Answers
8.1. If x is the distance from P to the flagpole and h is the height of the flagpole, then
tan(53°) = h/x
tan(28°) = h/(x + 20)
Solve for the first equation for h in terms of x :
h = x tan(53°)
Substitute this into the second equation and solve for x :
tan(28°) = x tan(53°) / (x + 20)
(x + 20) tan(28°) = x tan(53°)
x tan(28°) + 20 tan(28°) = x tan(53°)
x (tan(28°) - tan(53°)) = -20 tan(28°)
x = 20 tan(28°) / (tan(53°) - tan(28°))
x ≈ 13.4 m
8.2. By the law of cosines,
BD² = 7² + 11² - 2 • 7 • 11 cos(110°)
⇒ BD = √(170 - 154 cos(110°))
⇒ BD ≈ 14.9 cm
and
BC² = BD² + 16² - 2 • BD • 16 cos(40°)
⇒ BC = √(426 - 154 cos(110°) - 32 cos(40°) √(170 - 154 cos(110°)))
⇒ BC ≈ 10.6 cm
Now use Heron's formula. If S is the semiperimeter of ∆ABD and S' is the semiperimeter of ∆BCD, i.e.
S = (AB + BD + AD)/2 ≈ 16.5 cm
S' = (BC + CD + BD)/2 ≈ 20.7 cm
then
area ∆ABD = √(S (S - AB) (S - BD) (S - AD)) ≈ 36.2 cm²
and
area ∆BCD = √(S' (S' - BC) (S' - CD) (S' - BD)) ≈ 76.7 cm²
so that the total area of ABCD is approximately 112.9 cm².
Related Questions
A bottle of laundry detergent is 7/10
full. Jamie uses
3/10
of the bottle to
do her laundry. What fraction of the
bottle of laundry detergent is left?
Explain.
Answers
Answer:4/10 =2/5
Step-by-step explanation:
you subtract the numerator but the denominator stays the same. I then found a number that could be divided into both numbers and got 2/5.
This question is worth 20 points if someone answers it!
Answers
The maximum number of tourists in the third week will be maximum in the numberville city.The solution of f(x)=h(x) will be x(5,2).
What are equations?The equation is actually a relationship between the numbers and the variables.
To calculate the number of the tourists in the third week we will put the value 3 in every function:
[tex]f(x)=x^2+5x+10=(3)^2+(3\times 3)+10=29\\\\\\g(x)=3^x=3^3=27\\\\\\h(x)=10x=10\times 3=30[/tex]
So we can see that the function third h(x) numberville city is having a maximum number of tourists.
The solution of f(x)=h(x) will be calculated as:
[tex]x^2-3x+10=10x\\\\\\x^2-7x+10=0\\\\\\x^2-5x-2x+10=0\\\\\\x(x-5)-2(x-5)=0\\\\\\x=5,2[/tex]
Hence the solution of f(x)=h(x) will be x(5,2).
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The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. A 2-column table with 5 rows. Column 1 is labeled number of tickets with entries 1, 2, 3, 4, 5. Column 2 is labeled Probability with entries 0.17, 0.55, 0.20, 0.06, 0.02. What is the probability that a randomly selected purchase has less than two tickets? 0.17 0.55 0.72 0.83
Answers
Answer:
0.17
Step-by-step explanation:
The probability for purchasing 2 tickets at a time can be given as 0.17. The correct option is (A).
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Suppose X be the event to represent the number of tickets in purchase.
Then, as per the question distribution table can be formed as follows,
The number of tickets (X) P(X) Probability
1 0.17
2 0.55
3 0.20
4 0.06
5 0.02
Thus, the probability of selecting less than two tickets can be obtained as,
P(X < 2) = P(X = 1)
⇒ 0.17
Hence, the probability for a purchase to have less than two tickets is given as 0.17.
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
294 inches squred
Step-by-step explanation:
3 x 10 = 30
3 x 9 = 27
10 x 9 = 90
2(30) + 2(27) + 2(90) = 294
PLEASE HELP ILL MARK AS BRAINLEST
Which statement describes the speed of the remote-control car over time? O The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mili for the last 5 seconds. O The speed of the car increases from 4 mi h to 2 mih in the first 3 seconds, decreases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds. O The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 6 mi/h in the next second, and then remains at 6 mi/h for the last 6 seconds. O The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mih in the next 5 seconds, and then remains at 5 mi/h for the last 10 seconds,
Answers
Answer:
Step-by-step explanation:
The explanation of the problem is shown in the attached figure.
AS shown in the graph:
At t = 0 the speed = 4 miles/h then decrease to the speed = 2 miles/h during the first 3 seconds then increased to 5 miles/h during the next 2 seconds, then it became constant at 5 miles/h for the last 5 seconds.
So, the correct option is:
A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
Pls help me, this is due by tonight. What is the volume
Hopefully easy for some of you. :)
Answers
Answer:
115.86
Step-by-step explanation:
Which mixed number is equivalent to
19/3
Answers
Answer:
6 1/3
Step-by-step explanation:
You just have to see how many times it goes into it
Evaluate the expression:
-a^2 + c(a-c) - n^2 a= -3 c= -2 n= 3
Answers
Answer: -a^2+c\left(a-c\right)-n^2a=3\quad :\quad c=-\frac{-a+\sqrt{-3a^2-4an^2-12}}{2},\:c=-\frac{-a-\sqrt{-3a^2-4an^2-12}}{2}
Step-by-step explanation: YW! plese mark branlest!
For what values of a can you solve the linear system az + 3y = 2 and 4x + 5y = 6 by elimination without
multiplying first?
The values
and
Answers
Answer:
4, -4
Step-by-step explanation:
I think the first equation is ax + 3y = 2, not az + 3y = 2.
ax + 3y = 2
4x + 5y = 6
To use elimination, you need the coefficients of a to either add to zero, or to have a difference of zero if you subtract them.
a + 4 = 0
a = -4
a - 4 = 0
a = 4
Answer: a must be 4 or -4.
Answer:
-4 and 4
Step-by-step explanation:
Given linear system:
[tex]ax+3y=2[/tex]
[tex]4x+5y=6[/tex]
In order to solve the given linear system by elimination without multiplying first, [tex]a[/tex] must be either -4 or 4. That way, when you add or subtract the equations, the variable [tex]x[/tex] will be eliminated.
when [tex]a = -4[/tex]:
[tex]\large\begin{array}{ l r c c l r}& -4x & + & 3y & = & 2\\+ & 4x & + & 5y & = & 6\\\cline{1-6}& & & 8y & = & 8\\\cline{1-6}\end{array}[/tex]
when [tex]a = 4[/tex]:
[tex]\large\begin{array}{ l r c c l r}& 4x & + & 3y & = & 2\\- & 4x & + & 5y & = & 6\\\cline{1-6}& & & -2y & = & -4\\\cline{1-6}\end{array}[/tex]
How can I get 9th grade to add up to 500? You can only change summer and fall. Thank you
Answers
Answer:
8th fall- 203 9th fall-95
Step-by-step explanation:
the 9th total is 500
8th fall is 203
9th fall is 95
how to find 2 square root of 3
Answers
Answer:
sqrt12
Step-by-step explanation:
being given any problem like this, let's use the form y√x, y representint 2, and x is 3, but it's generalized
in order to find the unsimplified √ we would do 2(yx). Which in this case is 12
PLEASE HELP ME, I GIVE 69 POINTS FOR CORRECT ANSWER
A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
A: Sydney’s pyramid will have the same surface area because the One-half in the expression for the area of the triangular faces will make up for the slant height being doubled.
B: Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
C: Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
D: Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
(PS: If you choose C, you're wrong.)
Answers
Answer:
D
Step-by-step explanation:
I hope this helps! If it does, please mark me Brainliest! Thanks in advance!
what is the product ?
Answers
Explanation:
(5x+1) (5x-1)
(5x)^2 - 1^2
25x^2 - 1^2
Answer:
b) 25x² - 1
Step-by-step explanation:
→ (5x + 1)(5x - 1)
→ 25x² + 5x - 5x - 1
→ 25x² - 1
Thus, option (b) is the answer.
Evaluate: 2 • [(6 + 1)2 + 1]
Answers
Answer:
20
Step-by-step explanation:
2•[(6+1)2+1]
2•[(7)3]
2•10
• means times
2×10
20 answer
Answer:
p
Step-by-step explanation:
2 • [(6 + 1)2 + 1]
First The Brackets :
[(6 + 1)
->>> 6 + 1
= 7
But there's a bracket around 6 + 1 so now we multiply
-->>> [(7)2 + 1]
->>> 7 x 2
= 14
So now we add :
-->>> 14 + 1
= 15
And now we multiply:
->>> 15 • 2
--->>> 30
Hope it helps :))))
16) Graph g(x) = x + 3 + 2
Answers
please help thank you
Jack and Marcy are at an amusement park. Jack is standing 75 meters from a hot air balloon ride. He is recording Marcy with his cell phone as she gets into the basket of the balloon and the hot air balloon begins to rise.
Answers
Tan65°=h/75m
2.1445 × 75 = h
h = 160.83
Step-by-step explanation:
This is very very simple
Write an equation for the translation of y =5/x
that has the asymptotes x= -7 and y= 7
Answers
The equation for the translation of y = 5/x is y = 5/(x+7) + 7 if that has the asymptotes x= -7 and y= 7
What is hyperbola?
It is a curve in two-dimensional geometry having two parts, they both are symmetric. In other words, It can be defined as the number of points in the two-dimensional geometry that have a constant difference from that point to two fixed points in the plane.
We have:
[tex]\rm y = \dfrac{5}{x}[/tex]
Vertical asymptotes x= -7 and
Horizontal asymptotes y= 7
After translation:
[tex]\rm y = \dfrac{5}{x+7}+7[/tex]
Thus, the equation for the translation of y = 5/x is y = 5/(x+7) + 7 if that has the asymptotes x= -7 and y= 7
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Which sport is required to have both male and female competitors?
A. Water polo
B. Swimming
C. Hockey
D. Mixed doubles tennis
Answers
What is the volume of a cube with sides measuring 1.5 inches
Answers
Answer:
A cube with a side length of 3 inches has a volume of 27 cubic inches.
Step-by-step explanation:
yes
if you have 10 goldfish and 3 die how many are left
Answers
Answer:
7 goldfish
Step-by-step explanation:
10-3=7
Answer:
10-3=8
i think
Which expression is equivalent to 18x+8y?
Answers
Answer
2 (9 x + 4 y)
Hope this helps :)
3x+5y= -9
Y= 2x-7
Use substitution to solve the system
Answers
Answer:
x = 2
Step-by-step explanation:
3x + 5y = -9 ___(1)
y = 2x - 7
Substituting y's value in (1) ..
3x + 5( 2x - 7) = -9
3x + 10x -35 = -9
13x = -9 + 35
13x = 26
x = 26/13
x = 2
liam has 12 red ballons and 14 blue ballons he puts all of his ballons into 2 equal groups how many ballons are in each group
Answers
Answer: 6 red and 7 blue
Step-by-step explanation:
Cut in half the amount of each balloon
Then he divided 26 into 2 equal groups so divide 26 by 2 which is 13
13 is your answer :)
Five marbles labeled 1 through 5 are placed in a bag. A marble is randomly pulled and the number is recorded before the marble is
placed back in the bag. The results of the simulation of 20 marble pulls are shown in a dot plot.
Which dot plot models an unfair data-generating process?
Answers
Using the dot plot concept, it is found that the left plot on the bottom row shows an unfair data-generating process.
What does a dot plot show?The dot plot shows the number of times each measure appears in the data-set.
In this problem, each trial has 5 possible outcomes and there are 20 trials, hence each number should appear 20/5 = 4 times.
On the left plot of the bottom row, outcomes 1 and 5 appear 7 times, while outcomes 2, 3 and 4 appear 2 times, which are the furthest values from 5, hence it is an unfair data-generating process.
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Answer:
Step-by-step explanation:
Please help I need it quick!!!! Please
Answers
Answer:
Question 1
Cost per 10,000 Popsicle sticks = $725.20
⇒ Single Popsicle stick = 725.20 ÷ 10000 = $0.07 (nearest cent)
Question 2
Cost per 1,000 motherboards = $8,730
⇒ Cost of Single motherboard = 8730 ÷ 1000 = $8.73
Cost per 10 motherboards = $100
⇒ Cost of Single motherboard = 100 ÷ 10 = $10
Difference = 10 - 8.73 = $1.27
Question 3
Create a table with the cost per 1 unit:
[tex]\begin{array}{| c | c | c | c |}\cline{1-4} \sf PART & \sf COST\:PER\:1\:of\:10 & \sf COST\:PER\:1\:of\:1000 & \sf COST\:PER\:1\:of\:10000\\\cline{1-4} \sf Motherboard & \$10.00 & \$8.73 & \$7.04 \\\cline{1-4} \sf Processor & \$5.00 & \$1.25 & \$0.63 \\\cline{1-4} \sf Popsicle & \$0.10 & \$0.09 & \$0.07 \\\cline{1-4} \sf Motor & \$4.50 & \$0.18 & \$0.04 \\\cline{1-4} \sf Sensor & \$6.30 & \$4.54 & \$3.18 \\\cline{1-4} \sf Small\:gear & \$1.00 & \$0.80 & \$0.70 \\\cline{1-4} \end{array}[/tex]
From inspection of the table, the Motor saves the most money per unit when 10,000 is bought, since the difference between the cost of 1 unit is the greatest for this part.
Question 4
Cost of 1100 motherboards
= cost of 1000 + cost of 10 x 10
= 8730 + 100 x 10
= 8730 + 1000
= $9,730
Question 5
Cost of 12050 sensors
= cost of 10000 + cost of 1000 x 2 + cost of 10 x 5
= 31752 + 4536 x 2 + 63 x 5
= 31752 + 9072 + 315
= $41,139
The function h is defined as follows.
Screenshot shows the question.
Answers
[tex]\sf Simplified[/tex] ⇒ -2h
_______________________
[tex]\sf Given~h(-2)[/tex][tex]\sf Simply~move~2~to~the~left.[/tex]_______________________
Many counties in Florida missed many school days in the fall of 2004 due to hurricanes that year. To make up those days, they added time to each school day for a portion of the year. It was decided that in order to make up a 6 hour school day, 10 minutes would be added to each day. How many extended days would be needed to make up 3 school days?
Answers
Answer:
if 10 minutes was added each day 30 minutes is how long it would extend in 3 days
Tell whether the system has one solution, infinitely many solutions, or no solution.
Answers
Answer:
Has infinite solutions
Explanation:
-x + 5y = -3..... eq1
2x - 10y = 6 .... eq2
===============
make x the subject in equation 1
-x + 5y = -3
-x = -3 - 5y
x = 5y + 3
========= insert this in equation 2
2(5y + 3) - 10y = 6
10y + 6 -10y = 6
6 = 6
So, Has infinite solutions as L.H.S = R.H.S
Sand and gravel are mixed in the ratio 5:3 to form ballast.
How much sand is mixed with 750kg of gravel ?
Answers
Work Shown:
sand/gravel = 5/3
x/750 = 5/3
3x = 750*5
3x = 3750
x = 3750/3
x = 1250
Select the correct answer.
Factor completely
5x² - 45
OA (5x + 9)(x - 5)
O.B. 5(x - 45)
OC. 5(x-9)(x+ 9)
OD. 5(x+3)(x - 3)
Reset
Next
Answers
Answer:
D. 5(x + 3)(x - 3)
Step-by-step explanation:
Both terms are perfect squares, therefore we will factor using the difference of squares formula;a² - b² = (a + b) (a - b)
5(x + 3)(x - 3)
5(x² - 9)
(5x² - 45)
5x² - 45
Option D is correct, the factored form of the expression 5x² - 45 is 5(x+3)(x - 3)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 5x² - 45
Five times of x square minus forty five
x is the variable and minus is the operator
Let us take 5 common from the expression to find the factor form
5(x² - 9)
5(x² - 3²)
Now we know that a² - b² = (a+b)(a-b)
5(x+3)(x-3)
Hence, the factored form of the expression 5x² - 45 is 5(x+3)(x - 3)
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