Step-by-step explanation:
we have a right-angled triangle, that is "hovering" 1.61 m above the ground.
the Hypotenuse (the side opposite of the 90 degree angle) is the line of sight from the eye to the top of the skyscraper.
one leg is the height of the skyscraper (minus the 1.61 m).
the other leg is the ground distance from Jacob to the skyscraper (281 m).
we know already 2 angles : the 90° angle between the ground distance and the skyscraper height. and the 25° between the ground distance and the line of sight.
and as we know that the sum of all angles in a triangle is always 180°, we know that the third angle (between the line of sight and the skyscraper height) is
180 - 90 - 25 = 65°
now we can use the law of sines
a/sin(A) = b/sin(B) = c/sin(C)
(the ratio between a side and its opposing angle)
to get all missing side lengths.
the 25° angle is opposite of the skyscraper height, and the 65° angle is opposite of the ground distance (the only side length we know so far).
so,
height/sin(25) = 281/sin(65)
height = 281 × sin(25)/sin(65) = 131.0324519... m
to get the full height of the skyscraper, we need to add the 1.61 m that the described triangle was "hovering" above ground.
therefore, the height of the skyscraper is
131.0324519... + 1.61 = 132.6424519... ≈ 132.6 m
-453 divided by 15 = (simplest form)
Answer:
-453/15 = -30.2
Answer:
-30.2 or -30 1/5
Step-by-step explanation:
For #8 and #9, fill in the missing information for the following trapezoids. SHOW YOUR WORK to solve for the missing value.
9.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2
Applying the equation for the area of the trapezoid, it is found that the height is of 10 cm.
The area of a trapezoid is half the multiplication of the sum of the bases and the height, that is:
[tex]A = \frac{h}{2}(b_1 + b_2)[/tex]
For this problem, we have that: [tex]A = 205, b_1 = 20, b_2 = 21[/tex], hence:
[tex]A = \frac{h}{2}(b_1 + b_2)[/tex]
[tex]205 = \frac{h}{2}(20 + 21)[/tex]
[tex]20.5h = 205[/tex]
[tex]h = \frac{205}{20.5}[/tex]
[tex]h = 10[/tex]
The height is of 10 cm.
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Answer:
The height of trapezoid is 10 cm.
Step-by-step explanation:
Given :
»» [tex]\rm{b_1}[/tex] = 20 cm»» [tex]\rm{b_2}[/tex] = 21 cm»» [tex]\rm{area}[/tex] = 205 cm²To Find :
»» Height of trapezoidUsing Formula :
[tex]{\star{\small{\underline{\boxed{\sf{\red{Area_{(Trapezoid)} = \dfrac{1}{2} \Big(b_1 + b_2\Big)h}}}}}}}[/tex]
✧ [tex]\rm{b_1}[/tex] = 20 cm✧ [tex]\rm{b_2}[/tex] = 21 cm✧ [tex]\rm{area}[/tex] = 205 cm²Solution :
Substituting all the given values in the formula to find height of trapezoid :
[tex]{\dashrightarrow{\small{\sf{Area_{(Trapezoid)} = \dfrac{1}{2} \Big(b_1 + b_2\Big)h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \Big(20 + 21\Big)h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \Big( \: 41 \: \Big)h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \times 41 \times h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{ 41}{2}\times h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{h = 205 \times \dfrac{2}{41}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{h = \cancel{205} \times \dfrac{2}{\cancel{41}}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{h =5 \times 2}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{h =10 \: cm}}}}[/tex]
[tex]{\star{\small{\underline{\boxed{\frak{\pink{h =10 \: cm}}}}}}}[/tex]
Hence, the height of trapezoid is 10 cm.
[tex]\rule{300}{1.5}[/tex]
1. Which of the following is equivalent to x5/2?
1
(1)
5x
2
(3) Vr
2x
(2)
(4) Vx?
Given that the expression in the question is [tex]\displaystyle x^{\frac{5}{2} }[/tex], the equivalent expression
can be found using the rules of indices.
[tex]\displaystyle \underline{x^{\frac{5}{2} } \ is \ equivalent \ to \ x^2 \cdot\sqrt{x}}[/tex]Reasons:
The given expression is [tex]\displaystyle x^{\frac{5}{2} }[/tex]
Required:
To find the equivalent expression
Solution:
According to the rules of indices, we have;
[tex]a^{n + m} = a^n \times a^m[/tex]
[tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
Therefore, the above expression can be expanded as follows;
[tex]\displaystyle x^{\frac{5}{2} } = x ^{2.5} = \mathbf{x^{2 + 0.5}}[/tex]
[tex]\displaystyle x^{2 + 0.5} =\mathbf{ x^2 \times x^{0.5}}[/tex]
Which gives;
[tex]\displaystyle x^2 \times x^{0.5} = \mathbf{x^2 \times \sqrt{x}}[/tex]
Therefore;
[tex]\displaystyle x^{\frac{5}{2} } \equiv x^2 \cdot\sqrt{x}[/tex], which is the form [tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
[tex]\underline{An \ expression \ \mathbf{equivalent} \ to \ x^\frac{5}{2} \ is \ x^2 \cdot \sqrt{x}}[/tex]
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Is the following statement true or false? If false, replace the bold word to make the statement
true.
A rhombus is an equiangular quadrilateral
Answer:
replace rhombus with square, or rectangle
Step-by-step explanation:
In the summer reading program, a participant earns 50 stars for reading 10 books. The library tracks the number of stars(y, vertical axis) and books ( x, horizontal axis) on a graph. Which statements are correct.
A: Point(5,1) Represents the unit rate
B: Point(1,5) Represents the unit rate
C: Point(0,50) Represents the unit rate
D: Point(100,20) Represents reading 20 books
E: Point(20,100)Represents reading 20 books
Please help, I will give you the brainliest answer
Answer:
C: Point(0,50) Represents the unit rate
Step-by-step explanation:
Given that Ax - 4x² + 3x² + 4 = (x² - 2x + 1)(2x² + B) + C(x-1) + D for all values of x, evaluate A, B, C and D. Hence, deduce the remainder when Ar-4x+3x²+4 is divided by 2x² + B.
SANA MAKATULONG
#CARRYONLEARNING
when the area of a circle is increasing twice as fast as the radius, the radius is given by
Answer:
r = 1/π
Step-by-step explanation:
The area of a circle is given by ...
A = πr²
The rate of change of area is ...
A' = 2πr·r'
We want that rate of change to be twice as fast as the rate of change of radius:
2r' = 2πr·r'
1 = πr . . . . . . divide by 2r'
1/π = r
When the area is changing twice as fast as the radius, the radius is 1/π.
_____
Additional comment
The area and the radius have different units, so their rates of change must be compared numerically. The numerical value will depend on the units used. The radius for a circle whose area is measured in m² will be different than for one whose area is measured in ft².
At the beginning of the month you have $1500 in your bank account. Each time you visit the ATM you take $60 out. What is the rate at which your balance is changing each time you visit the ATM?
Group of answer choices
$3
-$60
$60
-$63
-$1500
-$3
HELP ME PLEASE I NEED HELPP
Answer:
4500 inches, check image below
Step-by-step explanation:
Simplify 7 1/3t−(10 2/3t−6) pls
Answer:
[tex]-\frac{10t}{3}+6[/tex]
Step-by-step explanation:
[tex]7 \frac{1}{3}t-(10 \frac{2}{3} t-6)[/tex]
Convert [tex]7\frac{1}{3}[/tex] to a mixed number
[tex]7\frac{1}{3}=\frac{7\cdot 3+1}{3}[/tex]
[tex]=\frac{22}{3}[/tex]
[tex]\bold{\frac{22}{3}t-\left(10\frac{2}{3}t-6\right)}[/tex]
Convert [tex]10\frac{2}{3}[/tex] into a mixed number
[tex]10\frac{2}{3}=\frac{10\cdot 3+2}{3}[/tex]
[tex]=\frac{32}{3}[/tex]
[tex]\bold{\frac{22}{3}t-\left(\frac{32}{3}t-6\right)}[/tex]
[tex]=\frac{22t}{3}-\frac{32t}{3}+6[/tex]
[tex]\bold{=\frac{-10t}{3}+6}[/tex]
Terms
Follow the PEMDAS order of operation:
P = ParenthesisE = ExponentsM = MultiplicationD = DivisionA = AdditionS = SubtractionYou do these steps in the order for which the equation comes. For example, start with the exponents if there are not any parentheses.
Which rule describes the composition of
transformations that maps AABC to AA"B"C"?
R0, 9000rx-axis(x, y)
Orx-axis Ro, 900(x, y)
RO, 1800 orx - axis(x, y)
Orx-axis Ro, 1800(x, y)
Answer:
The second one: r x-axis. R 90(x,y)
Step-by-step explanation:
You can see that from ABC to A'B'C', it's rotated a positive 90 degrees. then, from A'B'C' to A"B"C", reflected across x-axis. and when writing the transformation, it goes by last to first. that's why the R 90 comes first.
The rule which describes the composition of transformations that maps ΔABC to ΔA"B"C" is,
⇒ r _ x-axis. R _ 90(x, y)
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
To find the rule which describes the composition of transformations that maps ΔABC to ΔA"B"C".
Now, You can see that from ABC to A'B'C',
it's rotated a positive 90 degrees.
And, Then, from A'B'C' to A"B"C", reflected across x-axis.
Now, when writing the transformation, it goes by last to first. that's why the R 90 comes first.
Thus, The rule which describes the composition of transformations that maps ΔABC to ΔA"B"C" is,
⇒ r _ x-axis. R _ 90(x, y)
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Round 0.1 to the nearest whole number.
The formula to convert degrees Fahrenheit to degrees Celsius is: 'C = (5/9) ('F -32). The formula to convert degrees Celsius to degrees Fahrenheit is: 'F = 1.8 ('C) + 32. Using any of these formulas, determine, for what temperature the value of it in degrees Celsius is represented by the same number as its value in degrees Fahrenheit. Show your work. HINT: use either of those two equations, use x for 'C and use x for 'F, and solve it for x. The solution will be the answer to the problem (because the temperature is the same, and its numerical value in degrees Celsius in this case is the same as its number value in degrees Fahrenheit). *
Step-by-step explanation:
5/9 × (x - 32) = 1.8 × x + 32 = 9/5 × x + 32
5×(x - 32) = 9×9/5 × x + 32×9
5×5×(x - 32) = 9×9×x + 32×9×5
25x - 32×25 = 81x + 32×45
32×(-25 - 45) = 56x
4×(-70) = 7x
x = 4×(-10) = -40
-40° is the same temperature in Celsius and in Fahrenheit.
what are some expressions that are equivalent to
–
2(5n).
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\text{Gu\textbf{id}\textsf{e}}\bf\downarrow[/tex]
[tex]\large\textbf{2 negatives = positive}\\\large\textbf{2 positives = positive}\\\large\textbf{1 negative \& 1 positive = negative}\\\large\textbf{1 positive \& 1 negative = negative}\\\\\large\text{Negatives are BELOW 0}\\\large\text{Positives are ABOVE 0}\\\\\large\textsf{Negatives are on the LEFT side of zero.}\\\large\textsf{Positives are on the RIGHT side of zero.}[/tex]
[tex]\huge\textsf{-2(5n) \boxed{\rightarrow} \bf -10n}\\\\\\\\\huge\boxed{\rightarrow\text{-2n + (-2n) + (-2n) + (-2n) + (-2n)}}\\\huge\boxed{\rightarrow \text{\bf -2n - 2n - 2n - 2n - 2n}}\\\huge\boxed{\rightarrow{\text{-4n - 2n - 2n - 2n}}}\\\huge\boxed{\rightarrow \text{-6n - 2n - 2n}}\\\huge\boxed{\rightarrow \text{\bf -8n - 2n}}\\\huge\boxed{\rightarrow \boxed{\text{ -10n}}}[/tex]
[tex]\huge\text{\bf -5(2n)}\\\huge\boxed{\rightarrow \text{-10n}}[/tex]
[tex]\huge\boxed{\text{\bf Therefore, your answers \underline{\underline{could}} be: }}\\\huge\boxed{\bullet \textsf{ -2n - 2n - 2n - 2n -2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -8n - 2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -5(2n)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
4 more to go-2 + (-2) × -2 + (-2) ÷ -2
Let's se
-2+(-2)(-2)+(-2)/(-2)-2+(-2)^2+1-1+21Done!
The diameter of Mercury is approximately4.9×103 kilometers. The diameter of Saturn is approximately 1.2×105 kilometers. About how many times greater is the diameter of Saturn than the diameter of Mercury?
Answer: 378.7 kilometers (maybe, I am not sure)
Mercury: 4.9 * 103 = 504.7 kilometers
Saturn: 1.2 * 105 = 126 kilometers.
Why on earth is Mercury's diameter greater than Saturn's -
504.7 - 126 = 378.7 kilometers
Which expression would be easier to simplify if you used the commutative
property to change the order of the numbers?
O A. 80 + 20 + (-17)
O B. 2/3 +(-1/3) + 1/5
O C. (–19) + (-10) + 7/8
O D. (-80) + 43+ (-120)
Answer:
Step-by-step explanation:
THE ANSWER IS A. 80 + 20 + (-17)
Write an expression that is equivalent to 4(x + 1) - 7 (x + 3)
Answer:
-3x-17
Step-by-step explanation:
We need to expand this term by multiplying a term and an expression.
The following product distributive property will be used:
.
In our example, the resulting expression will consist of 2 terms:
the first term is a product of and .
the second term is a product of and .
Therefore, one expression that is equivalent to 4(x + 1) - 7(x + 3) is -3x - 17.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
what is the meaning of the word treacherous mean in the sentence below
QUICK plzzzz
i-ready lvl F
Answer: Guilty of or involving betrayal or deception.
Step-by-step explanation:
a student answered 86% of the questions on a test correctly. he received a grade of 98%. how many questions were on the test?
Let the number of questions on the test equal X which would be 100%
They answered 86 which equaled 98
Set up a ratio:
X/86 = 100/98
Cross multiply:
98X = 8600
Divide both sides by 98:
X = 87.75
Round to 87 questions
The total cost for attending the rodeo carnival can be found using the function f(x) = 2.25x + 18, where x is the number of food tickets purchased. If a family
purchases between 4 and 8 food tickets, what is the domain and range of this situation?
Answer:
domain is {4,5,6,7,8}, range is the other numbers in brackets
Step-by-step explanation:
mr farmer rectangular land measures 2000 meters by 3000 meters. if he walks around the perimeter of his land, how far does he walk
Answer:
10000 meters
Step-by-step explanation
To find perimeter you add the length of each side of the shape. Since the land is a rectangle there are two pairs that are parrallel, being 2000 and 3000. Making the distance 2000 + 2000 + 3000+ 3000 = 10000
Hope this helps!
A solid wood cone 12 cm in diameter and 8 cm high sells for $1.19. A second wood cone is 17 cm in diameter and 12 cm high. the fair price for this second cone rounded to the nearest cent, is
a) $2.53,
b) $3.58
c) $5.06
d) $10.75
e) $14.33
Answer:
Answer is a
Step-by-step explanation:
I think it's "A", im looking for answer as well :(
Plz, Help Me Quickly!!
I will mark Brainliest for the best answer.
Answer:
help you with what
Step-by-step explanation:
Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
The system of linear inequalities represented by the graph is 2 < x < 3.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The dotted lines represents strictly less than or greater than inequalities.
Inequality 1 represents x > 2 and inequality 2 represents x < 3.
The combined inequality can be represented as 2 < x < 3.
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Adam works for an agency.
His normal hourly rate is £8.32
The agency asks Adam to work 6 hours for a new company.
Adam will be paid time and a third of his normal hourly rate.
How much will Adam get paid in total when working for the new company
Adam receives 13.762 euros
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
Given
Adam normally earns 8.32 an hour.
1. 832 * 6 = 10.992 for 6 hours
Adam will be payed = 8.32 *1/3 = 2.77
Total payment = 10.992 + 2.77 = 13.762
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a swimming pool is drained at a rate of 50 gallons per hour. How many pints per minute is this?
Answer:
8
Step-by-step explanation:
Trey will be splitting 2 3/4 pies with himself and 5 friends. how much pie will each person get?
Answer: 11/24
Step-by-step explanation:I turned 2 and 3/4 into an improper fraction which got me 11/4.
There are 5 friends and him so that's 6 people.
So we can't do 11/4 divided by 6 so we must put 6 over 1.
So 11/4 divided by 6/1
Then we do "Keep Change Flip"
We keep 11/4
We change the division sign to multiplication
Then we flip 6/1 to 1/6
Then the problem is re wrote as:
11/4 times 1/6
And that equals 11/24 as your answer
So each person gets 11/24 of the pies.
Help please and thank you
Answer:
(a) P = 3000·1.15^t
(b) 12,137
Step-by-step explanation:
(a)The equation gets filled in so it looks like ...
P = (initial amount) × (1 +growth rate)^t
where t is in units compatible with the growth rate.
P = 3000·1.15^t
__
(b)Midnight is 10 hours later than 2 p.m., so the quantity will be ...
P = 3000·1.15^10 ≈ 3000·4.045558 ≈ 12,137
There will be 12,137 bacteria at midnight.
a statue of abraham lincoln casts a 9-foot shadow at the same time the white house casts 48-foot shadow . if the white house is 70 feet tall , how tall is the statue of abraham lincoln
Step-by-step explanation:
let's ignore the question, if the statue can cast an isolated shadow based on its location ...
2 objects and their shadows create 2 similar right-angled triangles.
that means all angles are the same, and the side lengths of one triangle correlate to the corresponding side lengths of the other triangle via the same factor.
so,
48 × f = 9
f = 9/48 = 3/16
therefore, the height of the statue is
70 × f = 70 × 3/16 = 210/16 = 13.125 ft