Identify a, b and c from the quadratic trinomial x^2-5x+6

The opposite sides are parallel to each other if diagonals of the quadrilateral bisect each other.

The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.

AC and BD bisect each other.

We know that in a quadrilateral if the diagonal of the quadrilateral bisect each other then the opposite sides are parallel to each other.

AC = BD         (Equal diagonal)

Then the side AB and CD are parallel to each other. And similarly, the sides BC and AD are also parallel to each other.

AB || CD or BC || AD

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The expression that is equivalent to (ab3rd power)4th power in the question is a4th power b 12th power.

Exponential expression is the power to which a given term of mathematical expression is raised to. The value of the power to which a variable is raised is not limited. Sometimes, some laws are required to solve some exponential expressions. An example is the law of indices which can be applied to solve some expressions in a given question with large numbered powers. The law of indices is one of the major law to refer to when discussing power of numbers or variables.

Thus the expression that is equivalent to (ab3rd power)4th power is:

(ab3rd power)4th power = (ab^3)^4

expand the given bracket to have;

         (ab^3)^4 = a^4 * b^(3*4)

                        = a^4b^12

Therefore the expression is equivalent to a^4b^12 i.e a4th power b 12th power.

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Answer:

x=16

Step-by-step explanation:

right!!

The length of the railing that was parallel to the steps is; 6.65 meters

Let us first of all convert the distance in meters to centimeters. From unit conversion, we know that 1 meter equals 100 centimeters. Thus;

3.6m * 100cm / 1m = 360cm

Now we calculate the number of steps as;

360 cm / 18 cm = 20 steps

Since each step measures 28 cm, it means that total measure of steps is;

20 * 28 = 560 cm

To calculate the length of the ladder, we must apply Pythagoras theorem: c² = a² + b²

From the question, we can say that;

a = 360; b = 560

Thus;

c² = 360² + 560²

c² = 443200

c = √443200

c = 665.73

Expressing 665.73 cm in meters would give us 6.65 meters.

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1) The triangle classified according to their sides is given as follows:

a) Isosceles triangle - It has two equal sides

b) Scalene Right Angled Triangle.

c)  obtuse scalene triangle -Has an angle that is over 90 degrees, as well as three unequal sides

d) Equilateral Triangle - Three equal sides and three equal angles

e) Isosceles Right Angled Triangle - Right angle with two equal sides and two equal angles

f) Scalene Triangle - Three unequal sides and three unequal angles.

g) Equilateral Triangle - Three equal sides and three equal angles

h) Obtuse Isosceles Triangle - has two equal sides with an angle measuring above 90 degrees.

2) Note that the value of x is 6, JK is 83, KL is 83 and JL is 83.

As indicated above, an Equilateral Triangle is one whose sides are equal. Thus,

JK = KL = JL

That means 13x + 5 = 17x -19 ..............1

Simplifying 1 by collecting like terms:

17x - 13x = 19 + 5

4x = 24

x = 24/4

x = 6

We can proceed to find the sides now

JK = 13x + 5

13 x 6 + 5

= 78 + 5

= 83

JK = 83

KL = 17x - 19

= 17 x 6 - 19

= 102 - 19

= 83

KL = 83

JL= 8x + 35​

= 8 x 6 + 35

= 48 + 35

= 83

JL = 83

Therefore, the value of x is 6, JK is 83, KL is 83 and JL is 83.

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Answer:

APR stands for Annual Percentage Rate, which is the interest charged on a loan expressed as a yearly rate. In this case, we are given the interest rate for a loan over 10 days.

To calculate the APR, we need to determine the annualized interest rate, which is the interest rate multiplied by the number of times the interest is compounded per year.

We know that the interest on the loan is $200. The loan amount is $800 and the loan period is 10 days.

First we need to calculate the daily interest rate:

Interest/Loan amount = 200/800 = 0.25

To find the annualized interest rate, we need to multiply the daily interest rate by the number of days in a year:

0.25* 365 = 91.25%

To the nearest percent the APR for this loan is 91%

The values of the expressions when x = -1 will be;

(i) 1

(ii) 0

(iii) 1

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra shows how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

when x = -1

(i) -x + 2

-1 + 2 = 1

(ii) x²+ 2x + 1

(-1)² + 2(-1) + 1

1 - 2 + 1 = 0

(iii) 2x² - x - 2

2(-1)² - (-1) - 2

2(1) + 1 - 2

2 + 1 - 2

3 - 2 = 1

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Answer:

[tex]b=3/11[/tex]

Step-by-step explanation:

[tex]-3b+11=8b+8 \\ \\ 11b+8=11 \\ \\ 11b=3 \\ \\ b=3/11[/tex]

The additional information needed to that triangle ADN is congruent to triangle DCO using SAS is

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent

The SAS says that the corresponding sides and the included angle must be congruent

the angles and side used here include

AN - < BAN - BA

DO - < CDN - CD

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Alyssa worked 1 hour walking dogs and 13 hours clearing tables. This solution satisfies all of the given conditions.

The first inequality represents the condition that Alyssa must work at most 3 hours walking dogs:

a ≤ 3

The second inequality represents the condition that Alyssa can work a maximum of 15 total hours:

a + y ≤ 15

The third inequality represents the condition that Alyssa must earn at least $130 in a given week:

8a + 10y ≥ 130

We can graph these inequalities on the same coordinate plane to find the region of possible solutions. The solution to the system of inequalities is the region of the plane that satisfies all of the inequalities.

The red line represents the first inequality, a ≤ 3. The blue line represents the second inequality, a + y ≤ 15. The green line represents the third inequality, 8a + 10y ≥ 130.

The region of the plane that satisfies all three inequalities is the area above the red line and below the green line, and to the left of the blue line. This region is shaded in the graph above.

Thus, one possible solution is point (1,13), which is the intersection of the red and blue lines. This corresponds to Alyssa working 1-hour walking dogs and 13 hours clearing tables. This solution satisfies all of the given conditions.

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Answer:

y + y + y + y + y + y

Step-by-step explanation:

6y =

6 * y =   ==> add y 6 times

Hence, 6 * y = y + y + y + y + y + y

The height of the mountain is derived to be 410 m approximately to 2 significant figure using the trigonometric ratio of tangent for angles of elevation 32° and 58°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We shall represent the length from point B to the foot of the mountain with x and the height of the mountain with h so that:

the distance from a to the foot of the mountain = 400m + x

tan 32° = h/(400 + x)

h = tan 32° (400 + x) {by cross multiplication}

h = 400 × tan 32° + xtan 32°

h = 249.9477 + xtan 32°

also;

tan 58° = h/x

h = tan 58° × x {by cross multiplication}

h = xtan 58°

so;

xtan 58° = 249.9477 + xtan 32°

xtan 58° - xtan 32° = 249.9477 {collect like terms}

x(tan 58° - tan 32°) = 249.9477

x(0.9755) = 249.9477 {divide through by 0.9755}

x = 249.9477/0.9755

x = 256.2252

h = 256.2252 × tan 58°

h = 410.9460.

Therefore, the height of the mountain is 410 m approximately to 2 significant figures using the trigonometric ratio of tangent for angles of elevation 32° and 58°.

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1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.

The idea of area is essential to contemporary mathematics. A two-dimensional shape, figure, or planar lamina in a plane will occupy a specific amount of space, which is denoted by the area.

The area can be simply defined as the volume of cloth, or other material with the specified thickness, required to construct a model of the shape, or as the volume of paint required to completely cover the surface of the shape in a single layer, or "coat," of paint.

It is a two-dimensional illustration of the length of a curve or the volume of a solid, where length is a one-dimensional concept and volume is a closely related concept that exists in three dimensions.

Area of national park = 9,542 miles²

14% of the area of the park is reserved for animal preservation

= 9542 × 14

= 9542 × 14/100

= 9542 × 0.14

=  1335.88 miles²

Thus, 1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.

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To evaluate the expression 5/6 - 3/4, we need to first convert the fractions to a common denominator. The least common multiple of 6 and 4 is 12, so we can rewrite the fractions as follows:

5/6 - 3/4 = (5/6)(2/2) - (3/4)(3/3)

= 10/12 - 9/12

= 1/12

Therefore, Devon used 1/12 of a cup more sugar than flour.

Answer:

x = 12

Step-by-step explanation:

3/9 = 4/x

3x = 36

x = 12

Answer:

The quadrilateral ABCD was dilated with a scale factor of 1.8

Take the value of x before the dilation (4), and multiply that by 1.8

The result should be 7.2

Hope this helps.

Rectangle measures 6 by 4 whereas rectangle b measures 6 by 2. A rectangle has two dimensions: a length and a width that are both perpendicular to it.

How to calculate a rectangle's dimensions: The perimeter equation can be expressed in terms of one of the following dimensions as follows: P = 2(a+b) b = P/2−a The equation for the area (A) plus the following one is as follows: The equation for area is A = ab.

We are given a square of 36 square centimeters.

The square's size will be 6 cm as a result.

Two rectangles are created by dividing the square into two equal-sized pieces.

Let the rectangles' measurements be 6*a and 6*b. Consequently, we can establish the ratio.

Moreover, we can set the combined area of rectangles equal to the area of square to form another equation:

Using substitution method, we can solve for 'a' and 'b' as shown below:

And

Therefore, dimensions of the two rectangles are 6x4 and 6x2, respectively.

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The equation that represent the proportional relationship is y = 11k.

Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.

Therefore, proportional relationship can be represented as follows:

y ∝ x

y = kx

where

Hence,

x = 2

y = 22

Therefore,

22 = 2k

k = 22 / 2

k = 11

Therefore, the equation is y = 11k

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Two-dimensional cross-sections could be obtained from a right rectangular prism a Rectangles. Option D

Generally, A right rectangular prism may give rise to three distinct varieties of two-dimensional cross-sections, and they are as follows:

A rectangle may be created by cutting the right rectangular prism along either of its faces to create a parallelogram, which can then be folded in half.

Obtaining a parallelogram requires cutting the correct rectangular prism at an angle that is not perpendicular to any of its faces. This will result in the formation of a parallelogram.

You may acquire a trapezoid by cutting the right rectangular prism at an angle that is not parallel to any of its faces. This will result in the formation of a trapezoid.

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Answer:

the slope is 9

Step-by-step explanation:

The slope is the number before the x.

Answer:

Slope = 9

Step-by-step explanation:

Now we have to,

→ find the slope of the equation.

Formula we use,

→ y = mx + b

→ m = Slope

Then the required slope will be,

→ y = mx + b

→ y = 9x + 0

→ y = 9x

→ [ m = 9 ]

Hence, the value of slope is 9.

The median distance is 5km.

The median distance, symbolized by δM, is the median value of the distance among any two node pairs. This is measured over each network's largest linked component, and takes into account pairs including of the same node.

In this case, the dots in the picture (attached) represent the number of matches.

So, if we write it all down here, the data will be:

3, 4, 4, 5, 5, 5, 5, 7, 7

Since the total of values in the data is odd number, that is 9, then the formula for the median distance will be:

Median = (n + 1) / 2

with n = 9

Thus, the median distance in this case:

= (n + 1) / 2

= (9 + 1) / 2

= 10 / 2

= 5

Hence, the median distance is 5km.

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Answer:

True.

Step-by-step explanation:

When two lines are crossed by a transversal, the interior angles between them will always add up to 180 degrees, which means they can never be parallel.

Answer:

Do you have answer choices?

The possible answers are Plane PLN, Plane LNR, Plane NRP, and Plane RPL.

The matching statements and reasons:

on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

equation given is 3(x+2)=7x-48

value of x

[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]

value of x from the given equation comes out to be 13.5

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The amount of money loaned at a rate of 7% will be $7,000.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A bank loaned out $10,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $1000.

Let 'x' be the amount of money loaned at a rate of 7%. Then the amount of money loaned at a rate of 17% will be ($10,000 - x). Then the equation is given as,

0.07x + 0.17($10,000 - x) = $1,000

0.07x - 0.17x + $1,700 = $1,000

0.10x = $700

x = $7,000

The amount of money loaned at a rate of 7% will be $7,000.

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The total number of pears consumed by all the 6 partridges is given by the equation A = 84 pears

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of pears be represented as A

Let the number of partridges be n = 6

Now , Pete the partridge eats 4 pears in 30 minutes

So , the number of pears in 1 hour = 2 x 4

The number of pears in 1 hour = 8 pears

The number of pears in 1 hour 30 minutes = 8 + 4 pears

The number of pears in 1 hour 30 minutes = 12 pears

The number of pears in 1 hour 45 minutes = 12 + 2 pears

The number of pears in 1 hour 45 minutes = 14 pears

So ,

The total number of pears by all 6 partridges A = 6 x number of pears in 1 hour 45 minutes

Substituting the values in the equation , we get

The total number of pears by all 6 partridges A = 6 x 14

On simplifying the equation , we get

The total number of pears by all 6 partridges A = 84 partridges

Therefore , the value of A is 84 partridges

Hence , the number of partridges is 84

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The profit the company would make over the course of its 5 years of operation, given the starting annual profit and the constant increase in the profit, is $ 998, 329.34

To find the total profit that the company would make over the first 5 years of the operation, use the future value formula :

= First profit x Future value interest factor of annuity, 27%, 5 years

First profit = $ 117, 000

Rate of increase = 27 %

Number of years = 5 years

The profit in 5 years is:

= 117, 000 x 8.53272941

= $ 998, 329.34

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Answer:  -0.04x + 0.09

Step-by-step explanation:

(0.95x - 0.04) - (0.99x - 0.13) = 0.95x - 0.04 - 0.99x + 0.13

                                             = 0.95x - 0.99x + 0.13 - 0.04

                                             = (0.95 - 0.99)x + (0.13 - 0.04)

                                             = -0.04x + 0.09

The value of k  for the point on the line is 63

We can find the value of k by using the slope formula. The slope of a line can is given by:

Slope = (y2-y1)/(x2-x1)

Since the pass through the origin (0,0), (k,7) and (-81,-9). we can write:

x1 = 0, y1 = 0 and x2 = -81, y2 = -9

Slope = (-9-0)/(-81-0) = 1/9

Also, we can write:

x1 = k, y1 = 7 and x2 = -81, y2 = -9. And the slope is still the same

1/9 =  (-9-7)/(-81-k)

1/9 = -16/(-81-k)

1/9(-81-k) = -16

-9 - k/9 = -16

-k/9 = -16 + 9

-k/9 = -7

-k = -7 × 9

-k = -63

k = 63

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The fruit salad that will taste more melody when the percent of melon in both Arturo and Nachelle are compared would be Nachelle's fruit salad.

The percentage of a quantity is determined when we divide the value by the total value and then multiply the resultant by 100.

For Nachelle;

Quantity of melon = 6 cups

quantity of apple = 1

Total quantity = 7

The percentage of melon = 6/7× 100

= 600/7 = 85.7%

For Arturo;

Quantity of melon = 10 cups

quantity of apple = 3

Total quantity = 13

The percentage of melon = 10/13 ×100

= 1000/13= 76.9%

Therefore,the fruit salad that will be melony would be Nachelle's fruit salad with the percentage of 85.7 of melon making up the salad.

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