Find values of a and b that make the following equality into identity:

Answer:

x=-2+sqrt(7)*i, -2-sqrt(7)*i

Step-by-step explanation:

x^2+4x=-11

x^2+4x-(-11)=0

x^2+4x+11=0

Apply the quadratic formula with a=1, b=4 and c=11.

Answer:

1.) 24

2.) 70°

Step-by-step explanation:

1.) 12*2=24

2.) 180°-110°=70°

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:

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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Answer:

159

Step-by-step explanation:

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

Answer:

Length = 17, Width = 6

Step-by-step explanation:

Let the length be L and width be W.

L = 3W - 1 , and,

2(L + W) = 46 => L+W = 23  => L = 23 - W, putting this into L = 3W - 1

23 - W = 3W - 1

24 = 4W

W = 6

therefore, L = 23 - W = 17

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:

Step-by-step explanation:

6*68=408

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

48/10=4.8

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

3.8=x/7.7

x=3.8*7.7x

x=29.26

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

x+5.1=13.4

x=13.4-5.1

x=8.3

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

8x=64

x=64/8

x=8

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

22=m+1

m=22-1

m=21

----------

45-4x for x=5

45-4(5)=45-20=25

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

256, 64, 16, 4

Answer:

6*68=408

Step-by-step explanation:

Answer:

8^5

Step-by-step explanation:

8^5

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:

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:

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

Answer:

2 dozen eggs are 24 eggs

The negative sign shows that they still owed $5000 to the creditors which shows a loss of money between June and December.

Step-by-step explanation:

Amount owed at the end of June = $3765

Amount owed at the end of December = $8765

As Hightop Roofing owed creditors the amount, therefore, we will consider the amount as negative, therefore,

Amount in June = -3765

Amount in December = -8765

To see the difference, we will subtract the amount owed in June from the amount owed in December.

[tex]Difference=(-8765)-(-3765)\\Difference=-8765+3765\\Difference=-5000[/tex]

The negative sign shows that they still owed $5000 to the creditors which shows a loss of money between June and December.

Keywords: difference, loss

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The equation of the line is y = [tex]\frac{2}{3}[/tex] x + 9

Step-by-step explanation:

The equation of a line in slope-intercept form is y = m x + b, where

∵ The line has a slope [tex]\frac{2}{3}[/tex]

∴ m = [tex]\frac{2}{3}[/tex]

∵ The y-intercept is 9

∴ b = 9

- Substitute the values of m and b in the form of the equation below

∵ y = m x + b

∴ y = [tex]\frac{2}{3}[/tex] x + 9

The equation of the line is y = [tex]\frac{2}{3}[/tex] x + 9

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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:

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:

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:

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:

amplitude = 3

Step-by-step explanation:

The standard form of a cosine function is

f(x) = a cos(bx + c) + d

amplitude = | a |, period = [tex]\frac{2\pi }{b}[/tex]

phase shift = - [tex]\frac{c}{b}[/tex], d is the vertical shift

Given the above function, then

amplitude = | - 3 | = 3

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:

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:

y=-2x+5

Step-by-step explanation:

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]

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: [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:

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:

A ) The selling price of radio is $ 81.64

B ) The selling price of microscope is $ 72.94

Step-by-step explanation:

Given as :

A ) Market price of radio = M.P = $ 125.60

Let The selling price of radio = S.P =  $ x

The discount = 35 %

So, Discount %  = [tex]\dfrac{M.P - S.P}{M.P}[/tex]

Or, [tex]\frac{35}{100}[/tex] = [tex]\dfrac{125.60 - x}{125.60}[/tex]

Or, [tex]\frac{x}{125.60}[/tex] = 1 - [tex]\frac{35}{100}[/tex]

Or,  [tex]\frac{x}{125.60}[/tex] =  [tex]\frac{100-35}{100}[/tex]

Or,  [tex]\frac{x}{125.60}[/tex] =  [tex]\frac{65}{100}[/tex]

∴  x = [tex]\frac{125.60\times 65}{100}[/tex]

I.e  x = $ 81.64

So, The selling price of radio is $ 81.64

B ) The market price of microscope = M.P = $ 96.25

    The discount = 20 %

    Tax percentage = 6 %

Let the selling price of microscope = $ y

Now, So, Discount %  = [tex]\dfrac{M.P - S.P}{M.P}[/tex]

Or, [tex]\frac{20}{100}[/tex] = [tex]\dfrac{96.25 - y}{96.25}[/tex]

Or, [tex]\frac{y}{96.25}[/tex] = 1 - [tex]\frac{20}{100}[/tex]

Or,  [tex]\frac{y}{96.25}[/tex] =  [tex]\frac{100-20}{100}[/tex]

Or,  [tex]\frac{y}{96.25}[/tex] =  [tex]\frac{80}{100}[/tex]

∴  y = [tex]\frac{96.25\times 80}{100}[/tex]

I,e y = $ 77

Again Tax of 6% is added

So , $ 77 - 6 % of $ 77

Or, $ 77 × 0.94 = $ 72.38

∴ The final cost of microscope after discount and tax is $ 72.94

Hence A ) The selling price of radio is $ 81.64

And     B ) The selling price of microscope is $ 72.94   Answer

Answer:

From figure A

The value of ∠ B = 75.74°   ,  ∠ C = 70.26° and  AB = 27.37

From figure B

The value of ∠ A = 42.8°   ,  ∠ B = 106.2° and  AC = 30.04

Step-by-step explanation:

Given first figure as :

AC = 28.2

BC = 16.5

∠ A = 34°

Let AB = c

From law of sines

[tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

Or, [tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex]

or, [tex]\dfrac{16.5}{Sin 34}[/tex] = [tex]\dfrac{28.2}{Sin B}[/tex]

Or,  29.506 =  [tex]\dfrac{28.2}{Sin B}[/tex]

Or, Sin B =  [tex]\dfrac{28.2}{29.5}[/tex]  

Or, Sin B = 0.955

∴  ∠B = [tex]Sin^{-1}[/tex] 0.955

I.e∠ B = 75.74

Now, ∠ C = 180° - ( ∠A + ∠B )

Or, ∠ C = 180° - ( 34° + 75.74° )

Or, ∠ C = 70.26°

Now, Again

[tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

so,  [tex]\dfrac{28.2}{Sin 75.74}[/tex] = [tex]\dfrac{c}{Sin 70.26}[/tex]

Or,   [tex]\dfrac{28.2}{0.9691}[/tex] = [tex]\dfrac{c}{0.9412}[/tex]

Or, c = 29.09 × 0.9412

∴    c = 27.37

I.e AB = 27.37

Hence,  The value of ∠ B = 75.74°   ,  ∠ C = 70.26° and  AB = 27.37

From figure second

Given as :

AB = c= 12

BC = a = 16

∠ C = 31°

let AC = b

From law of sines

[tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

Or, [tex]\dfrac{a}{SinA }[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

or,  [tex]\dfrac{16}{Sin A}[/tex] = [tex]\dfrac{12}{Sin 31}[/tex]

or,  [tex]\dfrac{16}{Sin A}[/tex] = [tex]\dfrac{12}{0.51}[/tex]

Or, [tex]\dfrac{16}{Sin A}[/tex] = 23.52

∴ Sin A = [tex]\dfrac{16}{23.52}[/tex]

I.e Sin A = 0.68

Or,  ∠ A = [tex]Sin^{-1}[/tex] 0.68

or,  ∠ A = 42.8°

Now,  ∠ B = 180° - ( 31° + 42.8° )

Or,  ∠ B = 106.2°

Now,  [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

or,  [tex]\dfrac{b}{Sin 106.2}[/tex] = [tex]\dfrac{16}{Sin 31}[/tex]

Or, [tex]\dfrac{b}{0.96}[/tex] = [tex]\dfrac{16}{0.51}[/tex]

or, b = 31.3×0.96

∴ b = 30.04

Hence The value of ∠ A = 42.8°   ,  ∠ B = 106.2° and  AC = 30.04

Answer