A church spire casts a shadow on the level ground. At the tip of the shadow, the tip of the spire lies 25° upward. Walking 100 m closer, the tip of the spire is at an angle of 55°. What must be the height of the spire in Figure 2?
Answers
Answer:
The height of the spire must be 69.24 m
Step-by-step explanation:
The information given are;
The initial angle of elevation of the tip of the spire from the tip of the shadow = 25°
The angle of elevation of the tip of the spire from the tip of the shadow after moving 100 m closer = 55°
The change distance moved closer to the church spire = 100 m
Let the base angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow be 25° and ∠x°
We have;
∠x° and the 55° angle of the ray from the tip of the spire to the tip of the shadow are supplementary angles (angle on a straight line)
Therefore;
∠x° = 180° - 55° = 125°
The calculated angle 125° above, the given 25° and the angle in between the two rays from the tip of the spire to the tip of the shadows are the interior angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow
Let the angle in between the two rays from the tip of the spire to the tip of the shadows = y
Therefore;
125° + y° + 25° = 180 (Angle sum theorem)
y° = 180° - (125° + 25°) = 30°
By sin rule, we have;
100/(sin (30°)) = (The length of the initial ray from the tip of the spire to the tip of the shadow before the shift)/(sin(125°))
Let the length of the initial ray from the tip of the spire to the tip of the shadow before the shift = l
100/(sin (30°)) = l/(sin(125°))
l = (sin(125°))×100/(sin (30°)) = 163.83 m
The height of the spire, by trigonometric ratio = sin(25°) × 163.83 m = 69.24 m
The height of the spire = 69.24 m.
Related Questions
you move left 1 unit and up 1 unit. you end at (-5, 5) where did you start?
Answers
Answer:-4,4
Step-by-step explanation:
Because, -4 plus -1 is -5 and 4+1 is 5, hope this helps
>~<
Step-by-step explanation:
(-6,1)
Which expression is equivalent to 2+9
Answers
Answer:
2+9 is 11
so write any expression that equals 11 like...
1+10=11
2+9=11
3+8=11
4+7=11
5+6=11
and those above are all example of expression that is equivalent to 2+9
Answer: C ON EDGE 2021
Step-by-step explanation:
write the equation of the line that passes through (3, 4) and (2,-1) in point slope form
Answers
Step-by-step explanation:
Using Point Slope formula :
[tex](y - y_1) = \frac{(y_2 - y_1)}{(x_2 - x_1)} (x - x_1)[/tex]
[tex](y - 4) = 5(x - 3)[/tex]
[tex]y = 5x - 11[/tex]
Answer:
The point slope formula is : y-y₁ =m(x-x₁), so first u need to find the value of slope.
Step-by-step explanation:
finding the value of slope:
slope(m)= y₂-y₁ ÷ x₂-x₁
= -1-4 ÷ 2-3
= 5
now finding equation;
y-y₁=m(x-x₁)
y-4 = 5(x-3)
11=5x - y
0= 5x - y -11
therefore equation of line in point slope is : 5x-y-11=0
A person ran 300 yards ran how many feet did he run
Answers
Answer:
900 feet
Step-by-step explanation:
300 yards converted to feet is 900 ft.
Kamal prepares 2 kilograms of dough every hour he works at the bakery. Write an equation that shows the relationship between the hours worked x and the dough prepared y. *
Answers
Answer:
2 into x into y
Step-by-step explanation:
5. The shape of a dome can be modeled by the equation h = - 2 d 2 + 100 where h is the height (in feet) of the dome from the floor d feet from its center. How far from the center of the dome is the height 50 feet?
6. A cab charges $0.10 per mile and a flat fee of $3.00. Write an equation to model the price y of an x-mile-long cab ride.
7. Use the discriminate to determine the number of solutions to the quadratic equation y = 3 x 2 - 4 x + 6. 8. If f ( x ) = 7 x 2 + 5, compute f ( )3 . 9. Write an equation representing the translation of f ( x ) = 7 x + 3 down 4 units.
Answers
Answer:
5. When the dome is 50 feet high, the distance from the center is 5 feet
6. The equation that model the price y of an x-mile long ride is given as follows;
y = 0.1×x + $3.00
7. The discriminant is < 0; The equation has no real root
8. f(3) = 68
9. The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is f(x) = 7·x + 7
Step-by-step explanation:
5. The given equation for the shape of the dome is presented as follows;
h = -2·d² + 100
Where;
h = The height of the dome (in feet)
d = The distance from the center
Therefore, we have;
When h = 50, d is found as follows;
h = -2·d² + 100
50 = -2·d² + 100
50 - 100 = -2·d²
-50 = -2·d²
∴ 2·d² = 50
d² = 50/2 = 25
d = √25 = 5 feet
Therefore when the dome is 50 feet high, the distance from the center is 5 feet
6. The given rate the cab charges per mile, x = $0.10
The rate the cab charges as flat fee = $3.00
Therefore, the price, y a person traveling by cab for x miles is given by the straight lie equation as y = m·x + c,
Where;
m = the slope or rate which in this case = $0.1/hour
c = A constant term which in this case = $3.00
Therefore
y = 0.1×x + $3.00
The equation that model the price y of an x-mile long ride is y = 0.1×x + $3.00
7. The discriminant, b² - 4·a·c of the quadratic equation is (-4)² - 4×3×6 = -56
which is < 0, the equation has no real root
8. Given f(x) = 7·x² + 5
f(3) = 7 × (3)² + 5 = 68
f(3) = 68
9. The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is given as follows;
Down 4 units is equivalent to subtracting 4 from the y-coordinate value, therefore, we have;
f(x) - 4= 7·x + 3
f(x) = 7·x + 3 + 4
f(x) = 7·x + 7
The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is f(x) = 7·x + 7
HELP ME ASAP PLEASE!!!
Answers
Answer:
idk
Step-by-step explanation:
The product of this number and 10 is equal to the square of this number
Answers
Answer:
___ x 10 = ____^2
Step-by-step explanation:
Factorise:
8 x 3 + 729 +10800² + 486X.
Answers
Answer:
(2x+9) ^3
Step-by-step explanation:
(((8 • (x3)) + 729) + (22•33x2)) + 486x
((23x3 + 729) + (22•33x2)) + 486x
Factoring: 8x3+108x2+486x+729
8x3+108x2+486x+729 is a perfect cube which means it is the cube of another polynomial
In our case, the cubic root of 8x3+108x2+486x+729 is 2x+9
Factorization is (2x+9)3
Hope this helped
Point M is the segment bisector. what is the value of x?
Answers
============================================
Explanation:
"Bisect" means to cut in half
M is the midpoint as it cuts segment ST in half
SM and MT are the same length
SM = MT
2x+3 = 4x-7
2x-4x = -7-3
-2x = -10
x = -10/(-2)
x = 5
----------
If x = 5, then
SM = 2x+3 = 2(5)+3 = 10+3 = 13
MT = 4x-7 = 4(5)-7 = 20-7 = 13
Both SM and MT are the same length (13 units). This confirms the answer.
Solve: -5 + 7 - 6 - (-4) *
Answers
Answer:
0
Step-by-step explanation:
-5 + 7 - 6 - (-4)
-11 + 7 - (-4)
-11 + 7 +4
-11 + 11
= 0
Answer: 0
Step-by-step explanation:
-5 + 7 -6-(-4)
-5 + 7 -2
-5+ 5 = 0
8+(-3) full work thx If u can help
Answers
Answer: 5
Step-by-step explanation:
8+(-3)
=8-3 ⇔ you don't need to change signs when it is positive(+) outside the parenthesis
=5 ⇔ subtraction
#CarryOnLearning
+(-)= -
8+(-3) =8-3
=5
What is the image point of (3,1) after a translation left 3 units and up 3 units?
Answers
Answer:
0,4
Step-by-step explanation:
When yo go 3 to the left for x you get back to 0 and when you go up 3 for 1 you go up to 4.
Answer:
(0,4)
Step-by-step explanation:
its right
For the residual plot below, explain whether the plot shows a linear or non-linear model and why.
Answers
Answer:
It is a linear model
Step-by-step explanation:
The answer choices imply that you can model the relationship between the variables with a line or curve.
find the relevant data points on the scatter plot and draw a line of best fit to visualize this relationship. The line of best fit should be drawn through appropriate points. The only far away point can be ignored. The line of best fit need not pass through the majority of the points.
According to the scatter plot and the line of best fit, it will be seen that as X - variables increases, Y - variable decreases, leading to a strong negative correlation.
The Majority of the data points are fairly close to the line of best fit, which means the correlation is strong.
WILL MARK BRAINLIEST IF CORRECT!!!!!!!!!!! :) (IMAGE ATTACHED)
Answers
Answer:
B
Step-by-step explanation:
just did it
Answer:
[tex]\huge\boxed{Option \ B: 5\sqrt[3]{10} + 4\sqrt[3]{10} }[/tex]
Step-by-step explanation:
[tex]\sf 9\sqrt[3]{10} \\We \ can \ split \ 9 \ into\ 5 \ and \ 4\\(5 + 4)\sqrt[3]{10} \\Applying distributive property\\5\sqrt[3]{10} + 4\sqrt[3]{10}[/tex]
Joshua sold his bike for 10% less than payed for it. If he sold the bike for $585, how much did he pay for it.
Answers
Answer: $650
Step-by-step explanation:
If he sold the bike 10% less than the original amount which means he sold it as a 10% discount so the person has to pay 90% of the price. And 90% of the price has to equal $585 so we could set up an equation and solve for the price.
90% * x = 585
0.9 * x = 585
0.9x = 585
x = 650
Which means he paid $650 for the bike.
Y = (x+2) (-X-1)
Answer the question using null law
Answers
Answer:
x = - 2, x = - 1
Step-by-step explanation:
Given
y = (x + 2)(- x - 1)
To solve for x let y = 0, that is
(x + 2)(- x - 1) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
- x - 1 = 0 ⇒ - x = 1 ⇒ x = - 1
Step-by-step explanation:
y=(x+2) (-x-1)
(45) - (+14)
y= (x+2) (-x-1)
y=-2
Let f(x) = 4x + 8 and g(x) = 2x - 12. Perform the function operation, (f - g)
(x), and then find the domain of the result.
Answers
Answer:
See below.
Step-by-step explanation:
So we know that:
[tex]f(x)=4x+8\text{ and } g(x)=2x-12[/tex]
First, know that:
[tex](f-g)(x)[/tex]
Is the same as:
[tex]=f(x)-g(x)[/tex]
Substitute:
[tex]=(4x+8)-(2x-12)[/tex]
Distribute:
[tex]=4x+8-2x+12[/tex]
Combine like terms;
[tex]=2x+20[/tex]
Thus:
[tex]f(g(x))=2x+20[/tex]
This is simply a linear equation.
Thus, the domain is all real numbers.
In interval notation, this is:
[tex](-\infty, \infty)[/tex]
This diagram is a straightedge and compass construction. A is the center of one
circle, and B
is the center of the other. Select all the true statements.
Answers
Answer:
True choices are 1, 2, 5
Step-by-step explanation:
As per diagram, the circles are equal.
Since the distance AB is the radius of both circles:
AB = AC = BC = BD = AD = rSo the answer choices:
1. AC = BC
Correct, both equal to r2. AC = BD
Correct, both equal to r3. CD = AB
Incorrect. Half of CD is the leg of 30-60-90 triangle and is equal to r√3/2, so CD = AB√34. ABCD is a square
Incorrect. ACBD is rhombus5. ABD is an equilateral triangle
Correct, all three sides are equal to r6. CD = AB + AB
Incorrect as CD = AB√312x+4(x-1)=60
solve please
Answers
Answer:
Hey there!
12x+4(x-1)=60
12x+4x-4=60
16x-4=60
16x=64
x=4
Let me know if this helps :)
Answer:
x=4
Step-by-step explanation:
Chloe wants to net 50000 on her house. Her closing costs will be 8000 plus 7% commission. She owes 200000 on her loan . What is the minimum contract price that she can accept for the property?
Answers
Answer:
$277,419
Step-by-step explanation:
Relevant Data provided as per the question is
Net amount = 50,000
Closing cost = 8,000
Loan amount = 200,000
Commission percentage = 7%
According to the given situation, the calculation of the minimum contract price is shown below:-
[tex]Minimum\ contract\ price = \frac{(Net\ amount\ +\ Closing\ cost\ +\ Loan\ amount) }{Remaining\ percentage}[/tex]
[tex]= \frac{(50,000 + 8,000 + 200,000)}{(100\% - 7\%)}[/tex]
[tex]= \frac{258,000}{93\%}[/tex]
= $277,419
Therefore for calculating the minimum contract price we simply applied the above formula.
3.3 x 10^11 in standard notation
Answers
Answer:
330,000,000,000
Step-by-step explanation:
Move the decimal to the right eleven times!
Answer:
3.3*10¹¹ = 330000000000
Step-by-step explanation:
3.3*10¹¹ = 330000000000
-4(x-5 ) - 25 = -5 x =?*
Answers
Answer:
x=0
Step-by-step explanation:
First distribute -4 to x and -5 and get -4x+20-25=-5
Then you combine like terms and get -4x-5=-5
Then add 5 to both sides and get -4x=0
Then divide both sides by -4 and get x=0
The test for goodness of fit a. is always an upper tail test. b. is always a two-tailed test. c. can be a lower or an upper tail test. d. is always a lower tail test.
Answers
Answer: a. is always an upper tail test.
Step-by-step explanation:
The chi-square goodness-of-fit test is a test to check whether the sample comes from the population with the expected distribution or not.
If the observed frequency is close to the expected frequency, then the square of the deviations will be small. The square of the deviation is divided by the expected frequency to get the weighted frequencies.
If the sum of these weighted squared deviations is large is then it creates a doubt for the distribution claimed other wise not. Therefore, the chi-square goodness-of-fit test is always a right tail test.
Hence correct option is "a. is always an upper tail test. "
2 3/7 - 1 1/4 please give the answer as a mixed number with the fraction part in the lowest terms :))
Answers
Answer:
9/28Step-by-step explanation:
2 3/7 - 1 1/4
2 3/7 - 1 1/4First turn the two mixed numbers into improper fraction:
2 3/7 - 1 1/4First turn the two mixed numbers into improper fraction:17/7 - 5/4
2 3/7 - 1 1/4First turn the two mixed numbers into improper fraction:17/7 - 5/4Next find the Lowest Common Denominator:
L.C.D = 28
L.C.D = 2821 - 12/28
L.C.D = 2821 - 12/28= 9/28
It won't be a mixed number because the denominator is bigger than the numerator.
how many centimetre square are there in a rectangle of 10cmby5cm
Answers
Answer:
30cm²
Step-by-step explanation:
Since there are two 10 centimeter sides, this can be shown as 10cm×2=20cm. Since there are two 5 centimeter sides, this can be shown as 5cm×2=10cm. 20cm+10cm=30cm².
2x - 3y = 16 5x - 3y = 13 solve the system of equations
Answers
Answer:
x=-1 y=-6
Step-by-step explanation:
i hope that helped
the sum of n and 7 is equal to 50
Answers
Answer:
43
Step-by-step explanation:
Sum means total
n+7=50
n=50-7
n=43
Which of the following is true given that 2.1 < 2.8?
A.
2.1 is to the right of 2.8 on a horizontal number line
B.
2.1 is at the same place as 2.8 on a horizontal number line
a.
2.1 is to the left of 2.8 on a horizontal number line
KDD
2.1 is the opposite of 2.8 on a horizontal number line
Answers
Answer:
[tex]\large \boxed{\mathrm{2.1 \ is \ to \ the \ left \ of \ 2.8 \ on \ a \ horizontal \ number \ line}}[/tex]
Step-by-step explanation:
[tex]2.1<2.8[/tex]
[tex]\sf 2.1 \ is \ lesser \ than \ 2.8.[/tex]
[tex]\sf A \ number \ that \ is \ lesser \ than \ another \ number \ is \ to \ the \ left \\ \ of \ that \ number \ on \ a \ horizontal \ number \ line.[/tex]
Answer:1 is to the left of 2.8 on a horizontal number line
Step-by-step explanation:
What will be the location of U’ in the image trapezoid S’T’U’V’?
Answers
Answer:
(14,1)
Step-by-step explanation:
You can see with the LKMJ rectangle, it moves over 7 and up 3.
We can do this for STUV and U is originally (7,-2) but moves up and right to the point (14,1)