The vertex form of the quadratic equation is f(x) = -3(x - 2)² + 5. The coordinates of the vertex are (2, 5).
We are given a quadratic function. The equation of the quadratic function is f(x) = -3x² + 12x - 7. We need to convert the equation to vertex form. We can convert a quadratic equation to its standard vertex form by "completing the square" method. The calculations are done below.
f(x) = -3x² + 12x - 7
f(x) = -3(x² - 4x) - 7
f(x) = -3(x² - 4x + 2² - 2²) - 7
f(x) = -3(x² - 4x + 2²) - 7 + 3*2²
f(x) = -3(x - 2)² - 7 + 12
f(x) = -3(x - 2)² + 5
The coordinates of the vertex are (2, 5).
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The line crossing the point (2,-2) and with the slope = -6.
Two consecutive Integers have a sum of 67. Find the Integers.
Answer:
33, 34
Step-by-step explanation:
we must start solving this equation by letting a variable equal the smaller number
let n = smaller number
now the larger number is consecutive so you add one to n to get it
n + 1 is the bigger number
if you add them you get 67
n + n + 1 = 67
now solve
add like terms
2n + 1 = 67
subtract 1 from both sides
2n = 66
n = 33
the smaller number is 33
adding one to that will get you the larger integer
33 + 1 = 34
that is the larger integer
Topic 6: Writing Linear Equations
26. Write a linear equation that passes through
the point (-6, 1) with a slope of 1/2
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-6)}) \implies y -1= \cfrac{1}{2} (x +6) \\\\\\ y-1=\cfrac{1}{2}x+3\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+4 \end{array}}[/tex]
company x has 50 employees and company y has 60 employees. both companies have the same number of full-time employees, but company y has 3 more than twice the number of part-time employees that company x has. how many part-time employees does company y have?
Using the simplification, company y has 17 number of part-time employees.
In the given question we have to find how many part-time employees does company y have.
From the question, company x has 50 employees and company y has 60 employees.
Both companies have the same number of full-time employees, but company y has 3 more than twice the number of part-time employees that company x has.
Let company x has A number of part-time employees.
According the given statement
Company y has number of part-time employees = 2A+3
Let company X and Y have B number of full-time employees.
So the total number of employees in company x;
A+B = 50....................(1)
The total number of employees in company x;
2A+3+B = 60
Subtract 3 on both side we get
2A+B=57....................(2)
Subtract Equation 2 and 1
2A+B-(A+B)=57-50
2A+B-A-B=57-50
A=7
Now putting the value of A in equation 1
7+B=50
Subtract 7 on both side we get
B=43
As, Company y has number of part-time employees = 2A+3
Company y has number of part-time employees = 2×7+3
Company y has number of part-time employees = 14+3
Company y has number of part-time employees = 17
Hence, company y has 17 number of part-time employees.
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The given lengths are two sides of a right triangle. All three sides of the triangle form a Pythagorean Triple. Find the length of the third side and tell whether it is a leg or the hypotenuse. 9 and 41
Answer:
40, leg
Step-by-step explanation:
The triangle has side lengths of 9, 40, and 41.
41 is the hypotenuse, so 40 is a leg.
PLS HELP ASAP!!!!!!
Are lines L1 and L2 Parallel? Are lines L1 and L4 perpendicular? Explain your thinking.
answer
Calculate the slopes of the 2 lines and compare them.
m = (y2 - y1)/(x2 - x1)
If they are equal, the lines are parallel. If one slope is the negative reciprocal of the other, the lines are perpendicular. If neither of these conditions are met, the lines are not parallel and are not perpendicular. You have all the information you need. Do the math.
Step-by-step explanation:
hope it helps
Lily has 16 hats. She has 80% as many hats as Miguel. How many hats does Miguel have?
Frequency of radiation with a wave length of 5.2 cm. (change to meters first)
Frequency of radiation with a wave length of 5.2 cm is 57.7x[tex]10^{8}[/tex]
What is frequency?The number of waves that pass a fixed point in unit time.
Given that, a frequency with a wave length of 5.2 cm
5.2 cm = 0.052 m
Frequency = f = c/λ
f = 3x[tex]10^{8}[/tex]/0.052 = 57.7x[tex]10^{8}[/tex] Hz
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What is the solution to the system of equations? y = –5x + 3 y = 1 (0. 4, 1) (0. 8, 1) (1, 0. 4) (1, 0. 8).
The solution to the system of equations (0.4, 1).
Given equations according to the question,
y = -5x+3
y = 1
Now we can use y = 1 and substitute the value of y in y = -5x+3
After substituting we get, the value of y we get,
= 1 = -5x+3
Now given points according to the questions are
(0.4, 1) , (0.8, 1), (1, 0.4), (1, 0.8).
We substitute these points in the equation to see which points satisfy the equation, the point satisfying the equation is our point.
First, we will use (0.4, 1)
= 1 = -5x+3
= 1 = -5×0.4 + 3
= 1 = -2+3
= 1 = 1
Hence (0.4, 1) is our first solution of the equation.
Then we will use (0.8 ,1)
= 1 = -5x+3
= 1 = -5×0.8 + 3
= 1 = -4+3
= 1 = -1
Hence (0.8, 1) is not out the solution to the equation.
Then we will use (1,0.4)
= 1 = -5x+3
= 1 = -5×1 + 3
= 1 = -5+3
= 1 = -2
Hence (1, 0.4) is not the solution to the equation.
Then we will use (1,0.8)
= 1 = -5x+3
= 1 = -5×1 + 3
= 1 = -5+3
= 1 = -2
Hence (1, 0.8) is not the solution to the equation.
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You use a pair of shoes to measure a distance. The shoes are 12 inches long. The distance is equal to the length of 21 of the shoes. What is the distance? i need help pls
The distance is 252 inches.
What is distance?
The distance between two points is the length of a straight line segment that links them. The distance of a point from a line is the length of the shortest line segment from the point to the line.
Given
the length of shoes = 12 inch
The distance is equal to length of 21 of the shoes.
The total distance = 12×21
=252 inch
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A bag containing 5 red and 7 green marbles.Two marbles are drawn consecutively without replacing them. Calculate the probability that both marbles are off the same color by using a tree diagram.
The probability that both marbles are of the same color is 31/66
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here, we have
5 red and 7 green marbles.
We have to calculate the probability of two marbles being drawn consecutively without replacing them.
The first is that if we define events R to be two red marbles, and G to be two green marbles, then we can verify that:
P(R) = (5/12)(4/11)
P(G) = (7/12)(6/11)
Then, P(R ∪ G) = P(R) + P(G)
= (5/12)(4/11) + (7/12)(6/11)
= 5/33 + 7/22
= 31/66
Hence, the probability that both marbles are of the same color is 31/66
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What is the value of tan A?
Margin of error: 0.007, confidence level 94%
The minimum sample size required for a 94% confidence interval with a margin of error of 0.007, using the z-distribution, is of:
18,033.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds obtained by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are presented and explained as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 94%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.94}{2} = 0.97[/tex], so the critical value is z = 1.88.
We have no estimate of the population proportion, hence we consider [tex]\pi = 0.5[/tex], which is when the largest sample size is required.
The margin of error is of M = 0.007, hence the sample size required is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.007 = 1.88\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.007\sqrt{n} = 1.88 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{1.88 \times 0.5}{0.007}[/tex]
[tex](\sqrt{n}) = \left(\frac{1.88 \times 0.5}{0.007}\right)^2[/tex]
n = 18,033.
The sample size was rounded up, as a sample size of 18,032 would result in a margin of error slightly above the desired 0.007.
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write an equation for the line in the slope-intercept form.
slope= 8/9, y-intercept=-4
A) f(x) = 9/8x +9/2
B) f(x) = -8/9x - 4
C) f(x) = 8/9x - 4
D) f(x) = -8/9x + 4
Answer:
the answer is c.
Step-by-step explanation:
the slope will always have an x behind it and the y intercept is exactly as written
Jackson is working two summer jobs, making $10 per hour washing cars and $12 per hour landscaping. Last week jackson worked a total of 14 hours and earned a total of $152. Determine the number of hours jackson worked washing cars last week and the number of hours he worked landscaping last week.
The number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours
The payment of car washing per hour = $10
The payment for landscaping = $12
Total number of hours worked = 14 hours
Number of hours worked in car washing = x
Number of hours worked in landscaping = y
Then the first equation will be
x + y = 14
x = 14 - y
Total amount he earned = $152
Next equation will be
10x + 12y = 152
Here we have to use substitution method
10(14-y) + 12y = 152
140 - 10y +12y = 152
140 + 2y = 152
2y = 152 - 140
2y = 12
y = 12/2
y = 6 hours
Then
x = 14 - y
x = 14 -6
x = 8 hours
Hence, the number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours
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need answer asap
Graph y <1- 3x
[tex]y < -3x+1[/tex]
Graph below:
The number of customers in a store on the first day is represented by (6x-3). The number of customers on the second day is represented by (x-1). Write an expression to find how many more customers visited the store on the first day.
The expression to find how many more customers visited the store on the first day is 5x - 2.
What is an expression?It's important to note that an expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the number of customers in a store on the first day is represented by (6x-3) and the number of customers on the second day is represented by (x-1).
The number of more customers will be:
= Customers on first day - Customers on second day
= 6x - 3 - (x - 1)
= 6x - 3 - x + 1
= 5x - 2
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Juan is learning about like terms in his math class. He must check all the combinations below that are like terms. Which ones should he check? 3x and x and 0.5 4 ✔ -m and 8m ✓ -xy² and 2xy² * y and y² * 4xy and -5x²y * m and n ✔ -7 and 6
the answers are 1,2,3,4,8 i just took it rn
From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²; –7 and 6 are the like terms combinations
Like and unlike terms in algebraic expression:In algebraic terms, the terms that contain the same variable and the same power or degree are called like terms, In algebraic like terms, the numerical coefficients can vary but are not variables.
Here are some examples of like terms and unlike terms,
4x and 9x are like terms
3x²y and 10x²y are like terms
2xy and 10yx are like terms
3x and 19y are unlike terms [ ∵ variable is different ]
2xyz and 2xy are unlike terms [ ∵ variables is missing in 2nd term ]
Here we have a set of algebraic terms that can be classified as given below
=> 3x and x - like terms
=> 1/4 and 0.5 - like terms
=> –m and 8m - like terms
=> –xy² and 2xy² - like terms
=> y and y² - unlike terms [ ∵ powers are not same ]
=> 4xy and –5x²y - unlike term [ ∵ powers are not same ]
=> m and n - unlike term [ ∵ variables are not same ]
=> –7 and 6 like terms
Therefore,
From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²; –7 and 6 are the like terms combinations
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The complete Question
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms. Which ones should he check? Choose all that apply.
=> 3x and x
=> 1/4 and 0.5
=> –m and 8m
=> –xy² and 2xy²
=> y and y²
=> 4xy and –5x²y
=> m and n
=> –7 and 6
is y=7-3x linear? if it is than why?
Yes y = 7 - 3x is a linear function
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
Definition of variables of a linear function
y = output variable
m = slope
x = input variable
c = y intercept
In comparison to the question asked
y = 7-3x
m = slope = -3
x = input variable
c = 7
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Find the measure of the that is supplementary to in the diagram below. Enter only the number.
Image showing line A B and line C D that intersect at point E. The angle A E D is labeled 65 degrees.
Answer: 115
Step-by-step explanation: trust me bro free lee
Two angles are supplementary if their sum is 180° thus the angle supplementary to angles m∠AED are m∠DEB and m∠AEC and their measure is 115° both.
What is an angle?The angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
As per the given lines, AB intersect CD at E has been drawn below,
m∠AED = 65° (given)
m∠AED + m∠DEB = 180° (supplementary)
m∠DEB = 180° - 65° = 115°.
m∠AED + m∠AEC = 180° (supplementary)
m∠AEC = 180° - 65° = 115°.
Hence "Two angles are supplementary if their sum is 180° thus the angle supplementary to angles m∠AED are m∠DEB and m∠AEC and their measure is 115° both".
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Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit fast charges a set fee per class. Stepping up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs? y = 5. 5x and y = 7. 5x + 10 y = 7. 5x and y = 5. 5x y = 7. 5x and y = 5. 5x + 10 y = 7. 5x + 10 and y = 5. 5x + 10.
The system of equations representing these costs is y = 7.5x and y = 5..5x + 10
Given,
Anna desires to enroll in fitness courses. She contrasts two gyms to see which offers the best value. Each class at Fit Fast costs a specified amount. Stepping up costs a monthly fee as well as a price for each lesson.
We have to find the system of equations representing these costs;
Fit Fast: a certain number of feet per class = y = Ax
Stepping Up: a monthly charge plus a cost for each additional class = h = Bx + C
The second and fourth systems can be ignored since they lack the form that is implied by the statement.
Given that it reflects a choice that is always preferable to the alternative, the first system produces an obvious result. There is no need to compare because, for any positive value of x, 5.5x will be less than 7.5x + 10,
The third system is
It is necessary to solve the equations y = 7.5x and y = 5.5x + 10 to decide when one rate is more practical than the other.
That is,
The system of equations representing these costs is y = 7.5x and y = 5..5x + 10
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Lauren is going to a carnival that has games and rides. Each game costs $2 and each ride costs $4.75. Lauren spent $50 altogether at the carnival and the number of rides she went on is 2 more than the number of games she played. Write a system of equations that could be used to determine the number of games Lauren played and the number of rides Lauren went on. Define the variables that you use to write the system.
Taking into account the definition of a system of linear equations, the system of equations to be solved is
r= g+2
2g + 4.75r= 50
where "g" is the number of games Lauren played and "r" is the number of rides Lauren went on.
System of linear equationsA system of linear equations is a set of two or more first degree equations, in which two or more unknowns are related and it is desired to find their value.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. Thit is, the values of the unknowns must be find, and when the are replacing, they must give the solution proposed in both equations.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"g" is the number of games Lauren played."r" is the number of rides Lauren went on.You know:
Each game costs $2 and each ride costs $4.75.Lauren spent $50 altogether at the carnival.The number of rides Lauren went on is 2 more than the number of games she played.The system of equations to be solved is
r= g+2
2g + 4.75r= 50
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This is 100% correct. Just got it right.
"g" is the number of games.
"r" is the number of rides.
System of equations
r = g + 2
2g + 4.75r = 50
f(x)=0.145x^2
The function above models f, the kinetic energy, in joules, of a baseball traveling at a speed of x meters per second. Based on the function, what is the kinetic energy, in joules, of a baseball traveling at a speed of 40meters per second?
A) 5.8
B) 58
C) 232
D) 2,320
Answer: A) 5.8
Step-by-step explanation: Hard guess
Determine the equation of the line that is perpendicular to the given line, through the given point
y=x-1; (-6,2)
Answer:
y = -x - 4
Step-by-step explanation:
Given line: y = x - 1
Slope of given line = 1
The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular line is -1.
slope = -1
point: (-6, 2)
y = mx + b
y = -x + b
2 = -(-6) + b
2 = 6 + b
b = -4
Equation:
y = -x - 4
naomi osaka plays tennis regularly with a friend, and from past experience, she believes that the outcome of each match is independent. for any given match she has a probability of 0.6 of winning. the probability that she wins the next two matches is:
The probability that she wins the next two matches is 36% or 0.36
How to calculate the probability of two matches?
Given,
She believes that the outcome of each match is independent. So, the outcome of next match does not depend on the previous match, is called independent event.
The probability of winning one match is 0.6
Since the outcome of each match is independent, we easily get the probability of she winning the next two matches by multiplying the probability of she winning per match. So,
Probability she wins the next two matches = 0.6 x 0.6
= 0.36 or 36%
Thus, the probability that she wins the next two matches is 36% or 0.36
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Simplify: |2-5|-(6 divided 2+1)^2
After simplification of |2-5|-(6/2+1)², the resultant answer is (A) -13.
What is simplification?To simplify simply means to make anything easier.
In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
Calculations and problem-solving techniques simplify the issue.
Substitute "of" for "multiplication," and "/" for "division."
Always carry out operations in accordance with "BODMAS."
Division and multiplication are equally important (Start from left) Both addition and subtraction are equally important.
So, simplify |2-5|-(6/2+1)² as follows:
|2-5|-(6/2+1)²
|-3| - (6/2 + 1)²
We know that : |-3| = 3 and (6/2 + 1)² = 16
Then, we have:
3 - 16
- 13
Therefore, after simplification of |2-5|-(6/2+1)², the resultant answer is (A) -13.
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Question 6 - (4 marks available) Sanjit drives the 45 km distance between York and Leeds. He then drives a further 42 km from Leeds to Blackpool. Sanjit's average speed between York and Leeds was 54 km/h. It also took Sanjit 35 minutes to travel from Leeds to Blackpool. Work out Sanjit's average speed (in km/h) for his total journey from York to Blackpool.
Answer:
58,5km/h
Step-by-step explanation:
Vyork-leeds=45km/h
Vleeds-blackpool=72km/h
(45+72):2=58,5km/h
3 tons of topsoil cost 2,520.00. What is the price per pound?
Answer:
$0.42
Step-by-step explanation:
3ton=6000pounds
2,520/6000=$0.42
Devaughn is 13 years older than Sydney. The sum of their ages is 99. What is Sydney's age?
Sydney's age is 43 years.
According to the question,
We have the following information:
Devaughn is 13 years older than Sydney. The sum of their ages is 99.
Let's take the age of Devaughn to be x years and the age of Sydney to be y years.
So, Devaughn's age can be expressed using the following expression:
y = 13+x years
Now, we have the following expression for the sum of their ages:
x+13+x = 99
2x+13 = 99
Moving 13 from the left hand side to right hand side will result in the change of the sign from plus to minus:
2x = 99-13
2x = 86
x = 86/2
x = 43 years
Hence, Sydney's age is 43 years.
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attending the university of houston main campus the bank agrees to give you a loan of 35000 with 2% simple interest over 8 years
As per the given data, loan amount is $35,000 with 2% simple interest for the time period of 8 years then monthly payment is equal to
$422.92.
As given in the question,
Loan amount taken from the bank is equal to $35,000
Simple interest rate is 2%
Time period = 8 years
Total interest paid is equal to
= Loan amount × Interest rate × time period
= 35,000 × 2% × 8
= (35,000 × 2 × 8) / 100
= $5600
Total amount to be paid
= Loan amount + Interest amount
= $35,000 + $ 5,600
= $ 40,600
Monthly payment done based on given interest and time period
= $40,600 / ( 8 × 12 )
= $ 40,600 / 96
= $ 422.92
Therefore, for the given data, loan amount is $35,000 with 2% simple interest for the time period of 8 years then monthly payment is equal to $ 422.92.
The complete question is:
Attending the university of Houston main campus ,the bank agrees to give you a loan of $35,000 with 2% simple interest over 8 years. How much will your monthly payments be?
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