Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 4 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W –0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cupsss

Answer:

Step-by-step explanation:

a1=-8

a2=3

D=11

n=-8+11(n-1)

Answer:

(13.5,-46.5)

Step-by-step explanation:

Since equation 2 is missing y, then x is a constant

-2x + 61 = 34

-2x = 34 - 61

-2x = -27

x = 13.5

Then plug x into the 1st

5x + y = 21

5 * (13.5) + y = 21

67.5 + Y = 21

y = 21 - 67.5

y = -46.5

So the point satisfying both equations is (13.5,-46.5)

Answer:

G = 140

Step-by-step explanation:

Linear pairs add to 180

H+G = 180

40+G = 180

G = 180-40

G = 140

Answer:

123,000 grams

Step-by-step explanation:

1000 mg is equivalent to 1 gram.

Answer:

123000g

Step-by-step explanation:

1000mg=1g

123000000mg= xgrams

cross multiplying,

you'll have

[tex] \frac{123000000}{1000} = 123000[/tex]

Answer:

a. GBC, FCB, DCH

b. FCD+HCD=180

Step-by-step explanation:

A

B

The angles that are congruent to ABE are BCF, DCH, and CBG

Angles FCD and HCD lie on the same straight line. This means that the sum of both angles will sum up to 180degrees since the sum of angle of a straight line is 180degrees (supplementary). Hence the required equation will be:

<FCD + <HCD = 180

An angle is a point where two lines meet or intersect.

The angles that are congruent to ABE are BCF, DCH, and CBG

ABE = BCE (corresponding angle)

Since BCE = DCH (vertically opposite angles), hence:

ABE = DCH (vertically opposite angles)

Also, we can see that DCH = CBG (corresponding angles), hence:

ABE = CBG (corresponding angle)

b) From the given diagram, we can see that angles FCD and HCD lie on the same straight line. This means that the sum of both angles will sum up to 180degrees since the sum of angle of a straight line is 180degrees (supplementary). Hence the required equation will be:

<FCD + <HCD = 180

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Answer:

Step-by-step explanation:

This question is asking us to find where sin(2x + 30) has a sin of 1. If you look at the unit circle, 90 degrees has a sin of 1. Mathematically, it will be solved like this (begin by taking the inverse sin of both sides):

[tex]sin^{-1}[sin(2x+30)]=sin^{-1}(1)[/tex]

On the left, the inverse sin "undoes" or cancels the sin, leaving us with

2x + 30 = sin⁻¹(1)

The right side is asking us what angle has a sin of 1, which is 90. Sub that into the right side:

2x + 30 = 90 and

2x = 60 so

x = 30

You're welcome!

Answer:

The length of the third side is 7.81 inches and the perimeter of the triangle is about 18.81 inches

Step-by-step explanation:

Answer:

We say that two lines (on the same plane) are parallel to each other if they never intersect each other, ragardless of how far they are extended on either side. Pictorially, parallel lines run along each other like the tracks of a train.

Hope this helps <3

Hi

5x²-x-4 = 0  

Δ= (-1)² - 4*5*(-4)

Δ =  1 -4*-20

Δ = 1  +80

Δ = 81  

√Δ=  9

as Δ ≥ 0 , so 2 solutions exist in R

S1 is :    ( 1+9) /2*5  =   10/10 = 1

s2 =      (1 -9)/2*5 =  -8/10 = -4*2 /2*5  = -4/5

Corrects answers are  A  and  D

Answer:

A. -4/5 And D. 1

Step-by-step explanation:

i just got it right

If [tex]P(x) = p_nx^n + p_{n-1}x^{n-1}+\ldots+p_0[/tex] is divided by [tex](x-a)[/tex], then [tex]P(x) = (x-a) \cdot Q(x) + R(x)[/tex] for some polynomials [tex]Q,R[/tex]. Moreover, [tex]\deg R < 1[/tex] (because [tex]\deg (x-a) = 1[/tex]), so there exists  [tex]\alpha \in \mathbb{R}[/tex] such that [tex]R(x) = \alpha[/tex] for all [tex]x \in \mathbb{R}[/tex]. But if we calculate [tex]P(a)[/tex], it turns out that [tex]P(a) = (a-a)\cdot Q(a) + \alpha[/tex], so [tex]R(x) = \alpha = P(a)[/tex]. [tex]\blacksquare[/tex]

Answer: the answer is

the option

B) Amy walks a distance equal to the radius, and Fraser walks a distance equal to the diameter of the lawn.

Step-by-step explanation:

Answer:

y=(3/4)x+2

Step-by-step explanation:

write the equation in slope-intercept form: y=(3/4)x - 3

since it is parallel the slope is the same so we have y=(3/4)x + b

then plug in the point (-1) = (3/4)(-4) + b

-1 = -3 +b, b=2

y= (3/4)x + 2

Cost of 1 kg = $9

So, cost of 5 kg = $9 × 5 = $45

Answer:

Greatest number is 65432

Lowest number is 23456

Step-by-step explanation:

[tex]65432+23456=88888[/tex]

Answer:

C2 because 40+40+25 equals 105 not 110

Answer:

x=12

Step-by-step explanation:

Since the polygons are similar, we can write a ratio to solve

red side / yellow side

4      2

--- = ---

x       6

Using cross products

4*6 = 2x

24 = 2x

Divide by 2

24/2 =2x/2

12=x

Answer:

12

Step-by-step explanation:

When two shapes are similar, you need to find the scale factor of two existing corresponding sides.

For example, you can do 6 and 2.

Divide:

6/2 = 3

The scale factor: 3

Now multiply 4 and the scale factor (3):

4 × 3 = 12

So, x = 12.

Hope this helped.

Answer:

l = (p - 2w)/2

Step-by-step explanation:

Answer:

45. -7.1, -7 1/7

46. 3.7

Step-by-step explanation:

45. y < -7

Answer: -7.1, -7 1/7

46.

z > 3 2/3

Answer: 3.7

Answer:

y(x)=12*(5)^x

Step-by-step explanation:

y=ab^x, y(0)=12. 12=a.

y=12*b^x, y(2)=300. 12*b^2=300. b^2=25. b=5

Answer:

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

5/15,20,25

3,4,5

5*4*3*5

300

Answer:

x=35/78

Step-by-step explanation:

3/2x-11/5=(7/8)*(64/49)

3/2x-11/5=8/7

3/2x=8/7+11/5

3/2x=117/35

x=(35*3)/(2*117)

x=35/78

The square root of 100 is 10.

To check, solve 10 x 10.

Hope this helps! Please mark me as brainliest!

Have a great day!

Answer:

(a-b)(b-c)(a-c)

Step-by-step explanation:

a^2(b - c) + b^2(c-a) + c^2(a - b)

= a^2b - a^2c + b^2c - b^2a + c^2a-c^2b

=a^2b - b^2a - a^2c + b^2c + c^2a -c^2b

= ab(a - b) - c(a^2 - b^2) +c^2(a - b)

=ab(a - b) -c(a - b)(a + b) +c^2(a - b)

=(a - b)(ab - c(a + b) +c^2)

=(a - b)(ab - cb -ca + c^2)

= (a - b)(b(a-c) -c(a-c))

=(a-b)(b-c)(a-c)

Answer:

GH = 8.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan J = opp side / adj side

tan J = HG / HJ

tan 40 = GH / 10

10 tan 40 = GH

8.39099=GH

Rounding to the nearest tenth

GH = 8.4

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through two points, (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁).

Also, for a given line:

y = m*x + s

A perpendicular line to that one must have a slope:

a = -(1/m)

And the intersection between two perpendicular lines forms four 90° angles.

So first, we need to find the slope of the line that passes through A and B.

A = (-3, 3)

B = (-1, -1)

Then the slope of the line is:

a = (-1 - 3)/(-1 - (-3)) = -4/2 = -2

a = -2

The slope of a perpendicular line should be:

slope = -(1/a) = -(1/-2) = 1/2

Then the perpendicular line will be something like:

y = (1/2)*x + b

To find the value of b, we can use the other restriction.

This line needs to pass through point C.

And we can see that point C is:

C = (1, 2)

This means that when x is equal to 1, y must be equal to 2.

Then replacing these in the above equation we get:

2 = (1/2)*1 + b

2 = 1/2 + b

2 - 1/2 = 4/2 - 1/2 = 3/2 = b

Then our equation is:

y = (1/2)*x+ 3/2

The graph of this line can be seen in the image below, the green line is the line that we found.

If you want to read more about linear relations, you can see:

https://brainly.com/question/19586594

Answer:

Step-by-step explanation:

Explanation:

For any 30-60-90 triangle, the short leg is half of the hypotenuse. The short leg is opposite the smallest angle 30 degrees.

So this means n = 10/2 = 5

Because n = 5, there's only one answer choice that fits and it's choice C.