Answer:
E
Step-by-step explanation:
The expression given is: sec β - cos β ( i will write "beta" instead of the symbol β)
We know that [tex]sec(x)=\frac{1}{cos(x)}[/tex]
Substituting this into the the expression and doing some algebra manipulation, we have:
[tex]sec(beta)-cos(beta)\\=\frac{1}{cos(beta)}-cos(beta)\\=\frac{1-cos^{2}(beta)}{cos(beta)}[/tex]
Using the identity [tex]cos^{2}(x)+sin^{2}(x)=1\\[/tex] (also [tex]sin^{2}(x)=1-cos^{2}(x)[/tex]), we can now write:
[tex]\frac{1-cos^{2}(beta)}{cos(beta)}\\=\frac{sin^2(beta)}{cos(beta)}\\=\frac{sin(beta)*sin(beta)}{cos(beta)}\\=\frac{sin(beta)}{cos(beta)}*sin(beta)[/tex]
We know [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex], substituting this, we have:
[tex]\frac{sin(beta)}{cos(beta)}*sin(beta)\\=tan(beta)*sin(beta)[/tex]
Answer choice E is the right answer.
The expression sec β - cos β in terms of sine and cosine simplifies to sin2 β. This is achieved by knowing that secant is the reciprocal of cosine and using the Pythagorean identity in trigonometry.
Explanation:To write the expression in terms of sine and cosine, we start by remembering that secant is the reciprocal of cosine, so sec β = 1/cos β. So, the expression sec β - cos β is equivalent to 1/cos β - cos β.
However, to remove the quotient from the expression, we multiply through by cos β to get 1 - cos2 β. So the expression sec β - cos β simplifies to 1 - cos2 β.
But remember, based on the Pythagorean identity in trigonometry, 1 - cos2 β is also equivalent to sin2 β. So that's our final simplified expression in terms of sine and cosine.
Learn more about Sine and Cosine here:https://brainly.com/question/22649800
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Geometry//Arcs and chords//Find the value of x // please explain
Answer:
x=22
Step-by-step explanation:
In the top lines, it is given they are perpendicular, in the bottom case, you don't know that. However, it is given that the line from the center intersects halfway the chord (I looked that up). By definition that means that these lines are also perpendicular. Since the line from the center is 12 units in both cases, the top chord must be the same size as the bottom chord.
x seems to denote the total length, so that's twice 11, x=22
Answer:
11
Step-by-step explanation:
if you folded the circle in help the 12s would line us and so would x and 11 so x = 11
Father gave me some money. I could choose between 15% of 1,500$ or 25% of 1,000$. Which amount did I choose
Answer:
25% of 1000 > 15% of 1500
Step-by-step explanation:
Lets calculate how much money you could receive
15% of 1500
.15 * 1500 = 225
25% of 1000
.25*1000 = 250
250>225
Final answer:
After calculating 15% of $1,500 and 25% of $1,000, it is evident that choosing the latter provides more money, amounting to $250 compared to $225 from the former option.
Explanation:
Choosing between percentages of different amounts involves straightforward arithmetic. To determine which option gives you more money, calculate the numerical value of each percentage. Option one is 15% of $1,500, which can be calculated as follows:
Convert the percentage to a decimal: 15% = 0.15.
Multiply the decimal by the total amount: 0.15 x $1,500 = $225.
Option two is 25% of $1,000:
Convert the percentage to a decimal: 25% = 0.25.
Multiply the decimal by the total amount: 0.25 x $1,000 = $250.
Now, compare the two amounts: $225 from the first option and $250 from the second option. It is clear that you would receive more money by choosing the 25% of $1,000, as it gives you a total of $250 compared to the $225 from the first option.
Can you help me solve that
Answer:2.6
Step-by-step explanation:
Use your graphing calculator of you have one and if you don't you can find one online and plug in the equation and find the intersection . If you get 2.5571 round it to the nearest tenth and you should get 2.6
Answer:2.6
Step-by-step explanation:
Use your graphing calculator of you have one and if you don't you can find one online and plug in the equation and find the intersection . If you get 2.5571 round it to the nearest tenth and you should get 2.6
[30 POINTS] An automobile steering wheel is shown. The ideal mechanical advantage of this wheel and axle = _____ .
The mechanical advantage is found by dividing Rw by Ra:
Mechanical advantage = 18 / 2 = 9
Answer:
Step-by-step explanation:
so it is basically nine
(x-2)(3x+4) destributive property
Answer:
FOIL IT:
First multiply the first terms in each parenthesis.
Outside is next. You multiply the terms on the outer edges of each parenthesis.
Inside is next. Multiply the terms on the inside edge of each parenthesis.
Last: Multiply last terms in each parenthesis.
YOU GET:
3x^2 - 2x - 8
One hot Saturday, Richard scooped 234 regular cones and 156 large cones. One scoop of ice cream is 3 ounces. A tub of ice cream weighs 10 pounds. How many tubs of ice cream did Richard use to make the cones?
Answer:
18
Step-by-step explanation:
The total number of scoops of ice cream that Richard got from the tub is,
(234 regular cones) x (2 scoops / 1 regular cone) + (156 large cones) x (2 scoops / 1 large cone) = 936 scoops
Given that each scoop weighs 3 ounces, the total weight of the ice cream is 2808 ounces. For the number of tubs,
(2808 ounces) x (1 lb / 16 ounces) x (1 tub /10 lb) = 17.55
Thus, the answer is 18.
Hope this helped!
Which graph represents a non proportional relationship?
The graph of a proportional relationship passes through origin (0, 0).
Therefore your answer is B).
Answer:
The answer is B
Step-by-step explanation:
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Apply distributive property to factor out the GCF
27+18r=
Answer: 9(3 + 2r)
Step-by-step explanation:
27 18r
∧ ∧
3 9 2 9r
∧ ∧
3 3 3 3r
27: 3 * 3 * 3
18r: 2 * 3 * 3 * r
Common Factors are 3 * 3 = 9
27: 9 * 3
18: 9 * 2r
27 + 18r = 9(3 + 2r)
Joe borrowed $9,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 2 years?
Joe paid $1,260 in interest over 2 years.
Explanation:To calculate the amount of interest Joe paid in 2 years, we can use the formula: Interest = Principal * Rate * Time. In this case, the principal is $9,000, the rate is 7% (which is equivalent to 0.07), and the time is 2 years. Plugging these values into the formula gives: Interest = $9,000 * 0.07 * 2 = $1,260. Therefore, Joe paid $1,260 in interest over 2 years.
find the next three term in the sequence-8, 24,-72,216
Answer:
- 648, 1944, - 5832
Step-by-step explanation:
the terms form a geometric sequence with
common ratio r = [tex]\frac{-72}{24}[/tex] = [tex]\frac{24}{-8}[/tex] = - 3
to obtain the next term in the sequence multiply the previous term by r
216 × - 3 = - 648
- 648 × - 3 = 1944
1944 × - 3 = - 5832
the next 3 terms are - 648, 1944, - 5832
Eliza travels 6 times as many minutes to school as ricky does.Altogether,they travel 63 minutes each day.How many minutes does Eliza travel?
Answer:
Eliza travels 54 minutes.
Step-by-step explanation:
Let's use the variable r to represent the number of minutes Ricky travles to school.
Eliza travels 6 times as many minutes as Ricky, so Eliza travels 6r minutes.
Altogether, they travel r + 6r minutes, or 7r minutes.
We are told they travel 63 minutes altogether, so 7r must equal 63.
7r = 63
Divide both sides by 7.
7r/7 = 63/7
r = 9
Ricky travels 9 minutes.
Eliza travels 6r minutes.
6r = 6 * 9 minutes = 54 minutes
Eliza travels 54 minutes.
you have a case of our mom's each one weighs 1.4 pounds and weight of 28 lb how many watermelons do you have
Answer:
20 watermelons
Step-by-step explanation:
28/1.4 = 20
Plz give me brainiest!!!!
You save $5,000.00 and invest 60% of it in stocks while leaving the rest in a savings account earning a 4.9% APR. The stock increases 9% in the first year and loses 4% of its value the second year. What would the gain have been if all of the investment had been left in the savings account?
Answer:
5,340
Step-by-step explanation:
Hi there:)
Amount invested in stock
=5000×0.6=3000
Amount invested in a saving account
5000-3000=2000
The stock increases 9% in the first year
3,000×(1+0.09)=3,270
and loses 4% of its value the second year
3,270×(1−0.04)=3,139.2
Amount of a saving account after two years
2,000×(1+0.049)^(2)=2,200.8
the total amount gained during the 2 years
3,139.2+2,200.8=5,340...answer
Hope it helps
Which statement shows the associative property of addition? 3⋅(5⋅x)=(3⋅5)⋅x 21 + 2y = 2y + 21 (u + 7) + 13 = u + (7 + 13) If m + 3 = 18, then 18 = m + 3.
Answer:
(u + 7) + 13 = u + (7 + 13)
Step-by-step explanation:
The associative property moves the parenthesis. We are doing addition , so we need to look for the problem that moves the parenthesis on addition.
find the value of x and y
Answer:
2x+10 // 2 • (x + 5)
Step-by-step explanation:
Final Result :
y + 10
Processing ends successfully
Under the dilation, the point (-3, -4) is moved to (-15, -20)
what is the scale factor of the dilation?
Answer:
The scale factor of dilation is: 5
Step-by-step explanation:
" A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
If the scale factor is greater than 1, the image is an enlargement (a stretch) " .
Whenever we multiply an coordinates or for some figure if all the coordinates get multiply by same factor 'a' then 'a' is called as scale factor in the dilation.
Here in this question:
(-3,-4) is moved to (-15,-20).
Here when (-3,-4) is multiplied by 5 we get the coordinate as: (-15,-20).
Hence, the scale factor is 5.
A flight from New York City to Chicago takes 3 1/2 hours
Answer:
8 HOURS PLEASE GIVE BRAINLIEST
Step-by-step explanation:
NY TO CHICAGO = 3.5 HOURS
CHICAGO TO LA = 4.5 HOURS
NY TO CHICAGO CHICAGO TO LA
3.5 + 4.5 = 8 HOURS
A line passes through the point , ( − 6, 1) and has a slope of − 4/3 .
Final answer:
A line with a slope of -4/3 passes through the point (-6, 1) can be represented by the equation y = -4/3x - 7.
Explanation:
A line with a slope of -4/3 passes through the point (-6, 1).
To find the equation of the line, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values into the equation, we get y - 1 = -4/3(x - (-6)).
Simplifying, we have y - 1 = -4/3(x + 6).
Expanding, y - 1 = -4/3x - 8.
Moving the constant term to the other side, we get y = -4/3x - 7.
what is the value of x in the diagram below ?
Answer:
x = 9
Step-by-step explanation:
12^2 + a^2 = 54^2
a^2 = 54^2 - 12^2
a = sqrt (54^2 - 12^2) = 6 * sqrt(77)
Then calculate it for another triangle, where each side is 6 times shorter (as 12/2 = 6):
2^2 + (sqrt(77))^2 = x^2
x^2 = 81
x = 9
Find the slope of the line represented by the table of values.
A) −4
B) −1/4
C) 4
D) 1/4
Answer:
B) −1/4
Step-by-step explanation:
The slope represents the change in y values divided by the change in x values. We can use the formula
slope = (y2-y1)/(x2-x1)
(2,4) (-2,5)
slope = (5-4)/(-2-2)
= 1/-4
slope = -1/4
Answer:
B. -1/4
Step-by-step explanation:
To get the slope you have to use the formula: y2-y1/x2-x1
y2-y1/x2-x1 = 4.47-5/-1-(-2)
4.75-5 = -.25
-1 - (-2) = 1
-.25/1 = -.25 or -1/4
Over time the value at property on 397 west lake street increased by 275. If the initial value of the property was p which expression represents the property current value? A) 375p B) 275p C) 3.75p D) 2.75p
Answer:
b
Step-by-step explanation:
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Initial value of the property = P
Rate of growth = 275%
So, we need to find the property's current value:
We will use "compound interest ":
What is the equation of the line that passes through the points (−2, 3) and (2, 7)?
x − y = −1
x − y = −2
x − y = − 5
x − y = − 6
The point-slope form of line:
[tex]y-y_1=m(x-x_1)[/tex]
The fomula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates of the points:
[tex]m=\dfrac{7-3}{2-(-2)}=\dfrac{4}{2+2}=\dfrac{4}{4}=1\\\\y-7=1(x-2)[/tex]
[tex]y-7=x-2[/tex] subtract y from both sides
[tex]-7=x-y-2[/tex] add 2 to both sides
[tex]-5=x-y\to\boxed{x-y=-5}[/tex]
determine two numbers that have a sum of 12 but a difference of 12
Answer:
0 And 12
Step-by-step explanation:
0 + 12 = 12
But 0 is 12 away from 12. hope i helped :)
Answer:
0 and 12
Step-by-step explanation:
0+12=12
12-0=12
Evaluate the expression 5x-3x for x=2
x is a placeholder for a number. Think of it as a box. Inside the box, we're told that 2 is there.
So we'll replace every x with 2 and use PEMDAS
5*x - 3*x = 5*2 - 3*2 = 10 - 6 = 4
After simplifying, the answer is 4.
Answer:
4
Step-by-step explanation:
5x-3x
We can simplify this expression
2x
Now we can substitute x=2
2(2)
=4
find the circumstances of a circle with a diameter of 27 cm
Answer:
84.78 cm
Step-by-step explanation:
The circumference = pi * d
d = 27
The circumference = 27 * pi
p = 3.14
The circumference = 84.78
If that is not among your choices, list what is.
What is a positive number that equals 30 when added to it squared
Answer: 5
Step-by-step explanation:
Let x represent the number, then
x² + x = 30
x² + x - 30 = 0
(x + 6) (x - 5) = 0
x + 6 = 0 x - 5 = 0
x = -6 x = 5
↓
not valid since the restriction is that x > 0 (a positive number)
So, x = 5
Find an equivalent ratio for the ratio 4 : 5.
400/500
10 : 12
48 to 60
20/30
Answer:
400/500
48 to 60
both are correct
Step-by-step explanation:
4/ 5
Multiply top and bottom by 100
4*100/ 5* 100 =400/500
400:500
4/5
Multiply top and bottom by 12
4/5 * 12/12 = 48/60
we can rewrite as 48:60
State the domain and range of the following function. {(2,3), (7,9), (4,-7), (6,2), (3,-5)}
Answer:
Domain: {2,3,4,6,7}
Range: { -7,-5,2,3,9}
Step-by-step explanation:
The domain is the input, or x, values.
The range is the output, or y, values.
They are normally written from least to greatest.
Answer:
Domain: 2,3,4,6,7
Range: -7,-5,2,3,9
Step-by-step explanation:
hope this helps :)
List the first 5 multiples,and find ALL the factors of 13.
11/12− 1/6q+5/6q−1/3
Answer:
16/12 = 1 4/12 or 1 2/6
Step-by-step explanation: