Answer:
25 meters .
Step-by-step explanation:
The actual width of the rectangle is 24.5 meters.
What is area of rectangle?The area of rectangle equals the base(width) times the height.
A = w × h
Given
Area of rectangle = 500 square meters.
Length of rectangle = 4x - 3 meters
Width of rectangle = 2x + 6 meters
Area of rectangle = length × width
500 = (4x - 3) (2x + 6)
⇒ 500 = [tex]8x^{2}+24x-6x-18[/tex]
⇒ 500 = [tex]8x^{2}+18x-18[/tex]
⇒ 500 = [tex]2(4x^{2}+9x-9)[/tex]
⇒ [tex]\frac{500}{2}=4x^{2}+9x-9[/tex]
⇒ [tex]250=4x^{2}+9x-9[/tex]
⇒ [tex]4x^{2}+9x-9-250=0[/tex]
⇒ [tex]4x^{2}+9x-259=0[/tex]
⇒ 4x(x + 7) -37(x + 7) = 0
⇒ (x + 7) (4x - 37) = 0
⇒ x = -7, x = [tex]\frac{37}{4}[/tex]
-7 is not satisfied because it is a negative number.
By substituting x = [tex]\frac{37}{4}[/tex] in width of rectangle
Actual width of rectangle = 2x + 6
= 2( [tex]\frac{37}{4}[/tex]) + 6
= [tex]\frac{37}{2}[/tex] + 6
= [tex]\frac{37+12}{2}[/tex]
= [tex]\frac{49}{2}[/tex]
= 24.5 meters
Hence, the actual width of the rectangle is 24.5 meters.
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the area of a circle is 100 square miles. What is the diameter?
Answer:
The diameter of a circle with an area of 100 square miles is 20/√π miles.
Step-by-step explanation:
Area =100 = πr^2.
diameter = d = 2r.
100 = πr^2.
100/π = r^2.
√(100/π) = r.
10/√π = r.
d = 2r.
d = 2 * 10/√π.
d = 20/√π
Find the equation of the line through the points (6, -9) and (-2, -1).
Enter your answer in slope-intercept form y = mx + b.
Answer:
y = -1x - 3
Step-by-step explanation:
y2 - y1 / x2 - x1
-1 - (-9) / -2 - 6
8/-8
= -1
y = -1x + b
-1 = -1(-2) + b
-1 = 2 + b
-3 = b
write a quadratic function h whose zeros are - 6 and -5 h (x) =
Answer:
h(x)= x^2+11x+30
Step-by-step explanation:
A quadratic function is in the form h(x) = ax^2 + bx + c.
Since the zeros are -6 and -5, take the opposite signs and add them to the variable x separately.
It should look like this: h(x)= (x+6)(x+5)
Since this is the factored form, we have to solve this equation further.
h(x)= (x+6)(x+5)
h(x)= x^2+6x+5x+30
h(x)= x^2+11x+30
A hot metal plate at 150°C has been placed in air at room temperature. Which event would most likely take place over the next few minutes?
- Molecules in both the metal and the surrounding air will start moving at lower speeds.
- Molecules in both the metal and the surrounding air will start moving at higher speeds.
- The air molecules that are surrounding the metal will slow down, and the molecules in the metal will speed up.
- The air molecules that are surrounding the metal will speed up, and the molecules in the metal will slow down.
Answer:
the last option, effectively cooling the hot plate down and heating the surrounding up
Rearrange x = 3g + 2 to make g the subject.
Answer:
g = ( x - 2 ) / 3
Step-by-step explanation:
x = 3g + 2
subtract 2 from each side
x - 2 = 3g + 2 - 2
simplify
x - 2 = 3g
Divide each side by 3
(x - 2)/3 = 3g/3
Simplify
( x - 2 ) / 3 = g
Flip equation
g = ( x - 2 ) / 3
And we are done!
Sketch the graph of y = 2 x squared + 7 x using your graphing calculator. What are the x-intercepts of this graph? a. (1, 0) and (-0.5, 0) c. There are no x-intercepts b. (0, 0) and (-3.5, 0) d. (-1.5, 0) and (-0.5, 0) Please select the best answer from the choices provided A B C D
Answer:
y= 2x²+7x
B is the answer
Ricky takes 2 coins at random from 3 quarters, 5 dimes, and two nickels in his pocket.
1) What is the (P) nickel then a quarter, without 2) What is the (P) nickel then a dime, with
replacement?
replacement?
3) What is the (P) quarter then a dime, with
replacement?
4) What is the (P) nickel then a nickel, without
replacement?
Answer:
Step-by-step explanation:
To calculate the probability of drawing a nickel followed by a quarter without replacement, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes: Ricky chooses 2 coins from a total of 3 quarters, 5 dimes, and 2 nickels. This can be calculated using combinations, denoted as C(n, r), which represents the number of ways to choose r items from a set of n items. In this case, Ricky is choosing 2 coins from a set of 10 coins:
Total possible outcomes = C(10, 2) = 45
Number of favorable outcomes: Ricky needs to select a nickel first, which leaves 9 coins remaining. Out of these remaining coins, there is 1 quarter. Thus, the number of favorable outcomes is 1.
Favorable outcomes = 1
Probability (P) of drawing a nickel then a quarter without replacement:
P = Favorable outcomes / Total possible outcomes
P = 1 / 45
Therefore, the probability of selecting a nickel followed by a quarter without replacement is 1/45.
To calculate the probability of drawing a nickel then a dime with replacement, we assume that after each selection, the coin is replaced, and the total number of coins remains the same.
Probability (P) of drawing a nickel then a dime with replacement:
P(nickel then dime) = (Number of nickels / Total number of coins) * (Number of dimes / Total number of coins)
P(nickel then dime) = (2/10) * (5/10)
P(nickel then dime) = 1/10
Therefore, the probability of selecting a nickel followed by a dime with replacement is 1/10.
To calculate the probability of drawing a quarter then a dime with replacement:
Probability (P) of drawing a quarter then a dime with replacement:
P(quarter then dime) = (Number of quarters / Total number of coins) * (Number of dimes / Total number of coins)
P(quarter then dime) = (3/10) * (5/10)
P(quarter then dime) = 3/20
Therefore, the probability of selecting a quarter followed by a dime with replacement is 3/20.
To calculate the probability of drawing a nickel then another nickel without replacement, we need to consider that the second draw must be a nickel and that the first nickel is not replaced.
Total number of possible outcomes: Ricky chooses 2 coins from a total of 3 quarters, 5 dimes, and 2 nickels:
Total possible outcomes = C(10, 2) = 45
Number of favorable outcomes: Ricky needs to select a nickel first, which leaves 9 coins remaining. Out of these remaining coins, there is only 1 nickel left.
Favorable outcomes = 1
Probability (P) of drawing a nickel then another nickel without replacement:
P = Favorable outcomes / Total possible outcomes
P = 1 / 45
Therefore, the probability of selecting a nickel followed by another nickel without replacement is 1/45.
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Need help with this
Find each indicated measure for circle O
Answer:
Angle A = 41, Arc CE = 42, Angle C = 41, Angle D = 40, Angle ABE = 61
Step-by-step explanation:
Angle A = Arc BD/2 (Inscribed Angle)
Angle A = 82/2
Angle A = 41
Arc CE = 2 x Angle CEB (Inscribed Angle)
Arc CE = 2 x 21
Arc CE = 42
Angle C = Arc BD/2 (Inscribed Angle)
Angle C = 82/2
Angle C = 41
Angle D = Arc AC/2 (Inscribed Angle)
Angle D = 80/2
Angle D = 40
Angle ABE = Arc AE/2
Angle ABE = Arc AC + Arc CE/2
Angle ABE = 122/2
Angle ABE = 61
m < A = [tex]39^{0}[/tex] , mCE = [tex]40^{0}[/tex], m < c = [tex]39^{0}[/tex], m < D = [tex]37^{0}[/tex] m < ABE = [tex]57^{0}[/tex]
What are angles in a circle ?A circle has a total of 360 degrees all the way around the center, so if that central angle determining a sector has an angle measure of 60 degrees, then the sector takes up 60/360 or 1/6, of the degrees all the way around.
a. m < A = [tex]\frac{1}{2}[/tex] mBD
= [tex]\frac{1}{2}[/tex] × [tex]78^{0}[/tex]
= [tex]39^{0}[/tex]
b. mCE = 2m < CBE
= 2 × [tex]20^{0}[/tex]
= [tex]40^{0}[/tex]
c. m < c = m < A = [tex]39^{0}[/tex]
d. m < D = [tex]\frac{1}{2}[/tex] mAC
= [tex]\frac{1}{2}[/tex] × [tex]74^{0}[/tex]
= [tex]37^{0}[/tex]
e. m < ABE = [tex]\frac{1}{2}[/tex] mAC + [tex]\frac{1}{2}[/tex] mCE
= [tex]37^{0}[/tex] + [tex]20^{0}[/tex]
= [tex]57^{0}[/tex]
Hence, m < A = [tex]39^{0}[/tex] , mCE = [tex]40^{0}[/tex], m < c = [tex]39^{0}[/tex], m < D = [tex]37^{0}[/tex] m < ABE = [tex]57^{0}[/tex]
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What is the slope of the line g(x) = -7x + 8?
Answer:
The slope is -7 and the y intercept is 8
Step-by-step explanation:
g(x) = -7x + 8
This is in the form y = mx +b where m is the slope and b is the y intercept
The slope is -7 and the y intercept is 8
Graph the function.
f(x) = 3 sin (x)
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
Answer:
Step-by-step explanation:
Mean line: y = -3
Period: 2pi ÷ ½ = 4pi
Amplitude = 5
Use the following points to sketch:
(0, -3)
(3.14, 2)
(6.28, -3)
(9.42, -8)
(12.56, -3)
The graph should look like a wave that oscillates between y = 3 and y = -3, crossing the midline at x-intercepts of every multiple of π.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To graph the function f(x) = 3 sin(x),
Steps:
- Draw the x and y axes on your graph paper.
- Mark the midline of the sine function at y=0.
- Choose a point on the midline to be the first point on your graph. Let's choose (0,0).
- To find the next point, identify a maximum or minimum value of the function closest to your first point.
In this case, the maximum value occurs at (π/2, 3) and the minimum value occurs at (3π/2, -3).
- Use the sine tool to draw the curve passing through your two points. Since the amplitude of the function is 3, the curve will reach a maximum of 3 and a minimum of -3.
Thus,
The graph should look like a wave that oscillates between y=3 and y=-3, crossing the midline at x-intercepts of every multiple of π.
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square root of 7 hole 18/49
Answer:
19/7
Step-by-step explanation:
7 18/49 = 361/49 = √361/√49 = 19×19/7×7 = 19/7
Square root of 7 18/49 is 19/7
Hope this answer helps you :)
Have a great day
Mark brainliest
Use the function below to find f(-2).
F(x)= 3^x
A. 1/6
B. -9
C. -6
D. 1/9
Answer:
D. 1/9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationExponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Step-by-step explanation:
Step 1: Define
Identify
f(x) = 3ˣ
f(-2) is x = -2 for function f(x)
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-2) = 3⁻²Exponents: f(-2) = 1/9HELP PLEASE
what is the base of this problem?
Answer:
8x8x8x8
Step-by-step explanation:
A 6 foot ladder is leaning against a wall and makes a 57 degree angle with the ground. How high does the ladder reach on the wall
Answer:
357
Son:tep-by-step explanati
Find the length of the arc in terms of pi. A 60° В С C 12 AB = [?] T T Hint: The arc is only part of the circle. Enter Corporation. All Rights Reserued.
10 hours ago — Find the length of the arc in terms of pi. A 60° В С C 12 AB = [?] T T Hint: The arc is only part of the circle. Enter Corporation. All Rights Reserued..
Need help ASAP. i forgot all the steps after the Area is solved with 5. or if 25pi is the right answer.
Answer:
[tex]42.5\:\mathrm{m^2}[/tex]
Step-by-step explanation:
The area of a sector with measure [tex]\theta[/tex] in degrees is given by [tex]r^2\pi\cdot\frac{\theta}{360}[/tex], where [tex]r[/tex] is the radius of the sector.
What we're given:
[tex]r[/tex] of 5 [tex]\theta[/tex] of [tex]195^{\circ}[/tex]Solving, we get:
[tex]A_{sector}=5^2\pi\cdot \frac{195}{360}=13.5416666667\pi=42.5424005174\approx \boxed{42.5\:\mathrm{m^2}}[/tex]
*Notes:
units should be in square meters (area) the problem does not say whether to round or leave answers in term of pi, so you may need to adjust the answer depending on what your teacher specifically wantsLeo is working part time as a server in a restaurant. He makes $8.14 for each hour he works, and on average earns an additional $300 per week in tips. Which function, f(x), can Leo use to model his average weekly salary in terms of the number of hours, x, he works?
Answer:
f(x) = 8.14x + 300
Step-by-step explanation:
The function of 8.14x + 300 can be used to model Leo's average weekly salary in terms of x.
What is a function?' A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.'
According to the given problem,
Amount Leo earns for each hour he works = $8.14
Amount Leo earns in x hours = $8.14x
Amount Leo earns as additional tip per week = $300
Therefore, the function of x is,
⇒ f(x) = 8.14x + 300
Hence, we can conclude, the function that can be used to model his weekly salary is 8.14x + 300
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Find the value of x in each case:
Step-by-step explanation:
angle MRP
angle PRS=angle RPN (alternate angles)
2x+x+x+78°=180°(sum of angles of a triangle)
4x+78°=180°
4x=180°-78°
4x=102°
4x/4=102°/4
x=25.5
Write the equation of a line passing through (-1,2) and perpendicular to y = 1/5x+5
Answer:
y = -5x - 3
Step-by-step explanation:
y = -5x + b
2 = -5(-1) + b
2 = 5 + b
-3 = b
ASAP ART!!!!!
Design your own rotational symmetry piece fulfilling at least ONE of the criteria listed AND coloring it
can you guys help me plz
Answer:
Step-by-step explanation:
x = 10sqrt(2)*cos(60) = 5sqrt(2) = 7.07 approx.
y = 10sqrt(2)*sin(60) = 10sqrt(2)*sqrt(3)/2 = 5sqrt(6)=12.25 approx.
Jane bought 6 banana at $250 per dozen. she sells four and a half dozen at $35 each and the others were sold at %20 each determine if she made a profit or loss state her profit or loss as a percentage. show working
Answer:
34.4% profit
Step-by-step explanation:
C.P. = 1500
S.P. = 2016
Profit% = 34.4%
Multiply : 2^3 root 3 by 3 root 2
Answer:
24 root 6
Step-by-step explanation:
Answer:
the answer is 58•78775383(that is 2^3√3×3√2)
Witch shows the correct way to convert 5 ounces to pounds ?
can anyone help meh with this i wasn't paying attention in class when my teacher was explaining how to do this :,)
Answer:
W=42°
X=29°
Step-by-step explanation:
180-138=42
90-42-19=29
Can anyone help me? With this Math problem ASAP
Answer:
amount is ≤ 500
Step-by-step explanation:
Maximum means less than or equal to
amount is ≤ 500
54 seconds to 2 minutes ( ratio )
Answer:
54:2 = 27:1
Step-by-step explanation:
54:2 use as fraction 54/2 then divide
Which of the following values of m will result in a true statement when substituted into the given equation?
m – 1.9 = 2.2
A. m = 2.8
B. m = 3.8
C. m = 4.1
D. m = 4.9
Answer:
C. m = 4.1 is the answer
what is the missing value for a on the diagram below?
Answer:
Step-by-step explanation:
The line that is going through the center of the circle is the diameter, which, like I just stated, goes through the middle of the circle (cutting it in half). Half of a circle measures 180 degrees. That means that x measures 180 - 122 which is 58 degrees.
median 10 24 9 18 15 28 12 27 25 29 10 26
Answer:
The median is 21
Step-by-step explanation:
Since you have 12 numbers in order, that's an even number, once you put them in numerical order and start crossing them off on both sides, you'll have 18 and 24 left, add them together and divide them by 2 and you'll have your median 21.