What is - 8/9 divided by 2/3

The results of factoring the polynomials are (x - 6)(x + 6), 3(x - 2)(x + 2), (x + 3)² and 4(x + 3)(x - 5)

First, we have

x² – 36

Applying the property of difference of squares, we have

(x - 6)(x + 6)

Next, we have

3x² - 12

Factor out 3

3(x² - 4)

Applying the property of difference of squares, we have

3(x - 2)(x + 2)

First, we have

x² + 6x + 9

Expand and factorize

x² + 6x + 9 = x² + 3x + 3x + 9 = (x + 3)²

Next, we have

4x² - 8x - 60

Expand and factorize

4x² - 8x - 60 = 4(x² - 2x - 15) = 4(x + 3)(x - 5)

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Answer:

C. (4, 0)

Step-by-step explanation:

(x, y)

a. (4, 3)

y = 12 - 3x

3 = 12 - 3(4)

3 = 12 - 12

3 = 0  false

b. (-4, 4)

y = 12 - 3x

4 = 12 - 3(-4)

4 = 12 + 12

4 = 24  false

c. (4, 0)

y = 12 - 3x

0 = 12 - 3(4)

0 = 12 - 12

0 = 0  true

d. (0, 4)

y = 12 - 3x

4 = 12 - 3(0)

4 = 12 - 0

4 = 12  false.

Answer:   C   (4, 0)

Step-by-step explanation:

your function y = 12 - 3x

They are asking which of those points are on the line

(x, y)   this is a format of a point where you can plug in x for x and y for y.

a.  (4, 3)  x=4  y=3  substitute and see if your answer is true

   3 = 12 -3(4)

   3 = 0   this is not true so (4, 3) is not a solution

b. (-4,4) x= -4 y=4

  4 = 12 - 3(-4)

  4 = 24  not true

c.  (4, 0)  x=4  y=0

  0 = 12-3(4)

  0 = 0  true      (4,0) is a solution

d. (0, 4)

4 =  12 - 3 (0)

4=12

The t-statistic value of the hypothesis is 2.236

The population mean is equal to 6,500 (H0: μ = 6500)

Alternative hypothesis:

The population mean is greater than 6,500 (Ha: μ > 6500)

We are given the sample mean (x) = 6,600, sample size (n) = 500, population standard deviation (σ) = 1,000, and level of significance (α) = 0.05.

First, we need to calculate the t-statistic using the formula:

t = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (6,600 - 6,500) / (1,000 / √500)

= 2.236

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The total volume of the original mixture is 4 liters.

Given that:

A mixture of 50% alcohol and 50% water has 4 liters of water added to it. It is now 25% alcohol.

Let 'x' be the amount of water and alcohol. Then we have

x / (x + x + 4) = 0.25

x/(x + 2) = 0.5

2x = x + 2

x = 2

The total volume of the original mixture is calculated as,

Total volume = x + x

Total volume = 2 + 2

Total volume = 4 liters

The total volume of the original mixture is 4 liters.

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Based on the conditions, the correct statements are,

⇒  Bracelet B has 8 more letter beads than Bracelet A.

We have to given that;

Donovahn made two bracelets for a friend.

And, Each bracelet is made of 36 beads. Bracelet A contains 12 letter beads Bracelet B contains 20 letter beads.

Hence, We have;

Based on the information provided, we can say that Bracelet B contains more letter beads than Bracelet A.

Specifically, Bracelet B has 8 more letter beads than Bracelet A.

Thus, Based on the conditions, the correct statements are,

⇒  Bracelet B has 8 more letter beads than Bracelet A.

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The values of AB and BC are equal and equal to

Information given in the problem includes

DE bisects AC at point B

AC = a + 23

AB = 3a + 4

From  the definition of a bisector, point B divides AC into two equal sides, this means that

AB = BC = (1/2) * AC

Substituting the value of AC and AB

AB = 3a + 4 = (1/2) * (a + 23)

3a + 4 = (1/2) * (a + 23)

solving for a

2 * (3a + 4) = a + 23

6a + 8 = a + 23

6a - a  = 23 - 8

5a = 15

a = 3

Then we have that:

AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13

and, AB = BC

so BC = 13

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Answer:

f(- 4) = 44 , g(5) = - 21

Step-by-step explanation:

to evaluate f(- 4) substitute x = - 4 into f(x)

f(- 4) = 2(- 4)² - 3(- 4) = 2(16) + 12 = 32 + 12 = 44

to evaluate g(5) substitute x = 5 into g(x)

g(5) = - 4(5) - 1 = - 20 - 1 = - 21

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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The value of x as shown in the triangular prism is 14 unit.

Triangular pyramids are formed solely from triangles. The 3 triangular sides slant upwards to form the triangular base.

To calculate the value of x of the rectangular pyramid, we use the formula below

Formula:

Where:

From the diagram and the question,

Given:

Substitute these values into equation 1 and solve for x

Hence, the value of x is 14 unit.

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Answer:

[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]

Step-by-step explanation:

As we know that

The standard equation of a parabola with vertex at point (h,k) is given by:

[tex]y = a(x-h)^2 + k[/tex]

where (h,k) is the vertex

and "a" is a coefficient that determines the direction and shape of the parabola.

We know that the vertex of our parabola is (-2, 6),

so we can substitute those values into the equation to get:

[tex]y = a(x + 2)^2 + 6[/tex]

Now finding a.

Since the parabola passes through point (-4, -5). Substituting these coordinates into the equation, we get:

-5 = a(-4 + 2)^2 + 6

-5 =a(-2)^2+6

-5=4a +6

-5-6=4a

4a=-11

a =- 11/4

Substituting the value of an equation second, we get

[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]

Therefore, the equation of the parabola with a vertex at (-2, 6) and passing through (-4, -5) is y =

[tex] \frac{-11}{4} (x + 2)^2 + 6[/tex]

Answer:

[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]

Step-by-step explanation:

The vertex form of a parabola is:

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

Given the vertex is at (-2, 6), substitute h = -2 and k = 6 into the equation:

[tex]y=a(x-(-2))^2+6[/tex]

[tex]y=a(x+2)^2+6[/tex]

To find the value of a, substitute the point (-4, -5) into the equation and solve for a:

[tex]\begin{aligned}-5&=a(-4+2)^2+6\\-5&=a(-2)^2+6\\-5&=4a+6\\-5-6&=4a+6-6\\-11&=4a\\\dfrac{-11}{4}&=\dfrac{4a}{4}\\-\dfrac{11}{4}&=a\\a&=-\dfrac{11}{4}\end{aligned}[/tex]

Substitute the found value of a back into the equation:

[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]

Therefore, the equation of a parabola with a vertex at (-2, 6) and that passes through the point (-4, -5) is:

[tex]\boxed{y=-\dfrac{11}{4}(x+2)^2+6}[/tex]

The bank employs a total of 32 bankers, and the answer is not listed among the options provided. The correct option is B.

Let's denote the number of bankers who manage only personal loans as P and the number of bankers who manage only business loans as B. Then, we can use the following information to form equations:

There are 20 bankers who manage personal loans, which means P + 3 bankers in total manage personal loans.

There are 25 bankers who manage business loans, which means B + 3 bankers in total manage business loans.

The bank has a total of X bankers.

Using these equations, we can solve for X as follows:

P + 3 = 20 (equation 1)

B + 3 = 25 (equation 2)

P + B + 3 = X (equation 3)

Solving equation 1 for P, we get P = 17.

Solving equation 2 for B, we get B = 12.

Substituting P = 17 and B = 22 into equation 3, we get:

17 + 12 + 3 = X

Simplifying, we get X = 32.

Therefore, the bank employs a total of 32 bankers, and the answer is not listed among the options provided.

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Answer:

x^2y^4

Step-by-step explanation:

b because u have to add the exponents of the like variable. x^4 and x^-2 are the like terms in this equations so 4+(-2) so its basically flipping the signs plus and the negative sign so it's just -2

The linear inequality with the solution set (2,-5), (-5,-5), (-5,5), (5,5), (5,-2) are x ≤ 5 and y ≤ 5

The solution set is given as

(2,-5), (-5,-5), (-5,5), (5,5), (5,-2)

We can see that the highest y value in the above ordered pairs is 5

So, we have

y ≤ 5

Also, we can see that the highest x value in the above ordered pairs is 5

So, we have

x ≤ 5

Hence, the linear inequality with the solution set is x ≤ 5 or y ≤ 5

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The task here is to determined where the table given is a function. Thus we can state that the above table is NOT a function. This is called Non-Function Relation.

The table given above is suggestive of the relationship between the values of x and y given.

It may be inferred that x values are the input values while the y values are the output.

So the criteria for the values on the table to constitute a function is that each input value (x) must be associated with only one value of y.

From the table, it is clear to see that this rule if violated. You have the x value (-1) being associated with the y values of 2 and 4 respectively, hence, it is proper to conclude that the table is NOT  a function.

This is called a Non-Function Relation.

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Answer:

A. 45(x+3)=60x

Step-by-step explanation:

Step-by-step explanation:

Use the Ratio Test since Ratio Test guarantee absolutely convergence.

[tex] \frac{ ( - 1) {}^{k + 1}(k + 1) {}^{a} }{5 {}^{k + 1}(3(k + 1) } \times \frac{5 {}^{k}(3k) }{(k) {}^{a} ( - 1) {}^{k} } [/tex]

This simplifes to

[tex] \frac{( - 1) {}^{k} ( - 1) ((k + 1)!) {}^{a} }{5 {}^{k}(5)(3k +1) ! } \times \frac{5 {}^{k} (3k)!}{( - 1) {}^{k} (k!) {}^{a} } [/tex]

[tex] \frac{ - (k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]

Take the absolute value

[tex] \frac{(k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]

In order for this series to be convergent,

the limit as k approaches infinity must be less than 1.

In order for this series to have a limit less than 1, our numerator and denominator degree must be equal or the denominator must have the larger degree.

Why

If the numerator has a larger degree, our test would make this divergent, so the limit would be infinity

Since the denominator have 3 binomials, our power for the denominator will be 3, this the numerator having a degree of 3 or less as well.

So one of the answer is 3.

The length of the arc FG is 12.56 units

Length of an arc is the distance that runs through the curved line of the circle making up the arc.

An arc is a cut out section of a circle. The circumference is the whole body of the circle.

The length of an arc is expressed as

(tetha))360 × 2πr

where r is the radius and tetha is the angle between the radii.

l = 72/360 × 2 × 3.14 × 10

l = 4521.6/360

l = 12.56 units

therefore the length of the arc FG is 12.56 units

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The volume of water in the aquarium up to the 15 inch mark is 3465 cubic inches.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

The volume of water in the aquarium up to the 15 inch mark will be equal to the volume of a rectangular prism with a length of 21 inches, a width of 11 inches, and a height of 15 inches.

This is because the water level is 15 inches from the bottom of the aquarium.

Hence, the volume of water in the aquarium up to the 15 inch mark is:

V = l × w × h

V = 21 × 11 × 15

V = 3465 cubic inches

Therefore, the volume of water in the aquarium is 3465 cubic inches.

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After 1 half-life, the amount of the element remaining is half of the original amount. After 2 half-lives, the amount remaining is half of the remaining amount after the first half-life. We can continue this pattern until we get to 30 days.

The number of half-lives in 30 days is 30/5 = 6.

So, after 1 half-life, the amount remaining is 948/2 = 474 grams.

After 2 half-lives, the amount remaining is 474/2 = 237 grams.

After 3 half-lives, the amount remaining is 237/2 = 118.5 grams.

After 4 half-lives, the amount remaining is 118.5/2 = 59.25 grams.

After 5 half-lives, the amount remaining is 59.25/2 = 29.625 grams.

After 6 half-lives, the amount remaining is 29.625/2 = 14.8125 grams.

Therefore, after 30 days, 14.8125 grams of the element remains

The minimum selling price per brownie to make a daily profit of at least $420 is $1.30.

Given that: A baker produces 400 brownies a day at a cost of 25 cents per brownie.

Let's begin by calculating the total cost of producing 400 brownies a day:

Cost per brownie = 25 cents = 0.25 dollars

Total cost = 400 × 0.25 = 100 dollars

To make a daily profit of at least $420, the total revenue should be:

Total revenue = Total cost + Minimum profit

Total revenue = 100 + 420 = 520 dollars

The minimum selling price per brownie to achieve this revenue can be calculated as:

Selling price per brownie = Total revenue / Number of brownies produced

Selling price per brownie = 520 / 400

Selling price per brownie = 1.3 dollars

Therefore, the minimum selling price is $1.30 per brownies.

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Answer:

$3.58

Step-by-step explanation:

Because we know that the 2 lbs of bananas will be purchased at the same rate, the price per pound for 5 lbs of bananas is proportional to the price per pound for 2 lbs of bananas.

Thus, we can solve for price, p of 2 lbs of bananas by setting up a proportion:

[tex]\frac{8.95}{5}=\frac{p}{2}\\ \\ 17.90=5p\\\\3.58=p[/tex]

The value of x in the triangle is 1/√3

We know that tan function is the ratio of opposite side and adjacent side

In triangle, for angle 60 degrees the opposite side is 1 unit

Adjacent side is x units

tan 60 = opposite side/adjacent side

√3= 1/x

We need to find value of x

Apply cross multiplication

x=1/√3

Hence, the value of x in the triangle is 1/√3

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Answer:

The answer is D.

[tex] \frac{1}{5}(12x - 10)[/tex]

The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)

From the question, we have the following function definition that can be used in our computation:

cos(xº)

Changing the degree into radian, we have

cos(xπ/180)

Express as a function

So, we have

y = cos(xπ/180)

When the cosine function is differentiated, we have

y' = -sin(xπ/180)

Hence, the differentiated function is y' = -sin(xπ/180)

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The graph of the function f(x) = 5(3)ˣ - 1 is represented as the diagram given in option C.

To find the main points of the function f(x) = 5(3)ˣ - 1, we can identify its key features such as the y-intercept, x-intercept, and any asymptotes.

Y-intercept:

To find the y-intercept, we set x = 0 and evaluate the function:

f(0) = 5(3)⁰ - 1 = 4

Therefore, the y-intercept is (0,4).

Asymptotes:

There are no vertical asymptotes for this function since the base of the exponential function, 3, is positive.

The graph of the function is given in the attached image.

Therefore, the correct option is C.

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If each tile cost $2 then the amount spend by  Nicole’s mother on tiles is $130

Given that Nicole‘s mother put tiles on a section of the kitchen floor.

The section included 5 rows with 13 tiles in each row

Each tile cost $2.

To find the total amount spend by Nicolas mother on tiles we have to find the number of tiles

Number of tiles =5×13

=65 tiles

Now let us find the amount

Total amount on tiles = 2×65

=$130

Hence, if each tile cost $2 then the amount spend by  Nicole’s mother on tiles is $130

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The maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.

It should be noted that upon deriving v(t), an equation of 12t² - 96t + 144 is produced. Subsequently, v'(t) must be set to zero, resulting in a quadratic equation of 12t² - 96t + 144 = 0, requiring division of both sides by 12 to produce t² - 8t + 12 = 0.

The quadratic can now be factored to obtain (t - 2)(t - 6) = 0, indicating that critical points lie on the values t = 2 and t = 6.

After calculating these values— v(1) = 100 m/s, v(2) = 64 m/s, v(6) = 16 m/s and v(7) = 1159 m/s—it is clear that the maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.

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The shapes that would be made if the figure is cut along the dotted line are  a right angled- triangle and a semi - circle.

Upon reviewing this shape, we observe that it is comprised of two distinct shapes: a right-angled triangle and a semicircle.

This means that if the figure was cut along the dotted lines that joined them, the shapes that would be made are the same shapes which are a right triangle and a semi - circle.

In conclusion, the shapes would be a semi - circle and right triangle.

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Answer:

$3

Step-by-step explanation:

since $12 is 4/4 and he save 1/4 its 12÷4

Answer:

$3

Step-by-step explanation:

12 divided by 4 is 3

(3+3)+(3+3)

6+6

= 12