what would the area a large rectangle has side lengths of 8 centimeters and 7 centimeters. a small square with side lengths of 4 centimeters is cut out of the large rectangle.

The length of the side RS in triangle RST as required to be determined in the task content is; 12 units.

The distance between two points defined by pairs of coordinates on the Cartesian plane can be determined by a modification of the Pythagoras theorem.

Hence, the distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:

AB= √{(y₂ - y₁)² + (x₂ - x₁)²}

Given that the vertices R and S of the triangle is at R(−3,3), S(-3,-9), hence:

RS= {( -9-3 )² + ( -3-(-3))² } = 12 units.

The length of the side RS in triangle RST is 12 units.

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The true statement about the graph of the parabola inequality given as y < x^2 + 2x - 6 is (b) the vertex is located at (-1,-7)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The parabola inequality is given as

y < x^2 + 2x - 6

Next, we plot the graph of the parabola inequality

To plot this graph, we simply enter the inequality y < x^2 + 2x - 6 in a graphing calculator

From the attached graph, we can see that the vertex of the parabola inequality is at (-1, -7)

Hence, the true statement about the graph of the parabola inequality given as y < x^2 + 2x - 6 is (b) the vertex is located at (-1,-7)

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The standard deviation of the response time is 1.2755 minutes.

Based on the information, the response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes.

The standard deviation of the response time will be illustrated thus:

It should be noted that the area under the one tailed standard normal curve is given as:

P(0 <= Z <= 1.96) = 0.475

The standards deviation will be:

= 2.5 / 1.96

= 1.2755

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The response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes. What is the standard deviation of the response time?

log₄x²y³ = log x² + log y² is solution of this logarithmic function.

What is an example of a logarithmic function?

What distinguishes exponential from logarithmic growth?

we use property [ log ( mn) = log +  log n ] in equation -

log₄x²y³ = log x² + log y²

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The best there terms of the sequence will be:

a. 10, 16

b. 211, 311

c. 10 , 12.5

d. -13, -22

It should be noted that in an arithmetic sequence, there is a constant difference, which is the difference between a term and the previous term.

We find the constant difference for each sequence, and we add it to the second term to find the third term. Then we add the constant difference to the third term to find the fourth term.

a. 4 - (-2) = 6

3rd term: 4 + 6 = 10

4th term: 10 + 6 = 16

b. 111 - 11 = 100

3rd term: 111 + 100 = 211

4th term: 211 + 100 = 311

c. 7.5 - 5 = 2.5

3rd term: 7.5 + 2.5 = 10

4th term: 10 + 2.5 = 12.5

d. -4 - 5 = -9

3rd term: -4 + (-9) = -13

4th term: -13 + (-9) = -22

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Here are the first two terms of some different arithmetic sequences:

a. -2,4

b. 11, 111

C. 5, 7.5

d. 5,-4

What are the next three terms of each sequence?

x = 4 is an extraneous solution.

√(5-x) -√x=1

√(5-x) = 1 + √x

Squaring both sides of the equations, we get

(√(5-x))² = (1 + √x)²

5 - x = 1 + x + 2√x

4 - 2x = 2√x

Squaring again both sides of the equations, we get

(4 - 2x)² = (2√x)²

16 + 4x² - 16x = 4x

4x² - 20x + 16 = 0         ...(1)

By middle term splitting equation (1) can be written as

4x² - 16x - 4x + 16 = 0  

4x(x - 4) -4(x - 4) = 0  

(x - 4) (4x - 4) = 0

4x - 4 = 0 and x - 4 = 0

x = 1 and 4

Check for Extraneous solution by putting value of x in the original equation -

Let x = 1

√(5-1) -√1=1

√4 - 1 = 1

2 -1 = 1

1 = 1

Since, LHS = RHS, so, x = 1 is not an extraneous solution

Let x = 4

√(5-4) -√4=1

√1 - 2 = 1

1 - 2 = 0

-1 = 0

which is a contradiction, so, x = 4 is an extraneous solution.

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Given that,

Mass of earth = 5.9 × 10²⁴ kg

Mass of   = 4.9 ×  10²⁴ kg

a) Combined mass of earth and

5.9 × 10²⁴ +  4.9 ×  10²⁴ = 10.8 × 10²⁴

b) If the mass of the sun =  1.9 × 10³⁰

Let's say the total gain of earth and  combined x

so it will equal the mass.

Then,

10.8 × 10²⁴ + x = 1.9 × 10³⁰

x = 18989.2 kg

Hence "Combined mass of earth and venues is 10.8 × 10²⁴ and there are a total of 18989.2 kg taking earth and venue to equal to the sun.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

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Answer:

The larger figures are 3 times the size of the smaller figures.

Scale factor = 3?

Step-by-step explanation:

Answer:

The scale factor is 3 :)

Step-by-step explanation:

The smaller figure multiplied by 3 is the larger figure.

Answer: Papst blue ribbon

Step-by-step explanation:

Ryan lives in a trailer park. He likes to drink papst blue ribbon and not wear satin robes.

In linear equation , the car y's price changes the most.

What are a definition and an example of a linear equation?

According to the question

a)  Car x : £ 10320  ≈  £ 10300        10320 - 10300 = 20

    Car y  : £ 15430 ≈ £ 15400          15430 - 15400 = 30

    Car z   :  £ 17490 ≈  £ 17500        17490 - 17500  = 10

                   10 < 20 < 30

so the car y's price changes the most.

b) this car's price change £ 30

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Answer:

75% filled

Step-by-step explanation:

Each triangle is 50%.

Half of 50% is 25%.

One full triangle, 50%, plus one half triangle, 25%, add up to 75% percent of the two triangles being filled.

Answer:

the answer is false

Step-by-step explanation:

this is an example: 22+1=23  23 is not an even number

Answer:

B. False

Step-by-step explanation:

Let the even number be x_e and odd be x_o

[tex]{ \tt{ = x _{e} + 1}}[/tex]

Assume the range is 2 ≤ x ≤ 4

[tex]{ \tt{x _{2} = 2 + 1}} \\ { \tt{x_{2} = 3 \: (odd)}}[/tex]

[tex]{ \tt{ x_{4} = 4 + 1}} \\{ \tt{x _{4} = 5 \: (odd)}}[/tex]

Therefore:

[tex]{ \tt{x _{n + 1} = x _{e} + n \: \: gives \: odd}}[/tex]

Hence;

[tex]{ \tt{ x_{e} + 1 = x _{o} }}[/tex]

For the given rational number, y=x-1/x²+4 x+4

Vertical Asymptotes: x= - 2

Horizontal Asymptotes: y = 0

A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar settings.

Given,

y=x-1/x²+4 x+4

y = x-1 / (x+2)²

x = -2, x = 0

So the horizontal asymptote will be 0.

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Answer: Yes √35 +5 is a rational number

Step-by-step explanation:

A rational number is any number that is a fraction, decimal, repeating decimal, or negative decimal.

Answer:

Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet.

Step-by-step explanation:

The domain and the range are  −∞ < x < ∞ and −∞ < y < ∞ while the intercept is (2, 0)

The domain of the function is the set of input values of the graph

The range of the function is the set of input values of the graph

The function is given as

g(x) = 3x + 6

The above function is a linear function

This means that the domain and the range of the function are the set of all real values

i.e. −∞ < x < ∞ and −∞ < y < ∞

Calculate x when g(x) = 0 to determine the x-intercept

So, we have

3x + 6 = 0

Divide through by 3

x + 2 = 0

This gives

x = -2

Hence, the domain and the range are  −∞ < x < ∞ and −∞ < y < ∞ while the intercept is (2, 0)

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Answer: 12346

Step-by-step explanation:

Firstly, to round the decimal number 12345.6789 to its nearest whole number we will look at the tenth place. the digit to the immediate right of the decimal point.

Here in the given example 12345.6789, the tenth digit is 6.

If the tenth place digit is equal to or more than 5 we will round up and if it is less than 5 we will round down.

If the hundredth digit of the decimal number is equal to or more than 5, then round up.

Since the tenth digit 6 is >= 5 we will round up i.e. ( ones place digit + 1 ) and the remaining all digits next to the decimal point are removed.

Therefore, the number 12345.6789 rounded to the nearest whole number is 12346. if this is wrong im sorry but i think this is how i even double checked.

The number of adults who have to attend the prom are 53

According to the question we have been given the ratio of number of adults to the number of students attending the prom which is :

                    [tex]\frac{x}{y} = \frac{1}{10}[/tex]          (1)

where, x = number of adults

and y = number of students attending the prom

Now equation (1) can be written as

                  y = 10x    (2)

That is number of students that attend the prom will be 10times the number of adults.

Now we have been given that there were 477 more students

                  y = x + 477

Now putting the value of y from equation (2) we get

               10x = x+477

                9x = 477

                  x = 53

Thus if the school is expecting the same attendance this year, then total 53 adults have to attend the prom.

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Answer:

2. 7x^2 + 4x + 2x

4. -x - 6

6. 4x^2

8. 7x - 2

10. 10x^2 + 5

PLEASE MARK AS BRAINLIEST!!!

Two parallel lines have equal slope.

Therefore, slope of line y = -2/9x + 6 is equal to the slope of the line joining the points (3,2).

Slope of line is given by :

m= -[(coefficient of x) / (coefficient of y)]

Where m= slope,

Slope of line y = -2/9x + 6

2/9x + y = 6

(m1) slope of equation g = -x/y

                                     = -(2/9)/1

                                     = -2/9

Since equation h is parallel to g

So, m1=m2

That is slope of equation h=slope of equation g

We know,

Equation of the line h having slope=m2= -2/9

passing through the slope of the point (3,2) is,

       y-y1=m(x-x1)

Replace with values x1,y1=(3,2) and m=-2/9

      y-2=(-2/9)(x-3)

We can solve it :      

       9y-18=-2x+6

       2x+9y=6+18

       2x+9y=24

       2x+9y-24=0

Hence,

     2x+9y-24=0 is the equation of h.

Therefore,

Line g has an equation of y = -2/9x + 6. Parallel to line g is line h, which passes through the point (3, 2), then the numbers in the equation of line h is 2x+9y-24=0

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Answer:

D) 7

Step-by-step explanation:

The answer is D because A, B, and C are not considered numbers that are natural, whole, integers, or fractional. Irrational numbers are numbers that cannot be quantified any other way, do not have repeating decimals, and never end. A good example of this is π or 3.14159265.... you get the picture.

Hope this helps!

The constant of variation is 3.6

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. That means, we can say that if one values will increase then other will automatically decrease and vice versa.

Let say if x and y are two values and k is a constant value, then

According to inverse variation

k = xy or y = k/x

In the given question,

Take the order pair (0.9,4)

As it is an inverse variation, we can substitute it

y=k/x  

Now find the constant of variation

4=k/0.9

K=3.6

Therefore, constant of variation is 3.6

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The value of m<1 is 65 degrees

From the diagram shown, we have that;

It is important to note that angles on a straight line sum up to 180 degrees

Also, corresponding angles are equal

Then, we have that;

m<2 + m<3 = 180°

Substitute the values

9x + 7 + 5x + 5 = 180

collect like terms

14x = 180 - 12

14x = 168

Make 'x' the subject

x = 168/ 14

x = 12

We have that;

m<3 = 5x + 5 = 5(12) + 5 = 60 + 5 = 65

But m<3 = m<1

m<1 = 65

Thus, the value of m<1 is 65 degrees

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The solution of the system of equation by elimination method is (-3, 3)

The system of equation can be solved using substitution, elimination and graphical method.

But we are asked to use elimination method.

Therefore,

2x + 6y = 12

2x - 3y=  - 15

Subtract equation(i) from equation(ii)

Therefore,

6y - (-3y) = 12 - (-15)

6y + 3y = 12 + 15

9y = 27

y = 27 / 9

y = 3

Therefore,

2x - 3y =  - 15

2x - 3(3) = - 15

2x - 9 = - 15

2x  = - 15 + 9

2x  = -6

divide both sides by 2

x = - 6 / 2

x = -3

Therefore, the solution of the system of equation by elimination method is (-3, 3)

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Answer:

0.119

Step-by-step explanation:

Based on the concept of conditional probability, the probability that the first iPod is defective and the others are not defective is approximately 0.1842

Conditional Probability is a term that is used to describe the chances that some outcome occurs given that another event has also occurred.

Generally, the functional probability is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening

In this case, to find the answer we break down the problem step by step:

Step 1: Find the probability that the first iPod is defective.

Since there are 3 defective iPods out of 20 total the probability of selecting a defective iPod on the first draw is 3/20.

Step 2: Find the probability that the second and third iPods are not defective.

After selecting a defective iPod there are 19 remaining iPods in the box out of which 17 are not defective.

Hence, the probability of selecting a non-defective iPod on the second draw is 17/19.

Also, given that the probability of selecting a non-defective iPod on the third draw (assuming the previous two iPods were not defective) is 16/18.

Step 3: Finding the overall probability.

The overall probability of the first iPod being defective and the second and third iPods being non-defective can be computed by multiplying the probabilities of each step:

Probability = (3/20) * (17/19) * (16/18)

= (51/380) * (16/18)

= 0.1842105

Therefore, in this case, it is concluded that the correct answer is approximately 0.1842 or 18.42%.

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Since the difference between consecutive terms is the same, the sequence is an arithmetic sequence, hence Mai is correct.

The sequence is missing, and has these following information:

We also have that:

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

From the values os the function, we have that:

The rate of change is the same, hence sequence is an arithmetic sequence, and Mai is correct.

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Answer:

112

Step-by-step explanation:

Find the lowest common multiple of 14 and 16.

To find the lowest common multiple:

1) Break the numbers down into their prime factors.

14 = [tex]2^{1}[/tex] x [tex]7^{1}[/tex]

16 = 2 x 8 = 2 x 2 x 4 = 2 x 2 x 2 x 2 =  [tex]2^{4}[/tex]

2) Multiply the highest power of each prime number.

We have three numbers, but only two are unique:  [tex]2^{1}[/tex] , [tex]7^{1}[/tex] and  [tex]2^{4}[/tex]

  [tex]2^{4}[/tex] >  [tex]2^{1}[/tex] , so we will use  [tex]2^{4}[/tex]

[tex]7^{1}[/tex] x  [tex]2^{4}[/tex] = 7 x 16 = 112

The simplest form of the expression [tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex] is [tex]13+7\sqrt{3}[/tex].

The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).

In elementary algebra, the procedure of rationalization is performed to get rid of the irrational number in the denominator. There are several methods for rationalizing the denominator.

An expression comprises a variable, a number, or a combination of a number, a variable, and operation symbols. An equation is created by joining two expressions with an equal sign.

Consider the expression,

[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex]

Rationalizing the denominator,

[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} } = \frac{5+\sqrt{3} }{2-\sqrt{3} } \times \frac{2+\sqrt{3} }{2+\sqrt{3}}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{(5+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}[/tex]

Using the identity,

( a + b )( a - b ) = a² - b²

Therefore,

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{5 \times 2 + 5 \times \sqrt{3} + \sqrt{3} \times 2 + (\sqrt{3} )^{2}}{(2)^{2}-(\sqrt{3} )^{2}}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{10+7\sqrt{3}+3}{4-3}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{13+7\sqrt{3}}{1}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = 13+7\sqrt{3}[/tex]

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The inequality is: 14.2 + 14.2 + x < 51.3

x < 22.9

We are given the following:

Perimeter of the triangle < 51.3 in.

The sides are 14.2 in., x in., and 14.2 in.

Therefore, we would have the following inequality:

14.2 + 14.2 + x < 51.3

Solve for x

28.4 + x < 51.3

x < 51.3 - 28.4

x < 22.9

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