The given expression written in the simplest radical form is 3√5
Writing an expression in radical formFrom the question, we are to write the given expression in the simplest radical form
The given expression is 45^(1/2)
From one of the laws of indices, we have that
[tex]x^{y/n} = \sqrt[n]{x^{y} }[/tex]
Thus,
Applying this rule, the given expression can be written as
√45
Now, we will express the given radical expression in the simplest radical form
Expressing in simplest radical form
√45
= √(9 × 5)
= √9 × √5
= 3 × √5
= 3√5
Hence, the given expression written in the simplest radical form is 3√5
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2. Amirah, Huixian and Priya make a total of 1530 toys in the ratio 12: 16:17.
(ii) the amount of money Priya earns if she is paid $1.65 for each toy.
Answer:
$953.70
Step-by-step explanation:
sum the parts of the ratio, 12 + 16 + 17 = 45 parts
divide the total number of toys by 45 to find the value of one part of the ratio.
1530 ÷ 45 = 34 , then
Priya makes 17 × 34 = 578 toys
she is paid $1.65 per toy, so is paid
578 × $1.65 = $953.70
An archer aims at a target that is 122 centimeters in diameter with 10 concentric circles whose diameters decrease by 12.2 centimeters as they get closer to the center. Find the probability that the archer will hit the center.
The probability that the archer will hit the center which is 122 centimeters in diameter with 10 concentric circles whose diameters decrease by 12.2 centimeters as they get closer to the center is 1/100.
As given in the question,
Total number of concentric circle=10
Outer circle diameter=122centimeters
Diameter decrease by 12.2 centimeters as they get closer to the center
Diameter of inner most circle= 122-9(12.2)
= 12.2centimeter
Probability that archer hit the center
= (Area of inner most circle)/ (Area of target)
= π(6.1)²/π(61)²
= {π(61)²/π(61)²}× 1/100
= 1/100
Therefore, probability that the archer will hit the center is 1/100.
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Sita walks from her house 160 meters north and from there 630 meters west to visit her friend. While comin back, she walked diagonally from her friend's house back to her home. What distance did she walk while coming back?
Answer:
650 meters
Step-by-step explanation:
Use the pythagorean theorem.
a²+b²=c²2
160²+630²=c²
c²=422500
√422500 = 650
Please help if you can
sustitucion de 18-3x=9
Answer: x=+9
Step-by-step explanation:
18=3x-9 18-(3x-9)=0 3x+9+18=0 -3x+27=0
-3x=-27
x=-27/-3
x=+9
Hope this helps! :) Have a great day! ^-^
Answer:
x=3
Step-by-step explanation:
18-3x=9
-18 -18 Subtract 18 from both sides of the equation to leave 3x by itself.
3x=9
/ /
3 3 Divide both sides by 3 to isolate x.
x=3 Final answer.
Solve for the value of t.
Answer: t =
(2t-4)
(5t+2)°
Submit Answer
Answer:
Step-by-step explanation:
If you are to check carefully you will find that the two angles are lying on a straight line of which is 180°
mathematically
[tex](2t-4)+(5t+2)=180\\2t+5t-4+2=180\\7t-2=180\\7t=180+2\\7t=182\\\frac{7t}{7} =\frac{182}{7} \\t=26[/tex]
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
r = 11 2/5ft, d=?, C =?
A circle is a curve sketched out by a point moving in a plane. The radius, diameter, and circumference of the circle are 11.4 ft, 22.8 ft, and 71.6283 ft, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that radius of the circle is 11 2/5 ft. Therefore, the radius of the circle in a simplified way can be written as,
The radius of the circle = 11 2/5 ft
= (11×5 + 2)/5 ft
= (55 + 2)/5 ft
= 57/5 ft
Now, the diameter and the circumference of the circle can be written as,
Diameter of circle = 2 × (Radius of the circle)
= 2 × 57/5 ft
= 114/5 ft
Circumference of circle = 2 × π × (Radius of the circle)
= 2 × π × 57/5 ft
= (114/5)π ft
Hence, the radius, diameter, and circumference of the circle are 57/5 ft, 114/5 ft, and (114/5)π ft, respectively.
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deas from earlier grades
5.
On a recent test, Mark got 6 questions out of 40
wrong. Which answer best describes the percent of
questions he got correct?
a. Less than 50%
b. More than 50%
c. Less than 25%
d. More than 75%
Explain or support your choice:
Answer:
D (he got 85% right which is more than 75%)
Step-by-step explanation:
because if you half 6/40 you get 3/20, now if you x by 5 you get 100 so do the same to the top (3x5 = 15)
Now you know that he got 15/100 = 15% wrong
so if you do 100 - 15 you get 85, so he got 85% right
85% is greater than 75% so therefore it is option D
hope this helps :)
PLEASE HELP!
Order the cube root of 51, four and two thirds, negative pi, and negative 17 over 5 from greatest to least.
four and two thirds, cubed root of 51, negative pi, and negative 17 over 5
four and two thirds, cubed root of 51, negative 17 over 5, and negative pi
cubed root of 51, negative pi, negative 17 over 5, and four and two thirds
cubed root of 51, four and two thirds, negative pi, and negative 17 over 5
The ordering of the rational and irrational numbers from greatest to least is given by:
4 and 2/3, cube root of 51, -π, -17/5.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.To order numbers on the number line, we have that:
For negative numbers, the smaller the integer part is, the greater is the number, for example -2 > -3.For positive numbers, the greater the integer part is, the greater is the number, for example 3 > 2.If the integer parts are equal, we look at the decimal part, following the same logic as above.
For this problem, the numbers are given as follows:
Cube root of 51 = 3.71.4 and 2/3 = 4.67.-π = -3.11415...-17/5 = -3.4.Hence the ordering of the rational and irrational numbers from greatest to least is given by:
4 and 2/3, cube root of 51, -π, -17/5.
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1.1 building blocks of geometry
Step-by-step explanation:
1. S
since PS = SQ, S must be exactly in the middle.
2. NQ = 3×PS = 3×3 = 9 cm
we see, NP = PS = SQ. so, NQ = NP + PS + SQ = e.q. 3×PS
3.
not sure what your teacher means.
line segment
line
NPS (as alternative to just NS)
4.
S is an endpoint of SQ.
5.
P is the midpoint of NS.
6.
NS is congruent to PQ.
7.
similar to 3.
line segment
line
SPN (as alternative to just SN)
Each statement :
1) 'S' is the midpoint of PQ.
2) NQ is 9cm long
3) Another name of NS is the line segment NS.
4) S is an endpoint of SQ.
5) P is the midpoint of NS.
6) NS is congruent to PQ
7) Another name of NS is the line segment NS.
Given, that line segment PS is 3cm long .
1.
'S' is the midpoint of PQ.
since PS = SQ, S must be exactly in the middle.
2.
NP = PS = SQ.
So, NQ = NP + PS + SQ
= 3 × PS
NQ = 3×PS
= 3×3
= 9 cm
Thus NQ is 9cm long .
3.
Another name of NS is the line segment NS.
P is the midpoint of NS.
So, NP = PS
4.
Line segment is starting from point S.
S is an endpoint of SQ.
5.
P is the midpoint of NS.
So, NP = PS
6.
In line segment NS,
NP = PS
In line segment PQ,
PS = SQ
NS is congruent to PQ.
7.
Another name of NS is the line segment NS.
P is the midpoint of NS.
So, NP = PS
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Evaluate each series to the given term. 2+4+6+8+ . . . . . . ; 10 th term
Finding the value of any term in a given sequence is known as an arithmetic sequence if each term in the sequence is equidistant from the terms before and after. To find any term in a sequence, we first have to find the pattern of the sequence. Then we can multiply the distance between any two terms by one less than the number of terms we are looking for. Adding this to the first term gives you the term you want.
Here the first term a=2,
Common difference d=4-2=2
We know that,
f(n)=a+(n-1) d
f (10) =2+(10-1) (2)
=2+(18)
=20
We know that,
Sn=n2[2a+(n-1) d]
∴S10=102⋅ [2(2) +(10-1) (2)]
=5⋅ [4+(18)]
=5⋅ [22]
=110
Hence, the 10th term of the given series is 20, and the sum of the first 10th term is 110.
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Solve each equation for y .
(3/4)y=15 x
After solving the equation, y = 20x is the value of y in (3/4)y=15 x
⇒ (3/4)y=15 x
⇒ y = 15x/(3/4)
⇒ y = 20x
How to solve an equation?To solve Linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Why is the slope of a vertical line undefined.
The slope of a line can be positive, negative, zero, or undefined. The horizontal line does not rise vertically (y1 − y2 = 0), so the slope is zero, but the vertical line does not extend horizontally (that is, x1 − x2 = 0), so the slope is undefined. As mentioned above, the horizontal line has zero slopes. This does not mean that the horizon has no slope. Since the horizontal line is m=0, it is represented symbolically by the expression y=b. Functions defined by horizontal lines are often called constant functions. The slope of the vertical line is undefined. Any two points on the vertical line have the same x-coordinate, so the gradient cannot be computed as a finite number according to the equation
M=(y2-y1)/(x2-x1)
This is because division by zero is an undefined operation.
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The age of a woman is four times the age of her daughter. Five years h:t 1ce, the age of the woman wili be three times the age of her daughter. What is the present age of the daughter
The present age of the daughter is 10 years old.
How to find the age of the daughter?The age of a woman is four times the age of her daughter.
let
x = age of the daughter
Therefore,
age of the woman = 4x
Five years later, the age of the woman will be three times the age of her daughter.
Therefore,
4x + 5 = 3(x + 5)
4x + 5 = 3x + 15
4x - 3x = 15 - 5
x = 10
Therefore, the present age of the daughter is 10 years old.
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Solve for the value of a
IM CURRENTLY BOUNCING BETWEEN ASSIGNMENTS AND I COULD REALLY USE THE HELP (PLEASE SEE THE ATTACHMENT)
Using linear function concepts, it is found that since the two lines have the same slope, they are parallel.
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.When two lines are parallel, they have the same slope.
The first road goes through points (0, 16) and (20,0), hence the slope is:
m = (0 - 16)/(20 - 0) = -0.8.
The second road goes through points (0,8) and (10,0), hence the slope is:
m = (0 - 8)/(10 - 0) = -0.8.
Since the two lines have the same slope, they are parallel.
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need help with a short word problem please!!!
Answer:
5
Step-by-step explanation:
You add 5.49 until it almost goes past 30
Then count how many times you added
I hope this helps!
write this ratio in the simplest frorm 6 to 21
Answer: 2 to 7
Step-by-step explanation:
divide both by three, it's the greatest common factor
1: Simplify:
-5+8-7
Answer:
Step-by-step explanation:
=(-5+8)-7=3-7=-4=-4
Step-by-step explanation:
-5(+8-7)
= -5+1
= -4
I hope this answers helps you a lot
3-4 The prime factorizations of 30 and 42 are shown. (D) 30 = 2 × 3 × 5 42 = 2 × 3 × 7 Which product is the greatest common factor of 30 and 42? A. 2 × 3 × 5×7 C. 5 × 7 TOSHIBA B. 2×2×3×3×5×7 D. 2 × 3
Answer:
D. 2 × 3
Step-by-step explanation:
Let's take the prime factorization of 30 and 42
30: 2*15=2*3*5
42: 2*21=2*3*7
Notice any common factors?
GCF: 2*3=6
GCF: 6
4. A conveyor belt moves at a constant rate
of 12 feet in 3 seconds. A second conveyor
belt moves 16 feet in 4 seconds. guys help !!!!
Solution :
Yes, the conveyors are in a proportional relationship.
Given,
A conveyor belt moves at a constant rate of 12 feet in 3 seconds.
A second conveyor belt moves 16 feet in 4 seconds.
There is a proportional relationship if the ratios of each pair of values are the same.
- First conveyor belt
12 feet in 3 seconds.
Ratio = 12 / 3 = 4
- Second conveyor belt
16 feet in 4 seconds.
Ratio = 16 / 4 = 4
Ratios are the same.
4 = 4
Thus the conveyors are in a proportional relationship.
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find the square root of 63.34 upto 2 decimals
The square root of 63.34 IS 7.95
The square root of decimal places can be found using long division method
The solution of this question in written form is attached so do check it out
first step is to find out the number whose square root is close but less than the given number as 7 in this case
second step add the divisor and the answer that is 7+ 7and make it our new divisor
Third step after carrying down the next pair of number write the number on once place that is 14_ which is 9 in our case and keep following the same steps unit the desired answer
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Question 15 of 25
Find the range of the graphed function.
0<y<8
given,
The y axis has a plot as low as 0.
soo it would be 0.
Then, the highest plot is marked as high as 8.
Therefore its 0<y<8.
a diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables
Types of Graphs and Charts;
Bar Chart/Graph.
Pie Chart.
Line Graph or Chart.
Histogram Chart.
Area Chart.
Dot Graph or Plot.
Scatter Plot.
Bubble Chart.
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The range of the graphical function is: 0<y<8
The graph of a function f is the set of ordered pairs, where {f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
Given that
The y axis has a plot as low as 0.
Soo it would be 0.
Then, the highest plot is marked as high as 8.
Therefore its 0<y<8.
Types of Graphs and Charts;
Bar Chart/Graph, Pie Chart, Line Graph or Chart, Histogram Chart, Area Chart, Dot Graph or Plot, Scatter Plot., Bubble Chart.
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5b = .1
solve the equation
b = 0.02
divide both side by 5
Answer:
I think that B equals 0.02
The difference between the product of eight and 47 the quotient of seven and five
Answer:
268.571429
Step-by-step explanation:
Evaluate each expression. Determine if the final simplified form of the expression is positive or negative.
HELP PLEASE!!
The values of the square numbers are:
a. -16
b. 16
c. 16
How to evaluate the valuesFrom the information given, we have the following expressions;
-4²(-4)²4²Let's write the squares in simpler form
-4² = - (4 × 4)
This is so because the square was only assigned to 4 and not the negative sign
(-4)² = - 4 × - 4
This is so because the square was assigned to both the negative sign and 4
4² = 4 × 4
This is so because the square was assigned to 4
Now, we have
- (4 × 4) = -16
- 4 × - 4 = 16
4 × 4 = 16
Thus, the values are - 16, 16 and 16 respectively.
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Determine the slope of the line that contains the given points.
C(3,1), D(-2,1)
The slope of the line containing (3,1) and (-2,1) is Zero(0).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = 1 , [tex]y_{1}[/tex] = 1 , [tex]x_{2}[/tex] = -2 , and [tex]x_{1}[/tex] = 3 .
On substituting the values of variables in equation1, we will get
m = ( (1)-(1) ) / ( (-2)-(3) ) = (0/(-5)) = 0.
As the slope of a line is Zero(0), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (7,-3) and (-8,-3) is Zero(0).
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rewrite each fraction
A. 5/20
B. 9/25
C. 6/7 - 2/5
This can be represented by the equation y = 30(0.92)d, where y is the number of phone calls after d days. how many phone calls should she expect after a week?
From the given equation y = 30(0.92)d, she should expect 193 phone calls after a week.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "="..
If the number of phone calls she should expect can be represented by the equation y = 30(0.92)d, where y is the number of phone calls after d days, then we can calculate the expected amount phone calls after a week.
To determine how much phone calls she should expect after a week, substitute the value of d.
y = 30(0.92)d
where d = 1 week = 7 days
y = 30(0.92)(7)
y = 193.2
Rounding off to the nearest whole number,
y = 193
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Each sequence has eight terms. Evaluate each related series. 1,-1,-3, . . . . . . -13
The sum of the 8 terms of the series 1-1-3-5- ... -13 is -48
The given sequence is:
1,-1,-3, . . -13
and there are 8 terms.
The related series of this sequence is:
1-1-3-5- ... -13
Notice that the series is an arithmetic series with:
first term, a(1) = 1
common difference, d = -1 - (1) = -2
last term, a(8) = -13
To find the sum of the series, use the sum formula:
S(n) = n/2 [(a(1) + a(n)]
Substitute n = 8, a(1) = 1, a(n) = a(8) = -13 into the formula:
S(8) = 8/2 [1 + (-13)]
S(9) = 4 . (-12) = -48
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