Step-by-step explanation:
[tex] \tt{2 {x}^{2} + x - 15 = 0}[/tex]
USING THE QUADRATIC FORMULA :
Here ,
a = 2 , b = 1 and c = - 15Substitute the values into the quadratic equation :
⇾ [tex] \tt{x \: = \: \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} \: }{2a} }[/tex]
⇾ [tex] \tt{x = \frac{ - 1\: ± \: \sqrt{ {1}^{2} - 4 \times 2 \times ( - 15) } }{2 \times 2}} [/tex]
Simplify
⇾ [tex] \tt{x = \frac{ -1 \:± \sqrt{1 - 8 \times ( - 15)} }{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 1\:± \: \sqrt{1 + 120} }{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 1 \:± \: \sqrt{121} }{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 1\: ± \: \sqrt{ {11}^{2} } }{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 1 \:± \: 11 }{4}} [/tex]
Now , we can split this into two answers because of the plus minus ( ± ) symbol.
Taking positive ( + ) sign :
⇾ [tex] \tt{x = \frac{ - 1+ 11}{4}} [/tex]
⇾ [tex] \tt{x = \frac{10}{4}} [/tex]
⇾ [tex] \boxed{ \tt{x = \frac{5}{2} }}[/tex]
Again , taking negative ( - ) sign :
⇾ [tex] \tt{x = \frac{ - 1 - 11}{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 12}{4}} [/tex]
⇾[tex] \boxed{ \tt{x = - 3}}[/tex]
☥ [tex] \red{ \bold{ \boxed{ \boxed{ \tt{Our \: final \: answer : x = \frac{5}{2} \: or \: - 3}}}}}[/tex]
⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆
[tex] \underline{ \underline{ \sf{Explore \: more !!}}} : [/tex]
There are various methods of solving quadratic equations. They are as follows :
Solving a quadratic equation by factorisation method : In this method , the second order of polynomial ax² + bx + c is factorised and expressed as the product of two linear factors. Then each linear factors is separately solved to get the required solutions of the equation by applying zero factor property. In zero factor property , if p • q = 0 then either p = 0 or q = 0 .In other words , if the product of two numbers is 0 , then one or both of the numbers must be zero.Solving a quadratic equation by completing the square : In this method , we transpose the constant term ( c ) to R.H.S , then L.H.S to expressed as perfect square expression.Solving a quadratic equation by using formula : In solving a quadratic equation of the form ax² + bx + c = 0 by completing the square , we obtain two roots of x , which are :[tex] \sf{ \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a}} [/tex] and [tex] \sf{ \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a}} [/tex]. These roots can be written as [tex] \sf{x = \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} }{2a}} [/tex] where a is the coefficient of x² , b is the coefficient of x and c is the constant term. We use this formula to find the required solutions of the given quadratic equation.Hope I helped! ツ
Have a wonderful day / night ! ♡
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The solutions to the quadratic equation [tex]2x^{2} + x - 15[/tex] are x = 2.5 and x = -3.
Given data:
The quadratic equation is represented as [tex]2x^{2} + x - 15[/tex].
Now, the roots are determined as:
[tex]x_{1}=\frac{-b+\sqrt[]{b^{2}-4ac} }{2a}[/tex]
[tex]x_{2}=\frac{-b-\sqrt[]{b^{2}-4ac} }{2a}[/tex]
The value of a = 2 , b = 1, and c = -1.5
Substituting the values in the equation:
[tex]x_{1}=\frac{-1+\sqrt[]{1^{2}-4*2*(-1.5)} }{2*2}[/tex]
So, the value of [tex]x_{1}=2.5[/tex].
[tex]x_{2}=\frac{-1-\sqrt[]{1^{2}-4*2*(-1.5)} }{2*2}[/tex]
The value of [tex]x_{2}=-3[/tex].
So, the roots are x = 2.5 and x = -3.
Hence, the quadratic equation is solved.
To learn more about quadratic equations, refer:
https://brainly.com/question/25652857
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Which ordered pair, when graphed, would not show a function?
(miles per gallon, gallons in tank)
(length of shadows/time of day)
(temperature in F, temperature in C)
O (number of employees, number of hours worked)
Answer: its the last answer I got it right
How many solutions does y=−2x−4
y=3x+3 have
Answer:
There is one solution
Answer:
It has one (-1.4,-1.2)
Step-by-step explanation:
I graphed both lines on desmos graphing calculator and they only crossed at one point.
Ms.Heinen's desk is 3 feet by 2 feet. What is the area of her desk?
Answer: The area would be 6 feet
Step-by-step explanation:
To find the area, we multiply the length and width
What is the GCF of the polynomial given below?
60ax - 40ay + 50az
Answer: 10a, all of the numbers can be divided by 10a
10a (6x − 4y + 5z) = 60ax - 40ay + 50az
Match the expression to the correct property that is shown.
Question 3 options:
Identity Property of Addition 1.
9+2+(4+3)=9+(2+4)+3
2.
y(xz)=(yx)z
3.
4+3+2=2+4+3
4.
5x ∙ 0=0
5.
-12 + 0 = -12
6.
−110×1=−110
7.
m∙4∙3=4∙m∙3
8.
4(3x+1)=12x+4
Associative Property of Addition
Commutative Property of Addition
Commutative Property of Multiplication
Identity Property of Multiplication
Multiplicative Property of Zero
Associative Property of Multiplication
Distributive Property
Answer:
Step-by-step explanation:
This is a help site, so I'll explain each property and see if you can match them yourself.
Associative property of addition, you can add 3 or more different numbers any which way, the sum will be the same.
Commutative Property of Addition - same as the associative property but with 2 numbers.
Identity Property of Multiplication - Any number multiplied by one is itself
Multiplicative Property of Zero: x * 0 = 0
Associative Property of Multiplication - Same as that of addition, yet with multiplication.
Distributive Property: Factoring Out.
EX: (12 x 15) = 3(4 x 5)
In ΔEFG, is it possible for segment GE to measure 4 units?
A. No, because 3 + 5 > 4, 5 + 4 > 3, and 4 + 3 > 5
B. Yes, because 3 + 5 4, 5 + 4 > 3, and 4 + 3 > 5
Answer:
Substitution
Step-by-step explanation:
We essentially have x = 180 and a+b+c = x.
So we are just substituting x for a+b+c
solve. 7/20n = 8/5. enter a fraction or a whole number
Answer:
7/32
Step-by-step explanation:
[tex]\frac{7}{20n}=\frac{8}{5}[/tex]
we can multiply the elements on the diagonal so
20n*8=7*5
160n=35
we divide the relation by 160
n=35/160=7/32
Help please! Help me please! I don’t understand! I’ll give you brainly!
Answer:
Its a monomial of degree 0
Step-by-step explanation:
pls mark brainliest
Answer:
The expression represents a polynomial. The polynomial is a monomial and has a degree of 1
Step-by-step explanation:
First lets look at the definitions of these words:
Monomial means that there is only one term in the equation
Binomial means there is 2 terms
Trinomial means there is 3
and polynomial means 4 or more
The equation would be a monomial because it only has 1 term in it.
Now lets look at the degree.
To find the degree lets take a look at how to make radicals into exponents
So you have [tex]-\sqrt{2}[/tex]
You know that when you square root something, the degree of the radical sign is 2.
That is not the degree its asking for though. Its asking for the degree of 2
In exponential form the equation is [tex]-2^{\frac{1}{2} }[/tex]
Reason for this being that the numerator is the exponent for whatever is inside the radical sign while the denominator is for the square root symbol.
So if you have [tex]-2^{\frac{3}{4} }[/tex] for example, the radical form is [tex]-\sqrt[4]{2^{3} }[/tex]
So the numerator would be the degree.
If there is no degree for the function, as in you don't see an exponent then that means the exponent = 1
If you need further assistance don't be afraid to reach out. I hope this helps!
The figure below is made up of two rectangular prisms.
3 m
7 m
10 m
4 m 1 m
Find the volume of the entire figure by adding the volumes of the separate figures.
Volume = 120 +
cubic meters
Answer:
Total Volume = 190 m³Step-by-step explanation:
Volume of the entire figure = L (Area 1 + Area 2)
where L = 10 m
Area 1 (blue prism) = 4 x 3 = 12 m²
Area 2 (brown prism = 1 x 7 = 7 m²
plugin values into the formula:
Volume of the entire figure = L (Area 1 + Area 2)
= 10 (12 + 7)
= 120 m³ + 70 m³
= 190 m³
Rewrite in simplest terms: -0.2t - 5 (-8t + 5)
Answer: 40.2t - 25
Step-by-step explanation:
-0.2t - 5 (-8t + 5)
-0.2t + 40t -25
39.8t - 25
An amusement park charges $5 for admission and $.80 for each ride. You go to the park with $13. Which inequality represents this situation
Answer:
Answer Placeholder (I'm going to solve it and answer when I'm done)
Step-by-step explanation:
write an equation in point slope form for the line through the given point with the given slope (-4, -3); m=8
Answer:
An equation in point-slope form for the line will be:
[tex]y - (-3) = 8 (x - (-4))[/tex]
Please check the attached line graph also.
Step-by-step explanation:
Given
The point (-4, -3)
The slope m = 8
To determine
Write an equation in point slope form for the line.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line(x₁, y₁) is the pointIn our case,
(x₁, y₁) = (-4, -3)The slope m = 8substituting the values m = 8 and the point (-4, -3)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - (-3) = 8 (x - (-4))[/tex]
Therefore, an equation in point-slope form for the line will be:
[tex]y - (-3) = 8 (x - (-4))[/tex]
Please check the attached line graph also.
The ratio of boys to girls in a class is 5:7.
There are 36 students in the class.
How many more
girls than boys are there?
Answer:
6 more girls than boys
Step-by-step explanation:
7+5=12
36 divided by 12 = 3
3x7=21
3x5=15
Advance Algebra Logarithm Task
Assume your friend, Natalie, has $10,000 to invest. Complete the following chart to show how
much she would earn if her money was invested in each of the specified accounts for 10 years.
Frequency of Annual interest Formula with values Amount after 10
compounding
substituted in
years
Quarterly 3.65%
Monthly
3.65%
Continuously
3.6%
rate
Which account would you suggest for Natalie? Continuously
9514 1404 393
Answer:
3.65% monthly
Step-by-step explanation:
The same amount is invested for the same period in all accounts, so we only need to determine the effective annual rate in order to compare the accounts.
For compounding annual rate r n times per year, the effective annual rate is ...
(1 +r/n)^n -1
For the same rate r, larger values of n cause effective rate to be higher. As a consequence, we know that 3.65% compounded quarterly will not have as great a yield as 3.65% compounded monthly. The effective rate for the monthly compounding is ...
(1 +0.0365/12)^12 -1 = 3.712%
The effective rate for continuous compounding is ...
e^r -1
For a continuously compounded rate of 3.6%, the effective annual rate is ...
e^0.036 -1 = 3.666%
This tells us the best yield is in the account bearing 3.65% compounded monthly.
_____
If i is the effective annual rate of interest as computed by the methods above, then the 10-year account balance will be ...
10000×(1 +i)^10
This is the formula used in the spreadsheet to calculate the balances shown.
The amount people who pay for cell phone service varies quite a bit, but the mean
monthly fee is $55 and the standard deviation is $22. The distribution is not Normal.
Many people pay about $30 for plans with 2GB data access and about $60 for 5GB
of data access, but some pay much more for unlimited data access. A sample survey
is designed to ask a simple random sample of 1,000 cell phone users how much they
pay. Let x be the mean amount paid.
Part A: What are the mean and standard deviation of the sample distribution of X?
Show your work and justify your reasoning. (4 points)
Part B: What is the shape of the sampling distribution of x? Justify your answer. (2
points)
Part C: What is the probability that the average cell phone service paid by the
sample of cell phone users will exceed $56? Show your work. (4 points) (10 points)
INTL
Answer:
a) The mean is $55 and the standard deviation is $0.6957
b) The shape of the sampling distribution of x is approximately normal.
c) 0.0749 = 7.49% probability that the average cell phone service paid by the sample of cell phone users will exceed $56.
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
Mean of the distribution: 55
Standard deviation of the distribution: 22
Sample of 1000.
This means that:
[tex]\mu = 55, \sigma = 22, n = 1000[/tex]
Part A: What are the mean and standard deviation of the sample distribution of X?
By the Central Limit Theorem, the mean is 55 and the standard deviation is [tex]s = \frac{22}{\sqrt{1000}} = 0.6957[/tex].
Part B: What is the shape of the sampling distribution of x?
By the Central Limit Theorem, the shape of the sampling distribution of x is approximately normal.
Part C: What is the probability that the average cell phone service paid by the sample of cell phone users will exceed $56?
This is 1 subtracted by the pvalue of Z when [tex]X = 56[/tex]. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 55}{0.6957}[/tex]
[tex]Z = 1.44[/tex]
[tex]Z = 1.44[/tex] has a pvalue of 0.9251
1 - 0.9251 = 0.0749
0.0749 = 7.49% probability that the average cell phone service paid by the sample of cell phone users will exceed $56.
answer quickly please Which number is the BASE?
2 = 8
Answer:
The base of the number is 8
Can you help me with this question?
Are the equations y – 5 = 2(x – 1)and y - 3 = 2(x + 3) the same equation? Explain
Answer:
No.
Step-by-step explanation:
y - 5 = 2(x - 1)
y = 2x + 3
y - 3 = 2(x + 3)
y = 2x + 9
Please help, will read you with Brainliest. Please check ALL that apply.
Answer:correct answers are:
A.m<JPX=90°
B.XY & JK form right angles
E. JP=KP
F.XY⊥JK
Step-by-step explanation:
hope this helps
what percent is a is b? pls help i need it right away
Answer:
what ???????????????????? repost this question
Whenever Jean sees the white streaks left in the sky by an airplane, she excitedly tells her kids it's Buzz Lightyear. One day, her son asked her how fast Buzz could fly. Jean, knowing that Buzz is really an airplane, told him about 500 miles per hour. How many feet per second can Buzz travel? Show your work, friends.
Answer:
The Buzz can travel 733.33 feet per second.
Step-by-step explanation:
An hour has 60 minutes, each of which has 60 seconds. So one hour has 60*60 = 3600 seconds.
The airplane can fly 500 miles per hour. Each mile has 5280 feet. So the plane can fly 500*5280 = 2640000 feet in one hour.
Per second, we have:
[tex]\frac{2640000}{3600} = 733.33[/tex]
The Buzz can travel 733.33 feet per second.
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!
Answer: C isn't correct.
Step-by-step explanation:
C is NOT correct
The equation that represents the situation is y = 50x not x = 50y
Hope I helped! :3
can u pls help me with this question
Answer:
0.12$ , I'm probably wrong lolol
a piggy bank has $6.95 and contains only nickles and dimes. If there are a total of 91 coins, how many nickles are there
Answer:
There are 43 nickels in the piggy bank.
Step-by-step explanation:
Given that:
Number of coins = 91
Worth of coins = $6.95 = 6.95*100 = 695 cents
Let,
x be the number of nickles
y be the number of dimes
According to given statement;
x+y=91 Eqn 1
5x+10y=695 Eqn 2
Multiplying Eqn 1 by 5
5x+5y = 455 Eqn 3
Subtracting Eqn 3 from Eqn 2
(5x+10y)-(5x+5y)=695-455
5x+10y-5x-5y=240
5y = 240
[tex]\frac{5y}{5}=\frac{240}{5}[/tex]
y = 48
Putting y=48 in Eqn 1
x+48=91
x=91-48
x= 43
Hence,
There are 43 nickels in the piggy bank.
Using powers of ten, which would be the best choice for the first number to subtract in the division problem 4860 divided by 15?
Identify all the corresponding angles below. Select all that apply.
Answer:
A,B,D,E
Step-by-step explanation:
hope u get to right
6) A garden measures p metres by 3p + 2 metres.
a) Write an expression that describes the perimeter of the garden.
b) The garden has a perimeter of 76 metres. Write an equation to show this.
c) Solve your equation to find the value of p.
ALL WORKING OUT NEEDED
p = 18.5
Step-by-step explanation:
a. to find perimeter you have to add all the sides together
So if one side is p, and the other side is 3p+2, just add them together like this
p + 3p + 2, then combine the ps so the expression is
4p + 2
b. now you find out the perimeter is 76
So put the original expression of your perimeter and 76 together like this
4p + 2 = 76
c. So now solve the equation
4p + 2 = 76
subtract 2 from both sides to get the ps alone
4p = 74
now divide by 4 to get the p by itself
74 ÷ 4 is 18.5, or 18 1/2
So p = 18.5 or 18 1/2
Rewrite each of the following expressions so that the number inside the radical is as small as possible. For example, rewrite √18 as 3√2.
√50=
√28=
√252=
Answer:
1) [tex]\mathbf{\sqrt{50}= 5\sqrt{2} }[/tex]
2) [tex]\mathbf{\sqrt{28}= 2\sqrt{7} }[/tex]
3) [tex]\mathbf{\sqrt{252}= 6\sqrt{7} }[/tex]
Step-by-step explanation:
We need to simplify the radicals:
1) [tex]\sqrt{50}[/tex]
First we find prime factors of 50
50 = 2 x 5 x 5
Now,
[tex]\sqrt{50}\\=\sqrt{2\times 5\times 5}\\=\sqrt{2\times 5^2}\\ =\sqrt{2} \sqrt{5^2}\\=5\sqrt{2}[/tex]
So, [tex]\mathbf{\sqrt{50}= 5\sqrt{2} }[/tex]
2) [tex]\sqrt{28}[/tex]
First we find prime factors of 28
28 = 2 x 2 x 7
Now,
[tex]\sqrt{28}\\=\sqrt{2\times 2\times 7}\\=\sqrt{2^2\times 7}\\ =\sqrt{2^2} \sqrt{7}\\=2\sqrt{7}[/tex]
So, [tex]\mathbf{\sqrt{28}= 2\sqrt{7} }[/tex]
3) [tex]\sqrt{252}[/tex]
First we find prime factors of 252
50 = 2 x 2 x 3 x 3 x 7
Now,
[tex]\sqrt{252}\\=\sqrt{2\times 2\times 3\times 3 \times7}\\=\sqrt{2^2\times 3^2 \times7}\\ =\sqrt{2^2} \sqrt{3^2}\sqrt{7} \\=2\times 3\sqrt{7}\\=6\sqrt{7}[/tex]
So, [tex]\mathbf{\sqrt{252}= 6\sqrt{7} }[/tex]
1. (04.01 LC)
Which unit rate is equivalent to 14 miles per gallon? (1 point)
2 gallons/32 miles
32 miles/2 gallons
3 gallons/42 miles
42 miles/3 gallons
Answer:
42 miles/3 gallons
Step-by-step explanation: Multiplying 14 by 3 and 1 by 3 will give you 42/3, which keeps the unit ratio.
Answer:
42 miles/3 gallons
Step-by-step explanation:
math geeks please help :(
9514 1404 393
Answer:
7th grade: 16
5th grade: 13
7th grade median is higher by 3 points
Step-by-step explanation:
There are 21 dots in each plot, so the median score will be the score associated with the 11th dot, counting from either end.
In the 7th-grade data, that dot is in the "16" column. The 7th grade median is 16.
In the 5th-grade data, that dot is in the "13" column. The 5th grade median is 13.
__
The 7th grade median is higher by 3 points.
_____
Additional comment
Your options for filling in the relationship of the scores are not shown. You may have to interpret the result according to the options available.