The slope of 3y = -5 is -5/3
We know that the slope-intercept form of equation of line is y = mx + c
where m is the slope of the line and c is the y-intercept of the line.
We have been given an equation of line 3y = -5
Consider given equation of line
3y = -5
Divide each side of above equation by 3
(3y)/3 = (-5)/3
y = -5/3
Comparing above equation with the slope-intercept form of equation of line y =mx + c we get,
m = -5/3 and c = 0
So, slope is -5/3
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meeny, miny and moe were playing tennis. from the second game on, the one who sat out the preceding game would replace the loser of that game. at the end, meeny played games and miny played games. how many games did moe play?
In the end, Moe played 51 games, while Meeny played 17 games and Miny played 35 games.
We can start solving the problem by using algebra. Let x be the number of games Moe played. Then, since Meeny and Miny played 17 and 35 games respectively, the total number of games played is 17 + 35 + x = x + 52.
We know that in the second game and on, the one who sat out the preceding game would replace the loser of that game. Therefore, the number of games played by Moe is one less than the number of games played by Meeny and Miny combined.
x = (17 + 35) - 1 = 51.
So, Moe played 51 games.
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The complete question is -
Meeny, Miny and Moe were playing tennis. From the second game on, the one who sat out the preceding game would replace the loser of that game. In the end, Meeny played 17 games and Miny played 35 games. How many games did Moe play?
What is factored form formula?
The equation y = [tex]ax^2[/tex] + bx + c is in factored form when it is written as
y = a(x - [tex]r_{1}[/tex])(x - [tex]r_{2}[/tex]).
The term "factored form" refers to a quadratic expression that is the product of two factors, each of which is a linear expression.
When an equation is in factored form, it can be expanded, which entails multiplying out the factors, to rewrite it in standard form. Factoring is the process of representing a given number or algebraic statement as the sum of its components.
The equation y = [tex]ax^2[/tex] + bx + c is in factored form when it is written as
y = a(x - [tex]r_{1}[/tex])(x - [tex]r_{2}[/tex]).
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Express 1.9 as a quotient of integers.
Expressing 1.9 as a quotient of integers is 19/10.
What is integers?An integer is a whole number (not a fractional number) that can be positive, negative, or zero. It is not a fraction, a decimal, or a percentage. A number such as 7, -11, or 0 is an integer. Integers are used in everyday life and are also used in computer programming.
This is equivalent to 1 9/10 which is a fraction. To write it as a quotient of integers, 19 is the numerator and 10 is the denominator. This means that if you take 19 parts of a whole and divide it into 10 equal parts, each part will be equal to 1.9.
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how to find the orthocenter of a triangle with coordinates
Orthocenter: Solve system of 3 eqs. using 3 altitudes' equation & vertices' coordinates.
What is coordinate ?
Coordinate is a value or set of values that identify the position of a point in a certain space. Represented by ordered pair or triple of numbers (x,y) or (x,y,z) respectively.
The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. To find the orthocenter of a triangle with coordinates, you can use the following steps:
1) Find the equation of the three altitudes of the triangle. To do this, you will need the coordinates of the three vertices of the triangle, as well as the slope of the line perpendicular to the side opposite each vertex.
2) Once you have the equations of the three altitudes, you can use them to find the coordinates of the orthocenter. To do this, you will need to solve a system of three equations with three variables (the x and y coordinates of the orthocenter, and the y-intercept of the altitude).
3) Once you have the coordinates of the orthocenter, you can use them to check your work by verifying that the point is indeed on each of the three altitudes.
Orthocenter: Solve system of 3 eqs. using 3 altitudes' equation & vertices' coordinates.
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What is the equation of a line perpendicular to y=-2/5x-1 that passes through (2,-8)
Please help ASAP
Answer:
y = 5/2 x - 13
Step-by-step explanation:
A line perpendicular to y=-2/5x-1 has a slope equal to the negative reciprocal of -2/5. The slope of the line passing through (2,-8) can be calculated as follows:
m = -(-5/2) = 5/2
The equation of the line in point-slope form is:
y - (-8) = (5/2)(x - 2)
Expanding the equation gives:
y + 8 = 5/2 x - 5
Solving for y:
y = 5/2 x - 5 - 8
y = 5/2 x - 13
The equation of the line is:
y = 5/2 x - 13
Question 4 pls answer
Answer:
Step-by-step explanation:
That equals 4/6 which is 2/3. Hope that was helpful!!!
please help and answer
Answer:
75.25
Step-by-step explanation:
to find the area of the square you multiply 5.5×5.5
you then add that to the are of the trapezoid using the formula a=a+b/2 h
you plug it all in and get (5.5×5.5)+((5.5+9.5/2)6)
the answer to that is 75.25
What are absolute value graphs called?
The graphs of absolute value functions are called "V-shaped" or "V-graphs" because their graph is in the shape of a "V".
The graph of an absolute value function is a V-shape that opens upward or downward, depending on the function.
The vertex of the V is the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line.
The absolute value function is defined as |x| where x is any real number and |x| represents the distance of x from zero on the number line, i.e., always non-negative.
Example of an absolute function is f(x) = |x + 3|. The vertex is where
x + 3 = 0
That is at x = -3.
Here the function opens upward, but if the function was -|x + 3|, it will open downward.
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what is the the ratio of the central angle measure to the circumference?
The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula:
arc measure = central angle measure / circumference
For a given central angle measure in degrees, the formula will be:
arc measure = (central angle measure in degrees) / 360
It's worth noting that this ratio is equal to the fraction of the circumference that the arc of the central angle measures.
For example, if the central angle measure is 90 degrees, the arc measure will be 90/360 = 1/4, meaning that the arc that is formed by the central angle measure is 1/4 of the circle's circumference.
It's also important to note that this ratio is also equal to the fraction of the total area of the circle that the sector formed by the central angle measures.
It's also worth noting that this ratio is always less than 1, since the central angle can't be greater than 360 degrees.
Therefore, The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula: arc measure = central angle measure / circumference
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Do you think you can determine the imaginary solutions by examining the graph? Explain your reasoning.
On solving the provided question, we can say that from graph we have a equation ,[tex]y = 4x^2[/tex] because it's a parabola
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here,
On solving the provided graph
we have a equation , [tex]y = 4x^2[/tex]
because it's a parabola
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According to the manufacturer, 20% of M&M's milk chocolate candies are orange and 23% of peanut M&Ms are orange. Suppose you take a random sample of 240 M/M^ prime s milk chocolate candies and 240 peanut M&M's. Let hat p 1 = sample proportion of M&M's milk chocolate candies that are orange and hat p 2 = the sample proportion of peanut M&M's that are orange. Find the probability that you select a greater proportion of orange peanut M&M's than of orange M&M's milk chocolate candies, assuming the company's claim is true?
The probability that you select a greater proportion of orange peanut M&M's than of orange M&M's milk chocolate candies is 0.7881
How to solve for the probabilityWe have to use the available data to solve this problem
We have The probability 1 = P1 = 20%
= 0.20
We have the probability 2 = p2 = 23%
= 0.23
The difference between p1 - p2
0.20 - 0.23
= - 0.03
n1 = 240
n2 = 240
[tex]\sqrt{\frac{p1 (1-p1)}{n1} +\frac{p2(1-p2)}{n2} } \\\\\sqrt{\frac{0.20 (1-0.20)}{240} +\frac{0.23(1-0.23)}{240} }[/tex]
= 0.0375
Then Z value = -0.03 / 0.0375
= -0.80
We have to find the p value
The p value = 1 - p(z ≤ -0.80)
= 1 - 2119
= 0.7881
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Solve x² - 11x - 42 = 0
O x = -3 and 14
O x = -14 and 3
O x = -6 and -7
O x = 6 and 7 < Previous
Answer: a = 1, b = -11, and c = -42.
Step-by-step explanation:
The solutions to the equation x² - 11x - 42 = 0 are x = -6 and x = 7.
You can find the solutions by factoring the equation, or by using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.
In this case, a = 1, b = -11, and c = -42.
A seed sprouted and grew 2 3 of a foot in 3 months. What was its rate of growth? simplify your answer and write it as a proper fraction, mixed number, or whole number. Feet per month.
If the seed sprouted and grew [tex]\frac{2}{3}[/tex] foot in 3 months , then the growth rate of the plant is [tex]\frac{2}{9}[/tex] foot per month .
the time in which the seed sprouted and grew [tex]\frac{2}{3}[/tex] feet = 3 months ,
to find the growth rate of the plant , we have to divide the length of plant grown by the time required for the growth .
that means , Growth Rate = [tex]\frac{\frac{2}{3} }{3}[/tex] ;
simplifying , we can write the fraction as : [tex]\frac{2}{9}[/tex] ;
So , the growth rate of the plant is [tex]\frac{2}{9}[/tex] foot per month , that means that there will be a [tex]\frac{2}{9}[/tex] foot increase in the length of the plant .
The given question is incomplete , the complete question is
A seed sprouted and grew 2/3 of a foot in 3 months. What was its rate of growth ?
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Which expression represents the volume of the prism, in cubic centimeters? 9x2 + 7x 14x2 + 7x 16x2 + 14x 28x2 + 14x.
Answer:
Step-by-step explanation:here is a example:Recall that the volume of a regular prism is given by the area of the base times the height.
Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.
The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.
Recall that the are of a triangle is given by 1/2 base times height.
Thus the area of of the pentagon base of the prism is given by
Therefore, the volume of the prism is given by volume=7x(2x+1)=14x2+7x
A toy train set includes a train station building which is a scale model of a real building. The area of the front side of the toy building is 1 square foot. The real building's front side has an area of 900 square feet. If we view the real building as a dilation of the toy, what is the scale factor?
The scale factor showing the view of the original building as a dilation of the toy is 0.00111.
What is the scale factor?The scale factor is a smaller or bigger representation of an object or shape.
The scale factor shows the ratio of the bigger or smaller scale to the original scale.
The scale factor shows the dilation of the toy when the new scale is reduced. It can also show the larger transformation of the toy when the original scale is increased by the scale factor.
The area of the scale model of the front side of the toy building = 1 ft²
The area of the front side of the original building = 900 ft²
The scale factor = 0.00111 (1 ft²/900 ft²)
Thus, we can conclude that the toy train's scale model is dilated by a scale factor of 0.00111.
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The cost c (in dollars) for the fuel and maintenance of a go-cart is given by c=10x+1200 , where x is the number of rides. It costs $40 per ride. How many rides does it take to break even?.
A go-fuel kart's and maintenance costs are calculated as follows: c=10x+1200, where x is the number of rides. $40 is the cost per ride. it takes x = 40 to break even.
What is meant by total cost?Total cost is the sum of all expenses incurred to obtain a particular level of output; average or unit cost is found by dividing total cost by the quantity produced.In order to calculate the average total cost, the total cost of production is divided by the total amount paid in money. The total-cost formula is a simple and user-friendly process that works by dividing the total cost of production by the quantity of goods produced.The total cost formula is used to total up the variable and constant expenses associated with providing commodities. Total cost = (Average Fixed Cost x Average Variable Cost) x Units Produced is the formula. You must be aware of the amounts for your fixed and variable costs in order to use this formula.The cost function given here is
c(x) = 10x + 1200
Where x = number of rides
c(x) is the total cost including the fixed cost.
Also it is given that each ride costs $40
So Revenue function for x number of rides shall be
R(X) = 40x
For break even
the cost must be equal to the revenue
Hence
R(x) = C(x)
40x = 10x + 1200
Subtracting 10x from both sides we get
30x = 1200
Dividing by 30 on both sides
We get
x = 40
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How do you do multiply and find the product?
To multiply two numbers, use the multiplication operator (*) between them. The product is the answer you get when you multiply the two numbers. For example, if you wanted to multiply 3 and 5, you would write 3 * 5 and the product would be 15.
1. Choose the two numbers to be multiplied.
2. Place the multiplication operator (*) between the two numbers.
3. Calculate the product of the two numbers.
4. The product is the answer you get when you multiply the two numbers.
To multiply two numbers, use the multiplication operator (*) between them. The product is the answer you get when you multiply the two numbers. For example, if you wanted to multiply 3 and 5, you would write 3 * 5 and the product would be 15.
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The table and corresponding image show the proof of the relationship between the slopes of two parallel lines. What is the missing statement in step 2?
Answer:
0-a/c-0 = -a/c
Step-by-step explanation:
The ratio of the number of comic books in Yazmin’s collection to the number of comic books in Itzel’s collection is 4:1. Itzel has 6 comic books. How many comic books does Yazmin have?
Answer: 35
Step-by-step explanation: 41 - 6 = 35
Jaidon counted dishes in the kitchen cabinet. The table shows what was found. Plates 8 Bowls 6 Cups 12 Write a ratio to compare bowls to all dishes. 6 to 12 6 over 26 26:6 6 over 18
The ratio comparing the 6 bowls to all the dishes will be 6 over 26. The correct option is B.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that Jaidon counted dishes in the kitchen cabinet. The table shows what was found. Plates 8 Bowls 6 Cups 12.
The ratio will be calculated as,
Ratio = 6 / ( 6 + 12 + 8 )
Ratio = 6 / 26
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Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options.
Nico, Raj and Sandra are correct.
And the explanation is given.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
An equation,
2/5(5 +x) = 8.
Nico, Aditi, Erick, Raj, and Sandra are solving the equation.
Approach 1:
Multiply by 5/2.
(5/2)(2/5)(5 +x) = 8(5/2)
5 + x = 20
x = 15.
Approach 2:
Multiply by 1/2 both sides
(1/2)(2/5)(5 +x) = 8(1/2)
5 + x = 4(5)
x = 15.
Approach 3:
Simplifying,
2 + 2/5x = 8
2x/5 = 6
x = 30/2
x = 15.
Therefore, Nico, Raj and Sandra are correct.
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an open-top storage bin in the shape of rectangular prism whose base is a square constructed such that the volume is 3500 cm^3. to minimize the weight of the storgae bin one must minimize the surface area. find the surface area (in cm^2) that minimizes the weight
The surface area that minimizes the weight of the storage bin is:
70x cm^2
To minimize the weight of an open-top storage bin in the shape of a rectangular prism, we need to minimize its surface area.
The volume of the storage bin is given as 3500 cm^3. Since the base of the bin is a square, we can let the length of one side of the base be x cm.
Therefore, the area of the base is x^2 cm^2.
The height of the bin is given by the equation:V = x^2 * h
where V is the volume and h is the height of the bin
So, we can substitute the value of V in the above equation to get:
3500 = x^2 * h
To minimize the surface area of the bin, we must minimize the sum of the areas of all its faces. The surface area of the rectangular prism is given by the formula:
2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism respectively.
Since the base of the bin is a square, we can let the length and width be equal to x. Therefore, we can use the equation of the height of the bin and the formula of the surface area of the rectangular prism to get:
2x^2 + 2xh = 2x^2 + 2x(3500/x^2)
Now, we can simplify the above equation to:
2x^2 + 2x(3500/x^2) = 2x^2 + 70x
To minimize the surface area, we need to minimize the value of x. We can see that the second term of the equation is a linear function of x and has a negative slope, which means that as x increases, the surface area decreases. Therefore, the surface area will be minimized when x is at its maximum value.
Therefore, the surface area that minimizes the weight of the storage bin is 70x cm^2.
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Which expression is equivalent to this sum?
O3(7+3)
O 3(7) +3
O 3+7+3
O 7(3+3)
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given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 2< x < 10
The rate of change of function is {r} = (1/8)(B - A).
What is rate of change of a function?Rate of change of a function between f(x) in the interval [a, b], is given as follows → {r} = {f(b) - f(a)}/{b - a}.In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a function f(x).
The given interval is - (2, 10). Since the table is not given, we can assume that -
f(10) = A
f(2) = B
Then, we can write the rate of change of functions as -
{r} = {f(b) - f(a)}/{b - a}
{r} = (B - A)/8
{r} = (1/8)(B - A)
Therefore, the rate of change of function is {r} = (1/8)(B - A).
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A salad dressing recipe uses 1. 5 cups of olive oil per batch and 0. 75 cups of vinegar per batch eden makes 3 1/2 batches of the salad dressing how many cups of salad does eden make
Please answer!!!!!!!!!!!!!!!!!
To make 3.5 batches of salad dressing, 7.875 cups of salad dressing are required.
What is equation?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 2.
Here,
1.5 cups of olive oil and .75 cups vinegar for 1 batch of salad dressing.
1.5+0.75=2.25 cups for 1 batch of dressing
3 1/2=3.5 batch
Total amount of cups=3.5*2.25
=7.875 cups of salad dressing
7.875 cups of salad dressing will be be needed to make 3.5 batches of salad dressing.
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if the zeros of the function are -2, 3, and 10 find the corresponding polynomial
Answer:
x³ - x² - 6x + 60
Step-by-step explanation:
you can write the polinom in this form: (x+2) × (x-3) × (x-10)
(x+2 = 0 => x = -2) same for other two zeros
(x² -3x +2x -6) × (x - 10) =
(x³ - 10x - 3x² + 30x + 2x² - 20x - 6x + 60) =
x³ - x² - 6x + 60
A line segment whose endpoint are on the circle is called a __________ of a circle .
Chord
Radius
Tangent
Diameter
A line segment whose endpoint are on the circle is called a __________ of a circle.
Chord
Radius
Tangent
Diameter
Answer: Chord
Find the value of x.
A. 41
B. 74
C. 82
D. 37
Answer:
37⁰
Step-by-step explanation:
180⁰ - 106⁰ =74⁰
74⁰ ÷ 2= 37⁰
The problem is on the picture. Thank you!
We can still simplify the fraction by dividing the numerator and denominator by 5 one more to obtain the final result, which is 29/40.
What is a Fraction?As the fraction's numerator, you should first write 725 because that is how the number appears after the decimal point.
We will take 1,000 as the fraction's denominator because there are three digits following the decimal point, allowing us to add three zeros and a one before it.
725/1000 is not the lowest word for the fraction.
The result of dividing the numerator and denominator by 5 is
145/200.
We can still simplify the fraction by dividing the numerator and denominator by 5 one more to obtain the final result,
which is 29/40.
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4. Each image shows a quadrilateral in a plane. The quadrilateral has been dilated using a center above the plane and a scale factor between 0 and 1.
Estimate the scale factor that was used for each dilation. (Lesson 5-3)
Dilation A
Dilation B
Dilation C
Given the above image, the estimated scale factor used in the dilation are given as follows:
Dilation A - 3/4
Dilation B - 1/4
Dilation C - 1/2
What is a scale factor?The scale factor is a metric for figures with similar appearances but differing scales or measurements. Assume two circles appear identical but have different radii. The scale factor specifies how much larger or smaller a figure is than the original figure.
When the new and original dimensions are specified, the scaling factor may be determined. The fundamental formula for determining a figure's scale factor is: Scale factor = Dimension of the new shape ÷ Dimension of the old shape.
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