4. (3x² + 3x-2) + (3x² - 5x - 3)
2​

Answer:

23

Step-by-step explanation:

Note there is a constant difference between consecutive terms

- 1 - (- 4) = - 1 + 4 = 3

2 - (- 1) = 2 + 1 = 3

5 - 2 = 3

This indicates that the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 4 and d = 3, thus

[tex]a_{10}[/tex] = - 4 + (9 × 3) = - 4 + 27 = 23

Answer:

2 dozen eggs are 24 eggs

Answer:

1.) 24

2.) 70°

Step-by-step explanation:

1.) 12*2=24

2.) 180°-110°=70°

Answer:

Domain- [-4,∞)  ; Range-  [-2,∞)

Step-by-step explanation:

[tex]y=\sqrt{x+4} -2[/tex]

For Domain, we need to find the range of value for x,

As the value for x+4 should be positive or 0 because it is under the square root bracket sign.

[tex]x+4\geq 0[/tex]

[tex]x\geq -4[/tex]

x ∈ [-4,∞)

For the range of values, we need to find all the possible value of y

As the value given by the square root will always be greater than equal to 0.

[tex]\sqrt{x+4}\geq 0[/tex]

[tex]\sqrt{x+4} -2\geq -2[/tex]

Therefore ,

y ∈ [-2,∞)

Answer:

The number of marbles does Tommy will get is 18 .

Step-by-step explanation:

Given as :

The total number of  marbles share between Tommy and Robbie = 48

The marbles were distributed between then in the ratio 3 : 5

Let the number of marbles does Tommy have = 3 x

The number of marbles does Robbie have = 5 x

Now,

According to question

The total number of  marbles share between Tommy and Robbie = 48

Or,  the number of marbles does Tommy have + The number of marbles does Robbie have = 48

Or, 3 x + 5 x = 48

Or, 8 x = 48

∴  x = [tex]\frac{48}{8}[/tex]

I.e  x = 6

So, the number of marbles does Tommy have = 3 × 6 =18

The number of marbles does Robbie have = 5 × 6 = 30

Hence the number of marbles does Tommy will get is 18 . Answer

Answer:

First situation matches to F(x) = 23(1.17)^x.

Second is 17x + 23 .

Third is 13x - 270.

Last one is 27(1.13)^x.

Step-by-step explanation:

Given the ratio of seats in the Circle to the Stalls is 2:5 and knowing the number of filled seats in the Circle, we can calculate that there were 1320 filled seats in the Stalls. This brings the total number of filled seats to 1848. However, without information on the theatre's total capacity, we cannot calculate the percentage occupancy.

The ratio of the number of seats in the Circle to the number of seats in the Stalls is 2:5. This means that for every 2 seats in the Circle there are 5 in the Stalls. Given that there were 528 seats filled in the Circle, we can use this ratio to calculate the number of filled seats in the Stalls.

Divide the number of filled Circle seats by 2 (which is 528/2 = 264) and then multiply by 5, which gives us 1320 filled seats in the Stalls. To calculate the total number of filled seats, we add the filled seats in the Circle and the Stalls together (1320 + 528), which gives us 1848 filled seats.

To work out the percentage of occupancy, we must first find out the maximum capacity of the theatre. All we know is the ratio of seats, we don't know the exact total number of seats. Unless we know the total number of seats in the theatre, we cannot work out the percentage of occupancy for last Friday.

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The number of occupied seats in the theatre, in both Circle and Stalls is summed up and divided by the total number of seats in the theatre. The result in decimal is multiplied by 100% to get the percentage occupancy. In this case, as all seats were occupied, the percentage is 100%.

The subject of your question involves ratio and percentage, which falls under the category of Mathematics, specifically proportions and ratios. We know that the ratio of the number of seats in the Circle to the number of seats in the Stalls is 2:5. This means that for every 2 seats in the Circle, there are 5 seats in the Stalls. If there were 528 seats occupied in the Circle, since the ratio is 2:5, the number of occupied seats in the Stalls would be (528/2)*5 = 1320. The total number of seats in the theatre is the sum of seats in both Circle and Stalls which is 528+1320 = 1848. The proportion of occupied seats is the sum of occupied seats in both levels (528+1320) divided by the total (1848), which gives us the decimal 1. The percentage of this is 1*100 = 100%. So the percentage occupancy of the theatre last Friday was 100%.

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Answer:

hnjmmm

Step-by-step explanation:

m,,\

l;'

Answer:

x = 2[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Given that y varies inversely as the square of x then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = yx² = 2 × 4² = 2 × 16 = 32

y = [tex]\frac{32}{x^2}[/tex] ← equation of variation

When y = [tex]\frac{4}{5}[/tex], then

[tex]\frac{4}{5}[/tex] = [tex]\frac{32}{x^2}[/tex] ( cross- multiply )

4x² = 160 ( divide both sides by 4 )

x² = 40 ( take the square root of both sides )

x = [tex]\sqrt{40}[/tex] = [tex]\sqrt{4(10)}[/tex] = 2[tex]\sqrt{10}[/tex]

Answer:

An open circle line going passed and from 3 that way --->

Step-by-step explanation:

Add 15 to both sides

12b > 36

Divide 12 to both sides

b > 3

Answer:

It will be an open circle going pass the 3 like this

o---------------------------------------------------------------->

Step-by-step explanation:

12b - 15 > 21

add 15:

12b - 15 > 21

      + 15  + 15

So now it's:

12b > 36

Now divide by 12:

12b > 36

/12     /12

And now your answer is:

b > 3

To find the unit rate representing how many patients each nurse is responsible for with 28 patients and 2 nurses, you divide 28 by 2, resulting in 14 patients per nurse.

Nurse Unit Rate Calculation:

Identify the total number of patients: 28 patients

Determine the number of nurses: 2 nurses

Calculate the unit rate by dividing the total number of patients by the number of nurses: 28 patients ÷ 2 nurses = 14 patients per nurse

Answer: [tex]H_0: p=0.30[/tex]

[tex]H_a: p <0.30[/tex]

Step-by-step explanation:

Definition:

Null Hypothesis : It is a statement about the population parameter that contains = , ≤ and ≥ signs.

Alternative hypothesis : It is also a statement about the population parameter against the null hypothesis that contains ≠  , < and > signs.

For the given situation.

Let [tex]\mu[/tex] be the population proportion of treated patients are uninsured.

A hospital director is told that 30% of the treated patients are uninsured.

Then, Null Hypothesis : [tex]H_0: p=0.30[/tex]

The director wants to test the claim that the percentage of uninsured patients is less than  the expected percentage.

i.e. Alternative hypothesis : [tex]H_a: p <0.30[/tex]

Hence, the set of hypothesis :

[tex]H_0: p=0.30[/tex]

[tex]H_a: p <0.30[/tex]

Answer:

D) 2

Step-by-step explanation:

5x + 7 [tex]\leq[/tex] 8x -3 +2x

5x + 7 [tex]\leq[/tex] 10x - 3

7 + 3 [tex]\leq[/tex] 10x - 5x

10 [tex]\leq[/tex] 5x

2[tex]\leq[/tex] x

x[tex]\geq[/tex]2

Answer:

[tex]\large\boxed{A.\ y^3}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\\dfrac{y^{10}}{y^7}=y^{10-7}=y^3[/tex]

[tex]\text{Other method:}[/tex]

[tex]\text{We know:}\ a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}\\\\y^{10}=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}_{10}\\\\y^7=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}_7}[/tex]

[tex]\dfrac{y^{10}}{y^7}=\dfrac{y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\cdot y\cdot y}{y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup}=y\cdot y\cdot y=y^3[/tex]

The correct answer is (a) a sheet of wet cardboard, which becomes limp when moistened as the material loses its rigidity and strength, unlike the other items listed which maintain their form and firmness.

Among the options provided, a sheet of wet cardboard is most likely to feel limp. When cardboard absorbs water, the material becomes weak and loses its rigidity, making it bend or flop easily. The other materials listed, such as a sheet of ice, a sleeping child, and a sheet of plywood, retain their form and rigidity better when they are not altered by external factors like moisture.

A sheet of ice remains solid until it melts, a sleeping child is not an inanimate object and doesn't become limp simply because they are asleep, and a sheet of plywood is a construction material designed to remain sturdy even when faced with various environmental conditions. Therefore, (a) a sheet of wet cardboard is the correct answer as it is the one that could be expected to feel limp when wet.

Answer: 3.75 gallons

Step-by-step explanation:

8 fl oz x 60 (minutes)=480 fl oz

480 fl oz ÷ 128=3.75 gallons

Water flow rate is defined as the volume of the fluid passing by some location. The water leaking from the pipe per hour is 3.75 gallons

A pipe is leaking at the rate of 8 fluid ounces per minute.

Water flow rate is defined as the volume of the fluid passing by some location.

As the flow rate is 8 fluid ounces per minute. In a hour there is total 60 minutes. Thus the flow rate of the pipe in fluid ounces per hour is,

[tex]Q=8\times60[/tex]

[tex]Q=480[/tex]

A fluid ounces is the unit of the measurement of the liquid. There is total 128 fluid ounces in a gallons. Thus the flow rate of the water in gallon can be calculated by dividing the 480 by 128. Thus the flow rate of pipe in gallons per hour is,

[tex]Q=\dfrac{480}{128}[/tex]

[tex]Q=3.75[/tex]

Hence the water leaking from the pipe per hour is 3.75 gallons.

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Answer:

Part 1:

Jose's Banquet Hall: 50g+100

Palace of Aaron: 45g+200

Part 2:

20 guests

Step-by-step explanation:

Part 1:

$50 per guest plus $100 fee

50g+100

$45 per guest plus $200 fee

45+200

Part 2:

$50(20)+$100=$1100

$45(20)+$200=$1100

Answer:

II. [tex]\displaystyle 20\:wedding\:guests[/tex]

I. [tex]\displaystyle 100 + 50g = 200 + 45g[/tex]

Step-by-step explanation:

100 + 50g = 200 + 45g

- 200 - 50g - 200 - 50g

___________________

[tex]\displaystyle \frac{-100}{-5} = \frac{-5g}{-5} \\ \\ 20 = g[/tex]

So, at twenty wedding guests, the cost will balance for both venues.

I am joyous to assist you anytime.

Answer: collision zone

Step-by-step explanation:As a result of this collision, the sedimentary rocks which were settled in the large-scale depression in the Earth's crust called Tethys were folded and formed the Himalayas.

C collision zone

The Himalayas are the world's highest mountains, straddling the Indian and Eurasian plates. The Himalayas were formed by a collision zone.

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Answer:

4th month

Step-by-step explanation:

As this graph shows the evolution of your collection over time, and not the number of key chains you collected in each month, you need to look for the month with the highest increase.

According to the graph on the first month you collected 4 key chains. After the 2nd month you had 6 key chains, so, you collected:

keys on 2nd month - keys on 1st month = 6-4 = 2 keys

In month 3 you went from 6 to 10 key chains, so you collected

keys on 3rd month - keys on 2nd month = 10-6 = 4 keys

On the next, month 4, you had 16, so you collected

keys on 4th month - keys on 3rd month = 16-10 = 6 keys

Finally, on the last month you had 18, having collected:

keys on 5th month - keys on 4th month = 18-16 = 2 keys

So, the month you most collected was the 4th, with 6 key chains. All the others months collected less keys (2 on the 2nd, 4 on the 3rd and 2 on the 5th).

I hope it is understandable.

Based on the graph, the month in which you collected the most key chains is May which is 4th month.

To determine this, we can look at the slope of the line between each pair of points. The slope of a line represents the rate of change, so a steeper slope indicates that the change is happening more quickly.

The slope of the line between the points for April and May is the steepest, which means that the number of key chains increased at the fastest rate during that month. Therefore, we can conclude that you collected the most key chains in May.

Here is a table of the slopes between each pair of points on the graph:

Month Previous Month Slope

May April 2.5

April March 2

March February 1.5

February January 1

As you can see, the slope between April and May is the highest, which indicates that you collected the most key chains during that month.

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Answer:

231

Step-by-step explanation:

Given

[tex]\frac{4}{77}=\frac{12}{x}[/tex]

Cross Multiply

[tex]x \times 4=12\times 77\\x=\frac{12\times 77}{4} \\x= 3\times 77\\x= 231[/tex]

Therefore x=231

Answer:

first proof should be cpctc, second proof is the triangle sum theorem

Answer:

165150 is the sum of the multiples of 3 between 100 and 1000.

Step-by-step explanation:

We need to find the sum of multiples of 3 between 100 and 1000.

First we will find the Total number of multiples of 3 between 100 and 1000.

Let a be the first multiple and l be the last multiple of 3

100 is not the multiple of 3.

101 is not the multiple of 3.

102 is the multiple of 3.

Hence first term a = 102

Similarly.

1000 is not a multiple of 3

999 is a multiple of 3

hence last term l = 999

Also d is the common difference.

hence d = 3.

Now by using Arithmetic progression formula we get;

[tex]T_n(l) =a+(n-1)d\\ 999=102+(n-1)3\\999-102=(n-1)3\\897=(n-1)3\\\frac{897}{3}=n-1\\\\n-1=299\\n=299+1\\n=300[/tex]

Hence there are 300 multiples of 3 between 100 and 1000

Now n=300, a=102, l = 999

Hence to find the sum of all the multiples we use the Sum of n terms in AP  formula;

Sum of n term [tex]S_n= \frac{n}{2}(a+l)[/tex]

[tex]S_{300}= \frac{300}{2}(102+999)\\\\S_{300}= 150(102+999)\\S_{300}= 150\times 1101\\S_{300}= 165150[/tex]

Hence,165150 is the sum of the multiples of 3 between 100 and 1000.

First find x and y.

Solve system of equations by elimination.

  3x-y=3

+(-x+y=3)

---------------

2x=6

x=3

Now plug in x into one of the equations to find y.

-3+y=3

y=6

xy=3x6=18

Final answer:

The product of xy, given the system of equations 3x - y = 3 and -x + y = 3, is 18. This is found by first solving for x and y using the elimination method and then multiplying the obtained values.

Explanation:

To find the product of xy, we need to solve the system of equations given by 3x - y = 3 and -x + y = 3. Here we'll use the elimination method. Adding both equations together, we eliminate y:

3x - y + (-x + y) = 3 + 3

Which simplifies to:

2x = 6

Dividing both sides by 2, we get:

x = 3

To find y, we substitute x back into one of the original equations, for example, the second equation -x + y = 3:

-(3) + y = 3

-3 + y = 3

Adding 3 to both sides gives us:

y = 6

Now we can find the product of xy:

xy = 3 * 6

xy = 18

Therefore, the product of xy is 18.

Answer:

The numerator is the first number in a division problem (dividend). The denominator is the second number in a division problem (divisor).

Answer:

Divisor

Step-by-step explanation:

The denominator is the divisor. This is the split apart quantity.

I am joyous to assist you anytime.

Answer:

A) The second day

B) 9/16 inches

Step-by-step explanation:

A) Elsa reached farther on the second day because -1/16 > -5/8

B) To calculate this we must first put both fractions above the same denominator. We can then subtract the smaller one from the bigger one:

-1/16 - (-10/16) = 9/16

Elsa reached 9/16 inches farther on the second day then she did on the first.

Final answer:

Elsa reached farther on the second day than the third day during her flexibility tests. She reached 9/16 inches farther on the second day compared to the third day.

Explanation:

Elsa is taking physical fitness tests in her strength training class where she tracks her progress by comparing her flexibility results to the baseline (first day). A negative value indicates she did not reach as far as the baseline.

A. On the second day, Elsa's flexibility test result was recorded as - 1/16 inches, and on the third day, it was -5/8 inches. Since -1/16 is greater than -5/8 (closer to zero), it means Elsa reached farther on the second day than the third day.

B. To find out by how much Elsa reached farther on the second day compared to the third day, we calculate the difference between the two measurements: (-1/16) - (-5/8) = 5/8 - 1/16. We must find a common denominator to subtract these fractions, which is 16. So we have (10/16) - (1/16) = 9/16 inches. Therefore, Elsa reached 9/16 inches farther on the second day compared to the third day.

Answer:

159

Step-by-step explanation:

Add 99 and 60 to get 159. Now subtract 99 from that and you will have 60.

Answer:

The Glee Club sold 90 Adult tickets.

Step-by-step explanation:

Let the number of Student ticket be x.

Let the number of Adult ticket be y.

Total Number of ticket sold is 150.

Hence,

Total Number of ticket = number of Student ticket + the number of Adult ticket

[tex]x+y=150 \ \ \ \ equation\ 1[/tex]

Also Given;

Student tickets cost $5.00 each.

Adult tickets cost $8.00 each.

Ticket Sales is $1,020.

hence,

[tex]5x+8y=1020 \ \ \ \ equation\ 2[/tex]

Now Multiplying equation 1 by 5 we get.

[tex]5\times(x+y)= 5\times150\\5x+5y=750\ \ \ \ equation \ 3[/tex]

Now Subtracting equation 2 from equation 3 we get;

[tex](5x+8y=1020)-(5x+5y=750)\\\\3y = 270\\y= \frac{270}{3}= 90[/tex]

Number of adult ticket sold is 90.

Also [tex]x+y=150\\x+90=150\\x=150-90=60[/tex]

Number of Student ticket sold is 60.

Hence, The Glee Club sold 90 Adult tickets.

By using a system of equations and the elimination method, we determined the Glee Club sold 90 adult tickets.

To help you understand how many adult tickets were sold by the Glee Club, we can use a system of equations to represent the situation. Let x represent the number of student tickets sold, and let y represent the number of adult tickets sold.

We have two equations based on the problem:

We can solve this system using the substitution or elimination method. Here, elimination will be more convenient:

Therefore, the number of adult tickets sold was 90.

Answer:

y=-2x+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side of a square

We have

[tex]A=1yd^2[/tex]

Therefore

[tex]s^2=1yd^2\to s=\sqrt{1yd^2}=1yd[/tex]

Answer:

x=0, y=2. (0, 2).

Step-by-step explanation:

3x+2y=4

8x-3y=-6

---------------

3(3x+2y)=3(4)

2(8x-3y)=2(-6)

-----------------------

9x+6y=12

16x-6y=-12

----------------

25x=0

x=0/25

x=0

3(0)+2y=4

0+2y=4

2y=4-0

2y=4

y=4/2

y=2

The solution of the systems of equations by substitution will be;

⇒ x = 0, y = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ 3x + 2y = 4

⇒ 8x - 3y = -6

Now,

Since, The system of equation are,

⇒ 3x + 2y = 4  ..(i)

⇒ 8x - 3y = -6  ..(ii)

Find the value of x from (i) as;

⇒ 3x + 2y = 4

⇒ 3x = 4 - 2y

⇒ x = 1/3 (4 - 2y)

Substitute above value in (ii), we get;

⇒ 8x - 3y = -6

⇒ 8 × 1/3 (4 - 2y) - 3y = -6

⇒ 32/3 - 16y/3 - 3y = - 6

⇒ 32/3 + 6 = 25y/3

⇒ 50/3 = 25y/3

⇒ 50 = 25y

⇒ y = 2

And, From (i),

⇒ 3x + 2y = 4

⇒ 3x + 2 × 2 = 4

⇒ 3x  = 4 - 4

⇒ x = 0

Thus, The solution of the systems of equations by substitution are;

⇒ x = 0, y = 2

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