1. If you were given a quadratic equation that will factor, explain how you would find thesolutions of the equation. (3 Points)

The number of millimeters in each glass is 200ml.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.

It is important to note that some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

Since Cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape. The amount in each will be:

= (2l - 400ml )/8

= (2000 - 400) / 8

= 1600 / 8

= 200ml

Therefore, based on the calculation, there'll be 200 millimeters on each glass.

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Complete question

cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape. How many ml will each contain?

The first equation is incorrect.

The second equation is correct.

The third equation is correct.

Let's go through each equation and determine whether it is correct or incorrect:

(b²+7b-9)+(4b-6b²) = -8b² + 14b-9

To determine if this equation is correct, we need to simplify both sides and check if they are equal.

On the left side:

(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9

On the right side:

-8b² + 14b - 9

Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.

(4a+6)-(3a²-9a+1)=-3a²+ 13a +5

Again, we need to simplify both sides of the equation and check if they are equal.

On the left side:

(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5

On the right side:

-3a² + 13a + 5

Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.

(12c-8c²)+(5c²- 10c) = -3c²+2c

Again, let's simplify both sides and compare them.

On the left side:

(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c

On the right side:

-3c² + 2c

Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.

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Answer:

x = 30

y = 2

Step-by-step explanation:

Please note: the value for x is correct only if this triangle is a right triangle.

This can be solved because 2(5y) = 20 and because if a triangle has all congruent angles then its side lengths are also congruent.

The dimensions of the rectangular garden which minimize the cost is equal to 9.6ft and 14.6ft respectively.

As given in the question,

Cost of brick wall is equal to $40/ft

Cost of metal fencing is equal to $20/ft

Let 'x' and 'y' are the dimensions of the rectangular garden

Area of the rectangular garden = 142 square feet

⇒ 142 = xy

⇒x = 142/y

Costing of four side fencing 'C' = 40x + 20x + 20y + 20y

⇒ C = 60x + 40y

⇒C = 60(142/y) + 40y

⇒C = 8520/y + 40y

Differentiate with respect to y

dC/dy = -8520/ y² + 40

Put dC/dy = 0

-8520/ y² + 40 = 0

⇒y² = 8520/40

⇒y = √213

⇒ y= 14.6 ft

⇒ x= 142/14.6

     = 9.7 ft

Therefore, the dimensions of the rectangular garden with the given area which minimize the cost is equal to 14.6ft and 9.7ft.

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Step-by-step explanation:

hey guys how do you put a picture like you did ?

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

The probability of forming this committee with equal representation is approximately 0.570 or 57.0%.

The total number of individuals in the ATU COVID-19 team of Marshalls is 50 (13+15+10+12). To form an executive committee of 16 with equal representation, we need to choose 4 individuals from each group (4 lecturers, 4 students, 4 administrative staff, and 4 medical personnel).
Using the combination formula, we can calculate the number of ways to choose 4 individuals from each group:
C(13,4) × C(15,4) × C(10,4) × C(12,4) = 715 × 1,455 × 2,385 × 4,095 = 7,976,476,875
Therefore, there are 7,976,476,875 possible ways to form the executive committee with equal representation.
To calculate the probability of forming this committee, we need to divide the number of possible ways by the total number of ways to choose any 16 individuals from the ATU COVID-19 team of Marshalls:
C(50,16) = 13,983,816
The probability of forming the executive committee with equal representation is:
7,976,476,875 / 13,983,816 = 0.570

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The graph of the Line Segment BC with the endpoints B(8,9) and C(-4,5) is shown below.

In the question ,

it is given that ,

the end points of the line segment is B(8,9) and C(-4,5) .

we have to graph the line segment BC.

first we mark the point on the coordinate plane , with point B and point C .

after that we join the points .

and the equation of the line segment is

(y - 5) = (9-5/8+4)*(x + 4)

(y - 5) = (1/3)*(x + 4)

3y - 15 = x + 4

x - 3y + 19 = 0

Therefore, the graph of the line segment BC is shown below.

The given question is incomplete , the complete question is

Graph line segment BC with endpoints B(8,9) and C(-4,5) and label the points.

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The center of the circle is (4, 7) and the radius is 7

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

(x - 4)^2 + (y - 7)^2 = 49

A circle equation is represented as

(x - a)^2 + (y - b)^2 = r^2

Where

Center - (a, b)

Radius = r

Using the above as a guide, we have the following:

(a, b) = (4, 7)

r^2 = 49

Evaluate

(a, b) = (4, 7)

r = 7

Hence, the radius of the equation is 7

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Answer:

Given Figure has set of Stacked cubes.

To Draw the Base Plan, lets see its right side, Left Side and Front side view.

Right side:

It has 3 cubes in base.

2 cubes in 2nd layer clearly seen in figure and only 1 cube in 3rd layer.

Left Side:

It has 2 Cubes in base.

Both Cubes attached to 1st and 2nd cube of right side cubes.

Front Side:

It can be seen that, here base only has 2 rows of cubes.

Therefore,  1st Figure is correct Base Plan (or enclosed figure)

Note: Numbers in enclosed figure just shows the total no. of cubes in that stack.

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Answer:

1.8 meters

Step-by-step explanation:

Multiply 12 by 0.15 to get your answer. You multiply because the question says "15% of 12 meters" which means you need to multiply.

Answer: 1.8

Step-by-step explanation:

Multiply 12 by .15 (15% as a decimal), and you'll get 1.8 meters. You multiply, because it says 15% of 12 meters.

Answer:

(4,0)

Step-by-step explanation:

You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!

Answer:

The mean of this set of numbers is 6.6.

Step-by-step explanation:

To find the mean, first add all of the above numbers together.

5+7+3+7+9+11+8+7+6+3= 66

Now, simply divide 66 by the number of numbers added together. In this case, that will be 10.

66/10=6.6

The mean of this set of numbers is 6.6.

Answer:

6.6

Step-by-step explanation:

Mean is found by adding up all the values of the numbers, and dividng by the amount of aforementioned numbers.In this case, the followign would occur...

First, we add up all the numbers:

5+7+3+7+9+11+8+7+6+3 =   66

Then, we count how many numbers there are:

10

Finally we divide the value from step 1 by the value from step 2:

66/10 = 6.6

Answer:

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

Let the numbers be s and l.

We are given that:

Set up equations:

Eliminate l:

Solve for s:

Find l:

It's not entirely clear to me what you're trying to solve, but it looks like the initial equation is

\(\dfrac{a-2}{a+3} -1 = \dfrac3{a+2}\)

First convert each term into a fraction with the same (i.e. the least common) denominator. The first term needs to be multiplied by a + 2; the second term by (a + 3) (a + 2); and the third term by a + 3 :

\(\dfrac{a-2}{a+3}\cdot\dfrac{a+2}{a+2} -1\cdot\dfrac{(a+3)(a+2)}{(a+3)(a+2)} = \dfrac3{a+2}\cdot\dfrac{a+3}{a+3} \\\\ \dfrac{(a-2)(a+2)}{(a+3)(a+2)} - \dfrac{(a+3)(a+2)}{(a+3)(a+2)} = \dfrac{3(a+3)}{(a+3)(a+2)}\)

Now that everything has the same denominator, we can combine the fractions into one. Move every term to one side and join the numerators:

\(\dfrac{(a-2)(a+2)-(a+3)(a+2)-3(a+3)}{(a+3)(a+2)} = 0\)

Simplify the numerator:

\(\dfrac{(a^2-4)-(a^2+5a+6)-(3a+9)}{(a+3)(a+2)} = 0 \\\\ \dfrac{-8a-19}{(a+3)(a+2)} = 0\)

If neither a = -3 nor a = -2, we can ignore the denominator:

\(-8a-19 = 0\)

Solve for a :

\(-8a = 19 \\\\ \boxed{a = -\dfrac{19}8}\)

Answer:

Option A: (4, -15).

Step-by-step explanation:

Given the quadratic function, y = x² - 8x + 1, where a = 1, b = -8, and c = 1:

We can use the following equation to solve for the x-coordinate of the vertex:

\(\displaystyle\mathsf{x\:=\:\frac{-b}{2a}}\)

Substitute the given values into the formula:

\(\displaystyle\mathsf{x\:=\:\frac{-b}{2a}\:=\:\frac{-(-8)}{2(1)}\:=\:\frac{8}{2}\:=\:4}\)

Hence, the x-coordinate of the vertex is 4.

Next, substitute the x-coordinate of the vertex into the given quadratic function to solve for its corresponding y-coordinate:

y = x² - 8x + 1

y = (4)² - 8(4) + 1

y = 16 - 32 + 1

y = -15

Therefore, the vertex of the given quadratic function, y = x² - 8x + 1, is: x = 4, y = -15, or (4, -15).  Thus, the correct answer is Option A: (4, -15).

Answer:

A. (4, -15)

Step-by-step explanation:

\(\underline{\mathrm{Parabola\:equation\:in\:polynomial\:form}}\)

\(\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:y=ax^2+bx+c\:\mathrm{is}\:x_v=-\frac{b}{2a}\)

\(\mathrm{The\:parabola\:params\:are:}\)

\(a=1,\:b=-8,\:c=1\)

\(x_v=-\frac{b}{2a}\)

\(x_v=-\frac{\left(-8\right)}{2\cdot \:1}\)

\(x_v=4\)

\(\mathrm{Plug\:in}\:x_v=4\:\mathrm{to\:find\:the}\:y_v\mathrm{value}\)

\(y_v=-15\)

\(\mathrm{Therefore\:the\:parabola\:vertex\:is}\)

\(\left(4,\:-15\right)\)

\(\mathrm{If}\:a<0,\:\mathrm{then\:the\:vertex\:is\:a\:maximum\:value}\)

\(\mathrm{If}\:a>0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}\)

\(a=1\)

\(\mathrm{Vertex\:of}\:x^2-8x+1:\quad \mathrm{Minimum}\space\left(4,\:-15\right)\)

Answer:

C and F

Step-by-step explanation:

Those two just work, that simple

The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Like usual, we can solve this question using an equation. Let’s assume that John’s age is x, and his sister’s age is y.

x = 2y

To figure out John’s age, we need to know his sister’s age. He’s 2 times older than his sister.

x + y = 27

The sum of their ages is 27, and we can substitute the value of x here to figure out y.

2y + y = 27

We can now simplify this, and get y by itself.

3y = 27

Now, we can divide by 3 to get the y by itself.

y = 9

We now know that John’s sister is 9.

Now, using our original equation, we can substitute in the value of y.

x = 2(9)

We can simplify this.

x = 18

John’s age is 18!

Hope this helps.

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Based on the statistical analysis, there is not enough evidence to conclude that the water from the new source contains unsafe levels of copper at the 0.05 significance level.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves applying mathematical and statistical techniques to extract meaningful insights from data, and to make decisions and predictions based on this information. Statistics is used in a wide range of fields, including business, economics, social sciences, health sciences, engineering, and more. It helps researchers, analysts, and decision-makers to identify patterns, relationships, and trends in data, and to draw conclusions based on statistical evidence.

(a) To test whether the water from this source contains unsafe levels of copper, we need to perform a one-sample t-test with the null hypothesis that the mean copper content in the water is less than or equal to 1.3 mg/l and the alternative hypothesis that the mean copper content in the water is greater than 1.3 mg/l.

The test statistic is calculated as:

t = (x - μ) / (s / √n)

where x is the sample mean (1.36 mg/l), μ is the hypothesized population mean (1.3 mg/l), s is the sample standard deviation (0.18 mg/l), and n is the sample size (30).

Plugging in the values, we get:

t = (1.36 - 1.3) / (0.18 / √30) = 1.47

The degrees of freedom for this test is n - 1 = 29.

Using a t-table or calculator, we find the p-value associated with a t-statistic of 1.47 and 29 degrees of freedom to be approximately 0.076.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence at the 0.05 level to conclude that the water from this source contains unsafe levels of copper.

Conditions for Independence: It is assumed that the water samples are independent of each other. This is because the sample is randomly selected and the size is less than 10% of the population. Also, it is assumed that the copper content in one water sample does not affect the copper content in another water sample.

Conditions for Normality: It is assumed that the distribution of the copper content in the population is approximately normal. We can justify this assumption based on the central limit theorem, which states that the distribution of the sample mean approaches normality as the sample size increases. Since the sample size is 30, we can assume that the sample mean follows a normal distribution. We can also check the normality assumption by creating a histogram or a normal probability plot of the data.

Therefore, based on the statistical analysis, there is not enough evidence to conclude that the water from the new source contains unsafe levels of copper at the 0.05 significance level.

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The function represented by the graph given is equivalent to -

g(x) = (x - 4)².

The function plotted represents a quadratic equation. A quadratic equation has a degree of 2. The given function is shifted to the left by 4 units. This means that the following transformation will take place on the x - coordinate of each and every point lying on the graph -

f(x, y) → f(x - 4, y)

So, we can write the function as -

g(x) = (x - 4)²

So, the function represented by the graph given is equivalent to -

g(x) = (x - 4)²

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Mr. Lloyd could use his credit card to buy the TV. Therefore, option  A is the correct answer.

Using a credit card to make a purchase requires that the buyer have a credit limit that is large enough to cover the amount of the purchase. Mr. Lloyd does not have enough money in his bank account to pay for the television, so he would not be able to use a credit card to make the purchase.

Options B, C, and D are all viable options for Mr. Lloyd. He could save up money and pay cash for the television at a later date, or he could use his debit card to make the purchase when he has enough money in his bank account. He could also save money and use his debit card at a later date when he has enough money in his bank account.

Therefore, option  A is the correct answer.

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Mr. Lloyd wants to buy a new television, but he does not have enough money in his bank account to pay for one. Which of these is NOT an option for Mr. Lloyd?

A) He can use his credit card to buy the television now.

B) He can save money and pay cash for the television at a later date.

C) He can use his debit card to buy the television now.

D) He can save money and use his debit card to buy the television at a later date.

Answer:

it would be what they said

Step-by-step explanation:

so sorry i need 50 pts

Answer:

Oh this is easy 24

Step-by-step explanation:

2x4=8x3=24

Answer:

There are 200 factory workers employed at steel mill.

Step-by-step explanation:

Let the total number of workers employed at steel mill be 'x'.

Now Given:

Percentile Number of workers purchased breakfast = 26%

So we can say that;

Number of workers purchased breakfast = \(\frac{26}{100}x=0.26x\)

Also Given:

Number of workers brought breakfast from home = 148

Solution:

Now we can say that;

total number of workers employed at steel mill is equal to sum of Number of workers purchased breakfast and Number of workers brought breakfast from home.

framing in equation form we get;

\(x=0.26x+148\)

Combining the like terms we get;

\(x-0.26x=148\)

\(0.74x=148\)

Dividing both side by 0.74 we get;

\(\frac{0.74x}{0.74} =\frac{148}{0.74}\)

\(x=200\)

Hence There are 200 factory workers employed at steel mill.