What type of transformation of △ABC results in △DEF ?​

Answer:

The answer is below

Step-by-step explanation:

A square is a quadrilateral (four sides and angles). All the sides and angles of a square are equal. Each angle of a square is 90° and the diagonals are equal.

In square ABCD:

AB = BC = CD = AC (all the sides of a square are equal)

Given that  P is the midpoint of BC and Q is the midpoint of CD. AP = a and AQ = b.

a) Triangle APB is a right angled triangle:

BC = AB (all sides of a triangle are equal)

PB = 1/2 (BC) = 1/2(AB) = 0.5AB

Using Pythagoras theorem:

AB² + PB² = AP²

substituting:

AB² + (0.5AB)² = a²

AB² + 0.25AB² = a²

1.25AB² = a²

AB² = 0.8a²

AB = a√0.8

b) Triangle AQD is a right angled triangle:

AD = DC (all sides of a triangle are equal)

DQ = 1/2 (DC) = 1/2(AD) = 0.5AD

Using Pythagoras theorem:

AD² + DQ² = AQ²

substituting:

AD² + (0.5AD)² = b²

AD² + 0.25AD² = b²

1.25AD² = b²

AD² = 0.8b²

AD = b√0.8

c) In right triangle ADB, Using Pythagoras theorem:

AB² + AD² = BD²

But AB = AD

Substituting:

0.8a² + 0.8b² = BD²

BD = √(0.8a² + 0.8b²)

But AD = AB, hence 0.8a² = 0.8b²

BD = √(1.6a²)    

BD = a√1.6

D) AC = AD (diagonals of a square are equal)

AC = √(0.8a² + 0.8b²)

AC = √(1.6b²) = b√1.6

Answer:

the us 113, hope this helps you out

Answer:

The ladder reaches (4)(√3) ft up the wall (6.93 ft)  

Step-by-step explanation:

Think of a triangle with a 60 degree angle in the lower left corner.  The lower right corner is a right triangle, and 8 ft is the length of the hypotenuse.  The other angle is 30 degrees.

We know the angle 60 degrees, plus the length of the hypotenuse, but need the length of the vertical side opposite the 60 degree angle.  Use the sine function here because it involves these knowns:

                               opposite side

sin 60 degrees = ------------------------ = x/(8 ft) = (√3)/2

Cross-multiplying, we get:

2x = (8 ft)(√3), or through reduction, x = (4)(√3)

The ladder reaches (4)(√3) ft up the wall (6.93 ft)                              

With the ground, [tex]6.92 ft[/tex] the wall does the ladder reach.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle.

According to the question

An eight foot ladder leans against a building. if the ladder makes an angle of 60° with the ground.

From the right angle triangle,

[tex]sin 60^{0} =\frac{h}{8}[/tex]

[tex]\frac{\sqrt{3} }{2}[/tex] =  [tex]\frac{h}{8}[/tex]

[tex]8\sqrt{3} =2h[/tex]

[tex]h = 4\sqrt{3}[/tex]

[tex]h = 6.92 ft[/tex]

Hence, With the ground, [tex]6.92 ft[/tex] the wall does the ladder reach.

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Answer:

A = 0.10m

Step-by-step explanation:

A = total amount spent

0.10 = cost per minute

m = how many minutes

Answer:

Step-by-step explanation:

First get rid of the parentheses. Distribute the - sign and the +6 to each one.

[tex]7-3x-5y+12x-18y+8y\\7+9x-5y-18y+8y\\7+9x-15y[/tex]

Answer:

Step-by-step explanation:

The $50 cleanup fee is a "fixed cost."

The "$30 per-person fee is a "variable cost."  That is, it varies with the number of people.

"within"  means "less than or equal to"

Cost = $50 + $30x       [where x = number of people]

Cost ≤  $4500              ["stay within their budget"]

$50 + $30x ≤ $4500           [substitute for cost]

 $30x ≤ $4450      [subtract $50 from both sides retains sense of inequality]

   x ≤ 148.3333     [divide by +$30 retains sense of inequality]

Mark and Heather may invite up to 148 guests.

     [note:  to be "≤," always truncate, never round up]

Check:

 148 people for $30 each + $50 is $4440+$50 = $4490.

One more person makes it $4520 -- that is too much.

There we go, my bad

Answer:

Step-by-step explanation:

First we need a linear equation for the situation. 50 cleanup fee applies regardless of how many people they have.  Even if NOBODY shows up, they will be charged $50, so $50 is our y-intercept. If they are charged $30 per person, and we are looking for the number of people they can invite, x will represent the number of people and y will represent the cost of everything. The linear equation is

y = 30x + 50. If they have 4500 to spend, then

4500 = 30x + 50, and now solve it for x:

4450 = 30x and now divide by 30 to get

148 1/3 = x. Now, you can't invite a third of a person, so it would be safe to invite 148 people and you won't go over your budget.

Answer:

the last one?

Step-by-step explanation:

i dont know, but that one seems like it would

Answer:

answer is A if only one can be chosen. if more than one can be, b might be an answer as well, but not c and d.

Step-by-step explanation:

think of a 3 4 5 triangle for answer a.

just remembered this method, do Pythagorean theorem for each answer. that will tell you which equals a triangle. answer a foe sure is one cmbecuase of a 3 4 5 triangle.

Answer:

750 is the answer. Hope it helps!

Answer:  The length is 510 and the width is 110.

Step-by-step explanation:

To find the area of a rectangle, you will have to add the 2 times the length plus 2 times the width because  a rectangle have 4 sides. Two widths and two  lengths.

You can now use the formula  P= 2l + 2w  

were P is the perimeter , l is the length, and w is the width.

the length is 400 more than the width, so we can represent that by the equation,  l = w + 400  

And now we know that the width is w.

So now we will input the perimeter, length, and into the formula to solve for w.

1240 = 2(w + 400) + 2w

1240 = 2w + 800 + 2w

1240 = 4w + 800

-800            -800

   440 = 4w

    w = 110

L= 110 + 400

L = 510  

Check :

1240 = 2(510) + 2(110)

1240 = 1020 + 220

1240 = 1240

Answer:

I really don't know I am sorry.

Step-by-step explanation:

Answer:

i = integers greater than n

n < i

n = smallest integer

a = 2nd largest integer

b = 3rd largest integer

c = largest integer

d = sum of all the integers

n + a + b + c = 2174

Step-by-step explanation:

Answer:

1 --- The cyclist's average speed was 18 miles per hour.

2 --- I would travel 280 miles far.

3 --- Your average speed was 52.5 miles per hour.

4 --- You should expect to arrive in Leeds at 11:50 AM.

5 --- The athlete will run 2000 m in 8 minutes and 20 seconds.

6A --- The average speed of the journey is 48 miles per hour.

6B --- It will take him 6 hours and 40 minutes.

Step-by-step explanation:

1) 90 / 5 = 18

2) 70 x 4 = 280

3) 315 / 6 = 52.5

4) 210 / 90 = 2.3333

   0.333 = 0:20

   9:30 + 2:20 = 11:50

5) 2000 / 4 = 500

   500 / 60 = 8.3333

   0.3333 = 0:20

   8.3333 = 8:20

6A) 0:45 = 0.75

     420 / 8.75 = 48

6B) 420 / 63 = 6.666

      6.6666 = 6:40

Answer:

dont know....mmm sorry

Answer

IM not too sure

Step-by-step explanation:

Not too sure sorry kid

Answer:

25 and 10 are the numbers

Step-by-step explanation:

Step-by-step explanation:

2x²+4x+5=0

.....

solve it by using the factorisation method or completing the square method

don't mind the hand writing

am I correct btw

Answer:

5.59

Step-by-step explanation:

Answer:

A 10

B10

C10

in total is 106

Answer:

Step-by-step explanation:

Looking at the y-values, it seems a geometric progression with the common ratio of 5. Therefore it can be exponential relationship.

By trying the values in the table we get the equation:

Answer:

x=11

Step-by-step explanation:

Since this is a 90º angle, 46º+(4x)º has to equal 90º, and you can make and solve an equation for this:

46+4x=90

4x=44

x=11

Check:

46+4x=90

46+4(11)=90

46+44=90

90=90

Answer:

8.96 g/cm3

Step-by-step explanation:

89.6 divided by 10 is 8.96

Answer

didn't know there was an image

Answer:

Janet put 6 red counters into the bag

Step-by-step explanation:

There are 5 yellow counters for every 1 red counter. If there are 20 yellow counters in the bag then there are 4 red counters. (20/5). If the ratio becomes 1:2 this means there are 2 yellow counters for every 1 red counter. There are 20 yellow counters so there must be 10 red counters in the bag. (20/2). 10 - 4 = 6. Janet put 6 red counters into the bag. (Brainliest would be appreciated!)

Answer: I think it's C.

Step-by-step explanation:

Answer:

Step-by-step explanación: La temperatura al interior de un congelador es de 20 °C y, luego de ... Por unidad su costo es $ 85 y el precio de venta es de $ 100. ... litros se pueden llenar 1 ​ latas de bebida, si cada una contiene con 15​ _ 2 0,35 litros? ... a los pies se demora 0,015 segundos,

Answer:

To determine the number of shirts that Lisa can buy, knowing that each one is worth $ 14, that she can spend a maximum of $ 150 and that she will also buy a pair of jeans for $ 58 and a pair of shoes for $ 39, the following calculation must be performed:

(150 - 58 - 39) / 14 = X

53/14 = X

3.78 = X

53 - (14 x 3) = X

11 = X

Therefore, Lisa can buy 3 T-shirts, and she will have 11 dollars left over.

Answer:

2

Step-by-step explanation:

Answer:

tree C was planted first

Step-by-step explanation:

Since Tree c was 10 inches tall when it was first grown and Tree A was 5 at first and Tree B was 3 inches tall. 10>5 10>3

Answer:

(2x+3)(x-7)

Step-by-step explanation:

2x^2+3x-14x-21

2x(x-7)+3(x-7)

The factors of the expression are (2x+3)(x-7).

Factorization is the breaking or decomposition of an entity (a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

For the given situation,

The expression is [tex]2x^{2} -11x-21[/tex]

The complete factorization of the expression is as,

⇒ [tex]2x^{2} -11x-21=0[/tex]

⇒ [tex]2x^{2} -14x+3x-21=0[/tex]

⇒ [tex]2x(x-7)+3(x-7)=0[/tex]

⇒ [tex](2x+3)(x-7)=0[/tex]

The value of x can be found as

⇒ [tex]2x+3 = 0[/tex] or [tex]x-7 = 0[/tex]

⇒ [tex]x=\frac{-3}{2}[/tex] or [tex]x=7[/tex]

Then -3/2 and 7 are the zeroes of the expression.

Hence we can conclude that the complete factorization of the expression are (2x+3)(x-7).

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