Answer:
y = (-2/9)x
Step-by-step explanation:
Rise over run so between (-7,-5) and (4,-3) it goes up -2 and over 9 so -2/9. Put this next to x and boom you have the slope equation.
The list represents the ages of students in a gymnastics class.
5, 7, 6, 9, 7, 5, 8, 8, 6, 9
If another student of age 5 joins the class, how is the mean affected?
The mean will remain the same at 7.
The mean will remain the same at about 6.3.
The mean will increase to about 7.2.
The mean will decrease to about 6.8.
The mean will decrease to about 6.8.
If another student of age 5 joins the class, how is the mean affected?The mean of the original ages is:
(5 + 7 + 6 + 9 + 7 + 5 + 8 + 8 + 6 + 9)/10 = 7
If another student of age 5 joins the class, the sum of the ages becomes:
5 + 7 + 6 + 9 + 7 + 5 + 8 + 8 + 6 + 9 + 5 = 75
And the number of students becomes 11. Therefore, the new mean is:
75/11 ≈ 6.82
So, the mean will decrease to about 6.8.
The correct answer is: The mean will decrease to about 6.8.
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please match the types of adaptive immunity with the statements that most accurately describe thme to test your understanding
The correct match for the adaptive immunity with the statement that best describes them are A - 1, B - 4, C - 2, D - 3.
Active immunity refers to the immune response developed by an individual's own immune system after exposure to a specific pathogen or through vaccination. It involves the production of specific immune cells, such as B-cells and T-cells, that recognize and respond to the antigens (foreign substances) present on the pathogen.
Artificial immunity refers to the acquisition of immunity against a specific pathogen through medical interventions rather than through natural exposure. It involves the administration of immunobiological substances or products that stimulate an immune response or provide preformed immune components to confer protection.
Passive immunity refers to the transfer of preformed antibodies or immune cells from one individual to another, providing immediate but temporary protection against a specific pathogen.
Natural immunity, also known as innate immunity, refers to the non-specific defense mechanisms that are present in an individual from birth and provide immediate protection against a wide range of pathogens.
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-- The given question is incomplete, the complete question is
"Match the statement to the type of adaptive immunity it most accurately describes to test your understanding of the adaptive immune states
A. Active Immunity 1. One's own body produces B-And T-Cell responses to SARS COV-2 Virus
B. Artificial Immunity 2. Individual receives immunotherapy containing antibodies against SARS COV-2 that were produced by another host.
C. Passive Immunity 3. Immunity is acquired through normal life experiences not through medical intervention.
D. Natural Immunity 4. Immunity is obtained through medical procedures such as COVID-19 vaccine." --
Click on photo if neccessary
Answer:
a i think
Step-by-step explanation:
Answer:
Your answer is A.
Step-by-step explanation:
5. Suppose X 1and X 2are random variables with mean 10,20 respectively, and SDs 2, 3 respectively.
Let T=11X 1−2X2
Find the mean and SD of T when X 1and X 2are independent.
Find the mean and SD of T when X1and X 2 have correlation of
−0.76
In the case that X1and X 2 are independent, normally distributed
variables, find P(T>30)
The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.
To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16. We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.
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NEED HELP ASAP!!! PLSSSSSSSSSSSSSSSSSSSS
Answer:
p(x) = 6x - 15
Step-by-step explanation:
So, first you subtract the cost of the necklace from the revenue, equating to 6x. Then, you take your constant, 15, and plug it into the equation for profit, giving you the finished equation of p(x) = 6x - 15. Hope this helps! (:
Answer: p(x) = 6x - 15 Answer is B
Step-by-step explanation:
They are wanting to know p(x)
Given:
r(x) = 10x
c(x) = 4x +15
p(x) = r(x) - c(x) >substitute r(x) and c(x)
p(x) = 10x - (4x + 15) >Distribute -
p(x) = 10x - 4x - 15 >combine like terms
p(x) = 6x - 15 Answer is B
Your uncle won the powerball jack[ot and decided to give you 50000 dollars. You want to save this money for college so you find an investment that has an anual interest rate of 3.75% and is compounded weekly. How much money will you have for college in 4 years
Answer: $58,088.57
Step-by-step explanation:
The investment is compounded weekly so you need to change the parameters of the equation to a weekly figure:
Interest rate is yearly so:
= 3.75%/52
= 3.75/52% per week
Number of periods is 4 years so:
= 4 * 52
= 208 weeks
Future value in 4 years is:
= 50,000 * ( 1 + 3.75/52%)²⁰⁸
= $58,088.57
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Question 14
\(\frac{\sin x}{26}=\frac{\sin 49^{\circ}}{25}\\\\\sin x=\frac{26\sin 49^{\circ}}{25}\\\\x \approx 51.7^{\circ}, 128.3^{\circ}\)
Both of these values satisfy the angle sum of a triangle.
Question 16
\(\frac{\sin x}{8}=\frac{\sin 105^{\circ}}{11}\\\\\sin x=\frac{8 \sin 105^{\circ}}{11}\\\\x \approx 44.6^{\circ}, 135.4^{\circ}\)
However, the second case exceeds the angle sum of a triangle, so \(x \approx 44.6^{\circ}\).
g 1. Let p equal the proportion of triathletes who suffered a training-related overuse injury during the past year. Out of 330 triathletes who responded to a survey, 177 indicated that they had suffered such an injury during the past year. a) Use these data to give a point estimate of p. b) Use these data to find an approximate 90% confidence interval for p. Interpret the interval in the context of the problem. c) Do you think that the 330 triathletes who responded to the survey may be considered a random sample from the population of triathletes
a) The point estimate of the proportion of triathletes who suffered a training-related overuse injury during the past year is approximately 0.5364. b) The approximate 90% confidence interval for the proportion of triathletes who suffered a training-related overuse injury during the past year is (0.4970, 0.5758). c) The random sampling assumption cannot be determined without additional information about the survey methodology and sampling process.
a) To obtain a point estimate of p, we divide the number of triathletes who suffered a training-related overuse injury (177) by the total number of respondents (330):
Point estimate of p = 177/330
≈ 0.5364
Therefore, the point estimate of p is approximately 0.5364.
b) To find an approximate 90% confidence interval for p, we can use the formula for the confidence interval of a proportion:
Confidence interval = p ± z * √((p(1-p))/n)
where:
p is the sample proportion (0.5364),
z is the z-score corresponding to the desired confidence level (90% corresponds to a z-score of approximately 1.645),
n is the sample size (330).
Substituting the values into the formula:
Confidence interval ≈ 0.5364 ± 1.645 * √((0.5364*(1-0.5364))/330)
Calculating the confidence interval:
Confidence interval ≈ 0.5364 ± 1.645 * √(0.2505/330)
Confidence interval ≈ 0.5364 ± 1.645 * 0.0239
Confidence interval ≈ 0.5364 ± 0.0394
Confidence interval ≈ (0.4970, 0.5758)
Therefore, the approximate 90% confidence interval for p is (0.4970, 0.5758).
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Consider these functions: f(x)=x+1, g(x)=2/x
Which polynomial is equivalent to (fog)(x)?
A.2/x+1
B.2x+2/x
C.2/x +1
D.2/x^2+x
Answer:
A.2/x+1 ............
The composite function f(g(x)) is 2/x + 1
Given the function
f(x)=x+1g(x)=2/xWe are to get the composite function (fog)(x)
This can be written as:
f(g(x)) = f(2/x)
f(2/x)= 2/x + 1
Hence the composite function f(g(x)) is 2/x + 1
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where is the altitude of polaris (the maximum)
The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.
The altitude of Polaris varies depending on the observer's latitude.
For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.
For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.
It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.
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78 is calories in 3/4. How many calories is in one cup
Answer:
208 or 104
Step-by-step explanation:
7. Due to a severe drought, a population of lions is decreasing at a rate of 3.5% per year. Scientists have noticed 80 lions in the area. After how many years will this population of 80 lions drop below 15 lions if this rate decrease continues?
Answer:
47 years
Step-by-step explanation:
The population decay can be modeled by an exponential function of the form ...
p = a·b^t
where a is the initial population, and b is the growth factor.
__
The growth factor is related to the given growth rate by ...
growth factor = 1 + growth rate
b = 1 + (-3.5%) = 1 -0.035 = 0.965
The initial population is given as a=80, so the exponential function is ...
p = 80·0.965^t
__
We want to find the value of t when p=15. This is solved using logarithms.
15 = 80·0.965^t
15/80 = 0.965^t . . . . . . . . . . . divide by 80
log(15/80) = t·log(0.965) . . . . take logs
t = log(15/80)/log(0.965) ≈ 46.985 . . . . divide by the coefficient of t
After 47 years, the population will drop below 15 lions.
does this interval give convincing evidence of a difference between the population proportions? justify your answer. no. because the interval does not contain 0, there is not convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. yes. because the interval does not contain 0, there is convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. no. because the interval does not contain negative numbers, there is not convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. yes. because the interval does not contain negative numbers, there is convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. no. because the conditions were not met, we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify egypt on the map is different from the true proportion of women that can identify egypt on a map.
The answer to the question is no, there is not convincing evidence of a difference between the population proportions.
Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.
In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.
Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.
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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.
Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.
In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.
Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.
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Find your own values that prove that tan(u-v) does not equal tan u - tan v. Show your work and explain why you chose these values.
To prove that tan(u - v) does not equal tan u - tan v, we start by assuming values for u and v.
To do this, we assume the following values
\(\mathbf{u = 75}\)
\(\mathbf{v = 45}\)
So, we have:
\(\mathbf{tan(u - v) \ne tan(u) - tan(v)}\)
Substitute the assumed values for u and v
\(\mathbf{tan(75 - 45) \ne tan(75) - tan(45)}\)
Subtract 45 from 75
\(\mathbf{tan(30) \ne tan(75) - tan(45)}\)
Using a calculator, calculate the values of tan(30), tan(45) and tan(75)
So, we have:
\(\mathbf{0.5774 \ne 3.7321 - 1}\)
Subtract 1 from 3.7321
\(\mathbf{0.5774 \ne 2.7321}\)
Notice that the expression on the left-hand side and the expression on the right-hand side are not equal.
Hence, \(\mathbf{tan(u - v) \ne tan(u) - tan(v)}\) is true
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What is the solution set of the equation 3x^2=48?
1) {-2,-8}
2) {2,8}
3) {4,-4}
4) {4,4}
A bicycle has a listed price of $765.95 before tax. If the sales tax rate is 9.5%, find the total cost of the bicycle with sales tax Included.
Answer:
The total cost is $ 589.06
Step-by-step explanation:
Answer:
$838.72
Step-by-step explanation:
$765.95 x 1.095 = $838.72
Alyssa swims 3 laps in 12 minutes. At this same
rate, how many laps will she swim in 30 minutes?
Answer:
I think 7
Step-by-step explanation:
By the way I'm a swimmer, and even I could swim 3 laps under 12 minutes. This poor girl is slow...
Calculate volume of hemisphere with radius 3.2 cm
The volume, V, of a sphere with radius r is V = [4/3 pi r^3]
Answer:
V ≈ 68.63 cm³
Step-by-step explanation:
the volume (V) of a sphere is calculated as
V = \(\frac{4}{3}\)πr³
the volume of a hemisphere is half the volume of a sphere, so
V = \(\frac{1}{2}\) × \(\frac{4}{3}\) πr³ = \(\frac{2}{3}\) πr³ , then
V = \(\frac{2}{3}\) π × 3.2³
= \(\frac{2}{3}\) π × 32.768
≈ 68.63 cm³ ( to 2 dec. places )
Two numbers multiply to be -40 and add to be 3. What are the numbers?
Answer:
The numbers are (x,y)=(-5,8) or (8,-5)
Step-by-step explanation:
Let two numbers be x and y,
We have,
x+y=3
x=3-y---(i)
Now,
xy=-40
(3-y)y=-40 [From (i)]
3y-y^2=-40
y^2-3y-40=0
Factoring,
(y + 5) (y - 8)=0
Either,
y+5=0 or, y-8=0
y=-5 y=8
When y=-5,
x=3-y
3--5
3+5
8
When y=8,
x=3-y
3-8
-5
Question 37 1 pts Which of the following is a solution to the differential equation: t². d^2y/dt^2 - 6t dy,dt + 12 = 0
a.y=t² + 1 b.y=t³+2t^4
c.no solution d.y = t-1 Question 38 1 pts Newton's law of cooliing states that the rate of change of the temperature T of an object is proportional to the temperature difference between the temperature S of the surroundings and the temperature T. Write down the differential equation. A cup of tea is prepared from boiling water at 100 degrees and cools to 50 degrees in 3 minutes. The temperature in the room is 20 degrees. What will the tea temperature be after a very long time? a.dT/dt=k(S-T); T≈ 20 degrees after a very long time b.dt/dT =k(ST); T≈ 30 degrees after a very long time c.dt/dT =K(S-T); T≈ 0 degrees after a very long time d.dt/dT = K (S+T); T≈ 30 degrees after a very long time
Question 37: The following is a solution to the differential equation y = t - 1. d.
Question 38: The tea temperature be after a very long time is dT/dt = k(S - T); T ≈ 20 degrees after a very long time. a.
To determine the solution to the given differential equation: t²(d²y/dt²) - 6t(dy/dt) + 12 = 0, we can solve the equation by assuming a solution in the form of y = tⁿ, where n is a constant.
By differentiating y with respect to t, we can substitute the derivatives into the differential equation to determine the value of n.
Let's differentiate y = tⁿ with respect to t:
dy/dt = n × tⁿ⁻¹
d²y/dt² = n(n-1) × tⁿ⁻²
Substituting these derivatives into the differential equation:
t²(n(n-1)tⁿ⁻²) - 6t(ntⁿ⁻¹) + 12 = 0
Simplifying the equation:
n(n-1)tⁿ - 6ntⁿ + 12 = 0
n(n-1)tⁿ - 6ntⁿ = -12
Since this equation must hold for all values of t, the coefficients of the tⁿ terms on both sides of the equation must be equal.
We can equate the coefficients:
n(n-1) = 0
n = 0 or n = 1
The general solution to the differential equation is y = c₁ + c₂ × t, where c₁ and c₂ are constants.
According to Newton's law of cooling, the rate of change of the temperature T of an object is proportional to the temperature difference between the object's temperature T and the surroundings' temperature S.
We can write the differential equation as follows:
dT/dt = k(S - T)
dT/dt represents the rate of change of temperature, k is the proportionality constant, and (S - T) represents the temperature difference between the object and the surroundings.
The cup of tea starts at 100 degrees and cools to 50 degrees in 3 minutes, with the room temperature at 20 degrees.
We can assume that the temperature of the tea will tend toward the room temperature as time goes to infinity.
This option correctly represents that as time goes to infinity, the temperature T of the tea will approach the temperature S of the surroundings, which is approximately 20 degrees.
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80 divided by 192.0!!!!!!!!!!!!!!!
Answer: .416666667
Step-by-step explanation: Take 80 and divide it by 192.0= .416666667
a pizza parlor offers a choice of 1010 different toppings. how many different 33-topping pizzas are there?
The permutation combination is 120 for 3 different topping pizzas are available.
Permutation Combination:
A variety of ways to select objects from a set, usually forming a subset without replacement. The selection of this subset is called a permutation if the order of selection is a factor, and a combination if the order is not a factor. The French mathematicians Blaise Pascal and Pierre de Fermat, in the 17th century, used many chances in his game of combinatorics and probability by considering the ratio of the number of required subsets to the number of all possible subsets stimulated the development of the theory.
The concepts of permutations and combinations and their differences can be illustrated by examining all the different ways of selecting pairs of objects from five identifiable objects such as the letters A, B, C, D and E.
According to the Question:
Given that :
Number of different toppings = 10
Number of Pizzas = 03
therefore,
The permutation combination are :
= 10!/7! 3!
= 15 × 8
= 120.
Therefore, there are 120 different combinations of toppings.
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Which equation has a graph that is a parabola with a vertex at (–2, 0)?
y = –2x2
y = (x + 2)2
y = (x – 2)2
y = x2 – 2
Comparing to the standard equation, the parabola with a vertex at (-2,0) is given by:
y = (x + 2)²
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, we have that h = -2 and k = 0, and all the options have leading coefficient a = 1, hence the equation is:
y = (x + 2)²
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Answer:
B. y = (x + 2)2What is equivalent to square root of 2 over 2? Select all that apply
Answer:
The answer is 2.
Step-by-step explanation:
The number of members in the band was 82 in 2000 and has decreased by 8% each year. Which model shows the band's membership in terms of t, the number of years since 2000?
Given:
The number of members in the band was 82 in 2000.
The number of members decreased by 8% each year.
Required:
We need to find the model for the given situation.
Explanation:
Let t be the number of years since 2000.
Let y be the number of members in t number of years since 2000.
The initial value is 82.
The number of members is decreasing.
Consider the exponential decay equation.
\(y=82(1-\frac{8}{100})^t\)\(y=82(1-0.08)^t\)\(y=82(0.92)^t\)Final answer:
\(y=82(0.92)^t\)
Assume that the demand curve D(p) given below is the market
demand for widgets:
Q=D(p)=2692−19pQ=D(p)=2692-19p, p > 0
Let the market supply of widgets be given by:
Q=S(p)=−5+10pQ=S(p)=-5+10p, p
The equilibrium price of widgets is $93, and the equilibrium quantity is 925 units.
The equilibrium price and quantity in the market for widgets can be determined by setting the quantity demanded equal to the quantity supplied. In this case, the demand curve for widgets is given by Q=D(p) = 2692 - 19p, and the supply curve is given by Q=S(p) = -5 + 10p.
To find the equilibrium price, we set the quantity demanded equal to the quantity supplied:
2692 - 19p = -5 + 10p
Combining like terms and isolating p, we have:
29p = 2697
p = 93
Therefore, the equilibrium price in the market for widgets is p = 93.
To find the equilibrium quantity, we substitute the equilibrium price back into either the demand or supply equation. Let's use the demand equation:
Q = 2692 - 19(93)
Q = 2692 - 1767
Q = 925
Therefore, the equilibrium quantity in the market for widgets is Q = 925.
In summary, the equilibrium price of widgets is $93, and the equilibrium quantity is 925 units.
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a constant force f 5, 3, 1 (in newtons) moves an object from (1, 2, 3) to (5, 6, 7) (measured in cm). find the work required for this to happen
The work required to move the object from point A to point B under the influence of the given constant force is 36 Joules.
To find the work required to move an object from point A to point B under the influence of a constant force, use the formula:
Work = Force * Displacement * cos(theta)
where:
- Force is the magnitude and direction of the constant force vector,
- Displacement is the vector representing the displacement of the object from point A to point B, and
- theta is the angle between the force vector and the displacement vector.
Given:
Force (F) = 5i + 3j + k (in Newtons)
Displacement (d) = (5 - 1)i + (6 - 2)j + (7 - 3)k = 4i + 4j + 4k (in cm)
First, let's calculate the dot product of the force vector and the displacement vector:
F · d = (5)(4) + (3)(4) + (1)(4) = 20 + 12 + 4 = 36
Since the force and displacement are in the same direction, the angle theta between them is 0 degrees. Therefore, cos(theta) = cos(0) = 1.
Now calculate the work:
Work = Force * Displacement * cos(theta)
= (5i + 3j + k) · (4i + 4j + 4k) · 1
= 36
The work required to move the object from point A to point B under the influence of the given constant force is 36 Joules.
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How do I do this, im not sure what im supposed to do
Answer:
Step-by-step explanation:
3<x<7
the set will contain all elements greater than 3 and less than 7
Roster form ={4,5,6}
b) Roster form :{-6,-5,-4,-3......}
set builder form is all numbers greater than -6
I hope it is right
hhhhhhhhhhhhhhellllllllllllllllllloooooooooooooppppppppppppppppp
Answer:
The answer is C. -3/4x+4
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
y=(-3/4)x + 4
take any point on the line and go up 3 than left 4 and you will end up on the line again because slope is rise/run
the slope is negative because from left to right the line is downhill
Pls help me really fast
\(\huge\text{Hey there!}\)
\(\huge\text{Square inches formula is: }\\\\\large\boxed{\mathsf{l}\rm{ength}\times\mathsf{h}\rm{eight} = \mathsf{s}\rm{quare \ inches}}}}}}}\)
\(\huge\text{So, your equation should look like:}\)
\(\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}\)
\(\huge\text{Now let us solve for your answer to this problem:}\)
\(\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}\)
\(\large\boxed{\mathsf{24\ inches\times 14\ inches = square\ inches^2}}\)
\(\large\boxed{\mathsf{336 = square\ inches^2}}\)
\(\huge\text{Therefore, your answer SHOULD be:}\)
\(\huge\boxed{\mathsf{Option\ D. \ 336}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)