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Answer:   y > -1.5 which is the same as y > -3/2

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Explanation:

As x goes off to negative infinity, the term 3^x gets closer to 0.

So the expression 0.5*(3^x - 3) approaches 0.5*(0-3) = 0.5*(-3) = -1.5 = -3/2

The y value will never actually get to -1.5 because 3^x never actually reaches 0. It only gets closer and closer.

So the range is the set of possible y outputs such that y > -1.5 or y > -3/2

This means the horizontal asymptote is y = -3/2 or y = -1.5 which is the horizontal "electric fence" of sorts that the function curve gets closer to, but never touches.

Answer:

The function is non-proportional.

Step-by-step explanation:

If the function was proportional, when the number of hours spent riding the bicycle is equal to 0, the total cost of renting the bicycle would also be 0. In other words, the function would be proportional if y=0 when x=0. However, this is not the case.

[tex]y=15x+10[/tex]

Plug 0 into the equation as x

[tex]y=15(0)+10\\y=10[/tex]

When 1 bicycle has been rented for 0 hours, the customer still has to pay 10 dollars just for renting it. When x=0, y=10. This means that the function is non-proportional.

I hope this helps!

Answer:

I hope this makes sense, sorry for the lack of proofs.

Step-by-step explanation:

It is given that S is the midpoint of line QT. The definition of a midpoint is that it bisects the line it is on. So, line QS and line TS are congruent, or the same.

Now, we also know that line QR and line TU are parallel. Because they are parallel, it means that they form congruent corners with lines QS and TS..I think the proof here is "angles opposite to congruent sides are congruent in a triangle." But I'm not sure if this is right. Anyways, this means angles RQS and UTS are congruent.

There's also some proof that when two lines cross, the opposite angles are congruent. This means that angles TSU and QSR are congruent.

Therefore, by ASA (angle-side-angle) ΔQRS ≅ ΔTUS.

Answer: -19x + 26y - 16

Step-by-step explanation:

Combine like terms:

= -4x + 3y - 6 -15x + 23y - 10

= -4x - 15x + 3y + 23y - 6 - 10

Simplifying the expression:

= -4x - 15x + 3y + 23y - 6 - 10

= -19x + 26y - 16

Answer:

41 kg of apples would cost $82.

Step-by-step explanation:

41 kg divided by 7 kg is 5.85714285714. 5.85714285714 multiplied by $14 is $82.

Answer:

1/3

Step-by-step explanation:

3/5 × 5/9 is 15/45 but simplified it is 1/3

Answer:

1/3

Step-by-step explanation:

3/5×5/9=?

      |

3/5×5/9= 15/45

      |

15/45 divided by 15= 1/3

      |

Therefore 3/5x5/9=1/3

Answer:

a

Step-by-step explanation:

irration minus rathional is a irrational number

Answer:

85 is the answer

Step-by-step explanation:

byeeeeee

Answer:

(f ￮ g)(- 64) = - 8

Step-by-step explanation:

Evaluate g(- 64) by substituting x = - 64 into g(x), then substitute the value obtained into f(x) , that is

g(- 64) = [tex]\sqrt[3]{-64}[/tex] + 1 = - 4 + 1 = - 3 , then

f(- 3) = (- 3 + 1)³ = (- 2)³ = - 8

Given that,

Length of a chord = 28 inches

Radius of the circle = 50 inches

To find,

The distance the chord from the center of the circle.

Solution,

Let the distance from the chord to the centre of circle is x.

It is denoted by OM.

Using Pythagoras theorem to find it.

[tex]50^2=28^2+x^2\\\\x=\sqrt{50^2-28^2} \\\\x=41.42\ \text{inches}[/tex]

So, the distance from the chord to the centre of circle 41.42 inches

Answer:

The answer is 30 :)

Step-by-step explanation:

I had this question on khan academy

have a good day and stay safe!

The value of expression at x = 3 is,

⇒ 30

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 6² + x - x²

Now, We can simplify as;

⇒ 6² + x - x²

⇒ 36 + x - x²

Put x = 3;

⇒ 36 + 3 - 3²

⇒ 36 + 3 - 9

⇒ 36 - 6

⇒ 30

Thus, The value of expression at x = 3 is,

⇒ 30

Learn more about the mathematical expression visit:

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the process by which green plants and some other organisms use sunlight to synthesize nutrients from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a by-product.

a. The circumference of Track 1 is  376.8 feet.

b. The circumference of Track 2 is  533.8 feet.

c. . The circumference of Track 3 is  690.8 feet.

The circular space Driver’s Delight has of 150 feet radius will have a circumference of  471 feet.

The circumference is the distance around the circle and he formula to calculate is 2πr, where r is the radius.

Driver’s Delight has 3 circular tracks for go-carting.

Track 1 has a radius of 60 feet therefore the circumference of this circular track will be,

Track₁ circumference = (2πr).

= (2×3.14×60) feet.

= 376.8 feet.

Track 2 has a radius of 85 feet therefore the circumference of this circular track will be,

Track₂ circumference = (2πr).

= (2×3.14×85) feet.

= 533.8 feet.

Track 3 has a radius of 110 feet therefore the circumference of this track will be,

Track₃ circumference = (2πr).

= (2×3.14×110) feet.

= 690.8 feet.

They also have a circular space of 150 feet there the circumference of this circular space will also be (2πr). And we know Diameter = Twice of radius.

So, we just have to multiply the diameter by π which has an approximate value of 3.14.

So, the circumference of this circular space is

= 150×π feet.

= 150×3.14 feet.

= 471 feet.

learn more about circumference here :

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Answer:

B

Step-by-step explanation:

12x = 72

x = 6

12 x 6 = 72

Answer:

it would be b.

Step-by-step explanation:

if u plug a number into the x spot it would be 12 x 6 = 72

Answer:

i think it's A but don't quote me on it

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

(10)^2 - (6)^2 = 64

Square root 64 = 8

Ans

$12.5/1 day

Step-by-step explanation:

Just cause

Answer:

y + 7 = x

Step-by-step explanation:

Answer:

36 inches²

Step-by-step explanation:

area of a triangle = length x base x ½

= 8 × 8 × ½

= 36in²

Answer:

10 % of the total time will be saved on the new route with the new speed.

Step-by-step explanation:

Let x miles  be the old route. Then the new route would be 1.26 x miles

Let y be the speed on the old route . Then the speed on the new route would be 1.4 y .

And let t be the time on the old route

Speed = Distance / Time

or

Time = Distance / Speed

t= x/y

     Time for the new route   = 1.26x/ 1.4y= 0.9 t

0.9 t means 90% of the old time will be required to cover 1.26x  miles with 1.4 y speed.

And 10 % of the total time will be saved on the new route with the new speed.

Answer:

(a) the cost per pint = $4 per pint

(b) the number of pints per dollar = 0.25 pints per dollar

(c) the number of pints you can afford for $20.00 = 5 pints of raspberries

(d) the cost of 8 pints of raspberries = $32

Step-by-step explanation:

Given;

cost of 3 pints of raspberries = $12.00

(a) the cost per pint

[tex]= \frac{\$12}{3 \ pints} = \$4 \ \ per \ pints[/tex]

(b) the number of pints per dollar

[tex]= \frac{ 3 \ pints}{\$12 } = \frac{3 \times\frac{1}{12} }{12 \times\frac{1}{12} } = \frac{\frac{1}{4} \ pints }{1\$} = \frac{0.25 \ pints}{1 \$} = 0.25 \ pints \ per \ dollar[/tex]

(c) the number of pints you can afford for $20.00

= (0.25 pints per dollar) x ($20.00) = 5 pints of raspberries

(d) the cost of 8 pints of raspberries

= ($4 per pints) x (8 pints) = $32

Answer:

compound

Step-by-step explanation:

it uses a comma and the conjunction but. so it is seen to be a compound sentence

1) equation: f(x) = 6e^(ln(⅓) • x) or 6(10)^(log(1/3) • x)

table:

x | y

-1 20

0 6

1 2

2) is cut off, I can't see the rest of the graph.

you already know i gotchu :)

Answer: u = 5

Step-by-step explanation:

first, i moved the terms.

-4u + 10u = 37 - 7

then, i collected the like terms and calculated them.

6u = 30

finally, i divided both sides.

u = 5

Answer:  0.714286

turn 7/10 into .7 and divide normally

Answer: 7a

Step-by-step explanation: Since they are like terms, you can just add or subtract them.

4a - 5a = -1a

2a + 6a = 8a

-1a + 8a = 7a

Answer:

-1

Step-by-step explanation:

This is the slope because x is the slope, and if there is no number in front of x then x is 1. There is also a negative in front of x which means the answer is -1.  

The slope of the equation y = -x + 7 equals -1.

Answer:

[tex]\bold{\frac{1}{6}}[/tex] of the bottle was used

Step-by-step explanation:

Amount of cleaning solution present in spray bottle = [tex]\frac{2}3[/tex] of the bottle

Amount of cleaning solution present in the spray bottle used = [tex]\frac{1}4[/tex] of the cleaning solution present initially

To find:

How much of the bottle was used?

Solution:

Here, we need to find how much amount of the cleaning solution spray was used from the complete bottle.

Amount of spray used = [tex]\frac{1}{4}\times \frac{2}{3}[/tex] of the cleaning solution = [tex]\bold{\frac{1}{6}}[/tex] of the cleaning solution.

Therefore, the answer is:

[tex]\bold{\frac{1}{6}}[/tex] of the bottle was used

Answer:

a. -⅓

b. 3

c. y = 3x - 10

Step-by-step explanation:

a. Gradient of line AB:

A(1, 3), B(7, 1)

[tex] Gradient = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{7 - 1} = \frac{-2}{6} = -\frac{1}{3} [/tex]

Gradient (m) = -⅓

b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.

Thus, the negative reciprocal of -⅓ = 3

Gradient of the line perpendicular to line AB = 3

c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:

We can write the equation using the point-slope form equation, y - b = m(x - a), where,

(a, b) represents a point on the line, and,

m = gradient/slope

We know that the gradient/slope (m) = 3

Also, a point, (a, b) = (4, 2).

Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)

Thus:

y - 2 = 3(x - 4)

y - 2 = 3x - 12

Add 2 to both sides

y = 3x - 12 + 2

y = 3x - 10