Answers
Statement 1:
ΔABC ≅ ΔCBD ≅ ΔACD
Reason: Given
_________________________________
Statement 2:
b/c = y/b; a/x = x/a
Reason: corresponding sides of similar triangles are proportional
(we want to have to have in the next statement that b² = cy; a² = cx
and proportionality is usually represented as fractions, if we observe the figure, the fractions of this statement correspond to the division of similar sides of the triangles)
________________________
Statement 3:
b² = cy; a² = cx
Reason: cross product property
(if we multiply both sides of b/c = y/b by b, we obtain b² = cy, and if we do the same for a/x = x/a we obtain a² = cx, since we are multiplying, it is called product, then, the option that best fit this field is cross product property)
_______________________________
Statement 4:
a² + b² = cx + cy
Reason: addition property of equality
(we want to prove that a² + b² = c², from the previous statement we can add both equalities so we obtain a² + b² , which is nearer to the conclusion we want to prove)
____________________
Statement 5:
a² + b² = c(x + y)
Reason: factor
(we find the common factor of cx and cy, it is c, then cx + cy = c(x + y))
___________________________
Statement 6:
c = x + y
Reason: Segment addition postulate
(we almost have the conclusion in the previous statement except for the (x + y) of the right part of the equality, since in the figure we observe that c = x + y, then we can use it to replace (x + y))
___________________________
Statement 7:
a² + b² = c²
Reason: substitution
(we substitute c by (x + y) of the statement 5)
⊕
Related Questions
Solve for y.2x – 8y = 24
Answers
Answer:
[tex]y=\frac{1}{4}x-3[/tex]Explanation:
Given the equation:
[tex]2x-8y=24[/tex]To solve for y, we follow the steps below:
Step 1: Rearrange to Isolate the term containing y.
[tex]8y=2x-24[/tex]Step 2: Divide both sides by 8.
[tex]\begin{gathered} \frac{8y}{8}=\frac{2x-24}{8} \\ y=\frac{2x-24}{8} \end{gathered}[/tex]Step 3: Simplify
[tex]\begin{gathered} y=\frac{2x}{8}-\frac{24}{8} \\ y=\frac{1}{4}x-3 \end{gathered}[/tex]A bus traveled on a level road for 6 hours at an average speed of 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 2 hour find the average speed on the level road if the entire trip was 360 miles.
Answers
Given:
A bus traveled on a level road for 6 hours at an average speed of 20 miles per hour .
The distance is calculated as,
[tex]\begin{gathered} d_1=r\times t \\ d_1=6\times20 \\ d_1=120\text{ miles} \end{gathered}[/tex]The distance covered by bus on level road is faster than it raveled on a winding road.
The time spent on the winding road was 2 hour. So, the distance is,
[tex]\begin{gathered} d_2=r\times t \\ d_2=2r\text{ miles} \end{gathered}[/tex]The total distance was 360 miles.
[tex]\begin{gathered} d_1+d_2=360 \\ 120+2r=360 \\ 2r=360-120 \\ 2r=240 \\ r=120 \end{gathered}[/tex]Answer: the average speed on the level road is 120 mph
Can I get an answer please?
Answers
the rule is reflextive
here(x, y) is changing into (x , -y)
the process is called translation
Find the slope between the points:(1,7)(-2,3)
Answers
Using the formula,
[tex]m=\frac{7-3}{1-(-2)}\rightarrow m=\frac{4}{1+2}\rightarrow m=\frac{4}{3}[/tex]Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 7 ) and (x₂, y₂ ) = (- 2, 3 )
m = [tex]\frac{3-7}{-2-1}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]
Solve: -2y ≥ 10y ≤ -5y ≤ 5y ≥ -5y ≥ 5
Answers
Given
[tex]-2y\ge10[/tex]Solution
Recall: Dividing by a negative number means you reverse the inequality symbol
[tex]\begin{gathered} -2y\ge10 \\ divide\text{ both sides by -2} \\ -\frac{2y}{-2}\ge\frac{10}{-2} \\ \\ y\leq-5 \end{gathered}[/tex]The final answer
[tex]y\leq-5[/tex]What are the coordinates of the point on the directed line segment from (-1,1) to (8, 10) that partitions the segment into a ratio of 2 to 1?
Answers
Point 1 = (x1,y1)= (-1,1)
Point 2 = (x2,y2)= (8,10)
xp,yp= ? (coordinates of the point)
a:b= 2:1
xp= x1+ a/a+b (x2-x1)
xp= -1+ 2/2+1 (8-(-1))
xp= -1+2/3 (8+1)
xp= -1+2/3(9)
xp= -1+ 6
xp= 5
yp= y1 + a/ a +b (y2-y1)
yp= 1 +2/3 (10-1)
yp =1+2/3 (9)
yp=1+6
yp=7
xp,yp = (5,7)
determine the solution to the system. Explain which method you used to determine your solution. 2x+y=-15y-6x=7
Answers
This is the system.
We will use the method of elimination to solve it.
So we will multiply the first equation by 3 and add it to the second one, this will gives us.
[tex]8y=4\rightarrow y=\frac{1}{2}[/tex][tex]2x+\frac{1}{2}=-1\rightarrow2x=-\frac{3}{2}\rightarrow x=-\frac{3}{4}[/tex]Josie sold 965 tickets to a local car show for a total of $4,335.00. A ticket for childrencosts $3.00 and an adult ticket costs $5.00. How many of each ticket did she sell?
Answers
Answer:
[tex]\begin{gathered} 245\text{ children tickets were sold.} \\ \text{ 720 adult tickets were sold.} \end{gathered}[/tex]Step-by-step explanation:
To approach this situation, we need to create a system of linear equations.
Let x be the number of children
Let y be the number of adults
For equation 1)
Since the sum of the tickets sold are 965, it means children plus adults is 965
[tex]x+y=965[/tex]For equation 2)
Since the price for children is $3, the adult ticket costs $5, and the total of tickets sold is $4,335:
[tex]3x+5y=4335[/tex]Now, we can solve this by using the substitution method, isolating one of the variables in equation 1 and plugging it into equation 2.
[tex]y=965-x[/tex]Plug it into equation 2:
[tex]3x+5(965-x)=4335[/tex]Solve for x.
[tex]\begin{gathered} 3x+4825-5x=4335 \\ 5x-3x=4825-4335 \\ 2x=490 \\ x=\frac{490}{2} \\ x=245 \\ 245\text{ children tickets were sold.} \end{gathered}[/tex]Knowing the value for x, we can plug it into equation 1, and solve for y.
[tex]\begin{gathered} y=965-245 \\ y=720\text{ } \\ \text{ 720 adult tickets were sold.} \end{gathered}[/tex]Unit cost of ring: $375Markup: 75%Retail Price?
Answers
Answer:
[tex]Retail=\text{ \$656.25}[/tex]Step-by-step explanation:
The retail price is represented by:
[tex]\text{ Retail= Cost*\lparen1+Markup \lparen as decimal\rparen\rparen}[/tex]Therefore, by the given information:
[tex]\begin{gathered} Retail=375*(1+0.75) \\ Retail=\text{ \$656.25} \end{gathered}[/tex]What is the value of sin E?Give your answer as a simplified fraction.
Answers
For this problem we first use the pythagorean theorem to find QH
[tex]\begin{gathered} QH^2+HE^2=QE^2 \\ QH^2=QE^2-HE^2=101^2-99^2=400 \\ QH=20 \end{gathered}[/tex]Then
[tex]\sin (E)\text{ =}\frac{QH}{QE}=\frac{20}{101}[/tex]9+9x=10x+2 Solve for x
Answers
This problem is about linear equations.
To solve it, we need to find the value of x.
[tex]9+9x=10x+2[/tex]First, we need to organize the equation, all terms without variables at the right side, and all terms with variables at the left side
[tex]9x-10x=2-9\text{ }\rightarrow-x=-7[/tex]Finally, we multiply the equation by -1 to get the proper answer
[tex]x=7[/tex]Therefore, the answer is 7.Enrique borrowed $23,500 to buy a car he pays his uncle 2% interest on the $4,500 he brought from him and he pays the bank 11.5% interest on the rest wherever interest rate does he pay the toll 23,500
Answers
Total borrowed: $23,500
$4,500 borrowed from his uncle: (2% interest)
Amount of interest paid to his uncle:
4,500 x 2/100 = $90
Amount borrowed from the bank: $23,500-$4,500 = $19,000
(11.5% interest)
Amount of interest paid to the bank:
19,000 x (11.5 /100) = 19,000 x 0.115 = $2,185
Total amount of interest:
23,500 (x/100) = 235 x
235x = 90+2185
Solve for x
235x = 2,275
x= 2,275/235 = 9.7
9.7 %
Find the 10th term of the geometric sequence whose common ratio is 3/2 and whose first term is 3.
Answers
ANSWER:
59049/512
EXPLANATION:
Given:
Common ratio(r) = 3/2
First term(a) = 3
Number of terms(n) = 10
To find:
The 10th term of the geometric sequence
We can go ahead and determine the 10th term of the sequence using the below formula and substituting the given values into it and evaluate;
[tex]\begin{gathered} a_n=ar^{n-1} \\ \\ a_{10}=3(\frac{3}{2})^{10-1} \\ \\ a_{10}=3(\frac{3}{2})^9 \\ \\ a_{10}=3(\frac{19683}{512}) \\ \\ a_{10}=\frac{59049}{512} \end{gathered}[/tex]Therefore, the 10th term of the sequence is 59049/512
2. Fill in the blanks below to show the sum of (2x2 + 4x) and (x2 + 8).
Answers
Given the function (2x^2+4x) and (x^2+8), we are to find the sum of both functions. This is as shown below;
(2x^2+4x) + (x^2+8) [sum means addition]
Next is to collect the like terms based on the power
= (2x^2+x^2)+4x +8
Evaluate the expression in parenthesis
= 3x^2 + 4x + 8
Hence the sum of (2x2 + 4x) and (x2 + 8) is 3x^2 + 4x + 8
You will have to fil the blanks with the corresponding coefficient of x^2 and x and the constant.
The first blank will be 3 (coefficient of x^2)
The second blank will be 4 (coefficient of x)
The third blank will be 8 (the constant value)Y
For a given set of rectangles, the length is inversely proportional to the width. In one
of these rectangles, the length is 25 and the width is 3. For this set of rectangles,
calculate the width of a rectangle whose length is 5.
Answers
Answer:
Step-by-step explanation:
Answer:
The width is 8 units
Step-by-step explanation:
This is a variation problem we are to work with.
Length is inversely proportional to width, let length be l and width be w
modeling the statement mathematically, we have lw = k where k is the proportionality constant
Now let’s get k from l = 12 and w = 6
k = 12 * 6 = 72
Now for the second rectangle also;
lw = k given l = 9
9w = 72
w = 72/9
w = 8
This is all the information I was given. O. 2.5.
Answers
The equation of a line in the slope-intercept form is y = mx + b, where m is the slope and b the y-intercept.
If it is known:
- The equation of a parallel line
- One point of the equation
To find the equation of the line, follow the steps:
1. Parallel lines have the same slope. So, use the slope of the parallel line to find the slope of the line.
2. Substitute the point in the equation to find b.
3. Since m and b are known, you found the equation of the line.
The birth weights of the 908 babies born at Valley Hospital in 2019 were normally
distributed with a mean of 7.2 pounds with a standard deviation of 1.5. Use the Z-
Score Table from the book to determine the number of babies that weighed more
than 10 pounds.
Answers
The number of babies that weighed more than 10 pounds is 43 using Z-
Score Table.
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a "bell curve."
Given that total number of babies is 908.
The mean of the normal distribution is 7.2 pound.
The standard deviation of the normal distribution is 1.5 pound.
The formula of z score is z = (x - μ)/σ
In the given question x = 10, μ = 1.5, σ = 7.2
z score = (10 - 7.2)/1.5 = 1.86667
P-value from Z-Table:
P(x<10) = 0.96903
P(x>10) = 1 - P(x<10) = 0.030974
The number of babies that weighed more than 10 pounds is ( 0.030974 × 908) = 43.39 = 43 (approx.)
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the approximate weights of two animals are 8.16 x 10 4 lbs. and 9.2 x 10 4 lbs. find the total weight of the two animals. write the final answer in scientific notation with the correct number of significant digits. 1.2 x 103 lbs. 1.19 x 103 lbs. 11 x 102 lbs. 5.8 x 102 lbs.
Answers
The scientific notation of weight of animal is 1.736 × 10^5.
What is scientific notation?
The scientific notation helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small. Learn power and exponents for better understanding.
The numbers can be written as a×10ⁿ.
Given, the weight of one animal is 8.16 × 10^4 and other animal is 9.2×10^4
Therefore, the sum of the weights in scientific notation is
=8.16 × 10^4 +9.2×10^4
Since they have same power of exponent, hence
=(8.16+9.2)10^4 =17.32×10^4
or we can write it as
1.732×10^5.
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I'm learning about Samples With the Mean Absolute Deviation but I have been having trouble with this type of math could you help me with my math?
Answers
Solution
For 3a)
[tex]\begin{gathered} \frac{30.1}{7.9}=\frac{3.81}{x} \\ \\ \Rightarrow x=\frac{7.9\times3.81}{30.1}=1 \end{gathered}[/tex]Sample W and Sample Z
match the property to the correct step in the problemA.) addition property of equality. B.) subtraction property of equalityC.) distributive property
Answers
In the first step
It is distributive property because we multiplied 10 by 2x and 10 by 4
1. C
In the second step
We add 6x to both sides, then
It is addition property of equality
2. A
In the third step
We subtract 40 from both sides, then
It is the subtraction property of equality
3. B
What is the perimeter of the composite figure?6 cm9 cm2 cm10 cm
Answers
As the given figure can be considered as two rectangles,
Consider the first rectangle,
The length is, 9-2 = 7 cm,
The width is, 10-6 = 4 cm.
Therefore, the perimeter is,
[tex]P=2(l+w)=2(7+4)=22\text{ cm}[/tex]For the second rectangle,
[tex]P=2(l+w)=2(10+2)=24\text{ cm}[/tex]Therefore, the total perimeter is,
22 cm + 24 cm = 46 cm.
In a class of students, the following data table summarizes how many students playan instrument or a sport. What is the probability that a student chosen randomlyfrom the class does not play a sport?Plays an instrument Does not play an instrumentPlays a sport34Does not play a sport136
Answers
First, let's calculate the total number of students in the class:
[tex]3+4+13+6=26[/tex]Out of those 26 students we have
[tex]13+6=19[/tex]19 that do not play a sport.
Therefore the probability that a student chosen randomly
from the class does not play a sport is:
[tex]\frac{19}{26}[/tex]You have to deliver medicines 1 mile away. In order to do that, you have to which drone to use depending on the size of the blade in the drone. The equation that gives the relationship between the size of the blade (b) in inches and speed (miles/hour) is as follows: Speed = 50-2b In order to deliver the medicine in time, the drone must travel faster than 37 miles/hour. Check the box underneath the blade that you would like to use. Then write the speed of the drone using this blade.
Answers
From the information given,
The equation representing the relationship between the size of the blade (b) in inches and speed (miles/hour) is given as
Speed = 50-2b
Also, the required drone must travel faster than 37 miles/hour.
For the small blade, b = 4 inches
speed = 50 - 2 * 4 = 50 - 8
speed = 42 miles/hour
For the medium blade, b = 6 inches
speed = 50 - 2 * 6 = 50 - 12
speed = 38 miles per hour
For the large blade, b = 8
speed = 50 - 2 * 8 = 50 - 16
speed = 34 miles per hour
Since the speed of the drone with small blade is greater than 37 miles per hour and it is the greatest among the three drones,
The speed of the drone will be 42 miles per hour
(x+3)^2+(y-4)^2=16please provide the center and the radius
Answers
Given:
Given the equation of the circle
[tex](x+3)^2+(y-4)^2=16[/tex]Required: Radius and center of the circle
Explanation:
The standard form of an equation of a circle is of the form
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the center and r is the radius.
Re-write the given equation of circle in standard form.
[tex](x-(-3))^2+(y-4)^2=4^2[/tex]Comparing with the standard form,
center: (h, k) = (-3, 4)
Radius: r = 4
Final Answer: Center = (-3, 4) and radius = 4.
Apply the distributive property to simplify the expression 8(12x – 20)
Answers
Answer:
[tex]\boxed{\bf {96x-160}}[/tex]
Step-by-step explanation:
[tex]\sf 8(12x - 20)[/tex]
Apply the Distributive Property :-
[tex]\boxed{\sf \:a\left(b-c\right)=ab-ac}[/tex]
[tex]\sf 8(12x - 20)[/tex]
[tex]\sf 8\times \:12x-8\times\:20[/tex]
[tex]\sf 8 \times 12x=\bf 96x[/tex]
[tex]\sf 8\times 20=\bf 160[/tex]
[tex]\bf 96x-160[/tex]
________________
Hope this helps!
Have a great day! :)
Answer:
96x - 160
Step-by-step explanation:
Given expression,
→ 8(12x - 20)
Let's simplify the expression,
→ 8(12x - 20)
→ (8 × 12x) - (8 × 20)
→ 96x - 160
Hence, answer is 96x - 160.
What is the solution to the system of equationsy = 3x - 2 and y = g(x) where g(x) is defined bythe function below?y=g(x)
Answers
we need to write the equation of the graph
it is a parable then the general form is
[tex]y=(x+a)^2+b[/tex]where a move the parable horizontally from the origin (a=negative move to right and a=positive move to left)
and b move the parable vertically from the origin (b=negative move to down and b=positive move to up)
this parable was moving from the origin to the right 2 units and any vertically
then a is -2 and b 0
[tex]y=(x-2)^2[/tex]now we have the system of equations
[tex]\begin{gathered} y=3x-2 \\ y=(x-2)^2 \end{gathered}[/tex]we can replace the y of the first equation on the second and give us
[tex]3x-2=(x-2)^2[/tex]simplify
[tex]3x-2=x^2-4x+4[/tex]we need to solve x but we have terms sith x and x^2 then we can equal to 0 to factor
[tex]\begin{gathered} 3x-2-x^2+4x-4=0 \\ -x^2+7x-6=0 \end{gathered}[/tex]multiply on both sides to remove the negative sign on x^2
[tex]x^2-7x+6=0[/tex]now we use the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a is 1, b is -7 and c is 6
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(1)(6)}}{2(1)} \\ \\ x=\frac{7\pm\sqrt[]{49-24}}{2} \\ \\ x=\frac{7\pm\sqrt[]{25}}{2} \\ \\ x=\frac{7\pm5}{2} \end{gathered}[/tex]we have two solutions for x
[tex]\begin{gathered} x_1=\frac{7+5}{2}=6 \\ \\ x_2=\frac{7-5}{2}=1 \end{gathered}[/tex]now we replace the values of x on the first equation to find the corresponding values of y
[tex]y=3x-2[/tex]x=6
[tex]\begin{gathered} y=3(6)-2 \\ y=16 \end{gathered}[/tex]x=1
[tex]\begin{gathered} y=3(1)-2 \\ y=1 \end{gathered}[/tex]Then we have to pairs of solutions
[tex]\begin{gathered} (6,16) \\ (1,1) \end{gathered}[/tex]where green line is y=3x-2
and red points are the solutions (1,1)and(6,16)
fill in the blank summataion notation
Answers
we have the sequence
5+9+13+...
we have an arithmetic sequence
a1=5
a2=9
a3=13
a2-a1=9-5=4
a3-a2=13-9=4
the common difference is d=4
the general expression is equal to
[tex]a_n=a_1+d\cdot(n-1)[/tex]we have
a1=5
d=4
substitute
[tex]\begin{gathered} a_n=5+4\cdot(n-1) \\ a_n=4n+1 \end{gathered}[/tex]therefore
the notation is equal to
see the attached figure
please wait a minute to fill the image
I am a rectangle with an area of 100 cm, what is the area of the one of my triangles A. 50 in B. 50 cm C. 100 cm D. 25 cm
Answers
the area of a triangle is half the area of the rectangle:
100 cm / 2 = 50 cm
Cindy is riding her bicycle six miles ahead of Tamira. Cindy is traveling at an average rate of 2 miles per hour. Tamira is traveling at an average rate of 4 miles perhour. Let a represent the number of hours since Tamira started riding her bicycleWhen will Tamira be ahead of Cindy? Write an inequality to represent thissituation
Answers
Given:
Cindy is riding her bicycle six miles ahead of Tamira at an average rate of 2 miles per hour.
Let 'a' represents the number of hours.
Distance travellled by Tamira in a hours = 4a
Distance travelled by Cindy in a hours=2a
[tex]4a>2a+6[/tex]Find the value of x if A, B, and C are collinear points and B is between A and C.AB=5,BC=3x+7,AC=5x−2A. 6B. 12C. 7D. 14
Answers
C. 7
Explanation:Given:
AB = 5
BC = 3x + 7
AC = 5x - 2
Since the points A, B, and C are collinear:
AB + BC = AC
Substitute the given values into the equation above:
5 + 3x + 7 = 5x - 2
Collect like terms
5x - 3x = 5 + 7 + 2
2x = 14
Divide both sides by 2
2x/2 = 14/2
x = 7