I.
Encircle the number(s) that is (are) not in the domain of the given
rational algebraic expression.

-1/4x

-3
-1
0
4

Step-by-step explanation:

[tex]p(x) = 3 {(x + 1)}^{2} - 3[/tex]

Answer: To find the percent increase in average movie theater ticket price, you can use the formula:

percent increase = (new value - old value) / old value * 100

Plugging in the values, we get:

percent increase = ($8.53 - $6.96) / $6.96 * 100 = 22.9%

So, the percent of increase in average movie theater ticket price for the 10-year period from 2007 to 2017 is 22.9%.

Step-by-step explanation:

Id the base BCDE of the pyramid is a horizontal square w side lengths 12cm . The size of the angle between AB and the base of the pyramid is 62 degree.

Side of square of base BCDE =12cm

Area of base =12² =144cm²

Volume of pyramid = 768cm³

1/3 a² × h= 768

1/3 × 144 × h =768cm³

h =768 × 3 /144

h =16 cm

BD² =BC² +CD²

BD² = 12² + 12²

BD² = 288

BD =√288 cm

BD = 16.97cm

BD = 17cm

So,

BF = 1/2 BD

BF = 1/2 × 17

BF =8.5cm

So since ΔABF  is angle between AB  and base of pyramid

tan <ABF = Tan-1 (16/8.5) = 62°

Therefore the size of the angle between AB and the base of the pyramid is 62 degree.

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Answer:

y = - 3

Step-by-step explanation:

A line parallel to the x- axis is a horizontal line with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (2, - 3 ) with y- coordinate - 3 , then

y = - 3 ← equation of line

Answer:

Step-by-step explanation:

Answer:

27/7

Step-by-step explanation:

First, note that 3 6/7 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

3 = whole number

6 = numerator

7 = denominator

To convert mixed number 3 6/7 to improper fraction, you follow these steps:

Multiply the whole number by the denominator

3 × 7 = 21

Add the product from Step 1 to the numerator

21 + 6 = 27

Write answer from Step 2 over the denominator

27/7

The mixed number 3 6/7 converted to improper fraction is therefore :

27/7

Answer:

27/7

Step-by-step explanation:

Answer:

y = 2x -2

Step-by-step explanation:

y = mx + b

We need the slope (m) and the y-intercept (b) to write the eqation.

The slope is the change in y over the change in x.  We can see from the table that the y is changing by 2 as the x changes by 1

So the slope is 2/1 which is the same as 2

The slope (m) is 2.

The y-intercept is the place where the line crosses the y axis.  It is at the point (0,b).  When x is zero, what is y?  If we follow the patter and move to the number before x is 1, we get x = 0.  That means that we have to move back 2 units of the y's.  That would be -2.  So the y-intercept is the point (0,-2).

The y-intercept (b) is -2

y = 2x - 2

The interest paid at the term end will be $5400.

What is interest and its types(Simple and compound interest)?

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

​The formula for these are

Simple Interest= P×r×n

where:

P=Principal amount

r=Annual interest rate

n=Term of loan, in years

Compound Interest=P×(1+r)^t−P

where:

P=Principal amount

r=Annual interest rate

t=Number of years interest is applied

Here,

Interest rate will be risk percentage + LIBOR

i.e.4.8%

Hence,  the interest can be found by using formula for simple interest

Therefore,

SI=P*r*t

=$450000*0.048*0.25               (Time is 3 month or  0.25 years.)

SI (Interest paid)=$5400

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The total interest paid for the period of three months will be $5225 on the loan amount of $450000.

What is interest?

The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.

Here in the question given data is

P= $450000

R=2.2%+2.8%=5%

T=1/4 years or three months

So from the simple interest formula

SI= PNR/100

SI=15000×5×1/`100×4

SI=$5625

Hence the total interest paid for the period of three months will be $5225 on the loan amount of $450000.

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The value of unknown side length x in simplest radical form is 4√37.

Option B is the correct answer.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Two right triangles.

Applying the Pythagorean theorem in the bigger triangle.

We get,

25² = 7² + Length²

25² = 49 + Length²

Length² = 625 - 49

Length² = 576

Length = √576

Length = 24

Now,

Applying the Pythagorean theorem in the smaller triangle.

We get,

x² = 4² + 24²

x² = 16 + 576

x² = 592

x² = 16 x 37

x = √(16 x 37)

x = √(4² x 37)

x = 4√37

Thus,

The value of x is 4√37.

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Answer:Angle

Step-by-step explanation:

A system of inequalities that can be used to model the scenario is d + a ≤ 300 and 10d ≥ 1,200.

A system of inequalities is two or more inequalities that must be proved simultaneously.

A system of inequalities contains at least two linear inequalities in the same variables.

Systems of inequalities are applied when there are a range of solutions and more than one constraint.

Inequalities may include greater than, less than, not equal to, equal to but less than, and equal to but greater than.

The total capacity of people the auditorium can hold = 300

The cost per ticket at the door = $10

The cost per ticket in advance = $7.50

Tickets cannot exceed 300

Door tickets must generate at least $1,200

Let the number of tickets sold at the door = d

Let the number of tickets sold in advance = a

10d + 7.5a ≤ 300

10d ≥ 1,200

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Answer:

Step-by-step explanation:

The general form of the equation for the line described by the point-slope form y + 3 = −2/7 (x − 5) is y = -2/7x + 19/7.

Answer: y= 5x - 9

Hope this will help

Answer:

y=5x-9

Step-by-step explanation:

In y=mx+b, m is the slope and b is the y intercept all you have to do is replace m and b with the numbers associated in the problem this case since 5 is the slope you put it where m is, and b being the y-intercept you put the -9 there!

In order to differentiate between objects, one must first recognise their distinctions.

In order to differentiate between objects, one must first recognise their distinctions. The difference between the chocolate sauce and the spicy bean dip, for instance, could be difficult to see if the party lighting is low. It is possible to distinguish between various.

To distinguish between objects being compared, to demonstrate, or to discover: On the basis of colour, religion, or country of origin, we do not make distinctions amongst our personnel. The majority of customers can easily distinguish between the cereal from our brand and that of our main rival.

-(x²yz³)³.(xyz)²​+z = (xy²z)². x²yz³ + (x²yz³)³.(xyz)²​.

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The derivative of the expression, x²yz³ + (x²yz³)³ with respect to z = (xy²z)² is:

d/dz (x²yz³ + (x²yz³)³) = d/dz (x²yz³) + d/dz ((x²yz³)³)

= 3x²y²z³ + 2x³yz⁴ + 3 * (x²yz³)² * (3x²y²z³ + 2x³yz⁴)

The derivative of the first term, x²yz³, with respect to z = (xy²z)² can be found using the chain rule:

d/dz (x²yz³) = d/dy (x²yz³) * dy/dz + d/dx (x²yz³) * dx/dz

= 3x²yz² * yz + 2x¹yz³ * xy²z

= 3x²y²z³ + 2x³yz⁴

The derivative of the second term, (x²yz³)³, with respect to z = (xy²z)² can be found using the chain rule and the power rule:

d/dz ((x²yz³)³) = d/dy (x²yz³)³ * dy/dz + d/dx (x²yz³)³ * dx/dz

= 3 * (x²yz³)² * (3x²yz² * yz + 2x¹yz³ * xy²z)

= 3 * (x²yz³)² * (3x²y²z³ + 2x³yz⁴)

Finally, the derivative of the expression, x²yz³ + (x²yz³)³ with respect to z = (xy²z)² is:

d/dz (x²yz³ + (x²yz³)³) = d/dz (x²yz³) + d/dz ((x²yz³)³)

= 3x²y²z³ + 2x³yz⁴ + 3 * (x²yz³)² * (3x²y²z³ + 2x³yz⁴)

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Answer:  Lily babysits for less than 4 hours.

Step-by-step explanation:

We can start by multiplying 4 hours by 7/8 to find out how many hours Lily spends babysitting.

4 * (7/8) = 7/2 = 3.5 hours

Since 3.5 is less than 4, Lily babysits for less than 4 hours.

Answer: Less than 4. (3 1/2 hours)

Step-by-step explanation:

When you multiply a number by a number smaller than 1, the answer gets smaller.

Lily babysits for 3 1/2 hours because 4 x 7/8 = 3 1/2

Answer:

Step-by-step explanation:

First, we will use the property of radicals that states that (a √b) * (c √d) = (ac) √(bd). Since the expression has both multiplication and addition, we will break the expression down into its components and simplify each component separately.

6√x+7√(54) = 6√x + 7√(27*2) = 6√x + 7√27 * 7√2 = 6√x + 7√27 * (2*√2) = 6√x + 14√27 * √2 .

Next, we will simplify the second component of the expression: 12√(6) = 12√(2*3) = 12√2 * 6√3 = (4*3)√2 * 6√3 = 12√2 * 6√3.

Finally, we can combine the two separate parts of the expression to get the simplified version: 6√x + 14√27 * √2 - 12√2 * 6√3 = 6√x + 14√27 * √2 - 12√6.

The simplified version of the expression is 6√x + 14√27 * √2 - 12√6, in exact terms (no decimals).

Based on the given derivative function, the function f is decreasing for a < x < b, because f'(x) < 0 for a < x < b (A).

The given derivative function is the first derivative of function f(x), where:

f'(x) = x² - (a+b) x + ab = (x - a) (x - b)

a < b

Since the first derivative function f'(x) is still in the form of x²  function, we can deduce that the original function f(x) has 2 extreme points, the maximum and the minimum. Those extreme points are (x = a) and (x = b).

However we cannot determine which one is the maximum point and which is the minimum one. We need to do another derivative work and check the second derivative function for each extreme points relevant to zero (0).

f'(x) = x²  - (a+b) x + ab

f''(x) = 2x - (a+b)

(x = a)

f''(a) = 2(a) - (a+b)

f''(a) = 2a - a - b

f''(a) = a - b < 0 --> because a < b

(x = b)

f''(b) = 2(b) - (a+b)

f''(b) = 2b - a - b

f''(b) = b - a > 0 --> because a < b

Based on the second derivative function, we can define that (x = a) is the maximum point because f''(a) < 0 and (x = b) is the minimum point because f''(b) > 0. Then the value of f(x) between a < x < b should be on a downward slope.

However wee need to reconfirm this statement by choosing one set of random number that meet the rules of a < x < b. For this time, we use:

a = 1

b = 3

x = 2

Then:

f'(x) = x² - (1 + 3) x + (1) (3)

f'(x) = x²  - 4x + 4

(x = 2)

f'(2) = (2)²  - 4(2) + 3

f'(2) = 4 - 8 + 3

f'(2) = -1 < 0 --> supported statement A

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Answer:

To determine which cream cheese is a better buy, we need to compare the price per unit of volume for each brand.

For Brand Y cream cheese:

Price per unit = 44 AED / 220 ml = 0.2 AED/ml

For Brand Z cream cheese:

Price per unit = 100 AED / 470 ml = 0.2127 AED/ml

Since the price per unit of volume for Brand Y cream cheese is 0.2 AED/ml and the price per unit of volume for Brand Z cream cheese is 0.2127 AED/ml, Brand Y cream cheese is cheaper per unit of volume. Therefore, Brand Y cream cheese is a better buy.

Using the details given, the area of the triangle in which the angles lies between the two sides is 90.3 units²

The area of a triangle can be calculated using the formula A = 1/2bh, where b is the base of the triangle and h is the height. Area of a triangle can be calculated using the formula: Area = (base x height) / 2, where base is the length of one side and height is the length of the side that forms the angle. In order to use this formula, you must know the length of two sides and the measure of the angle between them. However, this formula is subjective to details given

The area of a triangle can be calculated by

A = a×b×sinθ

a = 15

b = 8.1

θ = 132°

Substituting the values into the formula

A = 15 × 8.1 × sin 132

A = 90.3 units²

The area of the triangle is 90.3 units²

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Answer:

make the x and y variables to each other variables by addition or subtraction

173x-7x +4y-4y=5

166x + 0y=5

166x =5

x= 166/5

x=33.2

Salut/Hello!

Answer: a) 90 tiles ; b) 3 m

Step-by-step explanation:

a) First we need to imagine a drawing of the empty worktop. We know the width is equal to 6 tiles and the length is equal to 15 tiles. If the shorter edge fits 6 tiles then we have 6 sets of 15 tiles.
6 x 15 = 90 tiles

b) We know the length of one tile is 20 cm so the length of 15 tiles that fit in the worktop is equal to 300 cm or 3 m

I hope it was helpful!

a) To cover the workshop, he has to use 90 tiles altogether.

b) The length of the workshop is 3 meters.

We know that the area of the rectangle is

Area =  length × width

Here shorter edge is called width and the longer edge is called length.

Also given that,

The tiles required to cover the shorter edge are 6 tiles.

The tiles required to cover the longer edge are 15 tiles.

so, the total tiles required to cover the worktop are

Area = 15 tiles × 6 tiles

= 90 tiles

Therefore, 90 tiles are required to cover the worktop.

To find the length of the worktop,

Required length = length of each tile × no. of tiles

By applying the formula,

Required length = 20 cm × 15

= 300 cm

1 meter = 100 centimeteres

Therefore, the length of the worktop is 3 meters.

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Answer:

A = $400, B = $300, C = $240

Step-by-step explanation:

The ratio will be [tex]\frac{20}{60}:\frac{15}{60}:\frac{12}{60}[/tex], that means the total of them is (20 + 15 + 12 = 47).

Divide $940 by 47 to find the value of 1 unit [tex]\frac{940}{47}=20[/tex]

A = 20 × 20 = $400

B = 20 × 15 = $300

C = 20 × 12 = $240

Answer: looks like [tex]a^{7}[/tex]

Is that one of the answer choices?

answer is 25

use the formula to get the rest of the a's

Answer: To find the length of the diagonal cut, we can use the Pythagorean theorem.

The diagonal cut is the hypotenuse of a right triangle, with legs of length 9 and 12.

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. So, the length of the diagonal cut is the square root of (9^2 + 12^2)

So, the length of the diagonal cut is √(9^2 + 12^2) = √(81 + 144) = √225 = 15cm

Therefore, the diagonal cut that Danny made is 15 centimeters long.

Step-by-step explanation:

Answer:

The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In the case of the function H(x) = x+2/x^2+4x+4, we need to find the values of x for which the denominator x^2+4x+4 is not equal to zero.

x^2+4x+4 = 0

(x+2)^2 = 0

The denominator is always non-zero as the square of any real number is always positive. Therefore, the function H(x) = x+2/x^2+4x+4 is defined for all real values of x. Therefore, the function H(x) does not have any values that are not in its domain.

Step-by-step explanation:

Answer:

he never made a mistake, so the answer is A

Step-by-step explanation:

these are in line with integers and their rules.

The rule that's being applied there's if numbers of the same base are being divided, maintain the base and subtract the powers.

The speed of the boat against the current is (13+x)mph and with the current is (13-x) mph.

If boat goes along the stream flow (downstream), then the speed of boat will be increased as stream will help boat go faster. In contrast, the upstream flow of boat will be slower than its speed in normal flow due to stream resistance.

Speed of boat with the current = Speed of boat + Speed of current

Speed of boat against the current = Speed of boat - Speed of current

Given that the speed of a boat in still water is 13 mph. Also, the speed of the water current is x mph. Therefore, the speeds in the given cases can be written as,

a.) The of speed going against a current with a rate of x mph can be written as,

Speed of boat with against the water current

= Speed of Boat - Speed of water current

= 13 mph - x mph

= (13-x) mph

b.) The of speed going with a current with a rate of x mph can be written as,

Speed of boat with the water current

= Speed of Boat + Speed of water current

= 13 mph + x mph

= (13+x) mph

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