22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.
Since Amina recently moved and got a new job, and the quickest way to get to work is to take a freeway that charges a toll, and there are two options for paying the tolls:
Option A: No monthly fee, each trip on the tollway is $ 2.80.
Option B: $ 30 monthly fee, each trip on the tollway is half-priced at $ 1.40.
To determine how many trips on the tollway are needed for Option B to be cheaper; y, if Amina plans to travel to and from work 5 times a week, which option should she purchase; the following calculation must be performed:
Option A = 2.80X Option B = 30 + 1.40X 2.80 x 20 = 56 30 + 1.40 x 20 = 58 2.80 x 25 = 70 30 + 1.40 x 25 = 65 2.80 x 24 = 67.2 30 + 1.40 x 24 = 63.6 2.80 x 22 = 61.6 30 + 1.40 x 22 = 60.8
Therefore, 22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.
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factor this polynomial completely x^2-10x+25
x^2-10x+25
=x^2-5x-5x+25
x(x-5)-5(x-5)
=(x-5)(x-5)
x=5 , x=5
hope it's helpful to you
[tex]x^2 -10x +25\\\\=x^2 -2 \cdot 5 \cdot x +5^2\\\\=(x-5)^2\\\\=(x-5)(x-5)[/tex]
Which point represents the outlier
Answer:An outlier is any data point that falls above the 3rd quartile and below the first quartile. The inter-quartile range is and . The lower bound would be and the upper bound would be . The only possible answer outside of this range is .
Step-by-step explanation:
Answer: Select the correct answer.
Which point represents the outlier?
(3, 13)
Step-by-step explanation:
A. (2, 3)
B. (4, 5)
C. (3, 13)
D. (8, 9)
Mariana's office recycled a total of 9 kilograms of paper over 3 weeks. After 4 weeks,
how many kilograms of paper will Mariana's office have recycled? Solve using unit rates.
Answer:
9 kg per 3 weeks = 3 kg per week
Therefore, after 4 weeks it is (4 * 3) kilograms or 12 kilograms
Step-by-step explanation:
A jet plane can carry up to 200,000 liters of fuel. It used 130,000 liters of fuel during a flight. What percentage of the fuel capacity did it use on this flight?
Answer:
Step-by-step explanation:
65%
Step-by-step explanation:
Given: Full capacity= 200000 litres
Amount of fuel used during flight= 130000 litres
Now, finding percentage of fuel used on the flight.
∴ Percentage of fuel used=
Solving it, we will get
∴ 65% of fuel capacity been used in this flight.
Answer:
65%.
Step-by-step explanation:
(130,000/200.000) * 100
= 0.65 * 100
= 65%.
12POINTS PLEASE HURRY ASAPPPPP <3
ITS SQAURE 6
6 SQAURE OFTHE 6
sushi is a food peculiar to which country
Answer:
The concept of sushi was introduced to Japan
A 67-kilogram cannon fires a 1 kilogram cannonball at 45 m/sec. If the cannon is on wheels, at what speed does it move backward?
Answer:
-1.4 m/sec [backwards]
Step-by-step explanation:
The energy of the cannon moving should be equal to the energy contained in the cannonball. Kinetic energy for each is calculated using KE = (1/2)m[tex]v^{2}[/tex]
Let x be the speed of the cannon.
Cannonball:
KE = (1/2)m[tex]v^{2}[/tex]
KE = (1/2)(1kg)(45 m/sec)^2
KE = 22.5 kg*m/sec^2
Cannon: [The cannon will have the reverse energy]
KE = - (1/2)m[tex]v^{2}[/tex]
22.5 kg*m/sec^2 = -(1/2)(67 kg)x^2
22.5 kg*m/sec^2 = -(33.5 kg)x^2
x^2 = (33.5 kg)/(22.5 kg*m/sec^2)
x^2 = -1.4 m/sec [backwards]
Explain how the ratios 5 tacos for every 2 guest and 2 tacos for every 5 guests are different. Include a model in your explanation.
Answer:
5 tacos for 2 guests would mean more for each person, while 2 tacos for 5 guests would mean less for each person
plz help me to answer
Answer:
if you can only pick one it's e
Step-by-step explanation:
Im 90% sure a and c are both true answers while 70% sure that b and d are both true answers so unless someone says otherwise e is your best bet
Find the area of the composite figure.
Next, find the area of the parallelogram.
Triangle
Area = 77 cm
7 cm
Parallelogram
Area = [?] cm2
9 cm
Total Area of
Composite Figure = [ 1 cm2
22 cm
Answer:
Step-by-step explanation:
trapezoid is a 4-sided figure with one pair of parallel sides. For example, in the diagram to the right, the bases are parallel. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula looks like this:
area_trapezoid1.gif or area_trapezoid2.gif
Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height and · means multiply.
Each base of a trapezoid must be perpendicular to the height. In the diagram above, both bases are sides of the trapezoid. However, since the lateral sides are not perpendicular to either of the bases, a dotted line is drawn to represent the height.
Suppose theta is an angle in the standard position whose terminal side is in Quadrant II and tan0= -sqrt3 Find the exact values of the remaining five trigonometric functions of theta
The exact values of the remaining five trigonometric functions of theta are
sinθ = √3/2cosecθ = 2/√3cosθ = -1/2secθ = -2 cotθ = -1/√3Since tanθ = -√3.
The remaining five trigonometric functions of theta are sinθ, cosecθ, cosθ, secθ and cotθ.
The next trigonometric function of θ is cotθ.
cotθ = 1/tanθ
= 1/-√3
= -1/√3.
Also, tan²θ + 1 = sec²θ
Substituting tanθ = -√3 into the equation, we have
(-√3)² + 1 = sec²θ
3 + 1 = sec²θ
sec²θ = 4
secθ = ±√4
secθ = ±2
Since θ is in the quadrant II,
secθ = -2
Also, cosθ = 1/secθ
= 1/-2
= -1/2
Also, cot²θ + 1 = cosec²θ
Substituting cotθ = -1/√3 into the equation, we have
(-1/√3)² + 1 = cosec²θ
1/3 + 1 = cosec²θ
cosec²θ = 4/3
cosecθ = ±√(4/3)
cosecθ = ±2/√3
Since θ is in the quadrant II,
cosecθ = +2/√3
Also, sinθ = 1/cosecθ
= 1/2/√3
= √3/2
So, the exact values of the remaining five trigonometric functions of theta are
sinθ = √3/2cosecθ = 2/√3 cosθ = -1/2secθ = -2cotθ = -1/√3.Learn more about trigonometric functions here:
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EXERCISE 11D
1. Draw MON = 81° and bisect it.
2. Draw an angle of measure 175°.
3. Construct a right angle and then bisect it.
4. Draw ABC= 162º and divide it into four equal parts.
5. Construct the following angles using a ruler and compass. a 60° b. 30° C. 120° d. 135°
6. Draw an angle of 107° and make a copy of it. Verify your construction by ac measurement. a.
7. Draw an angle of 83º. Make a copy of its complementary angle.
✅help me to solve this
1. Draw MON = 81° and bisect it.
2. Draw an angle of measure 175
3. Construct a right angle and then bisect it.
Draw ABC = 162° and divide it into four equal parts.
5. Construct the following angles using a ruler and compass.
120°
5 x (3+H) = 15+45. What is H?
Answer:
9
Step-by-step explanation:
5 x 3 = 15 and 5 x H = 45
45 / 5 = 9
PLEASE HELP
solve for x?
please help me on this one would be great help.
Answer:
60
Step-by-step explanation:
Who are you favorite male country singers?
Answer:
kanye west
Step-by-step explanation:
I need help on this math question
Answer:
84
Step-by-step explanation:
7 Sizes * 3 Lengths * 4 Colors = 84
What is the answer to this problem
Answer:
Y=[tex]\frac{2}{3}[/tex]x+4
Step-by-step explanation:
Slope formula is y=mx+b
This is because the slope is 2 over 3: “rise over run”
Slope = m so: y=[tex]\frac{2}{3}[/tex]X+b
We need to find be, that easy because to find b, we have to look at the y axis. Were does the line intercept the y axis?
It is at (0,4) or just simply “4”
Now plug in b=4 into the equation:
y=[tex]\frac{2}{3}[/tex]X+4
Select the correct answer. This table represents the boiling point of water at different altitudes.Which equation represents water's boiling point (y) based on the change in altitude (x)? Altitude (thousands of feet) Boiling Point of Water (Fahrenheit) (sea level) 0 212 0.5 211.1 1.0 210 2.0 208.4 2.5 207.5 3.0 206.6 4.0 204.8 4.5 203.9
Answer:
Step-by-step explanation:
The net income reported on the income statement for the current year was $135,500 depreciation recorded on store equipment for the year amounted to $22,400 balances of the current asset and current libaility accounts at the beginning and end of the year are as follows
BraniliestBraniliestBraniliestBraniliest Braniliest
Answer:
-20.54 C
Step-by-step explanation:
Form an equation
-12.94 C = initial temperature
changes -1.9 per hour = -1.9h
h = hour
x = temperature after 4 hours
-12.94 -1.9h = x
substitute 4 for "h"
-12.94-1.9(4) = x
x = -20.54C
Answer:
-20.54Step-by-step explanation:
Just multiply -1.9 by 4 then add it to 12.94
Please answer question below (80)
Answer:
The last one is the right answer .
Help help help math math math math
Answer:
66 degrees.
Step-by-step explanation:
angle 4 is 124, and angle 1 and 4 make 180 degrees. that means angle 1 is 56 degrees (180-124). and the total angle in a triangle is also 180 degrees.
Add 56 and 58, you'd get 114.
180-114=66
angle 2=66 degrees.
Answer:
66
Step-by-step explanation:
1. The exterior angle theorem states that the measure of an exterior angle of a triangle is congruent to the sum of the two opposite interior angles.
Basically, exterior angle = opposite interior angle + opposite interior angle2. Now, let's see what information we have so far, and what we don't have.
m∠4 is 124 degrees, is the exterior angleThe angle with 58 degrees is one of the opposite interior angles∠2 is the other opposite interior angle, but we don't know its measure3. Now, let's set up the equation and solve it.
Step 1: Set up the equation.
[tex]124 = x + 58[/tex]Step 2: Subtract 58 from both sides.
[tex]124-58=x+58-58[/tex] [tex]66 = x[/tex]Step 3: Check if solution is correct.
[tex]124=66+58[/tex] [tex]124=124[/tex]Therefore, the answer is 66.
PLEASE HELP ME WITH GEOMETRY PLS AND TANKYOU
Answer:
68
Step-by-step explanation:
because 180-44=136
136:2=68 (since TRS=TSR, there is formula)
Solve the following exponential equation:
5^x=2
e^x=10
Number 1.
[tex]5^x=2[/tex], first we will take the [tex]log[/tex] of both of these numbers getting us,
[tex]x=\frac{log(2)}{log(5)}[/tex], which then gives us that [tex]x=0.4306777777....[/tex]
Number 2
[tex]e^x=10[/tex], solve for our exponent, [tex]2.718282^x=10[/tex], use the logarithmic formula, and we get,
[tex]x=\frac{log(10)}{log(2.718282)}[/tex], which then we get that [tex]x=2.302585[/tex]
An AC circuit operates at 60volts and 1000 Hz. The resistance is 500 ohms and the inductive reactance is 220 ohms. What is the current
The current flowing in the AC circuit is 0.11 A.
The given parameters:
Voltage in the circuit, V = 60 VResistance, R = 500 ohmsInductive reactance, Xl = 220 ohmsFrequency, f = 1000 HzThe impedance of the circuit is calculated as follows;
[tex]Z = \sqrt{R^2 + X_l^2} \\\\Z = \sqrt{500^2 + 220^2} \\\\Z = 546.26 \ ohms[/tex]
The current in the AC circuit is calculated as follows;
[tex]I = \frac{V}{Z} \\\\I = \frac{60}{546.26} \\\\I = 0.11 \ A[/tex]
Thus, the current flowing in the AC circuit is 0.11 A.
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Marty has 6 cans of pain that he can use for the 3 bedrooms he needs to paint. How much paint can Marty use in each bedroom?
A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is
if we can assume the ball is being thrown from the ground upwards, then we can say that the inital height of it is 0, whilst its initial velocity is 80 ft/s, thus
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+80t+0\implies h(t)=-16t^2+80t[/tex]
Factor Completely. 2a(x+y)+b(x+y)
Let's simplify step-by-step.
2a(x+y)+b(x+y)
Distribute:
=(2a)(x)+(2a)(y)+(b)(x)+(b)(y)
=2ax+2ay+bx+by
Answer:=2ax+2ay+bx+byThe simplification of the expression is 2ax+2ay+bx+by.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
An algebraic equation is a statement of the equality of two expressions formulated by applying algebraic operations to a set of variables.
Given expression is 2a(x+y)+b(x+y). The expression will be solved as below,
E = 2a(x+y)+b(x+y)
Multiply the values in the whole bracket and simplify,
E = (2a)(x)+(2a)(y)+(b)(x)+(b)(y)
E = 2ax+2ay+bx+by
The simplified expression is given as 2ax+2ay+bx+by.
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the orthocenter of a triangle is at the origin, and two of the vertices of the triangle are at (-5,0) and (3,4) Find the third vertex of the triangle
Answer:
(3, -6)
Step-by-step explanation:
The orthocenter is the point of intersection of the altitudes of the triangle. That is, each altitude goes through the orthocenter. Hence, the line from any given vertex through the orthocenter is perpendicular to the opposite side.
The attached figure shows the given points labeled A and B. Point A lies on the x-axis, as does the orthocenter, so the side opposite will be a vertical line (perpendicular to the x-axis).
The remaining side of the triangle will be perpendicular to the line from B through the origin. The line through B has slope 4/3, so the line containing side AC will have slope -3/4 and will go through point A. Its point-slope equation will be ...
y -0 = -3/4(x +5)
We already know the x-coordinate of vertex C is the same as that of vertex B, so is x=3. Using this in the equation for side AC, we find the y-coordinate to be ...
y = -3/4(3 +5) = -6
The coordinates of point C, the third vertex, are (3, -6).
_____
Additional comments
The slope of a line is given by ...
m = (y2 -y1)/(x2 -x1)
When (x1, y1) = (0, 0), this reduces to ...
m = y2/x2 . . . . . . the relation we used for the slope of line OB
__
The slope of a perpendicular line is the opposite reciprocal of the slope of a line. The line perpendicular to the one with slope 4/3 will be -1/(4/3) = -3/4.
__
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
What is the solution to the system of equations?
{2x + 3y = 6
x+y=1
Answer: {x,y} = {-3,-4}
Step-by-step explanation: