a spotlight has a parabolic cross section that is 4 ft wide at the opening and 2 ft deep at the vertex. how far from the vertex is the focus?
Answers
The distance from the vertex to the focus is :
8 feet
The spotlight has a parabolic cross-section with an opening width of 4 ft and a depth of 2 ft at the vertex. To find the distance from the vertex to the focus, we can use the equation for a parabola in the form y = (1/4f)x^2, where f is the distance to the focus.
Since the parabola is 4 ft wide at the opening, the value of x is 2 ft (half of the width). The depth at the vertex, which is the value of y, is 2 ft. Substituting these values into the equation, we get:
2 = (1/4f)(2^2)
2 = (1/4f)(4)
Now, we solve for f:
8 = f
So, the focus is 8 ft away from the vertex.
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Related Questions
Sofia ordered S pizzas for 24 guests at a party. Each guest will have 1/6 of a pizza. FIND S
Answers
Answer:
4 pizzas are needed.
Step-by-step explanation:
See image. You could totally think this through and use mental math to figure out how many pizzas are needed. See first image. Picture a pizza, cut it into 6 slices. It feeds 6 people. 2 pizzas feed 12 people. 3 pizzas feed 18 people. 4 pizzas feed 24 people.
If you have to write equations and show math work, you can write a single-variable equation or use a proportion. See image.
What is the value of x?
Answers
Answer:
12x+14=70
12x=70-14
12x=56
x=4.6
x=5
58:49 A pound of raisins costs $2.00, and a pound of almonds costs $5.00. Six pounds of a trail mix contains 2 more pounds of raisins than almonds. What is the cost of the 6 pounds of trail mix
Answers
Answer:
$18
Step-by-step explanation:
1 pound of raisins = $2
1 pound of almonds = $5
Let the number of raisins be represented by a
Let the number of almonds be represented by b
We are told in the question that:
Six pounds of a trail mix contains 2 more pounds of raisins than almonds.
a + b = 6 pounds
Hence, Almonds = 2 pounds
Raisins = 4 pounds
The cost of the 6 pounds of trail mix
= 4 × $2 + 2 × $5
=$8 + $10
= $18
Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months. Month 2 3 4 5 Sales 924 91
Answers
Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.
One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.
In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.
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six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?
Answers
If each child consumed the same quantity, then each would need to drink (63)x(4/n) of a gallon.
The US fluid ounce is equal to 1/128 of a US gallon since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint. The US gallon is accepted to be equivalent to around 3.785 L or 231 in inches, but the Imperial gallon is accepted to be equal to 4.54609 L. The liter is the unit of volume used by the great majority of people in the world. a volume measurement equal to eight pints.
An imperial gallon (Britain, Canada) is exactly 4.54609 liters. (US) 3.785 liters or around 231 cubic inches for liquids (a "U.S. liquid gallon")
Here gallon of lemonade to share = 63
let each children has 1 gallon of lemonade
so gallon=63
so portion =63/1
Formula = gallon to share x (4 parts of gallon shape / number of gallon)
which means if each one have n gallon then portion = (63)x(4/n)
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Each child would need to eat 63*4/n of a gallon if they all consumed the same amount.
Since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint, one US fluid ounce is equivalent to 1/128 of a US gallon. The Imperial gallon is acknowledged to be equal to 4.54609 L, but the US gallon is accepted to be about 3.785 L or 231 in. The vast majority of people in the world measure volume in litres. a volume that is eight pints in size.
In Britain and Canada, an imperial gallon equals precisely 4.54609 litres. 3.785 litres (US) or around 231 cubic inches (a "U.S. liquid")
Here, six thirty kids were sharing a gallon of lemonade.
each youngster should drink a gallon of lemonade.
Gallon = 63.
Hence part = 63/1
It indicates that the fraction is equal to 63*4/n if each has n gallons.
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Note: The complete question would be as bellow,
six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?
Ecological approach to algal bloom control. Algal blooms can have negative effects on an ecosystem by dominating its phytoplankton communities. Gonyostomum semen is a nuisance alga infesting many parts of northern Europe. Could the overall biomass of G. semen be controlled by grazing zooplankton species? A research team examined the relationship between the net growth rate of G. semen and the number of Daphnia magna grazers introduced in test tubes. A net growth rate was computed by comparing the initial and final abundances of G. semen in the experiment, with a negative value indicating a decrease in abundance. Here are the findings: 13 1 2 3 4 5 6 Number of grazers Net growth rate -1.9 -2.5 -2.2 -3.9 -4.1 -4.3 a. Make a scatterplot of number of grazers and net growth rate. Do you think that D. magna is an effective grazer of the G. semen alga? b. Find the correlation 1. How does it support your interpretation?
Answers
a. D. magna is an effective grazer of the G. semen alga. b. a very strong negative correlation between the number of grazers and the net growth rate of G. semen.
a. The scatterplot of the data shows a clear negative correlation between the number of D. magna grazers and the net growth rate of G. semen. As the number of grazers increases, the net growth rate of G. semen decreases. This suggests that D. magna is an effective grazer of the G. semen alga.
b. The correlation coefficient between the number of grazers and the net growth rate is -0.996. This indicates a strong negative correlation between the two variables, which supports the interpretation that D. magna is an effective grazer of G. semen. The closer the correlation coefficient is to -1, the stronger the negative correlation between the two variables. In this case, the correlation coefficient is very close to -1, which indicates a very strong negative correlation between the number of grazers and the net growth rate of G. semen.
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the manager of a local stadium is interested in how many fans purchase peanuts at events. in a random sample of ,200 fans chosen from several different events, 94 of them purchased peanuts. what does this data imply about the claim that half of the people who attend events purchase peanuts?
Answers
According to the given data 47% of the fans that attend the event, purchase the peanuts.
The sample collected was among 200 fans which means total fans = 200
out of which 94 fans purchased peanuts which means
Percentage of Fans purchased Peanuts = \(\frac{94}{200}\) X 100
= 47 %
Not exactly the half of the fans purchased the peanuts but approximately half that is 3% less than 50 % fans puchased the peanuts which implies => 47 % fans purchased peanuts.
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In ΔNOP, the measure of ∠P=90°, NP = 35, ON = 37, and PO = 12. What ratio represents the sine of ∠N?
Answers
Answer:
12/37
Step-by-step explanation:
SOH - CAH - TOA
O = opposite
A = adjacent
H = hypotenuse
Sin = O/H
Sin N = 12/37
Answer:Find sin N
sinN=
hypotenuse/opposite
12/37
Step-by-step explanation:
x and y each take on values 0 and 1 only and are independent. their marginal probability distributions are: f(x) =1/3, if x = 0 and f(x) = 2/3 if x = 1
Answers
the joint probability distribution for x and y is as follows:
f(x, y): x=0, y=0: 1/9
x=0, y=1: 2/9
x=1, y=0: 2/9
x=1, y=1: 4/9
Based on the given information, we can determine the marginal probability distributions for x and y:
For x:
f(x=0) = 1/3
f(x=1) = 2/3
For y, since it is independent of x, the probabilities remain the same:
f(y=0) = 1/3
f(y=1) = 2/3
To find the joint probability distribution, we multiply the probabilities for x and y since they are independent:
f(x=0, y=0) = f(x=0) * f(y=0) = (1/3) * (1/3) = 1/9
f(x=0, y=1) = f(x=0) * f(y=1) = (1/3) * (2/3) = 2/9
f(x=1, y=0) = f(x=1) * f(y=0) = (2/3) * (1/3) = 2/9
f(x=1, y=1) = f(x=1) * f(y=1) = (2/3) * (2/3) = 4/9
Therefore, the joint probability distribution for x and y is as follows:
f(x, y):
x=0, y=0: 1/9
x=0, y=1: 2/9
x=1, y=0: 2/9
x=1, y=1: 4/9
This represents the probabilities for each possible combination of x and y.
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The optimal amount of x1, x2, P1, P2 and income are given by the
following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I
=4189 The new price of P1 is the foll
Answers
The total change in the consumed quantity of x₁ as per given price and income is equal to 213.
x₁ = (21/7)P₁
x₂ = (51/7)P₂
P₁ = 10
P₂ = 5
P₁' = 81
To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',
The difference between the quantities consumed at the original price and the new price.
Let's calculate the quantity consumed at the original price,
x₁ orig
= (21/7)P₁
= (21/7) × 10
= 30
x₂ orig
= (51/7)P₂
= (51/7) × 5
= 36.4286 (approximated to 4 decimal places)
Now, let's calculate the quantity consumed at the new price,
x₁ new
= (21/7)P1'
= (21/7) × 81
= 243
x₂ new
= (51/7)P2
= (51/7) × 5
= 36.4286
The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,
Change in x₁
= x₁ new - x₁ original
= 243 - 30
= 213
Therefore, the total change in the quantity consumed of x₁ is 213.
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The above question is incomplete, the complete question is:
The optimal amount of x1, x2, P1, P2 and income are given by the following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?
Please answer step by step
3. What method is used to denote the following set? A={2,3,5,7,11}
a) Rule method
b) Listing method
c) Roster Method
d) borc
4. A diagram that makes use of geometric shapes to show relationships between sets.
a) Venn Diagram
b) Flow Chart
c) Unknown
d) Cannot be
Answers
Answer:
listing method
Step-by-step explanation:
pls make me brainliest pls
I hope this answer helps you with your test and/or homework
find a function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.
Answers
A function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f is f(x) = 3x^4/4 + 729/4.
In the given question, we have to find a function f such that f'(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.
The given function is f'(x) = 3x^3.
No integrating on both side,
f(x) = \(\int3x^3dx\) + C
f(x) = 3x^4/4 + C
As given, the line 81x + y = 0 is tangent to the graph of f.
So, slope at point of tangent; f'(x) = -81
So, 3x^3 = -81
Divide by 3 on both side, we get
x^3 = -27
Taking cube root on both side, we get
x = -3
So putting the value of x in 81x + y = 0, we get
y = 243
Thus, f(x) passes through (-3, 243).
So, 243 = 3/4(81) + C
Multiply by 4 on both side, we get
972 = 243 + 4C
Subtract 243 on both side, we get
4C = 729
Divide by 4 on both side, we get
C = 729/4
So, f(x) = 3x^4/4 + 729/4
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Find the radius of convergence, R, of the series.
[infinity] n = 1
(−1)nxn
5 n
R =
Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)
I =
Answers
The radius of convergence of the given series is 5. The interval of convergence is -5 ≤ x < 5, which means the series converges for all values of x between -5 and 5, excluding the endpoint x = 5.
To find the radius of convergence, we can use the ratio test
\(\lim_{n \to \infty}\) |(-1)ⁿ xⁿ⁺¹ 5ⁿ⁺¹ / (-1)ⁿ xⁿ 5ⁿ|
= \(\lim_{n \to \infty}\) lim |x|/5
The series converges if the ratio is less than 1, which occurs when |x| < 5. Therefore, the radius of convergence is R = 5.
To find the interval of convergence, we can test the endpoints x = -5 and x = 5.
When x = -5, the series becomes
∑ (from ∞ to n=1) (-1)ⁿ (-5)ⁿ / 5ⁿ
∑(from ∞ to n=1) (-1/5)ⁿ
which is an alternating geometric series with first term -1/5 and ratio -1/5. By the alternating series test, this series converges.
When x = 5, the series becomes
∑(from ∞ to n=1) (-1)ⁿ (5)ⁿ / 5ⁿ
∑(from ∞ to n=1) (-1)ⁿ
which is an alternating series that does not converge, since the terms do not approach 0 as n approaches infinity.
Therefore, the interval of convergence is -5 ≤ x < 5, or in interval notation, I = [-5, 5).
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Find the weighted average of the numbers 1 and 6, with weight four-fifths on the first number and one-fifth on the second number.a. 2b. 6.2 c. 3 d. 2.8
Answers
The weighted average of the numbers 1 and 6 is 2
What is a weighted average of two numbers?A weighted average is the average of a set of numbers, each with different associated “weights” or values. To find a weighted average, multiply each number by its weight, then add the results.
Given that, the weighted average of 1 and 6 in this instance, means the sum of the two numbers multiplied by their weights which are four-fifths and one-fourth respectively.
Weighted average = (first number x weight of first number)+(second number x weight of second number)
first number = 1
weight of first number = four fifths = 4/5
second number = 6
weight of second number = one fifth = 1/5
Therefore,
The weighted average = (1 x 4/5) + (6 x 1/5)
= 2
Hence, the weighted average of the numbers 1 and 6 is 2
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Which is greater?
\(4 \sqrt{20} \)
or
\( \sqrt{40} \)
Answers
Answer:
4√20
Step-by-step explanation:
√40 = √4 * √10 = 2√10
4√20 > 2√10
then:
the greater is:
4√20
USE LONG DIVISION
Divide.
(3x2 + 3x2 - 42x - 24) + (3x + 12)
Answers
Answer:
3x^2-39x-6
Step-by-step explanation:
because math easy
(93 points) Eloise bought 2 boxes of crackers to share with her friends. Her friends ate 12 of the first box and 34 of the second box.
A. 1/2 box
B. 2/3 box
C. 3/4 box
D. 1 1/3
Answers
Answer:
The answer is C, 3/4 of a box
arkadaşlar çanta yayınları deneme 10 daki çözümleri atarmısınız lütfen şık istemiyorum sadece çözümleri ACİL BAKARMISINIZ
Answers
Answer:
What you said doesnt make sense
Step-by-step explanation:
"
friends bag publications trial 10 could you throw the solutions please I don't want stylish, just look at the solutions urgently" Please say what you mean.
Which excerpt from the storyteller best supports the theme that the purpose of stories is to?
Answers
The purpose of stories "Here at the given any rate is said the bachelor, and then collecting his belongings preparatory to leaving the carriage, then he kept them quiet for ten minutes, which was more than you were able to do."
Here we need to excerpt from the storyteller best supports the theme that the purpose of stories.
While we look the bachelor says at the end they said that he kept them quiet for ten minutes, which was more than you were able to do and then he is implying that no matter what she thought of his story and how much "better" she thought she could've done it, and then his was able to capture the attention of these kids and that is the matter of the issue because, therefore for a story and then entertaining is more important than proper form
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In the diagram below, DE is parallel to XY. What is the value of y?
8
100
ya
O A. 120
B. 100
o
C. 80
o
D. 60
PREVIOUS
Answers
Answer:
100 is answer for math picture
Answer: 80
Step-by-step explanation:
180-100 = 80, y=80
2x+3(-6x-2)=18
Solve for X
Answers
Answer:
x = - 3/2
(the dash by the 3/2 is to show that it is negative, and is part of the answer)
Answer:
x= -3/2
Step-by-step explanation:
Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a survey and used to obtain the regression equation ŷ = –0. 227x + 50. 455, where x represents the price of bobbleheads (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). What is the predicted demand of a bobblehead that has price of $6. 00?
–1. 362 units
49. 093 units
51. 817 units
195. 837 units
Answers
The predicted demand of a bobblehead that has price of $6.00 is given as follows:
49.093 units.
What is the function?The function in the context of this problem is defined as follows:
y = -0.227x + 50.445.
In which:
x is the price of the bobblehead.y is the predicted demand.For a price of $6.00, the predicted demand is obtained with the numeric value at x = 6, replacing the lone instance of x by 6, hence:
y = -0.227(6) + 50.445
y = 49.093 units.
Meaning that the second option is the correct option.
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approximate the arc length of the curve y=14x4 over the interval [1,2] using the trapezoidal rule t7.
Answers
The approximate arc length of the curve y=14x^4 over the interval [1,2] using the trapezoidal rule t7 is approximately 27.78 units.
To approximate the arc length using the trapezoidal rule, we divide the interval [1,2] into seven subintervals of equal width. The formula for the arc length approximation using the trapezoidal rule is:
L ≈ h/2 * [f(x0) + 2f(x1) + 2f(x2) + ... + 2f(x6) + f(x7)],
where h is the width of each subinterval and f(xi) represent the value of the function at each corresponding x-coordinate.
In this case, h = (2-1)/7 = 1/7. Evaluating the function at the endpoints and midpoints of the subintervals, we can calculate the approximate arc length as 27.78 units.
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Help if u understand pleas and thanks
Answers
Answer:
3f
Step-by-step explanation:
f+f+f=3f
since every f has the same value
example
2+2+2=3(2)
6=6
Answer:
3f
Step-by-step explanation:
There are three f's added together, which makes 3f. If you had multiplied them all it would've been f^3, if you had divided f by 3 you would have f/3, and if f=1 it would've just been 3. This is why 3f is the best answer here.
Hope this helps :)
hey can someone help me pls *ANSWER ASAP*
Answers
This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,
Which is the translation applied?Remember that a vertical translation of N units is:
g(x) = f(x) + N
if N < 0 the translation is down.
if N > 0 the translation is up.
And a horizontal translation of N units is:
g(x) = f(x + N)
If N > 0 the translation is to the right.
if N < 0 the translation is to the left.
Here we have the transformation:
f(x) = x²
g(x) = (x + 2)² + 5
So this is a translation of 2 units to the left and 5 units up.
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show that the negative multinomial log-likelihood (10.14) is equivalent to the negative log of the likelihood expression (4.5) when there are m
Answers
The negative multinomial log-likelihood (Equation 10.14) is equivalent to the negative log of the likelihood expression (Equation 4.5) when there are 'm' categories.
Let's start by defining the negative multinomial log-likelihood (Equation 10.14) and the likelihood expression (Equation 4.5).
The negative multinomial log-likelihood (Equation 10.14) is given by:
L(θ) = -∑[i=1 to m] yₐ log(pₐ)
Where:
L(θ) represents the negative multinomial log-likelihood.
θ is a vector of parameters.
yₐ is the observed frequency of category i.
pₐ is the probability of category i.
The likelihood expression (Equation 4.5) is given by:
L(θ) = ∏[i=1 to m] pₐ
Where:
L(θ) represents the likelihood.
θ is a vector of parameters.
yₐ is the observed frequency of category i.
pₐ is the probability of category i.
To show the equivalence between the negative multinomial log-likelihood and the negative log of the likelihood expression, we need to take the logarithm of Equation 4.5 and then negate it.
Taking the logarithm of Equation 4.5:
log(L(θ)) = ∑[i=1 to m] yₐ log(pₐ)
Negating the logarithm of Equation 4.5:
-N log(L(θ)) = -∑[i=1 to m] yₐ log(pₐ)
Comparing the negated logarithm of Equation 4.5 with Equation 10.14, we can see that they are equivalent expressions. Therefore, the negative multinomial log-likelihood is indeed equivalent to the negative log of the likelihood expression when there are 'm' categories.
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please help due in 15 minutes!!!
Answers
Let the function P represent the population P(d), in thousands, of a colony of insects d days after first being measured. A model for P is P(d)=10⋅(1. 08)d. Select all the statements that are true about this situation.
There were 1,080 insects when the colony was first counted.
One week after the colony was first counted, there were 10,800 insects.
The growth factor per day is 1. 8.
The growth factor per week is 1. 08⋅7.
The growth factor per hour is 1. 8124
Answers
Answer:
c and e
Step-by-step explanation:
Lola likes to knit slippers and donate them to a nursing home. She has a bag of 60 pom-
poms in different colors that she puts on the top of the slippers. She randomly selects some
pom-poms from the bag to use. The table below shows the colors she selects.
Color Number
purple 4
orange
N
9
pink
yellow
5
Based on the data, estimate how many orange pom-poms were in the bag of 60 pom-poms.
If necessary, round your answer to the nearest whole number.
orange pom-poms
Submit
Answers
There were approximately 9 orange pom-poms in the bag.
How to estimate orange pom-poms?To estimate the number of orange pom-poms, we can use the proportion of orange pom-poms in the sample to the total sample size, and set it equal to the proportion of orange pom-poms in the bag to the total number of pom-poms in the bag.
Let x be the number of orange pom-poms in the bag. Then we have:
orange proportion in sample = 9/60 = 0.15
orange proportion in bag = x/60
Setting these two proportions equal, we get:
0.15 = x/60
Solving for x, we get:
x = 0.15 x 60
x = 9
Therefore, there were approximately 9 orange pom-poms in the bag.
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To estimate the number of orange pom-poms in the bag of 60, we use the ratio of selected orange pom-poms to the total number of pom-poms selected.
Explanation:To estimate the number of orange pom-poms in the bag of 60, we need to find the ratio of orange pom-poms to the total number of pom-poms selected. The table shows that Lola selected 9 orange pom-poms out of a total of 18 pom-poms. We can use this ratio to estimate the number of orange pom-poms in the bag by setting up a proportion:
Orange pom-poms in bag / Total pom-poms in bag = Orange pom-poms selected / Total pom-poms selected
By substituting the known values into the equation and solving for the unknown, we can estimate the number of orange pom-poms in the bag.
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find the lines slope and a point on the line y+4=-1/2(x-5)
Answers
Step-by-step explanation:
y+4 = -1/2(x-5)
y = (-x+5)/2 -4
y= (-x+5-8)/2
y= (-x-3)/2
when x=1
y=(-1-3)/2
y= -2
point on graph = (1,-2)
when x =3
y=(-3-3)/2
y= -3
point = (3,-3)
slope = (-2-(-3))/(1-3)
=1/-2
slope = 1/-2 , a point = (1,-2)
\(y + 4 = -\cfrac{1}{2}(x-5)\implies y-(\stackrel{y_1}{-4})= \stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{5}) \impliedby \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill m=-\cfrac{1}{2}\hspace{5em}(5~~,~~-4)~\hfill\)