Answers
Answer:
x=7
Step-by-step explanation:
7x-7 = 4x + 14
3x-7=14
3x = 21
x=7
Answer: 7
Step-by-step explanation:
Related Questions
Which statement could describe the dog’s movement 5 seconds after the command was given?
Answers
Final answer:
The dog’s movement 5 seconds after the command, considering different frames of reference for speed, can be described by the distance it would have traveled: either 25 meters on the sidewalk (at 5 m/s) or 10 meters from the student's perspective (at 2 m/s).
Explanation:
The student's question pertains to describing the dog’s movement 5 seconds after the command was given, considering the dog's speed. Since we have learned that the dog has different speeds in different frames of reference—5 m/s on the sidewalk and 2 m/s in the student’s frame—we can describe the dog’s movement based on these speeds. If the dog started moving at the moment the command was given and continued to move for 5 seconds, we can calculate the distance it would have covered in that time.
For the sidewalk's frame, where the dog's speed is 5 m/s, the dog would have covered a distance of:
Distance = Speed × Time
Distance = 5 m/s × 5 s = 25 meters
In the student’s frame, where the dog's speed is 2 m/s, it would have moved:
Distance = 2 m/s × 5 s = 10 meters
The statement that could describe the dog’s movement 5 seconds after the command was given is that the dog could have traveled either 25 meters from its starting point on the sidewalk or 10 meters from the student's perspective, depending on the frame of reference being considered.
What is the sign of -567.45 + 567.45?
Choose 1 answer:
A
Positive
B
Negative
(C) Neither positive nor negative-the sum is zero.
Answers
Answer:
C
Step-by-step explanation:
-567.45 + 567.45 = 0
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
36%
26%
45%
50%
Answers
Answer: 26%
Step-by-step explanation:
See attached photo. - my answer got deleted lol
Without additional information, we cannot determine the exact percentage of students age 15 and above who travel to school by bus.
Explanation:To find the percentage of students age 15 and above who travel to school by bus, we need to compare the number of students who travel by bus to the total number of students in that age group. However, we don't have that information in the given question.
We need more data to calculate the percentage. Without additional information, we cannot determine the exact percentage of students age 15 and above who travel to school by bus.
Evaluate the following expression (-3)^2
Answers
Answer:
9
Step-by-step explanation:
negative times a negative is a positive. Negative three squared is 9.
Roberta is on a hiking trip. On the first day, she starts hiking at an elevation of 223.3 feet. By the end of the first day, her elevation increases by 276.8 feet. On the second day, her elevation decreases by 59.2 feet. On the third day, her elevation decreases by 76.3 feet. What is Roberta's elevation at the end of the third day?
Answers
Answer:364.6
Step-by-step explanation:
Julie needs to cut 4 pieces of yarn, each with the same length and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut what is the equation that can be used to determine the total length of all of the yarn that she ends up, cutting,y? Is the graph of the equation continuous or discrete
Answers
Answer:
Total length of the x inches long pieces = 4x inches
She has to cut another piece = 7.75 inches
Total length = 4x + 7.75
This is what y represent, so
y = 4x + 7.75
The graph of the equation is continuous
Answer:
The required equation is [tex]y=4x+7.75[/tex] and the graph of the equation is continuous.
Step-by-step explanation:
Consider the provided information.
Julie needs to cut 4 pieces of yarn,
Let x represent the length of each yarn.
Then the length of 4 pieces will be: 4x
y represents the total length of all of the yarn that Julie decides to cut
Therefore the required equation that can be used to determine the total length of all of the yarn is:
[tex]y=4x+7.75[/tex]
Here, the graph is continuous, because the length of yarn can be any number.
In a right triangle, the hypotenuse has endpoints XY, shown on the graph.
below...
If Z represents the third vertex in the triangle and is located in the second quadrant with integer coordinates, what is the length of YZ?
A)3
B)4
C)5
D)6
Answers
Answer:
The correct option is C.
Step-by-step explanation:
In a right triangle, the hypotenuse has endpoints XY as shown in the given graph.
Since XY is hypotenuse and Z is third vertex in the triangle, therefore XZ and YZ must be perpendicular at point Z.
The coordinates of X are (-4,2), so draw a vertical line x=-4 and a horizontal line y=2.
The coordinates of Y are (-1,-3), so draw a vertical line x=-1 and a horizontal line y=-3.
From the below figure it is clear that the vertcal and horizontal lines intersect each other at [tex]Z_1[/tex] and [tex]Z_2[/tex].
It is given that Z is located in the second quadrant with integer coordinates, therefore the only possible location of Z is
[tex]Z=Z_2(-1,2)[/tex]
Since the length of YZ₂ is 5 units and Z=Z₂, therefore the length of YZ is 5 units.
Hence the correct option is C.
The population of a small town in northern California gradually increases by about 50 people a year. In 2010, the population was 8500 people. Write an equation for the population of this city and find its estimated population in 2017. The estimated population in 2017 is
Answers
The equation representing the population of the city is P = 50t + 8500. Substituting t=7 in this equation gives the estimated population in year 2017 as 8850 people.
Explanation:The question is asking for the population of the town in a given year, given it's steadily increasing each year. The original population, in 2010, is 8500 people and each year the number of people increases gradually by 50.
The general equation for a line is y = mx + c, where m is the slope (the rate of change), c is the y-intercept (the initial value), x is the input (in this case, the number of years since 2010), and y is the output (the population).
In this case, m = 50 (because the population increases by 50 people per year), c = 8500 (the population in 2010) and x will be the number of years since 2010. Therefore, the equation for the population of the town is: P = 50t + 8500
To find the population in 2017, you substitute t=7 (because 2017 is 7 years after 2010) into the equation: P = 50*7 + 8500 = 8850
So the estimated population in 2017 would be 8850 people.
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For f(x)=2x+1 and g(x)= x^2 -7, find (f•g)(x)
Answers
Answer:
[tex]\large\boxed{(f\cdot g)(x)=2x^3+x^2-14x-7}[/tex]
Step-by-step explanation:
[tex](f\cdot g)(x)=f(x)\cdot g(x)\\\\f(x)=2x+1;\ g(x)=x^2-7\\\\(f\cdot g)(x)=(2x+1)(x^2-7)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(2x)(x^2)+(2x)(-7)+(1)(x^2)+(1)(-7)\\\\=2x^3-14x+x^2-7[/tex]
Find all complex solutions of X^2-5X -5= 0
Answers
ANSWER
[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]
EXPLANATION
The given equation is
[tex] {x}^{2} - 5x - 5 = 0[/tex]
The solution is given by the formula
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
where a=1, b=-5, c=-5
We substitute into the formula to get;
[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)( - 5)} }{2(1)} [/tex]
We simplify to get,
[tex]x = \frac{ 5 \pm \sqrt{ 45} }{2} [/tex]
The solutions are:
[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]
The equation has no complex roots.
Answer:
x = [5 + 3√5]/2 or x = [5 -3√5]/2
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
To find the solutions of given equation
It is given x² - 5x - 5 = 0
here a = 1, b = -5 and c = -5
x = [-b ± √(b² - 4ac)]/2a
= [--5 ± √((-5)² - 4*1*-5)]/2*1
= [5 ± √(25 + 20)]/2
= [5 ± √(45)]/2
= [5 ± 3√5]/2
x = [5 + 3√5]/2 or x = [5 -3√5]/2
Jillana begins to solve a linear equation that results in a variable expression set equal to the same variable expression. Which is the best interpretation of this solution? The equation has one solution: x = 0. The equation has one solution: x = 1. The equation has no solution. The equation has infinite solutions.
Answers
Answer: infinite solutions
Step-by-step explanation:
If the left side equals the right side, then every value you input for the variable will make a TRUE statement --> which means there are infinite solutions.
For example: x + 1 = x + 1
Any value you choose for "x" will result in a true statement.
This is because they are the same line, which is another way of showing that they have infinite solutions.
The linear equation is an identity, which means that it has infinite solutions.
What is an identity?
We define an identity as an equation where we have the exact same expression in both sides of the equation.
For example, in:
f(x) = f(x).
Where f(x) is a function.
A easier example can be:
x + 5 = x + 5
Notice that we have the exact same thing in both sides, this is what Jilana gets when solving her linear equation.
This means that for any given value of x, the equation will be true. So, x can be any real value, which means that there are infinite solutions for the equation.
If you want to learn more about linear equations, you can read:
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In a young single person's monthly budget, $150 is spent on food, $175 is spent on housing, and $175 is spend on other items. Suppose you drew a circle graph to represent this information, what percent of the graph represents housing?
Answers
To find the percentage of the monthly budget that housing represents in a circle graph, divide the housing cost ($175) by the total monthly expenses ($500) and multiply by 100. This calculation shows that housing accounts for 35% of the monthly budget.
Explanation:When representing a monthly budget on a circle graph, or pie chart, you need to find out what percentage of the total budget each category represents. In this case, a young single person spends $150 on food, $175 on housing, and $175 on other items. To find the percentage that represents housing, we first need to calculate the total amount of monthly expenses which are $150 for food, $175 for housing, and $175 for other items, adding up to a total of $500.
Next, we calculate the percentage that the housing expense represents by dividing the housing cost by the total expenses and then multiplying by 100 to get a percentage:
Housing Percentage = (Housing Cost / Total Expenses) x 100Housing Percentage = ($175 / $500) x 100Housing Percentage = 0.35 x 100Housing Percentage = 35%Therefore, housing represents 35% of the total monthly budget on the circle graph.
The system of equations is solved using the linear combination method. What does 0= -12 mean regarding the solution to the system?
Answers:
There are no solutions to the system because the equations represent parallel lines.
There are no solutions to the system because the equation represent the same line.
There are infinitely many solutions to the system because the equations represent parallel lines.
There are infinitely many solutions to the system because the equations represent the same line.
Answers
Answer:
There are no solutions to the system because the equation represents parallel lines
Answer:
There are no solutions to the system because the equations represent parallel lines.Step-by-step explanation:
We know by given that the system result is 0 = -12.
This results means that there are no solutions in the system, because the statment 0 = -12 is false, also lines are parallels, that's the real reason why there's no solution.
Remember that parallel lines won't intercept, and a solution of a linear system means that those lines intercept. So, if they don't, then, there's no solution.
Therefore, the right answer is the first choice.
If the cost is $58 and the selling price is $63 then what is the percent of increase
Answers
For this case we can raise a rule of three:
$ 58 ----------> 100%
$ 63 ----------> x
Where "x" represents the percentage equivalent to $ 63.
[tex]x = \frac {63 * 100} {58}\\x = \frac {6300} {58}\\x = 108.62[/tex]
Thus, the percentage increase is 8.62%
Answer:
The percentage of increase is 8.62%
What is the product of the polynomials shown below?
Answers
Answer:
B. 14x^3+39x^2+18x+20
Step-by-step explanation:
Given polynomials are:
[tex](7x^2+2x+4)(2x+5)\\For\ product\\(2x+5)(7x^2+2x+4)\\= 2x(7x^2+2x+4)+5(7x^2+2x+4)\\= 14x^3+4x^2+8x+35x^2+10x+20\\Combining\ alike\ terms\\= 14x^3+4x^2+35x^2+8x+10x+20\\=14x^3+39x^2+18x+20[/tex]
The product of given polynomials is:
14x^3+39x^2+18x+20
Hence, Option B is correct ..
Answer:
B. 14x^3 + 39x^2 + 18x + 20.
Step-by-step explanation:
(7x^2 + 2x + 4)(2x + 5)
= 2x(7x^2 + 2x + 4) + 5(7x^2 + 2x + 4)
Distribute over the 2 parentheses:
= 14x^3 + 4x^2 + 8x + 35x^2 + 10x + 20
Add like terms:
= 14x^3 + 39x^2 + 18x + 20.
A representative from plan 1 wants to use the graph below to sell health plans for his company. How might the graph be redrawn to emphasize the difference between the cost per doctor visit for each of the three plans? The scale on the y-axis could be changed to 0–100. The scale on the y-axis could be changed to 25–40. The interval of the y-axis could be changed to count by 5s. The interval of the y-axis could be changed to count by 20s.
Answers
Answer:
B) The scale on the y-axis could be changed to 25–40.
Answer:
B the scale on the y-axis could be changed from 25-40
Step-by-step explanation:
just took test on edg and got a 100
A and B are independent events. P(A) =0.30 P(B) = 0.60
What is P(A|B)?
Answers
Answer:
P(A|B) = 0.30
Step-by-step explanation:
P(A) = 0.30
P(B) = 0.60
To Find:
P(A|B) = ?
P(A|B) means probability of occurring of event A when event B has occurred.
P(A|B) = P(A∩B)/P(B)
We know that for independent events;
P(A∩B) = P(A).P(B)
So, we have:
P(A|B) = P(A).P(B)/P(B)
P(A|B) = P(A)
So, probability of occurrence of an independent event does not depend on the probability of a different event.
A company manufactures its product at a cost of $0.50 per item and sells it for $0.85 per item daily overhead is $600 how many items must be manufactured each day in order for the company to break even
Answers
Answer:
1,715
Step-by-step explanation:
So, we have a product that is sold for $0.85 and costs $0.50 to produce, and we need to find the number is items needed to cover the $600 fixed costs of the company.
We can model this like that, where x is the number of items to make:
0.85x - 0.5x = 600
0.35x = 600
x = 1,714.29
So, to cover the fixed overhead/fixed expenses, they need to make at least 1,715 items, each day.
Samantha works in a bakery. The profit of cupcakes in dollars, after t weeks, is given by the function, C(t) = 0.1t3. The profit of cookies in dollars, after t weeks, is given by the function, K(t) = 5(1.07)t - 5. Which function describes the total profit, M(t), at the bakery after t weeks?
Answers
Answer:
M(t) = 0.1t3 + 5(1.07)t - 5
Step-by-step explanation:
Answer:
[tex]M(t) = 0.1t^{3}[/tex] [tex]+ 5(1.07)^{t}[/tex]- 5
Step-by-step explanation:
(on attachment with step by step explanation)
8x+5y=24
y=−4x
what is X and Y??
Answers
Answer:
Step-by-step explanation:
plug y into the first equation:
8x+5y=24
8x+5(-4x)=24
8x-20x=24
-12x=24
x=-24/12
x=-2
then plug x to the second equation
y=-4
y=-4(-2)
y=8
x=-2
y=8
8x + 5y = 24
You just told us that Y = -4x .
If that's true, then
8x + 5(-4x) = 24
8x - 20x = 24
-12x = 24
x = -2
y = -4x
y = -4(-2)
y = 8
How many kilograms are in 32,500 grams?
Answers
Hello There!
There are 32.5 kilograms in 32,500 grams.
STEPS
Write the number of grams
Divide by 1,000 because a kilogram is 1,000 grams
15 3/14+ 24 1/14+ 12 2/7+ 12 2/7+ 10 1/7 +10 1/7+ 35 3/7=
Answers
Answer:
it is :119.5714
Step-by-step explanation:
15 3/14+24 1/14+12 2/7+12 2/7+10 1/7+10 1/7+35 3/7=
step by step now:
15 3/14+24 1/14+12 4/14+12 4/14+10 2/14+10 2/14+35 6/14=118 22/14=118+1.5714=119.5714
Final answer:
The sum of the given mixed numbers is 119 and 2/7 after adding the whole numbers separately and then the fractions.
Explanation:
To calculate the sum of the given numbers, we start by adding the whole numbers and the fractions separately. All the fractions have a common denominator, which simplifies the process. Let's proceed with the calculation:
Adding the whole numbers: 15 + 24 + 12 + 12 + 10 + 10 + 35 = 118.
Adding the fractions: 3/14 + 1/14 = 4/14, simplifies to 2/7 because 4/14 is dividable by 2. Then, we add 2/7 + 2/7 + 1/7 + 1/7 + 3/7 = 9/7. But 9/7 is more than 1, so we rewrite 9/7 as 1 whole and 2/7.
Now let's combine the sums of whole numbers and fractions: 118 + 1 = 119.
Thus, the total sum is 119 and 2/7.
Which statements regarding EFG are true? Check all that apply.
Answers
Answer:
A and B
Step-by-step explanation:
You can tell by just looking. Also because it is a isosceles triangle.
We can see here that the statement that is true regarding ΔEFG are true:
A. EF + FG > EG
B. EF + FG > EF
C. EG - FG < EF
What is a triangle?A triangle is a polygon with three sides, three angles, and three vertices. It is one of the fundamental geometric shapes in Euclidean geometry. The sum of the internal angles of a triangle always adds up to 180°.
Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This theorem establishes a fundamental relationship between the lengths of the sides of a triangle.
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5 days 6 hours 20 minutes
- 3 days 8 hours 40 minutes
Answers
Answer: 1 day, 21 hours, and 40 minutes
Step-by-step explanation: To make it less confusing, you can convert all of the days into hours (24 hours in a day)...
126 hours and 20 minutes-80 hours and 40 minutes
7580 minutes-4840 minutes=2740 minutes
We can convert 2740 minutes back into hours and days now...
1 day, 21 hours, and 40 minutes
Or....
Step-by-step explanation: Or you can just subtract, start with minutes and go up from there...
20-40 would be in the negatives and time can’t be negative, so you need to borrow from the hours. So hours is now at 5 and minutes is at 20+40 which is 80. And 80-40=40
We now have...
5 days, 5 hours, and 40 minutes-3 days and 8 hours.
Now we can do the hours...
5-8 also is negative, so we need to borrow from the days. Days is now at 4. There are 24 hours in a day so 24+5=29. Now we can subtract 29-8=21
Now we have 4 days, 21 hours, and 40 minutes
And 4-3 is 1, which means we have 1 day,
21 hours, and 40 minutes as our answer!
The difference between the given time frames 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes after performing the subtraction operation is 1 day, 13 hours, and 40 minutes.
Explanation:The question is about an arithmetic operation involved in time. This arithmetic operation is subtraction. Given the time frames are 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes. Let's subtract the smaller time frame from the larger one.
First, convert all time periods into the smallest common unit (here, minutes). 5 days 6 hours 20 minutes equals to 7260 minutes and 3 days 8 hours 40 minutes equals to 5040 minutes.Next, subtract the two: 7260 - 5040 = 2220 minutes.Then, convert this result back into days, hours, and minutes to get the difference. So, 2220 minutes is equal to 1 day, 13 hours, and 40 minutes.So, the difference between 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes is 1 day, 13 hours, and 40 minutes.
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8 litres of paint can cover 129.6 m².
How much paint is required to paint an area of 243m²?
Answers
Answer:
15 litres
Step-by-step explanation:
129.6 m² needs 8L
1m² needs 8/129.6L
243m² needs (8/129.6)×243 = 15L
To calculate the amount of paint required for a 243m² area, determine the coverage rate from the given data (16.2 m² per litre) and then divide the desired area by the coverage rate. We find that 15 litres of paint are necessary to cover 243m².
Explanation:To find out how much paint is required to paint an area of 243m² when 8 litres of paint can cover 129.6 m², we need to calculate the paint coverage ratio and then apply it to the desired area.
First, we calculate the coverage rate of the paint:
Paint coverage rate = Area covered / Amount of paintPaint coverage rate = 129.6 m² / 8 litresPaint coverage rate = 16.2 m² per litreNext, we use this rate to determine the amount of paint needed for 243m²:
Required paint = Desired area / Paint coverage rateRequired paint = 243 m² / 16.2 m² per litreRequired paint = 15 litresTherefore, 15 litres of paint are required to paint an area of 243m².
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Which systems of equations will also have a solution of (2,0)
Answers
Final answer:
A system of equations will have the solution (2,0) if, when substituting x=2 and y=0, both equations are satisfied. This can be a linear equation where the y-intercept is set to be the negative double of the slope, or a conic section represented by a quadratic equation that intersects the x-axis at x=2.
Explanation:
Systems of equations that will have a solution of (2,0) must satisfy the condition that when x=2 and y=0, both equations are true. Considering the information provided about quadratic and differential equations, to find a system with the solution (2,0), one can set up a system of any two equations and test if the point (2,0) satisfies them. For instance, any linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept, will have a solution of (2,0) if b is set to -2m. Similarly, a second-order differential equation can be constructed with known solutions, including the point (2,0).
A system with a linear equation y = mx - 2m, where m can be any value.
A homogeneous linear differential equation with boundary conditions that result in the point (2,0) being a solution.
A conic section represented by a quadratic equation that intersects the x-axis at x=2.
For example, the quadratic equation ax² +2hxy+by² = 0, can be factored into two linear factors with no constant term, which means it represents two lines intersecting at the origin. If one of these lines passes through the point (2,0), it would confirm that our solution fits this system as well.
9. The maximum horizontal range of a projectile is given by the formula R= u2/g where u is the initial velocity and g is the acceleration due to gravity. Find the velocity with which a ball can be thrown to have a maximum range of 20 meters when the acceleration due to gravity is equal to 9.8 m/s.
(SHOW WORK)
Answers
The answer is:
The velocity with which the ball can be thrown to have a maximum range of 20 meters is equal to 14 m/s.
[tex]u=14\frac{m}{s}[/tex]
Why?To solve the problem and find the velocity, we need to isolate it from the equation used to calculate the maximum horizontal range.
We have the equation:
[tex]R=\frac{u^{2} }{g}[/tex]
Where,
R is the maximum horizontal range.
u is the initial velocity.
g is the gravity acceleration.
Also, from the statement we know that:
[tex]R=20m\\g=9.8\frac{m}{s^{2} }[/tex]
So, using the given information, and isolating, we have:
[tex]R=\frac{u^{2} }{g}[/tex]
[tex]R*g=u^{2}[/tex]
[tex]u^{2}=R*g=20m*9.8\frac{m}{s^{2} }=196\frac{m^{2} }{s^{2} }\\\\u=\sqrt{196\frac{m^{2} }{s^{2}}}=14\frac{m}{s}[/tex]
Hence, we have that the velocity with which the ball can be thrown to have a maximum range of 20 meters is equal to 14 m/s.
[tex]u=14\frac{m}{s}[/tex]
Have a nice day!
Answer:
The velocity with which a ball must be thrown to have a maximum range of 20 m is 14 m/s.
Note that this problem means to find the magnitude of the velocity and not the direction (it is implicit in the formula that the angle of the launch is 45°).
Explanation:
You just must use the given equation for the maximum horizontal range of a projectile and solve for u which is the unknwon:
Given equation: R = u² /gg = 9.8 m/s²R = 20 mu =?Solve for u:
u² = R × g = (20 m) × (9.8 m/s²) = 196 m²/s²Take square root from both sides:
u = 14 m/s ← answerThe radius of the large sphere is double the radius of the
small sphere
How many times is the volume of the large sphere than the
small sphere?a.2 b.4 c.6 d.8
Answers
Answer:
d. 8
Step-by-step explanation:
The volume of a sphere = 4/3πr³
Let the radius of the smaller sphere be r, then the volume of the large sphere will be 2 r
Finding the volumes of the 2 gives:
volume of large sphere = 4/3π (2r)³
= 32/3πr³
Volume of the smaller sphere = 4/3πr³
Dividing the two volumes we get the ratio of their volumes
32/3πr³÷4/3πr³= 8
Answer: Option d
[tex]\frac{V_2}{V_1}=8[/tex]
Step-by-step explanation:
The volume of a sphere is calculated using the following formula
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where r is the radius of the sphere and V is the volume.
If the radius of the small sphere is r and the volume is [tex]V_1[/tex] then:
[tex]V_1=\frac{4}{3}\pi r^3[/tex]
Let's call [tex]V_2[/tex] the volume of the large sphere. We know that it has a radius of 2r. So:
[tex]V_2=\frac{4}{3}\pi (2r)^3[/tex]
[tex]V_2=\frac{4}{3}*8\pi r^3[/tex]
Now we calculate the quotient of the volumes
[tex]\frac{V_2}{V_1}=\frac{\frac{4}{3}*8\pi r^3}{\frac{4}{3}\pi r^3}\\\\\frac{V_2}{V_1}=\frac{8r^3}{r^3}\\\\\frac{V_2}{V_1}=8[/tex]
The answer is the option d
Geometric sequence -1, -5, -25, -125 the 9th term
Answers
Final answer:
The 9th term of the geometric sequence -1, -5, -25, -125 is found to be -390625, using the formula for a geometric sequence nth term with a common ratio of 5.
Explanation:
To find the 9th term of the geometric sequence -1, -5, -25, -125, we need to determine the common ratio and apply the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and r is the common ratio.
The common ratio (r) is the factor that each term is multiplied by to get the next term. In this sequence, r is obtained by dividing the second term by the first term: r = -5 / -1 = 5. Therefore, to find the 9th term, we use the formula with a1 = -1, r = 5, and n = 9:
a9 = -1 × 5(9-1) = -1 × 58 = -390625
So, the 9th term of the geometric sequence is -390625.
Which statement accurately explains whether a reflection over the Y axis and a 270° counterclockwise rotation would map figure ACB onto itself?
Answers
When you reflect point C over (3,4) -> (-3,4) rotate 270 counter clockwise (-3,4) -> (4,3)
Neither the reflection over the y-axis nor the 270° counterclockwise rotation would map figure ACB onto itself.
Explanation:To determine whether a reflection over the y-axis and a 270° counterclockwise rotation would map figure ACB onto itself, we need to analyze the effects of these transformations.
A reflection over the y-axis would change the x-coordinates of the points, but not the y-coordinates. So, figure ACB would not be mapped onto itself after a reflection over the y-axis.A 270° counterclockwise rotation would change the position of the points by rotating them around the origin. After a 270° counterclockwise rotation, figure ACB would not be mapped onto itself as the shape and position of the points would change.Therefore, neither the reflection over the y-axis nor the 270° counterclockwise rotation would map figure ACB onto itself.