The area of the polygon is 4 square units
How to determine the area of the polygon?The vertices are given as:
(1, 2), (3, 2), (3, 0), and (1, 0)
The area is then calculated as:
A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |
So, we have:
A = 0.5 * |1 * 2 - 3 * 2 + 3 * 0 - 2 * 3 + 3 * 0 - 0 * 1 + 1 * 2 - 0 * 1|
Evaluate
A = 0.5 * |-8|
Remove the absolute bracket
A = 0.5 * 8
This gives
A = 4
Hence, the area of the polygon is 4 square units
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You are building a ramp that must cover a horizontal distance of exactly 13 feet. The angle of the ramp from the ground is 26 degrees. Determine the length of the ramp, in feet.
Answer: 18.6 feet
Step-by-step explanation: Horizontal distance = 17 feet and the angle
of elevation = 24°
On purchasing a cell phone, Tia got an offer and got the cell phone for $35\%$ less than the tag price. If she saved $\$140$ on that cell phone. Then price on the tag must be $\$$
On purchasing a cell phone, Tia got an offer and got the cell phone for 35% less than the tag price. If she saved 140 on that cell phone. Then price on the tag is 400.
Since, the cell pone is sold with 35% discount on it.
Tia got that phone at selling price with 35% discount on tag price. Also, she saved around 140 on buying the cell phone.
Therefore, the discount on the cell phone on the tag price is her saving on buying the cell phone.
Hence,
35% discount on tag price=Saved amount
(35/100)×T=140
where T is the tag price.
T=(140×100)35
T=14000/34
T=400
Therefore, on buying the cell phone with 35% discount on tag price costs around 140. Then the tag price is 400.
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If a truck traveled 75 miles in 3 hours, how many miles would the truck have traveled per minute?
The truck travelled 0.42 miles per minute
How to determine the miles per minute?The given parameters are:
Distance = 75 miles
Time = 3 hours
Convert time to minutes
Time = 3 * 60 minutes
Time = 180 minutes
The speed is calculated as:
Speed = Distance/Time
This gives
Speed = 75 miles/180 minutes
Evaluate
Speed = 0.42 miles per minutes
Hence, the truck travelled 0.42 miles per minute
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WORTH 50 points pls answer.
The two polygons are similar. Find the values of x and y
Answer:
y = 120
x = 10.6
Step-by-step explanation:
Given polygons are parallelograms.
In parallelograms, consecutive angles are supplementary which means their sum is equal to 180.
Since two parallelograms are similar:
60 + y = 180 subtract 60 from both sides
y = 120
To find the value of x:
side lengths are proportional because these are similar polygons
[tex]\frac{x+4}{22} = \frac{12}{18}[/tex] cross multiply fractions
18x + 72 = 264 subtract 72 from both sides
18x = 192 divide both sides by 18
x = 10.6 approximately
Genevieve wants to verify that negative x is the simplified expression of one-fifth (5 x minus 20) minus one-half (4 x minus 8). which procedure can genevieve follow to verify this? add one-fifth (5 x minus 20) minus one-half (4 x minus 8) and negative x. put an equal sign between one-fifth (5 x minus 20) minus one-half (4 x minus 8) and one-fifth (5 x minus 20) minus one-half (4 x minus 8) and then solve for x. substitute 5 into the first expression, substitute 4 into the second expression, and evaluate them. substitute 5 into each expression and evaluate them.
Answer: -x
Apply Multiplicative Distribution Law:- 1/5 * 5x - 1/5 * 20 - 1/2 * 4x - 1/2 *(-8)
Determine the sign for multiplication or division: 1/5 * 5x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8
Cross out the common factor: x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8
Cross out the common factor: x - 4 - 1/2 * 4x + 1/2 * 8 - 4 - 2x + 1/2 * 8
Cross out the common factor: x - 4 - 2x + 1/2 * 8
Cross out the common factor: x - 4 - 2x + 4
Reorder and gather like terms: (x - 2x) + (- 4 + 4)
Collect coefficients for the like terms: (1 - 2) * x + (- 4 + 4)
Calculate the sum or difference : - x + (- 4 + 4)
The sum of two opposites equals 0: -x
Answer: -x
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Answer:
D) Substitute 5 into each expression and evaluate them.
Step-by-step explanation:
Identify the scale of measurement for the following variable: The weight of a group of dieters. Group of answer choices nominal ratio ordinal interval
Ratio scale of measurement for the following variable, The weight of a group of dieters.
What scale of measurement is the variable of weight?Ratio measurement scale of ratio variables include height, weight, and distance. The ratio scale allows for the addition, subtraction, division, and multiplication of data. Additionally, ratio scales have a "real zero," which sets them apart from interval scales. The ratio scale is used to determine weight. The ratio is identical to the interval scale, with the exception that 0 on the scale denotes the absence of anything. serval scales can depict values lower than zero and do not hold a true zero. For instance, you can gauge temperatures as low as -10 degrees Celsius. Contrarily, ratio variables are always greater than zero. Height and weight are measured starting at 0 and never below it. Because they are numbers as we typically think of them, ratio scales are the simplest to comprehend. On a ratio scale, the distance between consecutive numbers is equal, and a score of zero indicates that there is no presence of the thing being measured. The majority of ratio scales are counts of items.
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What is the simplified form of startroot startfraction 2,160 x superscript 8 baseline over 60 x squared endfraction endroot? assume x ≠ 0.
The simplified form is [tex]6x^{3}[/tex].
What are indices in maths?
An index, or a power, is the small floating number that goes next to a number or letter.The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.The equation is -
[tex]\sqrt{\frac{2160x^{3} }{60x^{2} } }[/tex]
We can rewrite this using property of multiplication to obtain
[tex]\sqrt{\frac{2160}{60} * \frac{x^{8} }{x^{2} } }[/tex]
We simplify variable expression in the radicand using
[tex]\frac{a^{m} }{a^{n} } = a^{m - n}[/tex]
[tex]\sqrt{36 * x^{8 - 2} }[/tex]
[tex]\sqrt{36 * x^{6} }[/tex]
[tex]\sqrt{36 * (x^{3})^{2} }[/tex]
[tex]\sqrt{36} * \sqrt{(x^{3})^{2} }[/tex]
[tex]6 * x^{3}[/tex]
Therefore, the simplified form is [tex]6x^{3}[/tex]
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this table shows how many students fro two high schools attended a football game. A student is randomly selected. what is the probability that a student attended the game, given that the student if fro North Beach? Round your answer to two decimal places.
Using it's concept, the probability that a student attended the game, given that the student if fro North Beach is:
B. 0.65.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that 170 people attended the game, out of which 110 are from North Beach, hence the probability is:
p = 110/170 = 0.65.
Hence option B is correct.
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Answer:0.55 is the correct answer
Step-by-step explanation:
find area and perimeter show your work
Answer:
A= 16
P=16
Step-by-step explanation:
A=h^bxb/ 2
P= side+base+side
In general, the arithmetic average return is probably too _____ (low/high) for longer periods and the geometric average is probably too _____ (low/high) for shorter periods.
The arithmetic average return is probably too high for longer periods and the geometric average is probably too low for shorter periods.
What is Arithmetic Average Return?
When we look at historical returns, the difference between the geometric and arithmetic average returns isn't too hard to understand.
To put it slightly differently, the geometric average tells you what you actually earned per year on average, compounded annually. The arithmetic average tells you what you earned in a typical year. You should use whichever one answers the question you want answered. A somewhat trickier question concerns forecasting the future, and there's a lot of confusion about this point among analysts and financial planners.
Now, If we have estimates of both the arithmetic and geometric average returns, then the arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.
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If 0° < θ < 90° or 180° < θ < 270°, explain why sin 2θ is always positive.
Using a trigonometric identity, since in the first quadrant and in the third quadrant the sine and the cosine have the same sign, [tex]\sin{2\theta}[/tex] is always positive.
What is the trigonometric identity for sin 2θ?It is given by:
[tex]\sin{2\theta} = 2\sin{\theta}\cos{\theta}[/tex]
In the first quadrant(0° < θ < 90°) and in the third(180° < θ < 270°), the sine and the cosine have the same sign, hence the multiplication is positive and [tex]\sin{2\theta}[/tex] is always positive.
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Find the unknown angles
Answer:
Se below
Step-by-step explanation:
The two angles form a straight line which is 180° angle
4z + z = 180
5z = 180
z = 36 ° 4z = 144°
P(A) = 1/2
P(B) = 1/3
If A and B are independent, what is P(A ∩ B)?
Answer:
Step-by-step explanation:
hello :
P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6
Find the length of side a.
sorry for the bad quality, camera is broken. the one on top is 13 and the one below is 12.
SOLUTION :
a² = hypo² - base²
a² = 13² - 12²
a² = 169 - 144 = 25
a = √25
a = 5 units.
________________________________
HOPE IT HELPS
determine the slope of the line!!!!!
Answer: -3/2
Step-by-step explanation:
we could use the two points (2,3) and (0,4) from the graph
y2-y1/x2-x1
= 0-3/4-2
= -3/2
I don’t know what the second part of the question means
Answer:
Hello!
independent variable: variable in an experiment that is changed e.g. a plant's exposure to light
dependent variable: variable in an experiment that is measured e.g. a plant's height
The question is just asking to identify these variables.
Hope this helps! Feel free to ask further questions if need be.
NEED HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
A
Step-by-step explanation:
The function has vertical asymptotes at x=7 and x=-3, so the denominator needs to have factors (x-7) and (x+3).
This eliminates all the options except for A.
What is a Turned triangle?
Please tell me QUICKLY.
like the place where you are applying TURNED TRIANGLE.
coz literrally it means that if the trianlge has for example angle a on its right side then we turn the triangle as a whole and make the turn such that angle a is anywhere else but not on our right side....
I believe the explanation is clear, if not do contact me
Use the Law of Sines to solve (if possible) the triangle for the value of c. Round answers to the nearest tenths. A = 27.5°, a = 15.0 cm, b = 36.4 cm
The law of sines cannot be used to calculate the side c.
How to solve for side c?The given parameters are:
A = 27.5°, a = 15.0 cm, b = 36.4 cm
Based on the above values,
The law of sines cannot be used to calculate the side c.
This is so because the angle C is not given
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Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative three and negative four.
The equation of the graphed parabola is y=a[tex](x+3)^{2}[/tex]-4.
Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).
We are required to find the equation of the graphed parabola.
The equation of a quadratic function of vertex (h,k) is given by:
y=a[tex](x-h)^{2}[/tex]+k
In the above equation a is the leading coefficient.
We have been given point (-3,-4).
We have to just put the value of h=-3 and k=-4 and the required equation will be as under:
y=a[tex](x+3)^{2}[/tex]-4
Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a[tex](x+3)^{2}[/tex]-4.
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What is the area of the shape?
Answer: 21 units²
Step-by-step explanation:
Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where a and b are the parallel sides and h is the height.
Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.
[tex]A=\frac{1}{2}(5+9)*3[/tex]
[tex]A=\frac{1}{2}(14)*3[/tex] [Adding in the parentheses]
[tex]A=7*3[/tex] [Multiplying one-half by 14]
[tex]A=21[/tex] [Multiplying 7 and 3]
The area is 21 units².
Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle of elevation of 61°. Dan is standing on the ground at a point directly west of the base of the tower and must look up at an angle of elevation of 72° in order to see the top. If the CN Tower is 553.3 m tall,how far apart are Vic and Dan to the nearest meter? Include a well-labeled diagram as part of your solution.
Vic and Dan are 2, 897m apart.
How to determine the distance
It is important to note that the distance between Vic and Dan is the base of CN
Let's say the distance to Dan is x
The distance to Vic is y
Using cosine ratio, we have
cos α = opposite / adjacent
α = 72°
opposite = 553. 3cm
Adjacent = x
cos 72° = [tex]\frac{553. 3}{x}[/tex]
Cross multiply
[tex]cos 72[/tex] × [tex]x[/tex] = [tex]553. 3[/tex]
[tex]0. 3090x= 553. 3[/tex]
[tex]x = \frac{553. 3}{0. 3090}[/tex]
[tex]x = 1, 790. 61[/tex] m
The distance to Vic is y
Using the cosine ratio, we have
[tex]cos 60 = \frac{553. 3}{y}[/tex]
Cross multiply
[tex]0. 5y = 553. 3[/tex]
[tex]y = \frac{553. 3}{0. 5}[/tex]
[tex]y = 1,106. 6[/tex]m
To determine how far apart Vic and Dan, we use = x + y
= 1790. 61 + 1106. 6
= 2, 897. 21m
= 2, 897m
Thus, Vic and Dan are 2, 897m apart.
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What equation is parallel to 3y = 6x-10 and passes through A(4,5)?
Answer:
57?
Step-by-step explanation:
A student missed 45 problems on a mathematics test and received a grade of 39%. If all the problems were of equal value, how many problems were on the test
There were 74 problems in the test.
Rounding-off percentageLet the student got total number of problems in the test to be X.
Percentage of correct answer = 39 %
⇒ 61% of X were incorrect
⇒61/100 x X = 45
⇒61X = 45x100
⇒X = 4500/61
⇒X=73.77
After rounding off 73.77, we get 74.
Hence, we can say that there were total of 74 problems in the test.
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HELP!!!!!!QUICK!!!!!!!
If there are fifty raffle tickets in a jar, and only two will be drawn out, and you own two of them, what chance do you have of owning both winning tickets?
Answer:
1/25
Step-by-step explanation:
Answer:
I think it may be 1/1225
Step-by-step explanation:
first chance is 2/50 and second chance is 1/49 as one card decrease at first. So multiplying it we get 1/1225.
Which type of arc requires another entity to specify its start point?
A chemist has three different acid solutions. the first acid solution contains 20 % acid, the second contains 30 % and the third contains 60 % . he wants to use all three solutions to obtain a mixture of 54 liters containing 45 % acid, using 2 times as much of the 60 % solution as the 30 % solution. how many liters of each solution should be used? the chemist should use liters of 20 % solution, liters of 30 % solution, and liters of 60 % solution.
Let [tex]a,b,c[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% acid solutions, respectively. These quantities then contain [tex]0.20a[/tex], [tex]0.30b[/tex], and [tex]0.60c[/tex] liters of acid.
The chemist wants to end up with a total volume of 54 liters, so
[tex]a + b + c = 54[/tex]
and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so
[tex]0.20a + 0.30b + 0.60c = 24.3[/tex]
He will also use twice as much of the 60% solution as the 30% solution, so
[tex]c = 2b[/tex]
Substitute this into the first two equations and solve for [tex]a,b[/tex].
[tex]\begin{cases} a + 3b = 54 \\ 0.20a + 1.50b = 24.3 \end{cases}[/tex]
Eliminating [tex]b[/tex], we have
[tex](a + 3b) - 2 (0.20a + 1.50b) = 54 - 2(24.3) \implies 0.60a = 5.4 \implies \boxed{a = 9}[/tex]
Solve for [tex]b[/tex].
[tex]9+3b=54 \implies 3b=45 \implies \boxed{b=15}[/tex]
Solve for [tex]c[/tex].
[tex]c = 2(15) \implies \boxed{c=30}[/tex]
a = 9, b = 15 and c = 30 liters of each solution should be used.
What liter means?According to the metric system, a liter is a unit for measuring volume. A bottle of Coke that holds 33.76 ounces, or 1.0567 quarters, is an example of a liter. 2. The fundamental metric unit of liquid volume or capacity, which is equivalent to 1.06 quarts or 2.12 pints.What is a liter of water?Let's examine this with the help of the following justification. Despite the fact that there is no established standard size for glasses, their capacity varies. In contrast, we estimate that a glass of water holds 8 ounces, and a liter holds 32 ounces.According to the question:
Let a, b, and c stand for the relative volumes (in liters) of the 20 percent, 30 percent, and 60 percent acid solutions. The amount of acid in these amounts is 0.20a, 0.30b, and 0.60c liters.
a+b+c = 54 because the chemist wishes to have a final volume of 54 liters.
and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so
0.20a + 0.30b + 0.60c = 24.3
Additionally, he will consume twice as much of the 60% solution as the 30% solution, thus c = 2b.
Substitute this into the first two equations and solve for a,b
a + 3b = 54
0.20a + 1.50b = 24.3
Eliminating b, we have[tex](a+3 b)-2(0.20 a+1.50 b)=54-2(24.3) \\0.60 a=5.4[/tex]
a = 9.
Solve for b.9+3b = 54
3b = 45
b = 15.
Solve for c.c = 2(15)
c = 30.
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2 quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answer:
t = 60/n
Step-by-step explanation:
The original equation we know is y = k/n
Since 12 people can assemble the set in 5 hours, when y is 5, n will be 12.
We can now input that value into the equation.
--> 5 = k/12
--> 5(12) = k/12 (12)
--> 60 = k
--> k = 60
The equation to represent the situation can be written as:
t = 60/n
and that is our final answer!
12 people can assemble in 5hours
So
y=k/x12=k/5k=60Equation
y=60/xOr
t=60/nDetermine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
Step-by-step explanation:
Finding the third angle in triangle XYZ,
[tex]m\angle YXZ=180^{\circ}-77^{\circ}-48^{\circ}=55^{\circ}[/tex],
Thus, [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.