Answers
my brain is playing not smart on me right now
Related Questions
Find the value of the variable x. If your answer is not an integer, write it in simplest radical form with
the denominator rationalized h
Answers
The value of the variables y and z are 18
How to determine the value of the variablesFrom the question, we have the following parameters that can be used in our computation:
The special right triangle
The special right triangle has one of its angles to be 45 degrees
This means that
Legs = Hypotenuse/√2
Using the above as a guide, we have the following:
Legs = 18√2/√2
Evaluate
Legs = 18
Hence, the value of y and z are 18
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How to find the variance of uniform distribution?
Answers
We can find the variance of a uniform distribution, using the following formula: Variance = (b - a)² / 12. Here: a is the lower limit of the uniform distribution, b is the upper limit of the uniform distribution.
The formula for the variance of a uniform distribution is based on the fact that the variance of a continuous uniform distribution is equal to the square of the range (i.e., the difference between the upper and lower limits) divided by 12.
For example, let's say we have a uniform distribution between 0 and 10. To find the variance, we would use the formula:
Variance = (10 - 0)² / 12
Variance = 100 / 12
Variance = 8.33
Therefore, the variance of a uniform distribution between 0 and 10 is 8.33.
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image is the question
Answers
Answer:
350x + 200y - 4200 = 0
x intercept is (12,0)
y intercept (0,21)
steps:
ii
350x + 200y - 4200 = 0
Therefore, the equation in standard form that models the number of funnel cakes, x, and the number of deep-fried Oreos, y, Francis can buy if he spends $42.00 is:
350x + 200y - 4200 = 0
To find the x-intercept, we set y to zero and solve for x:
350x + 200(0) - 4200 = 0
350x = 4200
x = 12
Therefore, the x-intercept is 12. This means that if Francis only buys deep-fried Oreos (y = 0), he can buy 12 funnel cakes with $42.00.
Answer:
350x + 200y - 4200 = 0
x intercept is (12,0)
y intercept (0,21)
steps:
3.50x + 2.00y = 42.00
3.50x + 2.00y - 42.00 = 0
Multiplying both sides by 100 to eliminate the decimals, we get:
350x + 200y - 4200 = 0
x-intercept means what is x when y is 0
350x + 200(0) - 4200 = 0
350x = 4200
x = 12
y-intercept means what is y when x is 0
350(0) + 200y - 4200 = 0
200y = 4200
y = 21
So the x-intercept is (12, 0) and the y-intercept is (0, 21).
ChatGPT
To find the y-intercept, we set x to zero and solve for y:
350(0) + 200y - 4200 = 0
200y = 4200
y = 21
Therefore, the y-intercept is 21. This means that if Francis only buys funnel cakes (x = 0), he can buy 21 deep-fried Oreos with $42.00.
So the x-intercept is (12, 0) and the y-intercept is (0, 21).
ChatGPT
1. Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario?
2. Suppose that in her first month Yaseen is able to create 15 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work.
3. In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of business, she decides to supply 60 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work.
4. If Yaseen creates 60 kits in her second month of business and offers them for sale at $66 each, do you think she will sell all of them? Why or why not?
5. What family of functions do f(x) and g(x) belong to? How do you know?
6. If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking.
7. Use algebraic methods to find where Yaseen’s demand and supply functions intersect. What does this point(s) represent in context of this problem? Show all your work.
8. Confirm your answer from question 7 by using Desmos to create a single graph that shows both () and () with their domain restrictions. Provide a screenshot of your graph with the intersection point(s) marked.
Answers
To create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Yaseen can produce 15 kits, the cost per kit she should charge is
p = 10 + 0.5q
p = 10 + 0.5(15) (15)
p = $17.50
She can produce 15 kits, the cost per kit she should charge is:
p = 30 - 0.5(15) (15)
p = $22.50
She can provide 60 kits, the cost per kit should be as follows:
p = 10 + 0.5q
Here, q=60
p = 10 + 0.5(60)
p = $40
She can produce 60 kits, the cost per kit should be set at:
p = 30 - 0.5(60) (60)
p = $15
Therefore, to create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.
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Maya made fruit punch for a party. She mixed 2 gallons of orange juice, 5 quarts of pineapple juice, 4 pints of cranberry juice, and 6 cups of apple juice. How many quarts did she make in all?
Answers
Answer:
To add different quantities of liquids with different units of measurements, we need to convert them all to the same unit of measurement. In this case, let's convert everything to quarts since that is what we want the final answer to be in.
2 gallons = 8 quarts (since 1 gallon = 4 quarts)
5 quarts of pineapple juice = 5 quarts (no conversion needed)
4 pints of cranberry juice = 8 cups = 2 quarts (since 1 pint = 2 cups and 1 quart = 4 cups)
6 cups of apple juice = 1.5 quarts (since 1 cup = 0.25 quarts)
Now we can add up all the quantities:
2 + 5 + 2 + 1.5 = 10.5
Maya made 10.5 quarts of fruit punch in all
Bailey is asked to draw a circle. She is given the center and two points on the circle, but she isn't told which point is which. The points are (-6, 3), (-15, 3), and (3,3). Bailey draws an accurate circle from this information. What is the equation of the circle she drew?
O (= - 6)3 + (3 - 3)? = 3
O (= - 3)? + (y - 3)? = 3
O (* + 6)3 + (y - 3)? = 81
О (= - 3)3 + (y - 3)? = 81
〇(c+15)+(- 3) = 81
O (= - 6)? + (3 - 3)? = 81p
Answers
The Equation of Circle is (x+ 6)² + (y - 3)² = 9².
What is Equation of Circle?The equation for a circle is given by:
(x-h)² +(y-k)² = a²
Where (h,k) is the center and a is the radius of the circle.
Given:
We have the points A(-6, 3), B(-15, 3), and C(3,3).
Using Distance Formula
AB = √(-15 + 6)² + (3-3)²
AB = √9²
AB= 9 unit
BC= √(3 + 15)² + (3-3)²
BC = 18 unit
and, AC = √(3+6)² + (3-3)²
AC = 9 unit
As, AB = AC then A has to be the center (-6, 3) with radius 9 unit.
Thus, the Equation of Circle is
(x+ 6)² + (y - 3)² = 9²
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The area of a triangle is four times the area of a square. If the base of the triangle and a side of the square are equal, what is the ratio of the side of the square to the height of the triangle?.
Answers
Answer:
1:8
Step-by-step explanation:
since the base and sides are equal, I'll use 2 as a value for them. since all square sides are equal, we can find the area of the square. 2(2)=4. this means that in the situation the area of the triangle is 16.
16=1/2(2)h
32=2h
16=h
the height of the triangle is 16, while the side of the square is 2. the ratio is 2:16, or 1:8
Find the values of x and y for which △ABC and △XYZ are congruent.ABC: side lengths of 4x+3, 5, and 8y−1
XYZ: side lengths of 6x−1, 5, and y+6
Enter the correct values in the boxes.
Answers
Answer: Two triangles are congruent if and only if all corresponding sides are equal in length. So, to find the values of x and y for which ΔABC and ΔXYZ are congruent, we need to equate the corresponding side lengths:
4x + 3 = 6x - 1
5 = 5
8y - 1 = y + 6
Solving the first equation for x:
4x + 3 = 6x - 1
2x = -4
x = -2
Solving the third equation for y:
8y - 1 = y + 6
7y = 7
y = 1
So, the values of x and y that make ΔABC and ΔXYZ congruent are x = -2 and y = 1.
Step-by-step explanation:
help me this is like something else i dontunderstand it
Answers
The correct matching according to the given question is given in the image below.
What is the value of an expression?The value of an expression is obtained by substituting the variables with the specific values. The value may be any real number if the specific values are constants.
Substitute x=6 into the expression -2+2x/3.
-2+(2×6)/3=-2+12/3
=-2+4
=2
Substitute x=-3 into the expression 5-x/3.
5-(-3)/3=5-(-1)
=5+1
=6
Substitute x= 6 into the expression -3+x/2.
-3+6/2=-3+3
=0
Substitute x=4 into the expression 2-3x/4.
2-(3×4)/4=2-12/4
=2-3
=-1
Therefore, the answers are correctly matched by an arrow line.
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A hotel had 45 guests call for room service, and 200 who did not. What percentage of the guests called for room service?
Answers
Answer:
Step-by-step explanation:
Number of guests who called for room service = 45
Total number of guests = 45 + 200 = 245
Percentage of guests who called for room service = (45/245) x 100% ≈ 18.4%
Therefore, approximately 18.4% of the hotel's guests called for room service.
Explanation:
Add the number of people who called for room service which is 45 to the number of people who didn’t which is 200
200+45 = 245
(45/245) x 100% = 18.36%
Which rounds up to 18.4%
4v + 9 x 7? step by step
Answers
4v + (9 x 7)= 4v +56
First multiply 9x7 =63
So is going to be 4v + 63
Cz you cant add 4v to 63 bc 63 doesn’t have a v
SWIX (avio scab In circle O above, the length of arc BC is 2 cm, mZBOC = 32°, and m¿AOB = 96°. What is the length of arc AB?
Answers
The length of the arc AB is 6 cm when BC is 2 cm, ∠BOC = 32°, and ∠AOB = 96°.
What is the arc length of a circle?The arc length is the portion of the circumference of a circle. It is directly proportional to the central angle formed by an arc.
The center of the circle is O, where BC = 2 cm, ∠BOC = 32°, and ∠AOB = 96°. Draw the diagram as per the given data.
As 96° = 3×32°, it follows that ∠AOB = 3×∠BOC.
As the central angle formed by an arc is proportional to its length. It follows that AB = 3×BC.
Since, BC = 2 cm, it can be got that AB = 3×2 cm = 6 cm.
Therefore, the required answer is 6 cm.
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If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
tanΘ=1
Answers
Answer: Θ = [tex]45[/tex]
Step-by-step explanation:
tan x=sinx/cosx
and tan x is negative in the first and third quadrants.
tan x=1 for 45 degrees so tan x=-1 in the first quadrant 135 degrees and the third quadrant= 315 degrees
ILL GIVE BRAINLEST FOR SHOWING WORK, rail train scale of 1:87 model:11 in actual:?
Answers
The actual train is 957 inches long.
What is a Ratio?A ratio indicates the number of times one number contains another. The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of the model train to the actual train is 1 : 87.
The model train is 11 inches long, therefore,
1=11
Then, the value of 87 is:
87 = 87×11
= 957
Hence, the actual train is 957 inches long.
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Terri estimates that 30% of 123 is about 60.
Which statement correctly describes why this is not a reasonable estimate?
O The answer should be close to
O The answer should be close to
O The answer should be exactly
O The answer should be close to
of 120, which is 60.
of 120, which is 34.
of 120, which is 40.
of 120, which is 40.
Answers
The correct option regarding the estimate of the percentage is of:
The answer should be close to 1/3 of 120, which is 40.
How to estimate the percentage?The percentage is estimated applying the proportions in the context of the problem.
To estimate 30% of 123, we must multiply the total amount of 123 by the decimal equivalent of the percentage of 30%, which is 30/100 = 0.3, hence the estimate is given as follows:
0.3 x 123 = 36.9.
This is close to 1/3 of 120, which is of 40, hence the last option is correct.
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4, 8, 16, 32, 64
Write the explicit form of the sequence above.
Answers
Answer:
I think its
Step-by-step explanation:
2^(n+1) is the explicit form
How many packets,each of dimensions 16 cm by 9 cm by 4 cm can be placed in a cubical box of side 1.2m long ?
Answers
The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
The volume of each packet is given as,
v = 16 x 9 x 4
v = 576 cubic cm
The volume of the cubical box is given as,
V = (1.2 x 100) x (1.2 x 100) x (1.2 x 100)
V = 120 x 120 x 120
V = 1,728,000 cubic cm
Then the number of packets is given as,
n = V / v
n = 1,728,000 / 576
n = 3,000
The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.
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Shawn's mortgage balance of $263,000 is
compounded daily at a rate of 4.075%
annualized interest. If no payments are made
for 6 months, what will the balance be after
this time has passed?
Answers
The balance amount when compounded daily at a rate of 4.075% after 6 months is $269,320.60.
What is meant by compound interest?
The interest you earn on interest is known as compound interest. Compound interest, also known as interest on principal & interest, is the practice of adding interest to the principal amount of a loan or deposit. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even while the principal remains the same, the interest changes annually. We can observe that interest rises over time. Thus, we can infer that the interest the bank charges is compound interest rather than simple interest.
Given,
Principal amount P = $263,000
Rate of interest r = 4.075%
Time period t = 6 months = 0.5 years
Final amount = [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
where n = 365
A = [tex]P(1 + \frac{r}{n})^{nt} =263000(1 + \frac{0.04075}{365})^{365*0.5}[/tex] = $269,320.60
Therefore the balance amount when compounded daily at a rate of 4.075% is $269,320.60.
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Franco has a hat with 9 blue marbles, 4 yellow marbles, and 12 green marbles. He designs a binomial experiment by drawing a marble from the hat, recording whether the marble is green, and then laying the marble aside. He then repeats the process seven times. Which statement must be true?
The experiment is not a binomial experiment because there is not a fixed number of drawings.
The experiment is not a binomial experiment because the probability of choosing a green marble is the same for each drawing.
The experiment is not a binomial experiment because the probability of choosing a green marble is not the same for each drawing.
The experiment is not a binomial experiment because there are only two possible outcomes for each drawing.
Answers
Answer: c
Step-by-step explanation:
What is a unit normal table?
Answers
To calculate the z-score, the formula is: z-score = (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation. Once the z-score is calculated, it can be used to look up the area, or probability, in the table.
A unit normal table is a type of probability table that is used to determine the area, or probability, under the normal curve. It is based on the standard normal probability distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. To use the unit normal table, one first needs to calculate the z-score, which is the number of standard deviations away from the mean a given value is. To calculate the z-score, the formula is: z-score = (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation. Once the z-score is calculated, it can be used to look up the area, or probability, in the table.
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convert 1,235 to three decimal places
Answers
Answer: la response est 1,235 je pense
Step-by-step explanation: trois decimal veux dire trois chiffre après la virgule donc on decale la virgule de 3 vers la gauche
Two parallel lines are cut by a transversal as shown below.
Suppose m1=38°. Find m6 and m7.
Please help I don’t know how to do this
(See attached image)
Answers
Answer:
m∠6 = 142°
m∠7 = 38°
Step-by-step explanation:
You will be using postulates and theorems to solve this question.
Two parallel lines are cut by a transversal (Given)
- m∠1 = 38° (Given)
- m∠1 ≅ m∠3 (Vertical Angles Theorem)
∴ m∠3 = 38° (Definition of Vertical Angles Theorem)
- m∠3 ≅ m∠5 (Alternate Angles Theorem)
m∠3 = 38° ∴ m∠5 = 38° (Definition of Alternate Angles Theorem)
- m∠5 ≅ m∠7 (Vertical Angles Theorem)
m∠5 = 38° ∴ m∠7 = 38° (Definition of Alternate Angles Theorem)
m∠7 + m∠6 = 180° (Corresponding Angles Postulate)
m∠7 = 38° (Given above)
Plug in 38 for m∠7 and solve for m∠6:
(38) + m∠6 = 180
Isolate m∠6. Note the equal sign, what you do to one side, you do to the other. Subtract 38 from both sides of the equation:
m∠6 + 38 = 180
m∠6 + 38 (-38) = 180 (-38)
m∠6 = 180 - 38
m∠6 = 142°
-
Answers:
m∠6 = 142°
m∠7 = 38°
~
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HELPPPP ASAP 25 POINTSSS AND I WILL MARK YOU BRAINLIEST2. For a school Project, Ron recorded how much TV he watched in one weekend and what kinds of programs he watched. This chart shows the time he watched TV: SATURDAY: 9:30-10:30AM, 1:00-3:30PM; 8:00-10:00 PM SUNDAY: 1:00-2:30PM and 8:00-10:00PM Ron watched sports programs for one half of the time. He watched movies for one third of the time. He watched cartoons with his sister Ronnette the rest of the time. How many minutes did Ron watch cartoons? Show all work:
Answers
Ill try my best to "show my work" in text
First, we need to calculate the total amount of time Ron spent watching TV over the weekend.
On Saturday, he watched TV for 1 hour and 0 minutes from 9:30-10:30AM, 2 hours and 30 minutes from 1:00-3:30PM, and 2 hours from 8:00-10:00PM, for a total of 5 hours and 30 minutes on Saturday.
On Sunday, he watched TV for 1 hour and 30 minutes from 1:00-2:30PM, and 2 hours from 8:00-10:00PM, for a total of 2 hours and 30 minutes on Sunday.
The total time he spent watching TV over the weekend is 5 hours and 30 minutes on Saturday + 2 hours and 30 minutes on Sunday = 8 hours.
Next, we need to calculate the time he spent watching sports programs and movies.
He watched sports programs for half of the total time he spent watching TV, so he spent 8 hours / 2 = 4 hours watching sports programs.
He watched movies for one third of the total time he spent watching TV, so he spent 8 hours / 3 = 2 hours and 40 minutes watching movies.
Finally, we can calculate the time he spent watching cartoons with his sister.
He spent 8 hours watching TV total, and 4 hours watching sports programs and 2 hours and 40 minutes watching movies, so he spent 8 hours - 4 hours - 2 hours and 40 minutes = 1 hour and 20 minutes watching cartoons.
Since there are 60 minutes in an hour, the total time Ron spent watching cartoons is 1 hour and 20 minutes = 80 minutes.
Answer:
So Ron spent 1 hour and 40 minutes watching cartoons with his sister Ronnette.
Step-by-step explanation:
First, we need to calculate the total time that Ron spent watching TV. On Saturday, he watched TV for 1 hour in the morning, 2 hours and 30 minutes in the afternoon, and 2 hours in the evening, which adds up to 6 hours and 30 minutes. On Sunday, he watched TV for 1 hour and 30 minutes in the afternoon and 2 hours in the evening, which is a total of 3 hours and 30 minutes. So over the weekend, Ron watched TV for 6 hours and 30 minutes on Saturday and 3 hours and 30 minutes on Sunday, which adds up to a total of 10 hours.
Since Ron watched sports programs for half the time he watched TV, he spent 10 hours / 2 = 5 hours watching sports.
And since he watched movies for one-third of the time he watched TV, he spent 10 hours / 3 = 3 hours and 20 minutes watching movies.
Finally, we can calculate the time Ron spent watching cartoons by subtracting the time he spent watching sports and movies from the total time he spent watching TV:
10 hours - 5 hours - 3 hours and 20 minutes = 1 hour and 40 minutes
So Ron spent 1 hour and 40 minutes watching cartoons with his sister Ronnette.
Write and simplify an expression
for the perimeter of the triangle.
8x-4
x+5
6x
Will give Brain liest
Answers
Answer:
= 15x + 1.
Step-by-step explanation:
Sum and the length of all three sides
8x - 4 + x + 5 + 6x
8x + x + 6x - 4 + 5
15x + 1.
In the synthetic-division problem shown below, what number belongs in the
place of the question mark?
2 1 -2 -8 5
2
?
10☐☐.
Answers
The solution is, the remainder is 9.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
find the remainder in the synthetic division
1 4 6 -1
Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder
1 4 6 -1
0 4 10
--------------------------------
4 10 9 -> Remainder
So the remainder is 9.
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Compare / Contrast Exponential Equations
1.) 2 (1/5)x-5
2.) 3 (1/2)x-3
Answers
The main difference between the two equations is the rate at which the graphs increase (determined by the horizontal scaling factor) and the vertical position of the graph (determined by the vertical scaling factor and translation).
How did we get this assertion?Both exponential equations are in the form y = ab^x - c, where a is the vertical scaling factor, b is the horizontal scaling factor (also known as the growth factor), and c is the vertical translation. The difference between the two equations lies in the values of the parameters a, b, and c.
The first equation, 2 (1/5)x-5, has a vertical scaling factor of 2, a horizontal scaling factor of 1/5, and a vertical translation of -5. The graph of this equation will increase at a slower rate than the graph of the second equation.
The second equation, 3 (1/2)x-3, has a vertical scaling factor of 3, a horizontal scaling factor of 1/2, and a vertical translation of -3. The graph of this equation will increase at a faster rate than the graph of the first equation.
In summary, the main difference between the two equations is the rate at which the graphs increase (determined by the horizontal scaling factor) and the vertical position of the graph (determined by the vertical scaling factor and translation).
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2(x+4)=-6 what is x?
Answers
Answer: x = -7
explanation:
2(x+4)= -6
2x+8= -6
-8 -8
2x -14
Divide both sides by 2
X = -7
Answer:x=-7 I hope this helps
Step-by-step explanation:
2(x+4)=-6
Divide both sides of the equation by 2
X+4=-3
Move the constant to the right-hand side and change its sign
X=-3-4
Calculate the difference which means subtract-3 minus 4 which give you -7
X=-7
And that how you solve for X
This is Math and Science together for My Ap class environmental science class picture is below please help
Answers
a) Exponential growth: a type of population growth where the number of individuals increases rapidly over time. b) Logistic growth: a type of population growth where the growth rate decreases as the population size approach its carrying capacity. c) Carrying capacity: the maximum number of individuals that an environment can sustainably support. d) Limiting factors: environmental factors, such as the availability of resources, that limit the growth of a population.Some factors that has contributed to the worlds overall population growth in the last 150 years are: Advances in medicine, sanitation, etc.If the carrying capacity of the earth was 9 billion people, we would this number between 2035 and 2040.When the population surpasses the carrying capacity of the earth for a lengthy period of time, resources may be completely exhausted.Why is the study of population growth important?
The study of population growth is important because it helps us understand the factors that drive changes in population size, and the impacts that population growth can have on the environment, economy, and human well-being.
Understanding population dynamics is essential for developing sustainable policies and managing natural resources effectively.
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Solve for X (pls give explanation as well)
2x + 6
70°
Answers
The sum of all the angles of triangle is 180°
We have the following angles:
70°90°2x+6The sum of all these angles will be equal to 180°
[tex] \sf \: 70 + 90 + 2x + 6 = 180[/tex]
Add all the constants[tex] \sf166 + 2x = 180[/tex]
Move the constant to the right hand side and change its sign[tex] \sf2x = 180 - 166[/tex]
Subtract the numbers[tex] \sf2x = 14[/tex]
Divide both sides by 2[tex] \sf2x \div 2 = 14 \div 2[/tex]
[tex] \boxed{ \tt \: x = 7}[/tex]
Now,The given angle is 2x+6, So put the value of x in this and find the value of angle
2x+62×7+614+620°What are the coordinates of the point on the directed line segment from (-1,-9) to (8,9) that partitions the segment into a ratio of 4 to 5
Answers
Answer: To find the point on the directed line segment that partitions it into a ratio of 4 to 5, we can use the formula for a point on a line given two endpoints and a ratio. The formula is:
(x, y) = (1 - t) * (x1, y1) + t * (x2, y2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and t is a value between 0 and 1 that determines the location of the point along the line.
In this case, (x1, y1) = (-1, -9) and (x2, y2) = (8, 9), and we want the point that partitions the line segment into a 4 to 5 ratio, so:
t = 4 / (4 + 5) = 4 / 9
Plugging in the values into the formula:
x = (1 - t) * x1 + t * x2 = (1 - 4/9) * (-1) + (4/9) * 8 = (5/9) * 8 - (4/9) * 1 = 44/9 - 4/9 = 40/9
y = (1 - t) * y1 + t * y2 = (1 - 4/9) * (-9) + (4/9) * 9 = (5/9) * 9 - (4/9) * (-9) = 45/9 + 36/9 = 81/9
So the point that partitions the line segment into a 4 to 5 ratio is (40/9, 81/9).
Step-by-step explanation: