The path of a fast moving particle traces a circle with equation (x-3)² + (y-4)² = 25. It starts at point (3,-1), moves counter clockwise, and passes the point (8,4) for the first time after traveling 7 microseconds. Where is the particle after traveling for 20 microseconds. ​

Answer:

RT = 17.9

RS = 9.7

m<T = 33°

Step-by-step explanation:

sin R = opp/hyp

sin R = ST/RT

sin 57° = 15/RT

RT = 15/sin 57°

RT = 17.9

cos R = adj/hyp

cos R = RS/RT

cos 57° = RS/17.88544939

RS = 17.88544939 × cos 57°

RS = 9.7

m<R + m<S + m<T = 180°

57° + 90° + m<T = 180°

m<T = 33°

Step-by-step explanation:

that is really simple, because the additional half-circle compensates for the missing half-circle on the other side.

so, the area is plain and simple the area of the rectangle, which is

13×12 = 156 = 156.0

Answer:

a.  f+g = -3x+5 + x^2

b.  f-g =  -3x+5 - x^2

Step-by-step explanation:

g(x) = x^2

I'll assume the other two equations were meant to be:

f(x) = -3x+5, and h(x) = -4x-2

a.  f+g = -3x+5 + x^2

b.  f-g =  -3x+5 - x^2

The equation of the plane passing P (1,2,1) and orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is -3x-2y-z+8=0.

Equation of plane passing through (x1,y1,z1) is given by

A(x-x1)+B(y-y1)+C(z-z1)=0

where, A, B, and C are direction ratios

In the question, it is given that the plane passes through (1,2,1)

So, the equation of the plane will be in the form,

A(x-1)+B(y-2)+C(z-1)=0

It is also given that the plane is perpendicular to give 2 planes.

So, their normal to the plane would be perpendicular to the normal of both planes.

So, the required normal is a cross-product of the normals of planes

x-y-z-10=0 and x-2y+z-2=0

i.e,

-3i-2j-k=0

so, the direction ratios,

A=-3, B=-2, C=-1

putting the direction ratios in the previous equation of the plane,

-3(x-1)-2(y-2)-1(z-1)=0

-3x+3-2y+4-z+1=0

-3x-2y-z+8=0

is the required equation of the plane

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48.76%

Compound interest describes interest on the principal plus interest.

Compound Interest Formula

The formula to find compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]. In the formula:

We can plug in our information to find the rate.

Solving For Interest Rate

First, let's rewrite the equation with our information. Note that for simplicity I will write rounded values for each step, but in reality, no rounding should be done until the last step.

Then, simplify the exponent and divide both sides by 4700.

Take the 60th root of both sides.

Subtract 1 from both sides.

Finally, multiply both sides by 12.

This means that the rate is 0.04876. We can multiply this by 100 to get the rate as a percentage. The interest rate is 48.76%.

The height of a trapezoid  is 3cm

The formula for the area of a trapezoid is:

A = 1/2(base1 + base2)  × height

Where base1 and base2 are the lengths of the parallel sides of the trapezoid, and height is the distance between the bases.

That is:

A = 1/2(a+b)h

To  determine the height of a trapezoid using the formula substituting the given values and solve for h. That is:

A = 1/2(a+b)h

where A = 24 cubic centimeters, a = 9 cm and b = 7cm

24 = 1/2(9+7)h

24 = 1/2(16)h

24 = 8h

8h = 24

h = 24/8

h = 3 cm

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Answer:

x = 80

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Note that x is being divided by 4. To isolate x, do the opposite. Multiply 4 to both sides of the equation:

[tex]\frac{x}{4} = 20\\(\frac{x}{4} ) * 4 = (20) * 4\\x = 20 * 4\\x = 80[/tex]

x = 80 is your answer.

~

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The inequality statements are 1 < 0, x > 0, x = x and x = 5

An empty set

An empty set is a set with no elements.

An inequality statement with no solutions results in an empty set.

One example of an inequality statement with no solutions is 1 < 0.

Some solution but not all real numbers

An inequality statement whose solution is some but not all real numbers is x > 0.

The solution set is the set of all positive real numbers, excluding 0.

The number line is represented as follows

|------------------------------------| 0  |----------------------------- |

All real numbers

A statement whose solution is all real numbers is x = x

The solution set is the set of all real numbers

The number line is represented as follows

|--------------------------- | ...  | -2  | -1  | 0  | 1  | 2  | ... |

Exactly one number

A statement whose solution is exactly one number is x = 5.

The solution set is the set containing only the number 5

The number line is represented as follows

|--------------------------- | ...  | 4  | ... |

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Answer:

The range of a function is the set of all possible outputs (or y-values) of the function. To find the range of h, we can look at the y-values in the table.

The y-values for h(x) are: -27, -13, -3, 3, 5, 3, -3

The range of h is the set of all these y-values. We can see that the lowest y-value is -27 and the highest y-value is 5. So, the range of h is {-27,-13,-3,3,5}

Therefore, the range of h is from -27 to 5.

All of the zeros of f(x) algebraically are; x = -3, x = -1/2, x = -5/2

The zeros of a polynomial p(x) are defined as all the x-values that make the polynomial equal to zero.

The polynomial is;

f(x) = 4x³ + 24x² + 41x + 15

To find the x-intercept, we will equate the polynomial to zero to get;

4x³ + 24x² + 41x + 15 = 0

Since (x + 3) is a factor, then we can factorize the polynomial as;

(x + 3)(4x² + 12x + 5) = 0

Rewriting the quadratic term gives;

(x + 3)(4x² + 2x + 10x + 5) = 0

(x + 3)(2x(2x + 1) + 5(2x + 1)) = 0

Thus, the factors are expressed as;

(x + 3)(2x + 1)(2x + 5) = 0

Thus, the zeros are;

x + 3 = 0

x = -3

2x + 1 = 0

x = -1/2

2x + 5 = 0

x = -5/2

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The statement "The equation y = 3x - 5 represents a function." is; TRUE

The statement "A function can only be represented by a straight line on the coordinate plane." is; FALSE

A linear function is one that is formed when a variable y varies directly with a variable x. That is, when y increases, x also increases and the opposite is also true.

The equation y = 3x - 5 represents a function.  This statement is said to be true because every value of x gives a different value of y and as such we can say it maps different elements to different images.

A function can only be represented by a straight line on the coordinate plane.  This statement is false because a function can also be represented by a circle, ellipse, parabola, etc.

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Step-by-step explanation:

....................

Answer:

Step-by-step explanation:

top=125 degrees

second from the top= 55 degrees

3rd=35 degrees

4th=55 degrees

5th=125 degrees

Answer:

1:12, then 1 :11

wait unless its like in the same thing

wait sorry im confused

if its that then i think it would be 2:12

Step-by-step explanation:

sorry not too sure!!!

Answer:1

Step-by-step explanation:

0

The polynomial that represents the area of the new lot is x² +200x +9600 and the new area of the increase is 25 feet is 15225 ft²

A polynomial is an expression made up of variables (also known as indeterminates) and coefficients that only employs the addition, subtraction, multiplication, and non-negative integer exponents of the variables.

A single variable, x, is used as the only variable in the indeterminate polynomial x² - 4x + 7. Polynomials are used in many areas of science and mathematics.

They are employed in calculus and numerical analysis to approximate other functions, as well as in the definition of polynomial functions, which are used in a variety of fields, from basic chemistry and physics to economics and social science.

Simple word problems to sophisticated scientific conundrums can all be  represented using polynomial equations.

Polynomials are used to create algebraic varieties in higher mathematics.

Area = Length x Breadth

Area =(80 + x)x(120 + x) = x² +200x + 9600

Area = (80 + 25)x(120 + 25) = 105x145

Area = 15225 ft²

Therefore, the new area of the plot is 15225 ft²

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Answer:

To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:

Step-by-step explanation:

To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:

Find a factor pair of ac that has the sum of b. For example, if a = 2, b = -7, and c = -21, then the factor pair for -42 (2 * -21) that has the sum of -7 is (-7, -6).

Rewrite bx as a sum of those factors. In the example, -7x = -7x + (-6x).

Factor out the GCF (greatest common factor) from the two groups of terms. In the example, (2x - 7)(x - 6) = 2x(x - 6) - 7(x - 6) = 2x^2 - 14x + 12x - 42 = 2x^2 - 2x - 42.

Write the original trinomial as the product of two binomials. In the example, the trinomial 2x^2 + -7x + -21 can be factored as (2x - 7)(x - 6)

So the final factorization is (2x - 7)(x - 6)

If AB is parallel to CD and angle EAB =50°,angle ECD =100° then Angle AEC is 112∘

Since AB∥CD

∴∠CAB+∠DCA=180 ∘  (Co-interior angles)

The inside angles total 180 degrees and are known as co-interior angles. It indicates that two internal angles that are on the same side of the transversal have a sum that is additional.

∴22 ∘ +∠DCA=180 ∘

⇒∠DCA=180 ∘ −22 ∘ =158 ∘

Also, ∠ECD+∠DCA+∠y=360 ∘  (Angles about a point)

Angles around a point refer to the total number of angles that can be combined to produce a complete turn. A point's surrounding angles add up to 360°. The angles circling a point add up to 360° since they have completed a full turn and are identical in magnitude.

⇒90 ∘ +158 ∘ +∠y=360 ∘

⇒∠y=360 ∘ −(90 ∘ +158 ∘ )

⇒∠AEC=y=360 ∘ −248 ∘ =112∘

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The total interest that will be paid over the life is $5,28,000. The solution has been obtained using arithmetic operations.

What are arithmetic operations?

For all the real numbers, there are four basic mathematical operations which are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

We are given 30 year loan amounting $220,000 at interest rate of 8 percent with monthly payments of $1,614.28.

The annual interest comes out to be

8% of $220,000 = $17,600

The total interest = $17,600 * 30 = $5,28,000

Hence, the total interest that will be paid over the life is $5,28,000.

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The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.

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The system of equations is solved and the number of toy cars of each machine of Company A should produce to have equal number of toy cars is t = 375 toys

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of toy cars produced by Company A be A

Let the number of toy cars produced by Company B be B

The number of machines for A = 18 machines

The number of machines for B = 15 machines

The number of toy cars produced by A = t cars

The number of toy cars produced by B = 75 + t

And ,

The total number of toy cars of A = 18 x t

The total number of toy cars of B = 15 ( 75 + t )

So , in order for both the company's to have the same toys is

18t = 15 ( 75 + t )

On simplifying the equation , we get

18t = 1125 + 15t

Subtracting 15t on both sides of the equation , we get

3t = 1125

Divide by 3 on both sides of the equation , we get

t = 375 toys

Hence , the equations is A = 18t and B = 15 ( 75 + t )

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We can write the measurement of ∠DAC as -

∠DAC = ∠ADB - ∠DCA

A triangle is a polygon with three edges and three vertices.

Given is a triangle ABC.

The external angle is the sum of two interior opposite angles.

We can write -

∠ADB = ∠DAC + ∠DCA

So, we can write -

∠DAC = ∠ADB - ∠DCA

Therefore, we can write the measurement of ∠DAC as -

∠DAC = ∠ADB - ∠DCA.

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A customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.

Charge for first 5 charged = $ 4.50

Charge for additional time = $ 0.50 per minute

Starting time = 9:35 p.m.

End time = 11:15 p.m.

Total minutes = 100 minutes

Total charge = 4.50 + (95 x 0.50)

                  = 4.50 + 47.50

                  = 52.00

Hence, a customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.

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The focal radius of the ellipse of which the two foci seat are:  

An ellipse can be represented in the standard form as (x/a)² + (y/b)² = 1, where (a,b) is the center of the ellipse and a and b are the semi-major and semi-minor axes respectively.

Given the equation of the ellipse:

16x² + y² - 128x - 20y + 292 = 0

To put it in the standard form, we have to complete the square and then divide both sides by the constant on the right-hand side.

First, we complete the square by adding and subtracting (128/2)² and (20/2)² respectively:

16x² - 128x + (128/2)² + y² - 20y + (20/2)² = 292 + (128/2)² + (20/2)²

Then, we divide both sides by 292:

(16x² - 128x + (128/2)²)/292 + (y² - 20y + (20/2)²)/292 = 1

On simplifying we get:

(4x - 8)²/144 + (y - 10)²/36 = 1

Now we have the standard form of the equation of the ellipse and we can find the semi-major and semi-minor axis and the center of the ellipse.

The semi-major axis is equal to the square root of the coefficient of x squared (144) and the semi-minor axis is equal to the square root of the coefficient of y squared (36).

The center of the ellipse is (-8, 10) and the semi-major and semi-minor axis are 12, 6 respectively.

The focal radius is the distance between the center and the focus. The focal radius is equal to the square root of the semi-major axis squared minus the semi-minor axis squared.

Focal radius = √(a² - b²) = √(144-36) = √108 = 6√3

The two foci of the ellipse sit on the x-axis, symmetric about the center of the ellipse. The foci are located at (-8 ± 6√3, 10).

Therefore, the two foci of the ellipse are at (-8 + 6√3, 10) and (-8 - 6√3, 10).

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Answer:

t=1.92938456

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The fraction in eights of the Apple pie that the person baked, is 2 / 8 of the apple pie.

The number of pieces that the apple pie had was 8 pieces to start. This means that if the baker served 1 / 4 of this, you can find the fractions in eights by multiplying the fraction served by the number of pieces :

= Fraction served x Number of pieces

= 1 / 4 x 8

= 8 / 4

= 2 pieces

The fraction in eights of the Apple that was served was :

= Number of pieces served / Number of total pieces

= 2 / 8

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Answer:

142 bags

Step-by-step explanation:

0.5KG is half of a KG, so we can start by finding half of $9.90

$9.90/2 being $4.95

So each bag is $4.95

The total is $702.90

Dividing $702.90/$4.95 will equal the number of bags

702.9/4.95=142 bags

The probability of picking a green marble is 3/4 or 0.75. This means it is likely the event would occur. Therefore, option A is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, an experiment with a bag of marbles, P(green)=3/4.

Probability is used to determine how likely it is that a random event would happen. The probability that a random event occurs lie between 0 and 1.  The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability of picking a green marble is 3/4 or 0.75. 0.75 is more than 0.5. This means it is likely the event would occur.

Therefore, option A is the correct answer.

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To find the total cost of the pole at the store including sales tax, we need to multiply the price of the pole by the sales tax rate (expressed as a decimal).

$59.50 x 0.06 = $3.57

So the total cost of the pole at the store is $59.50 + $3.57 = $63.07.

To find the difference in price between the store and the website, we can subtract the website price from the store price:

$63.07 - $62.50 = $0.57

So the pole is $0.57 more expensive at the store than on the website.

Answer:

u

Step-by-step explanation