Answer: The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side. Use inverse operations to move terms.
Step-by-step explanation:
I need help solving this problem!
The value of a is = 4/3.
From the given figure:
((3/4)a+4)3 = 15
(3a+4*4 / 4)3 = 15
(3a + 16 / 4)3 = 15
3a*3 + 16*3 = 15*4
9a + 48 = 60
9a = 60 - 48
9a = 12
divide by 9 on both sides
9a/9 = 12/9
a = 12/9
= 4/3.
Therefore the value of a is = 4/3.
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A rectangular box has a square base. The combined length of a side of the square base, and the height is 20 in. Let x be the length of a side of the base of the box.
a. Write a polynomial function in factored form modeling the volume V of the box.
b. What is the maximum possible volume of the box?
c. Explain how you found the maximum possible volume.
Answer:
Step-by-step explanation:
V(x) = x3 + 2x2 - 11x - 12
To factor, you want 3 numbers that multiply to give -12 (the constant term) and add to give 2 (coefficient of the x2 term). The answer is 4, -3, and 1: (4)(-3)(1) = -12, 4 + (-3) + 1 = 2. So the volume polynomial factors to:
V(x) = (x+4)(x-3)(x+1)
Now the volume of a rectangular box is:
V = Length*Width*Height = (x+4)(x-3)(x+1)
So let's pick height = (x+1) = 4.5 (you could pick any one of the three factors).
x+1 = 4.5
x = 3.5
Length = (x+4) = 3.5+4 = 7.5
Width = (x-3) = 3.5 - 3 = 0.5
The box's dimensions are 7.5 m by 0.5 m by 4.5 m
A poster is to have an area of 200 square inches with 1 inch margins on the left and right sides, and 2 inch margins on the top and bottom. Varying the dimensions of the poster changes the area of the region inside the margins. What is the maximum area inside the margins?.
Using the Optimization problem solving strategy, the maximum area inside the margins is 108 inch².
Firstly , we can develope a function of two variables. let the length of poster be x inch and width be y inch.
total Area of poster (A ) = x × y = 200 inch² ---(1)
we have provided that bottom and top margin is 2 inch each and right -left margin is 1 inch each.
So, length of poster inside margin (l) = (x-4 ) inch
width of poster inside the margin (w) = (y-2) inch
Area inside the margins = l × w sq. inch
= (x-4)(y-2) sq.inch ---(2)
from (1) we can find out the value of one variable and put in equation (2) ,
from( 1), y = 200/x
Area inside margins= (x-4)(200/x - 2) = 2(x -4)( 100/x - 1) = 2( 100 - x - 400/x + 4)
Area inside margins = 2 ( -x - 400/x + 104)
To minimize the area inside the margins we take first order derivative of it
dA/ dx = d/dx[ 2( -x - 400/x + 104) ]
= 2 d/dx ( -x - 400/x +104) = 2 ( -1 + 400/x² )
critical points occurs when dA /dx = 0
2 ( -1 + 400/x² ) = 0 => 800/x² = 2
=> x² = 400 => x = 20
putting value of x in equation (1) we get ,
x×y = 200 = 20× y => y = 10
so, length of poster is 20 inch and width is 10 inch.
Now, length of poster inside margin (l) = 16 inch
width of poster inside margin (w) = 8 inch
maximum area inside margin is 108 inch².
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Four siblings have a dog walking business. The table shows the hours worked by each sibling. Each sibling earns $25.50 per hour and the total number of hours worked is represented by 10h+15 , where h represents the number of hours Michael worked.
The total amount of money the siblings earned is equal to $1504.5.
How to determine the total amount the siblings earned?From the information provided, the total number of hours worked is represented by this mathematical expression:
10h + 15
where:
h represents the number of hours Michael worked.
Next, we would determine the number of hours Michael worked by summing up all of the total number of hours worked by each of the four siblings and equating it to the total number of hours worked:
2.5(h + 3) + 4(h - 2) + 31 + h = 10h + 15
7.5h + 26 = 10h + 15
10h - 7.5h = 26 - 15
2.5h = 11
h = 4.4 hours.
For the total number of hours worked by each of the four siblings, we have:
Total hours = 10h + 15
Total hours = 10(4.4) + 15
Total hours = 44 + 15
Total hours = 59 hours.
At a rate of $25.50 per hour, the total amount the siblings earned is given by:
Total earnings = $25.50 × 59
Total earnings = $1504.5.
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Complete Question:
Four siblings have a dog walking business. The table shows the hours worked by each sibling. Each sibling earns $25.50 per hour and the total number of hours worked is represented by 10h + 15 , where h represents the number of hours Michael worked. What was the total amount the siblings earned?
What is the range of the data in how many teams complete the escape room this week
Please add an image or some more data.
Question 3(Multiple Choice Worth 2 points)
(01.07 LC)
Simplify the given expression below:
(3+4i)+(5-2i)
0-2+6i
02-2i
07+3i
08+2i
Kal practices lines for 28 minutes at his acting class. This is 70% of the entire acting class. How many minutes long is his acting class? use any strategy to solve.
Using percent method we can solve the problem. Kal's acting class is 40 minutes long in total.
In which he practices lines about 28 minutes.
let "x minutes" be the total timing of kal's acting class .
Percent is always running between 0 to 100 where 0 % means nothing and 100% total about which we are considering the percent.
so, here x mintues is equal 100% timing
we have given that, kal practice lines for 28 minutes at his acting class and in percent form his timing is equal to 70% .
That's 70% time of entire acting class = 28 min
but we have to find the 100% of entire acting class i.e x minutes
Now, 70% time of entire class = 28 minutes
1% time of entire acting class = 28/70 minutes
100% time of entire acting class i.e x = ( 28/70)100
= 40 minutes .
So, the entire kal's acting class runs for 40 minutes .
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One moving company charges $19.85 plus $0.20 per mile to rent a van. The company also rents truck for $24.95 plus $0.17 per mile. At how many miles is the price the same for renting vehicles?
answer:19.8 should be the answer?
Step-by-step explanation:
solve for the volume of the cylinders and sphere.
The volume of the cylinder with radius(r) 7 inches and height(h) 9 inches
is 1384.74 cubic inches.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, a cylindrical shape of radius(r) 7 inches and height(h) 9 inches.
We know the volume of a cylinder is πr²h.
∴ The volume of this cylinder is
= π×(7)²×9 cubic inches.
= 441π cubic inches.
= 1384.74 cubic inches.
For the volume of a sphere, it is (4/3)πr³.
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help needed asap!!!
find the equation of the line in point-slope form with the given slope passing through the given point
Option (a) is correct, i.e., the equation of the line in point-slope form with given slope -2/3 passing through the given point (2,-3) is y+3 = -2/3 (x-2).
What is point-slope form equation of a line?
Point slope form is used to represent a straight line using its slope and a point on the line.
The equation of a line in point-slope form whose slope is 'm' and which passes through a point (x₁ ,y₁) is
y - y₁ = m (x-x₁).
Here we have slope m= -2/3 and the point (x₁ ,y₁) = (2,-3).
Therefore, the point-slope form of the equation is
y- (-3) = - 2/3 (x-2)
⇒ y + 3= -2/3 (x-2).
⇒ Option(a) is correct.
Therefore, equation of the line in point- form slope is y+3 = -2/3 (x-2).
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You solve a system of equations in which x represents the number of adult memberships sold and y represents the number of student memberships sold. Can ( 6, 24) be the solution of the system? Explain your reasoning.
Answer:
picture please
Step-by-step explanation:
pic please
Factorise pm- pm + 3qm - 3qn
Answer:
3q(m-n)
Step-by-step explanation:
pm - pm + 3qm - 3qn
= 3qm - 3qn (pm-pm cancelled out such as 2x-2x=0)
= 3q(m-n)
Sketch a number line plot your age as a point on your number line
What would you consider as the starting point on a number line? Why?
The starting point of the number line drawn using the age is zero
What is a Number line?A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). The numbers on the left of zero are all negative, whereas the numbers on the right of zero are all positive.
The starting point of the number line drawn using the age is zero and it is why because every human life starts at the age of months/years.
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Which of the following are integers?
a. 9
b. 7
c. 0
d. 4
Answer: All of them are integer
Step-by-step explanation:
They are all integer.
solve the following quadratic equation 4x^2-31x-33=12
Once an antibiotic is given, number of bacteria decreases at a rate of 15%/day. There were about 15,000 bacteria prior to the treatment. The graph models the number of bacteria after x days of treatment. What are the key features of the exponential function modeled in terms of this situation and how can they be interpreted? Select each correct answer. 30 The line y = 0 is an asymptote of the graph. The x-intercept is 30. The line x = 0 is an asymptote of the graph. The asymptote indicates that there will never be more than 15,000 bacteria. The y-intercept is 15,000. The y-intercept represents the number of bacteria when treatment began. The asymptote indicates that as time increases, the number of bacteria approaches 0.
Answer:
The line y = 0 is an asymptote of the graph.
The y-intercept is 15,000.
The y-intercept represents the number of bacteria when treatment began.
The asymptote indicates that as time increases, the number of bacteria approaches 0.
Step-by-step explanation:
Took the test
a ____________ is a table in which frequencies correspond to two variables.
A contingency table is a table in which frequencies correspond to two variables.
Explanation:
In contingency table one variable is used to categorise rows and second variable is used to categories columns.In contingency table have at least two rows and at least two columns.What is frequency table?
A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.What does "two way frequency table" mean?
A two-way or contingency table is the name for this kind of table. A statistical table called a two-way or contingency table displays the observed number or frequency for two variables, with the rows denoting one category and the columns denoting the other. Example, the gender (male or female) row category.To know more about contingency table check the below link:
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The length of a rectangle i 7 inche le than twice the width, w, of the rectangle. Find the dimenion if the area i 30 quare meter
The dimensions of the rectangle are, length = 5 inch and width = 6 inch.
What is rectangle?
A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.
Let, the length of a rectangle is 7 inches less than twice the width, w, of the rectangle.
Suppose,
width = w = x, then,
length = l = 2x - 7
Since the area of the rectangle is 30 square inches.
We know that.
Area of rectangle = length x width
30 = (2x - 7) x (x)
30 = 2x^2 - 7x
2x^2 - 7x - 30 = 0
2x^2 - 12x + 5x - 30 = 0
2x(x - 6) + 5(x - 6) = 0
(2x + 5)(x - 6) = 0
⇒ 2x + 5 = 0, x - 6 = 0
⇒ x = -5/2, x = 6
Since length is not negative.
Therefore, w = 6.
So, l = 2(6) - 7 = 12 - 7 = 5
Hence, the length is 5 inches and the width is 6 inches.
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[tex]x\sqrt{2} +3=-2[/tex]
Value of x for the given expression x√2 + 3 = -2 is equal to (- 5√2)/2.
As given in the question,
Given expression is equal to :
x√2 + 3 = -2
Simplify the given expression x√2 + 3 = -2 to get the value of x we have,
x√2 + 3 = -2
Subtract 3 from both the side of the given expression we get,
x√2 + 3 - 3 = -2 - 3
⇒ x√2 + 0 = -5
Divide by √2 from both the side of the expression,
x√2/√2= -5/√2
⇒x = -5/√2
Multiply and divide by √2 on right-hand side we get
⇒ x = -5√2/ (√2×√2)
⇒ x= -5√2/2
Therefore, value of x for the given expression x√2 + 3 = -2 is equal to
(- 5√2)/2.
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what is 3/5 times 6/7
Answer:
Step-by-step explanation:
Ok:
1. Straight out Multiplication. Denominator to denominator and numerator to numerator!
3/5*6/7=
18/35=
Answer: 18/35
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∠A and angle ∠B are supplementary angles. If angle A=(5x-22) and m∠B=(x+28)
what are the mesaurements for ∠A?
The corresponding measurements for angles A and B are 123° and 57°
How to find the measurements of the angles?Supplementary angles are angles that sum up to 180 degrees e.g angle 140° and angle 40° are supplementary angles because the sum of 140° and 40° is equal to 180°
Given that: angle A= (5x-22) and m∠B= (x+28), and ∠A and angle ∠B are supplementary angles. Thus:
A + B = 180°
(5x-22) + (x+28) = 180°
5x-22 + x+28 = 180°
6x + 6 = 180
6x = 180 -6
6x = 174
x = 174/6 = 29°
∠A = (5x-22) put x = 29°
∠A = 5(29) -22
= 145-22
= 123°
∠B = 180 -123 = 57°
Therefore, the measurements for angles A and B are 123° and 57° respectively
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Answer:The corresponding measurements for angles A and B are 123° and 57°
The corresponding measurements for angles A and B are 123° and 57°
How to find the measurements of the angles?
Supplementary angles are angles that sum up to 180 degrees e.g angle 140° and angle 40° are supplementary angles because the sum of 140° and 40° is equal to 180°
Given that: angle A= (5x-22) and m∠B= (x+28), and ∠A and angle ∠B are supplementary angles. Thus:
A + B = 180°
(5x-22) + (x+28) = 180°
5x-22 + x+28 = 180°
6x + 6 = 180
6x = 180 -6
6x = 174
x = 174/6 = 29°
∠A = (5x-22) put x = 29°
∠A = 5(29) -22
= 145-22
= 123°
∠B = 180 -123 = 57°
Therefore, the measurements for angles A and B are 123° and 57° respectively
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james can go 144 miles with 12 gallons of gas in his truck.how far can he go on 17 gallons?
Answer:
425 Miles
Explaination:
Please give the brainliest.
Hailey is making floral centerpieces for a wedding. Each centerpiece has 17 flowers. She has 430 flowers for the project. She estimates that she can make between 20 and 30 complete centerpieces. Is her estimate reasonable?
Use your knowledge of place value and division to explain the reasonableness of her answer.
Nia knows that one apple bag and 6 kiwis cost $19.70.
She also knows that the same apple bag and 16 kiwis cost $43.7.
i.
What is the cost for each kiwi?
Answer:
each kiwi costs $2.40
Step-by-step explanation:
we set up our system of equations
x = bag of apples
y = kiwi
x + 16y = 43.7
x + 6y = 19.7
multiply any one of the equations by -1 to make x negative
-1(x+6y) = -1(19.7)
-x - 6y = -19.7
add the other equation and the new equation
-x - 6y = -19.7
x + 16y = 43.7
+ ____________
10y = 24
divide by 10 both sides
y = 2.4
we can also look for the cost of each bag of apples
plug in the y value to an original equation
x + 16(2.4) = 43.7
simplify
x + 38.4 = 43.7
subtract 38.4 from both sides
x = 5.3
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
The probability of type I error if the new blood test is used is 0.05
Given data;
It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested who do not have the condition received an incorrectly positive response. Take into account the null hypothesis that "the person does not have the disease."
The probability that the blood test report will be positive if someone has the disease = 0.97 The probability that the blood test report will be positive if someone does not have the disease is = 0.05
The null hypothesis is: "The individual does not have the disease."
The type I error occurs when we reject the null hypothesis, but it was true in reality.
Therefore, the probability of type I error = The probability that the blood test report will be positive if someone does not have the disease.
⇒ 0.05
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Write a linear equation that models the data in the table
X Y
-6 0
-3 2
0 4
3 6
Equation:?
to get the equation of any straight line, we simply need two points off of it, let's use the ones in red provided in the table in the picture below
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{4}{3 +3} \implies \cfrac{ 4 }{ 6 } \implies \cfrac{2 }{ 3 }[/tex]
[tex]\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}{2}=\stackrel{m}{ \cfrac{2 }{ 3 }}(x-\stackrel{x_1}{(-3)}) \implies y -2 = \cfrac{2 }{ 3 } ( x +3) \\\\\\ y-2=\cfrac{2 }{ 3 }x+2\implies {\Large \begin{array}{llll} y=\cfrac{2 }{ 3 }x+4 \end{array}}[/tex]
15 POINTS PLEASE HELP
The data in the table describes the preferred type of exercise of 9th graders.
Cycling Running Swimming Row Totals
Boy 12% 18% 16%
Girl. 14%. 21%. 19%
Column Totals blank blank 100%
Find the marginal relative frequency for students who prefer cycling as their preferred type of exercise.
12%
14%
26%
39%
Answer: its (C) 26%
Step-by-step explanation:
its easy you just have to do addition
Marginal relative frequency are the column totals and row totals without the 100% there, so basically all the blank spaces are marginal relative frequencies
And to calculate the marginal relative frequency for students who prefer cycling as their preferred type of exercise is 12% +14% = 26%
I also do flvs so believe me
Answer:
26, C
Step-by-step explanation:
I did the quiz
Bookwork code: J62
Copy and complete the table of values for
52 +3.
0 1
#| 3² | 9 | ¹ | 2 | ³ | 4 | 5 | 6
3
The values of y when x=-1,0,1,2,3,4,5,6 are 9,3,-1,-3,-3,-1,3,9 respectively.
Given the function is,
y = x²-5x+3
Finding the values we get,
substituting the value x=-1 we get,
y = (-1)²-5(-1)+3 = 1+5+3 = 9
substituting the value x=0 we get,
y = 0²-5*0+3 = 3
substituting the value x=1 we get,
y = 1²-5*1+3 = 1-5+3 = -1
substituting the value x=2 we get,
y = 2²-5*2+3 = 4-10+3 = -3
substituting the value x=3 we get,
y = 3²-5*3+3 = 9-15+3 = -3
substituting the value x=4 we get,
y = 4²-5*4+3 = 16-20+3 = -1
substituting the value x=5 we get,
y = 5²-5*5+3 = 25-25+3 = 3
substituting the value of x=6 we get,
y = 6²-5*6+3 = 36-30+3 = 9
Hence the values of y when x=-1,0,1,2,3,4,5,6 are 9,3,-1,-3,-3,-1,3,9 respectively.
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help me please.......................
the answer is (A) according to the cosine rule a^2=b^2+c^2-2(b)(c)cos(A)
Evaluate (-3 1/3) ^2 ( Need this by tomorrow, but that depends on time :] )
Answer:
[tex]33\frac{1}{3}[/tex]
Step-by-step explanation:
square is just multiplying things twice
(-3 1/3)(-3 1/3)
(-10/3)(-10/3)
100/3
33 1/3
Hopes this helps
Answer: 1
Step-by-step explanation:
(-3 1/3)= (-1/3)+(-1/3)+(-1/3) = -1
(-3 1/3)^2 = (-1)^2 = (-1)(-1) = 1