Geometry: write a formal proof, ASAP!!!

The quadratic equation whose roots -3 and 6 and leading coefficient 4 is 4x²-12x-72 = 0

A quadratic equation is an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x² + 3x + 1 , y = x²+x-1

If the root of the quadratic equation are -3 and 6

then, x = -3 and x= 6

therefore x+3 = 0 and (x-6) = 0

(x+3)(x-6) = 0

with leading coefficient 4,

then 4( x+3) ( x-6) = 0

4 ( x²-6x+3x-18) = 0

4( x²-3x-18) = 0

open the parentheses,

4x²-12x-72 = 0

Therefore, the quadratic equation with root -3 and 6 and leading coefficient 4 is 4x²-12x-72 = 0

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p ∧qp ∧~ q~p ∧q~ p ∧~q  is logically equivalent to~ (~p⇒q) for the given question

If p → q

and q →r , then  you can use the law of transitivity to conclude

q→r.

That is a basic law of sillogisms.

An example will help you to understand the transivity law:

Make p, stand for 3 > 3/4, q stand for 3/4 > 15 / 20, the you can conclude that 3 > 15 / 20.

3 > 3/4

3 /4 > 15 / 20

Then, 3 > 15 /20.

This is, from the fact that you know that 3 is gretar than 3/4 and that 3/4 is greater than 15/20, you can conclude that 3 > 15 / 20. That is transitivity and is a law of logic, which you can use to get conclusions.

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Answer: [tex]-2.2f-18[/tex]

Step-by-step explanation:

[tex]-2.6f+0.4f-14-4=f(-2.6+0.4)+(-14-4)=-2.2f-18[/tex]

The figure's scale factor and type of dilatation are

Scale factors are applied to alter the size of the image. The circumstance of increase is frequently referred to as enlargement or magnification.

Given that the preimage is smaller than the image, the situation is enlargement. This implies that the scale factor will also be higher than 1.

Establishing a baseline, say side 8 and side 20 in the preimage and the image respectively. Then, assuming the factor is k, get the factor.

8k = 20

k = 20/8

k = 2.5

The scale factor is 2.5

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Answer: 5.

Step-by-step explanation: The .57 doesn't matter so we can remove that.

Multiply 32 by 0.15

32 x 0.15 = 4.8

After you get your result, round it to the nearest tenths.

4.8 = 5

hope this helps

The exponential form of 64 is 2^6.

Answer:

x = -4

y = -1

Step-by-step explanation:

-5x+12y=8

2x-8y=0

We multiply the first equation by 2 and the second equation by 5

-10x + 24y = 16

10x - 40y = 0

-16y = 16

y = -1

Now put -1 back in for y and solve for x

-5x + 12(-1) = 8

-5x - 12 = 8

-5x = 20

x = -4

Let's check

-5(-4) + 12(-1) = 8

20 - 12 = 8

8 = 8

So, x = -4 & y = -1 is the correct answer.

To change the weight of kilograms into pounds, multiply the weight in kilograms by 2.2

According to the conversion systems, 1 kg = 2.2046 lbs

To facilitate conversion on a pen-paper basis we cannot use 2.2046 whole.

Hence we generally consider 1 k = 2.2 pounds.

The symbol for pounds is lbs and for kilograms is kg.

Now, 1 kg is 2.2 lbs

2 kg = 1 kg + 1 kg

= 2.2 lbs + 2.2 lbs

= 4.4lbs = 2 X 2.2

3 kg = 1 kg + 2 kg

= 2.2 lbs + 4.4 lbs

= 6.6 lbs. = 3 X 2.2

Hence we can see that for all these numbers we can multiply 2.2 to the given weight in kg to get the pounds form.

Hence we need to multiply 2.2

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Answer:

1. 6

2. 5

3. 4

Step-by-step explanation:

For each expression, Substitute the variable for what is given in the statement.

1. 8×(3/4)=6

2. 2.5×(2)=5

3. 10/2.5=4

To find out how much money you would save on car 1, you would multiply the sticker price by the discount percentage (expressed as a decimal). In this case, that would be $20,000.00 x 0.23 = $4,600.00. So you would save $4,600.00 on car 1.

To find out how much money you would save on car 2, you would multiply the sticker price by the discount percentage (expressed as a decimal). In this case, that would be $17,000.00 x 0.10 = $1,700.00. So you would save $1,700.00 on car 2.

Based on the calculations, Car 1 would be a better deal. Even though Car 2 is cheaper by $3,000.00 before discount, Car 1 saves more on discount of $4,600.00 compared to Car 2's $1,700.00. So Car 1 would be more affordable overall.

Answer:

x = 71/8

Step-by-step explanation:

Solve for x:

2 (x - (3 + 1/2)) = 10 + 3/4

Put 3 + 1/2 over the common denominator 2. 3 + 1/2 = (2×3)/2 + 1/2:

2 (x - (7/2)) = 10 + 3/4

2×3 = 6:

2 (x - (1/2 6 + 1/2)) = 10 + 3/4

6/2 + 1/2 = (6 + 1)/2:

2 (x - (7/2)) = 10 + 3/4

6 + 1 = 7:

2 (x - 1/2 7) = 10 + 3/4

Put each term in x - 7/2 over the common denominator 2: x - 7/2 = (2 x)/2 - 7/2:

2 ((2 x)/2 - 7/2) = 10 + 3/4

(2 x)/2 - 7/2 = (2 x - 7)/2:

2 (1/2 (2 x - 7)) = 10 + 3/4

(2 (2 x - 7))/2 = 2/2×(2 x - 7) = 2 x - 7:

(2 x - 7) = 10 + 3/4

Put 10 + 3/4 over the common denominator 4. 10 + 3/4 = (4×10)/4 + 3/4:

2 x - 7 = ((4×10)/4 + 3/4)

4×10 = 40:

2 x - 7 = 40/4 + 3/4

40/4 + 3/4 = (40 + 3)/4:

2 x - 7 = ((40 + 3)/4)

40 + 3 = 43:

2 x - 7 = 43/4

Add 7 to both sides:

2 x + (7 - 7) = 43/4 + 7

7 - 7 = 0:

2 x = 43/4 + 7

Put 43/4 + 7 over the common denominator 4. 43/4 + 7 = 43/4 + (4×7)/4:

2 x = (43/4 + (4×7)/4)

4×7 = 28:

2 x = 43/4 + 28/4

43/4 + 28/4 = (43 + 28)/4:

2 x = ((43 + 28)/4)

43 + 28 = 71:

2 x = 71/4

Divide both sides by 2:

x = (71/2)/4

4×2 = 8:

Answer: x = 71/8

Answer:

y = −x^2 + 4x

Step-by-step explanation:

x^2 = x (2x - 4) + y

Let's simplify it and we get

x^2 = 2x^2 - 4x + y

Now, we want to get the y by itself

x^2 = 2x^2 - 4x + y

-x^2 = -4x + y

-x^2 + 4x = y

So, our answer is  y = −x^2 + 4x

The amount of flour needed for 84 cups of sugar will be 14 cups of flour.

A property that can be measured like, mass, length, time, volume, and pressure. A unit is a standard quantity against which a quantity is measured for example, gram, metre, second, litre, pascal, which are units of the preceding quantities.

To measure the quantity of cups of flour needed to mix 84 cups of sugar;

24 cups of sugar = 4 cups of flour

84 cups of sugar = ? cups of flour = 84/24 x 4

for 84 cups of sugar = 3.5 x 4 = 14 cups of flour.

It will take 14 cups of flour to mix 84 cups of sugar.

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The answer is 24

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.

Given here:  A || B.

Now if transversal D intersects A and B we have

If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.

Thus we have 4x+5+3x+7=180

                               7x=168

                                 x=24

Hence, The value of x is 24

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The quadratic equation that describe the speed of Raj's car is c) x² + 5x - 500 = 0

speed of raj car = x km/h .

speed of ajay car = 5 km faster than speed of raj car = (x + 5) km/h .

Distance cover by ajay in 2 hours = 2(x + 5) km

time taken by raj to cover 400 km = D/S = (400/x) hours .

time taken by ajay to cover 400km = D/S = 400/(x + 5) hours .

A/q,

400/x - 400/(x + 5) = 4

400{1/x - 1/(x + 5)} = 4(x + 5 - x)/x(x + 5) = 1/100

x² + 5x = 5 * 100

x² + 5x - 500 = 0

In this case, it should be noted that the concept that was Illustrated here is the concept of quadratic equations.

Therefore, based on the calculation above, the correct option is C.

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Complete question

Which of the following quadratic equation describe the speed of Raj's car?

a) x² - 5 X - 500 = 0

b) x² + 4x - 400 = 0

c) x² + 5x - 500 = 0

d) x² - 4x + 400 = 0

No, number 48 is not the factor of 8 , 48 is a multiple of 8.

As given in the question,

Given number is equal to ,

48.

Factors are those numbers which divide the given number completely without leaving any remainder.

The factors of the number 48 are equal to:

1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Multiple of 8 are equal to :

8, 16, 24, 32, 40, 48, .....

48 is not considered as a factor of 8 it the multiple of the number 8.

8 is the factor of the given number 48.

Therefore, number 48 is not the factor of 8 , it is considered as the multiple of 8.

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Answer:

47 is a prime number because it has only two factors, 1 and 47.

Step-by-step explanation:

Your welcome.

Answer: A prime number is a number that can only be divided evenly by 1 and itself. 47 is a prime number because it can only be divided evenly by 1 and 47. It cannot be divided evenly by any other number. That's why we say 47 is a prime number. ✅

PLEASE MAKE THIS A BRANLIEST ANSWER!!!

Answer:

(-(11 w^2 - 13))

Step-by-step explanation:

Simplify the following:

2 w^2 - 13 w^2 + 13

Grouping like terms, 2 w^2 - 13 w^2 + 13 = (-13 w^2 + 2 w^2) + 13:

(-13 w^2 + 2 w^2) + 13

2 w^2 - 13 w^2 = -11 w^2:

-11 w^2 + 13

Factor -1 out of -11 w^2 + 13:

Answer: (-(11 w^2 - 13))

If a food delivery driver is 4 3/4 miles west of a city library when he gets a call to pick up food from a restaurant, the mixed fraction is 4.75 miles, and the overall distance is 6.25 miles.

The numerator, which is the portion of a fraction that is at the top, and the denominator, which is the portion that is at the bottom, are its two constituent parts.

It is given that:

A food delivery driver is 4 3/4 miles west of a city library when he receives the call to pick up food from a restaurant.

The restaurant is 1.5 miles east of the library.

The mixed fraction can be written as:

4 3/4 = 19/4 = 4.75

Total = 4.75 + 1.50 = 6.25 miles

Thus, If a food delivery driver is 4 3/4 miles west of a city library when he gets a call to pick up food from a restaurant, the mixed fraction is 4.75 miles, and the overall distance is 6.25 miles.

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Answer:

any number raised by power 0 is always one

ie 10000000000^0 = 1

99999999^0 =1

23^0 = 1

Answer:

Yes. If x=0, then 2ˣ = 0

Step-by-step explanation:

I presume you mean 2ˣ

Any number raised to the power zero is 1 so if x = 0, 2⁰ = 1. There are debates about what 0⁰ evaluates to but I don' think you need to worry about that for this question

I hope I interpreted your question correctly.

Answer:

cap: 17, wallet: 11

Step-by-step explanation:

45 - 28 = 17

45 - (17 x 2)  =

45 - 34 = 11

could also do:

28 - 17 = 11

Hope this helps have a good day

The required triangles are similar because Corresponding sides of the triangles are proportional and their corresponding angles are same.

For plants, an isotype is a replica of the logotype; holotype and isotypes are frequently taken from the same individual plant or samples from the same collection. Hence Isotypes are pairs of related holotypes. Therefore, choice D is the right response.

To prove the similarity of two triangles,Corresponding sides of the triangles are proportional and their corresponding angles are same.

The scale factor of their side = 33/11 = 3

So, ΔQRS ~  ΔTUV with scale factor of 3.

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Since the respective sides of the required triangles are proportional and their corresponding angles are identical, the required triangles are similar.

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The coordinates of the vertices of △ABC are A(-4,1), B(-2,4), C(-2,0), △CDE are C(-1,-1), D(1,1), E(4,-1), and △IHG are I(2,3),H(4,0), G(4,4).

The transformation is △ABC reflected with the line y =2 and shifted 6 units right sides.

What are the vertices of a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

There are three triangles. The vertices of △ABC are A(-4,1), B(-2,4), C(-2,0).

The vertices of △CDE are C(-1,-1), D(1,1), E(4,-1). The vertices of △IHG are I(2,3),H(4,0), G(4,4).

The △ABC is congruent with △IHG.

The difference between the x-coordinate of A and I is (2 - (-4)) = 6

The difference between the x-coordinate of B and H is (4 - (-2)) = 6

The difference between the x-coordinate of C and G is (4 - (-2)) = 6

The sum of the y-coordinate of A and I is (3+1) = 4

The sum of the y-coordinate of B and H is (4 + 0) = 4

The sum of the y-coordinate of C and G is (4 + 0) = 4

The midpoint of y-coordinate of △ABC and △IHG is 4/2 = 2

The △ABC is reflected by y = 2 and shifted 6 units right side.

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The question which can be answered by finding 4½ ÷ ¼ is "You are buying ¼ pound containers of fruit at the store. How many containers do you need to buy to have 4½ pounds of truit?".

The correct answer choice is option C

You have 4½ pounds of fruit and use ¼ pound. How much fruit is remaining

Pounds of fruits remaining = Pounds of fruits you have - pounds of fruits used

= 4½ - ¼

= 9/2 - 1/4

= (18-1)/4

= 17/4 pounds

How much is ¼ of 4½ pounds of fruit?

= ¼ × 4½

= ¼ × 9/4

= 9/16 pounds of fruits

You are buying ¼ pound containers of fruit at the store. How many containers do you need to buy to have 4½ pounds of truit?

Number of containers needed = 4½ ÷ ¼

= 9/2 ÷ 1/4

multiply by the reciprocal of 1/4

= 9/2 × 4/1

= 36/2

= 18 containers

Hence, The question which represents 4½ ÷ ¼ is "You are buying ¼ pound containers of fruit at the store. How many containers do you need to buy to have 4½ pounds of truit?".

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Answer:

from -5 to infinity

Step-by-step explanation:

Hope this helps.

The equation that represents the relationship between the number of apples a and the number of pears p is b. a = p + 3.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

From the information, in each basket of fruit, there are 3 more apples than pears.

Let p = pears

Let a = apple

Therefore, the equation that represents the relationship between the number of apples a and the number of pears p is a = p + 3.

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If a function yields the result y, then its inverse function, denoted by the symbol , will return the value x.

A function's output is returned when its inverse function does the same action variable. The inverse function of a function, or f-1(y), will return the value x if the function f(x) produces the output y.A function that reverses the action of a function, or f, is known as its inverse in mathematics.

Here,

A function that reverses the effects of another function is said to have an inverse. If y = f(x), then x must always equal g, then a function g is the inverse of a function f. (y). Application of f followed by application of g is equivalent to doing nothing, in other words. As g(f(x)) = x, this can be expressed in terms of the relationship between f and g.

Because they allow for the reversal of mathematical operations, inverse procedures are crucial for solving equations (e.g. logarithms, the inverses of exponential functions, are used to solve exponential equations). How to invert a mathematical technique is one of the most crucial questions whenever one is introduced.

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The complete question : " In Exercises 15-18, match the graph of the function with the graph of its inverse function. [The graphs of the inverse functions are labeled (a), (b), (c), and (d).]"

The origin in the complex plane is represented by the number 0. Therefore, the separation between a complex number and the complex plane's origin (zero) equals its absolute value.

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Answer:

Step-by-step explanation:

All except "E", "C", and "B".

A and D are true.

The line is negative and the slope is -5, not 5.