Answer:
The radius of the circle is 93.91
Step-by-step explanation:
In order to calculate the radius of this circle we can apply the formula to find the arc length. This formula is shown below:
length = [(angle)*pi*radius]/180
Since we want to find the radius we can isolate that variable, as shown:
(angle)*pi*radius = length*180
radius = (length*180)/(angle*pi)
radius = (12*pi*180)/(23*pi) = (12*180)/23
radius = 93.91
find the equation in standard form of the line passing through the points 3,-4 and 5,1
Answer:
5x - 2y - 23 = 0
Step-by-step explanation:
Line is passing through the points [tex] (3,\:-4)= (x_1, \:y_1) \: \&\: (5,\: 1)= (x_2,\:y_2) [/tex]
Equation of line in two point form is given as:
[tex] \frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \: \frac{y -( - 4) }{ - 4 -1} = \frac{x -3 }{3 -5 } \\ \\ \therefore \:\frac{y + 4 }{ - 5} = \frac{x -3 }{ - 2 } \\ \\ \therefore \: \frac{y + 4 }{ 5} = \frac{x -3 }{ 2 } \\ \\ \therefore \: 2(y + 4) = 5(x - 3) \\ \therefore \: 2y + 8 = 5x - 15 \\ \therefore \: 5x - 15 - 2y - 8 = 0 \\ \red{ \boxed{ \bold{\therefore \: 5x - 2y - 23 = 0}}} \\ is \: the \: required \: equation \: of \: line \: in \: \\ standard \: form.[/tex]
−15 ÷ 5 = A number line going from negative 30 to positive 30. An arrow goes from 5 to 10, from 10 to 15, from 15 to 20.
Emily used the number line to find the quotient for 15 ÷ 5. What errors did she make? Check all that apply.
A. The arrows should point in the negative direction.
B. The small arrows should end in the same place as the large one.
C. The arrows should end on negative 15.
E. The arrows should start at zero.
F. There should be 5 small arrows.
Answer:
-3
Step-by-step explanation:
-15 divided by 5= -3
Answer:
The answers are options A, C, and D
Step-by-step explanation:
A gift box is 12 inches long, 8 inches wide, and 4 inches tall. What is the volume of the gift box?
Answer: 384
Step-by-step explanation: 12x8x4=384
Answer:
V =384 inches^3
Step-by-step explanation:
The volume of a box is given by
V = l*w*h
V = 12*8*4
V =384 inches^3
What is the surface area of this design?
490in2
440in2
600in2
560in2
The answer is 440 in²
Here is what I added up!
25 + 4(40) + 4(20) + 100 + 75
I hope I helped :) Just comment if you have any questions and remember to vote me "brainliest" if you like my answer !!!
PLEASE ANSWER! IT'S SOO HARD FOR ME!!
a. Surya is competing in a triathlon that includes swimming, bicycling and running. For the first two segments of the race, Surya swam at an average rate of 4 kilometers per hour and bicycled at an average rate of 40 kilometers per hour. It took 81.75 minutes for Surya to swim and cycle a combined total of 43.29 kilometers, completing the first two segments of the race. How long, in minutes, did it take him to complete the swimming portion of the race? Express your answer to the nearest hundredth.
b. If an athlete who completes this triathlon swims, bicycles and runs a combined total of 52.95 kilometers, the distance the athlete swam is what percent of the total race distance? Express your answer as a percent to the nearest hundredth.
c. At what average rate, in kilometers per hour, must Surya run the third, and final, portion of the race if he wishes to complete the entire race in no more than 140 minutes? Express your answer to the nearest hundredth.
a) 18.68 minutes
b) 2.34%
c) 9.96 km/h
Step-by-step explanation:
a)
The velocity of Surya in the 1st segment (swimming part) is
[tex]v_1=4 km/h[/tex]
So, the distance covered by Surya in the swimming part is
[tex]d_1=4t_1[/tex]
where [tex]t_1[/tex] is the time taken to cover this part.
The velocity of Surya in the 2nd segment (biking part) is
[tex]v_2=40 km/h[/tex]
So the distance covered in the biking part is
[tex]d_2=40t_2[/tex]
where [tex]t_2[/tex] is the time taken to cover this part.
We know that the total distance covered in these 2 segments is
[tex]d=d_1+d_2=43.29[/tex]
So it can be rewritten as
[tex]4t1+40t_2=43.29[/tex] (1)
The total time taken to cover these two parts is
[tex]t=t_1+t_2=81.75 min =1.36 h[/tex]
So we have
[tex]t_2=1.36-t_1[/tex]
And substituting in (1) we can find t1:
[tex]4t_1 + 40(1.36-t_1)=43.29\\36t_1=11.21\\t_1=\frac{11.21}{36}=0.31 h = 18.68 min[/tex]
b)
The total distance covered in all 3 segments is
[tex]d=d_1+d_2+d_3=52.95 km[/tex]
where
where
d1 is the length of the swimming part
d2 is the length of the biking part
d3 is the length of the running part
We know that the distance covered in part 1 (swimming part) is
[tex]d_1=v_1 t_1 = (4)(0.31)=1.24 km[/tex]
Therefore we can find the percent that the swimming part correspond to the total race as:
[tex]\frac{d_1}{d}=\frac{1.24}{52.95}=0.0234 = 2.34\%[/tex]
c)
Here the total time taken by Surya for the race must be
[tex]t=140 min = 2.33 h[/tex]
And this is the sum of the times of the 3 segments:
[tex]t=t_1+t_2+t_3[/tex]
where
t1 is the time taken to complete the swimming part
t2 is the time taken to complete the biking part
t3 is the time taken to complete the running part
We know already that
[tex]t_1=0.31 h[/tex]
and
[tex]t_2=1.36-t_1=1.36-0.31=1.05 h[/tex]
So the time for the 3rd section must be
[tex]t_3=t-t_1-t_2=2.33-0.31-1.05=0.97h[/tex]
The distance to cover in the last part is
[tex]d_3=d-d_1-d_2=52.95-43.29=9.66 km[/tex]
So the average velocity of the last segment must be:
[tex]v_3=\frac{d_3}{t_3}=\frac{9.66}{0.97}=9.96 km/h[/tex]
What is the length of AC on the number line
According to the given question, the length of AC on the number line is 5 units
The length of AC on the number line can be determined by subtracting the coordinate of point A from the coordinate of point C. Let's say point A is located at coordinate 2 and point C is located at coordinate 7. To find the length of AC, we subtract the coordinate of A from the coordinate of C: 7 - 2 = 5
Therefore, the length of AC on the number line is 5 units. Another way to think about this is by considering the distance between the two points. In this case, the distance between point A and point C is the same as the length of AC. If you have any further questions, please, let me know.
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ILL GIVE YOU BRAINLIEST!! A survey of 500 people was taken regarding their favorite winter outdoor activity.The results are shown in the table below.
In a circle graph,what would be the measure of the central angle for snowmobiling?
A. 200°
B. 144°
C. 72°
D. 56°
E. 40°
Answer:
144°
If you look up 144° it matches exactly how it looks on a pie chart
I hope this helped
You randomly choose a marble from a jar. The jar contains 3 red marbles, 10
blue marbles, 8 green marbles, and 4 yellow marbles. Find the probability
of choosing a blue marble. *
The probability of choosing a blue marble is 2/5 or 0.4.
It is given that the jar contains 3 red marbles, 10 blue marbles, 8 green marbles, and 4 yellow marbles.
It is required to find the probability of choosing a blue marble.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have:
Number of total marbles = 3+10+8+4 ⇒25
Number of blue marble = 10
From the definition of the probability:
[tex]\rm Probability = \frac{Favourable \ outcomes}{Total \ outcomes}[/tex]
[tex]\rm Probability = \frac{10}{25}[/tex]
[tex]\rm Probability = \frac{2}{5 } \Rightarrow 0.4[/tex]
Thus, the probability of choosing a blue marble is 2/5 or 0.4.
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What polygon has 4 equal sides, 2 obtuse angles and 2 acute angles?
A.square
B.rectangle
C.trapezoid
D.fhombus
Three tanks, A, B and C are used to store oil.
Tank A contains n litres of oil. Tank B contains (n + 150) litres of oil.
Tank C is empty.
Oil is pumped from tank A and from tank B into tank C so that
all three tanks contain the same amount of oil.
500 litres of oil are pumped from tank A into tank C.
Work out the value of n.
Final answer:
To solve this problem, we set up a system of equations representing the amount of oil in each tank. Using the fact that all three tanks end up with the same amount of oil, we determine that Tank A must have started with 1000 litres of oil.
Explanation:
You need to find the value of n which represents the amount of oil initially in Tank A, given that 500 litres are pumped from Tank A to Tank C, and that Tanks A, B, and C eventually contain the same amount of oil.
After transferring 500 litres from Tank A to Tank C, Tank A will have n - 500 litres left. Since tank C was empty and now has 500 litres, Tank B must also transfer enough oil to Tank C such that both B and C have the same amount of oil. Tank B started with n + 150 litres and must end up with the same amount as tank C, which we will refer to as x.
Therefore, we need to solve the following system of equations:
Tank A: n - 500 = x
Tank B: n + 150 - x = x
Tank C: 500 = x
From Tank C's equation, we know that x = 500. Substituting this into the equations for Tanks A and B gives us:
Tank A: n - 500 = 500
Tank B: n + 150 - 500 = 500
From Tank A's equation, we see that n = 1000 litres.
What is the point-slope of a line that has a slope of -4 and passes through point(-3, 1)?
Answer:
y -1 = -4(x +3)
Step-by-step explanation:
The point slope form of a line is given by
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y -1 = -4(x --3)
y -1 = -4(x +3)
complete the number line model to find (-5) + 6.
Answer:
Step-by-step explanation:
Answer:
-11
Step-by-step explanation:
I think this is right
A sprinkler on a golf course is set to spray water over a distance of 75 feet and rotates through an angle of 135 degrees. Find the area of the fairway watered by the sprinkler
Answer:
6623.4375 feet²
Step-by-step explanation:
Distance is the radius
Area:
(135/360) × pi × r²
(135/360) × 3.14 × 75²
6623.4375 feet²
The area of the fairway watered by the sprinkler is 6,623.44 square feet
The shape of the golf course is a sector, Using the formula for calculating the area of a sector is expressed as:
[tex]A = \frac{\theta}{360} \times \pi r^2[/tex]
r is the radius = 75 feet[tex]\theta[/tex] is the angle subtended = [tex]135^0[/tex]Substitute the given parameters into the formula to have:
[tex]A=\frac{135}{360} \times 3.14 \times 75^2 \\A = \frac{2,384,437.5}{360}\\A= 6,623.4375ft^2[/tex]
Hence the area of the fairway watered by the sprinkler is 6,623.44 square feet
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Write 7 3/10 as an improper fraction
Answer:
73/10
Step-by-step explanation:
7*10+3/10=
70+3/10=
73/10
Your answer would be 73/10.
Step-by-step explanation:Think of it this way, each whole number counts as 10/10. So by using that, just do 10 * 7 / 10...
So you would get 70/10.
Then you would add on the left over 3/10 that you had at the beginning.
70/10 + 3/10 = 73/10
This would get your final answer of 73/10.
What is 17.043956 in decimal form
Answer:
17.043956
Step-by-step explanation:
Answer:
Step-by-step explanation:
17.043956 in decimal form
This is already in decimal form
Find the unit vector e which is collinear to vector a = (6,8) , and has the same direction.
the unit vector e which is collinear to vector a = (6,8) , and has the same direction is [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .
Step-by-step explanation:
Here we have , vector a = (6,8) . We need to find the unit vector e which is collinear to vector a = (6,8) , and has the same direction. Let's find out:
We know that for a vector [tex]a = (x,y)[/tex] the unit vector is given by :
⇒ [tex](\frac{x}{|a|} ,\frac{y}{|a|} )[/tex] , where |a| is modulus of vector a . So , Modulus of vector a is :
⇒ [tex]|a| = \sqrt{x^2+y^2}[/tex]
⇒ [tex]|a| = \sqrt{6^2+8^2}[/tex]
⇒ [tex]|a| = \sqrt{36+64}[/tex]
⇒ [tex]|a| = \sqrt{100}[/tex]
⇒ [tex]|a| =10[/tex]
Hence , unit vector is given by [tex](\frac{6}{10} ,\frac{8}{10})[/tex] or , [tex](\frac{3}{5} ,\frac{4}{5})[/tex] . Vector is already collinear as it's in same direction of original vector as :
⇒ [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex]
Therefore , the unit vector e which is collinear to vector a = (6,8) , and has the same direction is [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .
The area of a trapezium is 31.3cm if the parallel sides are of length 7.3cm and 5.3cm, calculate the perpendicular distance between them
Answer:
4.968 cm
Step-by-step explanation:
Given area of prism = 31.3 cm
This problem can be solved by using formula to calculate area of trapezium which is given below
Formula to calculate area of prism =( sum of parallel sides * perpendicular distance between parallel side )/2
let the perpendicular distance between parallel side = X
sum of parallel sides = 7.3+5.3 = 12.6 cm
Therefore by using formula
31.3 = (7.3+5.3)*X/2
=> 31.3 * 2 = 12.6*X
=> X = 62.6/12.6 = 4.968
Hence perpendicular distance between parallel side is 4.968 cm
i will mark Brainliest plzz help
1: 7x - 2 = 8 + 2x
2: 4 ( 3a + 1 ) = 3a + 22
3: 75 + 5 ( 2-5 ) = -10
4:a - 3 (2a) = -25
Answer:
1.7x-2=8+2x
Step-by-step explanation:
collect like terms
7x-2x=8+2
5x=10
divide 5 both sides to get the value of x
5x/5=10/5
x=2
Answer:
1. x = 2
2. a = 2
4. a = 5.
Step-by-step explanation:
1. 7x - 2 = 8 + 2x
7x - 2x = 8 + 2
5x = 10
x = 2.
2. 4 ( 3a + 1 ) = 3a + 22
12a + 4 = 3a + 22
12a - 3a = 22 - 4
9a = 18
a = 2.
4. a - 3(2a) = -25
a - 6a = -25
-5a = -25
a = 5.
( I couldn't do number 3 because there is no variable in the equation).
2/3 of a number is -6 find the number
Answer:
-12
Step-by-step explanation:
-6 times 3 is -18 and 2/3 of -18 is -12
The measures of the angles in A ABC are given by the expressions in the table
Angle
Measure
(3x - 10)
(2x)
Find the value of x. Then find the mZB and mZC
Enter your answers in the boxes.
mZB=
0
mZC=
Answer:
3x
Step-by-step explanation:
Using the triangle sum theorem the following are the missing values:
x = 25
m∠B = 65°
m∠C = 50°
What is the Triangle Sum Theorem?According to the triangle sum theory, all the interior angles of a triangle will add up to 180 degrees.
Given:
m∠A = 65°
m∠B = (3x - 10)°
m∠C = (2x)°
Therefore:
65 + 3x - 10 + 2x = 180
Combine like terms
55 + 5x = 180
5x = 180 - 55
5x = 125
x = 125/5
x = 25
m∠B = (3x - 10)° = 3(25) - 10 = 65°
m∠C = (2x)° = 2(25) = 50°
Therefore, using the triangle sum theorem the following are the missing values:
x = 25
m∠B = 65°
m∠C = 50°
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The range of F(x) = logbx is the set of all positive real numbers.
O A. True
O B. False
The statement about the range of the logarithmic function F(x) = log_bx being positive real numbers is false; the range includes all real numbers.
The statement that the range of F(x) = logbx is the set of all positive real numbers is False. The range of a logarithmic function like F(x) = logbx, where b is the base and x is the argument, is actually all real numbers, not just the positive ones. This is because you can take the log of any positive number, but the result can be any real number, negative, positive, or zero (when x=1).
For example, if the base b is greater than 1, as x approaches zero from the positive side, logbx will approach negative infinity, illustrating how the range includes negative numbers.
Jason walks 1/2 of a mile in 1/3 of an hour. If he walks at the same rate, how many miles does Jason walk each hour
Answer:
He would walk 1 1/2 a mile. Hope that helps
Step-by-step explanation:
What is y = -3(x – 7)(x + 3) in standard form?
Answer:
y=-3x^2+12x+63
Step-by-step explanation:
y=-3(x-7)(x+3)
y=-3(x^2-4x-21)
y=-3x^2+12x+63
10. The ages of participants in a relay race are 12.15, 14, 13, 15, 12, 22. 16, and
Identify the outlier in the data set. Determine how the outlier affects the
mean, median, and mode of the data. Then tell which measure of center best
describes the data with and without the outlier.
Please help with number 10 !!!!!! 40 points
Answer:
mean id 45.6
we get it by adding then subtracting
Which function is equivalent to f(x)=-4(x+7)^2-6
Answer:
f(x) = - 4x² - 56x - 202
Step-by-step explanation:
We can simplify this quadratic function given in vertex form into standard form by simplifying the exponents and adding like terms.
f(x) = -4(x+7)^2 - 6
f(x) = -4(x^2 + 14x + 49) - 6
f(x) = -4x² - 56x - 196 - 6
f(x) = -4x² - 56x - 202
Answer: b
Step-by-step explanation: just took the quiz on egde.
The diameter of the wheel is 22 inches what is the circumference of the world use 3.14 for pie
Answer:
69.08 inches
Step-by-step explanation:
Circumference of the wheel
= 2 pi r
Given
Pi = 3.14
Radius r = diameter/2 = 22/2
= 11
Therefore
Circumference = 2 x 3.14 x 11
= 69.08 inches
Dividing exponents in this equation
Answer:
18x^5y
Step-by-step explanation:
Divide 36 by 2 first : 18
since you are dividing, you subtract the exponents:
x^8 - x^3= x^5
y^4-y^3= y^1 but you usually just write y
Dividing exponents in this equation [tex]\frac{36x^{8}y^{4} }{2x^{3} y^{3} }[/tex] is [tex]18x^{5} y[/tex]
How can the expression be simplified?
A mathematical action called an exponent, sometimes referred to as a power, is the result of repeatedly multiplying a base number by itself. A little number or variable to the right and above the basic number serves as a symbol for it. For instance, in the notation 2^3, the base and exponent are 2 and 3, respectively, denoting three times the product of 2 and itself: 2^3 = 2 x 2 x 2 = 8.
Given that;
[tex]\frac{36x^{8}y^{4} }{2x^{3} y^{3} }[/tex]
Divide 36 by 2 first : 18
[tex]\frac{18x^{8}y^{4} }{x^{3} y^{3} }[/tex]
=[tex]18x^{5} y[/tex]
What is the length of each side ?
Answer:
36.3
Step-by-step explanation:
145.2/4 = length of each side
145.2/4 = 36.3
[PLEASE HELP] The area of Bethany's garden will be 48 square feet once she expands it. She is not going to change the measurement on one side, but the other side will be 8 feet longer than before. The equation that models this situation and can be used to determine the possible dimensions of Bethany's garden is x^2 +8x -48. Factor to determine the possible dimensions of Bethany's new garden.
Final answer:
To find Bethany's expanded garden dimensions, we factored the quadratic equation x² + 8x - 48 = 0 to find that the original dimension is 4 feet, resulting in the new dimensions of 4 feet by 12 feet.
Explanation:
The student is tasked with finding the possible dimensions of Bethany's expanded garden, which will have an area of 48 square feet. The side lengths of the new garden are related by the fact that one side will be 8 feet longer than the other. We can use the given quadratic equation x² + 8x - 48 = 0 to model this situation.
Step-by-Step Factoring
First, we identify the coefficients in the equation, which are A=1 (coefficient of x²), B=8 (coefficient of x), and C=-48 (constant term).
To factor the quadratic equation, we look for two numbers whose product is A*C (-48) and whose sum is B (8). These numbers are 12 and -4.
Rewrite the middle term (8x) using the numbers found: x² + 12x - 4x - 48 = 0.
Factor by grouping: (x² + 12x) - (4x + 48) = 0 becomes x(x + 12) - 4(x + 12) = 0.
Factor out the common factor: (x - 4)(x + 12) = 0.
Solve for x: x = 4 or x = -12. Since a garden's dimensions must be positive, we disregard the negative solution. This leaves us with x = 4 feet as the original dimension and x + 8 = 12 feet as the expanded dimension.
Thus, the dimensions of Bethany's new garden are 4 feet by 12 feet.
Suponiendo que el movimiento de un cuerpo se interpreta según la ecuación:
Y=3t²-2 determina la velocidad media considerando los 5 primeros segundos de caida
Answer:
Average speed = 15
Step-by-step explanation:
To find the speed of the body, we can take the position equation and take the derivative in relation to time:
Speed = dY/dt = 2*3*t = 6t
Then, we need to find the speed at t=0 and the speed at t=5:
Speed(t=0) = 6*0 = 0
Speed(t=5) = 6*5 = 30
Now, we just need to make the average of both speeds:
Average = (0 + 30) / 2 = 15