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Given:

The law of syllogism states that,

For the given data,

The steps that can be used are:

2(x² + 6x) = 3

2(x² + 6x + 9) = 3 + 18

Options B and C is the correct answer.

The solution for the quadratic equation is

x = (-12 + 2√42) / 4

x = (-12 - 2√42) / 4

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

2x² + 12x - 3 = 0

This is in the form of ax² + bx + c = 0

Now,

a = 2

b = 12

c = -3

We can solve this using the determinant formula.

Where,

D = -b ± √(b² - 4ac) / 2a

D = -12 ± √(144 +24) / 4

D = -12 ± √168 / 4

D = -12 ± √(4 x 42)/4

D = -12 ± 2√42 / 4

So,

x = (-12 + 2√42) / 4

x = (-12 - 2√42) / 4

The solution for the quadratic equation is

x = (-12 + 2√42) / 4

x = (-12 - 2√42) / 4

The following options are given:

2(x² + 6x + 9) = –3 + 9

2x² + 12x + 18 = -3 + 9

2x² + 12x + 18 + 3 - 9 = 0

2x² + 12x + 12 = 0

This is not true.

2(x² + 6x) = 3

2x² + 12x - 3 = 0

This is true.

2(x² + 6x + 9) = 3 + 18

2x² + 12x + 18 = 3 + 18

2x² + 12x - 3 = 0

This is true.

x + 3 = ± 21/2

Not true.

2(x² + 6x) = –3

2x² + 12x + 3 = 0

This is not true.

Thus,

The steps that can be used are:

2(x² + 6x) = 3

2(x² + 6x + 9) = 3 + 18

Options B and C is the correct answer.

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Answer:

length: 16ft

breadth:- 12ft

Slope intercept form:

y= mx + b

where:

m= slope

b= y intercept

m= 0

Replace (x,y) by the given point (3,-14) and solve for b

-14 = 0 (3)+ b

-14 = b

Slope intercept form:

y= - 14

Standard form:

Ax+BY = C

y = -14

Answer:

1) 15000*(1+0.0189)^(5*12) = 46130.16346

2) 15000*(1+0.01975)^(5*3) = 20113.9316

3) 15000*(1+0.0199)^5 = 16553.0954

4) 15000*(1+0.0325*5) = 17437.5

The first one is the best option.

The required solutions are x = 15/8 and y = 1/2 which is determined by the elimination method.

Given the linear system of equations as

y = 2 - 4x +6  or

4x + y = 8 …(i)

y= - 5² + 20x - 12 or

20x - y = 37 …(ii)

Equations (i) and (ii) constitute a system of two first-degree equations in the two variables x and y.

So, we have to find out the value of 'x’ and 'y’.

Add equation (i) and equation (ii), we get

4x + y + 20x - y = 8 + 37

24x = 45

x = 45/24

x = 15/8

Substitute the value of 'x’ into equation (i) and we get

4(15/8) + y = 8

60/8 + y = 8

y = 8 - 15/2

y = 1/2

Hence, the required solutions are x = 15/8 and y = 1/2.

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Answer:

[tex]c=\frac{t-10}{m}[/tex]

Step-by-step explanation:

[tex]t=10+cm[/tex]

Subtract 10 from both sides:

[tex]t-10=cm[/tex]

Divide both sides by [tex]m[/tex]:

[tex]\frac{t-10}{m}=c[/tex]

Placing [tex]c[/tex] on the left:

[tex]c=\frac{t-10}{m}[/tex]

For example, if the total charge is $27.50 and the distance ridden is 250 mi, we can calculate the additional cost per mile, as such:

[tex]c=\frac{27.50-10}{250}[/tex]

[tex]c=0.07[/tex]

Given:

Number of plants she has = 17

She will put 2 plants in some rows and i plant in other rows.

Let's determine the number of ways in which she plant the tomato plants.

Maximum number of rows with 2 plants = 17/2 = 8.5

There will be a maximum of 8 rows with 2 plants

To determine, let's solve using a table.

We have:

Rows with 2 plants: 1 2 3 4 5 6 7 8

Rows with plants: 16 13 11 9 7 5 3 1

Total plants: 17 17 17 17 17 17 17 17

We can see the maximum number of rows possible is 8 rows.

Therefore, Ms. Hernandez can plant the tomaoto plants 8 ways.

ANSWER:

8 Ways

The lines L1 and L2 are parallel and the Line L1 and L4 are not perpendicular .

In the question ,

it is given that ,

there are four line on the graph ,

to check whether lines are parallel or perpendicular , we need slope,

the Line L4 passes through the points , (0,-5) and (-2,-5),

slope = (-5+5)/(-2)

= 0

the Line L1 passes through the points (-3,-2) and (-6,-8) ,

slope = (-8+2)/(-6+3)

= -6/(-3)

= 2 ,

for the lines to be perpendicular the product of slope should be -1,

but the product of slope of Line1 and Line 4 is 0 .

So , they are not perpendicular .

the line L2 passes through the points (3 , 3.5) and (0 , -2.5) ,

slope = (3.5+2.5)/3

= 6/3

= 2 ,

Since the slope of Line1 and Line2 are equal ,

So , they are parallel .

Therefore , The lines L1 and L2 are parallel and the Line L1 and L4 are not perpendicular .

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a. The customer will earn $1440 as a interest after 20 years.

b. The account balance will be $5,940 after 20 years.

What is the simple interest?

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied.

The formula of simple interest is I = Prt.

P = principal

r = rate of interest per year.

t = time.

Given that, a customer deposits  $4,500 for 20 years.

According to question, P = $4,500, r =1.6% = 0.016, t = 20 year

Putting the value of P, r, and t in I = Prt:

I =4,500 × 0.016 ×20

I =4,500 × 0.016 ×20

I = 1440

The interest is $ 1440.

The account balance will be $(1440 + 4,500) = $5,940.

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Answer:

This table does not show a probability distribution because probabilities cannot be negative, and they cannot be greater than 1.

ANSWER

The closest measurement is 300cm³

EXPLANATION

The volume of a pyramid is:

where B is the ares of the base and h is the height.

In this problem, B = 64cm² and h = 14cm. The volume is:

The one that's closest is 300cm³

To find out the value of z we can use the formula

But we also have to find out the value of w, which be found using the equation

Which needs the value of x, which be found using

But instead of doing all that and finding the value of x, w and z. We can directly find z using the fact that

Because it's all angles opposite by a vertex, and the sum of them all will be 360º, then we can say that

Therefore, z = 110º.

♥ The given parameters are:

x = -2, y = 3 and z = -1/5

The expression is given as xyz

To evaluate the expression when x = -2, y = 3 and z = -1/5, we substitute x = -2, y = 3 and z = -1/5 in expression xyz

This is represented as xyz = -2 * 3 * -1/5

Evaluate the product in the above expression

So, we have xyz = 6/5

Hence, the value of the expression when x = -2, y = 3 and z = -1/5  is 6/5  ♥

We will find the vertex of the parabola as follows:

*Given a quadratic function of the form:

We will have that the vertex is given by:

So, for the function given we will have the following vertex:

So, the vertex for the function is given by the ordered pair (-4, 16).

We will have that the equation of the axis of symmetry is given by:

So, the axis of symmetry is x = -4.

We will determine the x-intercepts as follows:

So, we will have that the x-intercepts are located at x = -8 & x = 0.

From the previous point we can see that the point (0, 0) belongs to the parabola, thus the y-intercept is y = 0.

f(4) = -8 is another way of saying the point is (4 , -8)

f(-3) = 1 is another way of saying the point is (-3 , 1)

to get the equation of any straight line, we simply need two points off of it, so let's use those two provided

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{4}}} \implies \cfrac{1 +8}{-7} \implies \cfrac{ 9 }{ -7 } \implies - \cfrac{9 }{ 7 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{- \cfrac{9 }{ 7 }}(x-\stackrel{x_1}{4}) \implies y +8 = - \cfrac{9 }{ 7 } ( x -4) \\\\\\ y+8=- \cfrac{9 }{ 7 }x+\cfrac{36}{7}\implies y=- \cfrac{9 }{ 7 }x+\cfrac{36}{7}-8\implies {\Large \begin{array}{llll} y=- \cfrac{9 }{ 7 }x-\cfrac{20}{7} \end{array}}[/tex]

Explanation:

We're told from the question that 200 students took part in the exercise, so if the total number of girls is 100 then the total number of boys will be;

To find how many more girls than boys chose Biology, we'll have;

So 21 more girls than boys chose Biology.

To graph the inequality:

We use the x and y-intercepts.

When x=0

We have the point: (0, 5.5)

When y=0

We have the point: (-1.83, 0)

We plot the points (0, 5.5) and (-1.83,0).

The points are joined using a broken line because of the inequality sign: >

The graph is shown below:

To determine which side is required, we use the origin test.

When x=0 and y=0

This means the side of the line containing (0,0) is where we need. (Shaded above)

(a) Solve the inequality: n > 12

(b) The greatest amount of trips that Edwin can take up the mountain and still pay less than Rhea would be 63

What is Inequality?

Inequality of wealth in major cities Economic inequality comes in many forms, but two stand out above the rest: wealth inequality as measured by the distribution of wealth and income inequality as measured by the distribution of income.

Edwin and Rhea, two siblings, decide on distinct payment arrangements even though they are both going skiing.

In Edwin's proposal, rentals cost $45 and each lift up the mountain costs $5.25.

Rhea had an arrangement whereby her whole day would cost $108.

An inequaity that simulates the n trips up the mountain that Edwin will pay for out of pocket and Rhea won't.

45 + 5.25n > 108

45 is deducted from both sides.

-45 + 45 + 5.25n > 108 -45

5.25n > 63

5.25 times both sides.

n > 12

Also,

5.25 x 12

= 63

The most trips Edwin could make up the mountain and still make less money than Rhea is 63.

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Explanation

Question 3 wants us to determine the range of the function

The range will be

This is

∞

Point = (3,-4)

After a translation left 2 units(-2) and 2 units up

(3-2,-4+2) = (1,-2)

If we assume x and b are real numbers:

|x| = √(x²)

So:

√(x²) = b

Where b<0

x will be always positive, because every number squared is positive

So, the left hand side of the equation will be positive. And since the right hand side of the equation will be always negative, because they tell us that b<0, we can conclude that it is absurd:

√(x²) ≠ b

Therefore, no solutions exist

The answer is Zero

Answer:

800

Step-by-step explanation:

I need to find "S"

32 = s - 19

Add 19 in both sides

32 + 19 = s - 19 + 19

51 = s

Result

s = 51

Answer:

5,14

Step-by-step explanation:

Set of ordered pairs does not represent a function i

= {(2, 2), (0, -8), (2, 7), (-3, 8)}

A function relates an input to an output.  A function is generally denoted by f(x) where x is the input.

What is a set?

Any collection of objects , which are mathematical or not

Ordered pair are a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

From question given data is

{(4, 6), (9, -2), (3, -5), (6, 6)}

{(−1,−2),(−4,9),(8,−9),(1,2)}

{(-1, 9), (-7, 8), (3, -1), (4, -1)}

{(2, 2), (0, -8), (2, 7), (-3, 8)}

From the above options we can see that last option has same number in the x axis coordinate. Thus it does not represents a function.

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We will have that the $12 rate is given by:

B. A 12-pound bag of cat food cost $24, that is:

$24/12 = $2 per pound of food.

The equation is:

so is in the form y = mx + c

this means that C = 0 so the intersection when x = 0 y = 0 so the first point is (0,0)

we also know that the slope is negative, so only points in the II and IV cuadrant can be part of the line so we evaluate them:

For point A

point A is part of the line (-3,9)

For point D

So D is part of the line

So the solution is: PointsIf you don’t need further explanation on this question, we can end the session. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day! A, B, D

Answer:

correct answer: B and F

Step-by-step explanation:

Minimum number of glasses needed by the restaurant be 15

What do you understand by inequality?

Inequalities define the relationship between two different values. Inequality   implies  not to be equal. The "not equal symbol is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine if they are less than or greater than. If an inequality has just one variable, it is said to be an open sentence.

It is given that the restaurant needs at least 510 glasses.

Currently there are 231 glasses.

Number of glasses each set contain = 18 glasses

x is the minimum number of sets of glasses Isabella should buy.

Number of glasses in x number of sets = 18x glasses

According to question:

231 + 18x ≥ 510

18x ≥ 510 - 231

18x ≥ 279

x ≥ 15.5

Minimum number of sets of glasses ,x = 15

Therefore, minimum number of glasses needed by the restaurant be 15

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1. The total bill including sales tax is $34.72.

2. The amount the purchaser should pay the cashier is $34.72.

3. The denominations for the payment should be one $20 bill, one $10 bill, four $1 bills, and 72 cents (pennies).

The total cost payable to the grocery store cashier is the cost of the groceries plus the sales tax.

The cost for groceries = $32.75

Sales tax = 6%

Total cost = cost plus sales tax

= $34.72 ($32.75 x 1.06)

We can check the sum as follows:

Unit  Bill  Amount

1      $20    $20

1      $10       10

4       $1        4

Cents           0.72

Total        $34.72

Thus, the grocery purchaser will be spending $34.72, including the sales tax.

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