through the points (4, 18) and (6x, 2k) is (k - 9)/(3x - 2).
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a game arcade consists of a balloon that is inflated little-by-little during each round of play. The player wins when the balloon pops. The amount of air that is needed to make the balloon pop can be modeled bya. uniform distribution on the interval from 25 to 35 cubic inches of air.