Answer: The area of Triangle is A = 43.25
Step-by-step explanation:
In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3 [tex]s^{2}[/tex]* s = √3/4([tex]s^{2}[/tex])
Define Area of Triangle:
In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4([tex]s^{2}[/tex]) . The perimeter of an equilateral triangle is 3s.
So, we can write,
A = √3/4([tex]s^{2}[/tex])
It means, A = Area of the Triangle
S = length of Triangle = 10inches.
A = √3/4([tex]s^{2}[/tex])
A = √3/4([tex]10^{2}[/tex])
A= √3/4*100
A = 1.73/4*100
A = 0.4325*100
A = 43.25
The area of Triangle is A = 43.25
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Use the proportion d / 180° = r radians/πradians . Find the equivalent degree measure or radian measure 415°
Answer:
the answer is the 235⁰ ok that
Find the total cost of 901 computers that cost $508 each.
The postal service charges $2 to ship packages up to 5 ounces in weight, and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce.
Using it's concept, the domain of the relation is given as follows:
x ≥ 0.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input of the function.The range of a function is the set that contains all the values of the output of the function.In a graph, the domain and the range are found as follows:
The domain is given by the values of x, present in the horizontal axis of the graph.The range is given by the values of y, present in the vertical axis of the graph.From the graph, we have that the weights of the packages assume all values to the right of 0, hence the domain of the relation is given as follows:
x ≥ 0.
What is the missing information?The relation is incomplete, and is given by the graph at the end of the answer.
The question asked is the domain of the relation.
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2. Denesha is thinking of a number that is divisible by both 9 and 7. What is the smallest number Denesha could be thinking of?
Answer:
63
Step-by-step explanation:
Numbers divisible by 9:
18, 27, 36, 45, 63, 72, 81, 90 and 99.
Numbers divisible by 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.
Least common multiple=63
If the liquid continues to cool at the same rate , what will the temperature be at 3pm pls i need this answer
The temperature of the liquid at 3PM will be -7.5 °C
The initial temperature of the liquid at 9 AM = 0°C
Given that the temperature changes by -5/4 °C each hour.
That is the rate of change of temperature = -5/4 °C
We have to find the temperature of the liquid at 3 PM.
Let x denote the number of hours.
Then the temperature after x hours, t = 0 + ( -5/4)x = -(5/4)x is the linear equation modelling this set up.
So from 9 AM to 3PM, the number of hours = 6 hours
Put x = 6 .
Then, t = (-5/4) x 6
= -7.5
Therefore, the temperature of the liquid at 3 PM = -7.5°C
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14. The nth term of a quadratic sequence is n²+ 3n-2
(a) Find the fourth term of this sequence.
Here are the first five terms of a different quadratic sequence.
1, 7, 17, 31, 49
(b) Find, in terms of n, an expression for the nth term of this sequence.
Step-by-step explanation:
14a)
the 4th term = 4² + 3×4 - 2 = 16 + 12 - 2 = 26
b)
1, 7, 17, 31, 49
s1 = 1
s2 = s1 + 6
s3 = s2 + 10
s4 = s3 + 14
s5 = s4 + 18
the added term d grows with every step by 4. starting with a constant "+ 2" on top of -1 to create s1.
d1 = 2
d2 = d1 + 4
d3 = d2 + 4
dn = dn-1 + 4 = d1 + 4(n-1)
s1 = -1 + d1
s2 = s1 + d2 = -1 + d1 + d1 + 4
s3 = s2 + d3 = -1 + d1 + d1 + 4 + d1 + 4 + 4
s4 = s3 + d4 = -1 + d1 + d1 + 4 + d1 + 4 + 4 + d1 + 4 + 4 + 4
sn = -1 + n×d1 + sum(4(n - 1)) = -1 + 2n + 4n(n - 1)/2 =
= -1 + 2n + 2n(n - 1) = -1 + 2n(1 + n - 1) = -1 + 2n² =
= 2n² - 1
Using the graph below which of the following is a gas
A: NaCI
B: KCI
C: NaNO3
D: Ce2(SO4)3
Using the graph of solubility, D. Ce₂(SO₄)₃ is a gas
What is a gas?A gas is a state of matter with no fixed shape or volume.
What is solubility?Solubility of a substance is the amount of solute that can dissolve in unit volume of solvent at a given temperature.
Which of the following compounds is a gas?Note that the solubility of a substance depends on the temperature
For gases, the solubility decreses with incresing temperatureFor liquids, temperature has no effect on solubility and For solids, the solubility increases with temperature if the reaction is endothermixc and dedreases with temperature if the reaction is exothermic.From the graph above, we see that the compound with the least solubility is Ce₂(SO₄)₃. Since the solubility of gases derease with increasing temperature, thus Ce₂(SO₄)₃ is a gas
So, using the graph of solubility, D. Ce₂(SO₄)₃ is a gas
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What quartic polynomial equation has roots 2-3 i, 8,2 ?
The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96
Given,
Zeros are: x = 2, x = -3, x = 8, and x = 2
That is: x + 2 = 0, x - 3 = 0, x + 8 = 0, and x + 2 = 0
So the factors are: (x + 2) (x - 3) (x + 8) (x + 2) = 0
Multiply two at a time:
(x + 2)(x - 3) = x² - x - 6
(x + 8)(x + 2) = x² + 10x + 16
Now multiply those polynomials together using distributive method:
x² (x² + 10x + 16) - x(x² + 10x + 16) - 6(x² + 10x + 16)
= x⁴ + 10x³ + 16x² + x³ + 10x² + 16x - 6x² - 60x - 96
= x⁴ + 11x³ + 20x² - 44x - 96
The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96
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Identify if slope is negative or positive (please)
The slopes are:
the top graphs, we have (from left to right): Negative, positive, positive, positive.Now the bottom ones: Negative, positive, negative, positive.How to identify if the slope is positive or negative?A general linear equation in the slope-intercept form is written as:
y = m*x + k
Where m is the slope and k is the y-intercept.
Particularly, if the slope is positive, we will see that the line goes upwards when read from left to right, while if it is negative, it goes downwards.
First the top graphs, we have (from left to right)
Negative, positive, positive, positive.
Now the bottom ones:
Negative, positive, negative, positive.
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Two objects are similar if they have.
the same shape. a)different shapes. b)the same shape and size. c)different shapes and sizes.
Answer: Pretty sure its B. The same shape and size.
Step-by-step explanation:
Use synthetic division to determine whether each binomial is a factor of 3x³+10 x²-x-12 x+3.
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
Answer: |81 - (-29)|==> C
Step-by-step explanation:
h=high temperature
h=81
l=low temperature
l=-29
d=difference in high and low temperature
h-l=d
81-(-29)=d
81+29=d
d=110 ==> |81 - (-29)|=|81 +29|=|110|=110
|81 - (-29)|==> C
|81 -29|=|52|=52
-29 + 81=81-29=52
Which number is closest to 161 ?
positive square roots
in decimal form
The number that is closest to the square root of 161 is 13.
How to calculate the square root?In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer.
A number y such that y² = x, or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, -4 and 4 are the square roots of 16.
It should be noted that the square root of 161 is 12.689. Therefore, the number that is closest to the square root of 161 is 13.
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Which number is closest to the square root of 161 ?
The formula F(C) = 9/5C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius.
You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function’s
The function C(F) to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit will be equal to [tex][(\frac{5}{9}F) -\frac{160}{9}][/tex]
As per the question statement, the formula [F(C) = 9/5C + 32] is to calculate the temperature in degrees Fahrenheit for a given a temperature in degrees Celsius.
We are required to determine the function to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit.
Since, [F(C) = 9/5C + 32],
[tex]or, [F = \frac{9}{5} C + 32]\\or, (F-32)= \frac{9}{5} C\\or, \frac{9}{5} C=(F-32)\\or,C=\frac{5}{9} (F-32)\\or,C=\frac{5}{9}F-\frac{160}{9}[/tex]
That is, the function to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit is [tex]C(F)=[(\frac{5}{9}F) -\frac{160}{9}][/tex].
Function: In Mathematics, a function is an operator, which when fed with a input, will perform a specific set of operations on the input and then produce a certain output.To learn more about Functions, click on the link below.
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Answer:
inverse
C(F)=5/9F-106/9
check all
Step-by-step explanation:
23
6. application jeremy has a job at the movie theater.
his hourly wage is $7.38. suppose 15% of his income
is withheld for taxes and social security
a. what percent does jeremy get to keep?
b. what is his hourly take home wage?
a) Jeremy get to keep 85%
b) $6.273 is Jeremy's hourly take home wage.
Given,
Jeremy has a job at the movie theatre.
Hourly wage of Jeremy = $7.38
The % of income withheld for taxes and social security = 15%
7.38 × (15/100) = 1.107
That is, $1.107 from Jeremy's income is withheld for taxes and social security.
a) Percentage of income Jeremy get to keep:
= 100% - Withheld percentage
= 100 - 15
= 85
So, Jeremy gets 85% of his income to keep with him.
b) Jeremy's hourly take home wage:
Total income - Withheld amount
7.38 - 1.107 = 6.273
That is, Jeremy's hourly take home wage is $6.273.
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Write each logarithmic expression as a single logarithm. 3 log a-2 log b
The logarithmic expression as a single logarithm is log. a³/b²
What is defines as the logarithmic functions?A logarithmic and even sometimes log function is the inverse of an exponential function. We could employ a log function to find an exponent.
We should be able to transform between logarithmic as well as exponential forms in order to calculate earthquake magnitudes and otherwise correlate the magnitudes of two distinct earthquakes.
Let's use this information to make our log. Here is the logarithmic function:
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, as for the represented expression;
= 3 log a-2 log b
Using the power rule in both of the terms.
= log a³- log b²
Now, applying the Quotient Rule,
= log a³/b²
Therefore, the obtained single logarithm for the given logarithmic expression is log a³/b².
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if a bag contains 10 red 6 yellow 24 blue and 8 white balloons what si the part to whole ratio of blue balloons to all baloons
Answer: Part to whole is 1:2
3z - 7.1 = -4.1
What dose Z =
Answer:
4.1
Step-by-step explanation:
madookoo doo doo
Multiply and simplify. ∛9 . ∛9
Radical expression containing third root terms will be first multiplied and then simplified to its simplest form.
A radical expression is a mathematical expression containing a radical symbol (√). A radical expression contains three distinct parts:
1. A radical symbol which is the square root sign.
2. A radicand which is a component inside the radical,
3. A degree which is the root represented by the radical.
In the given expression, the radicand is 9 while the degree is 3.
As the degree is the same for both the terms, we can multiply the radicand.
Multiplying the radicand terms,
∛(9*9)=∛81
Simplifying the radicand,
∛(3*3*3*3)
Taking the cube root and simplifying,
3∛3
Hence, ∛9.∛9 = 3∛3
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SOMEONE TELL ME IF IM CORRECT AND TELL ME HOW MUCH TO COLOR IN!!!!
Answer:
Seems correct. I would never use pen for a math assignment though ;-;
Here’s the answer sheet lol.
Step-by-step explanation:
find the circumference and the area of a circle with diameter 8 cm.
Answer:
Step-by-step explanation:
If the diameter is 8 cm, and the formula is A=pie*radius^2, the radius is 4.
The area would be 16*pie
The formula for finding the circumference 2*pie*radius, so the circumference is 8*pie.
what is the equation 2(h+3.5)=-11
Answer:
h = -9
Step-by-step explanation:
Open the parentheses:
2(h+3.5) = -11
2h+7 = -11
Subtract 7 both sides
2h = -11 - 7
2h = -18
h = -9
solve: 1/2 x 3.4/4. Why is this your answer? How do you know this is correct?
Answer: 3.4/8 or 0.425
Step-by-step explanation:
Use this Rule: a/b * c/d = ac/bd
Simplify numerator (top): 1 * 3.4 = 3.4
Than Simplify denominator (bottom): 2 * 4 = 8
Finally: 3.4/8 or 0.425 (decimal)
This is my answer and I know this is correct because of using the Rule which demostrates that you should multiply top and bottom
Is it possible for a number to be both a whole number and an integer why and why not
A number system is defined as the representation of numbers by using digits or other symbols. It is possible for a number to be both a whole number and an integer.
What is a Number system?A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.
The given question is Is it possible for a number to be both a whole number and an integer why and why not.
The answer is yes because every whole number is an integer but not every integer to be a whole number.
For example 5 is both a whole number and integer but -5 is a integer but ot a whole number because in whole numbers we do not have negative numbers.
Therefore it is possible for a number to be both whole number and integer.
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What is the
equation of the line through (-2, 5) and (0, 3)?
Answer:
y=-x+3
Step-by-step explanation:
the gradient of the equation is -1
and the y intercept is 3
A cube has a side length of 3x^6 units. a smaller cube has a side length of x^2. how many smaller cubes will fit in the larger cube
[tex]27x^{12}[/tex] smaller cubes will fit in the larger cube.
Given,
Side length of the smaller cube = [tex]x^{2}[/tex] units.
Side length of the larger cube = [tex]3x^{6}[/tex] units.
We have to find the number of smaller cubes that can be fitted in the larger cube.
Volume of cube is given by the formula,
Volume = (side)³
Volume of the larger cube = [tex](3x^{6} )^{3}[/tex] = [tex]27x^{18}[/tex]units³
Volume of the smaller cube = [tex](x^{2} )^{3}[/tex] = [tex]x^{6}[/tex] units³
Let the number of smaller cube that can be fitted in the larger cube = n
Volume of n cubes = [tex]nx^{6}[/tex] units³
If space inside the larger cube will be occupied by 'n' smaller cubes,
volume of n smaller cubes = Volume of a larger cube
[tex]nx^{6}[/tex] = [tex]27x^{18}[/tex]
n = [tex]27x^{12}[/tex]
Therefore, [tex]27x^{12}[/tex] smaller cubes can be fitted in the larger cube.
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Which point is located at (5,-2)?
-7-8-54
+
point A
point B
point C
point D
revious Activity
0₂
8
7654
4
3-
2-
4
7 7 3 7 8 9
-2-
Mark this and return
1234567 x
16
C
D
Save and Exit
Next
Submit
Based on the attached graph, the point that is located at (5,-2) is point F
How to determine which point is located at (5,-2)?The graph that completes the question is added as an attachment
The point located at (5,-2) implies that the coordinates of the point are
x-coordinate = 5
y-coordinate = -2
From the attached graph, we can see that the point F has the following properties
x-coordinate = 5
y-coordinate = -2
This means that the point F is located at (5,-2)
Hence, the point that is located at (5,-2) is point F
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Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning.
Given: If a quadrilateral has diagonals that bisect each other, then it is a parallelogram.
The diagonals of quadrilateral PQRS bisect each other
No valid conclusion drawn from the statements.
You can "detach" the hypothesis from the conclusion using the law of detachment. More specifically, if p and p -q are known to be true, we can infer that q is true. On the other hand, we can cram conditional statements together using the law of syllogism. When p-q and q-r are known to be true, they can be combined to form p-r. After all, it would be silly-gism to go through q when we can just go from p to r.
P = quadrilateral has diagonals
Q = quadrilateral diagonals bisect each other
R= the quadrilateral is a parallelogram
Statement P is true because all quadrilaterals have 2 diagonals that runs from one edge to another eg square, rectangle, parallelogram, kite etc
Statement Q is False because not all quadrilateral's diagonals bisect each other as in the case of trapezium, likewise quadrilateral whose diagonals bisects each other are not only parallelogram, kite, square and rectangle diagonals bisect each other.
Statement R is False because a quadrilateral whose diagonals bisect each other is not only parallelogram. Square, rectangle and Kite diagonals also bisect each other, and they are also parallelogram.
Therefore, no valid conclusion made from the statements because parallelogram is not the only quadrilateral whose diagonals bisect each other and not all quadrilateral's diagonals bisect each other.
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Evaluate the expression. 1 4 + 1 2 ÷ 2 3 ÷ 3 5 Write your answer as a fraction or as a whole or mixed number.
The solution of the expression 1/4 + 1/2 ÷ 2/3 ÷ 3/5 is 1 1/2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
1/4 + 1/2 ÷ 2/3 ÷ 3/5
Express the quotient as a product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 1/2 x 3/2 ÷ 3/5
Evaluate the product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 3/4 ÷ 3/5
Express the quotient as a product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 3/4 x 5/3
Evaluate the product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 5/4
Evaluate the sum
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 6/4
Simplify
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1 1/2
Hence, the solution of the expression 1/4 + 1/2 ÷ 2/3 ÷ 3/5 is 1 1/2
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Use the graph to answer the following question.
The figure shown was transformed from Quadrant II to Quadrant IV .
Which of the following BEST represents this transformation?
reflection over the x-axis followed by a dilation of scale factor 2
rotation 90° clockwise followed by a reflection over the y-axis
reflection over the y-axis followed by a translation down 6 units
reflection over the x-axis followed by a translation right 5 units
The transformation is rotation 90° clockwise followed by a reflection over the y-axis
How to use the graph to answer the question?The question is given as
Which of the following BEST represents this transformation?
From the question, we have the figure shown to be
A transformation of a figure from Quadrant II to Quadrant IV
From the figure, we can see that the shapes in both quadrants have the same dimensions
This means that the shapes are not dilated
However, the orientation of the figures are difference
Because of the positioning of the shapes, we can conclude that the transformaton is rotation 90° clockwise followed by a reflection over the y-axis
Hence, the transformation is rotation 90° clockwise followed by a reflection over the y-axis
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