A point-slope form is an equation for a line, using a point and the slope of the line. So we have to find one x-coordinate and y-coordinate and write it in the form of (y-y₁) = m(x-x₁).
Here the total after 10 months is said to be 65 and number of months = 10. So we can calculate the set-up fee.
5 ×10 + x = 65
x = 65-50 = 15.
The only constant here is the set-up fee, 15.
Lets the number of months be x and total amount be y.
y- 5x = 15
Lets calculate the y intercept. x-term will be 0.
y+0 = 15
y = 15
Lets calculate the x-intercept. y term will be 0
-5x = 15
x = -3
Two points on the line are (-3,0) and (0,15)
slope = (15-0)/(0--3)
=15/3 = 5
So lets find out one point in the equation
If y=10,
10-5x = 15
-5x = 15-10
x = 5/-5 =-1
So a point on the line is (-1,10)
Point slope form,
(y-10) = 5 (x- ⁻1)
(y-10) = 5 (x+1)
So this is the point slope form.
y = 5x+15
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The ratio of the perimeter of a square piece of paper to the perimeter of a rectangular piece of paper is 2 : 5. Each side of the square piece of paper is 10cm. Find A. The perimeter of the square piece of paper B. The perimeter of the rectangular piece of paper C. The length of the rectangular piece of paper if its width is 15cm ( Please answer all parts!)
The perimeter of the square piece of paper is 40 cm .The perimeter of the rectangular piece of paper is 50 cm and the length of the rectangular piece of paper is 15 cm.
A. The perimeter of the square piece of paper is 40 cm.
This is calculated by multiplying the length of each side of the square by 4.
Length of each side = 10cm
Perimeter of square = 4 x 10 cm = 40 cm
B. The perimeter of the rectangular piece of paper is 50 cm.
This is calculated by multiplying the length and width of the rectangle by 2.
Length = 15 cm
Width = 15 cm
Perimeter of rectangle = 2 x (15 + 15) cm = 2 x 30 cm = 50 cm
C. The length of the rectangular piece of paper is 15 cm.
This is given in the question.
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Each kit to build a castle contains 235 parts.
How many parts are
in 4 of the kits?
evaluate h(x)= -10x when x= -3,0, and 4
In order to replace the value in the explicit expression for h, one must evaluate a function h(x) for a particular value of the independent variable x. h(-3)=30, h(0)=0, h(4)=-40
How to find the calculation?A function is evaluated by determining the value of f(x) =... or y =... that corresponds to a certain value of x. Simply substitute whatever x has been assigned for all of the x variables to do this.Meaning: Simplify and replace x with 5 Parentheses should be used to enclose the value that is being substituted.A variable is replaced with a provided number or expression when a function is evaluated. In order to replace the value in the explicit expression for h, one must evaluate a function h(x) for a particular value of the independent variable x.The task is as follows:h(x)=-10x
Let's determine the values below:
h(0)= -10 * (0) = 0 and h(4)= -10 * (4) = -40, respectively.
h(-3)=30, h(0)=0, h(4)=-40.
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The nature of the roots for the equation
If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.
What is Quadratic Equation ?
Quadratic equation can be defined as equation in which it is in the form of ax^2+bx+c = 0 .
Nature of Roots depending upon Discriminant
in step with the value of discriminant, we shall discuss the subsequent cases about the character of roots.
Case 1: D = 0
If the discriminant is same to 0 (b2 – 4ac = zero), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = zero, are real and equal. In this case, the roots are x = -b/2a. The graph of the equation touches the X axis at a single point.
Case 2: D > 0
If the discriminant is greater than zero (b2 – 4ac > 0), a, b, c are actual numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = 0, are actual and unequal. The graph of the equation touches the X-axis at two unique points.
Case 3: D < 0
If the discriminant is less than 0 (b2 – 4ac < 0), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = 0, are imaginary and unequal. The roots exist in conjugate pairs. The graph of the equation does not touch the X-axis.
Case 4: D > zero and perfect square
If D > zero and an excellent square, then the roots of the quadratic equation are actual, unequal and rational.
Case five: D > 0 and now not an excellent square
If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.
Therefore, If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.
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You are selling tickets for a high school play. Student
tickets cost $4 and general admission tickets cost $6.
You sell 31 tickets and collect $170. How many of each
type did you sell?
Answer:
sold 23 Tickets and 8 General Admission Tickets
Step-by-step explanation:
y = General Admission tickets
x = tickets
4x + 6y = 170
x + y = 31
Use the Substitution method:
4x + 6(31 - x) = 170
4x + 186 - 6x = 170
4x - 6x = -16
-2x = -16
x = 8
y = 31 - 8 = 23
Find the 67th term of the arithmetic sequence -17,-23,-29
The 67th term of the arithmetic sequence -17,-23,-29 is -413.
What is the arithmetic sequence?
An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always the same. This difference is called the common difference, and it can be represented by the variable d.
Given the sequence -17,-23,-29, we can see that the common difference is d = -23 - (-17) = -6
The nth term of an arithmetic sequence can be found using the formula:
a_n = a_1 + (n-1)d
where a_1 is the first term of the sequence, n is the term number and d is a common difference.
For the 67th term, a_1 = -17, n = 67 and d = -6
So the 67th term is:
a_67 = -17 + (67-1) * -6 = -17 + 66 * -6 = -17 - 396 = -413
Hence, the 67th term of the arithmetic sequence -17,-23,-29 is -413.
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Answer: -413
Step-by-step explanation:
A new long-life tire has a tread depth of 3/8 inches, instead of the more typical 7/32 inches. How much deeper is the new tire?
Using the subtraction operation, the new long-life tire with 3/8 inches depth is deeper than the more typical 7/32 inches by 5/32 inches.
What is a subtraction operation?Subtraction operations involve the minuend, the subtrahend, and the result called the difference.
It is one of the four basic mathematical operations, including addition, multiplication, and division.
The depth of the new long-life tire = 3/8 inches
The depth of the old tire = 7/32 inches
The difference = 5/32 inches (3/8 - 7/32)
Thus, the depth difference between the new long-life tire and the typical tire is 5/8 inches.
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Function rule or explanation of why it is not possible to find a function rule
Write the decimal as a fraction. 0.83 = F 10 x 0.83 = F x 10 8.33= [?]F
The decimal 8. 33 written as a fraction is 8 3/10
What is a fraction?
A fraction can be defined as the part of a whole number, variable, element,
The several types of fractions are;
Proper fractionsMixed fractionsImproper fractionsSimple fractionsComplex fractionsExamples of mixed fractions: 2 4/5, 7 1/2
Examples of simple fractions: 1/3, 1/4
Examples of improper fractions: 6/4, 7/5
Example of proper fractions: 2/3, 4/5
From the information given, we have that;
8.33
This is represented as;
8 3/10
Hence. the value is 8 3/10
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how to simplify 8(1+5x)
Answer:
0.2
Step-by-step explanation:
1. distribute 8 to 1 and 5
2. Now its 8+40x
3. Divide on both sides
4. 40x/40 cancels out
5. 8/40=0.2
Find the volume of the solid obtained by rotating the region bounded by y=x2 , y=0, and x=1, about the y-axis.
The volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis is π/2.
We have to determine the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis.
We will rotate the region near the y-axis using the disc method. Consequently, the curve's equation should be expressed in terms of y.
y = x^2
Taking square root on both side, we get
x = √y
We can write it as
x = y^{1/2}
The volume integral formula is
V = [tex]\pi\int_{a}^{b}R(x)^2dx[/tex]
The values of a and b are taken from the y-axis since the equation for the curve we need is expressed in terms of y.
Using the curve's equation, if x = 0, y = 0, and if x = 1, y = 1, respectively.
Thus, a = 0 and b = 1 are the values.
Now, we may use definite integral to express the volume.
V = [tex]\pi\int_{0}^{1}\left[y^{1/2}\right]^2dx[/tex]
Now simplify
V = [tex]\pi\int_{0}^{1}ydx[/tex]
Now integrating
V = [tex]\pi\left[\frac{y^2}{2}\right]_{0}^{1}[/tex]
V = [tex]\pi\left[\frac{(1)^2}{2}-\frac{(0)^2}{2}\right][/tex]
V = [tex]\pi\left[\frac{1}{2}-0}\right][/tex]
V = π/2
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Can someone please help me with this asap? I’ll give lots of points
A right triangle has 1 angle that measures 48 degrees. What is the measure of the third angle?
A: 64 degrees
B: 28 degrees
C: 42 degrees
D: 58 degrees
Step-by-step explanation:
always remember : the sum of all angles in a triangle is 180°.
so, one angle is 90° (it is a right triangle).
the second angle is 48°.
therefore,
180 = 90 + 48 + third angle
third angle = 180 - 90 - 48 = 42°
so, C is correct.
the preference card calls for 0.25% marcaine and 1% lidocaine to be equally concentrated. how much marcaine will you need to draw up to equal the 1% l
4.0 mL of marcaine will be needed to draw up to equal the 1%.
Marcaine is a brand name for the medication bupivacaine, which is a local anesthetic used to numb a specific area of the body during a surgical or medical procedure.
To determine the amount of marcaine that is needed to be drawn up to equal the 1% lidocaine, we can use the following formula:
(Concentration of Lidocaine) / (Concentration of Marcaine) = (Volume of Lidocaine) / (Volume of Marcaine)
In this case, we know that the concentration of lidocaine is 1% and the concentration of marcaine is 0.25%. So we can plug these values into the formula:
1 / 0.25 = (Volume of Lidocaine) / (Volume of Marcaine)
To solve for the volume of marcaine, we can multiply both sides of the equation by the volume of lidocaine:
(Volume of Lidocaine) / (Volume of Marcaine) = 4
Therefore, 4.0 mL of marcaine will be needed to draw up to equal the 1%.
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(4)(-0.5)(8)(-2/4) a positive product?
Answer: +8
Step-by-step explanation:
yes, it is going to be a positive product, since two negative signs multiply to give a positive sign.
⇒(4)(-0.5)(8)(-2/4)
⇒+8 ..Answer
hope that helps...
WILL GIVE BRAINLIEST
Find the average rate of change for the given function from x = −1 to x = 2
The average rate of change for the given function from x = −1 to x = 2 is -4/3
How to find the average rate of change for the given function from x = −1 to x = 2?The average rate of change of a function over an interval is a measure of how much the output of the function (y-value) changes as the input (x-value) changes over that interval. This is also the slope of the function or line.
average rate of change = (y2-y1)/(x2-x1)
From the graph, x1 = -1, y1 = 4 and x2 = 2, y2 = 0
average rate of change = (0-4)/(2-(-1)) = -4/3
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what is the value of the expression below? (15^1/5)^5
Answer:
15
Step-by-step explanation:
Given the expression:
[tex]\displaystyle{\left(15^{\frac{1}{5}}\right)^5}[/tex]
We can apply the law of exponent of:
[tex]\displaystyle{\left(a^m\right)^n = a^{mn}}[/tex]
Therefore, we will have:
[tex]\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15^{\frac{5}{5}}}\\\\\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15^{1}}\\\\\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15}[/tex]
Hence, the value of expression is 15.
(05.01 MC)
Currently, the temperature of an ice cream is 81°C below room temperature. The temperature of the ice cream decreases based on the
function f(t)=81(0.83) where t represents time elapsed in minutes. Where does the graph of f(t) cross the y-axis, and what does this represent
in the context of the problem?
The graph of f(t) crosses the y-axis at t = 0, which represents the initial temperature of the ice cream (81°C below room temperature).
What does this represent in the context of the problem?The graph of f(t) crosses the y-axis at y=81, which represents the initial temperature of the ice cream, 81°C below room temperature. This is the starting point of the graph, and all subsequent points on the graph represent the temperature of the ice cream as time progresses. As time passes, the temperature of the ice cream decreases, and the graph of f(t) illustrates this change.
The y-intercept of a graph measures the initial value of the function. In this case, the initial temperature of the ice cream is 81°C below room temperature. As the time passes, the temperature of the ice cream decreases at a rate of 0.83°C per minute. This rate of decrease is represented by the slope of the graph, which is 0.83.
The point where the graph of f(t) crosses the y-axis illustrates the initial temperature of the ice cream, and all subsequent points on the graph represent the temperature of the ice cream as time progresses. This is a helpful visual representation of the rate at which the temperature of the ice cream is decreasing. The graph of f(t) is a useful tool for understanding how the temperature of the ice cream changes over time.
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students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a
Students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a hypothesis.
A hypothesis is a proposed explanation or prediction about a phenomenon, based on limited information or data. It is a tentative statement about the relationship between variables that can be tested through further investigation or experimentation.
In scientific research, a hypothesis provides a framework for designing and conducting experiments to gather evidence to support or reject the hypothesis. It acts as a starting point for scientific inquiry and helps guide the research process.
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Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Gary would need 15.2 oz. of glue and 7.6 oz. of glitter to make 4 bottles.
The correct option is D.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
Given in the table,
Bottles Glue Glitter
1 3.8 1.9
Therefore
1 bottle = 3.8 oz. of glue + 1.9 oz. of glitter
Now,
Multiply 4 on both sides.
4 bottle = 4 x (3.8 oz. of glue + 1.9 oz. of glitter)
4 bottle = 15.2 oz. of glue + 7.6 oz. of glitter
Hence, 15.2 oz. of glue and 7.6 oz. of glitter is needed to make 4 bottles.
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The relationship between time in months and height in inches for Kylie's plant is represented by the
equation y = 12x. The relationship for Glen's plant is represented by the equation 2y = 24x. Is there a
time when the two plants are the same height?
Both equations are equivalent, which means that the two plants always have the same height.
Is there a time when the two plants are the same height?We know that the height in inches for Kylie's plant is represented by the
equation y = 12x, where x is the time in months.
And the height of Glen's plant is represented by the equation 2y = 24x
Notice that if we take the second equation and we divide both sides by 2, we will get:
2y = 24x
2y/2 = 24x/2
y = 12x
This is the same equation than the one that represents the height of Kylie's plant.
Then the two plantes have the same height always.
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Find the slope of the line through (-2,6) and (-5,9)
-1
Step-by-step explanation:Slope describes the rise over run for a graph.
Slope Formula
Slope is the change in y over the change in x. To find the slope of any line from two points we can use the slope formula. The slope formula is [tex]\displaystyle\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. We can plug the points we are given into this formula.
[tex]\frac{9-6}{-5-(-2)}[/tex]This equals [tex]\frac{3}{-3}[/tex] which is simply -1. The slope of the line is -1.
Counting the Change
The formula above just represents the changes in the y-values divided by the changes in the x-values. So, we can count that the y-values increase by 3. Then, the x-values decrease by 3. This creates the slope [tex]\frac{3}{-3}[/tex] (remember that increases are positive and decreases are negative). Once again this gives the slope of -1.
The average birth weight of a Boxer breed dog is 1.25 kilograms. What is the average birth weight in grams?The average birth weight of a Boxer breed dog is 1.25 kilograms. What is the average birth weight in grams?
Answer:
1250g
Step-by-step explanation:
1.25 kg × 1000 = 1250g
Sara says if you subtract 19 from my number and multiply the difference by -6 the result is -96,
what is saras number
PLEASE PLAE PLASE PALSE PLASEP APLSASEP PLASEP PLEASE PLAESESEEPZ.
3. I have two maps. One is of the Catskill mountains. The scale is 1.5 inches : 4 miles.
The other is of the Shawangunk mountains. The scale is 2 inches : 3.5 miles.
a) Find the distance of Slide mountain in the Catskills if on the map the trail is 2.325 inches.
b) Find the distance of Gertrude's nose in the Shawangunk's is 3.8 inches on the map.
a) Distance of Slide mountain in the Catskills is 6.2 miles
b) Distance of Gertrude's nose in the Shawangunk's = 6.65 miles
How to find a distance?To find a distance on a map, you need to use a ruler or a measuring device such as a pair of compasses. Firstly, place the ruler on the two points you want to measure the distance between. If you are using a pair of compasses, adjust the legs so that the two points are inside the circle created by the compasses. Then, read the distance on the ruler or across the arc of the compasses.
If the distance is relatively short, you can also use the map scale located at the side or bottom of the map. To use the scale, line up the starting point with the scale and then measure the length of the line on the scale. This will give you the distance between the two points.
Finally, if the map has a grid system, you can count the number of squares between the two points and then refer to the grid scale to calculate the distance.
By using one of the methods described above, you should be able to easily measure distances on a map.
a) 2.325 inches * 4 miles/1.5 inches = 6.2 miles
b) 3.8 inches * 3.5 miles/2 inches = 6.65 miles
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the diagonals of a trapezoid are perpendicular and have lengths $3$ and $4$. find the length of the median of the trapezoid.
The correct answer is 5/2. The median trapezoid is the line segment that bisects the area of the trapezoid and has its end points on the 2 bases of the trapezoid.
The median length is √( (3/2)^2 + (4/2)^2 ) = √(9/4 + 16/4) = √(25/4) = 5/2. So, the length of the median of the trapezoid is 5/2.
Since the diagonals of a median trapezoid bisect each other, the median of the trapezoid is the line segment that connects the midpoints of the diagonals. To find the median length, we can use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the 2 points. In this case, the median length is the square root of the sum of the squares of 1/2 length of the diagonals.
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The length of the median of the trapezoid will be 5/2 units.
Given that the median trapezoid is the line segment that divides the trapezoid's area and has its ends on its two bases,
The median length will be:
√( (3/2)^2 + (4/2)^2 )
= √(9/4 + 16/4)
= √(25/4)
= 5/ units
So, the length of the median of the trapezoid is 5/2.
The median of a median trapezoid is the line segment that links the midpoints of the diagonals since the diagonals of a median trapezoid bisect one another. We may use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the two points, to get the length of the median. The median length in this instance is equal to the square root of the sum of the squares of the diagonals' half-lengths.
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-2(c+2.5)-5(1.2c+4) simplify this expression
Answer: - 8c - 25
Step-by-step explanation:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.
5. Suppose the following table shows the number of labor hours needed to produce airplanes and automobiles in the United States and South Korea, but one of the numbers is unknown.
Number of Hours to Produce One Airplane
South Korea 2000 United States 1000
Number of Hours to Produce One Auto
?
10
a. Without knowing the number of labor hours required to produce an auto in South Korea, you can’t figure out which country has the comparative advantage in which good. Can you give an example of a number for the empty cell of the table that would give the United States the comparative advantage in the production of airplanes? What about South Korea?
b. What exact number would you have to place in the empty cell of the table for it to be impossible that trade between the United States and South Korea could benefit both
The number for an empty cell would be 20 so any number below this benefit South Korea and above this benefit the United States. This also makes it impossible for trade between these two countries.
If a country can manufacture a significant number of goods with the same resources as another country, it has an absolute advantage. If a country can manufacture a certain commodity more cheaply and with higher quality than another country, it has a comparative advantage.
In the given scenario, 1000÷10=100 autos are sacrificed by the United States to manufacture one airplane which is the opportunity cost. In comparison to the United States, South Korea requires twice (2000÷1000) as long to construct an airplane.
a) The number of hours for South Korea to produce one auto would be 2×10=20. Because of this, South Korea would benefit from any number below 20, while the US would benefit from any number above 20.
b) The empty cell value would be 20 for South Korea to have the same opportunity cost as the United States. So mutually beneficial trade cannot exist without comparative advantage.
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In a survey of 50 first graders, 30% said their favorite food is hot dog. Which box is correctly set up to show this?
The probability that the number of first graders who have liked the hot dog is 15
In math the term probability is defined as a number that reflects the chance or likelihood that a particular event will occur
Here we have know that in a survey of 50 first graders, and then 30% said their favorite food is hot dog.
Here we have to find the probability that the number of first graders who have liked the hot dog
As we know that the number of first graders is 50.
And here we also know that 30% of them are liked the hot dog.
Then it can be calculated as,
=> 50 x 30%
=> 50 x 30/100
=> 15.
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The cost of a bicycle wheel was $62 last week. This week, the cost rose to $79 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
the percentage increase is 27.4%
Step-by-step explanation:
To find the percentage increase, we can use the formula:
(New cost - Old cost) / Old cost x 100% = Percentage increase
(79 - 62) / 62 x 100% = 27.41%
The percentage increase is 27.41%. Rounded to the nearest tenth of a percent, the percentage increase is 27.4%
Difference of $62 and $79 is 24.1%
62 - 79/((62 + 79)/2) = 17/70.5 =
0.24113475177305 x 100 = 24.113475177305%
find -|-2/5|?
-2.5
2.5
2/5
-2/5
Answer:
(2/5)
Step-by-step explanation:
(-2/5) = -(2/5)
|-(2/5)| = (2/5)