Step-by-step explanation:
let's call the top of the pole T, and the ground point of the pole G.
so, the situation gives us 2 right-angled triangles:
PTG and QTB.
from both triangles we know one leg (TG, the pole = 9 m), the inner angles at G (90° in both cases), and actually the inner angles at T, because we know the angles of depression there.
the inner triangle angles at T are just the complementary angles of the angles of depression (that means they add up together to 90°).
the inner angle at PTG = 90 - 4 = 86°
the inner angle at QTG = 90 - 7 = 83°
and because the sum of all angles in a triangle is always 180°, we even know the third angles at P and Q :
angle P = 180 - 90 - 86 = 4°
angle Q = 180 - 90 - 83 = 7°
yes, they are the same as the angles of depression (must be the same).
so, we know from both triangles 1 side and all 3 angles.
with the law of sine we can get every missing side.
particularly we need the second legs (sides in the ground) to get the distance between both points.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides always opposite of their related angles.
TG/sin(4) = PG/sin(86)
PG = 9×sin(86)/sin(4) = 128.7059963... m
TG/sin(7) = QG/sin(83)
QG = 9×sin(83)/sin(7) = 73.29911785... m
the distance between P and Q can have now 2 solutions :
if P and Q are on different sides of the pole, then
PQ = 128.7059963... + 73.29911785... = 202.0051142... m
but if they are on the same side of the pole, then their distance is
PQ = 128.7059963... - 73.29911785... = 55.40687846... m
due to the phrasing of the first sentence I suspect the first solution to be right.
but just in case, I gave you also the second possible solution.
3. It snowed 80 inches over 10 days. What is the rate? What about the unit rate?
I can walk at 6km/hr and run at 15km/hr. On a journey I spend as long walking as I do running. If I had walked twice as long on the journey it would have taken me six minutes longer find how far I ran
He ran for 12 km in his journey.
What is an Equation ?An equation is formed when two algebraic expressions are equated by an equal sign.
It is given that
Speed of Walking =6km/hr
Speed of Running = 15km/hr
Let he walks and run x hours ( as given)
he covered distance = 21 x km
The total time taken in the journey is 2x
for the same distance
It is also given that
if for the total journey
if he walks walked twice as long on the journey
He walked 6x in the journey so new distance that he walked is 12x , then the total journey time = 6 minutes longer
Converting speed from km / hr to km/ min
1 km / hr = 60 km/ min
and forming an equation with the given data
12x * 60 /6 + 9x *60/15 = 2x * 60 + 6
120x + 36x = 120x +6
150x = 120
x = 120/150
x = 0.8 hours.
Therefore he spent 0.8 hours walking and 0.8 hours running and He ran 15 * 0.8 = 12 km
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How many sandwiches do
you think would be supplied by this
market if the price were $3.50?
=========================================================
Explanation:
Start at $3.50 on the vertical y axis. Draw a horizontal line until you reach the supply curve. Then drop straight down to land somewhere between 650 and 700 units supplied per day. Check out the diagram below.
A good estimate may be to use the midpoint. Add up those values and divide in half.
(650+700)/2 = 1350/2 = 675
Therefore, we estimate that 675 sandwiches per day would be supplied if the price was $3.50 per sandwich.
A fence is to be built to enclose a rectangular area of 200 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 12 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
y = 220/ ((10/3) * √22)
It is given that area is 200 square feet. Cost is 3 dollar per foot. Fourth side costs 12 dollars per foot.
This f(x,y) needs to represent the cost of the fence so we can look at each side's price. We can choose the fourth side to be along the x axis and be represented by 13x. The other sides therefore must be represented by 5y, 5y, and 5x.
So, our cost, f(x,y) = 13x + 5x + 5y + 5y = 18x + 10y
Our constraint is xy = 220 as defined by the area of a rectangle.
We can then take our constraint to be put in terms of exclusively x, giving us y = 220/x
Plugging this into our cost, the thing we are minimizing, we get f(x) = 18x + 2200/x
In order to find the minimum we use the first derivative test, taking f'(x) and finding the critical points.
f'(x) = 18 - 2200/x2
Setting this equation to be equal to 0 we find that x = ±√2200/18 . But the negative answer doesn't make sense because distance cannot be negative so we throw it out.
x = (10/3) * √22
We must verify that this is a minimum by confirming the following:
If x < (10/3) * √22, f'(x) < 0. So, f(x) is decreasing when x < (10/3) * √22.
If x > (10/3) * √22, f'(x) > 0. So, f(x) is increasing when x > (10/3) * √22.
Thus, we have guaranteed that (10/3) * √22 is the x dimension. Now we plug in this value in our original equation to find y and that is our y dimension. So, y = 220/ ((10/3) * √22)
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From the diagram below, given the side lengths marked, and if we know that < C is congruent to < E, we can say that ___.
Select one:
a.
the two triangles are similar by SAS
b.
the two triangles are not similar
c.
the two triangles are congruent
d.
the two triangles are similar by AA
Answer:
d) the two triangles are similar by AA
Step-by-step explanation:
Find the area of the shaded region. (Object is not drawn to scale.) GEOMETRY PLS HELPPPP
Answer:
101.5 cm
Step-by-step explanation:
You find the area of the rectangle and then the area of the triangle. Then, you subtract the area of the rectangle and the area of triangle.
Sherry Lebito bought 500 shares of stock at a quoted price of 83 1/4 What was the total purchase price?
$
A year later Sherry sold her stock at a quoted price of 95 1/2.
(b) Did she have a capital gain or a capital loss?
(c) How much of a gain or loss did she experience?
$
The total purchase price is $41,625.00
Capital gain was recorded
The capital gain is $41,625.00
What is total initial initial investment?
Was a capital gain or loss made?
What is the dollar value of gain or loss recorded?
Cost per share=$83.25(note 1/4=0.25)
Total purchase price=purchase price per share*number of shares
Total purchase price=$83.25*500
Total purchase price=$41,625.00
The fact that the price at which Sherry sold the stocks a year later is more than the initial purchase price of $83.25, means that a capital gain was recorded, in other words, she bought low and sold high.
The capital gain can be computed as the total selling price(selling price per stock multiplied by the number of shares sold) minus the total purchase price.
total selling price=$95.50(i.e. 1/2=0.500
total selling price=$95.50*500
total selling price=$47,750.00
capital gain=$47,750.00-$41,625.00
capital gain=$6,125.00
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What is the probability that the manufacturing unit has carbon emission beyond the permissible emission level and the test predicts this?
The probability that the manufacturing unit has carbon emissions beyond the permissible emission level is 0.2975
Given that the probability that carbon emissions from the company’s factory exceed the permissible level is 35% and the accuracy of the test is 85%.
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.
Event A: The given Carbon emission beyond to the given permissible emission level.
Event B: Test predicts this.
To get the probability of this problem, first we need to divide by 100 the given values.
A=35/100
A=0.35
The probability of event A is P(A)=0.35
And the probability is P(B|A)=85/100=0.85
Now, we will use the conditional probability formula, we get
P(B|A)=P(A∩B)/P(A)
0.85=P(A∩B)/0.35
P(A∩B)=0.85×0.35
P(A∩B)=0.2975
Hence, the probability that the manufacturing unit has carbon emissions beyond the permissible emission level and the test predicts is0.2975.
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The length of a rectangle is 7 centimeters less than three times its width. Its area is 40 square centimeters. Find the dimensions of the rectangle.
If the area of the rectangle is 40 square centimeters and length is 7 cm less than 3 times the breadth then the length will be 8 cm and breadth will be 5 cm.
Given area of the rectangle is 40 square centimeters and length is 7 centimeters less than 3 times the breadth.
let the breadth of rectangle be x.
According to question
Length=3x-7
Breadth=x
Area of rectangle=length* breadth
=[tex](3x-7)x[/tex]
=[tex]3x^{2} -7x[/tex]
Area is given as 40 square centimeters.
40=[tex]3x^{2} -7x[/tex]
[tex]3x^{2} -7x-40=0[/tex]
By factorization
[tex]3x^{2} -15x+8x-40=0[/tex]
3x(x-5)+8(x-5)=0
(3x+8)(x-5)=0
3x+8=0
x=-8/3
x-5=0
x=5
We should neglect x=-8/3 because side cannot be negative. So we have taken x=5.
Put x=5 in 3x-7 to get length
length=3(5)-7
=15-7
=8
Hence the length will be 8 cm and breadth will be 5 cm.
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The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
The answers to the various part as well as its reasons are given below
Part A:The x-intercepts shows a zero profit.The maximum value of the graph tells or depict the maximum profit.The function is one that goes up or increases upward until it reach the vertex and then it falls or decreases after it.This implies that the profit goes up as it reaches the peak at the vertex and it goes down after the vertex up until it gets to zero.The profits are negative as seen on the left of the first zero and on the right of the second zero.Part B:An approximate average rate of change of the graph from x = 3 to x = 5, shows the reduction in profit from 3 to 5.
Part C:Based on the above, the domain is one that is held back or constrained by x = 0 .
We are compelled at x = 6 due to the fact that we have to maneuver a negative profit.
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Miss Goh bought 6 blouses, 2 skirts and 2 dresses for $560. A blouse and a skirt cost $107. A blouse and a dress cost $134. What was the cost of a dress?
Answer:
$95 FOR A DRESS
Step-by-step explanation:
Let's rearrange the given:
She bought a blouse and skirt for two, a blouse and a dress for two, and a blouse for two.
A blouse and a skirt cost $107
A blouse and a dress cost $134
blouse cost x dollars
The equation:
2($107) + 2($134) + 2x = $560
SOLUTION:
$214 + $268 + 2x = $560
2x = $560 - $214 - $268
2x = $78
x = $39 for a single blouse
FIND THE COST OF DRESS:
A blouse and a dress cost $134 - $39 for a single blouse
$134 - $39 = $95
$95 IS THE COST OF DRESS
Which expression is equivalent to 3x2 + 7x + 4?
3(x2 + 7x + 4) – 14x - 8
3x2 + 7x + 4 – 14x
3x2 + 7x + 4 – 8
3x2 + 7x
Answer:
a.) 3(x^2 + 7x + 4) – 14x - 8
Step-by-step explanation:
a.) 3(x^2 + 7x + 4) – 14x - 8
3x^2 + 21x + 12 - 14x - 8
3x^2 + 7x + 4
b.) 3x^2 + 7x + 4 – 14x
3x^2 -7x + 4
c.) 3x^2 + 7x + 4 – 8
3x^2 + 7x - 4
d.) 3x^2 + 7x
Already simplified
a chemical company makes two brands of antifreeze the first brand is 20% pure antifreeze and the second brand is 45% pure antifreeze in order to obtain 70 gallons of the mixture that contains 30% antifreeze how many gallons of each brand of antifreeze must be used
Answer:
first brand: 42 gallons
second brand: 28 gallons
Step-by-step explanation:
So you know that the first brand is 20% antifreeze, this means that if you have x gallons then 0.20x is pure antifreeze. The same thing can be applied for the second brand except the coefficient is 0.45 and I'll just say the variable is y. If you haven't noticed, the coefficients are simply the percentages of antifreeze, but in decimal form. Anyways, since it's asking for a mixture that's 30% antifreeze and is 70 gallons that means 0.30(70) gallons is pure antifreeze. This simplifies to 21 gallons. So if we take the pure antifreeze of both mixtures we get the following equation:
[tex]21 = 0.2x + 0.45y[/tex]
the x represents how many gallons of the first brand, and the y represents how many gallons of the second brand. Since that's what it represents we also get the equation:
[tex]70=x+y[/tex]
In this equation there aren't any coefficients, since x and y represent the whole amount. the 0.2x and 0.45 simply represent how much is pure antifreeze.
So to solve this systems of equation we can solve for y or x, either works, and then substitute it into the other equation. So in this example I'll solve for y
Original equation:
[tex]70=x+y[/tex]
Subtract x from both sides
[tex]70-x=y[/tex]
So now we can substitute this into the pure antifreeze question
[tex]21 = 0.2x + 0.45y \implies21=0.2x+0.45(70-x)[/tex]
So now we can solve for x since it's the only variable in this equation
[tex]21=0.2x+31.5-0.45x[/tex]
Simplify
[tex]21=-0.25x+31.5[/tex]
Subtract 31.5 from both sides
[tex]-10.5=-0.25x[/tex]
Now divide both sides by -0.25
[tex]42=x[/tex]
So this means we have to use 42 gallons of the first brand, now we can substitute this into either equation to solve for y, but it's much easier to use the total gallon equation:
[tex]x+y=70\implies 42+y=70[/tex]
Subtract 42 from both sides
[tex]y=28[/tex]
So this means we need to use 42 gallons of the first brand and 28 gallons of the second brand
find the area of a circle whose radius is 'x', unit.
3.14 x² units
Step-by-step explanation:
Radius = x units. ----(given)
π = 3.14
Area of cirlce = πr²
= 3.14 * x²
= 3.14 x² units.
Hope it helps you!!Answer:
area = πx² square units
Step-by-step explanation:
Formula for the area of a circle:
area = πr²,
where r = radius.
In this problem, the radius is x, so we substitute r in the formula with x.
area = πx² square units
Mixed Practice
In the following exercises, solve.
358. The length of one leg of a right triangle is three more than the other leg. If the hypotenuse is 15, find the lengths of the two legs.
Answer:
9 units and 12 units to nearest hundredth.
Step-by-step explanation:
Let one leg be x units long then the other = x+3 units.
By Pythagoras:
x^2 + (x+3)^2 = 15^2 = 225
2x^2 + 6x + 9 = 225
2x^2 + 6x - 216 =0
x^2 + 3x - 108 = 0
(x - 9)(x + 12) = 0
x = 9
So the other 2 legs are 9 and 12.
8. What is the domain of [tex]\frac{x}{x^{2} +20x+75}[/tex] ? Hint: try factoring the polynomial.
9. What is the domain and range of [tex]\sqrt{13x-7}+1[/tex] ?
Please hurry! I really need help with this!
Answer:
8. Domain: (-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)
9. Domain: [7/13, ∞)
Range: [1, ∞)
Step-by-step explanation:
Question 8
Given rational function:
[tex]f(x)=\dfrac{x}{x^2+20x+75}[/tex]
Factor the denominator of the given rational function:
[tex]\implies x^2+20x+75[/tex]
[tex]\implies x^2+5x+15x+75[/tex]
[tex]\implies x(x+5)+15(x+5)[/tex]
[tex]\implies (x+15)(x+5)[/tex]
Therefore:
[tex]f(x)=\dfrac{x}{(x+15)(x+5)}[/tex]
Asymptote: a line that the curve gets infinitely close to, but never touches.
The function is undefined when the denominator equals zero:
[tex]x+15=0 \implies x=-15[/tex]
[tex]x+5=0 \implies x=-5[/tex]
Therefore, there are vertical asymptotes at x = -15 and x = -5.
Domain: set of all possible input values (x-values)
Therefore, the domain of the given rational function is:
(-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)
---------------------------------------------------------------------------------
Question 9
Given function:
[tex]f(x)=\sqrt{13x-7}+1[/tex]
Domain: set of all possible input values (x-values)
As the square root of a negative number is undefined:
[tex]\implies 13x-7\geq 0[/tex]
[tex]\implies 13x\geq 7[/tex]
[tex]\implies x\geq \dfrac{7}{13}[/tex]
Therefore, the domain of the given function is:
[tex]\left[\dfrac{7}{13},\infty\right)[/tex]
Range: set of all possible output values (y-values)
[tex]\textsf{As }\:\sqrt{13x-7}\geq 0[/tex]
[tex]\implies \sqrt{13x-7}+1\geq 1[/tex]
Therefore, the range of the given function is:
[1, ∞)
please help me on this question. im not the best at geometry
Answer: 48
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{x}{36}=\frac{64}{x}\\\\x^{2}=36 \cdot 64\\\\x=\sqrt{36 \cdot 64}\\\\x=\sqrt{36} \sqrt{64}=48[/tex]
A car rental company offers two plans for renting a car. Plan A: $30 per day and 18 cents per mile Plan B: $66 per day with free unlimited mileage How many miles would you need to drive for plan B to save you money
Answer:
200 miles
Step-by-step explanation:
Set up a cost equation for each plan using x for miles.
Set the equations equal.
Solve for x, the miles.
For a 1 day rental.
Plan A:
C = 0.18x + 30
Plan B:
C = 66
0.18x + 30 = 66
0.18x = 36
x = 36/0.18
x = 200
Answer: 200 miles
Find the value of each variable in the diagram given that a ∥ b.
Can you also explain please? Thank you!
The values are as follows:
z=50
v= 150
x= 100
y=15
w= 50
What is parallel lines?
Parallel lines are lines in a plane that are always the same distance apart.
z+130= 180 (Linear pair)
z=50
v+ 30 = 180 (Linear pair)
v= 150
x= 180- 30 - 50 (angle sum property)
x= 100
2y=30 (alternate interior angle)
y=15
w+x+2y=180 (Linear pair)
w+ 100 + 30 = 180
w= 50
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Manuel is blowing up balloons for a party at his house .he blows up 30 balloons in 10 minutes.how many balloons does he blow up in one minute ?
Answer:
it is 3 i think
Step-by-step explanatplease mark brainlest
find the values of x work 10% of my grade
Answer:
x = 35
Step-by-step explanation:
1. Add all angles
[tex]115+(x+36)+24+(2x+10)+2x[/tex]
= [tex]5x+185[/tex]
2. Match 360 and fix
[tex]5x+185=360[/tex]
[tex]5x=360-185[/tex]
[tex]5x=175[/tex]
[tex]x=175/5[/tex]
[tex]x=35[/tex]
Hope this helps
Answer:
[tex]\boxed{\sf x = 35^o}[/tex]
Step-by-step explanation:
Let's find the value of x :-
[tex]\sf 115 + x + 36 + 24 + 2x + 10 + 2x = 360^o[/tex]
Add the numbers.
[tex]\sf 185 + x + 2x + 2x = 360[/tex]Combine like terms.
[tex]\sf 5x + 185 = 360[/tex]Subtract 185 from both sides.
[tex]\sf 5x = 175[/tex]Divide both sides by 5.
[tex]\sf x = 35^o[/tex]--------------------------------------
The sum of two numbers is 724. one of the numbers is 217. what is the other number?
Answer:
507
Step-by-step explanation:
For the Algebraic Expression,
let the two numbers be X and y
lets assume x = 217
From the question,
217 + y = 724
y = 724-217
y = 507
Therefore, the other number is 507
Drag the tiles to the correct boxes to complete the pairs.
Match each question with its answer. The answers are in the form (quotient)r (remainder).
The number of books on each shelf is 11 remainder 11
The toffees left over is 22 r 4
The oranges that would remain is 11 r30
The pages left to read is 22 r 16
What are the matched questions and answers?Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
Number of books on each shelf = 3542 / 321 = 11 remainder 11
The toffees left over = 246 / 11 = 22 r 4
The oranges that would remain: 1702 / 152 = 11 r30
The pages left to read = 676 / 30 = 22 r 16
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12 A pilot needs to know the maximum height an aircraft can fly at. The cabin has been tested and is safe to a height of 15679 m. Round this height appropriately: a) to a whole number of kilometres b) to a whole 100 m.please help me
A manager measured the number of goods, y, that his company produced in x hours. The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.
Which equation, in point-slope form, correctly represents the goods produced by the company after x hours?
The equation, in point-slope form is (y - 45) = 5(x - 9) option first is correct.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
A manager measured the number of goods, y, that his company produced in x hours.
The slope:
m = 5
From the problem:
The point (9, 45) will satisfy the line.
(y - 45) = 5(x - 9)
Thus, the equation, in point-slope form is (y - 45) = 5(x - 9) option first is correct.
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find the root of the function f(x)= 1/(1/3)
Answer:
Hello, look at the picture
While driving, Carl notices that his odometer reads 25,952 miles, which happens to be a palindrome. He thought this was pretty rare, but 2.5 hours later, his odometer reads as 36,563 miles, anoher palindrome. What was Carl's average speed during those 2.5 hours
Carl's average speed was 4244 miles/hr during those 2.5 hours
First, the odometer showed palindromic no. 25952 miles
after 2.5 hours odometer showed the next palindromic no. is 36563.
hence the distance covered in 2.5 hours = 36563 - 25952 = 110611 miles.
Now, we have to find the average speed with the distance covered 110611 miles in a particular time of 2.5 hours.
Using formula,
average speed = total distance / total time
[tex]\frac{10611}{2.5}[/tex] =4244 miles/hour is the average speed
Hence, Carl's average speed was 4244 miles/hr during those 2.5 hours
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O Here is a list of numbers:
19, 4, 7, 2, 10, 5, 19, 2, 12
State the median.
Answer:
10
Step-by-step explanation:
median is the middle number of the list of numbers.
thereby counting through, the middle number which is the fifth number is 10
Answer:
7
Step-by-step explanation:
What is the smallest sample size that guarantees that the margin of error is less than 1% when constructing a 97% confidence interval for a population proportion
In order to get 97% confidence level, with confidence interval of
+/- 1%, and standard deviation of 0.5 our sample size should be 11,772 samples
A confidence interval for a population mean, when the population standard deviation is known based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution.
Accordingly, the Necessary Sample Size is calculated as follows:
Necessary Sample Size = [tex](Z-score)^{2} . StdDev*(1-StdDev) / (Margin Of Error)^{2}[/tex]
Given:-
At 97% confidence level Z-score = 2.17 Assuming standard deviation = 0.5, margin of error (confidence interval) of +/- 1%.Substituting in the given formula we get
Necessary Sample Size =
= ((2.17)² x 0.5(0.5)) / (0.01)²
= (4.7089x 0.25) / .0001
= 1.177225 / 0.0001
= 11,772.25
Hence in order to get 97% confidence level, with confidence interval of
+/- 1%, and standard deviation of 0.5 our sample size should be 11,772
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Trini rode her bike 12 miles on Friday. She rode 14 miles on Saturday and 15 miles on Sunday. How many miles did she ride in all?
Answer: 41
Step-by-step explanation:
12+14+15= 41