The directress of a parabola is represented by the linear equation y=2, and its vertex is located at (3,1).Both of these attributes of the parabola are graphed below. which of the following is the equation that represents this parabola?

In the given figure

There is a triangle RST

∵ RU is perpendicular on ST and bisects it

∴ Triangle RST is an isosceles triangle

∴ RS = RT

∵ RS = 3x + 9 and RT = 7x + 17

Equate them

∵ 7x + 17 = 3x + 9

Subtract 3x from both sides

∴ 7x - 3x + 17 = 3x - 3x + 9

∴ 4x + 17 = 9

Subtract 17 from both sides

∵ 4x + 17 - 17 = 9 - 17

∴ 4x = -8

Divide both sides by 4 to find x

∴ x = -2

Now substitute x by -2 in the expression of RS to find its length

∵ RS = 3(-2) + 9

∴ RS = -6 + 9

∴ RS = 3

The elements in the first 3 columns are the coefficients of system of equations.

The 4th column are the constants of the system of equations.

This is a system of 3 equations.

Let's write the system using the variables x, y, and z. Shown below:

Let's simplify and write the equations:

30,60,90,

Step-by-step explanation:

We need to estimate the sum:

In order to do so, we first round each term to the nearest integer. Then we add them.

We have:

Then, we can estimate the sum to be:

Therefore, option C is correct.

step 1

Find out sine

Remember the identity

substitute the given value of cosine

step 2

Find out cosecant

step 3

Find out secant

step 4

Find out tangent

step 5

Find out cotangent

For the first deal we get 6 goodie bags for $12, let's find how much each goodie bag cost in this case by dividing $12 by 6:

In the first deal, each goodie bag costs $2.

For the second deal, we get 4 goodie bags for $12, let's also find how much is 1 goodie bag in the scenario:

In the second deal, each goodie bag costs $3.

The better deal is the first one because each goodie bag is cheaper than in the second deal.

Answer: $12 for 6 goodie bags is the better deal

Answer:

y=5.5x+8

Step-by-step explanation:

The area of the larger triangle will be equal to 36 square units.

Triangle may be defined as a closed figure of three sides and three interior angles. Scaling of image may be defined as a ratio that can be used to represent the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object. Dilation may be defined as the process for creating similar figures by changing the size. A graph can be defined as a pictorial representation or a diagram that represents data or values. According to question the area of smaller triangle is given as 9 square units. After scaling the length of scale copies become double and the area becomes four times. So, the area of bigger triangle is 4×9 = 36.

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Complete Question:

These two triangles are scaled copies of one another. The area of the smaller triangle is 9 square units. What is the area of the larger triangle? Explain or show how you know.

Hence the second option, [tex]y=\frac{2}{3}x +\frac{11}{3}[/tex] is the correct option.

What is slope interception form?

Y=mx+b, where m is the slope and b is the y-intercept, is the slope intercept form. The graph of the linear equation can be drawn on the x-y coordinate plane using this form of the equation.

For the given question we are given,

slope (m) = 2/3

and we are also given the point that the line passes through to be,

(-1,3).

that is

(x,y)=(-1,3)

x=-1

y=3

we, know that slope interception form is of the form,

y=mx+c

substituting the value of m (slope) and the point (-1,3) we get

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

=   3= -2/3 +b

=   3+2/3=b

=    (9+2)/3=b

=     11/3=b

from this we get b=11/3

now substituting this again in

y=mx+b

we get

y=(2/3)x+(11/3)

Hence the second option [tex]y=\frac{2}{3}x +\frac{11}{3}[/tex] is correct.

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Answer:

Step-by-step explanation: To find the x-intercept, substitute in

0

for

y

and solve for

x

. To find the y-intercept, substitute in  0 for x

and solve for  y

x-intercept(s):  735,0

y-intercept(s):   0,490

Graph is attached. It will be a linearly increasing line.

Population for 0 months is 46

Population for 6 months is 88

Population for 12 months is 130

Population for 18 months is 172.

Given,

The equation for population, P = 7t + 46

P is the population

t is the time in months

We have to graph the equation using

t = 0, 6, 12 and 18.

For this we have to find P

1. t = 0

P = 7t + 46 = 7 × 0 + 46 = 0 + 46 = 46

2. t = 6

P = 7t + 46 = 7 × 6 + 46 = 42 + 46 = 88

3. t = 12

P = 7t + 46 = 7 × 12 + 46 = 84 + 46 = 130

4. t = 18

P = 7t + 46 = 7 × 18 + 46 = 126 + 46 = 172

The graph is given below and it will be a linearly increasing line.

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Answer:

Explanation:

Given the function:

The graph of G(x) is wider than the graph of F(x), so we can conclude that G(x) has been stretched vertically by a factor greater than 1 to obtain F(x).

Furthermore, G(x) was translated upwards by 2 units when we compare the vertices.

Thus, from the options,a possible equation for F(x) is:

Answer:F(x)=3x^2+2

Step-by-step explanation:

Step 1

Redraw the cyclic quadrilateral

From the image;

Step 2

Find the measure of angle R

Find the measure of angle T

Find the measure of angle U

Find the measure of Arc SRU

Find the measure of Arc mRUT

Find the measure of mRST

The given number 4,563 is 4558.437 times greater than 4.563.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point. 12.5 is a decimal number, for instance.

Using a single notation, decimals can convey both the entire number and the fraction. Whole numbers and fractions are separated from each other in decimals by a point called a decimal point. For instance, in the number 65.4, the entire number is 65, while the fractional half is 4 (10).

The given numbers are 4,563 that is four thousand five hundred sixty- three and 4.563 that is four point five six three.

The difference between these two numbers is 4558.437.

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We have to represent two real world situations that could be represented by the value -2.

(1) Let there be a fish which is 2 meter below the sea level.

Considering the sea level point to be zero and denoting the points above sea level as positive and the points below sea level as negative, like we do in a cartesian plane, the point which is 2 meter below the ground level will be -2.

(2) Let there be a box buried 2 feet under the ground.

Considering the ground level to be zero and denoting the point above the ground level as positive and the points below ground level as negative, the point which is 2 meter below the ground level will be -2.

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The mass of isotope 239-Pu left after 4000 years is approximately 3.3g

Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.

In solving the disintegration constant, we can use the half-life formula.

The half-life of a sample is given as;

[tex]T_\frac{1}{2} = \frac{ln2}{\lambda}[/tex]

Substituting the values into the equation;

[tex]T_\frac{1}{2} = \frac{ln2}{\lambda}\\24100 = \frac{ln2}{\lambda} \\\lambda = \frac{ln2}{24100} \\\lambda = 0.00002876years^-^1[/tex]

The formula of radioactivity is given as

[tex]N = N_oe^(^-^\lambda ^t)[/tex]

We can plug in the values and solve.

[tex]N = N_oe^(^-^\lambda ^t)\\N = 3.7e^-^(^0^.^0^0^0^0^2^8^7^6 ^*^4^0^0^0^)\\N = 3.297g\\N = 3.3g[/tex]

The amount left after 4000 years is 3.3g.

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Given that:

- A race car game takes 6 points each time the player hits a cone.

- You must find the integer that represents the change in total points if the player hits 10 cones.

It is important to remember that the Set of Integers contains the negative numbers, the positive numbers, and zero.

Then, by analyzing the data given in the exercise, you can identify two integers that must be multiplied, in order to calculate the total points if the player hits 10 cones. These are:

Since the game takes 6 points from the player each time this hits a cone, the integer that represents the points taken from the player must be negative.

In order to multiply the integers, you need to remember the Sign Rules for Multiplication:

Therefore, you get this result:

Hence, the answer is:

Answer:

57.97507788%

Step-by-step explanation:

Write the problem as a mathematical expression.

372.2

642    

Multiply by 100 to convert to a percentage.

372.2

642     * 100

Simplify

372.2.

642.      * 100 = 57.97507788%

Given a random sample of 269 students and a contigency table that gives the 2 way classification of their responses.

The probability formula is:

The conditional probability P(A/B) or P(B/A) arises only in the case of dependent events.

Hello!

We have the following multiplication:

To solve it, we have to multiply numerator with numerator and denominator with denominator, look:

So, the fraction in is the simplest form is 9/20.

The value of

which can be written as:

is

We have to add the jumping jacks from 4:00 (not included) to 11:00.

So we have to add:

The answer is option b) 56.

According to the problem:

• At 3:00 am the temperature was -8°.

• Then, it rose 25 degrees. ,This implies a sum.

• At last, it dropped 5 degrees. ,This implies a subtraction.

Remember that "rising" shows a positive direction and "dropping" shows a negative direction. Following this rule, we can form the following expression

There you can observe that the initial temperature (-8) increased (+)25, and then decreased (-)5.

Therefore, the temperature for the late day is

The value of the function f(x) = 2x -1 when f(x) = 7 is 13.

Function:

A function is defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given,

Here we have the function f(x) = 2x - 1.

Now, we need to find the value of the function when f(7).

To find the value of f(7), we have to replace the value of x with the value 7.

Then we get the equation like the following,

f(7) = 2(7) - 1

Now, we have to expand the terms in order to solve it,

f(7) = 14 - 1

When we subtract it, then we get the value of

f(7) = 13.

Therefore, the value of f(7) = 13.

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Answer:

Step-by-step explanation:

Given quadrilateral ABCD with AB≅AC, DA≅DC, ∠ABC≅∠ADC, and one of the corner angles equal to 150°, you want the measures of all corner angles.

The given congruent angles and sides are marked in the attached diagram. If we let ∠ACB = x and ∠ACD = y, we can write some equations involving the sums of the various angles.

First of all, we note that both triangles are isosceles. That means ...

The sum of angles in ∆ACD must be 180°, so we have ...

  x + 2y = 180°

We know that the isosceles triangle base angles cannot exceed 90°, so the angles at corners B and D cannot be 150°. That leaves two possibilities:

(a) Corner angle C is 150°   ⇒   x + y = 150°

(b) Corner angle A is 150°   ⇒   (180°-2x) +y = 150°

(a) Corner C is 150°

This makes the system of equations for x and y be ...

Subtracting the second from the first gives y = 30°, and substituting that value for y gives x = 120°. We already know x is the base angle of an isosceles triangle, so cannot have that value. This possibility is eliminated.

(b) Corner D is 150°

This makes the system of equations for x and y be ...

The second of these equations can be rearranged to ...

  2x -y = 30°

Adding twice this to the first equation, we have ...

  2(2x -y) +(x +2y) = 2(30°) +(180°)

  5x = 240°

  x = 48°

Substituting for x in the second equation gives ...

  2(48°) -y = 30°

  96° -30° = y = 66°

As we noted in the solution part (a), corner angle C is the sum of x and y:

  ∠BCD = x +y = 48° +66° = 114°

Then the corner angles are ...

The attached figure is drawn to scale.

Step-by-step explanation:

"with replacement" is important.

that means that the mixture of the marbles and therefore the chances to pull certain marbles does not change with the previous pull.

a probability is always

desired cases / totally possible cases

we have 14 marbles in the bag

4 orange

2 green

8 purple

the probability to pull an orange marble is therefore

4/14 = 2/7

the probability to pull a green marble is therefore

2/14 = 1/7

the probability to pull a purple marble is therefore

8/14 = 4/7

a.

a green marble is pulled AND then a purple marble is selected.

we need to combine both probabilities for one combined event :

1/7 × 4/7 = 4/49

b.

a purple marble and then a green marble is selected.

4/7 × 1/7 = 4/49

since we replace the marbles after every pull, both probabilities are the same, of course.

every pull has the same probability for each desired event.

c.

2 orange marbles are selected.

2/7 × 2/7 = 4/49

d.

2 non-orange marbles are pulled

there are 10 non-orange marbles. so this is

10/14 × 10/14 = 5/7 × 5/7 = 25/49

In the given situation the angle of depression is θ. To find it, use the trigonometric ratio of tangent of angle θ in a right triangle (the ratio of tangent is the relation between the two legs of a right traingle):

In the given situation the opposite leg to the angle of depresion is the distance between the base of the plateau and the Jedi Trainee and the adjacent leg is the sum of 500ft in the air and Chewbacca's eye height:

Answer:

iii) 501

iv) 110

Step-by-step explanation:

See picture

The inequality to solve is,

We will use the distributive property (shown below) to simplify the expression. Then, we will use algebra rules to solve the inequality.

Distributive Property

The simplification process >>>