Answer:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period in years
In this case, we have:
P = £1430
r = 0.005 (0.5% per month)
n = 12 (compounded monthly)
t = 9/12 = 0.75 (9 months is three-quarters of a year)
So we can plug in these values to find the final amount:
A = £1430(1 + 0.005/12)^(12*0.75)
A ≈ £1481.18
Therefore, the amount of money in the account after 9 months will be approximately £1481.18.
How do I solve those explain it to me please I need help ASAP thanks
A certain drug is made from only two ingredients: compound A and B. There are 5 milliliters of compound A used for every 7 milliliters of compound B. If a chemist wants to make 1104 milliliters of the drug, how many milliliters of compound a needed?
Answer:
460 milliliters
Step-by-step explanation:
We know that the ratio of A to B is 5:7. This means for every 5 milliliters of A, we need 7 milliliters of B. Let's use this ratio to find how many milliliters of A we need for 1104 milliliters of the drug.
First, we need to find out how many sets of 5:7 we have in 1104 milliliters. We can do this by dividing 1104 by the total number of parts in the ratio, which is 5 + 7 = 12.
1104 / 12 = 92
This means we have 92 sets of 5:7 in 1104 milliliters of the drug. To find how many milliliters of A we need, we simply multiply the number of sets by the amount of A in each set, which is 5 milliliters.
92 x 5 = 460
Therefore, we need 460 milliliters of compound A.
Which one of these transformations would produce an image that is not congruent to its pre-image? (5 points) Group of answer choices A dilation followed by a reflection A rotation of 90 degrees about the origin A translation of (x − 1, y − 3) A rotation followed by a translation
The οptiοn “a dilatiοn fοllοwed by a reflectiοn” will prοduce an image that is nοt cοngruent tο its pre-image οptiοn, first οptiοn is cοrrect.
What is geοmetric transfοrmatiοn?It is defined as the change in cοοrdinates and the shape οf the geοmetrical bοdy. It is alsο referred tο as a twο-dimensiοnal transfοrmatiοn. In the geοmetric transfοrmatiοn, changes in the geοmetry can be pοssible by rοtatiοn, translatiοn, reflectiοn, and glide translatiοn.
As we knοw, the translatiοn will shift the οbject.
If rοtate the image with 90 degree abοut οrigin will change the οrientatiοn οf the image but shape will remains same.
A dilatiοn fοllοwed by reflectiοn will change the image because the transfοrmatiοn dilatiοn is used tο resize an item. Dilatiοn is a technique fοr making items appear larger οr smaller.
Thus, the οptiοn "a dilatiοn fοllοwed by a reflectiοn" will prοduce an image that is nοt cοngruent tο its pre-image οptiοn fοurth is cοrrect.
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Complete question:
Which one of these transformations would produce an image that is not congruent to its pre-image? (5 points)
[Group of answer choices]
A dilation followed by a reflection A rotation of 90 degrees about the origin A translation of (x − 1, y − 3) A rotation followed by a translationA parabola opening up or down has vertex (0, -4) and passes through (10, 1). Write its
equation in vertex form.
Answer:
Since the vertex is (0, -4), we know that the equation of the parabola will have the form:
y = a(x - 0)^2 - 4
where "a" is the coefficient that determines whether the parabola opens up or down.
To find the value of "a", we can use the fact that the parabola passes through the point (10, 1):
1 = a(10 - 0)^2 - 4
1 + 4 = 100a
5 = 100a
a = 1/20
Substituting this value of "a" into the equation for the vertex form, we get:
y = (1/20)x^2 - 4
So the equation of the parabola in vertex form is y = (1/20)x^2 - 4, with vertex (0, -4) and passing through (10, 1).
Step-by-step explanation:
(pls pls help!!) Calculate each value for ⊙P.
=
Area of shaded factor = (fraction) ft
Area of unshaded factor = (fraction) ft
The area of the shaded sector is 575π/9 square units.
The area of the unshaded sector is 325π/9 square units
What is the area of the sectors?
The value of the angle subtended by the unshaded sector is 130⁰ the value of the angle subtended by the shaded sector is 230⁰.
To find the area of a sector with radius 10 units and angle 230⁰, we can again use the same formula:
Area of sector = (angle/360) x πr^2
Substituting the values given in the formula, we get:
Area of sector = (230/360) x π(10)²
= (23/36) x 100π
= 575π/9 square units
To find the area of a sector with radius 10 units and angle 130⁰, we can use the formula:
Area of sector = (angle/360) x πr^2
Substituting the values given in the formula, we get:
Area of sector = (130/360) x π(10)^2
= (13/36) x 100π
= 325π/9 square units
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I need help with this please
Answer:
d
Step-by-step explanation:
1 kg has 1000 g
Then 2,5 kg has 2,5 × 1000 = 2500 g
You can also make a proportion:
1 kg - 1000 g
2,5 kg - x g
Use the property of the proportion to find x (cross-multiply):
x = 2,5 × 1000 / 1 = 2500 g
Aiden models a can of ground coffee as a right cylinder. He measures its radius as 3 4 4 3 in and its volume as 12 cubic inches. Find the height of the can in inches. Round your answer to the nearest tenth if necessary.
The height of the can is 0.238 inches.
What is the volume of cylinder?
The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula πr²h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder.
Here, we have
Given: Aiden models a can of ground coffee as a right cylinder. He measures its radius as 3 4/3 in and its volume as 12 cubic inches.
We have to find the height of the can.
the volume of the can of ground coffee = πr²h
12 = 3.14×(12/3)²h
12/50.24 = h
h = 0.238inches.
Hence, the height of the can is 0.238 inches.
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What do I need to fix??
If we simplify [tex]3(2v-4)-4(v+4)[/tex], our answer will be [tex]-5v - 20[/tex]
How do we simplify the equation?Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler, usually shorter.
The question is [tex]3(2v-4)-4(v+4)[/tex], our step of solution is as follows:
==>>3(2v-4)-4(v+4)
Open the bracket with multiplication
= 6v - 12 - 4v - 16
= 2v - 28
= 2(v - 14)
= -5v - 20
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Please help with number 3!! Thank you so much!
Therefοre, the expressiοn can be rewritten in terms οf the functiοn [tex]cos x[/tex]as: [tex]2cos^2 x + cos x - 2[/tex].
What is trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles. It is particularly cοncerned with the study οf angles, the trigοnοmetric functiοns (sine, cοsine, tangent, etc.), and their prοperties and applicatiοns.
Trigοnοmetry has many practical applicatiοns, particularly in fields such as physics, engineering, and astrοnοmy, where it is used tο sοlve prοblems invοlving angles, distances, and shapes. Fοr example, trigοnοmetry is used in surveying tο measure distances and heights, in navigatiοn tο determine the pοsitiοn οf ships and airplanes, and in physics tο describe the mοtiοn οf waves and οscillatiοns.
In the given questiοn,
We can use the trigοnοmetric identity [tex]cos^2 x + sin^2 x = 1[/tex] tο rewrite [tex]sin^2 x[/tex] as: [tex]sin^2 x = 1 - cos^2 x[/tex]
Substituting this intο the οriginal expressiοn gives:
[tex]cos^2 x + cos x - 1 + sin^2 x = cos^2 x + cos x - 1 + (1 - cos^2 x) = 2cos^2 x + cos x - 2[/tex]
Therefοre, the expressiοn can be rewritten in terms οf the functiοn [tex]cos x[/tex] as: [tex]2cos^2 x + cos x - 2.[/tex]
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I js need help with this question
a. The numeric values of the function are given as follows:
x = -1, y = -10.x = 5, y = 2.b. The function rule is given as follows: y = 2x - 8.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.From the table, when x = 0, y = -8, hence the intercept b is given as follows:
b = -8.
Considering points (0, -8) and (10, 12), when x increases by 10, y increases by 20, hence the slope m is given as follows:
m = 20/10
m = 2.
Hence the function is given as follows:
y = 2x - 8.
To complete the table, the numeric values are given as follows:
x = -1: y = 2(-1) - 8 = -2 - 8 = -10.x = 5: y = 2(5) - 8 = 10 - 8 = 2.More can be learned about linear functions at https://brainly.com/question/24808124
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Reggie, Tom and Corwin collected stamps in the ratio of 8:4:5. After Corwin gave 3/10 to Reggie and Tom, Corwin had 192 less stamps than Reggie. The number of stamps that Tom had increased by 30%. How many stamps did Reggie and Corwin have in the end?
In the end, Reggie has 435.2 stamps and Cοrwin has 179.2 stamps.
What are the basic mathematical οperatiοns?The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Let's start by assigning variables tο represent the number οf stamps each persοn has.
Let x be the cοmmοn factοr, sο Reggie has 8x stamps, Tοm has 4x stamps, and Cοrwin has 5x stamps.
After Cοrwin gave 3/10 οf his stamps tο Reggie and Tοm, he had (1-3/10) οr 7/10 οf his οriginal number οf stamps, οr 7/10(5x) = 7x/2 stamps.
Reggie and Tοm each received 3/20 οf Cοrwin's οriginal number οf stamps, οr 3/20(5x) = 3x/4 stamps.
Sο Reggie nοw has 8x + 3x/4 stamps = 35x/4 stamps, and Tοm has 4x + 3x/4 stamps = 19x/4 stamps.
We are alsο given that Cοrwin had 192 less stamps than Reggie after the exchange, sο:
5x = 35x/4 - 192
Multiplying bοth sides by 4 tο get rid οf the fractiοn:
20x = 35x - 768
Subtracting 20x frοm bοth sides:
15x = 768
Dividing bοth sides by 15:
x = 51.2
Sο Reggie has 8x = 409.6 stamps, Tοm has 4x = 204.8 stamps, and Cοrwin has 5x = 256 stamps.
If Tοm's number οf stamps increased by 30%, he nοw has 130% οf his οriginal number οf stamps, οr 1.3(204.8) = 266.24 stamps.
Finally, adding up the number οf stamps each persοn nοw has:
Reggie: 409.6 + 3x/4 = 409.6 + 3(51.2)/4 = 435.2 stamps
Tοm: 266.24 stamps
Cοrwin: 7x/2 = 7(51.2)/2 = 179.2 stamps
Therefοre, in the end, Reggie has 435.2 stamps and Cοrwin has 179.2 stamps.
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We can let Reggie had 8x, Tom, had 4x, Corwin had 5x, Corwin gave Reggie y1, gave Tom y2,
So: We can know from the question
3/10 * 5x = y1 + y2
8x + y1 - 7/10 * 5x = 192 (2)
4x + y2 = 4x * 13/10 (3)
(1) + (2) + (3)
8x + 4x + 3/10 * 5x - 7/10 * 5x = 192 + 4x * 13/10
So x = 40
in the end
Corwin has 7/10 * 5x = 140
Reggie has 140 + 192 = 332
Tom has 13/10 * 4x = 208
332 + 140 = 472
So Reggie and Corwin have 472 stamps in the end.
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Decompose the composite figure to find its total area.
Answer: 36 m²
Step-by-step explanation:
First, we will solve for the area of the triangles. Since they are congruent, we will multiply the height times the base. Usually, you would have to divide by two. However, since we have two congruent triangles, we will not be doing this.
A = BH
A = (2 m)(6 m)
A = 12 m²
Next, we will find the area of the rectangle. We will multiply the length by the width.
A = BH
A = (6 m)(4 m)
A = 24 m²
Lastly, we will add these two values together.
24 m² + 12 m² = 36 m²
Please help Quick!! Will mark Brainliest too!
Answer:
52800 cm^3
Step-by-step explanation:
Given:
Rectangular prism
h = 6 cm (height)
l = 11 m = 1100 cm (length)
w = 8 cm (width)
[tex]v =a(base) \times h[/tex]
[tex]a(base) = l \times w = 1100 \times 8 = 8800 \: {cm}^{2} [/tex]
[tex]v = 8800 \times 6 = 52800 \: {cm}^{3} [/tex]
cos² (x)(1+tan²(x)) = 1, establish the identity
Answer:
see below.
Step-by-step explanation:
Use Trigonometric Expansion.
Verify the following identity:
[tex]cos(x)^2(tan(x)^2+1)=1[/tex]
Write tangent as [tex]\frac{sine}{cosine}[/tex]
[tex]cos(x)^2(\frac{sin(x)}{cos(x)} ^2+1)=1[/tex]
[tex]cos(x)^2(\frac{sin(x)}{cos(x)} ^2+1)=cos(x)^2(\frac{sin(x)^2}{cos(x)^2+1} )[/tex]
[tex](cos(x)^2(\frac{sin(x)^2}{cos(x)^2} +1))=1[/tex]
Put sin(x)^2/cos(x)^2 +1 over the common denominator cos(x)^2 : sin(x)^2/cos(x)^2+1 = cos(x)^2+sin(x)^2 /cos (x)^2:
cos(x)^2(cos(x)^2+sin(x)^2/cos(x)^2)=1
Cancel cos(x)^2 from the numerator to the denominator.
cos(x)^2(cos(x)^sin(x)^2)/cos(x)^2=cos(x)^2(cos(x)^2+sin(x)^2)/cos(x)^2=cos(x)+sin(x)^2:
(cos(x)^2+sin(x)^2=1
Substitute cos(x)^2 + sin (x)^2 = 1:
1 =1
A line in the coordinate plane has the equation 5a + b = 7,
where a represents the independent variable, and b
represents the dependent variable. Which of the following is
the equation of a line that is perpendicular to 5a+b=7?
A. b=5a+3
B. b=-5a-5
C. b= (1/5)a-2
D. b=(-1/5)a + 1
Explanation:
I'll use x in place of 'a'
I'll also use y in place of b.
The equation 5a+b = 7 turns into 5x+y = 7
Solve for y to get
5x+y = 7
y = -5x+7
This is in slope-intercept form y = mx+b
m = -5 = slopeb = 7 = y interceptThe negative reciprocal of the slope is 1/5. Flip the fraction and flip the sign. So if -5 is the original slope, then 1/5 is the perpendicular slope.
Of the answer choices, only choice C has a slope of 1/5. Think of b = (1/5)a-2 as y = (1/5)x - 2
Therefore, choice C is the answer.
The equation of a line that is perpendicular to '5a+b = 7' is 'b = (1/5)a + c'. Therefore, the correct option among given choices is 'b = (1/5)a - 2' (option C).
Explanation:To start with, the given line's equation, 5a + b = 7, can be converted to slope-intercept form (b = mx + c), where m represents the slope of line, and 'c' is the y-intercept.
Converting the equation, 5a + b = 7, we get b = -5a + 7. This tells us the slope of our original line is -5.
Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. So, the line perpendicular to the one with a slope of -5 would have a slope of 1/5. Therefore, the equation of a line perpendicular to '5a+b = 7' would be in the form 'b = (1/5)a + c'.
Thus, the correct answer is option C : b = (1/5)a - 2.
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Jami is an accountant at a mid-sized firm and has been hired by an investor to make recommendations about fi
local small businesses. These businesses are all in debt, but the investor sees potential in each idea. The investor wom
to know when each company is projected to break even and would prefer companies that will turn a profit with
the next 24 months. The investor secured the expense and revenue reports of each of the businesses to review.
Jami has created linear models to project the Cost and Revenue of each business and now must use the results
finalize her findings. In each equation x represents months. What should her recommendation be? How do
businesses rank?
Cost
Revenue
Blysis
of the evidence
Evidence
Appster
Enrich
(Technology Start-up) (Education Program)
y-13124.3190x y-6941915384x
y-3586x
y-21954x
¡.
Green Team
(Alternate Energy)
y 178420 64421x
y-68419x
Southwest Fusion
(Restaurant)
y-4289115387x
y-13174x
ons and show work.
Zoo to You
(Children's Parties)
y54209539
y-10381x
Conclusion
or Recommendation
e Clark Creative Ex
Answer:
To determine when each company is projected to break even, Jami needs to find the point where the Cost and Revenue equations intersect. This point will represent the month when the business is projected to break even, as the Cost and Revenue will be equal.
Using the given equations, we can set the Cost equation equal to the Revenue equation for each business:
Blysis: -13124.3190x + 3586 = -6941915384x + 21954
Solving for x, we get x = 0.00057 months.
Since this value is extremely small, we can assume that Blysis is already profitable.
Appster: -13124.3190x + 3586 = -6941915384x + 21954
Solving for x, we get x = 0.00057 months.
Since this value is extremely small, we can assume that Appster is already profitable.
Enrich: -3586x - 21954 = -6941915384x + 13174
Solving for x, we get x = 0.0035 months.
Since this value is also very small, we can assume that Enrich is already profitable.
Green Team: 178420.64421x - 68419 = -4289115387x + 13174
Solving for x, we get x = 0.0009 months.
Since this value is extremely small, we can assume that Green Team is already profitable.
Southwest Fusion: -13124.3190x + 4289115387x = 13174
Solving for x, we get x = 35.23 months.
This value indicates that Southwest Fusion is projected to break even in approximately 35 months.
Zoo to You: -13124.3190x + 54209539 = -10381x
Solving for x, we get x = 4.05 months.
This value indicates that Zoo to You is projected to break even in approximately 4 months.
Based on these projections, Jami should recommend Blysis, Appster, Enrich, and Green Team to the investor, as they are already profitable or expected to break even within the next 24 months. Southwest Fusion and Zoo to You may not be as attractive for investment, as they are projected to take longer to become profitable.
Step-by-step explanation:
YOU ARE GIVEN A MAGIC PENNY ON THE DAY YOU ARE BORN. YOU ARE TOLD THAT EACH YEAR ON YOUR BIRTHDAY, THE PENNY WILL MAGICALLY DOUBLE IF YOU DONT SPEND IT . HOW MUCH MONEY WILL YOU HAVE ON UR 10TH BIRTHDAY?
Answer:
20
Step-by-step explanation:
You have to multiply 10 by 2, which the ten represents ur 10th birthday, and the 2 represents the amount doubled. 10+2=20
A. Fill in the blanks to factor
3x² - 2x + 15x - 10 by grouping.
3x² - 2x + 15x - 10
=____(3x − ___) +___(___ — ____)
=(___+___)(____ — _____)
3x² - 2x + 15x - 10 can be factored by grouping as:
3x² - 2x + 15x - 10
= (3x - 2)(x + 5)
Explanation:
Group the first two terms and the last two terms together:
(3x² - 2x) + (15x - 10)
Factor out the GCF from each group:
3x(x - (2/3)) + 5(3x - 2)
Now we have a common factor of (3x - 2):
(3x - 2)(x + 5)
Step-by-step explanation:
3x² - 2x + 15x - 10
=x(3x-2)+5(3x-2)
=(x+5)(3x-2)
The average width of a movie theater seat is 23 inches. Thirty years ago, the typical movie theater seat was approximately 19 inches wide. Current movie theater seats are what percent of a theater seat from 30 years ago?
Thus, the current movie theater seats are 21.05 % of a theater seat from 30 years ago.
Explain about the percentage increase:The change between a final value and even an initial value, presented as a percentage of the starting value, is the percent increase over two values. Subtract the starting value from the ending value to get the percent increase.
Next, divide the difference by the starting amount. In order to convert this value to a percentage, multiply it by 100%. The difference in percentage between the two numbers will be shown in the final result.
Given data:
width of current movie theatre seat = 23 inches.
width of 30 years ago movie theatre seat = 19 inches.
Let x be the percentage increase:
19 + x%19 = 23
1 + x% = 23/19
x/100 = 23/19 - 1
x/100 = 4/19
x = 400/19
x = 21.05 %
Thus, the current movie theater seats are 21.05 % of a theater seat from 30 years ago.
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PROGRESSIVE
Employee: "When I started here, there were 500 employees. Since then, we have
added 35% more employees, so we now have a total of
employees."
175
350
535
635
Shanna Bedgood
675
Since the question is asking about total employees, we must add 175 to 500 to get 675. Therefore, the correct answer is 675.
What does increase mean?Increase means to grow or make larger in size, amount, degree, or intensity. It is the opposite of decrease, meaning to make or become less.
This is because when there were 500 employees, a 35% increase would be a total of 500 + 35% of 500
= 500 + 175
= 675.
To calculate 35% of 500, we use the formula:
(35/100) × 500 = 175
This means that 35% of 500 is 175, so when we add 175 to 500, we get 675.
Since the question is asking about total employees, we must add 175 to 500 to get 675.
Therefore, the correct answer is 675.
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find the length of the arc
(70 points)
can mark brainly
The calculated length of the arc has a value of 22.34 yards
Finding the length of the arcTo find the length of an arc, we can use the formula:
L = (θ/360) x 2πr
where L is the length of the arc, θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14.
In this case, the central angle is 160 degrees and the radius is 8 yards. So we can plug in these values to get:
L = (160/360) x 2π(8)
Evaluate
L = 22.34 yards
Therefore, the length of the arc is approximately 22.34 yards
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not sure what the answer is but I need the interpets
The x-intercepts of the given expression which is a rational function is calculated to be 0 and the y-intercepts are ±√25.
What does rational function mean?The given expression is a rational function and can be written as the quotient of two polynomials.
The numerator of the rational expression is -x⁷ and the denominator is x²−25. The numerator is a degree 7 polynomial and the denominator is a degree 2 polynomial.
To find the x-intercepts, we need to set the numerator equal to zero and solve for x.
-x⁷ = 0
x⁷ = 0
x = 0
To find the y-intercepts, we need to set the denominator equal to zero and solve for x.
x²−25 = 0
x² = 25
x = ± √25
Therefore, the x-intercepts of the given expression are 0 and the y-intercepts are ± √25.
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Question :
Find the intercepts of the given function.
y = (-x⁷)/(x²−25)
The answer is 4 but I don’t understand why the graph is starting at -2.
Answer:
graph 4 (reflected vertically)
Step-by-step explanation:
You want the graph that represents a cosine function with no horizontal shift, an amplitude of 2, and a period of 2π/3.
AmplitudeThe amplitude of a sine or cosine function is the difference between the positive peak and the centerline. All of the graphs show functions with an amplitude of 2.
Period/FrequencyThe period of the function is the difference of x-values between the first instance of the function and the first repeat: f(x) ≡ f(x+p) has a period of p.
Graphs 1 and 3 show periods of 2π/9; graphs 2 and 4 show periods of 2π/3, as required.
Horizontal shiftThere is an interaction between horizontal shift and vertical reflection. Sine or cosine functions are effectively inverted (reflected over the x-axis) if they are shifted horizontally by 1/2 period—and vice versa.
The function in graph 3 is a sine function, or a horizontally shifted cosine function.
The function in graph 4 is a cosine function that has been shifted 1/2 perior, OR a cosine function that has been reflected over the x-axis.
Graph 4 is the only viable choice for a cosine function with the correct period, so we have to assume it starts at -2 because it has been reflected vertically over the x-axis. (There seems to be no restriction on that in the problem statement.)
__
Additional comment
Ordinarily, you might not be expected to make any assumptions about vertical reflection. It seems a bit of a trick question.
What are two expressions that are equivalent to the expression 5(6j + 3 + j)
Answer:
5(7j+3) AND 35j +15 are both equal to the expression 5(6j + 3 + j)
The distance d(in miles) that you can see to the horizon with your eye level h feet above the water is given by d = √3h/2.
How far can you see when your eye level is 35 feet above the water?
With an eye level of 35 feet above the water, you can see approximately 7.24 miles to the horizon.
What is multiplication ?Multiplication is a mathematical operation that involves combining two or more numbers to find their total or product. It is often denoted by the symbol "×" or "*", and the result of multiplication is called the product. For example, multiplying 3 and 4 gives a product of 12, written as 3 × 4 = 12.
According to the given information:To find out how far you can see when your eye level is 35 feet above the water, we can use the given formula:
d = √(3h/2)
Plugging in h = 35, we get:
d = √(3 * 35/2)
d = √(105/2)
d = √52.5
d ≈ 7.24
So, when your eye level is 35 feet above the water, you can see approximately 7.24 miles to the horizon. Keep in mind that this is an approximation and actual visibility may vary due to factors such as atmospheric conditions and the height of objects obstructing the view.
Therefore, With an eye level of 35 feet above the water, you can see approximately 7.24 miles to the horizon.
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Express as a product "1 - sin(a) - cos (a)"
1 - sin(a) - cos(a) can be expressed as the product 2(cos(a)(sin)(a)).
What are Trigonometric Identities?
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
We can use the identity:
[tex]cos^2(a) + sin^2(a) = 1[/tex]
Substituting this into the expression 1 - sin(a) - cos(a), we get:
[tex]cos^2(a) + sin^2(a) - sin(a) - cos(a) \\\\cos^2(a) - cos(a) + sin^2(a) - sin(a) \\\\cos(a)( 1 - cos(a)) + sin(a)( 1- sin(a) )\\\\[/tex] eq2
It is given that
[tex]1 - sin(a) - cos (a)\ \text{this gives us}:\\\\1 - sin(a) = cos (a)\ \text{and} \ 1 - cos (a) = sin(a)[/tex]
Substituting these values in the eq2
[tex]cos(a)( 1 - cos(a)) + sin(a)( 1- sin(a) )\\\\cos(a)(sin(a)) + sin(a)(cos(a) )\\\\[/tex]
[tex]2(cos(a)(sin)(a))[/tex]
Therefore, 1 - sin(a) - cos(a) can be expressed as the product
[tex]2(cos(a)(sin)(a))[/tex]
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Rasheed signed a 2 year lease. He pays $565 a month. If he wants to move out 6 months early, how much money will he owe when he moves out?
Answer
3390
Step-by-step explanation:
rasheed still owes six months of rent because thats the lease that they signed so 565 times six is 3390. hope this helps.
Four consecutive odd integers add up to 48. What are the integers?
Answer:12
Step-by-step explanation: 48/4
Help with math problems
(1) The graph that shows the solution of the inequality 7 ≤ n + 5 is the graph of option A.
(2) Eduardo wrote at least 34 pages before today.
(3) The farmer needs to plant at least 8 rows of seeds to harvest at least 52 bushels of tomatoes.
What is the solution to the inequality 7 ≤ n + 5?The solution to the inequality 7 ≤ n + 5 is as follows:
7 ≤ n + 5
collect similar terms together
7 - 5 ≤ n
2 ≤ n
So we can interpret the result of this inequality as, n is greater than and equal to 2. Hence option A is the correct answer.
2. Let p be the number of pages Eduardo wrote before today. Then, the inequality that represents the situation is:
p + 16 > 50
To solve for p, first subtract 16 from both sides of the inequality:
p + 16 - 16 > 50 - 16
p > 34
Therefore, Eduardo wrote at least 34 pages before today.
3. Let r be the number of rows of seeds the farmer needs to plant. Then, the equation that represents the situation is:
6.5r ≥ 52
divide both sides of the equation by 6.5:
r ≥ 8
Therefore, the farmer needs to plant at least 8 rows of seeds to harvest at least 52 bushels of tomatoes.
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help pls show ur work
The height of the first floor above the second floor would be = 20 ft.
How to calculate the height of the first floor from the second floor?To calculate the height of the first floor from the second floor, the formula from SOHCAHTOA is used.
The opposite part of the triangle created by the escalator = ?ft
The hypotenuse of the triangle which is the height of the escalator = 40 ft
Sin 30° = X/40
X = sin30° × 40
X = 0.5×40
X = 20 ft
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