Answer:
7inches
Step-by-step explanation:
using Pythagoras a²+b²=c²
so it's rearranged to c²-b²=a² or c²-a²=b²
first we get 13²-11²
next we do 169-121
this makes 48
square root 48 is 6.90 inches
this rounds up to 7 Inches
your answer would be : 7 inches
Complete the table with ordered pairs that give coordinates of points that lie on the line shown in the graph
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
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
Lesson 1.2.2 Exit Ticket
Brown is making treat bags to give away on Halloween. He has 81 Snickers bars and 54 KitKat bars. He
ants to use all of the candy by making as many identical bags as possible.
a. How many treat bags can he make using all of the candy?
The most appropriate choice for LCM will be given by
He can make 162 treat bags using all the candy.
What is LCM?
Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.
Here,
Number of Snicker bars = 81
Number of kitkat bars = 54
Brown wants to use all of the candy by making as many identical bags as possible.
Number of treat bags he can make using all of the candy = LCM of 81, 54
81 = 3 x 3 x 3 x 3
54 = 2 x 3 x 3 x 3
LCM = 3 x 3 x 3 x 3 x 2
= 162
He can make 162 treat bags using all the candy.
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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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The formula for the circumference of a circle with diameter d is C = nd.
a. Solve the formula for d.
b. The circumference of a circle is 8 inches. What is the diameter of the circle?
Part (a)
[tex]C=\pi d \implies d=\frac{C}{\pi}[/tex]
Part (b)
[tex]d=\frac{8}{\pi}[/tex]
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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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.
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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HELPPPPPPPPPPPPPPPPPPPPP
Answer:
the answer to number 2 is: y=-4x-26
The answer to number 3 is y=5/2x+54
Step-by-step explanation:
Two hikers are 33 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 2.2 mph faster than the other.
The rate of the slow hike is 2.2 mph and the rate of the faster hiker is 4.4 mph.
Here in this issue, we are managing linear equations which is a condition of one variable regularly composed within the form ax+b=0 , where a and b are real numbers and x is an unknown variable. Solutions to linear equations allude to a linear equation that can have zero, one, or infinitely various solutions. A linear equation with no solutions simplifies to an untrue statement such as 1=0. A linear equation with one solution rearranges to a solution of the form x=n where n may be a real number. A Linear equation with infinitely various solutions simplifies to a true statement without a variable such as 1=1.
Here we considering the rate of the slow hiker to be x, so the rate for the fast hiker will be x+2.2
Since we know that distance = speed * time
therefore, the Distance covered in 5 hours by a slow hiker is 5x , wheras for fast hiker it will be 5(x+2.2)=5x+11 km
As we are given the condition that it i they are 33 miles apart, So
=>5x + 5x+11 = 33
=>10x = 33-11
=>10x = 22
x =22/10 => 2.2
So the rate of a slow hiker is 2.2 mph and the rate of a fast hiker is x+4.4= 4.4 mph.
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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]
DOMAIN AND RANGE, ANSWER ALL
The function is decreasing.
The domain is the set of x-values.
Interval: [tex](-\infty, \infty)[/tex]Inequality: [tex]-\infty < x < \infty[/tex]The range is the set of y-values.
Interval: [tex](0, \infty)[/tex]Inequality: [tex]x > 0[/tex]A quadrilateral is plotted on a coordinate plane. Each of the vertices of the quadrilateral undergoes the same transformation.Which transformation does not preserve the lengths of the sides of the quadrilateral?
Explanations :
(a) (x;y) →(x-3 ; -y+2 ) ; this preserves the lengths of the side, with a reflection across the x -axis .
(b) (x;y) →(2x +1 ; y-5 ); this does not preserve the length of sides, because the 2 multiply by x will change the length by factor of 2 .
(c) (x;y) → (-x+6 ;-y -8 ), preserves the lengths of sides, with reflection of y = -x .
(d) (x;y) →(-x -5 ; y+10 ) preserves the lenghts of the sides , with a reflection in the y -axis .
the following question
Answer:
angle ODC=30°
Step-by-step explanation:
Parallel to the line now draw another line PQ
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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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
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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EASY TRIG MATHEMATICS QUESTION! PLEASE HELP ME SOLVE! THANK YOU!
PLEASE LOOK AT IMAGE!
Based on table shown above, we have that: A. Yes, the table describe a function.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Based on table shown above, we have the following parameters:
Input value Output value
2001 30
2002 60
2003 30
2004 50
2005 40
In conclusion, we can reasonably infer and logically deduce that this table is a function because it has the different input values (x-values) for different or the same output values (y-values).
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5x3 × 2xy × 3xy2 is equivalent to
A.10x3y2
B.10x5y3
C.30x3y3
D.30x5y3
E.30x5y2
D
Step-by-step explanation:
....................
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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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
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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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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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.
any number raised to the 2nd power is said to be
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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(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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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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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