If the sum of six consecutive even integers is 390 what is the smallest of the six integers

Answer:

B. 1.43

Step-by-step explanation:

Because tan (180-θ)=-tan θ

[tex]tan (145) = tan (180 -35)= -tan 35 = -\frac{1}{1.43}\\tan 35 =\frac{1}{1.43}[/tex]

Because tan (90+θ) = -cot θ

tan (-125) can be written as:

[tex] tan(-125)=-tan (125) = - tan (90+35) = cot 35[/tex]

tan θ x cot θ =1

⇒tan 35 x cot 35 = 1

⇒[tex]\frac{1}{1.43} \times cot 35 =1 \\ cot 35 = 1.43[/tex]

⇒[tex] tan(-125)= cot 35 = 1.43[/tex]

To solve this question:

Doing this, we get that: [tex]c = -\frac{35}{4}[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

x²+x+c=0

Comparing with the standard second order equation, which is:

[tex]ax^2 + bx + c = 0[/tex]

We get that:

[tex]a = 1, b = 1[/tex]

Finding the roots:

[tex]\Delta = b^{2} - 4ac = 1^2 - 4(1)(c) = 1 - 4c[/tex]

[tex]x_{1} = \frac{-1 + \sqrt{1 - 4c}}{2}[/tex]

[tex]x_{2} = \frac{-1 - \sqrt{1 - 4c}}{2}[/tex]

Difference of 6

Thus:

[tex]x_1 - x_2 = 6[/tex]

[tex]\frac{-1 + \sqrt{1 - 4c}}{2} - \frac{-1 - \sqrt{1 - 4c}}{2} = 6[/tex]

[tex]-\frac{1}{2} + \frac{\sqrt{1 - 4c}}{2} + \frac{1}{2} + \frac{\sqrt{1 - 4c}}{2} = 6[/tex]

[tex]\frac{2\sqrt{1 - 4c}}{2} = 6[/tex]

[tex]\sqrt{1 - 4c} = 6[/tex]

[tex](\sqrt{1 - 4c})^2 = 6^2[/tex]

[tex]1 - 4c = 36[/tex]

[tex]-4c = 35[/tex]

[tex]4c = -35[/tex]

[tex]c = -\frac{35}{4}[/tex]

Thus, [tex]c = -\frac{35}{4}[/tex] is the value.

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Without the necessary figures or context, we cannot make a correct comparison between segment lengths s and t. The question lacks clarity and detail, therefore the answer is that no comparison can be made.

The geometrical figures and the comparison of segment lengths within these figures. Given the Pythagorean theorem and the details about forces and lines, we have information that could pertain to geometry, specifically to properties of triangles and the comparison of segment lengths or areas. However, without the actual figures or a clear indication of the context involving s and t, we cannot provide an accurate comparison between them. This implies that the answer would be D. No comparison can be made.

It is possible that s and t are referring to the lengths of sides in a triangle, but this question, as presented, lacks the clarity and detail required to make a precise calculation or comparison. For example, in the case of two segments being hypotenuse and side of right triangles, if we knew the lengths of the other sides, we could apply the Pythagorean theorem to find the relationship between s and t. But without this information or a clear diagram, we cannot conclude anything about the relationship between s and t.

Hi there! :)

Step-by-step explanation:

[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{1-7}{4-8}=\frac{-6}{-4}=\frac{-6/2}{-4/2}=\frac{-3}{-2}=\frac{3}{2}[/tex]

Slope is 3/2.

Final answer is 3/2.

Hope this helps!

Thanks!

Have a nice day! :)

:D

A)

S = Strawberry wafer packets

c = chocolate wafer packets

s +c = 22

3.00s +1.00c = 30.00

B)

 s + c = 22

s = 22-c

3.00(22-c) + 1.00c = 30.00

66.00 - 3.00c +1.00c = 30.00

66.00 -2.00c =30.00

-2.00c = -36.00

c = -36.00 / -2.00 = 18

 18 packets of chocolate wafers

4 packets of strawberry wafers

combine all the like terms

 4x^3  + 2x^2

 then you have -6x-6x which = -12x and -10+4 = -6

 so it becomes 4x^3+2x^2-12x-6

 Answer is A

The area of the rectangle is 80 square cm.

To find the area of a rectangle, we need to know the length and width. Let's denote the width of the rectangle as 'w'. As given, the length of the rectangle is 2 cm longer than its width, so the length can be represented as 'w + 2'.

The perimeter of a rectangle is the sum of all four sides. In this case, it is given as 36 cm. Using the formula for the perimeter of a rectangle, we can set up the equation:

2(w + w + 2) = 36

Simplifying the equation:

4w + 4 = 36

4w = 32

w = 8

Substituting the value of 'w' back into the expression for length:

Length = 8 + 2 = 10

The area of a rectangle is given by the formula: area = length × width. So, the area of this rectangle is:

Area = 10 × 8 = 80 square cm

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An equation in slope intercept form, passes through (-1,-10), parallel to y=7 is y = -10 .

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The slope of a line is the measure of the steepness and the direction of the line.  

The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

According to the question

An equation in slope intercept form,

passes through (-1,-10), parallel to y = 7

now,

When line is y = 7

that means , x = 0

and it is also a horizontal line , i.e slope (m) = 0

As, Parallel lines have same slope .

By using slope intercept formula for  (-1,-10)

y = mx + b

substituting the value

-10 = 0 + b

b = -10

Therefore, putting values in general equation of slope intercept for any point

y = mx + b

y = -10  

Hence, an equation in slope intercept form, passes through (-1,-10), parallel to y=7 is y = -10 .

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The expression solved for z is:

z = (4/3)*(y + w)

Here we have the expression:

y + w - 3/4z = 0

And we want to solve it for z, which means that we need to isolate z on one side of the expression.

If we add (3/4)z in both sides we get:

y + w = (3/4)z

Now if we multiply both sides by (4/3).

(4/3)*(y + w) = (4/4)*(3/4)z = z

Then we got:

z = (4/3)*(y + w).

Thus, the expression is solved for z.

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3 divided by 18.6 is 0.16129032258

Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.

Given expression,

3 divided by 18.6

To find the number :

We take division of 3 by 18.6.

3/18.6

= 0.16129032258

Therefore, the value is 0.16129032258

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The minimum of G(x) is -2 and of F(x) is 4 So, G(x) has the smallest minimum y-value.

The function G(x) is a sine function. The sine function, sin(x), has a range of -1 to 1. The minimum value of sin(x) is -1. Since G(x) = 2 sin(x - π), we multiply the minimum value of sin(x) by 2.

The minimum value of sin(x - π) is:

sin(x - π) = -1

Thus, the minimum value of G(x) is:

2 * (-1) = -2

To find the minimum value of a quadratic function, we use the vertex formula, x = -b / 2a. For F(x), a = 3, b = 12, and c = 16.

The x-coordinate of the vertex is:

x = -12 / (2 * 3) = -12 / 6 = -2

Substitute x = -2 into the function to find the minimum y-value:

F(-2) = 3(-2)² + 12(-2) + 16

F(-2) = 3(4) - 24 + 16 = 12 - 24 + 16 = 4

The correct description is about graph of an odd function is;

''The graph is symmetric about the origin''.

Option D is true.

What is odd function?

The function is said to an odd function if it satisfy the condition;

⇒ f (-x) = - f (x)

Given that;

The function is an odd function.

Now,

Since, The odd function is rotate by the figure 180 degree then it will remains same.

So, The graph of an odd function is symmetric about the origin.

Thus, The correct description is about graph of an odd function is;

''The graph is symmetric about the origin''.

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The amount of oil, in ounces, in the fuel mix can be found using a proportion with the given ratio and the amount of gasoline.

To find the number of ounces of oil, we need to use the given ratio and the amount of gasoline. The ratio of oil to gasoline is 5:18, meaning that for every 5 ounces of oil, there are 18 gallons of gasoline. Since we know that there are 36 gallons of gasoline, we can set up a proportion to find the number of ounces of oil:

5 ounces / 18 gallons = x ounces / 36 gallons

Cross multiplying, we get:

18x = 5 * 36

Simplifying further:

18x = 180

Dividing both sides by 18, we get:

x = 10 ounces

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The probability of drawing a diamond will be 1/4.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

An experiment consists of drawing 1 card from a standard​ 52-card deck.

Now,

Since, There are 13 diamond in 52 card deck.

So, The probability of drawing a diamond = 13 / 52

                                                                = 1 / 4

Thus, The probability of drawing a diamond will be 1/4.

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what are the Answer choices

Answer:

the answer would be B. N=4