What kind of Theorem is this? AAS, SAS, SSS, ASA, HL, or NP?

Let...

x=ones digit

x-3=tens digit

The number in terms of x would be...

10(x-3)+x = 11x-30

The number with its digits reversed would be...

10(x)+x-3 = 11x-3

And...

11x-30+11x-3=143     We can solve for x!

22x=176

x=8

The number would be 58.

answer: 58

The two digit number needed is valued 58.

Given that:

The tens of a two digit number  =  unit's digit - 3

Number reversed  + The number itself = 143

Let the ones digit of that two digit number be x and the tens digit be y. Then by place value concept, we have:

[tex]10(y) + x[/tex]

Since the tens digit = unit digit - 3

Thus we have:

[tex]y = x - 3[/tex]

or the number is :

[tex]10(x-3) + x = 11x - 30[/tex]

Now sum of the number and the number reversed is 143, which means:

[tex]143 = 10(x) + (y) + 10(y) + x = 10x + (x-3) + 11x - 30\\143 = 22x - 3 - 30\\x = 8[/tex]

Thus, the number is  [tex]10(x-3) + x = 50 + 8 = 58[/tex]

Thus, the two digit number needed is valued 58.

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Answer:

???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

Step-by-step explanation:

Answer:

The abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.

HL.

Step-by-step explanation:

The Figure is attached below

Given:

AB = DE ; BC = EF

∠C = ∠F = 90°

To Prove:

ΔACB ≅ ΔDFE

Proof:

Hypotenuse Leg Theorem:

The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.

The abbreviation is HL

In  ΔACB  and ΔDFE  

AB ≅ DE      ……….{Hypotenuse congruent Given}

BC  ≅ EF     ……….{Given}

∠C ≅ ∠F = 90°     …………..{Measure of each angle is 90° given}

ΔACB  ≅ ΔDFE   ….{Hypotenuse Leg ( HL ) Theorem}

Answer:

Step-by-step explanation:

ODYSSEY

Answer: 50%

Step-by-step explanation:

Answer: Nope it's 55%

Step-by-step explanation:

Answer:

 116 280

Step-by-step explanation:

number of combination = 20 x 19 x 18 x 17 = 116 280

HOPE THIS HELPED ;3

The number of different combinations are there if the numbers must be all different is 19380.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

Given that, a combination lock has 20 numbers on it.

Different three-number combinations

= 20!/3!(20-3)!

= 20×19×18×17!/3!×17!

= 20×19×18×17/(3×2×1)

= 10×19×6×17

= 19380

Therefore, the number of different combinations are there if the numbers must be all different is 19380.

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"Your question is incomplete, probably the complete question/missing part is:"

A combination lock has 20 numbers on it. How many different three-number combinations can be made? How many different combinations are there if the numbers must be all different?

Answer:

[tex]12-c[/tex]  Cookies

Step-by-step explanation:

The question is to find how many cookies did Cindy receive (write as an expression)?

Total cookies baked = 96

If evenly divided among 8 grandchildren, each would get:

[tex]\frac{96}{8}=12[/tex]

Each grandchildren would have gotten 12 cookies

Now, Cindy received "c" fewer than this (12), so Cindy received:

12 - c  Cookies

Cindy Received = 12 - c  Cookies

Answer:

96/8 - c.

Step-by-step explanation:

She is divideing among the grandkids so it would be 98/8-c

Answer: Area of Δ DUO = 12.0 square units.

Step-by-step explanation:

From the diagram, Δ DPA is a right angled triangle and right angled at P.

Therefore ∠D will be

Tan ∅° = PA/DP ie, opposite side all over the adjacent.

            = 4.5/3.75

Tan∅°   = 1.2

to calculate ∅°, we know find the inverse of Tan 1.2

∅ = Tan^-1 1 .2 from your log tables or calculator

         ∅° = 50.20°.

               = 50°

Since line DR is ⊥ to line OP

∠ADR = 90° - 50°

            = 40°.

From the diagram,

     ∠ADR = ∠UDR = 40°

Therefore,

    ∠ODU = 180 - ( 40 + 40 + 90 )  { Angle on a straight line }

                 = 180 - 170

                 = 10°

From Δ UDM , line MU is he height of the required Δ DUO whose area is to be determined.

Now find the height MU

            Tan10.0° = MU/10, where MU is the opposite side and 10.0 is the adjacent from the diagram given.

             MU = Tan10.0 x 10.0

                    =  0.1763 x 10.0

                    =  1.763

Therefore to calculate the area of Δ DUO

                    =   1/2 x base x height

                    = 1/2 x line OD x line MU

                    = 1/2 x 14.0 x 1.763

                    = 7 x 1.763

                    = 12.341

                    = 12.0 square units.

           =  

The cost of one sweatshirt is $19.

Step-by-step explanation:

Let,

Cost of one pair of jeans = x

Cost of one sweatshirt = y

According to given statement;

5x+2y=233     Eqn 1

3x+4y=193      Eqn 2

Multiplying Eqn 1 by 2

[tex]2(5x+2y=233)\\10x+4y=466\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](10x+4y)-(3x+4y)=466-193\\10x+4y-3x-4y=273\\7x=273[/tex]

Dividing both sides by 7

[tex]\frac{7x}{7}=\frac{273}{7}\\x=39[/tex]

Putting x=39 in Eqn 2

[tex]3(39)+4y=193\\117+4y=193\\4y=193-117\\4y=76[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4}=\frac{76}{4}\\y=19[/tex]

The cost of one sweatshirt is $19.

Keywords: linear equation, subtraction

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Answer:

8 1/3

Step-by-step explanation:

To write an improper fraction as a mixed number,

we divide the denominator into the numerator.

My work is attached below.

Answer:

There are 4 chairs in one row.

Step-by-step explanation:

Let [tex]$ x $[/tex] be the number of chairs in one row.

That is the length of one row.

Now, from the given data, three rows of length 3x can be formed with one chair left.

Or, if 15 extra chairs given, we can form 7 rows of the same length.

This means that there are [tex]$ 3x + 1 $[/tex] chairs in the first case. And since with 15 extra chairs we can form 7 rows, the equation would be

[tex]$ (3x + 1) + 15 = 7x $[/tex]

Solving this for '[tex]$ x $[/tex]', we get:

[tex]$ 3x + 16 = 7x $[/tex]

[tex]$ \implies 4x = 16 $[/tex]

[tex]$ \implies x = 4 $[/tex]

Therefore, the length of each row is four.

That is, there are four chairs in one row.

Answer:

396.584

Step-by-step explanation:

just move the decimal right 2 spaces when multiplying by 100

Answer:

396.584

Step-by-step explanation:

Step-by-step explanation: To determine whether the relation shown here is a function, it's important to understand that a function is a relation in which each x-term corresponds to exactly one y-term.

Each of the x-terms shown here 1, 2, 3, 4, and 5 appears only once so each x-term corresponds to only one y-term. So yes, this relation is a function.

The domain of a relation is the set of all the x-terms of the relation. So here, the domain will be the set of all the x-terms or {1, 2, 3, 4, 5}.

The range of a relation is the set of all the y-terms of the relation. SO here, the range will be the set of all the y-terms or {1, 2, 5, 10, 15}.

Answer:

$0.38

Step-by-step explanation:

Since there are two cups in a pint so you divide 0.76 by 2

Answer:

.38 cents

Step-by-step explanation:

Since there are 2 cups in one pint, you have to divided .76 (cents) by 2 and you get .38 (cents)

Answer:

The estimated population in 2025 will be 22261221.

Step-by-step explanation:

Let us assume that the annual growth rate is compounded annually on the population.

Now, in 2000, the population was 19169000 and the annual growth rate is 0.6%, the the population in the year 2025 will be given by  

[tex] 19169000(1 + \frac{0.6}{100} )^{25} = 22261220.7[/tex] ≈ 22261221

Therefore, the estimated population in 2025 will be 22261221. ( Answer )

Answer:

c

Step-by-step explanation:

c

Answer:

Step-by-step explanation:

2(5x - 1) - (2x - 5) =

10x - 2 - 2x + 5 =

8x + 3 <===

Answer:

They won [tex]\£63[/tex] in total

Step-by-step explanation:

Let

x ----> Mark's money

y ----> Henry's money

we know that

[tex]x=27[/tex] ----> equation A

[tex]\frac{x}{y}=\frac{3}{4}[/tex] ----> equation B

substitute equation A in equation B

[tex]\frac{27}{y}=\frac{3}{4}[/tex]

solve for y

[tex]y=27(4)/3\\y=36[/tex]

we have that

[tex]x+y=27+36=\£63[/tex]

Answer:

0.7

Step-by-step explanation:

Find Explanation attached

Answer:

The best could describe Anita's race from minute 3 to minute 5, She was standing, not moving, she could have been in an accident.

Step-by-step explanation:

See the attached figure.

As shown in the figure, we can note that the distance from minute 3 to minute 5 is constant which is equal to the distance at minute 3.

So, the average distance from minute 3 to minute 5 will be zero and hence the speed of Anita will be zero

So, From minute 3 to minute 5, She was standing, not moving.

Note: speed of Anita from minute 3 to minute 5

= ( distance difference) / (time difference) = zero / (5-3) = 0/2 = 0

To describe the race from minute 3 to 5, analyze the graph paying attention to the x and y axis and the slope of the curve. A straight line suggests constant speed, an upward line implies acceleration, and a downward line denotes deceleration.

To describe Anita's race from minute 3 to minute 5, we need to analyze the provided graph which depicts the distance from the start as a function of time for both racers. In this case, we do not have the actual graph so it's important that when you are presented with a graph you pay attention to the

x and y axis

, which in this instance are time and distance. It's vital to also look at the slope of the curve during those minutes 3 to 5 for Anita. If it's a straight line, it means Anita was biking at a

constant speed

. If the line is going upward, Anita was accelerating, and if the line is going downward, she was decelerating. Without the graph itself, it's hard to provide a definitive answer. But the basic method of reading the graph will help you understand the function of time and distance in the context of a race.

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Answer:

The numbers are 18, 22.5, and 13.5

Step-by-step explanation:

You first need to figure out what number you use to multiply to find your answer. I found 4.5

Now, multiply all numbers by 4.5

4 x 4.5 = 18

5 x 4.5 = 22.5

3 x 4.5 = 13.5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

For a function to be true, there cannot be the same x used for two different ys. D is the only table that follows this rule.

There are 59 eggs in the basket

Step-by-step explanation:

There are between 50 & 60 eggs in a basket

We need to find how many eggs in the basket

∵ When Roza counts by 3's there are 2 leftover

∵ When she counts by 5's there are 4 leftover

- That means the number of eggs when divided by 3 give

  remainder 2 and when divided by 5 give remainder 4

- To find the number look for the numbers that divisible by 5 and

  add 4 to them and then check the remainder when they divided

  by 3

∵ Between 50 and 60 there is only one number divisible by 5

  is 55 (not including 50 or 60)

∵ 55 + 4 = 59

∴ 59 gives remainder 4 when divided by 5

Let us check them with 3

∵ 59 - 2 = 57

∵ 57 is divisible by 3 ⇒ (57 ÷ 3 = 19)

∴ 59 when divide by 3 gives remainder 2

∴ 59 gives remainder 4 when divided by 5 and remainder 2 when

  divided by 3

∴ The number of eggs in the basket is 59

There are 59 eggs in the basket

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The domain of the function f(x) = (x - 5) / (2x - 3) is all real numbers except for x = 3/2 because this value would cause the denominator of the function to be zero, which is undefined.

The domain of a function refers to all possible values that can be inputted into the function, or 'x' values. For a rational function, such as f(x) = (x - 5) / (2x - 3), it is important to note that the function is undefined for values of x that would make the denominator equal zero. Because functions cannot have a denominator of zero, these values should be excluded from the domain.

To find these values, you would set the denominator equal to zero and solve. Thus, 2x - 3 = 0. Solving this, x = 3/2. Therefore, all real numbers except for x=3/2 are in the domain for this rational function.

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Answer:

x=-6

Step-by-step explanation:

3x-(2x-3)=2x+9

3x-2x+3=2x+9

x+3=2x+9

3=2x-x+9

3=x+9

x=3-9

x=-6

Answer:

3/2

Step-by-step explanation:

2+1=3

3*3/2=4.5

it would not make sense if it was 2/3 cuz look what u get.......

3*2/3=2

Answer:

Step-by-step explanation:

If x and y are proporttional then

[tex]\dfrac{y}{x}=costant\to\dfrac{y}{x}=a\to y=ax[/tex]

From the table we have x = 2 and y = 3.

Substitute:

[tex]3=2a[/tex]          divide both sides by 2

[tex]\dfrac{3}{2}=\dfrac{2a}{2}\\\\\dfrac{3}{2}=a\to a=\dfrac{3}{2}[/tex]

Therefore we have:

[tex]y=\dfrac{3}{2}x[/tex]

We increase x by 1:

[tex]y_1=\dfrac{3}{2}(x+1)[/tex]             use the distributive property

[tex]y_1=\underbrace{\dfrac{3}{2}x}_{y}+\dfrac{3}{2}\Rightarrow y_1=y+\dfrac{3}{2}[/tex]

Since the sales tax is 6%, the object will cost 1.06 (100% + 6%) times the original value.

1.06 × $95.00 = $100.70

The object will cost $100.70.

Let me know if you need any clarifications, thanks!

Answer: One small box of oranges costs $7 and one large box of oranges costs $13.

Step-by-step explanation:

Let be "s" the cost in dollars of one small box of oranges and "l"  the cost in dollars of one small box of oranges.

Based on the data given in the exercise, you can set up the following System of equations:

[tex]\left \{ {{3s+14l=203} \atop {11s+11l=220}} \right.[/tex]

Use the Elimination Method to solve it:

- Multiply the first equation by 11 and the second one by -3.

- Add the equations.

- Solve for "l".

Then:

[tex]\left \{ {{33s+154l=2233} \atop {-33s-33l=-660}} \right.\\...............................\\\\121l=1573\\\\l=13[/tex]

- Substitute the value of "l" into any original equation and solve for "s":

[tex]3s+14(13)=203\\\\3s=203-182\\\\s=\frac{21}{3}\\\\s=7[/tex]

Answer:

△JKL ≅ △XYZ by HL congruency for right triangles

Step-by-step explanation:

If only given two sides and an uncontained angle, the triangles may not necessarily be congruent. However, since the given angle is a right angle, they are congruent.

When given that the hypotenuse and any "leg" of the right triangles are equal, the triangles are congruent.

Since one angle is 90°, the other two angles must be acute. This is unlike the ambiguous case when given an uncontained acute angle, where two possible triangles can be made by making another angle obtuse.

Imagine an isosceles triangle cut in half at the altitude, creating two right triangles (JKL and XYZ). They have the same angle measures. Each with a right angle, the angle that had an equal measure in the isosceles, and the unequal angle bisected. For the triangles' sides, the isosceles base was bisected by the altitude, and they have the same altitude.

Answer:

A=πr^2 and A=πr'^2 by the definition of area

Answer:

(1) 9.106 cm

(2)  49.612 inches

Step-by-step explanation:

Answer:

1. C =9.106 cm              2.C =49.612 inches

Step-by-step explanation:

To solve these problems, we will follow the steps below;

First write down the formula for calculating the circumference of the circle

C= 2πr

where c is the circumference of the circle    and r is the radius of the circle

1) From the question diameter = 2.9 cm, but radius is half of the diameter, this implies that radius = [tex]\frac{d}{2}[/tex]= [tex]\frac{2.9}{2}[/tex]=1.45 cm  

We can now proceed to insert the values into the formula;

C= 2πr

   = 2×3.14×1.45

   =9.106 cm

C =9.106 cm

2) From the question, radius = 7.9 inches and π=3.14

We can now go ahead to insert the values into the formula  C= 2πr

C = 2×3.14× 7.9

    =49.612 inches

C =49.612 inches