Answers
Let x be the side opposite to angle 62 degrees
Let y be the adjacent angle.
The sine of the angle is given as follows:
[tex]\begin{gathered} \sin62=\frac{Opposite}{Hypotenuse}=\frac{x}{10} \\ \end{gathered}[/tex]The cosine is given as:
[tex]\cos62=\frac{Adjacent}{Hypotenuse}=\frac{y}{10}[/tex]Related Questions
complete the table to show the total change in the average mean daily in the price of for stocks over a five-day.
Answers
Answer: -$0.26, -$0.7, $0.65, and -$1.6
The number of days = 5
Average price = Total change in price / the number of days
For Stock A
Total change in price = -$1.30
Average price = - 1.30 / 5
Average price = -$0.26
STOCK B
Average change in price = -$0.14
From, Average price = Total price / number of days
Total price = Average price x number of days
Total price = -0.14 x 5
Total price = - $0.7
For stock C
Average price = 3.25 / 5
Average price = $0.65
Stock D
Average price = Total price / number of days
Total price = Average price x number of days
Total price = -0.32 x 5
Total price = - $1.6
The answer are -$0.26, -$0.7, $0.65, and -$1.6
7. Explain It Draw a net for a triangular pyramid. Explain how you know your dagram is correct.
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The definition of geometry net is the 2-dimensional shape that if folded, it will produce or yield to the 3-dimensional image
Since the triangular pyramid, has 4 sides (4 triangular faces), when we unfold it on the edges from one tip/corner, it will produce a 2-dimensional image of 3 triangles attached to the sides of one triangle
Consider the following expression-x + 8x2 - 9x?Step 2 of 2: Determine the degree and the leading coefficient of the polynomial.
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Solution
For this case we have the following polynomial:
[tex]-x+8x^2-9x[/tex]For this case the higher degree is 2 then the answer is:
Degree= 2
Leading Coefficient of the polynomial: 8
Convert to fractional Notation 4 19/100
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to solve this we need to convert the number 4 to a fraction with denominator 100 and add both fractions
to do that we can multiply 4 and 1 by 100, like this:
[tex]\frac{4\cdot100}{1\cdot100}=\frac{400}{100}[/tex]now we can add the fractions
[tex]\frac{400}{100}+\frac{19}{100}=\frac{419}{100}[/tex]So the answer is: 419/100
Amplitude, period, and phase shift of sine and cosine functions
Answers
We are given that
[tex]y=-2+2\cos (2x-\frac{\pi}{3})[/tex]Note: Given the cosine function
[tex]y=a\cos (bx-c)+d[/tex]then
[tex]\begin{gathered} Amplitude=a \\ Period=\frac{2\pi}{b} \\ PhaseShift=\frac{c}{b} \\ VerticalShift=d \end{gathered}[/tex]Comparing the question with what is written in the note
We have
[tex]\begin{gathered} a=2 \\ b=2 \\ c=\frac{\pi}{3} \\ d=-2 \end{gathered}[/tex]We want to find
(a). Amplitude
From the given question, the amplitude (a) is
[tex]\begin{gathered} a=2 \\ Amplitude=2 \end{gathered}[/tex](b).Period
From the given question, the period is
[tex]\begin{gathered} Period=\frac{2\pi}{b} \\ Period=\frac{2\pi}{2} \\ Period=\pi \end{gathered}[/tex](c). Phase Shift
From the given question, the phase shift is
[tex]\begin{gathered} PhaseShift=\frac{c}{b} \\ PhaseShift=\frac{\pi}{3}\times\frac{1}{2} \\ PhaseShift=\frac{\pi}{6} \end{gathered}[/tex]Drag each number to the correct location on the table
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Step-by-step explanation:
There is no table attached, please recheck and resend.
Alyssa will correctly label the numbers 48.4, 48482, 48.09, and 48on the number line below.
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The numbers under consideration are:
[tex]48.4,\text{ 48}\frac{1}{2},\text{ 48.09, 48}\frac{3}{5}[/tex]Converting all the numbers to decimal:
[tex]\begin{gathered} 48\frac{1}{2}=\text{ 48+0.5 = 48.5} \\ 48\frac{3}{5}=\text{ 48 + }0.6\text{ = 48.6} \end{gathered}[/tex]Therefore, the numbers can be written as:
48.4, 48.5, 48.09, and 48.6
Out of these numbers, only 48.6 is closest to 49
[tex]48\frac{3}{5}\text{ is closest to 49}[/tex]If the distance from the too of the building to the tip of its shadow is 150ft, what is the length of the buildings shadow
Answers
In order to know the length of the shadow, we will use a trigonometric function in this case for the data given and the distance we want to find we will use the sine
[tex]\sin (75)=\frac{S}{150}[/tex]we isolate S
[tex]S=\sin (75)\cdot150=144.89[/tex]the length of the shadow is 144.89ft
wich time of line are shown in the figure
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Solution
Step 1
Two distinct lines intersecting each other at 90° or at right angles are perpendicular to each other.
Hence apply this to question 8 the type of lines shown in the figure is perpendicular lines. Option C
Step 2
To explain this as stated above line A and line B intersect each other at a right angle hence line A and B are perpendicular lines. The line segments are seen below.
Need help with my math yall please??
Answers
The value of the expression after simplification is found as -3.
What is termed as simplification?Simplify simply way of making something easier to understand. Simply or simplification in mathematics refers to reducing an expression/fraction/problem to a simpler form. It simplifies the problem by calculating and solving it. We can —Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This helps make the expression simple to understand and solve.For the given expression;
5x + 8 = 2x - 1
Subtract 8 from both side.
5x + 8 - 8 = 2x - 1 - 8
Simplify
5x = 2x - 9
Subtract both side by 2x.
5x - 2x = 2x - 9 - 2x
3x = -9
Divide both side by 3.
3x/3 = -9/3
x = -3
Thus, the value of the expression is found as -3.
To know more about the simplification, here
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how many shirts can Jeanette sew at most of and still have 1. spool of thread left
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Answer:
The number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]Explanation:
Given a graph that relates the number of spools of thread left to the number of shirts sewn.
We want to find the number of shirts sewn at most, when there is just 1 spool of thread left.
To get that, let us draw a straight horizontal line from y=1 (spools of thread remaining =1) to join the line of the graph and also trace it down.
Tracing the line down we can observe that it is at shirt sewn equals 5.
So, the number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]prove the formula sin 3 A + sin A = 4 sin A cos2A
Answers
We proved that formula using the trigonometry relations sin3A + sinA = 4sinAcos^2A.
In the given question,
We have to prove the formula sin 3A+sin A = 4sinAcos^2A
The given expression is sin 3A+sin A = 4sinAcos^2A
To prove the formula we take the left side terms to the right side terms
The left side is sin 3A+sin A.
As we know that sin 3A = 3sinA − 4sin^3A
To solve the left side we put the value of sin 3A in sin 3A+sin A.
=sin 3A+sin A
=3sinA − 4sin^3A+sin A
Simplifying
= (3sinA+sin A) − 4sin^3A
= 4sinA − 4sin^3A
Taking 4sinA common from both terms
= 4sinA(1 − sin^2A)
As we know that cos^2A=1 − sin^2A. So
= 4sinAcos^2A
We proved the right hand side.
To learn more about formula of trigonometry terms link is here
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Find a unit vector u in the direction of v. Verify that ||0|| = 1.v = (4, -3)U =
Answers
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
A parallelogram has an area of 364.5 cm2. If the base is 27 cm, What is the height?
Answers
Answer:
Height = 13.5cm
Explanation:
The area of a parallelogram is obtained using the formula below:
[tex]\text{Area}=\text{Base}\times Height[/tex]Substituting the given values:
[tex]\begin{gathered} 364.5=27\times\text{Height} \\ \text{Height=}\frac{364.5}{27} \\ H\text{eight}=13.5\operatorname{cm} \end{gathered}[/tex]Jim baked 48 cookies with 4 scoops of flour. How many scoops of flour does Jim need in orderto bake 96 cookies? Assume the relationship is directly proportional.
Answers
Given:
Jim baked 48 cookies with 4 scoops of flour.
So, the unit rate will be = 48/4 = 12 cookies/scoop of flour
So, for 96 cookies, the number of scoops of flour will be =
96/12 = 8
So, the answer will be 8 scoops of flour
I need help please there are two parts when we are done with part one the next part shows :) now can I get help
Answers
The months in which the income was greater than the expenses are:
June, July and August
Find the value when x = 2 and y = 3.x ^-3y^ -3A. 54B. 216C. 1/216
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Explanation:
x ^-3y^ -3
1. Juan bought fruit from the grocery store. The variables below define his purchase. Juan's bananas cost half as much as apples. Which equations can be used to model his purchase? Select each correct equation.* a = the number of apples he bought b = the number of bananas he bought x= the cost of an apple in dollars y= the cost of a banana in dollars A- a= 1/2 bb- y=1/2 xc- a=2bd- x=2ye- y=2af- b=1/2 x
Answers
Juan's bananas cost half ( 1/2) as much as apples.
x= the cost of an apple in dollars
y= the cost of a banana in dollars
Multiply the cost of an apple by 1/2 (half). that expression must be equal to the cost of a banana.
y = 1/2 x (option b)
The graph shows a dilation of trapezoid TRAP with respect to the origin which statements are true about the figures select three
Answers
A dilation means an elongation of the sides of a figure
So in a dilation the sides are bigger than at the original figure
A key formula for found dilation is Pithagoras theorem
For calculate T'R'
T'R' is the exact diagonal of OT' and OR', that means
OT' + OR' = T'R' in vectorial sum
OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum
So then T'R'^2 = 5^2 + 5^2 = 50.
and T'R'= √50
Now find TR to find the factor of dilation that is
T'R'/TR
Find the surface area of the triangular prism. 13 in. 5 in. 4 in. 12 in.
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The first face is a triangle with height 5in and base 12in
Traingular face area = 1/2 x bh
=1/2 x 12 x 5
= 30 in^2
The area of the other triangular base = 30 in^2
Area of left side face = Length x breadth
= 5 x 4 = 20in^2
Area of the slant face = Length x breadth
= 13 x 4 = 52in^2
Area of the bottom face = Length x breadth
= 12 x 4 = 48in^2
Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2
=180in^2
4. AABC = ADBC by SSS. Select one set of corresponding parts that could be marked congruent by CPCTC.B.A11CDO CBDAO ZA ZDOZCZ ZBO ACBC
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We are given two triangles that are congruent and we are asked to mark the parts that are congruent by CPCTC, this stands for Corresponding Parts of Congruent Triangles are Congruent. This means that when two triangles are congruent then their corresponding sides and angles are also congruent.
We notice that the following segments are corresponding segments and therefore congruent:
[tex]\begin{gathered} AB=BD \\ AC=DC \\ CB=CB \end{gathered}[/tex]And also the following angles are corresponding angles and therefore congruent:
[tex]\begin{gathered} \angle A=\angle D \\ \angle ABC=\angle DBC \\ \angle ACB=\angle DCB \end{gathered}[/tex]Therefore, from CPCTC we know that the corresponding parts are:
[tex]\angle A=\angle D[/tex]Two companies provide service in a community.• The total cost of a service call for x hours of labor at company A is modeled byy = 28x+ 32.5.• The initial charge for a service call at company B is $3 less than at company A, but their hourly rate is 25% greater.What is the expected total cost of a service call for 6 hours of labor at company B?
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Answer:
The expected total cost of a service call for 6 hours of labor at company B is $239.5
Step-by-step explanation:
To solve this, we'll find the expression that models the cost at company B.
First, we'll calculate the hourly rate. We know that is 25% greater than the $28 rate from company A, so we can use a rule of three as following:
This way,
[tex]\begin{gathered} x=28\times\frac{125}{100} \\ \\ \Rightarrow x=35 \end{gathered}[/tex]Therefore, we'll have that the hourly rate for company B is $35.
Now, we know that the charge for service is $3 less than at company A. This way,
[tex]32.5-3=29.5[/tex]We can conclude that the charge for service at company B is $29.5
Using this data, we'll have that the expression that models the cost for company B is:
[tex]y=35x+29.5[/tex]Using x = 6 (six hours of labor),
[tex]\begin{gathered} y=35(6)+29.5 \\ \\ \Rightarrow y=239.5 \end{gathered}[/tex]Therefore, we can conclude that the expected total cost of a service call for 6 hours of labor at company B is $239.5
102,410,000,000,000,000,000,000,000 in scientific notation round to two digits after the decimal
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We have a big integer and want to write in scientific notation.
To do this we need to count how many places we need to move the decimal point.
In this case we need to move the decimal point to left so the exponent of 10 will be positive.
So,
[tex]\begin{gathered} 102,410,000,000,000,000,000,000,000=1.0241\cdot10^{29} \\ \text{Round to two digits after the decimal:} \\ 1.02\cdot10^{29} \end{gathered}[/tex]We move the decimal point 29 places to left so the exponent of 10 is 29.
Drag the tiles to the boxes to form correct pairs.Match each set of vertices to the triangle they form.acute equilateralright isoscelesacute isoscelesA(3,5),B(3,4),C(5,4)A(2,4), B(4,5), C(3,6)A(3,5),B(5,6),C(3,0)A(2,4),B(3,5), C(2,6)obtuse scaleneright scalene
Answers
Step 1
Plot the triangles
let
A)
we can see that angle in B is 90 ° and length AB is different to BC, When one of the three angles measure 90 degrees and the angles or lengths of other two sides are not congruent, then the scalene triangle is called right scalene triangle
right scalene
Step 2
triangle 2
[tex]A(2,4)\text{ B\lparen4,5\rparen c\lparen3,6\rparen}[/tex]in this case, we have that length AC equlas AB,also we can see that angle A is smaller than 90 ° ,an acute angle measure less than 90 degrees,so
so
[tex]AC=AB[/tex]a triangle in which two sides have the same length is called acute isosceles
Step 3
A(3,5),B(5,6),C(3,0)
an obtuse scalene triangle can be defined as a triangle whose one of the angles measures greater than 90 degrees but less than 180 degrees and the other two angles are less than 90 degrees. All three sides and angles are different in measurement.so this is an
obtuse scalene
Step 4
finally, A(2,4),B(3,5), C(2,6)
An isosceles right triangle is defined as a right-angled triangle with an equal base and height which are also known as the legs of the triangle.
we can see that
[tex]\begin{gathered} m\angle B=90 \\ AB=BC \end{gathered}[/tex]therefore, this is an
rigth isosceles
I hope this helps you
Answer:(3,5) (4,5) (3,6)
acute isosceles
Step-by-step explanation:
For each situation, an inequality is written. Which one has an incorrect inequality?АThree less than a number is greater than negative four and less than negative one; - 4 75DAll real numbers that are greater than or equal to - 7 1/2or less than or equal to zerox < 0 or x>-7 1/2
Answers
Option D has an incorrect inequality.
Since option D Says:
"All real numbers that are greater than or equal to - 7 1/2 or less than or equal to zero"
Greater than or equal is represented with the symbol ≤ or ≥.
So the correct inequality is for this statement is:
x ≤0 or x>-7 1/2
Not
x < 0 or x>-7 1/2
Note that the x and 0 part doesn't have an equal sign.
Fill in the missing number to complete the linear equation that gives the rule for this tablex: 4, 5, 6, 7y: 32, 40, 48, 56y = ?x
Answers
according to the equation and information given we can see that the equation is in the form
[tex]y=kx[/tex]in which k is the constant of proportionality
use one of the points to find the constant
[tex]\begin{gathered} 32=k(4) \\ k=\frac{32}{8} \\ k=8 \end{gathered}[/tex]replace withone of the points to see if its true in all the points
[tex]\begin{gathered} 40=8\cdot5 \\ 40=40 \end{gathered}[/tex]according to this the equation for the table will be
[tex]y=8x[/tex]how do i expand -4(-x-8)
Answers
Answer:
4x+32
Step-by-step explanation:
mutiply the -4 to both numbers inside parentheses. negative * negative= positive. -4*-x=4x, -4*-8=32
helpppppppppppppppppppppppppppppp
Answers
Answer:
[tex]f^{-1}[/tex](x) = x/2 - 3/2
Step-by-step explanation:
Swap x and y and solve for y.
Original equation:
y = 2x + 3
Swapped equation:
x = 2y + 3
Now, solve for y:
x -3 = 2y
y = (x-3)/2
If it's wrong, it might just be the way you format your answer, since Pearson (what I assume you're using) is specific about that.
Maybe, [tex]f^{-1}[/tex](x) = x/2 - 3/2 or [tex]f^{-1}[/tex](x) = (x-3)/2
an airliner travels 30 miles in 4 minutes. what is its speed in miles per hour?
Answers
We need to convert minutes to hours. We know that 1 hour is 60 minutes so we can use the conversion factor of 1 hour = 60 minutes. We make sure the minutes cancel in the top and bottom leaving
30 miles 60 minutes
------------- * --------------
4 minutes 1 hour
30 miles * 60
--------------------
1 hour
180 miles
--------------
hour
Can anyone help me with this I’m stuck and this is pretty difficult.
Answers
Answer:
x=-1
Explanation:
Given the equation:
[tex]$$ 24=4(x-7)+8(1-6 x) $$[/tex]First, expand the brackets:
[tex]24=4x-28+8-48x[/tex]Next, collect like terms and simplify:
[tex]\begin{gathered} 24=4x-48x-28+8 \\ 24=-20-44x \\ \text{ Add 20 to both sides} \\ 24+20=-44x \\ 44=-44x \\ \text{ Divide both sides by -44} \\ \frac{44}{-44}=\frac{-44x}{-44} \\ x=-1 \end{gathered}[/tex]The solution to the equation is -1.