(12, 10) , (-2, r) , m= -4
The value of r such that the slope associated with two points (12, 10), (-2, r) is -4 is 66.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
Given two points,
(12, 10) , (-2, r)
The slope associated with (x₁, y₁) and (x₂, y₂) →
Slope(m) = (y₂ - y₁)/(x₂ - x₁)
So,
m = (r - 10)/(-2-12)
(r - 10)/(-14) = -4
r - 10 = 56
r = 66
Hence "The value of r such that the slope associated with two points (12, 10), (-2, r) is -4 is 66".
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3. Jocelyn needs to study two stars for her astronomy research. She has narrowed her choices down to four stars that are located on a straight line from earth. Star Distance from earth Star A 0.176 times 10 to the power of 18 km Star B 22.13 times 10 to the power of 16 km Star C 31.42 times 10 to the power of 14 km Star D 125.5 times 10 to the power of 15 km Jocelyn wants to study the two stars that are closest to each other. (a) Which two stars should she study? (b) What is the distance between the two stars? Show or explain your work.
Which variable is most important to the following problem? At 9:00 a.m., a wind speed of 20 miles per hour was recorded. After that, the wind speed was recorded every hour. Each measurement showed an increase in wind speed of 3 miles per hour. The strongest wind was recorded at 4:00 p.m. After that, the wind speeds started to decrease. What was the top wind speed? A. the time of day the first measurement was made B. the miles-per-hour speed of the wind at its maximum point C. the number of hours it took for the wind speed to reach its minimum for the day
Final answer:
The most important variable to determine the top wind speed at 4:00 p.m. is B. the miles-per-hour speed of the wind at its maximum point. The calculation shows an initial speed of 20 mph at 9:00 a.m., with an increase of 3 mph each hour leading to a top speed of 41 mph at 4:00 p.m.
Explanation:
The variable most important to the problem of determining the top wind speed recorded is B. the miles-per-hour speed of the wind at its maximum point. To find the top speed, you can calculate the increase in wind speed from the initial measurement at 9:00 a.m. The wind was increasing by 3 miles per hour each hour until it reached its peak at 4:00 p.m.
Here is the calculation:
Top wind speed = Initial speed + (Increase per hour × Number of hours)
Top wind speed = 20 mph + (3 mph/hour × 7 hours)
Top wind speed = 20 mph + 21 mph
Top wind speed = 41 mph
Find an equation of the set of all points equidistant from the points a(−1, 6, 3) and b(4, 3, −2).
Choose the true statement.
-8 < 8
-8 > 8
-8 = 8
-8 < 8
since a negative number is below 0 and a positive number is above 0 the first statement is true
In the cafeteria 100 milk cartons were put out for breakfast. at the end of breakfast 27 remained what is the number of milk cartons taken to the total number of mil cartons
Which answer gives the number and type of solutions to the equation x2+14x+49=0 ?
The quadratic equation[tex]x^2 + 14x + 49 = 0[/tex]factors into [tex](x + 7)^2 = 0[/tex], yielding one real repeated solution, x = -7. This means the graph of the quadratic function touches the x-axis at precisely one point.
The given equation [tex]x^2 + 14x + 49 = 0[/tex] is a quadratic equation and can be factored or solved using the quadratic formula.
However, this particular equation is a perfect square trinomial because the constant term 49 is the square of 7 and twice the product of 7 and the linear coefficient 14 is equal to the middle term 14x.
[tex]x^2+2*7*x+7^2=0[/tex]
Therefore, the equation can be factored as
(x + 7)^2 = 0.
To find the solution, we set the factor equal to zero:
(x + 7) = 0
(x + 7) = 0
This equation has one unique solution, x = -7, which means the quadratic equation has one real repeated solution.
In the context of the number and type of solutions, it means the graph of the quadratic function touches the x-axis at one point (x = -7) and does not cross it.
Help plz someone give me an answer
What is 4h-3 expression factored
Which of the following statements says that a number is between -3 and 3?
A. |x| < 3
B. |x| > 3
Answer:
A. |x| < 3
Step-by-step explanation:
The absolute value of a number is the value that a number has beyond its sign. This means that the absolute value is the numerical magnitude of the number regardless of whether its sign is positive or negative. Formally, the absolute value of any real number x, is defined by:
[tex]|x|=\left \{ {{x,\hspace{3}if\hspace{3}x\geq0} \atop {-x,\hspace{3}if\hspace{3}x<0}} \right.[/tex]
In this sense, to satisfy the inequality [tex]|x|<3[/tex], the domain of x must be:
[tex]-3<x<3\\\\or\\\\(-3,3)[/tex]
Because for [tex]x<-3[/tex] or [tex]x>3[/tex] the inequality is absurd. For example if x=-4
[tex]|-4|=4<3[/tex] which is not true.
and for x=4
[tex]|4|=4<3[/tex] which is not true.
On the other hand to satisfy the inequality [tex]|x|>3[/tex], the domain of x must be:
[tex]-3>x>3\\\\or\\\\(-\infty,-3)\cup(3,\infty)[/tex]
Because for [tex]x<3[/tex] the inequality is absurd. For example if [tex]x=2[/tex]
[tex]|2|=2>3[/tex] which is not true.
and for x=-1
[tex]|-1|=1>3[/tex] which is not true.
Therefore the correct statement is:
A. |x| < 3
Is 0.245245245... a rational or irrational number?
James ran at a rate of 11.5 km per hour. What was james' speed in miles per hour? (NOT TO BE SOLVED. Needs to be an equation)
1km = 0.621371 miles
so equation is
total miles per hour = 11.5km * 0.621371
1/2(2d+6)=p solve for d
There are 12 signs of the zodiac. how many people must be in a group before you are guaranteed that at least 6 of them have the same sign
How many seconds are in 9 hours
Multiply.
(21)⋅(−7)
−147
−14
14
147
Answer:
-147
Step-by-step explanation:
12 cot2(x) = 4 find all values of x in the interval [0, 2π] that satisfy the equation
Final answer:
To solve 12 cot2(x) = 4, we simplify and use properties of the tangent function. The solution is x = π/3, 2π/3, 4π/3, and 5π/3 within the interval [0, 2π].
Explanation:
To solve the trigonometric equation 12 cot2(x) = 4, we first simplify it to find cot2(x) = 1/3 by dividing both sides by 12. To find cot(x), we take the square root of both sides, giving us cot(x) = ±1/√3. Remember that cot(x) is the reciprocal of tan(x), so we now have tan(x) = ±√3.
To find the values of x that satisfy this equation within the interval [0, 2π], we look at the unit circle. The tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants. Therefore, for tan(x) = √3, x = π/3, 4π/3, and for tan(x) = -√3, x = 2π/3, 5π/3. These are the values of x in the given interval that satisfy the equation.
Need help figuring out the equation for the linear line on the graph. Rise over run?
One of the factors of p^5 - 144p^3 is
A. P^3
B. P + 12
C. P - 12
D. All of the above
The perimeter of a rectangle is 50 centimeters. the length of the rectangle is one more than 3 times the width of the rectangle. what are the dimensions of the rectangle
The width of the rectangle is 6 centimeters and the length is 19 centimeters.
Explanation:To find the dimensions of the rectangle, we can assign variables to the length and width of the rectangle. Let's say the width is 'w' centimeters.
According to the information given, the length is '1 + 3w' centimeters. The perimeter of a rectangle is the sum of all its sides, so we can set up the equation: 2(length + width) = 50. Substituting the given expressions for length and width, we have: 2((1 + 3w) + w) = 50. Simplifying this equation, we get: 8w + 2 = 50. Solving for 'w', we find that the width of the rectangle is 6 centimeters. Substituting this value back into the expression for the length, we get: length = 1 + 3(6) = 19 centimeters.Therefore, the dimensions of the rectangle are width = 6 centimeters and length = 19 centimeters.
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The equation of a circle is x^2 + y^2 + Cx + Dy + E = 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are coefficients C, D, and E affected?
A) C, D, and E are unchanged.
B) C increases, but D and E are unchanged.
C) C and D decrease, but E is unchanged.
D) C, D, and E increase.
E) C and D are unchanged, but E decreases.
x and y are the center point so since C and D are multiplied by x an y they would remain the same
E = the center points squared plus the radius squared.
Since the radius is getting smaller E would also decrease
Answer is E
Convert the following: 22km = ________m A. 0.022 B. 2.2 C. 22 D. 22,000
1km = 1000 m
22*1000 = 22,000
Answer is D. 22,000
Ysidra paints a room that has 400 square feet of wall space in 2 and a half hours. at this rate, how long will it take her to paint a room that has 720 square feet of wall space?
The time taken to paint a room which has a wall space of 720 feet² is equal to [tex]4\frac{1}{2}[/tex] hours.
What is the unitary method ?
The unitary method is a method in which you find the value of one unit and then the value of required no. of units.
It is given that room is painted that has wall space of 400 feet². The time taken to paint this space is 2 and half hours.
So , the wall space painted per hour will be :
= 400 ÷ [tex]2\frac{1}{2}[/tex]
= 400 ÷ [tex]\frac{5}{2}[/tex]
= 400 × [tex]\frac{2}{5}[/tex]
= 160 square feet per hour
We have to find out the time taken to paint a room which has a wall space of 720 feet². So , this will be calculated by dividing 720 square feet wall space by the per hour painted wall space that is equal to:
= 720 / 160
= 4.5 hours
or
= [tex]4\frac{1}{2}[/tex] hours
Therefore , the time taken to paint a room which has a wall space of 720 feet² is equal to [tex]4\frac{1}{2}[/tex] hours.
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find the product of: (x+3vs)(2x+3vs)
Change the line 3x − 8y = 5 into slope-intercept form.
288 miles on 12 gallons of fuel; 240 miles on 10 gallons of fuel
Which figures are congruent? Will Give Brainliest Answer
A. B ≅D and A ≅C
B. B ≅D
C. B ≅D and E ≅F
D. B ≅D and E ≅F and A ≅C
If a person wanted to purchase their dream car, and keep it for many years, should they lease or buy? Why? (Site 1)
Buying an asset or a vehicle means paying off the entire sum of money that is the cost of the asset at the time of its purchase.
Leasing an asset means purchasing an asset by not paying the entire sum of money at the time of purchasing, rather paying in the form of rent over the period of time.
If a person wants to purchase his dream car for keeping for many years, then Buying Option is better because the payment of the overall cost in buying will be less than leasing.
This will also provide benefit that at the time of sale the owner will be paid off higher value of car as compared to car taken on lease.
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If a person wants to purchase their dream car and keep it for many years, it is generally recommended to buy rather than lease. Buying a car provides long-term ownership, customization options, and potential resale value, while leasing offers lower monthly payments but no ownership.
Explanation:If a person wants to purchase their dream car and keep it for many years, it is generally recommended to buy rather than lease. Here are the reasons why:
Ownership: When you buy a car, you become the owner and have the freedom to modify or personalize the vehicle as you wish. Leasing, on the other hand, only provides temporary possession of the car.Long-term cost: Buying a car may have higher upfront costs, such as a down payment and monthly loan payments, but in the long run, you will own the vehicle. Leasing involves lower monthly payments, but you will not own the car at the end of the lease term.Resale value: Owning a car allows you to build equity over time. You can sell the car later and recoup some of the cost. Leasing does not provide this opportunity.In conclusion, buying a car is a better option if you want long-term ownership and the ability to customize the vehicle. Leasing may be suitable for those who prefer lower monthly payments and don't want to commit to long-term ownership.
Real world equation that can be modeled by the equation y=1/20x
If Juan drives 50 mph for 1.5 hours and then 70 mph for 0.5 hours, then how far did he drive?
The total distance that he drive is:
110 miles.
Step-by-step explanation:We know that the distance is defined as the product of speed and time.
i.e.
[tex]Distance=Speed\times Time[/tex]
It is given that:
Juan drives 50 mph for 1.5 hours.
This means that at this rate the distance traveled by him is:
[tex]Distance_1=50\times 1.5\\\\i.e.\\\\Distance_1=75\ miles[/tex]
and he travels at the rate of 70 mph for 0.5 hours.
This means that the distance traveled by him at this rate is:
[tex]Distance_1=70\times 0.5\\\\i.e.\\\\Distance_1=35\ miles[/tex]
Hence, the total distance that he drive is:
[tex]Total\ distance=Distance_1+Distance_2\\\\Total\ distance=75+35\\\\i.e.\\\\Total\ distance=110\ miles[/tex]