Using the Pythagorean Theorem, the length of the third sides in a triangle that satisfy this criteria is given by:
[tex]l_2^2 = 49 - 2l_1^2[/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, considering the description of a Pythagorean triple, we have that:
[tex]h^2 + l_1^2 = 49[/tex].[tex]h^2 = 49 - l_1^2[/tex]Hence the length of the third side can be given as follows:
[tex]49 - l_1^2 = l_1^2 + l_2^2[/tex]
[tex]2l_1^2 + l_2^2 = 49[/tex]
[tex]l_2^2 = 49 - 2l_1^2[/tex]
Hence the length of the third sides in a triangle that satisfy this criteria is given by:
[tex]l_2^2 = 49 - 2l_1^2[/tex]
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The difference of two numbers is 29. The largest number is 3 more than twice the smallest number. What are the two numbers?
Group of answer choices
26 and 55
25 and 54
27 and 56
28 and 57
Answer:
x-x=29 answer is equal to 28and
Simplify. 4√162 +3 4√32
The question focuses on indices. Start by factorization of 162 and 32. Simplifying 32 yields 2^5 and 162 gives 3^4×2. Simplify the two expressions using the factors. Use the indices rule implying: b√a^c =a^(c⁄b)
∜162+3∜32
162= 81×2=3^4 ×2
32 = 2^5 = 2^4 ×2
∜(2×3^4 )+3∜(2^4×2)=∜(3^4 ) ∜2+3∜2^4 ∜2
3^(4⁄4)× ∜2+3×2^(4⁄4)×∜2 = 3×∜2+3×2∜2
3∜2+6∜2 = ∜2×(3+6) = 9∜2
= 9∜2
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The point J(4, – 4) is reflected over the y-axis. What are the coordinates of the resulting point, J'?
The coordinate of the resulting point J' is (-4, -4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the Coordinates.
The point is given as;
⇒ J (4, -4)
Now, The rule of the reflection of a point across the y-axis is equal to
(x, y) ⇒ (-x, y)
Hence, The coordinate of the resulting point J' after reflection over the y - axis of point J (4, -4) is,
(4, -4) ⇒ (-4, -4)
Hence, The coordinate of the resulting point J' is (-4, -4).
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What is the solution to the system of equations?
Y=2/3+3
y
x = -2
The solution to the given system of equations will be x = -2, y = 5/3. That is (-2, 5/3)
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given system of equation is;
y = 2/3 x + 3 ----------- (1)
x= -2 ----------- (2)
The value of x has been given in the second equation.
Now, we need to determine the value of y
From the second equation, we have that;
x = -2
Now Substitute the value of x into the first equation,
y = 2/3 x + 3
y = 2/3 (-2) + 3
y = -4/3 + 3
y = 5/3
Hence, the solution to the given system of equations will be x = -2, y = 5/3. That is (-2, 5/3)
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Recycling Center A processes aluminum at a rate of 100 pounds per hour, while Recycling Center B processes aluminum at a rate of 2 tons per week. Assuming that both centers operate all day every day, which center processes aluminum faster, and why?
1: Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 12 pounds per hour.
2: Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 24 pounds per hour.
3: Recycling Center B processes aluminum faster; its rate is about 120 pounds per hour.
4: Recycling Center B processes aluminum faster; its rate is about 240 pounds per hour.
We need to know about unitary method to solve the given question. Option () is correct, Recycling Center A processes aluminium faster; Recycling Center B's rate is about 24 pounds per hour.
Unitary method is a method to find out the value for a single quantity and then derive the value for the asked quantity. Here is this question we know Center A processes aluminium at a rate of 100 pounds per hour and center B processes 2 tons per week, we need to know who processes aluminium faster. To find the answer we need to first find how much aluminium center B processes per hour, to find that we need to use unitary method.
1 ton=2000 pounds
so, 2tons=2x2000=4000 pounds
Thus Center B processes 4000 pounds per week
A day has 24 hours, a week has 7 days, we know that the centers operate all day every day so number of hours in a week is
7x24=168 hours
Center B processes 4000 pounds in 168 hours
Center B processes 4000/168 pounds in one hour
Center B processes about 24 pounds in one hour
Therefore, we can see that Center A processes aluminium faster and Center B's rate is about 24 pounds per hour, thus option (2) is right.
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The per capita consumption (in pounds) of all poultry in a country is approximated by the function C(x) = 2.49x +93.19, where x is the number of years since 2001. Find and interpret C(1), and
estimate the per capita consumption of all poultry in the country in 2010.
a. Find and interpret C(1).
The value at intercept C(1) is 95.68 pounds
The estimated per capita consumption in the year 2010 will be 115.6 pounds
Part a:
Per capita consumption of all the poultry in a country is given by the function C(x) = 2.49x + 93.19
Finding intercept C(1):
For C(1) the value of x will be 1
C(1) = 2.49(1) + 93.19
C(1) = 95.68
Hence, the value at intercept C(1) is 95.68 pounds
Part b:
Finding the per capita consumption in the year 2010:
where x will be 9, as the time period from 2001 to 2010 is 9 years
C(2010) = 2.49(9) +93.19
= 22.41 + 93.19
= 115.6
Hence, the estimated per capita consumption of all the poultry in the country will be 115.6 pounds in the year 2010
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What happens to the value of the expression 5/x+5 as x decreases
What happens to the value of this expression 5/x + 5 as x decreases from a large positive number to a small positive number is that: A. It increases.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number. As a general rule, the smaller the divisor (denominator) of an expression, the larger would be the quotient.
Evaluating the given expression, we have:
When x = 3;
5/3 + 5 = 6.7
When x = 2;
5/2 + 5 = 7.5.
When x = 3;
5/1 + 5 = 10.
In conclusion, as x decreases from a large positive number to a small positive number in this expression 5/x + 5, its value would increase.
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Complete Question:
What happens to the value of the expression 5/x + 5 as x decreases from a large positive number to a small positive number? Choose 1 answer:
A. It increases.
B. It decreases.
C. It stays the same.
Select the expression that matches the scenario correctly. On January 1, the high temperature was 81 F in Kona, Hawaii the low temperature was -29 F in Barrow, Alaska. What was the difference between the two temperatures?
A. -29 + 81
B. |89 - 21|
C. |81 - (-29)|
D. 36 divided 6
The difference between the two temperatures is mathematically given as
|81 - (-29)| Option C
This is further explained below.
What was the difference between the two temperatures?Generally, the equation is mathematically given as
h-l=d
Therefore
81-(-29)=d
81+29=d
d=110
In conclusion,, in magnitude form
|81 - (-29)|=|81 +29|=|110|=110
|81 - (-29)|
Option C is correct
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Factor each expression completely. x²+4 x+4
The factoring of the expression x²+ 4x+4 is (x+2)²
To solve this exercise, we have to follow the rules of factoring:
x²+ 4x + 4
1. Looking for the a and b number that state the following equations:
a + b = 4a * b = 4Analyzing that (a*b) is a positive number, it means that (a) and (b) have the same signs.
The number could be:
a = 2
b = 2
Confirming:
a + b = 2 + 2 = 4
a * b = 2 * 2 = 4
2. Rewriting the factored expression (x+a)(x+b) with the obtained values, we get:
(x+2) (x+2)
3. Rewriting as the square of a binomial, we get:
(x+2)²
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
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The question is in the picture attached below. Pls answer, will give 50 points.
The required factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
An incomplete equation is given we have to determine the missing terms.
The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.
Here,
The given equation,
_x²y +_y² + 9_ = 3x_(_+ 4y + _).
So, factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
Thus, yhe required factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
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choose all the values that are equivalent to -(5/3)
1. -5/3 2. 5/-3 3. 5/3 4. -5/-3 5. - (-5/3)
Fractions represent the parts of a whole or collection of objects. the equivalent fractions to -(5/3) are -5/3, 5/-3.
What is Fraction?Fractions represent the parts of a whole or collection of objects.
-(5/3) is a fraction, Actually it a improper fraction with negative sign.
The equivalent fractions are obtained by multiplying same sign or same number in numerator and denominator.
-(5/3) is equivalent to -5/3
-(5/3) is equivalent to 5/-3
-(5/3) is not equivalent to 5/-3
-(5/3) is not equivalent to -5/-3 because when negative and negative are multiplied the result will be positive but to be equivalent fraction it should be negative.
-(5/3) is not equivalent to -(-5/3) because when negative and negative are multiplied the result will be positive but to be equivalent fraction it should be negative.
Therefore the equivalent fractions to -(5/3) are -5/3, 5/-3.
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A piece of ribbon of length 1m 10cm was cut off from a length 5m. What length remained?.
The length of ribbon that remained is 3m and 90 cm which is calculated by subtracting the cut length from the total length of the ribbon.
An arithmetic operation called subtraction simulates the process of removing items from a collection.
Subtraction can mean eliminating or lowering physical and abstract quantities utilizing a variety of things, such as negative integers, fractions, irrational numbers, vectors, decimals, functions, and matrices, however it is typically linked with natural numbers in mathematics.
The total length of the ribbon is is 5 meters or 500 centimeters. The length of the piece of ribbon that was cut is 1 m 10 cm=110 cm.
Length of the ribbon that remained is calculated by subtracting the total length form the cut off length 500-110 = 390 centimeters.
390 centimeters= 3 meters and 90 centimeters.
So the length that remained is 3 meters and 90 centimeters.
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Solve the equation
9x²29x28 = 0
Give your answers to 2 decimal places when appropriate.
Answer:
9x²29x28 = 0
The answer is 211932=0
9x2 - 29x - 28 = 0
The answer is 29x=−10
Step-by-step explanation:
what is the interval notation for the compound inequality x is less than or equal to -5 or x > 4
Answer:%
Step-by-step explanation:
PleSw help is it true or false
Answer:
It's True
Step-by-step explanation:
They both pass through the point 'U'ehich means they intersect.
PLEASE HELP ME WITH THIS
The correct way of using the equation is:
$25,475 = (1 - m)*$27,000
And with that we will get that the markdown is of the 5.6%
Which is the correct way of use the given formula?We know that the original price of the car is $27,000, and there is a markdown such that the new price of the car is $25,475.
Then, if m represents the markdown, we can write the equation:
$25,475 = (1 - m)*$27,000
Now we can solve this for m to get:
1 - $25,475/$27,000 = m = 0.056
If we want this in percentage form, we need to multiply it by 100%.
0.056*100% = 5.6%
the markdown in the price is of the 5.6%
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The depth of a local river averages 16 ft, which is represented as |−16|. In January, it measured 4 ft deep, or |−4|, and in July, it was 18 ft, or |−18|. What is the difference between depths in January and July?
22 feet
14 feet
10 feet
2 feet
Answer:14 ft
Step-by-step explanation:hope it helps, brainliest? i could really use it
mai bought some party supplies from an online store.the shop charges a 7.95 shipping fee or 6.25%of the total purchase.whichever is greater.suppose Mai's total purchase is 128.how much shipping will she pay?
The required amount of shipping paid by Mai is 8.
What is percent?In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".
Now it is given that,
Amount of shipping fee = 7.95
percentage of shipping fee = 6.25% of the total purchase
Total amount purchased = 128
Thus, amount of shipping for this purchase is given as,
Amount of shipping = 6.25% of 128
Solving,
Amount of shipping = 0.0625*128 = 8
Since the shop charges shipping fees of whichever is greater
and 7.95 < 8
Thus, amount of shipping paid by Mai = 8
Thus, the required amount of shipping paid by Mai is 8.
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Name a line that contains point b
Answer:
I think the answer is c.CB
the Martinez family has 3/4 a gallon of orange juice in the refrigerator. How many cups
of orange juice are in the refrigerator
Answer:
There are 12 cups of juice in the refrigerator.
Step-by-step explanation:
The conversion --> 1 gallon = 16 cups.
Therefore, [tex]\frac{3}{4}[/tex] a gallon x [tex]\frac{16 cups}{1 gallon}[/tex] = 12 cups.
--
Have a nice day!
A chemist is heating water so it can dissolve a larger amount of sodium chloride. The water's temperature increases 7°C each minute from an initial temperature of 21°C. How long will it take for the water to reach 49°C?
If water's temperature increases 7°C each minute from an initial temperature of 21°C. Then the time taken by the water to reach 49 degree Celsius is 4 minutes.
What is temperature?Temperature defines the atmosphere hotness. And it is expressed in different scales as well as in different parameters like Celsius etc. It is measured through the device known as thermometer.
According to the question, larger amount of sodium chloride is dissolved in the heating water. And the given data states that the water temperature increases 7 degree Celsius every minute.
Initial temperature of water is 21 degree Celsius.
Let us assume, water reaches at 49° C after 'x' minutes.
As per question, every minute temperature increases as 7°C. So, the expression can be written as: (21 + 7x)°C
⇒ 21 + 7x = 49
⇒x = 4 minutes
Hence, the time taken to reach 49° C is 4 minutes.
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Use the Venn diagram shown to list the set An C in roster form.
U
5
A 3
1
6
9
13
2
11
8
7
4
10
14
12
B
O A. (2, 3, 4, 6, 8, 9, 10, 11, 12, 13}
OB. {11}
O C. {4, 11, 12}
O D. (11, 13)
Answer:
Not Available
Step-by-step explanation:
Use the Venn diagram shown to list the set An C in roster form.
U
5
A 3
1
6
9
13
2
11
8
7
4
10
14
12
B
O A. (2, 3, 4, 6, 8, 9, 10, 11, 12, 13}
Set up a proportion and use it to solve for x.
The value of x is 7.
what is proportion?A proportion is an equation in which two ratios are set equal to each other.
Now, setting up the proportion we have
6/4 = x+6 / 4+8
3/2 = x+6 / 12
12*3 = 2(x+6)
36 = 2x + 12
2x = 36-12
2x= 14
x=7
Hence, the value of x is 7.
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Need answer asappppp
The Perimeter of the composite figure = 44.2 units.
How to Find the Perimeter of a Composite Figure?The perimeter of the composite figure = TU + UV + VW + WX + XQ + QR + RS + ST.
Length of TU = 3 units
Length of UV = 11 units
VW = 9 units
XQ = 5 units
QR = 2 units
Use the distance formula, d = [tex]\sqrt{(y_2 - y_1)^2 - (x_2 - x_1)^2}[/tex], to find the lengths of WX, RS, and ST.
W(-2, -6)
X(-5, -3)
R(-3, 2)
S(0, 0)
T(4, 5)
WX = √[(−5−(−2))² + (−3−(−6))²]
WX = √18 ≈ 4.2
RS = √(0−(−3))² + (0−2)²]
RS = √13 ≈ 3.6
ST = √[(0−4)² + (0−5)²]
ST = √41 ≈ 6.4
Perimeter of the composite figure = 3 + 11 + 9 + 5 + 2 + 4.2 + 3.6 + 6.4
Perimeter of the composite figure = 44.2 units.
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whats are equivalents to 9y +5y +4y
first person to answer gets brainliest
Given the dimensions of the shape, the length of PR can be found to be 19.8 units.
How to find the length of PR?The given triangle is an equilateral triangle which means that all the sides are equal.
That then means that:
PR = QR
So we can solve as:
2n + 9 = 7n - 18
Solving for n gives:
7n - 2n = 18 + 9
5n = 27
n = 5.4
The length of PR is therefore:
= 2n + 9
= 2 (5.4) + 9
= 19.8 units
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Three pins are inserted into a cork mat at points c, e, and d. the three pins are collinear. how much string is needed to reach from the pin at e to the pin at d and then to the pin at c? leave your answer as a decimal to the nearest tenth.
Answer:2.7 - 1.1 = 1.6
find the coordinates of the missing endpoint if b is the midpoint of ac
C(-5,4) B(-2,5)
step by step explanation
thank you!
Answer: (1,6)
Step-by-step explanation:
Let the coordinates of A be (x,y).
[tex]\frac{x-5}{2}=-2 \implies x=-4 \implies x=1\\\\\frac{y+4}{2}=5 \implies y+4 =10 \implies y=6\\\\\therefore A=(1, 6)[/tex]
A 99-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
Hello There!
The answer you are looking for is **8.25**.
Explanation:
If you do 8.25*12, you will get 99.
```Fact checking:
8.25*2= 16.50
8.25*4= 33.00
8.25*6= 49.50
8.25*8= 66.00
8.25*10= 82.50
and finally 8.25*12= 99.00
Since it is in inches- it would be 8 1/4in. or 20.955cm.
Hope this helps :)
Ukiah
Answer: 0.121212121
Step-by-step explanation: [tex]\frac{99}{1}[/tex]=[tex]\frac{12}{x}[/tex]
Cross multiply
99x= 12
divide both sides by 99
[tex]\frac{99x}{99} =\frac{12}{99}[/tex]
99 cancel 99 leaving x =[tex]\frac{12}{99}[/tex]=[tex]\frac{4}{33}[/tex]
in decimal
x= 0.121212121
/A and /B are vertical angles. If mA = (4x − 4)° and m/B = (5x – 29)°,
-
then find the measure of /A.
the measure of angle A is 96° when A and B are vertical angles.
We are given the two vertical angles as:
A = (4x − 4)° and B = (5x – 29)°
We know that, vertical angles are equal to each other.
So, we get that:
4 x - 4 = 5 x - 29
5 x - 4 x = 29 - 4
x = 25
A = 4 x - 4
A = 4 ( 25 ) - 4
A = 100 - 4
A = 96°
Therefore, the measure of angle A is 96° when A and B are vertical angles.
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