Answer:
~ 220.6
Step-by-step explanation:
sine rule : a/sinA =b/sinB = c/sinC
AB/sinC =BC/sinA
A = 180 - 110.2 - 13.5 = 56.3 degrees
AB/sin13.5 = 786/sin56.3
AB = 786sin13.5/sin56.3 = 220.5506
The distance across the river of AB is 220.55 m.
What is Law of Sines?Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.
That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,
a / sin A = b / sin B = c / sin C
Given a triangle ABC.
We have,
∠B = 110.2° and ∠C = 13.5°
We know that the sum of the interior angles of a triangle is 180°.
∠A = 180 - (110.2 + 13.5) = 56.3°
Using the law of sines,
BC / Sin A = AB / Sin C
Substituting the values,
786 / sin (56.3°) = AB / sin (13.5°)
AB = (786 / sin (56.3°)) sin (13.5°)
= 220.55 m
Hence the distance is 220.55 m.
Learn more about Law of Sines here :
https://brainly.com/question/13098194
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The van traveled 120 miles in 7 hours. How long would it take to travel 1400 miles at the same speed? (A) 5/3 hrs (B) 81 2/3 hrs (C) 49/6 hrs (D)24000 hr
Answer:
[tex]81\frac{2}{3}[/tex] hours
Step-by-step explanation:
Hi there!
1) Create a proportion
The van traveled 120 miles in 7 hoursThe van travels 1400 miles in x hours[tex]\frac{7h}{120mi}=\frac{x}{1400 mi}[/tex]
[tex]\frac{7}{120}=\frac{x}{1400}[/tex]
2) Solve for x
[tex]\frac{7}{120}=\frac{x}{1400}[/tex]
Multiply both sides by 1400
[tex]\frac{7}{120}*1400=\frac{x}{1400}*1400[/tex]
[tex]\frac{245}{3} =x[/tex]
[tex]\frac{245}{3} =x[/tex]
[tex]81\frac{2}{3} =x[/tex]
Therefore, it would take the van [tex]81\frac{2}{3}[/tex] hours to travel 1400 miles at the same speed.
I hope this helps!
here is another question can u help.
Answer:
The answer is (0,2)
Step-by-step explanation:
The second quadrant or Quadrant II has coordinates that are ALL positive.
(my favorite quadrant)
The coordinates would look like (4, 5) or (19, 69) and so on.
Write these sums as decimals:
2/100 + 3/1,000 =
1/10 + 4/10,000 =
Answer:
1 ) 0.023
2 ) 0.1004
Step-by-step explanation:
2 / 100 + 3 / 1000
= 0.02 + 0.003
= 0.020 + 0.003
= 0.023
1 / 10 + 4 / 10,000
= 0.1 + 0.0004
= 0.1000 + 0.0004
= 0.1004
Every bottle of supercharge vitamins contains 50 vitamins. Let v be the total number of vitamins and let b be the number of bottles.
Answer:
The answer is "[tex]v = \frac{50b}{v} = 50 \times b[/tex]".
Step-by-step explanation:
A single bottle of supercharging includes the equivalent of 50 vitamins.
Number of vitamins v = Total number of vitamins
b = the number of bottles that were used
Because each bottle contains one vitamin, you should multiply this total number of bottles (b) by the total amount of vitamins (50 vitamins).
[tex]v = \frac{50b}{v} = 50 \times b[/tex] so, Both are the same.
Answer:
i just did it- here ya go
Step-by-step explanation:
Algebra is confusing !! :(
Answer:
Step-by-step explanation:
Hello!
x²-4 = 5*5-4= 21
3x= 3*5 = 15
21/15 = 1,4
Answer: Fourth Choice. 1.4
Step-by-step explanation:
Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
Given
(x² - 4) / 3x
x = 5
Substitute the value of x
[(5)² - 4) / 3(5)
Simplify exponents
(25 - 4) / 3(5)
Simplify numerator with subtraction and denominator with multiplication
21 / 15
Simplify by division
7/5 = 1.4
Hope this helps!! :)
Please let me know if you have any questions
can someone help asap
This year, a small business had a total revenue of $42,900 . If this is 35% less than their total revenue the previous year, what was their total revenue the previous year?
if this value 35% less than the total, we conclude that:
42,900 = 65%
1% = 660
100% = 66,000
if you want to check the value, just do 65% of 66000, which equals to 42,900
hope it helps :)
below are properties of a square which one is not a all sides are equal b all angles are right angles C has five interior angles d diagonals are equal
Answer:
has five interior angles
a square is a quadrant meaning it has four interior angles
5th term of f(n)=3+2n
5th term of f(n)=3+2 5+_74+4-&;4-(4!
Step-by-step explanation:
5th term of f(n) = 3+ 2n
put n = 5
f(5) = 3 + 2 × 5
f(n) = 3+ 10
f(n) = 13
find the image of O(-1, -3) after two reflections, first in the line y = -2, and then in the line x = -2
Answer:
The image of point O after these reflections is (-3, -1)
Step-by-step explanation:
For a point (x, y) a reflection across the line y = a transforms the point to:
(x, a + (a - y))
and for a reflection across the line x = b, the new point will be:
(b + (b - x), y)
Then if we start with the point (-1, -3) and we do a reflection across the line y = -2
the new point is:
(-1, -2 + (-2 - (-3))
(-1, -2 + 1) = (-1, -1)
now we do a reflection across the line x = -2
Then the new point is:
(-2 + (-2 - (-1)), -1)
(-2 + (-2 + 1), -1)
(-2 - 1, -1)
(-3, -1)
The image of point O after these reflections is (-3, -1)
Ryan loves collecting keychains from his family vacations. He currently has 15 keychains in his collection and wants to add 5 keychains each year. How many keychains will be in his collection in 18 years?
A model of the Saturn V rocket has a scale of 1 inch = 12 feet. If the model rocket is 30 inches tall, how tall was the actual Saturn V rocket
Answer:
360 feets
Step-by-step explanation:
Given :
Scale : 1 inch = 12 feets
This means 1 inch on paper (model) represents 12 feets in real life
If the model height = 30 inches ;
The actual height of the Saturn V rocket will be :
1 inch = 12 feets
30 inch = x
x = (30 * 12)
x = 360 feets
Actual height = 360 feets
Which of the following are equations for the line shown below? Check all that
apply.
(-2,5)
5+
-5
5
(2,-3)
A. Y-5 = -2(x + 2)
B. y = -2x + 1
O c. y + 3 = -2(x - 2)
D. y = -2x - 7
c) y= -2x +1
Step-by-step explanation:
y= -2x +1
m= (- 3 -5)/2+2
= -2
c=1
y-(-3)= -2(x-2)
y= -2x +4 -3
y = -2x+1
Solve for 2. Round to the nearest tenth, if necessary.
B
X
A
7.9
154
Answer: <=
Submit Answer
attempt 1 out of 2
Answer:
x = 10.9
Step-by-step explanation:
Since this is a right triangle, we can us trig functions
tan theta = opp / adj
tan 54 = x / 7.9
7.9 tan 54 = x
x=10.87341
Rounding to the nearest tenth
x = 10.9
find the largest value :
A=5-x^2+2x
Answer:
6
Step-by-step explanation:
A=5-x^2+2x
Rewriting
A = -x^2 +2x+5
This is a downward opening parabola so the maximum value is at the vertex
Factor out the negative sign out of the first two terms
A = -(x^2 -2x) +5
Complete the square
-2/2 = -1 -1^2 = 1
Add 1 inside the parentheses Remember the negative sign out front so -1(1) is really adding -1 so we need to add 1 outside of the parentheses
A = -(x^2-2x+1) +1 +5
A = -(x-1)^2 +6
This is in vertex form
y = a(x-h)^2 +k where (h,k) is the vertex
The maximum occurs at x=h and the value is k
The maximum is 6
The cost of tickets of a comedy show of 'Gaijatra' is Rs 700 for an adult and Rs 500 for a child. If a family paid Rs 3,100 for 5 tickets, how many tickets were purchased in each category?
Answer:
Step-by-step explanation:
We need to create a system of equations here, one for the NUMBER of tickets sold and one for the COST of the tickets. They are very much NOT the same thing.
We have that the total number of tickets is 5, and that that total is made up of adult tickets and child tickets. The equation for the NUMBER of tickets, then, is:
a + c = 5
Now for the money.
If a child ticket costs Rc 500, the expression that represents that that is in fact the cost of the child ticket is 500c;
likewise for the adult ticket. If the adult ticket costs Rc 700, the expression that represents that is 700a.
And we know that a total of Rs 1300 was spent on the tickets. The equation for the COST is
700a + 500c = 1300
Now go back to the first equation and solve it for either a or c, it doesn't matter which. I solved for a:
a = 5 - c and we will sub that into the second equation for a:
700(5 - c) + 500c = 1300 and
3500 - 700c + 500c = 1300 and
-200c = -400 so
c = 2 tickets. That means that there were
a = 3 tickets sold for the adults.
The cars get miles to the gallon. After the car has traveled miles. 2 2/3 gallons of gas has been consummed
Answer:
80 miles
Step-by-step explanation:
Please find attached the graph used in answering this question
On the graph, the distance travelled is on the vertical axis while the gallons consumed in on the horizontal axis
from the graph, the following can be deduced :
0 gallons is consumed when the car travels 0 mile
1 gallon is consumed when the car travels 30 miles
2 gallons is consumed when the car travels 60 miles
total mile travelled when the gallons consumed is : 2 2/3 x 30
8/3 x 30 = 80 miles
the perimeter of the shape is
Answer:
94 cm.
Step-by-step explanation:
Perimeter = 25 + 2(10) + + 2(12) + 25
= 50 + 20 + 24
= 94 cm.
Plz see attachment below
Answer:
Step-by-step explanation:
Table I
Given function is,
f(x) = [tex]b^x[/tex]
From the table attached,
For x = 0.827, value of function f(0.827) = 5,
f(0.827) = [tex]b^{0.827}[/tex]
Therefore, [tex]b^{0.827}=5[/tex]
[tex]\text{log}(b^{0.827})=\text{log}(5)[/tex]
0.827[log(b)] = log(5)
log(b) = 0.8452
b = [tex]10^{0.8452}[/tex]
b = 7
Therefore, function 'f' will be,
f(x) = [tex]7^x[/tex]
For f(x) = 9,
9 = [tex]7^x[/tex]
log(9) = log([tex]7^x[/tex])
log(9) = x[log(7)]
x = 1.129
Table II
Given function is g(x) = [tex]\text{log}_b(x)[/tex]
From the given table,
For x = 7, g(x) = 1
1 = [tex]\text{log}_b(7)[/tex]
[tex]b^1=7[/tex]
b = 7
Therefore, the function 'g' will be,
g(x) = [tex]\text{log}_7(x)[/tex]
For g(x) = 1.318
1.318 = [tex]\text{log}_7(x)[/tex]
[tex]x=7^{1.318}[/tex]
[tex]x=12.9968[/tex]
[tex]x=13.997[/tex]
Find the vertex of the following equation: y = -0.25x2 + -1.5x + 6
Hi there!
[tex]\large\boxed{(-3, 8.25)}[/tex]
Solve for the vertex by completing the square:
y = -0.25x² - 1.5x + 6
Factor out a negative:
y = -(0.25x² + 1.5x) + 6
Remember that a square binomial is:
a² + 2ab + b²
We know that:
a² = 0.25, so a = 0.5
1.5 = 2ab, so:
1.5 = 2(0.5)b
b = 1.5
b² = 2.25
Thus:
y = -(0.25x² + 1.5x + 2.25) + 6 - (-2.25)
Simplify:
y = -(0.5x + 1.5)² + 8.25
Find the vertex by factoring out 0.5:
y = -0.5(x + 3)² + 8.25
Thus, the vertex is:
(-3, 8.25)
a teacher writes the following product on the board (3x) (x^2+6) = 3x^3 + 18x Eduardo says that 3x^3 + 18x is a factor of 3x
Your answer is attached above. hope it helps
20 points lovelys <3
Answer:
A) 2 cm
Step-by-step explanation:
By definition, regular polygons have equal sides and angles. Therefore, each side of the regular hexagon must be equal. Since one side is marked as 2 cm, the length of PQ must also be 2 cm.
Does the graph represent a linear expression?
Yes or No
Please answer fast!
Can anyone help me with this pls :)
THIS IS TIMED! Find the equation of the graphed line.
On a coordinate plane, a line goes through (negative 6, 0) and (0, negative 7).
a.
y = negative 6 x minus 7
c.
y = negative StartFraction 6 Over 7 EndFraction x minus 6
b.
y = 6 x minus 7
d.
y = negative StartFraction 7 Over 6 EndFraction x minus 7
Please select the best answer from the choices provided
A
B
C
D
Answer:
D
Step-by-step explanation:
x/(-6)+y/(-7)=1
7x+6y=-42
7x+6y+42=0
y=(-7/6)x-7
find the 10 degree value can u help me on it
Solution:-10
As <AGQ and <EQG are corresponding interior angles
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 60°+a=180[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow a=180-60[/tex]
[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow a=120}[/tex]
<AGQ=<PQR=60°<BHF=<PRQ=75°[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow b=75°}[/tex]
According to angle sum property
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow b+c+<PQR=180[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c+75+60=180[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c+135=180[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c=180-135[/tex]
[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow c=45°}[/tex]
help me fast pleaseee
Answer:
A
Step-by-step explanation:
The answer is A. Answered by Gauthmath
If I can read 10 pages in 50 minutes, how many pages will I read in an hour and a half
Answer:
18 pages
Step-by-step explanation:
that means you can read 2 pages in 10 minutes.
an hour and a half is 90 minutes.
90 is 9 times more than 10.
so we do 2 * 9 = 18 pages
What is the slope of the line that passes through (-4,5) and (2,-3)
Answer:
solution,
(X1,y1)= (-4,5)
(X2,Y2)=(2,-3)
slope of the line(m)= y2-y1/x2-x1
=-3-5/2-(-4)
=-8/6
=-4/3
A farmer has an orchard that covers an area of 40 acres. He grows apples on 25 acres, peaches on 7 acres, nectarines on 5 acres, and plums on 3 acres. The fruit trees are equally distributed within the orchard. A tree is chosen at random. Rounded to the nearest tenth of a percent, what is the theoretical probability that the tree is not within the acres of apple trees
Answer:
37.5%
Step-by-step explanation:
Calculation to determine the theoretical probability that the tree is not within the acres of apple trees
Using this formula
P=(Number of all orchard acres - Apple acres)/(Total orchard acres)*100
Where,
P represent Probability
Let plug in the formula
P=(40 acres- 25 acres)/40 acres
P=15 acres/40 acres *100
P=3/8*100
P=.375*100
P=37.5%
Therefore the THEORETICAL PROBABILITY that the tree is not within the acres of apple trees is 37.5%
Answer:
the answer is 37.5
Step-by-step explanation:
it is
