The equivalent expression for −12(8a − 7b) + 8(4x + 3y) is represented as - 96a + 84b + 32x + 24y
How to solve equivalent expression?Two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) can be solved as follows:
−12(8a − 7b) + 8(4x + 3y)
open the bracket
−12(8a − 7b) + 8(4x + 3y)
- 96a + 84b + 32x + 24y
Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) is - 96a + 84b + 32x + 24y
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write the equation of the line in point-slope form, that is parallel to y=5/2x + 1 and passes through the point (-3,1)
Answer:
[tex]\sf y = \dfrac{5}{2}x +\dfrac{17}{2}[/tex]
Step-by-step explanation:
[tex]\sf y =\dfrac{5}{2}x+1[/tex]
m= 5/2
Parallel lines have same slope.
Slope y-intercept form: y = mx +b
Here, m is the slope and b is the y-intercept
[tex]\sf y = \dfrac{5}{2}x + b[/tex]
Point (-3,1) passes through the required line. Substitute (-3,1) in the above equation and find 'b'.
[tex]\sf 1 = \dfrac{5}{2}*(-3)+b\\\\1 =\dfrac{-15}{2}+b\\\\[/tex]
[tex]\sf 1 +\dfrac{15}{2}=b\\\\\dfrac{2+15}{2}=b\\\\\\ \boxed{b= \dfrac{17}{2}}[/tex]
[tex]\sf \bf y = \dfrac{5}{2}x+\dfrac{17}{2}[/tex]
if the semi annual compound interest on rupees 8000 for 3/2 years is rupees 2648, what is the simple interest of the sum at the same rate and time?
The simple interest of the sum at the same rate and time is 2400
What is compound interest ?The interest that is paid on the principal and interest at regular intervals is known as compound interest.The difference between compound interest and simple interest starts to show after the first year, though.Beginning with the second year, interest is computed on both the principal amount and the interest from the prior year. As a result, interest on interest is another name for it.
Given that : Sum =8000 and time = [tex]\frac{3}{2} years[/tex] and rate is 20 %
When rate is calculate half yearly
R becomes [tex]\frac{R}{2}[/tex]
T becomes 2T
A = [tex]P(1+\frac{R}{100} )^{T}[/tex]
C.I = A-P
R = [tex]\frac{20}{2} = 10%[/tex]%
T = 2× [tex]\frac{3}{2} years[/tex] = 3years
A = [tex]P(1+\frac{R}{100} )^{T}[/tex]
A = 8000[tex]\frac{11}{10} ^{3}[/tex]
A = 8 ×1331
A = 10648
Now ,
C.I = A - P
C.I =10648 - 8000
C.I = 2468
The compound interest is 2468
Simple interest
A = P(1+rt)
A = 8000(1+0.2×1.5)
A =10400
S.I =A- P
= 10400 - 8000
=2400
The simple interest of the sum at the same rate and time is 2400
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the amount of sales tax paid on a purchase is proportional to the price of the item. suppose the sales tax rate is 6.25%. if p is the price of the item and t is the sales tax, which equation represents this?
The equation which represents the amount is p = 0.0625 t.
When a consumer buys a good or service from a retailer, sales tax, which is estimated as a percentage, is added to the cost of the item.
Sales tax rate = sales tax percent / 100.
Sales tax = list price * sales tax rate.
Total price including tax = list price + sales tax,
Total price including tax = list price + (list price * sales tax rate),
Total price including tax = list price * ( 1 + sales tax rate)
We have been given
sales tax rate = 6.25%.
The price of the item = p
The sales tax = t
We know that the amount of sales tax paid on a purchase is proportional to the price of the item.
p = 6.25% t
p = 6.25/100 t
p = 0.0625 t.
Hence , P = 0.0625 t is the equation used to represent the amount.
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Complete the table with ordered pairs that give coordinates of points that lie on the line shown in the graph
Which angle is an acute angle?
Answer:
<CPB
Step-by-step explanation:
Because <APE= right angle
<APC= Obtuse angle
<CPE= Obtuse Angle.
Also, <CPB because its the only angle below 90 degrees and an acute angle must be below 90 degrees.
how do I find the correct answer for the blank?
graph the linear equation 2x-4y=0
A graph of the linear equation (2x - 4y = 0) is shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
Generally speaking, the graph of any proportional relationship such as a linear equation is characterized by a straight line because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously as shown in the image attached below.
In conclusion, a graph which represents the linear equation (2x - 4y = 0) shows a proportional relationship between the value of x and y.
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omg im so sorry but i need help again guys:(
The expression for the side length of the bulletin board is √n (option B).
What is the expression for the side length?A square is an object with four sides that are of equal length. The sum of angles in a square is 360 degrees. A square has two diagonals that are of equal length that bisect each other at a right angle.
The area of a square can be determined by calculating the square of a side length.
The area of a square = length x length
= length²
If the area of a square is given, to determine its side length, find the square root of the area.
Length of a side = √area
√n
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the following question
Answer:
angle ODC=30°
Step-by-step explanation:
Parallel to the line now draw another line PQ
If I have £450 and I’m going away to India and currency conversion is £1=99.40 how much would I have
Answer:
Step-by-step explanation:
450 * 99.40 = 44730
what percent of 30 is 36
Answer:
10.8
Step-by-step explanation:
30% of 36
= 30/100 * 36
= 3/10 * 36
= 108/10
= 54/5
= 10.8
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a poker hand consists of five cards randomly dealt from a standard deck of 52 cards. the order of the cards does not matter. determine the following probabilities for a 5-card poker hand. write your answers in percent form, rounded to 4 decimal places.
The probabilities listed here, in percent form and rounded to the fourth decimal place, are 29.9474 for a 5-card poker hand.
How do probabilities work?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
According to given information;
C(4,3)C(48,2)/C(52,5) - 3 of 4 aces, 2 of 48 non-aces 0.1736%
C(13,5)/C(52,5) - 5 of 13 spades 0.0495%
There are 4 face cards, ace, king, queen, jack, and 4 suits for each. 16 face cards, and 36 non-face cards - C(16,3)C(36,2)/C(52,5) 13.5747%
There are 44 cards that are not aces or kings - C(4,2)C(4,2)C(44,1)/C(52,5) 0.0609%
There is 1 jack and 48 non-jacks C(4,1)C(48,4)/C(52,5) = 29.9474%.
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5.36 mixed number simplest form
To write a given number 5.36 in the mixed number is [tex]5\frac{36}{100}[/tex] and in the simplest form it is written as 134 / 25 .
As given in the question,
Given number in decimal form is equal to 5.36
5 is the whole number and 0.36 can be written as 36 /100.
Mixed number of the given number 5.36 is equal to
= 5 ( 36 / 100)
Reduced the mixed number to get the simplest form :
5 ( 36 / 100)
= 5 ( 9 / 25)
= 134 / 25
Therefore, to write a given number 5.36 in the mixed number is [tex]5\frac{36}{100}[/tex] and in the simplest form it is written as 134 / 25 .
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Use the parabola tool to graph the quadratic function f (X) =x2 - 12x +27
Answer:
Step-by-step explanation:
[tex]f(x)=x^2-12x^2+27\\f(x)=x^2-2(x)(6)+6^2-6^2+27\\f(x)=x^2-2(x)(6)+6^2-36+27\\f(x)=(x-6)^2-9[/tex]
This is the graph of the function f(x)=x² shifted right about the x-axis
by 6 units and dropped down about the y-axis by 9 units
an airline has 30 airplanes in los angeles (la), 12 airplanes in st. louis (sl), and 8 airplanes in dallas (d). during an eight-hour period, 20% of the planes in la fly to sl and 10% fly to d. of the planes in sl, 25% fly to la and 50% fly to d. of the planes in d, 12.5% fly to la and 50% fly to sl. how many planes are in each city after 8 hours?
Using proportions, the number of planes in each city after 8 hours is given as follows:
Los Angeles: 25.St. Louis: 13.Dallas: 12.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division, with the given ratios.
One example of application of proportions is for percentage problems, as the total amounts are multiplied by the decimal equivalent of the percentage to find the equivalent amounts.
The planes in Los Angeles after 8 hours are given as follows:
70% of 30 (that were already in Los Angeles).25% of 12(planes that were in St. Louis).12.5% of 8(planes that were in Dallas).Hence the amount is:
0.7 x 30 + 0.25 x 12 + 0.125 x 8 = 25.
The planes in St. Louis after 8 hours are given as follows:
20% of 30 (planes that were in Los Angeles).25% of 12(planes that were already in St. Louis).50% of 8(planes that were in Dallas).Hence the amount is:
0.2 x 30 + 0.25 x 12 + 0.5 x 8 = 13.
Initially, there were 50 planes, and 25 + 13 = 38 are in either Los Angeles or St. Louis, hence the remaining 50 - 38 = 12 are in Dallas.
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Multiply. 1. (5.2x)(1.9x)
Answer:
9.88x
Step-by-step explanation:
multiply both numbers together
Use the tangent identity to
find tan x.
sin x =
44
45
tan x =
COS X =
[?]√]
√89
4
Answer:
[tex]tan(x)=\frac{44\sqrt{89}}{89}[/tex]
Step-by-step explanation:
tan is defined as: [tex]tan(x)=\frac{opposite}{adjacent}[/tex]
sin is defined as: [tex]sin(x)=\frac{opposite}{hypotenuse}[/tex]
cos is defined as: [tex]cos(x)=\frac{adjacent}{hypotenuse}[/tex]
We can also define tan as: [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
because plugging in the definitions of sin and cos in we get: [tex]tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}[/tex]
which you'll notice is the original definition of tan(x)
So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)
[tex]sin(x)=\frac{44}{45}\\\\cos(x)=\frac{\sqrt{89}}{45}\\\\tan(x)=\frac{sin(x)}{cos(x)}[/tex]
plugging in sin(x) and cos(x) we get:
[tex]tan(x)=\frac{\frac{44}{45}}{\frac{\sqrt{89}}{45}}\\\\tan(x)=\frac{44}{45}*\frac{45}{\sqrt{89}}\\\\tan(x)=\frac{44}{\sqrt{89}}[/tex]
We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.
We can do this by multiplying the fraction by: [tex]\frac{\sqrt{89}}{\sqrt{89}}[/tex] which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator
[tex]tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}[/tex]
The Distributive Property Determine if the given expressions are equivalent
1. 3x + 12 and 3( 4 + x ) 2. 2( 3x - 30 ) and 6 - 30 3. 4 ( 5 - 4x ) and 20x - 16
The given expressions have been evaluated to be equivalent or not equivalent as follows:
3(4 + x) and 3x + 12: Equivalent.2(3x - 30) and 6 - 30: Not equivalent.4(5 - 4x) and 20x - 16: Not equivalent.What is the distribution property?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a specific number, the same output (result) would be produced as when each addend is multiplied respectively by the number, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
a(b + c) = ab + ac.
Next, we would determine whether or not the given expressions are equivalent:
3x + 12 and 3(4 + x):
Opening the bracket, we have:
3(4 + x) = 3x + 12 (Equivalent).
2(3x - 30) and 6 - 30;
Opening the bracket, we have:
2(3x - 30) = 6x - 60
2(3x - 30) = 6 - 30 (Not equivalent).
4(5 - 4x) and 20x - 16;
Opening the bracket, we have:
4(5 - 4x) = 20 - 16x
4(5 - 4x) = 20x - 16 (Not equivalent).
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Please help :)))
1. How are rational exponents and radicals related? Explain how to rewrite an expression from rational exponent form into radical form.
2. Explain how equations involving rational exponents or radicals are solved using the rules of exponents.
3. How do extraneous solutions arise from radical equations?
i'll lichuarlly give you so many points
Every radical can be rewritten has an exponent .
Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number).
1. Exponents that are written as fractions are referred to as rational exponents.
The top of the rational exponent is the new exponent on the radical, and the bottom of the rational exponent is the root, therefore a rational power can be reinterpreted as a radical in this fashion.
2. Separate the radical expression from the equal sign on one side. Put every every clause over there on the other side. Square both sides of the equation if the radical is a square root. Raise both sides of the equation to the third power if it is a cube root. Write an expression as a radical if the expression has a logical exponent. By examining the exponent's numerator, you may determine the power. By examining the exponent's denominator, you can get the root. Raise the radicand to the power while using the base as the radicand, and use the root as the index.
3. Extraneous Solutions appear because there are two solutions when you square the two sides of a square root equation (the positive and negative number). As a result, one of those figures will represent an extra solution, or a solution that is added but does not satisfy the initial equation.
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A skateboard in a
store in Charlottetown, PEI, costs
$39.99. It is on sale for 30% off.
The taxes are 16%. What is the sale
price of the skateboard including taxes?
A student says, “$39.99 – 30% discount
+ 16% taxes is the same as calculating
$39.99 – 14%.”
Is the student’s reasoning correct?
Answer:
No, the reasoning is not correct.
Step-by-step explanation:
39.99 x .14 = 5.5986 Does it make sense that the sales price plus the tax would be $5.60? Doesn't that seem really low?
39.99 x .3 = 11.997 is the amount that we are taking off of the original price.
39.99 - 12 (Rounded to the nearest cent) is 27.99.
Now we pay the tax on the discounted amount of the item.
27.99 x .16 = 4.4784 or 4.48 rounded to the nearest cent.
The out the door cost of the item
is 27.99 + 4.48 = 32.48
any number raised to the 2nd power is said to be
what is the value of 7 in the number 345.79
Answer: 345.79 - The value of the digit 7 is 7 thousandths, or 0.007.
sorry if this doesn't help..
The Value Of ( 3+ 4 + 5 ) ° Is Equal To
A) 0 B) 1 C) 12 D) -1
Answer:
( 3+ 4 + 5 ) °
=(3+9)°
=(12)°
C is the answer
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What is the equation of the line that is perpendicular to y = 2x + 3 and passes through the point (−4, 8).
y = 2x + 16
y = 2x − 20
y equals negative one-half times x
y equals negative one-half times x plus 6
The equation of the line that is perpendicular to y = 2x + 3 and passes through the point (−4, 8) is y = - 1 / 2 x + 6(y equals negative one-half times x plus 6)
How to find equation of a line?The equation of the line is perpendicular to y = 2x + 3 and passes through the point (−4, 8).
Therefore, perpendicular lines follows the rule:
m₁m₂ = -1
Hence,
2m₂= -1
m₂ = - 1 / 2
Therefore, let's find the slope of the line using (-4, 8)
8 = - 1 / 2 (-4) + b
b = 8 - 2
b = 6
Therefore, the equation of the line is y = - 1 / 2 x + 6
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Answer: The answer is D- y= -1/2x+6
another one i don’t get them that’s why
Answer:
x° = 100°
Step-by-step explanation:
Straight line angles add up to be 180°
Angles opposite eachother aka "vertical angles" are the same measurements.
If the quadratic equation is
y=x²
what is y when x = 3
Plug in 3 in the place of x and simplify
[tex]y=(3)^{2} \\y=3*3\\y=9[/tex]
y=9
5x3 × 2xy × 3xy2 is equivalent to
A.10x3y2
B.10x5y3
C.30x3y3
D.30x5y3
E.30x5y2
D
Step-by-step explanation:
....................
(Scientific Notation in the Real World MC)
A TV show had 5.6 x 105 viewers in the first week and 4.1 x 105 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation.
9.7 x 1010
9.7 x 105
4.85 x 1010
4.85 x 105
The average number of viewers over the two week is D. 4.85 x 10^5.
How to calculate the value?It should be noted that the scientific notation simply has to do with writing of numbers that are either too large or too small. This will be illustrated thus:
In this case, the TV show had 5.6 x 10^5 viewers in the first week and 4.1 x 10^5 viewers in the second week.
Therefore, the average number of viewers over the two weeks will be:
= (5.6 × 10^5) + (4.1 × 10^5) / 2
= 4.85 × 10^5
Note that we had to divide by 2 since it's average.
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"I NEED HELP PLS" The following figure is made of 1 triangle and 2 rectangles.
Find the area of each part of the figure and the whole figure.
Figure Area (square units)
Rectangle A
Triangle B
Rectangle C
Whole figure
The value of the area are;
Rectangle A = 54 square units
Triangle B = 2 square units
Rectangle C = 6 square units
Whole figure = 62 square units
How to determine the area of the composite figureThe formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleFrom the figure shown, we have two rectangles
Area of the bigger rectangle;
Length = 9
Width = 6
Now, substitute the value
Area = 9(6)
Multiply through
Area = 54 square units
Area of the smaller rectangle
Length = 9 - 7 = 2
Width = 9 - 6 = 3
Substitute the values
Area = 2(3)
Multiply through
Area = 6square units
The formula for area of a triangle is expressed as;
Area = 1/2 base× height
Base = 9 - 6 = 3
Height = 9 - 2 = 3
Substitute the value
Area = 1/ 2 ×2(3)
Area = 6/ 3
Area = 2
The total area = Rectangle A + rectangle B + Triangle
Total area = 54 + 6 + 2
Total area = 62 square units
Hence, the area is 62square units
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Answer:
A=54 B=3 Whole=73
Step-by-step explanation:
I know this because i did this aswell
How can you change the grouping of the addends. $5.50+$7.83+$3.50 what can they be changed to
They way you can change the grouping of the addends. in $5.50+$7.83+$3.50 is; $5.50 + ($7.83 + $3.50) = ($5.50 + $3.50) + $7.83
How to interpret Algebra Properties?There are different algebraic properties such as;
Commutative Property
Associative Property
Distributive Property
Now, the commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product. For example;
a + b + c = c + a + b or a* b = b * a
Now, the associative property states that the way in which factors are grouped in a multiplication or addition problems does not change the product. For example; x + (y + z) = (x + z) + y
Now, to our question, one way to group the addends using associative property is;
$5.50 + ($7.83 + $3.50) = ($5.50 + $3.50) + $7.83
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