Find the circumference of this circle.
Use 3.14 to approximate ™.
C = 2πr
14 ft
C = [?] ft
Entered

The zeros and the multiplicities of the polynomial are t = -7, t = -6 and t = -2 and 2, 3 and 6, respectively

The equation of the polynomial is given as

f(t) = -12(t+7)²(t+6)³(t+2)⁶

The multiplicities are the powers of the factors while the zeros are calculated by setting the factors to 0

So, we have

t + 7 = 0

t + 6 = 0

t + 2 = 0

Calculate the value of t

t = -7, t = -6 and t = -2

Hence the zeros are t = -7, t = -6 and t = -2

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According to the query that the function h is established, h(-3) = -1/2, h(2) = 4, and h(4) = -4/1 for all real integers.

An statement, rule, or law in mathematics that establishes the link between an independent variable and a predictor variables (the dependent variable). Equations may be found all around arithmetic, and they are essential for building physical connections in the sciences. A mappings between A and B will only be a function if every member in set A only has end and only 1 photo in set B. Where A & B even be two separate sets.

Have used the top form of h(x) for x = variables -3 and 4 (which deviate from 2):

[tex]\begin{aligned}& h(x)=-\frac{1}{2} x^2+4 \\& h(-3)=-\frac{1}{2}(-3)^2+4=-\frac{9}{2}+4=-\frac{9}{2}+\frac{4}{2}=-\frac{1}{2} \\& h(4)=-\frac{1}{2}(4)^2+4=-\frac{16}{2}+4=-\frac{16}{2}+\frac{4}{1}=-\frac{4}{1}\end{aligned}[/tex]

Alternatively, h(2) must be defined explicitly as stated in the function's second description (specific for when x equals 2). Thus, h(2) equals 4.

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Answer:6(a)+4(b)+9(c)

Step-by-step explanation:

Im pretty sure there was an equation that you did not put.

But the equal used to solve would be 6(a)+4(b)+9(c)

a= money earned pulling weeds

b=money earned raking leaves

c=money earned cutting grass.

Using tangent of the angle, the angle of elevation is 32.5 degrees

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

In this problem, we have to use the tangent of the angle since we know the opposite and adjacent sides

Tan θ = opposite / adjacent

tanθ = 222 / 348

tan θ = 0.6379

θ = tan⁻¹(0.6379)

θ = 32.5°

The angle of elevation is 32.5 degrees

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The solution for y in the inequality is (a) y ≥ 10

From the question, we have the following inequality expression that can be used in our computation:

42≤4.2y

Rewrite the expression properly

So, we have the following representation

42 ≤ 4.2y

Divide both sides of the inequality by 4.2

So, we have

42/4.2 ≤ 4.2y/4.2

Evaluate the quotients

So, we have the following representation

10 ≤ y

Rewrite the expression as

y ≥ 10

Hence, the solution is y ≥ 10

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Possible question

Solve for y. 42≤4.2y

y ≥ 10 y ≥ -10 y ≤ -10 y ≤ 10

The required inequality is 4¹/₃ > -5¹/8.

Inequality shows relation between two expression which are not equal to each others.

The given numbers are 4¹/₃ and -5¹/8.

The numbers are plotted on the number lines below,

To determine the number which is greater,

The number which is greater than zero will be greater from the numbers 4¹/₃ and -5¹/8.

4¹/₃  is a greater number.

The inequality can be written as,

4¹/₃ > -5¹/8.

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The answers of all the blanks are as:

a) 3200ft².

b)  8 times.

c) 100ft.

What is the area of the rectangle?

When calculating a rectangle's area, we multiply the length by the width of the rectangle.

we have,

length = 40ft

width = 10ft

Leila's vegetable garden has an area of 400 ft.

a)

new length = 40 * 2 =80ft

new width = 10 * 4 = 40ft

Therefore,  this describes the size of Leila's new garden :

= 80 * 40 = 3200ft²

b)

3200 / 400 = 8

The expansion changes the area of the garden:

The area of the new garden will be 8 times the area of the current garden.

c)

Leila's friend Keiko wants to expand her rectangular garden by 20 times the area of her current garden:

400 * 20 = 8000ft²

Keiko's garden length would be  5 times the current length:

40 * 5 = 80ft

and the new width would be the current width :

new width of Keiko's garden = 8000 / 80 = 100ft.

Hence, the answers of all the blanks are as:

a) 3200ft².

b)  8 times.

c) 100ft.

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Answer:

[tex]\huge\boxed{\sf < p = 36\°}[/tex]

Step-by-step explanation:

Since, the line is tangent to the circle, it is making an angle of 90 degree with the radius.

So,

∠p + 54 + 90 = 180 (Interior angles of a triangle add up to 180°)

∠p + 144 = 180

Subtract 144 to both sides

∠p = 180 - 144

[tex]\rule[225]{225}{2}[/tex]

Answer:

36°

Step-by-step explanation:

Tangent lines form Right Angles (90°) with all radii of circles.

Triangle Angle Sum: the three angles in a triangle add to 180°

90 + 54 + p = 180

144 + p = 180

p = 36

Answer:

$33.25

Step-by-step explanation:

Two packages cost $9.50

Divide $9.50 by two get the cost for one package

$4.75 per package

$4.75 * 7 to get the cost for 7 packages

$33.25

The number of student that took neither chemistry nor biology is 17.

A study of 50 high school students showed that exactly 25 of them took biology, exactly 20 of them took chemistry, and exactly 12 of them took both subjects.

The number of student that took neither biology nor chemistry can be calculated as follows;

Hence,

U = 50

n(C) = 20

n(B) = 25

n(B n C) = 12

n(B n C)' = ?

Therefore,

U = n(C) + n(B) - n(B n C)  + n(B n C)'

Therefore,

50 = 20 + 25  - 12 + x

50 - 45 + 12 = x

x = 5 + 12

x = 17

Therefore, 17 student took neither chemistry nor biology.

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Answer:

More than likely no full answer key however there might be answers for each individual question.

Answer: 4 feet of pipe

Step-by-step explanation:

1(f)+1(f)+(2(f)=4(f)

f=feet

The solutions using completing the square of quadratic equations are;

1) B: 2

2) A: Divide both sides by this coefficient

3) B: 5

4) All are quadratic equations

5) C. Quadratic Equation

1) Completing the square is basically a method for solving quadratic equations. Now, quadratic equations are second degree polynomials and as such have 2 roots. Thus, the solutions are 2.

2) Usually when using the method of completing the square, we are also trying to get rid of the coefficient attached to x squared and as such if we notice x squared has a coefficient, we will divide both sides by this coefficient.

3) The general form of quadratic equation is;

y = ax² + bx + c

Thus, we have;

2x² + 5x - 7 = 0

Thus, b = 5

4) They are all quadratic equations.

5) The correct one here is Quadratic Equation

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The total number of sandwiches they have in all on Sunday is 375 sandwiches.

The amount earned by the cafe if each sandwich cost $4.50 is $1,687.5

Total percentage of ham and turkey sandwiches = 35% + 25%

= 60%

So,

225 = 60% of x

225 = 0.60 × x

225 = 0.60x

divide both sides by 0.60

x = 225/0.60

x = 375

Hence,

Total number of sandwiches = 375

If the cafe sells all the sandwiches at $4.50 each

The total money earned by the cafe = cost of each sandwich × total number of sandwiches

= $4.50 × 375

= $1,687.5

Therefore, the total sandwiches sold in the cafe on Sunday is 375 sandwiches.

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{5x+2y=9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \atop {-0.5x-y=7.5\ \ \ \ \ \ \ \ |\cdot2}} \right. \\\\\\\left \{ {{5x+2y=9} \atop {-x-2y=15}} \right. \\+\\--------\\4x=24\ \ \Rightarrow\ x=24:4\Rightarrow\ x=6\\\\y=-0.5x-7.5=-0.5\cdot6-7.5=-3-7.5=-10.5\\\\\boxed{(x;y)=(6;-10.5)}[/tex]

Answer:

Step-by-step explanation:

4x-3y=11. 2 (2x-7y=22).=> 4x-14y=44. 4x-3y=11....................1. 4x-14y=44. 11y= -33. y= -3. then,putting it in 1. 4x-3 (-3)=11.

The distance between us and a star with a parallax angle of 0.1 arcsecond is 3.26 light years.

The distance between us and a star with a parallax angle of 0.01 arcsecond is 326 light years.

The distance between us and a star with a parallax angle of 0.001 arcsecond is 3260 light years.

The distance between us and a star with a parallax angle of 0.0001 arcsecond is 32600 light years.

The distance at which an object has a parallax of 1 arcsecond is known as a parsec. 3.26 light years are about how far this is.

The length of one parsec is 3.26 light years.

One arcsecond is equal to one parsec, which is equal to 3.26 light years.

We determine the other provided arcseconds based on this comparison.

3.26 light years make up a parsec.

0.1 arcsecond = 10 parsec

= 10 * 3.26 light years

= 32.6 light years

0.01 arcsecond = 100 parsec

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Answer 16

Step-by-step explanation:

The time taken by the ball to hit the ground is 9 seconds in quadratic equation .

What does quartic equation mean?

A fourth-degree equation, also known as a quartic equation, is one that reduces a quartic polynomial to zero and has the formula: where a 0. A quartic function's derivative is a cubic function.

a) The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.

          Differentiating both sides.

    δh/δt = -32t + 136

    -32t + 136    = 0

or, t = 136/32 = 4.5.

To check whether the value of h is maximum/minimum at t = 4.5, we differentiate

               δh/δt = -32t + 136

                 δh/δt = -32

which is < 0, which that implies, h is maximum at t = 4.5.

        the maximum height, by putting in t = 4.5, in the equation, to get:

h = -16(4.5)² + 136(4.5) + 72,

or, h = -16(20.25) + 612 + 72,

or, h = -324 + 684 = 360

Therefore, The maximum height of the ball is 360 feet.

b) the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.

Therefore, it can be written as:

0 = -16t² + 136t + 72.

or, 16t² - 136t - 72 = 0.

Solving this using the quadratic equation, we get

           t = - ( -136)± √(-136)² - 4( 16 ) ( -72)/2 * 16

           t =  136 ± √18496 + 4608/32

            t = 136 ± √23104/32

             t = 136 ± 52/32

Therefore, either t = (136+152)/32 = 9,

or, t  (136 - 152)/32 = -0.5.

Since t represents time, we won't take the negative value, and hence t = 9.

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Correct answer is:

27

Answer:

There would be 27 ounces of flour

Step-by-step explanation:

The ratio is 7:3 for sugar to flour.

I divided the 63 ounces of sugar by 7 to earn 9

Now, I multiplied 9 by 3 to get 27

Now thee ratio is 63:27

If you divide 7 and 3 you will get 2.3 repeating

If you divide 63 and 27 you will also get 2.3 repeating

Hope that makes sense! ;)

Step-by-step explanation:

5x³-6x³=-x³

5x²--3x²=8x²

-4x--5x= x

11--5=16

overall answer: -x³+8x²+x+16

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Answer:

(3, -5) or x=3, y=-5

Step-by-step explanation:

In a systems of equation, we're looking for what pair of (x, y) values make both equations true. When a pair of (x, y) makes an equation true, that just means it's on the line of the graph. So a pair of (x, y) values that makes both equations true, is simply when both lines intersect.

There are multiple methods to solve a systems of equation including: elimination, substitution, and graphing.

Each way has their advantages, and I'll show to to apply substitution and elimination

In this method we want to manipulate one of equations (or possibly both) so that they each have a variable with the "same coefficient" but different sign (one positive, one negative).

In the equations given, you may notice that the "y" variables each have the same coefficient, so we could multiply either of the equations by negative one, so one has positive y and another has negative y.

The reason we want the equations set up in this way, is so that we can add the equations which results in one of the variables being "eliminated" so that we can solve for a single value for the other variable.

So we start with:

[tex]x+y=-2\\2x+y=1[/tex]

let's multiply the top equation by -1 (remember to apply this to both sides so you don't actually change the equation)

[tex]-(x+y)=-(-2)\implies -x-y=2[/tex]

So now from here we have the two equations

[tex]-x-y=2\\2x+y=1[/tex]

If we add the two equations we get the following

[tex](-x+2x)+(-y+y)=(2+1)[/tex]

Notice how the -y and y cancel each other out? This is the entire point of the elimination method, so now we can solve for x

[tex]x=3[/tex]

This actually simplifies in our favor since -x + 2x = x, and the right side is just some constant, so we don't need to manipulate the equation anymore to solve for x.

Now that we know what the x-value is, we can plug this into either equation to solve for y. For simplicity I'll use the x + y = -2 equation.

[tex]3+y=-2\\y=-2-3\\y=-5[/tex]

So we know the solution is (3, -5) or [tex]x=3,\ y=-5[/tex]

The substitution method has the same goal as the elimination method, that is, get a one-variable equation so we can solve for one value. In this method, we want to define one variable in terms of the other variable, that way we can substitute this into the other equation, giving us a new equation with only one variable.

So let's just start with the top equation:

[tex]x+y=-2[/tex]

From here we can define "y" in terms of x, by subtracting x from both sides.

[tex]y=-2-x[/tex]

Now let's look at our other equation

[tex]2x+y=1[/tex]

Notice how it has a y variable, well we have one way of defining it: y = -2 - x. If we plug this into the bottom equation, now we only have x terms, giving us a one-variable equation.

[tex]2x+(-2-x)=1[/tex]

Now let's add 2 to both sides to cancel out the -2, and simplify 2x - x

[tex]x=3[/tex]

From here we essentially do the same thinkg we did in elimination method, except it may be a bit easier since we already have "y" solved for, we just need an x-value, which we now have!

[tex]y=-2-x\\\text{we know that x = 3}\\y=-2-(3)\\y=-5[/tex]

so now we have our solution: [tex](3, -5)\text{ or }x=-3, y=-5[/tex]

Answer:

Step-by-step explanation:

5 is D

6 is also D

Answer: c

Step-by-step explanation:

1) 2 2/5 + 5 2/10

2) 2 2/5 = 12/5 = 24/10

3) 5 2/10 = 52/10

4) 24 + 52 = 76

5) 76/10 = 38/5

6) convert to mixed number

Answer  :      x= [tex]\sqrt{2wy}[/tex]/ y

Step-by-step explanation:

Step-by-step explanation:

(X+3)/(x-2)=(x-4)/(X+5)

cross multiply

(x+3)(x+5)=(x-4)(x-2)

x(X+5)+3(X+5) = X(x-2)-4(x-2)

x²+5x+3x+15=x²-2x-4x+8

x²+8x+15=x²-6x+8

x²-x²+8x+6x=8-15

14x=-7

X=-7/14

X=-1/2

B)to verify substitute the answer in the equation given

that is RHS

X+3/x-2

=(-1/2+3)/(-1/2-2)

=5/2/-5/2

=-1

from LHS

x-4/(x+5)

=(-1/2-4)/(-1/2+5)

=-9/2/-9/2

=-1

the LHS= RHS

proved

Answer:

fourteen-sixteenths or  seven eights = 7/8 or 14/16

Step-by-step explanation:

Answer:

FINAL ANSWER: BODY B was moving at 1.35 m/s, 21 degrees above the x-axis.

Step-by-step explanation:

REFER TO THE IMAGES for the SOLUTIONS TO YOUR PROBLEM. Each step will be explained here.

When you solve for velocities before or after collision, you need to remember the law of conservation of moment which can be expressed through this formula:

 BEFORE                   AFTER

m1v1+m2v2      =     m1v1 + m2v2

This basically means, the sum of momentum of 2 objects BEFORE collision is equal to the same 2 objects AFTER collision.

The type of collision we have in your case is a 2D collision, where there is a gliding collision or they touch at an angle. So when you solve these type of problems, you have to consider the x and y components of motion. It makes things easier if you make a table like in the image to sort out your components.

STEP 1: COMPUTE FOR MOMENTUM BEFORE COLLISION for each OBJECT involved.

To solve for momentum, the formula is mass x velocity or mv:

STEP 1a: Body A: The problem states that before collision Body A is moving along the positive X-axis so the velocity will be +4.5 m/s. Notice that the velocity of the y component is 0 m/s. This is because BODY A is moving along the x-axis, with no mention that it deviated from it.

STEP 1b: Body B: Body B is at rest before collision, that is why it is not moving at all, which means both x and y components are equal to 0.

STEP 1c: Get the sum of all X components and the Sum of Y components.

STEP 2:   COMPUTE FOR MOMENTUM AFTER COLLISION for each OBJECT involved.

Step 2a: BODY A: Notice that we now have an angle. hence the cos and sin. We do this because we are breaking or decomposing the diagonal velocity into its x and y component. To get the x-component you get the cos of the angle and multiply it to the momentum of the diagonal or overall velocity. For y-component, instead of cos, you get the sin.

Step 2b: BODY B: Here we have unknowns, which we will derive later on. In this step, just plug in what you know into the formula.

Step 2c: We already know the x and y momentum of the objects BEFORE collision and the law of conversation of momentum states that the momentum AFTER is the same. With this total we can move onto the next step.

STEP 3: Solving for the X and y component of the velocity of BODY B AFTER collision.

Step 3a: Using the formula given in the image, we plug in what we know first. We know the momentum of the BODY A already, so we can put it into the equation. We also know the sum of both momenta and we put that into the equation too. Now all we do is derive the formula. DO NOT FORGET THAT WE ARE TO USE ONLY X COMPONENTS.

Step 3b: is the same as the previous step but instead, we use Y COMPONENTS only.

STEP 4: Combining X and Y components to get the resultant velocity:

For this step you need to remember the Pythagorean theorem. This is applied here because when you draw a free body diagram of the velocities, it creates a right triangle where :

the hypotenuse represents the final velocity

the opposite side represents the y-component and;

the adjacent represents the x-component.

Refer to the image for the solution.

STEP 5: Solving for the angle at which BODY B is moving:

For this step you need to remember SOH CAH TOA to find the angle at which BODY B is moving. You already have all the components you need, including the hypotheses. You can use any of the functions, and they should come up with the same approximation.

FINAL ANSWER: BODY B was moving at 1.35 m/s, 21 degrees above the x-axis.