Solve the following system of equations graphically. Select the graph that shows the correct solution of the system. 2x +y =3 3y= x - 12

12. If the first two terms of the sequence are -3 and 9, the next few terms are

-3 + 9 = 6

9 + 6 = 15

6 + 15 = 21

15 + 21 = 36

and so on. Continuing in this way, you'd find the 16th term to be 4359.

13. Let x be the cost of 1 floop.

31 floops cost less than $40, so 31x < 40 or x < 40/31.

32 floops cost more than $41, so 32x > 41 or x > 41/32.

Equivalently,

41/32 < x < 40/31

and

41/32 ≈ 1.28125

40/31 ≈ 1.29032

which means x = $1.29.

Answer:

Than the other one is a good idea for the angle measured

Measures of angles 3 and 6 is 60°

Parallel lines are those straight lines that are always the same distance apart from each other.

Given that, line m is parallel to line n and m ∠ 3 = (7x-10) and m ∠ 6=(5x+10)

Since m ║ n then

m ∠ 3 = m ∠ 6

(7x-10) = (5x+10)

2x = 20

x = 10

m ∠ 3 = 7x-10 = 7*10 - 10 = 60°

m ∠ 6 = (5x+10) = 5*10 + 10 = 60°

Hence, Measures of angles 3 and 6 is 60°

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The area of the banner, expressed in simplest form, is: (9 + 3x) ft²

The banner given in the image below has a rectangular shape. So, the area of the banner will be determined using the area of a rectangle.

Area of the banner = (3 + x)3

Area = (9 + 3x) ft²

Therefore, the area of the banner, expressed in simplest form, is: (9 + 3x) ft²

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Answer:

20

Step-by-step explanation:

I'm pretty sure its 20 but I could be wrong but 20 is my best guess.

Answer:

16 of the 33 plays none.

Step-by-step explanation:

From the list, we get that 18 students play football, 1 basketball, and 7 both.

What we need to do here is add up 18 and 1

then we subtract 19 by 7 to cancel out the people who play both

and then subtract the total number of 33 by 17,

which gives you 16.

Answer:

I do my love a ti love

Step-by-step explanation:

coroneta

Answer:

The sequence is a Gp

Each term can be gotten from multiplying the common difference (4)

Next three terms

(-192×4)= - 768

(-768×4)= - 3172

(-3172×4)= - 12688

Answer:

\(m\angle FGC =101\degree \)

Step-by-step explanation:

\(m\angle CBF = 46\degree\) (Given)

\(m\angle FIG = 55\degree\) (Given)

\(m\angle IFG = m\angle CBF\) (Corresponding angles)

\(\implies m\angle IFG = 46\degree\)

\(m\angle FGC =m\angle IFG+ m\angle FIG\)

(By exterior angle theorem)

\(m\angle FGC =46\degree+ 55\degree \)

\(m\angle FGC =101\degree\)

Here

Using the formula

sum of interiors=external

Answer:

7g + 3n - 2

Step-by-step explanation:

(7g - 6) - (-3n - 4)

7g - 6 + 3n + 4

7g + 3n - 2

I hope this helps!

The abbreviation used for pounds is "lbs" and for ounces is "oz".

When a baby is born, their weight is measured in pounds and ounces. The weight of a newborn can vary greatly, with an average weight ranging from 5.5 to 10 pounds. Newborns who weigh less than 5.5 pounds are considered small, while those who weigh more than 10 pounds are considered large.
The abbreviation used for pounds is "lbs" and for ounces is "oz". So, for example, a newborn who weighs 7 pounds and 2 ounces would be abbreviated as 7lbs 2oz. This is a common way of expressing a baby's weight, especially in medical settings such as the delivery room or the neonatal intensive care unit.
It is important to keep in mind that a baby's weight can change rapidly during the first few weeks of life. It is not uncommon for a newborn to lose some weight in the first few days after birth as they adjust to feeding. Typically, a baby will regain this weight within a week or two.
Overall, the weight of a newborn is an important factor in determining their health and development. Pediatricians and healthcare providers will monitor a baby's weight closely during their first few weeks of life to ensure that they are growing and developing properly.

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Answer:

Step-by-step explanation:

1. A given chord on a circle is perpendicular to a radius through its center, and it is at a distance less that the radius of the circle.

2. A circle of center O has a radius of 13 units. If a chord AB of 10 units is drawn at a distance, d, to the center of the circle, determine the value of d.

3. From question 2, the radius = 13 units, length of chord = 10 units and distance of chord to center of the circle is d.

A radius that meet the chord at center C, and divides it into two equal parts.

So that;

AC = CB = 5 units

Applying Pythagoras theorem to ΔOCB,

OC = d, CB = 5 units and OB = 13 units

\(13^{2}\) = \(5^{2}\) + \(d^{2}\)

169 = 25 + \(d^{2}\)

169 - 25 = \(d^{2}\)

144 = \(d^{2}\)

⇒ d = \(\sqrt{144}\)

       = 12 units

Therefore, the chord is at a distance of 12 units to the center of the circle.

A chord is a straight line joining 2 points on the circumference of a circle.

The line that connects any two points of the circumference of a circle is known as a chord.

Theorem: A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.

Converse: The perpendicular bisector of a chord passes through the center of a circle.

Problem: In the given figure the radius of the circle is 5 cms. what is the length of the chord?

Solution:

Given to us,

radius of the circle, r = 5 cms,

RA = 1 cm,

Radius, r = OA = OP = OQ = 5 cms.

Also, OR = OA - OR = 4 cms.

In ΔOPQ,

According to Pythagorus theorum,

OP² = OR² + RP²

5² = 4² + RP²

RP² = 25 -16 = 9

RP = 3,

We know,

A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.

A radius (OA) that is perpendicular to a chord divides the chord into two equal parts(RP = RQ).

Therefore, chord = RP + RQ = 3+3 = 6 cms.

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There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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Answer:

(0, 207)

Step-by-step explanation:

We calculate y-intercept by substituting 0 for x.

The equation becomes:

3*62-6*(0)+21=207

y intercept is (0, 207)

The volume of the given prototype is calculated as: Option B: 200in³

We are told that a watch company is developing packaging for its new watch. the designer uses an pentagonal prism with a base area of 20 in² and rectangles with a length of 10 in to create a prototype for the new package.

Since the designer uses pentagons with a base area of 20 in² and rectangles with a length of 10 in to create a prototype for the new package.

So here the volume is

= 20(10)

= 200

Therefore, The volume of the prototype is 200in³

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Answer:

4 + 16n

Step-by-step explanation:

4 (1 + 4n)

Use the distributive property & expand the expression .

= (4*1) + (4*4n)

= 4 + 16n

________

Hope it helps ⚜

Answer:

\(\Longrightarrow: \boxed{\sf{4+16n}}\)

Step-by-step explanation:

Use the distributive property.

Distributive property:

⇒ A(B+C)=AB+AC

Multiply expand.

4*1=4

4*4n=16n

Rewrite the expression down.

= 4+16n

I hope this helps! Let me know if you have any questions.

The volume of the tank can be found using the given information as:\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

Assuming that the area bounded is given by a function f(x), the volume of the oil storage tank can be calculated using the formula for the volume of a solid of revolution:

\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

where a and b are the limits of integration. In this case, the axis of revolution is the x-axis, so we are revolving the area about the x-axis.

Therefore, the volume of the tank can be found using the given information as:

\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

We need more information about the function f(x) or a curve that bounds the area in order to find the limits of integration and calculate the volume.

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A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.


A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.

Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.

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Answer:

2d

Step-by-step explanation:

Since Pete has double what Leo has, we need to multiply Leo's number of stamps by 2. But because we don't know how many he actually has, and the amount is represented by "d", we multiple "d" by 2

Answer:

Step-by-step explanation:

The difference is

Pete had d more stamps than Leo

The side of the square is x^5 .

Area of a square = (side)² = a²,

Given;

area of a square = \(x^{10}\)

Equating it with the general formula of square

Area of a square = a²,

          a² =  \(x^{10}\)

Taking square root on both sides,

\(a = \sqrt{x^{10}} \\\\a = x^5\)

Hence, the side of the square is x^5.

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S - 1 is also a rational number. If s is an irrational number, then s - 1 may be a rational or irrational number, depending on the specific value of s.

s and t are two rational numbers, are s + t and s - 1 rational or irrational explain your reasoning

If s and t are two rational numbers, then their sum s + t and difference s - t are also rational numbers.

To see why, let s = a/b and t = c/d, where a, b, c, and d are integers and b and d are not equal to zero. Then,

s + t = (a/b) + (c/d) = (ad + bc) / bd

Since ad + bc and bd are integers, we can see that s + t is also a rational number.

Similarly,

s - t = (a/b) - (c/d) = (ad - bc) / bd

Since ad - bc and bd are integers, we can see that s - t is also a rational number.

However, we cannot make any general statement about whether s - 1 is rational or irrational, as this depends on the specific value of s. If s is a rational number, then s - 1 is also a rational number. If s is an irrational number, then s - 1 may be a rational or irrational number, depending on the specific value of s.

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Answer:

Step-by-step explanation:

We know the bottom of the triangle is 5 cm and the top of the rectangle is 5 cm, but we need to find the sides.

The height of the triangle is 8 cm, we know this as we do 18 - 10 = 8 because we subtract the rectangle from the whole figure which leaves us the triangle.

We split the triangle into 2 parts. The bottom part is now each 2.5 cm.

Then we use the Pythagorean theorem.

Check my work on the picture for how I do it for which it leads to the sided of the triangle.

Now adding the sides of the whole perimeter we just focus on the outer regions.

Two parts from the triangle which both add up to 15.20 cm and the rectangle is 25 cm, you ignore the segment inside the figure.

25 + 15.20 = 37.20 cm.

Answer:

division

Step-by-step explanation:

We determined the points of intersection, identified which function is on top in different intervals, and integrated the absolute difference between the functions over the interval [-3, 5].

To find the area of the region enclosed by the graphs of f(x) = x^2 - x - 5 and f(x) = x + 10, we need to determine the points of intersection between the two functions and integrate the absolute difference between them.

First, let's find the points of intersection by setting the two equations equal to each other:

x^2 - x - 5 = x + 10

Rearranging the equation, we get:

x^2 - 2x - 15 = 0

Factoring the quadratic equation, we have:

(x - 5)(x + 3) = 0

So the two points of intersection are x = 5 and x = -3.

Next, we need to determine which function is on top in the region

between these two intersection points.

For x < -3, the function f(x) = x + 10 is on top.

For -3 < x < 5, the function f(x) = x^2 - x - 5 is on top.

For x > 5, the function f(x) = x + 10 is on top.

To find the area, we integrate the absolute difference between the two functions over the interval [-3, 5].

∫[from -3 to 5] |(x^2 - x - 5) - (x + 10)| dx

Simplifying, we have:

∫[from -3 to 5] |x^2 - 2x - 15| dx

Now, we split the integral into two parts based on the intervals where the absolute value changes its sign.

∫[from -3 to 5] (x^2 - 2x - 15) dx + ∫[from -3 to 5] -(x^2 - 2x - 15) dx

Integrating each part separately, we obtain:

[(1/3)x^3 - x^2 - 15x] from -3 to 5 - [(1/3)x^3 - x^2 - 15x] from -3 to 5

Simplifying further, we get:

[(1/3)(5)^3 - (5)^2 - 15(5)] - [(1/3)(-3)^3 - (-3)^2 - 15(-3)]

Calculating the values, we find:

[125/3 - 25 - 75] - [-27/3 - 9 + 45/3]

The final result is the absolute value of the difference of these two values.

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The inequality equation will be 0 < -15 - y. Then the value of the variable y is less than negative 15.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Zero is less than negative fifteen decreased by y, can be written as mathematically

0 < -15 - y

Then solving for y, we have

y < -15

The value of the variable y is less than negative 15.

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Answer:

B=54

C=54

Step-by-step explanation:

180-72=108

108/2=54

54*2=108

108+72=180

each child plays for 45 minutes.

To determine the number of minutes each child plays, we can divide the total playing time (90 minutes) by the total number of children (5). Since only two children can play at a time, we need to divide the playing time equally among the pairs of children.

Let's calculate:

Number of pairs of children = Total number of children / 2 = 5 / 2 = 2 pairs

Minutes each child plays = Total playing time / Number of pairs of children

Minutes each child plays = 90 minutes / 2 pairs = 45 minutes

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Answer:The number 0 falls in the interval -1 < x ≤ 1, so we use the formula f(x) = x to evaluate f(0).

The number 0 falls in the interval -1 < x ≤ 1, so we use the formula f(x) = x to evaluate f(0).f

The number 0 falls in the interval -1 < x ≤ 1, so we use the formula f(x) = x to evaluate f(0).f(

The number 0 falls in the interval -1 < x ≤ 1, so we use the formula f(x) = x to evaluate f(0).f(0

The number 0 falls in the interval -1 < x ≤ 1, so we use the formula f(x) = x to evaluate f(0).f(0)

The number 0 falls in the interval -1 < x ≤ 1, so we use the formula f(x) = x to evaluate f(0).f(0)=

The number 0 falls in the interval -1 < x ≤ 1, so we use the formula f(x) = x to evaluate f(0).f(0)=0

The number 0 falls in the interval -1 < x ≤ 1, so we use the formula f(x) = x to evaluate f(0).f(0)=0We get f(0) = 0. the answer is a

step by step:

Answer: 30%

15/50=.3

30%

I hope this is good enough:

The limit of (cosh(x) / x) * (3e^(-tx) * tan(t x)) as x approaches infinity is 0.

When evaluating the limit of the given expression, it is helpful to break it down into two parts: (cosh(x) / x) and (3e^(-tx) * tan(t x)).

For the first part, (cosh(x) / x), as x approaches infinity, the hyperbolic cosine function (cosh(x)) grows exponentially while x grows linearly. Therefore, the ratio cosh(x) / x approaches 0.

For the second part, (3e^(-tx) * tan(t x)), as x approaches infinity, the exponential term e^(-tx) approaches 0, and the tangent function (tan(t x)) oscillates between -1 and 1. Thus, the product 3e^(-tx) * tan(t x) approaches 0.

Combining these two results, the limit of the entire expression as x approaches infinity is 0.

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