The atrium was built in the shape shown. Find the area and perimeter of the atrium. Round to the nearest whole unit. (Dimensions are in m.)
Total area
A = semi circle + triangle.
1. Area of the semi circle:
[tex]A\text{ = }\frac{\pi\times r^2}{2}=\text{ }\frac{\pi\times3^2}{2}=\text{ 14.14 }[/tex]2. Area of the triangle:
[tex]A\text{ = }\frac{b\times h}{2}[/tex]h = 6; to find base we use the Pythagoras theorem, as follows:
[tex]b=\sqrt[]{10^2-6^2}=\text{ 8}[/tex]Then,
[tex]A\text{ = }\frac{8\text{ x 6}}{2}\text{ = 24}[/tex]Total area = 14 + 24 = 38 m²
Perimeter =
6 (π + 2) + 10 + 8 = 49 m
ramel borrows $4,000 from his local credit union, to be repaired with3.75% annual interest over 5 years, How Much money will ramel have paid back after 5 years
assuming is simple interest
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 3.75\%\to \frac{3.75}{100}\dotfill &0.0375\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000[1+(0.0375)(5)] \implies A=4000(1.1875)\implies A = 4750[/tex]
help
What is the relationship between Angle 1 and Angle 2
Any number of angles that add up to 180 are supplementary. Since a 180 degree angle is a straight line, these two angles, which lie on a straight line are supplementary.
helpp helppp ?????????????????????????/
Answer:
b
Step-by-step explanation:
please help!!!!! SOS 15 points!!!
To calculate monthly charges, a cellphone provider uses the equation: C=0.25m+60, with C being dollars and m representing minutes used beyond the ones provided by the plan. Assuming the plan allowed for 60 minutes, what would the charge be for a client that used 55 minutes? Put your answer in terms of dollars.
Answer:
C = $60
Step-by-step explanation:
To calculate monthly charges, a cellphone provider uses the equation: C = 0.25m + 60, with C being dollars and m representing minutes used beyond the ones provided by the plan. Assuming the plan allowed for 60 minutes, what would the charge be for a client that used 55 minutes? Put your answer in terms of dollars.
The customer used 55 minutes and did not max out the phone plan, and therefore does not pay any over charges of m.
C = 0.25m + 60 when m = 0
C = 0.25m + 60
C = 0.25(0) + 60
C = 0 + 60
C = $60
Answer:
C = $60
Step-by-step explanation:
Express each of the following in simplest radical form, combining terms where possible.
√25+√45-√20
5√2 is the solution of surd .
What does a math surd mean?
When a square root, cube root, or other root symbol is used in an expression, it is known as a surd. Irrational numbers cannot be stated accurately in decimal form because their decimals do not finish or recur. Surds are used to write irrational numbers precisely.In mathematics, an index is an exponent or power applied to a number or a variable. For instance, the index of 2 in the number 24 is 4.= √25+√45-√20
= √70 - √20
= √50
= 5√2
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View the attached image to answer.
The inequality that can be used with the squeeze theorem to calculate the limit of f(x) is [tex]-x^{2} \leq x^{2} cos\frac{1}{x^{2} } \leq x^{2} or -x^{2} \leq f(x)\leq x^{2}[/tex]
Squeeze Theorem,
If f(x)g(x)h(x) for all numbers and at some point x=k we get f(k)=h(k), then g(k) must also be equal to them, according to the squeeze (or sandwich) theorem. Theorem: By "squeezing" sin(x)/x between two better functions and using them to discover the limit at x=0, we can utilize them to obtain tricky limits like sin(x)/x at x=0.
The given function is [tex]f(x) = x^{2} cos(\frac{1}{x} )[/tex]
The range of the cos function is from -1 and 1.
We have,
[tex]-1\leq cos\frac{1}{x^{2} } \leq 1\\[/tex]
Multiplying the above inequality by x^2, we get :
[tex]-x^{2} \leq x^{2} cos\frac{1}{x^{2} } \leq x^{2}[/tex]
The above equation can be rewritten as,
[tex]-x^{2} \leq f(x)\leq x^{2}[/tex]
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How many grains of sand are there in 6,300 kg of sand?
(only need an answer to the second part)
When one grain of sand weighs 7×10⁻⁵ g, then there are 9.0 × 10¹⁰ grains of sand in 6300 kg of sand.
Given, one grain of sand approximately weighs 7×10⁻⁵ g.
Then how many grains of sand are there in 6300 kg of sand = ?
we know that one grain of sand weighs = 7×10⁻⁵ g.
therefore, 6300 kg = 6300 × 10³ g sand contains
= 6300 × 10³/7×10⁻⁵
= 900×10³/10⁻⁵
= 900 × 10³ × 10⁵
= 9.00 × 10² × 10³ ×10⁵
= 9.0 × 10²⁺³⁺⁵
= 9.0 × 10¹⁰
Hence there are 9.0 × 10¹⁰ grains of sand in 6300 kg of sand.
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whats 1+1
WRONG ANSWERS ONLY
The answer is number UNO
The answer can be window and 11
Answer:
answer is fish
Step-by-step explanation:
_______________________________
Can someone solve this and put down the reason.
Based on the figure shown the lines that are parallel are
line sline tHow to show that line s and line t are parallelUsing the given figure
line s has tow angles 115 and 65line t has one angle which is 65line u has one angle which is 115From the alternate internal angle postulate it can be shown that angle in both line t and line s are equal. This angle is 65 degrees.
The alternate angle postulate hold true for parallel lines hence it shows that line s is parallel to line t while line m is the transversal line required to complete the postulate.
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QUICK its the middle one
Answer:
25000000 should be the answer
Step-by-step explanation:
...
17+ 20 ÷ 4-5 = [?].
Answer:
Step-by-step explanation:
17+20/4-5
17+5-5
17-10
17
Suppose another tire is rolled 100 revolutions and travels about 7,540 inches, what is the radius of this tire?
The radius of the tire given the inches travelled in 100 revolution is 12 inches.
What is the radius?A tire has the shape of a circle. A circle is a bounded object which points from its center is equidistant to its circumference. One revolution is equal to the circumference of the tire. The circumference of a circle is the distance round the circle.
Circumference of a circle = 2πr
Where:
π = pi = 22/ 7r = radiusCircumference = total distance / number of revolutions
7540 / 100 = 75.40 inches
75.40 inches = 22/7 x r x 2
75.40 = 44/7 x r
r = 75.40 x 7/44 = 12 inches
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find the area of the triangle
Answer:
a=4, b=5, c=3
=4+5+3/2
=12/2
=s=6
Now,
we have,
√s(s-a)(s-b)(s-c)
√6(6-4)(6-5)(6-3)
√6×2×1×3
√36
=6
A parallelogram in a quadrilateral formed by two pairs of parallel lines. use what you know about parallel lines and for angles inside the parallelogram. Explain your answer.
Answer:
In a parallelogram:
Opposite sides are parallel.
Opposite sides and opposite angles are congruent.
Consecutive angles are supplementary.
an auto dealer would like to determine if there is a difference in the braking distance (the number of feet required to go from 60mph to 0mph) of two different models of a high-end sedan. six drivers are randomly selected and asked to drive both models and brake once they have reached exactly 60mph. the distance required to come to a complete halt is then measured in feet. the results of the test are as follows. can the auto dealer conclude that there is a significant difference in the braking distances of the two models? use α
According to the information, it can be concluded that there is no significant difference in the braking distances of the two models.
How to check if there is a wide difference in braking distances?To check if there is a wide difference between the braking distances of the two models we can use several alternatives. One of them is to add all the braking distance results of each car and take the average as shown below:
Model A: 150 + 145 + 160 + 155 + 152 + 153 = 915 / 6 = 152.5Model B: 152 + 146 + 160 + 157 + 154 + 155 = 924 / 6 = 154According to the above, it can be concluded that the braking distance of both models only varies by 2 feet, so it is considered that there is not a great difference in braking distances.
Note: This question is incomplete because there is some information missing. Here is the complete information:
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Serkannur
15 minutes ago
Mathematics
High School
PLEASE help me this is due in 1 hour, please try to answer at least 2
1. How do you evaluate an expression involving a rational and negative exponent?
2. How do you simplify rational variable expressions? Add, subtract, multiply or divide 2 rational variable expressions and then simplify.
3. Why are there sometimes restrictions in a rational expression? How do you determine those restrictions?
1)Use the following rule to rewrite with only a positive exponent: [tex]x^{-n}[/tex] = 1 ÷ [tex]x^{n}[/tex] and apply the exponent to both the numerator and the denominator of the fractional base using the rule: [tex](\frac{a}{b} )^{n} = \frac{a^{n} }{b^{n} }[/tex].
2) Simply add or subtract the numerators of two arithmetic operations with the same denominator and write the result to the common factor.
3) Yes, reasonable expressions have limitations at times. Check for zero just on the denominator side to identify those constraints.
1) To evaluate an expression with a rational and negative exponent, follow these steps:
Use the following rule to rewrite with only a positive exponent: [tex]x^{-n}[/tex] = 1 ÷ [tex]x^{n}[/tex]Apply the exponent to both the numerator and the denominator of the fractional base using the rule: [tex](\frac{a}{b} )^{n} = \frac{a^{n} }{b^{n} }[/tex].Rewrite as the reciprocal of the denominator.Write the fractional exponent as a radical and an exponent.Evaluate the radicals.Evaluate the exponents.2) To simplify rational variable expressions,
Simply add or subtract the numerators of two arithmetic operations with the same denominator and write the result to the common factor. If the denominators do not match, they must be changed until they are equal. That is, we need to find a common denominator.
3) The denominator can be any number, even zero. However, there are constraints based on not reducing by zero inside the case of a denominator. There is a limit to the value that may be used to replace our variable and get a denominator of 0.
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Zola is cutting a rope that is 3 yards long into pieces that are 4 inches long.
How many 4-inch pieces will Zola have in all? Enter the answer in the box.
Answer:
432. Zola will have 432 4-inch pieces of rope.
the image of (6,12)(6,12) after a dilation by a scale factor of \frac{1}{2}
2
1
The image of the point after the dilation is (3, 6)
What is dilation?Dilation involves changing the side length of a shape or a function
How to determine the equation of g(x)?The given parameters are:
Point = (6, 12)
The scale factor of dilation is given as
Scale factor = 1/2
Mathematically, this transformation can be represented as
(x, y) = 1/2(x, y)
So, we have
(x, y) = (1/2x, 1/2y)
When represented as a function, we have
Image = 1/2 * Point
Substitute the equation Point = (6, 12) in the equation Image = 1/2 * Point
So, we have the following equation
Image = 1/2 * (6, 12)
Evaluate the product
Image = (3, 6)
Hence, the image is (3, 6)
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Between which two whole numbers is square root of 12?
Which of the two numbers is a better estimate for square root of 12 explain.
Answer:
3 and 4
Step-by-step explanation:
square root 12 lies between (square root 9 and 16) so it is between 3 and 4
Answer: 3 and 4 is what your teacher is probably looking for, but there are technically infinite solutions to the first question.
3 is a better estimate for the square root of 12 since 3 times 3 = 9 which is 3 integers away from 12, where as 4 times 4 = 16, which is 4 integers away from 12.
Step-by-step explanation:
Calculate the square root of 12 which is roughly 3.464
Whole numbers are non-fractional. They can be any positive integer, as well as zero.
3.464 is between 3 and 4.
3 is less than 3.464 which is less than 4.
3 < 3.464 < 4
Technically there are infinite solutions to this problem, since 3.464 is also between 3 and 4, 3 and 5, 3 and 6, 2 and 4, 2 and 5, and infinitely more.
Question 2:
3*3 = 9.
4*4 = 16.
12-9 = 3.
16-12 = 4.
3 < 4.
12 is closer to 9 than it is to 16.
Keandra is taking a trip to visit her extended family and makes a stop somewhere during her trip. The distance between Cincinnati, where Keandra started, and Dayton, where Keandra made the stop is 54 miles. The distance between Dayton and Toledo, where Kendra’s family lives is 150.2 miles. How far did Keandra travel on her trip? Round to the correct number of significant figures.
Kendra travel a total of 204.2 miles
What is addition?
Addition is a basic arithmetic process in which we bring 2 or more number to get a new total. it is denoted by '+'
We are given that Kendra is going from Cincinnati to Toledo and she takes a halt at Dayton
Now the distance between Cincinnati and Dayton is 54 miles.
and the she has to travel 150.2 miles more
Hence the distance between Dayton and Toledo is 150.2 miles
To find out total distance travel add the two distances
We get 54+150.2 = 154.2 miles
Hence the total distance traveled by Kendra is 204.2 miles
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What is an equation of the line that passes through the points (-2, 7)(−2,7) and (-8, 4)(−8,4)?
Answer:y=1/2x+8
Step-by-step explanation: You find the slope using the equation
m= y2-y1/x2-x1= 1/2
and then you use point-slope form y-y1=m(x-x1)
Proof if the triangle is a right angled triangle or not
To proof if a triangle is a right angled triangle, Pythagoras theorems must be obeyed
Pythagoras theorem states that
[tex]\begin{gathered} c^2=a^2+b^2\text{ where c = hypotenus, i.e the longest sides} \\ a,\text{ and b are the other two sides} \\ \end{gathered}[/tex]nows, lets test the triangle with pythagoras theorem
longest side, c = 97, a = 65, b = 72
[tex]undefined[/tex]For the function f(x) = x + 4, what is the ordered pair for the point on the graph when x = 3p? (1 point)
(x, x + 4)
(x, 3p + 4)
(3p, x + 4)
(3p, 3p + 4)
Answer:
[tex](3p, 3p+4)[/tex]
Step-by-step explanation:
[tex]f(3p)=3p+4 \\ \\ \therefore (3p, 3p+4)[/tex]
Find the exact value of sim,cos, and ya for the angle below. Simply all roots.
Hello!
The angle of 30º is one of the remarkable angles (the others are 45º and 60º).
These angles are the most used in trigonometry, so it's good to memorize it.
Below, I'll explain to you one way to memorize it as a table:
For the sine and cosine, let's fill these spaces with 1 2 3 on the first line, and 3 2 1 on the second line. Then we're going to divide all of that by 2.
When the numerator is 2 or 3 we will put a square root in it.
For the tangent, it will be a little different:
• Tangent of ,30º ,is √3/3
,• Tangent of ,45º ,is 1
,• Tangent of ,60º ,is √3
So, the final answers for your exercise are:Sin 30º: 1/2 or 0.5
Cos 30º: √3/2
Tan 30º: √3/3
f(x) = 2x - 8
what is the transformation from y=2^-x
what does the graph look like
The parent function is the most basic example of the function type specified.
Solve the equation y=(2)x for y.
Lessen the steps you tap...
Take the parentheses out.
y=2x
Take the parentheses out.
Rmove parenthesis from y=(2)x.
y=2x
Assume that f(x)=2x for y=(2)x and g(x)=2x for y=2x8 respectively.
f(x)=2x\sg(x)=2x−8
Find a, h, and k for each equation to determine the transformation from the first equation to the second.
y=abx−h+k
For f(x)=2x a=1, find a, h, and k.
h=0\sk=0
Find a, h, and k for g(x)=2x8 with a=1, h=8, and k=0.
The value of h determines the horizontal shift.
The graph is moved to the left by h units, which is expressed as g(x)=f(x+h).
The graph is moved to the right by h units when g(x)=f(xh).
Right 8 Units Horizontal Shift
The value of k determines the vertical shift.
The graph is shifted up k units and is denoted by the expression: g(x)=f(x)+k).
g(x)=f(x)k shifts the graph down k units.
No vertical shift
The reflection that spans the x-axis is indicated by the symbol of a.
A signifies that the x-axis of the graph is reflected.
No reflection on the x-axis
The graph's vertical stretch or compression is indicated by the value of a.
A vertical stretch is a>1 (makes it narrower)
A vertical compression (which results in 0a1)
The graph's vertical stretch or compression is indicated by the value of a.
A vertical stretch is a>1 (makes it narrower)
A vertical compression is 0a1 (makes it wider)
Vertical Stretch or Compression: None
Compare the two functions and look for a horizontal or vertical shift, a reflection about the x-axis, and a vertical stretch to identify the transformation.
f(x)=2x is the parent function.
Right 8 Units Horizontal Shift
No vertical shift
No reflection on the x-axis
Vertical Stretch or Compression: None
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simplify the following to surd:
√3 + 1/√3 - 1/√27
Answer: -√3
Step-by-step explanation:
√3 + 1√3 - 1√27
√3 + √3 - √(3^2 x 3)
2√3 - 3√3
(2 - 3)√3
-1√3
-√3
Instructions
Choose the best answer. If necessary, use the paper you were given.
Question
A rectangular swimming pool is x meters wide. The length of the swimming pool is twice as long as the width.
If the perimeter of the pool is 64 meters, which of the following equations represents the given information?
x+x+2x+2x = 64
x+2x = 64
x+2+x+2 = 64
2x + 2x + 2x + 2x = 64
x + x +2x + 2x = 64 is the right equation
How to check perimeter of rectangle ?
In given question wide of swimming pool is xand the length of pool is twice of width that is 2x The given perimeter of pool is 64 meter.The formula for perimeter of rectangle is P = 2*(l+w)
we have perimeter , 64 = 2* (2x + x)
64 = x + x + 2x +2x
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a nutrition label states that there are 36g of carbohidrates in each serving. accounts for 12% of daily value. how many grams recommended per day?
There are 36 grams of carbohydrates in each serving. The total number of grams of carbohydrates that should be consumed daily is 300.
Given that,
There are 36 grams of carbohydrates in each serving, according to the nutrition label is 12% of the daily value.
We have to find how many grams are advised each day.
We can write 12% as 0.12.
Let x be the total number of grams of carbohydrates that should be consumed daily.
We can write the equation as
0.12x=36
x=36/0.12
x=3600/12
x=300
Therefore, the total number of grams of carbohydrates that should be consumed daily is 300.
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Two variables are connected by the relation: P∝1/Q^2
Q is increased by 40%
To the nearest percent, describe the change in P
in percentage terms.
The change in P in percentage terms is 51% decrease.
How to illustrate the information?Since the two variables are connected by the relation, this will be illustrated as:
P=k/Q^2
where k is the proportionality constant.
Now, If Q is increased by 40%, i.e. the update Q' = Q + 0.4Q.
Now, we have
P1 = k/Q^2 and P2 = k/(Q+0.4Q)^2
P2/P1 = {k/(Q+0.4Q)^2}/{k/Q^2}
P2/P1 = 1/(1.4)^2
P2=0.51*P1
P2 = 0.5P1
Hence P reduces by 51%.
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