The student got the solution to the quadratic equation wrong at step 2
What are quadratic equations?A quadratic equation is a mathematical equation in which it's higher power of unknown is 2.
A quadratic equation can be solved by using 4 different method of choice which are formula method, factorization method , completing the square and graphical method.
x^2+4x-12=0 is an example of quadratic equation.
using factorization method to solve the value of x
x^2+6x-2x-12=0
grouping the equation
(x^2+6x)(-2x-12)=0
x(x+6)-2(x+6)=0
(x+6)(x-2)=0
for the equation to be satisfied
(x+6)=0
or
(x-2)=0
Therefore x= -6 or+2
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Jenna bought a new car for $29,000. She paid a 10% down payment and financed
the remaining balance for 48 months with an APR of 4.5%. Determine the monthly
payment that Jenna pays.
If the remaining balance for 48 months with an APR of 4.5%. the monthly payment that Jenna pays is: $595.17.
How to find the monthly payment?Using this formula to determine the monthly payment
P = A ×r × ( 1 +r)^n ÷( 1+ r)^n -1
Where:
P = Principal = ?
A = Amount = $29,000 × ( 1- .10) = 26,100
r = Interest rate = 4.5% / 12 = 0.00375
n = number of months = 48 months
Let plug in the formula
P = 26,100 × 0.00375 × ( 1+ 0.00375)^ 48 ÷ ( 1+ 0.00375)^ 48 -1
P = 26,100 × 0.00375 × ( 1.00375)^ 48 ÷ ( 1.00375)^ 48 -1
P = 26,100 × 0.00375 × 1.196814377 ÷ 1.196814377 -1
P = 26,100 × 0.00375 × 1.196814377 ÷ 0.196814377
P = $117.1382456 ÷ 0.196814377
P = $595.17
Therefore $595.17 is the monthly payment.
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Find the measures of angle B (questions 1-6)
Answer:
1)
b = 42° (corresponding angles, parallel lines)
2)
b + 31 + 90 = 180 (sum of angles on a straight line=180)
b = 59°
3)
b + 34 = 180 (sum of angles on a straight line=180)
b = 146°
4)
b + 30 + 90 = 180 (sum of angles on a straight line=180)
b = 60°
5)
b + 35 + 90 = 180 (sum of angles on a straight line=180)
b = 55°
6)
b = 58° (alternate angles, parallel lines)
There is a negative correlation between the number of years in college and earnings.
Please select the best answer from the choices provided
Or T
F
Answer:
F (false)
Step-by-step explanation:
i hope this helps! Have a good day! c:
Assuming a direct proportion between the distance and time, how far would they travel in 5 hours?
A family taking a road trip vacation travels 126 miles in 3 hours.
We can calculate the constant of proportionality as:
[tex]\frac{126\text{ miles}}{3\text{ hours}}=42\text{ miles/hour}[/tex]Then, in 5 hours they would travel:
[tex]d=5\text{ hours}\cdot\frac{42\text{ miles}}{1\text{ hour}}=210\text{ miles}[/tex]In 5 hours they would travel 210 miles.
what percentage grade should a road have if the angle of elevation of the road is 44 degrees? (the percentage grade is defined as the change in the altitude of the road over a 100100 -foot horizontal distance. for example a 5%5% grade means that the road rises 55 feet for every 100100 feet of horizontal distance.)
For a 44° elevation angle, the grade will be 96%.
Given that,
if the angle of elevation of the road is 44 degrees,
The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)
A tangent ?
One of the six basic trigonometric functions is tangent, denoted as tan().
The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.
[tex]tan \alpha = sin\alpha /cos \alpha[/tex]
The tangent of the angle is the ratio of rise to run.
tan(angle) = grade
tan(44°) ≈ 0.96 = 96%
Therefore, The grade will be 96% for an angle of elevation of 44°.
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Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the
day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19,
22, 25}
Which equation represents the growth of the puppy?
Select one:
O
O
y = x + 3
y = 3x + 10
y = 10x + 3
y = x + 10
Equation (B) "y = 3x + 10" represents the growth of the puppy.
What are equations?An equation is a mathematical formula where the "equal to" sign appears between two expressions having the same value. Like 3x plus 5 equals 15, for example. Different types of equations exist, such as linear, quadratic, cubic, and others. The three primary forms of linear equations are the slope-intercept form, standard form, and point-slope form.So, the equation that represents the situation:
The weight increase is: (10, 13, 16, 19, 22, 25)We can observe that every time, there is a rise of 3lbs of weight.Now, let 10 be a constant as the weight is starting from 10 lbs.And 'x' be the number of time Salomon tracks the weight.Then:
y = 3x + 10For example, Salomon checks the weight for the 6th time then:
y = 3x + 10y = 3(5) + 10y = 15 + 10y = 25So, the equation is correct.
Therefore, equation (B) "y = 3x + 10" represents the growth of the puppy.
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The correct question is given below:
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19, 22, 25}
Which equation represents the growth of the puppy? Select one:
A. y = x + 3
B. y = 3x + 10
C. y = 10x + 3
D. y = x + 10
the population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard deviation is 15 milligrams. assume the variable is normally distributed. (a) find the probability the cholesterol content for a single egg is between 210 and 220. (b) find the probability the average cholesterol content for 25 eggs is between 210 and 220. (c) find the third quartile for the average cholesterol content for 25 eggs. (d) if we are told the average for 25 eggs is less than 220 mg, what is the probability the average is less than 210 mg?
Using the normal distribution, the probabilities are given as follows:
a) Between 210 and 220 for a single egg: 0.2586 = 25.86%.
b) Between 210 and 220 for the average of 25 eggs: 0.8164 = 81.64%.
c) Third quartile for the average of 25 eggs: 213 milligrams.
d) Less than 220 if less than 210: 0.1011 = 10.11%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation for the cholesterol levels are given as follows:
[tex]\mu = 215, \sigma = 15[/tex]
For item a, the probability is the p-value of Z when X = 220 subtracted by the p-value of Z when X = 210, hence:
X = 220:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (220 - 215)/15
Z = 0.33
Z = 0.33 has a p-value of 0.6293.
X = 210:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (210- 215)/15
Z = -0.33
Z = -0.33 has a p-value of 0.3707.
Hence the probability is:
0.6293 - 0.3707 = 0.2586.
For item b, we are dealing with a sample of 25, hence we apply the Central Limit Theorem as follows:
n = 25, s = 15/sqrt(25) = 3.
X = 220:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (220 - 215)/3
Z = 1.33
Z = 1.33 has a p-value of 0.9082.
X = 210:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (210 - 215)/15
Z = -1.33
Z = -1.33 has a p-value of 0.0918.
Then the probability is:
0.9082 - 0.0918 = 0.8164 = 81.64%.
The third quartile is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.675 = (X - 215)/3
X - 215 = -0.675 x 3
X = 213.
The conditional probability in item d is calculated as follows:
P(X < 210)/P(X < 220) = 0.0918/0.9082 = 0.1011 = 10.11%.
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hi I circled the answer but I just need to figure out how to do it
Let's begin by listing out the information given to us:
216^(-2n) = (1/6)^(3n+2)
6 is a factor of 216: 216 = 6³
1/6 = 6^(-1)
⇒ 6^(-2*3n) = 6^[(-1*(3n+2)]
⇒ 6^(-6n) = 6^(-3n-2)
Since both sides are in the same base, we equate the exponents. We have:
-6n = -3n - 2
Add "6n" from both sides, we have:
-6n + 6n = -3n + 6n - 2 ⇒ 0 = 3n - 2
⇒ 3n = 2
Two cars are initially 10 miles parat on the same straight road and are moving towards each other. One car is going 30 miles per hour and the other car is going 36 miles per hour. How far apart are the two cars 2 minutes later?
Answer:
Let's break down the given information.
Car A
Speed - 30 mph
Hence the distance traveled per minute would 30/60 mph which is 0.5 Miles every minute.
Car B
Speed - 36 mph
The distance traveled per minute would 36/60 mph which is 0.6 Miles every minute.
Initial distance between the cars is 10 Miles
Car A travels 1 miles in 2 minutes and Car B travels 1.2 miles in 2 minutes.
Hence to calculate the distance between the 2 cars we need to calculate
Initial distance - Distance travelled by Car A - Distance traveled by Car B
Which is
10 - 1 - 1.2
7.8 Miles distance between the 2 cars
please help me understand...
Answer:
A
Step-by-step explanation:
It is given that lines k and p are parallel. You also know that angles 2 and 3 are equal because of vertical angles. Due to the parallel lines, you can say that angles 1 and 2 are equal because they are corresponding angles (same-side).
These two angles are not alternate interior angles because angle 1 is exterior and on the same side as angle 2. The third option would not make sense because you are trying to prove two angles are equal, not that lines are parallel.
A package contains 11 resistors, 2of which are defective. If 4 are selected find the probability of getting the following results.P(1 defective)=
From the given values, we know there are 2 defective resistors and 9 not defective. then, we have
[tex]P(1\text{ defective)=}\frac{C^9_3\times C^2_1}{C^{11}_4}[/tex]where
[tex]C^9_3[/tex]denote the combinations of 9 elements taking in 3, that is 3 good resistor from the 9 which are not defective. Similarly,
[tex]C^2_1[/tex]denotes the combinations of 2 elements taking in 1, that is, 1 defective resistor form the 2 defective resistors.
Then, we have
[tex]P(1\text{ defective)=}\frac{84\times2}{330}[/tex]then, the answer is
[tex]P(1\text{ defective) =}0.509[/tex]apesville is a utopian island of 5000 square kilometers. there are currently 250,000 inhabitants of the island. last year, there were 12,000 new children born and 10,000 people were recorded as deceased. in how many years will the population of apesville double?
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Ans
Find the Tem 90 is in the
Ap-10₁-8,-6,-4
Answer:
a₉₀ = 168
Step-by-step explanation:
there is a common difference between consecutive terms, that is
- 8 - (- 10) = - 6 - (- 8) = 4 - (- 6) = 2
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 10 and d = 2 , then
a₉₀ = - 10 + (89 × 2) = - 10 + 178 = 168
a researcher obtains a list of all prisons in the u.s. she draws a random sample of 75 of the prisons on this list. she then obtains a list of all inmates from the warden at each of the 75 prisons and interviews a random sample of 30 inmates at each prison. this is a:
The researcher draws a random sample using a Multistage cluster sample
At each stage, you use smaller and smaller groups (units) to select a sample from a population. National surveys are frequently used to collect data from a large, geographically dispersed group of people. To use as your sample, you randomly select individual units from the cluster.
In multistage cluster sampling, the population is divided into clusters and some clusters are chosen in the first stage. You continue to break up the selected clusters into smaller clusters at each subsequent stage, and you do this until you reach the final step. In the final step, only a few members of each cluster are chosen for your sample.
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I need this answered please
The rate of the slowest car is 86 km/hr using the concept of relative velocity.
What is Relative velocity?Relative speed is the rate at which one moving body moves in relation to another. The differential between two moving bodies determines their relative speed while they are traveling in the same direction. However, when two bodies are traveling in opposition to one another, the relative speed is determined by averaging their respective speed.
Let the speed of 1st car is v₁.
Let the speed of 2nd car is v₂.
v₁- v₂ = 18 km/hr --- (1)
And using the concept of relativity.
S(rel) = D(rel)/time
S(rel) = 360 / 2
S(rel) = 190
v₁ + v₂ = 190 --- (2)
Adding equations 1 and 2 we get
v₁ = 104 km/hr
v₂ = 86 km/hr
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A bag contains:• 3 red marbles• 2 2 orange marbles• 1 yellow marble• 4 green marblesA marble is drawn from the bag and replaced 150times. How many times can you predict that a greenmarble or yellow marble will be drawn?
The probability of getting a green of a yellow marble can be determined like this:
Probability = (yellow marbles + green marbles) / total number of marbles
Probability = (1 + 4) / 10
Probability = 5 / 10
Probability = 1/2
By multiplying the given probability by the number of times a marble will be drawn, we get how many times we can predict that a green or a yellow marble will be picked, then we get:
Number of predictions = 150 × 1/2
Number of predictions = 75
Then, the answer is 75 times
Answer:
75 times.
Step-by-step explanation:
There are a total of 10 marbles in the bag.
Probability a green marble is drawn (in 1 draw) = 4/10 = 2/5.
In 150 draws you can expect to draw 150* 2/5 = 60 green marbles.
Probability a yellow marble is drawn (in 1 draw) = 1/10.
In 150 draws you can expect to draw 150* 1/10 = 15 yellow marbles.
So, the number of times for a green or yellow marble
= 60+15= 75.
Need an explanation why it’s 46.4
(Please help I need this asap)
Answer:
9 + 7 + 7.2 = 23.2
23.2 x 2 = 46.4
Step-by-step explanation:
-5/2 can be simplified?
If it can be simplified, would the answer be a fraction or a decimal?
Answer: -2 1/2 or -2.5
Step-by-step explanation:
Yes, it can be simplified.
-5/2 can be simplified to -2 1/2 which can be as a decimal as -2.5
5. Estimation What is the greatest possible integer solution of the inequality
3.806x< 19.902?
The greatest possible integer of the inequality is 19.902.
What is the inequality?
In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, as to if it is less than or greater than. The different inequality symbols, properties, and methods for resolving linear inequalities inside one variable and two variables will all be covered in this article along with examples.
Given that,
3.806< 19.902
In which, less than inequality is used.
The given numbers are in decimal form.
comparison be between the given numbers and check which one is greater.
3.806< 19.902
19.902 is the greater than 3.806
Hence, the greatest possible integer is 19.902.
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Simplify the expression, 2√54x8 - 4√24x8
Answer:
[tex]-2\sqrt{} 6x^{8}[/tex]
Step-by-step explanation:
f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))
Answer: 19
Step-by-step explanation:
[tex]g(5)=5-2=3\\\\\impies f(g(5))=f(3)\\\\=3(3)+10=19[/tex]
Which of the following rational functions is graphed below?
Answer: A.
Step-by-step explanation:
1. The function is even (symmetric about the y-axis)
2. The function F(x) is positive
[tex]\displaystyle\\Hence,\\F(x)=\frac{1}{x^2}[/tex]
1 billion, 1 million compare and give the factor
Answer:
1000000
Step-by-step explanation:
100000000: 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5
100000: 2 2 2 2 2 5 5 5 5 5
GCF: 2 2 2 2 2 5 5 5 5 5
The Greates Common Factor (GCF) is: 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 = 100000
Please help! Consider the following diagram where the regular polygon ABCDE has center at M, polygon DEHGF is irregular, and point D is on CF.Which of the following statements are correct? Select all that apply.
Solution:
From the given diagram;
The statements that are correct about the given diagram are
b)
[tex]m\angle EDC=108\degree\text{ \lparen Interior angle of a regular pentagon\rparen}[/tex]d) The sum of exterior angles of a polygon is 360°,
Hence, the sum of the exterior angles of polygon ABCDE and the sum of exterior angles of polygon DEHGF is 720°
e)
[tex]m\angle ABM=m\angle DCM[/tex]The lines represented by the equations
12
y
−
4
x
=
84
12y−4x=84 and
y
=
−
3
x
+
8
y=−3x+8 are
The two linear equations are perpendicular.
What are the lines?
Here we have the two linear equations:
12y - 4x = 84
y = -3x + 8
If we write both of them in the slope-intercept form (as the second one) we will get:
12y - 4x = 84
12y = 4x + 84
y = (4x + 84)/12
y = (1/3)*x + 7
Now, if we take the product of the slopes of the two lines, we get:
p = -3*(1/3) = -1
when this product is -1, the lines are perpendicular, so that is the relation between our lines.
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Given vectors a=(3, 2) and b=(-5, 6), find – 3a+2b.Write your answer in component form.-3a + 2b =
Vector a = (3, 2), then;
[tex]-3a=-3(3,2)\text{ = (-9,-6)}[/tex]Also, vector b = (-5, 6), then;
[tex]2b=2(-5,6)=(-10,12)[/tex]Then, -3a + 2b = (-9, -6) + (-10, 12)
[tex]\begin{gathered} -3a+2b=(-9+(-10),-6+12)_{} \\ -3a+2b=(-19,6) \end{gathered}[/tex]The answer is (-19,6)
haresh is writing a coordinate proof involving an isosceles triangle. haresh places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis. what coordinates should he assign to this third vertex of the isoceles triangle?
The third vertex of the isosceles triangle is (a/2, b).
Let one vertex of the triangle lies on the base of the x-axis as 'a' which is written as (a,0)
Similarly, the other vertex of the triangle lies on the base of the y-axis as 'b' which is written as (0,b)
Let other vertex be at origin (0, 0)
An isosceles triangle is a triangle that has at least two sides of equal length.
Hence, the vertex of the triangle is (a/2, b).
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23 - x < 23(1 + 7x)
What does x equal???
[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]
without given any restriction x is all the numbers greater than 0.
NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
The rental price of a dacha was $9000. At the end of each month
the price is increased by 6%.
a) Find the price of the house after 1 month.
b) Find the price of the house after 3 months.
c) Find the price of the house after 10 months
a) The price (amount) of the house after 1 month = $9540
b) The price (amount) of the house after 3 months = $10719.14
c) The price (amount) of the house after 10 months = $16117.629
a ) How to find the rental price of the house after 1 month ?
The rental price of a dacha = Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 1
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]
The rental price of the house after 1 month = $9540
b ) How to find the rental price of the house after 3 months ?
The rental price of a dacha = Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 3
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]
The rental price of the house after 3 months = $10719.14
c ) How to find the rental price of the house after 10 months ?
The rental price of a dacha =Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 10
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]
The rental price of the house after 10 months = $16117.629
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a container of milk contains 8 cups of milk. if paul sets aside $1\frac{2}{5}$ cups of milk for use in a recipe and divides the rest evenly among his three children, how much milk should each child receive? express your answer as a mixed number.
Each child will receive the 1.1 cup of milk.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that a container of milk contains 8 cups of milk. if paul sets aside [tex]1\dfrac{2}{5}[/tex] cups of milk for use in a recipe , then we get the leftover;
8 - [tex]1\frac{2}{5}[/tex] = 8 - 7/5
= 40- 7/5
= 33/5
= 6.6
The the rest cups of milk = 6.6
Then the rest evenly among his three children 6.6/3 = 1.1
Hence, Each child will receive the 1.1 cup of milk.
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