Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water, Marla's eye-level is 5.5 feet, and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, tothe nearest foot?
Answers
SOLUTION
Let us make a diagram to interpret the question
from the diagram above, we can make the right-angle triangle as follows
So we can use SOHCAHTOA to solve this. The opposite side to the angle 52 degrees is 45.5 ft, this is gotten by adding the height of the cliff to Maria's height from her feet to her eyes.
The adjacent side is d, that is the distance from the seal to the cliff, so we have
[tex]\begin{gathered} TOA\text{ tan}\theta\text{ = }\frac{opposite}{adjacent} \\ tan52\degree=\frac{45.5}{d} \\ cross\text{ multiply, we have } \\ tan52\degree d=45.5 \\ d=\frac{45.5}{tan52} \\ d=35.54849 \end{gathered}[/tex]Hence the answer is 36 foot to the nearest foot
Related Questions
At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway? A. 9y = 12x + 5B. 9x = 12y + 8C. 12y = -9x + 2 D. 12x = -9y + 4
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At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway?
A. 9y = 12x + 5
B. 9x = 12y + 8
C. 12y = -9x + 2
D. 12x = -9y + 4
______________________________________________________
Parallel equations have the same slope
6y = 8x - 11
y= 8/6 x - 11/6
y= 4/3 x-11/6
y = m x +b (m is the slope )
_____________________________________________
You need to find the other equation with the same slope
____________________________
A. 9y = 12x + 5
y = 12/ 9 x + 5/9
y = 4/3 x + 5/9
_________________________
B. 9x = 12y + 8
12 y= 9x-8
y= 9/ 12 x- 8/12
y= 3/4 x - 4/6
discarded
________________________
C. 12y = -9x + 2
y = -9/12 x + 2/12
y = -3/4 x + 1/6
discarded
_________________________
D. 12x = -9y + 4
12x -4 = -9y
y = -12/9 x +4/9
y = -4/3 x+4/9
discarded
_______________
So then, A 9y = 12x + 5 is the equation that could represent the new runway because is parallel to the highway 6y = 8x - 11.
Describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x. Look at image for example. Let’s do problem number 11
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given functions.
[tex]\begin{gathered} f(x)=-(x+5)^2-6 \\ h(x)=\frac{1}{3}f(x) \end{gathered}[/tex]STEP 2: Explain the transformation that occurs
What are Vertical Stretches and Shrinks?
While translations move the x and y intercepts of a base graph, stretches and shrinks effectively pull the base graph outward or compress the base graph inward, changing the overall dimensions of the base graph without altering its shape. When a graph is stretched or shrunk vertically, the x -intercepts act as anchors and do not change under the transformation.
This can be explained further as:
For the base function f (x) and a constant k > 0, the function given by:
[tex]\begin{gathered} h(x)=k\cdot f(x) \\ A\text{ vertical shrinking of f\lparen x\rparen by k factor where }0Calculate the equation that represents h in terms of x[tex]\begin{gathered} f(x)=-(x+5)^2-6 \\ h(x)=\frac{1}{3}\cdot f(x)=\frac{1}{3}\cdot-(x+5)^2-6 \end{gathered}[/tex]Hence, the transformation from the graph is a vertical shrinking by 1/3 factor and the equation that represents h in terms of x is given as:
[tex]\frac{1}{3}\times(-(x+5)^2-6)[/tex]26.219 Miles in 128 minutes. what is speed in km per minute?
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26.219 Miles in 128 minutes.
First we have to convert miles to km:
Since 1 mile = 1,609 km
26.219 x 1,609 = 42,041.561 km
Then divide the distance by the time:
42,041.561/ 128 = 192.85 km per minute
Use the following function rule to find f(48).
f(x) = 12 + x/4
Answers
Answer:
See image
depending on what is in the numerator of your question:
24 OR 15 SEE IMAGE!
Step-by-step explanation:
f(48) just means to use 48 in place of x in your work.
f(x) = 12 + x/4
f(48) = 12 + 48/4
Hopefully, your text/worksheet/screen is clear on which problem you are doing.
In the rhombus m<1 = 160 what are m<2 and m<3. This diagram is not drawn to scale. Show all work
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We are given a rhombus shape.
The measure of angle ∠1 = 160°
Recall that in a rhombus, the oppsite angles are equal, this means ∠1 = ∠2
So, ∠2 = 160°
Recall that the sum of all four interior angles in a rhombus must be equal to 360°
The diagonal line divides the angles in half.
This means that angle 3 and angle x are equal.
[tex]\begin{gathered} 160\degree+160\degree+2(\angle3+x)=360\degree_{} \\ 320\degree+2(\angle3+x)=360\degree \\ 2(\angle3+x)=360\degree-320\degree \\ 2(\angle3+x)=40\degree \\ \angle3+x=\frac{40\degree}{2} \\ \angle3+x=20\degree \end{gathered}[/tex]Since we know that ∠3 and ∠x are equal then
∠3 = 10° and ∠x = 10°
Therefore,
∠2 = 160°
∠3 = 10°
solve for x and y (2x+7)(x+1)(y+5)(x-4)
Answers
Answer:
I am assuming you are looking for the x-intercepts and y-intercepts...here they are.
x-intercepts: (-7/2,0) , (-1,0) , (4,0)
y-intercepts: (0,-5)
Hope this helps...if not, please expound your question more.
O GRAPHS AND FUNCTIONSDomain and range from the graph of a piecewise function
Answers
ANSWER:
[tex]Domain:(-5,-4]\cup[-1,2][/tex][tex]Range:[-3,0)\cup[1,4][/tex]EXPLANATION:
Given:
To find:
The domain and the range
Recall that the domain of a function is the set of possible input values for which the function is defined.
To determine the domain of a function from a graph, we consider the possible x-values from left to right.
So the domain of the given function can be written as;
[tex]Domain:(-5,-4]\cup[-1,2][/tex]The range of a function is the set of possible output values.
To determine the range of a function from a graph, we consider the possible y-values from the bottom to the top.
So the range of the given function can be written as;
[tex]Range:[-3,0)\cup[1,4][/tex]Give the slope and y - intercept for each of the following equations, then sketch the graph. Give the slope ofany line perpendicular to the given line.y =22 +5Slope =y - intercept = (0,_ ) Slope of a Line Perpendicular =
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The slope is 2.
The y-intercept is 5 or (0, 5)
See graph below
Explanation:Given:
y = 2x + 5
To find:
the slope, y-intercept, and plot a graph
To determine the slope and y-intercept, we will use the equation of line formula:
y = mx + b
m = slope
b = y-intercept
Comparing both equations:
y = y
2x = mx
m = 2
The slope = 2
5 = b
The y-intercept = 5
To plot the graph, we will assign values to x in order to get values to y that will be plotted:
let x = -4, 0, 4
when x = -4
y = 2(-4) + 5 = -3
when x = 0
y = 2(0) + 5 = 5
when x = 4
y = 2(4) + 5 = 13
Plotting the points:
Each line on the graph represents 1 unit
What 3D shape will be formed when the following are rotated around the axis
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a)
A washer will be formed
b)
A cone will be formed
C)
A sphere will be formed
I need help finding the exact perimeter. Special right triangles.
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Answer:
The exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]Explanation:
Given the square in the attached image.
The length of the diagonal is;
[tex]d=28[/tex]Let l represent the length of the sides;
[tex]\begin{gathered} l^2+l^2=28^2 \\ 2l^2=784 \\ l^2=\frac{784}{2} \\ l^2=392 \\ l=\sqrt[]{392} \\ l=14\sqrt[]{2} \end{gathered}[/tex]The perimeter of a square can be calculated as;
[tex]\begin{gathered} P=4l \\ P=4(14\sqrt[]{2}) \\ P=56\sqrt[]{2} \end{gathered}[/tex]Therefore, the exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]5. There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal ispoured into the bowl at a rate of 1.5 ounces per second. How many ounces are inthe bowl after 3 seconds?
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Question:
There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal is poured into the bowl at a rate of 1.5 ounces per second. How many ounces are in the bowl after 3 seconds?
Solution:
If additional cereal is poured into the bowl at a rate of 1.5 ounces per second, then in 3 seconds the additional cereal into the bowl is 1.5x 3 = 4.5 ounces. Thus after 3 seconds, the bowl has the original amount that it already had and the new aggregate:
9.75 ounces + 4.5 ounces = 14.25
then, the correct answer is:
14.25
Which system of inequalities is shown?-5O A. y>xy<4OB. y> xy> 4C. y< xy<4OD. y< xy> 45
Answers
Given:
a graph of the inequalities is given.
Find:
we have to find the correct inequalities.
Explanation:
From the graph , it is observed that the value of y > x and y < 4,
Therefore, the correct inequalities are y > x,
y < 4.
Hence, correct option is A.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answers
Answer:
translated 8 units down and then reflected across the y-axis
What is the domain for the following function? 2x . - 3 O A. (x+3) O B. {**-3) O c. {*#0 O D. all real number ers
Answers
Given,
y = 2x/x - 3
to solve this,
let's equate the denominator to 0
so,
y = 2x/0
this means undefined
recall,
Domain is the set of all possible values of x. Since the function is undeined when the denominator is zero, the domain is the set of all real numbers except the value which will make the denominator zero
so the domain for the function y = 2x/x - 3
is x is not equal to 3
therefore, the correct option is
[tex]A.\mleft\lbrace x\ne3\mright\rbrace[/tex]Soue se compound inequality and give your answer in intentel notation- 10 AND-80-72-1
Answers
S= (-4, 1 ]
1) Solving that compounded inequality
4x +6 > -10 and -8x+7 ≥ -1
2) Let's start by 4x +6 > -10
4x +6 > -10 Subtracting 6 from both sides
4x > -10-6
4x > -16 Dividing both sides by 4
x > -4
And with -8x+7 ≥ -1
-8x+7 ≥ -1 Subtract 7 from both sides
-8x ≥ -1 -7
-8x ≥ -8 Multiply by -1
8x ≤ 8
x ≤ 1
3) Graphing the solution interval:
So the solution is the interval S= (-4, 1 ] not including x= -4 and including the value x = 1
A school debate team has 4 girls and 6 boys. A total of 4 of the team members will be chosen top participate in the district debate. What is the probaility that 2 girland 2 boys will be selected?
Answers
The probability that 2 girls and 2 boys are selected is given by:
[tex]P(\text{ 2 boys, 2 girls })=\frac{4C2\times6C2}{10C4}=\frac{6\times15}{210}=\frac{3}{7}[/tex]Therefore, the correct choice is option D) 3/7.
What are the slope and the y-intercept of the linear function that is represented by the table? -- Nicol у 3 2 1 0 -2 / 0 Nlw 3 1 2 -1 The slope is -3, and the y-intercept is 3 The slope is -3, and the y-intercept is z. 1 The slope is 3, and the v-intercept is -
Answers
We will assume the next table to answer this question (a linear function) (since the data in the question is not clear):
Having this information, we can find the slope using the formula for it:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]If we pick up from the table the next points:
x1 = 1, y1 =6
x2 = 2, y2 = 8
Then
[tex]m=\frac{8-6}{2-1}=\frac{2}{1}\Rightarrow m=2[/tex]We can use the slope-point formula to find the y-intercept. We can use the point (3, 10). Then, we have:
[tex]y-y_1=m\cdot(x-x_1)\Rightarrow y-10=2\cdot(x-3)\Rightarrow y-10=2x-6[/tex][tex]y=2x-6+10\Rightarrow y=2x+4[/tex]We end up with the slope-intercept formula for the line. Then the y-intercept is 4. In other words, if we have x = 0, then y = 4.
Then the slope for the values represented in the proposed table is m = 2, and the y-intercept is y = 4.
are these places correctly.and yes it is math. pls answer fast
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we have that
Costs that stay the same from week to week or month to month
-savings for college
-Rent
Costs that cannot be adjusted within a budget
-Car insurance
-Health care
Costs that can be adjusted within a budget
-cell phone
-gasoline
-hair cut
-Groceries
Solve for the Limit of Function by applying appropriate Limit Theorems
Answers
Answer:
Given to solve,
[tex]\lim _{x\to-1}(2x+2)(x+2)[/tex]From the rules for limits, we can see that for any polynomial, the limit of the polynomial when x approaches a point k is equal to the value of the polynomial at k.
The given function of the limit is a quadratic function, the limit of the quadratic equation when x approaches a point -1 is equal to the value of the quadratic equation at -1.
we get,
[tex]\lim _{x\to-1}(2x+2)(x+2)=(2(-1)+2)((-1)+2)[/tex][tex]=(-2+2)(1)=0[/tex][tex]\lim _{x\to-1}(2x+2)(x+2)=0[/tex]
Answer is : 0
In New York, the tax on a property assessed at $520,000 is $10,400. If tax rates are proportional in this city, how much would the tax be on a property assessed at $370,000? Answer: $
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Given that the tax on a property assessed at $520,000 is $10,400 and the tax
there are twelve inches in one foot,creating the equation y=12x. if a door frame is 6.5 feet tall,how many inches tall is it
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Let's begin by listing out the information given to us:
[tex]\begin{gathered} 12in=1ft \\ y=12x \end{gathered}[/tex]The height of the door frame is 6.5 feet. To convert to inches, we have:
[tex]\begin{gathered} y=12(6.5)=78inches \\ y=78inches \end{gathered}[/tex]What is the missing coefficient of the x-term of the product (−x−5)^2 after it has been simplified?−25−101025
Answers
Given:
The terms is
[tex](-x-5)^2[/tex]Required:
What is the missing coefficient of the x-term of the product after it has been simplified?
Explanation:
We have to find the missing coefficient of the x term of the given product
We know
[tex](a-b)^2=a^2-2ab+b^2[/tex]So,
[tex](-x-5)^2=x^2+10x+25[/tex]Therefore, the missing coefficient of the x-term is 10.
Answer:
Therefore, the missing coefficient of the x-term is 10.
Dejah is comparing two numbers shown in scientific notation on her calculator. The first number was displayed as 7.156E25 and the second number was displayed as 3.498E-10. How can Dejah compare the two numbers?
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The first number is about
2 x 10¹⁵
2 x 10³⁵
2 x 10‐¹⁵
2 X 10‐³⁵
times bigger than the second number.
Answers
Answer:
2 x [tex]10^{35}[/tex]
Step-by-step explanation:
7 ÷ 3 is about 2
[tex]\frac{10^{25} }{10^{-10} }[/tex] = [tex]10^{35}[/tex] When you are dividing powers with the same bases, you subtract the exponents
25 - -10 = 25 + 10 = 35
Solve the equation-3 + a = 13a = ???
Answers
ANSWER
a = 16
EXPLANATION
To solve for a we have to add 3 on both sides of the equation:
[tex]\begin{gathered} -3+3+a=13+3 \\ a=16 \end{gathered}[/tex]Solve the inequality X - (5 - 3x) = 2x - 1
Answers
hi,
x - (5 - 3x) = 2x - 1
x - 5 + 3x = 2x - 1
x - 2x + 3x = -1 + 5
2x = 4
x = 4/2
x =< 2
[tex]\text{ x }\leq\text{ 2}[/tex]
The result is letter A, the first choice
quick!! will give brainliest!! Given g(x) = -x + 3, solve for a when g(2) = -1
Answers
We have the following:
[tex]g(x)=-x+3[/tex]replacing when x is 2:
[tex]g(2)=-2+3=1[/tex]Suppose a charity received a donation of $19.4 million. If this represents 43% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Answers
Given :
a charity received a donation of $19.4 million
Which represents 43% of the charity funds
Let the total funds = x
So,
43% of x = 19.4 million
So,
[tex]\begin{gathered} 43\%\cdot x=19.4 \\ \\ 0.43\cdot x=19.4 \\ \\ x=\frac{19.4}{0.43}\approx45.12 \end{gathered}[/tex]Rounding to the nearest million ,
The answer is : total donated funds = 45 million
how do you find the exponential equation for growth? or what is the exponential equation for growth?
Answers
Answer:
The equation f(x) = a(1 + r)x can also be used to compute exponential growth, where:
The function is represented by the word f(x).
The initial value of your data is represented by the a variable.
The growth rate is represented by the r variable.
Time is represented by the variable x.
Answer this, please
Zachariah and Khai collect stamps. Zachariah has 7 American stamps out of 12 stamps. Khai has 15 American stamps out of 24 stamps. Which statement is correct?
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is greater than 15 over 24.
Khai has a higher ratio of American stamps than Zachariah because 7 over 12 is less than 15 over 24.
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.
Zachariah and Khai have the same ratio of American stamps.
Answers
The last statement would be true, because you would convert 7/12 into a fraction and 15/24 into a fraction. From their fraction eyes to State you would turn them into decimals and then percentiles.
Answer:
D: They are both the same
Step-by-step explanation:
I took the test
Point S is on line segment \overline{RT} RT . Given RT=3x,RT=3x, RS=3x-5,RS=3x−5, and ST=3x-1,ST=3x−1, determine the numerical length of \overline{RT}. RT .
Answers
The numerical length of the line segment RT is 6.
Length:
Length is the measuring unit used to identifying the size of an object or distance from one point to the other.
Given,
There is a point on the line segment RT.
And the values of the pots are,
RT = 3x, RS = 3x - 5 and ST = 3x - 1.
Now we need to find the length of the line segment RT.
To find the line of the line segment RT,
We have to add the length of the segments,
That can be written as,
=> RT = RS + ST
Now, we have to apply the values of the point to the equation, then we get,
=> 3x = 3x - 5 + 3x - 1
=> 3x = 6x - 6
=> 6x - 3x - 6
=> 3x - 6
=> 3x = 6
=> x = 2
If the value of x is 2, then the length of the line segment RT is,
RT = 3x => 3 x 2 = 6
Therefore, the length of the line segment RT is 6.
To know more about Line Segment here.
https://brainly.com/question/25727583
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