Answers
Answer: 140 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\ and\ (x_3,y_3)[/tex] is given by
[tex]\text{Area}=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2][/tex]
Then area of triangle QRS with vertices (6,10), (2,-10) and (-9,5) is given by :-
[tex]\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-10-5)+2(5-10)-9(10-(-10))]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-15)+2(-5)+-9(20)]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[280]|\\\\\Rightarrow\text{Area}=140\text{ square units}[/tex]
Answer:
the answer is 140. I did the assignment
Related Questions
Maria needs $2.35 to buy a magazine. The only money she has is a jar of nickels and dimes. Write an equation in standard form for the different amounts of nickels x and dimes y she could use. Show your work :)
Answers
Evaluate 5 | x^3 - 2| + 7 when x = -2.
Answers
If two cylinders are similar and the ratio between the lengths of their edges is 4:3 what is the ratio of their volumes
Answers
volume scale factor is given by:
volume scale factor=(linear scale factor)^3
given that the linear scale factor is given by the ratio 4:3 which can be written as 4/3
thus the volume scale factor will be:
(4/3)^3
=64/27
this can be written as 64:27
Answer:
64:27
Step-by-step explanation:
what is 475.53 minus 67.37
Answers
The surface areas of two similar solids are 289 ft2 and 900 ft2. The volume of the larger solid is 1,755 ft3. What is the volume of the smaller solid?
Answers
In parallelogram ABCD, if angle C=110 and angle D=70, what is the sum of the measures of angle A and angle B?
Answers
To solve this problem, we must remember that the sum of interior angle of a polygon is:
Sum of interior angles = (n – 2) * 180˚
So, we can say that:
Sum of interior angles = angle A + angle B + angle C + angle D = (4 – 2) * 180˚
Where,
angle C + angle D = 110 + 70 = 180˚
Therefore substituting this value:
angle A + angle B + 180˚ = 2 * 108˚
angle A + angle B = 360˚ - 180˚
angle A + angle B = 180˚ (answer)
Hence we can also conclude that,
angle A + angle B = angle C + angle D
The answer is 180 degrees because...
angle A + angle B + 180˚ = 2 * 108˚
angle A + angle B = 3
angle A + angle B = 180˚ 60˚ - 180˚
Hope this helps, have a BLESSED and wonderful day! As well as as a safe one! :-)
-Cutiepatutie ☺❀❤
A 125-inch pipe is cut into two pieces. one piece is four times the length of the other. find the lengths of the two pieces.
Answers
You can calculate the length of the two pieces of pipe by setting up and solving a simple equation: 'x' stands for the length of the shorter piece, '4x' stands for the length of the longer piece, which will add up to the total length, 125 inches. You will find that 'x' equals 25, meaning the shorter pipe is 25 inches long and the longer one is 100 inches long.
Explanation:This question revolves around a simple equation in algebra. If we say that the shorter piece of pipe's length is 'x', we know from the problem that the longer piece's length is four times this length, or '4x'. The total length of the pipe, 125 inches, is made up of these two pieces. Therefore, those two lengths must add up to 125 inches.
This gives us the equation 'x + 4x = 125'. Combining like terms gives us '5x = 125'. To find 'x', we then divide both sides of the equation by 5, giving us 'x = 25'. Therefore, the shorter piece of pipe is 25 inches long, and the longer piece, being four times this length, is 100 inches long.
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How many revolutions will a car wheel of diameter 26 in. make as the car travels a distance of one mile? (round your answer to the nearest whole number.)?
Answers
there are 8280 feet in 1 mile
The number of revolutions in travelling 1 mile = 5280 * 6
----------- = 776 revs
13 pi
Answer:
776 revolutions per mile
Step-by-step explanation:
First we need to find the Circumference of the wheel.
Formula for circumference = πD
Where D = Diameter of the car wheel = 26 inches
Circumference of the car wheel = π × 26
= 81.68 inches
We have to find, how many inches make 1 mile.
1 mile = 63360 inches.
To determine the number of revolutions a car wheel of diameter 26 inches will travel,
= 63360 inches ÷ circumference of the car wheel
= 63360 inches ÷ 81.68inches
= 775.71 revolutions per mile
To the nearest whole number = 776 revolutions per mile.
To raise money for charity,Polly climbs the 1,776 steps in the CN Tower in Toronto,Canada.If it takes her 40 minutes to complete the climb,what is Polly's average rate per minute?
Answers
Which expression is equivalent to (4g^3h^2k^4)^3/8g^3h^2 - (h^5k^3)^5
Answers
Given expression:[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}-\left(h^5k^3\right)^5[/tex]
[tex]\left(4g^3h^2k^4\right)^3:\quad 2^6g^9h^6k^{12}[/tex]
[tex]8:\quad 2^3[/tex]
[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}=\frac{2^6g^9h^6k^{12}}{2^3g^3h^2}[/tex]
[tex]=2^3g^6h^4k^{12}[/tex]
[tex]\left(h^5k^3\right)^5=h^{25}k^{15}[/tex]
[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}-\left(h^5k^3\right)^5=2^3g^6h^4k^{12}-h^{25}k^{15}[/tex]
[tex]=8g^6h^4k^{12}-h^{25}k^{15}[/tex]
Therefore, correct option is 4th option [tex]8g^6h^4k^{12}-h^{25}k^{15}[/tex].
Answer:
ANSWER IS D
Step-by-step explanation:
Solve for t: 35t + 70 (7-t) = 385
Answers
To solve this equation, first, distribute the 70 across (7 - t). This creates the equation [tex]35t+490-70t=385[/tex]. Collecting like terms and subtracting 490 from both sides of the equation makes [tex]-35t=-105[/tex]. To finish solving for t, all you have to do now is divide by -35: [tex] \frac{-35t}{-35} = \frac{-105}{-35} [/tex], [tex]t=3[/tex].
What is the 32nd term of the arithmetic sequence where a1 = 4 and a6 = 34 ?
Answers
the nth term of an arithmetic sequence is :
An =Ap+(n-p)d ....a common difference is : d
in thie exercice : p=1 and n=6
A6 = A1 + (6-1)d
34 = 4 +5d
5d= 30
d= 6
A32 = A1+(32-1)(6) =4 + 31(6) = 190
Help identify measure of arc UV
Answers
45 = 1/2(94+20- arcUV)
45=57 - arcUV/2
arcUV / 2 = 57-45
arcUV / 2 =12
arcUV = 12(2)
arcUV = 24
answer is B. 24
The measure of arc UV is 24° .
What is arc?An “arc” is a smooth curve joining two endpoints. In general, an arc is one of the portions of a circle. It is basically a part of the circumference of a circle. Arc is a part of a curve.
According to the question
The Triangle formed inside the triangle
with angles 90° , 36° , ∠W
As sum of angle of triangle
99° + 36° + ∠W = 180°
∠W = 180° - 99° - 36°
∠W = 45°
Now,
According to the relation
∠W = [tex]\frac{1}{2}[/tex](arc SP - arc UV)
As
Arc SP = 94° + 20°
= 114°
so ,
45° = [tex]\frac{1}{2}[/tex]( 114° - arc UV)
90° = 114° - arc UV
arc UV = 114° - 90°
= 24°
Hence, the measure of arc UV is 24° .
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You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
10.1101 years
119.954 years
121.321 years
134.34 years
Answers
A=p (1+r/k)^kt
3000=150 (1+0.025/12)^12t
Solve for t
3000/150=(1+0.025/12)^12t
Take the log
Log (3000/150)=12t×log (1+0.025/12)
12t=Log (3000/150)÷log (1+0.025/12)
T=[Log (3000/150)÷log (1+0.025/12)]÷12
T=(log(3,000÷150)÷log(1+0.025÷12))÷12
T=119.954 years
The table below shows the surface area y, in square inches, of a shrinking puddle in x hours: Time (x) (hours) 1 4 7 10 Surface area (y) (square inches) 100 85 70 55 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the puddle. [Choose the value of the correlation coefficient from −1, −0.99, −0.5, −0.02.] (4 points) Part B: What is the value of the slope of the graph of surface area versus time between 1 and 4 hours, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
Answers
Part A. The correlation coefficient, R², is the quantitative evaluation of how the data points are well-fitted to a model. The closer it is to 1, the better. But a R²=1 is very ideal and rare. This can be only true if the points coincides exactly with the given model. Since we can see in the graph that the points are exaclty passed through by the linear model, the correlation coefficient is 1.
Part B. The slope of the graph is measured between two points as Δy/Δx. So, between 1 to 4 hours, the slope is: (85-100)/(4-1) = -5. The slope represents the instantaneous rate of change of surface area with time. It is called instantaneous because the change was only between than interval, not the whole set of data. Also, the negative sign signifies that the trend is decreasing.
Part C. The data represents causation if the time was the cause of the change of the pond's surface area. However, this is not technically true because there might be other factors to be considered like environmental conditions. But, definitely, these data are in correlation because together they show an observable trend.
Harmony can spend up to $100 on a shopping trip. She needs to buy socks and shoes. Each pair of socks costs $5.00 and each pair of shoes costs $20.00. Which graph shows all of the ways she can purchase shoes and socks, spending up to $100?
Answers
4y+x≤20 subtract x from both sides
4y≤-x+20 divide both side by 4
y≤-0.25x+5
So just in simplest terms, the slope is slightly negative and it should be shaded under the line since y is less than the line...so it is the second graph.
The size of a television is usually indicated by the length of the screens diagonal if a person buys a 20 inch television set that is 12 inches tall how wide is the television
Answers
diagonal = sqrt(a^2 +b^2)
20 = sqrt(12^2 +b^2)
20= sqrt(144+b^2)
20^2 = 144 + b^2
400 = 144 + b^2
256 = b^2
b = sqrt(256) = 16
it is 16 inches wide
Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.
According to the given information, quadrilateral RECT is a rectangle. By the definition of a rectangle, all four angles measure 90°. Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the Converse of the Same-Side Interior Angles Theorem. Quadrilateral RECT is then a parallelogram by definition of a parallelogram. Now, construct diagonals ET and CR. Because RECT is a parallelogram, opposite sides are congruent. Therefore, one can say that segment ER is congruent to segment CT. Segment TR is congruent to itself by the Reflexive Property of Equality. The _______________ says triangle ERT is congruent to triangle CTR. And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.
Which of the following completes the proof?
A (ASA) Theorem
B (HL) Theorem
C (SAS) Theorem
D (SSS) Theorem
Answers
|ER|=|CT| shown
(Therefore, one can say that segment ER is congruent to segment CT.)
m(R)=m(T)= 90°shown
(By the definition of a rectangle, all four angles measure 90°)
|RT|=|TR|
so we have Side Angle Side congruence.
By the (SAS) Theorem, the triangles are congruent.
Answer: C (SAS) Theorem
The answer is (SAS) Theorem. Because we know triangle ERT is congruent to triangle CTR, it has the sides ( C& E and R&T, and the angle T&R).
Hope its correct.
If a 72-candela light source is located at a distance of 3 meters from a surface, the illuminance on the surface is _______ lux.
Answers
The answer is 8 lux. Using the formula E= I/s^2, E stands for the illuminance on the surface that we are trying to solving, I stands for the intensity of the light from the sources it is candelas in the problem that we’re solving, and S stands for the distance from the light source to the surface it should be in meters.
E= I/s^2
E= 72/3^2
E=72/9
E= 8
Answer:
Penn Foster Students: 8
Step-by-step explanation:
Given the function f(x), you can get a picture of the graph of it inverse F^-1(x) by flipping the original graph f F(x) over the _____.
A. y=-1
B x= -1
C y=x
Answers
y=x
Answer:
y=x
Step-by-step explanation:
apex
(05.06)Which interval on the graph could be described as linear constant?
A
B
C
D
Answers
since A is a horizontal line it is constant
so A would be linear constant
By defining a constant line, we will see that the correct option is interval A.
What is a constant line?
A general linear equation is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
We say that a line is a constant line if the slope is equal to zero, so we get:
y = b
This would be graphed as a horizontal line.
So we only need to see which interval on the graph has a horizontal line. We will see that the interval is the A interval.
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*WILL GIVE BRAINLIEST*(08.03)Consider the following set of equations:
Equation A: y = 2x + 4
Equation B: y = 3x + 1
Which of the following is a step that can be used to find the solution to the set of equations?
2x + 4 = 3x + 1
2x = 3x + 4
2x + 4 = 3x
2x + 1 = 3x + 4
Answers
Finding the solution step by step:
Given- Equation A: y=2x+4; Equation B: y=3x+1
y=y, so 2x+4=3x+1
Get variables on one side and numbers on the other..
4-1=3x-2x
3=x
Substitute x into one of the equations (doesn't matter which): y= 2(3)+4
y=6+4
y=10
Solution- (3,10)
Hope the explanation helped!
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -5 - 5 cos θ
Answers
-5-5cos(theta)=r
-r=5+5cos(theta)
no y-axis symmetry
x-axis symmetry=(r,theta)=(r,-theta)
cosine is an even function, so yes it is symmetric around x-axis
origin symmetry=(r,theta)=(-r,theta) or (r, theta+pi)
no, as there is no y-axis symmetry
Answer:
x-axis symmetry
Step-by-step explanation:
OQ is a diagonal of quadrilateral NOPQ. If NO=PQ, NQO=7y-37, and POQ=2y+93, find POQ such that NOPQ is a parallelogram. A.26° B.63° C.97° D.145°
Answers
its not 26.
Just saying
its D. 145
Answer: D! 145!
Step-by-step explanation:
your almost done!!! Ah good luck xoxo
Find the midpoint of segment below
Answers
mp=((x1+x2)/2, (y1+y2)/2)
The sum of 3 consecutive even numbers is 78
Answers
3x+6=78
3x=72
x=24
Final answer: 24, 26, 28
Which number sentence below matches this word problem?
Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore. How far did they get? A.15 - 6 = 9
B. 9 + 15 = 24 C.15 - 9 = 6
D. 135 9 = 15
Answers
I'd say C.
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore
so, distance they travel before they ran out of gas = 15 miles
distance they floated back down river = 9 miles
So, they are at
[tex]15-9\\\\=6\ miles[/tex]
Hence, They are 6 miles far.
Therefore, Option 'C' is correct.
The minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let v
represent the wind speed.
Answers
The absolute value equation that represents the minimum and maximum speeds of a Category 1 hurricane is |v - 84.5| ≤ 10.5, where v is the wind speed.
Explanation:To write an absolute value equation that represents the minimum and maximum speeds of a Category 1 hurricane, you will center it around the average of the two, which is (74 + 95) / 2 = 84.5 mph. The difference between the maximum speed and the average speed is 95 - 84.5 = 10.5 mph. Thus, the absolute value equation to represent the wind speeds of this hurricane category is |v - 84.5| ≤ 10.5, where v represents the wind speed.
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An absolute value equation representing the minimum and maximum sustained wind speeds of a Category 1 hurricane can be written as |v - 84.5| = 10.5, where v is the wind speed in miles per hour. This equation indicates that the wind speed can deviate by 10.5 mph above or below 84.5 mph, encompassing the range of 74 to 95 mph.
Explanation:To represent the minimum and maximum sustained wind speeds of a Category 1 hurricane using an absolute value equation, we can use the variable v to stand for the wind speed. The absolute value of a number represents its distance from zero regardless of direction, which in the context of wind speed means how much the speed differs from a certain value.
For instance, if the center value is the average of the minimum and maximum speeds, that would be (74 + 95) / 2 = 84.5 miles per hour. Therefore, the absolute value equation that represents the wind speeds that form the boundaries of Category 1 could be written as |v - 84.5| = 10.5. This equation means that the Category 1 wind speed, v, can be 10.5 miles per hour above or below 84.5 miles per hour, which corresponds to the range between 74 and 95 miles per hour.
However, there usually isn't just one single absolute value equation to represent this range. Another approach could involve setting two absolute value inequalities that represent the minimum and maximum separately, such as |v - 74| ≥ 0 for the minimum speed and |v - 95| ≤ 0 for the maximum speed.
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Find the exact value of tan (arcsin (two fifths)). For full credit, explain your reasoning.
Answers
[tex]\bf sin^{-1}\left( \frac{2}{5} \right)=\theta \impliedby \textit{this simply means that} \\\\\\ sin(\theta )=\cfrac{2}{5}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{now let's find the adjacent side} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\bf \pm \sqrt{5^2-2^2}=a\implies \pm\sqrt{21}=a \\\\\\ \textit{we don't know if it's +/-, so we'll assume is the + one}\quad \sqrt{21}=a\\\\ -------------------------------\\\\ tan(\theta)=\cfrac{opposite}{adjacent}\qquad \qquad tan(\theta)=\cfrac{2}{\sqrt{21}} \\\\\\ \textit{and now, let's rationalize the denominator} \\\\\\ \cfrac{2}{\sqrt{21}}\cdot \cfrac{\sqrt{21}}{\sqrt{21}}\implies \cfrac{2\sqrt{21}}{(\sqrt{21})^2}\implies \cfrac{2\sqrt{21}}{21} [/tex]
[tex]\rm tan\theta = \dfrac{2}{\sqrt{21} }[/tex]
Step-by-step explanation:
Given :
[tex]\rm sin^-^1(\dfrac{2}{5})=\theta[/tex]
Calculation :
[tex]\rm sin\theta = \dfrac{perpendicular}{hypotenuse}[/tex]
According to Pythagorean theorem,
[tex]a^2+b^2=c^2[/tex]
here a = 2, c = 5. Then,
[tex]2^2+b^2=5^2[/tex]
[tex]b^2=25-4=21[/tex]
[tex]b=\pm\sqrt{21}[/tex]
Nothing is given in the question so we take positive
[tex]b = \sqrt{21}[/tex]
Therefore,
[tex]\rm tan\theta=\dfrac{perpendicular}{base}[/tex]
[tex]\rm tan\theta = \dfrac{2}{\sqrt{21} }[/tex]
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If y varies directly with x and y = 15 when x = 5, what is the value of k?
Answers
y = kx
15 = k5
k = 15/5
k = 3