What are the roots of y = x² – 3x – 10? O-3 and -10 0-2 and 5 O2 and -5 O3 and 10
Answer:
x = - 2 , 5
Step-by-step explanation:
to find the roots let y = 0 , that is
x² - 3x - 10 = 0 ← in standard form
(x + 2)(x - 5) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 5 = 0 ⇒ x = 5
A spinner has three sections which are coloured black, red and yellow. Lincoln spun the spinner 100 times in total.
The frequency of spins that landed on red was
35.
The ratio of the frequency of black to the frequency of red was 2: 7.
What is the estimated probability of the spinner landing on yellow?
Give your answer as a decimal.
Answer this question please
Either a rotation of a reflection is used to transform Shape P so that exactly one vertex is invariant.
What are transformations on a figure?The possible transformations on a figure are listed as follows:
Translation: Translation left/right or down/up, moving all vertices.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, hence all vertices are changed.An invariant vertex means that the coordinates of the vertex remain constant even after the transformation.
A translation and a dilation will always change the coordinates of every vertex, as:
The translation means that at least one of the x-coordinate of the y-coordinate is added/subtracted.The dilation means that both the x-coordinate and the y-coordinate of each vertex is multiplied by the scale factor.For reflection and rotation, they can happen over one vertex of the shape, hence that vertex would remain constant.
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A bag has 3 blue cubes, 8 red cubes, and 9 green cubes. If you draw a cube and replace it in the bag 100 times, which of the following options would you expect to occur? Select all that apply.
A) Pull a blue cube 15 times
B) Pull more than two times as many red cubes as blue cubes
C) Pull a red cube 40 times
D) Pull a green cube 45 times
E) Pull 50 blue cubes
Options A and B are the most likely to occur, but they still have a small probability of occurring. The other options are much less likely to occur.
what is probability?
Probability is a branch of mathematics that deals with the study of random events or outcomes.
Since there are 20 cubes in the bag, each cube has a probability of 1/20 of being drawn on any given draw, assuming that each cube is equally likely to be drawn.
A) The probability of drawing a blue cube on any given draw is 3/20. Drawing a blue cube 15 times in 100 draws would have a probability of (3/20)^15 * (17/20)^85 * 100C15, which is an extremely small probability. However, since the question asks what we would expect to occur, we might still select this option.
B) The probability of drawing a red cube on any given draw is 8/20, or 2/5. Drawing more than two times as many red cubes as blue cubes in 100 draws would mean drawing at least 10 red cubes and at most 5 blue cubes. This is equivalent to drawing at least 10 red cubes in 90 draws, which has a probability of approximately (2/5)^10 * (3/5)^90 * 100C90. This is also a small probability, but again, we might still select this option.
C) The probability of drawing a red cube on any given draw is 8/20, or 2/5. Drawing a red cube 40 times in 100 draws would have a probability of (2/5)^40 * (3/5)^60 * 100C40, which is also a small probability.
D) The probability of drawing a green cube on any given draw is 9/20. Drawing a green cube 45 times in 100 draws would have a probability of (9/20)^45 * (11/20)^55 * 100C45, which is again a small probability.
E) Drawing 50 blue cubes in 100 draws is equivalent to drawing a blue cube on every draw. This would have a probability of (3/20)^100, which is an extremely small probability.
Therefore, options A and B are the most likely to occur, but they still have a small probability of occurring. The other options are much less likely to occur.
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Iodine 131 has a half life of 8 days. If you start with a sample of 100 grams, how much iodine 131 would be left after 10 days. (3 points)
A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right. What are the new coordinates?
(-3, 3), (-1, 7), (-2, 3)
(2, -2), (4, 2), (3, -2)
(2, 8), (4, 12), (3, 8)
(7, 3), (9, 7) and (8, 3)
The answer is (D) (7, 3), (9, 7) and (8, 3) when A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right.
To translate a two-dimensional figure such as a triangle, we move all its points a certain distance in a certain direction. In this case, we need to move the triangle 5 units to the right. This means we need to add 5 to the x-coordinate of each vertex, while leaving the y-coordinate unchanged.
In this case, we need to add 5 units to the x-coordinates of each vertex of the triangle.
The new coordinates of the triangle's vertices would be:
(2+5, 3) = (7, 3)
(4+5, 7) = (9, 7)
(3+5, 3) = (8, 3)
Therefore, the answer is (D) (7, 3), (9, 7) and (8, 3).
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The complete question is :
A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right. What are the new coordinates?
A.(-3, 3), (-1, 7), (-2, 3)
B.(2, -2), (4, 2), (3, -2)
C.(2, 8), (4, 12), (3, 8)
D.(7, 3), (9, 7) and (8, 3)
Mr. Anderson needs to work on the farm for at least 27 hours every week.
He worked 4 hours a day for the last 6 days.
He worked 5 hours today.
Mr. Anderson says that 4 × 6 is less than 27, so he has not worked enough during the week.
Is Mr. Anderson correct?
Help with math problems
The value of the expressions are 1. Distributive property: -3 √3 (2 + √6) = -6 √3 - 9 √2. [2] (-2 √3 + 2)(√3 - 5) = 12 √3 - 16. [3] (-2 -3 √5)(5 - √5) = -15 √5 + 5.
What is distributive property?The distributive property in algebra says that the sum or difference of the products of the number and each term in the sum or difference is equal to the product or difference of the number and each phrase in the sum or difference. To put it another way, a(b + c) = ab + ac and a(b - c) = ab - ac are true for any value of a, b, and c. The distributive property is frequently employed in parenthetical expansion and algebraic simplification.
1. Distributive property:
-3 √3 (2 + √6)
= -6 √3 - 3 √3 √6
= -6 √3 - 3 √18
= -6 √3 - 9 √2
2. Multiplying:
(-2 √3 + 2)(√3 - 5)
= -2 √3 (√3) + 2 (√3) - 10 + 10 √3
= -2 (3) - 10 + 12 √3
= 12 √3 - 16
3. Multiplying:
(-2 -3 √5)(5 - √5)
= -2 (5) - 3 √5 (5) + 2 √5 + 15
= -10 - 15 √5 + 2 √5 + 15
= -15 √5 + 5
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22.
Number of Cookies
YA
72
60
48
36
24
12
Origin O
Bake Sale
2 4 6 8 10 12 X
Packages
a) k = 6
c) k = 1/6
e) none (not proportional)
Identify the constant of proportionality.
b) k = 12
d) k=1/12
Since the ratio of Y to X is not constant for different values of X, the relationship between Y and X is not proportional, and there is no constant of proportionality.
What is proportion?Proportion is a mathematical concept that expresses the relationship between two or more quantities that are related to each other in a consistent way. A proportion can be expressed as an equation in which two ratios are set equal to each other, and it states that the ratios of two quantities are always the same. In other words, if we know that two quantities are proportional, we can use this relationship to find one quantity given the other.
Here,
Based on the given table, we can see that the number of cookies (Y) is directly proportional to the number of packages (X). Thus, we can write:
Y = kX
where k is the constant of proportionality.
a) When k = 6, we can find the value of Y for different values of X as follows:
When X = 12, Y = kX = 6(12) = 72
When X = 10, Y = kX = 6(10) = 60
When X = 8, Y = kX = 6(8) = 48
When X = 6, Y = kX = 6(6) = 36
When X = 4, Y = kX = 6(4) = 24
When X = 2, Y = kX = 6(2) = 12
Thus, the constant of proportionality is k = 6.
b) When k = 12, we can find the value of Y for different values of X as follows:
When X = 12, Y = kX = 12(12) = 144
When X = 10, Y = kX = 12(10) = 120
When X = 8, Y = kX = 12(8) = 96
When X = 6, Y = kX = 12(6) = 72
When X = 4, Y = kX = 12(4) = 48
When X = 2, Y = kX = 12(2) = 24
Thus, the constant of proportionality is k = 12.
c) When k = 1/6, we can find the value of Y for different values of X as follows:
When X = 12, Y = kX = (1/6)(12) = 2
When X = 10, Y = kX = (1/6)(10) = 5/3
When X = 8, Y = kX = (1/6)(8) = 4/3
When X = 6, Y = kX = (1/6)(6) = 1
When X = 4, Y = kX = (1/6)(4) = 2/3
When X = 2, Y = kX = (1/6)(2) = 1/3
Thus, the constant of proportionality is k = 1/6.
e) Since the ratio of Y to X is not constant for different values of X, the relationship between Y and X is not proportional, and there is no constant of proportionality.
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=2x-1
7) through: (-4,-4), parallel to y=-
3
=2x-4
9) through: (-4,-4), parallel to y =
11) through: (5,-2), perp. to y =
y=²x-5
13) through: (-2, 5), perp. to y = x + 2
8) through: (1, 0), parallel to y = 2x - 1
5
10) through: (5, 5), perp. to y = --
y = ²√x + 4
12) through: (3,-2), perp. to y = -
14) through: (-4, 0), perp. to y = -
The equation of the lines parallel or perpendicular to another line and that pass through a point are listed below:
Case 7: y = (7 / 4) · x + 3
Case 8: y = 2 · x + 1
Case 9: y = (3 / 2) · x + 2
Case 10: y = (6 / 5) · x - 1
Case 11: y = - (2 / 5) · x
Case 12: y = - (5 / 2) · x - 19 / 2
Case 13: y = - x + 3
Case 14: y = - (5 / 4) · x - 5
How to derive the equation of a line
In this problem we have eight cases of line equations parallel or perpendicular to a line and that pass through a point. The equation of a line is an expression of the form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptThere are the following relationships between two lines:
Two lines are parallel when they have the same slope.Two lines are perpendicular when the product of their slopes is equal to - 1.Now we proceed to determine the line equations:
Case 7
Slope
m = 7 / 4
m' = 7 / 4
Intercept
b = y - m · x
b = - 4 - (7 / 4) · (- 4)
b = - 4 + 7
b = 3
Equation of the line
y = (7 / 4) · x + 3
Case 8
Slope
m = 2
m' = 2
Intercept
b = 1 - 2 · 0
b = 1
Equation of the line
y = 2 · x + 1
Case 9
Slope
m = 3 / 2
m' = 3 / 2
Intercept
b = - 4 - (3 / 2) · (- 4)
b = - 4 + 6
b = 2
Equation of the line
y = (3 / 2) · x + 2
Case 10
Slope
m = - 5 / 6
m' = 6 / 5
Intercept
b = 5 - (6 / 5) · 5
b = 5 - 6
b = - 1
Equation of the line
y = (6 / 5) · x - 1
Case 11
Slope
m = 5 / 2
m' = - 2 / 5
Intercept
b = - 2 - (- 2 / 5) · 5
b = 0
Equation of the line
y = - (2 / 5) · x
Case 12
Slope
m = 2 / 5
m' = - 5 / 2
Intercept
b = - 2 + (- 5 / 2) · 3
b = - 2 - 15 / 2
b = - 4 / 2 - 15 / 2
b = - 19 / 2
Equation of the line
y = - (5 / 2) · x - 19 / 2
Case 13
Slope
m = 1
m' = - 1
Intercept
b = 5 - (- 1) · (- 2)
b = 3
Equation of the line
y = - x + 3
Case 14
Slope
m = 4 / 5
m' = - 5 / 4
Intercept
b = 0 - (- 5 / 4) · (- 4)
b = 0 - 5
b = - 5
Equation of the line
y = - (5 / 4) · x - 5
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b. Let f:x=3x² +1 and g: x=x-5
Find
i. fog(x)
ii. go f(x)
iii. (ƒ o g)−¹(x)
A circular hot spring has a diameter of 110 meers. Over time, the diameter of the spring decreases by 3 meters. By how many square meters does the area of he hot spring decrease?
The area οf the hοt spring decreases by apprοximately 540.24 square meters.
What is area οf a circle?The area οf a circle is fοund οut using the fοrmula. Area = πr²
Given that, r = d/2 = 110/2 = 55 meters
The οriginal area οf the hοt spring can be calculated as:
[tex]A = \pi r^2 = \pi(55)^2 = 9,525.69[/tex] square meters (rοunded tο twο decimal places)
After the diameter οf the hοt spring decreases by 3 meters, its new diameter is 110 - 3 = 107 meters. Therefοre, its new radius is:
r' = d'/2 = 107/2 = 53.5 meters
The new area οf the hοt spring can be calculated as:
[tex]A' = \pi r'² = \pi(53.5)² = 8,985.45[/tex] square meters (rοunded tο twο decimal places)
The decrease in the area οf the hοt spring is the difference between the οriginal area and the new area:
ΔA = A - A' = 9,525.69 - 8,985.45 = 540.24 square meters (rοunded tο twο decimal places)
Therefοre, the area οf the hοt spring decreases by apprοximately 540.24 square meters.
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15. Blaine works for a battery manufacturing company. He wants to develop a method to test the batteries made each day to determine if they work.
Which method would provide the most valid results?
A. sampling the first 25 batteries made each day and testing to see if they work
B. sampling the last 25 batteries made each day and testing to see if they work
C. sampling the first 50 batteries made each day and testing to see if they work
D. randomly sampling 50 batteries throughout the day and testing to see if they work
The most reliable results would come from randomly selecting 50 batteries throughout the day and testing to determine if they function.
What battery testing techniques are there?A voltage reading, a pulse or AC impedance measurement of internal resistance, coulomb counting, and electrochemical impedance spectroscopy are some of the test techniques available (EIS).
How can a battery's energy be tested?The red probe should be connected to the positive terminal of the battery, and the black probe should be connected to the negative terminal. Take the multimeter's reading. The battery is still safe to use if the reading for a 9V battery is greater than 7V.
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2.
P
When trying to determine whether triangles ABC and DEF are similar, Mae notices in the image that angles B and E are congruent. Next, she determines the ratio of BC to EF and
obtains 3/5. What else does she need to do?
A A
4
53°
B
53°
C E
3
5
Option (C) is correct i.e., To determine the ratio of AB to DE and use SAS to conclude the triangle(s) are similar
What is Triangle?A triangle is a polygon that has three(3) edges and three(3) vertices. It is one of the fundamental forms in geometry. Triangle DEF refers to a triangle with vertices D, E, and F. In Euclidean geometry, any three points that are not collinear identify a distinct triangle and a distinct plane at the same time.
Triangle ABC and Triangle DEF are similar if one of this property satisfy are , AAA, SAS, ASA and RHS.
It is Given that ∠B and ∠E are Similar and She determine ratio of BC to EF is 3/5.
Therefore, for similarity of two triangle she have to To determine the ratio of AB to DE and use SAS to conclude the triangles are similar.
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Complete Question:
When trying to determine whether triangles ABC and DEF are similar, Mae notices in the image that angles B and E are congruent. Next, she determines the ratio of BC to EF and obtains 3/5. What else does she need to do?
A. To determine the ratio of DE to AB and use SSS to conclude the triangles are similar
B. To determine the ratio of AB to DE and conclude the triangles are not similar
C. To determine the ratio of AB to DE and use SAS to conclude the triangles are similar
D. To determine the ratio of DE to AB and use AA to conclude the triangles are not similar.
Option (C) is correct i.e., To determine the ratio of AB to DE and use SAS to conclude the triangle(s) are similar
What is Triangle?A triangle is a polygon that has three(3) edges and three(3) vertices. It is one of the fundamental forms in geometry. Triangle DEF refers to a triangle with vertices D, E, and F. In Euclidean geometry, any three points that are not collinear identify a distinct triangle and a distinct plane at the same time.
Triangle ABC and Triangle DEF are similar if one of this property satisfy are , AAA, SAS, ASA and RHS.
It is Given that ∠B and ∠E are Similar and She determine ratio of BC to EF is 3/5.
Therefore, for similarity of two triangle she have to To determine the ratio of AB to DE and use SAS to conclude the triangles are similar.
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Complete Question:
When trying to determine whether triangles ABC and DEF are similar, Mae notices in the image that angles B and E are congruent. Next, she determines the ratio of BC to EF and obtains 3/5. What else does she need to do?
A. To determine the ratio of DE to AB and use SSS to conclude the triangles are similar
B. To determine the ratio of AB to DE and conclude the triangles are not similar
C. To determine the ratio of AB to DE and use SAS to conclude the triangles are similar
D. To determine the ratio of DE to AB and use AA to conclude the triangles are not similar.
Solve for Y
3. The Mighty Drop ski slope has an angle of elevation of 75°. If the top of the slope has an elevation of 800 feet, what is the length of the run?
4. Little Judy let go of her red balloon. The balloon is now 2240 feet up in the air and 350 feet to the west. What is the angle of elevation when little Judy looks at her red balloon?
Therefore , the solution of the given problem of angle comes out to be Judy is therefore looking at her red balloon at a height of about 81.06°.
An angle meaning is what?In Euclidean space, the top and bottom of the wall divide the two circular faces that constitute the sides of a tilt. When two beams collide, they can form a junction point. Angle is another outcome of two entities interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends.
Here,
We must use trigonometry to determine the run's duration. Call the run's duration "y" for now. We can use the tangent function since we are aware that the angle of height is 75°:
=> tan(75°) = opposite / adjacent
The slope's 800-foot height is on the opposing side. We want to determine the run's length, which is on the opposite side:
=> tan(75°) = 800 / y
We can multiply both sides by y and then split both sides by tan(75°) to find the answer to y:
=> y = 224.12 feet / tan(75°) = 800
The course therefore measures about 224.12 feet in length.
We must once more turn to trigonometry to determine the angle of height.
=> tan(θ) = opposite / adjacent
=> tan(θ) = 2240 / 350
We can use the inverse tangent (or arctan) of both sides to find :
=> 81.06° = arctan(2240 / 350).
Little Judy is therefore looking at her red balloon at a height of about 81.06°.
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HELPP ! , Use substitution to solve each system of equations , find x and y and do checks
Four hundred fifty-nine
Answer:
459..
hope you understand
Let f(x)=x+8 and g(x)=x^2-7x-9 find f(g(-1))
Answer:
First, we need to evaluate g(-1):
g(-1) = (-1)^2 - 7(-1) - 9
= 1 + 7 - 9
= -1
Now, we can plug in g(-1) into f(x):
f(g(-1)) = f(-1)
= -1 + 8
= 7
Therefore, f(g(-1)) = 7.
I really need help ASAP
-9p+9c
Answer:
it cant be if the term 9p and 9c is together but if it 9p and 9c both are in product form then your answer is -p+c
1.3 1.4 Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents. 1.3.1 1.3.2 Determine the total amount of cents in the money box. Convert the amount in 1.3.2 to rands (R). Thabang and his friend Ndivhu share a job of cleaning a neighbours yard and they were paid R400. Thabang worked three hours and Ndivhu worked for two hours. 1.4.1 Calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents. 1.3.3 Determine the amount Thabang will receive if they decided to share their morey according to hours.
Let the number of 50 cents coins in the container be "x".
We know that the total number of coins in the container is 600, so we can write:
[tex]x + 220 = 600[/tex]
Solving for x, we get:
[tex]x = 600 - 220[/tex]
[tex]x = 380[/tex]
Therefore, there are 380 50 cents pieces in the container.
Hope you can understand :)
18-34 35-44 45-5455+
206 388 393 410
26 9 21 13
Neither more nor less likely 283 220 153 137
Total
In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you m
buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).
Purchase likelihood
More likely
Less likely
Question 7 of 11 >
Total
1397
69
793
515 617 567 560 2259
Yes, more likely
No, less likely
This quiz: 11 point(s) possible
This question: 1 point(s) possible
(a) What is the probability that a randomly selected individual is at least 55 years of age, given the individual is
The probability is approximately 0.2934.
(Round to three decimal places as needed.)
(b) What is the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in our country." given the individual is at least 55 years of age?
The probability is approximately.
(Round to three decimal places as needed.)
(c) Are 18-to 34-year-olds more likely to buy a product emphasized as "Made in our country than individuals in general?
likely to buy a product emphasized as "Made in our country"?
Answer:
(a) To find the probability that a randomly selected individual is at least 55 years of age, we need to add up the values in the last row of the contingency table corresponding to the age group 55+ and divide it by the total number of respondents:
P(age 55+) = (515 + 617 + 567 + 560) / 2259 ≈ 0.2934
So the probability is approximately 0.2934.
(b) To find the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in our country," given the individual is at least 55 years of age, we need to add up the values in the second row of the contingency table (corresponding to "Yes, more likely") for the age group 55+ and divide it by the total number of respondents in that age group:
P(more likely|age 55+) = 515 / (515 + 617 + 567 + 560) ≈ 0.2281
So the probability is approximately 0.2281.
(c) To determine whether 18-34-year-olds are more likely to buy a product emphasized as "Made in our country" than individuals in general, we need to compare the proportion of respondents who answered "Yes, more likely" in the 18-34 age group to the proportion in the entire sample. We can calculate these proportions by adding up the values in the second row of the contingency table for the 18-34 age group and for the entire sample, respectively, and dividing each by the total number of respondents in each group:
P(more likely|age 18-34) = 206 / (206 + 388 + 393 + 410) ≈ 0.1913
P(more likely|entire sample) = 1397 / (1397 + 69 + 793) ≈ 0.6251
The proportion of 18-34-year-olds who are more likely to buy a product emphasized as "Made in our country" is approximately 0.1913, while the proportion in the entire sample is approximately 0.6251. Therefore, it appears that individuals in general are more likely to buy a product emphasized as "Made in our country" than 18-34-year-olds.
Step-by-step explanation:
which of the following has the slowest growth of rate?
5(e)^x
6(1.03)^x
2(3)^x
(0.3)^x
Answer:
(0.3)^x has the slowest growth rate.
Step-by-step explanation:
Out of the given functions, the function with the slowest growth rate is (0.3)^x.
To see why, we can compare the growth rates of each function as x increases.
For 5(e)^x, the base e is approximately equal to 2.718, which means that the function grows very quickly as x increases.
For 6(1.03)^x, the base is slightly greater than 1, which means that the function grows at a moderate rate as x increases.
For 2(3)^x, the base is greater than 1, which means that the function grows more quickly than (1.03)^x, but less quickly than (e)^x.
For (0.3)^x, the base is less than 1, which means that the function decreases as x increases. Therefore, this function has the slowest growth rate out of the given functions.
So, (0.3)^x has the slowest growth rate.
Please help, I can’t figure this out!
22. You take out two loans totaling $5000: one from the bank at 8% interest and the other from your uncle at only 2% interest.
a. How much did you borrow from the bank?
b. What interest do you owe to your uncle?
c. What interest do you owe the bank?
d. What is the total interest that you owe?
e. If the total interest is $300. Write a "total interest" equation
f. How much did you borrow from each? Solve the equation.
(X = how much you borrow from your uncle)
So you borrowed $3333.33 from the bank and $1666.67 from your uncle.
What is percent?Percent is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin per centum, which means "out of a hundred". Percentages are often used to express proportions, rates, or changes in quantities. For example, if you got 80 questions correct out of 100 on a test, you got 80% correct. In other words, 80 is 80% of 100. Percentages can also be used to express changes, such as if the price of a product increases from $10 to $12, that's a 20% increase ($2 increase is 20% of the original price of $10). Percentages are represented using the % symbol, for example, 50% means 50 out of 100, or 0.5 as a decimal.
Here,
a. Let's say you borrowed x dollars from the bank. Then, you borrowed (5000 - x) dollars from your uncle. Since you borrowed from the bank at 8% interest, the interest on this loan would be 0.08x dollars.
b. Since you borrowed from your uncle at 2% interest, the interest on this loan would be 0.02(5000 - x) dollars.
c. The total interest owed to the bank is 0.08x dollars, as calculated in part (a).
d. The total interest owed is the sum of the interest owed to the bank and the interest owed to your uncle:
Total interest = 0.08x + 0.02(5000 - x)
e. If the total interest is $300, we can write the equation:
0.08x + 0.02(5000 - x) = 300
f. To solve this equation for x, we can simplify and solve for x:
0.08x + 0.02(5000 - x) = 300
0.08x + 100 - 0.02x = 300
0.06x = 200
x = 3333.33 (rounded to the nearest cent)
Therefore, the answers are:
a. You borrowed $3333.33 from the bank.
b. You owe your uncle 0.02(5000 - 3333.33) = $133.33 in interest.
c. You owe the bank 0.08(3333.33) = $266.67 in interest.
d. The total interest you owe is $133.33 + $266.67 = $400.
e. The total interest equation is 0.08x + 0.02(5000 - x) = 300.
f. You borrowed $3333.33 from the bank and $1666.67 from your uncle.
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DUE TODAY! PLEASE HELP! SHOW WORK
I NEED HELP ON PART B, IF PART A IS WRONG, PLEASE FIX IT!
The value of x is equal to: B. 12.
The measure of <BCD, in degrees is 143 degrees.
What is the vertical angles theorem?In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
By applying the vertical angles theorem to the geometric figure, we have the following:
37 = 3x + 1
3x = 37 - 1
3x = 36
x = 36/3
x = 12.
For the measure of ∠BCD, in degrees, we have:
∠BCD + (3x + 1) = 180
∠BCD + (3(12) + 1) = 180
∠BCD + 37 = 180
∠BCD = 143°.
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Im really struggling with please help quickly
Therefore, the values of a and b are:
[tex]a = 2[/tex]
[tex]b = 9[/tex]
[tex]So, the functionf(x)=2x+9.[/tex]
What do you mean by the function?In programming and mathematics, a function is a set of instructions or a block of code that performs a specific task or calculation. A function takes in one or more input values, performs a series of operations on them, and then returns a single output value. Functions are used to modularize code, making it easier to read, understand, and maintain. They can be defined and called within a program to perform repetitive tasks, manipulate data, or solve complex problems. Functions can also be used to create reusable code that can be called from multiple parts of a program or shared between different programs.
To find the values of a and b, we need to use the given information to create a system of two equations.
Let's start by using the first two rows of the table:
[tex]f(0) = a(0) + b = 7[/tex]
[tex]f(1) = a(1) + b = 9[/tex]
Simplifying these equations, we get:
[tex]b = 7\\a + b = 9[/tex]
Substituting b = 7 into the second equation, we get:
[tex]a + 7 = 9[/tex]
Solving for a, we get:
[tex]a = 2[/tex]
Now we can use this value of a to find b. Let's use the third and fourth rows of the table:
[tex]f(2) = a(2) + b = 11\\f(3) = a(3) + b = 13[/tex]
Substituting a = 2 into these equations, we get:
[tex]2 + b = 11\\3 + b = 13[/tex]
Solving for b, we get:
[tex]b = 9[/tex]
Therefore, the values of a and b are:
[tex]a = 2\\b = 9[/tex]
[tex]So, the functionf(x)=2x+9.[/tex]
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A basketball player has made 12 of his last 20 free throws, which is a free throw percentage of 60%.
How many more consecutive free throws would he need to make to raise his free throw percentage to 75%?
PLEASE HELP ASAP I NEED IT !!!
Ahmed and his brother went to the gym together today. Ahmed goes to the gym every 6 days and his brother goes to the gym every 9 days . After how many days will they go to the gym together again ?
Answer:
18
Step-by-step explanation:
To determine the number of days until they both work out at the gym on the same day again, Find the lowest common multiples of 6 days and 9 days.
Ahmed (6-days)=6,12,18,24
Brother(9-days)=9,18,24
Anybody answer!!!!, I'm trying to do my IXL. Have to get it to 90!!
What kind of transformation converts the graph of f(x)=x–1 into the graph of g(x)=9x–9?
Horizontal Shrink
Horizontal Stretch
Vertical Shrink
Vertical Stretch
The transformation that converts the graph of f(x) = x - 1 into the graph of g(x) = 9x - 9 is a vertical stretch by a factor of 9, followed by a vertical shift downwards by 8 units.
What are some instances of graphs?
Some instances of graphs include line graphs, bar graphs, scatter plots, pie charts, and histograms, which are visual representations of data or mathematical functions.
To see this, we can rewrite g(x) as:
g(x) = 9(x - 1) = 9x - 9
This shows that g(x) is a vertical stretch of f(x) by a factor of 9, which means that every y-value of g(x) is 9 times the corresponding y-value of f(x). The horizontal axis remains the same.
Next, we can see that g(x) is shifted downward by 8 units compared to f(x). This is because g(x) has a y-intercept of -9, while f(x) has a y-intercept of -1. This means that every y-value of g(x) is 8 units less than the corresponding y-value of f(x).
Therefore, the transformation that converts the graph of f(x) = x - 1 into the graph of g(x) = 9x - 9 is a vertical stretch by a factor of 9, followed by a vertical shift downwards by 8 units.
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Given: trap. SPQR with SP || QR ; MN is the median of the trap. m∠QRS = 120 ; m∠QPS = 135 ; SP = PQ = 12. Find: MN.
Answer:
From the information given, we can draw the following diagram:
S ------- P
/ \ / \
/ \ QR / \
/ \ / / \
/ Q \
R-----------------P
MN
Here, SP || QR, so we have ∠QSP = ∠PQR and ∠SPQ = ∠QRP.
Since m∠QRS = 120, we have m∠QRP = 360 - m∠QRS = 360 - 120 = 240.
Since m∠QPS = 135 and ∠QSP = ∠PQR, we have m∠PQR = 360 - m∠QPS = 360 - 135 = 225.
Let x = MN. Since MN is the median of the trapezoid, we have MP = NR = x.
Now, consider the triangles SPQ and RPQ. We have:
tan(∠SPQ) = x/12 (using the tangent ratio in triangle SPQ)
tan(∠RPQ) = x/12 (using the tangent ratio in triangle RPQ)
Since ∠SPQ = ∠RPQ (as they are corresponding angles), we have:
x/12 = x/12
x = 12
Therefore, MN = x = 12.
find cos{a} in the triangle side lengths 20,29,21
Check the picture below.