A polygon has 12 sides. Find the sum of its interior angles.
Answer: 1800°
Step-by-step explanation: In this problem, we're given that a polygon has 12 sides and we're asked find the sum of the measures of its interior angles.
The formula for finding the sum of the measures of the interior angles of a polygon is 180 (n - 2) where n represents the number of sides.
So here, since our polygon has 12 sides, we can plug a 12 in for the n in our formula and we have 180 (12 - 2) which is our equation.
Simplifying inside the parentheses first, 12 - 2 is 10 so we have 180 (10) which is 1800.
So if a polygon has 12 sides, then the sum of the measures of its interior angles is 1800°.
the speed limit on a highway is 70 miles per hour about how fast is this in miles per minute
The speed of 70 miles per hour is approximately equivalent to 1.17 miles per minute. This conversion is done by dividing the speed in miles per hour by 60, the number of minutes in an hour.
Explanation:To calculate the conversion from miles per hour to miles per minute, you divide the speed in mph by 60, as there are 60 minutes in an hour. So if we are given a speed limit of 70 miles per hour, that would convert to approximately 1.17 miles per minute.
This is calculated as 70 miles per hour ÷ 60 minutes per hour = 1.17 miles per minute
It's important to remember to use the correct conversion factor related to time, in this case that there are 60 minutes in an hour, to ensure the accuracy of the conversion.
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Which number produces an irrational number when added to 2/5
The correct answer to this is that:
Any irrational number when added to 2 / 5 still produces an irrational number.
For example, if we use π to add to 2/5 or 0.4. As far as we know the decimal digits for π just go on forever and do not have a repeating cycle hence making it an irrational number. Adding a rational number such as 0.4 to the value of π does not really greatly change the value of π. The decimal digits (hundredths place and so on) of the resulting number will still go on forever without a continual repeat.
So 0.4 + π is still irrational.
Answer:
5
Step-by-step explanation:
A tree is 6 feet 4 inches tall. How tall is it in inches?
The number of inches in 6 feet 4 inches tall is 76 inches.
Given that, a tree is 6 feet 4 inches tall.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 feet = 12 inches
So, 6 feet = 6×12
= 72 inches
Now, in inches = 72+4
= 76 inches
Therefore, the number of inches in 6 feet 4 inches tall is 76 inches.
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Water weighs about 8.34 pounds per gallon. About how many ounces per gallon is the weight of water?
What is the value of this expression? (-8)3
Answer:
Step-by-step explanation:
You could, if you wished, take out the negative sign, obtaining -(8)(3). That would be -24.
But if you meant exponentiation, it would look like (-8)^3, or (-8)³, and that would be equal to 8*8*8 = 512.
A 34 - m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 36 m . Find the length of the shadow. If necessary, round your answer to the nearest tenth.
Answer:
Length of the shadow is 11.8 meters.
Step-by-step explanation:
In the figure attached,
AB is a 34 meter tall building casting a shadow BC.
Let the measure of BC = x meters
It is given that the distance between A and C is 36 meters.
To find the length of BC we will apply Pythagoras theorem in the triangle.
AB² + BC² = AC²
(34)² + x² = (36)²
1156 + x² = 1296
x² = 1296 - 1156
x² = 140
x = √140
x = 11.832 meters
≈ 11.8 meters
Therefore, length of the shadow will be 11.8 meters.
A rectangle field with area 300 square meters has a length that is 5 meters more than it's width. If W represents the width of the field then an equation that can be used to determine the value of W is?
A) w^2-1500
B) w^2-295
C) w^2+5w-300
D) w^2-5w-300
E) 5w^2-300
The equation that would be used to determine the value of w is expressed as: C. w² + 5w - 300
What is the Area of a Rectangle?Area of a rectangle = (length)(width).
Given the following:
Area = 300 sq. mWidth = wLength = (w + 5) mTherefore, equation that would be used to find the value of w is:
(w + 5)(w) = 300
w² + 5w = 300
w² + 5w - 300
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an ellipse has a center at the origin, a vertex along the major axis at (13, 0), and a focus at (12, 0). What is the equation of the ellipse?
Answer: The equation of the ellipse is
[tex]\dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
Step-by-step explanation: We are given to find the equation of an ellipse that has a center at the origin, a vertex along the major axis at (13, 0) and a focus at (12, 0).
Since the focus lies on the X-axis, so the standard equation of an ellipse with major axis as X-axis is given by
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
According to given information, we have
a vertex along the major axis, (a, 0) = (13, 0)
⇒ length of the major axis, a = 13,
co-ordinates of focus, (c, 0) = (12, 0)
⇒ c = 12.
We know that
[tex]c^2=a^2-b^2.[/tex]
Therefore,
[tex]12^2=13^2-b^2\\\\\Rightarrow 144=169-b^2\\\\\Rightarrow b^2=169-144\\\\\Rightarrow b^2=25\\\\\Rightarrow b=5.[/tex]
Thus, from equation (i), we get
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\\\\\\\Rightarrow \dfrac{x^2}{13^2}+\dfrac{y^2}{5^2}=1\\\\\\\Rightarrow \dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
The equation of the ellipse is
[tex]\dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
The equation of the ellipse along the major axis at (13, 0), and a focus at (12, 0) is; x²/169 + y²/25 = 1
Equation of an ellipseThe equation of an ellipse whose center is the origin, (0,0) usually takes the form;
x²/a² + y²/b² = 1The coordinates of the vertex on the major axis is given as; (13,0) and the focus at (12,0)
Hence, the square of the length of the minor axis;
b² = a² - c²b² = 169 - 144b² = 25.Hence, the equation of the described ellipse is;
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write two different pairs of decimals whose sum are 14.1
Erica bought 3 1/2 yards of Frederick if she uses 2/3 of the fabric to make a curtain how much will she have left
For what value of a does 9=(1/27)^a+3
The value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3
Solving indical equationsThe given equation is:
[tex]9=(\frac{1}{27})^{a+3}[/tex]
This can be rewritten as:
[tex]9=27^{-1(a+3)}[/tex]
Which can be further simplified as:
[tex]3^2=3^{-3(a+3)}[/tex]
Since the bases are equal, they cancel out
The equation becomes:
2 = -3(a + 3)
2 = -3a - 9
2+9 = -3a
-3a = 11
a = -11/3
Therefore, the value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3
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A building 64 ft high casts a 288-ft shadow. Sarah casts a 18-ft shadow. The triangle formed by the building and its shadow is similar to the triangle formed by Sarah and her shadow. How tall is Sarah?
vito just put some money into a cd that pays 12.7 interest compound quarterly. according to the rule of 72,in the approximately how years will he have 4 times the amount of money that he has now
Answer:
11.34 years.
Step-by-step explanation:
We have been Vito put some money into a cd that pays 12.7 interest compound quarterly.
Since the rule of 72 states that to find the number of years it will take an amount to double, we need to divide 72 by annual interest rate.
First of all let us find the number of years it will take to double Vito's money by dividing 72 by 12.7.
[tex]\text{Time it will take to double Vito's money}=\frac{72}{12.7}[/tex]
[tex]\text{Time it will take to double Vito's money}=5.66929133858\approx 5.669[/tex]
Since it will take 5.669 years to double Vito's money, so to find the time it will take Vito to have 4 times the money, we will multiply 5.669 by 2.
[tex]\text{Time it will take to have 4 times Vito's money}=5.669*2[/tex]
[tex]\text{Time it will take to have 4 times Vito's money}=11.338\approx 11.34[/tex]
Therefore, approximately in 11.34 years Vito will have 4 times the amount of money that he has now.
Write the point in its current fraction form dog show all your work for full credit.
0.225
Consider △LNM. Which statements are true for triangle LNM? Check all that apply. The side opposite ∠L is NM. The side opposite ∠N is ML. The hypotenuse is NM. The hypotenuse is LN. The side adjacent ∠L is NM. The side adjacent ∠N is ML.
According the diagram given the correct statements are: The hypotenuse is LN; The side opposite [tex]\rm \angle L[/tex] is NM and The side opposite to [tex]\rm \angle N[/tex] is ML.
Given :
Triangle LNM.
Acccording to the given triangle (attached below):
The base of the triangle LNM is LM.The perpendicular of the triangle LMN is NM.The hypotenuse of the triangle LMN is LN.The opposite side of [tex]\rm \angle L[/tex] is MN.The opposite side of [tex]\rm \angle N[/tex] is LM.Therefore, the correct statements are: The hypotenuse is LN; The side opposite [tex]\rm \angle L[/tex] is NM and The side opposite to [tex]\rm \angle N[/tex] is ML.
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In triangle LNM, the side opposite angle L is NM, and the side opposite angle N is ML. The side adjacent to angle L is NM, and the side adjacent to angle N is ML. The hypotenuse of triangle LNM is LN, not NM.
Explanation:In triangle LNM, the side opposite angle L is NM, so the statement "The side opposite ∠L is NM" is true.
In triangle LNM, the side opposite angle N is ML, so the statement "The side opposite ∠N is ML" is true.
The hypotenuse of triangle LNM is LN, not NM, so the statement "The hypotenuse is NM" is false.
The side adjacent to angle L is NM, so the statement "The side adjacent ∠L is NM" is true.
The side adjacent to angle N is ML, so the statement "The side adjacent ∠N is ML" is true.
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Tim is 5 years older than Melissa. The sum of their ages is 21. This system is represented by the equations: t = 5 + m t + m = 21 What is the solution if you represent Tim's age on the y-axis and Melissa's age on the x-axis?
Makers Corp. had additions to retained earnings for the year just ended of $395,000. The firm paid out $195,000 in cash dividends, and it has ending total equity of $5.3 million. What is the net income?
Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = –3 and x = 3, the average rate of change is 0. Karly says that for the function, between x = –3 and x = 3, the graph goes up through a turning point, and then back down. Explain how Tucker and Karly can both be correct, using complete sentences.
If you flipped a fair coin 6 times and got 6 heads, what would be the probability of getting a head on the next toss? enter your answers as fractions.
a car is traveling at a rate of of 55 miles per hour. how many feet oer hour does the car travel?
Which is a better deal on a $39.99 item: 50% off original price or 40% off, plus additional 20% at the register?
2.5 million deaths per is how many deaths per minute
1) Which number rounds up when rounded to the nearest tenth?
55. 24
170.93
0.12
8.15
___________
2)
Estimate the value of 2968 + 9912 by rounding each number to the thousands.
14,000
13,000
12,000
7000
___________
3)
Which statement below shows the best use of friendly numbers to estimate the value of 27 ·times 4
25 times 4 = 100
30 times 5 = 150
27 times 4 = 108
20 times 4 = 80
_____________
4)
Marcus has 78 baseball cards and 45 basketball cards. Estimate the total number of cards Marcus has.
30
33
123
130
___________
5)
Determine which answer is reasonable for 4. 8 times 9.2.
14
45.36
432
870.4
(please be 100 sure)
write a formula for the nth term of the sequence. Identify your formula as recursive or explicit. -3,3,-3,3,-3,3
A total of 444 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
What is the value of 2xy if x = 3 and y = 2
Answer:
the value of 2xy if x =3 and y= 2 is 12
Step-by-step explanation:
The directions for mixing an insect spray say to use 1 3/4 ounces of chemical in each gallon of water. How many ounces of chemical should be mixed with 4 1/5 gallons of water?
7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.
To determine the amount of chemical to mix with 4 1/5 gallons of water, you need to use the given ratio of 1 3/4 ounces of chemical per gallon of water.
1.) Convert 4 1/5 gallons to a mixed number:
4 1/5 = 21/5 gallons.
2.) Multiply the amount of water by the chemical-to-water ratio:
(21/5) gallons * (7/4) ounces = 147/20 ounces.
3.) Convert 147/20 ounces to a mixed number:
147/20 = 7 7/20 ounces.
Therefore, 7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.
f(x) = 2/3 x -5 what is the value f(6)?
Given the function value of the acute angle find the other five trigonometric function values cos a= Sqrt 7/7