A line passes through the point (-2, -9) and has a slope of 8

Answer:

very very far indead he ran and ran without stopping

Answer:

a)  599 feet

Step-by-step explanation:

** As the measure of distance is in feet, we must use the value of gravity in ft/s² **

Constant Acceleration Equations (in ft)

Assuming that the projectile is fired at an angle of 12° above the horizontal.

Consider the vertical and horizontal motion separately.

Vertical motion

First, find time by resolving vertically, taking up as positive and
g = 32 ft/s²

[tex]\begin{aligned}\textsf{Using}\quad s & =ut+\dfrac{1}{2}at^2\\\implies 0 & = 217 \sin 12^{\circ}t+\dfrac{1}{2}(-32)t^2\\0 & = 217 \sin 12^{\circ}t-16t^2\\t(16t-217 \sin 12^{\circ}) & = 0\\16t & = 217 \sin 12^{\circ}\\t & = \dfrac{217 \sin 12^{\circ}}{16}\\t & = 2.819802307...\: \sf s\end{aligned}[/tex]

Horizontal motion

Resolving horizontally, taking right as positive:

(The horizontal component of velocity is constant, as there is no acceleration horizontally)

[tex]\begin{aligned}\textsf{Using}\quad s & =ut+\dfrac{1}{2}at^2\\\implies s & = (217 \cos 12^{\circ})(2.819802307...)+\dfrac{1}{2}(0)t^2\\& =598.5256808...\end{aligned}[/tex]

Therefore, the horizontal distance is 599 ft (nearest foot)

Answer:

  (x +2.5)² +(y -2)² = 6.25

Step-by-step explanation:

A radius of a circle is perpendicular to the tangent line at the point of tangency. This means the center of the circle lies on the horizontal line through the point (0, 2), which is on the vertical tangent x=0 (the y-axis).

The center of a circle lies on the perpendicular bisector of any chord, so the perpendicular bisector of the given two points will pass through the circle center.

__

The slope of the chord between the given points is found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (2 -0)/(0 -(-1)) = 2   ⇒   perpendicular has slope -1/2

The midpoint of the chord is ...

  M = (A +B)/2 = ((0, 2) +(-1, 0))/2 = (-1, 2)/2 = (-1/2, 1)

The point-slope form of the perpendicular through the midpoint of the chord is ...

  y -1 = -1/2(x -(-1/2))

__

For y = 2, the x-value is ...

  2 -1 = -1/2(x +1/2)

  -2 = x +1/2 . . . . . . multiply by -2

  -2.5 = x . . . . . . . subtract 1/2

The circle center is (-2.5, 2), and the radius is 2.5 (distance from center to y-axis).

__

The equation can be written as ...

  (x -h)² +(y -k)² = r² . . . . . . circle with center (h, k) and radius r

  (x -(-2.5))² +(y -2)² = 2.5²

  (x +2.5)² +(y -2)² = 6.25

Answer:

a⁴ - 81

Step-by-step explanation:

Identity applied :

(a + b)(a - b) = a² - b²

Simplifying :

Answer:

A

Step-by-step explanation:

Please see attached, I have colour coded for your convenience

Answer:

[tex]b = 2[/tex].

Step-by-step explanation:

By the factor theorem, if a monomial of the form [tex](x - a)[/tex] is a factor of the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex], then substituting in [tex]x = a[/tex] would set this polynomial to [tex]0[/tex].

Notice that in the factor theorem, the coefficient of [tex]x[/tex] in [tex](x - a)[/tex] is [tex]1[/tex], and the sign in front of the constant [tex]a[/tex] is a minus sign. Rewrite the given factor [tex](3\, x + 2)[/tex] in this form to find the value of [tex]a\![/tex]:

[tex]\begin{aligned}& (3\, x + 2) \\ =\; & 3\, (x + (2/3)) \\ =\; & 3\, (x - \underbrace{(-2/3)}_{a}) \end{aligned}[/tex].

Thus, [tex]x = (-2/3)[/tex] should set the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex] to [tex]0[/tex]:

[tex]\begin{aligned} & (3\, x^{3} + b\, x^{2} - 3\, x - 2) \\ =\; & 3\times (-2/3)^{3} + b\times (-2/3)^{2} - 3 \times (-2/3) - 2 \\ =\; & -3\times (2/3)^{3} + b\times (2/3)^{2} + 3 \times (2/3) - 2 \\ =\; & -\frac{8}{9} + \frac{4\, b}{9} + 2 - 2 \\ =\; & \frac{-8 + 4\, b}{9}\end{aligned}[/tex].

Set this expression to [tex]0[/tex] and solve for [tex]b[/tex]:

[tex]\displaystyle \frac{-8 + 4\, b}{9} = 0[/tex].

[tex]b = 2[/tex].

Answer:

130 cm³

Step-by-step explanation:

Volume of the pyramid = 1/3 × base area × height

Calculating base area;

Area = length × width

= 8 × 7

= 56 cm²

Now, Volume = ⅓ × 56 × 7

= ⅓ × 392

= 130.6 cm³.

Answer:

  $373.50

Step-by-step explanation:

Her monthly maximum obligation should be 15% of Bridgette's take-home pay of $2490.

  $2490×15% = $373.50

Probability that the next person will purchase more than one costume as a fraction in simplest form is; 11/113

We are given the data for number of people who visited the website and the number of costumes purchased in a single day as;

Number of visitors that purchased no costume = 27 visitors

Number of visitors that purchased exactly one costume = 75

Number of visitors that purchased more than one costume = 11

Total number of visitors = 27 + 75 + 11 = 113

Thus;

Probability that the next person will purchase more than one costume as a fraction in simplest form is;

P(purchase more than one costume) = 11/113

Read more about Probability at; https://brainly.com/question/251701

#SPJ1

Answer:

Step-by-step explanation:

In the question, it is given that a right cone has a diameter of 12 units and volume of 168π units³ and we have to find the height of the cone.

[tex] \: [/tex]

To Find the height of the cone, we must know this formula :

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi r^2h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]

Where,

Now, we will substitute the values in the formula :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times (6)^2 \times h = 168 \pi}}}}}}} \\ \\[/tex]

Cancelling π from both sides we get :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times 36 \times h = 168 \cancel\pi}}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \ \times 36 \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{36}{3} \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { 12 \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { h = \frac{168}{12} }}}}}}} \\ \\[/tex]

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h ={14 }}}}}}}} \\ \\[/tex]

Therefore,

Answer:

Which three questions?

Step-by-step explanation:

I've answered this first question, I guess I need two more...

Answer:

prior to

Step-by-step explanation:

The final matrix will be as follows   [tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns in mathematics.

The calculation of the given matrix is as follows:-

[tex]\rm D-C= \left[\begin{array}{ccc}13&2&-5\\6&-4&0\\\end{array}\right] - \left[\begin{array}{ccc}1&4&-8\\3&-5&2\\\end{array}\right] \\[/tex]

[tex]\rm D-C= \left[\begin{array}{ccc}(13-1)&(2-4)&(-5+8)\\(6-3)&(-4+5)&(0-2)\\\end{array}\right][/tex]

[tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

Hence the final matrix will be as follows   [tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

To know more about matrix follow

https://brainly.com/question/94574

#SPJ1

Answer:

Step-by-step explanation:

Volume

V = w h l

V = 2*15*13

V = 390 ft^3

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

Surface area

SA = b*h

SA = 15*13

SA = 195

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

b) Surface area

C) Volume

Answer:

21.54

Step-by-step explanation:

27.24 - 5.7

= 21.54

So, basically this is the formula to calculate weight mean.

Thank you.

Answer:

D. Coal.

Step-by-step explanation:

Doesn’t really affect the earth in any way.

Answer:

Domain: all real numbers (all reals)

Range: y> OR EQUAL TO -2

Step-by-step explanation:

Hope this helps! ;-)

Answer:

x + 7 = 5

Step-by-step explanation:

I think this should be an equation I’m in 7th and I am learning these again so it should be an equation.

original equation

[tex]v=\frac{d}{t}[/tex]

solve for t

[tex]t=\frac{d}{v}\\\\t=\frac{100}{6.25} \\\\t=16[/tex]

It took Dita 16 seconds to finish the race

Answer:

a

Step-by-step explanation:

aaaaaaa

its a

16 seconds

Answer:

true

Step-by-step explanation:

Examples :

180 = 5 × 2² × 3²

Then

The number 180 has perfect square factors which are 2 and 3

Then

The number √180 can be simplified because:

[tex]\sqrt{180} =\sqrt{5\times 2^{2}\times 3^{2}}[/tex]

        [tex]=\sqrt{5\times \left( 2\times 3\right)^{2} }[/tex]

        [tex]=\sqrt{5\times \left( 6\right)^{2} }[/tex]

        [tex]=\sqrt{5} \times \sqrt{6^{2}}[/tex]

        [tex]=6\sqrt{5}[/tex]

On the other hand :

10 = 5 × 2

Then

The number 10 has no perfect square factors

Then

The number √10 cannot be simplified because:

[tex]\sqrt{10} =\sqrt{5\times 2} =\sqrt{5} \times \sqrt{2}[/tex]

[tex]\text{and} \ \sqrt{5} \times \sqrt{2} \ \text{is not a simplified expression of} \ \sqrt{10} \ \\\text{,in fact it is more complicated than} \ \sqrt{10}[/tex]

Answer:

C) Revise

Step-by-step explanation:

A final draft needs to be revised before it can be published

The probability when x is greater than 120 is 0.0367. Then the correct option is D.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The mean is 95 and the standard deviation is 14. Then the probability when x > 120 will be

The z-score will be

z = (120 - 95)/ 14

z = 1.7857

Then the probability will be

P(x > 120) = P(z > 1.7857)

P(x > 120) = 1 - P(x<120)

P(x > 120) = 1 - 0.96293

P(x > 120) = 0.0367

More about the normal distribution link is given below.

https://brainly.com/question/12421652

#SPJ1

Answer:

0.0109056604

that is the answer, I used a calculator

Answer: Minimum: 0

Quartile Q1: 22.5

Median: 50

Quartile Q3: 77.5

Maximum: 100

Step-by-step explanation:

Answer:

Y less than or equal to zero

Step-by-step explanation:

The graph shows that its moving downwards, therefore the Y value is decreasing..

The area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The length of the rectangle = [tex]64\dfrac{5}{7}[/tex]  m = 453/7 m

The breadth of the rectangle = [tex]23\dfrac{3}{8}[/tex] m = 187/8 m

The area of the rectangle hall:

= (453/7)(187/8)  = 1512.69 ≈ 1512.7square m

Thus, the area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ1