A particle moves along the x-axis so that at time t ≥ 0 its position is given by x(t) = 2t3 - 21t2 + 72t - 53. At what time t is the particle at rest?

I think the y=ab^x goes with the first graph and the y=logbc goes with the second

Step-by-step explanation:

pictures

Answer:

y = 1/2x - 8

Step-by-step explanation:

Assuming that they want the equation in slope intercept form we would use the following form: y = mx + b

where m = slope and b = y intercept.

We are given the slope and a point on the line. We need to find the y intercept. We can do this by plugging in what we are given and then solving for b.

y = mx + b

slope (m) = 1/2

x value of given point (x) = 8

y value of given point (y) = -4

- plug in these values -

-4 = (1/2)(8) + b

now solve for b

multiply 1/2 and 8

-4 = 4 + b

subtract 4 from both sides

-8 = b

So the y intercept (b) is -8

We now plug in the slope and y intercept into slope intercept form

y = mx + b

m = 1/2 and b = -8

y = 1/2x - 8 is the equation of the line that passes through the point (8,-4) and has a slope of 1/2

For more validation refer to the attached image.

[tex]\text{Given that,}\\\\(x_1,y_1) = (8,-4), ~~ \text{and slope, m} = \dfrac 12\\\\\text{Equation with given points,}\\\\y -y_1 = m(x-x_1)\\\\\implies y -(-4) = \dfrac 12 (x-8)\\\\\implies y+4 = \dfrac 12 x - 4\\\\\implies y= \dfrac 12x -4 -4 \\\\\implies y = \dfrac 12 x -8\\\\\implies y = \dfrac{x-16}2\\\\\implies 2y = x -16\\\\\implies x -2y = 16[/tex]

Answer:

$24.00

Step-by-step explanation:

8x3=24

Answer:

Step-by-step explanation:

∠1 and 85 are supplementary

m∠1 = 180 - 85 = 95°

Answer:

45

Step-by-step explanation:

20 / 9 = 2.222222222223

100 / 45 = 2.222222222223

9 is 45% of 20 and 45 is 45% of 100.

Answer:

752

Step-by-step explanation:

7/20 of 2880 = 1008

2/9 of 2880 = 640

1/6 of 2880 = 480

2880 - 1008 - 640 - 480 = 752

Answer:

D

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Range is all the set y values.

Answer:

See image

Step-by-step explanation:

The range is all of the y-values. Look at the points on the graph, and make a list of all the y's That will be the range.

Answer:

i haven't done this in years but i'm pretty sure -19 meters

Step-by-step explanation:

Answer:

[tex]x^{2} -49[/tex]

Step-by-step explanation:

Answer:

[tex](x-7)(x+7) =x^2 -7^2 = x^2 -49[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) 11 + 11

2) 17 - n

3) x^2

4) 3^3

5) 88 / 8

6) 6 + 11

7) the quotient of 35 and 5

8) the sum of 4 and 5

9) 10 squared

10) 3 less than x

13) p^3 + qp

2^3 + 4(2)

8 + 8 + 16

14) (y^3)z / 3

(5^3)3 / 3

125(3) / 3

375 / 3

125

15) 2 + (j - h)^2

2 + (5 - 3)^2

2 + (2)^2

2 + 4

6

Answer:

[tex] \frac{5(x + y)}{ - 8x} [/tex]

Step-by-step explanation:

quotient means division

numerator is the top

denominator is the bottom

product means multiply

sum means add

Answer:

Step-by-step explanation:

6x + 10 + 2x + 26 = 180

8x + 36 = 180

8x = 144

x = 18

Answer:

Step-by-step explanation:

Answer:

See image

Step-by-step explanation:

Look at the front side of the building. It's a triangle, with the height given. We can see a right triangle here which means we can use the Pythagorean theorem. a^2 + b^2 = c^2 (a and b are the shorter sides called legs and c is the longest side called the hypotenuse)

20^2 + 13^2 = c^2

400 + 169 = c^2

569 = c^2 square root both sides

Sqrt 569 is approximately 23.85 ft. This is the length from the roof peak down the front edge to the bottom front right corner in the image.

Now, if we consider the roof itself. That edge is now a leg (on the front face it was the hypotenuse). The other leg is the 35 ft width given. So we'll use pythagorean theorem again to find the diagonal

23.85^2 + 35^2 = c^2

568.8 + 1225 = c^2

1793.8 = c^2

Square root both sides of the equation.

Sqrt 1793.8 = c

42.35 ft = c

The diagonal of the roof is just over 42 feet, that is 42.35 feet.

According to the desired test, the hypothesis are given by:

D) H0: μ=210

Ha: μ ≠ 210

At the null hypothesis, it is tested if the population mean is of 210 lbs, that is:

[tex]H_0: \mu = 210[/tex]

At the alternative hypothesis, it is tested if the population mean differs from 210 lbs, that is:

[tex]H_a: \mu \neq 210[/tex]

Hence, the correct option is:

D) H0: μ=210

Ha: μ ≠ 210

A similar problem is given at https://brainly.com/question/25707631

Answer:

3

Step-by-step explanation:

6 have visited a zoo.

6 have visited a factory.

3 visited both.

Of the 6 who visited a zoo, 3 also visited a factory.

Of the 6 who visited a factory, 3 also visited a zoo.

Here is the list of students:

3 visited a zoo but not a factory.

3 visited a factory but not a zoo.

3 visited both.

Answer: 3

Answer:

between midnight and 3am i think

Step-by-step explanation:

Answer:

$319

Step-by-step explanation:

Usually, sales tax is proportional to the amount of the sale, so if the sales tax is a factor of 22/16 times the original tax, then the sale amount must be 22/16 times the original item cost:

 (22/16)·$232 = $319

Answer:

$2.72

Step-by-step explanation:

2.74x0.89=2.4475

0.8x0.34=0.272

2.447+0.272=2.719, rounded is 2.72

Answer:

just the first on. upper left corner

Answer:

51

Step-by-step explanation:

The answer would be 51 because the numbers behind the decimal are below 5

Answer:

51

Step-by-step explanation:

51.33333333 rounds to 51 because 3 is less than 5.

When rounding, always look at the number before the first number in front of the decimal. If it is more than 5, round up. If it is less than, round down.

Answer: For in the inequality to be true, X must be less than or equal to 1. That represented as an in equality is X < 1.

x<1 true

Step-by-step explanation:

3(1+x)<+6= 3×1+3×X<+6=3+3x<6 then3x=6-3 solution 3x=3 devide by 3 both sides the answer is x=1 hence x<1 verified

Answer:

Distributive Property

Step-by-step explanation (if you were to show the steps):

(x+2)(y+z)   (first expression)

xy + xz + 2y + 2z (Distributive Property of Multiplication)

yx + 2y + zx + 2z (use the Commutative Property of Addition and Commutative Property of Multiplication to group xy (also known as yx) and 2y together, and to group xz (also known as zx) and 2z together)

y(x + 2) + z(x + 2) (use factoring to get the rewritten expression at the end)

Answer:

Let's neaten up that equation a bit:

trapezoid area = height * (sum of the bases) / 2

height = 2 * area / (short base + long base)

height = 2 * 78 / (5 + 8)

height = 156 / 13

height = 12 inches

Source: https://www.1728.org/quadtrap.htm

Step-by-step explanation:

The formula for the height is h = (b1+b2)/2A and the height of the trapezoid is 12 inches

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.

The area of a trapezoid is expressed as;

A = 1/2( a +b) h

where a and b are the parallel sides and h is the height.

Making h the subject

(a+b)h = 2A

h = 2A/( a+b)

h = 2A( b1 + b2)

A = 78 in²

a = 5 in

b = 8 in

h = 2 × 78/( 8+5)

h = 156/13

h = 12 in

learn more about area of trapezoid from

https://brainly.com/question/1410008

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Answer:

A. x = 96 and y = 42

Step-by-step explanation:

The required measure of the angle x and y is given as x =92° and y = 42°. Option A is correct.

Given that,
Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle as shown in the accompanying diagram what are the values of x and y is to be determined.

A triangle with two sides and two congruent angles that are equal each other is called an isosceles triangle.

Here,
For an isosceles triangle,
The measure of the angle opposite to the equal side is equal, So
y = 42°

Now,
The sum of the angles in the triangle° is equal to 180,
x + y + 42 = 180
x + 42 + 42 = 180
x = 96

Thus, the required measure of the angle x and y is given as x =92° and y = 42°. Option A is correct.

Learn more about the isosceles triangle here: https://brainly.com/question/2456591

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Area

[tex]\\ \tt\longmapsto \dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

[tex]\\ \tt\longmapsto \dfrac{1}{2}|(-2)(3+5)+(4)(-5-1)+(-2)(1-3)|[/tex]

[tex]\\ \tt\longmapsto \dfrac{1}{2}|-16-24+4|[/tex]

[tex]\\ \tt\longmapsto \dfrac{1}{2}|-36|[/tex]

[tex]\\ \tt\longmapsto 18units^2[/tex]

Answer:

Maria

Step-by-step explanation:

Sean - 2 minutes (1 mile/minute)

Maria - 4 minutes (0.5 miles/minute)

David - 3 minutes (1 mile/minute)

Carrie - 2 minutes (0.5 miles/minute)

Answer:

254.34

Step-by-step explanation:

Diameter: 2×radius

Radius:Diameter÷2

Area: pi×radius²

18/2=9

Radius=9

pi=3.14

3.14×9²=254.34

The area is 254.34