of lines with the following characterizing property. (h) mar + 2) = -1 (b) perpendicular to 3r + 2y = 7 (d) having inclination 60° (f) passing through the origin (h) having slope 6) x-intercept twice y-intercept
We need to write the equation of the family of the lines with the following characterizing property.
j) x - intercept is twice y - intercept
X- intercept is the value of x when y= 0
Y- intercept is the value of y when x = 0
so, let y- intercept = a
x- intercept = twice y- intercept = 2a
So, the line will pass through the points: ( 2a , 0 ) and ( 0 , a )
The general equation of the line is : y = m * x + b
Where m is the slope and b is y - intercept
[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{a-0}{0-2a}=\frac{a}{-2a}=-\frac{1}{2}[/tex]So, the equation of the family will be :
[tex]y=-\frac{1}{2}x+a[/tex]Find all real values of x such that f(x)=0 for f(x) = 2x^2 + 3x – 20
Consider first the general case of the equation
[tex]ax^2+bx+c\text{ =0}[/tex]The general formula that solves this problem is given by
[tex]x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, the number of real solutions depends on the value that is inside the square root. For it to have a real value, it must happen that
[tex]b^2-4ac\ge0[/tex]So first, let's check if this is our case. In our case a = 2, b = 3 and c = -20.
Then
[tex]b^2-4ac=(3)^2-4\cdot2\cdot(-20)\text{ = 9 +160 = }169\ge0[/tex]So in this case, the equation has real values. Now, recall that
[tex]169=13^2[/tex]So our general solution becomes
[tex]x\text{ = }\frac{-3\pm\sqrt[]{13^2}}{2\cdot2}[/tex]Then,
[tex]x\text{ = }\frac{-3\text{ }\pm\text{ 13}}{4}[/tex]The symbol in the middle means that we get one different solution whenever we take either the plus sign of the minus sign. So the first solution would be
[tex]x_{1\text{ }}=\frac{13-3}{4}\text{ = }\frac{10}{4}\text{ = }\frac{5}{2}[/tex]And the other solution would be
[tex]x_{2\text{ }}=\text{ }\frac{13+3}{4}\text{ = }\frac{16}{4}=4[/tex]
The graph shows the function f(x).
f(x)
Which equation represents f(x)?
a.f(x) = -√√x
b. f(x) = -√√x-1
c. f(x)=√√/-x-1
d. f(x)=√x
Answer:
The correct option is 3.
Step-by-step explanation:
The parent cube root function is
From the given graph it is clear that the graph of f(x) is transformed by reflecting the graph of g(x) across y-axis and shifting two units down.
If the parent cube root function is reflected across the y-axis, then x is replaced by -x.
Now, the graph of new function sifts 1 unit down. So, the required function is
The graph shows the function .
From the given graph it is clear that the graph passes through the points (-8,1), (0,-1) and (8,-3).
Check the above function by these points.
At x=-8,
At x=0,
At x=8,
All these points satisfy by the abobe function. It means the above function is correct.
Therefore the correct option is 3.
Shavon and Jesiah are having a race. Shavon can run 100 meters in 30 seconds. Jesiah can run 120 meters in 40 seconds. Who is running faster in meters per second, and by how much?
Shavon is running faster by 0.33 meter.
How to calculate the value?From the information, Shavon and Jesiah are having a race and Shavon can run 100 meters in 30 seconds. The speed will be:
= Distance / Time
= 100 / 30
= 3.33 meter per second
Jesiah can run 120 meters in 40 seconds. The speed will be:
= Distance / Time
= 120 / 40
= 3 meters per second.
Shavon runs faster. This is illustrated as:
= 3.33 - 3
= 0.33 meter
She's 0.33 meters faster.
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what’s the correct answer answer asap for brain list
Answer:
B is the correct answer
hope this helped:)
Simplify the expression below by applying the zero exponent rule. (5-8)^0 = Answer
Zero Exponent Rule:
[tex]\begin{gathered} a^0=1 \\ a\neq0 \end{gathered}[/tex]Thus, anything to the power of 0 is "1", except 0.
Let's simplify the expression shown:
[tex]\begin{gathered} (5-8)^0 \\ =(-3)^0 \\ =1 \end{gathered}[/tex]Answer1Mia Kaminsky sells shoes for Macy’s. Macy’s pays Mia $12 per hour plus a 5% commission on all sales. Assume Mia works 37 hours for the week and has $7,000 in sales. What is Mia’s gross pay
Mia's gross pay was $794 at the end of the week.
Mia's Gross PayTo calculate Mia's gross pay, we have to find how much she earned working 37 hours at a rate of $12 per hour.
Total number of hours worked = 37Rate per hour = $12We can simply multiply both variable to determine how much she earned working for 37 hours.
[tex]37 * 12 = 444[/tex]
Mia earned $444 for that week.
We can add this to her 5% commission which would be 5% of $7000
[tex]5\% of 7000 = 350[/tex]
The sum of Mia's gross pay for the week is
[tex]444 + 350 = 794[/tex]
She earned $794 in gross pay at the end of the week.
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PLS HELP WILL MARK BRAINLIEST
Answer:/Step-by-step explanation:
10. Write the phrase "20 divided by x minus 3 is 12" as a variable expression.
20
---------- = 12
x - 3
11. Write the phrase "4 plus the quotient of 9 and y equals 6" as a variable expression.
4 + (9 ÷ y) = 6
I hope this helps!
mark the red letter shown in the brackets the subject of the formula
Given equation is
[tex]A=lb[/tex]Now
[tex]b=\frac{A}{l}[/tex]I am having a hard time understanding explicit formulas with arithmetic sequences. The current sequence I am working with is:2, 8, 14, 20, 26The common difference is 6. I don't know how to come up with the explicit formula when given the sequence.
Solution
we are given the sequence
[tex]2,8,14,20,26,..[/tex]The first term = 2
Common difference = 6
The sequence is an arithmetic progression
The nth term is given as
[tex]\begin{gathered} a_n=a+(n-1)d \\ a=2 \\ d=6 \\ a_n=2+(n-1)(6) \\ a_n=2+6n-6 \\ a_n=6n-4 \end{gathered}[/tex]Therefore, the answer is
[tex]a_{n}=6n-4[/tex]Please help
12x2+20-3x−5
Factor out the GCF from the entire expression
I WILL FIRST GROUP THE LIKE TERMS AND SIMPLIFY THEM BEFORE FACTORISING
IT IS VITAL TO SIMPLIFY LIKE TERMS BEFORE FACTORISING.
[tex]12 {x}^{2} - 3x + 20 - 5 \\ = 12 {x}^{2} - 3x + 15[/tex]
THE GCF IN THE EXPRESSION IS 3 MEANING WE WILL DIVIDE EACH AND EVERY TERM IN THE P
EXPRESSION BY 3
[tex] = 3(4 {x}^{2} - x + 5)[/tex]
HOPE THIS HELPS.
Write the equation of a line that is parallel to the line whose equation is y = 1/3x +6 and passes through the point(-3,5).
Answer:
y = 1/3 x + 6
Explanation:
The slope of two parallel lines is the same; thereofre the equation of the line we are seeking looks like
[tex]y=\frac{1}{3}x+b[/tex]where b is a constant hitherto unknown.
Now, we know from point (-3, 5) that when when x = -3, y = 5; therefore,
[tex]5=\frac{1}{3}(-3)+b[/tex]the above simplifies to
[tex]5=-1+b[/tex][tex]\therefore b=6[/tex]Hence, the equation of the line is
[tex]y=\frac{1}{3}x+6[/tex]what the slope of the following equations y y equals -1/2x+4
the form or the slope-intercept form of the equation of the line is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
we have the next equation
[tex]y=-\frac{1}{2}x+4[/tex]as we can see the slope is m=-1/2, because we have the same form of the slope-intercept form
Compare and contrast the formulas for calculating the volume of a cone and the volume of apyramid. Give a mathematical example to illustrate your discussion.
SOLUTION:
Step 1:
In this question, we are given the following:
Compare and contrast the formulas for calculating the volume of a cone and the volume of a pyramid.
Give a mathematical example to illustrate your discussion.
Step 2:
The details of the solution are as follows:
The formula for calculating the volume of a cone:
The formula for calculating the volume of the pyramid:
Which is an algebraic expression for five more than z
The algebraic expression for 5 more than z is Z + 5.
Given,
5 more than z.
We need to find the algebraic expression.
What are the different algebraic expressions?
We have,
Examples:
- 3 more than M = M + 3
- 3 less than M = M - 3
- 3 times M = 3 x M
- 3 times M less than 2 = 3M - 2
- 3 times M more than 2 = 3M + 2
Find the algebraic expression for 5 more than Z.
We have,
5 more than Z = Z + 5
Thus the algebraic expression for 5 more than z is Z + 5.
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last monday two law students met up at Cafe literature after school to read the pages they were assigned in the legal methods class Alejandro can read one page per minute and he has 28 pages so far Carly who has a reading speed of two pages per minute has read 12 pages so far.Write an equation to describe the pages each student read.Graph the equations.Which are the ratios for each student?
Let x be the number of minutes they read and y the number of pages they read.
Since Alejandro read one page per minute and he has so far read a total of 28 pages he the total amount of pages he read is:
[tex]y=x+28[/tex]Now, Carly reads twice as much in the same time but she has read only 12 pages so far, then the amount of pages in her case is:
[tex]y=2x+12[/tex]The graphf of this equations are:
The rate of change:
Alejandro: 1
Carly: 2
MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $928 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin 13,800 . Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.
MotoWin can expected to make money from offering these warranties.
In the long-run, they should expect to make 514 dollars from each warranty sold
What is expected value of replacement?
The expected value to MotoWin Auto Superstore of a replacing a car is the sum of the costs to be incurred when there is replacement multiplied by its probability of occurrence plus the cost of no replacement multiplied by its likelihood of occurrence expressed in percentage terms
expected value of replacement=(cost of replacement*its probability)*(cost of no replacement*its probability)
cost of replacement=$13,800
probability of replacement=7%
cost of no replacement=$0(when there is no to replace no cost is incurred)
probability of no replacement=93%
expected value of replacement=($13,800*3%)+($0*97%)
expected value of replacement=$414
profit on replacement=replacement price-expected value of replacement
profit on replacement=$928-$414
profit on replacement=$514
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Simplify −6g(3g + 2).
−18g^2 + 2
−18g^2 − 12g
−18g + 2
−18g − 12g
Answer:
B. −18g^2 − 12g
Step-by-step explanation:
Hope this helps!
Please tell me if its incorrect
Please Help, thank you.
The interval notation for the change in temperature are-
Increasing temperature; (1, 3) ∪ (6, 8).Decreasing temperature; (0, 1) ∪ (3, 6).What is termed as the interval notation?An interval is represented on a number line using interval notation. In those other words, it is a method of writing real number line subsets. An interval is made up of numbers that fall between two particular given numbers.For the given function;
Increasing temperature; It is the temperature in which the graph is increasing or we can say that for as the vale of x increases the value of y also increases. Thus, the interval notations are-
Increasing temperature; (1, 3) ∪ (6, 8).
Decreasing temperature: It is the temperature in which the graph is decreasing or we can say that for as the vale of x increases the value of y also decreases. Thus, the interval notations are-
Decreasing temperature; (0, 1) ∪ (3, 6).
Thus, the interval notations for the function are found.
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Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1. The factors of the expression are______and_____
The factors of the expression are 2.5 and 11/5.
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions. Similar to this, we are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3.
Given Data
Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1.
Algebraic expression:
The factors of the expression are:
10 = 5y -1
11 = 5y
y = 11/5
y = 2.5
The factors of the expression are 2.5 and 11/5.
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Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of -3,-2, and 1, and a y-intercept of -14.
Recall that the general form of a third-degree polynomial is:
[tex]g(x)=k(x-a)(x-b)(x-c),[/tex]where k is a constant, and a, b, and c are the zeros of the polynomial.
Therefore:
[tex]p(x)=k(x+3)(x+2)(x-1).[/tex]Now, to determine the value of k, we consider the y-intercept:
[tex]p(0)=-14=k(0+3)(0+2)(0-1).[/tex]Solving for k, we get:
[tex]\begin{gathered} -14=-6k, \\ k=-\frac{14}{-6}, \\ k=\frac{14}{6}, \\ k=\frac{7}{3}. \end{gathered}[/tex]Finally:
[tex]p(x)=\frac{7}{3}(x+3)(x+2)(x-1).[/tex]Answer: [tex]p(x)=\frac{7}{3}(x+3)(x+2)(x-1).[/tex]what is the means proportional between 4 and 81
Given
4
18
Procedure
The mean proportional, or geometric mean, of two positive The mean proportional, or geometric mean, of two positive
[tex]\frac{a}{x}=\frac{x}{b}[/tex]When solving
[tex]\begin{gathered} x=\sqrt[]{a\cdot b} \\ x=\sqrt[]{4\cdot81} \\ x=\sqrt[]{324} \\ x=18 \end{gathered}[/tex]The answer would be 18
(3s)/(s^2 - 16) (s-4)/(s^2)
Answer: =111e3t(33cosh11−−√t+711−−√sinh11−−√t)
Step-by-step explanation:
Consider the equation below.
log4(x+3)= log2 (2+x)
Which system of equations can represent the equation?
Answer:
x=2log(2)−3log(4)log(4)−log(2)
Step-by-step explanation:
I hope this matches one of your answers
The decimal form is -4
Find the domain of the rational expression: 3x+21
all real numbers except 4
all real numbers except -7
all real numbers except 0
all real numbers except -21
Answer: The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Domain: (−∞,∞)
Range: (−∞,∞)
Hope this helps! :)
Find the sum and product of the roots of the equation 4x^2-12=3x
Given the equation:
[tex]4x^2-12=3x\text{ ----- equation 1}[/tex]Required: sum and product of the roots of the equation
solution:
For a quadratic equation of the form
[tex]ax^2\text{ + bx + c = 0 ------ equation 2}[/tex]the sum of the roots is expressed as
[tex]\text{sum of roots = -}\frac{b}{a}[/tex]the product of the roots is expressed as
[tex]\text{product of roots = }\frac{c}{a}[/tex]The given quadratic equation can be rewritten in the form as in equation 2 to be
[tex]4x^2-3x-12\text{ = 0 ----- equation 3}[/tex]In comparison to equation 2,
[tex]\begin{gathered} a\text{ = 4} \\ b\text{ = -3} \\ c\text{ =-12} \end{gathered}[/tex]Thus,
Sum of roots:
[tex]\begin{gathered} \text{sum of roots = -}\frac{b}{a} \\ =-\frac{-3}{4} \\ =\frac{3}{4} \end{gathered}[/tex]thus, the sum of the roots is
[tex]\frac{3}{4}[/tex]Products of roots:
[tex]\begin{gathered} \text{product of roots = }\frac{c}{a} \\ =\frac{-12}{4} \\ =-3 \end{gathered}[/tex]thus, the product of the roots is
[tex]-3[/tex]
Find the solution set for y = 4x - 3,
given the replacement set
{(-3, 9), (-2, -11), (0, -2), (2,5)}
The solution set for y = 4x-3 is {(2,5)} from the replacement set {(-3, 9), (-2, -11), (0, -2), (2,5)}.
The provided function is an equation of line in slope-intercept form of line.
According to which, if a line has slope m and it has the Y-intercept c, then the equation of line will be,
y = mx+c,
One thing to be noted here is, if the line passes through (a,b) then it will satisfy the equation and also, it will be called a solution of the equation.
The equation is y = 4x-3,
The given replacement sets is, {(-3, 9), (-2, -11), (0, -2), (2,5)}.
We will check for each and every element of the set,
1. For (-3,9)
Putting values in,
y = 4x-3
9 = 4(-3)-3
9 ≠ -15
Not a solution.
2. For (-2,11)
Putting values in,
y = 4x-3
11 = 4(-2)-3
11 ≠ -11
Not a solution.
3. For (0,-2)
Putting values in,
y = 4x-3
-2 = 4(0)-3
-2 ≠ -3
Not a solution.
4. For (2,5)
Putting values in,
y = 4x-3
5 = 4(2)-3
5 = 5
It is a solution for the equation y = 4x -3.
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Find the value of the expression: 12 ÷ 2 + ( 6 − 4 ) 2
Given:
[tex]12\div2+(6-4)2[/tex]Required:
To find the value of the given expression.
Explanation:
Consider the given expression,
[tex]\begin{gathered} 12\div2+(6-4)\times2 \\ =6+(6-4)2 \\ =6+2\times2 \\ =6+4 \\ =10 \end{gathered}[/tex]Final Answer:
The value of the given expression is 10.
True or False. 8 (12 + 3) is equivalent to 120
Use the order of operations and the distributive property to solve this expression. Work starting from the parenthesis.
8(12 + 3) = 120
8(15) = 120
120 = 120
The equation is true.
Answer:
True because you must do parentheses first so 12+3=15x8=120 so it is equivalent
Please help me with this question my son keeps getting this wrong, please help I have attached the image of the problem from his math paper.
The terms in the given expression are
[tex]8x^3y^2,4x^2y^3,40xy^3[/tex]The common factor in all the three time is
[tex]4xy^2[/tex]Take the common factor outside the brackets and write the remaining inside the brackets.
[tex]4xy^2(2x^2-xy+10y)[/tex]