(x^4+10x^3+10x^2-15x-6)/(x+2) Synthetic Division
The synthetic division for the polynomial (x^4+10x^3+10x^2-15x-6) divided by (x+2) would be:
x^3 + 8x^2 - 19x - 12 + (R)
Where R is the remainder.
The quotient is x^3 + 8x^2 - 19x - 12
What is a synthetic division for the polynomial?A synthetic division, also known as long division of polynomials or polynomial synthetic division, is a method of dividing polynomials that is faster and simpler than the traditional polynomial long division method. It is particularly useful for dividing a polynomial by a linear factor of the form (x - a), where a is a real number.
Synthetic division allows you to divide a polynomial by a linear factor without having to perform the traditional long division algorithm, by using the polynomial's coefficients instead of the polynomial itself. Synthetic division is also useful for finding the remainder of a polynomial division. The quotient and the remainder are written in a form of simplified polynomials.
Therefore, the correct answer is as given above
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The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810. Use the mean, median, mode, and range of the rents to answer the following question: Which measure of central tendency best described the advertised rents? Calculate the four measures of central tendency and provide two to four sentences supporting the answer. (I already calculate the four, I just need help with picking out the best one. Range: 880. Mode: 670. Mean: 898. Median: 790)
The MEAN best describes the monthly rents.
The best one is Mean : 898
Now, According to the question:
The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810.
We are required to use the mean, median and mode to explain which measure of central tendency best describes the monthly rent.
The mean, median and mode (as calculated) are the measures of central tendency for the data set given.
This measures which value is closest to the center such that it can conveniently represent every other data. Observe carefully that the least value is 670 while the highest is 1550.
Also, observe that the value which is "more central" to both extremes is the mean.
The median is closer to the lowest value and much farther from the highest value.
The mode is actually at the lowest end of the data set.
However, the mean is safely between both ends. Its farther away from the least value than the median which means its moving closer to the "center" unlike the other two measures.
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THE AREA OF A SECTOR IS A = 384 in².
A. IF THE RADIUS IS 24 IN. , WHAT IS THE MEASURE OF THE CENTRAL ANGLE, IN RADIANS?
B. IF THE CENTRAL ANGLE MEASURES RADIANS, WHAT IS THE RADIUS OF THE CIRCLE? ROUND TO THE NEAREST HUNDREDTH.
A) The measure of the central angle is [tex]\frac{4}{3} \pi[/tex] .
B) The radius of the circle is 55.43 in.
A) We know,
The area of a sector is [tex]\frac{n}{2\pi } \pi R^{2}[/tex]
where n = the degree of the central angle of the sector
R = radius of the circle
Suppose, the measure of the central angle is x.
[tex]\frac{x}{2\pi } .\pi .24^{2} = 384\pi[/tex]
⇒ [tex]\frac{x}{2\pi } = \frac{384\pi }{576\pi }[/tex]
⇒ [tex]x = \frac{384\pi }{576\pi } * 2\pi[/tex]
⇒ [tex]x = \frac{4}{3} \pi[/tex]
So, the measure of the central angle is [tex]\frac{4}{3} \pi[/tex].
B) Suppose the radius of the circle is r in.
[tex]\frac{\pi /4}{2\pi } .\pi .r^{2} =384\pi[/tex]
⇒[tex]\frac{1}{8} .\pi .r^{2} =384\pi[/tex]
⇒ [tex]r^{2} = 384\pi / \frac{1}{8} \pi[/tex]
⇒ [tex]r^{2} = 3072[/tex]
As r > 0
So, r = 55.43
Hence, The radius of the circle is 55.43 in.
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Select all the expressions which are equivalent to -5/2z-5/6
All the expressions which are equivalent to -5/2z-5/6 are given below.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression,
-(5/2)z - 5/6
Simplifying,
-(5/2)z - 5/6,
= -5(z/2 + 1/6) is an equivalent expression.
= -5/2 (z + 1/3) is an equivalent expression.
Therefore, -5(z/2 + 1/6) and -5/2 (z + 1/3) are the equivalent expressions
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A florist wants to determine if a new additive helps
extend the life of cut flowers longer than the original
additive does. The florist selects 20 flowers of different
types and puts each flower in its own vase with the
same amount of water. She positions the vases so they
also receive the same exposure to light. She numbers
the flowers 1-20, and places these numbers on equal-
sized slips of paper. The slips are placed in a hat and
mixed thoroughly. A slip is chosen and the
corresponding flower receives the new additive. After
the hat is shaken, another slip is chosen and the
corresponding flower also receives the new additive.
This procedure continues until 10 flowers have been
assigned to receive the new additive. The remaining 10
flowers receive the original additive.
"No, the flowers were not put into groups first and then randomly assigned the two additives.
Now, According to the question:
Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a random experiment. To avoid any ambiguity or surprise, a random experiment must be properly defined.
"Information available from the question"
The florist selects 20 flowers of different
And puts in each vase with same amount of water.
10 flowers have been assigned to receive the new additive.
The remaining 10 flowers receive the original additive.
Based on the data, this is not a randomized block design for the experiment because the flowers were not put into groups first and then randomly assigned the two additives.
Therefore, "No, the flowers were not put into groups first and then randomly assigned the two additives.
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A water sample shows 0. 097 grams of some trace element for every cubic centimeter
of water. Ayden uses a container in the shape of a right cylinder with a diameter of
16. 8 cm and a height of 10. 8 cm to collect a second sample, filling the container all
the way. Assuming the sample contains the same proportion of the trace element,
approximately how much trace element has Ayden collected? Round your answer to
the nearest tenth.
Adam has gathered 232.32 g of trace elements, which are contained in a cylindrical container with a radius of 8.4 cm and a height of 10.8 cm.
Radius of the cylinder 8.4 cm
Height of the cylinder = 10.8 cm
Volume of the cylinder = π r² h
When we change the values in the formula, we obtain:
V = π (8.4 cm)² (10.8 cm)
V = 22 / 7 (70.56 cm²) ( 10.8 cm)
V = 2395.008 cm³
Presence of particle = 0.097 g for every cm³
The element's trace for 2395.008 cm3 will be:
= 2395.008 × 0.097 g
= 232.315776 g
As a result, Adam has gathered 232.32 g of trace elements in the cylindrical container with a radius of 8.8 cm and a height of 15.9 cm.
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8 of the tables at Joy's Italian Restaurant are full and the other 13 tables are empty. What is the ratio of the number of empty tables to the total number of tables?
The ratio of the number of empty tables to the total number of tables 13:21.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that 8 of the tables at Joy's Italian Restaurant are full
13 tables are empty
The total number of tables in the restaurant are 8+13=21
We have to find ratio of the number of empty tables to the total number of tables
Empty tables = 13
Total number of tables=21
Ratio of the number of empty tables to the total number of tables 13:21
Hence, the ratio of the number of empty tables to the total number of tables 13:21.
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Solve the system by substitution. Check your solution. 0.5 x + 0.25 y = 36. y + 18 = 16 x. a. (36, 72) c. (49, 81) b. (9, 126) d. (21, 9) Please select the best answer from the choices provided A B C D
Answer:
Answer is in attached photo. (B)
Step-by-step explanation:
SolutionThe solution is in the attached photo , do note the question might specify the method to use to solve the equations, just like this the question:
1) Substitution Method
2) Elimination Method
Mary decided to look at new and used cars. Mary found a used car for $10000. Mary found that she paid 40% of the price of a new car. How much would a new car cost
Answer: i don't know sorry 99
Step-by-step explanation:
56+80
dr. green is interested in conducting a 2 x 2 x 3 within-group factorial design, with 20 participants in each cell. how many participants does she need overall?
she need 240 number of participant .
Graphing cell means to picture primary impacts and connections. The numbers in the secret elements address bunch implies in a 2 x 2 x 3 plan. The negligible means for factors An and B are likewise shown. The cell implies are plotted as line diagrams and as reference charts.
Now, According to the question:
We have Dr. Green is interested in conducting a 2 x 2 x 3 within-group factorial design.
There are 12 cells in factorial, and each cell 20 participant.
Then, number of participant = 20(12) = 240 participant.
Thus, she need 240 number of participant .
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Identify bias based on a survey of 2718 people the national opinion research center concluded that 30% 32% of americans always make a special effort to sort and recycle glass cans plastic or papers 24% americans often make such an effort
Based on a survey of 2718 people, a research center concluded that 32% of Americans "always" make a special effort to sort and recycle glass, cans, plastic, or papers. Participation bias is there in this case.
The bias would have no effect on a reader's perception of the assertion because no group of persons is much more likely to respond to the poll than any other.
When comparisons are performed between groups of patients who differ in outcome determinants and the differences are connected to the result, participation bias emerges.
1. Participation bias is inherent in studies that involve participant enrollment.
2 Because selective participation might jeopardize study external validity, determining the magnitude of participation bias is critical for optimizing inference from these investigations.
Few community studies have looked into the impact of participation bias. Nonparticipants in one population-based study of myocardial infarction (MI) were older, had more comorbidity, and had a lower survival rate than participants.
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a light post casts a shadow on a small boy. the boy, who is 4 feet 6 inches tall, notices that his shadow is 3 feet 4 inches long. he decided that if he measures how far he is from the light post, he can determine how tall the post is from the ground. explain how he can figure out the height of the light post. use mathematical reasoning.
The small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.
Similar triangles are triangles that have the same shape but can have different sizes. In this case, the shadow of the boy, the boy himself, and the light post form similar triangles.
Let h be the height of the light post, x be the distance between the boy and the light post, and s be the length of the shadow, we can use the following ratios -
(boy's height) / (boy's shadow) = (light post height) / (light post shadow)
i.e. (4 feet 6 inches) / (3 feet 4 inches) = (h) / (x)
Now, we can find the height of the light post by using the above equation and the given values of the boy's height and the shadow.
The small boy can measure the distance between him and the light post, and he can use this value in the above equation to determine the height of the light post. The equation is h/x = (4.5)/(3.33)
This is the ratio of the height of the light post and the distance between the boy and the light post, so h = (4.5 * x) / (3.33)
In this way, the small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.
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researchers collect data about juuling by asking users to keep track of the number of times per day they turn their device on and the number of inhalations each time they turn the device on. what type of data are these? group of answer choices interval nominal ratio ordinal
The given data is ordinal data.
This type of data is ordinal data, as the variables are collected on an ordered scale (the number of times per day the device is turned on and the number of inhalations per activation). Although the actual numerical values may not have equal distances, they can still be ordered and compared based on the magnitude of the numbers.
Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. These statistics are presented on an ordinal scale, one of the four measurement levels that S. S. Stevens described in 1946.
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earle bailey has 20 songs to choose from but can play only 7 in the next half-hour on sirius xm classic.how many different (ordered) playlists are possible
Applying combination, the number of playlist is: 75,435.
How to Apply Combination to Solve a Problem?A combination is a way of selecting a certain number of items from a larger set, without regard to the order of the items.
The number of possible playlists would be the number of ways to select 7 songs out of 20 without regard to order, which is commonly known as a combination.
The formula for combination is nCr, where n is the total number of items and r is the number of items being chosen at a time. So in this case, the number of possible playlists would be 20C7.
This can also be written as 20!/(7!*13!)
The answer is 75,435
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Divide the following: MUST SHOW WORK. (30 points)
On dividing the expression [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)], the value obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The expression is given as - [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)]
Apply the fraction rule, (a/b)/(c/d) = a·d/b·c
= [(x²-9) × (x²-2x-15)]/[(x²-4x-5) × (x²+5x+4)]
= [(x²-9) × (x+3)]/[(x²-4x-5) × (x+1)]
Expand the expression -
= [(x²-9) × (x+3)]/(x³-3x²-9x-5)
= (x³+3x²-9x-27)/(x³-3x²-9x-5)
= 1 + [(6x²-22)/(x³-3x²-9x-5)]
Therefore, the expression obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].
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The ratio of the volumes of the bags of dog food is [ Select ] which means the scale factor of the dimensions of the two bags is [ Select ] . Therefore the scale factor of the surface area of the two bags is [ Select ] .
Answer:
Step-by-step explanation:
Answer:
20, 2.7, 7.4
Step-by-step explanation:
I completed the assingment and got it 100
8x +x2/3 what is that answer
The solution to the expression when x = 3 is 26
How to determine the solution to the expressionFrom the question, we have the following parameters that can be used in our computation:
8x + x * 2/3
Also, we have
x = 3
substitute the known values in the above equation, so, we have the following representation
8 * 3 + 3 * 2/3
Evaluate the product
24 + 2
Evaluate the sum
26
Hence, the solution is 26
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Complete question
Given that 8x + x * 2/3, calculate the expression when x = 3
The algebraic expression 8x + 2x/3 is simplified to a simple fraction as 26x/3
How to simply the algebraic expressionWe shall first find the lowest common multiple (LCM) of the denominators of both terms to have a single fraction and then we simplify as follows;
The denominator of 8x is 1 and 2x/3 is 3
LCM of 1 and 3 is 3
we simplify to a single fraction;
multiply the term 8x by the LCM 3
(3 × 8x + 2x)/3
multiply the term 8x by the LCM 3
(24x + 2x)/3
add the algebraic terms 24x and 2x together
26x/3
Therefore, the algebraic expression 8x + 2x/3 is simplified to a simple fraction as 26x/3.
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Ella has .5 of sugar. How much water should she add to make 1.5% syrup concentration
We need to find how much water Ella needs to make the different concentrations of syrups. The solution will be for 1.5%, we need 32.83 lbs of water.
How to explain the concentration?The percentage in the concentration tells us how much in the mixture is sugar.
So for example, in the 50% syrup, we have a 50% of sugar, meaning that half of it is sugar, and we have 0.5 lbs of sugar, so we need to add the same amount of water, 0.5 lbs of water.
For the 1.5% syrup, this will be:
= (0.5 - 0.5 × 0.015) / 0.015
= 32.83 lbs
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Complete question
Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case. 1.5% syrup?
Set up a system of equations for the given information by filling in the boxes with the coefficients of the variables and the constant values, where is the amount invested in stocks, is the amount invested in bonds, and is the amount invested in CD's. If there is no visible coefficient, then enter for the coefficient. If a specific variable is not present in the equation, then enter for the coefficient. Country Day's scholarship fund receives a gift of $200000. The money is invested in stocks, bonds, and CDs. CDs pay 5% interest, bonds pay 2.9% interest, and stocks pay 10.9% interest. Country day invests $20000 more in bonds than in CDs. The total amount earned from the investments is $11165. Total amount invested: + + = Total amount earned from investements: + + = Relation of bonds and CDs: + + =
The system of equations is:
a + b + c = 2000000.109a + 0.029b + 0.05c = 11165b = c + 20000How to determine the system of equationsFrom the question, we have the following parameters that can be used in our computation:
Total amount invested = $110000
Using the fiollowing variable representations:
Amount invested in stocks = a Amount invested in bonds = bAmount invested in CD's = cWe have
a + b + c = 200000
Using the total interest earned of 7145, we have:
10.9% * a + 2.9% * b + 5% * c = 11165
So, we have
0.109a + 0.029b + 0.05%c = 11165
Country day invests $20000 more in bonds than in CDs.
So, we have
b = c + 20000
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y=x^2+6x+8
solve by using completing the square.
what are the roots/zeros/x-intercepts of your parabola?
The roots of the parabola are given as follows:
x = -2 and x = -4.
How to obtain the roots of the quadratic function?The quadratic function for this problem is defined as follows:
y = x² + 6x + 8.
Completing the squares, the quadratic function can be factored as follows:
y = (x + 4)(x + 2).
As:
The sum of the roots is of 6.The product of the roots is of 8.Then the roots are obtained as follows:
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t
he points that are on the graph of the function defined by y=2x+3
.
The point that lies on the function defined by the equation is (2, 7)
How to determine the point that lies on the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 3
The point in the ordered pair that lies on the graph of the equation is the solution set
Take for instance, we set x = 2
So, we have the following representation
y = 2 * 2 + 3
Evaluate the product and the sum
This gives
y = 7
When repesented as an ordered pair, we have
(2, 7)
Hence, the point is (2, 7)
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What do the measures of angles BDA and BEA and the fact that and are radii of circle A tell us about and Explain your answer
The measures of angles BDA and BEA is 90 degree and the fact that AD and AE are radii of circle A tell us about BD and BE must be a tangent to the circle.
The tangents to the circle are BD and BE.
∠BDA = 90
∠BEA = 90
Radii = AD and AE
A tangent's angle with a circle's radius is always measured as a 90-degree angle.
∠BDA = 90, and since AD is a radius, BD must be a tangent to the circle.
Similar, ∠BEA = 90 suggests that BE is a tangent to the circle and that AE is a radius.
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The complete question is:
What do the measures of angles BDA and BEA and the fact that AD and AE are radii of circle A tell us about BD and BE?
Use the box method to distribute and
simplify (-5x - 2) (5x + 4). Drag and
drop the terms to the correct locations of
the table.
( − 5x − 2)(5x+4)
You must answer all questions above
in order to submit.
Create a table with the place values for the first and second factors down the left and the top and bottom, respectively.
What is the box method?
Multiplication using the box method: Create a table with the place values of the first and second factors down the left and the top and bottom, respectively. Second step: multiply the place values and add the results to the table. Step 3: Add up all of the table's rows. Step 4: Add the sums of these rows.
Placing the first word in the first box and the last term in the last box is the first step in utilizing the box technique to factor a trinomial. Multiply the first and last boxes after that. Identify the first and last boxes' products, which together make up the middle word. Put these words in the remaining spaces.
Here's how you can use the box method to distribute and simplify the expression:
( -5x - 2 ) ( 5x + 4 )
⇒-5x -2
⇒5x 4
⇒-25x^2 -10x + 20x - 8
⇒-25x^2 + 10x - 8
So the simplified expression is:
-25x^2 + 10x - 8.
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how many 10-element subsets of {1, 2, 3, . . . , 20} contain at least one odd element? (hint: we are selecting a subset of the previous set, so {1,2,3,4,5,6,7,8,9,10} is the same as {1,2,3,5,4,6,7,8,9,10}.)
The no. of subsets with at least one odd number is ²⁰C₁₀ - 1
We have the sample set to be {1, 2, 3, 4, ... 20}
Now we need to make subsets of 10 from these 20 elements.
Hence, the number of possible subsets of 10 elements will be
²⁰C₁₀
Now, there are 10 odd elements in the given sample set.
Hence the number of sets that contain at least 1 odd element
= Total no. of possible sets - no. of possible sets with no odd no.
Now since there are only 10 even numbers, there can be only one such set possible.
Hence no. of the subsets with at least one odd number is
²⁰C₁₀ - 1
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Find the measures of the numbered angles.
Answer: ∠1= 75°, ∠2= 105°, ∠3=105°, ∠4=75°, ∠6=105°, ∠7= 105°, ∠8=75°
Step-by-step explanation:
∠1 is corresponding to angle 75° which make them equal.
∠2 is supplementary to ∠1 which means they add up to 180°. Since ∠1 is 75° you would subtract 75° from 180° to get 105°.
∠3 is vertical to ∠2 which makes them equal.
∠4 is vertical to ∠1 which makes them equal.
∠6 is corresponding to ∠2 which makes them equal.
∠7 is vertical to ∠6 which makes them equal.
∠8 is vertical to 75° which makes them equal.
a) Divide 260 in the ratio 1:3
Answer:
Step-by-step explanation:
Total number = 260
Ratio would be 1 : 3
So, the first part is given by
[tex]\frac{1}{4}[/tex] x 260
=[tex]\frac{260}{4}[/tex]
=65
And the second part is given by
[tex]\frac{3}{4}[/tex] x 260
=[tex]\frac{780}{4}[/tex]
=195
Hence, the first and second part are 65 and 195 respectively.
Think about what you know about breaking apart numbers with addition. Fill in each box. Use words,numbers. and picture. Show as many ideas as you can.
The breaking apart numbers with addition help us to solve an addition more efficient than left-to-right addition.
What is addition?Addition in math is a process of combining two or more numbers.
Given that, think about what you know about breaking apart numbers with addition.
What is it?Breaking apart an addend is a mental math strategy for addition. Some students may find this method more efficient than left-to-right addition.
What I know about it?This strategy involves breaking up one addend in an equation into more manageable parts.
Examples :-1) 32 + 46 =
Breaking the second term 46 in 40 + 6
32 + 40 + 6
= 72 + 6
= 78
2) 89 + 73 =
Breaking the second term 73 into 70 + 3
89 + 70 + 3
= 159 + 3
= 162
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Mr. Ramirez is always trying to clean up his garage. He has 1/5 liter of oil in one can and 2 5 liter of oil in another can. How much will he have if he pours them both into one can URGENT PLEASE ANSWER
The total amount of oil he would have if he pours them both in a can is 2.7 liters.
How much oil would he have?In order to determine the amount of oil he would have, add both numbers together. In order to add the numbers, both numbers have to be in the same form. One of the numbers is a decimal and the other is a fraction.
In order to convert the fraction to a decimal, divide the numerator by the denominator.
1/5 = 0.2
Total number of oil = 0.2 + 2.5 = 2.7 liters
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From the observation deck of a skyscraper, Morgan measures a 67
∘ angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
Angle of depression and elevation:The angle of depression refers to the angle above the hill.The ship is 349.8 feet away from the skyscraper's base horizontally.
How far does the ship extend horizontally from the skyscraper's base?You could calculate the angle of elevation, for instance, if you were standing on the ground and were looking up at a mountain's summit.
The angle between a line of sight's horizontal axis and its downward axis is known as the angle of depression.
The ship is 349.8 feet away from the skyscraper's base horizontally.
Angle of depression and elevation:The angle of depression refers to the angle above the hill.
given the aforementioned variables
The harbor is 824 feet tall.
Depression angle is 67 degrees.
SOH CAH TOA identification claims that:
Tan = opp/adj Tan = 824 Tan = 67
d = 824.8/tan67 d = 349.8 feet
Therefore, the vertical distance from the skyscraper's base to the ship is 349.8 feet.
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Does someone mind helping me with this problem? Thank you!
Answer:
0.01 goes in the first box
0.10 goes in the second box
Therefore, the first equation is 0.01p + 0.10d = 1.50
===========================================================
Reason:
The last part mentions "A penny is 0.01" which means $0.01 or 1 cent. The 0.01 is the coefficient of the variable p.
1 penny = $0.01
p number of pennies = 0.01p dollars
A similar situation happens with the dimes.
16/1 x 3/8 in simplest form
Answer: 6
Step-by-step explanation:
1. 16/1 × 3/8= 48/8
2. 48/8= 6