a subcommittee of the citys planning dept suggests a different plan for the walkways in a city's new park. in the revised blueprint shown below, the walkways are shown in blue and parallel lines indicated by red arrowheads.The right angles of the rectangular park are marked, and the other two angle measures are given in red, find the measure of each numbered angle in the blueprint
Answers
The angles are ∠1=42°
∠2=48°
∠3=90°
∠4=42°
∠5=48°
∠6=132°
∠7=90°
∠8=48°
∠9=90°
∠10=132°
∠11=90°
∠12=90°
∠13=48°
∠14=48°
∠15=90°
∠16=90°
∠17=90°
∠18=48°
∠19=48°
∠20=90°
∠21=48°
∠22=42°
What is an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. Angles formed by two rays are located in the plane that contains the rays.
An angle in Plane Geometry is a figure formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angulus," which means "corner." The two rays are referred to as the sides of an angle, while the common endpoint is referred to as the vertex.
In Euclidean geometry, an angle is the figure formed by two rays known as the sides.
∠1=42°
∠1+∠2=90°
∠2=48°
In ΔABF,
∠2+∠3+42°=180°
48°+∠3+42°=180°
∠3=90°
∠4=42°
Now, ∠3+∠4+∠5=180°
90°+42°+∠5=180°
∠5=48°
∠5+∠6=180°
∠6=132°
∠7=90°
∠8=48°
∠7+∠9=180°
∠9=90°
∠10=132°
∠11+∠3=180°
∠11=90°
∠11+∠12=180°
∠12=90°
∠16=∠11=90°
∠12=15=∠90°
∠13=48°
∠14=48°
∠17=90°
∠1+∠17+∠18=180°
42°+90°+∠18=180°
∠18=48°
∠19=48°
Now, ∠19+∠20+42°=180°
∠20=90°
∠21=48°
Now, ∠21+∠22=90°
∠22=42°
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Related Questions
in the photo below please!!!!
Answers
Answer:
[tex]\cos(\theta) + \sin(\theta)[/tex]
Step-by-step explanation:
Use the sine angle sum identity.
[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]
[tex]\sin(45\textdegree + \theta)=\sin(45\textdegree)\cos(\theta)+\cos(45\textdegree)\sin(\theta)[/tex]
Now, simplify [tex]\sin(45\textdegree)[/tex] and [tex]\cos(45\textdegree)[/tex] to [tex]\dfrac{\sqrt2}{2}[/tex]:
[tex]\sin(45\textdegree + \theta)=\dfrac{\sqrt2}{2} \cdot \cos(\theta)+\dfrac{\sqrt2}{2} \cdot \sin(\theta)[/tex]
Then, factor out [tex]\dfrac{\sqrt2}{2}[/tex] from each term.
[tex]\sin(45\textdegree + \theta)=\dfrac{\sqrt2}{2} \cdot ( \cos(\theta)+\sin(\theta))[/tex]
Finally, identify what is in the parentheses corresponding to the blank space in the question.
[tex]\cos(\theta) + \sin(\theta)[/tex]
For what value of x is line m parallel to n?
Answers
Answer: X is equal to 21
Step-by-step explanation:
Answer:
25 degrees
Step-by-step explanation:
5x - 10 = 115
5x = 115 + 10
5x = 125
5/5 x = 125/5
x = 25
ASAP PLEASE! A rectangular swimming pool is 8 ft deep. One side of the pool is 2.5 times longer than the other. The amount of water needed to fill the swimming pool is 2000 cubic feet. Find the dimensions of the pool.
The smaller dimension of the pool is {} ft and the larger dimension of the pool is {} ft.
Answers
The dimensions of the rectangular swimming pool are 25ft long 10ft wide and 8 feet deep.
What is a cuboid?A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height. Sometimes the cuboid shape is confused with a cube since it shares some properties of a cube, however, they are different from each other.
Volume of a cuboid = Length(L) x Width(W) x Depth(d)
but L = 2.5w
2.5w x w x 8 = 2000
20W^2 = 2000
W^2 = 2000/20
W^2 = 100
W = [tex]\sqrt{100}[/tex]
W = 10fft
L = 2.5W, but W = 10ft
L = 2.5 x 10
L = 25ft
In conclusion the length, width and depth are 25ft, 10ft, and 8ft respectively.
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For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a) A circle with radius 2 and center (3, 2).
(b) A circle centered at the origin with radius 1.
Answers
The equation of circle for both the parts will be as,
(a) (x-3)² +(y-2)²= 4
(b) x²+y² = 1
What is circle?
A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.
Main Body:
(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.
Circle centered at (h, k) with radius r:
(x -h)² +(y -k)² = r²
The given circle is ...
(x -2)² +(y -2)² =2²
(x -2)² +(y -2)² = 4
__
(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:
x²+y² = 1
Hence the equation of circle is such.
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Which congruency theorem can be used to prove that △ghl ≅ △khj? sss asa sas aas
Answers
We can prove that the given triangles GHL and KHJ are congruent using the ASA theorem. So, the second option is the correct answer.
We can say any two shapes are congruent if they have the same shape and size. For this, their sides and angles need to be mirror images of each other. We have four congruency theorems at hand here. These are side-side-side(SSS), angle-side-angle(ASA), side-angle-side(SAS), and angle-angle-side(AAS).
According to the ASA congruency theorem, one side and two angles of the triangles in question need to be similar. In the given image, we can see that two of the angles i.e., HGL and HKJ are congruent while GHL and KHJ are congruent. The sides GH and KH are also congruent. This makes the two triangles △GHL ≅ △KHJ by the ASA theorem. So, the second option is the correct answer.
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Let n be the number of trials and p be the probability of success in the binomial distribution. Under which conditions do the Binomial and Poisson distributions give approximate results? n → [infinity], p → 0 n → [infinity], p → 1 n → 0, p → 0 n → 0, p → 1
Answers
Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.
One of the common discrete distribution which is used in Statistics is the Binomial distribution. The Binomial distribution often deals with two types of situations, first, the occurring of an event and second, the non-occurring of an event termed respectively as success and failure. The Binomial distribution can be typically characterized by the two parameters namely “n” and “p” where “n” represents the number of trials and “p” represents the fixed probability of occurring of the desired event.
Further, the Binomial distribution can be visualized as an approach to determine the probability of observing a specified number of successes in a specified number of trials. The typical examples of Binomial distribution in our day-to-day life may include the survival of number of cancer patients, from the treatment offered, over a specified period of time;
Winning the number of seats against the number of candidates filed by a certain political party for an election;
Number of people benefiting from a certain house scheme when applied;
Number of covid patients discharged within three days from the hospital after their admission to a hospital for the treatment.
There is another discrete distribution which is equally popular as the Binomial distribution is the Poisson distribution. While the Binomial distribution deals with the number of trials and the probability of a success, Poisson distribution deals with the average number of successes per day or the number of successes observed per unit of time.
Unlike, in the case of a Binomial distribution, for a Poisson distribution, the knowledge of number of trials to get the observed number of successes is not required. The Poisson distribution has only one parameter namely “m” the mean number of successes per given unit of time.
The Poisson distribution is often taken as a limiting case of Binomial distribution, under the following conditions.
The number of trails is indefinitely large i.e., n → ∞
The probability of success, “p” is very small i.e., p → 0
np is finite i.e., np = m where p = m/n and q = 1 – m/n and m > 0.
However, it is not defined if “n” is large means how large and “p” is closed to zero means how small? It is left to the readers to assume how large n should be and how small p should be? As mentioned earlier, the Poisson distribution is often described as a limiting case of Binomial distribution.
Based on the results of the study , published by me clearly proves that even when 10 ≤ n ≤50 and p ≤ 0.2, the Poisson distribution can be a good approximation to Binomial distribution.
Hence the answer is Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.
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In the formula /=P-r-t, what does r stand for?
Answers
Answer:
The letter [tex]r[/tex] in the given formula represents the rate of interest.
Explanation:
Where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).
Hope this helps!
Water leaks from a crack in a vase at a rate of 0.5 cubic inches per minute. How long does it take for 20% of the water to leak from a full vase? I either got 10 minutes or 2.5...
Answers
The amount of time it would take for 20% of the water to leak from a full vase is equal to 24.128 minutes.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
V represents the volume of a cone.h represents the height.r represents the radius.From the diagram of the cone (see attachment), we have the following parameters:
Diameter of cone = 4.8 in.
Height of cone = 10 in.
Radius of cone = diameter/2 = 4.8/2 = 2.4 in.
Substituting the given parameters into the formula, we have;
Volume of cone, V = 1/3 × 3.142(2.4² × 10)
Volume of cone, V = 60.32 in³.
For the volume of water that has leaked, we have:
Volume of water leaked = 20/100 × 60.31
Volume of water leaked = 12.062 in³.
For the required amount of time, we have:
Time = Volume/Rate
Time = 12.064/0.5
Time = 24.128 minutes.
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if 40% of population is 4500 what is the total population?
Answers
Answer:
11250
Step-by-step explanation:
Write [tex]\frac{x^{2} - 5 }{x} + \frac{x + 8}{x-1}[/tex] as a single fraction.
Answers
The given expression can be simplified as (x³ + 3x + 5)/(x² - x).
How to add two fractions?If the fractions have the same denominators then their numerators are added keeping the denominators as the same.
For fractions with different denominators the LCM of the denominators are taken then that is divided by the numerators of each fraction and the number obtained is multiplied to each of them to get the equivalent fraction.
The given expression is as below,
(x² - 5)/x + (x + 8)/(x - 1)
It can be simplified as follows,
(x² - 5)/x + (x + 8)/(x - 1)
= ((x² - 5)(x - 1) + x(x + 8))/(x(x - 1))
= ((x³ - x² - 5x + 5) + x² + 8x)/(x² - x)
= (x³ + 3x + 5)/(x² - x)
Hence, the given expression can be written in the form of single fraction as (x³ + 3x + 5)/(x² - x).
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my last try anone willing to help
Answers
Logarithmic function log₍ₓ₊₂₎(4) = 3x can be written in exponential form as 4 = 3x ⁽ˣ⁺²⁾
Which property of log function is used?
The properties of log are nothing but the rules of logarithms and these are derived from the exponent rules.
These properties of logarithms are used to solve the logarithmic equations and to simplify logarithmic expressions.
A log function can be written in exponential form using
logₐ m = x ⇒ m = ax
According to the given question:
The given logarithmic function is
log₍ₓ₊₂₎(4) = 3x
On applying the property we get
4 = 3x ⁽ˣ⁺²⁾
Hence the required exponential form is 4 = 3x ⁽ˣ⁺²⁾
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please help meeeeeeeeeeeeeeeeeee
Answers
Answer:
6, 7, 10
Step-by-step explanation:
7 > x - 4 ( add 4 to both sides )
11 > x , then
x < 11
the values from the table which are solutions are 6, 7, 10
Answer:
Answer is 11
Step-by-step explanation:
7+4>z-4+4
11>z
Let F be the radial force field F(x, y) = xi + yj. Find the work done by this force along the following two curves, both which go from (0, 0) to (4, 16). (Use the Fundamental Theorem for Line Integrals instead of computing the line integral from the definition, as you did in the previous set. This way shows why the answers to the two parts must be the same - independence of path!) A. If C_1 is the curve: x = t, y = t^2, 0 lessthanorequalto t lessthanorequalto 4, then integral_C_1 F middot dr = B. If C_2 is the curve: x = 4t^2, y = 16t^2, 0 lessthanorequalto t lessthanorequalto 1, then integral_C_2 F middot dr =
Answers
To know the answer check the given file.
Question 1
Conor is going to the movie theater. A ticket to a movie costs t dollars, and there
is a 15% amusement tax on each ticket.
a. Conor buys a ticket to see a movie. Write two expressions in terms of t
showing his total cost.
Please help !!!!
Answers
The expressions of the total cost are 1.15t and t * (1 + 0.15)
How to determine the expression of the total cost?From the question, we have the following parameters that can be used in our computation:
Cost of a ticket = t dollars
Amusement tax on each ticket = 15%
The above parameters mean that the total cost of a ticket can be calculated using the following equation
The total cost of a ticket = Cost of a ticket * (1 + Amusement tax on each ticket)
Substitute the known values in the above equation, so, we have the following representation
The total cost of a ticket = t * (1 + 15%)
Evaluate the percentage
The total cost of a ticket = t * (1 + 0.15)
So, we have
The total cost of a ticket = t * (1.15)
Evaluate the product
The total cost of a ticket = 1.15t
Hence, the expression is 1.15t
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1. -2x² = -72
2. x² + 8 = -41
3. (2y - 3)² = 49
4. 4y² - 80 = 0
[ Solve the following quadratic Equations by extracting the square roots.] with solutions you can write in on paper:)
Answers
2. cant solve
3. y = 2,5 y = -4
4. y = 20
3
Select all the correct answers.
Which expressions are equal to ¹.2*?
O 12³
0 2³.33
0 26.33
O 125
Answers
It seems that there is perhaps some missing info here. Could you double check your question to validate the information being asked? Tysm!
john computes the sum of the elements of each of the 15 two-element subsets of $\{1,2,3,4,5,6\}$. what is the sum of these 15 sums?
Answers
Sum of the 15 two elements subset of $\{1,2,3,4,5,6} = ( N-1) (N)(N+1)/2
Three elements....two at time (1,2) (1,3) (2,3)....sum = 12
Four elements .... two at a time (1,2) (1,3) (1,4) (2,3) (2,4) (3,4) .....sum = 30
Five elements....two at a time (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5)
Note that for N elements taken 2 at a time....the pattern of sums seems to be
= (N-1)(N)(N+1) / 2
For taking 6 elements taking 2 at a time the sum should be
=(5)(6)(7) /2
=210 /2
=105
Therefore, total sum of those 15 sums of the elements of each of the 15 two-element subsets of $\{1,2,3,4,5,6\}$ = 105
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9. Melissa's front door is 36 inches by 82 inches. She bought a circular table that has a diameter of 91 inches. Will the table fit through the front door? Explain (Show your work).
Answers
Answer:
no it wont
Step-by-step explanation:
pls help me i really need help
Answers
Answer:
4 mph
1.5 mph
5 mph
Fastest: Kaliel, slowest: steve
Step-by-step explanation:
The unit for Melissia can be found by finding the slope of the line. The slope is shown to be 4 miles per hour. That is the unit rate, 4 miles per hour.
The unit rate for steve is also shown in the equation y = 1.5x. This equation is the filled in form of y = mx + b where m is equivalent to the slope. Therefore 1.5 is the slope meaning the unit rate is 1.5 miles per hour.
The unit rate for Kaliel is found using the information that he walks 10 miles in two hours. To find how much he goes in 1 hour divide by two getting you 5 miles per hour.
The fastest unit rate is Kalie with 5 miles per hour, and the slowest steve with 1.5 miles per hour.
Ella has 23 red blocks and 41 green blocks. She will use all of the blocks to build 8 equal towers.
Answers
Answer:
8
Step-by-step explanation:
23:41
41+23=64
64/8=8
What is the difference between survey and experiment?
Answers
The main difference between experiment and survey is that experiment is laboratory research and survey is field research. Experiments are used to prove theories or hypotheses. Surveys are used to understand the notions of a group of people.
A researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Which of the following tests is most appropriate?
analysis of variance
Answers
Since , a researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Therefore, the Multiple Regression method will be more appropriate analysis of variance.
Multiple regression analysis is a statistical technique that analyzes the relationship between two or more variables and uses that information to estimate the value of the dependent variable. The goal of multiple regression is to develop a model that describes the dependent variable y with multiple independent variables. Linear regression has only one independent and dependent variable. But for multiple regression, there are many independent variables that help explain or predict the dependent variable y better.
The multiple regression equation is given by
y = a + b 1×1+ b2×2+……+ bk xk
where x1, x2, ….xk are the k independent variables and y is the dependent variable
Advantages of multiple stepwise regression:
Only independent variables with non-zero regression coefficients are included in the regression equation. Several standard estimation errors and R-squared trends are displayed. Stepwise multiple regression is efficient for finding regression equations with only significant regression coefficients. The steps to create the regression equation are straightforward.Learn more about Multiple regression:
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Two occupations predicted to greatly increase in number of jobs are pharmacy technicians and network systems and data communication analysts. The number of pharmacy technician jobs predicted for
2003 through 2014 can be approximated by 7.3x-y=-256. The number of network and data analyst jobs for the same years can be approximated by 12.1x-y=-234. For both equations, x is the
number of years since 2003 and y is the number of jobs in thousands.
Answers
The year in which the number of both jobs pharmacy technicians and network systems and data communication analysts is equal is 2008.
Explain the term two variable linear equation?The linear equation in 2 variables is any equation that can be written as ax + by + c = 0, in which a, b, and c are all real values while a and b are not equal to zero.Considering the set of equations
7.3x - y = -256
12.1x - y = -234
where x represents the period of time since 2003.
y represents the quantity of jobs in thousands.
We have the answer after solving the system:
(x, y) ==> (4.5, 292)
Find the year where the total number of both jobs is equal.
At the solution point, the graphs of the two lines will collide.
The year in which the number from both jobs is equal will be 4.5 years after 2003, since x is the number of years after 2003.
So, here we are:
Year where the sum of the two jobs is equal:
2003 + 4.5 = 2007.5
= 2008 year
As a result, there will be an equal number of both jobs in 2008.
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There are 207 students in the 9 classes at East Middle School. At this rate, how many students are in 6 classes?
1: 54 students
2: 138 students
3: 69 students
4: 250 students
Answers
There are 207 students in the 9 classes at East Middle School. At this rate, how many students are in 6 classes?
1: 54 students
2: 138 students
3: 69 students
4: 250 students
207 / 9 = 23
23 * 6 = 138
Select the correct answer. The average rate of change of f(x) is given by the formula . Over what interval does this formula give the average rate of change for f(x)? A. [4, 7] B. [-7, 3] C. [3, 7] D. [3, 4]
Answers
Answer:
34
Step-by-step explanation:
hope u new it have fun hsm s
Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpoint
Answers
Answer: Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpoint
Step-by-step explanation: Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
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how many such tests would it take for the probability of committing at least one type i error to be at least 0.7? (round your answer up to the next whole number.)
Answers
The number of tests that it would take for the probability of committing at least one type I error to be at least 0.7 is 118 .
In the question ,
it is given that ,
the probability of committing at least , type I error is = 0.7
we have to find the number of tests ,
let the number of test be n ,
the above mentioned situation can be written as
1 - P(no type I error is committed) ≥ P(at least type I error is committed)
which is written as ,
1 - (1 - 0.01)ⁿ ≥ 0.7
-(0.99)ⁿ ≥ 0.7 - 1
(0.99)ⁿ ≤ 0.3
On further simplification ,
we get ,
n ≈ 118 .
Therefore , the number of tests are 118 .
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Line d pae through point (3, 5) and (10, 1). Line a pae through point (5, 8) and (2, 13). Are line d and line are parallel or perpendicular
Answers
lines a and d are neither parallel nor perpendicular.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
The given points of line d is (3,5) and (10,1)
and line an of line a is (5, 8) and (2, 13).
The slope of line d is m 1 = [tex]\frac{1-5}{10-3}[/tex]
m1 = -4/ 7
The slope of line d is m2 = [tex]\frac{13-8}{2-5}[/tex]
m2 = -5/3
if the slope of two lines is equal that is m1 = m2 , then the lines are parallel and the relation m1*m2=−1, then the lines are perpendicular to each other.
Here both condition fails.
Hence, lines a and d are neither parallel nor perpendicular.
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which is the inverse of graph f
Answers
Answer: the one in blue
Step-by-step explanation:
Draw a picture to show why this equation is true:
3/8 = 3 ÷ 8
Answers
Answer:
You can draw a picture like this:
Step-by-step explanation:
If we are working with fractions, then think of it as a circle.
3 circles divided by 8 people
(Draw 3 circles divided into eighths)
Now, on the first circle, write the number one into one of the slices.
Do the same to the second circle.
Now the third.
How many slices have the number 1 in it?
3 slices have the number 1 in it.
And each whole circle has 8 pieces.
3 (slices) divided by 8 (People) = 3/8