Answer: It is equidistant from the segment's endpoints
Step-by-step explanation: This can also be called "a locus of point" and this is now the perpendicular bisector theorem.
Write a real-world problem that you could represent with the equation 20 2n5 4. Solve the equation to find the answer to your problem
The solution of the given equation is 1.6. It has been represented and solved as a real-world problem below.
The given equation is = - 20 + 2x5 = 4
We can rewrite this equation as = - 4 + 2x5 = 20
Let us suppose that person A has x number of bananas that they have taken out from a stock full of bananas. They continue taking x number of bananas two more times. They then stop and see that person B has already taken 4 bananas from the stock. We can write this equation as -
= 4 + 2x
Person A saw knew that there were 20 bananas in total. So, we can write it as -
= 4 + 2x = 20
Person A then resumed and took x number of bananas again 5 more times. We can rewrite this as -
= 4 + 2x5 = 20
Solving this equation, we get -
= 4 + 10x = 20
= 10x = 20-4 = 16
= x = 16/10
= x = 1.6
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The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class, in which there are 20 girls. How many boys are there in Mandy’s science class? Show your work
Number of boys in Mandy’s science class is 5.
Now, According to the question:
The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class,
There are 20 girls.
To find the how many boys are there in Mandy’s science class?
Based on the given condition:
Let the ratio be 3x and 12x
Now, According to the statement:
12x = 20
x = 20/12
x = 5/3
So, Number of boys = 3 × 5/3 = 5
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Carmela's gross pay is $784.25. Her deductions total is $191.17. What percent of her gross pay is take-home pay?
The percent of Carmela's gross pay that is her take-home pay is 75%
How to calculate the percent of Carmela's gross pay that is her take-home pay?
Carmela's gross pay is $784.25
Her total deductions is $191.17
Therefore the percent of her gross pay can be calculated as follows
The first step is to subtract the deductions from the gross pay
784.25 - 191.17
= 593.08
The percent of the gross pay that is take-home pay is
593.08/784.24 × 100
= 0.75 × 100
= 75%
Hence 75% of her gross pay is take-home pay
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Does the point (0, 0) satisfy the equation y = x?
Answer:
yes
Step-by-step explanation:
when y equals 0, x equals 0 also
y = x will produce a straight line passing through the point of origin (0,0)
Select all the true statements about the table.
x y
2 7
6 21
8 28
14 49
The slope is 3.5.
There is a proportional relationship between the variables x and y.
The slope is 7.
There is a linear relationship between the variables x and y, but not a proportional relationship.
The graph does not pass through the point (0, 0).
Answer:
Slope is 3.5
There is a proportional relationship between the variables x and y
The other statements are false.
The slope is 3.5, not 7
A linear relationship is the same a proportional relationship so statement 4 is always false
The graph does pass through (0, 0)
Step-by-step explanation:
Consider the first 2 pairs of coordinates, (2, 7) and (6, 21);
The increase in x is from 2 to 6, i.e. an addition of 4, the increase in y is from 7 to 21, i.e. an addition of 14;
Now consider the the 2nd and 3rd pairs of coordinates, (6, 21) and (8, 28);
The increase in x is from 6 to 8, i.e. an addition of 2, the increase in y is from 21 to 28, i.e. an addition of 7;
So, with the first 2 pairs of coordinates, an increase of 4 in x resulted in an increase of 14 in y and with the second 2 pairs of coordinates, an increase of 2 in x resulted in an increase of 7 in y, i.e. (+4, +14) and (+2, + 7);
2 × (+2, +7) = (+4, 14)
Or:
(+4, +14) ÷ 2 = (+2, +7)
This means a line from the 1st point to the 2nd point and a line from the 2nd point to the 3rd point will have the same gradient:
To find the slope simple, find the increase in y resulting from an increase of 1 in x, so:
(+2, +7) ÷ 2 = (+1, +3.5)
The gradient (or slope) is 3.5;
If there is a line with a fixed gradient that passes through all the points, then the relationship is proportional, also linear;
This is the case for this question;
If we follow the pattern backwards as well, so the point:
(2, 7) - (+2, +7) = (0,0)
This means (0,0) lies on the line.
(0,0), (2, 7), (4, 14), (6, 21), (8, 28), (10, 35), (12, 42), (14, 49), etc.
All these points would lie on the line, just add 2 to x, add 7 to y;
You would find the same points plus others by the rule, add 1 to x, add 3.5 to y.
the sum of the cube of a number and the product of the number and twelve is equal to seven times the square of the number. find the number.
Answer:
4 or 3
Step-by-step explanation:
X³+12X=7X²
X³-7X²+12X=0
X(X²-7X+12)=0
SOLVING THE QUADRATIC EQUATION
you have X=3 or X=4
Find the inverse of this function question (i) only please
The inverse of the function will be x=(4y-2)/(y+2) where x is the inverse of the function given in i.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x.
Now,
As given
f(x)=2(x+1)/4-x
from here x will be inverse of the function
Therefore
y(4-x)=2x+2
4y-yx=2x+2
4y-2=x(y+2)
x=(4y-2)/(y+2)
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To be a member at Sal's gym, there is a one-time sign-up fee plus a monthly fee for each month of membership. The table shows the total cost to be a member of the gym for different numbers of months.
Number of Months Total Cost
3 $53. 97
6 $77. 94
12 $125. 88
Create a function that gives the total cost,
C
C
, in dollars, to be a member of the gym given the number of months,
m
m
, of membership.
Enter your function in the space provided
A function that gives the total cost, C in dollars, to be a member of the gym given the number of months, m is C = 7.99m + 30
The table that shows the total cost to be a member of the gym for different numbers of months is:
Number of Months Total Cost
3 $53. 97
6 $77. 94
12 $125. 88
The rate of change of total cost per month would be,
m = [tex]\frac{77. 94-53. 97}{6-3}\\\\[/tex]
m = 7.99
so, the function for the total cost would be,
C = 7.99m + d .......(1)
where d is the fixed cost of the gym
For m = 3, C = 53.97
53. 97 = 7.99m + d
53. 97 = 7.99(3) + d
d = 30
So, function (1) would be,
C = 7.99m + 30
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An experimental plant has an unusual growth pattern. On each day. The plant doubles its height of the previous day. On the first day of the experiment, the plant grows to twice, or 2 times, its original height. On the second day, the plant grows to 4 times its original height. On the third day, the plant grows to 8 times its original height.
A. How many times its original height does the plant reach on the sixth day? On the nth day?
A. On the sixth day, the plant grows to 64 times its original height.
B. On the nth day, the plant would [tex]2^n[/tex] time its original height.
A. From the given condition we can that the growth of the plant shows a geometric progression with a first term of 2 and a common ratio of 2.
On the first day, the plant grows to [tex]2^1[/tex] = 2 times its original height.
On the second day, the plant grows to [tex]2^2[/tex] = 4 times its original height.
Similarly, on the sixth day, the plant grows to [tex]2^6[/tex] = 64 times its original height.
B. The nth term of the progression can be calculated by multiplying the first term by the common ratio raised to the power of n-1.
In this case, the first term is 2 and the common ratio is 2. So the nth term is [tex]2 * 2^{n-1} = 2^n[/tex]
Hence, on the nth day, the plant grows to [tex]2^n[/tex] times its original height.
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Help pls I really need help
Answer:
b
Step-by-step explanation:
Mock June 22 1F Overview Question Progress Exam Paper Progress 42/80 Marks 10 Eric throws a biased coin 10 times. He gets 3 Tails. Sue throws the same coin 50 times. She gets 20 Tails. 10 Grade For This Paper U 3 Aadi is going to throw the coin once. (i) Which one of the following statements is correct about the probability of Aadi getting Tails? 2/5 (ii) Use Eric's and Sue's results to work out an estimate for the probability that Aadi will get Tails. Write your fraction in the form a/b 13 A Sue's estimate is best because she throws it 50 times. B Sue's estimate is best because she gets more Tails. C Sue's estimate is best because she throws it more times than Eric (1) (1) 15 Total marks: 2 16 17
The best estimate for the probability of getting tails is given as follows:
C Sue's estimate is best because she throws it more times than Eric.
How to obtain the probabilities?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
For this problem we calculate an experimental probability, as the outcomes are obtained from the previous trials of Eric and Sue.
The higher the number of trials, the closer the experimental probability is to the theoretical probability, meaning that the correct option is given by option C.
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At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
Some animal become endangered and a trict law ha to be
implemented to protect them. What will you do to protect and help
them?
One of the most important things to do to protect endangered animals is to reduce the amount of habitat destruction caused by human activities.
This can be done by creating protected areas and limiting or banning activities like logging, mining, or development in sensitive areas. Additionally, it is important to reduce over-hunting and poaching of these animals. This can be accomplished by establishing quotas and strict regulations on allowable hunting and fishing, as well as increasing enforcement efforts to catch violators. It is also important to understand the life cycles and behaviors of the threatened species so that we can better protect them. This can be done through field research, monitoring, and analyzing population trends. Finally, it is important to develop conservation plans and strategies to protect the species. These could include habitat restoration, reintroduction programs, captive breeding, and other measures to ensure their survival.
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A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. What is the surface area in square centimeters if the height is 2 centimeters?
60
120
180
240
*answer is 180. How?
The surface area of the triangular prism is 120[tex]cm^2[/tex]
Now, According to the question:
A triangular prism is a polyhedron with a triangle for a base, thus it is a three-sided prism. Given that the triangle has three sides and a height of h, the surface area would be A = Ph + ab where P is the perimeter of the triangle.
We have :
A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters.
Now,
Hypotenuse = 13
a = 5 cm
b = 12 cm
h = 2 cm
The perimeter of the triangle is the sum of all the sides or:
P = 13 + 5 + 12
P = 30 cm
To get the surface area, substitute the values in the formula below:
A = Ph + ab
A = (30)(2) + (5)(12)
A = 60 + 60
A = 120
Hence, The surface area of the triangular prism is 120[tex]cm^2[/tex]
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In right triangle ABC, ZC is a right angle, m ZA = 52, AC = 10. 01, and AB = c.
sin 52° 0. 788
cos 52° 0. 616
tan 52° 1. 280
What is the measurement of AB?
If necessary, round your answer to two decimal places, like this: 42. 53
The length of side AB rounded to two decimal places is 16.25.
In a right angle triangle, the side on the base of the angle in question is divided by the hypotenuse. In this case, we can use the cosine ratio to find the length of AB.
We are provided with the following information,
C is the right angle, C= 90°
A= 52°
AC = 10. 01
sin 52° = 0. 788
cos 52° = 0. 616
tan 52° = 1. 280
Now,
since angle C is the right angle, AB is the hypotenuse.
Therefore, with respect to Angle A, AC will be the base and BC will be the perpendicular.
We know, cos x= base/hypotenuse
In this case, cos A = AC / AB
cos 52° = 10. 01/ AB
AB = 10. 01 / 0. 616
AB = 16.25
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Need answer of number 3,4,5
A linear equation - y = 5x -7 is a slant line with intercepts for linear equations. A vertical line is x = 2. A line that runs through the origin is y = 3/4x.
A slant line with intercepts is y = 1/2x + 3. A horizontal line is y = 9. The line x = -1 runs vertically.
A linear equation is what?A direct condition is one that has a level of 1 as its most extreme worth. As a result, there is no variable in a linear equation with an exponent greater than 1. The graph of a linear equation will always be straight.
y = 5x -7 is the first line equation.This line is not horizontal or vertical when the equation is graphed; rather, it is slant.
Additionally, this line does not traverse the origin. As a result, this equation has intercepts and slant lines.
x = 2 is the second line equation.Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.
Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.
y = 3/4x is the third equation for the line.This line is not horizontal or vertical when the equation is graphed; rather, it is slant.
Additionally, this line actually traverses the origin. As a result, the origin of this equation is traversed by slant lines.
y = 1/2x + 3 is the fourth equation for a line.This line is not horizontal or vertical when the equation is graphed; rather, it is slant.
Additionally, this line does not traverse the origin. This equation is therefore a slant line with intercepts.
y = 9 is the fifth line equation.Since there is no x-intercept in this equation, it will be a horizontal line that runs parallel to the x-axis.
Additionally, this line does not traverse the origin. As a result, there is a horizontal line in this equation.
x = -1 is the sixth line equation.Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.
Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.
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Let f(x) = 3x2 – 2x + 6 and g(x) = 7x – 4. Identify the rule for f + g.
The sum between the functions:
f(x) = 3x² - 2x + 6
g(x) = 7x - 4
is (f + g)(x) = 3x² + 5x + 2
How to add the two functions?Here we have two functions which are:
f(x) = 3x² - 2x + 6
g(x) = 7x - 4
And we want to add these to get f + g, so we only need to add the two functions, we will get:
f(x) + g(x) = (3x² - 2x + 6) + (7x - 4)
Grouping like terms we will get:
(3x² - 2x + 6) + (7x - 4) = (3x²) + (-2x + 7x) + (6 - 4)
And now we can simplify that to get:
(3x²) + (-2x + 7x) + (6 - 4) = 3x² + 5x + 2
The sum is:
(f + g)(x) = 3x² + 5x + 2
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which inequality represents the graph??
Answer:
C
Step-by-step explanation:
Answer 8 and 9.
Find the measure of an arc from the central angle.
8) The Length of major arc MQN is; ⁵/₄πr
Length of minor arc MPN is; ³/₄πr
9) Length of major arc HJK is; ¹³/₁₅πr
Length of minor arc MPN is; ⁴/₁₅πr
How to find the length of an arc?The formula that is used to find the length of an arc is;
L = (θ/360) * 2πr
where;
L is length of arc
θ is central angle
r is radius
8) We are not given the radius and as such;
Length of major arc MQN = (225/360) * 2πr
= ⁵/₄πr
Length of minor arc MPN = ((360 - 225)/360) * 2πr
= ³/₄πr
9) Length of major arc HJK = (312/360) * 2πr
= ¹³/₁₅πr
Length of minor arc MPN = ((360 - 312)/360) * 2πr
= ⁴/₁₅πr
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Identify the number of terms and then the resend themselves for each algebraic expression
The number of terms in the algebraic expressions are:
6y + 14 ⇒ 2 terms3x³ + 7x² + x - 5 ⇒ 4 termsHow to determine the number of terms in the algebraic expressionsFrom the question, we have the following parameters that can be used in our computation:
6y + 14 and 3x³ + 7x² + x - 5
Consider an expression given as
ax + b
The number of terms in the expression is 2 and the terms are ax and b
Using the above as a guide, we have the following:
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Complete question
Identify the number of terms and then the resend themselves for each algebraic expression
6y + 14 and 3x³ + 7x² + x - 5
Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28 degrees
. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Step-by-step explanation:
this creates a right-angled triangle 2.5 ft above the ground.
the string is the Hypotenuse (the side opposite to the 90° angle). the air distance to the height of the kite is one leg, and the height of the kite minus the 2.5 ft is leg 2.
in the trigonometric triangle the up/down side is sine (multiplied by the Hypotenuse or radius of the circle) of the angle at the center of the circle. and the left/right side is cosine (again multiplied by the Hypotenuse or radius) of the angle.
so, the height of the kite above ground is
105×sin(28°) + 2.5 = 51.79451409... ≈ 51.79 ft.
Consider this series.
16+32/3 +64/9 +128/27 +...
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
The series Choose... You know this because the series is
Choose....
The series converges to 16 * 3 = 48
What is a series?A number series is a continues chain of number identical of non-identical depending on the logic behind the series. It can contain letters, number, variable, fraction, and numbers with power or exponents.
How to find the series coverage?The series converges.
This series is in the form of 16 * (1 + 1/3 + 1/9 + 1/27 + ...)
The series 1 + 1/3 + 1/9 + 1/27 + ... is a geometric series with a common ratio of 1/3.
A geometric series converges if |r| < 1, where r is the common ratio. In this case, |1/3| < 1, so the series converges to lim (1/(1-1/3)) = 3.
So the series converges to 16 * 3 = 48
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A student went on a two-day hike. • On day one, the student hiked 11 kilometers. On day two, the student hiked at a rate of 2 kilometers per hour for x hours. Which of the following graphs represents y, the total distance, in kilometers, the student hiked over both days after hiking for x hours on day two?
The slope is 2, which equals the distance travelled each hour. The total distance hiked at the start of the second day is represented by the y-intercept, which is 4, which is also the y-value. intercept's
Explain about the Slope?We locate the rise/run before calculating the slope. Since the line increases by 2 between each point, the rise is 2. It travels over 1 between the points, hence the run is 1. The slope is now 2/1, or 2.
Given that it is rise/run, this gives us miles/hours, which indicates the number of miles she treks per hour.
The line's crossing of the y-axis is known as the y-intercept. At four, this is.
The fact that the y-value at this time is 4 and the x-value at this point is 0 tells us that she has trekked 4 miles in the 0 hours since the start of the second day, which is the distance she has covered so far.
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how do i find the missing angles?! please help this is due today! please and thxx!
The measure of each angle are
<1 =46<2=164<3= 46<5= 46<6= 164<7= 46<8= 134What are Parallel lines?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
<4 = 134
So, <4 = <2 = 134 (Vertical opposite angle)
<4= <8= 134 (Corresponding Angle)
<1 + <4 = 180 (Linear Pair)
<1 = 180-134
<1 = 46
<1 = <3= 46 (Vertical opposite angle)
<2= <6= 164 (Corresponding Angle)
<3= <7 (Corresponding Angle)
<1= <5 (Corresponding Angle)
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2. Amy has a room that is 6 feet by 10 feet. She bought tiles
that are 8 inches by 6 inches. How many tiles will she
need to cover the floor?
A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
Because we are dealing with different units here, we first would need to know how many inches are in one foot.
1 foot = 12 inches
Now that we know how many inches are in a foot, we can convert the length and width of the room from feet to inches.
6 feet = 72 inches
10 feet = 120 inches
Taking these numbers, we now need to figure out the area of the floor.
72 × 120 = 8640
Now, find the area of each tile.
6 × 8 = 48
Taking 8640, we can now divide that by 48 to get the number of tiles needed.
8640 ÷ 48 = 180
Therefore, 180 tiles are needed to cover the floor.
the meaure of the exterior angel of a hexagon are x,3x,,4x,5x,8x, and 9x find the meaure of the larget exterior angel
The largest exterior angle of hexagone is 108°.
Given that exterior angle of a hexagon are x, 3x, 4x, 5x, 8x and 9x.
Exterior angles are those that run parallel to a polygon’s inner angles but are located outside of polygon.
We know that sum of exterior angle of any polygon is 360°.
So, sum of exterior angle of hexagon will be 360°.
x + 3x + 4x + 5x + 8x + 9x = 360°
30x = 360°
x = 360° / 30
x = 12°
Now the largest angle = 9 * 12 = 108°
Therefore, the largest angle of hexagon is 108°.
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since the mode is the most frequently occurring data value, . a. it can never be larger than the mean b. it is always larger than the median c. it is always larger than the mean d. more than one mode can exist
The distribution of the mean, median, and mode values will depend on how skewed the distribution is. As a result, mean or mode may be larger than or less than mode.
correct answer is D.
Different measures of the center in a set of numerical data include mean, median, and mode. They each attempt to condense a dataset into a single number that may be used to represent a "typical" data point.
The "mean" value is obtained by summing all the data points and dividing the result by the total number of data points.
The middle number, or median, is obtained by placing all data points in order and choosing the middle one (or, if there are two middle numbers, the mean of those two figures).
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HELP ASAP !! :80 POINTS
How long is the shortest route from Ellport to Union Falls using the roads shown?
If necessary, round your answer to the nearest tenth.
The shortest route from Ellport to Union Falls using road is 18 miles
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Pythagoras theorem is used to determine the measure of the sides of a right angled triangle. It is given by:
(hypotenuse side)² = (adjacent side)² + (opposite side)²
The distance from Larksville to Smithfield = 9 + 9 + 6 = 24 miles
The distance from Larksville to Union Falls = 19.5 + 6.5 = 26 miles
Let x represent the distance from Smithfield to Union falls, using Pythaoras:
26² = 24² + x²
x² = 100
x = 10 miles
the distance from Smithfield to Union falls is 10 miles.
Let y be the shortest route from Ellport to Union Falls, using Pythagoras:
y² = 10² + (9 + 6)²
y² = 10² + 15²
y² = 325
y = 18 miles
The distance from Ellport to Union Falls is 18 miles
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Select the procedures that cannot be used to show the converse of the Pythagorean theorem using side lengths chosen from 3 cm, 4 cm, 5 cm, and 6 cm.
A.
Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.
B.
Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
C.
Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.
D.
Knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
The procedure that cannot be used are:
A. Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.
B.
Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
C.
Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.
What is the Pythagorean theorem?The Pythagorean theorem states that the result obtained by squaring the value of the hypotenuse of a right angled triangle is equal to the sum of the squares of the values other two sides of the triangle.
The hypotenuse of a a given triangle is usually longer that the other two sides.
Therefore, the correct procedure when lengths such as 3 cm, 4 cm, 5 cm, and 6 cm should be knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
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For integers a, b, and c, define a*b*c to mean ab-bc+ca then 1*-1*2 equals
Options;
A; -4
B; -2
C; 0
D; 2
E; 4
The operation of 1 * (-1) * 2 equals option D. 2.
What are Binary Operations?Binary operations are the operations which are performed on a specific set.
If the operation is defined on a set X, then binary operation can be defined as,
* : X * X → X.
Addition, subtraction, ... are some of the binary operations.
The given binary operation is defined as,
a * b * c = [tex]a^b-b^c+c^a[/tex]
We have to find the value of 1 * (-1) * 2.
By the definition,
1 * (-1) * 2 = [tex]1^{-1}-(-1)^{2}+2^1[/tex]
= 1 - 1 + 2
= 2
Hence the correct option is D.
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