If the long chord and tangent length of a circular curve of radius R are equal the angle of deflection is 120 °
The term angle of deflection in math is defined as the angle of which the M particle is deviated
Here we know that the intersection point is the angle between the back tangent and forward tangent.
Here we have also know that the surveyor either computes its value from the preliminary traverse station angles or measures it in the field and it can be denoted by Δ.
Then the Tangent length is calculated as,
=> T = R tan Δ/2
Similarly, the long chord is calculated as,
=> L = 2 R sin Δ/2
Here we also know that Length of the long chord is defined as,
=> L = T
The it can be calculated as,
=>R tan Δ/2 = 2 R sin Δ/2
Here we know tanθ = sinθ/cosθ then it can be written as
=> 1/2 = cos (Δ/2)
=> Δ/2 = 60°
=> Δ = 120 °
Therefore option (d) is correct.
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Which expressions are equivalent to 10a - 25 + 5b?
The expressions are equivalent to 10a - 25 + 5b are option A, C and D.
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.
Given that the expression is 10a - 25 + 5b.
For the given options, simplify each individual expression to determine the answer:
A. 5(2a−5+b)
= 10a - 25 + 5b
Equivalent
B. -2(-5a-25+5b)
= 10a + 50 - 10b
Not equivalent
C. 10×(a − 2.5 + 0.5b)
= 10a - 25 + 5b
Equivalent
D. (−2a + 5 − b)⋅(−5)
= 10a - 25 + 5b
Equivalent
E. −10⋅(−a−2.5−0.5b)
= 10a + 25 + 5b
Not equivalent
Hence, the expressions are equivalent to 10a - 25 + 5b are option A, C and D.
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How are graphs with a nonzero axis most misleading?
Graphs with a nonzero axis most misleading as they distort differences between values.
What is a graph ?
Graph can be defined as the visual representation of data in the form of given ordered pairs.
A professional who specializes in interest rates might find the information in the left-hand graph quite useful.
They distort differences between values.
We have given that, a graph
They distort differences between values,
So distort differences between values can be,
Non-zero axes distort differences between values, but they are not always misleading.
It depends on who is looking at them.
Consider the bar graphs , showing the change in interest rates over time.
A reader might conclude that interest rates had risen sharply (the zero-axis shows that they have remained steady).
However, a professional who specializes in interest rates might find the information in the left-hand graph quite useful.
Hence, Graphs with a nonzero axis most misleading as they distort differences between values.
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Alexa is buying a car and needs to take out a loan for $22, 000. The bank is offerin
an annual interest rate of 6.3%, compounded monthly, for a 6 year loan. Using the
formula below, determine her monthly payment, to the nearest dollar.
M =
Pr(1+r)"
(1 + r)" − 1
According to the question, Alexa's monthly payment will be $448.59.
What is the payment ?Payment is the transfer of money from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment can take many forms, such as cash, check, credit or debit card, money order, bank transfer, or online payment. The most common form of payment is cash, followed by debit and credit cards. Payment also includes more modern forms such as digital currencies, mobile payments, and contactless payments. Payment is an important part of the exchange of goods and services, and it is essential for the functioning of a modern economy.
M = P x r x (1 + r)ⁿ / ((1 + r)ⁿ - 1)
M = 22,000 x 0.063 x (1 + 0.063)⁶ / ((1 + 0.063)⁶ - 1)
M = 22,000 x 0.063 x 1.3958 / 0.7236
M = $448.59
Therefore, Alexa's monthly payment will be $448.59.
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Anne is painting her house light blue. To make the color she wants, she must add 3 cans of white paint to every 2 cans of blue paint.
1. How many cans of white paint will she need to mix with 6 cans of blue?
2. Rate needed (white/blue)
3. What is the unit rate?
4. Interpretation of unit rate?
Anne should mix 9 cans white paint with 6 cans of blue paint.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, Anne wants to paint her house light, so she is mixing 3 cans of white paint to every 2 cans of blue paint.
So, the ratio of white paint to blue paint is 3:2
1) Multiply the ratio by 3, we get 9:6
So, Anne should mix 9 cans white paint with 6 cans of blue paint.
2) Rate = 3/2
= 1.5
Therefore, Anne should mix 9 cans white paint with 6 cans of blue paint.
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Triangle ABC has sides AB= 17cm, AC= 13cm and BC= 23cm, as shown
below.
13 cm
23cm
17 cm
Diagram not drawn to scale
Calculate the size of angle CAB to the nearest integer.
(3 marks)
Answer:
[tex]\boxed{m \angle CAB =99^{\circ}}[/tex]
Step-by-step explanation:
We can use the law of cosines to determine measure of ∠CAB
If a, b and c are the three sides of a triangle and C is the angle opposite side c then the law of cosines says
c² = a² + b² - 2ab cos(C)
Here we are asked to find m∠CAB
The side opposite ∠CAB is BC which is 23 cm long. This is c in the formula
The other two sides, a and b are 13 cm and 17 cm
Applying the formula, using C to represent m∠CAB
[tex]23^2=\:13^2+\:17^2-\:2\:\cdot 13\cdot 17\cdot \cos \left(C\right)[/tex]
First switch sides:
[tex]13^2+17^2-2\cdot \:13\cdot \:17\cos \left(C\right)=23^2[/tex]
[tex]\rightarrow 69+289-442\cos \left(C\right)=529\\\\\rightarrow 458 -4 42\cos \left(C\right) = 529\\[/tex]
[tex]\rightarrow -442\cos \left(C\right) = 529-458\\\\\rightarrow -442\cos \left(C\right) = 71\\\\[/tex]
[tex]\rightarrow \cos \left(C\right)=-\dfrac{71}{442}\\\\\rightarrow \cos \left(C\right) = - 0.16063\\\\[/tex]
[tex]\rightarrow C = \cos^{-1} (-0.16063)[/tex]
[tex]\rightarrow C = 99.2437^{\circ}[/tex]
Rounded to the nearest integer, this would become
[tex]\rightarrow C = \boxed{99^{\circ}}[/tex]
Emma practiced piano for 75% of the time that Olivia practiced. Emma practiced for 90 minutes. How long did Olivia practice?
Lauren worked for [tex]$7 / 24$[/tex] th of a day.
What is fraction?An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters. A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.A fraction is a concept where some portions of a full item are expressed in fraction form or division form. For example, if there are 150 students and 98 of them are female, the fraction can be written as follows. Similarly,
24 hours make up the entirety of a day.
In the morning, 1(1/4) hours, which equates to 5/4 hours, in the afternoon, 3 hours, and in the evening, 2 hours and 45 minutes, respectively, which may be stated as
=(2+45/60)
=2+3/4
=11/4hours
So, the total no of hours Lauren practised will be
Total [tex]$=\frac{5}{4}+3+\frac{11}{4}$[/tex]
[tex]$=\frac{5+12+11}{4}$[/tex]
[tex]$=\frac{28}{4}$[/tex]
[tex]$=7$[/tex] hours
Now we can express it in fraction form,
Fraction[tex]$7 / 24$[/tex]
Hence, Lauren worked for [tex]$7 / 24$[/tex]th of a day.
The complete question is,
Lauren practiced playing the piano 1 1/4 hours in the morning, 3 hours in the afternoon, and 2 hours and 45 minutes in the evening. For what fraction of the day did she practice?
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Solve each equation by factoring
1. 64p^2=9
2. 32-162k^2=0
3. 16/49-v^2=0
4. 27h^3=48h
PLS ANSWER QUICKLY!!!
If 3x + 10y=2 and -x + 7y = -4 are true equation what would be the value of 2x + 17y
Answer:
-2
Step-by-step explanation:
if we sum the 2 equations we will find it the the same equation they want so 3x+10y-x+7y=2-4
2x+17y=-2
I hope I help you in this ans and tq.
a square $abcd$ has an area of $4.$ the square is then dilated with a scale factor of $x,$ producing a square $a'b'c'd'$ of area $9.$ find the sum of all possible values of $x.$
The possible scales factors of the given dilation transformation are 3/2 and -3/2. Hence, their sum is zero.
A dilation is a transformation that results in an image with the same shape as the original but a different size.
In a dilation transformation, a negative scale factor enlargement will cause the enlargement to appear on the opposite side of the enlargement's center and will be inverted (upside down). The size of the shape will also alter depending on the degree of the enlargement.
The areas are scaled by 9/4
Since, the area of a square is the square of its side, then scale factor is:
Scale factor = ±√(9/4) = ± 3/2
Hence, the possible values are positive scale factor: 3/2 and negative scale factor = -3/2.
Their sum is: 3/2 + (-3/2) = 0
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Kenia want to buy a new tv. The regular price i $759. The tore i offering a 15% dicount and a ale tax of 7% i added after the dicount. What i the total cot of the tv to the nearet cent?
The total cost of the TV would be $690.00 to the nearest cent.
Given that,
The regular price of the TV is $759
So, the regular price of the TV = $759
The store is offering a discount of 15%. To calculate the discount amount, multiply the regular price by the discount rate (15% = 0.15).
So, the offered discount is 15% of $759 = $113.85
Subtract the discount amount from the regular price to get the price after the discount.
Then, the price after the discount is $759 - $113.85 = $645.15
To calculate the sales tax, multiply the price after the discount by the tax rate (7% = 0.07).
Then, the sales tax for the TV is 7% of $645.15 = $45.13
Add the sales tax to the price after discount
Then, total cost: $645.15 + $45.13 = $690.28
It is rounded to the nearest cent: $690.28 = $690.00
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if 20 men can complete a piece of work in 16 days how many men should be exiled to finish the work in 20 days?
Answer: 16 men should be assigned to finish the work in 20 days.
Step-by-step explanation:
Let's assume that the number of men needed to complete the work in 20 days is y. Then, the rate of work done by each man is given by 20/16=5/4 units of work per day.
So, the rate of work done by y men is given by 5/4 * y units of work per day.
Since the total work is constant, we have 20 men * 20/16 units of work per day = y men * 5/4 units of work per day.
Dividing both sides by 5/4, we get:
y = 20 * 20/16 / (5/4) = 20 * 4/5 = 16 men.
Therefore, 16 men should be assigned to finish the work in 20 days.
a student was adding the numbers 1, 2, 3, 4, and 5. they wrote: assuming these numbers are adjectives modifying the same noun, discuss what is incorrect about their equation.
The student's equation is incorrect because it contains only one part, and an equation requires two parts to be valid.
An equation is a statement that two things are equal, and it must contain two different parts. A single number, such as the five numbers that this student used, can't make an equation. The student was using the numbers as adjectives, which modify nouns, but adjectives can't be added to make an equation.
In order to have a proper equation, the student must have two parts, each with its own number or variable. For example, the student could have used 2 + 3 = 5, which is an equation with two parts.
The left side of the equation (2 + 3) is the sum of the two numbers, and the right side of the equation (5) is the result of that sum.
This equation would be correctly written and would produce the correct result.
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For the following exercises, find the level curves of each function at the indicated value of c to visualize the given function.14. z(x, y) = y²x², c = 115. z(x, y) = y²x², c = 416. g(x, y) = x² + y²; c=4,c=9
The level curve for the function z(x, y) = y²x², at the value c = 115 are the points that satisfy the equations y = (√115)/x and y = -(√115)/x .
The Level Curves of a function z(x,y) at a constant value "c" are defined as the set of points (x,y) where z(x,y) = c.
So, to find the level curves of z(x,y) = y²x² at the indicated value of c = 115, we need to solve the equation y²x² = 115 for x and y.
Starting with y²x² = 115,
Simplifying ,
we get ;
⇒ y² = 115/x²
Taking the square root(√) of both sides:
that means ⇒ |y| = sqrt(115/x²) ;
Since y can be either positive or negative, we have two equations:
⇒ y = sqrt(115/x²) ⇒ y = -sqrt(115/x²)
⇒ y = (√115)/x ⇒ y = -(√115)/x .
Therefore , the level curve for c = 115 is the set of points that satisfy either of these two equations.
The given question is incomplete , the complete question is
Find the level curves of each function at the indicated value of c to visualize the given function. z(x, y) = y²x², c = 115 .
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56% of men do not look forward to going clothes shopping for themselves. You randomly select 8 men. Find the probability that the number of men who do not look forward to going clothes shopping for themselves is EXACTLY FIVE.
Salut/Hello!
Answer: 0.625
Step-by-step explanation:
The probability will be 5 men in a selection of 8 random men
so 5/8 is equal to 0.625 which shows the probability.
I hope it was helpful! :]
Brennan wants to observe the moon as it completes one full orbit around the Earth. He plans to record the appearance of the moon in his journal. About how long will he need to make observations in order to view an entire cycle?
Responses
One day
One day
One Week
One Week
One Month
One Month
One Year
One Year
The amount of time it will take him to make an observations in order to view an entire cycle would be = one month. That is option C
What is moon cycle?Moon cycle is defined as the the series of phases that the moon takes to orbit around the earth as the earth moves round about the sun.
The difference phases of the moon include the following:
new Moon, waxing crescent, first quarter, waxing gibbous, full Moon, waning gibbous, third quarter and waning crescent.These cycles are repeated again after 29.5 days which is approximately 1 month, therefore, the amount of time it will take him to make an observations in order to view an entire cycle would be = one month
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when you do not learn for an exam with matzinger, the probability to get an f is 0:8. if you learn, the probability to get an f is 0:2.
The probability to get an f is 0:2 is 0.666
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
P(C/A) = 0.8
P(C/B) = 0.2
P(C)=0.4
P(A/C)= P(C/A)P(A)/P(C)
= 0.8*P(A)/0.4
P(C)= P(C/A) P(A)+ P(C/AC) (1-P(A)
0.4= 0.8*P(A)+0.2(1-P(A))
0.4 =0.6 P(A)+0.2
0.2/0.6 = P(A)
Hence
P(A/C)=0.8/0.4 *0.2/0.6
=2*2/6
=0.666
The probability to get an f is 0:2 is 0.666
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The vertices of a triangle are located at (-4, 1). (0, -2) and (3, 2). Select the correct option from the drop-down to complete the sentence.
The triangle is
Answer:
Isosceles Right Triangle.
Step-by-step explanation:
Let the points be A, B and C where A = (-4, 1), B = (0, -2) and C = (3, 2)
Slope of AB = (-2-1)/(0- -4) = -3/4
and its length = √(-2-1)^2 + (0- -4)^2 = √25 = √5.
Slope of BC = (2 - -2)/(3 - 0) = 4/3
and its length = √(2 - -2)^2 + (3)^2 = √25 = √5
Slope of AC = ((2-1)/3- -4) = 1/7
and its length = √((4--4)^2 + (2-1)^2 = √17
The product of the slopes of AB and BC = -3/4 * 4/3 = -1 so
m < ABC = 90 degrees.
Also, the sides AB and BC are equal in length
So. the Triangle is an isosceles right triangle.
simplify the expression - 4 1/2 ( - 2.5n + 3n - 4 ) .
Answer:
-2.25n + 18
Step-by-step explanation:
- 4 1/2 ( - 2.5n + 3n - 4 )
4 1/2 = 9/2
-9/2 (-2.5n + 3n - 4)
-9/2(0.5n - 4)
-2.25n + 18
PLEASE SHOW WORK…… I WILL GIVE BRAINLIEST
Answer:
11. 15°
I haven't learned how to find sides with only one side given yet I'm so sorry!!
Kala wrapped 48 gifts. Kala wrapped 6 times as many gifts as Juan. Let n be the number of gifts that Juan wrapped.
Answer:
Juan wrapped n gifts.
Kala wrapped 6n gifts. (because she wrapped 6 times as many gifts as Juan)
Kala wrapped 48 gifts in total (as stated in the problem)
So, 6n = 48
n = 8 (by dividing both sides by 6)
So, Juan wrapped 8 gifts.
Answer:
8 gifts.
Step-by-step explanation:
If Juan wrapped n gifts, then Kala wrapped 6n gifts because Kala wrapped 6 times as many gifts as Juan.
And we know that Kala wrapped 48 gifts, so we can set up an equation:
6n = 48
To find the number of gifts Juan wrapped, we can divide both sides of the equation by 6:
n = 48/6
n = 8
So Juan wrapped 8 gifts.
Rotate the triangle through 180° about the origin.
Answer:
(--1, -2)
(-4, -2)
(-4, -4)
Step-by-step explanation:
Rule ( x,y) ⇒ (-x, -y)
(1,2) ⇒ (-1,-2)
(4,2) ⇒ (-4,-2)
(4,4) ⇒ (-4,-4)
scalcet9 10.2.033. my notes ask your teacher practice another at what point(s) on the curve x = 9t2 2, y = t3 − 9 does the tangent line have slope 1 2 ?
The tangent line to the curve x = 9t^2 + 2, y = t^3 − 9 at the point (83, 18) has a slope of 1/2.
The slope of the tangent line to a curve at a point (x₀, y₀) can be found by taking the derivative of the equation for the curve at that point and evaluating it at x₀.
Given the curve x = 9t^2 + 2, y = t^3 − 9, we can find the derivative with respect to t, which is the slope of the curve at any point (x, y).
dx/dt = 18t
dy/dt = 3t^2
So, the slope of the tangent line at point (x₀, y₀) on the curve is given by:
m = dy/dt * (dt/dx) = (3t^2) * (1/18t) = (1/6) * t
To find the point(s) on the curve where the tangent line has slope 1/2, we set m = 1/2 and solve for t:
(1/6) * t = 1/2
t = 3
Substituting t = 3 back into the equation x = 9t^2 + 2, y = t^3 − 9, we get the point (x₀, y₀) = (83, 18).
--The question is incomplete, answering to the question below--
"at what point(s) on the curve x = 9t^2 + 2, y = t^3 − 9 does the tangent line have slope 1/2 ?"
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What’s the answer to the question?
A road i inclined at an angle of 3°. After driving 5403 feet along thi road, find the driver' increae in altitude. Round to the nearet foot. Ue ine coine and tangent
The increase in driver's altitude will be 283 feet based on the mentioned angle of elevation and distance travelled.
The road will represent hypotenuse and the altitude will represent the height of the triangle. Based on this, the formula to be used for calculation is -
sin theta = perpendicular ÷ hypotenuse, where theta is the angle of elevation.
sin 3° = altitude ÷ 5403
Rewriting the equation
Altitude = sin 3 × 5403
Keep the value of sine angle
Altitude = 0.05 × 5403
Performing multiplication
Altitude = 282.7 feet
Rounding off we get = 283 feet.
Thus, the altitude will be 283 feet.
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Express the following numbers in standard form
i) 5,00,00,000 ii) 39087.8 (iii) The distance between Earth and Moon is 384,000,000 m.
Answer:
i) 5,00,00,000 (5 billion) in standard form would be 5 x 10^9
ii) 39087.8 in standard form would be 3.90878 x 10^4
iii) The distance between Earth and Moon is 384,000,000 m (384 million meters) in standard form would be 3.84 x 10^8 m.
Step-by-step explanation:
Factor the expression completely.
x^4-4x^2-32
x
4
−4x
2
−32
X = -4,8 are the values of x in quadratic equation .
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem.
Let X² = X
= x^4 - 4x^2 - 32
= X² - 4X - 32
= X² - (8 - 4 )X - 32
= X² - 8X + 4X - 32
= X( X - 8 ) + 4( X - 8 )
= (X + 4 ) ( X - 8 )
= X = -4 , 8
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[tex] {2}^{2} \times {3}^{2} \times {5}^{2} [/tex]
I NEED HELP ASAP!!!! PLS!!!!
Is the prime factorization of what composite number?
A) 300
B) 900
C) 180
D) 240
Which list of numbers is ordered from least to greatest?
Answer: I want to say is this one: -6, -3, 2, 5
Step-by-step explanation: That one just look like its the one because the first option it goes from greatest to least and then repats itself so i know if not that one. then the next one also looks wrong. I saw is the 3rd one.
The radius of a quarter circle is 4 inches. What is the quarter circle's area
Answer:
i think its 3.14, im not sure though srry
Step-by-step explanation:
if the mean of a set of six numbers is 15, and the given numbers in the set are 5, 14, 10, 22, and 23, what is the value of the sixth number in the set? : * a) 0 b) 16 c) 22 d) 24
The value of the sixth number in the set of numbers is 16
The correct answer is an option (b)
Let us assume that 'p' be the value of the sixth number in the set.
So, the set of numbers is { 5, 14, 10, 22, 23, p}
The mean of a set of six numbers is 15.
We know that we can find the mean or average of a data set by adding all numbers in the data set and then dividing by the total number of values in the set.
Let m be the mean of set of numbers { 5, 14, 10, 22, 23, p}
So, m = 15
Here, the total number of values in set = 6
Using the formula for mean,
m = (5 + 14 + 10 + 22 + 23 + p)/6
15 = (5 + 14 + 10 + 22 + 23 + p)/6
15 × 6 = (5 + 14 + 10 + 22 + 23 + p)
90 = 74 + p
90 - 74 = 74 + p - 74
p = 16
Therefore, the sixth number is 16
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