4. (-/1 Points] DETAILS HARMATHAP12 10.4.007. 0/6 Submissions Used MY NOTES ASK YOUR TEACHER Suppose that the demand x (in units) for a product is x = 22,500 - 150p, where p dollars is the market price per unit. Then the consumer expenditure for the product is E = px = 22,500p - 150p2. For what market price will expenditure be greatest? $ Need Help? Read It Watch It Talk to a Tutor 5. [-/1 Points] DETAILS HARMATHAP12 10.4.011. 0/6 Submissions Used MY NOTES ASK YOUR TEACHER An inferior product with a large advertising budget sells well when it is introduced, but sales fall as people discontinue use of the product. Suppose that the weekly sales S are given by S. 300+ 20 (t + 7)21 where S is in millions of dollars and t is in weeks. After how many weeks will sales be maximized? weeks Need Help? Read It Watch it Talk to a Tutor 6. [-/2 Points] DETAILS HARMATHAP12 10.4.017. 0/6 Submissions Used MY NOTES ASK YOUR TEACHER A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on the side opposite the river costs $40 per foot, and the fence on the other sides costs $10 per foot. If the field must contain 72,200 square feet, what dimensions will minimize costs? side parallel to the river ft each of the other sides ft
Answers
4. To find the market price that will result in the greatest expenditure, we need to take the derivative of the expenditure function and set it equal to zero. So, E = 22,500p - 150p^2, and dE/dp = 22,500 - 300p. Setting this equal to zero and solving for p, we get p = 75. Therefore, the market price that will result in the greatest expenditure is $75.
5. To find when sales will be maximized, we need to take the derivative of the sales function and set it equal to zero. So, S = 300 + 20(t+7)^2, and dS/dt = 40(t+7). Setting this equal to zero and solving for t, we get t = -7. Therefore, sales will be maximized in week 0 (which is 7 weeks before the product is introduced).
6. Let x be the length of the side parallel to the river, and y be the length of the other sides. We know that xy = 72,200, and the cost function C = 40x + 20y. Solving for y in terms of x using the first equation, we get y = 72200/x. Substituting this into the cost function, we get C = 40x + 20(72200/x). Taking the derivative of this function and setting it equal to zero, we get 40 - 14444000/x^2 = 0. Solving for x, we get x = 60.17. Therefore, the side parallel to the river should be approximately 60.17 ft, and each of the other sides should be approximately 1203.33 ft to minimize costs.
4. To find the market price where the expenditure is greatest, we need to find the maximum value of the expenditure function E(p) = 22,500p - 150p^2. To do this, differentiate E(p) with respect to p and set it to 0:
dE(p)/dp = 22,500 - 300p = 0
300p = 22,500
p = 22,500 / 300 = $75
The greatest expenditure occurs when the market price is $75 per unit.
5. To find the number of weeks when sales are maximized, differentiate the sales function S(t) = 300 + 20(t + 7)^2 with respect to t and set it to 0:
dS(t)/dt = 40(t + 7) = 0
t + 7 = 0
t = -7
Since the number of weeks cannot be negative, there must be a mistake in the given function for S(t). Please double-check the function and provide the correct information.
6. Let x be the side parallel to the river and y be the other sides of the rectangular field. The area of the field is A = xy = 72,200 sq. ft, and the cost function C = 40x + 10y. To minimize the cost, we can substitute y from the area equation: y = 72,200/x. Now the cost function is C(x) = 40x + 10(72,200/x). Differentiate C(x) with respect to x and set it to 0:
dC(x)/dx = 40 - (10 * 72,200) / x^2 = 0
x^2 = (10 * 72,200) / 40
x ≈ 134.16 ft (side parallel to the river)
Substitute x back into the area equation to find y:
y = 72,200 / 134.16 ≈ 538.33 ft (each of the other sides)
To minimize the costs, the dimensions should be approximately 134.16 ft along the river and 538.33 ft for the other sides.
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Related Questions
Historically, WoolWord’s supermarket has found it sells an average of 2517 grapes per day, with a standard deviation of 357 grapes per day. Consider that the number of grapes sold per day is normally distributed. Find the probability (to 4 decimal places) that:
a) the number of grapes sold on a particular day exceeds 2300
b) the probability that the average daily grape sales over a three month (i.e. 90 day) period is less than 2500 grapes or more than 3000 grapes per day.
Answers
The probability that the number of grapes sold on a particular day exceeds 2300 ≈ 0.7291, and the probability that the average daily grape sales over a 90-day period is less than 2500 grapes or more than 3000 grapes per day ≈ 0.4252
We'll use the normal distribution and the properties of the z-score to solve these probability questions,
- Mean (μ) = 2517 grapes per day
- Standard deviation (σ) = 357 grapes per day
(a) We need to obtain the probability of the value being greater than 2300.
To do this, we'll calculate the z-score for 2300 and then use the standard normal distribution table or a calculator to find the corresponding probability.
z = (x - μ) / σ
z = (2300 - 2517) / 357
z ≈ -0.611
Using the z-table or a calculator, we can find the probability associated with a z-score of -0.611. Let's denote this probability as P(Z > -0.611).
P(Z > -0.611) ≈ 0.7291
(b) For the average daily grape sales over a 90-day period, we need to consider the distribution of the sample means.
Since the sample size is large (90), we can apply the Central Limit Theorem, which states that the distribution of sample means tends to follow a normal distribution regardless of the shape of the population distribution.
The mean of the sample means will still be 2517, but the standard deviation of the sample means (also known as the standard error of the mean, SEM) can be calculated as:
SEM = σ / √n
SEM = 357 / √90
SEM ≈ 37.66
Now we can calculate the z-scores for 2500 and 3000 using the sample mean distribution:
z1 = (x1 - μ) / SEM = (2500 - 2517) / 37.66
z1 ≈ -0.452
z2 = (x2 - μ) / SEM = (3000 - 2517) / 37.66
z2 ≈ 1.280
Using the z-table or a calculator, we can find the probabilities associated with these z-scores. Let's denote these probabilities as P1 and P2, respectively.
P1 = P(Z < -0.452)
P2 = P(Z > 1.280)
P1 ≈ 0.3249
P2 ≈ 0.1003
The probability that the average daily grape sales over a 90-day period is less than 2500 grapes or more than 3000 grapes per day is:
P = P1 + P2 ≈ 0.3249 + 0.1003 ≈ 0.4252
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Select the correct answer.
What is the simplest form of the ratio 11 : 16?
A.
1:6
B
5:8
c.
11.16
D.
22:32
Answers
Answer:
C
Step-by-step explanation:
The ratio 11:16 cannot be simplified
Answer:
Its already in simplest form
Step-by-step explanation:
You can think of it as a fraction. you cant divide 11 by anything besides 1 and itself. 11 doesnt go into 16 at all, completely. So the ratio cant be simplified
consider the parallelepiped with edges oa,ob, and oc, where a(2,1,0),b(1,2,0), and c(0,1,α). find the real number α>0 such that the volume of the parallelepiped is 3 units3. for α
Answers
The value of that makes the volume of the parallelepiped with edges oa, ob, and oc equal to 3 units is α = 1
What is the volume of a parallelopiped?The volume of a parallelopiped with sides a, b and c is V = a.(b × c)
Now, consider the parallelepiped with edges oa, ob, and oc, where a(2,1,0), (1,2,0), and c(0,1,α). To find the real number α>0 such that the volume of the parallelepiped is 3 units, we proceed as follows.
We know that the volume of the parallelopiped with sides a, b and c is a.(b × c) where
a(2,1,0),b(1,2,0), and c(0,1,α)Now a.(b × c) =det \(\left[\begin{array}{ccc}2&1&0\\1&2&0\\0&1&\alpha \end{array}\right]\)
So, a.(b × c) = 2(2 × α - 1 × 0) - 1(1 × α - 0 × 0) + 0(1 × 1 - 2 × 0)
= 2(2α - 0) - (α - 0) + 0(1 - 0)
= 2(2α) - (α) + 0(1)
= 4α - α + 0
= 3α + 0
= 3α
Now since the volume of the parallelopied is 3 units, we have that
a.(b × c) = 3
3α = 3
α = 3/3
α = 1
So, α = 1
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what do we mean when we say that a simple linear regression model is​ statistically useful?
Answers
A regular linear regression model is statistically helpful in providing a good fit to the information that can be used to make precise predictions about new information agendas.
A linear regression model is useful when the explanation of a significant amount of variation of the dependent variable utilizes one or more independent variables. The usability of a linear regression model can be comprehended by examining various statistical measures for instance
R-squared, adjusted R-squared, standard error of the estimate, p-values.R-squared value of 1 shows that all of the changes in the dependent variable are elaborated by the independent variable, Hence, an R-squared value of 0 points that none of the variations is elaborated
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Which description could be written as a linear function?
a) eight more than twice a number
b) three more than the product of two numbers
c) ten more than the square of a number
d) nine more than one divided by a number
Answers
Question:
Which description could be written as a linear function?
Answer:
Option a)
Explanation:
Let 2 numbers be x1 and x2.
For the first option:
Eight more than twice a number.
The graph would be y = 8 + 2x1 which is a linear function.
For the second option:
Three more than the product of two numbers.
The graph would be y = 3 + x1x2 which is a graph function.
For the third option:
Ten more than the square of a number.
The graph would be y = 9 + (x1)² which is a graph function.
For the fourth option:
Nine more than one divided by a number.
The graph would be y = 9 + 1/x1 which is a double-parabole function.
Hopefully this answer will help you.
Answer: option a
Step-by-step explanation:
Just took the test
Find the 7th term in the
sequence
-1, 2, -4, 8,...
Answers
Answer:
every other term is negative, so it would be -64
Step-by-step explanation:
hope it helps!
Solve the following equation for x to find the total number of people who downloaded songs from a music site for a certain month:
x = 0.6x + 384
How many people downloaded songs from the site that month?
Answers
Answer:
960 people.
Step-by-step explanation:
x = 0.6x + 384
x - 0.6x = 384
0.4x = 384
x = 384 / 0.4 = 960.
PLESSS help me I'm begging you
Answers
To find the volume of each pris you multiply the measures
So
first prism
\(15\operatorname{cm}\times12\operatorname{cm}\times5\operatorname{cm}\)then first blanck is 12
Second prism
\(5\operatorname{cm}\times14\operatorname{cm}\times4\operatorname{cm}\)if we multiply 5 and 14
\(70sq\operatorname{cm}\times4\operatorname{cm}\)then second blanck is 70
Total volume
\(\begin{gathered} (15\operatorname{cm}\times12\operatorname{cm}\times5\operatorname{cm})+(70sq\operatorname{cm}\times4\operatorname{cm}) \\ 900+280=1180 \end{gathered}\)then last blanck is 1180cu cm
a data set consists of the data given below plus one more data point. when the additional point is included in the data set the sample mean of the resulting data set is 26.5. what is the value of the additional data point?23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19
Answers
The value of the additional data point is 36
To find the value of the additional data point, we can use the concept of the sample mean.
Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.
The sample mean of this data set is 26.5.
To find the value of the additional data point, we can use the formula for the sample mean:
(sample mean) = (sum of all data points) / (number of data points)
In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.
Therefore, we can set up the equation:
26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12
Multiplying both sides of the equation by 12 to eliminate the fraction, we have:
318 = 282 + x
Subtracting 282 from both sides of the equation, we find:
x = 318 - 282
x = 36
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.
What is the circumference of a circle with a radius of 6?
Answers
hope it helps:)
Answer:
37.68 or 12π
Step-by-step explanation:
C = 2πr
C = 2(3.14)6 = 37.68
consider what you know about the sampling distribution of the sample proportion. this sampling distribution
Answers
Consider what you know about the sampling distribution of the sample proportion. this sampling distribution will have a centre equal to the population proportion, or p.
For determining the correct option, we will check one by one all the given options:
From the given statements, we can conclude that.
As the sample size of the data increases, the corresponding value of n also starts increasing.
The value on the denominator of the standard deviation equation is n.
Therefore, the standard deviation will decrease as the value of n increases.
A tiny variance is one with a low standard deviation.
As a result, the variance will be minor as the sample size increases.
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Actual questions should be:
Consider what you know about the sampling distribution of the sample proportion. This sampling distribution
(1) has a shape that is skewed to the right, regardless of sample size.
(2) is a collection of the parameters of all possible samples of a particular size taken from a particular population.
(3) Will become more variable as the sample size increases.
(4) will have a center equal to the population proportion, or p.
(5) will be Normal in shape only if the sample size is at least 100 .
Find the exact length of the midsegment of trapezoid JKLM with verticesJ(6, 10), K(10, 6), L(8, 2), and M(2, 2).The length of the midsegment is
Answers
The midsegment is equal to the average of the lengths of the bases, so:
\(M=\frac{JM+KL}{2}\)Where:
\(\begin{gathered} JM=\sqrt[]{(6-2)^2+(10-2)^2} \\ JM=\sqrt[]{80}=4\sqrt[]{5}\approx8.9 \end{gathered}\)and
\(\begin{gathered} KL=\sqrt[]{(10-8)^2+(6-2)^2} \\ KL=\sqrt[]{20}=2\sqrt[]{5}\approx4.47 \end{gathered}\)Therefore:
\(M=\frac{4\sqrt[]{5}+2\sqrt[]{5}}{2}=3\sqrt[]{5}\)
3/4x -9= 27 kinds need help
Answers
Answer:
X= 48
Step-by-step explanation:
math
Way
- It’s a calculator for algebra and stuff
Select the values that make the inequality -m≥4−m≥4 true.
Then write an equivalent inequality, in terms of mm.
(Numbers written in order from least to greatest going across.)
-9 -5 -4.1
-4 -3.9 -3
-1 0 1
3 3.9 4
4.1 5 9
Equivalent Inequality:
Answers
As for writing an equivalent inequality in terms of m, we can consider the original inequality -m ≥ 4 - m ≥ 4. Since this inequality does not hold true for any value of m, we cannot write an equivalent inequality.
To determine the values that make the inequality -m ≥ 4 - m ≥ 4 true, let's examine the given options:
-9, -5, -4.1
-4, -3.9, -3
-1, 0, 1
3, 3.9, 4
4.1, 5, 9
We need to identify the values that satisfy the inequality -m ≥ 4 - m ≥ 4.
Considering the inequality -m ≥ 4 - m, we can simplify it as follows:
-m ≥ 4 - m
-m + m ≥ 4 - m + m (adding m to both sides)
0 ≥ 4 (simplifying)
Since 0 is not greater than or equal to 4, this inequality is not true for any value of m.
Therefore, there are no values from the given options that satisfy the inequality -m ≥ 4 - m ≥ 4.
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determine the most suitable system of coordinates to describe the spherical shell between two concentric spheres centered at (4,1,2). the inner sphere has a radius of 7 and the outer sphere has a radius of 13.
Answers
The spherical coordinate system is the most suitable system of coordinates to describe the spherical shell between two concentric spheres centered at (4,1,2).
A system of coordinates is a set of numbers used to describe the position of a point in space. There are different types of coordinate systems, each with its own advantages and disadvantages.
The spherical shell is the region of space between two spheres with the same center, but different radii. In this case, the center of both spheres is at (4,1,2) and the inner sphere has a radius of 7 while the outer sphere has a radius of 13.
One of the most commonly used coordinate systems for describing spheres is the spherical coordinate system.
To use this system of coordinates to describe the spherical shell, we first need to determine the radial distance for each point in the shell. This distance is between 7 and 13, since the shell lies between the inner and outer spheres.
Therefore, to describe a point in the spherical shell using spherical coordinates, we use the radial distance, polar angle, and azimuthal angle. These coordinates can then be used to plot the spherical shell and understand its geometry and properties.
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Find an equation in point-slope for the line having the slope m m = - 6 and containing the point (8,6)
Answers
Answer:
y - 6 = - 6(x - 8)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
Here m = - 6 and (a, b ) = (8, 6 ) , then
y - 6 = - 6(x - 8) ← equation of line
Suppose that 3 is an equilibrium value of a differential equation. This means that if the initial value is 3 , then all of the values will be 3. all of the above. if the initial value is below 3 , the values will decrease. the values will approach 3.
Answers
If 3 is an equilibrium value of a differential equation, it means that all values will remain constant at 3. If the initial value is below 3, the values will approach 3.
In the context of a differential equation, an equilibrium value represents a stable solution where the derivative of the function is zero. In this case, if the equilibrium value is 3, it means that when the initial value of the function is set to 3, the function will remain constant at 3 for all time.
If the initial value is below 3, the values will tend to approach the equilibrium value of 3. As time progresses, the function will evolve, and its values will change. However, due to the nature of the equilibrium at 3, the values will gradually move closer to 3 over time, eventually stabilizing at that value. This behavior is characteristic of stable equilibrium points in differential equations.
On the other hand, if the initial value is above 3, the values will tend to move away from 3, either increasing or decreasing depending on the specific dynamics of the differential equation. The behavior of the system around the equilibrium value is determined by the equation's slope or rate of change
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Coffee is on sale for $7.99/lb.
If Callie buys 1.5 pounds of
coffee, how much will it cost?
Answers
Answer:
$11.99
Step-by-step explanation:
7.99/2 = 3.995
3.995 rounds up to 4
7.99 + 4 = 11.99
Answer:
11.99 is the answer
PLEASE HELP ASAP IM FREAKING OUT
Answers
Answer:
30 cm
Step-by-step explanation:
Make sure all units are the same!
P = Perimeter
A = Area
Formula used for similar figures:
\(\frac{A_{1}}{A_{2}} = (\frac{l_{1}}{l_{2}})^{2}\) —- eq(i)
\(\frac{P_{1}}{P_{2}} = \frac{l_{1}}{l_{2}}\) ———— eq(ii)
Applying eq(ii):
∴\(\frac{25}{P_{2}} = \frac{10}{12}\)
Cross-multiplication is applied:
\((25)(12) = 10P_{2}\)
\(300 = 10P_{2}\)
\(P_{2}\) has to be isolated and made the subject of the equation:
\(P_{2} = \frac{300}{10}\)
∴Perimeter of second figure = 30 cm
Write a two-column proof. Given: Quadrilateral ABCD is a parallelogram; M is a midpoint of Segment AB; N is a midpoint of Segment DC Prove: Quadrilateral AMCN is a parallelogram
Answers
Answer:
The answer is given below
Step-by-step explanation:
Statement Reasons
ABCD is a parallelogram; M is a midpoint Given
of AB and N is a midpoint of Segment
AB//DC, therefore AM//NC For a parallelogram, opposite . sides are parallel to each other
AB≅DC For a parallelogram, opposite . sides are equal to each other
1/2AB≅1/2DC Since both sides are equal to . each other
1/2AB = AM and 1/2DC = NC M is the midpoint of AB and N . is the midpoint of DC Midpoint
. theorem
AM≅NC Substitution, since AB is also
. equal to BC
Quadrilateral AMCN is a parallelogram If opposite sides of a
. quadrilateral is equal and .
opposite, it is a parallelogram
An office building to be constructed in Houston will be subjected to wind loads. The probability that the wind speed will exceed 100 miles per hour (mph) is 0.01% in any year. If the building subjected to wind speeds exceeding 100 mph, the damage will be $65,000. No damage occurs when the wind speed is less than 100 mph. To protect the building against winds of 100 mph or more, the engineers have determined that an additional capital investment of $35,000 is required. When the building is subjected to wind speeds in excess of 100 mph, the building damage is estimated to be $6,000. Use Decision Tree Analysis determine the best of the following alternatives: A. No additional investment for wind load damage B. $35,000 investment for wind load damage Assume a design life of 20 years and a yearly interest rate of 10 percent (See Engineering Economics Reference). You must draw the Decision Tree (with all pertinent information). Present detailed calculations to support your results.
Answers
Based on the given information, we can use Decision Tree Analysis to determine the best alternative for protecting the building against wind loads.
1. Decision Node: The first decision is whether to make an additional investment of $35,000 for wind load damage protection.
2. Chance Node: The probability of wind speeds exceeding 100 mph in any year is 0.01%. If the wind speed exceeds 100 mph, there are two possible outcomes:
a. Terminal Node: If no additional investment is made, the building damage is $65,000.
b. Terminal Node: If the additional investment of $35,000 is made, the building damage is $6,000.
3. Calculate the Expected Monetary Value (EMV) for each branch of the Chance Node:
a. EMV of no additional investment = Probability (0.01%) * Damage ($65,000)
b. EMV of $35,000 investment = Probability (0.01%) * Damage ($6,000) + (1 - Probability (0.01%)) * Additional Investment ($35,000)
4. Compare the EMV of both branches and select the alternative with the higher EMV as the best option.
Detailed calculations and drawing of the Decision Tree would be required to determine the specific values and make the final decision.
Decision Tree Analysis provides a structured approach to evaluate different alternatives and their associated probabilities and costs. By considering the potential outcomes and their probabilities, decision-makers can make informed choices that maximize expected value or minimize potential losses. It is important to conduct a thorough analysis and consider the financial implications over the design life of the project to make an optimal decision.
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Johan is selling baseball cards for 12 cents. He is selling 8 cards and says he’ll make $8.
Answers
In pretty sure that is the answer.
Evaluate the expression shown 6(14+8)+12
Answers
Answer:
144
Step-by-step explanation:
6(14+8)+12, Use distributive property
84+48+12, Just add all of them up
Bella wants to save for a vacation in three years and this vacation costs $2300. She deposits $2000 into a bank earning 5% interest compounded monthly. How much money does Bella have after 3 years?
Answers
Answer:
$2,323.2
Step-by-step explanation:
A = P(1 + r/n)^nt
Where,
A = future value = ?
P = present value = 2,000
r = interest rate = 5% = 0.05
n = number of periods = 12
t = time = 3 years
A = P(1 + r/n)^nt
= 2,000(1 + 0.05/12)^12*3
= 2,000( 1 + 0.00417)^36
= 2,000( 1.00417)^36
= 2,000(1.1616)
= 2,323.2
A = $2,323.2
A grocery store sells tangerines in 2/5 kg. bags. A customer bought 4 kg of tangerines for a school party. How many bags did he buy? ASAP
Answers
Answer:
There are 10 in 4kg
Step-by-step explanation:
Given
\(1\ Tangerine = \frac{2}{5}kg\)
Required
Determine the number in 4kg
Represent this with x.
To calculate this, we make use of the following:
\(x * \frac{2}{5}kg = 4kg\)
Multiply through by \(\frac{5}{2}\)
\(x * \frac{2}{5}kg *\frac{5}{2}= 4kg *\frac{5}{2}\)
\(x = 4*\frac{5}{2}\)
\(x =10\)
Hence, there are 10 in 4kg
Answer: the answer in that there are 10 in 4kg
Step-by-step explanation:
hi everyone freeeeeesss
Answers
Answer:
heyyyyyyyyyyyyy
Step-by-step explanation:
Hope you had a good day
Write the equation of a line through (-1,-5) parallel to 3x-y=5, and in slope intercept form
Answers
Answer:
y = 3x -2
Step-by-step explanation:
The general equation form is;
y = mx + b
where m is the slope and b is the y-intercept
For the equation given;
y = 3x -5
the slope from here is 3
If two lines are parallel, they have equal slopes
This mean that the slope of the line we want to calculate too is 3
Now we can use the point slope format to get the correct equation
y-y1 = m(x-x1)
y+ 5. = 3(x+ 1)
y = 3x + 3 -5
y = 3x -2
The coordinates of the vertices of AGH/ are G(-2, 3), H(-1, 2), and /(-3, 1). If AGH is reflected across the x-axis to
create AWVUV, find the coordinates of the vertex located at point W.
Answers
To reflect the triangle AGH across the x-axis, we need to keep the x-coordinates the same but negate the y-coordinates. So, the new coordinates of G' (the image of G) would be (-2, -3), the new coordinates of H' would be (-1, -2), and the new coordinates of A' would be (-3, -1). Now, to find the coordinates of W, we need to determine the intersection of the lines GH' and A'G'. To do this, we need to first find the equations of these lines.
The equation of a line can be found using the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula:
m = (y2 - y1) / (x2 - x1) For line GH', the two points are G(-2, 3) and H'(-1, -2). So, the slope of GH' is: mGH' = (-2 - 3) / (-1 - (-2)) = -5 / 1 = -5
Since the slope is 0, the line is horizontal and its equation is simply y = -1 (which is also the y-coordinate of A').
Now, to find the intersection of GH' and A'G', we can set their equations equal to each other and solve for x:
the y-coordinate of W, we can plug x = -6/5 into either equation:
y = -5(-6/5) - 7 = 1
the coordinates of W are (-6/5, 1).
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Solve the system of equations. y=-3/2+9
2x+2y=16
Answers
2x+2x7.5=16
2x+15=16
2x=16-15
2x=1
x=1/2
The sum of three consecutive even integers is 108. What is the largest number?
34
Answers
Answer:
It's 38.
Step-by-step explanation:
the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.
I hope this helps you!
Answer:
We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.
The problem states that the sum of three consecutive even integers is 108, so we can write an equation:
x + (x+2) + (x+4) = 108
We can simplify this equation by combining like terms:
3x + 6 = 108
3x = 102
x = 34
So, the smallest of the three consecutive even integers is 34.
The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38
The largest number of the three consecutive even integers is x+4 = 38.