Mikaela and Viktoria both competed in a curling match on opposing teams. Mikaela
said to Viktoria, "2 more than twice my team's score is the
same as three times your team's score reduced by 3." If
Viktoria's team's score was 7, what was Mikaela's team's
score?

Using translation concepts, it is found that the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

From triangle X′Y′Z′ to triangle X′′Y′′Z′′, the rule is given by:

(x,y) -> (x, -y)

Hence the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.

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The information we can see from the given data is that the speed of Julie is three times the speed of Bailey.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Given that:-

The speed of Bailey = x miles

The speed of the Julie = 3x miles

The ratio of the speeds will be given as:-

J / B = 3x / x

J / B = 3

J = 3 B

Therefore information we can see from the given data is that the speed of Julie is three times the speed of Bailey.

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Answer:

trapezoid

the horizontal side lengths wont touch each other if you extend them out

Answer:

Length = 16 yds

Width = 13 yds

Step-by-step explanation:

P = 2w + 2l

l = w + 3

58 = (2w + 2(w + 3))

58 = 4w + 6

52 = 4w

w = 13

L = w + 3

= 13 + 3

= 16

The length and width of the rectangle are 16,13yd.

The Length and Width of the rectangle can be found as:

The length of the rectangle is 3yds longer than the width which means length = w+3

and the perimeter is given by 58yd

Let W be the width and L be the length

We know that the perimeter of a rectangle is 2(L+w)

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle

2(w+w+3)=58

2(2w+3)=58

2w=29-3

w=13

then the length of the rectangle will be w+3

                                                              13+3 = 16

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The length of AD is 5 units. so, option A is the correct answer.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

The length of DC is given as 13 units.

The length of AC is given as 12  units. We can see that angle D is a right angle, so the triangle will be a right-angle triangle.

by Pythagoras theorem;

[tex]DC ^2 = AD^2 + AC^2\\\\13^2 = AD^2 + 12^2\\\\AD^2 = 169 - 144\\\\AD^2 = 25\\\\AD = 5[/tex]

Hence, the length of AD is 5 units. so, option A is the correct answer.

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The time spent by the repairman there will be 3 hours so the correct answer is option D.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195.

The time will be calculated as:-

Total amount =  $195

Now the fixed consulting cost will be $60 and will be deducted from the

total amount.

Variable cost = 195 - 60 = 135

The $45 per hour charge so for $145 the time will be:-

Time = 135 / 45

Time =  3 Hours

Therefore the time spent by the repairman there will be 3 hours so the correct answer is option D.

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The formula that can be used to find the number of bacteria is FV = 1000 x 2^t.

The formula that can be used to determine the number of bacteria is an exponential function with the form:

FV = P(1 + r)^t

Where:

1000 x ( 1 + 1)^t

FV = 1000 x 2^t

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The image was formed by a reflection of the letter M would be image A in the second quadrant b the reflection on X-axis. The correct option is A.

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in the opposite side of the axis as if we're seeing it in a mirror.

If you study it more, you will find that it's symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

Thus, if you're reflecting a point (x,y) along the x-axis, then its x abscissa will stay the same but y coordinates will negate.

Thus (x,y) turns to (x, -y)

Similarly, if you're reflecting a point (x,y) along the y -axis, the resultant image of the point will be (-x,y).

The image was formed by a reflection of the letter M would be image A in the second quadrant b the reflection on X-axis. The correct option is A.

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The reflection of letter M is (A)

A figure is said to be a reflection of the other figure, then every point in a figure is at equidistant from each corresponding point in another figure.

According to the graph the reflection of Of letter M is with same coordinates but with x as positive and y as negative.

Hence the reflection is (A).

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Answer:

centroid

Step-by-step explanation:

medians of the triangle intersect at point H, making this point centroid.

(essentially, it's the center of the triangle)

Answer:

18.18%

Step-by-step explanation:

(65000-55000)/55000×100

Answer:

120°

Step-by-step explanation:

x = angle       supplement = 180-x

x = 4(180-x) -120

x = 720 -  4x - 120

5x = 600°

x =120°

The Range of the function is  {y|y is a real number} , Option D is the correct answer

Range of a function is all the value a function can obtain.

From the figure it can be seen that the graph is moving slowly in either direction.

It extends from -∞ to +∞ ,

Therefore ,  {y|y is a real number} , Option D is the correct answer.

The complete question is

The graph shows a vertical translation of y = ³√x

What is the range of the translated function?

{y|y < 0}

{y|y ≥ 0}

{y|y is a natural number}

{y|y is a real number}

The image of the translated function is attached.

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Answer:

[tex]\boxed{\bf B. \: c = 4 \sqrt{3} }[/tex]

Step-by-step explanation:

Since a = 6, then, b = 3.47 ( opposite of 30°).

By applying the pythagoras theorem..

Answer:

4√3 or B

Step-by-step explanation:

Answer:

C)

Step-by-step explanation:

Prime factorize.

A) √30 is in its simplest form.

[tex]B) \sf \sqrt{45}= \sqrt{3*3*5} = 3\sqrt{5}\\[/tex]

[tex]C) \sqrt{75}=\sqrt{3*5*5}=5\sqrt{3}[/tex]

So, option C

The simplified expression of 5√3 is √75.

Hence, Option C is correct.

Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

The given expression is,

5√3

So it can be written as,

⇒√5² x √3

⇒ √25 x √3

Since we know that,

Square roots are multiplied by both the whole number component and the square root component individually.

Therefore,

⇒√(25x3)

⇒√75

Thus,

5√3  = √75

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[tex] \frac{ - 3}{5} \\ [/tex]

because , in the third quadrant , the value of cos is negative. Moreover , we can find the third side of the triangle using Pythagoras theorem.

then ,

[tex] \cos(\theta) = \frac{base}{hypotenuse} \\ \\ \dashrightarrow \: \cos(\theta) = \frac{ - 3}{5} [/tex]

hope helpful.

The answer is cos 0 = -3/5

Given :

tan 0 = 4/3 and is in the 3rd quadrant

this implies that both the perpendicular and base are negative.

Perpendicular = -4

Base = -3

Hypotenuse = [tex]\sqrt{(perpendicular)^{2} + (base)^{2} }[/tex]

Hypotenuse = [tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]

Hypotenuse = [tex]\sqrt{25} = 5[/tex]

cos 0 = [tex]\frac{Base}{Hypotenuse}[/tex]

cos 0 = -3/5

Therefore, cos 0 = -3/5

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Answer:

(2, - 3 )

Step-by-step explanation:

x + 4y = - 10 → (1)

2x - y = 7 → (2)

multiplying (2) by 4 and adding to (1) will eliminate y

8x - 4y = 28 → (3)

add (1) and (3) term by term to eliminate y

9x + 0 = 18

9x = 18 ( divide both sides by 9 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (1)

2 + 4y = - 10 ( subtract 2 from both sides )

4y = - 12 ( divide both sides by 4 )

y = - 3

solution is (2, - 3 )

Answer:

k = 11, if I understand the question.

Step-by-step explanation:

Please rephrase the question if my interpretation is incorrect.  (BTW, isn't (k,9) a dog?)

======================

I'll assume that we want to find the value of k as given by the equation of a line that has a slope of (1/2).  

Let's determine if we can establish an equation with what we know:

1.  It goes through point (3,5), and

2.  It has a slope of (1/2)

We'll look for a line with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

From (2) we know y = (1/2)x + b.

We can find b by using the one known point that lies on the line (3,5).  Use y = (1/2)x + b, insert the point (3,5), and solve for b:

y = (1/2)x + b

5 = (1/2)(3) + b

5 = 1.5 + b

b = 3.5

The line is y = (1/2)x + 3.5.

Now use the point (k,9):

y = (1/2)x + 3.5

9 = (1/2)k + 3.5

(1/2)k = 5.5

k = 11

The point is (11,9) so k = 9

See the attached graph.

Answer:

7 hours

Step-by-step explanation:

just multiply 3 and 7 to get 21

Answer:

[tex]\fbox {7 hours}[/tex]

Step-by-step explanation:

⇒ Rate = -3F/hour

⇒ Starting : -21F

Solving :

⇒ -21/-3

⇒ 7 hours

Answer:

  (b)  y = 18/x; y = 9/4

Step-by-step explanation:

Different kinds of variation are generally described by the equation ...

  y = k·( ) . . . . . . . where k is the constant of proportionality

__

What goes in parentheses depends on the kind of variation. Here is a partial list of kinds that may be seen in algebra problems.

The value of k can be found by solving the variation equation with given values of the variables.

__

The variables x and y are said to vary inversely, so the appropriate equation is ...

  y = k(1/x) = k/x

Using the given values, we can find k:

  9 = k/2

  9·2 = k = 18

So, the equation is ...

  y = k/18

__

Using the above equation, the value of y for x=8 is ...

  y = 18/8 = 9/4

Note: you can also get there by realizing that x=8 is 4 times x=2, so the new value of y will be the old value of y multiplied by the inverse of this factor. 1/4 times the old value of y: (1/4)9 = 9/4.

Answer:

Step-by-step explanation:

HOPE IT HELPS

Answer:

1

Step-by-step explanation:

[tex] log_{3}(5) \times log_{25}(9) = \frac{ log(5) }{ log(3) } \times \frac{ log(9) }{ log(25) } = \frac{ log(5) }{ log(3) } \times \frac{2 log(3) }{ 2log(5) } = \frac{2}{2} = 1[/tex]

By using trigonometry, we conclude that the horizontal distance is 785.15ft

We can think of this as a right triangle.

Where the height of the observation deck is one cathetus and the horizontal distance is the other cathetus,

We know that the depression angle when looking from above is 42°. If we step on this angle, the adjacent cathetus is the height of the deck, then the horizontal distance is the opposite cathetus.

Then we can use the relation:

tan(a) = (opposite cathteus)/(adjacent cathetus).

Replacing what we know:

tan(42°) = (distance)/(872ft)

tan(42°)*872ft = distance = 785.15ft

The horizontal distance is 785.15ft

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Step-by-step explanation:

[tex] = \frac{ \sqrt{12} }{ \sqrt{6} } [/tex]

[tex] = \sqrt{ \frac{12}{6} } [/tex]

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

The answer is A.

Step-by-step explanation:

i think b is right answer

Answer:

see photo for detailed analysis

Answer:

B. shifting

Step-by-step explanation:

When the price is rising or shifting higher, the demand curve moves to the left. But, t here is a corresponding change in the demand curve in that scenario while the cost stays unchanged. Since it relies on variables other than price, the simultaneous shift might go either left or right. However, the upward-pointing line depicts a rise in price and a fall in supply.