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According to the Pythagorean Theorem, if A and B are the legs of a right triangle and C is the hypotenuse, then:
[tex]A^2+B^2=C^2[/tex]The legs of the first right triangle are 5 and x, and its hypotenuse is 13. Use the Pythagorean Theorem and solve for x:
[tex]\begin{gathered} x^2+5^2=13^2 \\ \Rightarrow x^2+25=169 \\ \Rightarrow x^2=169-25 \\ \Rightarrow x^2=144 \\ \Rightarrow x=\sqrt[]{144} \\ \Rightarrow x=12 \end{gathered}[/tex]The legs of the second right triangle are 8 and x+3. Replace x=12. Then, the legs have measures 8 and 15. Use the Pythagorean Theorem to find the hypotenuse y:
[tex]\begin{gathered} 8^2+15^2=y^2 \\ \Rightarrow64+225=y^2 \\ \Rightarrow289=y^2 \\ \Rightarrow y=\sqrt[]{289} \\ \Rightarrow y=17 \end{gathered}[/tex]The legs of the third right triangle have measures m and 2y-2x+10, and the hypotenuse has length 29. Replace x=12 and y=17. Then, the legs of the third right triangle are m and 20, and the hypotenuse has length 29. Solve for m:
[tex]\begin{gathered} m^2+20^2=29^2 \\ \Rightarrow m^2+400=841 \\ \Rightarrow m^2=841-400 \\ \Rightarrow m^2=441 \\ \Rightarrow m=\sqrt[]{441} \\ \Rightarrow m=21 \end{gathered}[/tex]Therefore, the solutions for x, y and m are:
[tex]\begin{gathered} x=12 \\ y=17 \\ m=21 \end{gathered}[/tex]Related Questions
I’m having trouble figuring out this problem . Could you please help me ?
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SOLUTION:
Case: Rate of change. Also called slope (or gradient)
Problem description: The change of d with respect to t is described as every 3 units increase in t leads to a corresponding 8 units increase in d.
Final answer:
Rate of change is caculated as:
[tex]\begin{gathered} \text{Rate of change= }\frac{\Delta d}{\Delta t} \\ \text{Rate of change= }\frac{8}{3}\text{ OR }2\frac{2}{3}\text{ OR 2.67 (approx)} \end{gathered}[/tex]Need help solving number 8But it says you need to find the indicated function values for the following function “f(x)=3x^2+3x-1”
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Answer:
c.
Explanation:
We are given that:
[tex]f\mleft(x\mright)=3x^2+3x-1[/tex]We will proceed to obtain f(3a) as shown below:
[tex]\begin{gathered} f\mleft(x\mright)=3x^2+3x-1 \\ when:x=3a \\ \text{Substitute this into the function, we have:} \\ f(3a)=3(3a)^2+3(3a)-1 \\ f(3a)=3(9a^2)+9a-1 \\ f(3a)=27a^2+9a-1 \\ \\ \therefore f(3a)=27a^2+9a-1 \end{gathered}[/tex]Therefore, the answer is c
how many like terms are in the expression:5a^2+6b+a^2-3b-2+4c.
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Solution
Part 3
For this case we have 6 different terms
Part 4
We can do the following:
[tex]5a^2+a^2+6b-3b+4c-2[/tex]Part 5
And we can simplify on this way:
[tex]6a^2+3b+4c-2[/tex]
a.) 40 - 8 = 40 + n what is n25+ (-100) = 25 – n what is n
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Explanation
Step 1
a)
[tex]40-8=40+n[/tex]add like terms
[tex]\begin{gathered} 40-8=40+n \\ 32=40+n \end{gathered}[/tex]now, subtract 40 in both sides to isolate n
[tex]\begin{gathered} 32=40+n \\ 32-40=40+n-40 \\ -8=n \\ n=-8 \end{gathered}[/tex]Step 2
b)
[tex]\begin{gathered} 25+(-100)=25-n \\ break\text{ the parenthesis by multipling +}\cdot-100 \\ 25+(-100)=25-n \\ 25-100=25-n \\ \text{add like terms} \\ -75=25-n \\ \text{subtract 25 in both sides} \\ -75-25=25-n-25 \\ -100=-n \\ \text{Multiply both sides by -1} \\ -100\cdot-1=-n\cdot-1 \\ 100=n \\ n=100 \end{gathered}[/tex]I hope this helps you
Point M is the midpoint of AB. M has coordinates of (6.-4) and A has coordinates of (3.-7).Part A: What are the coordinates of point B?
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We will solve as follows:
[tex](\frac{x+3}{2}=6,\frac{y-4}{2}=-4)=(x=9,y=-1)[/tex]So, the coordinates are (9, -1).
graph at least one full cycle of the of the following trig function label the amplitude midline minimum and the intervalsf(x)=1/3cps 2(x+pi)
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Given the function
[tex]f(x)=\frac{1}{3}\cos (2(x+\pi))[/tex]Which is equivalent to
[tex]\Leftrightarrow f(x)=\frac{1}{3}\cos (2x+2\pi))[/tex]In general, a trigonometric equation has the following structure
[tex]g(x)=A\cos (B(x-C))+D[/tex]Where A is the amplitude.
Therefore, the amplitude of our function is 1/3.
As for the minimum and maximum of the function, remember that the range of the cosine function is [-1,1]; therefore,
[tex]\begin{gathered} \text{minimum(f(x))}=\frac{1}{3}(-1)=-\frac{1}{3} \\ \text{maximum(f(x))}=\frac{1}{3}(1)=\frac{1}{3} \end{gathered}[/tex]Furthermore, the midline of the graph is a parallel line to the x-axis that crosses the midpoint between the maximum and the minimum; in our case,
[tex]\begin{gathered} \frac{\frac{1}{3}+(-\frac{1}{3})}{2}=0 \\ \Rightarrow\text{midline is y=0} \end{gathered}[/tex]Finally, the graph of the function in the [0,2pi] interval is
If a spinner is pointed in front of the digit 6 space and the question is on the spinner what is P(5, and a number greater than 3?
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The number of element sample space for the experiment is n(T) = 8.
Determine the probability for the number 5.
[tex]P(5)=\frac{1}{8}[/tex]The possible number greater than 3 are 4, 5, 6, 7, and 8. So number of possible outcome for greater than 3 are 5.
Determine the probaility for the number greater than 3.
[tex]P\text{ (number greater than 3)=}\frac{5}{8}[/tex]Both events are independent. So probability for number 5, and greater than 3 is,
[tex]\begin{gathered} P\text{ (5,greater than number 3)=P(5)}\cdot P\text{ (number greater than 3)} \\ =\frac{1}{8}\cdot\frac{5}{8} \\ =\frac{5}{64} \end{gathered}[/tex]Answer: 5/64
Question 513 pointsFind the slope of the line passing through the points (2,1),(0,1).DiscussА 0B 1C 1/2D 2/1E-1
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Answer
Option A is correct.
Slope = 0
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (2, 1) and (0, 1)
x₁ = 2
y₁ = 1
x₂ = 0
y₂ = 1
[tex]\text{Slope = }\frac{1-1}{1-2}=\frac{0}{-1}=0[/tex]Hope this Helps!!!
6. Find the difference of the twoexpressions.(4/5k+1)-(3/5k-2)
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We will find the difference as follows:
[tex](\frac{4}{5}k+1)-(\frac{3}{5}k-2)=\frac{4}{5}k+1-\frac{3}{5}k+2=\frac{1}{5}k+3[/tex]So, the difference is:
[tex]\frac{1}{5}k+3[/tex]k
The formula for the circumference of a circle is C- 2. Determine the circumference when the radius r is 10 cm.a.100 g cmC.20 cmb.20x cmd.100 cm
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To calculate the circumference of a circle with a radius of 10 cm you have to apply the following formula:
[tex]C=2\pi r[/tex]Where
C is the circumference
r is the radius
π is the number pi
Replace the formula with r=10 and solve:
[tex]\begin{gathered} C=2\pi r \\ C=2\pi\cdot10 \\ C=20\pi cm \end{gathered}[/tex]The circumference of the circle is 20π cm.
I need help with this geometry question I’m confused for some reason.
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We are asked to determine which of the triangles is a right triangle. To do that we can apply the Pythagorean theorem, taking the larger side as the hypotenuse. If the Equality of the Pythagorean theorem holds, then the triangle is a right triangle.
Let's take triangle P. The largest side is 30, therefore, we take this as the hypotenuse. The Pythagorean theorem is as follows:
[tex]h^2=a^2+b^2[/tex]Where:
[tex]\begin{gathered} h=\text{ hypotenuse} \\ a,b=\text{ sides} \end{gathered}[/tex]Now we substitute the values:
[tex]30^2=12^2+24^2[/tex]Now we solve the squares:
[tex]900=144+576[/tex]Adding the terms:
[tex]900=720[/tex]Since the terms on the right side and the left side are not equal, this means that the given triangle is not a right triangle.
Now, let's do the same procedure for triangle Q. We have that the hypotenuse in this triangle is 41. Therefore, substituting in the Pythagorean theorem we get:
[tex]41^2=40^2+9^2[/tex]Solving the square:
[tex]1681=1600+81[/tex]Adding the terms:
[tex]1681=1681[/tex]Since we got the same result on both sides this means that the triangle Q is a right triangle.
For each description of a net, select the three-dimensional figure the net represents Triangular Prism Triangular Pyramid Rectangular Prism Rectangular Pyramid 6 rectangles A D 2 triangles and 3 rectangles G 4 triangles K 4 triangles and 1 rectangle M o (Р)
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(1) 6 rectangles = Rectangular Prism (C)
(2) 2 triangles and 3 rectangles= Triangular prism (E)
(3) 4 triangles = Triangular Pyramid (J)
(4) 4 triangles and 1 rectangle =Rectangular Pyramid (P)
John was given the equation 5(x - 2) - 2(7-5) = 9 to solve. Some of the steps and their reasons have already beencompleted. State a property of numbers for each missing reason.5(x - 2)-2(x - 5) = 9(1) 5x - 10 - 2x + 10 = 9(1)(2) 5x - 2x - 10+ 10 = 9(2)3x + 0 = 93x = 9x = 3
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(1) is due to the distributive property of the multiplication over the addition of numbers .
(2) is due to the commutative property of the addition of numbers.
Which of the following is the statement below describing ? In a right triangle, the sum of the squares of the leg lengths is equal to the square of the hypotenuse length
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According to Pythagorean Theorem,
Consider that the given statement exactly matches the statement of the Pythagorean Theorem.
So option A is the correct choice.
I attached the photo below. Can you answer the question in written form?
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The Solution:
Given:
We are required to solve for x and y by the Substitution Method.
Step 1:
Substitute the for y. This means we should equate both equations.
[tex]3x+3=x-1[/tex]Solving for x in the above linear equation, we get:
[tex]\begin{gathered} 3x-x=-1-3 \\ \\ 2x=-4 \end{gathered}[/tex]Divide both sides by 2.
[tex]\begin{gathered} \frac{2x}{2}=\frac{-4}{2} \\ \\ x=-2 \end{gathered}[/tex]Step 2:
Substitute -2 for x in any of the given equations.
[tex]\begin{gathered} y=x-1 \\ y=-2-1 \\ y=-3 \end{gathered}[/tex]Thus, the correct answer is (-2, -3)
I need help solving this practice problem for my calculus prep guide
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Okay, here we have this:
Considering the provided terms, we are going to identify the formula of the arithmetic sequence and later we will calculate the term number 84, so we obtain the following:
Difference=a2-a1=-1269-(-1286)
Difference=-1269+1286
Difference=17
Now, let's replace in the arithmetic sequence form, so we have the following sequence:
[tex]\begin{gathered} a_n=a_1+\mleft(n-1\mright)d \\ a_n=-1286+(n-1)17 \\ a_n=-1286+17n-17 \\ a_n=17n-1303 \end{gathered}[/tex]Finally, let's replace with n=84, then:
[tex]\begin{gathered} a_{84}=17\mleft(84\mright)-1303 \\ =1428-1303 \\ =125 \end{gathered}[/tex]Finally we obtain that the 84th term of the sequence is 125.
Is the sequence an arithmetic sequence? 2. -12,4, 0, 2 ....... O Yes or o No3. -6,0, 6, 12 ..... O Yes or o No
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2. since we can find a common difference, then it is not a an arithmetic sequence
3. since it has a common difference, then yes it is an arithmetic sequence.
Translate the figure 2 units left and 2 units down.
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The coordinates of the pre-image are:
(1,3) (2, -1) and (4,3)
The coordinates of the image are:
(-1, 1) (0,-3) and (2, 1)
find the value of x and the measure of Arc AD
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First DB is a chord.
Line AC divide the chord DB into two equal length.
Hence
DE = EB
11x - 33 = 8x + 9
Collect like terms
11x - 8x = 9 + 33
3x = 42
x = 42/3
x = 14
Arc of AD
A circle is 360 degrees. Line AC divide circle into two semi circles. Hence, angle of a semi circle is 180 degrees.
Arc AD = 180 - 58 = 122
A vertical meter stick casts a shadow 40 cm long at the same time a flagpole casts a shadow 10 feet long. How tall is the flagpole?
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The first step we need to take is to convert the size of the meter stick to centimeters. This is done below:
[tex]1m=100\operatorname{cm}[/tex]Now that both the height and the shadow are on the same unit, we can create a proportion to determine the height of the flag. Which is done below:
[tex]\frac{100\text{ cm}}{40\text{ cm}}=\frac{x\text{ ft}}{10\text{ ft}}[/tex]We can eliminate the units, then cross multiply to determine x.
[tex]\begin{gathered} \frac{100}{40}=\frac{x}{10} \\ 40\cdot x=100\cdot10 \\ 40\cdot x=1000 \\ x=\frac{1000}{40}=25 \end{gathered}[/tex]The flag has a height of 25 ft.
Select all of the ordered pairs that are solutions to the equation y= -5x + 30
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´We must substitute each pair into our equation:
A. If we substitute poin (45,3), we have
[tex]\begin{gathered} 3=-5(45)+30 \\ 3=-195\text{ !!!!} \end{gathered}[/tex]that is, this point doesnt belong to the line.
B. If we substitute poin (3,45), we have
[tex]\begin{gathered} 45=-5(3)+30 \\ 45=-15+30 \\ 45=15\text{ !!!!} \end{gathered}[/tex]then, this point doesnt belong to the line.
C. If we substitute poin (0,30), we have
[tex]\begin{gathered} 30=-5(0)+30 \\ 30=0+30 \\ 30=30 \end{gathered}[/tex]then, this point is a solution.
D. If we substitute poin (30,0), we have
[tex]\begin{gathered} 0=-5(30)+30 \\ 0=-150+30 \\ 0=-120\text{ !!!} \end{gathered}[/tex]then, this point doesnt belong to the line.
Therefore, the answer is option C
The function we need to use answer this is h(r)= √4-r
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Given:
[tex]\begin{gathered} h(r)=\sqrt{4}-r............(1) \\ 3h(r)+2=4..............(2) \end{gathered}[/tex]To find:
The value of r.
Explanation:
Using function (1) in (2),
[tex]\begin{gathered} 3(\sqrt{4}-r)+2=4 \\ 3(2-r)=4-2 \\ 6-3r=2 \\ -3r=-4 \\ r=\frac{4}{3} \end{gathered}[/tex]Therefore, the value of r is,
[tex]\frac{4}{3}[/tex]Final answer:
The value of r is,
[tex]\frac{4}{3}[/tex]A copy machine makes 24 copies per minute. How long does it take to make 126 copies?
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a runner ran 100 meters in 10.49 seconds. using dimensional analysis and using 3.28 feet per meter and 5,280 feet per mile, how fast did they do this in miles per hour? Please include all multiplication and division steps when you write out the answer
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a runner ran 100 meters in 10.49 seconds. using dimensional analysis and using 3.28 feet per meter and 5,280 feet per mile, how fast did they do this in miles per hour? Please include all multiplication and division steps when you write out the answer
step 1
Convert meters to feet
we have that
3.28 ft ------------> 1 m
so
100 m=100*(3.28)=328 ft
step 2
Convert ft to miles
we have that
5,280 ft ----------> 1 mi
so
328 ft=328/5,280 mi
step 3
Convert sec to hours
we have that
1 h----------> 3,600 sec
so
10.49 sec=10.49/3,600 h
step 4
Find the speed in miles per hours
Divide the distance in miles by the time in hours
so
(328/5,280)/(10.49/3,600)=(328*3,600)/(10.49*5,280)
21.32 miles/hourBy 9pm Friday night, a restaurant had sold 200 entrées, 50 of which were steak. The restaurant makes a greater profit on steak than on any other entrée, so they want steak to represent at least 50% of their total number of entrées sold. If they sell no additional other types of entrées, what is the minimum number of steak entrées that the restaurant must sell in order to reach their goal?
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We are told that the restaurant sold 200 entrees, 50 of which where steak.
If they want steak to represent at least 50% of their total number of entrées sold that means that steak must represent at least half of the total steaks sold.
Therefore, half of the total entrees sold would be;
[tex]\begin{gathered} \frac{\text{Total entre}es}{2}=\frac{200}{2} \\ =100 \end{gathered}[/tex]Since they have sold 50 entrees, this implies that the restaurant must sell at least an extra 50 entree to meet the goal they required.
Therefore, 50 entrees innitially sold, plus 50 entrees that would be sold would give the minimum number of steak entrées that the restaurant must sell in order to reach their goal.
This implies
[tex]\text{minimum}=50+50=100\text{ steaks}[/tex]They must therefore sell 100 steaks to achieve their goals.
ANSWER: 100 STEAKS
This is a practice assessment ( I will send the other half)
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Since R is the center of the circle, then the angle ARD has the same measure than the arc AD, which is 120°.
On the other hand, the measure of the arc ABC will be the same as the measure of the angle ARC, which is 180°.
The measure of the arc ADB is the same as the sum of the measures of the angles ARD, DRC and CRB, which is 120°+60°+40°=220°.
Finally, the measure of arc BD is the same as the sum of the angles BRC and CRD, which is 40°+60°=100°.
What is 192 in simplest form? OA 323 OB. 3V8 OC 83 OD D. 2148
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Form of 192
192 = 3x 2^6
192 = 3x 8^2
Complete the follow 2 examples on paper and upload your work below
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So, in order to translate the statements into algebraic expressions, we will write it using variables/unknowns:
Seven times the absolute value of six minus a number squared:
7*I6I - x²
The sum of the squared root of x and the cubed root of y:
[tex]\sqrt[]{x}+\sqrt[3]{y}[/tex]Fort Forte is due north of camp Campbell. A Stealth helicaptor flight takes off from the fort and heads towards the camp. At one Point in the helicaptor flight it's in line of sight distance is 10 miles from the Fort at a angle of elevation of 27°. The chopper radios the camp and reports that they can see the camp at an angle of depression of 18°. How far apart are the two military installations?
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the dark point is the helicaptor. So we get that the height of the helicaptor is
[tex]\begin{gathered} 10\cdot\sin 27=h \\ h\approx4.54mi \end{gathered}[/tex]So we get that
[tex]\begin{gathered} x=10\cdot\cos 27\approx8.91mi \\ \tan (18)=\frac{4.54}{y}\rightarrow y=\frac{4.54}{\tan 18}\approx13.97mi \end{gathered}[/tex]so the distance between the two military installations is
[tex]x+y=8.91+13.97\approx22.88mi[/tex]there is a house that measures 12×15 and it has 7 rooms how much living space is there?
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Let's begin by listing out the information given to us:
Area of each room (a) = 12 * 15 = 180
Number of rooms (n) = 7
Area of living space is given by:
[tex]A=a\cdot n=180\cdot7=1260unit^2[/tex]