While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 25 degrees. After walking 350 ft closer, he guessed that the angle of elevation had increased by 14 degrees. Approximately how tall is the hill?A. 475 feetB. 385 feetC. 608 feetD. 202 feet
Answers
The line sketch of the movement and positioning of Joe and the hill are shown below.
Brief description of the sketch made.
From the sketch, point A is where Joe started from heading towards the hill.
The hill is represented by BC and the height is h
25 degrees was the initial angle of elevation.
After moving 350 ft closer to the hill, the angle of elevation increased by 14 degrees to 25 + 14 = 39 degrees.
From triangle BCD,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 39=\frac{h}{x} \\ 0.8098=\frac{h}{x} \\ \text{Making h subject of the formula,} \\ h=0.8098x \end{gathered}[/tex]From triangle ABC,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 25=\frac{h}{350+x} \\ \text{Substituting the value of h gotten from the previous triangle,} \\ \tan 25=\frac{0.8098x}{350+x} \\ 0.4663=\frac{0.8098x}{350+x} \\ C\text{ ross multiplying,} \\ 0.4663(350+x)=0.8098x \\ 163.205+0.4663x=0.8098x \\ C\text{ ollecting the like terms,} \\ 163.205=0.8098x-0.4663x \\ 163.205=0.3435x \\ \text{Dividing both sides by 0.3435 to get x,} \\ x=\frac{163.205}{0.3435} \\ x=475.124ft \\ \\ \text{The height, h of the hill is;} \\ h=0.8098x \\ h=0.8098\times475.124 \\ h=384.755ft \\ h\approx385ft \end{gathered}[/tex]Therefore, the height of the hill is 385 feet
The correct answer is option B.
Related Questions
5. What is the value of the 4th term of the expansion of (y + 2z)³?
Answers
The 4th term of the expansion is 8z³.
How to expand in mathematics?The expression to be expanded is (y + 2z)³
To expand a bracket means to multiply each term in the bracket by the expression outside the bracket
Therefore,
(y + 2z)³ = (y + 2z)(y + 2z)(y + 2z)
Therefore,
(y + 2z)(y + 2z) = y² + 2yz + 2yz + 4z²
y² + 2yz + 2yz + 4z² = y² + 4yz + 4z²
Hence,
y² + 4yz + 4z² (y + 2z) = y³ + 2y²z + 4y²z + 8yz² + 4yz² + 8z³
Therefore,
(y + 2z)³ = y³ + 2y²z + 4y²z + 8yz² + 4yz² + 8z³
(y + 2z)³ = y³ + 6y²z + 12yz² + 8z³
Therefore, the 4th term is 8z³
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3 × 3/2 answer as a fraction
Answers
Evaluate the value of expression.
[tex]\begin{gathered} 3\times\frac{3}{2}=\frac{3\cdot3}{2} \\ =\frac{9}{2} \\ =4\frac{1}{2} \end{gathered}[/tex]So answer is 9/2 or 4 1/2.
The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies.
Note
C
D
E
F
G
A
B
Frequency(Hz)
261.6
293.7
329.6
349.2
392.0
440.0
493.9
Determine the ratio of the note A to middle C.
a.
1.6818
c.
1.5348
b.
1.4983
d.
1.3654
Answers
4. What value of c would make the function below have two real solutions? y= -3x^2 – 4x+c
Answers
The quadratic equation is,
[tex]y=-3x^2-4x+c[/tex]The value of coefficients of square term, x term and constant terms are,
a = -3
b = -4
and c = c.
For two real roots,
[tex]b^2-4ac>0[/tex]Dubstitute the values in the equation to obtain the value of c.
[tex]\begin{gathered} (-4)^2-4\cdot(-3)\cdot(c)>0 \\ 16+12c-16>0-16 \\ \frac{12c}{12}>\frac{-16}{12} \\ c>-1.333 \end{gathered}[/tex]So value of c should be greater than -1.333, and from from the options it can be observed that value more than -1.333 is only c = -1.
So answer is c = -1.
PLEASE HELP ME I WAS SICK AND I DONT UNDERSTAND.DUE IN 1 HOUR!!!!
Answers
Answer:
x = 11
Step-by-step explanation:
(3x + 12) + (7x + 15) = 137 (exterior angle: angle KFG = angle g + angle h)
10x + 27 = 137
10x = 110
x = 11
What is the best estimate for this sum1/4+2/7=
Answers
Let's determine the sum of the following:
[tex]\text{ }\frac{\text{ 1}}{\text{ 4}}\text{ + }\frac{\text{ 2}}{\text{ 7}}[/tex]Step 1: Make the two fractions into similar fractions.
The LCM of 4 and 7 is 28, thus, let's convert each fraction into one with a denominator of 28.
We get,
[tex]\text{ }\frac{\text{ 1}}{\text{ 4}}\text{ = }\frac{\text{ 1 x }7}{\text{ 28}}\text{ = }\frac{7}{28}[/tex][tex]\text{ }\frac{\text{ 2}}{\text{ 7}}\text{ = }\frac{\text{ 2 x 4}}{\text{ 28}}\text{ = }\frac{\text{ 8}}{\text{ 28}}[/tex]Step 2: Add the fractions.
[tex]\text{ }\frac{\text{ 1}}{\text{ 4}}\text{ + }\frac{\text{ 2}}{\text{ 7}}[/tex][tex]\text{ }\frac{7}{28}\text{ + }\frac{8}{28}\text{ = }\frac{15}{28}[/tex]Therefore, the answer is 15/28.
2(a + b) + 4m(a + b)
Answers
Answer:
(a+b) 2+4m
Step-by-step explanation:
(a+b) 2+4m
take (a+b) out
Answer: 4am+4bm+2a+2b
Step-by-step explanation:
Distribute: 2(a+b)+4m(a+b)
2a+2b+4m(a+b)
Distribute: 2a+2b+4m(a+b)
2a+2b+4am+4bm
Rearrange terms: 2a+2b+4am+4bm
4am+4bm+2a+2b
Solution: 4am+4bm+2a+2b
What’s the correct answer answer asap for brainlist i really need help
Answers
Answer:
C, a transcript of information from DNA
Step-by-step explanation:
mRNA is option C.) “a transcript of information from DNA.”
The role of messenger RNA is to transfer information across the cell. This process has to work this way because DNA cannot leave the nucleus, while RNA can. mRNA uses ribose to provide instructions to ribosomes on how the cell makes proteins.
Write an inequality and make a number line that shows the situation. 1. A cruise ship can carry up to 3000 passengers. How much passengers might be in the cruise ship?2. Rafael drinks more than 3 pints of water a day. How many pints of water might Rafael drink?
Answers
1. Variable
• x: number of passengers
From the description of the problem, the number of passengers must be at most 3000. Mathematically:
x ≤ 3000
This inequality can be represented in a number line as follows:
PLEASE I NEED THIS REALLY REALLY BAD
Answers
The quadratic function that includes the given points is given by y = 3/5x² + 6/5x + 6.
what is a quadratic function?When a polynomial function has one or more variables and the highest exponent of any one of the variables is two, the function is said to be quadratic. A "polynomial function of degree 2," then, is a quadratic function.
The definition of a quadratic function:A quadratic function is one that has the formula f(x) = ax2 + bx + c, where a, b, and c are all integers with a not equal to zero. A parabola is the shape that makes up the graph of a quadratic function. The basic "U" shape of a parabola is the same whether it opens upward or downward, or with a different "width" or "steepness."
According to the given data:If we put the values of points in the above equation, then we get.
Putting point (0,6) we get
6 = 0 + 0 + c
=> c = 6
Putting point (2,8) we get
8 = 4a + 2b + 6
=> 2 = 4a + 2b
=> = 2a + b ......(1)
Putting point (3,-3) we get
-3 = 9a + 3b + 6
=> -9 = 9a + 3b
=> -3 = 3a + b ......(2)
From equation (1) b = 2a. Substitute the value of b in equation (2) we get
3 = 3a + 2a
=> a = 3/5
Now, b = 6/5
The quadratic function that includes the given points is given by y = 3/5x² + 6/5x + 6.
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write an equation for each translation of y=|x|a) 3 units upb) left to units
Answers
In a translation, the general translation of y=f(x) is that y=f(x+a) if f(x) is translated by a units towards left direction or downward and y = f(x) = f(x-a) is f(x) is translated by "a" units towards right direction or upward
Hence:
Translation of y =|x|
a) 3 units up
y = | x - 3|
b) left 2 units
y = | x+2|
What is the total surface area of a cylinder With a radious of 1 cm and a height of 12 cm.
Answers
ANSWER
SA = 26π
EXPLANATION
The total surface area is the sum of the areas of the sides of the cylinder:
In this problem r = 1cm and h = 12cm. The areas to sum are the area of the top and the base, which are identical circles, and the area of the rectangle that forms the side:
[tex]undefined[/tex]What is equivalent to 7-5x=10-(6x+7)
Answers
In order to find the equivalent of the expression we will need to simplify it, this is done by combining terms with the same variable.
[tex]\begin{gathered} 7\text{ - 5x = 10 -6x + 7} \\ 7\text{ - 5x = 17 - 6x} \end{gathered}[/tex]The correct answer would be the fourth option.
Label the coefficient constant exponent and verbal 5X^2-7
Answers
The labels of the expression given as 5x² - 7 are
Coefficient = 5Constant = 7Exponent = 2Variable = xHow to label the expression?The expression is given as
5x² - 7
As a general rule:
Expressions are represented using variables, terms, factors, coefficients, operators, constant, etc.
Each of these make up an expression
Take for instance, the following expression
axⁿ + b
The features are
Coefficient = aConstant = bExponent = nVariable = xUsing the above as a guide, the labels of 5x² - 7 are:
Coefficient (5), Constant (7), Exponent (2) and Variable (x)
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5. A. How do we know if an ordered pair is an x-intercept? Explain with specific detail.B. How do we know if an ordered pair is a y-intercept? Explain with specific detail.C. In the table, which order pair is the x-intercept, and which is the y-intercept?х4XNOу-10-24123
Answers
a) x-intercept: the y coordinate will be zero while the x coordinate will have a value different from zero.
b) y-intercept: the x coordinate will have a value of zero while the y-coordinate will have a value that is non-zero.
c) The x-intercept: (2, 0)
The y-intercept: (0, 1)
Explanation:5) a) x-intercept is the value of x when the value of y is zero.
To determine if an ordered pair is an x-intercept, the y coordinate will be zero while the x coordinate will have a value different from zero.
b) y-intercept is the value of y when x is equal to zero.
To determine if an ordered pair is a y-intercept, the x coordinate will have a value of zero while the y-coordinate will have a value that is non-zero.
c) To get the x-intercept: From the table, we will check for the of x when the value of y = 0
The value of y = 0 when x = 2
The ordered pair: (x, y)
The x-intercept: (2, 0)
To get the y-intercept: we will check for the value of y when x = 0
The value of x = 0 when y = 1
The ordered pair: (x, y)
The y-intercept: (0, 1)
Write an absolute value inequality whose solution set is shown by the graphs. Each mark on the graph represents a whole number. (Your answers will have the absolute value symbols, | |.)
Answers
To answer this question we will use the following:
[tex]\begin{gathered} |a|\ge b\text{ if and only if} \\ a\ge b\text{ or }a\le-b. \end{gathered}[/tex]Notice that the given set consists of the real numbers that are greater than or equal to 3 or that are less than or equal to -3, the above statement in algebraic notation is:
[tex]x\geq3\text{ or }x\leq-3.[/tex]Using the first equations we get that the given set can be represented by the following absolute value inequality:
[tex]|x|\ge3.[/tex]Answer:
[tex]|x|\ge3.[/tex]A math student has a plan to solve the following system by the elimination method. To eliminate the x-terms, he wants to multiply the top equation by 7 . What should he multiply the second equation by so that when he adds the equations, the x-terms are eliminated?
Answers
Answer
To eliminate x, we will multiply the second equatio by -3.
x = 7
y = 5
Explanation
To solve this, we first write the two equations
-3x - 7y = -56
-7x + 10y = 1
So, to solve this, we need to make sure the factors of x are the same numbers and of opposite signs
So, if we multiply the first equation by 7, we will need to multiply the second equation by -3 to obtain 21x and -21x for the two of them.
(-3x - 7y = -56) × 7
(-7x + 10y = 1) × -3
-21x - 49y = -392
21x - 30y = -3
We will then add the two equations and then the solution for the equation is obtained by solving for y first.
-21x + 21x - 49y - 30y = -392 - 3
0 - 79y = -395
-79y = -395
Divide both sides by -79
(-79y/-79) = (-395/-79)
y = 5
We can then solve for x using any of the two equations
-7x + 10y = 1
-7x + 10(5) = 1
-7x + 50 = 1
-7x = 1 - 50
-7x = -49
Divide both sides by -7
(-7x/-7) = (-49/-7)
x = 7
Hope this Helps!!!
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
The amount of coffee that was imported in 2007 is 2.0606 million pounds.
What is a function?It should be noted that a function simply s used to illustrate the relationship between the variables given.
From the information, the function is illustrated as:
= 0.7166x² + 6.267x + 1.344
x represents 1997 which was given as 0.
Therefore, the amount in 1997 will be:
= 0.7166x² + 6.267x + 1.344
= 0.7166(0)² + 6.267(0) + 1.344
= 0.7166 + 1.344
= 2.0606 million pounds.
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10. Find the value of k such that the line through (5, 1) and (k, 7) is parallel to the line
y = 3x.
Answers
Answer:
k = 7
Step-by-step explanation:
y = 3x
The slope is 3
Parallel lines have the same slope so a line parallel will have a slope of 3
Using the slope formula
m = (y2-y1)/(x2-x1)
3 = ( 7-1)/(k-5)
3 = 6/(k-5)
Multiply each side by k-5)
3 * (k-5) = 6
Divide each side by 3
k-5 = 6/3
k-5 = 2
Add 5 to each side
k = 7
If angle T = x degrees and angle V = 3x + 60, then angle V = ___ degrees.
Answers
Given data:
The given circle.
The quadrilateral inside the circle is cyclic in nature, the expression for the cyclic quadrilateral is,
[tex]\begin{gathered} \angle V+\angle T=19=180^{\circ} \\ 3x+60+x=180 \\ 4x=120 \\ x=30 \end{gathered}[/tex]The value of angle V is,
[tex]\begin{gathered} \angle V=3(30^{\circ})+60^{\circ} \\ =150^{\circ} \end{gathered}[/tex]Thus, the value of angle V is 150 degrees.
interest : 40principal: xrate: 1.66%time : 4
Answers
The simple interest is given by:
[tex]I=PVrt[/tex]Where:
PV = Present value or principal
I = Interest
r = rate
t = time
Solve for PV:
[tex]\begin{gathered} PV=\frac{I}{rt} \\ so\colon \\ PV=\frac{40}{0.0166\cdot4} \\ PV=602.4 \end{gathered}[/tex]Answer:
$602.4
Given: 3x + 16 = 4x - 9
Prove: x = 25
Answers
Answer:
x=16
Step-by-step explanation:
Simplifying
3x + 16 = 4x
Reorder the terms:
16 + 3x = 4x
Solving
16 + 3x = 4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x' to each side of the equation.
16 + 3x + -4x = 4x + -4x
Combine like terms: 3x + -4x = -1x
16 + -1x = 4x + -4x
Combine like terms: 4x + -4x = 0
16 + -1x = 0
Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16
Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16
Combine like terms: 0 + -16 = -16
-1x = -16
Divide each side by '-1'.
x = 16
Simplifying
x = 16
I Need Help Please This Will Only Take 1min…
Answers
The (C) solution of the equation is the value of the variable that causes an equation to be a true statement.
What are equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others.So, the Root or solution of the equation is the value of the variable that turns an equation into a true statement.
An equation that compares two mathematical expressions is a sentence or mathematical statement.The value of the variable that makes the equation true or satisfies it is referred to as the equation's root or solution.For instance,
"x + 2 = 0"The equation's solution in this case is x = - 2.
x² - 1 = 0Here, the equation's roots or solutions are x = 1 and -1.
Therefore, the (C) solution of the equation is the value of the variable that causes an equation to be a true statement.
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The complete question is given below:
The value of the variable which makes an equation a true statement is called the ________ of the equation.
A. Coefficient
B. Equation
C. Solution
D. Algebraic expression
E. Constant
F. Variable
Which values of x and y would make the following expression represent a real number?
(4 + 5i)(x + yi)
x = 4, y = 5
x = –4, y = 0
x = 4, y = –5
x = 0, y =
Answers
The values of x and y that makes the expression are x = 4 and y = -5
How to determine the values of x and y?The expression is given as
(4 + 5i)(x + yi)
The above expression is a complex expression
As a general rule, complex expressions are represented as a + bi
Where a is the real part and bi is the complex part
Also, we have
i = √-1
Using the above as a guide, we have
(4 + 5i)(x + yi)
For the above expression to be a real number, then the following must be true
(4 + 5i) must be a conjugate of (x + yi)
This means that
x + yi = 4 - 5i
By comparison, we have
x = 4 and y = -5
Hence, the values are x = 4 and y = -5
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A professor has recorded exam grades for 10 students in his class, but one of the grades is no longer redable.if the mean score on the exam was 80 and the mean of the 9 readable scores is 84, what is the value of the unreadable score.
Answers
We have The mean of a data-set is given by the sum of all values in the data-set divided by the number of values, so:
data set has 10 values
mean data set is 80
The 9 readable scores have a mean of 84, this is: 9 x 84 = 756
the value of the unreadable score is x
Therefore, the mean is:
[tex]\frac{756+x}{10}=80[/tex]then solve for x:
[tex]\begin{gathered} 10\times\frac{756+x}{10}=80\times10 \\ 756+x=800 \\ 756+x-756=800-756 \\ x=44 \end{gathered}[/tex]Answer: the value of unreadable score is 44
When 2 triangles are congruent, you can move 1 figure and it fits exactly on the other. Which transformation from Unit 1 would not result in congruent figures?
Answers
The non-rigid transformation will not result in congruent figures because they will change the size or shape.
Hence, the answer is dilation because if we dilate the figures they will not be congruent after the transformation.
Identify the quadratic function(s). (Select all that apply.) 2b(b - 7) + b = 0 (4a + 2)(2a - 1) + 1 = 0 2y + 2(3y - 5) = 0 8 - 5x = 4(3x - 1)
Answers
The quadratic equations are 2b(b - 7) + b = 0 and (4a + 2)(2a - 1) + 1 = 0 .
what is Quadratic Equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x² (a ≠ 0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.
Given:
a) 2b(b - 7) + b = 0
2b² - 14b + b = 0
2b² - 13b = 0
b) (4a + 2)(2a - 1) + 1 = 0
8a² - 4a + 4a + 1 =0
8a² 1 =0
c) 2y + 2(3y - 5) = 0
2y+ 6y- 10 = 0
8y -10=0
d) 8 - 5x = 4(3x - 1)
8- 5x= 12x- 4
Hence, the quadratic equations are 2b(b - 7) + b = 0 and (4a + 2)(2a - 1) + 1 = 0 .
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1. WHAT IS THE STANDARD DEVIATION FOR THE FOLLOWING DATA. ROUND YOUR ANSWER TO TWO DECIMAL PLACES 6 8 5 11 4 22.WHAT IS THE STANDARD DEVIATION FOR THE FOLLOWING DATA.90 90 90 90 90 90?3.) IF THE STANDARD DEVIATION IS 9, WHAT IS THE VARIANCE?
Answers
Solution:3.16
Analysis: In the first step, we need to find the mean of values we have in the exercise:
[tex]Mean=(6+8+5+11+4+2)/6=36/6=6[/tex]Now, let's find the standard deviation:
Subtract the mean from each of the data values and list the differences.
6-6=0
8-6=2
5-6=-1
11-6=5
4-6=-2
2-6=-4
Now, let's square each of the differences from the previous step and make a list of the squares.
[tex]\begin{gathered} 0^2=0 \\ 2^2=4 \\ (-1)^2=1 \\ 5^2=25 \\ (-2)^2=4 \\ (-4)^2=16 \\ \end{gathered}[/tex]Now, let's add the squares from the previous step:
0+4+1+25+4+16=50.
Let's use the formula
[tex]S=\sqrt{\frac{\sum_{i=1}^n(x_i-\bar{x})^2}{n-1}}=\sqrt{\frac{50^{}}{6-1}}=\sqrt{10}=3.16[/tex]Find the direction angle of v for the following vector.v=7i−2jPart 1What is the direction angle of v?
Answers
Given: the vector v
[tex]v=7i-2j[/tex]To Determine: The direction of the given vector
The vector diagram is as shown below
The direction of a vector is calculated by the formula
[tex]\theta=\tan ^{-1}(\frac{y}{x})[/tex]From the given vector, determine x and y
[tex]x=7,y=-2[/tex]Note, the vector is on the fourth quadrant
[tex]\begin{gathered} \theta=\tan ^{-1}(\frac{7}{-2}) \\ \theta=74.05+270=344.05 \\ \theta\approx344.1^0 \end{gathered}[/tex]Hence, the direction of v is 344.1⁰(nearest one decimal place)
prove that the medians to the legs of an isosceles triangle are congruent
I need the step by step proof on this
Answers
The median of the legs of a triangle joins the vertex to the midpoint of the opposite side of the triangle. Hence, they are congruent. The correct postulate is (D) SAS See proof below.
What exactly are Congruent Triangles?Congruent triangles are those with the same size and form. This signifies that the respective sides are equal, as are the corresponding angles.
The median of a triangle's legs connects the vertex to the midway of the opposing side of the triangle. An isosceles triangle has two sides and angles that are congruent.
This suggests that postulates AAA and SSS are ruled out.
This is because both postulates entail that the triangles' sides and angles are congruent.
Sides AB and AC are congruent (S)
Sides CD and BD are also congruent (S)
Angles at D on both triangles are congruent (A)
These mean that:
The triangles are congruent by the SAS postulate. Thus, the correct postulate is (d) SAS
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Full Question:
Prove that the medians to the legs of an isosceles triangle are congruent. What rule did you use to prove triangles congruent:
1. AAA
2. ASA
3. Cannot be determined
4. SAS
5. SSS
