El reto consiste en convertir la igualdad en verdadera, haciendo 1 movimiento y luego, otra opción, haciendo dos movimientos. (no está permitido retirar fósforos)

Answer:

47°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles

124° is an exterior angle , thus

77 + ? = 124 ( subtract 77 from both sides )

? = 47°

Answer:

2 1/3 cupcakes

Step-by-step explanation:

A cupcake can make 3 four cups of flour

In 8 fourteen cups of flour, require (14 X 4)/(3 X 8) of cupcakes

  = 56/24 = 2 1/3 cupcakes

Answer:

36 answered correctly

Step-by-step explanation:

Hey there!

Well 90% of 40 is 36.

This is true because 90% as a fraction not simplified is 36/40 and when we do,

36 ÷ 40 we get .9.

And we move the decimal places 2 times to the right in .9 and we get 90%.

Hope this helps :)

Answer:

36

Step-by-step explanation:

Answer:

  C.  7 hours

Step-by-step explanation:

Let the time for the trip out be represented by t. Then the time for the return trip is t-1. The distance was the same for both trips, so we have ...

  distance = speed × time

  300t = 350(t -1)

  300t = 350t -350 . . . . eliminate parentheses

  350 = 50t . . . . . . . . . . add 350-300t

  7 = t . . . . . . divide by 50

The trip out took 7 hours.

Answer:

Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4

Part B:

P''(-1, 0)

Q''(0, -1)

R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are not congruent

Step-by-step explanation:

The coordinates of triangle PQR are;

P(4, 0)

Q(0, 4)

R(-8, -4)

The coordinates of triangle P'Q'R' are;

P'(1, 0)

Q'(0, -1)

R'(-2, -1)

Part A:

The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' can be found from the ratio of the respective coordinates as follows;

The ratio of the x, and y coordinates of the points are;

P'/P  = x'/x = 1/4, y'/y =0/0

R'/R = x'/x = -2/-8 = 1/4, y'/y =-1/-4 = 1/4

Therefore, the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' = 1/4

Part B: For reflection across the y-axis, we have;

Pre-image (x, y) becomes the image, (-x, y)

Therefore, we have;

Reflection of P'(1, 0) about the y-xis becomes P''(-1, 0)

Reflection of Q'(0, -1) about the y-xis becomes Q''(0, -1)

Reflection of R'(-2, -1) about the y-xis becomes R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are similar but they are not congruent as the dimensions of PQR are larger than the dimensions of the sides of triangle P''Q''R''.

(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/4

(B) Coordinates of Δ P"Q"R"

P" (-1,0)

Q"(0,-1)

R"(2,-1)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (4,0),

Q(0,-4)

R(-8,-4)

Coordinates of P'Q'R' are

P'(1,0)

Q'(0,-1)

R'(-2,-1)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = [tex]D= \sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2 }[/tex]

Where D = Distance between two points [tex](X_1.Y_1) \; and\; (X_2.Y_2)[/tex]

from distance formula we can write that

[tex]PQ = \sqrt{(0-4)^2+ (-4-0)^2} }\\[/tex]

PQ = [tex]4\sqrt{2}[/tex]

Similarly

P'Q'= [tex]\sqrt{2}[/tex]

PQ /P'Q' = 4

hence the scale factor of dilation is 1/4 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

[tex](x,y ) \; as \; (-x,y)[/tex]

So the Coordinated of Δ P"Q"R" can be written as

P" (-1,0)

Q"(0,-1)

R"(2,-1)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

For more information please refer to the link below

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Answer:

5 ratio 4 is

35 ratio 28

they both multiply by 7.....

Answer:

[tex]\large \boxed{x=28}[/tex]

Step-by-step explanation:

[tex]5:4=35:x[/tex]

Ratios can be expressed as fractions.

[tex]5/4=35/x[/tex]

Cross multiply.

[tex]5 \times x = 4 \times 35[/tex]

[tex]5x=140[/tex]

Divide both sides by 5.

[tex](5x)/5=140/5[/tex]

[tex]x=28[/tex]

Answer:

1 pint

Step-by-step explanation:

You need 2 * 2 = 4 pints to make 12 cookies. Since 3 cookies is 1/4 of 12 cookies, you would need 1/4 * 4 = 1 pint of milk to make 3 cookies.

Answer:

1 pint

Step-by-step explanation:

12c=4p

divide both sides by 4

3 cookies needs 1 pint!!!!

HOPE I HELPED

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DESPERATELY TRYING TO LEVEL UP

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The ratio 2:11 means for every 3 apple trees they will plant 11 pear trees.

They are planting 150 apple trees. Divide total apple trees by the ratio: 150/3 = 50

Multiply that by the ratio of pear trees:

50 x 11 = 550

They need to plant 550 pear trees.

Answer:

Step-by-step explanation:

Given one side and diagonal of rectangle we can use Pythagorean theorem to calculate the other side of it.

[tex]L=40\, cm\\D=41\,cm\\W=\ ?\\\\W^2+L^2=D^2\\\\W^2+40^2=41^2\\\\W^2+1600=1681\\\\W^2=81\\\\W=9[/tex]

Perimeter:

P = 2W + 2L = 2•40 + 2•9 = 80 + 18 = 98

Answer:

T(H) = -3H + 50.

Step-by-step explanation:

The constant will be 50 degrees Celsius. The surface temperature at the location will not change. The temperature decreases by 3 degrees Celsius for every kilometer going up, so the slope will be -3 degrees.

You are trying to find the temperature on the planet, and you are changing the kilometers of altitude to find the temperature. The x-variable is your independent variable, which means that you will be changing the x-variable. So, H is your x-variable while T is your y-variable.

T = -3H + 50.

To graph, we can use the Math is Fun Function Grapher and Calculator. The graph is seen below.

Hope this helps!

Answer:

Step-by-step explanation:

Given the set T{X: 2<x ≤ 9} where x is an integer, the element of the set T will be {3, 4, 5, 6, 7, 8, 9}.  note that from the inequality set 2<x ≤ 9, x is not equal to 2 but greater than 2. The inequality can be divided into two as shown;

If 2<x ≤ 9 then 2<x and x≤9

If 2<x, this means x>2 but not equal to 2. This is the reason why 2 is not contained in the set T.

Similarly if x≤9, this shows that x can not be greater than 9 but less than or equal to 9.

Since the set T =  {3, 4, 5, 6, 7, 8, 9}, we are to find n(T). n(T) means cardinality of the set T and cardinality of a set is defined as the total number of element in a set.

Hence n()n(T) = 7 (since there are 7 elements in the set T)

Answer:

x = 3

Step-by-step explanation:

Given

5 - (4 - 3x) = 10 ← distribute the terms in the parenthesis by - 1

5 - 4 + 3x = 10, that is

1 + 3x = 10 ( subtract 1 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

Answer:

See below.

Step-by-step explanation:

[tex]\cot(x-\frac{\pi}{2})=-\tan(x)[/tex]

Convert the cotangent to cosine over sine:

[tex]\frac{\cos(x-\frac{\pi}{2} )}{\sin(x-\frac{\pi}{2})} =-\tan(x)[/tex]

Use the cofunction identities. The cofunction identities are:

[tex]\sin(x)=\cos(\frac{\pi}{2}-x)\\\cos(x)=\sin(\frac{\pi}{2}-x)[/tex]

To convert this, factor out a negative one from the cosine and sine.

[tex]\frac{\cos(-(\frac{\pi}{2}-x ))}{\sin(-(\frac{\pi}{2}-x))} =-\tan(x)[/tex]

Recall that since cosine is an even function, we can remove the negative. Since sine is an odd function, we can move the negative outside:

[tex]\frac{\cos((\frac{\pi}{2}-x ))}{-\sin((\frac{\pi}{2}-x))} =-\tan(x)\\-\frac{\sin(x)}{\cos(x)} =-\tan(x)\\-\tan(x)\stackrel{\checkmark}{=}-\tan(x)[/tex]

Answer:

1:55 pm

Step-by-step explanation:

So, you arrive at 4: 15 pm in Orlando after a 2 hr and 20 minute flight from Houston.  So, lets start with the easy part: let's subtract the 2 hrs part.  

2 hrs earlier from 4:15 pm is 2:15 pm.

Then, you have to subtract the 20 minutes.  Well, it's quite obvious that if you left at 2:00 pm, that would be a total of 2 hrs and 15 minutes.  Just subtract the 15 minutes from the 2:15 pm.  However, it's 20 minutes, not 15, so you have to still subtract that last five minutes.  

So, 2:00 pm minus 5 minutes would equal 1:55 pm.

Answer:

U B = 100.5

Step-by-step explanation:

the upper bound of the size of the television screen= 95.5 since it is corrected to the nearest 5 then the U B =100.5 cm

The upper bound of the size of the television screen is 100.5 cm

The conversion of the size of the television screen to the nearest 5cm from the initial size of 95 cm is = 100 cm.

Now, the upper bound of the size of the television screen which is 100 is can be determined by the addition of a half value to 100 cm:

i.e.

= (1/2) + 100 cm

= 0.5 + 100 cm

= 100.5 cm

Therefore, we can conclude that the upper bound of the size of the television screen is 100.5 cm

Learn more about nearest value here:

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Answer:

343

Step-by-step explanation:

7^3 =

7*7*7

343

Answer:

[tex]\Large \boxed{11.08}[/tex]

Step-by-step explanation:

The triangles are congruent, we can use ratios to solve.

AD/DC = BE/EC

Let the length of EC be x.

6/14 = 4.75/x

Solve for x.

Cross multiply.

6 × x = 14 × 4.75

6x = 66.5

Divide both sides by 6.

(6x)/6 = (66.5)/6

x = 11.083333...

Greetings from Brasil...

Here we can use similarities of triangles

AC/DC = BC/EC

20/14 = (4.75 + X)/X

X ≅ 11.1

see attachment

Answer:

6/80, 9/120, 12/160 etc

Answer:

3/40 = 6/80 = 9/120 = 12/160 etc......

Hope it helps

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Answer:

$1.80

Step-by-step explanation:

2/3x = 1.2

x = 1.2 / (2/3)

x = 1.2 * (3/2)

x = 1.80

Answer:

2

Step-by-step explanation:

because ther is in the picture

Answer:

9 small boxes and 15 large boxes

Step-by-step explanation:

x = small box

y = large box

x + y = 24

9x + 24y = 441

-9x - 9y = -216

15y = 225

y = 15

x + 15 = 24

x = 9

Answer:

Let x be the small boxes

Let y be the large boxes

x+y=24

9x+24y=441

Step-by-step explanation:

2x+10=14

x=2

Area: 14.4= 56

3x+16=25

3x=9

x=3

17x-1,7=37,4

17x=39,1

x=2,3

This Question is incomplete

Complete Question:

The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}

What is the five number summary:

a) Minimum

b) Q₁

c) Median

d) Q₃

e) Maximum

Answer:

a) Minimum = 18

b) Q₁ = 27.5

c) Median = 39.5

d) Q₃ = 43

e) Maximum = 49

Step-by-step explanation:

From the above diagram, we were given the following set of data.

{18, 49, 38, 41, 33, 44, 42, 22}

Before answering any of the questions, we have to rearrange the data from the lowest to the highest (ascending order). Hence, we have:

{18, 22, 33, 38, 41, 42, 44, 49}

a) Minimum

{18, 22, 33, 38, 41, 42, 44, 49}

Looking at this set of arranged data, the minimum number is the least or lowest number.

This number is 18

b) Q₁

{18, 22, 33, 38, 41, 42, 44, 49}

Q₁ means First Quartile. The formula is = ¼(n + 1)th value

n = Number of terms in the data set = 8

= ¼(8 + 1)th value

= ¼(9)th value

= 2 1/4 value

= 2.25 value

In the above Question, the 2.25 value is the value between the second and third number.

Hence:

22+33/2 = 55/2 = 27.5

Therefore, Q₁ = 27.5

c) Median

{18, 22, 33, 38, 41, 42, 44, 49}

The median of the number is the number in the middle

For this data, we have 8 number, Hence the median is the sum of the 4th and 5th term divided by 2

4th term = 38

5th term = 41

= 38 + 41/ 2 = 79/2

= 39.5

Hence, the median = 39.5

d) Q₃

{18, 22, 33, 38, 41, 42, 44, 49}

Q₃ means Third Quartile. The formula is = ¾(n + 1)th value

n = Number of terms in the data set = 8

= ¾(8 + 1)th value

= ¾(9)th value

= 6 3/4 value

= 6.75 value

In the above Question, the 6.75 value is the value between the sixth and seventh number.

Hence:

42+44/2 = 86/2 = 43

Therefore, Q₃ = 43

e) Maximum

{18, 22, 33, 38, 41, 42, 44, 49}

Looking at this set of arranged data, the Maximum number is the highest number.

This number is 49

Answer:

174

Step-by-step explanation:

Given

132, 145, 97, 112, 128, 82

Required

Estimate amount of students in an art class

This is calculated by obtaining the mean of the given data

[tex]Mean = \frac{\sum x}{n}[/tex]

Where n is the number of observations

So;  n = 6

[tex]Mean = \frac{132+ 145+ 97+ 112+ 128+ 82}{6}[/tex]

[tex]Mean = \frac{696}{6}[/tex]

[tex]Mean = 174.0[/tex]

Hence, the estimated number of students is 174

Answer:

Step-by-step explanation:

Hello,

26 = 2 * 13

8 = 2 * 4

so we can simply as below.

[tex]\dfrac{26}{8}\\\\=\dfrac{2*13}{2*4}\\\\\boxed{=\dfrac{13}{4}}[/tex]

Thank you

[tex]\dfrac{26}{8}=\dfrac{13\cdot2}{4\cdot2}=\,\boxed{\,\dfrac{13}4\,}\,=\dfrac{3\cdot4+1}4=3\frac14[/tex]

or if its 20, not 26:

[tex]\dfrac{20}{8}=\dfrac{4\cdot5}{4\cdot2}=\, \boxed{\,\dfrac{5}2\,}\, =\dfrac{2\cdot2+1}2=2\frac12[/tex]

Answer:

hey here is the answer

Step-by-step explanation:

Subject of the formula:

It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

For example:

In the formula v = u + at, v is the subject.

To find v in the example, we substitute the values u, a and t in the R.H.S. of the equation.

Changing the subject of the formula:

To change the subject of a formula, begin with the variable to become the new subject, and apply inverse operation as for solving equations in the opposite order to the order conventions.  

1. To make ‘u’ the subject of the formula in v = u + at,  

  [subtract at from both sides]

v - at = u

or, u = v - at

2. To make ‘t’ the subject of the formula, v = u + at,

 [subtract u from both sides]

v - u = at

or, (v - u )/a = t

or, t = (v - u)/a

Change the Subject of a Formula

The value of the equation is v = 96 when u = 6 and t = 9

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

v = u + 10t   be equation (1)

when u = 6 and t = 9

Substitute the value of u and t in the equation , we get

v = 6 + 10 ( 9 )

On simplifying the equation , we get

v = 6 + 90

v = 96

Therefore , the value of v is 96

Hence , the equation is v = 96

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Answer:Let x km/hr be the speed of train

Let y be the time taken by the train

Distance = speed x time

= x y

To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.

it clearly says that speed is increased by 6 and time is reduced by 4

So , (x + 6) (y - 4) = x y

x y - 4 x + 6 y - 24 = x y

x y - x y - 4 x + 6 y = 24

- 4 x + 6 y = 24

divided by (-2) => 2 x - 3 y = -12 ----- (1)

To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.

it clearly says that speed is reduced by 6 and time is increased by 6

So , (x - 6) (y + 6) = x y

x y + 6 x - 6 y - 36 = x y

x y - x y + 6 x - 6 y = 36

6 x - 6 y = 36

divided by (6) => x - y = 6 ----- (2)

2 x - 3 y = -12

(2) x 2 => 2 x - 2 y = 12

(-) (+) (-)

---------------

- y = -24

y = 24

Now we have to apply the value of y in the first equation to get value of x

Substitute y = 24 in the first equation we get

2 x - 3 (24) = -12

2 x - 72 = -12

2 x = -12 + 72

2 x = 60

x = 60/2

x = 30

Speed of the train = 30 km/hr

Time taken by the train = 24 hours

Distance covered by the train = x y = 30 x 24 = 720 km

Verification:

2 x – 3 y = -12

2(30) - 3(24) = -12

60 - 72 = -12

-12 = -12

Answer:

Step-by-step explanation:

Distributive property of multiplication has to do with the multiplication of numbers by the sum of that number

say in our given example $2.05.

When we decide to multiply 3 property with $2 and $0.5 which when added together will still give  $2.05, we are using distributive property of multiplication.

Hence according to distributive property 3*$2.05 is the same as

3*$2 + 3*$0.5

Answer:

False

Step-by-step explanation:

Because the question says you pick a different shirt on Tuesday than on Monday, that means you have one less shirt you can select, so the event is dependent.

G(f(10))

First solve f(x) by replacing x with 10:

F(x) = x-4 = 10-4 = 6

Now replace x in g(x) with 6

G(x) = 6-x = 6-6 = 0

So g(f(10)) = 0