Identify the domain and range of the relation. Represent the relation with a
mapping diagram. Is the relation a function?
{(−1, 1), (−2, 2), (4, −4), (7, −7)}

Answer: x < 3

Step-by-step explanation:

NOTE: [tex]\sqrt{(x+5)^2} = |x + 5|[/tex]

Rewrite the equation:

| x + 5 | < | x + 1 |

Remember that absolute value makes the "inside" value positive, so we need to solve for 2 case of x + 5 (inside is positive or negative) and 2 cases of x + 1.

± (x + 5) < ± (x + 1)

Case 1: +  +

x + 5 < x + 1

    5 < 1

  FALSE

Case 2: - -

-(x + 5) < -(x + 1)

 x + 5 > x + 1   divided both sides by -1

      5 > 1

     TRUE so this works when both "insides" are negative

⇒   x + 5 < 0     and      x + 1 < 0

          x < -5     and           x < -1

since it has to satisfy both, x < -5

Case 3: + -

x + 5 < -(x + 1)

x + 5 < -x - 1     distributed -1 on right side

2x + 5 < -1

2x       < -6

 x       < -3

Case 4: - +

-(x + 5) < x + 1

-x - 5 < x + 1     distributed -1 on left side

   -5 < 2x + 1

   -6 < 2x

   -3 < x

     x > -3

This is a contradiction of Case 3 so need to choose a test point.

TEST POINTS (I choose -6, -4, and -2)

 | -6 + 5 | < | -6 + 1 |

 |    -1     | < |    -5   |

          1   <   5

        TRUE so x < -5 is valid

 | -4 + 5 | < | -4 + 1 |

 |     1     | < |    -3   |

          1   <   3

        TRUE so x < -3 is valid

 | -2 + 5 | < | -2 + 1 |

 |     3     | < |    -1   |

          3   <   1

        FALSE so x > 3 is NOT valid

Note that x < -3 includes all the values of x < -5, so x < -3 is the answer.

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This is a faster way to solve it. Thank you @proner26 !

| x + 5 | < | x + 1 |

(| x + 5 |)² < (| x + 1 |)²

x² + 10x + 25 < x² + 2x + 1

       10x + 25 <       2x + 1

        8x + 25 <                1

        8x         <             -24

          x         <              -3

Answer: x < -3

Answer:

45=5t

Step-by-step explanation:

im doing it right now and got it right

This is true.  The slope of the perpendicular line is equal to the negative reciprocal.  This means that you "flip" the fraction and multiply by negative 1.  Since the reciprocal is also the multiplicative inverse (something you multiply by a number to get 1), and the signs are different (one is positive, one is negative) it equals -1.

Hope this helps!

The statement is true that the product of the slopes of perpendicular lines, excluding vertical lines, always equals -1. This is a basic rule in geometry, where two lines are perpendicular if their slopes multiply to -1.

The statement that 'the product of the slopes of perpendicular lines (excluding vertical lines) always equals -1' is true.

In the coordinate system, two lines are perpendicular if the product of their slopes is -1. This is because the slope is a measure of the steepness of a line. Imagine you have two lines with slopes m1 and m2. If these lines are perpendicular to each other, then m1 * m2 = -1.

For example, if one line has a slope of 2 (m1 = 2), the line perpendicular to it will have a slope of -1/2 (since 2 * -1/2 = -1).

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Answer:

[tex]x^{\circ}=56^{\circ};[/tex]

The exterior angle has measure [tex]116^{\circ}.[/tex]

Step-by-step explanation:

Angle QRP and angle with measure of (2x+4)° are supplementary, then

[tex]m\angle QRP+(2x+4)^{\circ}=180^{\circ},\\ \\m\angle QRP=180^{\circ}-(2x+4)^{\circ}.[/tex]

The sum of the measures of all interior angles of the triangle is equal to 180°, then

[tex]m\angle PQR+m\angle QRP+m\angle RPQ=180^{\circ},\\ \\x^{\circ}+180^{\circ}-(2x+4)^{\circ}+60^{\circ}=180^{\circ},\\ \\x^{\circ}-2x^{\circ}=-60^{\circ}+4^{\circ},\\ \\-x^{\circ}=-56^{\circ},\\ \\x^{\circ}=56^{\circ}.[/tex]

The exterior angle has measure

[tex](2\cdot 56+4)^{\circ}=116^{\circ}.[/tex]

Answer:

x=56 and the exterior angle is 116

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +4) form a straight line so they make 180 degrees.

y + 2x+4 =180

Solve for y by subtracting 2x+4 from each side.

y + 2x+4 - (2x+4) =180 - (2x+4)

y = 180-2x-4

y = 176-2x

The three angles of a triangle add to 180 degrees

x+ y+ 60 = 180

x+ (176-2x)+60 = 180

Combine like terms

-x +236=180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply each side by -1

-1*-x = -56*-1

x=56

The exterior angle is 2x+4.  Substitute x=56 into the equation.

2(56)+4

112+4

116

Answer:

50 C = 122 F

Step-by-step explanation:

50°C × 9/5 +32

Answer:

50°C = 122°F.

Step-by-step explanation:

Given  : The formula to convert F° to C° is [tex]C = \frac{5}{9}( f - 32)[/tex].

To find :  Convert 50°C to °F

Solution : We have given

[tex]C = \frac{5}{9}( f - 32)[/tex].

On multiplying by 9 both sides.

[tex]9 C = 5( f - 32)[/tex].

On dividing both sides by 5

[tex]\frac{9C}{5} =( f - 32)[/tex].

On adding both sides by 32

[tex]\frac{9C}{5}+ 32 = f[/tex].

Then plug C = 50°

[tex]\frac{9 * 50 }{5}+ 32 = f[/tex].

[tex]\frac{450}{5}+ 32 = f[/tex].

[tex] 90+ 32 = f[/tex].

[tex] 122°= f[/tex].

Therefore,  50°C = 122°F.

Answer:

260 in economy

100 in business

Step-by-step explanation:

ok so out of 18 seats 13 are economy and 5 are business and since 18 times 20 is 360 we multiply each of these by 20 so 13 times 20 is 260 20 times 5 is 100 there you go

Answer:

b. 3 4/6 cant equal 3 2/3

Step-by-step explanation:

Answer:

y + 2 = 23(x - 3)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 23 and (a, b) = (3, - 2), hence

y + 2 = 23(x - 3) ← equation in point-slope form

Answer:

C  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

4.20 ÷ 60 = 0.07

sales tax is 7% and this is your constant of variation

The answer is 0.07 hope this helps you ! :)

Answer:

- c = 9

Step-by-step explanation:

given c = - 9 ← multiply both sides by - 1

c × - 1 = - 9 × - 1 ⇒ - c = 9

Answer:

SSS - Two triangles have to have 3 congruent pairs of sides.

ASA - Two triangles have to have 2 congruent pairs of angles with an included congruent pair of sides.

SAS - Two triangles have to have 2 congruent pairs of sides with an included congruent pair of angles.

AAS - Two triangles have to have 2 pairs of congruent angles with a non-included congruent pair of sides.

Answer:

313

Step-by-step explanation:

Quotient - Division

5,008 ÷ 16 = 313

Hope this helps you! And btw, you can use a calulator. :D

Answer:

313

Step-by-step explanation:

5,008/16 equals 313

Answer:

Estimate is 150 and actual product is 138.

Step-by-step explanation:

To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.

Given are the numbers 3 and 46.

We can round 46 ≈ 50.

So Estimation would be 3 x 46 ≈ 3 x 50

3 times 5 is 15 and we can add zeros after it.  

So estimation is 3 x 46 ≈ 150.

Now actual product would be...

3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.

3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.

It means the actual product is 3 x 48 = 138.

Answer:

6. d.

8. see below

Step-by-step explanation:

6.

A large pizza costs $4.25 more than a medium pizza.

L = $4.25 + M

4 large & 6 medium cost $99.50.

4L + 6m = $99.50

Answer d.

8.

A large river runs right through a city called Chestnutville. There are many bridges and tunnels connecting the two sides of the river. The total number of bridges and tunnels is 15. The number of tunnels is 3 more than twice the number of bridges. How many bridges, b, are there in Chestnutville, and how many tunnels, t, are there in Chestnutville?

Answer:

a) There is no solution

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

while rounding the fraction to half,it is to remember that

anything less than 1/4 can be rounded to zero.

anything equal or 1/4 or greater and less than 3/4 can be rounded to 1/2.

anything greater than 3/4 and less than 1 can be rounded to one.

so,1/9<1/4

the value is 0.

Final answer:

The fraction 1/9, when rounded off to the nearest 1/2, is closest to 0, so it rounds down to 0.

Explanation:

To round the fraction 1/9 to the nearest 1/2, you must decide which multiple of 1/2 (0, 1/2, or 1) it is closest to. Since 1/9 is less than 1/2, the first decision is whether it's closer to 0 or to 1/2. Since 1/9 is much smaller than 1/2, it makes sense to round it down to 0. Therefore, when rounding 1/9 to the nearest 1/2, the answer is 0.

Answer:

Whats the question?

Step-by-step explanation:

Answer:

Tony

Step-by-step explanation:

Tony:

3 Packs = 12 dollars

1 Pencil Box = 7 dollars

Mario:

4 Binders = 24 dollars

-6.

12+7= 19

24-6=18

Tony spent more money.

Answer:

The annual percentage yield is 6.609%

Step-by-step explanation:

Let's assume

amount invested=$1

so, P=1

APR of 6.4% compounded daily

so, r=6.4%=0.064

n=365

t=1

now, we can use formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

now, we ca plug values

[tex]A=1(1+\frac{0.064}{365})^{365\times 1}[/tex]

we get

[tex]A=1.06609[/tex]

now, we can find APY

[tex]APY=\frac{A-P}{P}\times 100[/tex]

now, we can plug values

[tex]APY=\frac{1.06609-1}{1}\times 100[/tex]

we get

APY is 6.609%

Answer:

The annual percentage yield is 6.609%.

Step-by-step explanation:

The annual percentage yield is calculated by:

APY = [tex](1+\frac{r}{n} )^{n} -1[/tex]

where r is the percentage rate and n refers to the number of times compounded.

So, r = [tex]\frac{6.4}{100}[/tex] = 0.064

Since the APR is compounded daily,

n = 365

Now,

APY = [tex](1+\frac{0.064}{365} )^{365} -1[/tex]

= 6.609% approximately

Answer:

A - $2240

Step-by-step explanation:

120(12) + 800 =

1440 + 800 = 2240

Answer:

2.04

Step-by-step explanation:

The question about the height of a tree on a scale drawing did not provide enough information for a certain answer. However, given a hypothetical height for the drawn tree, the actual height can be determined by multiplying this by the scale factor.

The subject of this question is mathematics, specifically dealing with ratios and proportions related to scale drawings. Given that the scale of the drawing is 1 in: 5 ft, this means that 1 inch on the drawing corresponds to 5 feet in real life. However, the specific height of the tree on the drawing in inches is not provided in the question, making it impossible to give a definite answer.

As an example to further explain, if the tree is drawn as 2 inches on the scale drawing, you would simply multiply by 5 (since the scale is 1 in: 5 ft) to find the actual height of the tree. So, for a 2 inch drawn tree, the actual tree would be 2 in * 5 ft/in = 10 ft tall.

But given the current information, a definite height cannot be provided. Please provide the height of the tree in inches on the scale drawing.

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Answer:

-2b/(a-b)

Step-by-step explanation:

1− (a+b/a−b)

We need to get a common denominator of a-b

1 = (a-b)/(a-b)

Replace 1 with (a-b)/(a-b)

(a-b)/(a-b) - (a+b)/(a-b)

Put over the common denominator

(a-b) - (a+b)

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

(a-b)

Distribute the minus sign.

(a-b) - a-b)

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

(a-b)

a-a-b-b

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

a-b

-2b

----------

a-b

Answer:

y = 0 and z = 5

Step-by-step explanation:

the denominator of the expression cannot equal zero as this would make the expression undefined Equating the denominator to zero and solving gives the values that y and z cannot be

solve y(z - 5) = 0

equate each factor to zero and solve

y = 0 ← excluded value

z - 5 = 0 ⇒ z = 5 ← excluded value

Answer:

These fractions are not equivalent.

Step-by-step explanation:

To tell whether the fractions are equivalent, get a common denominator.

The common denominator is 10

1/2 *5/5 = 5/10

2/5 *2/2 = 4/10

5/10 ≠4/10

These fractions are not equivalent.

Answer:

- 405

Step-by-step explanation:

the recursive formula given allows us to find the next term in the sequence by multiplying the previous term by - 3

[tex]b_{2}[/tex] = [tex]b_{1}[/tex](- 3) = 15 × - 3 = - 45

[tex]b_{3}[/tex] = [tex]b_{2}[/tex](- 3) = - 45 × - 3 = 135

[tex]b_{4}[/tex] = [tex]b_{3}[/tex](- 3) = 135 × - 3 = - 405

Answer:

2693.45

Step-by-step explanation:

step 1 - 2615*3%=78.45

step 2 - 2615+78.45=2693.45

Answer:

Function 2 has a greater rate of change

Step-by-step explanation:

Function 1:

Number of Weeks (x)               1     2      3     4

Amount Remaining (dollars) (y) 40   36    32   28

We can find the slope by using

m = (y2-y1)/ (x2-x1)

  = (40-36)/ (1-2)

  = 4/-1

 = -4

Function 2:

y = −5x + 40

Using y = mx+b

The slope is -5

Function 2 has a greater rate of change

Answer:

Function 2, because Steve spends $5 each week and Ada spends $4 each week

Step-by-step explanation:

I took the test

Answer:

5 is the initial value

Step-by-step explanation:

From the table we can see that the values of y are increasing by 4

Lets use two points and find out slope

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

we use points (0,5) (1,9)

[tex]slope = \frac{9-5}{1-0}=4[/tex]

slope m= 5

Now we use y=mx+b equation

m= slope and b= y intercept, plug in (0,5)  and find out b

y=4x+b

5= 4(0) +b

so b= 5

b=5 is the initial value of the function

Answer:

5 is the initial value

Step-by-step explanation:

From the table we can see that the values of y are increasing by 4

Lets use two points and find out slope

formula of slope

slope=m=[tex]\frac{y2-y1}{x2-x1}[/tex]

putting points (0,5) (1,9) in equation of slope

m=[tex]\frac{9-5}{1-0}[/tex]

slope m= 4

we know y=mx+b

m= slope and b= y intercept, plug in (0,5)  and find out b

b=?

x=0

m=4

y=5

putting these values in y=mx+b

y=4x+b

5= 4(0) +b

so b= 5

b=5 is the initial value of the function