Identify and extend the pattern to find the next number in the sequence 3, 12, 48, 1 92

Answer:

No solution.

Explanation:

Given expression:

when x = 3, y = 4

Substitute these values inside expression:

6(3) + 4(4) = 36

18 + 16 = 36

34 = 36

As the statement "34 = 36" not true. The solution is false or no solution.

Answer:

The given values are wrong.

Step-by-step explanation:

Given information,

→ x = 3

→ y = 4

Solving the given equation,

→ 6x + 4y = 36

→ (6 × 3) + (4 × 4) = 36

→ 18 + 16 = 36

→ 34 ≠ 36

Hence, there is no solution.

Using the Factor Theorem, the non-real solutions are given as follows:

[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the function is:

f(x) = 3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48.

The function can be written as:

f(x) = g(x)h(x).

In which:

Using a calculator, as the graph is not given, the real solutions are given as follows:

[tex]x_1 = -6, x_2 = -4, x_3 = 1[/tex]

Hence:

g(x) = (x + 6)(x + 4)(x - 1)

g(x) = (x² + 10x + 24)(x - 1)

g(x) = x³ + 9x² + 14x - 24.

f(x) is of degree 5, g(x) of degree 3, hence h(x) is of degree 2 and:

f(x) = g(x)h(x)

3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48 = (x³ + 9x² + 14x - 24)(ax² + bx + c)

Hence:

-24bx + 14cx = 76x

-24b + 28 = 76

-24b = 48

b = -2.

Then the equation with the non-real solutions is:

h(x) = 3x² - 2x + 2.

Which is a quadratic equation with coefficients a = 3, b = -2 and c = 2, thus:

Hence the non-real solutions are:

[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]

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Step-by-step explanation:

(5 ,_4) it the location this is the answer

Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21% were taken in a 24-hour period from the pie chart.

Given that,

In the figure there is a chart pie chart with 4 parts and 4 colors.

Six cotton mice, nine Norway rats, 17 pine voles, and two eastern chipmunks were taken in a 24-hour period.

We have to find by use the information below to calculate the percentage of each species of captured mammal, and then use that information to name the various pie-shaped sections.

Each value must be converted into a circle's angle for the pie chart.

Total=6+9+17+2=34

Cotton mice=(6/34)×360°=64°

Norway rats=(9/34)×360°=95°

Pine voles=(17/34)×360°=180°

Eastern chipmunks=(2/34)×360°=21°

Therefore, Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21%.

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The model that best described the statement is an exponential model and the function that models the situation is A(t) = 4^t

The statement is given as:

The above statement is a population function

Population functions are best represented by an exponential function

Hence, the model that best described the statement is an exponential model.

Here, we have

Initial value, a = 1

Rate, r = 3

The function is represented as

A(t) = A * (1 + r)^t

So, we have

A(t) = 1 * (1+3)^t

Evaluate

A(t) = 4^t

Hence, the function that models the situation is A(t) = 4^t

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Answer:

67,500

Step-by-step explanation:

i think this is the answer.

Answer:  67500

This is because 536 is closer to 500 than it is to 600

Answer:

c

Step-by-step explanation:

Answer: x=21, y=8

Step-by-step explanation:

18y+5=10x-61  ==> 18y+5 and 10x-61 are congruent angle, so they're equal

x+10+10x-61=180 ==> x+10 and 10x-61 are supplementary angles since they're on a straight line(a straight line measures 180 degrees and is called a straight angle), so they add up to 180 degrees.

x+10x+10-61=180

11x-51=180

11x=231

x=21

18y+5=10(21)-61

18y+5=210-61

18y+5=149

18y=144

y=8

The reciprocal of 0.375 is gotten by Dividing 1 by 0.375 and Solving the equation 0.375x = 1

The reciprocal of a number is the multiplicative inverse of that number. For a number x, the reciprocal is x⁻¹

Hence, the reciprocal of 0.375 is:

a) Dividing 1 by 0.375

b) Solving the equation 0.375x = 1

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Answer: Y = -8 or Y = 8

Step-by-step explanation:

Y² = 64

Y = -8 or Y = 8 ==> yes there is more than one answer

$3,708.33 is withheld monthly for state taxes.

Some states have a graduated income tax that involves a different tax rate for each of several levels of income. The tax rate increases as income increases.

Tax Withheld per Pay Period = Annual Tax Withheld/ Number of Pay Periods per Year

Here, we are given that Kerry McCarthy is a news traffic reporter with an annual gross pay of $44,500.

Thus, the Annual Tax Withheld = $44,500.

He is paid on a monthly basis ⇒ Number of Pay Periods per Year = 12

Hence, we get-

Tax Withheld per Pay Period = 44,500/ 12

= 3,708.33

Thus $3,708.33 is withheld monthly for state taxes.

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The function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.

Given that the table which shows the capacities at which U.S. nuclear power plants are working and a model of the situation is f(t)=0.027t²+0.216t+53.296.

The Scatter plot for our function and points is shown in attached image and the point are highly related to the curve .

So the function is good model.

The year 2014 means t=2014-1970=44

So to get the population,put t=44 in equation

f(t)=0.027(44)²+0.216(44)+53.296

f(t)=0.027(1936)+0.216(44)+53.296

f(t)=52.272+9.504+53.296

f(t)=115.072

And on rounding it we get 115%.

Now, to find year at which capacity is 100% ,put f(t)=100 and solve for t

f(t)=0.027t²+0.216t+53.296=100

0.027t²+0.216t+53.296=100

0.027t²+0.216t+53.296-100=0

0.027t²+0.216t-46.704=0

Now, we will solve this using quadratic formula for f(x) =ax²+bx+c=0

[tex]\begin{aligned}x&=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end[/tex]

for our function a= 0.027 , b=0.216 ,c=-46.704 substitute this value and we get

[tex]\begin{aligned}t&=\frac{-0.216\pm \sqrt{(0.216)^2-4\times 0.027\times (-46.704)}}{2\times 0.027}\\ &=\frac{-0.216\pm \sqrt{0.046656+5.044032}}{0.054}\\ &=\frac{-0.216\pm \sqrt{5.090688}}{0.054}\\ &=\frac{-0.216\pm 2.256}{0.54}\\ &=37.78, -45.78\end[/tex]

As we all know time cannot be negative so t=-45.78 will be rejected.

So, t=37.78=38

Now, we will find the corresponding year

1970+38=2008

Hence, from the given table the function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.

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this is what you need?if yes than look and write

From the graph of the function, we have that:

a) The domain is all real values.

b) The range is y ≤ 4.

c) The x-intercepts are x = -4 and x = 1.

d) The y-intercept is y = 3.

e) f(-2) = 3, f(2) = -5.

Hence, for this problem:

a) The domain is all real values.

b) The range is y ≤ 4.

Hence:

c) The x-intercepts are x = -4 and x = 1.

d) The y-intercept is y = 3.

For the graph, when x = -2 y = 3 and when x = 2 y = -5, hence:

f(-2) = 3, f(2) = -5.

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[tex] \green\star\:{\underline{\underline{\sf{\orange{Answer:}}}}}[/tex]

¡Hello :D!

To solve the similar terms we must eliminate the parentheses and then put the parentheses back but this time it would be like this: (4 x + x) + ( 2 - 2)

Once we have done that we must restore the ones on the right side which gives us the result of 1 then as we see that there is + in the Parenthesis and another + outside the Parenthesis we do not care + since we are using the law of signs .

We proceed to solve:

[tex]\: \: \: \: \: \: \bold \: \bold \: \bold \: ( \bf4x+2)+(x-2)[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \bf \bold4x + 2 + x - 2[/tex]

[tex] \: \: \: \: \: \: \: \: \bf\tt( \bf4x + x) + (2 - 2)[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf5x[/tex]

So the result is 5x

I hope I've helped XD

The inequality that describes the possible temperatures on Mars is

 -133°c ≤T≤ -7°c .

Inequality compares two values by if they are less than or greater than each other.

According to the given question Mars has a maximum temperature of -7°c at the equator and a minimum temperature of -133°c at the winter pole.

We have to write an inequality that describes the possible temperatures on Mars.

Let us denote all the possible range of temperatures by T,

∴ T is less or equal to the maximum temperature and T is greater than or equal to the minimum temperature.

So,    -133°c ≤T≤ -7°c .

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Answer: 4 seconds

Step-by-step explanation:

c=cheetah. a=antelope

a=c+120

c/90=a/60

c/90=(c+120)/60

60*c/90=60*(c+120)/60

6*c/9=c+120

2c/3=c+120

(2c/3=c+120)*3   ==> multiply the equation by 3 to get rid of fractions

2c=3c+360

2c-3c=3c-3c+360

-c=360

c=-360  feet==> position of cheetah before catching up to the antelope. This means that the cheetah needs to travel 360 feet before reaching 0 ft when it catches the antelope.

360 feet * 1 second/90 feet=

360*1/90=

360/90=4 seconds

As per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.

As given,

Total number of potential customers =40

Number of  respondents from bar graph

At grocery stores= 40

At drugstores respondents =32

At health food stores =8

At big box stores =20

Average number=(40 +32+8+20)/40

                            = 100 /40

                            =2.5

Therefore, as per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.

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f(x)=x+1 is a formula for a function f(x) that has f(9)=10

What is a simple definition for function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

a constant function is a function whose (output) value is the same for every input value. For example, the function y(x) = 10 is a constant function because the value of y(x) is 10 regardless of the input value x

if we take f(x)= x+1

then put x=9 we get f(9)= 10

Hence , f(x)=x+1 is a formula for a function f(x) that has f(9)=10

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The original amount for the laptop that Candace bought when the markup rate is 20% will be $4375.

It should be noted that she added 875 markup amount to the original price and the markup rate used was 20%,

Therefore, 20% of x = 865

0.2x = 875

Divide

x = 875 / 0.2

x = 4375

Therefore, the original amount for the laptop is $4375.

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Answer:

y= (x+9)^2

Step-by-step explanation:

If h<0 ( negative) then it shifts to the right, if it is is h>0 ( positive number) then it shift to the left!

y = x2

Shift 2 units left:  y = (x+2)2

Then, shift up 9 units:  y = (x+2)2 + 9

Then, reflect in the x-axis:  y = -(x+2)2 - 9

Answer: 0.3574 miles

Step-by-step explanation:

22647 inches = 0.3574 miles

The polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).

Polar and rectangular forms are related by this relation: (x, y) → (r · cos θ, r · sin θ), where r is the radial distance with respect to the origin and θ is the angle in standard position. We can use this fact to change the given expression into its rectangular form:

r = - 4 · (x / r)

r² = - 4 · x

x² + y² = - 4 · x

y² = - (x² + 4 · x)

y² - 4 = - (x² + 4 · x + 4)

y² - 4 = - (x + 2)²

(x + 2)² + y² = 4

(x + 2)² + y² = 2²

In a nutshell, the polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).

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Answer:

10

Step-by-step explanation:

1 Simplify 10-910−9 to 11.

1+8-7+{(6-(5+4)\div 3)}^{2}-1

1+8−7+(6−(5+4)÷3)

2

−1

2 Simplify 5+45+4 to 99.

1+8-7+{(6-9\div 3)}^{2}-1

1+8−7+(6−9÷3)

2

−1

3 Simplify 9\div 39÷3 to 33.

1+8-7+{(6-3)}^{2}-1

1+8−7+(6−3)

2

−1

4 Simplify 6-36−3 to 33.

1+8-7+{3}^{2}-1

1+8−7+3

2

−1

5 Simplify {3}^{2}3

2

to 99.

1+8-7+9-1

1+8−7+9−1

6 Simplify 1+81+8 to 99.

9-7+9-1

9−7+9−1

7 Simplify 9-79−7 to 22.

2+9-1

2+9−1

8 Simplify 2+92+9 to 1111.

11-1

11−1

9 Simplify.

10

Answer: 17/14 or 1 3/14 simplified

Step-by-step explanation:

14 is the least common multiple of denominators 7 and 2. Use it to convert to equivalent fractions with this common denominator.

Answer: x^3y^2(x+y)

Step-by-step explanation:

x^4y^2+x^3y^3​=

x*(x^3y^2)+(x^3y^2)*y=x^3y^2(x+y)

Answer:

13

Step-by-step explanation:

Simplify the following:

(7 - (sqrt(16))/4)^2 + 2 - 5^2

sqrt(16) = sqrt(2^4) = 2^2:

(7 - (2^2)/4)^2 + 2 - 5^2

2^2 = 4:

(7 - 4/4)^2 + 2 - 5^2

(-4)/4 = 4/4×-1 = -1:

(-1 + 7)^2 + 2 - 5^2

7 - 1 = 6:

6^2 + 2 - 5^2

5^2 = 25:

6^2 + 2 - 25

6^2 = 36:

36 + 2 - 25

36 + 2 - 25 = 13:

Answer:  13

The correct option is b. -30x + 32 = 182.

After combining the like terms, the equation that represents -8x + 23 - 22x + 9 = 182 is -30x + 32 = 182, where x = -5.

In its most basic form, an equation is a statement that demonstrates that 2 mathematical expressions have been equal.

Now, as per the given question;

The stated equation in the question is is,

-8x + 23 – 22x + 9 = 182

Considering like terms together;

-8x – 22x + 23 + 9 = 182

Further simplifying;

– 30x + 32 = 182

Subtracting 32 from the both sides.

– 30x + 32 - 32 = 182 - 32

On solving;

– 30x = 150

⇒ x = -5

Therefore, the expression which defined the equation after taking alike terms is -30x + 32 = 182 for which the value of 'x' comes to be -5.

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The complete question is;

Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms?

-8x + 23 – 22x + 9 = 182

a. 14x + 32 = 182

b. -30x + 32 = 182

c. 14x + 14 = 182

d. -30x + 14 = 182

Answer: probably like 1.8%

Step-by-step explanation: