Answer:
62.83 m²
Step-by-step explanation:
The area of the path is calculated as
area of outside circle - area of reservoir
= πr₁² - πr₂²
where r₁ is the radius of the outer circle and r₂ the radius of the reservoir
diameter of reservoir = 8 m, hence radius = 4 m
radius of outer circle = radius of reservoir + width of path = 4 + 2 = 6 m, thus
area of path = π × 6² - π × 4² = 36π - 16π = 20π ≈ 62.83 m²
40 POINTS Geometry - When you know the scale factor (e.g. 3), why does the point of dilation matter? Wouldn't each coordinate be multiplied by the scale factor no matter where it was dilated? (e.g. 3, 6 becomes 9, 12) Or am I missing something?
Hey!
Answer and Explanation:
When the scale factor is 1 and lower then that means its a reduction. When the scale factor is 1 and higher it's an enlargement.If (3, 6) becomes (9, 12) then the scale factor is not possible. Because when you divide you would get (2, 3).If you had (3, 6) and (6, 12) then the scale factor would be 2. Which is an enlargement.Hope This Helped! Good Luck!
NEED ASAP PLEASE!!!!!!!!!!
To find the answer first we make an equation. This equation works for both.
c+(a*y) where c = Current height, a = Annual growth and Y = Years of growth.
Substitute for the correct numbers.
For Tree A:
38+(4*y)
And for Tree B:
45.5+(2.5*y)
Then add some to find that both are the same in 5 years for 58 inches each.
Answer:
you might neees to see if thyeare not ggoing tose if thye are noty the same because is rh on thta thye could do all the smaet hinbg
Step-by-step explanation:
nect thing they could npt going and thye are
1. A rectangle has a length of 15 centimeters and a width of 8
centimeters. Which of the following is closest to the radius of a
circle that has an area equal to the area of the rectangle?
Answer: radius = 6.18 (I don't know what solutions you have, but the actual answer for the radius is about 6.18 cm so which ever is closest.)
Step-by-step explanation:
the area of a circle is \pi r^{2}
*rewrite your equation solving for radius
r=\sqrt{A/\pi } =\sqrt{120/\pi } = 6.18
To find the Radius of a circle with an area equal to the area of a rectangle, multiply the length and width of the rectangle to get its area, then use the formula A = πr² to solve for the radius.
To find the Radius of a circle with an area equal to the area of a rectangle, we need to find the area of the rectangle and then calculate the radius of the circle using that area.
The area of the rectangle is found by multiplying the length and width, which in this case is 15 cm * 8 cm = 120 cm².
The area of a circle is given by the formula A = πr², where A is the area and r is the radius. Since the area of the rectangle is equal to the area of the circle, we can set up the equation 120 cm² = πr².
Solving for r, we get r ≈ 6.94 cm (rounded to two decimal places).
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Find the side length s of the square.
Area = 441 cm
S=
cm
[tex]\huge\boxed{\text{21 cm}}[/tex]
The area of a square is equal to the square of its side length. [tex]A=s^2[/tex]
Substitute in the known variable. [tex]441=s^2[/tex]
Now, find the square root of each side of the equation. [tex]\sqrt{441}=s[/tex]
Find the square root of [tex]441[/tex]. [tex]\boxed{21}=s[/tex]
Write cos(arcsin3x +arccos x) as an algebraic expression of x that does not involve trigonometric functions.
Answer:
[tex]x \sqrt{1-9x^2} -3x \sqrt{1-x^2}[/tex]
Step-by-step explanation:
Since we have to analyze the cosine of an addition of angles, let's recall that cos of an addition is:
[tex]cos (\alpha +\beta ) = cos(\alpha ) cos(\beta) - sin(\alpha) sin(\beta)[/tex]
Let's also use those Greek letters [tex]\alpha[/tex] and [tex]\alpha[/tex] to represent the inverse functions we are dealing with:
[tex]\alpha =arcsin(3x)[/tex] and therefore, [tex]sin(\alpha ) = 3x[/tex]
[tex]\beta =arccos(x)[/tex] and therefore [tex]cos(\beta ) = x[/tex]
Now use these identities to re-write the equation for the cos of an addition given above:
[tex]cos (\alpha +\beta ) = cos(\alpha ) cos(\beta) - sin(\alpha) sin(\beta)\\cos (\alpha +\beta ) = cos(\alpha ) x - 3x sin(\beta )[/tex]
Now recall that the sine of an angle can be written in terms of the cos of the same angle via the Pythagorean identity: [tex]sin(\beta ) = \sqrt{1-cos^2(\beta) }[/tex]
In our case, and with our particular values, this gives:
[tex]sin(\beta ) = \sqrt{1-cos^2(\beta)} = \sqrt{1-x^2}[/tex]
Similarly we can write the cos of an angle in terms of the sine of the same angle:
[tex]cos(\alpha ) = \sqrt{1-sin^2(\alpha) }[/tex]
In ours case, using our values, this gives:
[tex]cos(\alpha ) = \sqrt{1-sin^2(\alpha) }= \sqrt{1-(3x)^2}= \sqrt{1-9x^2}[/tex]
So replacing these in the cos of an addition of angles formula, we obtain that the given expression equals:
[tex]x \sqrt{1-9x^2} -3x \sqrt{1-x^2}[/tex]
We can simplify the expression cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions by using sin(arccos(x)) = sqrt(1 - x^2). The simplified expression is sqrt(1 - (3x)^2) * x - 3x * sqrt(1 - x^2).
Explanation:To simplify the expression cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions, we can use the fact that sin(arccos(x)) = sqrt(1 - x^2). Let's start by finding sin(arccos(x)).
arccos(x) gives us an angle whose cosine is x. We can then take the sine of this angle to get sin(arccos(x)). We know that sin^2(arccos(x)) + cos^2(arccos(x)) = 1, so sin(arccos(x)) = sqrt(1 - x^2).
Now, let's substitute the values in the original expression:
cos(arcsin(3x) + arccos(x)) = cos(arcsin(3x)) * cos(arccos(x)) - sin(arcsin(3x)) * sin(arccos(x))
Substituting the values, we have: cos(arcsin(3x)) * cos(arccos(x)) - sin(arcsin(3x)) * sin(arccos(x)) = sqrt(1 - (3x)^2) * x - 3x * sqrt(1 - x^2)
This is the simplified expression of cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions.
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Help with this math homework
Answer:
5. 2
6. 51
7. X
Answer
For 5, the answer is 3
Step-by-step explanation:
Fibonacci Sequence: Start at 1
1+0=1
1+1=2
1+2=3
3+2=5
etc.
write a division sentence that divides a negative integer by a positive integer. Then write a multiplication sentence that proves your division sentence is correct.
Answer:RULE 1: The quotient of a positive integer and a negative integer is negative. RULE 2: The quotient of two positive integers is positive. RULE 3: The quotient of two negative integers is positive. If the signs are different the answer is negative.
Hope this helps
Step-by-step explanation:
We used -12 and 3 to demonstrate negative integer divided by a positive integer resulting in -4. We confirmed this by multiplying -4 by 3 to get -12 back.
Explanation:Let's use -12 and 3 as examples for a negative integer and a positive integer respectively. The division sentence would be -12 ÷ 3 = -4. To prove this division is correct using multiplication, you would multiply the quotient by the divisor. So, -4 * 3 = -12, which is equivalent to the dividend. Therefore, the multiplication shows the accuracy of the division.
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The figure shown is a rectangular prism. Which edges are perpendicular QE?
Select each correct answer
A. TQ
B. PR
C. RA
D. QP
E. EJ
The edges which are perpendicular to edge QE are TQ, QP and EJ. Thus, option (A), (D) and (E) are correct.
In a rectangular prism, the edges that are perpendicular to QE are those that intersect QE at right angles.
So, for an edge to be perpendicular to QE, it should be parallel to the other two edges of the rectangle that contains QE.
From the given options:
A. TQ: This edge is perpendicular to QE because it is parallel to the edges TP and EQ.
B. PR: This edge is not perpendicular to QE because it is parallel QE.
C. RA: This edge is not perpendicular to QE because it is parallel to QE.
D. QP: This edge is perpendicular to QE as it is parallel to the edges PQ and TE, not QE.
E. EJ: This edge is perpendicular to QE as it is parallel to the edges EK and QJ, not QE.
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Which of the following can be written as a fraction of integers? CHECK ALL THAT APPLY.
2.5
square root of 14
square root of 16
-1.25
5.333333...
pi
0.6
Answer:
2.5
√16,
-1.25,
5.33333...
0.6
Step-by-step explanation:
A decimal number can be written as the fraction of integers ( i.e. rational number ) if it is terminating or recurring non terminating,
2.5 is terminating decimal,
⇒ it can be written as a fraction of integers,
√14 = 3.7416573...... is not recurring non terminating decimal,
⇒ it can not be written as a fraction of integers,
√16 = 4 is an integer,
an integer can always written as a fraction of integers,
-1.25 is terminating decimal,
⇒ it can be written as a fraction of integers,
5.333333... is a recurring non terminating decimal,
⇒ it can be written as a fraction of integers,
[tex]\pi[/tex] = 3.14159265359.... is not recurring non terminating decimal,
⇒ it can not be written as a fraction of integers,
0.6 is terminating decimal,
⇒ it can be written as a fraction of integers
Determine the missing information in the paragraph proof.
Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).
Prove: The slopes of perpendicular lines are negative reciprocals.
The slopes of lines PQ and P’Q’ can be determined using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction
The product of these slopes is ________. This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.
Answer:
A) [tex](\frac{d-b}{c-a} )(\frac{c-a}{-d+b} )[/tex]
The product of these slopes is -1
Step-by-step explanation:
The slope of perpendicular lines are negative reciprocal.This means that when you multiply the two slopes you get -1.
To find slope of a line you apply;
m=change is y-axis values/change in x-axis values
Given that there are two lines, PQ and P'Q' then to find slope you follow;
Line PQ where P(a,b) and Q (c,d) slope,m= (d-b / c-a )
Line P'Q' where P'(-b,a) and Q'(-d,c) slope , m= ( c-a / -d+b)
Multiplying the two slopes
[tex]\frac{d-b}{c-a} *\frac{c-a}{-d+b} \\\\\\\frac{d-b}{-d+b} \\\\=-1[/tex]
Answer:
a
Step-by-step explanation:
took the test today
5. Jenny earns $30 a day working part time at a supermarket. Write an algebraic expression to
represent the amount of money she will earn in d days.
A 30d
B. 30
30
€ 30+ 0
D. None of the above
The algebraic expression to represent the amount of money Jenny will earn in d days, given that she earns $30 per day, is 30d.
Explanation:The question is asking to write an algebraic expression to represent the amount of money Jenny will earn working at a supermarket for a certain number of days, where she earns $30 per day. In algebra, we often use variables to represent unknown quantities. In this case, we will use d to represent the number of days.
In one day, Jenny earns $30. Therefore, to determine how much she earns in multiple days, we multiply the number of days by the amount she earns each day. If she works 'd' days, Jenny will therefore earn 30d dollars.
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Complete the steps to solve the equation 4e2 + 2x = x-3 by graphing.
1. Write a system of equations.
y = 4e2 + 2x and y =________
2. Graph the system. Use the graphing calculator to graph each equation.
3. Identify the solutions. The
_________ of the points where the graphs of the equations
intersect are the solutions to the original equation.
The equation 4e2 + 2x = x-3 has __________
Answer:
1. x-3
3. x -coordinates
has no solution
Step-by-step explanation:
Answer:
x-3
x -coordinates
has no solution
Step-by-step explanation:
Round 440.221281415 to 2 decimal places.
Answer:
440.22
Hope this helps you!
How do you solve this?
Answer:
Step-by-step explanation:
set it up like this
19x + 11 = 11x + 4
then self like algebra
19x + 11 -4 = 11x + 4 - 4
19x + 7 = 11x
19x -11x + 7= 11x -11x
8x ÷ 8 + 7 ÷ 8
x = 0.875
plug it into
19x + 11
19 × 0.875 + 11 = 27.625
so 27.625 should be your answer
How many tens make the number 600
Answer:
60
Step-by-step explanation:
60*10=600
Answer:
[tex]60[/tex]
Step-by-step explanation:
Simple. Tens represent the value as 10
If we have more than one zero, as in two for example.
The number is in the hundreds place.
Then just multiply the different number by the 10 value
100 * 6 = 600
It is sixty tens
which product is greatest? (-9)*(-3) or (-7)*(-2)? explain
Answer:
-9 x -3
Step-by-step explanation:
-7 x -2 will give +14.
-9 x -3 will give +27
+27 is greater than +14.
Two negative numbers multiplied will give a positive answer. (Always)
Multiplying two negative numbers gives a positive product. Therefore, both (-9)*(-3) and (-7)*(-2) result in positive numbers. However, (-9)*(-3) equals to 27, which is greater than (-7)*(-2) equals to 14.
Explanation:In Mathematics, when you multiply two negative numbers together, the product is a positive number. This is because the rules of sign in multiplication state that a negative times negative equals to a positive. Therefore, both (-9)*(-3) and (-7)*(-2) will result in positive numbers. (-9)*(-3) equals 27, while (-7)*(-2) equals 14. So, the product of (-9)*(-3), which is 27, is greater than the product of (-7)*(-2), which is 14.
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Combine like terms to create an equivalent expression . Make sure to simplify coefficients and constants as well. - 6/5 - 2/3 * v + 4/15 + 1/3 * v
Help please
Answer:
the answer is -1/3v-14/15
-1/3v -14/15 is the required solution for combine like terms to create an equivalent expression to - 6/5 - 2/3 * v + 4/15 + 1/3 * v.
Given that,
To combine like terms to create an equivalent expression and to Make sure to simplify coefficients and constants as well,
- 6/5 - 2/3 * v + 4/15 + 1/3 * v
The algebraic expression consists of constant and variable. eg x, y, z etc.
Here,
= - 6/5 - 2/3 * v + 4/15 + 1/3 * v
In the above expression, -2/3 and 1/3 is the coefficient and -6/5 and -2/3 is constant while adding like termes the coefficient combines with coefficient and constant with constant.
= -2/3v + 1/3v -6/5 + 4/15
= -1/3v -14/15
Thus, -1/3v -14/15 is the required solution for combine like terms to create an equivalent expression to - 6/5 - 2/3 * v + 4/15 + 1/3 * v.
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Candi Barr has a mobile hanging in her window, and it's balanced because the weight on each side is the same.
a.) If Candi takes two triangles off of the left side and three triangles off of the right side, will the mobile still be in balance, or will it tip to one side? If so, which side? Explain how you know.
Plz help. A tram moved upward 3 meters per second for 24 seconds. What was the total change in the tram's elevation?
Answer:
Step-by-step explanation:
[tex]\frac{3 meters}{1 second} * 24 seconds[/tex]
[tex]72 meters[/tex]
The total change in the tram's elevation is found by multiplying the speed (3 meters per second) by the time (24 seconds) which gives us a result of 72 meters.
Explanation:The total change in the tram's elevation can be found using the formula for distance travelled which is speed times time. We know that the speed of the tram is 3 meters per second, and it moved for 24 seconds. To find the total distance travelled or the total change in elevation, we simply multiply the speed by the time.
So, 3 meters per second multiplied by 24 seconds equals 72 meters. Therefore, the total change in the tram's elevation was 72 meters.
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571÷24 PLZ help. ❤❤
Answer:
23.79
Step-by-step explanation:
You can use a calculator or use the give and take method. when using the calculator always take the first two numbers after the decimal.
Suppose you bought eight oranges and one grapefruit for a total of 4.60. Later that day, you bought six oranges and three grapefruits for a total of 4.80. What is the price of each type of fruit?
Answer:
a grapefruit would cost $0.06 and an orange would cost $0.05
Step-by-step explanation:
The price of an orange is 0.5 dollars and price of a grape is 0.6 dollars.
What is linear equation in two variable ?A linear equation has highest degree of a and contains two variables generally in x and y.
According to the given question you bought eight oranges and one grapefruit for a total of 4.60.
Let oranges be denoted by O and grapefruit be denoted by G.
∴ 8O + 1G = 4.60...(i)
Later that day, you bought six oranges and three grapefruits for a total of 4.80.
∴ 6O + 3G = 4.80...(ii)
Now multiplying (i) by 3 and subtracting it from (ii) to cancel out one variable and get the value of the other.
We get O = 0.5 dollars and G = 0.6 dollars.
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What is the unit form for 10 x 3tens
Answer:
3 hundreds
Step-by-step explanation:
10*3*10=300
unit for is 3 hundreds standard form is 300
Evaluate the expression when k=-4
|k-2 • |3k|,- 1
a. 72
b. 71
c. 66
d. -73
The value of the expression | (k - 2) × (3k) | - 1 at k = -4 will be 71. Then the correct option is B.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ | (k - 2) × (3k) | - 1
The value of the expression at k = -4 will be
⇒ | (-4 - 2) × 3 × -4 | - 1
⇒ | (- 6) × (-12)| - 1
⇒ | 72 | - 1
⇒ 72 - 1
⇒ 71
The value of the expression | (k - 2) × (3k) | - 1 at k = -4 will be 71. Then the correct option is B.
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4 fair coins are tossed. What is the probability that all the outcomes are heads?
1/16 You need to multiply 2x2x2x2 since all the coins are both two sided
If x=1, then 9x-4x=2x+3x
Answer:
Is true
Step-by-step explanation:
9(1)-4(1)=2(1)+(3)
5=5
Answer:
5 = 4
Step-by-step explanation
9(1) - 4(1) = 2(1) + 2(1)
so its pretty much just
9 - 4 = 2 + 2
5 = 4
Select all statements that are true about the linear equation.
y=4x−3
The graph of the equation is the set of all points that are solutions to the equation.
The point (1, 1) is on the graph of the equation.
The point (0, −3) is on the graph of the equation.
The graph of the equation is a single point representing one solution to the equation.
Answer:
The graph of the equation is the set of all points that are solutions to the equation.
The point (1, 1) is on the graph of the equation.
The point (0, −3) is on the graph of the equation.
Step-by-step explanation:
The statements that are true about the linear equation are:
The point (1, 1) is on the graph of the equation.The point (0, −3) is on the graph of the equation.The graph of the equation is the set of all points that are solutions to the equation.What is true of the linear equation ?The graph of a linear equation is a line. The line is made up of all points that satisfy the equation. To find the points that satisfy the equation, we can substitute different values for x and solve for y.
If we substitute x=1, we get y=4(1)−3=1. So, the point (1, 1) is on the graph of the equation.
If we substitute x=0, we get y=4(0)−3=−3. So, the point (0, −3) is also on the graph of the equation.
The graph of the equation is a line that passes through the points (1, 1) and (0, −3).
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Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1.5 ft/s. When Graham's
arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable
continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which
system of equations can be used to model this situation?
(n-18+1.51
In-5+242-167
(n-18+1.57
In-5+24+167
(n-18+1.51
[h=5+241
(n=18+1.54-167
In=5+241- 1672
Answer:
If Hunter is right beneath Graham ( 18ft-5ft=13ft) and G's arms are 18ft above ground ( and going up, no bending) the question would be at what hight would Graham catch the ball and and how soon.
The maximum hight that the ball can reach before falling ( when the vector F - force of throwing the ball to Graham, would be equal in module to gravitational force - considering gravitational velocity of 13ft/s^2
The equation of Graham cable is h(t) = -16t² + 1.5t + 18
The equation of Hunter ball is h(t) = -16t² + 24t + 5
What is an equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Now, The height of a projectile at time t is:
h(t) = -16t² + ut + h'
Where u is the initial velocity and h' is the initial height.
So, the equation of Graham cable is:
h(t) = -16t² + 1.5t + 18
and, the equation of Hunter ball is:
h(t) = -16t² + 24t + 5
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The product of a number and 10, increased by 1
Answer:
10x+1
Step-by-step explanation:
The expression of the given description could be 10n + 1.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.
For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.
If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
We have been given a statement as 'The product of a number and 10, increased by 1'
Where" the product " means multiply.
" increased " means add
Let the unknown number be n
So the expression could be;
10n + 1
Therefore, the expression of the given description could be 10n + 1 .
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The length and width of a rectangle is (x-2) and (4-y) respectively. Express the area, A, of the rectangle in terms of x and y.
Answer:
4x + 2y - xy - 8
Step-by-step explanation:
The area (A) of a rectangle is calculated as
A = length × width , that is
A = (x - 2)(4 - y)
Each of the terms in the second factor is multiplied by each of the terms in the first factor, that is
x(4 - y) - 2(4 - y) ← distribute both parenthesis
= 4x - xy - 8 + 2y, thus
A = 4x + 2y - xy - 8
Answer: 4x - xy - 8 + 2y
Step-by-step explanation:
(x-2)(4-y) = 4x - xy - 8 + 2y
a function is defined as shown