Triangle VWX is formed by connecting the midpoints of the side of triangle STU.
The lengths of the sides of triangle VWX are shown. What is the length of SU?
Figures not necessarily drawn to scale.
Answers
The length of the side SU will be equal to 4√2.
What is a Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The formula for the Pythagorean theorem will be given as:-
H² = P² + B²
Here,
H = Hypotenuse
P = perpendicular
B= Base
The length of the sides of the triangle is formed by joining the midpoints of the bigger triangle are xw=2, xv=2, and vw = 3.
Here sv = vt = xw = 2 units. Apply the Pythagorean theorem in a triangle xsv.
H² = P² + B²
sx² = xv² + sv²
sx = √ ( 2² + 2² )
sx = √8
sx = √ ( 2 x 2 x 2 )
sx = 2√2
SU = 2 sx
SU = 2 x 2√2
SU = 4√2
Therefore, the length of the side SU will be equal to 4√2.
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Related Questions
write the answer in standard form(-3x^4 + x^6 – 9x^5+ 2x^2– 7) + (-2x^5 + x - 4x^2– x^4 + 12)
Answers
Simplify the expression and express in standard form.
[tex]\begin{gathered} (-3x^4+x^6-9x^5+2x^2-7)+(-2x^5+x-4x^2-x^4+12) \\ =-3x^4+x^6-9x^5+2x^2-7-2x^5+x-4x^2-x^4+12 \\ =x^6-11x^5-4x^4-2x^2+x+5 \end{gathered}[/tex]So answer is,
[tex]x^6-11x^5-4x^4-2x^2+x+5[/tex]thanks in advance for the help
Answers
a. The decrease road line verified by given function while increase in the highway The function representing the railroad miles has a negative slope, indicating a decrease. The function representing the highway miles has a positive slope, indicating an increase.
b. It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
Given
The function y =-1518x + 144.068 represents the railroad miles.
While the function y =-360.5x + 155.18models the number of highway miles.
For each function, x is the number of years after 1995.
The year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.
Therefore,
-1518x + 144.068= -360.5x + 155.18
-1518x+360.5x = 155.18-144.068
1157.5x = 11.112
x = 9
Then,
1995 - 9 = 1986
It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
What are miles?A mile, sometimes an international mile or base mile to distinguish it from other miles, is an imperial unit in the United Kingdom and a standard unit of distance in the United States. both are based on the older English unit of length, which is 5280 English feet or 1760 yards. The legal mile was standardized by an international agreement between the Commonwealth of Great Britain and the United States in 1959, when it was officially redefined in SI units to exactly 1609.3 meters.
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1.
Rule/Equation: y = slope (x) +/- y-intercept
OR y = m(x) +/- b
X
2
6
10
14
18
y
12
8
4
0
TABLES TO EQUATIONS #2
-4
Slope (growth rate):
y-intercept (starting value):
2
Equation:
Answers
Answer:
Step-by-step explanation:
x y
2 12
6 8
10 4
14 0
18 -4
The slope is the Rise/Run, or change in y over the change in x. Pick any two points. I'll choose (2,12) and (18,-4),
Rise = (-4 - 12) = -16
Run = (18 - 2) = 16
Slope = Rise/Run = -16/15, or -1
The equation becomes y = -1x + b
To find b, use any of the points in the equation and solve for b. I'll use (14,0):
y = -1x + b
0 = -1(14) + b
b = 14
The equation is y = -x + 14
See the attached graph.
25.6 = 8x solve for x
Answers
Answer:
x = [tex]\frac{16}{5} = 3\frac{1}{5} = 3.2[/tex]
Step-by-step explanation:
25.6 = 8x
Divide both sides by 8.
[tex]\frac{25.6}{8} = x\\[/tex]
Expand [tex]\frac{25.6}{8}[/tex] by multiplying both numerator and the denominator by 10.
[tex]\frac{256}{80} = x[/tex]
Reduce the fraction [tex]\frac{256}{80\\}[/tex] to lowest terms by extracting and canceling out 16.
[tex]\frac{16}{5} = x[/tex]
Swap sides so that all variable terms are on the left-hand side.
[tex]x = \frac{16}{5}[/tex]
If you answer is meant to be a fraction, then your correct answer is [tex]3\frac{1}{5}[/tex] and if you answer is meant to be a decimal then you correct answer is 3.2.
Hope I helped and have a good day. ~sunshine~ =D
a $25$ foot ladder is resting against a wall so that the bottom of the ladder is $7$ feet from the wall. the bottom of the ladder starts slipping away from the wall at a rate of $1$ foot per second. how many feet per second is the top of the ladder sliding down the wall when it is $15$ feet above the ground?
Answers
The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. When the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.
Given that,
The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. A feet per second of the ladder's bottom begins to slide away from the wall.
We have to find when the ladder is 15 feet above the ground, how many feet per second is the top of the ladder falling down the wall.
Let us take x = height where the ladder hits the building
7 squared + x squared=25 squared
49+x squared=625
x squared=576
x=24 feet
Now,
If it slips 15 feet that 24-15=9 feet
Let x = distance from wall:
x² + 9² = 25²
x² + 81= 625
x² = 544
x = 23.3 feet
Therefore, when the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.
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Can somebody help me with number 11?
Answers
The unknown angles are as follows:
m∠EFH = 80°m∠EFG = 160°The value of ST in the line segment is 22 units.
How to find angles and mid points?An angle bisector is a bisector that bisect an angles into two equal parts.
Therefore, EF is the angle bisector of ∠EFG.
The bisector divides the ∠EFG equally into ∠EFH and ∠HFG.
Hence,
∠EFH = ∠HFG
m∠HFG = 80°
m∠EFH = 80°
m∠EFG = 80 + 80
m∠EFG = 160°
12.
Let's find ST in the line segment.
PT = 40
QS = 12
PQ = QR = RS = x
QR + RS = QS
2x = 12
x = 12 / 2
x = 6
Therefore,
PQ = QR = RS = 6 units
PS = PQ + QR + RS
PS = 6 + 6 + 6
PS = 18 units
Hence,
ST = PT - PS
ST = 40 - 18
ST = 22 units
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Graph the solution to the following system of inequalities. Don’t forget to answer the point in the solution set.
Answers
Given the following System of Inequalities:
[tex]\begin{cases}7x+4y<16 \\ -5x+4y\ge12\end{cases}[/tex]You need to remember that the Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
The steps to graph the System of Inequalities are:
1. In this case, you know that the first line is:
[tex]7x+4y=16[/tex]So you need to solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 4y=-7x+16 \\ \\ y=\frac{-7}{4}x+\frac{16}{4} \\ \\ y=-\frac{7}{4}x+4 \end{gathered}[/tex]You can identify that the y-intercept is:
[tex]b_1=4[/tex]2. Since the value of "y" is zero when the line intersects the x-axis, you can substitute that value into the equation and solve for "x", in order to find the x-intercept:
[tex]\begin{gathered} 7x+4y=16 \\ 7x+4(0)=16 \\ 7x=16 \\ \\ x=\frac{16}{7}\approx2.286 \end{gathered}[/tex]3. Now you know that the first line passes through these points:
[tex](0,4);(2.286,0)[/tex]4. The second line is:
[tex]-5x+4y=12[/tex]So you can solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 4y=5x+12 \\ \\ y=\frac{5}{4}x+\frac{12}{4} \\ \\ y=\frac{5}{4}x+3 \end{gathered}[/tex]Notice that the y-intercept is:
[tex]b_2=3[/tex]5. Knowing that "y" is zero when the line intersects the x-axis, you can substitute that value into the equation of the second line and solve for "x" to find the x-intercept:
[tex]\begin{gathered} -5x+4y=12 \\ -5x+4(0)=12 \\ -5x=12 \\ \\ x=\frac{12}{-5} \\ \\ x=-2.4 \end{gathered}[/tex]Reflect the figure over the line y = 1. Plot all of the points of the reflected figure. You may click a plotted point to delete it.
Answers
Answer:
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Triangle XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form triangle X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4). The type of transformation that triangle XYZ undergoes is a
.
Triangle X′Y′Z′ then undergoes a transformation to form triangle X′′Y′′Z′′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4). The type of transformation that triangle X′Y′Z′ undergoes is a
.
Answers
Answer:
1. (x+6, y-2)
2. reflection across the x-axis
Step-by-step explanation:
two functions are given below: f(x) and h(x). state the axis of symmetry for each function and explain how to find it
HELP ME PLEASE
Answers
The axis of symmetry for function
f(x) is x = 8 and for h(x) is x = 3.
We know that the quadratic equation in vertex form is, y = a (x - m)² + n
where (m, n) is the vertex of the parabola.
And, the axis of symmetry is x = m.
Consider function f(x)
f(x) = -4(x - 8)² + 3
This function represents a quadratic equation in vertex form with vertex (8, 3)
So, the axis of symmetry for function f(x) would be x = 8
We know that the axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetrical.
Consider the function h(x)
We can observe that the vertex of parabola is (3, 2)
So, the axis of symmetry would be x = 3.
Therefore, the axis of symmetry for function
f(x) is x = 8 and for h(x) is x = 3.
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Emily is designing a t-shirt logo for her company. The t-shirt printing company offers 11 colors to choose from for the logo design. If any number of colors can be chosen, how many different color combinations are possible?
Answers
39,916,800 color combinations are possible
Here, we want to get the possible number of color combinations possible.
Since any number of colors can be chosen, there are no restrictions here
That means the number of possible color combinations will be;
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800 color combinations
O is the center of the regular decagon below. Find its perimeter. Round to the nearest
tenth if necessary.
16
Answers
Answer:
Step-by-step explanation:
The perimeter of the given polygon rounded to the nearest tenth is; 24.7
What is the perimeter of the Polygon?
The given polygon as we can see has 10 sides.
Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.
Thus, the other two angles will be; (180 - 36)/2 = 72° each
Using sine rule, we can find the length of a side of the polygon as;
x/sin 36 = 4/sin 72
x = (4 * sin 36)/sin 72
x = 2.472
Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7
How do you solve -m=9
Answers
Hello!
So, we are given the following to solve:
[tex]-m=9[/tex]
To solve this, simply divide both sides by -1.
[tex]\frac{-m}{-1}= \frac{9}{-1}[/tex]
Then, simplify the expression and you have your solution.
[tex]m=-9[/tex]
Hope this helps! If so, please lmk! Thanks and good luck!
Answer:
m= -9
Step-by-step explanation:
Divide both sides by -1
[tex]\frac{-m}{-1} =\frac{9}{-1}[/tex]
Simplify m = - 9
What is the area of trapezoid ABCE?A20 mB16 mEDC25 msq m
Answers
Given data:
The given figure of the trapezium.
The expression for the area of the trapezium is,
[tex]\begin{gathered} A=\frac{1}{2}(20\text{ m+25 m)(16 m)} \\ =360m^2 \end{gathered}[/tex]Thus, the area of the given trapezium is 360 sq-m.
Given the 2 statements: "If you study for your test, then you will pass
your test," and "If you passed your test, then you studied for your
test." the biconditional is:
Answers
The biconditional statement is "You study for your test if and only if you passed".
What is biconditional statement?
A biconditional statement combines a conditional statement with its opposite expressed in the form of "if and only if."
The given statements are,
"If you study for your test, then you will pass your test" and "you passed your test then you studied for your test".
The biconditional statement is: "You study for your test if and only if you passed".
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In a company 80/ of workers are men if 1120 people workfor the company who aren’t men how many workers are there in all
Answers
Answer:
if you meant %, the answer is 2016
Step-by-step explanation:
1120 + 80% is 2016
What is the answer to this question
Answers
The angles are which alternate exterior angles include the following: A. ∠XWY and ∠STR.
What are parallel lines?Parallel lines can be defined as two (2) lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.
In conclusion, we can logically deduce that both ∠XWY and ∠STR are alternate exterior angles because they lie outside the two (2) parallel lines and are located on opposite sides of the transversal.
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Algebra homework pls help
Answers
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The equation 9 x 5 = 45 consists of the two equations are separated by the 'equal' sign.
Detailed explanation:Assume that a team has N players.
Each squad may have anywhere from 3 to 5 players, so
3 ≤ 5 ...(i)
Let P represent a player's total points in a single game round.
Each round of the game allows for a maximum of 10 points for each player, so
0 ≤ p ≤ 10 ....( i)
(1) Elena assembled a team of five people.
As a result, 5 players' points in 1 round equal 5P.
Equation (ii) yields the range of
0 ≤ 5p ≤ 50.
As a result, Elena's team's points total ranges from 0 to 50.
(2) If each shot is off by one point, then
One player's points in one round are equal to 10-1=9.
So, 9 x 5 = 45 points were collected by 5 players in 1 round.
(3) Assume that R represents the number of teams as an integer.
the game involves at least three teams, therefore
R ≥ 3 ...( iii)
Given that N players make up one team,
R team has NR players, where R is 3, 4, or more.
Next, using equation (i)
3R ≤ 5R
Therefore, the number of players ranges from 3R to 5R if there are at least 3 teams.
The game can have anywhere from 3x3=9 to 5x3=15 players when R=3.
Answer:
(I) Between 0 and 50.
(ii) Between 3 and 5.
(iii) Between 3R and 5R, where R = 3,4,5,...
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27. A table and five chairs cost $3500. The cost of three chairs is $1050. What is the cost of a table if all the chairs cost the same price?
Answers
What is 3 2/5 plus 2 1/5?
Answers
Answer: 5 3/5
Step-by-step explanation:
3 + 2 = 5
2/5 + 1/5 = 3/5
5 + 3/5 = 5 3/5
Hope this helps!
Solve for m/UVX.
Answer: m/UV X =
O
72°
42°
Submit Answer
Answers
The measure of angle UVX is 30°
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. The arc is centered at the vertex and defined by the sides in the case of a geometric angle.
Given, measure of angle UVW = 72°
measure of angle XVW = 42°
So, the measure of angle UVX = 72° - 42° = 30°
Hence, the measure of angle UVX is 30°
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PLEASE HELP!! Will mark brainliest!!
Answers
Answer:
-1, 0, 1, 2
Step-by-step explanation:
[tex]\sqrt{5-5} -1\\\sqrt{0} -1\\0-1\\-1[/tex]
[tex]\sqrt{6-5} -1\\\sqrt{1} -1\\1-1\\0[/tex]
[tex]\sqrt{9-5} -1\\\sqrt{4} -1\\2-1\\1[/tex]
[tex]\sqrt{14-5} -1\\\sqrt{9} -1\\3-1\\2[/tex]
Ciara how’s it going with the total area of (3x^2+4x) Square feet.What is the length and the width of the garden? explain
Answers
Ok, since we know that the area of a rectangle is given by the product of the width times the length, and the area is given to us by the function 3x^2+4x, we then factor the function of area:
[tex]3x^2+4x=x(3x+4)[/tex]By the previous definition, we will have that the lenght of the garden will be 3x+4 and the widht of the garden will be x.
2 Four friends go to the ice cream shop to purchase frozen
yogurt. Each friend gets a part strawberry and part
vanilla.
• Lucas gets 0.25 strawberry.
Adrianna gets % strawberry.
Ricardo gets 0.8 strawberry.
Jasmine gets % strawberry.
•
•
Arrange the friends in order from least to greatest amount of
strawberry in their yogurt.
Least
Greatest
Answers
Answer:
12
Step-by-step explanation:
Under his cell phone plan, Rahul pays a flat cost of $36 per month and $4 per
gigabyte. He wants to keep his bill under $95 per month. Which inequality
can be used to determine g, the maximum number of gigabytes Rahul can use
while staying within his budget?
Answers
The inequality of the function is 36 + 4x < 95 and Rahul can use 14 gigabyte while staying within his budget
How to determine the inequality of the function?The given parameters are:
Flat cost = $36 per monthRate per gigabyte = $4 per gigabyteRahul's bill = Under $95The above means that;
The total charges per month is
C(x) = Flat cost + Rate per gigabyte x Number of gigabyte
So, we have
C(x) = 36 + 4x
For the bill to be under $95, we have
36 + 4x < 95
Solving further, we have
4x > 59
Divide by 4
x < 14.75
Hence, the inequality is 36 + 4x < 95
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A boat can travel 228 miles on 19
gallons of gasoline. How much gasoline
will it need to go 48 miles?
Round the answer to two decimal digits
Answers
Answer: 4 gallons
Step-by-step explanation:
The boat can travel 228 miles on 19 gallons of gasoline. We can divide 228 by 19 to find out how many miles the boat can travel on 1 gallon of gasoline, which is 12. For the boat to go 48 miles, we can divide 48 by 12 to get the answer, which is 4. The boat can travel 48 miles with 4 gallons of gasoline.
My penMath The area of a triangle can be found using the formula: Area = 1/2 · base · height. Find the area of the triangle pictured below, where the measurements are given in meters (m) 2 m 10 m
Answers
Answer:
The area of the given triangle is 10 sq meters
Explanation:
The area of a triangle is given by the formula:
Area = 1/2 base . height
Given that the triangle has base = 10m, and height = 2m
Area = 1/2 * 10 * 2
= 10 square meters
the registrar of a college examined the grade point averages of different categories of students. the results showed that the probability of a meaningful difference between men and women was .27. using the most common standard, is this a statistically significant difference?
Answers
The difference of 0.27 is not statistically significant.
A statistically significant difference indicates if the responses of one group differ significantly from those of another when using statistical testing.
The statistically significant differences between the numbers really aid in your data analysis. It is up to you how to interpret or act on your results, therefore you should also think about if they are significant.Let's imagine, for instance, that you get more consumer complaints from women than from men. How do you know that this is a genuine issue that has to be addressed? To find out if your male consumers are significantly more satisfied with your goods, doing a poll is a terrific technique. Our statistical significance tool can assist you in determining whether males are considerably more satisfied with your goods than women using a statistical formula. This enables you to base decisions on facts rather than anecdotes.Now we know that any data of t-statistic that is greater than 1.96 is statistically significant.
Now the difference is 0.27. Hence it is not statistically significant.
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When an integer is subtracted from 2 times the next consecutive odd integer, the
difference is 9. Find the value of the greater integer.
Answers
Answer:
7
Step-by-step explanation:
Let x be the "integer." We'll assume it is odd.
The next consecutive odd integer would be x+2.
(2(x+2) - x) =9 [When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9]
(2(x+2) - x) =9
(2x+4) - x) =9
x+4 =9
x = 5
The greater integer is x+2 or 7
Check:
If 5 is subtracted from 2 times the next consecutive odd integer, 7, is the difference 9?
2*7 - 5 = 9?
14 - 5 = 9?
14 - 5 = 9? YES
Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for sor">=" for >.5(-3,0)5(0, -3)
Answers
we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is
[tex]\begin{gathered} m=\frac{-3-0}{0-(-3)} \\ m=\frac{-3}{3} \\ m=-1 \end{gathered}[/tex]where we used the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, our searched line has the form:
[tex]y=-x+b[/tex]where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:
[tex]\begin{gathered} -3=-(0)+b \\ b=-3 \end{gathered}[/tex]then, the searched line in slope-intercept form is
[tex]y=-x-3[/tex]Therfore, the given area can be modeled as
[tex]y>-x-3[/tex]because when a line is dashed it doesn't belong to the given area.
