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NOTE: Figure not drawn to scale.
Which statement can be used to prove that the triangles above are congruent?
A If two triangles have three pairs of corresponding sides that are congruent, then the triangles are congruent.
B If two triangles have three pairs of corresponding angles that are congruent, then the triangles are congruent
If two triangles have two pairs of corresponding sides that are congruent, and the included angles are congru
triangles are congruent.
D
If two triangles have to pairs of corresponding angles that are congruent, and the included sides are congru
triangles are congruent.

 By the property of alternate interior angles, Option (1) is the correct statement.    

  ∠XWY ≅ ∠ZYW

   Property of the alternate angles states, if two parallel lines are cut by a transversal, then the alternate angles are congruent.

By this property,

Lines XW and YZ are the parallel lines intersected by a transversal WY.

Here, ∠XWY and ∠ZYW represent the interior angles between the parallel lines and the transversal.

Therefore, interior alternate angles ∠XWY and ∠ZYW will be congruent.

Hence, Option (1) will be the correct option.

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The slope of the given straight line equation 3x+y=-12 is m=-3.

Finding the change in values divided by the change in values will reveal the slope between two places. As long as the line is linear, you can really use any two locations along the line to get the slope (straight line). An easy approach to do it is to use the end points since they are provided.

Negative, positive, zero and undefined are four types of slope.

The equation is given as:

3x+y= -12

Separate y we get:

y= -3x-12

This is a straight line equation and we can compare it with y=mx+c where m is the slope.

Upon comparison with general equation slope m=-3.

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The solution of three consecutive numbers is the addition of one more value to a base number.

For example, the solution of three consecutive numbers of 5 is 6, 7, 8.

Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.

When we want to find the consecutive numbers of a base number we only have to do a sum, which we can express in the following way:

Cn = N + n

Example:

N = 5

Three consecutive numbers are:

n= 1, 2, 3

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Answer:

16x^8y^3

Step-by-step explanation:

Simplify the expression.

Answer:

[tex]-8x^7(-2xy^3) = 16x^8y^3[/tex]

Step-by-step explanation:

⭐Multiplication rules

⭐ Exponent multiplication rule

⭐ Multiplying two terms with variables

We need to utilize these 3 key points (⭐) when multiplying to terms with variables.

First, let's multiply the coefficients:

-8 * -2 = 16

Next, let's multiply the variables:

[tex]x^7 * xy^3[/tex]

These two variables have the same base (x), so we will add their exponents up.

* remember: if you see a variable without an exponent, it has an exponent of 1 *

[tex]x^7 * x = x^8[/tex]

The variable [tex]y^3[/tex] will stay the same because there is no other y variable.

= [tex]x^8y^3[/tex]

Now, "attach" the variables to the product of the coefficients:

= [tex]16x^8y^3[/tex]

Answer:

3x3 is a cubic polynomial

Step-by-step explanation:

Since the highest degree of exponent in 3x3 is 3, the polynomial is a cubic polynomial.

... Hope this helped! Have a wonderful New Year!

Replacing the values of h and k to create the equation of the transformed function gives us; y = [∛(x - 4)] - k

The graph represents a transformation of the parent cube root function.

The parent cube root function is; y = ∛x

In this parent function, we see that the value of h  and k are equal to 0. Where;

h = 0, k = 0 in parent function

Then the graph changes direction at the coordinate (0,0) in parent function.

From the given graph, we can see that it changes direction at the coordinate (4,-1)

This tells us that the graph is shifted by 4 units to the right and then by 1 unit downwards.

Thus, it means that the value of h = 4  and the value of k = 1.

Thus, the equation of the transformed function will be written as;

y = [∛(x - 4)] - k

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The symbol that should be used is the division symbol. On the other hand, in the result the whole number represents the number of curtains, while the fraction represents a fraction of the next curtain.

Given :

The numerator: Number above.

The denominator: Number below.

A whole number: Optional element.

The number of curtains the tailor can make is equal to the total fabric divided by the fabric required for one curtain. Based on this, the symbol should be ÷.

= 18 1/2 ÷ 2 3/4

The whole number represents the number of curtains. The division of the total fabric and the total fabric required for one curtain will include a whole number and a fraction. In this situation, the whole number represents the number of curtains that can be made from the total fabric.

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Sanjay needs 90 meters of fence to surround a rectangular garden. The length of the garden is three times its width, w.

What is an equation in maths?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Given that we have all the equations set up, we need to solve for W.

1.) w+3w=90

4w=90

w=22.5

2.) w+3w+w+3w=90

8w=90

w=11.25

3.) 2*w+2*3w=90

2w+6w=90

8w=90

w=11.25

4.) 2*(3w+w)=90

6w+2w=90

8w=90

w=11.25

Now, out of all those which one was different?

A. (w+3w=90)

This equation did not match with all the others is (w+3w = 90)

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Answer:

Step-by-step explanation:

put it into the y=mx+c equation

y=-2x+8

therefore th y intercept is at (0,8)

and the gradient in -2

The value of function  (f + g)(x) is 7x² + x - 4.

Here the functions provided are,

f(x) = 4x² - 5x

g(x) = 3x² + 6x - 4

The p addition property of functions (f + g)(x) allows them to be written as,

(f + g)(x) = f(x) + g(x)

In the above equation, we can substitute the values of each function.

(f + g)(x) =  4x² - 5x + 3x² + 6x - 4

We have to combine the similar terms,

(f + g)(x) =  4x² - 5x + 3x² + 6x - 4

             = 7x² + x - 4

So (f + g)(x) = 7x² + x - 4

Therefore the correct answer is option B.

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If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.

A number that is not negative and doesn't have any fractional or decimal components. Anything that isn't a whole number is a fraction. most often expressed with a numerator (top) and denominator (bottom). All fractions should ideally be "correct" fractions, that is, less than 1.

You can multiply a fraction by a whole number by only multiplying the numerator which is the top number on the bar. for example:

E = 2 x 3/4

E = 6/4

E = 1²/₄

Hence, If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.

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Answer:

the snail was going 0.005m/second

Step-by-step explanation:

15m/3000

The one-time administration fee is (d) $60

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

12 months costs $660.

15 months costs $810.

This means that

(x, y) = (12, 660) and (15, 810)

For the one-time administration fee, we have

(x, y) = (0, y)

So, we calculate the slope using

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(y - 660)/(0 - 12) = (810 - 660)/(15 - 12)

This gives

(660 - y)/12 = 50

So, we have

660 - y=600

This gives

y = 60

Hence, the administration fee is $60

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The average speed of Chen when skating is 5 miles per hour

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

Time = 3/4 of an hour

Distance covered = 3 3/4 miles

The average speed can be calculated using the following equation

Average speed = Distance covered/Time

Substitute the known values in the above equation, so, we have the following representation

Average speed = (3 3/4)/(3/4)

Evaluate the quotient

Average speed = 5

Hence, the average speed is 5 miles per hour

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Answer:

16 inches

Step-by-step explanation:

Using the Pythagorean theorem, the distance is [tex]\sqrt{65^2-63^2}=16[/tex].

The factors of x³ 4x² x 6 are (1) x³, (2) 4x², (3) x and (4) 6. These factors are the numbers that can be multiplied together to give x³ 4x² x 6 as the product.

To find the factors of x³ 4x² x 6, we must first expand the expression. x³ 4x² x 6 can be expanded to x³ x x 4x² x 6, which can be further simplified to x³ + 4x² + 6. The factors of this expression are the numbers that can be multiplied together to give x³ 4x² x 6 as the product. In this case, the factors are (1) x³, (2) 4x², (3) x, and (4) 6. In other words, x³ 4x² x 6 can be written as (x³)(4x²)(x)(6). Understanding the factors of an expression is an important skill in algebra, as it can help you simplify and solve equations.

The factors of x³ 4x² x 6 can be calculated by factoring the expression:

x³ 4x² x 6 = (x³)(4x²)(x)(6)

This can be further simplified to:

x³ 4x² x 6 = x⁴ (4x²)(6)

Therefore, the factors of

x³ 4x² x 6 are (1) x³, (2) 4x², (3) x, and (4) 6.

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Answer:

If each shopping trolley is 1 meter long, and each trolley in the stack adds 0.25 meters, then the total length of the stack will be equal to the length of each trolley plus the length added by each additional trolley in the stack. This means that the total length of the stack will be equal to 1 + 0.25 = 1.25 meters per trolley.

If the stack has a total length of 10 meters, and each trolley adds 1.25 meters to the stack, we can divide the total length by the length added by each trolley to find the number of trolleys that can be stacked in a single line of 10 meters:

10 / 1.25 = <<10/1.25=8>>8 trolleys

Therefore, if each shopping trolley is 1 meter long and each trolley in the stack adds 0.25 meters, a single line of 10 meters could hold a stack of 8 trolleys.

Step-by-step explanation:

The incorrect answer is b) The difference between their speeds is exactly 1.5 miles per hour.

What is distance?

The distance between two sites is the length of the route. The metre is the SI unit for distance.

What is speed?

The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.

What is time?

The amount of time that something happens, goes through a process, or remains the same.

Let distance be Y and time be X.

Distance (Y) travelled by William after X hours;

Y= 19X

Speed of Leo = [tex]\frac{distance}{time}[/tex]

= [tex]\frac{8}{0.5}[/tex]= 16 m/hr

Difference in speed= 19-16= 3m/hr

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A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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Put the polynomial in conventional form. Count the number of terms in the polynomial. The degree of the polynomial is one more than the number of terms.

Begin by writing the polynomial in standard form. This means that the terms should be written in descending order of degree, with the coefficient of the leading term being positive. Make sure that each term is separated by a plus or minus sign.Count the number of terms in the polynomial. Include the constant term, even if it is equal to zero.The degree of the polynomial is one more than the number of terms. For example, if the polynomial has two terms, its degree is three. If the polynomial has three terms, its degree is four.If the polynomial has an exponent that is not a whole number, it is called a rational polynomial. The degree of a rational polynomial is equal to the degree of the numerator of the rational expression. If the polynomial has a negative exponent, it is called an inverse polynomial. The degree of an inverse polynomial is equal to the negative of the exponent. If the polynomial is a combination of rational and inverse polynomials, the degree is equal to the highest

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The image is the final appearance of a figure after a transformation operation. The pre-image is the original appearance of a figure in a transformation operation.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.

Preimages are the original, unaltered shapes, and images are the new (transformed) shapes. To put it another way, a transformation is a process that maps a preimage onto an image.

Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.

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There probability two ways to pick two representatives with one majoring in mathematics and the other majoring in computer science.

In order to pick two representatives with one majoring in mathematics and the other majoring in computer science, there are two approaches that can be taken. The first approach is to pick one representative who majors in mathematics first, then the second representative who majors in computer science. The second approach is to pick one representative who majors in computer science first, then the second representative who majors in mathematics. Both of these approaches would yield two representatives, one with a mathematics major and the other with a computer science major. It is important to note that whichever approach is taken, both representatives must be chosen from the same pool of potential representatives. Thus, the pool of potential representatives should be large enough to encompass both mathematics and computer science majors in order to successfully pick two representatives with one majoring in mathematics and the other majoring in computer science.

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Answer:

550 kWh

Step-by-step explanation:

To find the number of kilowatt hours of electricity the Abubakar family will be using 12 months after they've started decreasing their usage, we can substitute 12 for x in the equation y = –25x + 850. This gives us y = –25 * 12 + 850 = –300 + 850 = 550.

Therefore, the Abubakar family will be using 550 kilowatt hours of electricity 12 months after they've started decreasing their usage.

False , the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

Given :

A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

False, it is the y-intercept of the function that indicates the amount at the start of the experiment.

B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

True, the y-intercept is given when x = 0, indicating the initial value of the function.

C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.

False, because the maximum value of each table is given in different times, and also the initial value of each table is different.

D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.

False, the growth rate is not given by the inicial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.

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Full question :

is in the image uploaded.

A geometric sequence is an exponential function. Instead of y=ax, we write an=crn where r is the common ratio and c is a constant (not the first term of the sequence, however). A recursive definition, since each term is found by multiplying the previous term by the common ratio, ak+1=ak * r.

Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem.

There are many shapes in geometry based on their dimensions. Circle, Triangle, Square, Rectangle, Kite, Trapezium, Parallelogram, Rhombus and different types of polygons are the 2-d shapes. Cube, Cuboid, Sphere, Cone and Cylinder are the basic three-dimensional shapes.

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A function is a mathematical relationship between the domain and the range, two sets of values. The range is the set of output values that the function produces, and the domain is the set of input values for which it is defined.

What is a function, exactly?

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

Consider the function f(x) = x^2 as an illustration. This function generates the value f from the supplied value x. (x). This function will return the value 9 if the given value is 3, since 3^2 = 9.

Generally speaking, a function describes the relationship between two sets of values (the domain) (the range). For instance, the relationship between the input value x and the output value f(x) is described by the function f(x) = x^2.

A formula, which is a guide that explains how to calculate the output value for a specific input value, is typically used to express a function. For instance, the function f(x) = x^2 has the formula f(x) = x^2. We just enter the input value into the formula and simplify to determine the output value for a particular input value.

A fundamental idea in mathematics, functions are used to model and describe a wide variety of real-world occurrences. For instance, the quadratic function f(x) = x^2 + 2x + 1 can be used to simulate how an item would move in the presence of gravity. A population's expansion over time can be predicted using the exponential function f(x) = 3^x.

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The complete two-way frequency table is shown below.

what is frequency table?

a table that displays the distribution of a characteristic's occurrence frequency in accordance with a specific set of class intervals.

explanation:

Denote the events as follows:

U = a member have been to the United States

NU = a member have not been to the United States

A = a member have been to Australia

NA = a member have not been to Australia

The information provided is:

             A         NA        Total

U          5          __           11

NU       __         __           __    

Total      12         __           19

Complete the table as follows:

n (U ∩ NA) = n (U) - n (U ∩ A)

               = 11 - 5

                = 6

n (NU) = N - n (U)

          = 19 - 11

          = 8

n (NU ∩ A) = n (A) - n (U ∩ A)

                = 12 - 5

                = 7

n (NA) = N - n (A)

         = 19 - 12

         = 7

n (NU ∩ NA) = n (NA) + n (U ∩ NA)

                    = 7 - 6

                    = 1

Therefore, the complete 2-way Frequency table is:

            A         NA        Total

U          5           6           11

NU        7            1           8    

Total      12          7           19

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The height of pyramid if the length and slant height is known is . h² = S² - (x/2)².

We can employ the Pythagoras theorem to accomplish this as the triangle is right-angled and is created by the slant height (s), its altitude (h), and 1⁄2 of side length of a base (x/2).

As a result, (x/2)² + h² = s².

We can utilize this while figuring out how to find the pyramid's volume given the slant height.

h² = S² - (x/2)²

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