Answer:
We can use the tangent function to solve for the height of the tower. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle.
First, we'll find the opposite side (the height of the tower) using the angle of elevation:
tan(21°) = opposite / 300
opposite = 300 * tan(21°)
Then we'll find the opposite side (the depth of the base of the tower below the window) using the angle of depression:
tan(20°) = opposite / 300
opposite = 300 * tan(20°)
Now we can add the two opposite sides we found to get the total height of the tower
height = opposite(elevation) + opposite(depression)
height = 300 * tan(21°) + 300 * tan(20°)
The angle should be converted to radians before using the tangent function, and the final answer should be rounded to 2 decimal places.
Step-by-step explanation:
2) In 2000, the population of a town in 20,000 and decreased by 2% each year.
a) Write an equation to model this scenario.
b) What will the population be in 2025?
The equation which states that the population of a town is 20,000 and decreased by 2% each year is y=20000(1-0.2x)
What is an equation example?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What are the types of equations?Different Types of Equations
Linear Equation.
Radical Equation.
Exponential Equation.
Rational Equation.
Let the population be y and the of years be x
According to the question, the equation should be
y=20000(1-0.02x)
In 2025 the population will be
y=20000(1-0.02*25)
y=100000
The population will become 10000
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1. What is the sum of the first 20 multiples of five?
OS20 = 1,050
OS20 = 1,000
OS20 = 1,550
OS20 = 2,100
What is the difference when -2 is subtracted from 2?
Answer:
Step-by-step explanation:
2-(-2)
=2+2
=4
Answer: the difference when -2 is subtracted from 2 will be 4
Step-by-step explanation: according to question
2 -(-2)
=2+2 ( - + - = +)
= 4
A cyclist travels 2 miles in 10 minutes and then a further 8 miles in 30 minutes without stopping. Calculate the cyclist's average speed in mph.
The cyclist's average speed is
14.93
mph.
Total
distance
covered is=2+8=10
Total time =10+30=40
=40/60 min
=.0.67 hours.
Convert miles per min to miles per hour,
average speed= 10 miles/0.67 hours,
=14.93 mph.
The average speed is =4.93 mph
The total distance covered is 2 + 8 = 10 miles. The total time taken is 10 minutes + 30 minutes = 40 minutes. To convert minutes to hours, divide the time in minutes by 60. So, the total time taken in hours is 40 minutes / 60 = 0.67 hours. To convert miles per minute to miles per hour, multiply the speed in miles per minute by 60. So, the average speed in miles per hour is
10 miles / 0.67 hours = 14.93 mph
The average speed is =14.93 mph
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Calculate ( – 2 – 3i)^4. Give your answer in a + bi form
Answer:
-34 - 24i
Step-by-step explanation:
To calculate ( – 2 – 3i)^4, we can use the property that (a + bi)^n = a^n + (n*a^(n-1)b)i + (na^(n-2)*b^2)i^2 + ...
So, ( – 2 – 3i)^4 = (-2 - 3i) * (-2 - 3i) * (-2 - 3i) * (-2 - 3i)
= -2^4 - 2^3 * 3i - 2^2 * 3^2i^2 - 2 * 3^3i^3 - 3^4i^4
= -16 - 24i + 18i^2
= -16 - 24i -18
= -34 - 24i
ayo earns 50,000 monthly and he spends 35,000 altogether. if he saves the rest, find the percentage of his savings
Answer:
30%.
Step-by-step explanation:
Ayo earns 50,000 monthly and he spends 35,000 altogether, so he saves the rest of his income. To find the percentage of his savings, we can divide his savings by his total income and multiply by 100.
His total income is 50,000
His total expenditure is 35,000
His savings = total income - total expenditure = 50,000-35,000 = 15,000
So the percentage of his savings = (savings / total income) x 100 = (15,000 / 50,000) x 100 = 0.3 x 100 = 30%
Therefore, Ayo's savings percentage is 30%.
7.86x4.564 report the following answer into significant figures
Answer:
35.87
Step-by-step explanation:
First, what is 7.86 by 4.564?
It is 35.87304.
But the answer needs to be in significant figures, so how do we do that?
Well, significant figures are the numbers that comes after the decimal place. For example, 0.52, which has 2 significant figures.
So with 7.86, there are 2 significant figures and with 4.565, there are 3.
We want to use the one with the least amount of significant figures, so we would round our answer to the hundredth:
35.87
Hope this helps!
The required answer is 35.8730
The number of significant figures in a measurement represents the level of precision in that measurement. In general, the last digit in a number is considered uncertain and is rounded based on the number of significant figures.
When performing arithmetic calculations, the result should be rounded to the same number of significant figures as the least precise measurement used in the calculation.
In this case, the least precise measurement is 4.564, with four significant figures. Therefore, the final result of the calculation 7.86 x 4.564 should be reported with four significant figures.
The answer is 35.87304 and should be reported as 35.8730
(Please mark my answer Brainliest if this helped.)
Solve for t.
t − 4/3 = 1
Answer:
t = [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
t - [tex]\frac{4}{3}[/tex] = 1 ( multiply through by 3 to clear the fraction )
3t - 4 = 3 ( add 4 to both sides )
3t = 7 ( divide both sides by 3 )
t = [tex]\frac{7}{3}[/tex]
converting within measurement sytems
Converting within measurement systems means that we are changing the unit of measurement from one to another.
What is Converting within measurement systems?It is referred to as converting units within measuring systems if we do it using the metric or conventional systems. The conventional system and the metric system are the two most widely used measurement systems. In other words, we are not converting units from customary to metric or vice versa.
Simple unit conversions can be performed mentally or with one-step multiplication or division. There are, however, more difficult conversions that call for many conversions between a wide range of units.
The Unit Factor Method, another name for the Dimensional Analysis process, is a mathematical technique that takes advantage of the fact that any number or statement may be multiplied by "one" without changing its value. By multiplying the previous measurement by one (or more) different representations of the number 1, you can convert units. Although the measurement's value is unaffected by the factor of 1, the measurement's units are.
A ratio of one is referred to as a conversion ratio or unit factor. The names of the units that will be used in the conversion are listed in this ratio. It can be used to convert values both within the English and Metric Systems and between the two. The idea of equivalent values serves as the foundation for the conversion ratio.
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Complete question:
What do you mean by converting within measurement systems?
5 2 (3x4) divided by 3-5
The solution to the expression 5 2 (3x4) divided by 3-5 is -312
What are fractions?Fractions are simply described as part of a whole number or variable.
There are different types of fraction which includes;
Complex fractionsImproper fractionsProper fractionsMixed fractionsSimple fractionsWhat is PEDMAS?PEMDAS is a mathematical acronym used to give the order of operations to be followed in solving expressions.
It stands for;
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionGiven the expression;
52(3×4)/3 - 5
expand the parentheses
52(12)/-2
624/-2
Divide the values
-312
Hence, the values is -312
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T √ 8
60
80%
75%
60%
30%
Explore
Here are four tape diagrams. Each diagram is split into
two pieces that add up to 100%.
The top diagram has a length of 60 units.
Determine the length of the bottom diagram.
The length of the bottom diagram in the final tape diagram is 5.04 units.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.
The top diagram length is 60 units.
20 % of the 60 units is carried down, the length of the new section is:
20/100 * 60 = 12units.
60% of the next 12 units are carried down, the length of the new section is:
60/100 * 12 = 7.2 units
Similarly, when 70% of the section is carried down the length of the new section is:
70/100 * 7.2 = 5.04 units.
Hence the length of the bottom diagram is 5.04 units.
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do you know the ansawer ?
Answer:
1/70
Step-by-step explanation:
(63-40) (21-10) 23 11 23-22 1
(---------)-(--------)=------ - ------ = -------- = --
( 70 ) ( 35 ) 70 35 70 70
The equations x + 5 y = 10, 3 x minus y = 1, x minus 5 y = 10, and 3 x + y = 1 are shown on the graph below.
On a coordinate plane, there are 4 lines. Green line goes through (0, negative 1) and (1, 2). Blue line goes through (0, 1) and (1, negative 2). Pink line goes through (0, 2), and (2, 1.5). Orange line goes through (negative 2, negative 2.5) and (2, negative 1.5).
Which is the approximate solution for the system of equations x + 5 y = 10 and 3 x + y = 1?
(–0.3, 2.1)
(–0.3, –2.1)
(0.9, –1.8)
(0.9, 1.8)
They intersect in the 2nd quadrant. Only one answer choice (–0.3, 2.1)
What is y-intercepts?
Horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.
The graph shows you the lines all differ in their y-intercepts. This means you can identify the y-intercepts of the equations of interest, and you will know which lines to look at.
The y-intercept is found by setting x=0 and solving for y:
x +5y = 10
0 + 5y = 10
y = 10/5 = 2
3x +y = 1
3·0 +y = 1
y = 1
The two lines of interest are the ones that have y-intercepts of 2 (pink) and 1 (blue). They intersect in the 2nd quadrant. Only one answer choice can apply: (–0.3, 2.1)
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The equation y = 4x + 3 models the data below.
x 12 3 4 5 6 78
y 8 13 16 21 26 29 33. 37
a. Calculate the residuals and use the points (x, residual) to make a scatter
plot.
b. Complete the statement below to explain why the model is or is not a good
fit.
The points
So, the equation y = 4x +3
a good fit.
5
2
4-
-2
44
-5-
Point
1
Undo
2
3
Redo
7
x Reset
8
9 10
the plot is attached below and the slope is 4.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
The equation y = 4x + 3 models the data below.
x 1 2 3 4 5 6 7 8
y 8 13 16 21 26 29 33 37
The plot will be using this data.
Hence the plot is attached below and the slope is 4.
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A checkout clerk at a department store is expected to complete 16 transactions every hour. In the past 20 minutes, he completed 6 transactions. Choose True or False for each statement. If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour. Choose... At his current rate, the clerk will complete 12 transactions in 1 hour. Choose... At his current rate, the clerk will complete 9 transactions every half hour. Choose... If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions. Choose...
Step-by-step explanation:
16 transactions per hour (60 minutes).
in short :
16/1
or 16/60 (for minutes instead of 1 hour)
in 20 minutes 6 transactions.
so,
6/20
hour many transactions then in 1 hour (60 minutes) ?
60 = 20×3
so, to bring the ratio to 1 hour (60 minutes) we need to multiply the denominator by 3. and to keep the ratio value, we need to to do the same thing also to the numerator.
therefore,
6/20 × 3/3 = 18/60
so, the clerk will do 18 transactions per hour.
he will meet his goal of 16 : true
he will even exceed but definitely meet his goal.
12 transactions in 1 hour : false
9 transactions every half hour : true
as he will do 18 transactions in 1 hour, he will do half of these transactions (9) in half an hour.
96 transactions in 6 hours : false
18/1
6 = 1×6
so, with the same trick as above we get
18/1 × 6/6 = 108/6
and we see, he would complete 108 transactions in a 6- hour shift.
96 would be right, if the actual ratio would be 16/1 :
16/1 × 6/6 = 96/6
The table describes the quadratic function h(x).
x h(x)
−3 1
−2 −2
−1 −3
0 −2
1 1
2 6
3 13
What is the equation of h(x) in vertex form?
h(x) = (x − 1)2 + 1
h(x) = (x − 1)2 + 3
h(x) = (x + 1)2 − 1
h(x) = (x + 1)2 − 3
The required quadratic equaiton is h(x) = (x + 1)² -3. Option D is correct.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
From the data select 1 pair of values,
x = 0, when h(0) = -2
Now, put this pair in each quadratic equation, since the equation that satisfies this fair will be the required quadratic equation.
A,
h(x) = (x − 1)² + 1
h(0) = (0 − 1)² + 1
h(0) = 2
B.
h(x) = (x − 1)² + 3
h(0) = 4
C.
h(x) = (x + 1)² - 1
h(0) = 0
D.
h(x) = (x + 1)² - 3
h(0) = 1 - 3 = -2
h(0) = -2
Thus, the required quadratic equaiton is h(x) = (x + 1)² -3. Option D is correct.
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How to write this number in standard form (8*10)+(6*10,000)+(3*100,000)(2*100)+(9*1,000)+(7*1)
Answer:
369,287 in the US
3.69287×10⁵ in the UK
Step-by-step explanation:
Given the number (8*10)+(6*10,000)+(3*100,000)+(2*100)+(9*1,000)+(7*1), you want it written in standard form.
Standard formThe "standard form" of a number is different depending on your local culture.
In the US, the standard form of this number can be had by performing the indicated addition.
(8*10)+(6*10,000)+(3*100,000)+(2*100)+(9*1,000)+(7*1)
= 80 +60,000 +300,000 +200 +9,000 +7
= 300,000 +60,000 +9,000 +200 +80 +7 . . . . more useful order
= 369,287
In the UK, "standard form" of a number refers to "scientific notation". The leading digit is shown to the left of the decimal point, and the multiplier is the power of 10 corresponding to that digit's place value.
= 3.69287×10⁵
A bank has launched a three-year structured deposit that offers an effective annual interest of 8% for the first 18 months, quarterly interest of 1.5% for the next 6 months and semi-annual interest of 2% for the last 12 months. If I wish to receive $100, 000 on the maturity date (that is, on the last day of the third year), how much, to the nearest dollar, should I invest? (Assume that interest rates and principal are guaranteed)
Answer:
To determine how much you should invest to receive $100,000 on the maturity date, you will need to calculate the present value of the cash flows at the beginning of the investment. The present value is the amount of money you would need to invest today to receive a certain amount at a future date, taking into account the time value of money and the interest rate.
You can calculate the present value by using the formula:
PV = CF / (1 + r)^t
Where:
PV = present value
CF = cash flow (the amount you will receive at the maturity date)
r = interest rate
t = time (in years)
The first 18 months, the interest rate is 8% per year, which is equivalent to 8/12 = 0.67% per month.
The next 6 months, the interest rate is 1.5% per quarter, which is equivalent to 1.5/4 = 0.375% per month.
The last 12 months, the interest rate is 2% per semi-annual, which is equivalent to 2/2 = 1% per month.
For the first 18 months, the present value of the cash flow is:
PV = 100,000 / (1 + 0.0067)^(18/12) = 95,167
For the next 6 months, the present value of the cash flow is:
PV = 95,167 / (1 + 0.00375)^(6/12) = 94,853
For the last 12 months, the present value of the cash flow is:
PV = 94,853 / (1 + 0.01)^(12/12) = 94,853
So, to receive $100,000 on the maturity date, you should invest 94,853 dollars to the nearest dollar.
Which ratio is the odd one out 8:39, 6:30, 2:10, 4:20, 1:5
Answer:
8:39 is the answer.
The rest, when simplified, change to 1:5.
8. Find the area of the triangle using trigonometry
Using the details given, the area of the triangle in which the angles lies between the two sides is 90.3 units²
What is Area of TriangleThe area of a triangle can be calculated using the formula A = 1/2bh, where b is the base of the triangle and h is the height. Area of a triangle can be calculated using the formula: Area = (base x height) / 2, where base is the length of one side and height is the length of the side that forms the angle. In order to use this formula, you must know the length of two sides and the measure of the angle between them. However, this formula is subjective to details given
The area of a triangle can be calculated by
A = a×b×sinθ
a = 15
b = 8.1
θ = 132°
Substituting the values into the formula
A = 15 × 8.1 × sin 132
A = 90.3 units²
The area of the triangle is 90.3 units²
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what is the area to 14cm and 14cm 17cm 16 cm
Answer:
Area =312cm²
Step-by-step explanation:
since two rectangle are joined together you will find each area of the diagram and finally you add the two rectangle.
so the value for A1
A1 × Length × width.
A1 =16 ×17
A1 =272cm²
the value for A2
A2 Length × width
A2 = 14 × 3
A2 =42cm²
The area of the diagram
=A1 + A2
=272 + 42
=312cm².
The total area of the given figure is 468 cm².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
From the given figure,
Larger rectangle has length=30 cm and width=14 cm.
Smaller rectangle has length=16 cm and width=3 cm.
We know that, the area of a rectangle is Length×Width
Area of Larger rectangle is
30×14 = 420 cm²
Area of Smaller rectangle is
16×3 = 48 cm²
Total area = 420+48 =468 cm²
Therefore, the total area is 468 cm².
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If BD=7x-10, BC=4x-29, and CD=5x-9, find each value
Answer: We know that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using the triangle inequality theorem, we can set up the following inequality:
BD + BC > CD
7x - 10 + 4x - 29 > 5x - 9
Simplifying, we get:
11x - 39 > 5x - 9
Subtracting 5x from both sides, we get:
6x - 39 > -9
Adding 39 to both sides, we get:
6x > 30
Dividing by 6 from both sides, we get:
x > 5
So x must be greater than 5.
To find the value of BD, we can substitute the value of x in the equation:
BD = 7x - 10
BD = 7(5) - 10 = 25 - 10 = 15
To find the value of BC, we can substitute the value of x in the equation:
BC = 4x - 29
BC = 4(5) - 29 = 20 - 29 = -9
To find the value of CD, we can substitute the value of x in the equation:
CD = 5x - 9
CD = 5(5) - 9 = 25 - 9 = 16
So, BD = 15, BC = -9, CD = 16
Step-by-step explanation:
James has a $7,500 unsubsidized 10-loan with an interest rate 4.29%. He wants to pay only the interest while attending school. His payments is due on the 10th of each month. He made his last payment on February 10th, and this is a leap year. Calculate the amount that he will pay on March 10th. (Keep in mind that they are 366 days in a leap year.)
The amount that he will pay on March 10th is $1287 with interest rate.
What does the arithmetic behind interest rates mean?The annual rate that is charged for borrowing (or made by investing), given as a single percentage number, represents the real yearly cost of money throughout the course of a loan.
Given that he is aware that he can begin loan repayment on a $7,500 loan in 4.5 years at the present interest rate of 4.29%, the following will be applicable:
4.29% of 7500 after the first year
4.29 × 7500/100
321.75
After the 4.5-year term, multiply the interest by 4.5 to determine the overall interest:
321.75 × 4
$1287.
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Please look at the picture and answer the question thank you
Answer:
-2x^2+5y^3+
Step-by-step explanation:
Bodens account has a principal of $700 and a simple interest rate of 3.3%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any number?
Answer:
The interest earned is $92.40
The amount in the bank is 92.40 + 700 = $792.40
Step-by-step explanation:
I do not see a number line
Interest = principle x rate x time
Interest = 700 x .033 x 4
Interest = 92.40
Help Please.
The difference between two numbers is 9. Four times the larger number plus one-half the smaller is 45. What are the numbers?
Answer:
To solve this problem, we will use the following steps:
Step 1: Let's assume that the larger number is x and the smaller number is y, we know that the difference between the two numbers is 9, so we can write the equation: x-y = 9
Step 2: We know that Four times the larger number plus one-half the smaller is 45, so we can write the equation: 4x + 0.5y = 45
Step 3: Now we have two equations with two unknowns, we can solve for one of the unknowns by isolating it in one of the equations.
x-y = 9
x = y+9
Step 4: Now we can substitute the value of x in the second equation
4(y+9) + 0.5y = 45
4y + 36 + 0.5y = 45
4.5y + 36 = 45
4.5y = 9
y=2
Step 5: We can substitute the value of y in one of the equation, to find the value of x
x-2 = 9
x = 11
Final Answer: The two numbers are 11 and 2.
Triangle abc undergoes a sequence of transformations 1 reflection across line x=1. 2 dilation by a factor of 2 centered at the origin. What is the resulting image
The resulting image of the triangle ABC after the transformations is given by the image presented at the end of the answer.
How to obtain the image of the triangle?The vertices of the original triangle ABC are given as follows:
A(0,2), B(3,2), C (2,7).
First we have the reflection across the line x = 1, which is a vertical line, meaning that:
The x-coordinate remains the same distance from x = 1, however on an opposite direction.The y-coordinate remains constant.Hence the vertices after the reflection are given as follows:
A'(2,2), B'(-1,2), C'(0,7).
For example, a coordinate of 0 is one unit left of x = 1, hence the coordinate of the image will be one unit right, at x = 2.
The dilation with a scale factor of 2 centered at the origin means that the coordinates are multiplied by 2, hence:
A''(4,4), B''(-2,4), C''(0,14).
Missing InformationThe vertices of the original triangle ABC are given as follows:
A(0,2), B(3,2), C (2,7).
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Consider parallelogram JKLM below.
Use the information given in the figure to find x, mZM, and mZMJ
M
J
51°
3.
3x
L
70°
K
Two consecutive integers are such that 3 times the larger exceeds twice the smaller by 24. find the integers.
Answer:
26 and 27
Step-by-step explanation:
If the smaller integer is represented using the variable n, then the next consecutive integer is n + 1
3 times the smaller => 3n
2 times the larger => 2(n + 1 = 2n + 2
We are given 3 times the larger exceeds twice the smaller by 24 which can be represented as:
3n - (2n + 2) = 24
3n - 2n - 2 = 24
n - 2 = 24
n = 24 + 2 = 26
So the integers are 26 and 27
Mr. and Mrs. DiNapoli have two sons and three daughters, When the whole family is together for dinner, they have to bring one extra chair to the table. How many chairs do they usually have around the table?
Answer:
6
Step-by-step explanation:
You want to know how many chairs are usually around the table if 1 chair must be added to accommodate Mr. and Mrs. DiNapoli and their two sons and three daughters.
TotalThe number present for a family dinner is ...
1 (Mr. DiNapoli) +1 (Mrs. DiNapoli) +2 (sons) +3 (daughters) = 7
ChairsIf one chair is added to make 7, then there are usually ...
7 - 1 = 6 . . . . chairs at the table
