[tex]2 = {x}^{2} + 5x[/tex]
Arrange the expression into the standard form.[tex]0 = {x}^{2} + 5x - 2 \\ {x}^{2} + 5x - 2 = 0[/tex]
DiscriminantFrom the standard form equation and from the given equation.
[tex]a {x}^{2} + bx + c = 0 \\ a = 1 \: \: \: b = 5 \: \: \: c = - 2[/tex]
Discriminant Formula
[tex]D = {b}^{2} - 4ac[/tex]
Substitute the value of terms in the discriminant formula.
[tex]D = {(5)}^{2} - 4(1)( - 2) \\ D = 25 - 4( - 2) \\ D = 25 + 8 \\ D = 33[/tex]
Discriminant Types
[tex]D > 0 \: \: \: \: 2 \: \: real \: \: roots \\ D = 0 \: \: \: \: 1 \: \: real \: \: root \\ D < 0 \: \: \: imaginary \: \: roots[/tex]
We can rule out the Imaginary root and double root because the discriminant is greater than 0. Therefore, the only choices are either Irrational or Rational.
However, we cannot factor the expression by using two brackets or common factor. We can say that the equation has two real irrational roots.
Answerreal and irrational rootAlice walks 6/10 miles every day. how many miles does she walks 5 days?
3 miles
6 / 10 × 5 = 30 / 10
30 / 10 = 3
Please help I am having a really bad day and crying all the time.
Answer:
7 dollars
Step-by-step explanation:
I hope this helps and i hope you have better days and stop crying because life is way to short for all of that and i dont know you but you dont deserve to cry all the time you should be happy if you want to talk about anything im here!
help me plz One line of text on a page uses about 4/15 of an inch. There are 0.5-inch margins at the top and bottom of a page. Write and solve an inequality to find the number of lines that can be typed on a page that is 17 inches long.
Answer:
60 lines can be typed in the page
Step-by-step explanation:
Given:
Length of the page = 17 inches
Length of the margin = 0.5-inch
length of one line = 4/15
To Find:
The number of lines that can be typed on a page
Solution:
Let the number of line that can be typed be n
then
n <=
the top and bottom margins are 0.5 inches each
so we will be having
=>
=>
=>
=>
=>
If Matt buys 3 oranges for $2.79 at the fruit start, what is the rate per orange.
Answer:
the rate is $0.93 per orange
Answer: $0.93
Step-by-step explanation:
F(-2)=x^2-3x+4; find f(-2)
A triangle has sides with lengths of 8 miles, 15 miles, and 18 miles. Is it a right triangle?
Answer:
No
Step-by-step explanation:
for it to be a right triangle, a² + b² = c². C must be the larger of the 3 sides, which in this case is 18. if you substitute 8 for a and 15 for b, you do not get C = 18, meaning that this is not a right triangle
Miko has a vast collection of books in her library. English books make up
3
8
of her collection.
5
7
of the remaining books are Chinese books and the rest are German books. How many books are there in her book collection if there are 75 Chinese books?
Answer:
168 books
Step-by-step explanation:
Given
[tex]English = \frac{3}{8}[/tex]
[tex]Chinese = \frac{5}{7}[/tex] of the remaining books
Required
Determine the total number of books
If the proportion of the English books is 3/8, the the remaining is:
[tex]Remaining = 1 - English[/tex]
[tex]Remaining = 1 - \frac{3}{8}[/tex]
Take LCM
[tex]Remaining = \frac{8 - 3}{8}[/tex]
[tex]Remaining = \frac{5}{8}[/tex]
From the question, we understand that:
[tex]Chinese = \frac{5}{7}[/tex] of the remaining books
This means:
[tex]Chinese = \frac{5}{7} * \frac{5}{8}[/tex]
[tex]Chinese = \frac{5*5}{7*8}[/tex]
[tex]Chinese = \frac{25}{56}[/tex]
From the question, we also understand that 75 are Chinese books.
The total number of books can then be calculated using:
[tex]Chinese = \frac{25}{56} * Total[/tex]
Substitute 75 for Chinese
[tex]75 = \frac{25}{56} * Total[/tex]
Make Total the subject:
[tex]Total = \frac{56 * 75}{25}[/tex]
[tex]Total = \frac{4200}{25}[/tex]
[tex]Total = 168[/tex]
There are 168 books are there in her book collection if there are 75 Chinese books.
Given
Miko has a vast collection of books in her library.
English books = 3/8
Chinese books = 5/7.
Ratio proportion;A ratio is a comparison of two or more numbers that indicates their quantities in relation to each other.
The proportion of the English books is 3/8, the remaining is:
[tex]\rm Remaining\ books=1-\dfrac{3}{8}\\ \\ Remaining\ books=\dfrac{8-3}{8}\\\\ Remaining\ books=\dfrac{5}{8}[/tex]
Then,
Chines books = ratio of Chinese book × ratio of remaining books × Total books
[tex]\rm 75=\dfrac{5}{7}\times \dfrac{5}{8}\times Total \ books\\\\Total \ books =\dfrac{75 \times 7\times 8}{5\times 5}\\\\Total \ books =3\times 56\\\\Total \ books=168\\[/tex]
Hence, there are 168 books are there in her book collection if there are 75 Chinese books.
To know more about proportion click the link given below.
https://brainly.com/question/12674321
Help ASAP! And explain!
Answer:
Option (2)
Step-by-step explanation:
Given:
AC is an angle bisector of ∠DAB and ∠DAB
m∠BCA ≅ m∠DCA
m∠BAC ≅ m∠DAC
To Prove:
ΔABC ≅ ΔADC
Solution:
Statements Reasons
1). m∠BCA ≅ m∠DCA 1). Given
2). m∠BAC ≅ m∠DAC 2). Given
3). AC ≅ AC 3). Reflexive property
4). ΔABC ≅ ΔADC 4). ASA property of congruence
Therefore, Option (2) will be the correct option.
What is the radius of a circle with a diameter of 12 inches?
Answer:6
Step-by-step explanation:
the radius of a circle is half of the length of the diameter
Answer:
diameter of circle=12 inches
radius of circle = half of diameter
=12÷2
=6 inches
Nine times the sum of a number and ten is the difference of a number and six
Answer:
The answer is -2.
Select the point shown on the coordinate plane for each ordered pair. Point is located at (3, 9). Point is located at (9, 3). Point is located at (6, 5). Point is located at (5, 6).
Answer:
A D B C in ORDER
Step-by-step explanation:
Answer:
Point
✔ A
is located at (3, 9).
Point
✔ D
is located at (9, 3).
Point
✔ B
is located at (6, 5).
Point
✔ C
is located at (5, 6).
Step-by-step explanation:
I hope this helps doing the Assignment!
A package of spaghetti weighs 238 grams. How many ounces does the package weigh? 1 oz = 28 g.
Answer: 8.5
Step-by-step explanation: 238 / 28 = 8.5
8.5 oz
The package of spaghetti weighs 8.5 ounces.
To find out how many ounces the package of spaghetti weighs, we can use the conversion factor that 1 ounce is equal to 28 grams.
Given that:
package of spaghetti weighs 238 grams, we can convert this to ounces by dividing it by the conversion factor:
= 238 grams / 28 g/oz
= 8.5 ounces
Therefore, the package of spaghetti weighs 8.5 ounces.
Learn more about Unit Conversion here:
https://brainly.com/question/28600662
#SPJ6
The polygons are similar. Solve for x.
scale factor from A to B = 3:5
Answer:
9
Step-by-step explanation:
if scale factor is 3/5, then
(x+12):35=3:5, ⇒
[tex]\frac{x+12}{35} =\frac{3}{5}; x=21-12; x=9[/tex]
hey this subjects really hard for me can someone answer please its 50 points
The circumference of a roll of party streamers is 11 inches. The circumference decreases by 3 inches after you use the streamers to decorate for a birthday party. Find the diameter of the roll after the decrease. Round your answer to the nearest hundredth.
Answer:
2.54 inches
Step-by-step explanation:
Dakota and Justine are training to be in the Sweat for Fun Run. They ran the same distance on Saturday, but Dakota finished in less time. They each plan to run for the same amount of time on Sunday. If their average speeds are consistent, who will run farther on Sunday?
Answer:
Dakota will run farther on Sunday.
Step-by-step explanation:
when they ran the same distance Dakota finished first, so she ran more miles per hour than Justine did. If they both run at the same speed on sunday that they ran on saturday, dakota will run farther because her speed is greater than justine's speed
Answer:
Dakota will run farther on Sunday.
Step-by-step explanation:
Jordan has a checking account. he withdrew $90 from an ATM Tuesday. Thursday he deposited $20. Friday he wrote a check for $15 what was the total change in Jordan account
Answer:
The total change in his account is of -$85, that is, a loss of $85
Step-by-step explanation:
We combine these changes. So
On Tuesday, he withdrew $90 from his account, which means that, the total change, initially of $0, is now of -$90.
On Thusday, he deposited $20, which means that the total change of -$90 is now of -$90 + $20 = -$70
On Friday, he wrote a check of $15, removing 15 from his account, which means the total change will be of -$70 -$15 = -$85
36 x - 8y2 when x=3 and y= 6
Step-by-step explanation:
multiply the numbers
36×3=108. 8×6×2=96
subtract the numbers
108-96
=12
great day :)
Answer:
12
Step-by-step explanation:
x = 3
36 x 3 = 108
y = 6
8 x 6 x 2 = 96
= 108 - 96
= 12
Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. Roughly what percentage of regulation basketballs weigh more than 23.1 ounces
Answer:
13.567%
Step-by-step explanation:
We solve the above question, using z score formula
z = (x-μ)/σ, where
x is the raw score = 23.1 ounces
μ is the population mean = 22.0 ounces
σ is the population standard deviation = 1.0 ounce
More than = Greater than with the sign = >
Hence, for x > 23.1 ounces
z = 23.1 - 22.0/1.0
= 1.1
Probability value from Z-Table:
P(x<23.1) = 0.86433
P(x>23.1) = 1 - P(x<23.1)
P(x>23.1) = 1 - 0.86433
P(x>23.1) = 0.13567
Converting to percentage
= 0.13567 × 100
= 13.567%
Therefore, the percentage of regulation basketballs that weigh more than 23.1 ounces is 13.567%
plz solve for brainlyest
Answer:
1.80
Step-by-step explanation:
multiply the binomials (2x-7)(x-5)
Graphing Polynomial Functions
Graph the following functions by making a table
of values
f(x)=x^5-3x^4+9x^3-x^2+2
Answer:
table and graph attached
Step-by-step explanation:
Apply the distributive property to factor out the greatest common factor. 30 + 42
Answer:
The answer is 6(5+7)
Step-by-step explanation:
What is the slope of the function?
4. If Nick goes swimming 7 times, what would he need to pay with each payment plan? Which is
the best payment method for him?
5. If Nick goes swimming 9 times, what would he need to pay with each payment plan? Which is
the best payment method for him?
6. If Nick goes swimming 13 times, what would he need to pay with each payment plan? Which is
the best payment method for him?
Answer:
number 4 and plz thank me if this is right plz
(PLEASE HELP ASAP)
A plumber has a 12-foot piece of pipe. He needs 8 feet, 6 inches of pipe to repair a leak in a water line. How many inches of pipe will he have left after he makes the repair?
Answer:
3ft 6in or 42 inches in total
Step-by-step explanation:
hope this helps
What is the perpendicular slope of m=0?
Answer: The slope of a line perpendicular to a line with a slope of 0 is undefined. The perpendicular line is a vertical line. A line with a slope of 0 is a horizontal line.
Step-by-step explanation:
A radio DJ frequently announces how much money is currently in a jackpot. Every day several randomly selected residents are called and asked to identify the amount, and thereby win it. Those who keep track of the jackpot amount are most likely to be reinforced on a __________ schedule.
Answer:
"Variable interval" is the right solution.
Step-by-step explanation:
A variable-interval timetable seems to be a fiber-reinforced routine where another sensitivity or reaction would be commended because an unanticipated or unstable transaction has taken place, which would be the exact reverse of either a fixed-interval routine. The whole such schedule results in a slow or predictable, fairly constant targeted respondents.What is the simplest way to explain scale drawings for middle school math?
Answer:
The simplest way to teach middle school math scale drawings is to use real pictures to relate to each other to explain the concept. For example, scaling a red ball of 1" to a ball of 2" and so on. This will show how the ball increases by size by adding 1" each time.
Simplify the following expression. Rationalize all denominators.
Answer:
[tex]\frac{\sqrt{3}x}{2y^{\frac{2}{3} } }[/tex]
Step-by-step explanation:
√3x^6/√2x^4y^3
~Factor
(√3)x^3/(√2)x²y√y
~Cancel
(√3)x/(√2)y√y
~Rationalize
(√6)x/2y^(2/3)
Best of Luck!
