Answer:
Intersecting (fourth answer choice)
Step-by-step explanation:
If the lines are perpendicular, parallel, or intersecting, they are not skew. Thus, we need to check if the lines can be classified as either perpendicular, parallel, or intersecting first. If the lines are classified as neither, then they are skew.First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Converting y - 3x = 4x to slope-intercept form:
(y - 3x = 4x) + 3x
y = 7x
Thus, the slope of this line is 7 and the y-intercept is 0.
Converting 6 - 2y = 8x to slope-intercept form:
(6 - 2y = 8x) - 6
(-2y = 8x - 6) / -2
y = -4x + 3
Thus, the slope of this line is -4 and the y-intercept is 3.
Checking if y = 7x and y = -4x + 3 are perpendicular lines:
The slopes of perpendicular lines are negative reciprocals of each other.We can show this in the following formula:
m2 = -1 / m1, where
m1 is the slope of one line,and m2 is the slope of the other line.Thus, we only have to plug in one of the slopes for m1. Let's do -4.
m2 = -1 / -4
m2 = 1/4
Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.
Checking if y = 7x and y = -4x + 3 are parallel lines:
The slopes of parallel lines are equal to each other.
Because 7 and -4 are not equal, the two lines are not parallel.
Checking if the lines intersect:
The intersection point of two lines have the same x and y coordinate. To determine if the two lines intersect, we treat them like a system of equations.Method to solve the system: Elimination:
We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:
add the two equations, eliminate the ys, and solve for x:-1 (y = 7x)
-y = -7x
----------------------------------------------------------------------------------------------------------
-y = -7x
+
y = -4x + 3
----------------------------------------------------------------------------------------------------------
(0 = -11x + 3) - 3
(-3 = -11x) / 11
3/11 = x
Now we can plug in 3/11 for x in y = 7x to find y:
y = 7(3/11)
y = 21/11
Thus, x = 3/11 and y = 21/11
We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3. If we get the same answer on both sides of the equation for both equations, the lines intersect:
Checking solutions (x = 3/11 and y = 21/11) for y = 7x:
21/11 = 7(3/11)
21/11 = 21/11
Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:
21/11 = -4(3/11) + 3
21/11 = -12/11 + (3 * 11/11)
21/11 = -12/11 + 33/11
21/11 = 21/11
Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).
This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.
quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 62
minutes with a mean life of 606
minutes.
If the claim is true, in a sample of 99
batteries, what is the probability that the mean battery life would be greater than 619
minutes? Round your answer to four decimal places.
Answer:
Step-by-step explanation:
Find the area of
the parallelogram.
8
11
7
Use the
formula:
a = bh
area = base x height.
b = 11
h = 7
a = [?]
Answer:
77 units^2
Step-by-step explanation:
Since the formula for the area of a parallelogram is Area = Base x Height, you can multiply the Base (11) by the Height (7)
So, A = (7) x (11) = 77 units^2
The 8 in this case is not necessary. You only need the base and height. Hope this helps!
In the following figure, assume that a, b, and c = 5, e = 12, and d = 13. What is the area of this complex figure? Note that the bottom triangle is a right triangle. The height of the equilateral triangle is 4.33 units.
Answer:
The area of the complex figure is approximately 210.92 square units.
Step-by-step explanation:
Let's calculate the area of the complex figure with the given information.
We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.
1. Equilateral Triangle:
The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:
Area of Equilateral Triangle = (base^2 * √3) / 4
In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.
Area of Equilateral Triangle = (13^2 * √3) / 4
Area of Equilateral Triangle ≈ 42.42 square units
2. Right Triangle:
The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).
Area of Right Triangle = (base * height) / 2
In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).
Area of Right Triangle = (5 * 5) / 2
Area of Right Triangle = 12.5 square units
3. Rectangle:
The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).
Area of Rectangle = length * width
Area of Rectangle = 13 * 12
Area of Rectangle = 156 square units
Now, to get the total area of the complex figure, we add the areas of each component:
Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle
Total Area = 42.42 + 12.5 + 156
Total Area ≈ 210.92 square units
Therefore, the area of the complex figure is approximately 210.92 square units.
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.
For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).
Applying this transformation to each vertex of triangle NMO, we get:
N' = (2(-1) - (-5), 2) = (5, 2)
M' = (2(-1) - (-2), 1) = (2, 1)
O' = (2(-1) - (-3), 3) = (3, 3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
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need help with this ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]\dfrac{120}{169}[/tex]
Step-by-step explanation:
Find the exact value of the given trigonometric expression.
[tex]\sin(2\sin^{-1}(\frac{12}{13} ))= \ ??\\\\\hrule[/tex]
The method I am about to show you will allow you to complete this problem without the use of a calculator. Although, memorization of the trigonometric identities is essential.
Apply the following double-angle identity.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Double-Angle Identity:}}\\\\\sin(2A)=2\sin(A)\cos(A)\end{array}\right}[/tex]
[tex]\sin(2\sin^{-1}(\frac{12}{13} ))\\\\\\ \\\Longrightarrow 2\sin(\sin^{-1}(\frac{12}{13} ))\cos(\sin^{-1}(\frac{12}{13} ))\\\\\\ \\\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\sqrt{1-(\frac{12}{13} )^2} \Big)\\\\\\ \\\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\sqrt{1-(\frac{12}{13} )^2} \Big)\\\\\\ \\\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\sqrt{1-\frac{144}{169}}} \Big)\\\\\\ \\\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\sqrt{\dfrac{25}{169}}} \Big)[/tex]
[tex]\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\dfrac{5}{13} } \Big)\\\\\\\\\Longrightarrow \boxed{\boxed{\frac{120}{169} }}[/tex]
Thus, the problem is solved.
Celeste is planting a rectangular flower garden in which the width will be 4 feet less than its length. She has decided to put a birdbath within the garden that will occupy a space 3feet by 4 feet how many feet are now left for planting? Express your answer on factored form
Answer:
(L-6)(L+2)
Step-by-step explanation:
Let L be the length of the flower garden.
Then the width will be L-4.
The area of the flower garden = L*(L-4) =L²-4L
The area of the birdbath is 3*4 = 12 ft²
The area of the remaining space for planting is
= Area of flower garden - area of birdbath
L² - 4L - 12We can factor the expression as follows:
L² - 4L - 12 L²-(6-2)L-12L²-6x+2x-12taking common frome each two terms
L(L-6)+2(L-6)(L-6)(L+2)Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.
Simplify 3r^4 • (-4r^0)
what is the result of converting 2.3 miles into yards ? remenber that 1 mile=1760 yards.
4048 yards is the answer
Step-by-step explanation:
2.3 × 1760
Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A' is at (−4, 2) and the image of D' is at (−2, 1).
polygon ABCDE is on a coordinate plane with point A at 2, 4 and point B at 4, 3 and point C at 3, 2 and point D at 1, 2 and point E at 0, 3
Which transformation can be used to show that ABCDE and its image are congruent?
The transformation used to show congruence between polygon ABCDE and its image is a translation of 6 units to the left and 1 unit down.
To show that polygon ABCDE and its image are congruent, we need to determine which transformation was used. In this case, the transformation that can be used to show congruence is a translation.
A translation is a transformation that moves every point of a figure by the same distance and in the same direction. Since the image of A' is at (-4, 2) and the image of D' is at (-2, 1), we can see that the polygon was shifted 6 units to the left and 1 unit down.
Therefore, the transformation used is a translation of -6 units in the x-direction and -1 unit in the y-direction. This translation preserves the shape and size of the polygon, making ABCDE congruent to its image.
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Is the expression quadratic 3x+5y-2
No, the expression 3x + 5y - 2200 is not a quadratic expression.
A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.
It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.
"3x + 5y - 2" is a linear expression, not a quadratic expression.
In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.
The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.
It is a first-degree polynomial, meaning that the highest power of the variable is 1.
Linear expressions often have a graph that is a straight line.
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No. The expression, 3x + 5y - 2, is not quadratic.
What are quadratic expressions?The expression "3x+5y-2" is a linear expression, not quadratic.
Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.
The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.
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See picture dfown below for refgerecnce
The value of the quadratic function y = x² - 4x + 3 is determined by substituting the given value of x into the equation and performing the necessary calculations.
1. Start with the quadratic function: y = x² - 4x + 3.
2. Determine the value of x for which you want to find the value of y.
3. Substitute the given value of x into the equation.
4. Perform the necessary calculations to simplify the expression.
5. Evaluate the expression to find the value of y.
For example, let's find the value of y when x = 2:
1. Start with the quadratic function: y = x² - 4x + 3.
2. We want to find the value of y when x = 2.
3. Substitute x = 2 into the equation: y = (2)² - 4(2) + 3.
4. Simplify the expression: y = 4 - 8 + 3.
5. Perform the necessary calculations: y = -1.
6. Therefore, when x = 2, the value of the quadratic function y = x² - 4x + 3 is -1.
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40,328*77 =
Remainder:
Answer: Step-by-step work:
40,328
77
3,105 (Carry the 3)
27,468
302,976
1,609,432
Add the numbers horizontally:
2,943,941
So, 40,328 * 77 = 2,943,941
The remainder when divided by 10 is:
2,943,941 % 10 = 1
Therefore, the remainder is 1.
More concisely:
40,328 * 77 = 2,943,941
2,943,941 % 10 = 1
So the remainder when 2,943,941 is divided by 10 is 1.
Hope this helps! Let me know if you have any other questions
Step-by-step explanation:
1. Obtener el área del siguiente rectángulo.
13
2
74
The area of the given rectangle is determined by multiplying its length of 13 units by its width of 2 units, resulting in an area of 26 square units.
To find the area of the rectangle, we need to multiply its length by its width. The length of the rectangle is given as 13 units and the width is given as 2 units.
The formula to calculate the area of a rectangle is: Area = Length × Width.
Using the given measurements, we substitute the values into the formula:
Area = 13 × 2 = 26 square units.
Therefore, the area of the given rectangle is 26 square units.
To provide a more detailed explanation, the area of a rectangle represents the total amount of space enclosed by its four sides. In this case, the rectangle has a length of 13 units and a width of 2 units. When we multiply the length by the width, we are essentially finding the product of the two dimensions, which gives us the total area.
The resulting area of 26 square units implies that within the boundaries of the rectangle, there are 26 square units of space. It is important to note that the unit of measurement used for the length and width should be consistent to ensure the accuracy of the area calculation.
In summary, the area of the given rectangle is determined by multiplying its length of 13 units by its width of 2 units, resulting in an area of 26 square units.
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9 ft
4.7 ft
6.5 ft
6.5 ft
Find the area of the triangle.
Answer: 21.15 ft²
Step-by-step explanation:
We can use the formula for the area of a triangle:
(b×h)/2
In this case, the base is 9 and the height is 4.7.
So, we substitute the variables with the numbers in this problem.
(9 × 4.7)/2
9 × 4.7 = 42.3
42.3/2 = 21.15
So, our final answer is 21.15 ft²
Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$1300/semiannual period for 8 years at 4.5%/year compounded semiannually
Answer:
Therefore, the amount (future value) of the ordinary annuity is approximately $19,446.27.
Step-by-step explanation:
We can use the formula:
FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)
where we will consider :
FV is the future value,
P is the periodic payment,
r is the interest rate per period,
n is the number of compounding periods per year, and
t is the number of years.
Now given :
P = $1300 (payment per semiannual period)
r = 4.5% per year (or 0.045 as a decimal)
n = 2 (compounded semiannually)
t = 8 years
Plugging in these values into the formula, we will be getting:
FV = 1300 * [(1 + 0.045/2)^(2*8) - 1] / (0.045/2)
Calculating this expression will give us the future value (amount) of the ordinary annuity:
FV = 1300 * [(1 + 0.0225)^(16) - 1] / 0.0225
FV ≈ $19,446.27 (rounded to the nearest cent)
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what is da rate to question
The calculated value of the rate of the graph is 0.8
How to determine the rate of the graphfrom the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
(0, -16) and (20, 0)
The rate of the graph is calculated as
Rate = Change in y/x
using the above as a guide, we have the following:
Rate = (0 + 16)/(20 - 0)
Evaluate
Rate = 0.8
Hence, the rate is 0.8
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Which linear equation shows a proportional relationship?
y equals negative one sixth times x
y equals one sixth times x minus 8
y = −6x + 1
y = 6
Answer:
y = (-1/6)x represents a proportional relationship.
Shireen had a nap for 2 h. After her nap, she played badminton for 1/2h and swam for 1/5h.
(a) How long did Shireen exercise?
(b) How much more time did Shireen spend on her nap than on
her exercise?
give me a solution just the answer
Answer:
If the tickets are priced at $20 each, the total amount of money taken in would be $88,000.
Step-by-step explanation:
To write the number of tickets sold, n, as a function of the ticket price, p, we can use the given information that for every $1 increase in price, 200 tickets go unsold.
Let's define the slope of the line as the decrease in tickets per dollar increase in price. Since 200 tickets go unsold for every $1 increase, the slope of the line is -200.
Now, let's find the equation of the line through the given points: (12, 6000), (13, 5800), (14, 5600), and so on.
Using the point-slope form of a linear equation, we have:
n - 6000 = -200(p - 12)
Simplifying the equation, we get:
n - 6000 = -200p + 2400
Rearranging the equation to solve for n, we have:
n = -200p + 8400
This equation represents the number of tickets sold, n, as a function of the ticket price, p.
To find how much money will be taken in if the tickets are $20 each, we substitute p = 20 into the equation:
n = -200(20) + 8400
n = -4000 + 8400
n = 4400
If the tickets are $20 each, the number of tickets sold would be 4400. To calculate the total amount of money taken in, we multiply the number of tickets sold by the ticket price:
Money taken in = Number of tickets sold * Ticket price
Money taken in = 4400 * $20
Money taken in = $88,000
Hope this helps.
you ran 4 1/2 times around a quarter mile track. how far did you run?
Answer:
1 1/8 of a mile.
Step-by-step explanation:
The distance around the track is one quarter of a mile. Therefore, if you run around the track 4 times, you will have ran 1 mile, as 4 * 1/4 = 1. You would also run the other 1/2 of the lap, and to find that distance, you would multiply 1/2 * 1/4, because you only ran 1/2 of a lap and not one whole lap, which would come out to 1/8 of a mile. So, your final answer would be 1 + 1/8 of a mile, which comes out to 1 and 1/8 of a mile.
4 is the product of 8 and b simplify all fractions
The value of b in the Problem given is 0.5
Simplifying Word problemsThe given problem can be represented mathematically as below :
4 = 8 * bWe can find be in the expression thus :
4 = 8b
divide both sides by 8 in other to isolate b
4/8 = 8b/8
0.5 = b
Therefore, value of b in the expression is 1/2.
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What change do you have to make to the graph of f (x) = 7x in order to graph the function g (x) = 7x+10?
To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.
To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.
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If GE is the angle bisector of
A green grocer buys a box of 150 grapefruit for $12. He sells them for 12 cents each. What is the profit percent
The profit percent made by the green grocer on the sale of the grapefruits is 50%.
To calculate the profit percent, we need to determine the profit made on the sale of the grapefruits.
The grocer buys a box of 150 grapefruits for $12, which means the cost of each grapefruit is $12/150 = $0.08.
The grocer sells each grapefruit for 12 cents, which is $0.12.
The profit made on each grapefruit is the selling price minus the cost price: $0.12 - $0.08 = $0.04.
Now, we can calculate the total profit by multiplying the profit per grapefruit by the number of grapefruits: $0.04 * 150 = $6.
To find the profit percent, we divide the profit by the cost price and multiply by 100: ($6 / $12) * 100 = 50%.
Therefore, the profit percent is 50%.
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A ____ is just another way of saying what we want to count by on our graph.
Answer:
A scale is just another way of saying what we want to count by on our graph.
Step-by-step explanation:
A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.
Which value is equilivent to x+4/4+x
Answer:
It's 1
Step-by-step explanation:
any number or expression divided by itself is 1
Answer:
1
Step-by-step explanation:
The expression (x + 4) / (4 + x) simplifies to 1 because no matter what value you choose for x, when you add 4 to it and add the same value to 4, you always get the same result in the numerator and denominator, making them cancel out and equal to 1.
A study was completed in Georgia. In northern Georgia, the study involved 3,000 patients; 84% of them experienced flulike symptoms during the month of December. The study had a margin of error of 1.7% What does that mean for the study?
Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
Each pair of figures is similar. Find the value of the missing side (x). Round your answer to the nearest tenth if necessary.
Answer:
4.9 in
Step-by-step explanation:
6/11 = x/9
6/11 times 9 = x
x = 4.9
Which graph shows a dilation? On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 0.5, 0), (negative 1, 2), (1, 2), (1.5, 0).
Make sure to maximize the question window to get the best view of this problem.
Give the formulas for the piecewise function graphed below.
Make sure the top row is for the left piece, the second row is
for the middle plece, and the bottom row is for the right piece.
f(x) =
The formulas for the piecewise function graphed below are:
f(x) = x + 3 for -2 ≤ x < 0, 3 for 0 ≤ x < 2, -2x + 7 for 2 ≤ x ≤ 4.
The piecewise function graph provided consists of three distinct pieces.
To give the formulas for each piece, we can break it down as follows:
For the left piece:
The left piece of the graph starts at x = -2 and ends at x = 0. It appears to be a linear function with a positive slope. Let's call this function f₁(x).
The formula for the left piece, f₁(x), can be written as:
f₁(x) = mx + b
To find the slope (m) and y-intercept (b), we can use two points on the graph.
From the graph, we can see that when x = -2, y = 1. And when x = 0, y = 3.
Using the formula for slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 1) / (0 - (-2))
m = 2 / 2
m = 1
Substituting the values of m and one of the points (x, y) into the equation, we can solve for the y-intercept (b):
1 = 1(-2) + b
1 = -2 + b
b = 1 + 2
b = 3
Therefore, the formula for the left piece is:
f₁(x) = x + 3
For the middle piece:
The middle piece of the graph starts at x = 0 and ends at x = 2. It appears to be a horizontal line.
Let's call this function f₂(x).
The formula for the middle piece, f₂(x), can be written as:
f₂(x) = c
To find the value of c, we can observe that the y-values of this piece are all equal to 3.
Therefore, the formula for the middle piece is simply:
f₂(x) = 3
When x = 2, y = 3. And when x = 4, y = -1.
Using the formula for slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
m = (-1 - 3) / (4 - 2)
m = -4 / 2
m = -2
Substituting the values of m and one of the points (x, y) into the equation, we can solve for the y-intercept (b):
3 = -2(2) + b
3 = -4 + b
b = 3 + 4
b = 7
Therefore, the formula for the right piece is:
f₃(x) = -2x + 7
To summarize, the formulas for the piecewise function graphed below are:
f(x) =
x + 3 for -2 ≤ x < 0
3 for 0 ≤ x < 2
-2x + 7 for 2 ≤ x ≤ 4
For more related questions on piecewise function:
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