Find the sine, cosine, and tangent for the angle whose measure is pi/6...pi divided by 6.

The equation of a parabola with a focus at (-2,-3) and a directrix at y = -5  is y =  1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)

What is Parabola?

A parabola is the location of a moving point whose distance from a given focus point and directrix line, respectively, is always constant.

let's keep it simple: (x, y). Focus is on (7,5)

When the separation from focus is

[tex]\sqrt{(x - (-2)^{2}) + (y - (-3)^{2} ) }[/tex] . Its distance from directrix y = -5 i.e.

y + 5 = |y + 5|^2

Hence, equation of parabola:

(x - (-2))^2 + (y - (-3))^2 = |y + 5|^2

or, (x + 2)^2 + (y + 3)^2 = |y + 5|^2

x^2 + 4x + 4 + y^2 + 3y + 9 = y^2 + 10y + 25

or, x^2 + 4x + 13 + y^2 + 3y = y^2 + 10y + 25

x^2 + 4x - 12 = 7y

y = (x^2 + 4x - 12)/7

y = 1/7(x^2 + 4x +4 - 4) - 12/7

y = 1/7(x + 2)^2 - 12-4/7

y =  1/7(x + 2)^2 - 8/7

Hence, parabola's equation is y =  1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)

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The polynomial for the given graph is P(x) = (x+2)(x+8)(x-1)(x-4)

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

Given,

The polynomial for the given graph is:

P(x) = (x+2)(x+8)(x-1)(x-4)

Each non-zero term in a polynomial function is made up of a number, known as the term's coefficient, and a variable raised to a non-negative integer power. A polynomial function can be either zero or the sum of a finite number of non-zero terms.

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The solution to the given expression is 7,677.6.

This is a question of multiplication.

Multiplication

In mathematics, multiplication is used as a method of finding the product of two or more numbers. It is one of the arithmetic operations,  like addition, subtraction and division that we use in everyday life. The major application we can see in multiplication tables.

In arithmetic, the multiplication of two numbers is represented by  the repeated addition of one number with respect to another.

Given expression:-

[−3*914]*[(−0.1)*(−28)]

We have to find the solution of the given expression.

We have,

-3*914 = -2742

(-0.1)*(-28) = 2.8

Hence, we can write,

[−3*914]*[(−0.1)*(−28)] = (-2742)*(2.8)

(-2742)*(2.8) = 7,677.6

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The value of y when x is 9 for the proportional relationship between is 31.5.

The constant of proportionality is used to show the proportional relationship between the numbers given.

In this case, when x is 2, y is 7. This will be illustrated thus:

y = kx

7 = 2k

Divide

k = 7/2

k = 3.5

Therefore, when x is 9, the value of y will be:

y = kx

y = 3.5 × 9

y = 31.5

Therefore, y is 31.5.

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Answer:

x = 12

Step-by-step explanation:

since the triangles are congruent then corresponding angles are congruent, so

∠ CBD = ∠ ABD , that is

9x - 9 = 99 ( add 9 to both sides )

9x = 108 ( divide both sides by 9 )

x = 12

The domain is the set of all real numbers and the range is the set of all real numbers larger than -4, so the correct option is the third one.

For a function y = f(x) we define the domain as the set of the x-values (horizontal axis) and the range as the set of the y-values (vertical axis).

Here we have a parabola, in this case the domain is always the set of all real numbers, and the range is all the values above or equal to the vertex (in cases like this, where the parabola opens up).

We can see that the vertex is at y = -4

So the range is.

[-4, ∞]

So the correct option is 3.

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To determine the percet of shoppers that use coupons, the manager interviews every shopper thay enters the greeting aisle and records wether they use or not coupons.

Since he does not take any measures, nor divide the shopers into groups or, for example, interviews one every k number of shoppers, the sampling method he used is the most simple and common one, named

"Simple random sample" or "random sample"

Answer: [tex]2/63, -52/63, 83/63[/tex]

Step-by-step explanation:

[tex]h(1)=-\frac{6}{7}(1)+\frac{8}{9}=\frac{2}{63}\\\\h(2)=-\frac{6}{7}(2)+\frac{8}{9}=-\frac{52}{63}\\\\h(-1/2)=-\frac{6}{7}(-1/2)+\frac{8}{9}=\frac{83}{63}[/tex]

The number of customers he would have in the seventh week is 37.

The customers of Felix grow at a linear rate. A linear growth rate is when a value increases a constant rate. The customers would increase by 2 each week.

The linear equation that represents the number of customers in the seventh week:

Initial number of customers + [ rate of increase x (number of weeks - 1)]

25 + [2 x (7 - 1)]

25 + (2 x 6)

25 + 12 = 37

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Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy are 16.

Sample timings as observed are 3.5, 3.1, 4.0, 3.5, and 3.9.

Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5

The average sample time (X) is 3.6.

Observed time (T) Mean (X) (X - T) (X - T)^2

3.5 3.6 0.1 0.01

3.1 3.6 0.5 0.25

4.0 3.6 -0.4 0.16

3.5 3.6 0.1 0.01

3.9 3.6 -0.3 0.09

Allow Standard deviation to be S.

2 in (X-T) - 1 n

[tex]S=\sqrt{\frac{0.52}{4}}[/tex]

S = 0.3605

Considering that (h) = 0.05,

Given that 95% of the time,

Z value at 95% confidence interval = 1.96

Let N be the number of observations.

2 N= Z.S hX

[tex]N=(\frac{1.96X0.3605}{0.05X3.6})[/tex]

N = 15.4

N = 16 (rounded off to next whole number) (rounded off to next whole number)

Consequently, 16 observations are required.

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Answer:

Step-by-step explanation:

Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy of 16.

Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5

The average sample time (X) is 3.6. Observed time (T) Mean (X) (XT) (X-T)^2

3.5 3.6 0.1 0.01

3.1 3.6 0.5 0.25

4.0 3.6 -0.4 0.16

3.5 3.6 0.1 0.01

3.9 3.6-0.3 0.09

Allow Standard deviation to be S.

2 in (X-T) - 1n

S=√0.52/4

S=0.3605

Considering that (h) = 0.05,

Given that 95% of the time,

Z value at 95% confidence interval = 1.96 Let N be the number of observations.

2 N=Z.S hx

N=(1.96X0.3605)÷(0.05×3.6)

N = 15.4

N = 16 (rounded off to next whole number) (rounded off to next whole number) Consequently, 16 observations are required.

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Answer:

it can't be in a whole number since it is a fraction and will go in decimals

Answer: You always use circumference if you are talking about a round object.

Expression ( w+4)(w + 7) represent the total area of the garden and walkway.

The area of Rectangle is length times of width.

Given that  the width of the garden, in feet be w.

The length is 3 feet longer than its width, hence:  w + 3

The entire garden is surrounded by a 2-foot-wide cement walkway. Therefore:

garden and walkaway length= (w + 3) + 2 + 2 = w + 7

garden and walkaway width = w + 2 + 2 = w + 4

The area of garden and walkaway

= length times of width

=Length × Width

= (w + 7)(w + 4)

Hence expression ( w+4)(w + 7) represent the total area of the garden and walkway

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Answer:

x<-2, x>-7

Step-by-step explanation:

1st one

add 7 to 3 =10

-5 divide by 10 = -2

2nd one

add 7 to -42 = -35

-35 divided by 5 = -7

Using the Pythagorean Theorem, it is found that:

A. The straight line distance between the school and the fire station is of 4.62 miles.

B. The distance between the school and the hospital is of 2.08 miles.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In the context of this problem, the distance between the school and the fire station is the hypotenuse of a right triangle with sides 4.3 and 1.7, hence:

d² = 4.3² + 1.7²

d = sqrt(4.3² + 1.7²)

d = 4.62 miles.

The hospital is 3.1 miles west of the fire station, hence the distance between the school and the hospital is the hypotenuse of a right triangle of sides 1.7 and 4.3 - 3.1 = 1.2, hence:

d² = 1.2² + 1.7²

d = sqrt(1.2² + 1.7²)

d = 2.08 miles.

The complete problem is given by the image at the end of the answer.

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Answer:

1256

Step-by-step explanation:

A=3.14*20^2

=400*3.14

=1256

Answer: what sentence ?

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The sentence is true because if it is true, then the sentence is false.

You are asking if the sentence is false, and it is false, so the question you asked is true.

This is so confusing though...

Answer:

option 4

Step-by-step explanation:

let c represent the old amount , then twice the old amount is 2c.

1.5 less than twice the old amount is 2c - 1.5 , so

2c - 5 = 6

20 + xy - 3 + 4y^2 + 10 - 2y^2

(20 - 3 + 10) + (4y^2 - 2y^2) + xy

27 + 2y^2 + xy

Given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.

So, the likelihood that a pupil is between the ages of 6 and 8 can be calculated using the techniques below:

P = 28/89

Therefore, given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.

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The complete question is given below:

Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age group. One student from the school will be selected at random. What is the probability that the student is in the age group of 6 to 8 years given that the selected student responded with joy?

Percent of the original is the radius of the reduced artery is 0.070 times the original radius.

Given that,

A blood clot has lowered the flow rate in an artery to 8.5% of its usual value, and the average pressure difference has increased by 20.5%.

p1 = 8.5 % ,

p2 = 20.5 %

The equation is using here is From Poiseuille's equation

Q = \Delta p \pi r4 / 8 \eta L

now

Q1 = \Delta p1\pi r14 / 8 \eta L

and

Q2 = \Delta p2\pi r24 / 8 \eta L

Q1 = \Delta p1\pi r14 / 8 \eta L / Q2 = \Delta p2\pi r24 / 8 \eta L

Q1 / Q2 = \Delta p1 ro4 / \Delta p2 r24

r24 = ( 0.085 Q1 / Q1 ) ( \Delta p1 / \Delta p1 + 0.20 \Delta p1 ) ro4

r24 = 0.085 X ( 1 / ( 1 + 0.20 ) ro4  

r2 = 0.070 ro  

As a result, the shortened artery's radius is 0.070 times its original radius, or percent of the original.

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Angle d is exterior angle . and an exterior angle is equal to addition of two interior angles .

What is the formula for the exterior angle theorem?

In this figure,

       Angle d is exterior angle . and an exterior angle is equal to addition of two interior angles .

So, According to  Exterior Angle Theorem,

                        ∠D = ∠A + ∠B

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Answer:

See explanation below.

Step-by-step explanation:

There is a theorem about the sum of the measures of the angles of a triangle.

In this case, with the interior angle measures called a, b, and c, the theorem states:

Theorem:

The sum of the measures of the interior angles of a triangle is 180°.

a + b + c = 180°

Now we will prove the theorem and answer why a + b = d.

Look at angles c and d. They form a linear pair. Angles that form a linear pair are supplementary angles. By the definition of supplementary angles, the sum of the measures of angles c and d is 180°.

We have

c + d = 180°              Eq. 1

By the theorem above, we have

a + b + c = 180°        Eq. 2

Let's subtract Eq. 1 from Eq. 2:

    a + b + c       = 180°

 -              c + d = 180°

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

   a + b        - d = 0

a + b - d = 0

Add d to both sides.

a + b = d

That is a proof of the Exterior Angle Theorem.

The system of quadratic equations obtained on solving general equation of parabola are

a. 5=36a - 6b +c

   -2=64a+8b+c

    3=16a+4b+c

b. 1=289a+17b+c

   -1=81a-9b+c

  2=11025a+105b+c

the equation parabola

the general equation of Parabloa is written as-

y=a[tex]x^{2}[/tex]+bx+c

if the parabola passes through the point. then this point must satisfy the equation of the parabola. so, by putting the value of points we get a set equations-

5=a[tex]6^{2}[/tex]+b(-6)+c

5=36a - 6b +c

and for other two points we get equations

-2=64a+8b+c

and 3=16a+4b+c

and for other three points we get the equations

1=289a+17b+c

-1=81a-9b+c

2=11025a+105b+c

so on solving we get these three set of quadratic equations.

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Answer: E

Step-by-step explanation:

Option A is a reflection over the y-axis.

Option B is a rotation of 180 degrees about the origin followed by a dilation.

Option C is a reflection over the line y=x.

Option D is a reflection over the y-axis.

Option E is a reflection over the x-axis.

The quantity of salt in the tank at period t equivalents A(t) = 200 - 130 e(-t/40).

Initially, the tank has A(0) = 50 g of salt.

The rate of salt entryway is (1 g/L) × (5 L/min) = 5 g/min

And a rate of (A(t) ÷ 200 g/L) × (5 L/min) = (A(t) ÷ 40) g/min,

As an outcome, the quantity of salt in the tank modifications as

A'(t) = (5 - A(t)) ÷ 40.

Solve ODE for A(t):

A'(t) + (A(t) ÷ 40) = 4

[tex]e^{\frac{(t)}{40} }[/tex] A'(t) + ([tex]e^{\frac{(t)}{40} }[/tex] ÷ 40 A(t)) = 4[tex]e^{\frac{(t)}{40} }[/tex]

([tex]e^{\frac{(t)}{40} }[/tex] A(t))' = 4[tex]e^{\frac{(t)}{40} }[/tex]

[tex]e^{\frac{(t)}{40} }[/tex] A(t) = 160[tex]e^{\frac{(t)}{40} }[/tex] + C

A(t) = 160 + C[tex]e^{\frac{(t)}{40} }[/tex]

Given A(0) = 30, conclude that

30 = 160 + C

C = -130,

This denotes that the quantity of salt in the tank at period t equivalents

A(t) = 200 - 130 e(-t ÷ 40).

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ANSWER:

139 square yards

STEP-BY-STEP EXPLANATION:

We have that the formula for the surface area of a triangular prism is the following:

Where p, is the perimeter is the base and h is the height, while b is the area of the base, we replace and calculate the area like this:

The area is 139 square yards

Answer:

i = 74

j = 47

Step-by-step explanation:

to find "i" add 16 & 90 which is 106. subtract 106 from 180 to get 74.

to find "j" add 43 & 90 which is 133. subtract 133 from 180 to get 47

Answer:

5x-4

Step-by-step explanation: