A 37-ft ladder leans against a building so that the angle between the ground and the ladder is 73°. How high does the ladder reach up the side of the building?
Answer:
35.4 ft
Step-by-step explanation:
To solve this problem, we need to represent the statement in the question in a diagram.
Please see attached photo.
In the attached photo, x is the height of the building.
Thus, we can calculate the value of x as shown below:
Angle θ = 73°
Opposite = x
Hypothenus = 37 ft
Using the Sine ratio, the value of x can be obtained as follow:
Sine θ = Opposite /Hypothenus
Sine 73 = x /37
Cross multiply
x = 37 × Sine 73
x = 35.4 ft
Therefore, the ladder reached up to 35.4 ft of building.
If $17,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is: (a) 7% simple interest: $ (b) 7% compounded annually: $ (c) 7% compounded quarterly: $ (d) 7% compounded monthly: $
Answer:
a.) $29,750.00 simple interest
b.) $75,266.35 Compounded annually
c.) $79,358.65 compunded quarterly
d.) $80,332.11 compounded monthly
Step-by-step explanation:
a.) Formula: I = p x r x t
Where:
P is the principal amount, $17000.00.
r is the interest rate, 7% per year, or in decimal form, 7/100=0.07.
t is the time involved, 25....year(s) time periods.
So, t is 25....year time periods.
To find the simple interest, we multiply 17000 × 0.07 × 25 to get that:
The interest is: $29750.00
______________________________
b.) $75,266.35
c.) $79,358.65
d.) $80,332.11
Is 5.231 rational or irrational
Answer:
Rational
Step-by-step explanation:
A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Hope This Helps :)
What do you think is going to be the most challenging part of Alg.1 and why?
Answer:
I think Factoring is going to be the most challenging part of Alg.1 because it seems like there are a lot of steps before finding the answers.
Explanation:
When I took algebra I, the most difficult part for me was inequalities.
I had been used to linear equations and even quadratic equations, where the operative rule is "keep the equal sign sacred" (whatever you do to one side must also be done to the other side). Once I figured out that multiplying or dividing inequalities by a negative number reverses the comparison, I was good to go.
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These days, algebra I also includes a good dose of statistics. That seems to trip up a number of people, including me. The main thing, I think, is to stay clear on the definitions, and whether you're talking about a population or a sample. A lot of the math is easily handled by a graphing calculator or spreadsheet, so familiarity with the use of those is a great bonus (almost required).
__
You will be better equipped to go into algebra I if you have memorized multiplication tables, rules of divisibility, some mental math procedures, and squares and cubes of small integers (square ≤ 20^2, cubes ≤ 10^3). This will help immensely when it comes to factoring. Similarly, you need to be familiar with arithmetic involving decimals, fractions, and mixed numbers. Numbers in one form should offer you no more challenge than numbers in any other form.
__
A big challenge for many people is the fact that math builds on previous learning. If you don't learn the early stuff well, and practice it a lot, then you will find you have difficulty drawing on that knowledge to make the later stuff easier. It's NOT a "test and forget" sort of deal. It's a "remember this forever" sort of deal.
Please help!!
Darrel’s baby sister was 8 pounds at birth. She gained 4 pounds each year. She now weighs 32 pounds. How old is she?
Subtract to find the weight she gained since birth.
32 - 8 = 24
Divide to see how many years passed.
24 / 4 = 6
Therefore, Darrel's baby sister is 6 years old.
Best of Luck!
Adela, Tony, Pang, and Ruben are all in 6th grade. Their average age is 11 years old. The list shows the difference from average for each.
Age Difference
Adela: 0.75 year
Tony: 11
10
years
Pang: –0.8 year
Ruben: -1
2
year
Which lists shows the values of the differences ordered from least to greatest?
Adela, Tony, Pang, Ruben
Adela, Pang, Ruben, Tony
Pang, Ruben, Adela, Tony
Tony, Adela, Ruben, Pang
Answer:
Pang, Ruben, Adela, and Tony is the correct answer.
Step-by-step explanation:
I got it right on edge2021
The order of differences ordered from least to greatest
Pang, Ruben, Adela, Tony.
What is Ascending Order?The arranging of numbers from least to largest is known as ascending order. For instance, the digits 3, 15, 28, and 49 are listed in ascending order.
Given:
Age Difference
Adela: 0.75 year
Tony: 1 1/10 years = 11/10= 1.1 year
Pang: –0.8 year
Ruben: -1 / 2 year = -0.5 year.
So, the differences ordered from least to greatest
-0.8 < -0.5 < 0.75 < 1.1
Hence, Pang, Ruben, Adela, Tony.
Learn more about ascending order here:
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what is the reciprocal of -5.2/2.5 ?
need an answer fast please
Answer:
− 0.48076923
Step-by-step explanation:
Under which conditions does the commutative property apply to compositions of f(x) and g(x)?
A) when f(g(x)) and g(f(x) are inverse functions
B) when f(g(x)) and g(f(x) are equal for at least one value of x
C) when f(g(x)) and g(f(x) are equal for all values of x
D) when f(g(x)) and g(f(x) are not inverse functions
Answer:
The correct option is;
C) When f(g(x)) and g(f(x)) are equal for all values of x
Step-by-step explanation:
To have commutative property is to have the property to move around or change position, as such the commutative property is the property concerns the changing of the positioning of items
The commutative property for addition is a + b = b + a while the commutative property for multiplication is a×b = b×a
For functions , the commutative property can therefore, be expressed as follows;
Commutative property of f(x) and g(x) gives f(g(x)) = g(f(x)) for all values of x.
Answer:
c
Step-by-step explanation:
Find the 7th term in the
sequence
-4, -8,-16,
Answer:
-256
Step-by-step explanation:
Given:
a₁ = -4 (First term) r = -8 ÷ -4 = 2 (Common ratio) n = 7 (Number of term)Find:
a₇ = ?Formula:
aₙ = a₁ · rⁿ⁻¹Solve:
a₇ = -4 · 2⁷⁻¹a₇ = -4 · 2⁶a₇ = -4 · 64a₇ = -256Find the slope of the line passing through (3,5) and (-4,-10)
Answer:
[tex] \frac{15}{7} [/tex]
Step-by-step explanation:
Please see attached picture for full solution.
Can someone help please
Answer:
13.2
Step-by-step explanation:
11/5=x/6
66/5=×
13.2
If a=3, b= -5
then who has
2b + a
Answer:
-7
Step-by-step explanation:
2b+a
2(-5)+3
-10+3
-7
Answer:-7
Step-by-step explanation:
2b+a
2×-5=-10
-10+3=-7
Choose the best description of the ratio:
220 seventh grade students
630 middle school students
is a
DRAG & DROP THE ANSWER
<
part-to-part ratio
part-to-whole ratio
rate
unit rate
a polynomial of degree 4 in y has at most
A: 4terms
B: 3terms
C: 5 terms
D: 8 terms
Answer:
C.
Step-by-step explanation:
The highest term must be of x^4, then decreasing to x^3, x^2, x and the constant term.
Altogether there are at maximum 5 terms.
A polynomial of degree 4 in y has at most 5 terms, the correct option is C.
What is a Polynomial of degree 4 ?A polynomial is an expression of variables and mathematical operators.
The polynomial in degree 4 can be written as
ay⁴ +by³ +cy² +dy +e
The polynomial of degree 4 can have 5 terms, 4 in decreasing power of y and a constant.
To know more about Polynomial
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There are 72 boys and 28 girls. What percent are girls? I'm not sure if it is 28% or 18%?
Answer:
28%
Step-by-step explanation:
do 28/28+72=28/100
then multiply 28/100 by 100 which equals 28%
PLEASE HELP!!
Draw a line segment between each vertex of ABCD and the corresponding vertex of AEFBEFCEFDEF.
There are four line segments in all. Then move polygon ABCD around the coordinate plane. What do
you observe about the angle formed between the line segments you drew and the line of reflection,
EF? Use the tools available in GeoGebra to confirm your hypothesis.
Answer:
Each line segment joining a vertex of ABCD to the corresponding vertex in the image is perpendicular to the line of reflection, EF. That is, the lines intersect at a 90 degree angle.
Bo is buying a board game that usually costs B dollars. The game is on sale, and the price has been reduced by 18%. Which of the following expressions could represent how much Bo pays for the game? Choose 2 answers: A 0.82B B 1.18B C B - 0.18 D B - 18 E B - 0.18B
Answer:
a and b
Step-by-step explanation:
Josie hikes a trail that is 2574 meters long at the same rate of speed. She completes the trail in exactly 33 minutes.
How many meters did Josie travel each minute?
O A. 43 m/min
OB. 78 m/min
C. 594 m/min
OD. 1287 m/min
o
E
1980 m/min
Answer:
B. 78 meters
Step-by-step explanation:
2574 divided by 33 equal 78
hope this helps you :)
Multiply your answer should be a monomial in standard form (-4x^2)(7x^3)
answer: -28x^5
exlaningtion:I used my brain dhdhdishdhdhdhdhdh
The statement “1cm represents 2m” is the scale of the drawing. It can also be expressed as “1cm to 2m” or “1cm for every 2m.” What do you think the scale tells us?
Answer:
A scale is a way to resize drawings or figures to make them fit into a particular size.
Step-by-step explanation:
In 2D drawing or diagrams, a scale factor greater than 1 enlarges the object, while a scale factor between 0 and 1 shrinks the objects, also using a scale factor of 1 changes nothing or leaves the drawing the way it is.
Furthermore, scales are represented in ratio form 1:2, telling us that say 1cm in the virtual environment or paper represents 2km in reality
remove parentheses by applying the distributive property 10x(4 - 3x)
Answer:
40x - 30 x²
Step-by-step explanation:
When x is multiplied by x it become x².
10x(4 - 3x)
10x times 4 = 40x
10x times -3x = -30x
40x - 30 x²
4(3x-1)=9-x
Thank you !
Step-by-step explanation:
4(3x-1)=9-x
12x-4=9-x
12x+x=9+4
13x=13
x=13/13
x=1
6x* 10 = 160
what the result of X ?
Answer:
x=8/3
Step-by-step explanation:
6x*10=160
6x=16
x=16/6
x=8/3
Answer:
[tex]x = 8 \div 3 \\ \\ [/tex]
Is the function even or odd?
Answer:
[tex]f(\theta)=\cos(\theta)[/tex] is an even function.
Step-by-step explanation:
Recall when it means when a function is even or odd. An even function has the following property:
[tex]f(-x)=f(x)[/tex]
And an odd function has the following property:
[tex]f(-x)=-f(x)[/tex]
So, let's test some values for cos(x).
Let's use π/3:
[tex]f(\pi/3)=\cos(\pi/3)[/tex]
From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).
Now, let's find -π/3. This is the same as 5π/3. Thus:
[tex]f(-\pi/3)=\cos(-\pi/3)[/tex]
And again from the unit circle, we can see that this is 1/2.
Therefore, despite the negative, the function outputs the same value.
Cosine is an even function.
Notes:
Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!
rewrite 3/4x - 5 = 7/12 so it does not have fractions .
Answer:
Answer
Step-by-step explanation:
0.75x -5 = 0.583333333333...
Answer:
x = 7.4444
Step-by-step explanation:
3/4 x - 5 = 7/12
3x/4 - 5 = 7/12
3x/4 = 7/12 + 5
3x/4 = 7/12 + 60/12
3x/4 = 67/12
3x = 4*67/12
3x = 268/12
3x = 22.3333
x = 22.3333/3
x = 7.4444
Check:
3*7.4444/4 - 5 = 7/12
5.58333 - 5 = 0.58333
In city A, the temperature rises 9° F from 8am then the temperature drops 8°F from 9am to 10am in city B the temperature drops 1°F from 8am to 9am then the temperature drops 3°F from 9am to 10am write an expression that represents the change In temperature from 8am to 10am for each city. Simplify and interpret each sum. Which expression represents the change in temperature for city A?
Answer:
For City A, the expression for temperature change is 9 + (-8)
The amount the temperature changes for City A = 1°F
For City B, the expression for temperature change is -1 + (-3) = -4°F
The amount the temperature changes for City B = -4°F
Step-by-step explanation:
The given information are;
In City A, the temperature rise from 8 am to 9 am = 9°F
In City A, the temperature drop from 9 am to 10 am = 8°F
In City B, the temperature drop from 8 am to 9 am = 1°F
In City B, the temperature drop from 9 am to 10 am = 3°F
The expression for that represents the temperature change from 8 am to 10 am is therefore;
For City A
Temperature change from 8 am to 10 am are
8 am to 9 am = +9°F
9 am to 10 am = -8°F
Sum, change from 8 am to 10 am = 9 + (-8) = 1°F
For City B
Temperature change from 8 am to 10 am are
8 am to 9 am = -1°F
9 am to 10 am = -3°F
Sum, change from 8 am to 10 am = -1 + (-3) = -4°F
An is climbing down a ladder. Each time he descends four rungs on the ladder, he stops to see how much farther he has to go. Which word in the problem indicates that a negative integer should be used?
Answer:
Descends
Step-by-step explanation:
The word descend is what indicates that a negative integer should be used.
When we talk about height we should be regarding it in increments which makes its integers positive, that is something that increases. But the question says descends, descends means a reduction in height. which is a way of describing height in an opposite or negative direction.
decendsStep-by-step explanation:
The third angle of an isosceles triangle is 16 o less than the sum of two equal angles. Find
three angles of the triangle.
Answer: 49°, 49°, 82°
Step-by-step explanation:
Let x represent the base angles
then 2x - 16 is the vertex angle.
Triangle Sum Theorem states that the sum of the angles is 180°
(x) + (x) + (2x - 16) = 180
4x - 16 = 180
4x = 196
x = 49
Base angles: x = 49
Vertex angle: 2(49) - 16 = 82
What is the distance between the points (−3, 5) and (−3, −9)? A) 4 B) 6 C) 11 D) 14
Answer: D)14
Step-by-step explanation: The x-factors are both -3 but the y-factors are different so you count the distance between them
find the value of h
Answer: The value of h is -1.
Step-by-step explanation:
The function F(x) = ║x║ has been shifted 1 unit to the right. H in this case represents if the function has been shifted to the right or to the left. If the function is being shifted to the right then H is negative and if the function is shifted to the left, x is positive. In this case the value of h is -1.