Using only the markings given in the diagram, which triangle congruence criterion can be used to prove that PQR and STU are congruent?
Answers
Answer: HL
Step-by-step explanation:
If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. The correct option is D, HL.
What is the HL theorem?According to the HL theorem, If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore, the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
In the two of the given triangle, ΔPQR and ΔSTU, the following things can be seen,
PR ≅ SU (Leg of the triangle)
RQ ≅ TU (Hypotenuse)
Also, since the two of the triangles are right angle triangle, and the length of the one leg of the two triangles is equal, also, the hypotenuse of the two triangle is equal. Therefore, Using the HL postulate. The two triangles can be said to be congruent.
Hence, the triangle congruence criterion can be used to prove that PQR and STU are congruent is HL Congruency.
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Related Questions
find all solutions to the problem: 2/x+6 - 1/x+3 =2
Answers
Answer:
[tex]\displaystyle x=-\frac{9}{2},\:x=-4[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{2}{x+6}-\frac{1}{x+3}=2\\\\\frac{2(x+3)}{(x+6)(x+3)}-\frac{(x+6)}{(x+6)(x+3)}=2\\ \\\frac{(2x+6)-(x+6)}{(x+6)(x+3)}=2\\ \\\frac{x}{(x+6)(x+3)}=2\\ \\x=2(x+6)(x+3)\\\\x=2(x^2+9x+18)\\\\x=2x^2+18x+36\\\\0=2x^2+17x+36[/tex]
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-17\pm\sqrt{(17)^2-4(2)(36)}}{2(2)}\\\\x=\frac{-17\pm\sqrt{289-288}}{4}\\\\x=\frac{-17\pm\sqrt{1}}{4}\\\\x=\frac{-17\pm1}{4}\\ \\x_1=\frac{-18}{4}=-\frac{9}{2},\: x_2=\frac{-16}{4}=-4[/tex]
Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14
Answers
The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.
How to find slope and y-intercept?The slope and y-intercept of an equation can be easily found using slope intercept equation.
y = mx + b
where
m = slopeb = y-interceptTherefore,
3x + 2y = 14
2y = -3x + 14
y = -3 / 2 x + 7
Therefore,
slope = - 3 / 2
y-intercept = 7
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Paul and Krystal spent 1 1/2 hours at the pool
Answers
Answer:
Paul and Krystal spent 13 hours at the pool
Step-by-step explanation:
I Thank
is f(x)=x^(2)-4 and f(x)=3(2-x) functions?
Answers
Answer:
Yes
Step-by-step explanation:
There is only one output value for each input value, which is the definition of a function.
Somebody please help me with this question
Answers
Answer:
-2
-1
-2
-3
Step-by-step explanation:
For an odd function, f(-x) = -f(x).
f(2) = 2; f(-2) = -2
f(3) = 1; f(-3) = -1
f(4) = 2; f(-4) = -2
f(6) = 3; f(-6) = -3
Describe how the product of 0.08 x 8 would look on a one hundred-square grid.
The product would have ____
squares shaded out of 100.
Answers
0.08 x 8 = 64 which means, 64 would be shaded. Hope this helps!
XY and BD are parallel lines
X is a point on AB and C is a point on BD.
XB = XC
a) Complete this sentence.
Angle XBC = 55° because = ?
b) Work out angle BXC.
Give a reason for each angle you work out.
Answers
Answer:
a) they are corresponding angles
b) B=55° (proven)
C=55 (Angles opposite equal sides)
B+C+X=180° ( sum of angles of a triangle)
55°+55°X=180
110°+X=180°
X=180°-110°
X=70°
Which of the following rules is the composition of a dilation of scale factor 2, then a translation of three units to the right? a) (2x+3,y) b) (2x+6, 2y) c) (2x +3, 2y) d) (2x+6, y)
Answers
Answer:
The answer is C: (2x +3, 2y)
Step-by-step explanation:
When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.
Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.
(x, y) -----> (2x, 2y)
Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.
Translation 2 units right:
(2x, 2y) -----> (2x +3, 2y)
The equation of line LM is y = 5x + 4. Write an equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2).
Answers
When the line is Perpendicular, you make it the opposite reciprocal.
Now you want to find b so plug in the coordinate provided.
2=-1/5(-3)+b 2 is y -3 is x
2=0.6+b
Subtract 0.6 from both sides
1.4=b
y=-1/5x+1.4
which equation represents circle n? (17 points & will mark branliest)
Answers
Answer:
c. (x+7)^2+(y-6)^2=50
Step-by-step explanation:
The equation of a circle is; (x+7)²+(y-6)² = 50
What is circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The points on the circle are L(-2, 11) and centre is N(-7, 6)
Find the radius,
D = √(-7+2)²+(6-11))²
D = √25+25
D = √50
We know that, the equation of a circle is given by,
( x − a )² + ( y − b )² = r² , where ( a , b ) represents the centre of the circle,
Here, centre is N(-7, 6)
Therefore, the equation of a circle is;
(x+7)²+(y-6)² = 50
Hence, the required equation is (x+7)²+(y-6)² = 50
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What is the probability of rolling a 6 sided die 4 times and getting an even number all 4 times?
Answers
Explanation:
There are three even numbers in a six sided die, so the automatic fraction form would be 3/6, with 6 being the total number of numbers on the die. Reducing this to simplest form would give you 1/2, or 50%.
Number 4, Use the net to complete the sentences. The square pyramids base that is_____ units on each side. The height of each triangular face is ______ units.
Answers
Find the slope of the line.
Answers
Answer:
2
Step-by-step explanation:
we know the line goes through the origin, so we have point (0,0). next, find another point the line goes through. for example, point (2,4)
the slope formula for points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1). plug in the 2 points to get (4-0)/(2-0) = 4/2 = 2
The box is 450 square. The length is 10 inches and the width is 5 inches. What is the height of the box
Answers
Answer:
9 inches
Step-by-step explanation:
I assume you mean the volume of the box is 450.
In that case, to figure out for the volume we multiply 10 by 5. This gives us 50.
450/50=9
The height of the box is 9 inches
Give brainliest please!
hope this helps :)
3z+35=47 solve
help, i need answer
Answers
Answer:
z=4
Step-by-step explanation:
subtract 47-35
3z=12
divide both sides by 3
z=4
Solve for x in the triangle. Round your answer to the nearest tenth.
X
5
22°
Answers
Ryder used front-end estimation to estimate the product of (–24.98)(–1.29). What was his estimate?
–32
–20
20
32
Answers
Answer:
(d) 32
Step-by-step explanation:
An estimate is a value that is intended to approximate the result of a detailed calculation. Often, the target is an estimate that is within about 10% of the actual value. A "rough order of magnitude" (ROM) estimate is intended to be within about a factor of 3 of the actual value.
__
An estimate is generally made by using a reduced number of significant figures in the calculations. Often, the numbers used will be rounded to 1 or 2 significant figures. The math is often accomplished mentally, so methods of mental arithmetic are often used to simplify the calculations.
rounded valuesWe are asked for an estimate of the product (-24.98)(-1.29). We notice there are an even number of minus signs, so the result will be positive. The values are (25)(1.3) when rounded to 2 significant figures.
Along with the rounded values, it is often useful to make note of the direction and magnitude of the errors due to rounding. Here, we have rounded both numbers up. The number 25 is high by 0.02, and the number 1.3 is also high by 0.01. These can be used to estimate the error in the estimated value.
the productThe desired product can be computed several different ways. Either or both of the numbers 25 and 1.3 can be represented in a fashion that facilitates the (mental) arithmetic. Here are three (3) methods that could be used.
(25)(1.3) = 25(1 +0.3) = 25 +7.5 = 32.5 (a little high, so we can choose to round down to 32)(25)(1.3) = (100/4)(1.3) = 130/4 = 65/2 ≈ 64/2 = 32 (again, rounding down because we know 32.5 is too high)(25)(1.3) = 2.5(13) = 2(13) +13/2 = 26 +6.5 = 32.5 ≈ 32Ryder's estimate was 32.
_____
Additional comment
The actual product is ...
(25 -0.02)(1.3 -0.01) = (25)(1.3) -0.02(1.3) -0.01(25) +(0.02)(0.01).
As a first approximation of the error in the product 32.5, we can sum the middle two terms:
-0.02(1.3) and -0.01(25) = -0.026-0.25 = -0.276.
Then the first refinement of the estimate will give us ...
32.500 -0.276 = 32.224
The actual value is obtained by adding the final error term:
32.224 +0.0002 = 32.2242 . . . . the actual product with estimate errors resolved.
Answer:
yo
Step-by-step explanation:
its C, or 20
edge
ur welcome
I am not divisible by 2,3,5 or 7. My two digits are not the same, but they are both squares. What two numbers could I be?
I NEED HELP FASTTT
Answers
Answer:
19 is suitable no in which 1 is square of itself and 9 is of 3
The only square single digits are 1, 4 and 9
Possible two digit numbers are:
14 - divisible by 2
19
41
49 - divisible by 7
91 - divisible by 7
94 - divisible by 2
Submitting a Bid
You want to bid on a project for the pool shown. The project involves ordering and installing the brown tile that borders the pool, and ordering a custom-made tarp to cover the surface of the pool. In the figure, each grid square represents 1 square foot.
You pay $5 per linear foot for the tile.
You pay $4 per square foot for the tarp
It takes about 15 min to install each foot of the tile
A) estimate the total cost for the tile and the tarp
Answers
Answer:
5,125
Step-by-step explanation:
hello fellow indians Question: Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).
Answers
Answer: andres is 5 years old pls banned him he called e a mean word like the N word
Step-by-step explanation:
An arithmetic sequence has this recursive formula:
What is the explicit formula for this sequence?
Answers
Answer:
C
Step-by-step explanation:
the explicit formula for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
from the recursive formula in the form
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
given
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 7
with d = - 7 and a₁ = 4 , then explicit formula is
[tex]a_{n}[/tex] = 4 + (n - 1)(- 7)
What is the derivative of the function f(x)= 4cos2x + logx + x?
Answers
Answer:
[tex]f'(x)=-8\sin2x+\frac{1}{x} +1[/tex]
Step-by-step explanation:
I assume by [tex]\log(x)[/tex], the base is [tex]e[/tex], so let [tex]\log_e(x)=\ln(x)[/tex]:
[tex]\displaystyle f(x)=4\cos2x+\ln x+x\\\\f'(x)=\frac{d}{dx}(4\cos2x+\ln x + x)\\\\f'(x)=\frac{d}{dx}(4\cos2x)+\frac{d}{dx}(\ln x)+\frac{d}{dx}(x)\\\\f'(x)=-8\sin2x+\frac{1}{x}+1[/tex]
Remember that by the chain rule, to find the derivative of [tex]4\cos2x[/tex], you must find the derivative of the inside, which is [tex]\displaystyle \frac{d}{dx}(2x)=2[/tex], and multiply it by the outside derivative. Recall that [tex]\displaystyle \frac{d}{dx}\cos(x)=-\sin(x)[/tex], so replace [tex]-\sin(x)[/tex] with [tex]-4\sin(2x)[/tex], and multiply by 2 to get [tex]-8\sin(2x)[/tex] as your derivative.
Also remember that [tex]\displaystyle \frac{d}{dx}\ln(x)=\frac{1}{x}[/tex], one of the more basic derivatives.
The derivative of the function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given function is four times of cos2x plus logx plus x.
f(x)= 4cos2x + logx + x
We need to find the derivative of it f'(x)
d/dxf(x)=d/dx(4cos2x)+d/dx(logx)+d/dx(x)
f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)
We know that
d/dx(cosx)=-sinx
d/dx(logx)=1/x
d/dx(x)=1
Apply in above equation
f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)
f'(x)=4.2(-sin2x)+1/x+1
f'(x)=-8sin2x+1/x+1
Hence the derivative of function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.
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Matthew is grocery shopping for a taco Tuesday Bloc Party he is expecting 60 people including himself, and for each person to have 1 soft and 1 crispy taco. Soft tortillas coke in packs of 10. Crispy taco shells come in packs of 12. How many packages of each tortilla type does Mathew need to feed everyone?
Answers
The number of each tortilla type that Mathew would need to feed everyone is = 6 packages of Soft tortillas and 5 packages of Crispy taco shells.
Calculation of number of tortillaThe number of people Matthew is expecting including himself = 60
The Soft tortillas coke appear = 10/pack
The Crispy taco shells appear = 12/pack
Since each person is to get 1 soft and 1 crispy taco, the number of tortilla type that Mathew would need to feed everyone is
= 60/10 = 6 packages of Soft tortillas
= 60/12 = 5 packages of Crispy taco shells
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The distance to your brother's house is 481 miles, and the distance to the Grand Canyon is 814 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to the Grand Canyon to take?
Answers
The time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
The distance to your brother's house is 481 miles, and the distance to the Grand Canyon is 814 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to the Grand Canyon to take?The time will be calculated as:-
First, we will calculate the speed to cover the distance of Brother's house:-
Speed = Distance / Time
Speed = 481 / 13 = 37 miles per hour.
Now the time to cover a distance of 814 miles will be calculated as:-
Time = Distance / Speed
Time = 814 / 37
Time = 22 hours
Therefore the time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.
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Mollie wants to measure the capacity of the kitchen sink.
She has a 1 L container and a 10 mL container. Which should she use and why?
A.
10 mL container; the capacity of the sink is close to 10 mL.
B.
10 mL container; the capacity of the sink is less than 1 L so the 1 L container would not give an accurate measurement.
C.
1 L container; the capacity of the sink is at least 1 L.
D.
Either container; or the 10 mL container can measure the capacity as quickly as the 1 L container.
Answers
Answer:
1L container as the capacity of the sink is obviously at least 1L and most probably much more than 1L
Step-by-step explanation:
letter C
6. Solve the equation: h/9 = 7.
A. h = -63
B. h=63
C. h=127
D. h = 7/g
Answers
Answer:
B) h=63
Step-by-step explanation:
Multiply both sides by 9.
h/*9=9*7
Simplify
h=63
[tex]\bf{\dfrac{h}{9}=7 \ \ \to \ \ \ Exercise \ to \ solve }[/tex]
Multiply both sides by 9.
h = 7 × 9Multiply 7 and 9 to get 63.
h = 63 ===> AnswerTherefore, the correct option is "B".
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Find the volume of the prism.
9km 8km 6km
Answers
The correct answer is option B which is the volume of the prism is 216 km³.
What is the volume of the prism?A prism is a three-dimensional solid with a triangular base called a triangular prism. The volume of the triangular prism is equal to the product of the area of the base and the height of the prism.
The volume of the prism will be calculated by using the formula below:-
V = Area of the base x Height
Since the base is a right-angle triangle so we will calculate the area of the right-angle triangle.
V = Area of the triangle x Height
V = ( 1/2 ) x 8 x 6 x ( 9 )
V = 216 km²
Therefore the correct answer is option B which is the volume of the prism is 216 km³.
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PLEASE HELP ME WITH THIS!!!
Answers
Answer:
68 inches
Step-by-step explanation:
y = x + 2
x = 66
y = 66 + 2
y = 68
Between which two tenths is the decimal approximation of √7?
Answers
Answer:
2.6 and 2.7
Step-by-step explanation:
The actual square root of 7 is 2.64 and that is between 2.6 and 2.7.
Urgent! Brainliest to whoever solves it
Quadrilateral HGFJ is a rhombus
Answers
Answer:
16cm and 48 degrees
Step-by-step explanation: