Find the discriminant of the following equation.

4x2 + 12x + 9 = 0

Final answer:

To find the ratio that forms a proportion with 9/5, we can find a common multiplier for each option and check if the resulting ratios are equal to 9/5.

Explanation:

If we want to determine which ratio forms a proportion with 9/5, we can find a common multiplier. We can multiply both the numerator and denominator of each ratio by the same number and check if the resulting ratios are equal to 9/5.

Let's check each option:

Therefore, the ratio 54/30 (option a) forms a proportion with 9/5.

The possibility statements are:

Statement 1

The function is defined on [2.4]

The above means that, the minimum is 2, and the maximum is 4

However, since the function is continuous at [2,4), the close bracket ")" means that the function extends indefinitely i.e. no maximum.

Hence, this statement is possible

Statement 2

The function is defined on [4.5]

The above means that, the minimum is 4, and the maximum is 5

However, since the function is continuous at [4,5], the close brackets "[" and "]" mean that the function have finite values

Hence, this statement is possible

Statement 3

The function is defined on [2,5]

The above means that, the minimum is 2, and the maximum is 5

However, since the function is continuous at [2,5], the close brackets "[" and "]" mean that the function have finite values and it has bounded intervals

Hence, this statement is not possible

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Let

x------> the biggest number

y------> the middle number

z------> the smallest number

we know that

[tex]x=2y[/tex] -------> equation [tex]1[/tex]

[tex]x+y=4z[/tex] -------> equation [tex]2[/tex]

[tex]z+y=x-2[/tex] -------> equation [tex]3[/tex]

substitute equation [tex]1[/tex] in equation [tex]2[/tex] and equation [tex]3[/tex]

[tex][2y]+y=4z[/tex] ------> [tex]3y=4z[/tex] ------> equation [tex]4[/tex]

[tex]z+y=[2y]-2[/tex] ----> [tex]z+2=y[/tex] ------> equation [tex]5[/tex]

using a graph tool-----> to resolve the system of equations

see the attached figure

the solution is the point [tex](6,8)[/tex]

[tex]z=6\\y=8[/tex]

Find the value of x

[tex]x=2y[/tex]

[tex]x=2*8=16[/tex]

therefore

the answer is

the biggest number is [tex]16[/tex]

the the middle number is [tex]8[/tex]

the smallest number is [tex]6[/tex]

Answer: There are 17.5 minutes for which it costs the same amount to use each card for a single call.

Step-by-step explanation:

Let the number of minutes be x

To use card A, the cost is $1.00 to connect and then $0.04 per minute.

So, our expression becomes,

[tex]1+0.04x[/tex]

To use card B, the cost is $0.65 to connect and then $0.06 per minute.

So, our expression becomes,

[tex]0.65+0.06x[/tex]

According to question, if it cost the same amount to use each card for a single call, then it will be

[tex]1+0.04x=0.65+0.06x\\\\1-0.65=0.06x-0.04x\\\\0.35=0.02x\\\\\frac{0.35}{0.02}=x\\\\17.5=x[/tex]

Hence, there are 17.5 minutes for which it costs the same amount to use each card for a single call.

Answer:

First option is correct.

Step-by-step explanation:

In triangle ABC, [tex]\angle A=8x-2[/tex], [tex]\angle B=2x-8[/tex] and [tex]\angle C=94-4x[/tex].

According to angle sum property of a triangle, the sum of interior angles of a triangle is 180 degree.

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]8x-2+2x-8+94-4x=180[/tex]

[tex]6x+84=180[/tex]

[tex]6x=96[/tex]

Divide both sides by 6.

[tex]x=16[/tex]

Therefore the value of x is 16. The measure of angles are

[tex]\angle A=8(16)-2=126[/tex]

[tex]\angle B=2(16)-8=24[/tex]

[tex]\angle C=94-4(16)=30[/tex]

The opposite angle of shortest side is always smallest interior angle. Similarly the opposite angle of longest side is always largest interior angle.

[tex]\angle B<\angle C<\angle A[/tex]

[tex]AC<AB<BC[/tex]

Therefore option 1 is correct.

"The sum of 58 and 76 is 134.

To find the sum of two numbers, one simply needs to add them together. In this case, the numbers are 58 and 76.

The addition can be performed as follows:

[tex]\[ 58 + 76 = 134 \][/tex]

Thus, the correct answer to the question ""What is the sum of 58 and 76?"" is 134."

Answer:

9 months!!

Step-by-step explanation:

Mr. and Mrs. Number are so happy because they are both prime numbers, which are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.

For example:

Mr. Number could be 2, as it is divisible only by 1 and 2.

Mrs. Number could be 3, as it is divisible only by 1 and 3.

Prime numbers have unique properties and are considered special in mathematics. They play a fundamental role in number theory and various mathematical algorithms. Additionally, prime numbers are essential in cryptography, ensuring secure communication and data encryption.

So, Mr. and Mrs. Number are happy because they share the special quality of being prime numbers, making them quite unique and valuable in the mathematics.

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Answer:

90 degree and  [tex]\frac{pi}{180}[/tex] radians.

Step-by-step explanation:

Given  :  Angle formed by the hands of a clock at 3:00

To find : Write in  term of degrees and radians ...

Solution : We have given that a clock show the time 3 :00

We know that at 3 : 00 clock show hour hand at 3 and minute hand at 12.

Angle formed by the minute hand at 12 and hour hand at 3 is 90 degree.

90 degree =  [tex]\frac{pi}{180}[/tex] radian.

Therefore, 90 degree and  [tex]\frac{pi}{180}[/tex]radians.

Answer:

option (c) is correct,

[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

Step-by-step explanation:

Given expression ,  [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

We have to choose an equivalent fraction from the given options.

Consider expression (c) ,

[tex]3x^2+17-\frac{82}{x+5}[/tex]

Taking LCM , Multiply [tex]3x^2+17[/tex] by (x+5) , we get,

[tex]\frac{3x^2(x+5)+17(x+5)-82}{x+5}[/tex]

On solving , we get,

[tex]\frac{3x^3+15x^2+17x+85-82}{x+5}[/tex]

On simplifying, we get,

[tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

Which is equal to the given expression.

Thus, option (c) is correct,

[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

The answer is A. 10 feet, on Plato.

The given equation in slope-intercept form is y = -2x - 2.

Slope of a line is defined as the change in the value of y-coordinate with respect to the x-coordinate value. It is usually denoted by 'm'.

It can also be defined as the tangent of the angle that the given line is making with the X-axis.

That is m = tan θ, where θ is the angle that line is making with the X-axis.

The equation of a line in slope-intercept form is given by,

y = mx + c

Here, c is called the y-intercept, the value of which is the value of the y-coordinate when the line touches the Y-axis.

Now,

y + 4 = -2 (x - 1)

y + 4 = -2x + 2

y = -2x + 2 - 4

y = -2x - 2

The equation of the line in slope-intercept form is y = -2x - 2.

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The answer is c.

F(x)=5x^3+7x^4-1/2x

Answer:

x = -2

Step-by-step explanation:

To find the height that allows a person to see 50 kilometers, we set the given function equal to 50 and solve for h. This calculation gives us the height as approximately 0.2 kilometers.

The question requires us to find the height h that would allow a person to see 50 kilometers, given the function D(h)=111.7 * sqrt(h).

We can solve this by setting the function equal to 50 and then solving for h. Like so: 50 = 111.7 * sqrt(h).

To isolate sqrt(h), we divide both sides of the equation by 111.7: sqrt(h) = 50 / 111.7.

Then we square both sides of the equation to solve for h: h = (50 / 111.7)^2.

Upon calculating the right side of this equation, we find that the height is approximately 0.2 kilometers.

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The answer for this question is 0.2 Kilometers or 200 meters(approx.)

The detailed explanation is as follows :

The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given by the function D(h)=111.7 times square root of h. We need to find the height that would allow a person to see 50 kilometers.

To solve this problem, we need to find the height h that allows a person to see a distance of 50 kilometers. We start with the given function:

D(h) = 111.7 * sqrt(h)

We set D(h) to 50 kilometers:

50 = 111.7 * sqrt(h)

To isolate sqrt(h), we divide both sides by 111.7:

sqrt(h) = 50 / 111.7

Next, we calculate the division:

sqrt(h) ≈ 0.4475

Now we square both sides to find h:

h = (0.4475)^2 ≈ 0.2002

Therefore, the height that allows a person to see 50 kilometers is approximately 0.2002 kilometers, or 200.2 meters above the ground.

Hence the required answer is 0.2 kilometers or 200 meters(approximately)

Answer:

Option 1,2 and 3.

Step-by-step explanation:

An algebraic expression is such a mathematical representation of variables

Algebra is relation with variables a,y,z and so on

So, Option 2 is correct that is it will contain variable in numerator.

Similarly, Option 3 is correct that is it will contain variable in denominator.

Option 4 is incorrect because if it  contains variable with an exponent then it will not be algebraic it will become exponent function.

Option 1 is correct because it may have common denominator an algebraic fraction will have common denominator.

Answer:

n = 3years

Step-by-step explanation:

If Gary buys a van £27500 and sell the van at a value of the £11264 after n years, depreciation will give us;

£27500-£11264 = £16236

If the van depreciates by 20% each year, yearly depreciation will be;

20% of £27500 = £5500

To get the total number of years n it takes the van to depreciate to £11264 will give total depreciation amount/yearly depreciation amount which gives;

£16236/£5500 = 2.9years

This means that the van has depreciate from £27500 to £11264 after 3years

Answer:

C) circle

Step-by-step explanation:

To find out how many people responded Orlando, we need to add up the fractions for Miami, Kissimmee, Fort Lauderdale, Key West, and Tampa and then set up a proportion to find the number of people who said Orlando. The answer is approximately 47 people.

To find out how many people responded Orlando, we need to add up the fractions for Miami, Kissimmee, Fort Lauderdale, Key West, and Tampa since the rest said Tampa. The fractions we need to add are 1/4, 1/8, 1/16, and 1/32. Let's calculate each fraction to get a common denominator.

1/4 = 8/32, 1/8 = 4/32, 1/16 = 2/32, 1/32 = 1/32.

Now we can add them up: 8/32 + 4/32 + 2/32 + 1/32 = 15/32.

Since the remaining fraction is Tampa, which corresponds to 22 people, we can set up a proportion: 15/32 = 22/x to find out how many people said Orlando. Cross-multiply and solve for x: 32 * 22 = 15x, 704 = 15x, x = 704/15, x ≈ 46.93.

Therefore, approximately 47 people responded Orlando.

Using the compound interest formula, it will take approximately 24.53 years for an initial investment of $1,500 to grow to $7,300 at an annual interest rate of 6.75%. This is calculated by solving for t in the rearranged compound interest formula.

To determine how many years it will take for your $1,500 investment to reach $7,300 with an interest rate of 6.75% compounded annually, we use the formula for compound interest:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:

We rearrange the formula to solve for t:

t = (log(A/P) / log(1 + r/n)) / n

Plug in the known values:

t = (log(7300/1500) / log(1 + 0.0675)) / 1

Calculate the logarithms:

t ≈ (log(4.8667) / log(1.0675))

t ≈ (0.6887 / 0.0281)

t ≈ 24.53

It will take approximately 24.53 years for the investment to grow to $7,300.