Please solve with explanation (high points)
Step-by-step explanation:
so, we have a large triangle made of the 2 cables as legs and the ground distance AB as baseline.
the tower is the height to the baseline of that large triangle.
let's call the top of the tower T.
and remember, the sum of all angles in a triangle is always 180°.
we know the angle A = 62°, and angle B = 72°.
assuming that AB is a truly horizontal line that means that the 2 legs (cables) have different lengths, the triangle is not isoceles, and the tower is not in the middle of the baseline.
so, the height (tower) splits the baseline into 2 parts. let's call them p and q.
p + q = 12 m
p = 12 - q
let's simply define that p is the part of the baseline on the A side, and q is the part of the baseline on the B side.
we have now 2 small right-angled triangles the large height (tower) splits the large triangle into.
one has the sides
AT, height (tower), p
angle A = 62°
angle T = 180 - 90 - 62 = 28°
the other has the sides
BT, height (tower), q
angle B = 72°
angle T = 180 - 90 - 72 = 18°
now remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with the sides and the associated angles being opposite.
p/sin(28) = height/sin(62)
q/sin(18) = height/sin(72)
we know from above that
p = 12 - q
so,
(12 - q)/sin(28) = height/sin(62)
height = (12 - q)×sin(62)/sin(28)
q/sin(18) = height/sin(72)
height = q×sin(72)/sin(18)
and therefore, as height = height we get
(12 - q)×sin(62)/sin(28) = q×sin(72)/sin(18)
(12 - q)×sin(62)×sin(18) = q×sin(72)×sin(28)
12×sin(62)×sin(18) - q×sin(62)×sin(18) =
= q×sin(72)×sin(28)
12×sin(62)×sin(18) = q×sin(72)×sin(28) + q×sin(62)×sin(18) =
= q×(sin(72)×sin(28) + sin(62)×sin(18))
q = 12×sin(62)×sin(18) / (sin(72)×sin(28) + sin(62)×sin(18))
q = 4.551603755... m
p = 12 - q = 7.448396245... m
height = q×sin(72)/sin(18) = 14.00839594... m ≈ 14 m
the cell tower is about 14 m tall.
What is an equation of a circle whose center is at (2,-4) and is
tangent to the line x = -2?
(1) (x - 2)2 + (y + 4)² = 4
(2) (x - 2)² + (y + 4)² = 16
(3) (x + 2)² + (y - 4)² = 4
(4) (x + 2)² + (y - 4)² = 16
The equation of the circle with center at (2,-4) and tangent to the line x = -2 is given by:
(2) (x - 2)² + (y + 4)² = 16
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The circle has center at (2,-4), hence [tex]x_0 = 2, y_0 = -4[/tex].
The center is tangent to the line x = -2, hence it has a point at x = -2, since |-2 - 2| = 4, r = 4 -> r² = 16.
Hence the equation of the circle is given by:
(2) (x - 2)² + (y + 4)² = 16
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9. Marianna is making a piñata that has a ball-like shape. The piñata has a surface area of 60 square feet. Use
the formula for the surface area of a sphere (S = 4m2) to find the radius of the piñata.
a
About 22.80 ft
C.
About 3.87 ft
D
la
b. About 4.78 ft
d.
About 2.19 ft
-2 6-2
1
Answer:
D. 2.19
Step-by-step explanation:
ok so the formula for the surface area of a sphere is 4[tex]\pi[/tex][tex]r^2[/tex]
We see that 4[tex]\pi[/tex][tex]r^2[/tex]=60.
To find the radius we must isolate r on one side of the equations.
[tex]r^2[/tex]=60/4[tex]\pi[/tex]
[tex]r^2[/tex] = 4.77464829276
r = [tex]\sqrt{4.77464829276}[/tex]
That is approximately equal to 2.19
x²-3x+1=0
O A. 3±√15
OB. 3+√5
3± √5
o c. 2121224
OD. 5±10
3
Answer:
X=3+-√5/3
Step-by-step explanation:
x=-b+-√b^2-4ac/2
=3+-√(-3)^2-4(1)(1)/2
Find the total selling price.
Alonzo and Catalyn Diaz paid a total of $23,289.26 for their new automobile. If the sales tax rate in their community is 6.5%, what was the total selling price of the Diaz's new automobile?
the assumption being that the tax is added to the amount advertised for the vehicle, namely 23289.26 + 6.5% of that.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 23289.26}}{\left( \cfrac{6.5}{100} \right)23289.26}\implies 1513.8~\hfill \underset{\textit{total selling price}}{\stackrel{23289.26~~ + ~~1513.8}{24803.06}}[/tex]
The length of a rectangle is 3 inches more than the width. The area is 10 square inches. Find the dimensions
Answer:
Width = 2
Length = 5
Step-by-step explanation:
let A be the area of the rectangle
L be the length of the rectangle
w be the width of the rectangle
Formula: ‘area of a rectangle’
A = L × w
…………………………………………………
A = L × w
⇔ 10 = (w + 3) × w
⇔ 10 = w² + 3w
⇔ w² + 3w - 10 = 0
Solving the quadratic equation w² + 3w - 10 = 0 :
Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49
then √Δ = 7
[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]
[tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]
-5 is not valid ,because w represents the width
which must be a positive number
Then w = 2
Conclusion:
Width = 2
Length = 2 + 3 = 5
At their last practice, the basketball team shot free throws for 17 minutes, ran for 12 minutes, and then passed the ball for 16 minutes.
For how many minutes was the team practicing? Explain how you got your answer.
Answer:
45 minutes
Step-by-step explanation:
If you're trying to find the total number of minutes, they practiced you'd have to add.
So, if they did free throws for 17 minutes
Ran for 12 minutes
And passed the ball for 16
You'd add those up
17+16+12 = 45
In conclusion they practiced for a total of 45 minutes.
Help me answer this question, please
Kylee is playing a game she has to receive more than 20 points average of five games to move onto the next level which inequality represents the situation is T represents the total number of points Kylee earned for five games choices are
T/5 < 20
T/5 <_ 20
T/5 >_ 20
T/5 > 20
The inequality T/5 > 20 represents and T is the total number of points Kylee earned for five games situation option fourth is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Kylee is playing a game she has to receive more than 20 points on average of five games to move onto the next level.
T is representing the total number of points Kylee earned for five games
The average is 20.
T/5 is also representing the average points of five games.
She has to receive more than 20 points on average in five games:
T/5 > 20
Thus, the inequality T/5 > 20 represents and T is the total number of points Kylee earned for five games situation option fourth is correct.
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Solving two-step equations 3x-2=16
Hey there!
Solve for x :
Answer:x = 6 ✅
Explanation:3x - 2 = 16
>> Add 2 to both sides :
3x - 2 + 2 = 16 + 2
3x = 18
>> Divide each side by 3 :
3x / 3 = 18 / 3
x = 6
▪️Let's verify :
3(6) - 2 ⇔18 - 2 ⇔ 16
Therefore, your answer is x = 6
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3x−2=16
Add 2 to both sides.
3x=16+2
Add 16 and 2 to get 18.
3x=18
Divide both sides by 3.
x = 18 /3
Divide 18 by 3 to get 6.
x = 6 ===> Answer
Verification
Let x = 6
3×6−2=16
18-2= 16
16 = 16
Checked ✅
{ Pisces04 }
Using the graph of the function g(x) = log5 (x – 3), what are the x-intercept and asymptote of g(x)? The x-intercept is 4, and the asymptote is located at x = 3. The x-intercept is 3, and the asymptote is located at x = 4. The x-intercept is 4, and the asymptote is located at y = 3. The x-intercept is 3, and the asymptote is located at y = 4.
The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.
What is an Asymptote ?An asymptote is a line that a curve approaches but it never reach.
The given equation
y = log₅(x-3)
To find the asymptote
Set the argument of the logarithm equal to zero.
x - 3 = 0
The vertical asymptote occurs at
x = 3
The equation can also be written as
[tex]\rm 5^y = x-3[/tex]
To find the x intercept we will put the value of y = 0 ;
therefore
5⁰ = x -3
1=x-3
x = 4
Therefore ,The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.
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Answer:
The x-intercept is 4, and the asymptote is located at x = 3.
Step-by-step explanation:
I got it right on the test.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice. 120
Yam. 100
Beans. 140
Vegetable 140
Meat. 180
Sugar. 40
Palm oil. 60
Display using a pie chart
The pie chart for the expenditure of a housewife for a particular day is shown below.
What is a pie chart?A map wherein the round is split into segments, each one representing a percentage of the total.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice - 120
Yam - 100
Beans - 140
Vegetable - 140
Meat - 180
Sugar - 40
Palm oil - 60
The pie chart is given below.
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The right pengtagonal prism has a height of of 14 units.
A pentagonal prism has a perpendicular distance of 14 units between the bases. An apothem has a length of 4 units.
The volume of the prism is 840 cubic units. What is the perimeter of the base?
12 units
15 units
21 units
30 units
2 units
3 units
4 units
The perimeter of the base of the right pentagonal prism is 30 units
How to determine the perimeter of the base?The given parameters are:
Volume = 840 cubic unitsHeight, h = 14 unitsApothem, a = 4 unitsThe volume of a right pentagonal prism is:
V = 0.5Pah
Where P represents the perimeter of the base.
So, we have:
0.5 * P * 14 * 4 = 840
Divide both sides by 0.5 * 14 * 4
P = 30
Hence, the perimeter of the base is 30 units
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ABC DEF. The area of ABC is given. Find the area of DEF
Answer: B
Step-by-step explanation:
The ratio of the areas of similar figures is the square of the scale factor.
Scale factor = image/preimage = 48/12 = 4.So, the ratio of the areas is 16, and thus the area of DEF is (16)(90)=1440
Triangle Sum Theorem: The 3 angles inside a triangle add up to 180. Example: 1 + 2 + 3 = 180 Exterior Sum Theorem: The 3 exterior angles of a triangle add up to 360. Example: 4 + 5 + 6 = 360 Remote Exterior Angle Theorem: The 2 remote interior angles of a triangle add up to be the same size as the exterior angle. Example: 1+2 = 4 someone please answer this quickly
Answer:
What exactly is the question here?
The average Wealth of a person in Richville is $150,000 and the average wealth of a
person in Poorville 15 $20,000. Suppose Richville and Poorville combine to form Mediumville.
Translate the sentence into an inequality.
Four times the sum of a number and 17 is at least −26.
The sentence "Four times the sum of a number and 17 is at least −26" translated to an inequality is 4(x+17) ≥ -26
Translating sentences into inequalityFrom the question, we are to translate the given sentence into an equality.
The given sentence is
Four times the sum of a number and 17 is at least −26
Let the unknown number be x
Then,
The sum of a number and 17 will be
x + 17
Then,
Four times the sum of a number and 17 can be written as
4(x+17)
Now,
"At least -26" means it is greater than or equal to -26
Thus,
Four times the sum of a number and 17 is at least −26 becomes
4(x+17) ≥ -26
Hence, the sentence "Four times the sum of a number and 17 is at least −26" translated to an inequality is 4(x+17) ≥ -26.
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Write 3 + 2 log z - log(x² + 2x + 1) +1/2 log y as a single logarithm with coefficient 1.
Answer:
[tex]\displaystyle \log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex] OR [tex]\displaystyle 3+\log\frac{z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]
Choose the more appropriate answer
Step-by-step explanation:
I read your problem as [tex]3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y[/tex]:
[tex]\displaystyle 3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y\\\\\log1000+\log z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log1000z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2}{(x+1)^2}+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]
Question 2 Write the following paragraph proof as a two-column proof. Given: AB = CD and BC = DE Prove: AC = CE A B C D E We're given that AB = CD. By the addition property of equality, we add BC to both sides of the equation to get AB + BC = CD + BC. Since we're also given that BC = DE, we use the substitution property of equality to replace BC with DE on the right side of the equation. So, AB+ BC = CD + DE. Next, by segment addition, we get that AB + BC is equal to AC and that CD + DE is equal to CE. Finally, we use the substitution property of equality on the equation AB + BC = CD + DE to replace AB + BC with AC and CD + DE with CE to get that AC = CE. Type the correct answer in the box. BIUX² X₂ 14pt === Statements Reasons B.
Answer: See below
Step-by-step explanation:
Given:
AB = CD and BC = DE
To prove:
AC = CE
Statements Reasons
AB = CD GivenAB + CB = CD + BC Addition property of equalityAB + BC = CD + DE Given: BC = DEAC = CE By segment addition: AB + BC = AC and CD + DE = CETherefore, AC = CE has been proved
Which algebraic rule describes the translation of quadrilateral ABCD to quadrilateral A’B’C’D?
The algebraic rule that best describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is P'(x, y) = (x + 8, y + 7). (Correct answer: A)
How to determine the translation of a quadrilateral on a Cartesian plane
According to the image attached we understand that the quadrilateral ABCD is transformed into quadrilateral A'B'C'D' by applying pure translation. Translations are a kind of rigid transformation, defined as a transformation applied on a geometric locus such that Euclidean distance is conserved at every point of the construction.
Vectorially speaking, translations are described by the following formula:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vector.By direct comparison, we conclude that the quadrilateral ABCD is translated 8 units in the +x direction and 7 units in the +y direction. Hence, the algebraic rule that describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is:
P'(x, y) = (x, y) + (8, 7)
P'(x, y) = (x + 8, y + 7)
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PLS HELP ASAP!… WILL MARK BRAINLIEST
Which of the following are exterior angles? Check all that apply.
The exterior angles in the given triangle are angles 4 and 5.
What are the exterior angles?
The given shape is a triangle. A triangle is a three-sided polygon that has angles that sum up to 180 degrees. The exterior angle is the angle that is formed when a line is extended from the next side and the other side of the triangle. Simply put, it is the angle that is not inside the triangle.
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PLEASE HELP!!!
Which point is tangent to the circle?
A
D
M
Q
Answer:
M is target to the circle
please help asap
6
9
18
Answer:
18
Step-by-step explanation:
The value of n = 1 , 2 , 3. Find the first 3 term and add them.
3*1 + 3*2 + 3*3 = 3 + 6 + 9
= 18
Susan, Enrique and Martin are going for a meal.
Susan pays £26, Enrique pays £20 and Martin pays £18.
What fraction of the meal did each friend pay for?
Answer:
13/32 Susan
5/16 Enrique
9/32 Martin
Step-by-step explanation:
26+20+18=64
26/64=13/32
20/64=5/16
18/64=9/32
Describe the solution(s) to 9x² - 36x + 36 = 0 by just determining the radicand. Show your work. (10 points) Part B: Describe the solution (s) to x²-x + 4 = 0 by just determining the radicand. Show your work. (10) points) Part C: Solve 4x² + 23 – 35 using an - appropriate method. Show the steps of your work and explain why you chose the method used
The solution to the equations are:
9x² - 36x + 36 = 0 has two equal real solutionsx² - x + 4 = 0 has no real solutionsThe factored expression of 4x² + 23 – 35 is 4(x² -3)Part A: Describe the solutionThe equation is given as:
[tex]9x\² - 36x + 36 = 0[/tex]
The above equation is a quadratic equation which can be represented as:
[tex]ax\² + bx + c = 0[/tex]
The discriminant (d) is calculated as:
[tex]d = b\² - 4ac[/tex]
So, we have:
[tex]d = (-36)\² - 4 * 9 * 36[/tex]
[tex]d = 0[/tex]
A discriminant of 0 means that the equation has two equal real solutions
Hence, 9x² - 36x + 36 = 0 has two equal real solutions
Part B: Describe the solutionThe equation is given as:
[tex]x\² - x + 4 = 0[/tex]
The above equation can be represented as:
[tex]ax\² + bx + c = 0[/tex]
The discriminant (d) is calculated as:
[tex]d = b\² - 4ac[/tex]
So, we have:
[tex]d = (-1)\² - 4 * 1 * 4[/tex]
[tex]d = -15[/tex]
A discriminant of -15 means that the equation has no real solutions
Hence, x² - x + 4 = 0 has no real solutions
Part C: The solution to the expressionWe have:
[tex]4x\² + 23 - 35[/tex]
Evaluate the difference
[tex]4x\² -12[/tex]
Factor out 4
[tex]4(x\² -3)[/tex]
Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)
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help please!!! i need to turn this in tomorrow
Answer:
$10955.6157151671
Step-by-step explanation:
Amount [A] = [tex]P(1+r)^{t}[/tex]
Here, P = principal (which is $5000)
r = rate of interest in decimal form(which is 0.04)
t = time in years (which is 20)
Substituting,
[tex]$5000(1+0.04)^{20}[/tex] = $10955.6157151671
SOMEONE PLS HELP ME. ASAP PLSSS
The formula that can be used to find the area of the figure shaded green is 9² - 4². The correct option is c 9² - 4²
From the question, we are to determine the formula that could be used to find area of the figure shaded green
From the formula for calculating area of a square
A = s²
Where A is area
and s is the side length
Then, the area of the bigger square will be
A = 9²
NOTE: Side length of the bigger square is 9m
Then,
For the smaller square, which is not shaded green
A = 4²
NOTE: Side length of the smaller square is 4m
∴ Area of the figure shaded green = 9² - 4²
Hence, the formula that can be used to find the area of the figure shaded green is 9² - 4². The correct option is c 9² - 4²
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What is the range of this exponential function?
f(x) = 2.7x
The range of the exponential function f(x) = 2.7ˣ will be from zero to infinity that is (0, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The exponential function is given below.
f(x) = 2.7ˣ
We know the value of the exponential function is always positive.
Then the range of the exponential function f(x) = 2.7ˣ will be from zero to infinity that is (0, ∞).
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This means that 0.3 is a (n)
number. Rational or irrational
0.3 is a Rational Number written in Decimal Form
0.3 is neither an Integer nor a Whole number.
The cylindrical storage shed shown below is completely filled with road salt to make a town's roads safer during snow storms. About 21,000 cubic feet of road salt is used during a typical snow storm.
a. What is the total volume of the storage shed?
b. How many snow storms can the town expect to handle before the storage shed needs to be refilled with additional road salt?
Answer:
a. 40000pi ft^3
b. 5 times
Step-by-step explanation:
a. the volume of a cylinder is pi * h * r^2
r = 20ft, h = 100ft
so V = pi * 100 * 20^2 = 40,000pi or around 125663.7 ft^3
b. to find the number of times, divide the volume by the amount of salt needed per storm then round down:
40000pi/21000 = 5.98 so 5 times. notes: depending on the teacher you might just round to the nearest integer