Given: A, B, and C are collinear, AB=BD, and BD=BC
Prove: B is the midpoint of AC

The values of the coefficients and constant in the quadratic function are a = 1, b = -5, and c = 6, where a and b are coefficients and c is the constant.

Given quadratic function f(x) = x² - 5x + 6.

The values of the coefficients and constant in the function are

a = 1

b = -5

c = 6

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The saved amount after selling the tank and by using the code is $21.24.

What is selling price?

The selling price is the amount in the form of extra charges which was decided by the shopkeepers for the different commodities. The cost spent by the shopkeeper for the purchase is the cost price. And for profit selling price should be more than the cost price.

According to the question, the given parameter is as written below:

The selling price of the Jellyfish tank is: $24.99

And the discount with special code is: 15 percent

The calculated money saved by using the special code is:

Discount Amount = (24.99 x 15)/100 = 3.7485

Saved money = $24.99 - $ 3.7485 = $ 21.2415 ≅ $ 21.24

Hence, the saved amount after selling the tank and by using the code is $21.24.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Scale factor: 1 : 8

Scale drawing:

A = 2 cm²

Object:

A = ?

Step 02:

A = 2 cm² * (8 / 1) = 16cm²

Answer:

45

Step-by-step explanation:

In this picture we can see that they gave us 2 angles.

Angle V has an angle of x+83

Angle S has an angle of 4x - 53

As one of the circle thermoses in mathematics said when there is an angle in the center of the circle, the angle at the circumference is half the angle at the center, which means we could create and equation such that:

angle of angle V = 2 times the angle of angle S

x + 83 = 2(4x - 53)

x + 83 = 8x - 106

189 = 7x

27 = x

Since we know x = 27, we can substitute into the equation angle of S to find what is the angle of TSU:

4x - 53

= 4(27) - 53

= 108 - 53

= 45

Answer:

<TSU = 55°

Step-by-step explanation:

We know that,

Angle at the circumference of a circle is twice the angle at the centre.

Therefore,

2 × <UST = <UVT

Given that,

< UVT = x + 83

< TSU = 4x - 53

Accordingly, we can make an expression like this.

[tex] \sf2 × <UST = <UVT[/tex]

[tex] \sf2(4x - 53) = x + 83 \\ [/tex]

And now solve the above expression and find the value of x.

Let us solve it now.

[tex] \sf8x - 106 = x + 83 \\ \sf8x - x = 106 + 83 \\ \sf7x = 189 \\ \sf \: x = 27[/tex]

And now, according to the question they've asked us to find the value of <TSU.

As we mentioned earlier, they've given that, <TSU = 4x - 53.

So, to find the value of Angle TSU, we have to replace x with 27 and find the value of angle TSU.

Let us solve it now

[tex] \sf \: <TSU = 4x - 53 \\ \sf \: <TSU = 4 \times 27 - 53 \\ \sf \: <TSU = 108 - 53 \\ \sf \: <TSU = 55 \degree[/tex]

Answer:

y=12x+40

Step-by-step explanation:

The earnings are the initial payment per month plus the pay per hour times the number of hours.

Answer:

2.5

Step-by-step explanation:

if it is divison then the answer would be 2.5

if its additin is  35

if subtraction it is 15

if multipcation  250

could you please re post the question clearly as right now I don't understand what this means, you can try just taking a picture of the question and attach it to your post

The multiplication of the mixed fractions as 4²/₇ * 2¹/₅ gives; 9³/₇

A mixed fraction is one that has a part that is a whole number and a part that is a proper fraction.

Now, a proper fraction has its' numerator lesser than its' denominator while an improper fraction has it's numerator greater than its' denominator.

Let us convert each fraction into an improper fraction before multiplication.

4²/₇ = 30/7

2¹/₅ = 11/5

Thus, we have;

30/7 * 11/5

This can be reduced to;

66/7 which can be converted back to a mixed fraction to get 9³/₇

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The percentage of the tip that Serena's father paid was 20%.

Mathematically, a percentage is a numerical ratio, usually expressed as a fraction of 100 and denoted by the percent sign (%).

Percentages show the proportional relationship between two fractions, like proportions and ratios.

The amount of the tip = $5

The cost of the ride = $25

The total amount paid by Serena's father = $30 ($5 + $25)

The percentage of tip to the ride's cost = The amount of the tip divided by the cost of the ride.

= 20% ($5/$25 x 100)

Thus, in percentage terms, the amount that Serena's father tipped the taxi driver is 20% of the ride's actual cost.

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Answer:

0

Step-by-step explanation:

7 is not in the sample space, meaning it is impossible. Therefore, the probability is 0.

Answer:

No solution.

Step-by-step explanation:

 Solving using elimination method:

           3a = - 5b - 2

    3a + 5b = -2 ------------------(I)

            10b = 1 - 6a

   6a + 10b = 1 --------------------(II)

[tex]\sf \dfrac{a_1}{a_2}= \dfrac{3}{6}=\dfrac{1}{2}\\\\\dfrac{b_1}{b_2}=\dfrac{5}{10}=\dfrac{1}{2}\\\\\dfrac{c_1}{c_2} = \dfrac{-2}{1}[/tex]

[tex]\sf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}[/tex]

So, this system of linear equations are two parallel lines and has no solution.

Answer:

Option 4: a reflection over the y-axis and a translation 4 units down

Step-by-step explanation:

f(x) = 3x + 1 ---> g(x) = -3x - 5

to go from 3x to -3x is a reflection across the y axis

to go from 1 to -5 is a shift 4 units down

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices.

10. In the given figure,

l ║m

(3x - 29)° + (8y + 17)° = 180° [Because they are linear pairs]

⇒ 3x -29 + 8y + 17 = 180

⇒ 3x + 8y - 12 = 180

⇒ 3x + 8y = 192 ............ (1)

Now,

8y + 17 = 6x -7 [Alternate interior angles]

⇒ 6x - 8y = 24 ..............(2)

On adding (1) and (2),

(3x + 8y) + (6x - 8y) = 192 + 24

simplifying the above equation, we get

⇒9x = 216

⇒ x = 216/9 = 24

⇒ x = 24

Now, 6x - 8y = 24

⇒ 8y = 6(24) - 24

⇒ y = (144 - 24)/8

⇒ y = 120/8 = 15

So, x = 24 and y = 15

11. In this given figure,

l ║m

7x - 23 = 49 + 3x ...... (Alternate interior angles)

⇒ 7x - 3x = 49+23

⇒ 4x = 72

⇒ x = 18

11y -1 = 3x [Alternate exterior angles]

⇒ 11y - 1 = 3 x 18

⇒ 11y = 54 + 1

⇒ 11y = 55

⇒ y = 5

Therefore, the value of x = 18 and y = 5

12. 11. In this given figure,

l ║m

3x - 4 = 5x - 38 [Alternate interior angles]

⇒ 5x - 3x = 38 - 4

⇒ 2x = 34

⇒ x = 17

7y - 20 + 5x - 38 + 90° = 180° [Angle sum property of a triangle]

⇒ 7y - 20 + 85 - 38 + 90 = 180

⇒ 7y + 117 = 180

simplifying the above equation, we get

⇒ 7y = 180 - 117

⇒ 7y = 63

⇒ y = 63/7 = 9

Therefore, the value of x = 17 and y = 9

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The angle whose supplement is 12 degrees less than twice its measure is 64 degrees.

supplementary angles are angles that add up 180 degrees.

Given the data in the question;

Let x represent the first angle.

Since the angle are supplementary, sum of angles = 180°

First angle + second angle = 180

x + ( 2x - 12 ) = 180

Solve for x

x + 2x - 12 = 180

3x - 12 = 180

3x = 180 + 12

3x = 192

x = 192/3

x = 64

Therefore, the measure of the angle 64 degrees.

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Let the original amount be n.

(n) (percentage) = (final amount)

We're given:

Organize this information into an equation:

n(13.5%) = 27

⇒ Convert 13.5% into a decimal:

0.135n = 27

⇒ Divide both sides by 0.135:

n = 27 ÷ 0.135

n = 200

Therefore, the original amount is 200.

200

After thoroughly calculating the equation, we conclude that x⁴ + 4x³ - 6x² - 2x + 25  is the simplified form of 3/x - 1 - 4x - 1/x + 1 = x² +(5/x)²- 1 - 5

When the top and bottom of a fraction are the same size and still whole numbers, the fraction is said to be in its simplest form or simplified form.

Using 2/4 as an example, 1/2 can be written.

Simplify a fraction by multiplying its top and bottom by the biggest number that will divide them both exactly (they must stay whole numbers). the outcome will be what we call the simplified form.

We have been asked to simply the equation

3/x - 1 - 4x - 1/x + 1 = x² +(5/x)²- 1 - 5

⇒ 3/x - 4x - 1/x + 6 = x² +(5/x)²

⇒ 2/x - 4x + 6 = x² +(5/x)²

⇒ 2/x - 4x²/x + 6x/x = x² +(5/x)²

⇒ (2 - 4x² + 6x)/x = x² +(5/x)²

Multiplying x to both side

⇒ 2 - 4x² + 6x = x² +(5/x)² × x

⇒ 2 - 4x² + 6x = x³ + 25/x

​⇒  x³ + 4x² - 2 = 6x - 25/x

​⇒ x³ + 4x² - 2 = 6x²/x - 25/x

​⇒ x³ + 4x² - 2 = (6x²- 25)/x

Multiplying x to both side

​⇒ (x³ + 4x² - 2) x = 6x²- 25

​⇒ ​x⁴ + 4x³ - 2x = 6x²- 25

​⇒ x⁴ + 4x³ - 6x² - 2x + 25

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The answer is C:38

explanation: you multiply 8x4=32, so then you add 6 to 32

Hope this helped!

If an experiment with a random outcome is repeated a large number of​ times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called​ The Law of Large Numbers.

The Law of Large Numbers states that on the off chance that a test with an irregular result is repeated a huge number of​ times, the empirical probability of an event is likely to be near the true probability. The bigger the number of​ redundancies, the closer together these probabilities are likely to be.The law of large numbers does not ensure that a given test, particularly a little test, will reflect the genuine population characteristics or that a test that does not reflect the genuine population will be adjusted by a subsequent sample. The law of large numbers demonstrates a greater test will speak to a population mean, whereas the central tendency theorem states a greater test will speak to a population's distribution.

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Answer:

205

Step-by-step explanation:

we first enter the desired number equaling the equation, so 21. then we enter the first term and find the common difference, in this case it's going up by 9. then we take the desired term, subtract 1 and we end up with 205 as the 21st term.

21 = 25 + 9 (21 - 1)

He buy 10 games that costs $13.

Equation, also known as a statement of equivalence between two expressions with variable- and/or number-based components. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Given Data

John has $160 to spend on video games.

He spent $30 on a controller the rest on video games.

If each game costs $13

Equation

30 + 13g = 160

13g = 130

g = 10

He buy 10 games that costs $13.

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The graph of the inequality 7< f has been plotted.

The given inequality is 7 < f

The inequality states that the the relationship between two numbers. The relationships are greater than, greater than or equal to , less than, less than or equal to, equal to. These are the commonly used relationship between the two number in the inequality.

Here the inequality is 7 < f

The value of f is greater than 7

Plot the inequality in the graph

At the point 7 we use a small circle to represents the term greater than, if it was greater than or equal to we use a dot at that point

Hence, the graph of the inequality 7< f has been plotted

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Answer:

I see a right angle, so the transversal is perpendicular to the parallel lines. Therefore, x and y are supplementary and congruent, and so we have x = 90 and

y = 90.

Answer:

207/4 some other forms are 51 3/4 or 51.75

Step-by-step explanation:

Answer:

24  3/4 gal

Step-by-step explanation:

2 3/4 gal / bucket    *   9 bucket   = 24 3/4 gal

If A is in the interior of NFL. If m/NFA = 5x+10, m/AFL = 30-2x, and m/NFL = 58°, the value of x would be 6

It is important to note that the formula for determining the sum of interior angles of a shape is expressed as;

(n-2) 180

Where 'n' is the number of sides

From the information given, we have that the shape has 3 sides, so we have

(3 -2)180

180°

Give the angles as;

Equate the angles to m/NFL, we have

5x+10 + 30-2x = 58

Now, collect like terms

5x - 2x = 58 - 40

Subtract like terms

3x = 18

Make 'x' the subject by dividing both sides by 3, we have

x = 18/3

x = 6

Thus, the value of 'x' is 3

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Answer:

Green

Verde = green

Answer:

Total width of the gate in cm is equal to=> 109.9+89.4=199.3 cm

Step-by-step explanation:

GIVEN-

A gate is made out of 7 panels of wood, each of which is 15.7 cm wide. between the panels, there is a gap of 14.9 cm

THIS IS AN EASY SUMMATION PROBLEM-

FOR ONE PANEL WIDTH =15.7

FOR 7 PANEL'S WIDTH =15.7*7=109.9;

NOW, between the 7 panels, 6 gaps create

one gap =14.9 cm

six gap =14.9 * 6 =89.4 cm

so, the total width of the gate in cm is equal to=> 109.9+89.4=199.3 cm

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The two solutions of the quadratic function are 0.58 and -1.1.

The solution of a quadratic equation can be obtained using the substitution method or formula method.

The solution of the given quadratic function is determined as follows;

f(x) = 8x² + 4x - 5

0 =  8x² + 4x - 5

The formula method of a quadratic function is given as;

[tex]x = \frac{-b \ \ \pm \ \sqrt{b^2 - 4ac} }{2a}[/tex]

from the above equation, a = 8, b = 4, c = -5

[tex]x = \frac{-4 \ \ \pm \ \sqrt{4^2 - 4(8\times -5)} }{2a}\\\\x = \frac{-4 \ \ \pm \ \sqrt{16 + 160} }{2(8)}\\\\[/tex]

x = 0.58 or -1.1

Thus, the function has two solutions, a negative and positive solution.

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Answer:

D

Step-by-step explanation:

[tex]2x-12y=24 \\ \\ x-6y=12 \\ \\ 6y-x=-12 \\ \\ 6y=x-12 \\ \\ y=\frac{1}{6}x-2[/tex]

The slopes of the lines are neither the same nor are they negative reciprocals, so the answer is D.