Given: ∠T ≅ ∠V; ST || UV
Prove: TU || VW

4 connected lines are shown. A line from point S goes slightly down and to the left to point T to form S T. A line from point T goes slightly down and to the right to point U to form T U. A line from point U goes slightly down and to the left to point V to form U T. A line goes slightly down and to the right to point W to form point W.

Complete the two-column proof.

edge 2022 pls helpppppp

The linear equation is y = (1/7)*x + 11/7.

The general linear equation is:

y = a*x + b

Where a is the slope.

Here we know that a = (1/7), then the line is:

y = (1/7)*x + b

We also know that the line contains the point (-4, 1), this means that when x = -4, we must have y = 1.

Replacing that, we get:

1 = (1/7)*(-4) + b

1 + 4/7 = b

7/7 + 4/7 = b

11/7 = b

So the linear equation is:

y = (1/7)*x + 11/7.

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The equation of the linear function of the line is: y = 1/7x + 11/7.

A linear function equation is modelled as, y = mx + b, where m is the slope and b is the y-intercept.

Slope (m) = 1/7, and the line passes through (-4, 1), therefore, substitute (x, y) = (-4, 1) and m = 1/7 into y = mx + b:

1 = 1/7(-4) + b

1 = -4/7 + b

1 + 4/7 = b

11/7 = b

b = 11/7

Plug in the values of m and b into y = mx + b:

y = 1/7x + 11/7

The equation of the linear function is: y = 1/7x + 11/7

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Answer:

See below

Step-by-step explanation:

To construct a circle, one must know the center point of the circle, and the circle's radius.
The circle that circumscribes a triangle (called a circumcircle), has a circumcenter (center point) that is the point of concurrency (a point where more than two lines intersect at the same point) of all three perpendicular bisectors (perpendicular lines that happen to cut a given line segment exactly in half) of the sides of the triangle.

Construct the circle with a center at the circumcenter, and a radius out to any one of the vertices of the triangle.  The circumcenter is equidistant from all three vertices, so the circle draw will contain all three vertices.

To construct perpendicular a bisector, recall that a perpendicular bisector is a line containing all points that are equidistant the end points of a line segment (each point on the line is the same distance from both segment endpoints simultaneously).

So, if we can find two points that are the equidistant from the two segment endpoints, we'll have two points on the line, and to draw any line, one only needs two distinct points, and the straightedge.

Finding a point that is equidistant from two given points

Set the compass to any radius that is larger than half the distance between the two endpoints.  If uncertain of a "good" choice, one can simply choose the length of the line segment itself as a radius.

Setting the center of the compass circle on one endpoint, draw an arc such that the arc will pass through the perpendicular line we're trying to construct twice.  If uncertain, draw the entire circle.  Keeping the radius saved.

With the same radius, setting the center of the compass circle to the second endpoint, draw and arc such that the arc intersects the first circle two times.  If it doesn't intersect two times, the radius chosen at the beginning was too small.  Start the entire process over with a larger radius.

These two points of intersection are equidistant from the two endpoints of the line segment, and thus, they are on the perpendicular bisector of the line segment.

Using those two points, and a straightedge, draw the line containing those two points, and extend it generously in both directions.

Steps 1-5 in pink; steps 6-10 in green; steps 11-15 in blue (see diagram):

Note:  Since all three perpendicular bisectors intersect at the same point, it is only necessary to find two of three, not all three.  So, one could skip constructing one of those three perpendicular bisectors (either steps 1-5, 6-10, or 11-15), and still be able to construct the circumcircle correctly.

Step-by-step explanation:

9, 430, 049 = 9 million four hundred thirty thousand and fourtynine....

[tex]...[/tex] :)..

Answer:

x= 6 , y = 3

Step-by-step explanation:

x + 5y = 21

i am using trail and error method and i got the answer easily

the logic behind this is simple

the first equation is x + 5y = 21 so we can say that y  will be 5 x 1 , 5 x 2 , 5 x  3 , 5 x 4

first i did 5 x 4 = 20

x + 5 x 4 = 21

x= 1 but the equation x + y = 1 + 4 = 5  which is not equal to 9

second i tried with 5 x 3 =15

and the equation will be

x + 5 x 3 = 21

6 + 15 = 21

this time the second equation became true

x + y = 9

6 + 3 = 9

the no of pounds of salsa = 6

no of pounds of tomato = 3

The expression for YYY is (d) (x >= 50) && (x <= 100)

The instruction is given as:

If (YYY) {

// Output "50, 51, ..., 99, 100"

}

The value of x is given as:

x = 50 to 100 (inclusive)

This means that:

x must be greater than or equal to 50 AND x cannot exceed 100

The keyword AND is represented as &&.

So, the condition is:

x >= 50 && x <= 100

Hence, the expression for YYY is (d) (x >= 50) && (x <= 100)

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Answer:

3/4 = -3* 2*(c-

I hope it helps!

if it does pls mark me brainliest answer

The fraction of players who don't stretch and get injured = 4/9.

The frequency tree is shown in the image attached.

The total number of footballers = 45.

The total number of footballers who stretch = 36.

Therefore, the number of footballers who don't stretch = 45 - 36 = 9.

The total number of injured footballers = 10.

The number of injured footballers from the players who stretch = 6.

Therefore, the number of injured footballers from the footballers who don't stretch = 10 - 6 = 4.

The total number of footballers who don't get injured = 45 - 10 = 35.

The number of footballers who stretch and don't get injured = 36 - 6 = 30.

The number of footballers who don't stretch and don't get injured = 9 - 4 = 5.

Therefore, the frequency tree can be shown in the image attached.

The fraction of players who don't stretch and get injured = 4/9.

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It will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.

When two numbers can be written as p/q is called a Ratio , and when two ratios are equal they are said to be in proportion .

It is given that

Jeremy is reading a 60-page book.

The time taken to read  20 pages is 30 minutes

Then it can be written as 20:30 = 2:3

The rate of reading is same so To read the rest 40 pages is given by

40:x

40: x = 2:3

40*3/2 = x

x = 60 minutes

Therefore it will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.

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Answer:

[tex]\huge\boxed{\sf L = 78\°}[/tex]

Step-by-step explanation:

Exterior angle of L = 5x + 12

M = 3x - 2

N = 50

So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.

Here,

Exterior angle of L = M + N

5x + 12 = 3x - 2 + 50

5x + 12 = 3x + 48

Subtract 12 to both sides

5x = 3x + 48 - 12

5x - 3x = 36

2x = 36

Divide 2 to both sides

x = 18

So,

= 3x - 2

= 3 (18) - 2

= 54 - 2

= 52°

Now,

We know that,

L + M + N = 180°

L + 52 + 50 = 180

L + 102 = 180

Subtract 102 to both sides

L = 180 - 102

L = 78°

[tex]\rule[225]{225}{2}[/tex]

Answer:

0.00305 (rounded)

Step-by-step explanation:

this is a geometric sequence so the formula is

an=a×r×n-1

Answer:

The man is 27 years old.

Step-by-step explanation:

You can create a system of equations.
Let x = the age of the man
Let y = the age of his son
You can create the following equations based on what was given in the problem:
1. x = y + 18
2. (x - 3) = 4(y - 3)
You can simplify the second equation:
x - 3 = 4y - 12
x = 4y - 9
Then, solve the system of equations:
x = y + 18
-
x = 4y - 9
____________
0 = -3x + 27
The son's age is 9, therefore the father is 27 years old.

Answer:

17 in.

Step-by-step explanation:

There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.

Answer:

I don't see the equation options.  See below for a predicted equation.

y= (2/3)x + 4

Step-by-step explanation:

The points are (-3,2), (0,4), and (3,6).  I will assume they lie in a straight line.

Find an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

m, the slope, is also known as the "Rise/Run."

Pick any two points.  I'll use (0,4) and 3,6)

Rise = (6-4) = 2

Run  = (3-0) = 3

Slope = 2/3

The equation becomes y = (2/3)x + b

B is easy in this case.  Point (0,4) tells us that y = 4 when x = 0 (the definition of b).

The equation is y= (2/3)x + 4

See the attached graph.

Answer:

54 degrees!

Step-by-step explanation:

its a right triangle so we know 2 out of the 3 angles

so 36 + 90 = 126

180 - 126 = 54!

hope this helps :)

Answer:

48 Square Centimeters

Step-by-step explanation:

The red triangular exterior pieces are all equilateral triangles with some side length.

We don't need to know what that side length is. It doesn't matter.

The area of one red equilateral triangle is some area A.

There are 6 of these red triangles, so the red exterior triangular parts combine to a total area of 6*A.

The hexagon is composed of equilateral triangles as well.

Each of these blue equilateral triangles is congruent to any outer red triangle because the side length is the same.

Therefore, the 6 blue equilateral triangles composing this hexagon combine to get a total area of 6*A

The area of the star overall is 12*A because we have 6 blue triangles combining with the 6 red triangles.

There is a total of 12 triangles.

Answer:

x = $1 & y = $2.

Each doughnut cost $1 and hot chocolate cost $2.

Answer:

B and C

Step-by-step explanation:

Answer:

The probability of selecting two democrats is 1/380

Step-by-step explanation:

Here we are given the people as,

8 democrats, 8 republicans and 6 independent.

So total number of people are: 8+6+6=20

Probability of choosing first democrat = 1/20

Probability of choosing first democrat = 1/19

Thus P( two democrats in succession ) = 1/20 ×1/19

                                                                = 1/380

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The statement D is false that No irrational number is rational.

The set of real numbers includes integers, rational numbers, and irrational numbers.

This implies that all irrational numbers and integers are also real numbers.

Thus, statements A and B are correct.

Rational numbers are numbers that can be written as the division of two integers, which thus also include all integers.

The set of irrational numbers then contains all real numbers that are NOT rational numbers

Therefore, the set of irrational numbers does not include integers, which implies that statement D is false.

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Answer:

Option (C)

Step-by-step explanation:

The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.

So, this means that adding 1 to this, the range matches with option C.

The value of sin(30°) is 1/2.

The branch of mathematics concerned with specific functions of angles and their application to calculations.

The diagram is attached below:

We know,

sin 30= Perpendicular/ Hypotenuse.

As, the hypotenuse is the opposite side of the right angle and the perpendicular is opposite to the given angle.

So,

sin 30 = 5/10

sin 30 = 1/2

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The coordinates of the vertices of the reflected image are (-3,4)  (0,4) (-3, 2) (0,2).

Reflection is a mathematical transformation of a shape by moving the vertices of the shape across a line of reflection.

Analysis:

coordinates of the shape before transformation are: (-3, 0) (0,0) (-3, -2) 0, -2)

Across the line of transformation, the corresponding vertices(old and new) must be equal distance from the line of reflection.

Also for reflection on y-axis only y-coordinates are affected.

so for point(-3, 0) 0 is 1 unit away from y = 1 so the other coordinate 1 unit away from y = 1 is y = 2 making the new point (-3, 2) same as others .

Find the image in the attached file below.

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The amount of oil required for 1 liter of fuel is 111.11 mL.

Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.

Given that the fuel is the mixture where 8 parts are petrol and 1 part is oil in the whole part of the fuel.

The total part of the fuel is 8+1=9

the portion of the petrol is = parts of petrol/total parts of the fuel= 8/9

the portion of the oil = parts of oil /total parts of the fuel= 1/9

Now we have to calculate the amount of oil required for 1 liter of fuel.

As discussed before, 1/9 parts of the fuel is oil.

So the amount of oil is= (1/9)*1 liter= (1/9)litre= 1/9* 1000 mL= 111.11 mL

Similarly, we can calculate the amount of petrol which will be

the amount of petrol= (8/9)*1 liter= (8/9) liter= 8/9*1000 mL= 888.88 mL

Therefore the amount of oil required for 1 liter of fuel is 111.11 mL.

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The value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

The value of x that will satisfy this condition can be found by simplifying the given inequality. Therefore, The given inequality can be simplified as,

4x + 1 - 1 ≥ -8

4x ≥ -8

x ≥ -2

Hence, the value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.

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The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.

Given the table

x         f(x)

-2        -46

-1         -22

0         -10

1           -4

2          -1

We have to choose which statement describes better about function

Let us assume [tex]f(x)=ab^x+c[/tex]

at x=0, f(0)=-10

So, -10 =a+c

Similarly, by satisfying the above table in the f(x)

[tex]f(x)=\frac{33}{5} (\frac{1}{11})^x-\frac{17}{5}[/tex]

[tex]f'(x) > 0[/tex]

So we can say that f(x) is an increasing function.

[tex]g(x) = - 18 (\frac{1}{3} )^ x + 2[/tex]

[tex]g^ \prime (x) = - 18 (\frac{1}{3} )^ x ln(1/3)[/tex]

ln(1/3) < 0

So, g^ \prime (x) > 0

So, g(x) is an increasing function.

For any x∈f(x) and  x∈g(x) [tex]g'(x) > f'(x)[/tex]

So, g increases at a faster average rate

Thus, Both functions are increasing, but function g increases at a faster average rate.

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Answer:

can you rephrase it? how many pounds are there?

Step-by-step explanation:

Answer:

Formula for a linear sequence is

Tn=a+(n-1)d

where Tn is the nth term

a is the first term

n is the number of term

d is common difference

Answer:

4.5-1.4=3.1

Step-by-step explanation:

Hope this answers your question!

If not, I am sorry.