Use a quadratic equation to find two real numbers that satisfies the situation. The sum of the two numbers is 2, and their product is –48.

Answers

Answer 1

Final answer:

To find two real numbers whose sum is 2 and product is -48, we form a quadratic equation x^2 - 2x - 48 = 0. Using the quadratic formula, we get two pairs of numbers (8, -6) and (-6, 8) that satisfy the given conditions.

Explanation:

To find two real numbers that satisfy the given conditions, namely their sum being 2 and their product being –48, we can set up a system of equations or use a . Let's denote the two numbers as x and y. We know:

x + y = 2xy = -48

We can express y in terms of x from the first equation: y = 2 - x. Substituting this into the second equation gives us:

x(2 - x) = -48

This simplifies to a quadratic equation:

x^2 - 2x - 48 = 0

Using the, x = (-b ± √(b^2 - 4ac)) / (2a), with a = 1, b = -2, and c = -48, we find the two possible values for x, which in turn gives us the corresponding values for y:

x = (2 ± √(4 + 192)) / 2

x = (2 ± √196) / 2

x = (2 ± 14) / 2

Therefore, the two solutions are x = 8 or x = -6. Since we were looking for two numbers, using x + y = 2, the corresponding y values are y = -6 and y = 8, respectively. Hence, the two pairs of numbers that satisfy the conditions are (8, -6) and (-6, 8).

Related Questions

ed is using the recipe shown to make fruit salad he wants to use 30 diced stawberries in his vruit sald how many bananas apples and pears should ed use in his fruit sald

Answers

We know that 1 serving = 4 bananas
3 apples
6 pears
and 20 strawberrys
To get 30 we need to half 20 =10 20+10=30

That means we also needs to half the other ones
1/2 of 4 = 2 4+2=6
1/2 of 3 = 1.5 3+ 1.5=4.5
1/2 of 6 = 3 6+3=9

6 Bananas
4.5 Apples
9 Pears
30 strawberries diced.

Answer:

Step-by-step explanation:

Which of the following statements about bullying is true? A. Children will independently learn positive behaviors as they mature B. Bullying is not harmful. C. Bullying is just a phase and children will grow out of it. D. Types of bullying include physical, verbal, emotional, and cyberbullying.

Answers

D is correct........ .

Types of bullying include physical, verbal, emotional, and cyberbullying about bullying is true. Correct option is D.

Option D is the correct statement. Bullying can take various forms, and the four main types of bullying are physical (e.g., hitting, pushing), verbal (e.g., name-calling, teasing), emotional (e.g., spreading rumors, excluding someone), and cyberbullying (bullying that takes place online or through digital means). It is essential to recognize and address these different types of bullying to create a safe and supportive environment for children and prevent harm.

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Tasha earns $400 per week plus a commission of 10% on her weekly sales. Each week she saves of her earnings. In the expression , what does the expression 400 + 0.1s represent in this situation?

the amount Tasha saves each week
the amount Tasha earns each hour
Tasha's weekly commission
Tasha's weekly earnings

Answers

D.) Tasha's weekly earnings.

Tasha makes a commission and an hourly wage, so B and C are out.

And it couldn't be A because Tasha could save more or spend more, either way D is the best answer

Answer:

its D

Step-by-step explanation:

How many sides does a polygon have if the sum of interior angles is 11700

Answers

The sum of the measures of the interior angles of a polygon of n sides is
180(n - 2)

180(n - 2) = 11700

n - 2 = 65

n = 67

It has 67 sides.

Assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of $26,000 and a standard deviation of $5000. what is the cutoff salary for teachers in the bottom 10%?

Answers

To solve this we would need to find the bottom 10% z-score and find c such that Pr(X<c)=0.1. We find that c = -1.2815 using normal distribution. The cutoff salary for teachers in the bottom 10% would be X=26000 + 5000 x (-1.28155) or 19,592.24.

Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. Her graph is shown below. What are the solutions of –x2 + 4x = x – 4? A.–5 and 0
B.–5 and –1
C.–1 and 4
D.0 and 4

Answers

C -1 and 4 i just did the test on this

Answer

C.–1 and 4

Explanation

Solving the equations y = –x² + 4x and y = x – 4

–x² + 4x = x – 4

x² - 4x + x = 4

x² - 3x = 4

x² - 3x + (3/2)² = 4 + (3/2)²

(x - 3/2)² = 4 + 9/4

= 6.25

x - 3/2 = √6.25 or x - 3/2 = -√6.25

x = 2.5 + 1.5 x = -2.5 + 1.5

= 4 = -1

1. Find the length (distance) of segments AB, CD, and EF.

AB =

CD =

EF =
2. Find the midpoint of segments AB, CD, and EF.

AB =

CD =

EF =

3. Find the slope of the segments AB, CD, and EF.

AB =

CD =

EF =

Answers

1. AB = 7 units
CD= 3 units
EF= 5 units
2.AB= (-0.5, 2)
CD= (-4,-2.5)
EF=(2.5,-3)
3.AB=0
CD=undefined
EF=-4/3

Answer:

1) AB=7 CD=3 EF=[tex]3\sqrt{5}[/tex] 2) [tex]M_{AB}=\frac{-1}{2},2[/tex] [tex] \\ M_{EF} =(\frac{5}{2}-3)[/tex] \\ [tex] \\ M_{EF} =(\frac{5}{2}-3)[/tex] 3) AB not inclined CD not inclined EF 6/5

Step-by-step explanation:

1) We can use the Distance Formula to answer the 1st. question.

But in the first case AB I'd rather doing it intuitively because it is a straight line parallel to the x-axis

A(-4,2) and B(3,2)

In this segment, also parallel we can calculate the length as |-4|+|3|=7 since both have the same y coordinate.

Using the Distance formula to check it:

[tex]D=\sqrt{(3--4)^{2}+(2-2)^{2}}\\D=\sqrt{49}\\D=7[/tex]

C(-4,-1) D(-4,-4)

Similar to the first one but this time with different y coordinates.

The length will be calculated by subtracting the absolute values for y:

|-4|-|-1|=4-1 = 3

Using the Distance formula to check it:

[tex]D=\sqrt{(-4--1)^{2}+(-4--4)^{2}}\\D=\sqrt{9}\\D=3[/tex]

E (1,-1) F(4,-5)

In this case there's no straight line.

So right to the Distance Formula:

[tex]D=\sqrt{(-5-1)^{2}+(4-1)^{2}}\\ D=\sqrt{36+9}\\D=\sqrt{45}\\D=3\sqrt{5}[/tex]

2) To find the Midpoints we need to calculate the Mean of these two points.

A(-4,2) and B(3,2)

[tex]M_{AB} =\frac{-4+3}{2},\frac{2+2}{2}\\M_{AB}=\frac{-1}{2},2[/tex]

C(-4,-1) D(-4,-4)

[tex]M_{CD} =\frac{-4-4}{2} ,\frac{-1-4}{2} \\M_{CD} =(0,\frac{-5}{2})[/tex]

E (1,-1) F(4,-5)

[tex]M_{EF} =\frac{4+1}{2} ,\frac{-1-5}{2} \\ M_{EF} =(\frac{5}{2}-3)[/tex]

3) To find the Slope let's calculate the quotient of a difference between y-coordinates over x-coordinates of two given points.

[tex]m_{AB}=\frac{2-2}{3--4}=\frac{0}{7}=0[/tex]

AB is not inclined.

C(-4,-1) D(-4,-4)

[tex]m_{CD}=\frac{-4--1}{-4--4}=\frac{-3}{-4+4}=\frac{-3}{0}[/tex]

Not Defined for all Real Set of Numbers

The line CD is not inclined.

E(1,-1) F(4,-5)

[tex]m_{EF}=\frac{-5-1}{4--1}=\frac{6}{5}[/tex]

The line EF has a slope of 6/5

Shirley measures the thickness of a piece of cardboard with a ruler that has centimeter and inch markings. Which of the following is most likely the value that Shirley measures?

Answers

Centimeter would most likely use to measure the thickness

3 inches is most likely what she measures because the ruler only has inches and centimeters so inches would be more logical

A student earned 37 out of 50 points on the last test. What percent correct did the student earn?

Answers

percent = part / whole * 100

% correct = 37/50 * 100 = 74%

The answer is: " 74% " .
_____________________
% = percent = parts per 100 = x/ 100 ;

37/50 = x/100 ;

Looking at the denominators;

50 * (what value?) = 100 ?

→ 100 ÷ 50 = 2 ;

So; 50 * 2 = 100 ;

So; 37/50 = (37*2) / (50*2) = 74/100 = 74 % .
_______________________________________
The answer is: " 74% " .
_______________________________________

work out the height of a parallelogram with a base of 10m and an area of 60m2

Answers

Area formula of a parallelogram is
A = base x height

Given are the
Area = 60 m² and base = 10 m

Substitute the given:

60 = 10h (divide by 10 to find value of h)
[tex] \frac{60}{10} = \frac{10h}{10} [/tex] (10 and 10 cancels out)

h = 6
The height of a parallelogram with a base of 10m and an area of 60m² is 6m

Write a compound inequality to represent all of the numbers between -4 and 6.

Answers

-4 < x < 6

could also be : x > -4 and x < 6

Answer:-4 < x < 6

Step-by-step explanation:

The price of a set of kitchen cabinets is $1,500 in January. In February, the price is increased by 10%. After not selling, the price is reduced by 5% in March. What is the price in March?

Answers

The answer would be 1,567.50

What do you do if you're looking for least common multiple and all your numbers are prime?

Answers

It’s important to remember the distinction between “greatest common factor” and “least common multiple.” A factor of a particular number is a bit like a multiplicative LEGO piece that makes it up; they’re the numbers that other natural numbers can be broken down into by division. A multiple is the opposite; a number and the number that it’s multiplied by (say, 8 x 5) *become factors* of a new number (40, in this case).

When we talk about finding the “least common multiple” of a set of numbers, what we’re asking is this: if you list out multiples of each number, what’s the *first* number in those lists they all have in common? For instance, if we wanted to find the least common multiple between 3 and 5, we could list out their multiples:

3, 6, 9, 12, 15, 18, 21
5, 10, 15, 20, 25, 30

15 is the first multiple that appears in both lists, so the least common multiple of 3 and 5 is 15.

Problem page a light bulb consumes 2400 watt-hours per day. how many watt-hours does it consume in 3 days and 6 hours?

Answers

Calculate for 3 days: 2,400 x 3 = 7,200

Calculate 1 day per hour: 2,400 ÷ 24 = 100
Calculate for 6 hours: 100 x 6 = 600

7,200 + 600 = 7,800 watt-hours

Final answer:

The light bulb consumes 7800 watt-hours in 3 days and 6 hours, calculated by summing the daily consumption over three days and additional energy consumed in 6 hours.

Explanation:

To calculate the energy consumption in watt-hours, we first understand that the light bulb consumes 2400 watt-hours in one day. To find out how much it consumes in 3 days and 6 hours, we multiply the daily consumption by the number of days and then add the consumption for the additional 6 hours:

Energy consumed in 3 days = 2400 watt-hours/day imes 3 days = 7200 watt-hours

Energy consumed in 6 hours = (2400 watt-hours/day) / (24 hours/day) imes 6 hours = 600 watt-hours

Adding these two amounts gives us the total energy consumption in the specified time:

Total energy consumption = 7200 watt-hours + 600 watt-hours = 7800 watt-hours

Therefore, the light bulb consumes 7800 watt-hours in 3 days and 6 hours.

The length of a side of an equilateral triangle is 12. find the length of the altitude

Answers

Final answer:

To calculate the altitude of an equilateral triangle with side length 12, divide the side by 2 and multiply by [tex]$\sqrt{3}$[/tex] giving an altitude of approximately 10.3923 units.

Explanation:

To find the length of the altitude of an equilateral triangle with a side length of 12, you can use the Pythagorean theorem. The altitude of the equilateral triangle creates two 30-60-90 right triangles. The altitude is the longer leg in this case, and the side of the triangle is the hypotenuse. In a 30-60-90 triangle, the longer leg (altitude) is [tex]$\sqrt{3}$[/tex]times the shorter leg (half of the side of the triangle).

First, divide the side of 12 into two to get the shorter leg of the right triangle, which is 6. Then, multiply 6 by $\sqrt{3}$ to find the length of the altitude. This results in:

[tex]$6 \times \sqrt{3} = 6\sqrt{3} \approx 10.3923$[/tex]

Therefore, the altitude of the equilateral triangle is approximately 10.3923 units long.

divide this polynomial:
(x^2-6x-20) divided by (x+2)
* if someone would be able to tell me how to divide this it would be very MUCH appreciated

Answers

Hi!

So I'll show you how to divide the polynomial step-by-step

First you want to write this out like any long division problem.

After that you need to see what times x is x^2?

x*x is x^2 so you want to write x over -6x, you have to make sure that you write it over the same degree term.

Now you multiply both x and 2 (which came from the x +2) by x (which was what you wrote in your first part of the quotient)

Then you subtract what you got from multiplying the x and 2 by x (you should have gotten -8x)

Now you want to bring down the next term in the dividend.

So you want to see what times x is -8x? (This should be -8)

Now you write -8 in the quotient. Now your quotient should be x-8.

After that, you want to multiply x+2 by the -8 and subtract again. (you should get -4)

Since you've filled in the last space in your quotient you have a remainder of -4. Remember to write the remainder as a fraction, -4/x+2

Hope this helped! Let me know if you still have any questions!

hi friend
here's your answer looking for

u can take the help of the attachment here

hope you are satisfied with my answer

Which ordered pair is a solution to this equation? 2x+3y=16 A.) (11, 1)
B.) (7,2)
C.) (5,2)
D.) (3,2)

Answers

C.) (5,2) as we put these values in the above equation we get 16 on both sides and hence the equation is satisfied.if we put values in the above equation the answer is `16. from above equation 2x+3y=16 put x=5 y=2 2(5)+3(3)=16

5,2 is the answer, this is such easy question my baby brother could do it easy

To find the value of an expression is called

Answers

We have learned that, in in an algebraic expression, letters can stand for numbers. When we substitute a specific value for each variable, and then perform the operations, it's called evaluating the expression. Let's evaluate the expression 3y + 2y when 5 = y.

Tony is now three years older than howard. five years ago the sum of their ages was 59. now, tony is

Answers

Tony's age now is 36.

The Tony age and Howard age be 36 and 33 respectively.

It is required to find the age of tony.

What is age?

The amount of time during which someone or something has lived or existed. The length of time that a person has lived or a thing has existed.

Given:

Let Howard age=x

Tony age=x+3

Before 5 year we have,

Howard age=x-5,

Tony age=x+4-5=x-1

Some of there age=59

According to given question we have,

x-5+x-1=59

2x-6=59

2x=65

X=65/2

x=32.5

The age can't be fraction or decimal so we take 33.

Howard age=33

Tony age=33+3=36

Therefore, the Tony age and Howard age be 36 and 33 respectively.

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The cost of an oil change is $21.95. The markup rate is 65%. What is the selling price?

Answers

the answer is $36.22 because you need to times 21.95 by 0.65 and you get 14.27 and add that to the original price.

it $36.22 because you need to times 21.95 by 0.65 and you get 14.27 and add that to the original price.

because i already did this

Matt has a block. He uses one of the flat surfaces of the block to trace a triangle. What type of solid figure is Matt's block?

Answers

it will be a square since the surface area is 3-D

The types of 3D objects on which one face is triangular are triangular prism, triangular-based pyramid, and square-based pyramid so Matt's solid figure can be anyone among the three.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given,

Matt used a 3D block to draw a triangle on the paper.

Now in order to draw a triangle there are three types of 3D objects that can be used,

01) Triangular prism,

02) Triangular-based pyramid

03) Square-based pyramid

Hence "The types of 3D objects on which one face is triangular are triangular prism, triangular-based pyramid, and square-based pyramid so Matt's solid figure can be anyone among the three".

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The great pyramid in Egypt was built around 2560 BC over the years it has lost 30 feet of height off its top and is now 451 feet tall. Find the original height of the great pyramid

Answers

You add 30+451= 481

the number of peaches, p, is three less than half the number of grapes, g. which expression represents the number of peaches in terms of the number of grapes
A.g/2-3
B.2g-3
C.g-3/2
D.3g-2

Answers

peaches = 3 less than one half the number of grapes

so from the written problem you can get:

p=1/2g-3

1/2g is the same as g/2

so answer is A. p= g/2-3

A patchwork blanket is made up of 10 identical squares.Liam has made 14 squares,Raj has made 12 squares and Gemma has made 15 squares.How many patchwork blankets have they made between them ?

Answers

they will make 4 blankets, because when you add the patchwork squares they have made 41 patchwork squares, so 41 divided by 10 is 4, with one left over

They can make one each so in total three blankets because each one can only make one. This is because they all make patches and assuming that they all make them identical in their own piles then they would only be able to make 3 with some left over from each

I need help solving 206x12

Answers

206
X 12
--------
2472

The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 2. What percent of the class is boys?

Answers

60% please make me as the most brainlyest

since the ratio is boys to girls 3:2.
Then the percentage is 3/5 which then can be changed to 60 %

When the Citizens United decision was handed down, a flood of corporate cash was expected to enter the political system. The ruling did result in more corporate and union spending, but far less than anticipated because__________.?

Answers

Many businesses and organizations were afraid of taking stances on hot-button topics or candidates. There was a fear that this would alienate a sector of their membership or customer base, and would therefore be seen as a risky investment. Much of the money that was raised was from individual donors, in actuality.

The measure of each interoir angle of a regualr polygon is 144 . how many sides does this polygon have

Answers

Each Interior Angle = 180 - (360 / number of sides)
# of sides = -360 / (Each Interior Angle -180)
# of sides = -360 / (144 -180)
# of sides = -360 / -36
# of sides = 10

How is interest similar to sales tax in markup

Answers

Sales tax, interest, and markup is a raise in the money of a cost. Hope I helped: )

4.624 to the nearest 10m

Answers

4620 mhope this helps

The value of the decimal number 4.624 to the nearest 10 places is 4.6

What is rounding off the numbers?

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.

Given decimal number is 4.624. The rounding off is:-

4.624 = 4.6 at 10 places

Therefore, the value of the decimal number 4.624 to the nearest 10 places is 4.6

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