A quadratic equation is shown below: 9x2 − 16x + 60 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answers

Answer 1

9x^2 - 16x + 60
Find the discriminant, b^2 - 4ac, which is the same as the value of the radicand.
(-16)^2 - 4 * 9 * 60 = -1904
Since the discriminant is negative, there will be NO real solutions, and 2 complex solutions.

Part B.
4x^2 + 8x - 5 = 0
You can tell if a quadratic is factorable if you find the discriminant and it is a perfect square. The discriminant for this quadratic is 144 so it is factorable.
(2x + 5)(2x - 1) = 0
Set each factor equal to zero.
2x + 5 = 0 2x - 1 = 0
subt 5 from both sides add 1 to both sides
2x = -5 2x = 1
divide both sides by 2 divide both sides by 2
x = -5/2 x = 1/2

Related Questions

On a test hailey answered 64 out of 75 questions correctly. What percent of her answers
Were correct?

Answers

Answer:

[tex]\bold{85\frac13\,\%}[/tex]

Step-by-step explanation:

[tex]\dfrac{64}{75}\cdot100\,\%=\dfrac{64}{3}\cdot4\,\%=\dfrac{256}{3}\,\%=85\frac13\,\%[/tex]

Which expressions are equivalent to 3(x + 3y + 2x − y)?

Answers

3(x + 3y + 2x − y) = 3(3x + 2y)
= 9x + 6y
See if any of these match an answer option.

Use distributive property, and simplify like terms.

3(x + 3y + 2x - y)
= 3(x) + 3(3y) + 3(2x) + 3(-y)
= 3x + 9y + 6x - 3y
= 9x + 6y

Therefore, 9x + 6y is equal to 3(x + 3y + 2x - y)

Also, 9x + 6y can be factored into 3(3x + 2y).
3(3x + 2y)
= 3(3x) + 3(2y)
= 9x + 6y

So this pair is equivalent: 3(3x + 2y) and 9x + 6y

Ira purchased a new dishwasher for $361.35. The dishwasher was on sale for 17.5% off. What was the original price of the dishwasher, to the nearest dollar?

Answers

Answer: $438
To solve this equation, you cross multiply. I first subtracted 17.5 from 100 in order to get the percentage value that $361.35 was of its original price. Since 100 - 17.5 = 82.5, the washing machine is 82.5% of its original price.

I cross multiplied by writing [tex] \frac{361.35}{1} * \frac{82.5}{100} [/tex], and multiplying [tex]361.35 * 100[/tex] and [tex]82.5 * 1[/tex]. The result was [tex] \frac{36135}{82.5}[/tex]. This becomes $438. There is no rounding needed to be done.

The original price of the dishwasher with a 17.5 percentage discount is $361.

We have,

To find the original price of the dishwasher, we need to figure out what the discount amount is and subtract it from the sale price.

The discount amount is 17.5% percentage of the original price, which can be expressed as:

Discount amount = 0.175 x Original price

We can rearrange this equation to solve for the original price:

Original price = Discount amount / 0.175

The discount amount is:

Discount amount = 0.175 x $361.35 = $63.25

So the original price of the dishwasher was:

Original price = $63.25 / 0.175 = $361.43

Rounding this to the nearest dollar gives an original price of $361.

Thus,

The original price of the dishwasher with a 17.5 percentage discount is $361.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ7

In which situation is the distance traveled proportional to time? A: An airplane landing
B;A soccer ball you kick across a field C:A person running on a treadmill at 3 mph for 6 minutes D:A 3 -minute ride on a roller coaster

Answers

Answer:

Step-by-step explanation:

you add it my g

Answer:

C: A person running on a treadmill at 3mph for 6 minutes

Step-by-step explanation:

I just had the question and got it right.

Translate the sentence into an inequality.

Three subtracted from b is less than or equal to −17.

Answers

B-3 [less than or equal to sign] -17

"Three subtracted from b" = b-3

"is less than or equal to" = ≤

"-17" = -17

Putting it all together...

b-3≤-17

What's 2 ways to write 100203

Answers

100000 + 200 + 3 (expanded form)

one hundred thousand two hundred and three (word form)

hope this helps

The center of an ellipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x = 14 1/12.
what is the equation that represents the ellipse?????????

Answers

The standard equation for an ellipse is
[tex] \frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1[/tex]
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes

Refer to the figure shown below.
The center of the ellipse is at (0,0).
Therefore, h=0, k=0.

One focus is at (12, 0)
Therefore
c = 12

One directrix is at 14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13

Because c² = a² - b², obtain
b² = a² - c²
= 169 - 144 = 25
b = 5

Answer:
The equation for the ellipse is
[tex] \frac{x^{2}}{169} + \frac{y^{2}}{25} =1[/tex]

Final answer:

The equation that represents the ellipse with the given coordinates of the center, one focus, and one directrix is x^2/144 + y^2/(25/12) = 1.

Explanation:

The equation that represents the ellipse with the center at (0, 0), one focus at (12, 0), and one directrix at x = 14 1/12 can be found using the standard form of the equation for an ellipse:

(x - h)^2/a^2 + (y - k)^2/b^2 = 1

where (h, k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.

Since the center is at (0, 0), the equation becomes:

x^2/a^2 + y^2/b^2 = 1

The distance from the center to one focus is 12, so the value of a is 12. To find the value of b, we need to use the distance from the focus to the directrix. Since the directrix is x = 14 1/12, the distance from the focus to the directrix is |14 1/12 - 12|. Simplifying, we get |14 1/12 - 12| = 2 1/12. Therefore, the value of b is 2 1/12.

Substituting these values into the equation, we get:

x^2/144 + y^2/(25/12) = 1

Learn more about Ellipse equation here:

https://brainly.com/question/33868440

#SPJ3

An acute angle θ is in a right triangle with sin θ = seven eighths. What is the value of cot θ?

ANSWERS
square root of fifteen divided by eight
eight divided by the square root of fifteen
seven divided by the square root of fifteen
square root of fifteen divided by seven

Answers

Draw a right triangle ABC, with m(CAB)=∅.

Let CB=7 units, AC=8 units, so by the Pythagorean theorem:

[tex]AB= \sqrt{ AC^{2} - BC^{2} }= \sqrt{ 8^{2} - 7^{2} }= \sqrt{64-49} = \sqrt{15} [/tex] (units)

so we have drawn a triangle where sin∅=7/8

in this triangle, cot∅=(adjacent side)/(opposite side)=[tex] \frac{ \sqrt{15} }{7} [/tex]

Answer: square root of fifteen divided by seven

How many feet are in 30 yards?

Answers

Hi!

For every 1 yard, we have 3 feet. So, in order to find out how many feet are in 30 yards - we must multiply 3 by 30.

3 * 30 = 90.

This means there are 90 feet in 30 yards.

Hopefully, this helps! =)

Answer:

90 feet

Step-by-step explanation:

Formula we use,

→ 1 yd = 3 ft

Then no of feet in 30 yards is,

→ 30 × 3

→ 90 ft

Hence, the answer is 90 ft.

In my block of 100 flats a painter is kept employed by painting one flat each month from January to November. The flats are painted in the same order and he takes a holiday every December. If my flat was last painted in August 2010 when will it be next painted?

Answers

January to November == 11 months.

11 flats are painted every year.

100 flats / 11 flats per year = 9 years + 1 month

the next time it will be painted is September 2019.

Answer:

The answer is September 2019.

Step-by-step explanation:

In order to determine the date of the painting flat, we have to know how the painter works.

Every year, the painter paints 11 flats, because he paints one flat each month and he doesn't work in December.

Also, if we consider that "my flat" is currently in the first position, we have to wait until the painter paints the 100 position because the painter has to paint 99 flats more.

So, "my flat was painted in August 2010", then the painter paints 3 flats more that year (September, October, November).

Now we add more painted flats every year:

3+11+11+11+11+11+11+11+11=91

At beginning of 2019, the painter has painted 91 flats. So in 9 months later, the painter will be paint the 100 position, that is in September 2019.

Finally "my flat" will be painted in September 2019.

How many tenths are equal to 4/5 mile using a diagram

Answers

4/5 as a decimal is 0.8

One tenth equals to 0.1

0.8 = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1

We need ten lots of 0.1 to make 0.8

Carlos can print a document on apricot printer which the speed is 8 in 4.5 minutes how long would it take him to print the same document on a sure-fire printer which the speed is 12

Answers

The apricot printer has a speed of 8.
The surefire printer has a speed of 12.

The surefire is faster than the apricot printer, so it wll take less time to print a document.
The apricot printer takes 4.5 minutes.
Therefore by proportion, the surefire printer takes
(8/12)*4.5 = 3 minutes.

Answer: 3 minutes

What is the prime factorization of 162?

Answers

2*3 to the power of 4

Prime factorization of 162:
Start by dividing by the smallest prime number.
162/2 = 81
81/3 = 27
27/3 = 9
9/3 = 3

2 * 3 * 3 * 3 * 3 = 2 * 3^4

60,000 is ten times as much as

Answers

is ten times as much as 6,000

10 times x=60000

x=6000

Which equation represents an exponential function with an initial value of 500

Answers

Exponential function is characterized by an exponential increase or decrease of the value from one data point to the next by some constant. When you graph an exponential function, it would start by having a very steep slope. As time goes on, the slope decreases until it levels off. The general from of this equation is: y = A×b^x, where A is the initial data point at the start of an event, like an experiment. The term 'b' is the constant of exponential change. This is raised to the power of x, which represents the independent variable, usually time.

So, the hint for you to find is the term 500 right before the term with an exponent. For example, the function would be: y = 500(1.8)^x.

There is a 70% chance of rain tomorrow and a 20% chance that the volleyball game will be postponed. What is the probability that it will rain tomorrow and the volleyball game will be postponed?

Answers

0.20/0.70 = 0.2857

28.6% chance

round the answer as needed.

I believe it is 14%

because 20% = 0.2 and 70% = 0.7

then 0.2 * 0.7 = 0.14

0.14 = 14%

14% is answer srry if wrong

What is an expression that is equal to 12m+12n

Answers

Since 12 = 3+9, we could write 3m+9m+12n = 12m+12n

a person or company that allows others to borrow money is called

Answers

Answer:

ummm its called a lender since that person is "lending" you something

Step-by-step explanation:

A person or company that allows others to borrow money is called a "lender".

What is a Lender?

A lender is a person, a group (public or private), or a financial organization that makes cash accessible to a person or business with the expectation of repayment. Payment of any interest or fees will be included in the repayment.

Repayment might take place in installments (such as a monthly mortgage payment) or as a flat amount. A mortgage is one of the largest loans that individuals obtain from lenders.

The loan duration varies depending on the type of debt. While some loans are for 1-2 years, the majority are for 6-12 months.

Thus, a person or company that allows others to borrow money is called a "lender".

To learn more about the Lender link is given below.

https://brainly.com/question/26106234

#SPJ2

Two trucks leave from the same truck stop at the same time. One travels east on interstae 80 and the other travels west. The eastbound truck averages 40 miles per hour, and the westbound truck averages 50 miles per hour. In how many hours will the trucks be 300 miles apart?

Answers

My answer comes out to 3hrs. Thats the closest i got to 300 Miles.

Answer:

About 3 hours

Step-by-step explanation:

Imagine one truck going West and the other East. One is going 50 miles per hour and the other is going 40 miles per hour. Because you need to use the equation 50x+40x=300. You should get x = 3.3.

If f(x)= -x²+3x+5, find f(-3), f(0), f(2), f(5), and f(8).

Answers

f(-3)
-(-3)^2+3(-3)+5
-9-9+5
-18+5
-13 <======

f(0)
-(0)^2+3(0)+5
-0+0+5
5 <=======

f(2)
-(2)^2+3(2)+5
-4+6+5
7 <=======

f(5)
-(5)^2+3(5)+5
-25+15+5
-5 <======

f(8)
-(8)^2+3(8)+5
-64+24+5
-35 <======

use the numbers 2,3,5, and 8 to write an expression that has a value of -1

Answers

(5 x 3) - (8 x 2) = -1

Cat breeders often mate cats that have special traits that they will pass on to offspring. This is an example of

Answers

probably it is inherited trait????

blame it on me if you get it wrong:C

Video DVDs (ignoring the hole in the middle) have an area of 36π cm^2 The formula to calculate the circumference, C, for a circle is c=2√Aπ, where A is the area of the circle. What is the circumference of the disc?
12πcrr
18πcrr
24πcrr
30πcrr

Answers

it's 12π, because √36=6. 6×2= 12 :)

Final answer:

The circumference of a DVD with an area of 36π cm^2 is 12π cm.

Explanation:

The question asks for the circumference of a DVD with an area of 36π cm2. The circumference C of a circle is related to its area A by the formula C = 2√(Aπ). In this case, we need to substitute the given area of the disc into the formula to calculate the circumference.

First, we'll start by plugging in the area into the formula:

C = 2 √(36π π)
C = 2 √(36)√(π)√(π)
C = 2 × 6 × π
C = 12π

Therefore, the circumference of the disc is 12π cm.

what is ten times as much as 4.9

Answers

it would be 4.9 x 10 so 49

Final answer:

The question wants to find out what is ten times as much as 4.9. By multiplying 4.9 by 10. The answer is 49.

Explanation:

The student is asking about multiplication which is an operation in Mathematics. In this case, the student wants to know what is ten times as much as 4.9. To find the answer, we need to multiply 4.9 by 10. The multiplication process is as follows:

4.9 x 10 = 49

So, ten times as much as 4.9 is 49.

Learn more about Multiplication here:

https://brainly.com/question/5992872

#SPJ2

HELP??
A scatter plot is shown below

Which two ordered pairs can be joined to draw most accurately the line of best fit on this scatter plot?

(4, 9.5) and (10, 5.5)
(5, 0) and (10, 10)
(0, 6) and (5, 0)
(0, 9.5) and (10, 1.5)

Answers

The correct answer is (0, 9.5) and (10, 1.5).

Answer: The correct answer is D!

Step-by-step explanation:

-8*-4^2/7

i got 32/7?

Answers

The answer is: " -128 / 7 ; or; " -18 6/7 " ;
or: " -18.2857142857142857 " ; or, round to: " -18.286 " .
_____________________________________________________

Using the correct order of operations, the "exponents" function come first.

The problem is written:
__________________________
" -8*-4^2/7 " ,

In this case, we take the "-4² " ; which is: " (-4)*(-4) = 16.

Then we do the multiplication and division, in the order in which they occur, from left to right.

So, we would have: " (-8)*(16) = -128. \

Then: " (-128)/ 7 = -18.2857142857142857 = -18 6/7 " .

or: round to: " -18.286 " .
________________________________________________________

Please help to solve... Need steps

Answers

x + y = 360
x =0.25y

substitute x = 0.25y into x + y = 360
x + y = 360
0.25y + y = 360
1.25y = 360
y = 288

x = 288 (0.25) = 72

Jose has 72 stamps
Maria has 288 stamps

288 - 72 = 216

answer
Maria has 216 more stamps than Jose

help me please. I don't know how to do this. so can you take me step by step if possible.

Answers

Ok divide 3.15 and 9 by nine. You will get .35 over one or .35 of a cup. Next divide 2.4 and 8 by 8 you will get .3 or .30. Finally, subtract .35 by .30 and you will get .05.

You are studying for your final exam of the semester. up to this point, you received 3 exam scores of 67%, 68%, and 78℅. to receive a grade of C in the class, you must have an average exam score between 70% and 79% for all 4 exams including the final.

Answers

(67 + 68 + 78 + x) / 4 = 70
(213 + x) / 4 = 70
213 + x = 70 * 4
213 + x = 280
x = 280 - 213
x = 67

(213 + x) / 4 = 79
213 + x = 79 * 4
213 + x = 316
x = 316 - 213
x = 103

lowest u can make is 67, highest u can make is 100

Answer: its 68,100 on plato

What is the place value of 8 in 0.829

Answers

the answer is the tenths place

The 8 is in the tenths place, the 2 is in the hundredths place, and the 9 is in the thousandths place. Hope this helps, please mark brainliest Have a great night.

Other Questions

In what ways does lennie meet george's need for a companion The step of making a tentative plan in the troop-leading procedure usually has six steps. what is step six? What pronoun completes Tu_das los regalos a ellos. Help? Sampling A toy bin has twenty toys in it, five of each type. Storm wants to know which type of toy he would pick if he pulled out one.Which of the following would be the most appropriate sampling technique? A. He could use a spinner with four equal-sized sections, one for each toy. B. He could make a chart to show all of the toys that other people pulled out. Molecules containing a large number of hydroxyl groups are What is hooke's law? does it apply to elastic materials or to inelastic materials? The area, a, of an ellipse can be determined using the formula a=TTxy where x and y are half the lengths of the largest and smallest diameters of the ellipse. Which is an equivalent equation solved for y How does the video make the atom bomb seem less threatening than it actually was? Why did the London Company send settlers to Virginia Socialist economies have experienced a recent slowdown in growth because of: An ore contains fe3o4 and no other iron. the iron in a 36.6-gram sample of the ore is all converted by a series of chemical reactions to fe2o3. the mass of fe2o3 is measured to be 29 g. what was the mass of fe3o4 in the sample of ore? How many citizens did the constitution initially mandate that each member of the house of representatives should represent? Spanish speakers? help? Choose the best translation for the following sentence. I know the truth. Yo sabo la verdad. Eric plans to rent a Beach House for a week. He has a coupon for 20% off the daily base rate of $200. He will also have to pay an additional $20 a day for utilities. Which expression represents the situation. (d represents the number of days) Article I, Section 8 of the Constitution describes what kind of congressional powers? a. properb. expressedc. reservedd. necessary Uranium-233 undergoes alpha decay, and then the daughter isotope undergoes another alpha decay. Which equation correctly describes this decay series? Use the periodic table link from the tools bar to answer the question. A citys population, P (in thousands), can be modeled by the equation P = 130( 1.03)^x where x is the number of years after January 1, 2000. For what value of x does the model predict that the population of the city will be approximately 170,000? Why is the development of agriculture called a revolution What effect does adding a constant have on a exponential function? By how much does a^3 - 2a exceed a^2 + a - 6? Steam Workshop Downloader