Select the correct answer.Solve the equation using the method of completing the square.A. B. C. D.

we have the new function

The vertex of this function is the ordered pair (0,3)

The coordinates of the second point

(2,2) ------------> (2,f(2))

Find the value of f(2)

the new coordinates of point (2,2) are (2,13/3)

see the attached figure

One daylily $10 and 1 shrub $11

1) Gathering the data from the question

Erica spent $200 on 9 daylillies and 10 shrubs

Megan spent $185 on 13 daylilies and 5 shrubs

9d+10s=200

13d+5s=185

2) Let's solve this system of linear equations now

9d+10s=200

13d+5s=185 Multiply by (-2)

9d +10s=200

-26d-10=-370

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

-17d =-170

17d=170

d=10

9(10) +10s=200

90+10s-90=200-90

10s=200-90

10s=110

s=11

So the cost of one daylily is$10 and 1 shrub is $11

ANSWER

x + y = 4

EXPLANATION

The standard form of a linear equation is given as:

ax + by = c

To do this, we have to find the equation of the line using point-slope method:

y - y1 = m(x - x1)

where (x1, y1) is the point the line passes through

m = slope

The given slope is -1 ad the point the line passes through is (1, 3).

Therefore, we have:

y - 3 = -1(x - 1)

y - 3 = -x + 1

=> x + y = 1 + 3

x + y = 4

That is the equation of the line in standard form.

The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.

The mid-way between the least value and the greatest value of the data set is called the midrange, and the median is the middle number in a sorted list of numbers.

Given a data 10,3, 11,3, 12,4, 13,5, 14,2, 15,3

Mean = (2+3+3+3+4+5+10+11+12+13+14+15)/12 = 7.92

Median = 15/2 = 7.5

Mode = 3

Midrange = (2+15)/2 = 8.2

Hence, The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.

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Answer:

Explanation:

Here, we want to determine the most precise name for the quadrilateral

At first sight, the image plot looks like a kite. We will have to confirm this using the properties of a kite

One of the important properties is to check that the diagonals intersect at right angles

Looking at the plot, QS and PR must be perpendicular

This is correct as they meet at right angles at the line through the origin

Also, for us to have a kite, PQ and QR must be equal

This is also correct as PQ and QR are equal in length

Furthermore, PS and RS must be equal in length

This is alo correct as the two are equal in length

We thus conclude that the quadrilateral is a kitecohis is als

plot looks like a kite. We will have to confirm this using the properties of a kite

plot looks like a kite. We will have to confirm this using the properties of a kite

Since AB is tangent to the circle, the angle BAO equals π/2.

The same happens to BC, so the angle BCO also equals π/2.

Now, for any quadrilateral, the sum of the internal angles is 2π. Therefore:

ABC + AOC + BAO + BCO = 2π

ABC + 3π/7 + π/2 + π/2 = 2π

ABC = 2π - 3π/7 - π/2 - π/2 = π - 3π/7 = (7π - 3π)/7

ABC = 4π/7

We have the next equation

We sum similar terms

then we clear x

the value of x=4

Solution

we are given that

Notice the lettering on each triangle, they both represent the triangle we are given in the question

The postulate here is Sides, Angle, Sides (SAS)

Option C

Answer:

(x + 7 ) ( x - 12 )

Explanation:

We know that if we multiply any two expressions x + a and x + b then we have

Now similarly,

meaning

In other words, what are the two numbers that if I add them together I get -5 and If I multiply them I get -84. The answer comes from educated guesses. We guess that if we add 7 and -12 we get 5 and if we multiply then we get -84; therefore,

Hence, the expression can be factored as

which is our answer!

A table showing the number of graduates by subject from a university's faculty of natural science in 2002.

1) To calculate the number of students that graduated, find the sum of the number of graduates from each subject.

The number of students that graduated is 60.

2) To determine the sector angle that will represent the number of graduates in each subject, divide the number of graduates in each subject by the total number of students and then multiply by 360º.

3) To construct a pie chart with radius, 4cm to represent the information, draw a circle of radius 4cm and partition it into sectors with central angles as calculated in (2) above.

7) The angle asked is ajacent to the leg given and we also have the hypotenuse. So we can use cossine:

8) Here we want the hypotenus given an angle an its opposite leg. So we can use sine:

9) We want the leg which is opposite of a given angle and we have the hypotenuse. So we can use sine again:

5 guys are putting yogurt in a girl's mouth

Each of the yogurt is 5 liters

The total yogurt the girl is carrying = 5 x 5

= 25

The answer is 25 liters of yogurt

Given the function:

For the given function, we will determine the concavity between x = -1 and x = 5

By the average rate of change over the interval 3 ≤ x < 5

We will use the following formula:

First, we will find the value of f(5) and f(3)

Substitute into the formula:

So, the average rate of change will be as follows:

As the average rate of change is negative, the concavity of the graph will be concave down

We have values of x and f(x) and choices for the expression of f(x).

We can easily found the correct option just evaluating the expressions in the x values and see which have the correct value of f(x):

For x=2 the outpur=f(x)=9:

You can evaluate in the other values of x and proof that the corretc option is the first.

In order to determine the required probability, calculate the total area of the shaded regions frist:

Consider that there is a rectangle and a triangle with shaded area, then, you have:

A1 = (1 ft)(2 ft) = 2 ft² rectangle area

A2 = (2 ft)(2 ft)/2 = 2ft² triangle area

Then, the total shaded area is:

A = A1 + A2

A = 2 ft² + 2 ft²

A = 4 ft²

Next, calculate the total area of the given figure:

A' = (3 ft + 1 ft)(2 ft) = 8 ft²

Next, the probability is the quotient in between the area of th shaded regions over the area of the total figure:

p = A/A'

p = (2 ft²)/(4 ft²)

p = 0.50

Hence, the probability that a point chosen is inside a shaded region is 0.50

The value of m∠JSM is 17 degrees.

Given data;

The measure of the ∠JAE = 48 degrees.

The measure of the ∠AEJ = 90 degrees.

The measure of the ∠EMS = 59 degrees.

In triangle JEA;

By angle sum property, we know that;

∠JAE + ∠AEJ + ∠EJA = 180 degree

Substitute the given values in the above expression.

48 degree + 90 degree + ∠EJA = 180 degree

∠EJA = 42 degrees

The angle JMS is,

∠JMS = 180 - ∠EMS (Linear pair)

∠JMS = 180 degrees - 59 degrees = 121 degrees.

In triangle JMS,

By angle sum property, we know that;

∠JMS + ∠JSM + ∠EJA = 180 degree

121 degree + ∠JSM + 42 degree = 180 degree

∠JSM = 17 degree

Thus, the measure of ∠JSM is 17 degrees.

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Given: The amout charged per ticket is $8.50

If x tickets are sold

Then the total revenue (amount made) will be =>

If t(x) represents how much the studio collects

and k(x) represents how much is kept

Given: t(x) = 75% then

k(x)= (100 -75)%= 25 %

So that

The total amount that will be kept will be

25% of $8.50x

=>

The amount that will be kept will be

= > $2.125x

Where x is the number of tickets

Average batting rate for the season is 0.432.

Given,

Number of hits in first half of the season =11

Number of hits in second half of the season = 5

Number of times at bat during first half of the season = 30

Number of times at bat during second half of the season = 7

then,

Total number of hits in the season = 11+5 = 16

Total number of times at bat during the season = 30+7 =37      

To find average batting rate use formula,

                                                      [tex]Average batting rate of season =\frac{Total number of hits in season}{Total number of at bat during season} \\\\=\frac{16}{37}\\\\ =0.432[/tex]

Hence, the batter's average batting rate for the season is 0.432.

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we can take any equation and solve for any variable, for example y will solve x from the second equation

now replace the value of x on the first equation

simplify

and solve for y

Value of y is 0 now we can replace y=0 on any equation and solve for x

for example I will replace y=0 on the second equation to find x

Value of x is 2

If we want to represent the solution as a point, the solution is

Answer:

405

Step-by-step explanation:

don't forget to follow rate like

Consecutive interior angles (Same side)

x = -8

The two angles are 136 + x and x + 56

The two angles are consecutive-interior angles because they are on the same side of the transversal.

Note that consecutive -interior angles are supplementary and they add up to 180 degrees.

Applying this rule to the diagram shown:

(136 + x) + (x + 56) = 180

136 + 56 + x + x = 180

192 + 2x = 180

2x = 180 - 196

2x = -16

x = -16 / 2

x = -8

To find the solution, lets first simplify the inequality:

Cube root of 30 is 3.107.

Cube root is the number that needs to be multiplied three times to get the original number.

The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:

Step 1: Start with the prime factorization of the given number.

Step 2: Then, divide the factors obtained into groups containing three same factors.

Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.

We have to find the cube root of 30.

Prime factorization of 30 = 2*3*5.

Therefore the cube root of 30 = ∛(2*3*5)= ∛30 .

As ∛30 cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.

So here we will use approximation method to find the cube root of 30 using Halley's approach:

Halley’s Cube Root Formula: ∛a = x[(x³ + 2a)/(2x³ + a)]

The letter “a” stands in for the required cube root computation.

Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.

Here we have a = 30

and we will substitute x = 3 because 3³ = 27< 30 is the nearest perfect cube.

Substituting a and x in Halley's formula,

∛30 = 3[(3³ + 2*30)/(2*3³ + 30)]

       = 3[(27+60)/(54+30)]

       = 3(87/84)

       = 3*1.0357

∛30 = 3.107.

Therefore the cube root of 30 is 3.107.

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Since the function starts at it maximum value, let's use a cosine function to represent it:

Since the midline of the periodic function is y = 2, we have A = 2.

The period of the function is 4pi/3, so we have:

Since the function already starts at its maximum value, there is no horizontal phase shift, so D = 0.

The amplitude is 1 (it goes up and down 1 unit from the midline), so we have B = 1.

Therefore the function is:

Answer:

B) 6.5

Step-by-step explanation:

Complementary angles are angles that are put together to equal 90 degrees.

Angle one is 32 degrees.

90-32= 58

So we need to get the number 58 for it to be complementary. The reason for this is because 32+58=90. Which would make it complementary.

When we plug in 6.5 we get 58, which is what we want.

12(6.5)- 20= 90

78-20=58

Hope this helps!!!

The value of x is 6.5.

Complimentary angles are known as angles which makes the sum of 90°.

The angles sum up to form a right angle. When two angles complement each other they sum up to be 90°.

According to question one angle - 32° and other angle [12x - 20].

⇒ 32 + [12x - 20] = 90

⇒ 12x - 20 = 58

⇒ 12x = 78

⇒ x = 6.5

Hence, the value of x is 6.5.

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The line y = -7x/3 is a line of symmetry to the given hexagon while the line y=x is not a line of symmetry to it

This makes the answer to the first statement Yes and the second statement No. That is

Reflective symmetry over the line y=-7x/3 -------------------Yes

Reflective symmetry over the x-axis ------------------------------------No

The vertices of the given figure are

A(1, -1), B(5.-6), and C(1, - 6).

For a 90 counterclockwise about the origin, a coordinate, (x, y) would be (- y, x)

This means that after the 90 degrees rotation,

coordinate A would be (- - 1, 1) = (1, 1)

Coordinate B would be (- - 6, 5) = (6, 5)

Coordinate C would be (- - 6, 1) = (6, 1)

a.

The dilation is a reduction, this comes from the fact that the dilation factor is less than 1.

b.

A point after a dilation is given as:

where k is the dilation factor.

In this case we need to divide all the coordinates by two, then we have that:

Given the algebraic expression below

Collect like terms

Add possible like terms using the distributive property of algebra

Hence, the final answer is 9a + 4y

Option D is correct

We can add the are of the 3 rectangle, so we get that the area is: