The co-ordinate of the point of trisection of the line joining the (25,10) (-5,-5) is (15,5).
Given - Line joining the points (25,10) (-5,-5)
To find - The co-ordinate of the point of trisection
The points that divide a line segment AB in a ratio of 1:2 or 2:1 are known as points of trisection.
The point that splits a line segment AB in the ratio m:n is determined by the following formula,
\(\frac{mx_{2}+ nx_{1} }{m+ n}\) , \(\frac{my_{2} + ny_{1} }{m + n}\)
Accordingly,
\(\frac{1(-5) + 2(25)}{3}\) , \(\frac{1(-5) + 2(10)}{3}\)
\(\frac{-5 +50}{3}\) , \(\frac{-5 + 20}{3}\)
Solving,
\(\frac{45}{3}\) , \(\frac{15}{3}\)
(15, 5)
The co-ordinate of the point of trisection of the line joining the (25,10) (-5,-5) is (15,5).
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With a tailwind , a bird flew at a ground speed of 3mi/h. Flying the same path against the same wind, the bird travels at a ground speed of 1.5mi/h. What is the bird's air speed? what is the wind speed?
The speed of a bird with respect to the wind Bird's air speed is 2.25 mi/h. The speed of the wind with respect to the ground wind's speed is 0.75 mi/h.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Relative speed is usually given in terms of the speed of body A with respect to another body B (Vab)
Vab = Va - Vb
Vab = Speed of A relative to B
Va = Speed of A
Vb = Speed of B
So, for this question, when the bird is travelling in the same direction of the wind, the speed of the bird with respect to the ground is 3 mi/h
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
Speed of bird with respect to the wind = x
Speed of bird with respect to ground = 3 mi/h
Speed of the wind with respect to the ground = y
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
x = 3 - y
When the bird is travelling in the opposite direction, the speed of the bird with respect to the ground is 1.5 mi/h
Speed of bird with respect to the wind = x
Speed of bird with respect to ground = 1.5 mi/h
Speed of the wind with respect to the ground = -y (Negative since the wind is in the opposite direction)
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
x = 1.5 - (-y)
x = 1.5 + y
We can then solve this system of equations
x = 3 - y
x = 1.5 + y
1.5 + y = 3 - y
y + y = 3 - 1.5
2y = 1.5
Divide both sides by 2
(2y/2) = (1.5/2)
y = 0.75 mi/h
x = 1.5 + y
x = 1.5 + 0.75
x = 2.25 mi/h
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what is the best way to show your work for 2/3 times 9/12?
If anyone can help please help me
Answer:
Well the answer is 1/2
Step-by-step explanation:
The best way to show your work is writing it out.
please help me with this question
Retail price : $67.60
Markup percent : 150%
What is the original price?
Answer:
The original price is $45.06
Step-by-step explanation:
Let x represent the original price
x * 1.5 = 67.6
We isolate x by dividing both sides by 1.5
x * 1.5 / 5 = 67.6 / 1.5
x = $45.06
Plz help very important question
9514 1404 393
Answer:
g(2a) = 8a
Step-by-step explanation:
Put the argument where the variable is and simplify.
g(a) = 4a
g(2a) = 4(2a) = 8a
g(2a) = 8a
a random sampling of sixty pitchers from the national league and fifty-two pitchers from the american league showed that 10 national and 9 american league pitchers had e.r.a's below 3.5. suppose that this sample data is used to test the claim that there is a difference in the proportion of pitchers with era's below 3.5 in the two leagues. find the test statistic for the test. group of answer choices -0.090 28.197 -0.117 2.428
The test statistic for the test of proportions comparing the proportions of pitchers with ERA's below 3.5 in the National League and American League is approximately 2.428.
To find the test statistic for the test of proportions, we can use the formula
test statistic = (p₁ - p₂) / √(p(1 - p) (1/n₁ + 1/n₂))
where p₁ and p₂ are the proportions of pitchers with ERA's below 3.5 in the National League and American League, respectively, and p is the pooled proportion.
In this case, the proportions are p₁ = 10/60 = 1/6 and p₂ = 9/52. The pooled proportion is given by:
p = (x₁ + x₂) / (n₁ + n₂)
= (10 + 9) / (60 + 52)
= 19 / 112
Substituting the values into the formula, we get:
test statistic = (1/6 - 9/52) / √((19/112) (1 - 19/112) (1/60 + 1/52))
After evaluating this expression, the test statistic is approximately 2.428.
Therefore, the test statistic for the test is 2.428.
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ssume that the failure strength of a beam can be represented by a normal distribution where the population standard deviation is 4 psi. if you need the width of the 95% confidence interval to be 3 psi, how large of a sample do you need?
The failure strength of a beam can be represented by a normal distribution where the population standard deviation is 4 psi, we get a test measure of 7. Subsequently, we would require a test of at slightest 7 pillars to attain a 95% certainty interim with a width of 3 psi...
To discover the test measure required to realize a 95% certainty interim with a width of 3 psi, we ought to utilize the equation:
n = [ (z*σ) / E ]\(^{2}\)
where:
n is the test measure
z is the z-score related to the specified level of certainty (in this case, 95% compares to a z-score of 1.96)
σ is the populace standard deviation
E is the specified edge of blunder (in this case, 3 psi)
n = [ (1.96 * 4) / 3 ]\(^{2}\)
n = [ 2.61 ]\(^{2}\)
n = 6.82
we get a test measure of 7. Subsequently, we would require a test of at slightest 7 pillars to attain a 95% certainty interim with a width of 3 psi.
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7. A triangle has side lengths of 9 and 5. Which of the following cannot be the length of the third side? *
The values less than 4 or greater than 14 cannot be the length of the third side
Which cannot be the length of the third side?From the question, we have the following parameters that can be used in our computation:
Side lengths of 9 and 5.
Represent the third length of the triangle with x
So, we have the following representation (using the triangle inequality theorem)
a + b ≥ c.
Substitute the known values in the above equation, so, we have the following representation
9 + 5 ≥ x
9 + x ≥ 5
5 + x ≥ 9
Evaluate the sum
14 ≥ x
x ≥ -4
x ≥ 4
So, we have
14 ≥ x
x ≥ 4
Combine
4 ≤ x ≤ 14
This means that values less than 4 or greater than 14 cannot be the length of the third side
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The measure that cannot be the length of the third side is 14. Option
How to determine the lengthAn important rule to remember about triangles is called the third side rule:
Third side rule of triangles states that;
The length of the third side of a triangle is less than the sum of the lengths of the other two sides and greater than the (positive) difference of the lengths of the other two sides.
For this triangle, the length of the third side must be greater than
9- 5= 4
Also, the length of the third side must be less than
9 + 5 = 14
Hence, all the answers are possible except for answer D, which is equal to 14 but not less than 14.
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The Complete question is added as:
A triangle has side lengths of 9 and 5. Which of the following cannot be the length of the third side? *
a. 4
b. 5
c. 11
d. 14
find the odds in favor of getting four different numbers when tossing four dice.
The odds are 5 to 18 in favor of getting four different numbers when tossing four dice.
To find the odds in favor of getting four different numbers when tossing four dice, we need to first determine the total number of possible outcomes. With four dice, there are 6 possible outcomes for each die, resulting in a total of 6 x 6 x 6 x 6 = 1296 possible outcomes.
Next, we need to determine the number of outcomes that result in four different numbers being rolled. To do this, we can use the combination formula. There are 6 ways to choose the first number, 5 ways to choose the second number (since it cannot be the same as the first), 4 ways to choose the third number (since it cannot be the same as the first or second), and 3 ways to choose the fourth number (since it cannot be the same as the first, second, or third). This gives us a total of 6 x 5 x 4 x 3 = 360 outcomes where four different numbers are rolled.
Therefore, the odds in favor of getting four different numbers when tossing four dice are:
360 favorable outcomes / 1296 possible outcomes = 5/18
So the odds are 5 to 18 in favor of getting four different numbers when tossing four dice.
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a form of reasoning called is the process of forming general ideas and rules based on your experiences and observation
A form of reasoning called induction is the process of forming general ideas and rules based on your experiences and observations.
What is the Induction?The process of welcoming newly hired employees and assisting them in adjusting to their new positions and working surroundings is known as induction. Beginning a new work can be stressful, so new hires require assistance adjusting to their new environment.
The action or process of inducting someone to a position or organization.
We have given that,
A form of reasoning called is the process of forming general ideas and rules based on your experiences and observations.
As a result, the process of formulating general hypotheses and rules based on your observations and experiences is known as induction.
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plz help it’s been due and it’s almost brake
Answer:
thanks for the points
Step-by-step explanation:
3. Find a quadratic polynomial whose one zero is 5 + √3 and sum of the zeroes is 10.
Answer:
f(x) = x² - 10x + 22
Step-by-step explanation:
Let's assume the quadratic polynomial as:
f(x) = ax² + bx + c
Now we know that if one of the zeroes is 5 + √3, then the other zero must be 5 - √3 (because complex roots always come in conjugate pairs).
So the sum of the zeroes will be:
(5 + √3) + (5 - √3) = 10
10 = 2 * 5
The product of the zeroes will be:
(5 + √3) * (5 - √3) = 25 - 3 = 22
Now, using the sum and product of zeroes, we can write:
b/a = 10
c/a = 22
Solving for b and c, we get:
b = -10a
c = 22a
Substituting these values in f(x), we get:
f(x) = a(x - 5 - √3)(x - 5 + √3)
Expanding the right-hand side:
f(x) = a[(x - 5)² - (√3)²]
f(x) = a(x² - 10x + 22)
Comparing the coefficients of f(x) with ax² + bx + c, we get:
a = 1, b = -10, c = 22
Therefore, the quadratic polynomial is:
f(x) = x² - 10x + 22
A rectangular garden is fenced on all sides with 132 feet of fencing. The garden is 6 feet longer than it is wide. Find the length and width of the garden
Answer:
129: width
135:length
what is -3 = -8x - 9 + 5x
Answer: x = -2
Step-by-step explanation:
To begin, consider the following equation:
-3 = -8x - 9 + 5x
To begin, add the x terms on the right side of the equation:
-3 = -8x + 5x - 9
Simplifying even more:
-3 = -3x - 9
We wish to get rid of the constant term on the right side (-9) in order to isolate the variable x. This can be accomplished by adding 9 to both sides of the equation:
-3 + 9 = -3x - 9 + 9
To simplify: 6 = -3x
We can now calculate x by dividing both sides of the equation by -3: 6 / -3 = -3x / -3
To simplify: -2 = x
As a result, the answer to the equation -3 = -8x - 9 + 5x is x = -2.
PLEASE HELP ME I’LL GIVE BRILLIANCE TO YOU
Answer:
y=-2x+8
Step-by-step explanation:
y intercept is at 8, and there is a decrease in 2x per 1y
Answer:
the answer is the second one do nitrotype. com
Step-by-step explanation:
get rid of the space in .com
The graph below shows the time Andrea spent reading one day. Write a few sentences to describe the relationship between the time Andrea spent reading and the number of pages she read.
Answer:
the more pages she read, the more time she read for.
Step-by-step explanation:
What is the domain of the function y=2x-6?
-00
O 0
o 3
O 6
help
Answer:
6≤x<∞
Step-by-step explanation:
y=2√x-6
The domain is all values of x that makes the expression defined.
Set-Builder Notation: {x| x ≤ 3 }
Interval Notation: (-∞,3]
What is the domain of function?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Given the function in the question;
y = 5√(6−2x)
To find the domain, set the radicand greater than or equal zero and solve for x.
6 - 2x ≥ 0
Subtract 6 from both sides
6 - 6- 2x ≥ 0 - 6
-2x ≥ -6
Divide both sides by -2
-2x/-2 ≤ -6/-2
x ≤ -6/-2
x ≤ 3
Therefore, the domain is;
Set-Builder Notation: {x| x ≤ 3 }
Interval Notation: (-∞,3]
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complete question:
What is the domain of the function y=5√6−2x
if there were 1580 people who participated in the survey then how many people said they had 4 members in their family?
Answer:
632
Step-by-step explanation:
1580*0.4=632
The formula for finding the surface area of a rectangular solid with length 1, width w, ~ and height h is SA = 2/w + 21h + 2wh. Find the surface area of a rectangular solid with length 5 inches, width 2 inches, and height 4 inches. A. 28 square inches B. 36 square inches C. 72 square inches D. 76 square inches
The surface area of the rectangular solid with length 5 inches, width 2 inches, and height 4 inches is 76 sq inch. The answer is D.
What is surface area of rectangular solid ?
The surface area of a rectangular solid (also known as a rectangular prism) is the total area of all its faces. It can be calculated using the formula:
SA = 2lw + 2lh + 2wh
where l is the length of the rectangular solid, w is its width, and h is its height.
The rectangular solid has six faces: a top face, a bottom face, a front face, a back face, a left side face, and a right side face. The formula above accounts for the area of each of these faces.
According to the question:
The formula for the surface area of a rectangular solid is:
SA = 2lw + 2lh + 2wh
We are given that the length (l) of the solid is 5 inches, the width (w) is 2 inches, and the height (h) is 4 inches. Substituting these values into the formula, we get:
SA = 2(5)(2) + 2(5)(4) + 2(2)(4)
= 20 + 40 + 16
= 76 square inches
Therefore, the surface area of the rectangular solid with length 5 inches, width 2 inches, and height 4 inches is 76 square inches. The answer is D.
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A baketball player attemptd 15 baket in a game he make 9 which ratio decribe the number of baket the player made to the number of baket the playerd attempted
The ratio that describes the number of baskets the player made to the number of baskets the player attempted is 9:15. This can be simplified to 3:5.
The ratio of the number of baskets made by the player to the number of baskets attempted is 9/15. This ratio can be simplified to 3/5, which means that for every 5 baskets attempted, the player made 3 baskets. This ratio can also be expressed as a percentage by dividing the number of baskets made by the number of baskets attempted and multiplying the result by 100%. In this case, the percentage of baskets made by the player is 60% (9 baskets made / 15 baskets attempted * 100% = 60%). This means that out of every 100 baskets attempted by the player, he made 60 baskets.
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Calculate the present value annuity of 5000per annum for 12years and interested being 4% per annually compounded annually
\(~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}}\\ \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount} \\ pymnt=\textit{periodic payments}\dotfill &\$5000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}\)
\(A=5000\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1\cdot 12}-1}{\frac{0.04}{1}} \right]\implies A=5000\left( \cfrac{1.04^{12}~~ - ~~1}{0.04} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 75129.03~\hfill\)
Picture⬇️. Thank you!
Answer:
The bottom most option
Step-by-step explanation:
Lets divide 3 2/5 and 3 1/6
3 2/5 = 17/5 and 3 1/6 = 19/6
17/5/(19/6) = 17/5 x 6/19 = 102/95 = 1 7/95 or the last option.
Pls mark as brainliest for no real reason. Cheers
help please will mark branniest
thanks :)
Answer:
the first one is the 2 method for cpm and the second one is to seperate the other variable. the last one is say its a combination of both removing zeros and balanced sets. hope this helped :)
You randomly select a number from 0 to 39 (inclusively) and then randomly select a number from 0 to 9 (inclusively). What is the probability of selecting a 7 both times? The probability is (Type an integer or a decimal. Do not round.)
The probability of selecting a 7 on the first draw is 1/40, since there are 40 equally likely numbers to choose from. The probability of selecting a 7 on the second draw is 1/10, since there are 10 equally likely numbers to choose from. Since these events are independent, we can multiply the probabilities to find the probability of selecting a 7 both times:
1/40 * 1/10 = 1/400
So the probability of selecting a 7 both times is 1/400, or 0.0025.
To find the probability of selecting a 7 both times, we'll calculate the individual probabilities and then multiply them.
There are 40 numbers from 0 to 39 (inclusive) and only one of them is 7. So, the probability of selecting a 7 in the first draw is 1/40.
There are 10 numbers from 0 to 9 (inclusive) and again only one of them is 7. So, the probability of selecting a 7 in the second draw is 1/10.
Now, multiply the probabilities: (1/40) * (1/10) = 1/400.
The probability of selecting a 7 both times is 1/400.
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1. At Parker’s Pizza Parlor, the total cost of an order of 5 slices of pizza is $12.37. This price includes $1.12 in sales tax. Let p represent the cost of 1 slice of pizza. (a) Write an equation to represent this scenario. (b) Solve the equation for p to determine the cost of 1 slice of pizza.
Step-by-step explanation:
p = 5 ÷ (12.37 - 1.12)
p = 5 ÷ 11.25
p = 2.25
Answer:
$12.37-1.12=$11.25
let p =1 slice
5(p)=11.25
5p=11.25
=2.25a feature was created using a triangle and a semicircle . use the ruler provided to measure the dimensions of the triangle and semicircle to the nearest centimeter . which measurement is closest to the area of the feature in square centimeters .
The area of a circle is given by:
\(\begin{gathered} A=r^2\pi \\ \text{Where:} \\ r=\frac{8}{2}=4 \\ \text{ Since it is a semicircle, the area is:} \\ A=\frac{4^2\pi}{2}=8\pi \end{gathered}\)And the area of the triangle is:
\(\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{where:} \\ b=8 \\ h=7 \\ A=\frac{8\cdot7}{2}=28 \end{gathered}\)Therefore, the total area is:
\(A_T=8\pi+28\approx53.13\operatorname{cm}\)Aubrey walks 15 miles in 4 hours. At what unit rate does Aubrey walk?
A.
4 miles
15 hours
O B.
15 miles
4 hours
C.
4 hours
15 miles
O D.
15/4 miles
1 hour
Answer:
Answer is A.
Step-by-step explanation:
What is the nth term rule of the linear sequence below?
-9,-5,-1,3,7,.....
what is the TN=
explain to me, please?
Thanks
Answer:
4n -13
Step-by-step explanation:
notice that the difference between the adjacent terms is 4.
nth term is given by:
nth term = first term + (n-1) × difference -n is any number
= -9 + (n-1) × 4
= -9 + 4n -4
= 4n -13
Find the product
(7+2u) (7-2u)
Options:
a) 49+4u
b) 49-4u(square root sign)
c) 4u(square root sign) - 49
Answer:
b
Step-by-step explanation:
if you mean squared and not square root, then it would be b because if you factor it back out, you will get the original expression back because of the subtraction of perfect squares.
Answer:
b) \(\boxed{\bold{(7+2u)(7-2u)=49-4u^2}}\)Step-by-step explanation:
\((7+2u) (7-2u)=(7)(7)+(7)(-2u)+(2u)(7)+(2u)(-2u)=\\\\=49-14u+14u-4u^2=\ \underline{49-4u^2}\)
1 sack of flour contains 21 cups. It takes 3 cups of flour to make a batch of cookies. How many batches of cookies can you make with TWO sacks of flour?
Answer:
14 batches
Step-by-step explanation:
If 1 sack of flour = 21 cups, and 1 batch of cookies need 3 cups, all you have to do is find out how many batches can be made with 1 sack and double the number:
3 × _ = 21
21 ÷ 3 = 7
7 × 2 = 14
You can make 14 batches of cookies with 2 sacks of flour.
Hope this helped.