We know that the lines (AC) and (BD) are parallel.AE = 4.2 × 10^4; BE = 3.2 × 10^3; CE = 6.8 × 10^5Calculate ED length
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1) Since the lines AC and BD are parallel and given the measurements, we tell these triangles are similar.
2) Based on that we can write out the following ratios:
[tex]\begin{gathered} \frac{3.2\cdot \:10^3}{4.2\cdot \:10^4}=\frac{x}{6.8\cdot \:10^5} \\ \frac{x}{6.8\cdot \:10^5}=\frac{3.2\cdot \:10^3}{4.2\cdot \:10^4} \\ x=51809.52380 \\ x=5.18\cdot10^4 \end{gathered}[/tex]Rounding off to the nearest hundredth.
Related Questions
Write As An Algebraic Expression For The Following:3 Times A Number Decreased By 5The Quotient Of A Number and 3The Product Of Three Times A Number And 62 Less Than The Product Of A Number And 6
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3x - 5
In answering the question, our chosen unknown number will be represented by a variable x
3 times a number
= 3 * x = 3x
decreased by 5 means we are going to subtract 5 from our previous answer
Thus, we have 3x - 5
What is the solution to the equation 4x = 44?x = 10x = 40x = 11x = 4
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Dividing the given equation by 4 we get:
[tex]\frac{4x}{4}=\frac{44}{4}.[/tex]Simplifying the above result we get:
[tex]x=11.[/tex]Answer: Third option.
[tex]x=11.[/tex]
Hong is participating in a 6-day cross-country biking challenge. He biked for 71, 59, 68, 70, and 68 miles on the first five days. How many miles does he need to bike on the last day so that his average (mean) is 64 miles per day?
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Based on the given information, we can express the following
[tex]64=\frac{71+59+68+70+68+x}{6}[/tex]We formed that equation from the mean formula. Now, we solve for x,
[tex]\begin{gathered} 64\cdot6=336+x \\ x=384-336 \\ x=48 \end{gathered}[/tex]Hence, he needs to bike 48 miles on the last day to have an average of 64 miles per day.In a paragraph, explain what the domain and range is for the function, and how you found your answer: f(x) = x^2+6x - 25.
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A function's domain is the set of all points across which it is defined. That is all the x - values it can takes. The range is values that the function takes on as output. That is all y - values it is defined.
for f(x) = x^2+6x - 25.
domain: all ℝ numbers
range: [-34, ∞)
Evaluate.36² + 6 + - 15 + (30/-6)
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Solving the operation in parenthesis gives us:
[tex]36^2+\text{ 6 + - 15 +}-5[/tex]Now we need to solve the power, which is done below:
[tex]1296\text{ + 6 + - 15 + - 5}[/tex]Adjusting all the signals:
[tex]1296+6-15-5[/tex]Performing the operations:
[tex]\begin{gathered} 1302\text{ -15 -5} \\ 1287\text{ -5} \\ 1282 \end{gathered}[/tex]If a 5 km race is approximately 3.1 miles, how many meters would you have to run to complete ahalf marathon (13.1 miles)
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we know that
5 km race is approximately 3.1 miles
or
5,000 meters ----------> 3.1 miles
so
Applying proportion
Find out how many meters are 13.1 miles
5,000/3.1=x/13.1
solve for x
x=(5,000/3.1)*13.1
x=21,129 metersSophia and Emilio are looking for a daycare for their son, Michael. They want to make sure the daycare is midway between their jobs. Sophia works at the HEB located at (4, 6), and Emilio works at the Home Depot located at (1, 2). Where should the daycare be located?1.(2.5, 4)2.(1.5, 5)3.(1.5, 2)4.(2, 3)Sophia and Emilio are looking for a daycare for their son, Michael. They want to make sure the daycare is midway between their jobs. Sophia works at the HEB located at (4, 6), and Emilio works at the Home Depot located at (1, 2). Where should the daycare be located?a.(2.5, 4)b.(1.5, 5)c.(1.5, 2)d.(2, 3)
Answers
Solution
We have the two points (4, 6) and (1, 2)
We only need to find the midpoint
[tex]\begin{gathered} Midpoint=(\frac{4+1}{2},\frac{6+2}{2}) \\ \\ Midpoint=(\frac{5}{2},4) \\ \\ Midpoint=(2.5,4) \end{gathered}[/tex]Correct Option (2.5, 4)
Find the equation of the line that is parallel to the line 4x+2y=24 that goes through the point (6,4)
Answers
We have that the linear equation is:
4x + 2y = 24
We need to convert this standard form of the line equation into the slope-intercept form of the line equation, that is, y = mx + b. Then, we can do as follows:
1. Subtract 4x from both sides of the equation:
[tex]4x-4x+2y=24-4x\Rightarrow2y=-4x+24[/tex]2. Divide both sides of the equation by 2 (to isolate y):
[tex]\frac{2y}{2}=-\frac{4}{2}x+\frac{24}{2}\Rightarrow y=-2x+12[/tex]Now, we have the slope-intercept form of the line equation. The slope, m, is m = -2.
Since we need to find a parallel line to this line, the new line needs to have the same slope, that is, m = -2.
Then, we have the slope, m = -2, and the point (6, 4). We can use the point-slope form of the line equation to find the parallel line. Therefore, we have:
[tex]y-y_1=m(x-x_1)\Rightarrow y-4=-2(x-6)[/tex]And then, expanding this equation, we finally have that the parallel line is:
[tex]y-4=-2x+12\Rightarrow y=-2x+12+4\Rightarrow y=-2x+16[/tex]what is the equation in standard form y= -3x - 4
Answers
The standard form of equation of a line is expressed as y = mx+c where;
m is the slope of the line
c is the intercept
Given the equation of the line y = -3x - 4
you can see that the equation given is already in its standard form with -3 as the slope and -4 a the intercept.
Hence the standard form of the equation is still y = -3x - 4
A regular octagon has eight sides of equal length.A stop sign is in the shape of a regular octagon.Find the perimeter of a stop sign with a side length of 12 in. Answer in inches
Answers
Recall that the perimeter of a polygon is the sum of the lengths of each side of the polygon.
Since a regular octagon has 8 sides of equal length, and the stop sign is a regular octagon with a side length of 12 in, then its perimeter is:
[tex]\text{Perimeter}=8\times12in\text{.}[/tex]Simplifying the above result we get:
[tex]\text{Perimeter}=96in\text{.}[/tex]Answer:
[tex]96in\text{.}[/tex]Find the volume of saup in a cylindricd can thatBaches til and inches across the lid
Answers
The volume of the cylinder is
[tex]V=\pi\times r^2\times h[/tex]Where:
r is the radius of the base of the cylinder
h is the height of the cylinder
Since the cylinder is 8 inches tall, then
h = 8 inches
Since it is 4 inches across the lid, then
The diameter of the base is 4 inches
Divide it by to get the radius of it, then
r = 2 inches
Now, substitute them in the rule above
[tex]\begin{gathered} V=\pi\times2^2\times8 \\ V=\pi\times4\times8 \\ V=32\pi in^3 \end{gathered}[/tex]We can use pi = 3.14, then
[tex]V=100.48in^3[/tex]The volume of the soup is 100.48 inches^3
what is that simplify24/36 using that Giant one
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so the answer is 2/3
how is 2/4 and 3/6 related
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Stacy is building a candy house. She worked on it 3 2/3 hours before lunch and 6 1/4 hours after lunch. How many total hours did Stacy spend working on the candy house?
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To calculate the total nmber of hours, we will simply add
[tex]3\frac{2}{3}+6\frac{1}{4}[/tex]Let's add the whole number part, then add the fraction part
That is;
[tex]3+6+\frac{2}{3}+\frac{1}{4}[/tex][tex]=9+\frac{8+3}{12}[/tex][tex]=9\frac{11}{12}\text{ hours}[/tex]The above is the total number of hour she spent.
A target with a diameter of 70 cm has 4 scoring zones formed by concentriccircles. The diameter of the center circle is 10 cm. The width of each ring is 10cm. A dart hits the target at a random point. Find the probability that it will hit apoint in the yellow region.
Answers
The probability is equal to divide the area of the yellow region by the area of the complete circle
so
step 1
Find the area of teh complete circle
r=70/2=35 cm
substitute
[tex]\begin{gathered} A=\pi\cdot35^2 \\ A=1,225\pi\text{ cm2} \end{gathered}[/tex]step 2
Find the area of the yellow region
[tex]\begin{gathered} A=\pi(35^2-25^2) \\ A=600\pi\text{ cm2} \end{gathered}[/tex]step 3
find the probability
P=600pi/1,225pi
P=0.4898
or
P=48.98%
What is the value of the expression 7x2+ 9x-3 when x = 3?
Answers
Answer:
87
Explanation:
To find the value of the expression at x = 6, we simply replace x with 6. This gives
[tex]7(3)^2+9(3)-3[/tex]which we simplify to get:
[tex]\begin{gathered} 7\times9+27+-3 \\ =63+27-3 \\ =\boxed{87.} \end{gathered}[/tex]Hence, the value of the expression is 87 when x = 3.
How do you know that all four sides of this shape are congruent?
Answers
Quadrilateral QRST is given as a parallelogram. Hence, opposite sides are congruent.
That is
Line segment QT is congruent to line segment RS
and
Line segment QR is congruent to line segment TS
Since it is given that QR is congruent to QT, then all the four sides of the quadrilateral QRST are congruent.
How do I solve for 15? It says to use tan30=20/a
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Since we have a right triangle, we can relate the given angle and the legs a and 20 by means of the tangent function ,that is,
[tex]\tan 30=\frac{20}{a}[/tex]Since tangent of 30 degrees is
[tex]\text{tan}30=\frac{\text{ opposite side to angle 30}}{\text{ adjacent side to angle 30}}=\frac{1}{\sqrt[]{3}}[/tex]we have that
[tex]\frac{1}{\sqrt[]{3}}=\frac{20}{a}[/tex]Then, by cross multiplying the numbers, we have
[tex]1\times a=20\times\sqrt[]{3}[/tex]Therefore, we have:
[tex]a=20\sqrt[]{3}=34.64[/tex]By rounding to the nearest whole number, the answer is: 35 units
Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.2лम2л五COS(15) w() - Sin(ਤੋਂ ) sin()-(COS
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The sum identity for Cosine is given as:
[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]This is the same for the given equation in the equation, assuming:
[tex]\begin{gathered} A=\frac{2\pi}{5} \\ B=\frac{\pi}{12} \end{gathered}[/tex]Hence, the correct answer is:
[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]Is the answer A. or C.? Can you explain, please?
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The correct answer is A.
In Panel 3, option C is what you found on the top of the box with a smiley face, if you flip it side ways like in panel 4, the direction of the shape will also change that is the same with option A.
Luther started collecting lunch boxes when he was 5 years old. He had 12 superhero lunch boxes, 19 outer space lunch boxes, and 26 rock band lunch boxes.Then Luther's cousin started her own lunch box collection. Luther wanted to help her get started, so he gave his cousin 17 lunch boxes from his collection. How many lunch boxes does Luther have left in his collection?
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Solution
For this case we have the following lunch boxes
12 from superhero
19 from outer space
26 from rock bands
A total of: 12+19+26= 57 lunch boxes
And he gave to his cousin 17 lunch boxes so then the remaining are:
57-17= 40 lunch boxes
The ratio soccer balls to basebalss is 12 to 15. If there are 48 soccer balls, how many baseballs are there?
Answers
Answer
60baseballs
Explanation
Given the ratio soccer balls to basebalss is 12 to 15, this is expressed as:
12:15
Ratio of soccerball = 12
Ratio of baseball = 15
Total ratio = 12+15
Total ratio = 27
First let us calculate the total balls, this is expressed as:
12/27 * x = 48 (using soccerball)
x is the total balls
12x/27 = 48
cross multiply:
12x = 27*48
12x = 1296
x = 1296/12
x = 108
The total number of balls is 108 balls
Since baseball + soccerball = 108
baseball + 48 = 108
baseball = 108-48
baseball = 60
Hence the total number of baseball is 60.1
Find the area of the shaded piece. Round the nearest HUNDREDTH, if needed. AC = 30 and m
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Solution
The diagram below will be of help
Note: Area of a Sector Formula
[tex]Area=\frac{\theta}{360}\times\pi r^2[/tex]Here
[tex]\begin{gathered} r=15 \\ \theta=55^{\circ} \end{gathered}[/tex]Substituting the parameters
[tex]\begin{gathered} Area=\frac{\theta}{360}\pi r^{2} \\ Area=\frac{55}{360}\times\pi\times15^2 \\ Area=\frac{275}{8}\pi \end{gathered}[/tex]There are two shaded portion (with the same Area)
Therefore, the area will be
[tex]\begin{gathered} Area=2\times\frac{275}{8}\pi \\ Area=\frac{275}{4}\pi \\ Area=215.9844949 \\ Area=215.98\text{ square unit \lparen to the nearest hundredth\rparen} \end{gathered}[/tex]The answer is
[tex]\begin{equation*} 215.98\text{ square unit \lparen to the nearest hundredth\rparen} \end{equation*}[/tex]The area of the triangle has a height of 10.2ft and base of 28ft. What is the area of the shaded region
Answers
The area of a triangle is computed as follows:
[tex]A=\text{base}\cdot\text{height}\cdot\frac{1}{2}[/tex]Substituting with base = 28 ft, height = 10.2 ft, we get:
[tex]A=28\cdot10.2\cdot\frac{1}{2}=142.8ft^2[/tex]The area of a rectangle is computed as follows:
[tex]A=\text{base}\cdot\text{height}[/tex]The rectangle of the graph has a base of 29.8 ft and a height of 23 ft. Its area is:
[tex]A=29.8\cdot23=685.4ft^2[/tex]Therefore, the area of the shaded region is:
[tex]\text{area of the rectangle - area of the triangle = 685.4-142.8 = }542.6\text{ sq. ft}[/tex]If 6/7 of a class was absent due to illness and 2/5 of the school was absent due to illness, is the fraction of the class that was absent equivalent to the fraction of the entire school that was absent?
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We have to convert the fraction to a decimal number, because the fractions given are in the simplest form
[tex]\frac{6}{7}=0.86[/tex][tex]\frac{2}{5}=0.4[/tex]as we can see the fractions given are not equivalent because the decimal number must be the same in equivalent fractions.
Therefore
3)225 using partial quotients.
Answers
75
-----------
3I225 I
- 210 I 70 ( because 70*3 = 210)
-------------- I +
15 I5 (because 5*3=15)
- 15 I
--------------------
0 75
Quotient is 75 and the remainder is 0
Could you please check my answer? Use elimnation to solve the system of equations:3x+4y=82x+3y=8My answer: (-8, 8)
Answers
According to the given data we have the following system of equations:
3x+4y=8
2x+3y=8
In order to calculate the variables x and y we would make the following calculations:
3x+4y=8
2x+3y=8
First we would multiply 3x+4y=8 times 2 and 2x+3y=8 times -3 So:
3x+4y=8
2x+3y=8
0 -y=-8
y=8
If y=8, hence, we would substitute the value of y into the first equation so we can finally calculate the variable x.
So:
plug y=8 into 3x+4y=8
3x + 4(8)=8
3x+ 32=8
3x=-24
x=-24/3
x=-8
Hence, the values of x and y would be (-8,8)
Rex wanted to estimate the mean finishing time for the finishers at the New York CityMarathon. He took a random sample of 10 finishers' times, which were skewed to the right witha sample mean of 271.5 minutes. He's considering using his data to make a confidence intervalfor the mean finishing time, has he met the conditions for creating a confidence interval for thetrue mean finishing time?
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No, he isn't the sample is just a few finishers. He must increase the size of the sample. Or at least calculate which could be the size of the sample to determine if he's right or wrong.
Express the following fraction in simplest form, only using positive exponents. 5 3(v1) 2v-1
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So we brought the numbers out and worked on v alone
The graph below shows a displacement(m)-time(s) graph for a particle moving in a straight line.The speed of the particle in the first T seconds was half the speed of the particle in the last 3 seconds.Find the value of T.
Answers
The value of T = 6 sec
Explanation:We need to find the relationship between displacement, speed and time
The formula relating the displacement to speed and time:
[tex]\text{speed = }\frac{displacement}{time}[/tex]For the first T seconds:
time = T
displacement = 4m
[tex]speed_1\text{ = }\frac{4}{T}[/tex]For the last 3 seconds:
time = 14 sec - 11 sec = 3 sec
displacement = 4 - 0 = 4 m
[tex]speed_3\text{ = }\frac{4}{3}\text{ m/s}[/tex]From the question:
The speed of the particle in the first T seconds was half the speed of the particle in the last 3 seconds
[tex]\begin{gathered} speed_1\text{ = }\frac{1}{2}(speed_3) \\ \frac{4}{T}\text{ = }\frac{1}{2}(\frac{4}{3}) \\ \frac{4}{T}=\text{ }\frac{4}{6} \\ \frac{4}{T}=\text{ }\frac{4}{6} \\ \text{cross multiply:} \\ 4(6)\text{ = 4(T)} \\ 24\text{ = 4T} \end{gathered}[/tex][tex]\begin{gathered} \frac{24}{4}\text{ = }\frac{4T}{4} \\ T\text{ = 6 sec} \end{gathered}[/tex]