In the diagram, the base of the tower is at point H, and the top of the tower is at point F. If the distance from the base of the tower to point G is 7x feet and the distance from the base of the tower to point E is 6x + 12 feet, find GE, the distance across the lake.
A. 84 feet
B.
94 feet
C. 168 feet
D. 186 feet
Answers
This problem can be solved using triangle similarities:
Consider the Pythagorean Theorem with the formula; c^2=a^2+b^2
let: a=height from base to point
b1=base of the first triangle formed
b2-base of the second triangle formed
c1=c2= hypotenuse of the two triangles,
note:
they have equal hypotenuse and share the same height, thus a1=a2
sqrt[(a^2+(7x)^2)]=sqrt[a^2+(6x+12)^2]
sqrt(49x^2) =sqrt[(6x+12)^2]
7x=6x+12
x=12
GE=7x+6x+12
GE=7(12)+6(12)+12
GE= 168 feet
Thus, the answer is:
C. 168 feet
Related Questions
of the pizzas sold last week at vondras pizzaria 7/12 were large pizzas and 1/4 were extra large pizzas, what fraction of the pizzas aild were either large or extra large? enter your answer simplified and as a proper fraction
Answers
7/12 + 3/12 = 10/12
10/12 of the pizzas sold were either large or extra large
I hope this helps :)
Answer:
Step-by-step explanation:
7/12 + 1/4
7/12 + 3/12 = 10/12
10/12 of the pizzas sold were either large or extra large
What is the y-intercept of the quadratic y=-2x^2-4x-5 ?
(-5,0)
(0,-2)
(-1,3)
(0,-5)
Answers
We have:
[tex]y=-2x^2-4x-5\to f(0)=-2(0)^2-4(0)-5=-5[/tex]
Answer: (0; -5)
Find F'(x) for F(x) = [x^3,1] integral cos(t^4)dt
A. cos(1)-cos(x^12)
B. -3x^2cos(x^12)
C. cos(x^7)
D. -cos(x^12)
Answers
F'(x) = 0 -cos((x^3)^4)·3x^2
Simplifying, ...
F'(x) = -3x^2·cos(x^12)
The appropriate choice is ...
B. -3x^2cos(x^12)
Over 4 hours, the temperature in Miami, Florida, rose 8ºF. How many degrees, on average, did the temperature rise per hour
Answers
Answer:
The correct answer is 2°F
Step-by-step explanation:
Your equation is 8÷4
8÷4=2
I hope this helps :)
Sergio runs 2 1/4 miles in 30 minutes. Write the ratio in fractional form and determine Sergio's speed in miles per hour.
Answers
4.5 miles per hour.
Hope this helps. - M
Sergio runs at a speed of 4.5 miles per hour. The ratio of his running distance to time is 9/2.
Explanation:To determine Sergio's speed in miles per hour (mph), we use the equation: speed = distance/time. Sergio runs 2 1/4 miles in 30 minutes. First, we need to convert the fractional distance to a decimal and the time to hours. 2 1/4 miles is equal to 2.25 miles and 30 minutes is equal to 0.5 hours.
Substitute these values into the equation:
speed = 2.25 miles/0.5 hour = 4.5 mph.
Therefore, Sergio's running speed is 4.5 miles per hour. The ratio of distance to time in fractional form would be 9/2.
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22x+70=17x-95 show step by step please
Answers
[tex]22x + 70 = 17x - 95[/tex]
Move variables to the left by adding their opposites to both sides. Eliminate the opposites.
[tex]22x - 17x + 70 = - 95[/tex]
Move constants to the right by adding their opposites to both sides. Eliminate the opposites.
[tex]22x - 17x = - 95 - 70[/tex]
Collect the like terms by subtracting their coefficients and numbers.
[tex]5x = - 95 - 70[/tex]
Calculate the sum or difference. Extract the negative sign from the expression. Add the numbers.
[tex]5x = - 165[/tex]
Divide both sides of the equation by 5 and calculate the quotient.
[tex]x = - 33[/tex]
Answer:
Value of x is -33.
Step-by-step explanation:
[tex] \sf22x+70=17x-95 [/tex]
We combine x term together. In this equation there are two extra 22x and 17x and 17x is right hand side and we have to shift it left hand side so we have to change sign. 17x is a positive number so we have to shift in left hand side so it convert into negative number means - 17x.
[tex]\sf22x - 17x=-95 - 70[/tex]
Now, we combine next terms together and in right hand side we shift -70. Because in left hand side 70 is a positive number then we have to shift it right hand side so it change into negative.
[tex] \sf5x = - 165[/tex]
We write 5x because we subtract 22 with 17 and in right inside we write minus 165 because we add - 95 and -70. we can't subtract minus 95 and -70 because in front of the both of number there is a sign of minus.
Remember :-
- and - = + + and - = -- and + = -[tex]\sf x = \dfrac{ - 165}{5} [/tex]
We divide -165 by 5. Because in Left hand side 5x is in multiple so we shift it Right hand side and it turns into divide.
[tex] \sf \:x = - 33[/tex]
Now, we get value of x is -33.
Verification :-
Put values of x -33
22x+70
22×(-33) +70
= -726 + 70
= -656
Now, in R.H.S
17x-95
17×(-33) -95
= - 561 - 95
= - 656
L.H.S = R.H.S
Hence, proved
Note :-
L.H.S = Left hand side
R.H.S = Right hand side
giovanni justifies what is expression -4x - 8 is equivalent to -2( x + 1) - 2 ( x + 3 ) by letting x equal 3 in both expressions what is the value of each expression when x equals 3
Answers
You put 3 in for x in both equations
Equation 1
-4(3) - 8 =
Multiply
-12 - 8 = -20
The answer is one of the ones with -20
------------------------------------------------------------------------------------------------------
Equation 2
-2(3 + 1) - 2(3 + 3)
Do what is in paraenthesis
-2(4) - 2(6)
Multiply
-8 - 12 = -20
------------------------------------------------------------------------------------------------------
The answer is C) -20 and -20
Hope this helps!
Answer:
C. -20 & -20
Step-by-step explanation:
If you substitute x for 3 in the expressions, they will both evaluate to -20.
Thus, the answer is -20
A cross-section of a light reflector is a parabola. The bulb is located at the focus. Suppose the bulb is located 11 in from the vertex of the reflector.
Use this information to make the following determinations.
Model a cross section of the reflector by writing an equation of a parabola that opens upward and has its vertex at the origin.
Answers
An equation of a parabola that opens upward and has its vertex at the origin,
⇒ y² = - 8 x
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Now,
The equation of the parabola turned to the left is to the negative side of the coordinate system is:
⇒ y² = - 2 p x
where, p is the parameter of the parabola
The relationship between the parameter and the focus is.
⇒ p = 2 f
=> p = 2 × 2
⇒ p = 4 cm
Then, the equation of the parabola is:
y² = - 2 p x
= - 2 × 4 x
= - 8 x
Therefore, An equation of a parabola that opens upward and has its vertex at the origin,
⇒ y² = - 8 x
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Suppose you choose two families at random. what is the chance that family a owns exactly one car and family b owns exactly one car?
Answers
What is 134,500 rounded to the nearest ten thousand
Answers
Q #15 Graph ARTS With vertices R(6, 6), S(3, -6),and T(0, 3) and its image. over the Y -axis
Answers
(x,y) ⇒⇒⇒ (-x,y)
Note point T will not change
the solution is as shown in attached figure
What is the growth factor of the following example? Assume time is measured in the units given. A forest shrinks 80% per century.
Answers
The growth factor is 0.20 per century.
need help fast don't understand both A and B show work please
Answers
Usually the number of bits in a byte is 8 or 16 or 32 and recently 64. You don't have to write a formula to restrict it to this number of bits. You are not asked to do so. The general formula is 2^n - 1 for the problem of Millie and her golden keys. Somehow the system can be made to choose the right number of bits. Apple IIe s for example, used 8 bits and there was a location that told the processor that fact.
2^n - 1 <<<<< Answer
Problem B
In this case n = 4
2^n - 1 = 2^4 - 1 = 16 - 1 = 15
Millie can collect 15 keys <<<<<< Answer
hey can you please help me posted picture of question
Answers
C (n) = 20n + 15
Clearing t we have:
20n = c - 15
n = c / 20 - 15/20
Rewriting:
N (c) = (c-15) / 20
Answer:
The inverse function for this case is given by:
N (c) = (c-15) / 20
option B
MpRashawn recently spent $100 to open a store selling tee-shirts. At his business, he purchases plain tee-shirts for $11 each, prints graphics on them, and then sells them for $26 each. What is the minimum number of tee-shirts that Rashawn would need to sell in order to make a profit (total income minus total expenses) of at least $400?
Answers
400÷15=26,(6)
He would need to sell 27 T-shirts
Rashawn would need to sell 20 T-Shirts in order to make a profit of at least $400.
What is profit percentage?SP-CP divided by CP multiplying with 100 we get profit percentage.
P= [(SP-CP)/CP ] × 100
Given the following details about Mr. Rashawn.
Mr. Rashawn recently spent = $100 to open a store selling tee-shirts
He purchases plain tee-shirts for = $11 each
Then sells them for = $26 each
Profit on each shirt = $26 - $11 = $15
Profit = $400 -$100= $ 300
Number of t- shirts= $300/15 = 20 T -shirts.
Thus, Rashawn would need to sell 20 T-Shirts in order to make a profit of at least $400.
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-845 degree coterminal angle
Answers
with negative angles, we go "clockwise", the same direction a clock hands move.
so -360-360-125 = -845.
so as you see in the picture, you go around twice, and then a little bit more, an extra 125°, landing you at -125°, or its positive counterpart, 235°.
twice the difference of p and 10
Answers
2( p-10)
2p-20
The American flag is customarily made with its width and length in the ratio of 10 to 19. Which of the following dimensions is in the correct ratio for the flag?
Answers
Final answer:
The given dimensions do not match the American flag's customary ratio of 10 to 19. To find the correct dimensions, the numbers must divide to equal approximately 0.5263. None of the provided options are correct.
Explanation:
The American flag is customarily made with its width and length in the ratio of 10 to 19. To ensure the dimensions are correct, we must find a pair of numbers that, when divided, are in the same proportion as 10/19 (approximately 0.5263). Looking at the listed dimensions:
51 H (Height is not a width or length measurement, so we cannot confirm the ratio)
53 x 38 (53/38 = 1.3947 which is not equal to 10/19)
55 x 0.025 (55/0.025 = 2200 which is not equal to 10/19)
57 x (2.93, 3.59) (This does not provide a pair of length and width measurements)
59 (This is not a dimension)
Since none of the provided options has numbers that mirror the 10 to 19 ratio of the flag, none of these dimensions would be correct for an American flag. If we want to find dimensions that are proportional, we have to look for any two numbers that, when divided, equal approximately 0.5263. Hence, an example of a correct dimension following the flag's ratio would be 10 inches by 19 inches or any multiple thereof.
When multiplied, what is the simplified form of (5 − 2i)(1 − 2i)? Write the answer in standard form, a + bi, where a and b are real numbers.
Answers
F: 5*1 = 5
O: 5 *(-2i) = - 10i
I : -2i * (1) = - 2i
L: (-2i)(-2i) This may take a bit. There's a few signs hanging around.
L: (-2 * -2)*(i * i)
L: 4 (i *i)
L: 4(-1)
L: - 4 So combine these results.
FOIL: 5 - 10i - 2i - 4 Group the like terms
FOIL: 5 - 4 - 10i - 2i Now collect them
FOIL: 1 - 12i <<<<<<< Answer
s=4h+4w solve for h.
Answers
s - 4w = 4h
Now you are going to divide both sides by 4 to isolate the variable h. This gives you your answer:
[tex]h = \frac{(s-4w)}{4} [/tex]
please help me out i will reward brainliest
Answers
Write down and simplify the following algebraic expressions. The sum of −3x+5 and 7−4x is subtracted from 5x+17.
Answers
-3x+5+7-4x = -7x+12
That subtracted from 5x+17:
5x+17-(-7x+12) = 12x+5
What is the equation in slope-intercept form of the linear function represented by the table? x y –6 –18 –1 –8 4 2 9 12
Answers
y = (y₂ -y₁)/(x₂ -x₁)×(x -x₁) +y₁
If we let (x₁, y₁) = (4, 2) and (x₂, y₂) = (9, 12) this becomes
y = (12 -2)/(9 -4)×(x -4) +2
y = (10/5)×(x -4) +2
y = 2x -6
The equation in slope-intercept form of the given function is ...
y = 2x -6
Answer: y=2x-6
Step-by-step explanation:
Evaluate 7i^4-12i^2
-5
19
19i
Answers
Hope this helps
The powers of i repeat every four terms, so i⁴ equals 1 and i² equals -1. The result of the evaluation is 19.
To evaluate the expression 7i⁴-12i². In complex numbers, i is the imaginary unit with the property that i² = -1. The powers of i repeat every four terms:
i¹ = i
i² = -1
i³ = -i
i⁴ = 1
Using these properties, we can simplify the expression:
7i⁴ is 7 times 1, which equals 7.
-12i² is -12 times -1, which equals 12.
Adding these together, we get 7 + 12 = 19.
Therefore, the evaluated expression is 19.
Anyone have the answer?!!!
Answers
reflection across y = x.
Which of the following shows the length of the third side, in inches, of the triangle below?
Hypotenuse is 74 and one leg is 24
Answers
c² = a² + b²
Filling in your numbers, we can solve for b.
74² = 24² + b²
74² - 24² = b² = 4900
b = √4900 = 70
The length of the third side is 70.
Answer:
70 inches
Step-by-step explanation:
205/1000 is less then are greater then 0.205
Answers
The Tigers’ first play when they had possession of the ball went for -3 yards. Did the Tigers gain or lose yards on that play? How many yards did they gain or lose?
Answers
Answer:
The correct answer is (The Tigers lost 3 yards on that play.)
Evaluate the expression. 32 + 6 × 22 – 42 ÷ 2
Answers
Do 6 x 22:
= 32 + 132 – 42 ÷ 2
Do: 42 ÷ 2:
= 32 + 132 – 21
Do: 32 + 132:
= 164 – 21
Do 164 -21:
= 143
Answer: 143
Here is your answer:
The proper answer to this question is "143".
Reason:
Use PEMDAS:
Write the problem then solve:
32 + 6 × 22 – 42 ÷ 2=
↓
6×22=132
↓
32+132-42÷2=
↓
42÷2=21
↓
32+132-21
↓
32+132=164
↓
164-21
↓
164-21=143
↓
=143
Therefore your answer is 143!
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Pythagorean theorem to determine if a triangle with sides 2 ft,5ft,4ft is a right triangle
Answers
[tex] 2^2 + 4^2 = 5^2 [/tex]
[tex] 4 + 16 = 25 [/tex]
[tex] 20 = 25 [/tex]
Since 20 = 25 is clearly a false statement, the three side lengths 2 ft, 4 ft, and 5 ft do not form a right triangle.