Find the lengths of UV and ST and determine whether they are congruent.
Hint: Congruent line segments have the same length.
The length of both UV and ST is [tex]3\sqrt{2}[/tex] and hence they both are congruent.
Here, we are given two lines- UV and ST.
We can find the length of the lines using distance formula. According to distance formula, distance between two points- (x1, y1) and (x2, y2) is given as-
[tex]\sqrt{(x2-x1)^{2} + (y2 - y1)^{2} }[/tex]
Here, for UV,
the two endpoints are- (1,0) and (4,3)
thus, the length of UV will be-
[tex]\sqrt{(4-1)^{2} + (3 - 0)^{2} }[/tex]
= [tex]\sqrt{(3)^{2} + (3 )^{2} }[/tex]
= [tex]\sqrt{9 + 9 }[/tex]
= [tex]\sqrt{18}[/tex]
= [tex]3\sqrt{2}[/tex]
Similarly, the two endpoints of ST are- (-2,-1) and (1,-4)
thus, the length of UV will be-
[tex]\sqrt{(1+2)^{2} + (-4 +1)^{2} }[/tex]
= [tex]\sqrt{(3)^{2} + (-3)^{2} }[/tex]
= [tex]\sqrt{9 + 9 }[/tex]
= [tex]\sqrt{18}[/tex]
= [tex]3\sqrt{2}[/tex]
So we can see that UV = ST = [tex]3\sqrt{2}[/tex], which means that both of them are congruent. Hence, option 1 is the correct answer.
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Your question was incomplete. Check for the missing figure below.
List the domain and range of the relation.
{(5,-3), (2.2), (0, -3), (2.1) (5,3)}
The domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}
The domain of a function is the set of inputs that are accepted by the function. The range, also known as the codomain, is the set of all the output values of the function.
Here, we are given a relation with the following set of solutions-
{(5,-3), (2,2), (0, -3), (2,1) (5,3)}
We know that all x values will form the domain and all the y values will make up the range.
Here the x values are: 5, 2, 0, 2, 5
and the y values are: -3, 2, -3, 1, 3
Thus, the domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}
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name the relationship, corresponding laternate interior alternate exterior same side interior vertical linear
Answer:
see explanation
Step-by-step explanation:
the relationship between angles a and b
they are alternate interior angles
these angle pairs are on opposite ( alternate) sides of the transversal and are in between ( in the interior of )the parallel lines.
Transitive Property of Equality
If a +5=b+3 and a +5 = 12, then b + 3 =?
b+3=12
because a+5=b+3 and a+5=12 which means b+3 must be 12 as well
The sum of three times a number and nine is 12 
Answer:
1
Step-by-step explanation:
let the number be n
3n + 9 = 12
3n = 12 - 9 = 3
n= 3/3
n= 1
Which statement about AABC and ADEF is true?
Answer: D.
hope this helps
Dave and Sandy Hartranft are frequent flyers with a particular . They often from City A to City a of 840 On particular tripthey wirdand the flight takes 2 hoursThe return trip, with the wind behind them, only takes 1 1/2 * t hoursthe wind speed is the same on tripthe wind and find the speed of the plane in still air The wind speed ismph The speed of the plane ismph
It should be noted that the wind speed is 70km per hour and the plane speed is 490km per hour.
How to illustrate the information?Based on the information given, the following an be illustrated.
Let P = speed of plane
Let w = speed of wind
The appropriate equation will be:
(P + W) (3/2) = 840 ....... i
(P - W) × 2 = (840 / 2) ...... ii
P + W = 560 .....i
P - W = 420 ......ii
Subtract the equations
2P = 980
P = 980 / 2 = 490
P + W = 560
490 + W = 560
W = 560 - 490
W = 70
Therefore, the wind speed is 70km per hour and the plane speed is 490km per hour.
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Can somebody help me if you know what this is
Answer:The LCM of 15 and 20 is 60.
Step-by-step explanation: I used the internet/gggle
Solve the following proportion for 8/11 = v/6 .
Round your answer to the nearest tenth.
Answer:
v = 4.4
Step-by-step explanation:
Let's solve your equation step-by-step.
8/11 = v/6
Step 1: Cross-multiply.
8/11 = v/6
(8)*(6)=v*(11)
48=11v
Step 2: Flip the equation.
11v=48
Step 3: Divide both sides by 11.
11v/11 = 48/11
v= 48/11
v = 4.4
The population of a town increased from 3,250 in 2008 to 4,300 in 2010. Find the
absolute and relative (percent) increase.
The absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.
Here, we are given that the population of a town increased from 3,250 in 2008 to 4,300 in 2010.
The absolute change can be calculate as-
Final population count - initial population count
= 4,300 - 3,250
= 1,050
Thus, absolute increase = 1,050
Now, the percentage increase can be calculated as follows-
percentage change = absolute change in population/ initial population count × 100
= 1,050/ 3,250 × 100
= 10500/ 325
= 32.3%
Thus, the absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.
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will give brainliest if correct
The value of f(5) is 4375.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(1)= 7,
f(n) = 5f(n-1)
f(2) = 5f(1)
=5*7
f(2)= 35
f(3) = 5f(3-1)
f(3) = 5f(2)
f(3) = 5*35
f(3) = 175
f(4) = 5f(4-1)
f(4) = 5f(3)
f(4) = 5*175
f(4) = 875
f(5) = 5f(5-1)
f(5) = 5f(4)
f(5) = 5*875
f(5) = 4375
Hence, the value of f(5) is 4375.
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Suppose the tangent line to the curve
y = f(x)
at the point
(1, 1)
has the equation
y = 7 − 6x.
If Newton's method is used to locate a solution of the equation
f(x) = 0
and the initial approximation is x1 = 1, find the second approximation x2.
Answer:
x2 = 7/6
Step-by-step explanation:
You want the second approximation using Newton's method, given that the first approximation is x1=1 and the function tangent at x=1 is y=7-6x.
Newton's methodNewton's method approximates the function by its tangent line at the point (x, f(x)). That is, the second approximation is the x-intercept of the tangent line y = 7 -6x. That value of x is ...
0 = 7 -6x
6x = 7 . . . . . add 6x
x = 7/6 . . . . divide by 6
The second approximation is x2 = 7/6.
The blueprint specifications for a machined part call for its thickness to be 3.145 in.
with a tolerance of +-0.010 in. Find the limit dimensions of the part?
The limit dimensions of the part are 3.135 inches and 3.155 inches
How to find the limit dimensions of the part?The given parameters are
Thickness = 3.145 inches
Tolerance = 0.010 inches
The limit dimensions of the part are calculated as
Limit = Thickness +/- Tolerance
So, we have
Limit = 3.145 inches +/- 0.010 inches
Expand the above expression
So, we have
Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)
Evaluate the sum
Limit = (3.135 inches, 3.155 inches)
Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches
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How many 4/13 pound boxes of cereal can be made from 11,804 pound of cereal?
the length of a rectangle is three more than double the width. if the perimeter is 126 inches, find the dimensions.
The dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.
Leth the width of the revtangle be x.
According to the given question.
The perimeter of the rectangle is 126 inches.
The length of the rectangle is three more than double the width.
⇒ Length of the rectangle = 3 + 2x
Now, according to the given conditions we can say that
Perimeter of the rectangle = 2( length + width)
⇒ 126 = 2(3 + 2x + x)
⇒ 126 = 2(3 + 3x)
⇒ 63 = 3 + 3x
⇒ 63 - 3 = 3x
⇒ 60 = 3x
⇒ x = 20 inches
Therefore, the length of the rectangle = 3 + 2(20) = 3 + 40 = 43
Hence, the dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.
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Which expression shows another way to write -2/5 divided by 3/2?
The expression that shows another way to write -2/5 divided by 3/2 will be -2/5 ÷ 3/2.
How to calculate the value?It should be noted that an expression simply shows the relationship between the variables.
Therefore, the expression that shows another way to write -2/5 divided by 3/2 will be:
= -2/5 ÷ 3/2
= -2/5 × 2/3
= -4/15.
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a rectangular room measures 17 feet by 6 feet. find the cost of installing a strip of wallpaper around the room if the wallpaper costs $0.94 foot.
Answer:
$95.88
Step-by-step explanation:
multiply 6 by 17 and get 102
multiply 102 by 0.94 and get 95.88
A can of soda takes an average (mean) of 26 minutes to move through an assembly line. If the standard deviation is 2 minutes and the distribution is normal, what is the probability that the can will take over 29 minutes?
The probability that a can will take more than 29 minutes is approximately 0.66807
How can the probability of an event be determined in a normal distribution?The mean time taken by the soda to move through the assembly line = 26 minutes
The standard deviation of the time it takes = 2 minutes
Required: The probability that the can takes more than 29 minutes
Solution: The Z-Score formula is presented as follows;
[tex]Z = \frac{x - \mu}{ \sigma} [/tex]
The Z-Score of a can that takes 29 minutes is given as follows;
[tex]Z = \frac{29 - 6}{ 2} = 1.5[/tex]
Which gives;
Z = 1.5
The probability P(x < Z) obtained online or from the Z-Score table gives;
P(x < 1.5) ≈ 0.93319Which gives;
The probability that the can will take more than 29 minutes P(x > Z) ≈ 1 - 0.93319 = 0.66807
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Which of the following represents "the square of the sum of a number and 4 is 36"?
Ox²+42=36
(x+4)2 = 36
Ox²+4=36
Answer:
[tex](x + 4)^{2}[/tex] = 36
Step-by-step explanation:
So the "sum of a number and 4" is what gets squared and that together is equal to 36.
9888-1111+4444
...........
Answer:
the answer is 13,221 ...........
Answer:
13221...........
Step-by-step explanation:
9888-1111=8777
8777+4444=13221
Confused on Math
Solve the Systems
x+2y+2z=-2
2x-y-2z=-5
x+2y+4z=0
x=?
y=?
z=?
Answer:
Step-by-step explanation:
HELLP
Find the coordinates of the point 3/10 of the way from A to B
The coordinates of the point
3/10 of the way from A to B are
Step-by-step explanation:
this is similar to the complete approach to find the midpoint. just instead of 1/2 we are looking for 3/10 of the distance.
the general approach is
A + (B - A)×factor
factor can be 1/2 or 3/10 or 7/10 or 24/29 or ...
so, we have
(-3, -6) + ((9 - -3)×3/10, (5 - -6)×3/10) =
= (-3, -6) + (12×3/10, 11×3/10) =
= (-3, -6) + (3.6, 3.3) = (0.6, -2.7)
the point 3/10 of the way from A to B is
(0.6, -2.7)
Evaluate 4|-2| - |-3|
5
-5
11
Answer:
5
Step-by-step explanation:
4(|−2|)−|−3|
=(4)(2)−|−3|
=8−|−3|
=8−3
=5
Consider 2 cylinders. The volume of these two cylinders are. If another cross section is taken at a different height, the areas of the cross sections will be
The volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.
The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it.
The formula for the volume of a cylinder is given as:
V=π r² h
Now from the figure,
We have, for the first cylinder the height is 16 units and the radius is 7 units.
Hence,
V = 22/7 × 7² × 16
V = 22/7 × 7 × 7 × 16
V = 2424
Therefore the volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.
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Show that the roots of the quadratic equation given by(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are real and they can not be equal unless a=b=c
Expanding out the equation, we get
[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]
Considering the discriminant,
[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]
This is always non-negative, meaning the roots are real.
The roots are equal if and only if the discriminant is 0, which is when a=b=c.
The length of a rectangle is nine more than triple the width. If the perimeter is 154 inches, find the dimensions.
Answer:
Length = 60 inches
Width = 17 inches
Step-by-step explanation:
Let width = w
Length = 3w + 9
Perimeter = 154
Perimeter = 2(length + width)
2(3w + 9 + w) = 154
8w + 18 = 154
8w = 154 - 18
8w = 136
w = 136/8
w = 17 inches
Length = 3w + 9 = 3(17) + 9 = 60 inches
Given [tex]$\triangle RST \cong \triangle XYZ$[/tex]. Points [tex]$P$[/tex] and [tex]$W$[/tex] lie on [tex]$ST$[/tex] and [tex]$YZ$[/tex], respectively. Which of the following statements are true?
A) If [tex]$P$[/tex] is the midpoint of [tex]$\overline {ST}$[/tex] and [tex]$W$[/tex] is the midpoint of [tex]$\overline {YZ},$[/tex] then [tex]$\triangle RSP\cong \triangle XYW$[/tex].
B) If [tex]$\overline {RP}$[/tex] bisects [tex]$\angle SRT$ and [tex]$\overline {XW}$[/tex] bisects [tex]$\angle YXZ$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].
C) If [tex]$RP=XW$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].
D) If [tex]$\overline {RP}\perp\overline {ST}$[/tex] and [tex]$\overline {XW}\perp\overline{YZ}$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].
The triangles ΔRST and ΔXYZ are congruent, then all the same construction make triangles congruent. All the options are correct.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
If two triangles are congruent, then the ratio of the corresponding sides will be one.
The triangles ΔRST ≅ ΔXYZ. Points P and W lie on ST and YZ, respectively.
The diagram is given below.
A) If P is the midpoint of ST and W is the midpoint of YZ then ΔRSP ≅ ΔXYW is true.
B) If RP bisects ∠SRT and XW bisects ∠YXZ, then ΔRSP ≅ ΔXYW is true.
C) If RP = XW, then ΔRSP ≅ ΔXYW is true.
D) If RP ⊥ ST and XW ⊥ YZ, then ΔRSP ≅ ΔXYW is true.
All the options are correct.
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"Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator."
Can someone please explain the answer to me
Step-by-step explanation:
[tex] \frac{1}{ {x}^{ \frac{ - 1}{3} } } \times \frac{1}{3x} \\ \frac{1}{ {3x}^{ \frac{2}{3} } } \\ \frac{1}{ 3\sqrt[3]{x {}^{2} } } [/tex]
A blogger found that the number of visits to her Web site increases 5.6% annually. The Web site had 80,000
visits this year. Write an exponential model to represent this situation. By what percent does the number of
visits increase daily? Explain how you found the daily rate.
f(t) = 80,00[tex](1+ 0.056)^{t}[/tex] is the exponential function that represents the model. The number of visits increase by 0.015% daily.
Here, we are given that a blogger found that the number of visits to her Web site increases 5.6% annually.
The exponential function is given as-
Final value = initial value [tex](1 + r)^{t}[/tex]
where r = rate of change
and t = time
here, r = 5.6%
r = 0.056
Further, the Web site had 80,000 visits this year ⇒ initial value = 80,000
Thus, we can get the following function-
f(t) = 80,00[tex](1+ 0.056)^{t}[/tex]
where f(t) represents the views after t years.
Now, since we are given that the views increase by 5.6% in 1 year
and 1 year = 365 days
⇒ daily rate = 5.6/365
= 0.015
Thus, the number of visits increase by 0.015% daily.
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-5•g(4)-1 If g(x)=1-3/4x
The value of -5*g(4)-1 is 9.
It is a question of functions.
Here, g is a function of x.
Function
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Let X and Y be any two non-empty sets; mapping from X to Y will be a function only when every element in set X has one end, only one image in set Y.
Given that:-
g(x) = 1 - (3/4)x
We have to find the value of -5*g(4)-1
First we will find g(4),
g(4) = 1 - (3/4)*(4) = 1 - 3 = -2
-5*g(4) - 1 = -5*(-2) - 1 = 10 - 1 = 9
Hence, the value of -5*g(4) - 1 is 9.
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