The value of the angle 16°43'27"is approximately 16.724167 degrees.
A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees.
The radian is the SI unit for measuring angles.1 degree = [tex]\frac{\pi}{180}[/tex] radiansA complete rotation around a circle is 180°.A degree is a narrow enough angle for many practical tasks where full degrees are enough for precision. In those instances when this is not the case, such as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be expressed in decimal degrees.To convert a degree from minutes and seconds to decimal we must know the relation between degree and minutes and seconds.
1 degree=60 minutes.
1 minute = 60 seconds.
The given angle is 16°43'27"
27 seconds = 27 ÷ 60 minutes = 0.45 minutes = 0.45 ÷ 60 degree =0.0075 degree
43 minutes= 43 ÷ 60 degree = 0.71666666..
Total angle in decimal = 16+0.71666666+0.0075 =16.7241666...
Therefore required angle ≈ 16.7241667 degrees.
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Do you know the muffin man?
Please answer following question in picture
1. The line passing through (-14,-9) and (7,9) has the equation:
y = 6/7x + 3/2
2.The line passing through (0,-3) and (0,15) has the equation:
since the slope is undefined, hence equation of the line is not formed.
3.The line passing through (-24,-16) and (-8,-6) has the equation:
y = 5/8x - 1
4.The line passing through (-8,-12) and (12,13) has the equation:
y = 5/4x - 2.
Given we have the pair of points, through which we need to determine the equation of the line:
1. (-14,-9) and (7,9)
first we need to find the slope
(-14,-9) = (x₁,y₁)
(7,9) = (x₂,y₂)
m= y₂₋y₁/x₂₋x₁
= 9-(-9)/7-(-14)
= 18/21
m= 6/7
Use the slope and one of the points to find the y-intercept b:
(7,9) and m= 6/7
substitute in y=mx+b
9=6/7(7) + b
b = 9/6
b= 3/2
now substitute m=6/7 and b= 3/2 in slope intercept form.
y = 6/7x + 3/2
2. (0,-3) and (0,15)
first we need to find the slope
(0,-3) = (x₁,y₁)
(0,15) = (x₂,y₂)
m= y₂₋y₁/x₂₋x₁
= 15-(-3)/0-0
= undefined
hence we can't frame the equation of the line.
3. (-24,-16) and (-8,-6)
first we need to find the slope
(-24,-16) = (x₁,y₁)
(-8,-6) = (x₂,y₂)
m= y₂₋y₁/x₂₋x₁
= -6-(-16)/-8-(-24)
= -6+16/-8+24
= 10/16
m= 5/8
Use the slope and one of the points to find the y-intercept b:
(-8,-6) and m= 5/8
substitute in y=mx+b
-6=5/8(-8) + b
b = -1
now substitute m=5/8 and b= -1 in slope intercept form.
y = 5/8x - 1
4. (-8,-12) and (12,13)
first we need to find the slope
(-8,-12) = (x₁,y₁)
(12,13) = (x₂,y₂)
m= y₂₋y₁/x₂₋x₁
= 13-(-12)/12-(-8)
= 25/12+8
= 25/20
m= 5/4
Use the slope and one of the points to find the y-intercept b:
(12,13) and m= 5/4
substitute in y=mx+b
13=5/4(12) + b
b = -2
now substitute m=5/4 and b= -2 in slope intercept form.
y = 5/4x - 2.
hence we get the acquired results.
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4/3 times 6/5 in simplest form
Answer:
8/5 or 1 3/5
Step-by-step explanation:
Answer:
Exact form: 8/5
Mixed Number form: 1 3/5
Step-by-step explanation:
First, let's cancel the common factor of 3
4/3 * 6/5
4 * (3*2/5)
4 * 2/5
Next, lets combine 4 and 2/5
4*2/5
8/5
We can finish this off by simplifying 8/5
8/5 = 1 3/5
Write an absolute value inequality for the graph below.
Use x for your variable.
←++
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
An absolute value inequality for given graph is |x| ≤ 6
In this question, we have been given a graph of a number line.
We need to write an absolute value inequality for given graph.
From the given graph, we can observe that the value of x lies between -6 to 6.
i.e., -6 ≤ x ≤ 6
We know that, for a real number 'm', the absolute value function for m would be,
|±m| = m
So, -6 ≤ x ≤ 6
|x| ≤ 6, which is required inequality.
Therefore, an absolute value inequality for given graph is |x| ≤ 6
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Triangle `CDA` is the image of Triangle `ABC` after a `180°` rotation about the midpoint of segment `AC`. Triangle `ECB` is the image of Triangle `ABC` after a `180°` rotation about the midpoint of segment `BC`.
ABCD and ABEC are parallelograms becayse a parallelogram can be divided into congruent triangles of different orientations
How to explain why ABCD and ABEC are parallelograms?The pre-image of the rotations are given as:
Triangle ABCTriangle ABCThe image of the rotations are given as:
Triangle CDATriangle ECBNotice that the triangles ABC and CDA have a common line segment AC, while the triangles ABC and ECB have a common line segment CB
The above is true, because the triangle is rotated by 180 degrees through its own midpoint
When the images of the rotations are viewed as a single shape, the view of the shape is a parallelogram
Because a parallelogram can be divided into congruent triangles of different orientations, then ABCD and ABEC are parallelograms
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Complete question
Triangle CDA is the image of triangle ABC after a 180º rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180º rotation around the midpoint of segment BC.
Explain why ABCD and ABEC are parallelograms.
See attachment for image
Solve for h s=2pie r squared =2 pie rh
H = S/2πr + r or (S + 2πr²)/2πr simplified and solved for the value S = 2πr² + 2πrh
Here given that S = 2πr² + 2πrh
Lets simply the equation
⇒ S = 2πr² + 2πrh
⇒ S = 2πr(r + h)
⇒ S/2πr = r + h
⇒ h = S/2πr + r or (S + 2πr²)/2πr
What is an equation?In mathematics, an equation is a formula that indicates the equality of two expressions by connecting them with the equals sign =.
The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.
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PLEASE ANSWER NOW
What is the distance between -22 and 12 on a number line? Write an expression using subtraction and absolute value to show the distance.
Answer:
34
Step-by-step explanation:
How can you write and evaluate an nth root of a number?
Let's say you wanted to find the cube root of 8
You write it on your paper like this: [tex]\sqrt[3]{8}[/tex]
In your calculator, you'd type this in: 8^(1/3)
The exponent of 1/3 corresponds to a cube root.
In general, the exponent of 1/n is for the nth root
The connection is [tex]\sqrt[n]{\text{x}} = \text{x}^{1/n}[/tex]
The pentagons ABCDE and PQRST are similar.
Find the length x of PQ .
The measure of the length PQ is 7.2
Similar shapesFigures are known to be similar if the ratio of the sides is equal to a constant "k".
In order to determine the value of k, we will use the following ratio as shown:
AB/BC = PQ/QR
Substitute the given parameters
6/2 = x/2.4
Cross multiply
2x = 2.4(6)
2x = 14.4
x = 14.4/2
x = 7.2
Hence the measure of the length PQ is 7.2
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a rectangle that is 3 inches by 5 inches has been scaled by a factor of 6. What are the side lengths of the scaled copy?
The lengths of the scaled copy of rectangle is 18 inches by 30 inches .
Scaled by a factor : Whenever something is scaled by a factor it means that it is multiplied by that factor .
For Example , if 3 is scaled by a factor of 2 , means 3 is multiplied by 2 that is 3*2=6.
In the given question
length of rectangle = 3inches
it is scaled by factor of 6 , that means
length of scaled copy of rectangle = 3*6= 18inches.
breadth of the rectangle = 5 inches
it is scaled by factor a factor of 6 , that means
breadth of scaled copy of rectangle = 5*6 = 30inches.
Therefore , the lengths of the scaled copy of the rectangle will be 18inches by 30inches.
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pls help me
Drag the tiles to the boxes to form correct pairs.
Consider functions f and g.
(a) The answer of (g.f)(2) is [tex]\sqrt{23}[/tex] .
(b)The answer of (g + f) (2) is [tex]\sqrt{3}[/tex] - 3 .
(c)The answer of (g - f) (-1) is [tex]\sqrt{15}[/tex] .
(d)The answer of [tex]\frac{f}{g}(-1)[/tex] is 0 .
The composition of functions f(x) and g(x) on which g(x) acts first is denoted by f(g(x)) or (f ∘ g)(x). It combines two or more functions to provide another function. In function composition, the output of the function inside the parentheses becomes the input of the outer function.We have given two functions f(x) = [tex]1-x^2[/tex] and g(x) = [tex]\sqrt{11-4x}[/tex]
(a) Put x = 2 in f(x) we get f(2) = 1 - 4 = -3
(g.f)(2) = g(f(2))
= g(-3)
[tex]=\sqrt{11-4(-3)}\\=\sqrt{11+12} \\=\sqrt{23}[/tex]
which is option (c) .
(b) Put x = 2 in f(x) we get f(2) = 1 - 4 = -3 and g(2) = [tex]\sqrt{11-8} =\sqrt{3}[/tex]
(g + f) (2) = g(2) + f(2)
= [tex]\sqrt{3}[/tex] + (-3)
= [tex]\sqrt{3}[/tex] - 3
which is option (a)
(c) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]
(g - f) (-1) = g(-1) - f(-1)
= [tex]\sqrt{15}[/tex] + 0
= [tex]\sqrt{15}[/tex]
which is option (b)
(d) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]
[tex]\frac{f}{g}(-1)[/tex] = f(-1) / g(-1)
= 0 / [tex]\sqrt{15}[/tex]
= 0
which is option (d)
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write the equation of the line through the points (-6,-9) and (2,5)
Answer: y2-y1 and x2-x1
Step-by-step explanation:
5-9=-4
2--6=8
-4,8
What is the slope of y = -19
Answer: 0
Step-by-step explanation: the slope intercept form is y= mx +b. The equation here is y = -19. It means that the slope, m, is 0. You can also think about it this way. y= -19 graph will show you that for every x value, the y is at -19 since there is no rise over run. it is just a straight line at y= -19
find the value for x
(x+63)
(4x)
Answer:
x = 21
Step-by-step explanation:
You are given expressions (x+63)° and (4x)° for alternate interior angles at a transversal crossing parallel lines. You want to know the value of x.
Alternate interior anglesWhere a transversal crosses parallel lines, alternate interior angles are congruent. That means ...
(4x)° = (x +63)°
3x = 63 . . . . . . . . divide by °, subtract x
x = 21 . . . . . . . . . divide by the coefficient of x
plssss help 10 if corrret
The difference between -4/5 and -3/5 will be -7/5.
How to express the fraction?It should be noted that the difference between 4/5 and 3/5 will be illustrated thus:
= 4/5 - 3/5
= 1/5
Subtracting -3/5 from -4/5 will be:
= -3/5 - 4/5
It should be noted that they both have negative signs.
Therefore, the value will be -7/5 or - 1 2/5.
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Compute using long division 342÷23
Answer:
342 ÷ 23 = 14.869565217 or 14 r 20
Check step-by-step explanation below for 2 methods to solve.
14.869565217 method right below
14 r 20 method at the bottom in bold and underlined
Hope this helps :)
Step-by-step explanation:
divisor
↓ ? <------ quotient
23 | 342 <------ dividend
remainder = r (the number that the divisor can't go into.
1) 23 goes into 34 one time, so we write the one on top.
1
23 | 342
2) 23 • 1 = 23 so then we subtract 23 from 34 and get 11.
1
23 | 342
- 23
1 1
3) Now we carry down the 2 and get 112.
1
23 | 342
- 23 ↓
1 1 2
4) 23 goes into 112 four times, so we write the four on top.
1 4
23 | 342
- 23 ↓
1 1 2
5) 23 • 14 = 92 so we subtract 92 from 112 and get 20.
1 4
23 | 342
- 23 ↓
1 1 2
- 92
20
6) 23 can't go into 20 so we add a decinal and a zero to 342 (dividend) and add a decimal to 14 too.
1 4.
23 | 342.0
- 23 ↓
1 1 2
- 92
20
7) Repeat the same steps again (Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor (if greater use it if less than take the next number). Then divide it by the divisor and write the answer on top as the quotient. Subtract the result from the digit and write the difference below. Bring down the next digit of the dividend (if present). Repeat the same process.)
1 4.8
23 | 342.0
- 23 ↓↓
1 1 2
- 92
200
- 1 84
16
8) Keep repeating and then we get 14.8695652174
*However, if the directions say to not continue and add the decimal and zero then we must put a remainer (r).*
1 4 r 20
23 | 342
- 23 ↓
1 1 2
- 92
20
Dan's has a current credit card statement of $785. His credit card APR is 24.42%. What would be his finance charge if he does not pay the balance in full?
The $785 balance on Dan's credit card is currently due. The APR on his credit card is 24.42%. He has to pay the full balance that is $785.2442.
Given that,
The $785 balance on Dan's credit card is currently due.
The APR on his credit card is 24.42%.
We have to find what finance fee would he pay if he didn't pay the balance in full.
To find the balance full he has to pay.
We have to add the balance of current due and APR .
We get,
=$785+24.42%
=$785+0.2442
=$785.2442
Therefore, he has to pay the full balance that is $785.2442.
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Rewrite in simplest terms: (x +9y) — (9x -8y)
Answer:Your answer would be -8 x - 17 y
Step-by-step explanation: x - 9 x would be - 8 x
You would have to distribute the negative in the problem -(9 x- 8 y) which would make it -9 x +8 y and 9 y + 8 y is 17 y so there fore the answer is -8 x - 17 y
Write a⇀ with magnitude 10 and direction 42° in component form. Round to the nearest tenth.
The component form of the given magnitude and direction is 7.4 + 6.7i.
What is component form?A vector's component form is the ordered pair that explains the changes in the x- and y-values. A vector v's component form is written as v=vx,vy, where vx represents the horizontal distance between the initial and terminal points and vy represents the vertical displacement between both the initial and terminal points.To find the component form of magnitude 10 and direction 42°:
component form = x + iy
Then,
x = 10 cos 42° = 7.43 = 7.4y = 10 sin 42° = 6.69 = 6.7Component form: 7.4 + 6.7iTherefore, 7.4 + 6.7i is the component form of the given magnitude and direction
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Which equation has no solution?
O 14x-21 = -6
O 1-2-x1=9
O 13x + 61 = 6
O 1-2x + 81 = 0
Equation has no solution is |4x-2|=-6
checking option A
|4x-2|=-6 . . . .1
if 4x-2≥0
4x≥2
x≥1/2
then |4x-2| = 4x-2
So , .. . . 1 becomes
4x-2=-6
4x=-4
x=-1
But x≥1/2
So x=-1 is not a solution.
if 4x-2≤0
4x≤2
x≤1/2
then |4x-2| = -(4x-2)
So , .. . . 1 becomes
-4x+2=-6
4x=8
x=2
but x≤1/2
So x=2 is not a solution.
checking option B
|-2-x| = 9 . . . 2
if -2-x ≥ 0
x≤-2
then
|-2-x| = -2-x
So, . . .. . 2 becomes
-2-x=9
x=-11
so it has a solution .
checking option C
|3x+61| = 6 . . . . . 3
if 3x+61≥0
x≥-61/3
then
|3x+61| = 3x+61
So, . . .3 becomes
3x+61=6
x=-55/3
So it has a solution.
checking option D
|-2x+8|=0 . . . . .4
if -2x+8≥0
x≤4
then |-2x+8| = -2x+8
So , .. . . . .4 becomes
-2x+8=0
x=4
So it has a solution.
Hence option A |4x-2|=-6
has not a solution.
Sometimes equations have no solution. This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction.
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There are hard sweets and soft sweets in a bowl in the ratio 3:5 The hard sweets are blue and red in the ratio 1:4 The soft sweets are blue and red in the ratio 2:3 What fraction of the sweets are blue?
The fraction of the sweets that are blue given the ratios is 13/40.
What is the fraction of blue sweets?A fraction is a non-integer that is made up of a numerator and a denominator. An example is 2/3. 2 is the numerator and 3 is the denominator.
Ratio shows the relationship between two or more numbers. It is the number of times that one value is contained in other value(s). Ratios are used to compare two or more numbers.
We would be assuming the numbers of sweet based on the given ratios.
The number of hard sweets = 30
The number of soft sweets = 50
Number of hard sweets that are blue = (1/5) x 30 = 6
Number of soft sweets that are blue = (2/5) x 50 = 20
Total number of blue sweets =20 + 6 = 26
Total number of sweets = 30 + 50 = 80
Fraction of blue sweets = 26/80 = 13 /40
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Convert 121 lb to kg and round to the nearest tenth
Answer: 54.9
Step-by-step explanation:
121 lb converted to kk is 54.885
54.885 rounded to the nearest tenth is 54.9
Hey guys please help me with this thanks
Answer:
Step-by-step explanation:
boy just include the unit rate of mph and make the question solvable as easy as that, or you could use the example and change the mph
Find the other endpoint of the segment with a midpoint of (-6, 4) and endpoint of (4, 8).
Show your own work
Answer:
(-16, 0)
Step-by-step explanation:
The midpoint can be found using the formula below, where [tex](x_1,y_1)[/tex] is the first endpoint and [tex](x_2, y_2)[/tex] is the other endpoint.
[tex]\boxed{\text{Midpoint}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )}[/tex]
Let the other endpoint be (x, y).
Substitute the given midpoint and one endpoint into the formula above:
(-6, 4)= [tex](\frac{x+4}{2},\frac{y+8}{2} )[/tex]
Comparing the x-coordinate:
[tex]-6=\frac{x+4}{2}[/tex]
Multiply both sides by 2:
x +4= -12
Subtract 4 from both sides:
x= -12 -4
x= -16
Comparing the y-coordinate:
[tex]4=\frac{y+8}{2}[/tex]
Multiply both sides by 2:
y +8= 8
Subtract 8 from both sides:
y= 8 -8
y= 0
Thus, the other endpoint is (-16, 0).
Supplementary:
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Solve for x.
3x+2
70°
Answer:
it 21
Step-by-step explanation:
rr
Solve the following compound inequality. −x−4≤x−12≤−x+2 Submit your answer by dragging the movable blue points on the number line.
Solution:
Inequality Form: [tex]4\leq x\leq 7[/tex]
Interval Notation: [tex][4,7][/tex]
_________________________________________________________
As for plotting on your line graph, one point should be a closed circle on 4, then the next should be a closed circle on 7.
__________________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Eli broke a cell sample into 14 batches, each weighing 4.7 x 10-8 grams. How much
did the original sample weigh? Use scientific notation to express your answer.
The weight of the original sample from which all 14 batches in the task content is; 65.8 x 10-8 grams.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that Eli broke a cell sample into 14 batches, each weighing 4.7 x 10-8 grams. which follows that the task content; the weight of the original sample from which the eight batches were obtained be determined.
Hence, since each of the 14 batches weighs;
[tex]4.7 \times 10^{-8}[/tex]
Therefore, the weight of the original sample can be obtained as;
[tex]4.7 \times 10^{-8} \times 14\\\\65.8 \times 10^{-8}[/tex]
However, when the weight is expressed in scientific notation, thus the weight of the original sample is;
[tex]65.8 \times 10^{-8}[/tex]
Hence, The weight of the original sample from which all 14 batches which each weighed 4.7 x 10-8 grams are obtained as required in the task content is; 65.8 x 10-8 grams.
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Find the lengths of UV and ST and determine whether they are congruent.
Hint: Congruent line segments have the same length.
Answer:
-2, S, U, V. that was a good question.
Step-by-step explanation:
Thanks. You are known.
USING TOOLS The table shows the numbers y (in thousands) of people in a city who regularly use sharable
electric scooters x weeks after the scooters are introduced.
Time, x Number of users, y
1, 1.5
4, 2.2
6, 2.4
10, 3.9
12, 5.5
15, 6.8
20, 12.3
24, 16.4
25, 17.6
1. Write function that models the data
2. Use the model to predict the number of users after 32 weeks
From the data given, we have that:
1. The linear regression equation is given by:y = 0.69684x - 1.43675.
2. 21 users during the 32th week.
How to find the equation of best fit using a calculator?To find the equation, we need to insert the points (x,y), given in a scatter plot or in a table, in the calculator. We also have to identify the type of data that models the situation, such as linear, quadratic or exponential.
For this problem, the data is increasing somewhat linearly, hence linear regression is used.
The points of the function, from the table, are given as follows:
(1, 1.5), (4, 2.2), (6, 2.4), (10, 3.9), (12, 5.5), (15, 6.8), (20, 12.3), (24, 16.4), (25, 17.6).
Hence the the linear equation that models the data is:
y = 0.69684x - 1.43675
The value during the 32th week is found when x = 32, hence:
y = 0.69684(32) - 1.43675 = 21 (rounded up, as the first decimal digit is greater than 0.5).
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Identify and extend the pattern to find the next number in the sequence 3, 12, 48, 1 92
Answer:
768
Step-by-step explanation:
The numbers are multiplying by 4 each time, Therefore the next number will be 768.