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[tex]y=14x[/tex], where x is the number of gallons used and y is the distance driven in miles.
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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
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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]Hello! I need some help with this homework question, please? The question is posted in the image below. Q3
Answers
As given by the question
There are given that the function:
[tex]f(x)=x^2+3[/tex]Now,
From the given formula:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Then,
First find the equation for f(x + h)
So,
[tex]\begin{gathered} f(x)=x^2+3 \\ f(x+h)=(x+h^{})^2+3 \\ f(x+h)=x^2+h^2+2xh+3 \end{gathered}[/tex]Then,
Put both values into the given formula:
So,
[tex]\frac{f(x+h)-f(x)}{h}=\frac{x^2+h^2+2xh+3-x^2-3}{h}[/tex]Then,
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{h^2+2xh}{h} \\ =\frac{h(h^{}+2x)}{h} \\ =h+2x \\ =2x+h \end{gathered}[/tex]Hence, the difference quotient is 2x + h.
An item is regularly priced at $43. It is on sale for 15% off the regular price.Use the ALEKS calculator to find the sale price.
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$36.55
Explanations:
Given the following parameters
Regular price of a ticket = $43
Sales discount = 15%
Determine the discounted price
Discount price = 0.15 * 43
Discount price = $6.45
Determine the sales price
Sales price = Regular price - discount
Sales price = $43 - $6.45
Sales price = $36.55
Hence the sales price for the item will be $36.55
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
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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 maximum value of
C = x + 4y
subject to the following constraints:
x ≥ 0
x≤ 12
y ≤ 10
2x + 3y ≥ 24
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The maximum value of the linear equation is obtained as 52.
What is termed as the maximum value of function?The maximum value of such a function is the point on a graph where the function achieved its maximum point, or vertex.There are several ways to find the maximum value of the a quadratic equation.The first method is graphing. Visually, you can determine the highest value by graphing the equation and locating the maximum point of the graph. This is especially simple if you have a graphing calculator. There are three ways to calculate the maximum value of the a quadratic equation. Each of them can be employed to ascertain the maximum in their own specific context.For the given question;
The linear equation is defined as;
C = x + 4y
The constraints are-
x ≥ 0
x≤ 12
y ≤ 10
2x + 3y ≥ 24
From the constraints, the maximum value for x and y are taken as;
x = 12 and y = 10.
Put the the equation, to find the maximum value.
C = x + 4y
C = 12 + 4×10
C = 52
Thus, the maximum value of the function is obtained as 52.
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*THIS IS AN ANSWER BECAUSE I CAN'T ANSWER SOMEONE'S QUESTION*
Bob can do a job in 5 hours, while Bill can do the same job in 8 hours. How many hours would it take them, working together, to do this job?
ANSWER:
The one in the following equation stands for ONE WHOLE JOB.
[tex]\frac{1}{5}x+\frac{1}{8}x=1\\\\[/tex]
[tex]x=\frac{40}{13} hours[/tex]
hence, this is the answer.
Answers
Answer:
x=40/13
Step-by-step explanation:
tex]\frac{1}{5}x+\frac{1}{8}x=1\\\\[/tex]
[tex]x=\frac{40}{13} hours[/tex]
Find the value of the expression: 12 ÷ 2 + ( 6 − 4 ) 2
Answers
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.
What is the solution to the rational inequality?
3 - x / 2x + 1 ≥ 2
( - 1/ 2 , 1 / 5)
( - ∞ ; - 1 /2)
( - 1 / 2 , 1 / 5)
( - ∞ , - 1/ 2 ) ∪ ( 1 /5 , ∞ )
Answers
The solution to the rational inequality given in this problem is as follows:
(-1/2, 1/5].
Rational inequalityThe rational inequality is defined as follows:
[tex]\frac{3 - x}{2x + 1} \geq 2[/tex]
The first step to solve the inequality is isolate 0 on the right side of the inequality, hence:
[tex]\frac{3 - x}{2x + 1} - 2 \geq 0[/tex]
Then the least common multiplied is applied to represent the left side of the inequality as a single fraction, as follows:
[tex]\frac{3 - x - 2(2x + 1)}{2x + 1}\geq 0[/tex]
[tex]\frac{3 - x - 4x - 2}{2x + 1}\geq 0[/tex]
[tex]\frac{-5x + 1}{2x + 1}\geq 0[/tex]
There are two cases for the solution to the inequality:
Case 1: numerator and denominator positive.Case 2: numerator and denominator negative.The solution is the union of the solution of each of these cases.
Case 1-5x + 1 ≥ 0
-5x ≥ -1
5x ≤ 1
x ≤ 1/5
2x + 1 > 0 (only > as the denominator cannot be zero)
2x > -1
x > -1/2
The intersection of these solutions is given by the following interval:
(-1/2, 1/5].
Case 2-5x + 1 ≤ 0
-5x ≤ -1
5x ≥ 1
x ≥ 1/5
2x + 1 < 0
2x < -1
x < -1/2.
The intersection of these two cases is empty, hence the solution to the inequality is given by the following interval:
(-1/2, 1/5].
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a group of six people has 10 pizzas to share if they divide the pizzas evenly how much does each person get
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We will have that if they divide them evenly they will end up with:
[tex]\frac{10}{6}=\frac{5}{3}[/tex]So, each one will end up with option D.
PLS HELP WILL MARK BRAINLIEST
Answers
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!
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.
Answers
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:
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?
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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
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.
Answers
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]I only need the answer
THANK YOU!!
Answers
After simplifying the expression to a singles complex number, it becomes 1+√3i.
A complex number is a unique kind of number in the number system, it has two parts. One it called the real part which is a real number and an imaginary part which is also a real part but accompanied by the specific notation called iota.
Here a complex number Z is provided to us,
Z = [2+√(-12)]/2
As we can see,
Here we have √-12
We can write it as,
√(-2×2×3)
= 2√(-3)
Here, √-1 is given that special notation "IOTA (i)" which we mentioned earlier.
=2√3i
So, Z becomes,
Z = (2+2√3i)/2
Z= 1+√3i
So, the simpler form of Z = [2+√(-12)]/2 is Z= 1+√3i.
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Find all real values of x such that f(x)=0 for f(x) = 2x^2 + 3x – 20
Answers
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]
Redondea 5,951 a la decena más cercana
Answers
Answer:
6
Step-by-step explanation:
5.951
porque 1 no es mas o menos que 5, no vamos arriba
5.95
porque 5 es igual o mas que 5, vamos arriba
1 mas 9, es 10
pero este diez en el .9 is basicamente 1.0
entonces se combireta a uno entero
dejando nos con
6
f(x) = 2^3x-1 - 2find the inverse function of f(x)
Answers
Given the function
[tex]f(x)=2^{3-x}-2[/tex]Substitute y = f(x) into the function above
[tex]y=2^{3-x}-2[/tex]Make 'x' the subject of the formula
[tex]y+2=2^{3-x}[/tex]Take the log₂ of both sides
[tex]\begin{gathered} \log _2(y+2)=\log _22^{(3-x)} \\ \log _2(y+2)=3-x\log _22 \\ \end{gathered}[/tex]Note:
[tex]\log _22=1[/tex]Therefore,
[tex]\begin{gathered} \log _2(y+2)=(3-x)\times1 \\ \log _2(y+2)=3-x \end{gathered}[/tex]Isolating 'x'
[tex]x=3-\log _2(y+2)[/tex]Replace 'x' with 'y'
[tex]y=3-\log _2(x+2)[/tex]Hence,
[tex]f^{-1}(x)=3-\log _2(x+2)[/tex]The correct option is Option 2.
Marian purchased a home valued at $465,000. She purchased homeowner insurance for 75% of the value of the home. If the annual premium on the policy was $0.74 perhundred-dollar unit, how much did she pay to the nearest whole cent)?$2,875.50$2,695.00$2,580.75$3,050.74None of these choices are correct.
Answers
The value of the police if fot the 75% of the total value of the home value. The 75% of $465000 is:
[tex]465000\cdot0.75=348750[/tex]The value of the insurance is then for $348750. The annual premium of the policy is $0.74 per hunder-dollar unit. Then, we need to estimate the hundred-dollar units in $348750. To estimate them, we need to divide the value by 100:
[tex]\frac{348750}{100}=3487.5[/tex]The value of the policy is then by 3487.5 hundreds of dollars. Now, we can estimate the amount to be paid yearly:
[tex]0.74\cdot3487.5=2580.75[/tex]Then, the amount to pay, according to the given conditions is $2580.75. Correct answer is the third option.
Martin charges $10 for every 5 bags of leaves
Answers
Answer: each bag is 2$
Step-by-step explanation: 2+2= 4 4+2 = 6 6+2=8 8+2= 10
If Martin charges $10 for every 5 bags of leaves, then we divide the total price by the number of bags, then
Price $10 ➗ 5 bags = $2 each bag of leaves.Answer: In total, each bag of leaves counts $2✅ .
what’s the correct answer answer asap for brain list
Answers
Answer:
B is the correct answer
hope this helped:)
What is the solution of the following system? {6x+2y=−10 5x−5y=5
Answers
Answer below:
Step-by-step explanation:
6x+2y=-10
(-5/3,0) x-int
(0,5) y-int
slope= -3
5x-5y=5
slope= 1
(1,0) x-int
(0,-1) y-int
mark the red letter shown in the brackets the subject of the formula
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Given equation is
[tex]A=lb[/tex]Now
[tex]b=\frac{A}{l}[/tex]f(a)=-3a-5; Find ƒ(-7)
Answers
Step-by-step explanation:
the answer is attached
hope it helps
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.
Answers
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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If Z is a standard normal variable, find P(-1.2 < Z < 0.4). Round your answer to 3 decimal places.
Answers
If Z is a standard normal variable, The value of P(-1.2 < Z < 0.4) is
0.5403
This is further explained below.
What is a standard normal variable?Generally, A random variable with a normal distribution and mean equal to zero and standard deviation equal to one is referred to as a standard normal random variable. The letter Z will never be used to represent it in any context.
Given that, we have to find, P(-1.2<z<0.4)
P(-1.2<z<0.4) =P(z<0.4)-P(z<-1.2)
Using, the z-distribution table determine the values
=0.6554-0.1151
=0.5403
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If figure, angle ABE & angle DBC are right angles. Prove that angle ABD ≊ angle EBC
Hurry and answer please
Answers
Angle ABE & angle DBC are right angles then ∠ABE≅ ∠EBC
What is complementary angle theorem?
If two angles are complementary to the same angle, then they are congruent.
1.∠ABE and ∠DBC are right angles(Given)
2. m∠ABE=90⁰
m∠DBC=90⁰
By definition of right angles
3.∠ABE and ∠DBE are complementary.
∠DBE and ∠EBC are complementary.
(By complementary theorem)
two angles are complementary to the same angle, then they are congruent.
4. ∠ABE≅ ∠EBC (is complementary to same)
Hence ∠ABE≅ ∠EBC.
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When Mr. Jackson got in his car yesterday, the odometer read 187,198.9 km. When he got home, the reading was 187,399.4 km. How far did Mr. Jackson drive?
Answers
The distance Mr. Jackson drove from when he got in his car to when he got home is 200.5 km.
Given:
The odometer reading when Mr.Jackson got in his car = 187,198.9 km
The odometer reading when Mr.Jackson got home = 187,399.4 km
An odometer is a device used to calculate the distance traveled by a vehicle.
To determine the distance Mr.Jackson drove we subtract the odometer readings from when he got home minus when he got into his car.
⇒ (187,399.4 - 187,198.9) km
⇒ 200.5 km
Therefore, Mr. Jackson drove 220.5 km from when he got in his car to when he got home.
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Mia 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
Answers
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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determine the maximum or minimum of the quadratic function. express your answer in the form (x,y) and using decimals rounded to the hundredths.f(x)=2x^2+7-10
Answers
We are given the following quadratic equation
[tex]f(x)=2x^2+7x-10[/tex]The vertex is the maximum/minimum point of the quadratic equation.
The x-coordinate of the vertex is given by
[tex]h=-\frac{b}{2a}[/tex]Comparing the given equation with the general form of the quadratic equation, the coefficients are
a = 2
b = 7
c = -10
[tex]h=-\frac{b}{2a}=-\frac{7}{2(2)}=-\frac{7}{4}=-1.75[/tex]The y-coordinate of the vertex is given by
[tex]\begin{gathered} f(x)=2x^2+7x-10 \\ f(-1.75)=2(-1.75)^2+7(-1.75)-10 \\ f(-1.75)=2(3.0625)^{}-12.25-10 \\ f(-1.75)=6.125^{}-12.25-10 \\ f\mleft(-1.75\mright)=-16.13 \end{gathered}[/tex]This means that we have a minimum point.
Therefore, the minimum point of the given quadratic equation is
[tex](-1.75,-16.13)[/tex]Answer:
Exact Form:x=±√6/2
Decimal Form:x=1.22474487,−1.22474487
Step-by-step explanation:
what the slope of the following equations y y equals -1/2x+4
Answers
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