take the square root of both sides of the equation from part B (n↑2−c↑2=0) and write the resulting equation.
Answers
Given:
A right angled triangle named as triangle 2 with sides perpendicular height(a),
base(b) and hypotenuse(n).
Required:
Find the resultant equation using two sides.
Explanation:
By Pythagoras theorem we know that sum of square of base and perpendicular height of triangle equal square of hypotenuse.
Here, perpendicular height(a) and base(n)
[tex]a^2+b^2=n^2[/tex]This is the resulting equation.
Answer:
Hence, resulting equation is above.
Answer:
Part A
The equation for triangle 2 will be: a² + b² = n².
Part B
We know,
Now, we substitute a^2+b^2=c^2 in the second equation
So, the new equation is c^2 = n^2
Part C
Now, taking the square root of both sides of the equation from part B, we get
Part D
The equation obtained is true thanks to the Pythagorean theorem, because the corresponding legs in both triangles are of equal measure, we will obtain that their hypotenuse is also equal.
You can see that the 90° angles is conformed by 2 sides, these sides are the legs and the last side is the hypotenuse.
Part E
This means that the 2 triangles are equal, they have 3 sides equals.
The triangles also meet the criterion that explains that if two sides and the angle opposite the longest side are equal, the triangles are equal.
Part F
Yes, the triangle 1 is a rigth triangle because this has a right angle, that is, a 90 degree angle
Step-by-step explanation: Hope it helps!
Related Questions
what is 48 divided by 9 in long division
Answers
We need to divide 48 by 9 using long division. This is done below:
The first step is to try to divide 4 by 9, which we can't do, therefore the result is "0", then we multiply the result with the divisor and subtract from the dividend, which gives us 48 - 0 = 48. Now we need to try to divide 48 directly by 9, which is equal to 5, then we multiply this result to the divisor and subtract from the dividend, resulting in a remainder of 3.
The result of the division is 5 with remainder 3.
Answer:
5.3333 or 5 3/9
Step-by-step explanation:
Which of the following represents z equals negative 4 radical 3 end radical plus 4 times i in trigonometric form?
Answers
Notice that
[tex]\begin{gathered} z=-4\sqrt[]{3}+4i=8(-\frac{\sqrt[]{3}}{2}+\frac{1}{2}i) \\ \Rightarrow z=8(-\frac{\sqrt[]{3}}{2}+\frac{1}{2}i) \end{gathered}[/tex]Set,
[tex]\begin{gathered} z=8(\cos x+i\sin x) \\ \Rightarrow8(\cos x+i\sin x)=8(-\frac{\sqrt[]{3}}{2}+\frac{1}{2}i) \\ \Rightarrow\cos x=-\frac{\sqrt[]{3}}{2},\sin x=\frac{1}{2} \end{gathered}[/tex]Then, angle x is in the second quadrant since cosx is negative and sinx is positive-
On the other hand,
Therefore, using the unitary circle,
Therefore, the angle that produces such values for the cosine and sine function is x=150°; thus,
[tex]\begin{gathered} x=150\degree \\ \Rightarrow z=8(-\frac{\sqrt[]{3}}{2}+\frac{1}{2}i)=8(\cos (150\degree+i\sin (150\degree))) \\ \Rightarrow z=8(\cos (150\degree+i\sin (150\degree))) \end{gathered}[/tex]The answer is option 4 (top to bottom)
If A and B are sets whose union is B, then it must be true that
Answers
Since A and B are sets whose union is B, then it is true that A is a subset of B
Answer: A.
y=x – 2 when X = = 3.5
Answers
Answer:
y = 1.5
Step-by-step explanation:
Given equation,
→ x = 3.5
→ y = x - 2
Then required value of y is,
→ y = x - 2
→ y = 3.5 - 2
→ [ y = 1.5 ]
Hence, the value of y is 1.5.
Find the area of the trapezoid.A trapezoid with the top base labeled five inches and the bottom base labeled seven inches. The height is labeled three inches.Enter the correct answer in the box.
Answers
We can divide the trapezoid into a triangle and a rectangle:
Find the area of each figure, and then add them:
Area of a triangle = 1/2 x base x height
A1 = 1/2 x 2 x 3 = 3 in2
Area of a rectangle: base x height
A2 = 5 x 3 = 15 in2
Total area = A1 + A2 = 3 + 15 = 18 in2
can Someone help me with number 4 i dont understand
Answers
Two lines are parallel if their slopes are equal.
In this case we have the lines:
[tex]\begin{gathered} y-7x=6 \\ y+7x=8 \end{gathered}[/tex]If we rearrange them in slope-intercept form, we get:
[tex]\begin{gathered} a)y-7x=6\longrightarrow y=7x+6 \\ b)y+7x=8\longrightarrow y=-7x+8 \end{gathered}[/tex]As line a has a slope m=7 and line has a slope m=-7, the lines have different slopes so they are not parallel.
[tex]\begin{gathered} m_a=7 \\ m_b=-7 \\ 7\neq-7\longrightarrow\text{not parallel} \end{gathered}[/tex]Answer: The lines are not parallel
The length of a rectangle is 2m-5. Width is 4m-2. If the perimeter is 382 inches, find the length and the width.
Answers
Given:
• Length of a rectangle = 2m-5
,• Width of the rectangle = 4m-2
,• Perimeter of the rectangle = 382 Inches
We know that:
[tex]\begin{gathered} Perimeter\; of\; a\; rectangle=2(\text{Length}+Wi\differentialD tth)th).th) \\ \text{Therefore:} \\ 382=2\left(2m-5+4m-2\right) \\ 382=2(2m+4m-5-2) \\ 382=2(6m-7) \\ 382=12m-14 \\ \text{Add 14 to both sides} \\ 382+14=12m-14+14 \\ 396=12m \\ \text{Divide both sides by 12} \\ m=33 \end{gathered}[/tex]Can you please help me with the second and third problem they are really hard and im struggling to solve them
Answers
Given:
Tameka made x 2 points shots and y 3 points shots.
To find:
a) The expression that represents the total number of points.
b) Calculate points when x = 5 and y = 2.
Explanation:
a) The total number of points can be calculated as follows,
[tex]T=2x+3y[/tex]Where T represents the total number of points.
b) Substituting x = 5 and y = 2, we get
[tex]\begin{gathered} T=2(5)+3(2) \\ T=10+6 \\ T=16 \end{gathered}[/tex]So, the total number of points she got is 16 points.
Final answer:
The expression that represents the total number of points is,
[tex]T=2x+3y[/tex]The total number of points she got is 16 points.
Express as an inequality. Then graph the solution to the compound inequality and write the solution in interval notation. A can of soda is not properly filled if the amount of soda x in the can is more than 12.1 ounces or fewer than 11.6 ounces
Answers
Let 'x' be the amount of soda in the can.
The first condition can be written like this:
[tex]undefined[/tex]The 10th term of an A.P is double the 2nd term Find the 8th term, given that the first term is 7
Answers
Step 1
The nth term of an A.P is given as;
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ a_1=7 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} a_2=7+(2-1)d \\ a_2=7+d \\ a_{10}=2(7+d)=14+2d \\ a_{10}=7+9d \\ 7+9d=14+2d \\ 7d=7 \\ d=1 \end{gathered}[/tex]Hence the 8th term will be;
[tex]\begin{gathered} a_8=7+(8-1)d \\ a_8=7+7(1) \\ a_8=14 \end{gathered}[/tex]When does ball 2 reach the ground? round to the nearest hundredth.
Answers
Solution:
Given the function:
[tex]\begin{gathered} f(t)=-16t^2+h---\text{ equation 1} \\ where \\ f(t)\Rightarrow current\text{v height} \\ t\Rightarrow time \\ h\Rightarrow height \end{gathered}[/tex]When ball 2 reaches the ground, we have
[tex]f(t)=0----\text{ equation 2}[/tex]By substitution, we have
[tex]\begin{gathered} 0=-16t^2+h \\ add\text{ -h to both sides of the equation} \\ 0-h=-16t^2+h-h \\ \Rightarrow-h=-16t^2 \\ \therefore \\ t^2=\frac{h}{16}---\text{ equation 3} \end{gathered}[/tex]To find the time ball 2 reaches the ground, we have
[tex]\begin{gathered} From\text{ equation 3,} \\ t^2=\frac{h}{16} \\ but\text{ h = 277} \\ t^2=\frac{277}{16} \\ take\text{ the square root of both sides} \\ \sqrt{t^2}=\sqrt{\frac{277}{16}} \\ t=\pm4.16082 \\ but\text{ t cannot be negative.} \\ \therefore \\ t\approx4.16\text{ \lparen nearest hundredth\rparen} \end{gathered}[/tex]Hence, ball 2 reaches the ground at
[tex]t=4.16[/tex]
I need help with the first question and x^2-8x is not the right answer
Answers
Given
[tex]f(x)=x^2-8x[/tex]To find the standard form of the quadratic equation.
Explanation:
It is given that,
[tex]f(x)=x^2-8x[/tex]That implies,
[tex]\begin{gathered} f(x)=(x-4)^2-4^2(by\text{ completing the square method}) \\ =(x-4)^2-16 \end{gathered}[/tex]Hence, the standard form of the quadratic equation is,
[tex]f(x)=(x-4)^2-16[/tex]what is the inverse of the function y=2 log ^3 x
Answers
Given the following function:
[tex]y=2\log ^3\text{ x}[/tex][tex]\begin{gathered} y=2\log ^3\text{ x} \\ x=2\log ^3(y) \\ x=2\log ^3=3^{\frac{x}{2}} \\ =3^{\frac{x}{2}} \end{gathered}[/tex](If it isn't the given function in the question please feel free to reopen a new session, wasn't able to confirm with you on the function)
What is the scale factor used in the enlargement from drawing 1 to draining 2(Express as a percent or a decimal)
Answers
The length of drawing 1 is 1.5 inches
Drawing 2 is 1.8 inches
We need to use the same side
Take Drawing 2 over drawing 1
1.8/1.5
1.2
The scale factor is 1.2
A recipe calls for 2 cups of flour. Lee has only a 3-cup measuring cup. How many 3-cup measuring cups of flour does she need?
Answers
Answer: 2
Explanation:
With the 2cup measauring cup, Lee can measure cups in multiples of 2:
2, 4, 6, 8,...
And with the 3cup measuring cup, Lee can measure cups in multiples of 3:
3, 6, 9, 12,...
As we can see the common number is that both can measure 6 cups. (this is the minimum common multiple).
Lee neds 2 measuring cups of 3 cups. This is so that Lee can measure 6 cups of flour wich is a multiple of the 2 cups of flour that the recipe needs.
The store is selling a shirt that costs $32. You have a couponfor 10% off. How much will the shirt cost after you use thecoupon?
Answers
The cost of the shirt = $32
Reduction percentage = 10%
Therefore, the reduction is,
[tex]\frac{10}{100}\times32=3.2[/tex]The cost of the shirt is
[tex]32-3.2=28.8[/tex]The cost of the shirt after using the coupon is $ 28.8.
I need help on this problem. m/np^2=kplease help me with the steps
Answers
Answer
n = (m/p²k)
Explanation
We are told to solve for n, that is, make n the subject of formula.
[tex]\frac{m}{np^2}=k[/tex]To solve this, we first cross multiply
[tex]\begin{gathered} \frac{m}{np^2}=k \\ np^2\times k=m \\ np^2k=m \end{gathered}[/tex]np²k = m
Divide both sides by p²k
[tex]\begin{gathered} \frac{np^2k}{p^2k}=\frac{m}{p^2k} \\ n=\frac{m}{p^{2}k} \end{gathered}[/tex]Hope this Helps!!!
you have saved up $52 by earning $4 for each lawn you mow how many more lawns do you need to mow to reach a total of $74
Answers
Given:
Amount saved = $52
Amount you earn on each lawn = $4
Let's find how many more lawns you need to mow to reach a total of $74.
Let x represent number of lawns needed to reach a total of $74
We have the equation:
[tex]x=\frac{74-52}{4}[/tex]Let's solve for x:
[tex]\begin{gathered} x=\frac{74-52}{4} \\ \\ x=\frac{22}{4} \\ \\ x=5.5\approx6 \end{gathered}[/tex]Therefore, you need to mow 5.5 lawns which is approximately 6 lawns to reach a total of $74
A group of 25 people is going to run a race. The top three runners earngold, silver, and bronze medals.This is an example of ____ (combination or permutation?)n=r =There are ____ of ways to choose the gold,silver, and bronze medal winners.
Answers
Solution
The permutation is the number of possible ways to select the specified objects from the total number of objects in which the orders matters. The total objects is represented by n and selected objects is represented by the r.
Answer and Explanation:
This is an example of Permutation
Number of people: n = 25
Type of medals: r = 3
[tex]\begin{gathered} n_{Pr}=\frac{n!}{(n-r)!} \\ 25P_3=\frac{25!}{(25-3)!} \\ =\frac{25!}{22!} \\ =\frac{25\times24\times23\times22!}{22!} \\ =13800 \end{gathered}[/tex]There are 13800 of ways to choose the gold,
silver, and bronze medal winners.
Solve and graph the following system. Please use my graph to plot the points. 3x-2y=182x+4y=-4
Answers
We have to solve and graph the following system of equations:
[tex]\begin{gathered} 3x-2y=18 \\ 2x+4y=-4 \end{gathered}[/tex]We can solve this graphically: the solution will be the intersection of both lines, as this is the only point that satisfy the two equations.
We start by graphing the first equation.
We have it expressed in standard form, so we can find the x-intercept and y-intercept.
The x-intercept (y = 0) will be:
[tex]\begin{gathered} 3x-2(0)=18 \\ 3x=18 \\ x=\frac{18}{3} \\ x=6 \end{gathered}[/tex]Then, the x-intercept is (6,0).
The y-intercept (x = 0) will be:
[tex]\begin{gathered} 3(0)-2y=18 \\ -2y=18 \\ y=\frac{18}{-2} \\ y=-9 \end{gathered}[/tex]Then, the y-intercept is (0,-9).
With two points we can graph the line as:
We can repeat the process for the second line.
First we simplify it:
[tex]\begin{gathered} \frac{2x+4y}{2}=\frac{-4}{2} \\ x+2y=-2 \end{gathered}[/tex]Then, we can find the x-intercept (y = 0) as:
[tex]\begin{gathered} x+2(0)=-2 \\ x=-2 \end{gathered}[/tex]The y-intercept (x = 0) will be:
[tex]\begin{gathered} (0)+2y=-2 \\ y=-\frac{2}{2} \\ y=-1 \end{gathered}[/tex]Then, we have the two intercepts: (-2, 0) and (0, -1).
We can graph this line as:
The lines intersect at (4,-3) which is the solution to the system.
Can you please help me
Answers
In order to find the area of the trapezoid, consider the figure as formed by two right triangles with the same area, and one rectangle.
Then, if A1 is the area of one triangle and A2 is the area of the rectangle, you have for the area of the trapezoid:
A = 2A1 + A2
where, for the triangle you have:
A1 = b·h/2
b = (16 ft - 6ft)/2 = 5 ft
h = 12 ft
A1 = (5 ft)(12 ft)/2 = 30 ft²
and for the rectangle:
A2 = w·h
w = 6 ft
h = 12 ft
A2 = (6 ft)(12 ft) = 72 ft²
next, replace the values of A1 and A2 to get the area of the trapezoid:
A = 2(30 ft²) + 72 ft²
A = 60 ft² + 72 ft²
A = 132 ft²
Hence, the area of the given trapezoid is 132 ft²
the following is a figure of the trapezoid as formed by two triangle and one rectangle:
it wont let me load the image in . Create a box plot with the following data:574, 526, 512, 579, 595, 517, 524, 552, 558, 541
Answers
Step 1
Given; 574, 526, 512, 579, 595, 517, 524, 552, 558, 541
Required; To create a box plot
Step 2
Arrange in ascending order
[tex]512,\:517,\:524,\:526,\:541,\:552,\:558,\:574,\:579,\:595[/tex]Find the lower quartile
[tex]\begin{gathered} \mathrm{The\:first\:quartile\:is\:computed\:by\:taking\:the\:median\:of\:the\:lower\:half\:of\:a\:sorted\:set.} \\ 524 \end{gathered}[/tex]Find the upper quartile
[tex]\begin{gathered} The\:third\:quartile\:is\:computed\:by\:taking\:the\:median\:of\:the\:higher\:half\:of\:a\:sorted\:set \\ 574 \end{gathered}[/tex]The median is the middle number of the entire data
[tex]=\frac{541+552}{2}=546.5[/tex]The maximum and minimum values are;
[tex]595\text{ and 512 respectively}[/tex]This is the clearest photo i can getDetermine the equation of the circle graphed below
Answers
Given the graph of the circle
To write the equation of the circle , we need to find the radius and the coordinates of the center
As shown in the figure :
The center of the circle = (h,k) = ( 7 , 5 )
And the radius of the circle = r = 3
The general equation of the circle is :
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substitute with the values of h, k and r :
So, the equation of the given circle is :
[tex]\begin{gathered} (x-7)^2+(y-5)^2=3^2 \\ \\ (x-7)^2+(y-5)^2=9 \end{gathered}[/tex]What is the surface area of the cube?
Answers
Answer: A=6a^2
Step-by-step explanation:
This is the equation to solve any Surface area of a cube question.
The table shows the types of movies and the numbers of DVDS rented by customers at a store in one day. Based on the data in the table, what is the probability that random customer will rent a drama?
Answers
Let:
A = Rental a Drama Movie
a = Number of rentals of drama movies
N = Total number of rentals
the probability that random customer will rent a drama is:
[tex]\begin{gathered} P(A)=\frac{a}{N} \\ where\colon \\ a=25 \\ N=25+35+50+15=125 \\ so\colon \\ P(A)=\frac{25}{125} \\ P(A)=\frac{1}{5}=0.2 \end{gathered}[/tex]Answer:
20%
Find the distance between the two pony in simplest radical form (-9,3) and (-3,-5)
Answers
Given the points ( -9 , 3 ) and ( -3 , -5 )
And we need to the distance between them
The formula to find the distance d is :
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]so, the distance =
[tex]\begin{gathered} d=\sqrt[]{(-3-(-9))^2+(-5-3)^2} \\ d=\sqrt[]{(-3+9)^2+(-5-3)^2} \\ d=\sqrt[]{6^2+(-8)^2} \\ d=\sqrt[]{36+64}=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]so, the distance = 10
How to find percentages in numbers?
Answers
Percentages are expressed in terms of 100. The symbol is %. Assuming the total number of oranges shared among 2 boys is 60. If one boy gets 40 oranges, the percentage of the total orange that the boy got would be expressed as
40/60 * 100 = 66.67%
The percentage is calculated with respect to the total.
Again, we can express a given number in terms of percentage. If we want to express 3/4 in terms of percentage, it becomes
3/4 * 100 = 75%
The table represents some points on the graph of an exponentialfunction.x-2-1012f(x)12.5 15 18 21.6 25.92 Which function represents the same relationship?A f(x) = 15(5/6)xB f(x) = 18(6/5)xC f(x) = 15(6/5)xD f(x) = 18(5/6)x
Answers
Take into account that the general form of an exponential function is:
f(x) = a(r)^x
if r is lower than one the function increases, otherwise the function decreases.
Based on the information of the table, you can identify that the function increases. Then, r > 1. From the given options, 6/5 is a number greater than 1.
To determine what is the value of a, in the general expression, you can use any pair of values of the table, replace in the general form of the function and solve for a, as follow:
12.5 = a(6/5)⁻²
12.5 = a(0.694)
a = 12.5/0.694
a = 18
Hence, the exponential function of the data of the table is:
f(x) = 18(6/5)^x
Find the value of x. Then select the correct set of angle measures for this triangle.
Answers
ANSWER
B. 31°, 106°, and 43°
EXPLANATION
First, we have to find the value of x. Knowing that the sum of the measures of all the interior angles of a triangle is 180°, we can write an equation for x,
[tex](5x-7)+(11x-4)+(3x+1)=180[/tex]Add like terms,
[tex]\begin{gathered} (5x+11x+3x)+(-7-4+1)=180 \\ \\ 19x-10=180 \end{gathered}[/tex]Add 10 to both sides,
[tex]\begin{gathered} 19x-10+10=180+10 \\ \\ 19x=190 \end{gathered}[/tex]And divide both sides by 19,1
[tex]\begin{gathered} \frac{19x}{19}=\frac{190}{19} \\ \\ x=10 \end{gathered}[/tex]Now, replace the value of x = 10 in the expressions for each angle's measure to find their values,
[tex]\begin{cases}5x-7=5\cdot10-7=50-7=43 \\ {11x-4=11\cdot10-4=110-4=106} \\ {3x+1=3\cdot10+1=30+1=31}\end{cases}[/tex]Hence, the set of angle measures for this triangle is 31°, 106°, and 43°.
I you could just give me the answer that would be great no explanation needed:) I will give you a highesr rating if you do thank you
Answers
The correct answer is:
C) Dilation with respect to the origin by a scale factor of 2 followed by a traslation of 2 units left
