The pavement at the new shopping mall is being laid. Which transformation is applied from brick A to brick B?
A. reflection
B. rotation
C. dilation
D. translation

The average rate of change of g(x) = -x3 + 2 is therefore -51/5 from x = -1 to x = 4.

The slope of the secant line connecting two points on a function across an interval represents the average rate of change of that function over that interval. We must determine the slope of the secant line that connects the points (-1, g(-1)) and (4, g(4)) in order to calculate the average rate of change of g(x) = -x³ + 2 from x = -1 to x = 4.

g(-1) = -(-1) (-1)

4³ + 2 = -1 + 2 = 1 \sg(4) = -4^3 + 2 = -52 + 2 = -50

The secant line's slope is therefore ((-50) - 1) / (4 - (-1)) = -51 / 5

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Step-by-step explanation:

The equivalent expression in the form of a product is:

(8x) * (4x + 6)

Answer: 4

Step-by-step explanation:

3x4+12

------------ (over)

6

12+12

---------

6

24

----- = 4

6

X2 + 7x + 10 = 0 has roots -5 and -2, the answer.

x2 + 7x + 10 = 0 is a mathematical equation.

x2 + 5x + 2x + 10 = 0 [dividing the middle term] is another way to express the aforementioned equation.

After factoring 2 from the second term of the expression, 2x + 10, and x from the first term of the expression, (x2 + 5x), the expression may be broken down into its constituent parts.

We obtain the factorized equation as follows: x (x + 5) + 2 (x + 5) = 0.

Now we can calculate (x + 2) (x + 5) = 0 by utilizing the distributive property.

The result of separately equating both terms with 0 is,

The equation x2 + 7x + 10 = 0 has -5 and -2 as its roots.

The Complete Question is :

How to Find the roots of the equation x2 + 7x + 10 = 0?

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On solving the provided question, we can say that A Equation is[tex]y=100/3 e^{(ln3/2) t}[/tex]

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

[tex]Y= ce^{kt}[/tex]

Sub in [tex]300= ce^{4k}[/tex]

[tex]100= ce^{2k}[/tex]

Divide to get[tex]3= e^{2k[/tex]

Take log of both sides    ln3= 2k lne

So k=ln3/2

We now have y=ce^(ln3/2)t

Sub in to solve for t

100= ce^ln3

c=100/3

A Equation is[tex]y=100/3 e^{(ln3/2) t}[/tex]

B At t=0 there were approx 100/3 or 33 filies.

C After 10 days there will be 100/3 e^(ln3)/2 *10 or approx  8100 flies.

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The fraction 6/5 represents the scale factor of one rectangle towards the other. The figure has been shown.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
one rectangle = 6/5 [original rectangle]
one rectangle / original rectangle = 6 / 5
Scale factor [for the rectangle] = 6/5

Thus, the fraction 6/5 represents the scale factor of one rectangle towards the other. The figure has been shown.

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The larger television is Vehicle Viewing, explanation is mentioned below,

The diagonal of a television refers to the length of a line segment connecting two opposite corners of the screen. It is a way of measuring the size of the television screen, rather than its width or height. The diagonal measurement gives a good indication of the overall screen size and is commonly used as a specification for television screens.

Given that,

Two television,

Vehicle Viewing having diagonal 75 inches

Traveling TV Co having diagonal 8.5 inches

larger television =?

Vehicle Viewing, Inc. has the larger television with a diagonal of 75 inches compared to Traveling TV Co.'s diagonal of 8.5 inches.

This can be determined by simply comparing the two diagonal measurements given.

Hence, the larger television is Vehicle Viewing.

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The correct option is A. 30° for the value of x in the similar triangles right triangles DEF and WXY.

The hypotenuse-leg congruent theorem states that if two right-angled triangles have congruent legs, then their hypotenuses are also congruent.

it also implies that angle D is equal to angle W and angle F is equal angle Y

so;

x + 2x + 90 = 180° {sum of interior angles of a triangle}

3x + 90° = 180°

3x = 180° - 90° {subtract 90° from both sides}

3x = 90°

x = 90°/3 {divide through by 3}

x = 30°

Therefore, the value of x in the similar triangles right triangles DEF and WXY is equal to 30°

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The results of the expressions are;

1)  192

2) 3

3) 1024

We have to note that when we say that there is an expression, the implication of that is that the equality sign is missing in the mathematical statement as it has been written.

We know that;

1) a*b

a=8

b=24

8*24

= 192

2)  b/a

b/a

b=24

a=8

24/8

= 3

3)  (a+b)^2

a=8

b=24

(8+24)^2

= 1024

This is the way that we can be able to obtain all the expressions that we have in the question that is shown here.

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Missing parts;

Use a = 8 and b = 24 to work out the value of these expressions. b) ab c) b/a d) (a + b)^2

Answer:

Step-by-step explanation:

The graph of y = 2x + c is a straight line with a slope of 2 and a y-intercept of c. The value of k cannot be determined from the equation alone, as it depends on the value of the constant c. To find the value of k, you would need additional information such as the coordinates of a point on the line or the x and y values that correspond to a specific k.

Answer:

25 is X

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

1+3=4

4+5=9

9+7=16

16+9=25

3+2=5

5+2=7

7+2=9

Answer: 67.1 cm

Step-by-step explanation:

Using the Law of Sines:

[tex]\frac{i}{\sin I}=\frac{h}{\sin H}\\\\\frac{i}{\sin 24^{\circ}}=\frac{97}{\sin 144^{\circ}}\\\\i=\frac{97 \sin 24^{\circ}}{\sin 144^{\circ}}\\\\i \approx 67.1 \text{ cm}[/tex]

Answer:  67.1

Step-by-step explanation:

The quantity that will be left after 35 seconds would be =-71.5%

The quantity of radioactive Beryllium-11 isotope that was used to start the experiment = 100%

The rate at which the isotope decays= 4.9%/second

The quantity that will remain after 35 seconds = ?

That is;

4.9% = 1 second

x% = 35 seconds

make X the subject of formula;

X = 4.9×35

X= 171.5

The quantity that will be left = 100-171.5 = -71.5%

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The expression can be written as: a * b + 5.

From the question, we have the following parameters that can be used in our computation:

The product of a and b increased by 5.

The product of a and b is represented as

a * b

Increased by 5 means

a * b + 5

So, the expression is a * b + 5

The expression "a * b + 5" represents the mathematical operation of first multiplying two values, 'a' and 'b', and then adding 5 to the result.

The '*' symbol is used for multiplication, and the '+' symbol is used for addition.

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a) The possible rational zeroes of the function are: ±1, ±2, ±3, ±6

b) The possible number of positive, negative, and imaginary roots of the function are: 0 to 2 positive roots, 0 to 2 negative roots, An odd number of imaginary roots.

What is Descartes' Rule?

The number of real zeros in a polynomial function is determined using Descartes' rule of sign. It states that the number of positive real zeros in a polynomial function f(x) is equal to or fewer than the number of changes in the sign of the coefficients.

a) To find the possible rational zeroes of the function, we can use the Rational Root Theorem, which states that if p/q is a rational zero of a polynomial with integer coefficients, then p must divide the constant term (in this case, -6) and q must divide the leading coefficient (in this case, 2).

The possible rational zeroes of the function are: ±1, ±2, ±3, ±6

b) To use Descartes' Rule of Signs to determine the number of positive, negative, and imaginary roots of the function, we count the number of sign changes in the coefficients of the polynomial. In this case, the signs are +, +, -, +, +, so we have two sign changes. Descartes' Rule of Signs states that a polynomial with n sign changes will have either n or n-2 positive roots. Since n=2 in this case, the polynomial can have either 0 or 2 positive roots. The same is true for negative roots. Additionally, if the degree of the polynomial is odd and the leading coefficient is positive, the polynomial will have an odd number of imaginary roots.

Therefore, The possible number of positive, negative, and imaginary roots of the function are:

0 to 2 positive roots

0 to 2 negative roots

An odd number of imaginary roots.

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Answer:

16.7%

Step-by-step explanation:

84 - 70 = 14

14 divided by 84, times 100 = 16.7%

So, it increase by 16.7%

Answer:1. y=2x+3

             2. y=-1x-2  

             3. y=-3x+4

             4= y=3x+0

The maximum height the ball reaches is 132 feet.

A ball is tossed upward, and the height H is calculated as follows:

h(t)=  1/2 gt 2 +V 0 t +H 0.

t is the amount of time spent.

The equation in this instance is expressed as h(t)=16t 2 +64t +100.

The solution of the equation h=0 gives the time t at which the item strikes the ground if h(t) is zero, which implies that the ball is at the ground at h=100.

h=−16t 2  +64t+100

h=−16(t 2  + 2+ 2)+ 100−(−16×2 )

h=−16(t−2) 2  + -100 − (−32)

h=−16(t−2 ) 2  +132

The vertex is (2 ,132 ), therefore, the maximum height is 132 feet.

The maximum height the ball reaches is 132 feet.

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Note that where Tom Harris is 24 years old and he wishes to purchase a $7,000 value 10-year term insurance, his annual premium will be:  $290.5.

Gross premiums written in the insurance sector are the sum of direct and assumed premiums written before subtracting ceded reinsurance. Direct premiums written are the premiums on all policies issued by the company's insurance subsidiaries throughout the fiscal year.

To compute Tom's insurance premium we must use the information given as well as the table above:

Given:

Tom's Age = 24 years

Value of Insurance Cover Requested = $7,000

Type of Insurance cover requested = 10-Year Term

The rate for the Type of Insurance Cover requested: Since he 24 and wants a 10-year term, the rate applicable from the table is; 4.15%

Thus, his annual premium  = 7000 * 4.15%
= 29050/ 100
= $290.5

Thus, Tom Harris' annual insurance premium is: $290.5

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On solving the provided question we cans ay that the increasing order of the function is  y = 5/2x +10 < y = 3/2x+1/2 < y = 1/2x - 2 < y = 3/4x - 7/3 < y = -1/2x + 1/2 < y = 3/2x - 11/2

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the increasing order of the function is

y = 5/2x +10 < y = 3/2x+1/2 < y = 1/2x - 2 < y = 3/4x - 7/3 < y = -1/2x + 1/2 < y = 3/2x - 11/2

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The amount of compound remaining from a 84-ounce sample after seven weeks is 4.32 ounces.

Given a half-life of 5 days and a sample of 84 ounces, the exponential decay function can be represented as:

A(t) = 84 * (1/2)^(t/5)

Where A(t) represents the amount of the compound remaining after t days.

To find the amount of compound remaining after 7 weeks

7 weeks * 7 days/week = 49 days,

we can substitute t = 49 into the function:

A(49) = 84 * (1/2)^(49/5)

A(49) = 84 * (1/2)^9.8

A(49) ≈ 4.32 ounces

So, the amount of the compound remaining after 7 weeks would be approximately 4.32 ounces.

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The exact values of the unit circle is cos θ = 9/25 and sin θ = ( √544/25 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

The terminal side of angle θ intersects the unit circle in the first quadrant at ( 9/25 , y )

So , the equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r²   be equation (1)

Substituting the values of x and y in the equation , we get

( 9/25 )² + y² = 1²

On simplifying the equation , we get

( 81/625 ) + y² = 1

Subtracting ( 81/625 ) on both sides of the equation , we get

y² = 544/625

Taking square roots on both sides of the equation , we get

y = √544/25

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

So , the value of cos θ = 9/25 and sin θ = ( √544/25 )

Hence , the equations are solved

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The percentage of the tip at the restaurant will be 15%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Kim and sam went to a Mexican restaurant for lunch the total bill including tip was 25.46. They left 3.82 for a tip.

The percentage of the tip will be calculated as:-

Percentage = 3.82 / 25.46

Percentage = 0.15 x 100
Percentage - 15%

Hence, the percentage of the tip at the restaurant will be 15%.

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Answer: Undifined!

Step-by-step explanation: Division by zero is considered an invalid operation in mathematics because there is no number that can be multiplied by zero to produce the original number. In other words, there is no single valid answer to dividing by zero. Example: You have 0 cookies and you want to share them among 9 friends. There's no way to share, since you don't have cookies haha!

Answer:

Step-by-step explanation:

An expression without a value is referred to as being undefined; it has an indeterminant form. When a number is divided by zero, it usually has no specified meaning. Mathematically, we can't divide by zero because the result is an equation we can't compute.

Answer:

To solve the expression [(4r²t)³]², you need to follow the order of operations (PEMDAS):

Calculate the expression inside the outermost parenthesis first: (4r²t)³ = (4 * r^2 * t)^3, where r and t are variables.

Raise the result to the power of 3: (4 * r^2 * t)^3 = 64 * r^6 * t^3.

Raise the result to the power of 2: (64 * r^6 * t^3)^2 = 4096 * r^12 * t^6.

So, [(4r²t)³]² = 4096 * r^12 * t^6.

Step-by-step explanation:

Answer:A. 315,000 ÷ 900 = 350

Step-by-step explanation:

A. 315,000 ÷ 900 = 350

Answer:1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.

1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.

To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.

You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.

Step-by-step explanation:

1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.

1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.

To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.

You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.

The predicted interval for the given function is, f(x) ≥ 0 over the interval [-1,1]. So Option C is correct

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The ordered pairs of the given function

(-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

It can be observed from the values of f(x) with respect to x, that the function reaches zero at x = -1, then then reach up to 5 at x = 0 and then again reaches zero at x = 1

Hence, the value of f(x) remains positive within the interval of [-1,1].

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