find the discriminant and determine the number of real solutions : 4x^2 + 7x - 15 = 0

Answers

Answer 1
The discriminant of a quadratic expression [tex]\displaystyle{ ax^2+bx+c[/tex] is 
                          [tex]\displaystyle{ D=b^2-4ac[/tex].

In the quadratic [tex]4x^2+7x-15[/tex], a=4, b=7, and c=-15.

Thus, [tex]\displaystyle{ D=b^2-4ac=7^2-4(4)(-15)=49+240=289>0[/tex].


The discriminant is positive, this means that the equation has 2 real solutions.

Answer: 2

Related Questions

Factor the expression.

4d + 12

Answers

4d+12
Lets put out the 4 because it can also be pulled out of 12
4(d+3)

Shoutout to @Mdarrow01

Have an amazing day!
4d + 12 = 4(d+3)
I hope this helps

PLEASE HELP WITH THIS!
In "Brer Rabbit Goes Back to Mr. Man's Garden," how does Brer Rabbit end up in the box?

A.
Brer Rabbit jumps into the box because he thinks it contains lamb.

B.
Brer Fox traps Brer Rabbit in the box to help Mr. Man.

C.
Janey asks Brer Rabbit to get into the box before giving him any peanuts.

D.
Mr. Man sets a trap for Brer Rabbit in the peanut patch, and it works.

Answers

CI think that it is C.

you have a $100 gift card to spend at a store. You buy a portable compact disc player for $45. Compact discs are on sale for $11 each. How may compact discs can you buy with the money remaining on gift card?

Answers

You can buy 4 compact discs
Let's create an expression with the given variables and values to better understand the problem.

y=100-(45+11c)

This equation subtracts the value of the cd player and the CDs from the money on the gift card. 

We can simplify the equation a little more to make it easier to solve.
y=55-11c

Now, we can see how many CDs we can buy with the remaining money on the gift card by solving for 'c'.
11c=55
c=5

We can buy 5 CDs with the money remaining on the gift card.

Consider the following statement. Five less than 4 times a number equals 2 more than 3 times the number. a. Write an equation to represent the statement. Use n for the unknown number. b. Solve the equation. c. Explain how you solved the equation.

Answers

4n-5 = 3n+2  thats taking the word problem and writing it out
Now solve

4n-5=3n+2
n = 7

n  = unknown number

5 less than 4 times a number = 4n-5

2 more than 3 times a number = 3n+2

 so you have 4n-5 = 3n +2

add 5 to both sides:

4n=3n+7

subtract 3n from both sides:

n = 7


name an angle with vertex n that appears obtuse

Answers

Final answer:

An obtuse angle is one measuring between 90 and 180 degrees. Without a diagram, one cannot name a specific obtuse angle with vertex 'n', but generally, any angle appearing to open wider than 90 degrees at vertex 'n' can be considered obtuse.

Explanation:

To determine an angle with a vertex named 'n' that is obtuse, you need to know that an obtuse angle is one that measures more than 90 degrees but less than 180 degrees. Unfortunately, without a diagram or more context, it's impossible to provide a specific example. However, if you're looking at a diagram where an angle is labeled with the vertex 'n', and you can see that the angle opens wider than a right angle (which is exactly 90 degrees), then that angle is likely obtuse.

For instance, let's consider an angle named angle XnY, where 'n' is the vertex or corner point. If the measure of angle XnY is say, 120 degrees, it is definitively an obtuse angle because it falls between 90 and 180 degrees. The notation for an obtuse angle with vertex 'n' could be written as angle XnY (where 'X' and 'Y' stand for the names of the other points that form the angle with vertex 'n').

Any angle with its vertex at point "n" that measures more than 90 degrees and less than 180 degrees would be considered an obtuse angle.

An angle is a measure of the amount of rotation needed to bring one line or plane into coincidence with another, generally measured in degrees or radians.

An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. Therefore, any angle with its vertex at point "n" that measures more than 90 degrees and less than 180 degrees would be considered an obtuse angle. An example of such an angle could be ∠ABC, where point B is the vertex and the angle measures, for instance, 120 degrees.

Stephanie says of the graph of Y is equal to 3X +2 and why is it going to 3X -2 are parallel. Isabella says the grass are perpendicular who is correct? explain your reasoning

Answers

parallel because the Y moved 4 units down and the slope hasnt changed

A pump can move 42 gallons of water in 7 minutes. Find the unit rate

Answers

in 1 min the thing can pump 6 gallons of water

What is the square root of 6 between what two integers

Answers

The square root of 6 is2.44948974278

What are the laws of exponents

Answers

the exponent of a number says how many times to use the number in multiplication.

Answer:

One rule to remember that everyone forgets is, multiply the base number as many times as what the exponent is. So for example, 3² is not 3 x 2 = 6, it's    3 x 3 = 9. Hope that makes sense! :)

Step-by-step explanation:


Greg builds a new pond which has a volume of 7.35 m3. It is 4.2 m long and 50 cm deep. What is the width of the pond? m

Answers

I believe that the formula to get the volume of a regular prism is V = L × W × H. And so with that being said, Let's just say the pond is rectangular in shape, therefore we can use that formula.
Width = Volume/(Length x Depth)
Plug in your variables.
Width = 7.35/4.2 × 0.5 = 7.35/2.1 = 3.5 m
So, your width of the pond is equal to 3.5m.

Hope this helped, and if it did I'd appreciate if you marked me as brainliest as I need it to get to a higher rank. If you need any more help, feel free to add me and/or message me :)
Width = 7.35/4.2*0.5 = 7.35/2.1 = 3.5 m

a cell phone distributor earns a yearly salary of $28,000 plus a 17.5% commission on sales. find the total earnings for a year when the sales are $38,000

Answers

28000 salary + 17.5% commish * 38000 in sales .
28000 + 6650 = 34650

hope this helps , give brainliest

How many solutions does the following equation have ?

Answers

This problem has no solution. The answer is A. Hope I helped.

In the equation 4(y - 30) =4y + 12, the correct option is no solution. Therefore, option A is correct.

What is an equation?

Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation. For an unknown quantity represented by an unknown variable, equations are then solved to determine its value. It is clear that a statement is not even an equation if there is no "equal to" sign in it.

Let's solve the equation,

4(y - 30) =4y + 12

4y - 120 = 4y + 12

The value of 4y is got cancelled from both the sides, then the equation has no solution.

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Which of the following fractions is not in simplest form?
5/11
4/9
8/15
2/14

Answers

2/14 is not in simplest form

My answer would be the fourth one... 2/14

Jason draws a line in the sand at the beach. The line is 7/8 ft long. He wants to divide the line into sections that are each 1/8 ft long. How many sections will the line be divided into?

Answers

into seven sections.

Answer: 7 sections.

Step-by-step explanation:

Given : Jason draws a line in the sand at the beach.

The line is [tex]\dfrac{7}{8}[/tex] ft long.

He wants to divide the line into sections that are each  [tex]\dfrac{1}{8}[/tex] ft long.

Then, the number of section will the line be divided into is given by using division operation:-

[tex]\dfrac{7}{8}\div\dfrac{1}{8}[/tex]

[tex]\dfrac{7}{8}\times8=7[/tex]  [Change [tex]\dfrac{1}{8}[/tex] by its reciproval (8) to convert division operation into multiplication]

Hence, the line will divided into 7 sections.

To which real number sets does the number −1.7 belong? Choose all answers that are correct. A. natural numbers B. whole numbers C. integers D. rational numbers

Answers

To which real number sets does the number −1.7 belong?


C. integers

which statement describes the difference in energy between an ice cube and liquid water.

Answers

ice cubes are solid witch gives it less energy than i liquad for example if ice thoches a wire than it well take time for effect but if water touches water it comes in effect way faster

Mr. Henderson has 2 bouncy ball vending machines. he buys one bag of the 27 millimeter balls and one bag of the 40 millimeter balls .he puts a n equal number of each in the 2 machines. how many bouncy balls does he put in each machine

Answers

You need to subtract 27 from 40 so it should look like this 40-27= and 40-27=13 so he put 13 balls in each machine.

Answer:

Total Number of bouncy balls in two bags

    =One bag contains 27 millimeter balls + One bag contains 40 millimeter balls

   =27 +40

    =67

Now ,67 balls are put equally in 2 machines.

67 is an odd number which can't be divided into equal parts.

→67=33(Machine 1) +34(Machine 2)

          or

→67=34(Machine 1) +33(Machine 2)

Don’t understand please help meeeeee!!!!!!

Answers

you would count by threes

A driveway is 40 yards long. About how many meters long is it?

Answers

About 45 meters... or 44.8
The answer to this is 36.576.

What is the product of −2 1/2 and −3 1/2 ? Enter your answer as a mixed number, in simplified form, in the box.

Answers

8 3/4 is your answer in a mixed number form
the answer wouldbe -2 1/2

$500, 12%,18 months


HELP!!!!!!!!!!

Answers

A man borrowed $500 at a 12% annual interest rate and repaid it after 18 months. The calculated simple interest on the loan is $6.00.

To calculate simple interest, you can use the formula:

Simple Interest = [tex]\frac{P \times R \times T}{100}[/tex]

where:

- P is the principal amount (the initial amount borrowed),

- R is the rate of interest per annum, and

- T is the time the money is borrowed for in years.

In this case:

- P = $500,

- R = 12%(or 0.12 as a decimal), and

- T = 18 months (which is 1.5 years since [tex]\( \frac{18}{12} = 1.5 \))[/tex].

Now plug these values into the formula:

Simple Interest = [tex]\frac{500 \times 0.12 \times 1.5}{100}[/tex]

Calculate this expression to find the simple interest.

Simple Interest = [tex]\frac{500 \times 0.12 \times 1.5}{100}[/tex]

Simple Interest = [tex]\frac{90}{100}[/tex]

Simple Interest = $6.00

Therefore, the simple interest on a $500 loan at an annual interest rate of 12% over 18 months is $6.00.

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The complete question is:

A man borrows $500 and pays it back after 18 months at 12% per annum. Find the simple interest.

The simple interest is $90.

The formula for simple interest is:

I = PRT

Where:

I = the interest paid

P = the principal amount borrowed

R = the interest rate

T = the time period (in years)

We know that P = $500, R = 12% = 0.12, and T = 18 months = 18/12 = 1.5 years. We can now plug these values into the formula to solve for I:

I = $500 * 0.12 * 1.5 = $90

Therefore, the simple interest is $90.

The complete question is:

A man borrows $500 and pays it back after 18 months at 12% per annum. Find the simple interest.

Tina bought 15.25 gallons of gasoline at a price of $2.31 per gallon. What is the total cost of the gasoline rounded to the nearest hundredth?

Answers

To find the total cost, we must multiply the amount that was bought by the price of each individual item. So we need to multiply the price of one gallon by how many gallons Tina bought:

[tex] 15.25*2.31=35.227 [/tex]

However, the question says to round to the nearest hundredth, so we must round up. Therefore the total amount Tina paid for the gasoline was $35.23.

If Tina bought 15.25 gallons of gasoline at a price of $2.31 per gallon. The total cost of the gasoline rounded to the nearest hundred will be: $35.23

Using this formula

Total cost=Quantity ×price

Where:

Quantity=15.25 gallons

Price=$2.31 per gallon

Let plug in the formula

Total cost=15.25×$2.31

Total cost=$35.2275

Total cost=$35.23 (Approximately)

Inconclusion if Tina bought 15.25 gallons of gasoline at a price of $2.31 per gallon. The total cost of the gasoline rounded to the nearest hundred will be: $35.23

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Please help me out with this simple math question. Thanks

Answers

the answer is -243 because you just have to plug in the correct values and figure out the answer

Question for the people out there hungry for brainliest and points.

What's the absolute value of negative 3?

Answers

Positive 3. Absolute values are never negative, they are either 0 or a positive. so -3 would be +3
i think its zero ;))

A company produces 4.56*10^3 light bulbs each week. Written in scientific notation, which is the best estimate of how many light bulbs the company will make in 9.36*10^2 weeks?

Answers

[tex]\(4.56 \times 10^3\) bulbs/week. After \(9.36 \times 10^2\)[/tex] weeks, approximately [tex]\(4.27 \times 10^6\)[/tex] bulbs produced.

To find the total number of light bulbs the company will produce in [tex]\(9.36 \times 10^2\)[/tex] weeks, you multiply the number of light bulbs produced each week by the number of weeks:

[tex]\[(4.56 \times 10^3) \times (9.36 \times 10^2)\][/tex]

When you multiply numbers in scientific notation, you multiply the coefficients and add the exponents. So:

[tex]\[(4.56 \times 10^3) \times (9.36 \times 10^2) = (4.56 \times 9.36) \times (10^3 \times 10^2)\]\[= 42.6816 \times 10^{3+2}\]\[= 42.6816 \times 10^5\][/tex]

Now, we rewrite [tex]\(42.6816\)[/tex] in scientific notation:

[tex]\[42.6816 = 4.26816 \times 10^1\][/tex]

So, the total number of light bulbs the company will produce is:

[tex]\[4.26816 \times 10^1 \times 10^5 = 4.26816 \times 10^{1+5} = 4.26816 \times 10^6\][/tex]

In scientific notation, the best estimate of the number of light bulbs the company will make in [tex]\(9.36 \times 10^2\) weeks is \(4.27 \times 10^6\).[/tex]

What is 60% out of 20

Answers

it is 20% because it is 20 out of 60%
I hope this helps you out

How do you solve the problem

Answers

Since the two labelled angles are corresponding angles, they are equal.
10x = 9x + 10
Subtract both sides by 9x 
x = 10
Also, if you need to know, the angle length is 100 degrees.

Have an awesome day! :)

Solve the inequality 2 ways
Which is easier?

Answers

hope this help to answer you question.

after driving 117 km 3/5 of a trip is completed how long is the total trip how many more kilometers must be driven to complete the trip simplify your answer

Answers

the trip will be completed after 195 km

The printer charges $4 per book to print it, and you spent $3500 on advertising. you sell the book for $15 a copy. How many copies must you sell so that your income from sales is greater than your total cost?

Answers

15x > 4x + 3,500 ($15 per copy must exceed $4 per copy of a printer and an initial amount of $3,500 from advertising)
11x > 3,500 (Simplify, subtract 4x from both sides)
x > 318 2/11 (Divide both sides by 11)
You cannot sell part of a book, so you round to the higher whole number.
You must sell at least 319 books.
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