The two ways to generate fractions equivalent to a given fraction include:
A Multiply the numerator by a nonzero number or divide the denominator by a nonzero number.
B..Multiply or divide the numerator and denominator by the same nonzero number.
How to illustrate the fraction?It should be noted that equivalent fractions simply means the fractions that are the same when reduced to their lowest terms.
It should be noted that multiplying the numerator by a nonzero number or divide the denominator by a nonzero number as.also.doung the same for the numerator and denominator by the same nonzero number will given an equivalent fraction.
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How much will a person pay for 5.5 pounds of bananas at a price of $1.66 per pound?
...
The person pay $9.13 for 5.5 pounds of bananas .
The unit method is a method of finding the value of one unit and then finding the value of the required number of units."It's a way to get a single unit value from a multiple unit value and a multiple unit value from a single unit value." or should find a lesser value. To do this, you must first find the value of one thing by division, and then find the value of more or less by multiplication. For simplicity, we always write the computed side on the right and the known side on the left.It is given that $1.66 per pound of bananas .
1 pound of banana cost = $1.66
5.5 pounds of banana cost will be [tex]=5.5\times1.66[/tex]
[tex]=\$9.13[/tex]
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Solve. 3+(4-x)³/₂=11
Values of x are 0, 6 + ✓48i/2 and 6 - ✓48i/2.
3 + [tex]{(4 - x)}^{3/2}[/tex]= 11
Subtracting 3 on both sides of the equation, we get
3 + [tex]{(4 - x)}^{3/2}[/tex]- 3 = 11 - 3
[tex]{(4 - x)}^{3/2}[/tex] = 8
Squaring both the sides of the equation, we get
[tex] {(4 - x)^{3/2 \times 2} }[/tex] = 8²
(4 - x)³ = 64
Using the identity (a - b)³ = a³ + b³ + 3a²b - 3ab², we get
4³ + x³ + 3×4²x - 3×4×x² = 64
64 + x³ + 48x - 12x² = 64
x³ - 12x² + 48 = 0
Taking x common from the above equation, we get
x(x² - 12x + 48) = 0
x = 0 and x² - 12x + 48
Sovling the quadratic equation x² - 12x + 48, we get
x = -b+✓(b² - 4ac)/2a and -b-✓(b² - 4ac)/2a
x = -(-12)+✓((-12)² - 4(1)(48))/2(1) and -(-12)-✓((-12)² - 4(1)(48))/2(1)
x = 12+✓(144-192)/2 and 12-✓(144-192)/2
x = 12+✓-48/2 and 12-✓-48/2
x = 12+✓48i/2 and 12-✓48i/2
x = 6+✓48i/2 and 6-✓48i/2
Thus, the values of x are 0, 6+✓48i/2 and 6-✓48i/2
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Using the Change of Base Formula, what is the value of log₇15 rounded to the nearest hundredth?
The required value up to the nearest hundredth of change of base of the log function is given by1.39.
What is a logarithmic function?
A function which is the inverse of the exponential function is called a logarithmic function. It is depicted by writing a log before any number, variable or function. Log functions are strictly increasing functions in nature.
Calculation of the value of log₇15
We know that log₇15 can be written as log15 / log7, using the properties of the logarithmic function, log
Now, log₇15 = 1.1761 / 0.845
= 1.392
Hence, the required value up to the nearest hundredth is given by 1.39.
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What is the axis of symmetry of h(x) = 5x2 + 40x + 64?
x = −16
x = −4
x = 4
x = 16
Answer:
x = - 4
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 ) then the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex]
h(x) = 5x² + 40x + 64 ← is in standard form
with a = 5 , b = 40 , then axis of symmetry is
x = - [tex]\frac{40}{10}[/tex] = - 4
a regular hexagon is shown below. suppose that the hexagon is rotated counterclockwise about its center so that the vertex at O is moved to K. how many degrees does the hexagon rotate?
If the hexagon is rotated counterclockwise about its center so that the vertex at O is moved to K. The amount of degrees that the hexagon rotate is: 120°.
Hexagon rotationLet P represent the center point
First step is to calculate or to determine the central angle
Central angle=360°/6
Central angle=60°
Second step is to calculate the degree that hexagon rotate if it rotate counterclockwise about its center
Hence,
∠KPO=2×60°
∠KPO=120°
Therefore If the hexagon is rotated counterclockwise about its center so that the vertex at O is moved to K. The amount of degrees that the hexagon rotate is: 120°.
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need some help on thisss one
Answer:
in order from greatest to least, 9.7 times 10^5, 9/7, 7/9, 10^-5
Step-by-step explanation:
if you put them in a graphing calculator you'll get the answers. try desmos
Evaluate 3.5 raised to the seventh power divided by 3.5 raised to the sixth power, all raised to the second power.
1
3.5
7
12.25
The value of the expression (3.5^7/3.5^6)^2 is 12.25
How to evaluate the expression?The expression is given as
3.5 raised to the seventh power divided by 3.5 raised to the sixth power, all raised to the second power.
Rewrite properly as
(3.5^7/3.5^6)^2
Apply the law of indices
So, we have
(3.5^7/3.5^6)^2 = (3.5^7-6)^2
This gives
(3.5^7/3.5^6)^2 = (3.5)^2
Evaluate the exponent
(3.5^7/3.5^6)^2 = 12.25
Hence, the value of the expression (3.5^7/3.5^6)^2 is 12.25
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could you graph the function f(x)=5x using itercepts? explain you reasoning
Answer:
The xxx-intercept is the point where a line crosses the xxx-axis, and the yyy-intercept is the point where a line crosses the yyy-axis.
Step-by-step explanation:
Two interior decorating teams are competing in a kitchen remodel competition. their remodels are graded on the following categories, each worth 18 points; time to complete, design, and total cost. time to complete is worth 75% of their final score, design is 15%, and total cost is 10%. whoever has the largest final score wins $150,000. suppose team a received 15 points for time to complete, 9 points for design, and 14 points for total cost. suppose team b received 17 points for time to complete, 7 points for design, and 13 points for total cost. using technology, determine which team won the competition. team a won by 1.9 points. team a won by 1.1 points. team b won by 1.9 points. team b won by 1.1 points.
Answer:
team b by 1.1
Step-by-step explanation:
everything else was wrong when i did it
Find f(8)
f(x) =
7, x>3
5x − 3, x<3
Since 8>3
[tex]f(8) = 7[/tex]
Suppose that A and B are points on the number line.
If AB=9 and A lies at 7, where could B be located?
If there is more than one location, separate them with commas.
On the number line, if 'A' lies at 7 then 'B' could lie at -2, 16.
What is a number line?
A number line can be stretched in either direction indefinitely and is commonly displayed horizontally.
The numerals on the number line grow as one goes from left to right and drop as one moves from right to left.
Given, AB = 9 and 'A' lies at 7
So, basically 'B' can be at -2 on the number line which makes the distance between 'A' and 'B' 9 units. The same is possible for B at 16 on the number line.
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Determine whether the function has line symmetry.
Nope, the domain is not centered at any point, let along that this is a linear function.
DIG DEEPER A three-dimensional printing pen uses heated plastic to create three-dimensional objects. A kit comes with one 3D-printing pen and p packages of plastic. An art club purchases 6 identical kits for (180+58.5p) dollars. Write an expression that represents the cost of one kit.
Answer:
Step-by-step explanation:
mdcmmmm
Choose the correct term to complete each sentence.
The number under a radical sign is called the (index/radicand).
The number under a radical sign is called the Radicand .
Radicals : A no . of the form [tex]\sqrt[n]{x}[/tex] is called a radical , where x is the radicand and n is the index of the radical . Ex . of radicals [tex]\sqrt[3]{5}[/tex] , [tex]\sqrt{7}[/tex] , [tex]\sqrt[5]{3}[/tex] and so on .
It can be expressed in the form of rational exponent ( [tex]x^{1/n}[/tex] ) . This can be done by keeping the radicand as it is and raising the index to the power of exponent hence , it will be converted to rational exponent .
For ex . [tex]\sqrt{2}[/tex] = [tex]2^{1/2}[/tex] , [tex]\sqrt[3]{5}[/tex] = [tex]5^{1/3}[/tex] , [tex]\sqrt[5]{7}[/tex] = [tex]7^{5}[/tex] , and so on .
Hence , the number under a radical sign is called the Radicand .
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Given f(x) = 3x + 3, write a new function if the y-intercept is increased by two units.
Answer:
f(x) = 3x + 5
Step-by-step explanation:
Because if the y-intercept is increased by two units in the slope formula where b is the y-intercept, then the answer is 3x + 5.
Which table represents y as a function of x? HELP PLEASEEEE
1. Mr. Mady opens a savings account with principal P dollars that pays 2.11% interest compounded
quarterly. Express his ending balance after one year algebraically
If Mr. Mady opens a savings account with principal P dollars that pays 2.11% interest compounded quarterly. His ending balance after one year algebraically is: A = P(1 + 0.0211/4)^4.
Compound InterestGiven:
Rate= 2.11%
Now let express Mr Mady ending balance after one year algebraically by using this formula
A=P(1+r/n)^n
Where:
A = Future value
P=Principal
r= Rate
N=Number of period
Let plug in the formula
A = P(1 + 0.0411/4)^4
Therefore If Mr. Mady opens a savings account with principal P dollars that pays 2.11% interest compounded quarterly. His ending balance after one year algebraically is: A = P(1 + 0.0211/4)^4.
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Tickets to a sporting event cost $125 each. What's a reasonable domain and range.
The domain and the range of a function is the set of input and output values of the function.
The domain is the set of all whole numbers.
The range is the set of all whole numbers.
Let the number of tickets be x, and the revenue be y.
So, the revenue function will be:
y = 125
The number of tickets cannot be less than 0.
So, the domain of the revenue function is
domain=0,∞
The above means that, the domain is the set of all whole numbers
Similarly, the revenue cannot be less than 0.
So, the range of the revenue function is
range = 0,∞
The above means that, the range is also the set of all whole numbers (in multiples of 125).
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c rounded to the nearest 10 is 640.
d rounded to the nearest 10 is 420.
what are the lower and upper bounds of c + d?
The bounds of C is 635 - 644
The bounds of D is 415 - 424
The lower bounds of C + D can be found by adding 635 + 415, which is 1050
The upper bounds of C + D can be found by adding 644 + 424, which is 1068
So, the lower bounds of C + D is 1050 and the upper bounds is 1068
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
The upper bound is 1068 and the lower bound is 1050
What is the upper bound and lower bound of a number?The lower bound is the smallest value that would round up to the estimated value. The upper bound is the smallest value that would round up to the next estimated value.
Given here, c rounded to the nearest 10 is 640 and d rounded to the nearest 10 is 420. Then we have the minimum and maximum value as
Min C = 635 and Max C = 644 & Min D=415 and Max D = 424
Therefore the upper bound for c+d = 644+424
= 1068
And the lower bound for c+d = 635+415
=1050
Hence The upper bound is 1068 and the lower bound is 1050
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Estimate the mean lifetime of a bulb.
Give your answer rounded to 2 DP
?hours
The mean lifetime of a bulb is 31. 57
What is mean?Mean can be defined as the average of a given set of values or elements.
The formula for the mean of a given set of values is expressed as;
Mean = sum of the occurrence of the values/ number of values
Or
Mean = sum of terms/number of terms
From the information given, the frequency of the lifetime of the bulbs were given as;
34, 31, 94, 40 , 0 , 17, 5
The sum of the terms is given as:
= 34 + 31 + 94 + 40 + 0 + 17 + 5
= 221
The number of terms = 7
Substitute into the formula
Mean = 221/ 7
Mean = 31. 571
In 2 decimal place
Mean = 31. 57
Thus, the mean lifetime of a bulb is 31. 57
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4x-5=7+4y solve for y.
Answer:
y=x-3
Step-by-step explanation:
4x-5=7+4y
Subtract 7 from both sides.
4x-12=4y
Divide 4 from both sides.
x-3=y
y equals x minus 3.
y=x-3
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Given: angle COB=3x+16 and angle AOD=5x-42
Prove: x=29
Answer:
if your asking how to get 29 then here is how
Step-by-step explanation:
Evaluate
3x+16=5x−42
Move the variable to the left side
3x+16−5x=−42
Subtract the terms
−2x+16=−42
Move the constant to the right side
−2x=−42−16
Subtract the terms
−2x=−58
Divide both sides
2x divided by -2
-58 divided by 2
Solution
x=29
1 Find the value of 5 x
(a) 500
(b) 50
(c) 5000
(d) 5
2 Find the product of 3.6 x 100
(a) 36
(b) 360
(c) 0.36
(d) 0.0036
3 The additive inverse of is ------------
(a) -1
(b)
(c) -5
(d) 1
4 Find the mode of the data 4, 3, 5, 11, 4, 7, 5, 4, 3
(a) 4
(b) 3
(c) 5
(d) 7
5 Write the base of
(a) p
(b) 10
(c) 1
(d) 0
6 Find the value of
(a) 2
(b) 6
(c) 3
7 Write the value of 5
(a) 3
(b) 0
(c) 1
(d) 15
8 Find the value of
(a) 100000
(b) 10000
(c) 100
(d) 10
9 Find the range of the following observations 48, 62, 78, 12, 96, 34, 25
(a) 84
(b) 78
(c) 80
(d) 69
10 ------- is the multiplicative inverse of 60
(a) 60,
(b) -60
(c) 1
11 The value of (
(a) -1
(b) 1
(c) 8
(d) -8
12 3.45 × -1000 is-------------
(a) -3450
(b) -345
(c) 0
(d) 3450
13 Number of edges of the cylinder is ----------------
(a) 8
(b) 6
(c) 2
(d) 4
14 Number of faces in a cube is -------------
(a) 12
(b) 8
(c) 6
(d) 10
SECTION – B
II. Solve the problems ( 11 x 2 = 22 )
15 Write four rational numbers equivalent to
16 Find the value of the following
3365 x 164 – 2365 x 164
17 Evaluate of 105
18 Divide the following
(a) 168.96 8
(b) 505 ÷ 100
19 Express 15625 as a power of 5
20 Multiply the following
(a) 4.9 x 0.005
(b) 0.0016 x 625
21 Find the value of
22 Find the mean of the data 3.2, 4.8, 18.9, 7.8, 10.3
23 The median weight of the data set 16, 5, 11, 19, x, 4 is 9 . Find the value of
24 The distance between the sun and the Jupiter is 778,500,000,000 m . Express it in standard form.
25 A rectangular garden has an area of 25.3 and a width of 4.4 m . What is the length of the garden.
SECTION C
III. Solve the problem with proper steps ( 8 X 3 = 24)
26 Arrange the rational numbers in descending order
, , , and
27 The mean of 8numbers is 27. Find the sum of these 10 numbers.
28 Find 10 rational numbers between -2 and -3
29 Simplify and express in the exponential form using laws of exponents.
30 Represent on a number line
31 A rectangular garden has a length m and a width of m . What is the perimeter of the garden ?
32 Find the value of
33 Find value using properties
(19 × 5) + (19 × 21)
SECTION - D
IV. Solve the problems with proper steps ( 5 X 4 = 20 )
34 From a ribbon of length 7 m , Shreya used 4 m of ribbon . How much ribbon is left ?
35 The product of two numbers is 173.502. If one of them is 18.9, then find the other number ?
36 Express each of the following as a product of powers of prime numbers
(a) 1296
(b) 625
37 The scores that two gymnastic and Josh obtained in six events of parallel bars were as follows
Asif : 8.1, 9.6, 9.2 , 7.5, 9.4, 9.0,
Josh : 9.3, 9.5, 8.0, 9.1, 7.8, 8.5
(a) Find the mean score of Asif
(b) Find the mean score of Josh
(c) Whose performance was better.
38 The table shows the favourite pets of 40 children in a class . Draw Bar graph for this data.
PETS DOG CAT RABBIT FISH
NUMBER OF
CHILDREN
14 8 10 8
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The solution to all parts is shown below.
What is Mean of data?Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.
1. The value of 5 in 2875 is 5.
2. The product is 360
3. Additive inverse is -1
4. Mode = 4
9. Range = 96 - 12 = 84
10. 1/60
12. -3.45 x -1000 = 3450
13. Number of edges of the cylinder is 2.
14. Faces = 6
16. 3365 x 164 – 2365 x 164
= 164( 3365 - 2365)
= 1640
17. (a) 168.96 /8 = 21.12
(b) 505 ÷ 100 = 50.5
18. 15625 = [tex]5^6[/tex]
19. Mean = 45/5= 9
21. 778,500,000,000 m = 7.7785 x [tex]10^{11[/tex] m
22. length of the garden = 25.3 / 4.4 = 5.75 m
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Simplify each expression.
ln e³
ln e³ = 3, by definition and properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
As seen by the definition of logarithms, [tex]log_b(a)=x[/tex]
In case of natural logarithm, b = e, i.e., [tex]log_e(a)[/tex] = ln (a) = x
In the question, ln (e)³, a = e
By property of logarithms, [tex]log_b(a^m) = m(log_b(a))[/tex] ,
=> 3 (ln (e)) = 3 [tex]log_e(e)[/tex]
Since, [tex]log_e(e)[/tex] = 1, ln (e)³ = 3 (1) = 3.
Hence, ln e³ = 3, by definition and properties of logarithm.
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Use the Change of Base Formula. What is the value of each expression?
b. log₄18
The value of the given expression that is log₄ 18 = 2.084
A logarithm operation can be rewritten as a fraction of logarithms with a new base using the change of base formula.
Example: logₐ b = (logₓ b) / logₓ a)
Therefore, log₄ 18 = (log₁₀ 18) / (log₁₀ 4).....eq(i)
We know, log₁₀ 4 = 0.602
We can write log₁₀ 18 as log₁₀(2x9).
Using the product rule of logarithms, log₁₀ 18 = log₁₀2 + log₁₀9log₁₀ 18 = 0.301 + 0.954log₁₀ 18 = 1.255
Substituting the value of log₁₀ 18 = 1.255 in eq(i) we get,
log₄ 18 = 1.255/0.602log₄ 18 = 2.084
The final answer to the question is log₄18 = 2.084 using the change of base formula.
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After making several scale drawings,Joseph decides on the best placement for a new grill on his desks.He uses a scale of 2 cm for every 5 in. what is the actual area of the space for Joseph's new grill in square inches?
The actual area of the space for Joseph's new grill in square inches is 1280cm².
How to calculate the value?It should be noted that Joseph uses a scale of 2 cm for every 5 inches.
It should be noted that the drawing is 80inches by 100 inches.. Therefore, the original shape will be:
= 80 × 2/5 = 32
= 100 × 2/5 = 40
Therefore, the area will be:
= Length × Width
= 32 × 40
= 1280cm².
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Jospwh has a drawing of 80 inches by 10 inches. After making several scale drawings,Joseph decides on the best placement for a new grill on his desks.He uses a scale of 2 cm for every 5 in. what is the actual area of the space for Joseph's new grill in square inches?
The value of the perimeter of the figure is equal to the value of the area. Find the value of X.
The value of x if the value of the perimeter of the figure is equal to the value of the area is 1.5
Area and perimeter of rectangleLength of the rectangle = 6 inWidth of the rectangle = 2x inArea of rectangle = perimeter of rectangle
Length × width = 2(length + width)
6 × 2x = 2(6 + 2x)
12x = 12 + 4x
collect like terms12x - 4x = 12
8x = 12
divide both sides by 8x = 12 / 8
x = 1.5
So,
Width of the rectangle = 2x in
= 2(1.5)
= 3 in
Therefore, the length and width of the given rectangle is 6 in and 3 in respectively
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A scale model of a bus is 12 inches long. The scale is 1:21. How many inches long is
the bus it represents?
According to the scale model, the bus has a real length of 252 inches (21 feet).
How to use scales to estimate the real length of a bus
Scales are ratio between two lengths, scales are an useful resource to represent systems in affordable dimensions (i.e. The Empire State Building in a piece of paper). In this case, scales are defined by the following formula:
r = l' / l
Where:
r - Scale factorl' - Reduced length, in inches.l - Real length, in inches.If we know that r = 1 / 21 and l' = 12 in, then the real length of the bus is:
l = l' / r
l = 12 in / (1 / 21)
l = 252 in
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Find the coordinates of the triangle after the transformations. Translate the triangle 1 unit right and 5 units down. Then reflect the triangle in the y-axis.
The coordinates of the sequence of transformations is R' (3, -4), S' (3, -1) and T' (1, -4)
How to determine the image of the transformation?The complete question is added as an attachment
The coordinates of the triangle are given as
R = (-4, 1)
S = (-4, 4)
T = (-2, 1)
The sequence of transformations is given as
Translate the triangle 1 unit right and 5 units down. Reflect the triangle in the y-axis.The rules of the above sequence of transformations are
Translate the triangle 1 unit right and 5 units down: (x + 1, y - 5)Reflect the triangle in the y-axis: (-x, y)When the above transformations are combined, we have
(x, y) = (-x - 1, y - 5)
So, we have
R' = (4 - 1, 1 - 5) = (3, -4)
S' = (4 - 1, 4 - 5) = (3, -1)
T = (2 - 1, 1 - 5) = (1, -4)
Hence, the image of the sequence of transformations is R' (3, -4), S' (3, -1) and T' (1, -4)
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A week before an election 1,5000 people were asked who they planned to vote for. Of the people asked 45% said they planned to vote for candidate x and 38% said they planned to vote for candidate y the rest said they had not decided yet how many of the people that were asked have not yet decided who they plan to vote for?
Answer:
2 550
Step-by-step explanation:
Total no. of people who already have a decision, as a % = 45%+38% = 83%
No. of people who haven't decided yet, as a % = 100% - 83% = 17%
No. of people who haven't decided = 15 000 x 17/100 = 2 550