same side interior angles are _____ congruent

A.always
B.never
C.sometimes

Answer:

8

Step-by-step explanation:

To one decimal place:

[tex]2 \sqrt{10} = 6.3[/tex]

[tex]10 \sqrt{2} = 14.1[/tex]

So there are eight integers between 2√10 and 10√2: 7, 8, 9, 10, 11, 12, 13, and 14.

We will apply the Pythagoras theorem to find the measure of the unknown leg in a triangle when one leg and the hypotenuse are provided dimensions.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

[tex]\rm h^2 = p^2+ b^2[/tex]

Where,

h is the hypotenuse

p is the perpendicular

b is the base

If any of the two is given the third side will be obtained using the  Pythagoras theorem.

In a triangle with given measurements for one leg and the hypotenuse, we will determine the measure of the unknown leg by the Pythagoras theorem.

Hence we willl apply the pythogorous theorem for finding the unknown side.

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Answer:

11 and 22

Step-by-step explanation:

let one positive integer be n then the other is 2n , so

n × 2n = 242

2n² = 242 ( divide both sides by 2 )

n² = 121 ( take square root of both sides )

n = [tex]\sqrt{121}[/tex] = 11

2n = 2 × 11 = 22

the 2 integers are 11 and 22

Step-by-step explanation:

tan x = sin x / cos x

[tex]tan \: x \: = \frac{ \frac{7}{15} }{ \frac{4 \sqrt{11} }{15} } = \frac{7}{4 \sqrt{11} } [/tex]

Triangle ABC is similar to triangle DEC, ∠B ≅ ∠E and 3DE = 2BC

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Right triangle ABC is reflected over AC, then dilated by a scale factor of 2/3 to form triangle DEC, hence:

Triangle ABC is similar to triangle DEC, corresponding angles are congruent (∠B ≅ ∠E) and DE = (2/3)BC i.e. 3DE = 2BC

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Answer: C

Step-by-step explanation:

The inverse of a function maps the domain onto the range.

Answer:

center = (-5, -7)

radius = 21

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given equation:

[tex](x+5)^2 + (y+7)^2 = 21^2[/tex]

Comparing the given equation with the standard equation of a circle:

Hence, the coordinates of centre is (-5,-2).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The given equation  of circle,

(x+5)² + (y+7)² = 21²

We know that,

Equation of a circle is:

(x-a)² + (y-b)² = r²

where:

(a, b) is the center

And r is the radius

Comparing with the given equation we have,

center = (-5,-7)

And radius = 21 units

Thus,

Coordinates =  (-5,-7).

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53) Vertical angles are congruent, so [tex]m\angle IDA=121^{\circ}[/tex]

54) [tex]\angle YDA[/tex] and [tex]\angle YDF[/tex] are supplementary, so [tex]m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}[/tex]

55) Because vertical angles are congruent, [tex]m\angle FDI=59^{\circ}[/tex]. Now, because DR bisects [tex]\angle FDI[/tex], this means [tex]m\angle RDI=\frac{59}{2}=29.5^{\circ}[/tex]

56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32

Cooper left his dinner server a 19% tip.

To find the percent tip, we need to first subtract the cost of the meal from the total amount paid, which will give us the tip amount:

Tip amount = Total amount paid - Cost of the meal

Tip amount = $33.32 - $28

Tip amount = $5.32

Now we can calculate the percentage of the tip by dividing the tip amount by the cost of the meal and multiplying by 100:

Percent tip = (Tip amount / Cost of the meal) x 100

Percent tip = ($5.32 / $28) x 100

Percent tip = 0.19 x 100

Percent tip = 19%

Therefore, Cooper gave a 19% tip on his dinner.

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Answer:

  B. II  (6, 8, 10)

Step-by-step explanation:

A set of triangle side lengths will form a right triangle if they satisfy the Pythagorean theorem. The sum of squares of the shortest two sides must equal the square of the longest side.

__

Sets of integers that satisfy the Pythagorean theorem are called "Pythagorean triples." Some of these for smaller integers are ...

  (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)

If small integer side lengths are not one of these triples, or a multiple of one of these triples, they will not form a right triangle.

I. not a match to any triple

II. matches (3, 4, 5) multiplied by 2 -- a right triangle

III. not a match to any triple

IV. not a match to any triple

_____

Of course, you can actually compute the squares to see if they satisfy the Pythagorean theorem:

I. 4² +5² = 41 ≠ 6² (acute triangle)

II. 6² +8² = 100 = 10² -- right triangle

III. 5² +13² = 194 ≠ 14² (obtuse triangle)

IV. 7² +11² = 170 ≠ 13² (acute triangle)

__

The sum f = a² +b² -c² (where c is the longest side) can be considered to be a "form factor" for the triangle. For ...

This "form factor" is related to the largest angle (C) by ...

  cos(C) = f/(2ab)

Answer:

A. 4 root 3

Step-by-step explanation:

Answer: C. Parabola

Definition: a parabola is a conic section in which it is mostly characterised of having a U-shape wherein it is symmetrical and an open plane curve.

Answer:

y = x/2 -3

Step-by-step explanation:

x - 2y = 6

Slope intercept form is y = mx+b  where m is the slope and b is the y intercept

We need to solve for y

Subtract x from each side

x-2y-x = -x+6

-2y = -x+6

Divide each side by -2

-2y/-2 = -x/-2 +6/-2

y = x/2 -3

The slope intercept form is

y = x/2 -3

Answer: slope intercept form is

y = x/2 -3

Step-by-step explanation:

hope this helps ; )

The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²

The angles will be calculated as follows:-

13x² + 12x² + 20x² = 180

45x²  =  180

x²  =  4

x   =  ±2

The angles will be:-

∠ABC = 13x²  = 13 x ( 2² ) = 52

∠ACB = 12x²  = 12 ( 2² )    = 48

∠CAB = 20x²  = 20 ( 2² )  = 80

Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

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Answer:

the angles of a triangle always equal 180 so

34+x-5+4y=180

simplify

29+x+4y=180

-29

x+4y=151

-4y

x=-4y+151

then put this into the original equation

29-4y+151+4y=180

simplify

29+151=180

so this proves that this works

-1/4x-151=y

Hope This Helps!!!

Answer:

Step-by-step explanation:

Ray can be defined as a part of a line that has a fixed starting point but no end point.

The starting point is B and on its way to infinity, it passes through point A.

Correct sign is

[tex]\huge\boxed{\overrightarrow{BA}}[/tex]

Answer:

50.007131355

Step-by-step explanation:

A calculator lol?

Factor the rational function,

.

.

.

.

Notice that the denominator and numerator both have x-1. This means that we have a removable discontinuity there so set x-1=0.

.

.

So our domain can be all reals except 1.

Range: First factor out the x-1. We will be left with

.

Since 1 isn't in the domain, plug in 1 to find the what won't be in the range

.

So 7 isn't in the range,

End Behavior:

Since the rational function numerator is a quadratic and the denominator is a linear function, the rational function will approach will not have a horizontal asymptotes.

The range of shelter A is 22.  The range of shelter B is 18.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number. The range is the difference between the two numbers.

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The probability of the 90th percentile given a mean of 262 and a standard deviation of 45 is 319.672

Here,

The formula for the percentile probability is

[tex]P=\mu+z\sigma[/tex]

P=262 + 1.2816(45)

P = 319.672

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Sin3A=Cos3A

Cos(90-3A)=Cos3A

90-3A=3A

90=3A+3A

90=6A

90/6=A

^•^

The answer is A=15

The domain will be ( 0, ∞) and the range of the function F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] will be [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and [ [tex]\dfrac{3\pi}{8}[/tex],3].

Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The range of the function we can see from the graph of the function will be from  [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and  [ [tex]\dfrac{3\pi}{8}[/tex],3]

The domain of the function will be all the values of the real numbers for the function ranges from  ( 0, ∞ ).

Therefore the domain will be ( 0, ∞) and the range of the function F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] will be [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and [ [tex]\dfrac{3\pi}{8}[/tex],3].

The complete question is given below:-

what is the domain and range of the function

F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] .

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Answer:

the answer is $62

Step-by-step explanation:

if you subtract 110 by 98 you get 12 and the same for the rest so if you subtract 74 by 12 you get 62

Hope that help :)

Answer:

62

Step-by-step explanation:

Answer:

I believe the terms would be 31, 35, 39.

Step-by-step explanation:

We know this because 43-27 is 16. since there are 3 terms missing, we divide the answer by 4, and you get 4. The number you get there is how many you add to each term to get the missing ones. For example, 27+4=31. The pattern is adding 4 to each term. Hope I helped!

The income elasticity for the household is -1.05.

Income elasticity measures how quantity demanded changes when there is a change in the income of a person / household

Income elasticity = percentage change in quantity demanded / percentage change in income

Income elasticity = -21% / 20 = -1.05

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Answer:

∠ EAB = 85°

Step-by-step explanation:

∠ EBC and ∠ BCD are same- side interior angles and sum to 180° , so

∠ BCD = 180° - ∠ EBC = 180° - 148° = 32°

the sum of the 3 angles in Δ ADC = 180° , that is

∠ EDC + ∠ BCD + ∠ EAB = 180°

63° + 32° + ∠ EAB = 180°

95° + ∠ EAB = 180° ( subtract 95° from both sides )

∠ EAB = 85°

Answer:

first of all the line EAB is a triangle and all the angles in a triangle equate to 180° therefore;

[tex]angle \: ebc = 148 \\ angle \: edc = 63 \\ 148 + 63 = 180[/tex]

next I subtract 148 from 63 which gives 85⁰ therefore eab is equals 85⁰