Answer:
[tex]\large\boxed{A=6.25\pi\ km^2\approx19.625\ km^2}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have the length of a diameter d = 5 km
We know: d = 2r. Therefor r = 5km : 2 = 2.5 km.
Substitute:
[tex]A=\pi(2.5)^2=6.25\pi\ km^2[/tex]
If you want an approximation, then
[tex]\pi\approx3.14\to A\approx(6.25)(3.14)=19.625\ km^2[/tex]
Hey!
-----------------------------
Formula: A = πr²
Diameter: d / 2 = r
-----------------------------
Solution:
A = (3.14)(2.5)²
A = (3.14)(6.25)
A = 19.625km.
-----------------------------
Answer:
The area of the circle is 19.625km. or 6.25π km.
-----------------------------
Hope This Helped! Good Luck!
Solve for w.
-12 = -|w|
Write your answers as integers or as proper or improper fractions in simplest form.
w= or w =
Hey!
-----------------------------------------------
Answer:
w = -12 or w = 12
-----------------------------------------------
Explanation:
The lines on each side of the w stands for "absolute value". This means that whatever number is inside the two lines is positive regarding its sign.
|12| = 12
|-12| = 12
Since the equation has the negative symbol outside the two lines, it means that the absolute value will remain negative.
-----------------------------------------------
Hope This Helped! Good Luck!
** A rock is thrown upward from the top of
a 25 foot tower with an initial upward
velocity of 100ft/sec. The height of a rock
above the ground as a function of time can
be modeled by the equation: h(t) =
- 16t? + 100t + 25. How long does it take
for the rock to fall back to the ground?
Answer:
The rocket will take 6.49 seconds to fall back to the ground
Step-by-step explanation:
* Lets explain how to solve the problem
- A rock is thrown upward from the top of a 25 foot tower with an initial
upward velocity of 100 ft/sec
- That means at t = 0 the height of the rock is 25 feet above the ground
- A function of time can be modeled by the equation:
h(t) = - 16t² + 100t + 25, where h is the height of the rocket from the
ground at time t
∵ h(t) = -16t² + 100t + 25
- The height of the rocket is 25 feet above the ground when it
is thrown up
∴ h(t) = 25 at t = 0 ⇒ initial position of the rocket
- The height of the rocket when hits the ground is zero
∴ h(t) = 0 when the rocket hits the ground ⇒ final position of it
- We need to find the time that the rocket takes to fall back to
the ground
∵ h(t) = 0
∵ h(t) = -16t² + 100t + 25
∴ -16t² + 100t + 25 = 0
- Lets solve it to find the value of t
∵ -16t² + 100t + 25 = 0
- Multiply both sides by -1 to make the coefficient of t² positive
∴ 16t² - 100t - 25 = 0
- Use your calculator to find the values of t
∴ t = 6.49 sec and t = -0.24 sec
∵ We will reject the value of t = -0.24, because time can not be
negative value
∴ The rocket will take 6.49 seconds to fall back to the ground
The length of a rectangle is 6 inches longer than it is wide. If the area is 40 square inches, what are the dimensions of the rectangle?
Answer:
The length is 10 inches, and the width is 4 inches.
By creating a quadratic equation using the known facts and algebra, we can determine that the dimensions of the rectangle with an area of 40 square inches are length= 10 inches and width= 4 inches.
Explanation:This problem is a classic example of using algebra to solve for unknown dimensions. Given that the area (A) of a rectangle equals its length (L) times its width (W), written as A = L x W, you can substitute the given values into this formula. You're told the length is 6 inches longer than the width, which you can denote in algebra as L = W + 6. Secondly, you're given that the area is 40 square inches. Substituting these values gives us the following equation: 40 = W(W + 6).
Solving this equation will give us the width, and substituting the width into the formula L = W + 6, gives us the length.
Solving the Equation:
First, distribute the width on the right side of the equation to get 40 = W^2 + 6W. Re-arranging terms gives W^2 + 6W - 40 = 0. Factoring this quadratic equation yields (W - 4)(W + 10) = 0. Setting each factor equal to zero and solving for W gives W = 4 and W = -10. Because a width cannot be negative, the width of the rectangle is 4 inches. Substituting W = 4 into the length equation results in L = 4 + 6 = 10 inches. Hence, the dimensions of the rectangle are Length = 10 inches and Width = 4 inches.
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Six less than a number is greater than 54
Answer:
6<x>54 ASK YOUR TEACHER
Step-by-step explanation:
Please help me I help with this.
Answer:4(y+6)
Step-by-step explanation: y from -9 to 9
go to wolfram math to see the graph because i cant draw it
I hope this helps you.
Solve by elimination
-5x+8y=-27
-8x+7y=-20
Answer:
x = -1 , y = -4
Step-by-step explanation by elimination:
Solve the following system:
{8 y - 5 x = -27 | (equation 1)
7 y - 8 x = -20 | (equation 2)
Swap equation 1 with equation 2:
{-(8 x) + 7 y = -20 | (equation 1)
-(5 x) + 8 y = -27 | (equation 2)
Subtract 5/8 × (equation 1) from equation 2:
{-(8 x) + 7 y = -20 | (equation 1)
0 x+(29 y)/8 = (-29)/2 | (equation 2)
Multiply equation 2 by 8/29:
{-(8 x) + 7 y = -20 | (equation 1)
0 x+y = -4 | (equation 2)
Subtract 7 × (equation 2) from equation 1:
{-(8 x)+0 y = 8 | (equation 1)
0 x+y = -4 | (equation 2)
Divide equation 1 by -8:
{x+0 y = -1 | (equation 1)
0 x+y = -4 | (equation 2)
Collect results:
Answer: {x = -1 , y = -4
find the possible values of a if the points with the given coordinates are the indicated distance apart.
1. (1, a), (3, -2); d=5
Answer:
Possible values of a = 2.58 and -6.58.
Step-by-step explanation:
Using the distance formula
√(3- 1)^2 + (-2-a)^2) = 5
(3- 1)^2 + (-2-a)^2 = 25
4 + 4a + a^2 + 4 = 25
a^2 + 4a - 17 = 0
a = [-4 +/- √(4^2 - 4*1*-17) ] / 2
a = -2 +/- √84 / 2
a = 2.58, -6.58.
ILL MARK BRAINLIEST ASAP IF CORRECT Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1).
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h. k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (- 6, - 1), thus
y = a(x + 6)² - 1
To find a substitute one of the roots into the equation
Using (- 3, 0), then
0 = a(- 3 +6)² - 1
0 = 9a - 1 ( add 1 to both sides )
1 = 9a ( divide both sides by 9 )
a = [tex]\frac{1}{9}[/tex], thus
y = [tex]\frac{1}{9}[/tex](x + 6)² - 1 ← in vertex form
Expand factor and simplify
y = [tex]\frac{1}{9}[/tex] (x² + 12x + 36) - 1 ← distribute
y = [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 4 - 1
= [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 3 ← in standard form
One Solution
no solution
infinitely many solutions
3x + 9 + 4x + x =
_x+_
The simplified equation from the given 3x + 9 + 4x + x = _x + _ is 8x + 9 = _x + _. This equation cannot be solved further without the values for the variables represented by the underscores.
Explanation:The first step to solving the equation is to simplify it. Your original equation is 3x + 9 + 4x + x = _x + _. When we simplify the left side of the equation by combining like terms we get 8x + 9 = _x + _. However, the variables in the blanks on the right side of equation are unknown, so we can't solve it fully. But now you have a simpler equation to work with, and if you receive any additional information, you can substitute those values into your simplified equation.
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convert 3.62x10^-2 into expanded form
Answer:
0.0362
Because the exponent is negative, you move the decimal to the left 2 times.
Factor the expression: (9x)(9x)+12x+4
Answer:
81x^2 + 12x + 4
Step-by-step explanation:
This expression doesn't factor
Depending on the cycle, washing a load of
clothes takes from 22 to 28 minutes. Diying
takes an additional 20 to 30 minutes. What
are the woun and maximum total times
to complete a load of laundry?
Final answer:
The time to complete a load of laundry ranges from a minimum of 42 minutes to a maximum of 58 minutes, combining the shortest and longest durations for both washing and drying cycles respectively.
Explanation:
The question asks about calculating the minimum and maximum total times for completing a load of laundry, including washing and drying cycles. The minimum time for washing is 22 minutes, and the minimum time for drying is 20 minutes. Therefore, the minimum total time to complete a load of laundry is 22 + 20 = 42 minutes.
On the other end, the maximum time for washing is 28 minutes, and the maximum time for drying is 30 minutes. The maximum total time to complete a load of laundry is 28 + 30 = 58 minutes.
In conclusion, the entire process of doing laundry, including both washing and drying, takes between 42 and 58 minutes in total.
CAN SOMEONE HELP ME WITH THIS????????????????
[tex]\text{Hello there!}\\\\\text{We're trying to find the area of the shape}\\\text{We can do this by finding the area for the different shapes, then adding}\\\text{them together}\\\\\text{We can find the area of the rectangle,} \,\,84\cdot66=5,544\\\\\text{To find the area of the half circle, we would use the equation:}\,\,A=\frac{3.14r^2}{2}\\\\\text{The radius is half of the diameter, therefore it is 33. Plug 33 in r}\\\\A=\frac{3.14(33)^2}{2}\\\\\text{Solve:}\\\\A=\frac{3.14(33)^2}{2}\\[/tex]
[tex]A=\frac{3.14(1089)}{2}\\\\A=\frac{3419.46}{2}\\\\\text{Divide by 2}\\\\A=1709.73\\\\\text{Since there's two half circles, we would add 1709.73 twice}\\\\\text{Add all the areas together}\\\\1709.73+1709.73+5,544=8963.46\\\\\large\boxed{\text{Area:}\,\,8963.46\,\,\text{m}^2}}[/tex]
what is the total amount?
Total amount of what?
$8.75 * 7.5
about $65.63
Forgive me if I'm wrong
Hope this helps!
If Bob paid $41.44 for 14 gallons what is the price of gas per gallon
In segment AC, the midpoint is B. If segments AC = 5x-9 and AB = 2x, what is the measure of segment AC.
Answer:
The measure of segment AC is 36 units
Step-by-step explanation:
- The mid-point divides the segment into two equal parts in length
- B is the mid point of segment AC
- That means B divides segment AC into two equal parts in length
∴ AB = BC
∵ AC = 5x - 9
∵ AB = 2x
- The two parts AB and BC are equal in length
∴ BC = 2x
∵ AC = AB + BC
- Substitute the values of AB and BC in the expression of AC
∴ AC = 2x + 2x
∴ AC = 4x
∵ AC = 5x - 9
- Equate the two values of AC
∴ 5x - 9 = 4x
- Add 9 to both sides
∴ 5x = 4x + 9
- Subtract 4x from both sides
∴ x = 9
- Substitute the value of x in any expression of AC
∵ AC = 4x
∵ x = 9
∴ AC = 4(9) = 36
* The measure of segment AC is 36 units
Starting from the origin, how is point ( – 5, 4) plotted?
Question 1 options:
Move 5 units left and 4 units up.
Move 5 units down and 4 units right.
Move 4 units down and 5 units right.
Move 4 units left and 5 units up.
Move 5 units left and 4 units up
Final answer:
To plot the point (-5, 4) from the origin, move 5 units to the left and 4 units up in a standard Cartesian coordinate system.
Explanation:
To plot the point (-5, 4) starting from the origin in a standard Cartesian coordinate system, you would need to move 5 units left and 4 units up. This is because the x-coordinate is negative, indicating a movement to the left of the origin, and the y-coordinate is positive, indicating a movement above the origin.
The correct steps are as follows:
Starting at the origin (0,0), move 5 units to the left along the horizontal axis. This brings you to the point (-5,0).From there, move 4 units upward along the vertical axis. This brings you to the final position, which is the point (-5, 4).This method adheres to the standard convention that in an xy-coordinate system, right and up are positive directions, while left and down are negative.
Factorise fully 5x-15
To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms. The expression 5x - 15 can be factorised fully by finding the greatest common factor, which is 5. So the expression factorised fully is 5(x - 3).
Explanation:To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms.
The GCF of 5x and 15 is 5. Thus, we can pull 5 outside of the equation and divide each term by 5.
The equation becomes: 5(x - 3).
So, the expression 5x - 15 factorised fully is 5(x - 3).
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Help it’s due by the end of class
Answer:
A
Step-by-step explanation:
Let's see...
It's a cube, so the total volume will be one length cubed or 10^3 which is 1000.
(2500 g)/(1000 cm^3) = [tex]2.5 g/cm^3[/tex]
I'm pretty sure the answer is A because it's the only one with correct scientific notation.
Consider the expression (x 6) – 3x
What is the value of the expression evaluated for x = 12?
Answer:
-26
Step-by-step explanation:
What does 70 times 500
Answer:
35000
Step-by-step explanation:
Multiply 7 by 5 and you would get 35, then add the zeros
Answer:
70*500= 35000
Step-by-step explanation:
10 + 3(x + 2) = 31
Solve the equation
Answer:
x = 5
Step-by-step explanation:
Screenshot below will explain the answer
please help 21 points!!!!!
Step-by-step explanation:
The measure of angle y is 62°.
I solve this by
We know: Measures of interior angles in a triangle add up to 180°.
Therefore we have the equation:
60° + 58° + y = 180°
118° + y = 180° subtract 118° from both sides
118° - 118° + y = 180° - 118°
y = 62°
The measure of angle x is 122°.
I solve this by
Angles 58° and x are supplementary angles.
Supplementary angles add up to 180°.
Therefore we have the equation:
x + 58° = 180° subtract 58° from both sides
x + 58° - 58° = 180° - 58°
x = 122°
19.38 in word form ?
Answer:
nineteen and thirty - eight hundredths
Step-by-step explanation:
Find the values of x and y.
(10x – 61)°
(18y + 5)°
(x + 10)°
Answer:
Part 1) The value of x is 21
Part 2 The value of y is 8
Step-by-step explanation:
step 1
Find the value of x
we know that
[tex](10x-61)\°+(x+10)\°=180\°[/tex] ------> by supplementary angles (linear pair)
[tex]11x-51=180[/tex]
[tex]11x=180+51[/tex]
[tex]11x=231[/tex]
[tex]x=21[/tex]
step 2
Find the value of y
we know that
[tex](10x-61)\°=(18y+5)\°[/tex] ----> by vertical angles
substitute the value of x and solve for y
[tex](10(21)-61)\°=(18y+5)\°[/tex]
[tex](149)\°=(18y+5)\°[/tex]
[tex]18y=149-5[/tex]
[tex]18y=144[/tex]
[tex]y=8[/tex]
Answer:
x=21 y=8
Step-by-step explanation:
Find the product using suitable identities.
a) [tex](\frac{x}{3} - 6)^{2}[/tex] step by step
Answer:
[tex]\frac{x^2}{9}[/tex] - 4x + 36
Step-by-step explanation:
([tex]\frac{x}{3}[/tex] - 6)² = ([tex]\frac{x}{3}[/tex] - 6)([tex]\frac{x}{3}[/tex] - 6)
Each term in the second factor is multiplied by each term in the firs t factor, that is
[tex]\frac{x}{3}[/tex]([tex]\frac{x}{3}[/tex] - 6) - 6([tex]\frac{x}{3}[/tex] - 6)
Distribute both parenthesis
= [tex]\frac{x^2}{9}[/tex] - 2x - 2x + 36 ← collect like terms
= [tex]\frac{x^2}{9}[/tex] - 4x + 36
Step by step answer for
1/2n +3/4n=1/2
let's keep in mind that we have denominators of 2, 4 and 2, and thus we can use their LCD of 4, and multiply both sides by that LCD to do away with the denominators, let's proceed,
[tex]\bf \cfrac{1}{2}n+\cfrac{3}{4}n=\cfrac{1}{2}\implies \stackrel{\textit{multipying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{2}n+\cfrac{3}{4}n \right)=4\left( \cfrac{1}{2} \right)}\implies 2n+3n=2 \\\\\\ 5n=2\implies n=\cfrac{2}{5}[/tex]
Simplify 8^-5 over 8^-3
Answer:
64-5 divided by 64-3 is 59 divided by 61. 59
8 squared is equal to 64. -----
61
Step-by-step explanation:
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{8^{-5}}{8^{-3}}\implies \cfrac{1}{8^{-3}\cdot 8^5}\implies \cfrac{1}{8^{-3+5}}\implies \cfrac{1}{8^2}\implies \cfrac{1}{64}[/tex]
Find Sn for the given arithmetic series.
a1 = –74, d = –3, n = 20
Answer:
- 1050
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], thus
[tex]S_{20}[/tex] = [tex]\frac{20}{2}[/tex] [ (2 × - 74) + (19 × - 3) ]
= 10 ( - 148 - 57) = 10 × - 105 = - 1050
X over 4 greater than or equal to negative 8
x/4 >= -8
Multiply both sides by 4.
x >= (-8)(4)
x >= -32
The value of X is greater than or equal to -32.
Explanation:To solve the inequality X/4 ≥ -8, we need to isolate the variable X. Firstly, we can multiply both sides of the inequality by 4 to get rid of the denominator: X ≥ -32. This means that the value of X is greater than or equal to -32. In interval notation, we can represent this as (-32, ∞).
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