SOLUTION:
Step 1:
In this question, we are given the following:
The radius of a circle is 9 inches.
What is the length of a 45° arc?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Arc\text{ length = }\frac{\theta}{360^0}\text{ x 2}\pi r \\ where\text{ }\theta\text{ = 45}^0 \\ Radius\text{ = 9 inches} \\ \end{gathered}[/tex][tex]\begin{gathered} Arc\text{ length =}\frac{45^0}{360^0}\text{ x 2 x }\pi\text{ x 9} \\ =\frac{1}{8}\text{ x 2 x }\pi\text{ x 9} \\ =\text{ }\frac{18\pi}{8} \\ =\text{ }\frac{9\pi}{4} \\ =\text{ 7.068583471} \\ \approx\text{ 7.07 inches \lparen correct to 2 decimal places\rparen} \end{gathered}[/tex]CONCLUSION:
The length of the Arc = 7.07 inches ( correct to 2 decimal places )
There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be 36°. From the same location, the angle of elevation to the top of the lightning rod is measured to be 38°. Find the height of the lightning rod. To earn full credit please share a diagram and include all your work and calculations
To better analyze the problem, let us draw an illustration:
To determine the height of the lightning rod, we have to determine the height of the building and the height of the building + lightning rod using the given angles and distance from the base.
Let's solve for the height of the building itself first. Use the 36-degree angle.
[tex]tan36=\frac{height\text{ }of\text{ }the\text{ }building}{distance\text{ }from\text{ }the\text{ }building}[/tex]Let's plug in the data to the function above and solve for the height of the building.
[tex]\begin{gathered} tan36=\frac{x}{500ft} \\ 500tan36=x \\ 363.2713ft=x \end{gathered}[/tex]Therefore, the height of the building itself is 363.2713 ft.
Moving on to the height of the building + lightning rod, use the tangent function still but this time, use the 38-degree angle.
[tex]\begin{gathered} 500tan38=x \\ 390.6428=x \end{gathered}[/tex]Therefore, the height of the building + lightning rod is 390.6428ft.
So, to determine the height of the lightning rod only, let's subtract the two calculated heights.
[tex]\begin{gathered} lightning\text{ }rod=390.6428ft-363.2713ft \\ lightning\text{ }rod=27.3715\approx27.37ft \end{gathered}[/tex]Answer:
The height of the lightning rod is approximately 27.37 ft.
For jewelry prices in a jewelry store, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed rightChoose the correct answer below."O UniformO Skewed rightSkewed leftO Bell shaped+
For jewelry prices in a jewelry store, histogram of the data will be bell-shaped .
A rectangular pool is surrounded by a walk 3 meters wide. The pool is 5 meters longer than its width. If the total area of the pool and walk is 270 square meters more than the area of the pool, find the dimensions of the pool.
The length and width of the rectangular pool are respectively; Length = 22 meters and Width = 17 meters
What is the area of the rectangle?Area of the pool which is a rectangle has the formula;
A = Length(L) * Width(w)
Let the width of the pool = x
Then the length will = (x + 5)
Since the walkway is 3 meters wide, It means that the overall dimensions will be (x + 6) by (x + 5 + 6) or (x + 11)
Total area - pool area = 270
Thus;
(x + 11) * (x + 6) - x(x + 5) = 270
x² + 11x + 6x + 66 - x² - 5x = 270
17x - 5x + 66 = 270
12x + 66 = 270
12x = 270 - 66
x = 204/12
x = 17
Length of pool = x + 5 = 17 + 5 = 22 meters
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Choose a sequence of similarity transformations that maps ABC to DEF
A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation.
When a figure is transformed by a similarity transformation, an image is created that is similar to the original figure
In this case, the sequence of transformation that maps ABC to DEF is as follow:
• Reflection across the x-axis
,• A scale factor of 2
It is a reflection across the x-axis because the image is turned upside down and it is enlarged because:
[tex]\frac{DE}{AC}=\frac{4}{2}=2[/tex]Hence Option A is correct
A party rental company has chairs and tables for rent. The total cost to rent 12 chairs and 2 tables is $39. The total cost to rent 3chairs and 5 tables is $57. What is the cost to rent each chair and each table?00Х$?Cost to rent each chair: slCost to rent each table: s]
let
x = cost of single chair
y = cost of single table
[tex]\begin{gathered} 12x+2y=39 \\ 3x+5y=57 \\ 2y=39-12x \\ y=\frac{39}{2}-6x \\ \\ 3x+5(\frac{39}{2}-6x)=57 \\ 3x+\frac{195}{2}-30x=57 \\ -27x=57-\frac{195}{2} \\ -27x=97.5 \\ x=\frac{-40.5}{-27} \\ x=\text{ 1.5} \\ \\ 12x+2y=39 \\ 12(1.5)+2y=39 \\ 18+2y=39 \\ 2y=39-18 \\ y=\frac{21}{2} \\ y=10.5 \end{gathered}[/tex]cost of rent of each chair = $1.5
cost of rent of each table = $10.5
What is it called when two numbers have a product of one
Answer: Reciprocals
Explanation isn't really needed but reciprocals are basically
Example:
3/4's reciprocal is 4/3 and multiplying 3/4 x 4/3 = 1
17. 17. The scores for a math test are shown below, ordered from smallest to largest. 60 61 62 63 63 64 64 65 66 66 66 69 72 72 72 74 75 80 82 84 86 86 87 87 89 89 90 93 94 98 Fill out the stem and leaf plot below for this data. Enter the leaves separated by commas (ex: 1,1,2,3). Stems Leaves
Answer:
Filling the values we have;
Explanation:
Given the data on the given table, we want to fill them in a stem leaves plot.
The tens values would be in the stems while the unit values will be written in their corresponding leaves.
Filling the values we have;
Pluto has a diameter of 1,413 miles. What does this distance equal in kilometers?
(1 mile = 1.6 kilometers)
A. 12,761 km
B. 2,275 km
C. 3,476 km
D. 143,042 km
Answer:
B
Step-by-step explanation:
since 1 mile is 1.6 kilometers we multiply 1,413 with 1.6 and it equals 2260.8
And since 1.6 was a approximation the closest answer is B
Hopes this help please mark brainliest
find the equation of the line when 6 is the y intercept
...........................................
The winner of a card game is the person closest to 0.The second place player was 8 points behind.If the winner had a score of -3 then what was the score for 2nd place?
ANSWER:
-11
STEP-BY-STEP EXPLANATION:
We have that the winner has a score of -3, and the second place, 8 points behind, therefore, the score of the second place would be:
Therefore:
[tex]-3-8=-11[/tex]The score is -11
A concession stands sells drinks and hotdogs the number of drinks sold is five more than four times the number of hotdogs sold the stands sells 500 items how many hotdogs were sold
Answer:120
Step-by-step explanation:
Please help me with this : For the coordinate grid to the right, identify a pair of congruent figures. Then determine a congruence transformation that maps the preimage to the congruent image.
SOLUTION:
From the image;
The congruent triangles are;
[tex]\Delta ZTF\cong\Delta BQY[/tex]2. The transformation that maps these triangles is;
[tex]T(-5,-1)\circ r_{(180^o,O)}(\Delta ZTF)[/tex]This means triangle ZTF was translated 5 units to the left and 1 unit down and rotated 180 degrees about the origin to get triangle BQY,
help meeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
33
Step-by-step explanation:
you are scamming everyone. why?
Given mn, find the value of x.
t
(9x+7)°
(10x-10)°
(9x+7=10x-10)
All terms are shifted to the left:
(9x+7-(10x-10))=0
Parentheses are used to compute terms: +(9x+7-(10x-10)), so:
9x+7-(10x-10)
the Function Domain determination
9x-(10x-10)
+7
We eliminate parenthesis.
9x-10x+10+7
All the numbers and variables are added together.
-
1x+17
Returning to the equation
+(-1x+17)
We eliminate parenthesis.
-1x+17=0
We shift every term that contains x to the left and every other term to the right.
-x=-17 \sx=-17/-1 \sx=+17
Relation of degrees of polynomials:How can you determine an equation's degree?
The degree of a term in the polynomial expression is expressed as a + b if a and b are the exponents of the many variables in a term.
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1,3/5,9/25 find the 8th term
Answer:
2187/78125
Step-by-step explanation:
T(n) = 3^(n-1) / 5^(n-1)
4x^(2)+4=20 solve by using square roots
Explanation
We are told to resolve the quadratic equation
[tex]4x^2+4=20[/tex]To do so, we will have to collect like terms
[tex]\begin{gathered} 4x^2=20-4 \\ 4x^2=16 \end{gathered}[/tex]Then we will divide both sides by 4
[tex]\begin{gathered} \frac{4x^2}{4}=\frac{16}{4} \\ \\ x^2=4 \end{gathered}[/tex]Thus the value of x will be obtained using square root
[tex]\begin{gathered} x=\pm\sqrt{4} \\ x=\pm2 \end{gathered}[/tex]Therefore, the values of x are: x=2, x=-2
3/4=6/x proportionsolve for x
5) x = 8
Explanation:[tex]\frac{3}{4}=\frac{6}{x}[/tex]cross multply:
[tex]\begin{gathered} 3\times\text{ x = 4 }\times\text{ 6} \\ 3x\text{ = 24} \end{gathered}[/tex]divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3\text{ }}=\text{ }\frac{\text{24}}{3} \\ x\text{ = 8} \end{gathered}[/tex]Sue learned to sing a total of 10 pieces over the course of 5 weeks of voice lessons. After 8
weeks of voice lessons, how many pieces will Sue be able To sing total?
Answer:
2 pieces per week. 10 pieces/ 5 weeks. 16 pieces for 8 weeks. ? 16 pieces total.
Step-by-step explanation:
Hope you help me, I need help with the check part
1.- 3(x - 2) = 15
Solve for x 3(x - 2)/3 = 15/3
Simplifying x - 2 = 5
(x - 2) = 15/3
(x - 2) = 5
x - 2 = 5
x = 5 + 2
x = 7
Check. Substitute the value of x in the original equation and solve it
3(7 - 2) = 15
3(5) = 15
15 = 15 As the two value are the same, the solution of x is
correct.
2.- 4y + 9 - 7y = -6
Solve for y
Simplify like terms
4y - 7y + 9 = -6
- 3y + 9 = -6
-3y = -6 - 9
-3y = -15
-3y/-3 = -15/-3
y = 5
Check
4(5) + 9 - 7(5) = -6
20 + 9 - 35 = -6
29 - 35 = -6
-6 = -6 The solution is correct because both numbers are the same.
Consider the quadratic equation y = ×^2 + 4x + 7 Complete the square to express the quadratic in standard form y = a(x - h)^2+ k a= h = k = [tex]y = {x}^{2} + 4x + 7[/tex]complete the square
To write the equation;
[tex]y=x^2+4x+7[/tex]in standard form, we will follow the steps below:
From the above
a=1
b=4
c=7
So find (b/2a)²
=[4/2(1)]²
=(4/2)²
=2²
=4
We will now have;
y = (x²+4x+4) + 7-4
y=(x+2)² +3
comparing with;
y=a(x-h)² + k
a=1
h=-2
k=3
Find the selling price of a $89.50 jacket with a 25% markup. Round to the nearest cent when necessary. $113.85 $111.22 $127.50 $111.88
$111.88 (option D)
Explanation:Selling price = ?
Cost price of jacket = $89.50
Markup % = 25% = 0.25
We'll apply markup formula:
[tex]markup\text{ \% = }\frac{selling\text{ price - cost price}}{\cos t\text{ price}}\text{ }\times\text{ 100}[/tex][tex]\begin{gathered} 0.25\text{ = }\frac{selling\text{ price - 89.50 }}{89.50} \\ \\ 0.25(89.50)\text{ = selling price - }89.50 \\ 22.375\text{ = selling price - 89.50} \\ 22.375\text{ + 89.50 = selling price} \end{gathered}[/tex][tex]\begin{gathered} \text{selling price = 111.875} \\ To\text{ the nearest cent,} \\ \text{Selling price = \$111.88 (option D)} \end{gathered}[/tex]How many thousands are in 50,000
ANSWER
50
EXPLANATION
We want to know how many thousands there are in 50,000
To do this, we have to find what we will multiply by 1000 to get 50,000
That is:
[tex]\begin{gathered} x\cdot\text{ 1000 = 50000} \\ \Rightarrow\text{ x = }\frac{50000}{1000} \\ x\text{ = 50} \end{gathered}[/tex]The answer is 50.
simplify the equation
The simplified expression of the equation given as (x² - 16)/(x² -2x - 3) ≤ 4 is 3x² -8x + 4 ≥ 0
How to simplify the equation?From the question, we have the following parameters
(x² - 16)/(x² -2x - 3) ≤ 4
Multiply both sides of the expression by (x² -2x - 3)
So, we have the following representation
(x² -2x - 3) * (x² - 16)/(x² -2x - 3) ≤ 4 * (x² -2x - 3)
Evaluate the products in the above expression
So, we have the following equation
(x² - 16) ≤ 4 * (x² -2x - 3)
Open the brackets
This gives
x² - 16 ≤ 4x² -8x - 12
Collect the like terms in the above expression
So, we have the following equation
0 ≤ 3x² -8x +4
Rewrite the expression as
3x² -8x + 4 ≥ 0
Hence, the simplified expression of the equation is 3x² -8x + 4 ≥ 0
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which expression is equivalent to. -2(5x + 3y)
A. 3y(5x - 2)
B 5x(-2+3y)
c -10x - 6y
-10x + 3y
The -2 multiplies each every term in the brackets. meaning -2 will multiply 5x and also 3y
[tex] = - 2(5x) - 2(3y) \\ = - 10x - 6y[/tex]
OPTION C MATCHES AS THE SOLUTION.
GOODLUCK
Identify the 25th term of an arithmetic sequence where a1 = −7 and a18 = 95
The 25th term is 137
Explanation:[tex]\begin{gathered} \text{Given:} \\ a_1\text{ = -7} \\ a_{18}\text{ = 95} \\ a_{25}\text{ = ?} \end{gathered}[/tex]To get the 25th term, we need to find the common difference.
An arithmetic sequence is given as:
[tex]\begin{gathered} a_n=a_1\text{ + (n - 1)d} \\ \text{where a}_1\text{ = first term} \\ n\text{ = number of terms} \\ d\text{ = co}mmon\text{ difference} \end{gathered}[/tex]The formula for the 18th term will be used to find the common difference:
[tex]\begin{gathered} \text{where n = 18} \\ a_{18}=a_1\text{ + (18 - 1)(d)} \\ 95\text{ = -7 + 17d} \\ 95\text{ + 7 = 17d} \\ 102\text{ = 17d} \\ d\text{ = }\frac{102}{17} \\ d\text{ = 6} \end{gathered}[/tex]Now we can find the 25th term:
[tex]\begin{gathered} \text{where n = 25} \\ a_{25}=a_1\text{ + (25 - 1)d} \\ a_{25}=a_1\text{ + 24d} \\ a_{25}=\text{ -7 + 24(6) }=\text{ 144 - 7} \\ a_{25}=\text{ }137 \end{gathered}[/tex]The 25th term is 137
Need help asap extra points
The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]8x - 5y = 26[/tex] is the required equation of line.
What is equation of line in slope intercept form?
General form of equation of line in slope intercept form is given by
y = mx + c where m is the slope of the line and c is the y intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept
The distance from the origin to the point where the line cuts the x axis is the x intercept
Here,
[tex]8x - 5y = 4\\5y = 8x - 4\\y = \frac{8}{5}x - \frac{4}{5}[/tex]
Slope of [tex]8x - 5y = 4[/tex] is [tex]\frac{8}{5}\\[/tex]
Slope of the line parallel to the given line = [tex]\frac{8}{5}[/tex]
The line passes through (2, -2)
Equation of line =
[tex]y - (-2) = \frac{8}{5}(x - 2)\\5y + 10 = 8x -16\\8x - 5y = 16+10\\8x - 5y = 26[/tex]
This is the required equation of line.
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9
You're applying for a job that has a skills test requirement. In order
to pass you need to get 48 of the 55 questions correct. What
percent of the questions do you need to answer correctly?
O
55%
Using the given percentages we can calculate that the 87.27 percent of questions needed to be answered correctly .
The word "percent" comes from the Latin phrase per centum, which meaning "hundred" or "by the hundred."
Per was regularly abbreviated to "p" and eventually disappeared entirely. The Italian term per cento, which means "for a hundred," progressively reduced to become the symbol for "percent." The current "%" symbol is derived from the "cento," which was composed of two circles and a horizontal line. Due to inconsistent usage, it is not always clear from the context what a% is in reference to. The usual interpretation of a quantity's "10% rise" or "10% drop" is that it refers to the quantity's initial value.The number of questions that are required to pass = 48
total number of questions = 55
Percentage of questions = 48/55 × 100 = 87.27 %
Therefore he will need to answer 87.27 % question correctly to pass.
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how can you represent all the solutions y=2x
All the solutions of the equation y=2x can be represented by the points in the straight line.
We are given an equation. The equation is linear in nature. The equation is given below :
y = 2x
An equation is a mathematical statement that includes the sign 'equal to' between two expressions with equal values.
We can see that the equation is a straight line. A line is an endlessly long object with no breadth, depth, or curve in geometry. Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. All the solutions to the equation can be represented by the coordinates of the points that satisfy the equation of line. The graph is attached below.
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if a population of a town decreases by 5% every 3 years would it be exponential ?
Yes, the population would be exponential.
What are exponents?
Exponentiation is a numerical technique denoted by the symbol bn that involves two integers, the base b and the exponent or power n, and is spoken as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bn is the product of multiplying n bases. Typically, the exponent is displayed as a superscript to the right of the base. In such scenario, bn is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or simply "b to the nth."
Yes, the population would be exponential.
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can someone solve this?2 > -3t - 10and is it an open or closed circle?
Given data:
The given inequality is 2> -3t-10.
The given inequality can be written as,
[tex]\begin{gathered} 2>-3t-10 \\ 12>-3t \\ 4>-t \\ t>-4 \end{gathered}[/tex]Thus the value of t is (-4, ∞), and it is open interval.
