To construct a perpendicular bisector, we have to draw two arcs using each of the endpoints as centers
What is a perpendicular bisector?
A perpendicular bisector is said to be a line that intersects the segment of another line perpendicularly and also divides it into two equal parts.
The properties of a perpendicular bisector include:
It divides a line segment into two equal parts It makes right angles with the line segment.Points in the perpendicular bisector are equal from the line of the segment.Hence, all the mentioned properties are correct except that to construct it, we have to draw two arcs using each of the endpoints as centers.
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how do i find the answer of this math question or problem f(x) = 4x − 9?
Answer:
x = 9/4
Step-by-step explanation:
f(x) = 4x - 9
(first substitute f(x) with 0)
0 = 4× - 9
(Move four)
-4x = -9
=> x = -9/-4
= 9/4
the probability that an at home pregnancy test will correctly identify a pregnancy is 0.98. suppose 11 randomly selected pregnant women with typical hormone levels are each given the test. rounding your answer to four decimal places, find the probability that all 11 tests will be positive at least one test will be negative
The probability that all 11 tests will be positive is 0.8007
The probability that at least one test will be negative is 0.1993
Finding the probability that all 11 tests will be positiveFrom the question, we have the following parameters that can be used in our computation:
p = 0.98
n = 11
The probability that all 11 tests will be positive is
P = pⁿ
So, we have
P = 0.98¹¹
Evaluate
P = 0.8007
Finding the probability that at least one test will be negativeHere, we use
P = 1 - P(No negative)
So, we have
P = 1 - 0.8007
Evaluate
P = 0.1993
Hence, the probability is 0.1993
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I need help! I provided a screenshot below. Rotations and Transformations - Geometry
Given the above transformation by counterclockwise rotation, the new coordinates will be given as:
F (7, -18)
G (12, -15)
H (12, -11)
I (7, -7).
What is a transformation?In math/geometry, the reconfiguration of a geometric shape such that there is a change from it's initial image is called transformation.
In this case, the actual dimensions of the shape were unaltered but it's coordinates did change.
See the attached and:
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20 % of the m&ms are red. There were 40 m&ms in the bag . How many red m&ms are there?
Answer:
8 Red M&M's
Step-by-step explanation:
40 M&M's × 0·20 = 8 red M&M's in the bag
Hope this helps, plz mark brainliest!
answer 8 red m&ms are there
Step-by-step explanation:
20/100*40
100/20=5
40/5=8
answer is 8red m&ms are there
thisss guyyy iss looooking fine . but why so serioussss hahahaha. when guysss be looking at you like this. does it make you blush what do u doo.
Answer:
no- it doesnt make me blush- and uh- i look at them and then away- and then start to draw or read-0-0
Step-by-step explanation:
A student is planning to attend college in 5 years. The student has saved $1,200 and plans to save another $50 per month over the next 60 months. Based on this information about the student’s plan, which statement about the possible choices for a college is true?
The correct answer choice:
The student would be able to afford the in-state cost for one year at a public 2-year college.
The correct option is D.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
A student is planning to attend college in 5 years.
The student has saved $1,200 and plans to save another $50 per month over the next 60 months.
The total savings,
= 1200 + (50 x 60)
= $4200
That is equivalent to the cost of one year at a public 2-year college.
Therefore, the saving amount is equivalent to the cost of one year at a public 2-year college.
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The table shows the cost per year of attending different types of colleges.
A student is planning to attend college in 5 years. The student has saved $1,200 and plans to save another $50 per month over the next 60 months.
Based on this information about the student's plan, which statement about the possible choices for a college is true?
Answer choices
The student would be able to afford the cost for one year at a private 4-year college.
The student would be able to afford out-of-state cost for half a year at a 4-year public college.
The student would be able to afford in-state cost for half a year at a public 4-year college.
The student would be able to afford in-state cost for one year at a public 2-year college.
Find a particular solution to the equation dạy dy et = - 2 dt2 +y dt t Please use exp(a*t) to denote the exponential function eat. Do not use e^(at). Powers may be denoted by **: for instance t2 = **2 = g(t) = =
Particular solution to the given differential equation is dy/dt =\(e^t / (-2dt^2 + y dt)\), the constant d represents any arbitrary constant value,
To find a particular solution to the given differential equation:
dy/dt = \(e^t / (-2dt^2 + y dt)\)
We can use the method of undetermined coefficients. Let's assume the particular solution has the form:
y_p(t) = A ×\(e^{at)\)
where A and a are constants to be determined.
Now, we'll differentiate y_p(t) to find dy_p/dt and substitute it into the differential equation:
dy_p/dt = A * a * \(e^{at}\)
Substituting this into the differential equation, we get:
A * a *\(e^{at}\) = \(e^{t}\) / (-2dt² + A * \(e^{at}\) dt)
Now, let's solve for the values of A and a.
Comparing the terms on both sides, we can equate the coefficients:
A * a = 1 (equation 1)
-2d = A (equation 2)
From equation 2, we can solve for A:
A = -2d
Now, substitute this value of A into equation 1:
-2d * a = 1
Solving for a:
a = -1 / (2d)
Therefore, the particular solution to the given differential equation is:
y_p(t) = (-2d) * \(e^{-t/2d}\)
Note: The constant d represents any arbitrary constant value, and it is included in the particular solution.
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6th Grade Math:
A 5-pound bag of cat food costs $11. What is the unit price of the cat food?
Answer:
The unit rate is 2.20. For a single pound of cat food it would cost $2.20
Explain why the confidence intervals you constructed using the percentile method and the standard error method are not exactly the same.
The confidence intervals created using the percentile method and the standard error method are not exactly the same for two reasons:
First, the two methods are based on different assumptions about the population distribution of the sample. Second, the percentile method and the standard error method use different formulas to compute the confidence intervals. The standard error method assumes that the population is normally distributed, while the percentile method does not make any assumptions about the distribution of the population. As a result, the percentile method is more robust than the standard error method because it is less sensitive to outliers and skewness in the data. The percentile method calculates the confidence interval using the lower and upper percentiles of the bootstrap distribution, while the standard error method calculates the confidence interval using the mean and standard error of the bootstrap distribution.
Since the mean and percentiles are different measures of central tendency, the confidence intervals will not be exactly the same.
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if s and l are independent, both should be accepted. true or false?
if s and l are independent, both should be accepted False.
If s and l are independent, it means that the occurrence of one event does not affect the occurrence of the other event. However, this does not necessarily mean that both events should be accepted. It depends on the specific criteria and requirements for acceptance of each event.
Therefore, the statement "if s and l are independent, both should be accepted" is false.
If s and l are independent, it means that they have no direct influence on each other. However, this does not necessarily mean that both should be accepted. The acceptance of s and l will depend on their individual merits and the specific context or criteria being considered.
The independence of s and l does not automatically imply that both should be accepted. Instead, evaluate each one separately based on the relevant factors.
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True. If s and l are independent variables, then accepting one does not affect the acceptance or rejection of the other. Therefore, both can be accepted if they meet the necessary criteria.
However, it's important to note that this assumption of independence should be confirmed through statistical analysis before making any conclusions.
If s and l are independent variables, then accepting one does not affect the acceptance or rejection of the other. This means that both can be accepted if they meet the necessary criteria. However, it's important to ensure that this assumption of independence is valid before making any conclusions. The independence of the variables can be tested through statistical analysis. Therefore, it's essential to examine the relationship between s and l before accepting or rejecting them. In general, if s and l are independent, then both can be accepted without any issues.
In conclusion, if s and l are independent variables, then both can be accepted. However, the independence assumption should be confirmed before making any decisions. This can be achieved through statistical analysis, which is a crucial step in data analysis.
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6 74/500 as a decimal (giving another chance for brainliest)
Answer:
6.148
Step-by-step explanation:
Brainlyst if u are right
Answer:
D. (2, 7)Step-by-step explanation:
The solution is the coordinates of the point (p,n) of intercept of lines described by given equations.
what percent of 260 is 143
Answer:
55%
Step-by-step explanation:
To find what percent of 260 is 143, we can set up a proportion:
x/100 = 143/260
Cross-multiplying, we get:
260x = 14300
Dividing both sides by 260, we get:
x = 55
Therefore, 143 is approximately 55% of 260.
which expressions are equivalent to 8 13 ?
The next four equivalent fractions of 8/13 are:
16/2624/3932/5240/65What are some equivalent fractions of 8/13?Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.
In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.
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Can someone plz help me ty
Answer:
8/15
Step-by-step explanation:
you first want to change your whole number, 4, into a fraction so all you have to do is add a 1 in the denominator so it will be 4/1
then you multiply across
2/15 * 4/1
you first multiply 2 and 4 and your answer will be 8 which is the numerator
then multiply 15 and 1 which is 15, the denominator
then you get
8/15
the random variable is geometric with a parameter which is itself a uniform random variable on . find the value of the conditional pdf of , given that . hint: use the result in the last segment.
The conditional PDF of X given Y = y is a geometric distribution with parameter 1-p.
Let X be a geometric random variable with parameter p, and let Y be a uniform random variable on the interval [0,1], which means the PDF of Y is fY(y) = 1 for 0 ≤ y ≤ 1 and 0 otherwise. We want to find the conditional PDF of X given Y = y.
By Bayes' theorem, the conditional PDF of X given Y = y is given by:
fX|Y(x|y) = fY|X(y|x) fX(x) / fY(y)
where fX(x) is the PDF of X, which is given by fX(x) = (1-p)^(x-1) p for x = 1, 2, 3, ..., and fY|X(y|x) is the PDF of Y given X = x, which is given by fY|X(y|x) = 1 for 0 ≤ y ≤ p and 0 otherwise.
To find fY(y), we use the law of total probability:
fY(y) = ∑ fX(x) fY|X(y|x) for all x
Plugging in the values of fX(x) and fY|X(y|x), we get:
fY(y) = ∑ (1-p)^(x-1) p for 0 ≤ y ≤ p and 0 otherwise.
Since Y is uniform on [0,1], we have fY(y) = 1 for 0 ≤ y ≤ 1 and 0 otherwise. Therefore, the above sum simplifies to:
∑ (1-p)^(x-1) p = p / (1 - (1-p)) = 1
Now we can plug in the values of fY(y) and fX(x|y) into the formula for the conditional PDF of X given Y = y:
fX|Y(x|y) = fY|X(y|x) fX(x) / fY(y)
fX|Y(x|y) = (1/p) (1-p)^(x-1) p / 1 = (1-p)^(x-1)
Thus, the conditional PDF of X given Y = y is a geometric distribution with parameter 1-p.
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a Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
y = 2/5x +24/5, is the equation which represents a line that passes through (-2, 4) and has a slope of 2/5.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = 2/5 x +b
Substitute the point (-2,4) into the equation and solve for b
4 = 2/5(-2)+b
4 = -4/5 +b
Add 4/5 to each side
20/5 +4/5 = b
24/5 = b
Hence, y = 2/5x +24/5, is the equation which represents a line that passes through (-2, 4) and has a slope of 2/5.
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suppose that a store offers gift certificate in denominations of 25 dollars and 50 dollars. determine the possible total amounts you can form using these gift certiciates
The possible total amounts can be formed by combining various quantities of 25-dollar and 50-dollar gift certificates in accordance with your needs.
To determine the possible total amounts that can be formed using gift certificates in denominations of $25 and $50, we can use a simple formula. Let x represent the number of $25 gift certificates and y represent the number of $50 gift certificates.
The formula for finding the total amount is:
Total amount = 25x + 50y
To find all possible total amounts, we need to consider all possible combinations of x and y.
For example:
- If we have 1 $25 gift certificate and 0 $50 gift certificates, the total amount is $25.
- If we have 2 $25 gift certificates and 0 $50 gift certificates, the total amount is $50.
- If we have 0 $25 gift certificates and 1 $50 gift certificate, the total amount is $50.
- If we have 1 $25 gift certificate and 1 $50 gift certificate, the total amount is $75.
- If we have 2 $25 gift certificates and 1 $50 gift certificate, the total amount is $100.
In general, any total amount can be formed using a combination of $25 and $50 gift certificates. The possible total amounts are:
$25, $50, $75, $100, $125, $150, $175, $200, $225, $250, and so on.
Hi! I'd be happy to help you with this question. To determine the possible total amounts you can form using gift certificates in denominations of 25 dollars and 50 dollars, follow these steps:
Step 1: Identify the minimum amount.
The minimum amount you can form is with one 25-dollar gift certificate, which gives a total of 25 dollars.
Step 2: Determine the increments.
Since the denominations are 25 dollars and 50 dollars, the possible amounts will increase in increments of 25 dollars.
Step 3: List the possible amounts.
Using the minimum amount (25 dollars) and the increments (25 dollars), the possible total amounts you can form using these gift certificates are:
- 25 dollars (1 x 25-dollar gift certificate)
- 50 dollars (2 x 25-dollar gift certificates or 1 x 50-dollar gift certificate)
- 75 dollars (3 x 25-dollar gift certificates or 1 x 25-dollar + 1 x 50-dollar gift certificates)
- 100 dollars (4 x 25-dollar gift certificates or 2 x 50-dollar gift certificates)
- ... and so on, increasing in 25-dollar increments.
The possible total amounts can be formed by combining various quantities of 25-dollar and 50-dollar gift certificates in accordance with your needs.
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Solve the equation for r. s=7r-33.
Answer: \(r=\frac{s+33}{7}\)
Step-by-step explanation:
s = 7r -33. add 33 to both sides +33 -33 =0 ."cancels"
s + 33 = 7r divide both sides by 7 7r/7 7/7 = 1 'cancels' and leaves r
(s + 33) / 7 = r
\(r=\frac{s+33}{7}\)
A rectangle has a perimeter of 64. the width is 3 less than the length. the equation for the scenario is 2x 2(x â€"" 3) = 64. what does the variable x represent in the equation? what will finding x â€"" 3 determine?
The variable x represent the length of rectangle.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Perimeter= 64 units
let the length be x.
So, width = x - 3
So, Perimeter of rectangle = 2 ( l + w)
64 = 2( x+ x -3)
32 = 2x -3
29= 2x
x= 29/2
Hence, the variable x represent the length of rectangle.
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the humane society reports that of 428 animals at their local animal shelter, 376 are household pets and the remaining 52 are wildlife animals. over the weekend, 29 of the household pets were adopted and 10 of the wildlife animals were released back into the wild. is there sufficient evidence to indicate a difference in the number of animals leaving the shelter over the weekend for the two types (household pets and wildlife animals)? use the p-value approach at the 1% level of significance.
There is sufficient evidence to believe that the number of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.
How to prove it there's sufficient evidenceTo determine if there's sufficient evidence,
Let us define the null and alternative hypotheses for this test as follows:
Null hypothesis (H0): The proportion of household pets leaving the shelter over the weekend is the same as the proportion of wildlife animals leaving the shelter over the weekend.
Alternative hypothesis (Ha): The proportion of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.
The test statistic for two sample test is given by:
z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))
where
p1 and p2 are the proportions of household pets and wildlife animals leaving the shelter over the weekend, respectively,
p is the pooled proportion,
n1 and n2 are the sample sizes for household pets and wildlife animals, respectively.
Pooled proportion is
p = (x1 + x2) / (n1 + n2)
where x1 and x2 are the number of household pets and wildlife animals leaving the shelter over the weekend, respectively.
Given
-n1 = 376, n2 = 52, x1 = 29, x2 = 10
p = (29 + 10) / (376 + 52) = 0.091
The observed proportions are:
p1 = x1 / n1 = 29 / 376 = 0.0771
p2 = x2 / n2 = 10 / 52 = 0.1923
The test statistic value
z = (0.0771 - 0.1923) / sqrt(0.091 * (1 - 0.091) * (1/376 + 1/52)) = -3.04
By using a standard normal distribution table,
The p-value is 0.00238.
Since the p-value (0.00238) is less than the level of significance (0.01), we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the number of animals leaving the shelter over the weekend for household pets and wildlife animals.
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Find the absolute values of 1 1/4 + - 11/6
The absolute value of 1 1/4 + - 11/6 is 7/12
The absolute value of any number is the non-negative value. Therefore, the absolute value is always positive. It is the distance of a number from zero. The absolute value is represented by the modulus sign 'l l'.
Given, 1 1/4 + - 11/6
We have to find the absolute value of the given equation.
1 1/4 + - 11/6 or 5/4 - 11/6
By solving the equation, we get (-7/12)
The absolute value of l-7/12l is 7/12.
We can conclude that the absolute value of a negative number is a positive number. The absolute value of a positive number is also a positive number.
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Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.
Describe in your own words, at least one benefit of using tables to compare
ratios?
Step-by-step explanation: it would help to compare whitch the answer would be 5 to 7
20 points plz just help me. Explain how you would use fraction bars to find the quotient of StartFraction 10 Over 12 EndFraction divided by StartFraction 4 Over 6 EndFraction. What is the quotient?
Answer:
5/4
Step-by-step explanation:
(10/12) / (4/6)
Reduce the fractions:
(5/6) / (2/3)
Multiply by the reciprocal:
(5/6) × (3/2)
15/12
Reduce:
5/4
Answer:
Draw one whole fraction bar. Next, draw 6 equal bars under it, since you are dividing by sixths. Then draw a twelfths fraction bar with 2 twelfths for each sixth bar. Above the twelfths bar, circle groups of 4 sixths. There is one group of 4/6 with 1/6 remaining. Since 1/6 is 1/4 of 4/6, the quotient is 1 1/4.
Step-by-step explanation:
why did someone remove ma answer :l
please help me simplify
Answer:
-25/6 is the closest
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
18+7=25
16+26=42
25/10-42/6
75/30-210/30=-135/30
-27/6
If x is a positive integer, then x is _____ negative.
a. never
b. sometimes
c. always
Solve each equation and show all your work.
6x - 5 = 2x + 7
3z - 2 = 5z + 19
5x - 15 + 2x = 4x + 12
35x + 2 = 7
Answer:
x = 3
z = (-21)/2
x = 9
x = 1/7
Step-by-step explanation:
Solve for x:
6 x - 5 = 2 x + 7
Subtract 2 x from both sides:
(6 x - 2 x) - 5 = (2 x - 2 x) + 7
6 x - 2 x = 4 x:
4 x - 5 = (2 x - 2 x) + 7
2 x - 2 x = 0:
4 x - 5 = 7
Add 5 to both sides:
4 x + (5 - 5) = 5 + 7
5 - 5 = 0:
4 x = 7 + 5
7 + 5 = 12:
4 x = 12
Divide both sides of 4 x = 12 by 4:
(4 x)/4 = 12/4
4/4 = 1:
x = 12/4
The gcd of 12 and 4 is 4, so 12/4 = (4×3)/(4×1) = 4/4×3 = 3:
Answer: x = 3
____________________________________
Solve for z:
3 z - 2 = 5 z + 19
Subtract 5 z from both sides:
(3 z - 5 z) - 2 = (5 z - 5 z) + 19
3 z - 5 z = -2 z:
-2 z - 2 = (5 z - 5 z) + 19
5 z - 5 z = 0:
-2 z - 2 = 19
Add 2 to both sides:
(2 - 2) - 2 z = 2 + 19
2 - 2 = 0:
-2 z = 19 + 2
19 + 2 = 21:
-2 z = 21
Divide both sides of -2 z = 21 by -2:
(-2 z)/(-2) = 21/(-2)
(-2)/(-2) = 1:
z = 21/(-2)
Multiply numerator and denominator of 21/(-2) by -1:
Answer: z = (-21)/2
________________________________________
Solve for x:
5 x + 2 x - 15 = 4 x + 12
Grouping like terms, 5 x + 2 x - 15 = (5 x + 2 x) - 15:
(5 x + 2 x) - 15 = 4 x + 12
5 x + 2 x = 7 x:
7 x - 15 = 4 x + 12
Subtract 4 x from both sides:
(7 x - 4 x) - 15 = (4 x - 4 x) + 12
7 x - 4 x = 3 x:
3 x - 15 = (4 x - 4 x) + 12
4 x - 4 x = 0:
3 x - 15 = 12
Add 15 to both sides:
3 x + (15 - 15) = 15 + 12
15 - 15 = 0:
3 x = 12 + 15
12 + 15 = 27:
3 x = 27
Divide both sides of 3 x = 27 by 3:
(3 x)/3 = 27/3
3/3 = 1:
x = 27/3
The gcd of 27 and 3 is 3, so 27/3 = (3×9)/(3×1) = 3/3×9 = 9:
Answer: x = 9
__________________________________________
Solve for x:
35 x + 2 = 7
Subtract 2 from both sides:
35 x + (2 - 2) = 7 - 2
2 - 2 = 0:
35 x = 7 - 2
7 - 2 = 5:
35 x = 5
Divide both sides of 35 x = 5 by 35:
(35 x)/35 = 5/35
35/35 = 1:
x = 5/35
The gcd of 5 and 35 is 5, so 5/35 = (5×1)/(5×7) = 5/5×1/7 = 1/7:
Answer: x = 1/7
The area between two negative scores can be found by
The area between two negative scores can be found by taking the absolute difference between the two scores.
The area between two negative scores can be found by taking the absolute difference between the two scores. This is because the absolute difference gives us the distance between the two scores without considering their signs.
To calculate the area between two negative scores, follow these steps:
1. Identify the two negative scores.
2. Subtract the smaller negative score from the larger negative score.
3. Take the absolute value of the result to remove the negative sign.
4. The absolute difference between the two negative scores represents the area between them.
For example, let's say we have two negative scores, -5 and -10. To find the area between them, we subtract -5 from -10, resulting in -10 - (-5) = -10 + 5 = -15. Since we are interested in the distance, we take the absolute value of -15, which gives us 15. Therefore, the area between -5 and -10 is 15.
The absolute difference between two negative scores gives us the area between them. This approach is applicable whenever we want to find the distance or area between any two numbers, not just negative scores.
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Explain how the distance formula can prove Pythagoras' Theorem. In your
explanation use the Pythagoras Theorem and how the distance formula can be used
with a right triangle when only given the hypotenuse.
Answer:
Given a triangle ABC, Pythagoras' Theorem shows that:
\(c^2=a^2+b^2\)
Thus,
\(c = \sqrt{a^2+b^2}\)
The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.
\(d^2 = (x_{2} -x_{1})^2 + (y_{2} -y_{1})^2\)
\(d = \sqrt{(x_{2}-x_{1})^2 + (y_{2} -y_{1})^2 }\)
Therefore when given the hypotenuse with endpoints at
\((x_{1}, y_{1}) and {(x_{2}, y_{2})\)
We know that the third point of the right triangle will be at
\((x_{2}, y_{1})\)
and that the two side lengths will be defined by the absolute values of:
\((x_{2} - x_{1}) = a\)
\((y_{2} - y_{1}) = b\)