The expression represented by the given number line is f(x) = -k(x+2.5)(x-3) where k > 0.
The expression represented by the given number line can be determined by identifying the values that correspond to the endpoints of each arrow and the direction of the arrow.
Starting from the left endpoint, the arrow goes from -2.5 to -1. This means that the expression is positive between -2.5 and -1. To determine the exact expression, we need to know the interval of the arrow.
The arrow starts at 0 and ends at 3, which means the expression is positive between 0 and 3. Finally, the arrow goes from 3 to -2.5, which means the expression is negative between 3 and -2.5.
Putting all of this information together, we can write the expression as:
f(x) = k(x+2.5)(x-3)
where k is a constant that determines the overall scale of the expression. Since the expression is positive between -2.5 and -1, we know that k must be negative. Since the expression is negative between 3 and -2.5, we know that k must be positive.
Therefore, the expression represented by the given number line is:
f(x) = -k(x+2.5)(x-3) where k > 0.
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Ellus
These prisms are similar. Find the surface
area of the larger prism in decimal form.
5 m
7 m
Surface Area
90 m2
Surface Area = [? ] m2
please helppp. :)
If two prisms are similar, their corresponding dimensions are proportional.
Let's assume that the ratio of the corresponding lengths of the smaller prism to the larger prism is k:1, where k is a constant.
Then the ratio of the corresponding surface areas of the smaller prism to the larger prism is [tex](k^2):1[/tex], because the surface area of a prism is proportional to the square of its length.
In this problem, the surface area of the smaller prism is not given.
However, we can find the ratio of the corresponding lengths of the smaller prism to the larger prism using the fact that they are similar.
The height of the smaller prism can be found as follows:
[tex]7/5 = h/L[/tex]
where h is the height of the smaller prism and L is the length of the larger prism.
Solving for h, we get:
[tex]h = (7/5)L[/tex]
The ratio of the corresponding lengths of the smaller prism to the larger prism is 7:5.
The ratio of the surface areas of the smaller prism to the larger prism is:
[tex](7/5)^2 : 1 = 49/25 : 1[/tex]
We know that the surface area of the larger prism is [tex]90 m^2.[/tex]
Let's denote the surface area of the smaller prism by A. Then we can set up an equation:
(49/25)A = 90
Solving for A, we get:
A = (25/49) * 90 = 45/7 ≈ 6.4
The surface area of the smaller prism is approximately [tex]6.4 m^2.[/tex]
(Note: The units of the surface area are not provided for the smaller prism, so I assumed the same units as the larger prism.
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Consider the following 8 numbers, where one labelled
x
is unknown. 32
,
46
,
46
,
x
,
35
,
9
,
4
,
38
Given that the range of the numbers is 55, work out 2 values of
x
Two possible values of x are 10 and 40.
To find two possible values of x, we need to first determine the highest and lowest numbers in the set.
Highest number: 46
Lowest number: 4
To get a range of 55, we need the highest number minus the lowest number to equal 55.
46 - 4 = 42
But we know that there are 8 numbers in the set, so the range must be spread out over those 8 numbers. To get an idea of how much each number should increase, we can divide 42 by 7 (the number of gaps between the numbers) to get an average increase of 6.
Now we can use this average increase to find two possible values of x.
1) If x is 6 more than the lowest number (4 + 6 = 10), then the set becomes:
4, 9, 10, 32, 35, 38, 46, 46
And the range is:
46 - 4 = 42
2) If x is 6 less than the highest number (46 - 6 = 40), then the set becomes:
4, 9, 35, 38, 40, 46, 46, 32
And the range is:
46 - 4 = 42
Therefore, two possible values of x are 10 and 40.
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Frank has four different credit cards, the balances and interest information of which are outlined in the table below. he would like to consolidate his credit cards to a single credit card with an apr of 18% and pay off the balance in 24 months. what will his monthly credit card payment be? credit card balance apr a $2,380 19% b $4,500 15% c $1,580 17.50% d $900 21% a. $390.00 b. $462.91 c. $467.29 d. $52.00 please select the best answer from the choices provided a b c d
Frank's monthly credit card payment for consolidating his credit cards will be $467.29.
Option C is the correct answer.
We have,
To calculate the monthly credit card payment for consolidating Frank's credit cards, we can use the formula for the monthly payment on a loan:
[tex]M = P (r (1 + r)^n) / ((1 + r)^n - 1),[/tex]
where M is the monthly payment, P is the total loan amount (sum of all credit card balances), r is the monthly interest rate, and n is the number of months.
First, let's calculate the total loan amount:
Total loan amount = $2,380 + $4,500 + $1,580 + $900 = $9,360.
Next, let's calculate the monthly interest rate:
Monthly interest rate = APR / 12 = 18% / 12 = 1.5%.
Now, let's calculate the monthly payment using the formula:
[tex]M = $9,360 \times (0.015 (1 + 0.015)^{24}) / ((1 + 0.015)^{24} - 1).[/tex]
Using a calculator, we can compute the value of M:
M ≈ $467.286.
Rounding to the nearest cent,
Frank's monthly credit card payment for consolidating his credit cards will be $467.29.
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How many triangles are represented in a=120 degrees a=250 b=195
To determine how many triangles are represented by the angles a=120 degrees, a=250 degrees, and b=195 degrees, we need to use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
First, we need to determine which angle corresponds to which side. Let's assume that angle a is opposite to the longest side, and angle b is opposite to the shortest side. Therefore, we have: a = 250 degrees (longest side) a = 120 degrees b = 195 degrees (shortest side) Next, we need to use the triangle inequality theorem to determine which combinations of sides can form a triangle. For any two sides a and b, the third side c must satisfy the following condition: c < a + b Using this condition, we can determine the valid combinations of sides: - a + b > c: This is always true, since a and b are the longest and shortest sides, respectively. - a + c > b: This is true for all values of c, since a is the longest side. - b + c > a: This is true only when c > a - b.
Substituting the given values, we get: c > a - b c > 250 - 195 c > 55 Therefore, any side c that is greater than 55 can form a triangle with sides a and b. We can use this condition to count the number of valid triangles: - If c = 56, then we have one triangle. - If c = 57, then we have two triangles (c can be either adjacent side). - If c = 58, then we have three triangles (c can be any of the three sides). Continuing this pattern, we can count the number of triangles for each value of c: c = 56: 1 triangle c = 57: 2 triangles c = 58: 3 triangles c = 59: 4 triangles c = 60: 5 triangles c = 61: 6 triangles c = 62: 7 triangles c = 63: 8 triangles c = 64: 9 triangles c = 65: 10 triangles c = 66: 11 triangles c = 67: 12 triangles c = 68: 13 triangles c = 69: 14 triangles c = 70: 15 triangles c > 70: 16 triangles (since all three sides can form a triangle) Therefore, there are 16 possible triangles that can be formed with the given angles and side lengths.
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A bicycle wheel has a diameter of 26 inches. Isabelle rides the bike so that the wheel makes two complete rotations per second. Which function models the height of a spot on the edge of the wheel?
A. h(t) = 13 sin(2π t) + 13
B. h(t) = 13 sin(4π t)
C. h(t) = 13 sin(4π t) + 13
D. h(t) = 13 sin(2π t)
Answer:
I can definitely help you with that math problem! Given the information about the bicycle wheel, we need to find the function that models the height of a spot on the edge of the wheel. We know that the wheel has a diameter of 26 inches, which means the radius is half of that, or 13 inches. Isabelle rides the bike so that the wheel makes two complete rotations per second, which means the period of the function is 1/2 second (since it takes half a second for the wheel to complete one rotation).
Using the formula for a sinusoidal function, we can write the function as h(t) = A sin(2π/B (t - h)) + k, where A is the amplitude, B is the period, h is the horizontal shift, and k is the vertical shift. We can determine the values of these parameters as follows:
- Amplitude: The amplitude is half the distance between the highest and lowest points of the function. Since the radius of the wheel is 13 inches, the highest and lowest points are 26 inches apart. Therefore, the amplitude is 13 inches.
- Period: We know that the period is 1/2 second, so B = 2π/1/2 = 4π.
- Horizontal shift: The function starts at its highest point, so there is no horizontal shift. Therefore, h = 0.
- Vertical shift: The center of the wheel is at a height of 13 inches above the ground, so the vertical shift is also 13 inches.
Putting it all together, we get the function h(t) = 13 sin(4πt) + 13, which corresponds to option C. This function models the height of a spot on the edge of the wheel as Isabelle rides the bike. I hope this explanation helps! Let me know if you have any other questions or if there's anything else I can assist you with.
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You doing the practice 1
Using the intersection of sets we find that A ∩ B = {1, 3}
What is a set?A set is a collection of well ordered items.
Givent hat set A = {x| x is an od number greater than 0 and less than 10} and set B = {1, 2, 3, 4}, we desire to find A ∩ B. We proceed as follows.
First since set A = {x| x is an odd number greater than 0 and less than 10}, its elements are A = {1, 3, 5, 7, 9}
Also, set B = {1, 2, 3, 4}
Since we require A ∩ B which is the intersection of both sets and is the elements that both sets have in common. Since both sets have element 1 and 3 in common, we have that
A ∩ B = {1, 3}
So, A ∩ B = {1, 3}
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True or false kites are never rhombuses
Answer:
Step-by-step explanation:
false i think
Answer:
True
Step-by-step explanation:
If AB is tangent to circle P at B, find Measure of angle 1
To find the measure of angle 1 when AB is tangent to circle P at point B, we must consider some properties of tangents and circles.
A tangent line to a circle is a line that touches the circle at exactly one point, known as the point of tangency. In this case, line AB is tangent to circle P at point B. A crucial property of tangents is that they are perpendicular to the radius of the circle at the point of tangency. Therefore, the radius PB of circle P is perpendicular to tangent AB at point B.
Now, let's examine angle 1. If angle 1 is the angle formed by the tangent AB and the radius PB at point B, then it is a right angle due to the aforementioned property. In this case, the measure of angle 1 is 90 degrees.
However, if angle 1 is not directly formed by the tangent and radius, more information is needed to determine its measure. For example, if angle 1 is an angle inside the circle, you would need to know the measure of other angles or lengths of chords within the circle to calculate it.
In summary, if angle 1 is formed by tangent AB and radius PB at point B, its measure is 90 degrees because tangents are perpendicular to the radius at the point of tangency. If angle 1 is not formed by the tangent and radius, additional information is required to determine its measure.
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The temperature at sunrise was T degrees. By noon the temperature had tripled. By sunset, the temperature was only half of what the
temperature was at noon.
Which expression shows the temperature at sunset in terms of T?
OA (T+3) = Ź
(T+3)
2
Ос. 37 = 5
1 / 2
3. 37 를
D
The expression that shows the temperature at sunset in terms of T is 3T/2.
Let's call the temperature at sunrise T. According to the problem statement, the temperature tripled from sunrise to noon, so the temperature at noon is 3T.
Then, from noon to sunset, the temperature halved, so the temperature at sunset is (1/2) of the temperature at noon, or (1/2)(3T), which simplifies to 3T/2. Therefore, the expression that shows the temperature at sunset in terms of T is 3T/2.
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Charles draws △PQR, with m∠QPR = 130°, m∠PQR = 30°, and m∠PRQ = 20°.
Which triangle represents Charles’s triangle??
Answer:
Please look at the picture provided to see the correct triangle because each figure has no a,b, or c. Thanks
Goldilocks walked into her kitchen to find that a bear had eaten her tasty can of soup. All that was left was the label below that used to completely cover the sides of the can (without any overlap). What was the volume of the can of soup that the bear ate? The label is 22 in. (top) by 9 in. (side).
The volume of the can of soup that the bear ate was approximately 4644.64 cubic inches.
To solve this problem, we need to make some assumptions about the can of soup. Let's assume that the can is cylindrical and that it is completely filled with soup. We also need to assume that the label covered the entire surface area of the can without any overlap.
The label is 22 inches tall and 9 inches wide, so it covered a total surface area of 22 x 9 = 198 square inches. Since the label completely covered the sides of the can without any overlap, we can use this surface area to find the surface area of the can itself.
The surface area of a cylinder is given by the formula A = 2πrh + 2πr², where r is the radius of the base of the cylinder, and h is the height of the cylinder. In this case, we know that the height of the cylinder is 22 inches (the height of the label), and the circumference of the base of the cylinder is 9 inches (the width of the label).
Using these values, we can solve for the radius of the cylinder:
9 = 2πr
r = 4.53 inches
Now we can use the formula for the surface area of a cylinder to solve for the volume of the can:
A = 2πrh + 2πr²
198 = 2π(22)(4.53) + 2π(4.53)²
198 = 634.26
A = πr²h
V = A x h/3
V = 634.26 x 22/3
V ≈ 4644.64 cubic inches
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Blank 1 or B =
Blank 2 or P =
Blank 3 or l =
The part of the surface area equation are
Part 1 = B = Base areaPart 2 = P = Perimeter of basePart 3 = l = Height of pyramidCompleting the part of the surface area equationFrom the question, we have the following parameters that can be used in our computation:
SA = B + 1/2Pl
In the equation, we have
Part 1 = B
Part 2 = P
Part 3 = l
When the above parts are labelled, we have
Part 1 = B = Base area
Part 2 = P = Perimeter of base
Part 3 = l = Height of pyramid
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to increase strength and/or muscle mass, weight trainers will try different approaches. one approach is to apply an electrical impulse through a
muscle as the person is lifting a weight. a researcher wants to determine if adding this electrical impulse increases the amount of weight a person
can lift. to conduct his research, he selects one hundred people, and randomly divides them into two groups. one group wears a device that
sends an electrical impulse through the muscle used to repeatedly lift a 5 pound weight. the other group lifts the same weight without the electrical
impulse. the researcher counts the number of repetitions until the subjects can no longer lift the weight. is this an example of an observational
study or an experiment?
This is an example of an experiment. In an experiment, researchers manipulate the independent variable (in this case, the presence or absence of an electrical impulse) to determine its effect on the dependent variable (the number of repetitions the subjects can lift a weight).
The researcher randomly assigned subjects to either receive the electrical impulse or not, which is a key feature of experimental design.
By doing so, the researcher can ensure that any differences observed between the two groups are due to the manipulation of the independent variable, rather than any pre-existing differences between the groups.
In contrast, an observational study merely observes existing characteristics or behaviors of a population, without any manipulation or control of variables.
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what is the percent of 11/20
Answer: 55%
Step-by-step explanation:
To find the percentage of 11/20, we can use the following formula:
Percentage = (Numerator ÷ Denominator) × 100
Substituting the values from 11/20 into the formula, we get:
Percentage = (11 ÷ 20) × 100
Percentage = 0.55 × 100
Percentage = 55%
Therefore, the percentage of 11/20 is 55%.
Answer:
Solution: 11/20 as a percent is 55%
Step-by-step explanation:
First, convert the fraction into a decimal by dividing the numerator by the denominator:
11/20 = 0.55
If we multiply the decimal by 100, we will get the percentage:
00.5 * 100 = 55
We can see that 11/20 is percentage is 55.
12. Higher Order Thinking Q'R'S' T' is the image
of QRST after a dilation with center at the origin.
a. Find the scale factor.
b. Find the area of each parallelogram. What is
the relationship between the areas?
Considering the figures the scale factor is 1/4
Area of parallelogram QRST
= 9 square units
Area of parallelogram Q'R'S'T'
= 144 square units
How to find the scale factor of the parallelogramThe scale factor is solved using a reference side say QR and Q'R'
with QR = 12 and Q'R' = 3
the relationship is
QR * scale factor = Q'R'
12 * scale factor = 3
scale factor = 3/12 = 1/4
Area of parallelogram QRST
= base * height
= 3 * 3
= 9 square units
Area of parallelogram Q'R'S'T'
= 12 * 12
= 144 square units
The relationship between the areas are
9 square units * ( scale factor)² = 144
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Jyllina created this box plot representing the number of inches of snow that fell this winter in different nearby cities
Snowfall Summary
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Number of inches
(a) What was the greatest amount of snowfall in any of the cities?
(b) In which quarter is the data most concentrated? Explain how you know. (c) In which quarter is the data most spread out? Explain how you know
(a) The greatest amount of snowfall in any of the cities = 50 inches.
(b) The data is most concentrated in the second quarter (Q₂), ranging from 6 inches to 20 inches.
(c) The data is most spread out in the fourth quarter (Q₄), ranging from 32 inches to 50 inches.
What is a Box plot:A box plot is a type of graphical representation that summarizes the distribution of a dataset based on the five-number summary: the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.
A box plot consists of a rectangular box, which spans from Q1 to Q3, with a vertical line inside it representing the median. The length of the box represents the interquartile range (IQR), which is the range between Q1 and Q3.
Whiskers, which are lines extending from the top and bottom of the box, indicate the range of the dataset outside of the IQR.
Here we have
Jyllina created this box plot representing the number of inches of snow that fell this winter in different nearby cities
The data ranges from 4 to 50 inches
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
(a) The greatest amount of snowfall in any of the cities will equal the highest value which is 50 inches.
(b) The data is most concentrated in the second quarter (Q₂), which ranges from 6 inches to 20 inches.
This can be inferred from the fact that the box plot shows the smallest range between the minimum and maximum values, as well as the smallest size of the box, which represents the interquartile range (IQR).
(c) The data is most spread out in the fourth quarter (Q₄), which ranges from 32 inches to 50 inches.
This can be inferred from the fact that the box plot shows the largest range between the minimum and maximum values, as well as the largest size of the box, which represents the IQR.
Additionally, the whiskers, which represent the range of values outside the IQR, are also the longest in this quarter, indicating that there are more extreme values in this range compared to the other quarters.
Therefore,
(a) The greatest amount of snowfall in any of the cities = 50 inches.
(b) The data is most concentrated in the second quarter (Q₂), ranging from 6 inches to 20 inches.
(c) The data is most spread out in the fourth quarter (Q₄), ranging from 32 inches to 50 inches.
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Complete Question:
The dotted line is the perpendicular bisector of side AB. The distance between points E and A is 7 units. What is the distance between points E and B? Explain or show your reasoning
The distance between points E and B is (2/3)*AB, or (2/3)*(7+x) units.
Since the dotted line is the perpendicular bisector of side AB, it means that it cuts the line AB into two equal halves. Thus, the distance between points E and the dotted line is equal to the distance between point A and the dotted line.
We know that the distance between points E and A is 7 units, and since the dotted line bisects AB, the distance between point A and the dotted line is equal to the distance between point B and the dotted line. Let's call this distance 'x'.
Therefore, we have two equal distances (7 units and 'x') that add up to the length of AB. This means that:
AB = 7 units + x
However, we also know that the dotted line is the perpendicular bisector of AB, meaning that it forms right angles with both A and B. This creates two right-angled triangles, AED and BED, where DE is the perpendicular line from point E to AB.
Using Pythagoras' theorem, we can find the length of DE in terms of 'x':
(DE)² + (AE)² = (AD)²
(DE)² + (7)² = (AB/2)²
(DE)² + 49 = (AB²)/4
(DE)² = (AB²)/4 - 49
(DE)² = (AB² - 196)/4
(DE)² = (x²)/4
DE = x/2
Therefore, the distance between points E and B is equal to the length of DE plus the distance between point B and the dotted line, which is also equal to 'x'. Therefore, the distance between points E and B is:
EB = (x/2) + x = 1.5x
We can substitute this into the equation we found earlier:
AB = 7 units + x
AB = 7 units + (2/3)*EB
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During a sale, a store offered a 20% discount on a stereo system that originally sold for $720. After the sale, the discounted price of the stereo system was marked up by 20%. What was the price of the stereo system after the markup? Round to the nearest cent.
The price of the stereo system after the discount and markup is $691.20.
How to determine the markup:The markup price represents the price after adding a percentage of the discounted price.
The markup can be determined using the markup factor, which increases 100% by the markup percentage.
The discount offered on the stereo system = 20%
Original sales price of the system = $720
Discount factor = 0.8 (1 - 0.2)
Discounted price = $576 ($720 x 0.8)
Markup percentage after the discount = 20%
Markup factor = 1.2 (1 + 0.2)
Marked up price = $691.20 ($576 x 1.2)
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The visitors to a certain website were questioned about their favorite soups.
If 180 people were surveyed, how many more people voted for split pea soup than for potato soup?
Answer:
.15(180) - .10(180) = .05(180) = 9
9 more people voted for split pea soup than for potato soup.
You are choosing between two different cheese wedges at the grocery store. Assume both
wedges are triangular prisms with bases that are isosceles triangles. The first wedge has a base
that is 2. 5 in. Wide and a height of 4. 5 in. , with the entire wedge being 3 in thick. The second
wedge has a base that is 3 in, wide and a height of 4 in. , with the entire wedge being 3. 5 in.
thick. Which wedge has a greater volume of cheese, and by how much?
The first wedge by 6. 375 cubic inches
The first wedge by 12. 75 cubic inches
The second wedge by 8. 25 cubic inches
The second wedge by 4. 125 cubic inches
The second wedge has a greater volume by 4.125 cubic inches. Therefore, the correct option is 4.
To determine which cheese wedge has a greater volume, you need to calculate the volume of each triangular prism using the given dimensions.
For the first wedge:
1. Calculate the area of the base (isosceles triangle):
(base x height) / 2 = (2.5 in x 4.5 in) / 2 = 5.625 square inches
2. Calculate the volume of the prism:
base area x thickness = 5.625 sq in x 3 in = 16.875 cubic inches
For the second wedge:
1. Calculate the area of the base (isosceles triangle):
(base x height) / 2 = (3 in x 4 in) / 2 = 6 square inches
2. Calculate the volume of the prism:
base area x thickness = 6 sq in x 3.5 in = 21 cubic inches
To find which wedge has a greater volume and by how much, subtract the smaller volume from the larger volume:
21 cu in - 16.875 cu in = 4.125 cu in.
Therefore, the correct answer is option 4: The second wedge has a greater volume by 4.125 cubic inches.
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In triangle ABC, A is (0,0), B is (0,,3) and C is (3,0). What type of triangle is ABC? SELECT ALL THAT APPLY
The triangle has two sides with equal lengths (AB and AC) and one side with a different length (BC). This makes it an isosceles triangle.
How to find the type of triangle
Triangle ABC has vertices A(0,0), B(0,3), and C(3,0).
To determine the type of triangle, we can find the lengths of the sides using the distance formula:
AB = sqrt((0-0)^2 + (3-0)^2) = sqrt(0 + 9) = 3
BC = sqrt((3-0)^2 + (0-3)^2) = sqrt(9 + 9) = sqrt(18) = 3√2
AC = sqrt((3-0)^2 + (0-0)^2) = sqrt(9 + 0) = 3
The triangle has two sides with equal lengths (AB and AC) and one side with a different length (BC). This makes it an isosceles triangle.
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find the coordinates of p so that p partitions the segment of AB in the ratio 7 to 2 if A( -5,4) and B( -8,-2)
The coordinates of p so that p partitions the segment of AB in the ratio 7 to 2 if A( -5,4) and B( -8,-2) is P(x, y) = [-22/3, -2/3].
How to determine the coordinates of point P?In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to 4.
In Mathematics and Geometry, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical equation:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
By substituting the given parameters into the formula for line ratio, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(7(-8) + 2(-5))/(7 + 2)], [(7(-2) + 2(4))/(7 + 2)]
P(x, y) = [(-56 - 10)/(9)], [(-14 + 8)/9]
P(x, y) = [-66/9], [(-6)/(9)]
P(x, y) = [-22/3, -2/3]
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Two forces of 39n (newtons) and 46n act on an object at right angles. find the magnitude of the resultant and the angle that it makes with the smaller force.
The magnitude of the resultant force is approximately 60.28 newtons. The angle between the resultant force and the smaller force is approximately 50.5 degrees.
To find the magnitude of the resultant force, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the two forces are acting at right angles, so we can treat them as the sides of a right triangle:
resultant force^2 = (39n)^2 + (46n)^2
resultant force^2 = 1521n^2 + 2116n^2
resultant force^2 = 3637n^2
resultant force = sqrt(3637n^2) = 60.28n
So the magnitude of the resultant force is approximately 60.28 newtons.
To find the angle that the resultant force makes with the smaller force, we can use trigonometry.
We know that the two forces are at right angles, so the angle between the resultant force and the smaller force is the same as the angle between the resultant force and the larger force. Let's call this angle θ. Then we have:
tan θ = (larger force) / (smaller force)
tan θ = 46n / 39n
θ = tan^-1(46/39) = 50.5°
Therefore, the angle between the resultant force and the smaller force is approximately 50.5 degrees.
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Hillary used her credit card to buy a $804 laptop, which she paid off by making identical monthly payments for two and a half years. Over the six years that she kept the laptop, it cost her an average of $0. 27 of electricity per day. Hillary's credit card has an APR of 11. 27%, compounded monthly, and she made no other purchases with her credit card until she had paid off the laptop. What percentage of the lifetime cost of the laptop was interest? Assume that there were two leap years over the period that Hillary kept the laptop and round all dollar values to the nearest cent)
Percentage of lifetime cost that was interest = $407.
Let's begin by finding the monthly payment that Hillary made to pay off her laptop over two and a half years.
If she paid off the $804 balance with identical monthly payments, then the total amount she paid is equal to the balance plus the interest:
Total amount paid = balance + interest
We can use the formula for the present value of an annuity to solve for the monthly payment, where PV is the present value (in this case, $804), r is the monthly interest rate (which we can find from the APR), n is the total number of payments (30 months), and PMT is the monthly payment:
PV = PMT * (1 - (1 + r)^(-n)) / r
We can solve this equation for PMT:
PMT = PV * r / (1 - (1 + r)^(-n))
The monthly interest rate is the annual percentage rate divided by 12, and the number of payments is the number of years times 12:
r = 0.1127 / 12 = 0.009391667
n = 2.5 * 12 = 30
Using these values, we get:
PMT = 804 * 0.009391667 / (1 - (1 + 0.009391667)^(-30)) = $33.00
So Hillary made 30 monthly payments of $33.00 to pay off her laptop.
Next, we can calculate the cost of electricity over six years. There are 365 days in a year, and 2 leap years in the six-year period, for a total of 6*365+2 = 2192 days.
At $0.27 per day, the total cost of electricity is:
2192 * $0.27 = $592.64
Now we can calculate the total cost of the laptop over six years.
Hillary paid $33.00 per month for 30 months, or a total of 30 * $33.00 = $990.00. She also paid $592.64 for electricity. Therefore, the total cost of the laptop is:
$990.00 + $592.64 = $1582.64
The interest she paid on her credit card is the difference between the total amount she paid and the cost of the laptop:
Interest = Total amount paid - Cost of laptop
Interest = $990.00 + interest on $804 balance - $804 - $592.64
Simplifying this expression, we get:
Interest = $185.36 + interest on $804 balance
To find the interest on the $804 balance, we can use the formula for compound interest, where P is the principal (in this case, $804), r is the annual interest rate (11.27%), and t is the time in years (2.5 years):
A = P*(1 + r/n)^(n*t)
Here, we can set the number of compounding periods per year, n, to 12 since the interest is compounded monthly. Substituting the given values, we get:
A = $804*(1 + 0.1127/12)^(12*2.5) = $1026.12
So the interest on the $804 balance is:
Interest on $804 balance = $1026.12 - $804 = $222.12
Plugging this value into our expression for Interest, we get:
Interest = $185.36 + $222.12 = $407.48
Finally, we can find the percentage of the lifetime cost of the laptop that was interest:
Percentage of lifetime cost that was interest = Interest / Total cost of laptop * 100%
Percentage of lifetime cost that was interest = $407.
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6 Evaluate without using calculators. -4(-2)+(-12)÷(+3)+-20+(+4)+(-6
Answer:
Its 12
Step-by-step explanation:
1. Following PEMDAS, we first solve the equation inside the parentheses.
-4(-2) = 8
-12 ÷ 3 = -4
-20 + 4 = -16
2. Now, we have the following expression:
8 + (-4) + (-16)
3. Again, following PEMDAS, we solve the equation inside the parentheses first.
8 + (-4) + (-16) = 8 - 4 - 16
4. Finally, we solve the equation from left to right.
8 - 4 - 16 = 8 - (4 + 16)
8 - (20) = -12
Therefore, the value of the expression is -12.
So far you have completed 816 miles
which is 48% of the trail.
Assuming that the trail is a total of "x" miles, we can set up the following equation to solve for "x":
816 = 0.48x
To solve for "x", we can divide both sides by 0.48:
x = 1700
Therefore, the total length of the trail is 1700 miles.
When a figure is translated on the coordinate plane you should add or subtract x and y? Is this statement true or false?
Answer: True
Step-by-step explanation:
Help pls I need help with sand and a word with my
Answer: X= 4/5x + 8
Step-by-step explanation: Distribution factor
Reema and Quinton both babysit for extra money. Reema charges $10 per hour and
Quinton charges based on the equation m= 5h + 25. Where h is the number of hours
worked and m is the total amount of money charged. Who would make more money if
they both worked 4 hours?
o Quinton would make $10 more than Reema
O Quinton would make $5 more than Reema
o Reema would make $10 more than Quinton
O Reema would make $5 more than Quinton
On babysitting for four hours, the differently earned money will be Quinton would make $5 more than Reema.
Reema's charge for babysitting for four hours = 10 × 4
Reema's charge = $40
For Quinton, keep the value of hours in expression -
Quinton's charge = 5 (4) + 25
Quinton's charge = 20 + 25
Quinton's charge = $45
As Quinton's charge is greater than Reema, she makes more money.
Amount of more money made by Quinton = 45 - 40
Subtract to find the difference
Amount of more money made by Quinton = $5
Hence, correct answer is Quinton would make $5 more than Reema.
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Write 7.725666118 as a percentage
please show the method too.
The number written as a percentage is:
772.5666118%
How to write any number as a percentage?To do this, just multiply the number by 100%.
For example, for any number A, the percentage form of A is:
p = A*100%
Here the number is 7.725666118, then the percentage form of this number will be:
N = 7.725666118*100% = 772.5666118%
That is the number as a percentage.
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