Write the recursive formula for 5, 15, 30, 50...........

Answer:

  9.  (x +3)² +4x = x² +10x +9

  10.  (5 +3m)/15

  11.  x = (-1±i√14)/3

Step-by-step explanation:

You want help with practice test questions involving quadratics and rational numbers.

For this, it is perhaps easiest to show equivalence by multiplying out the second form of the quadratic:

  (x +3)² +4x

  = (x +3)(x +3) +4x

  = x(x +3) +3(x +3) +4x

  = x² +3x +3x +9 +4x

  = x² +(3 +3 +4)x +9

  = x² +10x +9 . . . . . . . . equivalent form

As you know, fractions can be added by adding their numerators when they have a common denominator. Here, the denominators of 3 and 5 have no common factors, so the least common denominator is their product, 3·5 = 15. Writing equivalent fractions with denominators of 15, we have ...

  [tex]\dfrac{1}{3}+\dfrac{m}{5}=\dfrac{5}{5}\cdot\dfrac{1}{3}+\dfrac{3}{3}\cdot\dfrac{m}{5}\\\\=\dfrac{5}{15}+\dfrac{3m}{15}=\boxed{\dfrac{5+3m}{15}}[/tex]

It can be worthwhile to remember that you can always add fractions with the formula ...

  [tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]

The solution to 3x² +2x +5 = 0 is found using the quadratic formula with ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-2\pm\sqrt{2^2-4\cdot3\cdot5}}{2\cdot3}\\\\=\dfrac{-2\pm\sqrt{-56}}{6}=\dfrac{-2\pm2i\sqrt{14}}{6}\\\\\boxed{x=\dfrac{-1\pm i\sqrt{14}}{3}}[/tex]

__

Additional comment

It can be useful to remember ...

  (a ±b)² = a² ±2ab +b²

where the sign of the middle term matches the sign in the binomial. This is also used for "completing the square" where the b² term is the square of the middle term after it is divided by 2a.

Answer:  135 + x = 258; x = distance driven on second day (in km).

Step-by-step explanation: Another alternative way to write the equation could be "258 - 135 = x" where x = distance driven on second day (in km).

"x" itself in the case of these equations would be 123km.

The circumference of the outer circle is 72 and circumference of the inner circle is 66.Therefore, the circumference of the outer circle is 6ft greater than the circumference of the inner circle.

We know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

Given that the circumference of the inner circle is 66ft, we can find its radius by dividing the circumference by 2π:

r = C/2π = 66/(2π) ≈ 10.52ft

The distance between the inner and outer circles is 3ft, so the radius of the outer circle is 3ft greater than the radius of the inner circle:

r_outer = r_inner + 3ft = 10.52ft + 3ft = 13.52ft

Now, we can find the circumference of the outer circle using the same formula as before:

C_outer = 2πr_outer ≈ 72ft

Finally, to find the difference between the circumference of the outer circle and the circumference of the inner circle, we subtract the circumference of the inner circle from the circumference of the outer circle:

C_difference = C_outer - C_inner ≈ 72ft - 66ft = 6ft

Therefore, the circumference of the outer circle is 6ft greater than the circumference of the inner circle.

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Answer:

The answer is 6

Answer:

c

Step-by-step explanation:

Using the surface area of the rectangular prism we know that the dimensions of the base are 2in x 2in.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism.

A rectangular prism also refers to a cuboid.

A cuboid and a rectangular prism have the same cross-section.

The surface area of the rectangular prism: A=2(wl+hl+hw)

Insert values: A=2(wl+l+hw)

232=2(wl+28l+28w)

232 = 2wl + 56l + 56w

We know that w and l are equal as: w = l as the base is square:

So, we can write:

232 = 2wl + 56l + 56w

232 = 2w² + 56w + 56w

232 = 2w² + 112w

2w² + 112w - 232 = 0

2w² + w(116 - 4) -232

2w² + 116w - 4w - 232

2w(w+58) -4(w+58)

Then, we have:

w+58 = 0 ⇒ w = -58

2w-4 = 0 ⇒ w = 2

Since the base measurements cannot be negative.

Then, the dimensions of the base are: 2in x 2 in

Therefore, using the surface area of the rectangular prism we know that the dimensions of the base are 2in x 2in.

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The closest distance that a cinema can put seats to the screen is approximately 3.2 meters.

the trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

We can use trigonometry to find the closest distance that a cinema can put seats to the screen.

Let "d" be the closest distance between the screen and the seats. Then, we can form a right triangle with the distance "d" as the adjacent side, the height of the screen (7.3 m) as the opposite side, and the height of the customer's eyes above the floor (1.2 m) plus the height of the seat above the floor (which we can assume is 0.5 m) as the hypotenuse.

Using the tangent function, we can write:

tan(31°) = (7.3)/(d + 1.7)

Solving for "d", we get:

d = (7.3)/(tan(31°)) - 1.7 ≈ 3.2 m

Therefore, the closest distance that a cinema can put seats to the screen is approximately 3.2 meters.

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Answer:

(x, y ) → (x + 2, y + 3 )

Step-by-step explanation:

consider the coordinates of the centres of circles A and B

A (- 1, - 1 ) and B (1, 2 )

- 1 → 1 in the x- direction is + 2

- 1 → 2 in the y- direction is + 3

then translation rule is

(x, y ) → (x + 2, y + 3 )

Answer: Well, there are 12 months in a year, so that's 12 people at least, and if we wanted to make sure that we had at least 4 people of the same month, we'd want 4 times 12, so 48 people is my guess

sorry if it's wrong. Hope this helps!

Step-by-step explanation:

The required quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] expressed in scientific notation is [tex]$3.1966 \times 10^{-6}$[/tex].

To express the quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] in scientific notation, we can write:

[tex]$\frac{1.888 \times 10}{5.9 \times 10^6}$[/tex]

We can simplify the numerator by moving the decimal point one place to the left:

[tex]$\frac{0.1888 \times 10^1}{5.9 \times 10^6}$[/tex]

Now, we can divide the coefficients and subtract the exponents:

[tex]$\frac{0.1888}{5.9} \times 10^{2-6}$[/tex]

[tex]$= 0.031966 \times 10^{-4}$[/tex]

Finally, we can express the result in proper scientific notation by moving the decimal point one place to the right:

[tex]$= 3.1966 \times 10^{-6}$[/tex]

Therefore, the quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] expressed in scientific notation is [tex]$3.1966 \times 10^{-6}$[/tex].

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Option B is best represents for the answer. A. 84.13%. B. 15.87%. 99.87%. D. 81.86%. To create the distribution curve, we can use the normal distribution formula:  [tex]f(x) = (1/σ√(2π)) * e^(-0.5((x-μ)/σ)^2)[/tex]

where:

f(x) = probability density function at value x

μ = mean = 16.2

σ = standard deviation = 0.3

Using this formula, we can calculate the probabilities for the given scenarios:

a. Probability of a coke having less than 16.5 ounces:

We need to find P(X < 16.5), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 16.5:

z = (16.5 - 16.2) / 0.3 = 1

P(Z < 1) = 0.8413

Therefore, the probability of a coke having less than 16.5 ounces is 84.13%.

b. Probability of a coke having less than 15.9 ounces:

We need to find P(X < 15.9), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 15.9:

z = (15.9 - 16.2) / 0.3 = -1

P(Z < -1) = 0.1587

Therefore, the probability of a coke having less than 15.9 ounces is 15.87%.

c. Probability of a coke having more than 15.3 ounces:

We need to find P(X > 15.3), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 15.3:

z = (15.3 - 16.2) / 0.3 = -3

P(Z > -3) = 0.9987

Therefore, the probability of a coke having more than 15.3 ounces is 99.87%.

d. Probability of a bag having between 15.9 and 16.8 ounces:

We need to find P(15.9 < X < 16.8), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the values of 15.9 and 16.8:

z1 = (15.9 - 16.2) / 0.3 = -1

z2 = (16.8 - 16.2) / 0.3 = 2

P(-1 < Z < 2) = 0.8186

Therefore, the probability of a coke having a volume between 15.9 and 16.8 ounces is 81.86%.

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Answer: a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (4 in 4xy)

Step-by-step explanation: the coefficient is the number or digit that is being multiplied and it is placed before a constant quantity

Answer:

3588

Step-by-step explanation: prime factorize and find common factors, only count those once, take the rest and the common factors and multiply

Based on the line of best fit, the length of this catfish can be predicted to be 38 inches.

Given the following data:

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.

From the graph of the data, we have the following linear equation:

[tex]y=\dfrac{1}{2}x+18[/tex]

Substituting the value of x, we have:

[tex]y=(\dfrac{1}{2}\times40)+18[/tex]

[tex]y=20+18[/tex]

[tex]\bold{y = 38 \ inches.}[/tex]

Answer:

the average weight of the students in Class A is 25.92 kg.

2x^-4y=2(2)^-4.4

2\2^16

1\2^15

The answer is not in the options

The total unpainted surface area of these cubes is: 12cm

Therefore, the formula for the volume of a rectangular prism is, volume of a rectangular prism (V) = l × w × h, where. To find the volume of the rectangular prism, we multiply the length, width, and height, that is the area of the base is multiplied by the height.

The unpainted ones will be the ones in the middle of the prism

Let 3 be the height

There will be 2 × 6 × 5  =  60  painted cubes on the top and bottom

There will  2 × 6  +   2 × 3  =  18 more painted cubes "sandwiched" between the top and bottom surfaces

So...the total unpainted cubes  is  90  - 78   =   12

So their total surface area is just   [12 × 6 ] cm^2   =  72 cm^2

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The given question is incomplete, complete question is:

A rectangular prism 3cm by 5cm by 6cm is painted mauve and is then cut into 1 cm cubes what is the total unpainted surface area of these cubes

Answer:

Step-by-step explanation:

Strap in man I can only do so much with 5000 characters:

1) 8 outcomes

2) Fried rice - chicken adobo - pineapple juice

   Fried rice - pinakbet -  pineapple juice

   Steamed rice - chicken adobo - pineapple juice

   Steamed rice - pinakbet - pineapple juice

3) 4

4) 2

5) 2

6) 2

7) 4/8 or 1/2 or 50%

8) 2/8 or 1/4 or 25%

9) 2/8 or 1/4 or 25%

10)2/8 or 1/4 or 25%

That's it! I hope this helps you out. Got any questions. I'll uh...be here :)

The missing numbers 50% of 60 = 30

A number is a numerical unit of measurement and labeling in mathematics.

The natural numbers 1, 2, 3, 4, and so on are the first examples.

Number words are a linguistic way to express numbers.

Most commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five.

Basic numerals are frequently grouped in a numeral system, which is an ordered manner to represent any number, because only a small number of symbols can be learned.

The most widely used number system is the Hindu-Arabic number system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."

50*60/100

30

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An equation that shows an example of the associative property of addition is: a. (- 4 + i) + 4i = -4 + (i + 4i)

Associativity, which applies only to addition and multiplication, states that any sum or product of 3 or more numbers is unaffected by how the numbers are grouped in parentheses. In other words, if the same numbers are grouped differently for addition and multiplication, their results will always be the same.

The associative property of the addition states that the addition of numbers cannot affect by the grouping of the number.

A+(B+C) = (A+B) +C

Here, in the above equation the value of A+(B+C)  is always equal to the value of (A+B)+C whether the grouping of number is changes or not.

That is:

The expression that complies with this property is given by:

(-4+i) + 4i = -4 + (i+ 4i)

Complete Question:

Which equation shows an example of the associative property of addition?

a.(–4 + i) + 4i = –4 + (i + 4i)

b.(–4 + i) + 4i = 4i + (–4i + i)

c.4i × (–4i + i) = (4i – 4i) + (4i × i)

d.(–4i + i) + 0 = (–4i + i)

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Answer:

The angle measures from least to greatest are 30°, 30° and 120°.

Step-by-step explanation:

The interior angles of a triangle sum to 180°.

Given the ratio of the interior angles of a triangle is 1 : 1 : 4 then:

x + x + 4x = 180°

Solve the equation for x:

⇒ 6x = 180°

⇒ x = 30°

Therefore, the angle measures are:

So the angle measures from least to greatest are 30°, 30° and 120°.

Answer:

30 , 30 , 120 .

Step-by-step explanation:

Given :

To find :

Solution :

As we know that the angle sum property is 180° , that is the sum of all the interior angles is 180° .

Let us take the given ratio to be 1x:1x:4x .

Sum of these= 1x + 1x + 4x = 6x .

So we can create a equation as ,

==> 6x = 180°

==> x = 180°/6

==> x = 30°

Now we can find the angles as ,

Hence the angles of the triangle are 30° , 30° and 120° .

Answer: Yes, they are similar

Step-by-step explanation: HAVE AN AMAZING DAY AND GOOD GRADES!!!!! :D

If  a deadly disease infected the hummingbird population, what would most likely happen to the plants option (b) They would become endangered

If a deadly disease infected the hummingbird population, it would most likely lead to a decrease in the pollination of plants that rely on hummingbirds for pollination. Without the hummingbirds to transfer pollen between flowers, these plants would have a reduced rate of successful pollination, which would result in a decrease in their ability to reproduce.

However, it is unlikely that the plants would die within hours or become endangered immediately, nor would they need to migrate. The effect of the loss of hummingbird pollinators on the plants would depend on the specific plant species, their pollination requirements, and the availability of alternative pollinators. Some plants may be more adaptable to using alternative pollinators, while others may suffer more severe consequences. It is also possible that the loss of hummingbirds could lead to a decline in the populations of other animals that depend on the plants, creating a ripple effect in the ecosystem.

Therefore, the correct option is (d) They would become endangered

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We can estimate that approximately 14.17% of students in the district are interested in playing hockey.

Total interested students = 0.1417 x 4,000 = 567.

An average proportion is the sum of a set of proportions divided by the number of proportions.

It represents the average or typical value of the proportions in the set, and can be used to estimate the overall proportion or percentage of a larger population

To estimate the total number of students in the district who are interested in playing hockey, we can first find the proportion of students in each sample who said yes, and then use the average proportion across all four samples to estimate the proportion of students in the district who are interested.

Finally, we can multiply this proportion by the total number of students in the district to estimate the total number of interested students.

The proportion of students in each sample who said yes is:

Sample 1: 4/30 = 0.1333

Sample 2: 5/30 = 0.1667

Sample 3: 5/30 = 0.1667

Sample 4: 3/30 = 0.1000

The average proportion across all four samples is:

(0.1333 + 0.1667 + 0.1667 + 0.1000) / 4 = 0.1417

To estimate the total number of interested students, we can multiply this proportion by the total number of students in the district: Total interested students = 0.1417 x 4,000 = 567.

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Notes:

Hi,

I don't really know what you're asking, so if you could clarify, that would be great. Thanks!

(Do you want me to simplify the equation? Find out what x is?)

- 201600823

Answer:

none of the above

Step-by-step explanation:

3(x − 4)² +6 = 0

3(x − 4)² = -6 / : 3

(x − 4)² = -2

x² - 8x + 16 = -2

x² - 8x + 16 + 2 = 0

x² - 8x + 18 = 0

D = b² - 4ac = (-8)² - 4 * 1 * 18 = 64 - 72 = -8 < 0

Since the discriminant is less than zero, this quadratic equation has no solutions, the graph would not cross the x-axis and therefore have no zeros.

Answer:

Step-by-step explanation:

Advik spends $24.50 at the home goods store on a bird bath and $2.79 a bag for multiple mulch bags. His total before tax for the purchase is $66.35. 15 sacks of mulch were bought by Advik.

Let's start by first finding the total cost of the bird bath and the mulch bags.

The cost of the bird bath is $24.50.

Let's use "x" to represent the number of bags of mulch that Advik purchased. Each bag costs $2.79, so the total cost of the mulch bags is 2.79x.

The total cost of the purchase before tax is $66.35. So we can write an equation:

24.50 + 2.79x = 66.35

To solve for x, we can first subtract 24.50 from both sides:

2.79x = 41.85

Then we can divide both sides by 2.79:

x = 15

So Advik purchased 15 bags of mulch.

The complete question is:-

At a home goods store, Advik buys a bird bath for $24.50 and several bags of mulch that cost $2.79 each. The total for his purchase is $66.35 before tax.

Find how many bags he purchased.

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Answer:

A) 39

B) 900

C) 60%

A) proportion:

21.84 is 56% of x number

x number = 100%

If you want to calculate x you can use proportion. First of all make this kind of system..

x - 100%

21.84 - 56%

Then multiply numbers diagonally.

56x = 2184

Finally solve x

x = 2184/56

x = 39