Prove that,if one root of the equation ax^2+bx+c=0 is twice the other,then 2b^2=9ac

Answer: 1*5=5 is the counterexample.

Step-by-step explanation: The conjecture stated is that the product of two positive numbers is always greater than either number. We have to find certain values to check and see if this conjecture is false. We can use the numbers 1 and 5 to multiply. This would be the identity property of multiplication. 1 and 5 are both positive numbers and therefore that 1*5=5 is the counterexample.

Data:

• B = 70°

• b = 19ft

• C = 90°

Procedure:

• Finding the angles

We know that C = 90° as the image shows the symbols. Also, we know that the sum of the interior angles of a triangle are 180°. Then, to get A we have to do the following:

Isolating for A:

Replacing the values we know:

• Finding side ,a

Using trigonometric functions, we can get a.

As we already know the value of A and b, we can isolate for a:

Replacing the values:

• Finding side ,c

Finally, using the Pythagorean Theorem, we can calculate c:

Isolating for c:

Replacing the values:

Answer:

• A = 20°

• a = 6.92 ft

• c = 20.22 ft

Blanks to be filled by 4,3,8 and 3.

Multiplication in mathematics is the same as adding equal groups. As we multiply, there are more items in the group. The product, the two factors, and the product are all components of a multiplication problem. The numbers 6 and 9 are the factors in the multiplication equation 6 x 9 = 54, and 54 is the result.

Given Data

           3 __ 8

×            7 8 4

_____________

       1 _    9 2

    2 7 __ 4

_   4 3  6

_____________

 2  7 2 8 __ 2

_____________

Solving

Multiplying and adding,

           3 _4_ 8

×            7 8 4

_____________

       1 3_    9 2

    2 7 _8_ 4

_   4 3  6

_____________

 2  7 2 8 _3_ 2

_____________

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The value of complex number is [tex]ab^{2}[/tex] = 36+18i

What is complex number?

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number.

The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers.

Given,

a = 4+2i

b = 3

[tex]b^{2}[/tex] = 3(3)

= 9

Hence, the value of

[tex]ab^{2}[/tex] = (4+2i)9

=36+ 18i

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commutative property

That's what you call the property 7x8 = 8x7

commutative property!

The required metric conversion is:

96 times 1/2 inch is equal to 4 feet

In this question, we need to find convert 1/2 inch to 4 feet

We need to convert metric unit.

We know that, 1 feet = 12 inches

So, 4 feet would be 48 inches

We can write 48 inches as,

48 inches

= 96 × (1/2) inches

This means, if we add 1/2inch 96 times then it is equal to 4 feet

Therefore, the required metric conversion is: 96 times 1/2 inch is equal to 4 feet

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The evaluated value of x from the line geometry given is 36.

An angle is the point where two lines meet. From the given diagram, the sum of the angles on the line is 180 degrees.

Take the sum to have

x + 3x + x = 180

Simplify

4x + x = 180

5x = 180

Divide both sides by 5

5x/5 = 180/5

x = 36

Hence the value of x from the diagram is 36

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a) The distance that the bus traveled varies directly with time.

b) If the journey of 60 km takes 8 hours, the speed of the bus is 7.5 km/h.

The relationship between distance and speed can best be explained below:

For a constant speed, for example, 60 km/h, the distance traveled, 60 km, is proportional to the time used.

But if the distance is fixed at 60 km, the time it takes the bus, for example, 8 hours, is inversely proportional to the speed.

Total distance = 60 km

Steady speed = 60 km/h

Thus, for every kilometer, the bus takes one minute (60/60) and for every minute, the bus travels a kilometer.

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The formula to obtain the future value (FV) is,

Where,

Therefore,

ence, there will be $6`166.13 in the account after 5years.

Answer: X1= 7 - sqrt{17} over 4

              X2= 7 + sqrt{17} over 4

A store sold 22 colored shirts and 8 white shirts.

Let x be the number of colored shorts and y be the number of white shirts.

A store sold 14 more colored shirts than white shirts.

so, we get an equation,

x = y + 14                       ....................(1)

The white shirts cost $9.95, and the colored shirts cost $10.50. The store sold $310.60 worth of shirts.

So we get an equation,

10.50x + 9.95y = 310.60           .............(2)

Substitute above value of x in equation (2)

10.50(y + 14) + 9.95y = 310.60          

10.50y + 147 + 9.95y = 310.60          

20.45y = 310.60 - 147

20.45y = 163.6

y = 8

Substitute above value of y in equation (1)

So, x = 8 + 14

x = 22

Therefore, a store sold 22 colored shirts and 8 white shirts.

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C(x) is related to its parent function c(x) = 0.75|x| + 25.

The function in the context of the situation illustrated that the cost is the same.

It should be noted that a function is used to show the relationship between the variables.

In this case, the cost to travel X miles east or west on a train is the same. The function for the cost is given as c(x) = 0.75|x| + 25.

Let East = positive direction

Let West = negative direction

Let the travel distance in East = x

Travel distance for West = -x mile

The cost to travel East x miles will be:

= 0.75(x) + 24

= 0.75x + 25

The cost to travel West will be:

c(-x) = 0.75x + 25

This shows that the cost will be the same even though there in different directions.

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Angle JKL has a measure of 24 degrees while angle LKM has a measure of 12 degrees

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following angles

From the attached figure, we can see that:

Angle 1 is twice the measure of angle 2

This is so because, the angle 1 is the vertex angle of an isosceles triangle

While the angle 2 is half of it

So, we have

Angle 1 = 2 * Angle 2

Substitute the known values in the above equation

So, we have

2 * 3x = 5x + 4

Evaluate the product

So, we have

6x = 5x + 4

Evaluate the like terms

x = 4

Substitute x = 4 in the equations JKL=5x+4 and LKM=3x

So, we have

JKL= 5 x 4 + 4

LKM = 3 x 4

Evaluate the equations

So, we have

JKL= 24

LKM = 12

Hence, the measures of the angles are JKL= 24 and LKM = 12, respectively

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Answer:

The smallest of the three integers is 17. (17, 19, 21)

Based on the equations given, the best comparison between them is that they are intersecting but not perpendicular.

When lines are perpendicular to each other, one line will have a slope that is the negative reciprocal of the other. For instance, if the slope of one line is 2, the slope of the perpendicular line will be -1/2.

Parallel lines will have the exact same slope.

The slope of the first line is:

2x - 7y = -5

(2x - 7y = -5) x 1/7

2/7x - y = -5/7

Slope = 2/7

The slope of the second line is:
x - 3y = 4

(x - 3y = 4) x 1/3

1/3x - y = 4/3

Slope = 1/3

The slopes are neither negative reciprocals nor the same so the lines must be intersecting but not perpendicular.

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Answer:

it's easily 47 as it's finished basement ALONE and b is 3 car garage ALONE while c is both so it's asking who has a finished basement ALONE/ONLY

Answer:

38

Step-by-step explanation:

The total homes are 85

Of the homes with finish basements it is 47

Then you find the difference: 85-47 =

The final answer is 38

a ) The value is 4.472

b)2 decimal place is 4.47

When expressing a whole number and a fraction together, decimals are utilized. Here, we shall use a "." (also known as a decimal point) to demarcate the full number from the fraction. Say, for illustration, that you intend to bring a cone of ice cream. You are informed by the vendor that ice cream costs $2 and 50 cents. Now, if you wanted to sum up this cost in a single number, you would say that an ice cream cone costs $2.50. You may be utilizing decimals without even recognizing it in a variety of everyday settings.

[tex]\sqrt{4.5^{2} -0.5^{2} }\\ \sqrt{20.25-0.25} \\\sqrt{20}\\ 4.4721[/tex]

a ) The value is 4.472

b)2 decimal place is 4.47

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Answer: Use the quotient rule to solve this problem (formula attached). g(x) would be -sqrt x and f(x) would be x^2 - 4x +5.

Answer: 3.55, 6.187, 9.312, 27.132

Step-by-step explanation:

The easiest way I do this is by rounding all the numbers to the nearest hundredths, tenths, or whole numbers.

3.55 = 4
6.187 = 6
9.312 = 9
27.132 = 27

[tex] = (a + 1)(b(a + 1) - 5)[/tex]

HOPE THIS HELPS

Given the expression below

We can evaluate the expression by simplifying the parenthesis

Answer: 54

Answer:

VERY

Step-by-step explanation:

VERY

Answer:

74.44

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]

A number line that plots the integers –12, –3, and 7 will be A. A number line going from negative 15 to positive 10. Points are at negative 12, negative 3, and 7.

It should be noted that a number line simply means the straight line that can be used to show the addition and subtraction of numbers.

It should be noted that the negative numbers are on the left hand side and the positive numbers are on the right hand side.

Therefore, this is conveyed effectively by option A.

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Answers to all the problems using BODMAS property are:

So, (A) 107-[59-(18+9-(12-18+6) +3}]:

(B) [222- 486 of 8]+(58-45) × 8

(C) 1500-[160+ (40-(120-100)}]

Therefore, answers to all the problems using BODMAS property are:

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Answer:Explanation:

Option 1: Vertically compressed by a factor of 4, reflected across the x-axis, and shifted right 6 units and down 2 units.

iven the parent function:

If y is vertically compressed by a factor of 4, we have:

Next, a reflection across the x-axis will give:

If the result is shifted

Finally, a shift downwards by units gives:

Thus, the graph of g(x) is the graph of y vertically compressed by a factor of 4, reflected across the x-axis, and shifted right 6 units and down 2 units.

he firsyt option is correct.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given data

STEP 2: answer question a

To get the answer,

Hence, 120 different toppings pizza are possible

STEP 3: Answer question b

Hence, 1215450 mini-boxes are possible

Charlie used 400 milliliters of Solution B if the resulting mixture is a 12% alcohol solution.

An algebraic equation is a declaration of the equality of two expressions created by applying the algebraic operations to a set of variables.

Monomial expressions, binomial expressions, and polynomial expressions are the three main categories of algebraic expressions.

Given : Solution A contains 20% alcohol, while Solution B contains 6% alcohol.

It is  also given that Charlie uses 300 milliliters of Solution A.

Let's say that the mixture contained x ml of the 6% solution B.

x + 300 = resulting mixture of 12 % alcohol.

20% (300) + 6% (x) = 12% (x+300)

60 + 0.06x = 0.12x + 36

0.06x = 24

x = 400 milliliters

As a result, if the resulting mixture is a 12% alcohol solution, he used 400 milliliters of Solution B.

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