The function f is defined by f(x) = x^2 + 3x -10 , if f(x + 5) = x^2 + kx + 30, k=

It will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet option third is correct.

It is defined as the equation by which we can find the motion of a physical particle with respect to time. It is the representation of physical entity movement in a mathematical function.

We have:

The height of the Sharon from the diving board = 18 feet

The initial upward velocity of the Sharon = 4 ft/s

The height of the Megan from the ground = 5 feet

The initial upward velocity of the beach ball = 16 ft/s

We know the equation of motion is given by:

[tex]\rm h(t) = x + ut+\frac{1}{2} gt^2[/tex]

Put x = 18 feet and u = 4 ft/s in the above equation, we get:

[tex]\rm h(t) = 18 + 4t+\frac{1}{2} \times9.8t^2[/tex] ....(1)     [g = 9.8 m/s²]

Put x = 5 feet and u = 16 ft/s in the equation of motion, we get:

[tex]\rm h(t) = 5 + 16t+\frac{1}{2} \times9.8t^2[/tex]  ....(2)

Equate the equation (1) and equation (2), we get

[tex]\rm 18 + 4t+\frac{1}{2} \times9.8t^2= 5 + 16t+\frac{1}{2} \times9.8t^2\\[/tex]

18 + 4t = 5 + 16t

12t = 13

t = 1.08 seconds

Thus, it will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet.

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Answer:

768

Step-by-step explanation:

I hope you mean this, if you don't say so

So

here

If hours be x

Question asked to plot a equation to calculate profit so all the expenses or loss should be deducted,here the constant loss is of 150 so 150 should be subtracted

The equation in slope intercept form

Answer:

d)  y = 30x - 150

Step-by-step explanation:

Let x = number of hours worked

Let y = profit earned

Profit is the amount left after expenses are deducted.

Given:

⇒ y = 30x

Given:

This is Terry's expenses, so we must deduct this amount from the amount he earns walking the dogs to calculate the final profit:

⇒ y = 30x - 150

The quotient of the provided division in which binomial is divided by a quadratic equation is x+2.

Quotient is the resultant number which is obtained by dividing a number with another. Let a number a is divided by number b. Then the quotient of these two number will be,

[tex]q=\dfrac{a}{b}[/tex]

Here, (a, b) are the real numbers.

The given division expression is,

[tex]\dfrac{x^2+3x+2}{x+1}[/tex]

Let the quotient of this division problem is f(x). Thus,

[tex]f(x)=\dfrac{x^2+3x+2}{x+1}[/tex]

Factor the numerator expression as,

[tex]f(x)=\dfrac{x^2+2x+x+2}{x+1}\\f(x)=\dfrac{x(x+2)+1(x+2)}{x+1}\\f(x)=\dfrac{(x+2)(x+1)}{x+1}\\f(x)={x+2}[/tex]

Thus, the quotient of the provided division in which binomial is divided by a quadratic equation is x+2.

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Answer:

its A. on edge 2023

Step-by-step explanation:

Answer:

√3

Step-by-step explanation:

To recall trigonometric ratios, there is a special acronym known as sohcahtoa which stands for

Finding the angle [tex]\theta[/tex]

We are given that,

[tex] \displaystyle \sin( \theta) = \frac{ \sqrt{3} }{2} [/tex]

To find the angle [tex]\theta[/tex] , take inverse of sin of both sides,

[tex] \displaystyle { \sin}^{ - 1}( \sin( \theta) )= { \sin}^{ - 1} \bigg(\frac{ \sqrt{3} }{2} \bigg )[/tex]

with the help of unit circle,we acquire:

[tex] \displaystyle \boxed{\theta= {60}^{ \circ} }[/tex]

Finding [tex]\tan\theta[/tex]

simply plug in the value of theta:

[tex] \tan( {60}^{ \circ} ) [/tex]

using unit circle,we get:

[tex] \implies \tan( {60}^{ \circ} ) = \boxed{\sqrt{3} }[/tex]

and we're done!

Let's solve

[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{\sqrt{3}}{2}[/tex]

[tex]\\ \rm\Rrightarrow \theta=sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right)[/tex]

[tex]\\ \rm\Rrightarrow \theta=\dfrac{\pi}{3}[/tex]

Now

[tex]\\ \rm\Rrightarrow tan\theta=tan\dfrac{\pi}{3}[/tex]

[tex]\\ \rm\Rrightarrow tan\theta=\sqrt{3}[/tex]

Answer:

1

Step-by-step explanation:

in this constellation the upper left vertex corresponds to the bottom right vertex. and the upper right vertex to the bottom left vertex.

so, the side x corresponds to the side x+2.

and, of course, the top side corresponds to the bottom side.

going from the small to the large triangle the scaling factor is 6/2 = 3/1 = 3.

therefore

3 × x = x + 2

3x = x + 2

2x = 2

x = 1

Answer:

2√5.

Step-by-step explanation:

Using the Pythagoras theorem

x^2 = (√10)^2  + (√10)^2

x^2 = 10 + 10

x^2 = 20

x = √20

= √4*√5

= 2√5

Answer: 1) 4%/40% 2)4%/40% 3)5%/50% 4)4%/40%

Step-by-step explanation:

i think those are the answers

Answer:

4

Step-by-step explanation:

All you need to do is plug in each value for x & then solve the equation to see if it equals 7.  When a number, like 2, is next to an x you multiply the two of them.  So when you substitute a number for x, you multiply it by the 2.

2(3)-1= 5

2(4)-1= 7

2(5)-1=9

The bottom figure, answer A

D has infinite lines of symmetry

B can be split from top left to bottom right, as well as from the top right corner to the bottom left corner

C can be split from left to right and top to bottom

A can only be split from left to right, as the sides aren’t equal to each other

Answer:

ABD

Step-by-step explanation:

Answer: x = 1/4

Step-by-step explanation:

Lo primero que harías es restar 7 de ambos lados de la ecuación debido a tu propiedad de igualdad, que te permite hacer esto.

24x+7=13

      -7   -7

24x=6

Ahora lo que harás es dividir ambos lados entre 24 para que puedas aislar x.

24x=6

/24    /24

x=6/24

Finalmente, puedes simplificar la fracción dividiendo el numerador y el denominador por 6.

x=6/6  /  24/6

x=1/4

AREA Fomula: A = πr²

where:

Find the Area of a 6 cm radius.

Solved:

CIRCUMFERENCE Formula: 2πr

where:

Find the Circumference of a 6 cm radius

Solved:

Answer:

A third degree or cubic polynomial with three terms. The constant term is -1/7, the leading term is -10x³ and the leading coefficient is -10

Answer:

12 ft ^3

Step-by-step explanation:

I assume you are looking ofr the volume of this pyramid

V = 1/3 base area * height

base area = area of 3-4-5 triangle =  1/2 * 3 * 4 = 6   ft^2

so Volume is :

1/3  * 6 * 6 = 12 ft^3

Answer:

y = 9x

Step-by-step explanation:

Answer:

4.5x          OR           9/2x

Step-by-step explanation:

We know this is a lineasr equation isnce it is a straight line and goes by a slope factor.

We know that for every change in 9 on the y axis, there is a change of two on the x- axis. This slope is now 9/2

The equation can be 9/2x OR 4.5x depending on whether your teacher will accept decimal answers or fractional answers.

Answer: 4.71

Step-by-step explanation:

The circle can be illustrated by its equation, and the equation that represents the circle is (x + 4)² + (y - 9)² = 5²

The center of the circle is given as:

Center, (a,b) = (-4,9)

The diameter is given as:

d = 10

Calculate the radius (r)

r = 10/2 = 5

The circle equation is then calculated using:

(x - a)² + (y - b)² = r²

So, we have:

(x + 4)² + (y - 9)² = 5²

Hence, the equation that represents the circle is (x + 4)² + (y - 9)² = 5²

Read more about circle equations at:

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Answer:

B on edge

Step-by-step explanation:

(x + 4)^2 + (y – 9)^2 = 25

Answer:

4:10

simplify = 2:5

Answer:

5 pounds

Step-by-step explanation:

Answer: 1. Not dependent 2.2.Not dependent 3. Not dependent 4. Not dependent 5. Choosing marble without replacement is dependent

Step-by-step explanation: if you concert the decimals to fractions in each question, they are not related

Answer:

60.9 mi

Step-by-step explanation:

Circumference of circle:

diameter = 19.4 mi

Circumference of circle = πd

                                        = 3.14 * 19.4

                                        = 60.9 mi

Answer:

C. The principal randomly selects homeroom classes and surveys each student in the chosen classes.

Step-by-step explanation:

Middle school is 6-8th. Surveying only the eighth-grade students won't give a representative sample of the whole school only the eighth-graders. Option A is incorrect.

Surveying only the students in detention represents a very small amount of students compared to the school, therefore it is not a representative sample. Option B is incorrect.

Yet again, the students in the math club is a small amount of students compared to the school. It does not represent the entire, or majority of the population. Option D is incorrect.

Picking students from homeroom classes and surveying each will give a wider variation of opinions from each grade and therefore a representative sample. Option C is the correct answer.

Answer:

C

Step-by-step explanation:

I just did the quiz and it was correct

Answer:

G

Step-by-step explanation:

really look at the position of point A on the number line.

it is a little bit to the right of -2, but clearly to the left of -1 and especially 0.

so, A must be negative.

that eliminates already H and J.

remember, that e.g. -2 < -1.

so, seemingly "adding" something to the description of a value of a negative number makes that negative number even smaller.

-1 7/8 is for example NOT the same as -1 + 7/8.

it is the same as

-1 - 7/8 = -1 7/8

so, -1 7/8 is indeed smaller than -1.

but it is still larger than -2 (e.g -1 8/8 = -2).

therefore, only G makes sense.

Answer:

63.59 in²

Step-by-step explanation:

The formula to find the area of a square: a², where a is the side.

The formula to find the area of a circle: πr², where r is the radius (diameter ÷ 2), and the pi is alterable (3.14 or 3.142 or 22/7).

1) Find the diameter of the circle. The side of a square is the diameter.

a²

a = √81

a = 9

2) Plug the values into the formula of the area of a circle. 9 ÷ 2 = 4.5 (radius).

= 3.14 x 4.5²

= 3.14 x 20.25

= 63.585

3) Round off the result to the nearest hundredth.

= 63.59

The largest circle possible from the square piece of yellow felt material to create a sun for her art project is of area 63.585 square inches.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface

According to the question

Square piece of yellow felt that has an area = 81 square inches

Now ,

Area of square of yellow felt =  81 square inches

⇒     [tex]Side^{2} = 81[/tex]

⇒      Side = ± 9      (where -ve 9 cannot be side )

⇒      Side =  9      

The largest circle possible from the material is

where, side of square = diameter of circle  ( figure attached )

        ⇒  9   = diameter of circle

       ⇒   9 = 2r

       ⇒   [tex]\frac{9}{2}[/tex] = r or  r = 4.5

Area of circle = [tex]\pi r^{2}[/tex]

                      =  3.14 * 4.5 * 4.5

                     = 63.585 square inches.

Hence, Area of the largest circle cut from the  square piece is of 63.585 square inches.

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# SPJ2

Answer:

V ≈ 258 ft³

Step-by-step explanation:

I given the diameter d= 7.9 ft so the radius is r = d/2 = 7.9/2  ft

Volume of a sphere is

V = (4/3) π·r³ = (4/3) · π · (7.9/2)³ = 258.1546167 ft³