The radius of the sector is 10.27 miles
How to find the radius of a sector?The area of a sector can be represented as follows;
area of a sector = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
∅= 25 degrees
area of the sector = 23 miles²
area of a sector = ∅ / 360 × πr²
23 = 25 / 360 × πr²
cross multiply
23 × 360 = 25πr²
8280 = 25πr²
divide both sides by 25
πr² = 8280 / 25
πr² = 331.2
r² = 331.2 / 3.14
r² = 105.477707006
r = √105.477707006
r = 10.2702336877 miles
Therefore, the radius of the sector is 10.27 miles
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In a local shop some items are being sold at a third off. They now cost the following amounts. What was the original full price? 40 POINTS AND BRAINLIEST
1.£6.46
2.£58.24
3.£114.28
4.£12.50
5.£10.86
Answer:
1) 9.69
2) 87.36
3) 171.42
4) 18.75
5) 16.29
Step-by-step explanation:
Treat each value's full price as x. then, all of the values are (2/3)x. To get (2/3)x back to x, we must multiply (2/3)x*(3/2)=x. Multiply each of the questions given by 3/2 or 1.5
20 PTS! Please Help!!!! Will Give Brainliest!! This is a Khan Academy Problem!!!
Find the approximate perimeter of pentagon ABCDE plotted below. A(0,7) B(6,0) C(3,-4) D(-3,-4) E(-6,0)
Using it's concept, the approximate perimeter of pentagon ABCDE is given as follows:
34.4 units.
What is the perimeter of a figure?The perimeter of a figure is given by the sum of the lengths of it's outside dimensions.
In this problem, the vertices are in a coordinate-plane, hence the distances are found using the formula for the distance between two points.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The length of segment AB is:
[tex]AB = \sqrt{(6 - 0)^2+(0 - 7)^2} = 9.2[/tex]
The length of segment BC is:
[tex]BC = \sqrt{(6 - 3)^2+(0 + 4)^2} = 5[/tex]
The length of segment CD is:
[tex]CD = \sqrt{(-3 -3)^2+(-4 + 4)^2} = 6[/tex]
The length of segment DE is:
[tex]DE = \sqrt{(-6 + 3)^2+(0 + 4)^2} = 5[/tex]
The length of segment EA is:
[tex]EA = \sqrt{(-6 +0)^2+(0 - 7)^2} = 9.2[/tex]
Hence the perimeter is:
P = AB + BC + CD + DE + EA = 9.2 + 5 + 6 + 5 + 9.2 = 34.4 units.
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the x and y intercept
12 in.
14 in.
14 in.
Find the area of the figure above.
[?] square inches please explain how you got the answer for future questions
Answer:
168 square inches
Step-by-step explanation:
A = BH
or
Area = Base x Height
In other words multiply 12 and 14.
Resolver xfa... El taller trata de division de polinomios o algo asi
La altura del triangulo está dada por el polinomio:
p(x) = a + 4
¿Cual es la altura del triangulo?Recordar que para un triangulo de base B y altura H, el area es
A = B*H/2
En este caso, sabemos que la base es B = (4*a^2 + 6)
Y el area es A = 2a^3 + 8a^2 +3a +12
Entoces la altura será un polinomio tal que:
P(a)*(4*a^2 + 6)/2 = 2a^3 + 8a^2 +3a +12
P(a)*(4*a^2 + 6) = 2*(2a^3 + 8a^2 +3a +12) = 4a^3 + 16a^2 + 6a + 24
Podemos ver que p(a) va a ser un polinomio de grado 1, entonces:
p(a) = (c*a + b)
Reemplazando eso:
(c*a + b)*(4*a^2 + 6) = 4a^3 + 16a^2 + 6a + 24
Expandiendo:
(4c)*a^3 + (6c)*a + (4b)*a^2 + 6*b = 4a^3 + 16a^2 + 6a + 24
Comparando terminos del mismo exponente, podemos ver que:
(4c) = 4
6c = 6
4b = 16
6b = 24
Resolviendo esas ecuaciones para c y b, podemos ver que:
b = 16/4 = 4
c = 4/4 = 1
Entonces la altura del triangulo está dada por el polinomio:
p(x) = a + 4
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Suppose we are given the following information.
Line 1 passes through (0, 6) and (6, 4).
Line 2 passes through (-1, -7) and (1, -1).
Are these lines parallel, perpendicular, or neither?
Group of answer choices
Since the product of the slope is -1, hence the lines are perpendicular
Parallel and Perpendicular linesTwo lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1
Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;
Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3
Similarly for the coordinate points (-1, -7) and (1, -1).
Slope = -1+7/1+1
Slope of line 2 = 6/2
Slope = 3
Take the product of the slopes
Slope = -1/3 * 3
slope = -1
Since the product of the slope is -1, hence the lines are perpendicular
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Julie spent 6 hours on the phone in 2 days. How many hours will she spend on the phone in a week?
If the p-value is smaller than the level of significance, what conclusion should we reach?
If the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.
In this question,
A p-value is a probability, calculated after running a statistical test on data and it lies between 0 and 1. The p-value only tells you how likely the data you have observed is occurred under the null hypothesis.
One of the most commonly used p-value is 0.05. If the value is greater than 0.05, the null hypothesis is considered to be true. If the calculated p-value turns out to be less than 0.05, the null hypothesis is considered to be false, or nullified (hence the name null hypothesis).
A small p-value (< 0.05 in general) means that the observed results are unusual, assuming that they were due to chance only. Now, the smaller the p-value, the stronger the evidence that should reject the null hypothesis.
Hence we can conclude that if the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.
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Question 2 of 10 Based only on the information given in the diagram, it is guaranteed that PQR~ STU.
A. True B. False
please!? thanks!
The given statement is false because the triangles may not be identical if their corresponding angles are genuinely different.
What is the triangle?Three sides, three vertices, and three angles make up a triangle. A triangle's three interior angles are always added up to 180 degrees. A triangle's two longest sides are always longer than its third side. A triangle with the vertices P, Q, and R symbol is △PQR.Based only on the information given in the diagram, it is guaranteed that PQR~ STU:
Two right triangles, ΔPQR and ΔSTU—are shown in the illustration with their right angles at ∠P and ∠S, respectively.
It is also demonstrated that TU = 12 units and QR = 6 units.
Because we only provided one set of congruent angles, we are unable to apply the A postulate of similarity to it.
Additionally, since there is only one pair of comparable sides, we are unable to determine whether they are proportionate.
The statement "based purely on the information presented in the diagram, it is assumed that triangle PQR triangle STU" is False because the triangles may not be identical if their corresponding angles are genuinely different.
Hence, The given statement is false.
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Elliott is standing at the top of a store escalator that leads to the ground floor below. the angle of depression from the top of the escalator to the floor is 42.51°, and the escalator is 16 feet long. how far is the top of the escalator from the ground floor? round your answer to the nearest foot.
By using what we know about right triangles, we conclude that the height is 11ft.
How far is the top of the escalator from the ground floor?We can think of this as a right triangle.
Where the length of the escalator is the hypotenuse
We know that the angle of depression is 42.51°, then the top angle of our right triangle is:
90° - 42.51° = 47.49°
Now, the height of the top of the escalator would be the adjacent cathetus to said angle, then we can use the relation:
cos(a) = (adjacent cathetus)/(hypotenuse)
Replacing what we know:
cos(47.49°) = height/16ft
cos(47.49°) *16ft = height = 10.8ft
Rounding to the nearest foot, we get:
height = 11ft
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For each graph below,state whether it represents a function
Answer:
1. No
2. No
3. Yes
4. No
5. Yes
6. No
Step-by-step explanation:
If you want to check if a graph is a function, do a vertical line test. For every vertical line, there should be only 1 point on the line if the graph is a function.
Determine the size of the unknown angle to the nearest tenth of a degree.
tan Y : 0.2334
Also, two different questions down below.
Answer:
shown below
Step-by-step explanation:
1) tanY = 0.2334
Y = arctan(0.2334)
Y = 13.14 degrees
2) X = 12 / tan(40)
X = 14.3km
3) x = arctan(5/8)
x = 32°
Gwen and $660 per week and has 18% of this amount withheld for taxes Social Security and Medicare find amount withheld
Can the mixed number 7 and 13/100 be simplified?
Step-by-step explanation:
Reduce 13/100 to lowest terms
13
100
is already in the simplest form. It can be written as 0.13 in decimal form (rounded to 6 decimal places).
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 13 and 100 is 1
Divide both the numerator and denominator by the GCD
13 ÷ 1
100 ÷ 1
Reduced fraction:
13
100
Therefore, 13/100 simplified to lowest terms is 13/100.
The mixed number [tex]7\dfrac{13}{100}[/tex] is [tex]\dfrac{713}{100}[/tex] on simplification.
A mixed number is a mathematical representation of a number that consists of a whole number and a fraction. It's called a "mixed number" because it combines both a whole number and a proper fraction. The whole number part represents a whole quantity, while the fractional proportion represents a proportion of a whole.
Mixed numbers are generally employed to represent measures that aren't whole numbers but are still greater than 1. They're particularly useful when dealing with magnitudes, such as lengths or quantities of things, that concern both whole units and fractional parts.
Given that
[tex]7\dfrac{13}{100}[/tex] [tex]= 7 + \dfrac{13}{100}[/tex]
[tex]= \dfrac{700}{100}+ \dfrac{13}{100}\\= \dfrac{700+13}{100} \\= \dfrac{713}{100}[/tex]
Hence, The mixed number [tex]7\dfrac{13}{100}[/tex] can be simplified as [tex]\dfrac{713}{100}[/tex].
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The dashed triangle is the image of the solid triangle. The center of dilation is (6, 6).
What is the scale factor used to create the dilation?
Enter your answer as an integer or decimal in the box.
The two right triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 1. The vertical y-axis ranges from negative 10 to 10 in increments of 1. A dashed triangle has vertices at begin ordered pair 6 comma 6 end ordered pair, begin ordered pair 6 comma 9 end ordered pair, and begin ordered pair 9 comma 6 end ordered pair. A solid triangle has vertices at begin ordered pair 6 comma 6 end ordered pair, begin ordered pair 6 comma negative 9 end ordered pair, and begin ordered pair negative 9 comma 6 end ordered pair.
Answer:
The scale factor is 1/5.
Step-by-step explanation:
You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached. I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15. What do I need to multiple 3 by to get 15? 5. That is the scale factor from the little triangle to the big triangle. If I go the other way, the scale factor is the reciprocal of 5 or 1.5
you purchased 18.000 milliliters of juice. Juice costs $2 per liter. The cashier
ays you owe $12,000 for the juice, but you know that is not correct. Look at
the cashier's work and figure out how much you should pay. Explain what
he cashier did wrong.
18,000 + 3 = 6,000 liters
6,000 liters x $2 = $12,000
Answer:
cashier needed to divide by 1000, not 3.
Step-by-step explanation:
there are 1000ml in one liter. in order to find the amount of liters, youd have to divide the milliliters by 1000. its only after then that you can multiply by $2. answer would be $36
What equation represents a line that passes through points (-1,2) and (3,1)
4x - y = -6
X + 4y = 7
X - 4y = -9
4x + y = 2
Answer:
B.) x + 4y = 7
Step-by-step explanation:
(Step 1) ----------------------------------------------------------------------------------------------
To find the equation, we first need to find the slope using the point-slope form:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope, "x₁" and "y₁" represent the values from the first point, and "x₂" and "y₂" represent the values from the second point.
Point 1: (-1, 2) Point 2: (3, 1)
x₁ = -1 x₂ = 3
y₁ = 2 y₂ = 1
y₁ - y₂ = m(x₁ - x₂) <----- Point-slope form
2 - 1 = m(-1 - 3) <----- Insert values
1 = m(-4) <----- Subtract
-1/4 = m <----- Divide both sides by -4
(Step 2) ---------------------------------------------------------------------------------------------
The given equations are in the slope-intercept form. The general structure looks like this:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. To find the y-intercept, you can plug the newfound slope and values from one point into the equation.
x = -1
y = 2
m = -1/4
y = mx + b <----- Slope-intercept form
2 = (-1/4)(-1) + b <----- Insert values
2 = 1/4 + b <----- Multiply -1/4 and -1
8/4 = 1/4 + b <----- Make common denominators
7/4 = b <----- Subtract both sides by 1/4
(Step 3) ---------------------------------------------------------------------------------------------
The equation in slope-intercept form is thus: y = -1/4x + 7/4.
While this equation is accurate, it seems that it must be slightly manipulated. Therefore, we need to alter this equation to look like one of the answer choices. For instance, we can multiply the entire equation by 4 to remove the denominator.
y = -1/4x + 7/4 <----- Equation
4y = -x + 7 <----- Multiply all terms by 4
x + 4y = 7 <----- Add "x" to both sides
Identify ER rounded to the nearest tenth. The Figure shows right triangle M E R with right angle E. The length of hypotenuse M R is equal to 37 units. Angle R measures 61 degrees.
Answers;
a) ER ≈ 66.7
b) ER ≈ 32.4
c) ER ≈ 17.9
d) ER ≈ 22.3
Please give an explanation! :)
The value of length ER rounded to the nearest tenth is 17.9 units (Option C)
Trigonometric ratiosThe trigonometric ratios which has been proven as regarding right angle triangles are given below:
Sine θ = Opposite / Hypothenus
Cos θ = Adjacent / Hypothenus
Tan θ = Opposite / Adjacent
With above information in mind, we can easily determine the length of ER in the question. This is illustrated below:
How to determine the length of ERFrom the question given above, which is summarized in the diagram (see attached photo) the following data were obtained:
Hypothenus (MR) = 37 unitsAngle R = 61 °Adjacent (ER) = ?Since we looking for the Adjacent (ER), the best trig ratio to use is the Cos θ ratio. This can be obtained as illustrated below:
Cos θ = Adjacent / Hypothenus
Cos 61 = ER / 37
Cross multiply
ER = 37 × Cos 61
ER = 37 × 0.4848
ER = 17.9 units
Thus, the length of ER to the nearest tenth is 17.9 units
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What is the slope of a line perpendicular to the line whose equation is 3x + y = -9.
Fully simplify your answer.
Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is [tex]\frac{1}{3}[/tex].
Linear equationA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles.
Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseIn this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -3. So:
(-3)× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-3)
slope perpendicular line= [tex]\frac{1}{3}[/tex]
Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is [tex]\frac{1}{3}[/tex].
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Solve the inequality and enter your solution as an inequality comparing the variable to a number x+25>50
Let's solve your inequality step-by-step.
x+25>50
Step 1: Subtract 25 from both sides.
x+25−25>50−25
x>25
Answer:
x>25
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to make purple he must mix red and blue in ratio 5:3 if he uses 3.5 liters of red paint how much blue paint should he use
Answer:
2.1 litres
Step-by-step explanation:
the 5 part of the ratio refers to 3.5 litres of red paint
divide this amount by 5 to find the value of one part of the ratio
3.5 litres ÷ 5 = 0.7 litres ← value of 1 part of the ratio , then
3 parts = 3 × 0.7 litres = 2.1 litres ← amount of blue paint used
At the city museum, child admission is $6.20 and adult admission is $9.40. On Thursday, 163 tickets were sold for a total sales of $1221.80. How many adult
tickets were sold that day?
To form a system of equation from a word problem, we must recognize different variables to form different equations.
Solving the QuestionLet a represent the number of child tickets.
Let b represent the number of adult tickets.
We're given:
1a = $6.201b = $9.40a and b in total is 163Total sales = $1221.80Because we're given that a and b in total is 163, we can form the following equation:
[tex]a+b=163[/tex]
We're also given that the total sales made is $1221.80. Because we know that 1a = $6.20 and 1b = $9.40, we can also form the following equation:
[tex]6.2a+9.4b=1221.8[/tex]
Here are our two equations:
[tex]a+b=163[/tex]
[tex]6.2a+9.4b=1221.8[/tex]
Solving the System of EquationsWe can solve using the method of elimination. Multiply both sides by 6.2 in the first equation:
[tex]6.2(a+b)=6.2(163)\\6.2a+6.2b=1010.6[/tex]
Subtract this new equation from the second equation to cancel out a:
[tex]\hspace{10}6.2a+9.4b=1221.8\\- 6.2a+6.2b=1010.6\\\rule{100}{0.5}\\3.2b=211.2[/tex]
Solve for b:
[tex]b=66[/tex]
Therefore, the number of adult tickets sold is 66.
Answer66
Use the recursive formula to find the first five terms in the arithmetic sequence.
Answer:
3, 1, - 1, - 3, - 5
Step-by-step explanation:
using the recursive formula and f(1) = 3 , then
f(2) = f(1) - 2 = 3 - 2 = 1
f(3) = f(2) - 2 = 1 - 2 = - 1
f(4) = f(3) - 2 = - 1 - 2 = - 3
f(5) = f(4) - 2 = - 3 - 2 = - 5
first 5 terms are 3, 1, - 1, - 3, - 5
-0.8662866239 . . . is:
rational
irrational
Answer:
irrational, it can't be written as a fraction
Step-by-step explanation:
Volume=
Help me please thanks so much asap
Answer:
600
Step-by-step explanation:
since it is a right triangle based pyramid, 2 of them will make a cube. so, it is bwh / 2.
base = 24
width = 10
height = 5
volume = 1200
volume of pyramid = 600
does anyone know how to do this? pls help
Answer:
-3
Step-by-step explanation:
If you reflect over the y-axis and then move 2 units to the left(x-2), then ABCD will be 3 units above EHGF. Since you need to move it down 3 units to map ABCD onto EHGF, you will need to do y-3, which is the same as y+-3
What is the fiftieth term in the sequence 5, 7, 9, 11, 13 …?
The 15th term in the given A.P. sequence is a₁₅ = 33.
According to the statement
we have given that the A.P. Series with the a = 5 and the d is 2.
And we have to find the 15th term of the sequence.
So, for this purpose we know that the
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
And the formula is a
an = a + (n-1)d
After substitute the values in it the equation become
an = 5 + (15-1)2
a₁₅ = 5 + 28
Now the 15th term is a₁₅ = 33.
So, The 15th term in the given A.P. sequence is a₁₅ = 33.
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What is the solution to the system of equations?
y = A system of equations. y equals StartFraction one-half EndFraction x minus 6. x equals negative 4.x – 6
x = –4
The solution to the system of equations y = 1/2x - 6, x = -4 is x = -4 and y = -8. (x, y) = (-4, -8)
EquationThere are different types of equation. Namely;
Linear equationQuadratic equationSimultaneous equationy = 1/2x - 6
x = -4
Substitute x = -4 intoy = 1/2x - 6
y = 1/2(-4) - 6
= -4/2 - 6
= -2 - 6
y = -8
Therefore,
The solution to the system of equations y = 1/2x - 6, x = -4 is x = -4 and y = -8. (x, y) = (-4, -8)
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sketch graphs of the following on the same plane using different colours y=2x-3;y=-3;x=-3;2x+3y-6=0
The graph of the four linear equations is the one we can see below, such that:
Blue line is y = -3Green line is x = -3Orange line is y = 2x - 3Purple line is 2x + 3y - 6 = 0.How to graph the linear equations?
Here we have the set of linear equations:
y = 2x - 3y = -3x = -32x + 2y - 6 = 0We want to graph these 4 lines on the same coordinate axis.
The line:
y = -3
Is an horizontal line at y = -3
The line:
x = -3
Is a vertical line at x = -3.
And the other two are common linear equations that are graphed in the usual way, then the graph of all the linear equations is the one you can see below.
Where:
Blue line is y = -3Green line is x = -3Orange line is y = 2x - 3Purple line is 2x + 3y - 6 = 0.If you want to learn more about linear equations:
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if x : y = 0.75 : 0.90 and y : z = 1/3 : 1/4
(A) simplify the ratio x : y and y : z
(B) find x : y : z
Step-by-step explanation:
x:y=0.75:0.90
Here,
Dividing by the value of y=0.90,
x:y=0.75/0.90:0.90/0.90
=5/6:1
Similarly,
y:z=1/3:1/4
Dividing by 1/3,we get,
y:z=1:3/4
Now,
X:y:z=5/6:1:3/4
Multiplying by both value of y,0.90×1/3=3/10
x:y:z=5/6×3/10:1×3/10:3/4×3/10
By solving this,
x:y:z=1/4:3/10:9/40