Write a two-column proof.

Given: BA ≅ DC, ∠ B A C ≅ ∠ D C A
Prove: BC ≅ DA

Two sides without an angle measurement, such as a = 6 m and b = 9 m, can be used to create an infinite number of acute triangles.

How many distinct acute triangles can we make, for instance, if our side lengths are 6 m and 9 m and our angle value ranges from 0 to 90 degrees?

Create a triangle with a 45-degree angle, sides that are 10 and 10 meters long, and a third side that can be stretched to the required length. You've constructed a triangle.

We can create a whole different Acute triangle that is identical to this one by altering the length and angle of the third side.

Never overlook picking the side angles and lengths. It's possible that you'll choose to proceed in a different way. There are an infinite amount of distinct triangles that can be created with the same angles.

As a result, we can make an infinite number of acute triangles using a single angle and a single side length.

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Given that line AT bisects angle CAR, the measure of angle TAR is 35 degree.

Given the data in the question;

Since Line AT bisects ∠CAR

m∠CAR = 2 × m∠CAT

9x + 7 = 2( 5x )

We solve for x

9x + 7 = 10x

10x - 9x = 7

x = 7

We know that a bisector divides a line or angle into two equal halves.

Hence, m∠CAT = m∠TAR

m∠TAR = m∠CAT = 5x

m∠TAR = m∠CAT = 5(7)

m∠TAR = m∠CAT = 35°

Given that line AT bisects angle CAR, the measure of angle TAR is 35 degree.

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A particular kind of relation called a function is one in which every input value has only one and only one output value. The value of an input is the independent value, but the value of an output is dependent on the value of the input.

The independent variable is the cause. The other study factors have no impact on its value. The dependent variable is effect. Its value is affected by changes in the independent variable.

It is an independent variable that has no bearing on the other factors you are attempting to evaluate. For example, age may be an independent variable.

The graph's x-axis (horizontal line) should contain the independent variable, and the y-axis should contain the dependent variable (vertical line).

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Answer:

Step-by-step explanation:

true if 10=x and y equals 33

Answer:

x = -1

Step-by-step explanation:

1. Remove parentheses

-2 * 3x + x = 5

2. Multiply

-6x + x= 5

3. Add like terms

-5x = 5

4. Divide both sides by -5

-x = -1

Answer:

r = C/2n

Step-by-step explanation:

that's the solution above

The correct choice is B

In the given statement is:

The Great Pyramid of Giza in Egypt originally had a height of about 148 meters. The base of the pyramid was a square with 230-meter sides.

To find the original volume of the pyramid.

We know that, the Volume of the Pyramid is V = 1/3 Bh,

Where B is the area of the base and h is the height of the pyramid.

Now, V = 1/3 Bh

V = [tex]\frac{1}{3}[/tex](230 x 230)148

V~ 2,609,733[tex]m^{3}[/tex]

Hence, The correct choice is B

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Step-by-step explanation:

lex x be the common ratio/ scale factor

the sides and 13x

sum of the sides defines perimeter

that is

5x12x13x=15

30x=15

x=15/30

x=0.5

the sides of the triangle are 0.5(5)=2.5

0.5(12(=6

0.5(12)=6.5

2.5,6 6.5 All in inches

Lisa's hand is located twenty-five feet distant from the rock.

This is further explained below.

Generally, If the rock is falling at a rate of 5 inches per second, then you can easily calculate how deep below the surface of the lake it was after 5 seconds by multiplying 5 by 4.

After four seconds, the rock will have dropped -20 inches.

Because Lisa's hand is five feet above the water's surface, we need to add five to the distance between her hand and the rock in order to calculate how far away it is.

After four seconds, Lisa's hand is located twenty-five feet distant from the rock.

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Mary used 96 pounds of type b coffee this month.

Using algebraic expression and equation, we can solve how much of each type of coffee did Mary used that month.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Given that that month, Mary made 181 pounds of the blend that is a mixture of two types of coffee, we can express this as:

181 = a + b

where a = pounds of type a coffee that costs $5.35 per pound

b = pounds of type b coffee that costs $4.15 per pound

Also, the total cost of the blend that month is $853.15, which is the sum of the total cost of the two types of coffee. We can express that as:

$853.15 = $5.35(a) + $4.15(b)

Using substitution method to solve the two equations,

181 = a + b   ⇒   a = 181 - b

$853.15 = $5.35(181 - b) + $4.15(b)

853.15 = 968.35 - 5.35b + 4.15b

5.35b - 4.15b = 968.35 - 853.15

1.2b = 115.2

b = 96

a = 181 - b

a = 181 - 96

a = 85

Hence, Mary used 85 pounds of type a coffee and 96 pounds of type b coffee that month.

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Answer:

-2/5 or -10/15

Step-by-step explanation:

find the common denominater in this case you can multiplie 5 by 3 to get 15

no your question looks like -1/15+-9/15 just add -1 and -9 which gets you -10 so now you end up with -10/15 if you want it simplified just divide by 5 and you get -2/3

The ratio of the number of white shoes to the number of black

shoes Alex owns is 2:3

Let the number of red shoes be x

Then from the given information, we know that

brown shoes = 3 times red shoes = 3x

black shoes = 2 times brown shoes = 2(3x)= 6x

white shoes = 4times  red shoes = 4x

We need to find the ratio between the number of white shoes and the number of black shoes owned by Alex

So, the ratio of the number of white shoes to the number of black

shoes he owns is number of white shoes : number of black shoes

= 4x: 6x

which can be simplified as 2: 3

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Answer:

The answer is x=14

Step-by-step explanation:

(4x14 - 1)

(56 - 1)

Hope this helps ( ˊᵕˋ )♡

For given equilateral triangle ΔFGH, x = 15. And the measure of each side is 35 units.

In given question,

ΔFGH is equilateral triangle.

The sides of ΔFGH are:

FG = 3x - 10,  

GH =2x + 5 ,

and HF = x + 20 .

We need to find the value of x.

Since ΔFGH is an equilateral triangle, FG = GH = FH

⇒  3x - 10 = 2x + 5 = x + 20

Consider  3x - 10 = 2x + 5

⇒ 3x - 2x = 5 + 10

⇒ x = 15

Now we find the measure of each side.

FG = 3x - 10

FG = 3(15) - 10

FG = 35 units

But FG = GH = FH

So, the measure of each side is 35 units.

Therefore, for given equilateral triangle ΔFGH, x = 15. And the measure of each side is 35 units.

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The linear equation that describes the amount of data you can use in terms of the amount of money that you are willing to spend is q= (p-500)/3

P=3q + 500 is a linear equation where p is the price of the cellular plan and q is the amount of data used in the form of GB

In order to form a linear equation that describes the amount of data you can use in terms of the amount of money that you are willing to spend, we just need to shuffle the linear equation in order to get the coefficient if q as 1

First step, we need to move 500 from right hand side to left hand side which would change the sign from + to -.

=p - 500 = 3q

Second step, we need to move 3 from right hand side to left hand side which would change the sign from × to ÷.

= (p-500)/3 = q

Which can also be written as q= (p-500)/3

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The eighth term of the given geometric sequence is: 384.

Now, given: -3, 6, -12, ....

Here, [tex]\frac{6}{-3}=\frac{-12}{6} = -2[/tex]

Thus this geometric progression has the common ratio = -2.

The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, a₈ = a₁ ( r⁸⁻¹)

=> a₈ = (-3)(-2)⁷

=> a₈ = 3 ( 128) = 384.

Hence, The eighth term of the given geometric sequence is: 384.

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Answer:

Step-by-step explanation:

Hello, I have a Wonderfull website that can help you with this question. (Mathgenius.com) it should pull it up. its all and every subject you can imagine.

Answer:

Chicago to Cleveland- 350 miles

Cleveland to Cincinnati-250 miles

Cincinnati to Chicago-300 miles

Type of triangle formed? - Scalene

Step-by-step explanation:

so I first give each of them a letter, so I chose a for Chicago to Cleveland, b for Cleveland to Cincinnati, and c for Cincinnati to Chicago. Then I write some equations.
a+b+c =900

b=c-50

a=50+c

i then plug the a and b equation into the first one to get

50+c+c-50+c=900

The fifties cancel out, so we are left with 3c =900 so c=300

From this we can figure out the rest by substituting in 300 for c in the an and b equations.
300-50=250

300+50=350

Answer:

Step-by-step explanation:

Im not so sure about this one but I think it is D

The most likely next step in the series is:

Blue color with 7 rays.

Option D is the correct answer.

A series containing figures will have a pattern between each consecutive figure.

We have,

From the series,

First figure:

Blue color and 3 rays.

Second figure:

Red color and 5 rays

We can assume that the color alternates and the number of rays increases by 2.

So,

Third figure.

Blue color and (5 + 2) rays.

Thus,

Option D is the third figure in the series.

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Answer:

49

Hope this hleps :)

Step-by-step explanation:

19.6 ÷ 0.4 = 49

Check:

49 × 0.4 = 19.6 ✓

The option that identifies the mistake that Miguel made is that Miguel found 5.78 ÷ 2 as 2.89, but incorrectly found the power of 10.

It should be noted that the number given is illustrated as:

5.78 × 10^5× 0.000002

= 2.89 × 10^5

Therefore, the mistake that Miguel made is that Miguel found 5.78 ÷ 2 as 2.89, but incorrectly found the power of 10.

In conclusion, the correct option is D

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Recognize the Error Miguel found the quotient

5

.

78

×

10

5

0

.

000002

as 0.289. Which of the following correctly identifies his mistake

These are independent events because the likelihood of the first event has no bearing on the probability of the second event. Let V represent choosing holidaymakers from the previous summer.

Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true.

P(V)= (8/10)*(8/10)*(8/10)

P(V)= 512/1000

= 51.2%.

The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.

Basic probability is governed by three primary rules: the addition rule, the multiplication rule, and the complement rule.

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Answer: a) $3.57   b) 600 g

Step-by-step explanation:

a)  1 kg=1000g

Let's do the proportion:

$7.00 - 1000 g

  $x    -  510 g

Hence,

[tex]\displaystyle\\x=\frac{7*510}{1000} \\\\x=\frac{3570}{1000} \\\\x=3.57\ dollars[/tex]

b)  

Let's do the proportion:

$7.00 - 1000 g

$4.20 -    x g

Hence,

[tex]\displaystyle\\x=\frac{4.2*1000}{7} \\\\x=\frac{4200}{7} \\\\x=600 g[/tex]

a) The cost of a taro that weighs 510 grams is, $3.57

b) The weight of the taro in grams (g) is, 600 g

a) Here, Taro costs $7.00 per kilogram.

Hence, the cost of a taro that weighs 510 grams is,

= 1000 grams = $7.00

510 grams = $7.00 x 510 / 1000

                = $3.57

Hence, the cost of a taro that weighs 510 grams is, $3.57

b) Since, A taro costs $4.20

Now, WE can change the weight of the taro in grams (g) as,

$7.00 = 1000 g

Hence, $4.2 = 1000 x $4.2 / 7

                    = 600 grams

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The midpoint is at ([tex]\frac{10\sqrt{3} }{2} , \frac{9}{2} , \frac{9\sqrt{2} }{2}[/tex])

In the given statement is

To find the midpoint of the line segment joining the pair of points

S(6√3, 4,4√2) and T(4√3, 5, √2)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =(  [tex]\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} , \frac{z_{1} +z_{2} }{2}[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points S(6√3, 4,4√2) and T(4√3, 5, √2)

Solving for the midpoint , we have,

m = ([tex]\frac{6\sqrt{3}+4\sqrt{3} }{2} ,\frac{4+5}{2} , \frac{4\sqrt{2}+5\sqrt{2} }{2}[/tex])

m = ([tex]\frac{10\sqrt{3} }{2} , \frac{9}{2} , \frac{9\sqrt{2} }{2}[/tex] )

Therefore, the midpoint is at ([tex]\frac{10\sqrt{3} }{2} , \frac{9}{2} , \frac{9\sqrt{2} }{2}[/tex] )

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Answer:

16x + 10y = 21

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

[tex]\frac{4}{3}[/tex] x + [tex]\frac{5}{6}[/tex] y = [tex]\frac{7}{4}[/tex]

multiply through by 12 ( the LCM of 3, 6 and 4 ) to clear the fractions

16x + 10y = 21 ← in standard form

The coordinates of the point T is a T(2,-4).

According to the statement

We have to find that the the coordinates of T.

So, For this purpose, we know that the

Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.

From the given information:

the midpoint of line RT is M=(3,0). If R has the coordinates (-1,-4),

Then

For the coordinates of the t

We know that the from the description of the given points of the line RT

T = R+M

It means the coordinates of the t is the sum of the coordinates of the r and the M.

Then

T (x,y) = R(-1,-4) + M(3,0)

T (x,y) = R+M (-1+3,-4+0)

T (x,y) = R+M (2,-4)

So, The coordinates of the point T is a T(2,-4).

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The multiples of 2 from 101 to 200 will be all the even numbers starting from 102 to 200.

It should be noted that multiples simply mean the product that can be gotten when a number is multiplied by another number.

It should be noted that the multiples of 2 from 101 to 200 will be all the even numbers starting from 102 to 200.

In this case, the odd numbers aren't multiple of 2.

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Answer: The answer is:  360

Step-by-step explanation:

Subtract 450 by 90

450 - 90 = 360.

Hope this helped <//3

  The total score in the six tests (average) is:

P = 85

 A sequence is defined by an order of values and/or elements that have a relationship of variation as a ratio or proportion that makes them predictable.

 The first thing to do in this problem is to compare the behavior of the first three trials (variation between each number):

75, 79, 83

   We must find an expression that models a variable behavior of 4 starting at 75

An = A1 + (n - 1)x : Where x = 4

A(4) = 75 + (4 - 1)4

A(4) = 87

A(5) = 75 + (5 - 1)4

A(5) = 91

A(6) = 95

Average to know the score of all tests

P = (75 + 79 + 83 + 87 + 91 + 95) / 6

P = 85

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