Answers
SOLUTION
From the question given the following statements to prove are correct, then the last part
[tex]\Delta RSU\cong\Delta TSV[/tex]The reason is Side-side-side triangle theorem
This theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
Hence the answer is Side-side-side triangle theorem
Related Questions
Solve the equation:2(x + 3) = 8
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First, we have to apply distributive property:
[tex]2(x)+2(3)=8[/tex][tex]2x+6=8[/tex]Subtract 6 from both sides of the equation:
[tex]2x+6-6=8-6[/tex][tex]2x=2[/tex]Finally, divide both sides of the equation by 2:
[tex]2x/2=2/2[/tex][tex]x=1[/tex]
I am doing my math homework and I can’t really understand it
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simplify: value of x , f(x)=-3
Explanation: we can clear see from the given table that when x= -7 , f(x) will -3
so x=-7 for f(x)=-3
Final answer: x=-7 is required answer.
Rewrite the expression 1/2p - (1 - 1/4p) without parentheses.
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Question:
Rewrite the expression 1/2p - (1 - 1/4p) without parentheses.
Solution:
Consider the following expression:
[tex]\frac{1}{2}\text{ p - (1-}\frac{1}{4}p\text{)}[/tex]putting together like terms, we get:
[tex]\frac{1}{2}p\text{ + }\frac{1}{4}p-1[/tex]this is equivalent to:
[tex]\frac{2p\text{ + p}}{4}-1[/tex]finally, this is equivalent to:
[tex]\frac{3\text{ p}}{4}-1[/tex]then, the correct answer is:
[tex]\frac{3\text{ p}}{4}-1[/tex]factorizar 4y^2= -16y
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Para factorizar la ecuación
[tex]4y^2=-16y[/tex]Primero pasamos el -16y sumando al lado izquierdo:
[tex]4y^2+16y=0[/tex]Notamos que 4y es factor común en ambos términos de la ecuación. por lo cual podemos factorizar este factor común.
[tex]4y(y+4)=0[/tex]This is the graph of f(x)=-0.05(x^ 1 2-26x-120 .What are the zeros of this function? Circle them on the graph
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Answer:
Zeros are at x = 30 and x = -4.
Explanation:
The zeros of a function are the points where it intersects the x-axis. in other words, the zeros are solutions to the following equation.
[tex]f(x)=0.[/tex]which in our case is
[tex]f\mleft(x\mright)=-0.05\left(x^2-26x-120\right)=0[/tex]Now looking that the graph of the function given we see that the parabola intersects the x-axis at x = -4 and x = 30.
Therefore, the zeros of the function are at x = -4 and x = 30.
I dont know how to do number 21 on my homework
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A point has the form:
[tex](x,y)[/tex]Where "x" is the x-coordinate and "y" is the y-coordinate.
To plot a point you must identify the x-coordinate and the y-coordinate. You need to:
- Move "x" units to the right (if it is positive).
- Move "x" units to the left (if it is negative).
- Move "y" units up (if it is positive).
- Move "y" units down (if it is negative).
Remember that you must move "x" or "y" spaces from the origin, which is the point (0,0).
In this case, given the points:
[tex]\begin{gathered} a.\left(3,2\right) \\ b.(6,4) \\ c.(8,1) \\ d.(2,8) \end{gathered}[/tex]For "a", for example, you must move 3 units to the right and and then 2 units up. Apply this procedure to each point.
Therefore, you can plot them as you can see in the picture attached:
Enter an estimate. Round each mbxed number to the nearest half in your estimate. 1 6 2 5 Estimate : Find the difference and enter it in simplest form. 62-5 5- =
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Let's begin by listing out the given information:
the graph represents an object that is shot upward from a tower and then falls to the ground. The independent variable is time in seconds and the dependent variable is the object's height above the ground in meters. 1. How tall is the tower from which the object was shot?2. when did the object hit the ground?3. estimate the greatest height the object reached and then the time it took to reach that heightindicate this situation on the graph below by drawing on the graph given
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In the graph, the height, measured in meters, is on the y-axis and the time, measured in seconds, is on the x-axis. It shows the variation of the height of an object shot from a tower with respect to the time.
1. Since the shot was made from the top of the tower, the starting height of the object (time zero) is equal to the height of the tower. This is represented in the graph by the y-intercept of the function, that is, the value of y when x=0.
The y-intercept is at (0,10) which indicates that the height of the tower is 10m
2. The point where the object hit the ground, the height is zero meters, so in the graph, it is determined by the point where the parabola reaches the x-axis (y=0) known as the x-intercept.
The coordinates of the x-intercept are (6,0)
This indicates that the object hit the ground 6 seconds after being shot.
3. The variability of the object's height describes a parabola, where the vertex of the parabola indicates the highest point the object can reach.
You have to determine the coordinates of the vertex by looking at the graph. These are, approximately (2.8,93)
The y-coordinate of the vertex indicates the highest point of the object, which is 93meters.
The x-coordinate of the vertex indicates the time it took the object to reach said height, which is 2.8 seconds
Solve the following system of linear equations.x + 2y + z = - 32x - 3y - 3z = 173x - 2y + 4z = - 23Answerx =y =z =
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ANSWER
[tex]\begin{gathered} x=1 \\ y=1 \\ z=-6 \end{gathered}[/tex]EXPLANATION
We want to solve the given system of linear equations:
[tex]\begin{gathered} x+2y+z=-3 \\ 2x-3y-3z=17 \\ 3x-2y+4z=-23 \end{gathered}[/tex]From the first equation, make x the subject of the formula:
[tex]x=-2y-z-3[/tex]Substitute the equation above into the second and third equations:
[tex]\begin{gathered} 2(-2y-z-3)-3y-3z=17 \\ -4y-2z-6-3y-3z=17 \\ \Rightarrow-7y-5z=23 \end{gathered}[/tex]and:
[tex]\begin{gathered} 3(-2y-z-3)-2y+4z=-23 \\ -6y-3z-9-2y+4z=-23 \\ \Rightarrow-8y+z=-14 \end{gathered}[/tex]Now, we have a system of two equations with two variables:
[tex]\begin{gathered} -7y-5z=23 \\ -8y+z=-14 \end{gathered}[/tex]From the second equation, make z the subject of the formula:
[tex]z=8y-14[/tex]Substitute the equation above into the first equation and solve for y:
[tex]\begin{gathered} -7y-5(8y-14)=23 \\ -7y-40y+70=23 \\ \Rightarrow-47y=23-70=-47 \\ \Rightarrow y=\frac{-47}{-47} \\ y=1 \end{gathered}[/tex]Substitute the value of y into the equation for z:
[tex]\begin{gathered} z=8(1)-14=8-14 \\ z=-6 \end{gathered}[/tex]Finally, substitute the values of y and z into the equation for x:
[tex]\begin{gathered} x=-2(1)-(-6)-3 \\ x=-2+6+3 \\ x=1 \end{gathered}[/tex]Hence, the solution to the system of linear equations is:
[tex]\begin{gathered} x=1 \\ y=1 \\ z=-6 \end{gathered}[/tex]an artist is painting a mural in the shape of a rectangle that has an area of 216 ft the mural is 8 feet high. how long it is it
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The area of the rectangle is given by:
[tex]A=h\cdot l[/tex]Where:
A = Area = 216ft²
h = Height = 8ft
l = Length
Solve for l:
[tex]\begin{gathered} 216=8l \\ l=\frac{216}{8} \\ l=27ft \end{gathered}[/tex]Answer:
27ft
_______ 10. Given the following information, find the length of chord AC.OA = 5. OB = 3A. 4B. 5C. 6D. 8
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Hello there. To solve this question, we'll have to remember some properties about the radius of a circle and the Pythagorean Theorem.
Given the following diagram:
We want to determine the length of the chord AC.
We already know that the length of the segments OA = 5 and OB = 3.
In the diagram, we get
Notice this is a right triangle, therefore we can determine the length of the segment AB by using the Pythagorean Theorem.
We know that
[tex]\overline{AB}^2+\overline{OB}^2=\overline{OA}^2[/tex]Hence we get that
[tex]\begin{gathered} \overline{AB}^2+3^2=5^2 \\ \\ \overline{AB}^2+9=25 \\ \\ \overline{AB}^2=25-9=16 \\ \\ \overline{AB}=\sqrt{16}=4 \\ \end{gathered}[/tex]Since OA is the radius of the circle and D is the midpoint of the arc AC, we get that
[tex]\overline{OA}\equiv\overline{OC}[/tex]Which means that
[tex]\overline{AB}\equiv\overline{BC}[/tex]Since
[tex]\overline{AC}=\overline{AB}+\overline{BC}[/tex]We get that
[tex]\overline{AC}=4+4=8[/tex]This is the final answer and contained in the last option, D. 8;
solve for v9= 5v+27+4v
Answers
Let's satrt by copying the equation:
[tex]9=5v+27+4v[/tex]Firslty, let's leave the equation with all the terms with v on one side and all the term without v on the other.
The right side has all the terms with v, but there is one without v that we need to pass to the other side., we can do that by substracting both sides by 27:
[tex]\begin{gathered} 9-27=5v+27+4v-27 \\ 9-27=5v+4v+27-27 \\ 9-27=5v+4v \end{gathered}[/tex]Now, we evaluate the like-terms on each side:
[tex]-18=9v[/tex]Now, we can invert the sign so that the variable v go to the left side, as usual:
[tex]9v=-18[/tex]To finish the solve. we can divide both sides by 9:
[tex]\begin{gathered} \frac{9v}{9}=\frac{-18}{9} \\ v=-2 \end{gathered}[/tex]I need help with the number one question it's my homework and can a tutor please help me nothing much, please. Thanks for the help.
Answers
An example of The Whole is the Sum of Its Parts is the addition of angles. Notice that angle SAC is formed by the addition of SAT and TAC.
So, we can express the following as an example of the axiom
[tex]m\angle SAC=m\angle SAT+m\angle TAC[/tex]make sure to abide by the difference quotient part of the question
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We have to find the tangent line to y = x² - 3 at x = a.
The slope of the tangent line will be equal to the first derivative at that point.
We start by calculating the first derivative using the definition of the derivative:
[tex]\begin{gathered} y^{\prime}=\lim_{h\to0}\frac{f(x+h)-f(x)}{h} \\ y^{\prime}=\lim_{h\to0}\frac{(x+h)^2-3-x^2+3}{h} \\ y^{\prime}=\lim_{h\to0}\frac{x^2+2xh-h^2-x^2-3+3}{h} \\ y^{\prime}=\lim_{h\to0}\frac{2xh-h^2}{h} \\ y^{\prime}=\lim_{h\to0}2x-h \\ y^{\prime}=2x \end{gathered}[/tex]As we have to calculate the tangent line at x = 2 and a = 2, we can replace x with 2 to find the slope of the tangent line:
[tex]m=y^{\prime}(2)=2(2)=4[/tex]We now need a point of the line to find its complete equation.
As the line is tangent to (a, f(a)) we can calculate the value of f(a) = f(2) as:
[tex]f(2)=(2)^2-3=4-3=1[/tex]Then, with a slope m = 4 and tangent to point (2, 1) we can write the equation of the line as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-1=4(x-2) \\ y=4x-8+1 \\ y=4x-7 \end{gathered}[/tex]We can check this with a graph as:
Answer:
The tangent line is y = 4x - 7
218Note: Where appropriate use either the pi button on your calculator or the approximation of"3.14". Round answers to the nearest tenth.Circumference of the base =Area of the base =Height =Lateral Area =Surface Area = 125.6Volume =Blank 1: 12.6Blank 2: 12.6Blank 3: 8Blank 4: 100.5Blank 5: 125.6Blank 6:
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Answer:
The volume of the cylinder is;
[tex]V=100.5\text{ cubic units}[/tex]Explanation:
Given the figure in the attached image.
The height and radius of the cylinder are;
[tex]\begin{gathered} h=8 \\ r=2 \end{gathered}[/tex]Recall that the volume of a cylinder can be calculated using the formula;
[tex]V=\pi r^2h[/tex]Substituting the given values;
[tex]\begin{gathered} V=\pi\times2^2\times8 \\ V=32\pi \\ V=100.5\text{ cubic units} \end{gathered}[/tex]Therefore, the volume of the cylinder is;
[tex]V=100.5\text{ cubic units}[/tex]A bag has 7 red marbles, 8 blue marbles, and 5 purple marbles, Rachel draws a marble from the bad without looking.What is the probability that Rachael draw a blue marbleA. 4%B.8%C.12%D.40%E.66.7%
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To find the probability of drawing a blue marble we have to divide the number of blue marbles and the total number of marbles. There are 8 blue marbles, and there are 20 total marbles.
[tex]P_{\text{blue}}=\frac{8}{20}=\frac{2}{5}=0.4[/tex]Hence, the probability is 40%.What additional piece of information is needed to show triangle ABC is congruent to triangles DEF by SSS.
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SOLUTION
Given the question in the image, the following are the solution steps to get the correct piece of information needed
Step 1: Define the SSS postulate
If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent. We can determine that the three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Step 2: Find the correct statement
From the image, the following can be seen:
[tex]\begin{gathered} AB\cong ED\text{ (given)} \\ AC\cong FD(given) \\ BC\cong EF \\ By\text{ SSS postulate }ABC\cong DEF \end{gathered}[/tex]Hence, it can be deduced from above that the correct piece of information needed to use the SSS postulate is:
[tex]BC=EF[/tex]I just need the answers for questions 9 and 10
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Hello. To answer this questions, we need to remember some properties about fractions and equivalences.
Starting by the question 9:
Call the population 5 years ago by P. If the population has decreased 12000 in these 5 years and this represents a decrease of 3%, so it means the new population is 0.97P.
With this, we can make the following equation:
P - 12000 = 0.97P
Subtract 0.97P and sum 12000 in both sides of the equation
0.03P = 12000
Divide both sides of the equation by a factor of 0.03
P = 3600000
A population of bacteria is growing according to the equation P(t)=600e0.03t . In how many years will the population will exceed 708? Round your answer to one decimal place.t =
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Given
[tex]P=600e^{0.03t}[/tex]Find
time,t
Explaination
[tex]\begin{gathered} P=600e^{0.03t} \\ 708=600e^{0.03t} \\ 1.18=e^{0.03t} \end{gathered}[/tex]Taking log on both sides
[tex]\begin{gathered} ln(1.18)=0.03t \\ 0.165514438=0.03t \\ t=5.5\text{ sec} \end{gathered}[/tex]Final Answer
t = 5.5 sec
63. 7+ (-26)Decimal plus a negative
Answers
63.7+(-26)
If we add a negative number, is the same as subtracting that number:
63.7-26
37.7
−5r+8r+5=please help
Answers
-5r + 8r + 5
-5r and 8r can be combined as follows:
(-5r + 8r) + 5 =
= 3r + 5
At a blood drive, 6 donors with type O + blood, 4 donors with type A + blood, and 2 donors with type B + blood are in line. In how many distinguishable ways can thedonors be in line?The donors can be in line in different ways.2
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First, let's state the given information:
The number of donors with the blood of type O+ is 6.
The number of donors with the blood of type A+ is 4.
The number of donors with the blood of type B+ is 2.
we will label these numbers as follows for reference:
[tex]\begin{gathered} a=6 \\ b=4 \\ c=2 \end{gathered}[/tex]We will also need the total number of donors "n":
[tex]\begin{gathered} n=6+4+2 \\ n=12 \end{gathered}[/tex]Since we are asked to find the distinguishable ways in which the donors can be in line, we need to find the number of permutations.
The formula for permutations is:
[tex]P=\frac{n!}{a!b!c!}[/tex]Where "!" means factorial, and is defined as follows, for example, 4! is:
[tex]4!=4\times3\times2\times1[/tex]And so on depending on the number.
In this case, the operation we have to solve is:
[tex]P=\frac{12!}{6!4!2!}[/tex]Solving this division we get the result for the number of distinguishable ways in which the donors can be in line:
[tex]P=13,860[/tex]Answer: 13,860
Which fraction in simplest form) is equivant to 0.66/106/1003/53/50
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Simplify the expression 0.6 in decimal and simplfy further.
[tex]\begin{gathered} \frac{0.6}{10}=\frac{6}{10} \\ =\frac{3}{5} \end{gathered}[/tex]So answer is 3/5
a class rolled number cubes. their results are shown in the table. what is the experimental probability of rolling number 1? round your answer to the nearest tenth.
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Answer: 15.7%
Explanation
The probability of an event A is given by:
[tex]P(A)=\frac{\text{ occurence of events A}}{\text{total occurrences}}[/tex]In our case, event A is rolling the number 1. Thus, we have 42 occurrences, while the total occurrences are:
[tex]\text{ Total occurrences}=42+44+45+44+47+46=268[/tex]Then:
[tex]P(A)=\frac{42}{268}=0.1567[/tex]Changing to percent:
[tex]0.157\times100\%\approx15.7\%[/tex]Solve the system of equations by the addition method3x - 2y = 74x + 6y = 5
Answers
Answer:
x = 2
y = -1/2
Explanation:
First, we need to multiply the first equation by 3 as:
3x - 2y = 7
3*(3x - 2y) = 3*7
9x - 6y = 21
Now, we can add this equation to the second equation, So:
9x - 6y = 21
4x + 6y = 5
13x + 0 = 26
So, we can solve for x, as:
13x = 26
x = 26/13
x = 2
Finally, we can replace x by 2 on the first equation and solve for y as:
3x - 2y = 7
3*2 - 2y = 7
6 - 2y = 7
-2y = 7 - 6
-2y = 1
y = 1/(-2)
y = - 1/2
Triangle PQR has coordinates P(2,4),(-2,4), R(0,-6). Write the coordinates of the vertices of theimage of a triangle after a dilation of 1.5.
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Triangle PQR has coordinates P(2,4),(-2,4), R(0,-6). Write the coordinates of the vertices of the
image of a triangle after a dilation of 1.5.
i will assume that the center of dilation is the origin (0,0)
so
the rule of the dilation is
(x,y) ------> (1.5x, 1.5y)
therefore
the vertices of the image are
P(2,4) ------> P'(3,6)
Q(-2,4) -----> Q'(-3,6)
R(0,6) -----> R'(0,9)
use the slope intercept form to graph the equation y= -3/8x-4
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we have that the line pass trough (0,-4) and (8,-7) so its graph is
3.3125 as converted to a precent
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Sasha, this is the solution:
3.3125 to percent
Let's recall that for converting a decimal number to percent, we should multiply by 100, this way:
3.3125 * 100 = 331.25%
The graph above is a transformation of the function x ^ 2 Write an equation for the function graphed aboveg(x)=
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Answer:
[tex]g(x)\text{ = -}\frac{1}{4}(x+1)\placeholder{⬚}^2+1[/tex]Explanation:
Here, we want to write an equation for the graph shown
The graph of x^2 is an upward-facing graph
The graph we have shown below is a graph that has been reflected and shifted
To get the equation of the graph we need to write it in the vertex form
The vertex form is:
[tex]y\text{ = a\lparen x-h\rparen}^2+k[/tex]The vertex of the graph is at (h,k)
Looking at the given graph, we have the vertex at (-1,1)
Thus, we have the equation as:
[tex]y\text{ = a\lparen x+1\rparen}^2+1[/tex]Lastly, we need to get the value of a
We can use the point (1,0)
Substituting this value:
[tex]\begin{gathered} 0\text{ = a\lparen1+1\rparen}^2\text{ + 1} \\ 0\text{ = 4a + 1} \\ 4a\text{ = -1} \\ a\text{ =- }\frac{1}{4} \end{gathered}[/tex]Thus, we have the equation of the plotted graph as:
[tex]g(x)\text{ = -}\frac{1}{4}(x+1)\placeholder{⬚}^2+1[/tex]If three tacos and two drinks cost $13.00, and four tacos and one drink costs $15.25, how much does a taco cost?
Answers
Answer: $3.5
Step-by-step explanation:
3x+2y=13
4x+y=15.25
System of equations
I solved using elimination but there are other methods
3x+2y=13
-8x-2y=-30.5
The y cancels out
3x=13
-8x=-30.5
=
-5x= -17.5
Solve
x=3.5
ANSWER: $3.5