11. Ryan and Kathy each drew a triangle with an angle of 20 degrees. Under which condition would the
triangles be similar?

a) if both are right triangles

c) if the triangles have the same area

b) if both are obtuse triangles

d) if the triangles have the same perimeter

The given function are

r(x) = 2 - x²    and     w(x) = x - 2

(w*r)(x) can be obtained by multiplying the both function together

So, (w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)

(w*r)(x) = x (2-x²) - 2(2-x²)

           = 2x - x³ - 4 + 2x²

∴ (w*r)(x) = -x³ + 2x² + 2x - 4

It is a polynomial function with a domain equal to R

The range of (w*r)(x) can be obtained by graphing the function

To graph (w*r)(x), we need to make a table between x and (w*r)(x)

See the attached figure which represents the table and the graph of (w*r)(x)

As shown in the graph the range of (w*r)(x) is (-∞,∞)

Answer: -3

Step-by-step explanation: Used calculator

The comparison of the linear functions to line A are given as follows:

A linear function is defined as follows:

y = mx + b.

In which the coefficients are listed as follows:

The slope determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, the function is:

y = 4x - 6.

Hence the slope is of:

m = 4.

Then the functions, relative to y = 4x - 6, are classified as follows:

The problem gives three lines with different slopes, and you have to define if they are parallel, perpendicular or neither parallel nor perpendicular.

The intercepts are not relevant and I couldn't find the problem on the internet, hence I say that they are constants.

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Answer:

x=246 or x=-266

Step-by-step explanation:

First you bring 12x to the other side and simplify to give

x²+20x+116=0

Then solve by completing the square:

(x+10)²-100+116=0

(x+10)²+16=0

(x+10)²=-16

x+10=±256

x=±256-10

x=246 or x=-266

Hope this helps

Answer: Yes

Step-by-step explanation:

Add all of their best times.

11.9 + 12.6 + 12.52 + 11.95 = 48.97

48.97 < 49.6

The domain and range of the relation shown in the table include the following: A. domain:{−3, −1, 2, 4}, range:{0, 2, 4}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined.

This ultimately implies that, a domain is the set of all possible input values (x-values) to a relation, and the domain of a graph comprises all the input values which are located on the x-coordinate from the least to the greatest.

Additionally, a range is the set of all real numbers that is associated with the elements of a domain i.e all of the y-values shown on the y-coordinate of the graph of a relation, from the least to the greatest.

By critically observing the table of this relation shown, we can reasonably infer and logically deduce the following:

Domain = {−3, −1, 2, 4}.

Range = {0, 2, 4}.

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Function A has a rate of change of 5 & function B has a rate of change of -4.5. so, function A has a greater rate of change.

What is the rate of change?

The rate at which a variable changes over a given time period. It is frequently used when discussing momentum, and it can be expressed as a ratio of a change in one variable to a corresponding change in another. This ratio is represented graphically by the slope of a line.

For the first function, we can use the equation of the slope

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

take any two points,

m = (25-15)/5.5-3.5 = 10/2 = 5

The general equation of a straight line is;

y = mx + c

where m is the slope

Therefore, in the case of the second equation, -4.5 is the slope

Hence, function A has a rate of change of 5 & function B has a rate of change of -4.5. so, function A has a greater rate of change.

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The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)

We are given from the question that the triangle P'Q'R' was transformed from the triangle PQR.

We see from the image that the coordinates of the original triangle PQR are;

P(-1, 1)

Q(2, 0)

R(-1, -2)

We also see that the coordinates of the transformed triangle P'Q'R' are;

P(-5/2, 5/2)

Q(5, 0)

R(-5/2, -5)

Thus, we can conclude that the transformation rule used here is;

(x, y) → (⁵/₂x, ⁵/₂y)

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The equation represents the price of a pumpkin is p = 5 + 0.35x

The cost of each pumpkin = $5.00

The cost of the pumpkin per pound = $0.35

Consider the price of the pumpkin = p

Consider the number of pounds = x

The equation is the mathematical statement that shows the relationship between two expression with an equal sign. In equation the inequality will not be a part. The expression is the combination of two expression and an equal sign

Then the equation will be

p = 5  + 0.35x

Hence, the equation represents the price of a pumpkin is p = 5 + 0.35x

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Answer:

Step-by-step explanation:

Ok:

1. This is a percent problem!

45/100*15=

675/100=

6.75

2. Subtract:

15-6.75=

8.25$

Answer: 8.25$

The distance from an angle of depression to the boat at 21° to angle of depression of 50° is 112 feet

Information from the question

A boat is heading towards a lighthouse, where Yaritza is watching from a vertical distance of 139 feet

Yaritza measures an angle of depression to the boat at point AA to be 21°

Yaritza takes another measurement and finds the angle of depression to the boat (now at point BB) to be 50°

the distance from point AA to point BB = ?

The direction of movements describes a right triangle of

opposite =  ?

adjacent = 139 feet

The distance is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

for x = 21 point AA is solved

tan 21 = ? / 139

? = 139 * tan 21

? = 53.357

for x = 50 point BB is solved

? = 139 * tan 50

? = 165.654

the distance from point AA to point BB

= 165.654 - 53.357

= 112.297

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The length of the base edge of the pyramid is 1.71 feet

In order to find the total surface area, we will need to add up the areas of the base and the three other sides. SA=B+12(P×h), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid.

If l is the length of the square base and h is the height of the pyramid, then h =2/3l

from the formula, SA= B+12(P×h)

the perimeter of a square is 4l

the base area of square is l^2

therefore 96= l^2+ 12(4l×2/3l)

96= l^2+ 12×8/3l^2

96=l^2+32l^2

96= 33l^2

divide both sides by 33

l^2= 96/33

l=√2.91

l=1.71 feet

therefore the length of the base edge is 1.71 feet

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Answer:

145 degrees

Step-by-step explanation:

The side through L is at a 35 degree angle, and the side through N is at a 180 degree angle. Taking the difference, we get 145 degrees.

Answer:

HL

Step-by-step explanation:

Since the two triangles are right triangles and have 2 sets of congruent sides, you can use the HL congruence theorem to prove that they are congruent.

**HL only works with right triangles

Answer:

4.5 miles

Step-by-step explanation:

0.5 of a mile per 1/9 of an hour.

rate x time=distance and you need to find distance for one hour not 1/9 so multiply it by 9 so

0.5*9=4.5, 1/9*9=1

rate   time   distance

4.5  *    1   =  d

4.5*1=d

4.5=d

so the distance traveled in one hour is 4.5 miles

Answer:

4.5 miles

Step-by-step explanation:

Given:

Let x be the distance Julia rides in one hour.

Create an equivalent ratio of miles to hours:

[tex]\implies \dfrac{1}{2}:\dfrac{1}{9}=x:1[/tex]

[tex]\implies \dfrac{\frac{1}{2}}{\frac{1}{9}}=\dfrac{x}{1}[/tex]

[tex]\implies \dfrac{1}{2}\times \dfrac{9}{1}}=x[/tex]

[tex]\implies \dfrac{9}{2}=x[/tex]

[tex]\implies x=4.5[/tex]

Therefore, Julia rides 4.5 miles in one hour.

The mathematical expression is 3/5b -7 = a.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

7 less than three fifths of b is a

So, the mathematical expression for the above statement is

(3/5)b - 7 = a

3b - 35 = 5a

3b- 5a= 35

Hence, the mathematical expression is 3/5b -7 = a.

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Answer: regularly patterned or that occur in regular intervals.

Step-by-step explanation: took it

The total cost of the cosmetics including 2% processing fee rounded up to the nearest cent is $26.27

The cost of the cosmetics is $25.75

The 2% processing fee is calculated as follows:

2/100 × $25.75 = $ 0.515

The total cost including processing fee is $25.75 + $ 0.515 = $26.265 rounded up to $26.27

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Answer:

When we reflect over the x-axis the answer will be (6, -2)

Then when we go 4 units right it will turn into (10,-2)

And lastly, when we go 3 units down, it will be (10,-5)

The Answer is (10,-2)

(Brainiest is optional)

Answer:

y = x - 12

Step-by-step explanation:

slope = (-9 - (-5))/(3 - 7) = -4/(-4) = 1

y = mx + b

y = x + b

-5 = 7 + b

b = -12

y = x - 12

Answer:

las fórmulas de 3 dividir por r te va a dar igual a 1.862

Answer:

Step-by-step explanation

C

Answer:

2.5x

Step-by-step explanation:

Given information for width:

Model: 10 in.

Real: 25 in.

Solve: How much times wider is real than model?

To find this, lets divide 25in. by 10in to find the scale factor.

25/10 = 2.5

2.5

We can verify this by multiplying 10 by 2.5

10 x 2.5 = 25

980g of sulphuric acid (H₂SO₄) is needed to prepare 5.0L of a 2M solution.

So, the grams of H₂SO₄ needed will be:

Therefore, 980g of sulphuric acid (H₂SO₄) is needed to prepare 5.0L of a 2M solution.

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Answer:

42

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] x = [tex]\frac{1}{7}[/tex]x + 15  Clear the fraction by multiplying all the way through by 14

7x = 2x + 210  Subtract 2s from both sides

5x = 210  Divide both sides by 5

x = 42

The percent of increase in Zach's finishing time is 5%.

From the information, at a race a few months ago, he finished in 280 minutes and yesterday, he completed another triathlon and finished in 294 minutes.

The increase in time will be:

= New time - Old time

= 294 - 280

= 14 minutes

The percentage increase will be:

= Increase in time / Original time × 100

= 14 / 280 × 100

= 1/20 × 100

= 5%

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The probability that the person is over 40 years of age is 32/51 or 62.75%.

(the table is attached as image)

We know that,

The ratio of the size of the event space to the size of the sample space is the probability of an event.

The total number of possible outcomes is the size of the sample space.

The number of outcomes in the event you are interested in is called the event space.

Using the formula,

P = size of the event space/size of the sample space

⇒The probability that the person is older than 40,

sample size=255

size of the event space=85

P=85/255------> P=1/3

⇒the probability that the person drinks root beer,

sample size=255

size of the event space=75

P=75/255------> P=5/17

⇒the probability that the person is older than 40 of age or that they drink root beer,

P=(1/3)+(5/17)-----> P=(17*1+3*5)/51------> P=32/51-----> 0.6275----> 62.75%

therefore,

the answer is

32/51 or 62.75%

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(complete question)

if one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.

The option that shows the equation for the line in the graph is

A graph is a pictorial representation of data. The graph shows a linear function which will be written in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as B(-5. 5)  (-2, -4)

m = (y₂ - y₁) / (x₂ - x₁)

substituting the values

= ( -4 - 5 ) / ( -2 - -5 )

= -9 / -2 + 5

= -9 / 3

= -3

y intercept, c

this is a point where the graph cuts the y axis

c = -10

hence the equation is written using y = mx + c and substituting the values

y = -3x - 10

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