The 125 feet long line and the angles 65°10', and 60°10' obtained from the surveying equipment gives the length of the bridge as approximately 1234.2 feet.
Which rule can be used to find the length of the bridge?Given;
Location of the tree = The other side of the river from the surveyor
Length of the line measured along the river, L = 125 feet
Angle to the tree from the start of the line = 65°10'
1° = 60'
10' = ((1/60)×10)° = (1/6)°
65°10' = (65 + 10/60)° = (65 + 1/6)°
Angle measured at the end of the line, E = 60°10'
Similarly;
E = 60°10' = (60 + 1/6)°
The interior angle, S, of the triangle formed by the tree and the line, at the start of the line is therefore;
Angle S = 180° - (65 + 1/6)° = (114+5/6)° (linear pair angles)
S = (114+5/6)°
From the angle sum property of a triangle, angle formed at the tree, T, is therefore;
T = 180° - ((114+5/6)° + (60 + 1/6)°) = 5°
According to the rule of sines, we have;
l/(sin T) = b/(sin E)
Where;
b = The length of the bridge
Which gives;
124/(sin 5°) = b/(sin (60 + 1/6)°)
b = (sin (60 + 1/6)°) × (124/(sin 5°)) ≈ 1234.2
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M angle JKL=
Help me please! Asap thanks so much :)
The measure of the angle <JKL is 56 degrees
Tangent secant theorem of a circleThe theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Given the following parameters
m<IL = 112 degrees
Since the measure of the vertex is half the measure of its intercepted arc, hence;
<JKl = 1/2(m<IL)
Substitute the given parameters into the formula to have;
<JKl = 1/2(112)
<JKL = 56 degrees
Hence the measure of the angle <JKL is 56 degrees
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Identify the slope of a line perpendicular to the given line Y=2x-4
[tex]m = \frac{ - 1}{a} = \frac{ - 1}{2} \\ y = \frac{ - 1}{2} x + b[/tex]
In each of the following, the type of variation is given along with 1 data point. Find the variation constant. a. direct variation; y = Kx where x = 3 and y = 6 b. inverse square variation; y = K/x2 where x = –2 and y = 1 c. inverse variation; y = K/x where x = 8 and y = 10 d. inverse variation; y = K/x where x = 3 and y = 3 e. direct square variation; y = Kx 2 where x = 5 and y = 15 f. direct variation; y = Kx where x = –7.5 and y = 6.3
For direct variation, variation constant = 2.
For inverse square variation, variation constant = 4.
For inverse variation, variation constant =80.
For inverse variation, variation constant = 9.
For direct square variation, variation constant = 0.6
For direct variation, variation constant = -0.84
(a) Direct variation: y = Kx where x = 3 and y = 6
Variation constant(k) = y/x = 6/3 =2
(b) Inverse square variation: y = K/[tex]x^{2}[/tex] where x = -2 and y = 1
Variation constant(k) = y[tex]x^{2}[/tex] = 1(-2)(-2) =4
(c) Inverse variation: y = K/x where x = 8 and y = 10
Variation constant(k) = y*x = 8*10 =80
(d) Inverse variation: y = K/x where x = 3 and y = 3
Variation constant(k) = y*x = 3*3 =9
(e) Direct square variation: y = K[tex]x^{2}[/tex] where x = 5 and y = 15
Variation constant(k) = y/[tex]x^{2}[/tex] = 15/25 =0.6
(f) Direct variation: y = Kx where x = -7.5 and y = 6.3
Variation constant(k) = y/x = -6.3/7.5 = -0.84
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What are the points if the slope is 4 and the point is (1,-1)
The points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the points?The given parameters are:
Slope = 4
Point = (1, -1)
The slope of 4 means that as x changes by 1, the value of y changes by 4
This means that, we have:
(x + 1, y + 4)
Substitute the known values in the above equation
(1 + 1, -1 + 4)
Evaluate
(2, 3)
Hence, the points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)
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Select the correct answer.
What is the solution to the equation?
2(x + 7) = 8
OA. -15 and 1
OB. -15
OC. 1
OD.
no solution
Answer:
Option D is correct.
No solution
Step-by-step explanation:
2(x+7)=8
Apply 2 into bracket:
2x+14=8
2x=8-14
2x=-6
Divide both sides by 2:
x=-3
hence here is no option for x=-3, so answer is no solution.
i need help with this ;n;
Find the width and heigth of a newer 47-inch television whose screen has an aspect ratio of 4:3
Find the área of the screen
Answer:
width: 37.6 inheight: 28.2 inarea: 1060.32 in²Step-by-step explanation:
The measurement used to describe a television is the length of its diagonal. The relation between the width, height, and diagonal is described by the Pythagorean theorem.
Diagonal unitsThe Pythagorean theorem tells us the relation between the sides of a right triangle and its hypotenuse. The diagonal of a rectangle is the hypotenuse of a right triangle whose sides are the width and height of the rectangle. If 'c' is the number of "ratio units" in the diagonal, we have ...
4² +3² = c²
c = √(16 +9) = 5
The diagonal of the screen is 5 ratio units, so the width is 4/5 of the length of the diagonal, and the height is 3/5 the length of the diagonal.
Screen dimensionsThe width is ...
(4/5)(47 in) = 37.6 in . . . width
The height is ...
(3/5)(47 in) = 28.2 in . . . height
AreaThe area is the product of the width and height:
A = WH = (37.6 in)(28.2 in) = 1060.32 in²
The area of the screen is 1060.32 square inches.
What is the next number in the arithmetic sequence below??
I think it's D but I'm not sure.
What is the area of the sector of the circle below, if the radius is 5 m. and the central angle < AOB measures 88 °. (round answer to the nearest tenth)
Answer:
b 19.2
Step-by-step explanation:
a = [tex]\pi[/tex][tex]r^{2}[/tex] for a circle. We do not want to find the area for a whole circle. We only want to find the area for part of a circle. a hole circle is 360 degrees.
a = [tex]\frac{88}{360}[/tex][tex]\pi[/tex][tex]r^{2}[/tex]
a = [tex]\frac{88}{360}[/tex][tex]\pi[/tex]([tex]5^{2}[/tex])
a = 19.2 rounded.
The area of the sector of circle is b. 19.20 square meter.
What is the area of sector of circle?The space enclosed by the sector of circle is called area of the sector of circle.Mathematically,
Area of the sector of circle, A = θ/360πr²
where θ is the angle of the arc and r is the radius of the circle.
Now it is given that,
radius of the circle, r = 5m
Angle of arc, θ = 88°
Therefore, area ofsector of circle A = θ/360πr²
Put the values,
A = 88/360 π 5²
Solving the equation we get
A = 19.20 square meter.
Hence,the area of the sector of circle is b. 19.20 square meter.
So the correct answer is b.) 19.20 square meter.
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if the earth is 12.5 million years old, how old is the earth in hours?
Answer:
1.09575e+11
Step-by-step explanation:
find PQ if possible
Answer: 11 units
Step-by-step explanation:
We can say that [tex]\triangle TSQ\sim\triangle PSR[/tex] by AA Similarity Postulate. This is since [tex]\angle T\cong\angle P[/tex] and both ∠TSQ and ∠RSP are right angles, making them congruent.
Similar triangles have a property that corresponding sides are proportional. Hence, we can say that
[tex]\frac{ST}{PS}=\frac{SQ}{SR}\\\frac{15}{PS}=\frac{9}{12}\\\frac{15}{PS}=\frac{3}{4}\\60=3*PS\\PS=20[/tex]
We also know that PS is the combined length of PQ and QS. Since we know that QS is 9, let's substitute PQ + 9 in and solve.
[tex]PQ+9=20\\PQ=11[/tex]
Jamie is 6 years older than tyrion now. in 2 years, jamie will be one year less than twice tyrion's current age. what is jamie's current age?
Answer:
Jamie is currently 15.
Step-by-step explanation:
How many integers between $1$ and $200$ are multiples of both $3$ and $5$ but not of either $4$ or $7$
There are only 13 multiples of both 3 and 5, since
[tex]200 = 3\cdot5\cdot13 + 5[/tex]
From these integers, we eliminate any that are also divisible by 4 or 7.
[tex]3\cdot5\cdot4 = 60 \implies \{60,120,180\}[/tex]
[tex]3\cdot5\cdot7 = 105 \implies \{105\}[/tex]
so there are 13 - 4 = 9 such integers.
c) Shin thinks of a number. She multiplies it bye 5 then subtract 7. The answer is he
same as 3 times a number plus 11. What number did shin think of?
Answer:
9
Step-by-step explanation:
let the number be y
5×y - 7 = 3×y + 11
5y-7 = 3y+11
collect like terms
5y-3y = 11+7
2y = 18
y = 18/2
y = 9
Scalcet8 4. 2. 26. suppose that 2 ≤ f '(x) ≤ 4 for all values of x. what are the minimum and maximum possible values of f(4) − f(1)? ≤ f(4) − f(1) ≤ show my work (optional)
The minimum value of f(4) - f(1) is 6.
The maximum value of f(4) - f(1) is 12.
In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.
Taking the given inequality as (i).
We are asked to find the minimum and maximum possible values of f(4) - f(1).
We multiply (i) by dx throughout, to get:
4dx ≤ f'(x)dx ≤ 5dx.
To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:
[tex]\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12[/tex]
Thus, the minimum value of f(4) - f(1) is 6.
The maximum value of f(4) - f(1) is 12.
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answer????? with steps
WILL GIVE CROWN
What is the remainder of 2x^2+7x-39/x-7
show work
On dividing we get 69/2 or 34.5 as remainder.
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor if and only if f=0.
Long division is best suited for such expressions:-
On applying long division and factor theorem we get
2x²+7x-39 = (2x - 1/2)(x-7) + 69/2
Thus on dividing we get 69/2 or 34.5 as remainder.
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A man left rs 1,800,000 as inheritance.his heirs are 6 daughters and 2 sons.find the share of each heir
Answer:$225,000 each
Step-by-step explanation: Assuming that they each get an equal share of the inheritance, there are 8 shares of the inheritance so we divided the $1.8m by 8 which equals $225,000 each.
find the value of n:
[tex]\frac{10}{n} =\frac{15}{6}[/tex]
find the value of x and y that satisfies both the equaties x/y= 2/3 and y/24=3/4
Answer:[tex]\Large\boxed{x=12~;~y=18}[/tex]
Step-by-step explanation:
Given a system of equations
[tex]1)~\frac{x}{y} =\frac{2}{3}[/tex]
[tex]2)~\frac{y}{24} =\frac{3}{4}[/tex]
Multiply 24 on both sides of 2) equation to isolate y-value
[tex]\frac{y}{24}\times24 =\frac{3}{4}\times24[/tex]
[tex]\Large\boxed{y=18}[/tex]
Substitute the y-value into the 1) equation
[tex]\frac{x}{18} =\frac{2}{3}[/tex]
Multiply 18 on both sides of 1) equation to isolate y-value
[tex]\frac{x}{18}\times18 =\frac{2}{3}\times18[/tex]
[tex]\Large\boxed{x=12}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. What is the measure of the final interior angle?
108°
127°
150°
487°
Answer:
127
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Charlie began hiking from her campsite back to her car. Her campsite was located 9 miles from her car. She had walked for 1 hour and was 2 miles from her campsite when she realized she had forgotten her water bottle. She hurried back to her campsite in 0.5 hours, collected her water bottle, and rested for 0.5 hours. Then she began hiking back to her car at a quicker pace. She hiked for 3 more hours before she reached her car. Which graph represents Charlie's distance from her car at different times?
The Distance - Time graph that represents that represents Charlie's trip is attached accordingly.
What is a Distance - Time Graph?A distance-time graph can be used to illustrate the distance traveled by an item moving in a straight line.
The gradient of the line in a distance-time graph equals the speed of the item. The quicker the item moves, the higher the gradient (and the steeper the line).
What is the use of a Distance - Time Graph?Some of the uses of the distance-time graph are;
The position of the object at a time can be detected using the distance - time graphThe D-T Graph can provide the speed at which a person or an object is traveling.Learn more about Distance - Time Graph:
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Use the bisection method to find solutions accurate to within 10−2 for x 4 − 2x 3 − 4x 2 4x 4 = 0 on each interval.
(a) [−2, −1].
(b) [0, 2].
(c) [2, 3].
(d) [−1, 0].
The solution accurate to equation within [tex]10^{-2}[/tex] for [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] lies in [0,2].
Given the equation [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] and range is [tex]10^{-2}[/tex].
We are required to find the interval in which the solution lies.
The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the mid point of the interval is found. The sign of its relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than [tex]10^{-2}[/tex].
Interval:[0,2], signs [+,-],mid point:1, sign at midpoint +.
[1,2] 3/2
[1,3/2] 5/4
The rest is in the attachment. The listed table values are the successive interval mid points.
The final midpoint is 181/128=1.411406.
This solution is within 0.0002 of the actual root.
Hence the solution accurate to equation within [tex]10^{-2}[/tex] for [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] lies in [0,2].
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Graph paper recommended***
Quadrilateral MATH includes the points M(2,-4) and A(5,-2).
Part A: Find coordinates for T and H such that quadrilateral MATH is a rectangle.
Part B: Prove that the resulting quadrilateral is a rectangle.
18
a) The coordinates for T and H such that quadrillateral MATH is a rectangle are T(x, y) = (2, - 2) and H(x, y) = (5, - 4).
b) The quadrilateral MATH is a rectangle.
How to create and analyze quadrillateral on a Cartesian plane
Quadrilaterals are figures with four sides and whose internal angles sums a total of 360 degrees. A quadrilateral is a rectangle when each pair of opposite sides are parallel and have the same length to each others, each of the four angles are right angles and each pair of perpendicular sides.
a) Vectorially speaking, we can construct a rectangle by using the following definitions:
M(x, y) = (a, b), A(x, y) = (c, d), T(x, y) = (a, d), H(x, y) = (c, b)
If we know that a = 2, b = - 4, c = 5, d = - 2, then the points T and H are described below:
T(x, y) = (2, - 2), H(x, y) = (5, - 4)
The coordinates for T and H such that quadrillateral MATH is a rectangle are T(x, y) = (2, - 2) and H(x, y) = (5, - 4).
b) To prove that quadrilateral MATH, we need to prove that:
MT = HA
(2, - 2) - (2, - 4) = (5, - 2) - (5, - 4)
(0, 2) = (0, 2)
TA = MH
(5, - 2) - (2, - 2) = (5, - 4) - (2, - 4)
(3, 0) = (3, 0)
MT • TA = 0
(0, 2) • (3, 0) = 0 · 3 + 2 · 0 = 0
MH • HA = 0
(3, 0) • (0, 2) = 3 · 0 + 0 · 2 = 0
Therefore, the quadrilateral MATH is a rectangle.
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PLS HELP IM SO STUCK
3x-2y= 7
Slope intercept form y= mx+b
3x- 2y= 7
- 3x -3x
-2y/-2= 3x/-2 - 7/2
y= 3x/-2 -7/2
Answer:
3x/2 and the second 7/-2y
Step-by-step explanation:
thats how is what i got
what is the equivalent expression (3*5)^6=?
Answer:
15^6
Step-by-step explanation:
According to BODMAS
where;
B - Bracket ()
O - Off (*)
D - Division (/)
M - Multiplication (*)
A - Addition (-)
S - Subtraction (+)
Bracket should be solved first
therefore;
(3*5)^6
15^6 = 11390625
Which can be approximately in standard form written as 1.1*10^7
Thirty percent of high-school senior boys play in the school band. If a certain high school has 60 senior boys, how many boys play in the school band?
(A) 12
(B) 18
(C) 22
(D) 30
Write a series of instructions that will multiply eax by 18, using a combination of shift, mov, and add instructions
MOV EBX,EAX
SHL EAX,4
SHL EBX,1
ADD EAX,EBX these are the series of instructions that will multiply eax by 18, using a combination of shift, mov, and add instructions.
STEPS:
1. Copy EAX into another register, say EBX
2. We know that shift left by 'n' bits results in multiplication with 2^'n' , so perform shift left operation of EAX by 4 bits ( results in multiplication of EAX with 16) and perform shift left operation of EBX by 2 bits(results in multiplication of EBX with 2)
3. Now add EAX and EBX which is the required answer ( Since, i*16 + i*2 equals to i*18 )
INSTRUCTIONS:
mov ebx,eax ; make copy
shl eax,4 ; eax * 16
shl ebx,1 ; ebx * 2
add eax,ebx ; answer
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PLSSS
C= [tex]\frac{12^{3} . 6^{5} }{9^{4} . 2^{10}}[/tex]
Answer:
2
Step-by-step explanation:
The trick here is to reduce each of the bases to lowest form first
[tex]12 = 3.4 = 3 .2.2 = 3.2^{2}\\12^{3} = (3.2^{2} )^{3} = 3^{3}2^{6} \\6 = 3.2\\6^{5} = (3.2)^{5} = 3^{5} .2^{5} \\\\Numerator = 3^32^63^52^5 = 3^82^{11}\\Denominator computation\\9 = 3^2\\9^{4} = (3^{2} )^4 = 3^{8} \\Denominator = 3^82^{10} \\\\\frac{Numerator}{Denominator } =\frac{{3^8}{2^{11} }}{3^82^{10}} = \frac{2^{11}} {2^{10}} = 2^1 = 2[/tex]
what is 5/8 divided by 1/2?
Answer:
5/4
Step-by-step explanation:
(5/8)(2/1)
(Reciprocal of 1/2 is 2/1 as shown above)
(5)(2)/(8)(1)=10/8
10/8=5/4
