5x + 13y=232
12x + 7y= 218

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:

∠ 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

Answer:

Sweater: 392 [tex]\frac{6}{7}[/tex]

Hat: 78[tex]\frac{4}{7}[/tex]

Scarf: 83[tex]\frac{4}{7}[/tex]

Step-by-step explanation:

Set the sweater = x

The hat = [tex]\frac{1}{5}[/tex] x

The scarf = [tex]\frac{1}{5}[/tex] x + 5

x + [tex]\frac{1}{5}[/tex] x + [tex]\frac{1}{5}[/tex] x + 5 = 555

Combine like terms

1[tex]\frac{2}{5}[/tex] x + 5 = 555

Subtract 5 from both sides

1[tex]\frac{2}{5}[/tex] x = 550

Divide by 1[tex]\frac{2}{5}[/tex]

x = 392 [tex]\frac{6}{7}[/tex] This is how much wool was used for the sweater.

Divide by 5 to get the hat = 78 [tex]\frac{4}{7}[/tex]

Add 5 to that to get the scarf: 83[tex]\frac{4}{7}[/tex]

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:

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.

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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By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:

[tex]x \to y[/tex]

[tex]f(x) \to x[/tex]

[tex]x = \frac{-2\cdot y + 2}{y+7}[/tex]

x · (y + 7) = - 2 · y + 2

x · y + 7 · x = - 2 · y + 2

2 · y + x · y = - 7 · x + 2

y · (2 + x) = - 7 · x + 2

[tex]g(x) = \frac{- 7\cdot x + 2}{x + 2}[/tex]

By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

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Answer:

  [c] The value of w cannot be a negative number.

  [d] Substitution is used to replace the variable l with a value of 20.

  [e] The subtraction property of equality is used to isolate the term with the variable w.

Step-by-step explanation:

     To figure out which steps of the solution are true, let us solve.

2 l plus 2 w equals 62 -> 2l + 2w = 62

----

2l + 2w = 62

2(20) + 2w = 62  <- Substitution is used to replace the variable l with a value of 20.

40 + 2w = 62

2w = 22 <- The subtraction property of equality is used to isolate the term with the variable w.

w = 11

     This means that the value of w is not 10 feet so the first option is incorrect. This shape is a rectangle, so the value of w cannot be 0. Since we cannot have a negative measurement, option three is incorrect. This leaves us with the last three options as our answer, shown by the work above.

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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:

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]

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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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:

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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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]

Answer:

A. 4 root 3

Step-by-step explanation:

Answer:

(-1, -4)

Step-by-step explanation:

y = -x² - 2x - 5

y = -1(x² + 2x + 5)

y = -1(x² + 2x + 1 - 1 + 5)

y = -1(x² + 2x + 1) - 4

y = -(x + 1)² - 4

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!

Answer:

50.007131355

Step-by-step explanation:

A calculator lol?

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

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

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: 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.

The volume of 10% solution will be 6 l and 9 litre of the 30 % solution will be taken.

Volume is the space occupied by a three dimensional object .

The concentration of solution required is 22% acid

The concentration of solution available is 10% and 30%

The total volume required is 15 liters

The formula for making a mixture is

Concentration = ( m₁x₁ +m₂x₂) / (x₁+x₂)

22 = (10 * x + 30 *(15 -x))/( 15)

10 x + 450 - 30x =330

-20x = -120

x = 6

The volume of 10% solution will be 6 l

and 9 litre of the 30 % solution will be taken.

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Answer: C

Step-by-step explanation:

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

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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