For each function, determine whether y varies directly with x . If so, what is the constant of variation?
b. y = x/9

a. 95 b. kite

Step-by-step explanation:

a. all quadrilaterals add up to 360° angle with all angles, so 100+100+65=265, 360-265=95.

b. most quadrilaterals have 2 pairs of 2 equilateral angles, and this is one of the only ones that doesnt.

Answer:

a)  95°

b)  Kite

Step-by-step explanation:

Theorem:  Interior angles of a quadrilateral sum to 360°.

Given angles:

Let x be the unknown angle.

⇒ 100° + 65° + 100° + x = 360°

⇒ 265° + x = 360°

⇒ 265° + x - 265° = 360° - 265°

⇒ x = 95°

Therefore, the fourth angle is 95°.

A kite is a quadrilateral that has one pair of congruent opposite angles.

Therefore, as two of the interior angles of the given quadrilateral are equal, the shape may be a kite.

The equation of the circle x^2 + y^2 = 2 has a radius of √2 and a center located at (0 , 0).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, x^2 + y^2 = 2, is in standard form, then

h = 0

k = 0

r = √2

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The number of milliliters of blood the volunteers donated will be given by expression 470(32 - n).

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

There were 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470 milliliters each.

Then the expression will be given as

⇒ 470(32 - n)

The number of milliliters of blood the volunteers donated will be given by expression 470(32 - n).

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Answer:

$6.95

Step-by-step explanation:

Kole: $ 6.50

His sister : $6.50+$0.40

= $6.90

Half of his sister: $6.90/2 =$3.45

$10-($6.50 +$3.45)

=$10-$3.05

=$6.95

Answer:

I don't know rjdjdjjdjddjidis

=====================================================

Explanation:

Multiply the given values. This is because,

total mass = (number of paperclips)*(mass per paperclip)

So,

(5.0 x 10^−4)(6.85 x 10^4)

(5.0 * 6.85) x (10^−4 * 10^4)

34.25 x 10^(-4+4)

34.25 x 10^0

(3.425 x 10^1) x 10^0

3.425 x 10^(1+0)

3.425 x 10^1

3.4 x 10^1

We round the first value to 2 sig figs because it is the smaller sig fig count of 5.0 and 6.85; the 0 in 5.0 is significant.

Notice how I rewrote 34.25 into 3.425 x 10^1. I did this to get the number in the form a x 10^b, where [tex]0 \le a < 10[/tex], which fits scientific notation form.

The value 3.4 x 10^1 simplifies to 34. So an estimate of the total mass is about 34 mg. But we'll stick with scientific notation since your teacher instructed it.

To find the discontinuities, we need to factor the polynomial below. Once we have the two binomials, we set each to 0. This way, you can find the value that produces 0 in the denominator.

Let's factor x2−5x+6

x2−5x+6

The middle number is -5, and the last number is 6.

Factoring means we want something like

(x+_) (x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -5

Multiply together to get 6

Can you think of the two numbers?

Try -2 and -3:

-2+-3 = -5

-2*-3 = 6

Fill in the blanks in

(x+_) (x+_)

with -2 and -3 to get...

(x-2) (x-3)

Since you cannot divide by 0, the discontinuities at these points exist as a vertical asymptote. Therefore, the vertical asymptote exists at x= two and x= 3.

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The numeric value of the question is present in the in the option B. Thus, Option B is a correct option.

According to the statement

We have to find that the Numeric value.

So, For this purpose, we know that the

The Number value is the value refers to the worth of each digit depending on where it lies in the number.

From the given information:

The given value is a -2½.

And we have to find that the in which option the given value in the question is placed.

For example, if the value in the given question is a 1 then the in which option we have given value is 1.

Then

according to the statement,

In option B the value is similar to the those value which is given in the question.

So, The numeric value of the question is present in the in the option B. Thus, Option B is a correct option.

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It can be solved using a Venn diagram. Total 8 students took both subjects.

A Venn diagram uses overlapping circles or other shapes to represent the relationships between two or more groups of objects. They typically serve to attractively organize objects, highlighting both the similarities and differences between the components. In the fields of mathematics, statistics, logic, education, linguistics, computer science, and business, Venn diagrams are extensively utilized.

It can be solved using a Venn diagram as

14 students take Physics, 6 students take mathematics and the rest 8 take both subjects.

where, 14(Physics) + 6(mathematics) + 8(both) = 28 (which is the total no. of students).

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Answer:

1) the center is (3,4), radius is 3. 3)  ( x − 2 )^2 + ( y − 14 )^2 = 9, 5) the center is (12,5), the radius is 4

Step-by-step explanation:

For the graphs just look for the middle point, and thats essentially your center, and the radius is how many units the edge of the circle is to the center. So for 1 the center would be (3,4) and the radius 3. For problem 3 use the equation  ( x − a )^2 + ( y − b )^2 = r^2, where you substitute the radius for r, your x center coordinate as a, and your y coordinate as b. In problem 5, use 12 as your x value for the center coordinate, and 5 as your y value. Then just take the root of 16 to get your radius, and apply that to the other problem. Hope this helps :)

Answer:

last one is the correct one

Mark please

Given statement is False and the True statement is 'In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes.'

The correct answer is an option (B)

In this question, we have been given a statement 'In a frequency​ distribution, the class width is the distance between the lower and upper limits of a class.'

We need to determine whether the given statement is True or False.

We know that, the class width is the distance between the lower limits of consecutive classes.

So, the given statement is False.

The correct statement is 'In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes. '

Therefore, given statement is False and the True statement is 'In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes.'

The correct answer is an option (B)

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neverminding the amount of $3000, we know the compound interest is 1.1%, we also know that the compounding period is daily, so hmmm let's assume there are 365days in a year, so

[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+\frac{r}{n}\right)^{n}-1~\hfill \begin{cases} r=rate\to 1.1\%\to \frac{1.1}{100}\dotfill &0.011\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, so let's assume 365} \end{array}\dotfill &365 \end{cases} \\\\\\ \left(1+\frac{0.011}{365}\right)^{365}-1 ~~ \approx ~~ 0.01106055 ~~ \approx ~~ 1.106055\% ~~ \approx 1.11\%[/tex]

The point slope form finds the equation of a straight line that passes through a given point and is inclined to the x-axis. Each point on a line must satisfy the line's equation. Two-variable linear equations symbolize lines. The point slope formula is utilized when we know the line's slope and a point. The next section explains the point slope form and how to calculate its formula.

The equation of a straight line that is inclined at a particular angle to the x-axis and passes at a given point may be found by using the point slope form. This form is used to get the equation of the line. An equation may be said to be the equation of a line if it can be shown to be fulfilled by every point along the line. This indicates that a line is represented by a linear equation that has two variables. Whereas the Point slope formula is only used in situations in which both the slope of the line and a point on the line are known. In the next part, let's get more in-depth knowledge about the point slope form as well as how to derive the formula that is used to express the point slope form.

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The equation of the line h. 5x + 6y = 9 is parallel with the equation of the line 5x + 6y = 30.

Two lines are parallel with each other if they do not intersect no matter how much you extend both lines. Parallel lines have equal slopes.

The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. In an equation in slope-intercept form, y = mx + b, the slope, m is the coefficient of x.

Determine the slope of the given line and each given choices by transforming each into slope-intercept form.

5x + 6y = 30

6y = -5x + 30

y = -5/6 x + 30/6

y = -5/6 x + 5

m = -5/6

f. 5x + 9y = 30

9y = -5x + 30

y = -5/9 x + 30/9

y = -5/9 x + 10/3

m = -5/9

g. 9x + 6y = 30

6y = -9x + 30

y = -9/6 x + 30/6

y = -3/2 x + 5

m = -3/2

h. 5x + 6y = 9

6y = -5x + 9

y = -5/6 x + 9/6

y = -5/6 x + 3/2

m = -5/6

i. 6x + 5y = 30

5y = -6x + 30

y = -6/5 x + 30/5

y = -6/5 x + 6

m = -6/5

Since h. 5x + 6y = 9 has a slope of -5/6 and equal to the slope of the given line, then they are parallel lines.

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The linear equation with a direct variation function always passes through the origin.

What are direct variation functions?

The direct variation function defines a linear function of the form y = kx, where y varies as a multiple of x and x 0. These always follow the origin test.

Calculation

Yes, the method will always work because the linear equations having direct variations are those equations which always pass through the origin.

For example: If we consider an equation y = 3x. Then, it will always pass through the origin as y changes with respect to some multiples of x.

Hence, the direct variation function always passes through the origin.

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Answer:

I would say y=3x+6

Step-by-step explanation:

Answer:

it is not factorable

Step-by-step explanation:

If Jenny's Bakery sells carrot muffins at 2 each and the electricity to run the oven is 120 per day and the cost of making one carrot muffin is 1.40, then the number of muffins needed to be sold each day to break even is equal to 200.

The number of muffins needed to be sold each to break even can be determined by forming a linear equation.

A linear equation, sometimes also referred to as a first-degree equation can be described as an equation that contains variables that have the maximum power of not more than one.

The linear equation for this problem will be,

Cost of electricity to run the oven + Cost of making x number of muffins = Sale price of x number of muffins

120 + 1.40 (x) = 2 (x)

Here x is equal to the number of muffins

Rearranging the equation,

120 = 2(x) - 1.40 (x)

120 = 0.6 (x)

120/0.6 = x

x = 200

Hence, 200 muffins are needed to be sold each day to break even.

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Answer: 5, 7, 13, 15, 18

Step-by-step explanation:

The line's equation is y=3x-4.

What is Equation of line?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation where the slope of line is m and b is the y- intercept. The slope is defined as

m = (y-y1)/(x-x1)

Given:

For two lines to be perpendicular to each other, they must have slopes that are negative reciprocals of each other (i.e. the negative reciprocal of n is -1/n). The slope of the given line is –1/3 which means the slope of a line perpendicular to it would be 3.

From the given slope equation of the line

y=3x+b,

where b is the y-intercept. Since we know the line passes through the point (2,2).

(y-2)/(x-2) = 3

y-2 = 3*(x-2)

y=3x-6+2

y=3x-4

The value of b = -4

Therefore, the equation of the second line is y=3x-4.

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The pattern exists described as a sequence of repeating objects, shapes, or numbers. Patterns can also occasionally be referred to as a series.

The pattern follows the rule tn = t(n-1) × 3

The next three numbers be 1, 3, 9, 27, 81, 243, 729, 2187.

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

Let the numbers in the pattern be 1, 3, 9, 27, 81, . . .

t2 = 1 × 3 = 3

t3 = 3 × 3 = 9

t4 = 9 × 3 = 27

t5 = 27 × 3 = 81

t6 = 81 × 3 = 243

t7 = 243 × 3 = 729

t8 = 729 × 3 = 2187

Thus the pattern follows the rule tn = t(n-1)×3

Therefore, the next three numbers be 1, 3, 9, 27, 81, 243, 729, 2187.

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Step-by-step explanation:

2x=1.2-0.8

2x=0.4

x=0.4/2=0.2

The speed of the wind today is 6 miles per hour.

We know that speed = distance / time        .........(1)

You ride your bike to a store, 4 mi away, to pick up things for dinner.

Here, distance = 4 miles

When there is no wind, you ride at 10 mi/h.

So, using above formula (1),

⇒ 10 = 4 / t

⇒ t = 10/4

⇒ t = 2.5 hours

This means,  it takes 2.5 hours for you to get to the store on a day without wind.

Today your trip to the store and back took 1 hour.

We need to find the speed of the wind.

Let 's' be the speed of the wind.

So using above formula (1),

⇒ (10 - s) = 4 / 1

⇒ 10 - s = 4

⇒ s = 6 mi/h

Therefore, the speed of the wind today is 6 miles per hour.

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Answer:

a₁ = 15

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

given S₁₄ = - 63 , then

[tex]\frac{14}{2}[/tex] [ 2a₁ + 13d ] = - 63

7(2a₁ + 13d) = - 63 ( divide both sides by 7 )

2a₁ + 13d = - 9 → (1)

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₁₄ = - 24 , then

a₁ + 13d = - 24 → (2)

subtract (2) from (1) term by term to eliminate d

a₁ + 0 = - 9 - (- 24)

a₁ = - 9 + 24 = 15

The spinner's point has a 11.11% chance of landing on red.

A pie chart is a type of chart which displays data as a circular graph.

We comprehend that the pie's total value is always 100%. It is also assumed that a circle has a circumference of 360°. As a result, the sum of all pieces of data equals 360°. Based on these, there appear to be primarily two pie chart formulas:

Now, the stated data of the pie chart are-

When a circle is wholly rotated, the center forms a 360-degree angle.

A complete rotation at the central point of the circle yields 360 degrees.

The total color percentage is 100%.

Divide a red value by 3.6 because 360 ° / 100% = 3.6.

The spinner's pointer displays an overall percentage of red of 40%.

P = 40/3.6 (probability of each pointer landing on red).

P = 11.111.. = 11.11 (pointer landing on red) (approx.)

As an outcome, the pointer has a 11.11% chance of landing on the red.

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45 because it's 45 and I'm smart with a PhD in maths