Answer:
t(1) = -3.5, Recursive equation is t(n) = t(n-1) + 4.5
Step-by-step explanation:
t(n)=4.5n-8
Let find the sequence
Plug in n=1,2,3,4.....
n=1 t(1)=4.5(1) -8= -3.5
n=2 t(2)=4.5(2) -8= 1
n=3 t(3)=4.5(3) -8= 5.5
n=4 t(4)=4.5(4) -8= 10
so sequence is -3.5, 1, 5.5, 10................
Now we find the common difference
1 - (-3.5) = 4.5
5.5-1 = 4.5
10 - 5.5 = 4.5
common difference d = 4.5
Formula for recursive function is
t(n) = t(n-1) + d
We got d= 4.5
t(n) = t(n-1) + 4.5 , also t(1) = -3.5
Final answer:
The student seems confused between a linear and a quadratic equation. The provided equation is linear (t(n) = 4.5n - 8), while the supporting information describes how to solve a quadratic equation using the quadratic formula with specified coefficients.
Explanation:
The question posed by the student pertains to a recursive equation, which is a formula that defines each term of a sequence using preceding terms. However, the recursive equation mentioned (t(n) = 4.5n - 8) seems to be a simple linear equation rather than a recursive one. The student may be asking for a recursive form, but has provided a linear formula instead.
The additional information provided references a quadratic equation where the coefficients a, b, and c are given as 4.90, ±14.3, and ±20.0, respectively. The general form of a quadratic equation is at² + bt + c = 0. The solutions to this quadratic equation can be found using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). To find the solutions to the given quadratic equation, the values of a, b, and c would be substituted into the quadratic formula and the resulting expression solved.
For clarity, it seems there might be some confusion in the question as it mixes linear and quadratic equations. It is important to correctly identify the type of equation and its coefficients to proceed with finding a solution.
What is the length of PR
Answer:
B 7
Step-by-step explanation:
Since the triangles are similar by AAA
We can use ratios to find the length x (which is PR)
5 15
-------- = ------------
x 21
Using cross products
5 * 21 = 15 *x
Divide each side by 15
5/15 * 21 = 15x/15
1/3 * 21 =x
7 =x
Answer:
here is how i did it.
travis has three moths to save money for a trip. an airplane ticket costs more than 300 . if he saves the same amount of money ,a,each month,how much does he need to save each month to pay for the ticket
Answer:
He needs to save $100 a month.
Step-by-step explanation:
Since Travis needs $300 in 3 months, you divide 300 by 3.
300/3 = 100
Therefore, Travis needs to save $100 a month.
Travis needs to save more than $100 each month for three months to afford an airplane ticket that costs more than $300.
Explanation:To determine how much Travis needs to save each month to pay for his airplane ticket, which costs more than $300, we can set up an equation. Let's assume the minimum amount he needs for the ticket is $300. If Travis is saving for three months, he needs to divide the total cost of the ticket by the number of months he has to save.
Let the amount he needs to save each month be represented by a. Therefore, we have the following equation: 3a = 300, which simplifies to a = 300/3. Solving this, we find that a = $100.
However, since the ticket costs more than $300, he will need to save slightly more than $100 each month.
30 pts + BRAINLIEST
Using the letters in the word INNOVATIVE, find the number of permutations that can be formed using 4 letters at a time. Show your work or explain how you got your answer.
Answer:
Number of permutations = 5040
Step-by-step explanation:
We are given the word 'INNOVATIVE', that has total 10 letters.
Now, we are asked to form words using exactly 4 letters at a time i.e. out of 10 letters we are using 4.
Therefore, the number of permutations that can be formed using 4 letters are = P(10,4)
i.e. [tex]10_{P_{4} }[/tex]
= [tex]\frac{10!}{(10-4)!}[/tex]
= [tex]\frac{10!}{6!}[/tex]
= [tex]\frac{10*9*8*7*6!}{6!}[/tex]
= 10*9*8*7
= 5040
Answer: 5040
Step-by-step explanation:
npr = n! / (n - r)!
numbers of letters given = 10
permutation that can be formed using 4 letters at a time= 10 P ₄
=10! / (10 - 4)! = 10! / 6!
= 10 ×9 ×8×7 ×6! /6! ( the 6! will cancel out)
= 10×9 ×8×7=5040
Therefore, the number of permutations are 5040
The gray figure is the image of the black figure after a dilation. Which represents the dilation?
Answer:
B.
Step-by-step explanation:
The original function in 8 wide, the new function is 4 wide. That means the original function was shrunk by half (4/8)
(x,y)--> (1/2x, 1/2y) represents the dilation.
What is Dilation?Dilation defines changing the size of an object without changing its shape.
How to Solve the problem?This problem can be solved by following steps
In black figure X-axis = 8 units , Y axis = 8 units.In grey figure X-axis = 4 units , Y axis = 4 units.X-axis of grey figure = 1/2*X-axis of Black figure.= 1/2*8
= 4 units.
Y-axis of grey figure = 1/2*Y-axis of Black figure
= 1/2*8
= 4 units
Therefore,
(x,y)--> (1/2x,1/2y) represents the dilation.
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each bowl can hold 1/4 cup of nuts. Taisha has 3 3/8 cup of nuts. How many full bowls can she make?
Answer:
13 bowls
Step-by-step explanation:
To figure out how many bowls of nuts she can make, we divide how many cups of nuts she has by how many cups of nuts in a bowl
3 3/8 ÷ 1/4
Lets change 3 3/8 into an improper fraction
3 3/8 = (8*3 +3)/8 = 27/8
27/8 ÷ 1/4
Copy dot flip
27 /8 * 4/1
27/2
2 goes into 27 13 times with 1 left over
13 1/2
She will have 13 full bowls of nuts
How do you set up an equation for this problem??
Answer:
2x + 7 = 3x - 5
Step-by-step explanation:
Since triangle RTS is isosceles, RT is congruent to RS. So you can set up the equation 2x + 7 = 3x - 5 to find x. Then you can input the value of x into 2x +7 or 3x - 5 to find the measure of the congruent sides.
What is the slope of the line represented by the equation 6y-14x=5
Answer:
14/6
Step-by-step explanation:
To find the slope, we can put it into slope intercept form. So 6y=14x+5. So y=14/6+5/6.
A survey at your school found that 792 in 1,220 students have a cell phone. What percent of the a poinp students in school have a cell phone? Round to the nearest hundredth where necessary
Answer: 100/1220*792= 64.9 have cell phones.
Step-by-step explanation:
Answer:
The percentage of students with cell phone is 64.92%
Step-by-step explanation:
Given
Sample Size = 1,220
Number of student with cell phones = 792
Required
Percentage of students with cell phone
To calculate the percentage of students with cell phone, we take a ratio of the number of students with cell phone to the sample size.
Mathematically, this is represented as
[tex]Percentage = \frac{Students-with-cell-phone}{Sample Size}[/tex]
By Substitution,
[tex]Percentage = \frac{792}{1220}[/tex]
[tex]Percentage = 0.64918032786[/tex]
[tex]Percentage = 64.918032786[/tex]%
[tex]Percentage = 64.92[/tex]% Approximated to nearest hundredth
Hence, the percentage of students with cell phone is 64.92%
What is the volume of a cylinder with a diameter of 6m and a height of 5m?
Final answer:
The volume of a cylinder with a diameter of 6m and a height of 5m is calculated using the formula V = πr²h. With a radius of 3m, the volume is 141.39m³.
Explanation:
To find the volume of a cylinder with a diameter of 6m and a height of 5m, we first need to calculate the radius of the cylinder. The radius is half of the diameter, so in this case, the radius (r) is 3m. The formula for the volume (V) of a cylinder is V = πr²h, where π (pi) is approximately 3.142, r is the radius, and h is the height of the cylinder.
Using this formula, we get:
V = π × (3m)² × 5m
V = 3.142 × 9m² × 5m
V = 3.142 × 45m³
V = 141.39m³
Therefore, the volume of the cylinder is 141.39 cubic meters.
Abbie recorded the temperatures at which two oils freeze: Oil Temperature Cottonseed oil −48.1 °C Coconut oil 24.8 °C Which statement about the temperatures at which these oils freeze is true? Coconut oil freezes at a higher temperature than cottonseed oil because 24.8 °C < −48.1 °C. Coconut oil freezes at a lower temperature than cottonseed oil because 24.8 °C < −48.1 °C. Coconut oil freezes at a higher temperature than cottonseed oil because 24.8 °C > −48.1 °C. Coconut oil freezes at a lower temperature than cottonseed oil because 24.8 °C > −48.1 °C.
Answer:
The correct answer is option (C).
Coconut oil freezes at a higher temperature than cottonseed oil because 24.8 > -48.1
Step-by-step explanation:
We have been given the freezing temperatures of cottonseed oil and coconut oil. The freezing temperature of cottonseed oil is -48.1 degree celsius and the same for coconut oil is 24.8 degree celsius.
We are supposed to compare the two freezing temperatures. We know that 24.8 is higher than -48.1, therefore, we can conclude that freezing temperature of coconut oil is higher than the freezing temperature of cottonseed oil because 24.8 is more than -48.1. Thus, correct answer is option (C).
Answer:
C
Step-by-step explanation:
what is m+4(2m-3)=-3
Answer:
m = 1
Step-by-step explanation:
distribute and simplify the left side of the equation
m + 8m - 12 = - 3
9m - 12 = - 3 ( add 12 to both sides )
9m = 9 ( divide both sides by 9 )
m = 1
In a certain bag of candies, 2/5 of the candies are grape flavored and 3/10 are lemon flavored. What fraction of the candies is either grape flavored or lemon flavored?
A. 1/10
B. 2/3
C. 7/10
To find the fraction of candies that are either grape or lemon flavored, we add the fractions representing each flavor: 2/5 for grape and 3/10 for lemon. After finding a common denominator, we get 4/10 + 3/10, yielding 7/10 of the candies being either grape or lemon-flavored.
To find the fraction of candies that are either grape-flavored or lemon-flavored, we need to add the fractions that represent each flavor. We are told that 2/5 of the candies are grape-flavored and 3/10 are lemon-flavored.
First, we need a common denominator to add these two fractions. The least common denominator for 5 and 10 is 10. We can convert 2/5 to a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2. This gives us 4/10. Now we can add:
4/10 (grape flavored)
+ 3/10 (lemon flavored)
= 7/10 (either grape or lemon flavored)
Hence, the fraction of the candies that are either grape-flavored or lemon-flavored is 7/10.
On Monday Kennedy spent $2 on lunch. On Tuesday she spent $1 on a snack on Wednesday, her sister gave her $3. Graph the integers on the number line.
Answer:
-2, -1, 3.Step-by-step explanation:
Money per day:On Monday: $2 on lunch.
On Tuesday: $1 on a snack.
On Wednesday: her siter gave her $3.
Now, before we graph the integers, first you need to think about those number and their meaning. If the number represents debt or expenses, then it must be a negative number. But, if the number represents money received, then it must be a positive number.
So, we have the following integer: -2, -1, 3.
If we graph these integers, it would be like the images attached shows.
the permitir of the garden is (6x+2) units. Find the length of the missing side .
Answer: ? = x + 1
Step-by-step explanation:
The perimeter of the garden is x + 3x + 1 + x + ?
The perimeter of the garden is also (6x + 2)
Therfore:
x + 3x + 1 + x + ? = 6x + 2
Collect like terms:
5x + 1 + ? = 6x + 2
Subtract 5x from both sides:
1 + ? = x + 2
Subtract 1 from both sides:
? = x + 1
You cannot find ? as a number, only in terms of x.
At a pizzeria, the ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday. The pizzeria made a total of 84 pizzas that day. How many of those pizzas were topped with vegetables?
A. 12
B. 36
C. 48
D. 63
Answer:
Option B is correct
36 pizzas were topped with vegetables
Step-by-step explanation:
Let x be the number.
As per the statement:
At a pizzeria, the ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday.
The ratio of pizza topped with meat to pizzas topped with vegetables = 4 : 3
then;
the number of pizza topped with meat = 4x
and
the number pizza topped with vegetables = 3x
It is also given that the pizzeria made a total of 84 pizzas that day.
[tex]\text{Total Pizzas} = \text{Number of pizzas topped with meat}+ \text{Number of pizzas topped with vegetables}[/tex]
Substitute the given values we get;
[tex]84 = 4x+3x[/tex]
Combine like terms;
[tex]84= 7x[/tex]
Divide both sides by 7 we get;
12 = x
The pizza were topped with vegetables = 3x = 3(12) = 36
therefore, 36 pizzas were topped with vegetables
Answer:
The correct answer is option B.
Step-by-step explanation:
The ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday.
Let the pizza's topped with meat be 4x
Let the pizza's topped with vegetable be 3x
Total pizzeria made a Saturday = 84
4x + 3x = 84
7x = 84
x = [tex]\frac{84}{7}=12[/tex]
Pizza's topped with meat = 4x = 4 × 12 = 48
Pizza's topped with vegetable = 3x = 3 × 12 = 36
12 pizzas were topped with vegetables.
What is the slope of A-line that is perpendicular to the line shown, (0,-2) (-3,2)
Answer:
3/4
Step-by-step explanation:
Answer:
-3/4 I think hope this helps
Beth walked around her neighborhood. In 1/2 hour, she walked 1 1/4 miles. What was Beth’s rate in miles per hour
Answer:
2.5 miles per hour
Step-by-step explanation:
ok, so we already know how long she walked in 1/2 hour and we need to find out how many miles in one full hour. So, i multiplied 1 1/4 times two to make up the one full hour and I got 2.5 miles. So the rate is 2.5 mph.
Speed of walking is 2.5 miles per hour
Given that;
Time taken to walk = 1/2 hour = 0.5 hour
Distance cover = 1¹/₄ = 5 / 4 = 1.25 miles
Find:
Speed of walking
Computation:
Speed of walking = Distance cover / Time taken
Speed of walking = 1.25 / 0.5
Speed of walking = 2.5 miles per hour
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Find the value of y when x = 4 in the equation 1/7(3x + y) = x Show your work help
whats -2/3+(-7 4/9) please solve
Answer:-8.1111111
Step-by-step explanation:
Given a circle with measures of (C, d, and r) and a circle with measures of (C', d', and r'), what is r' if C/C' = 0.75 and d = 6.0?
A) 2
B) 4
C) 8
D) 12
Answer:
B
Step-by-step explanation:
All circles are similar and therefore proportional. C/C' is the ratio of Circle C to Circle C'. Since it is 0.75, this means that C is 75% of C'. We know that radius of C will also be 75% of the radiuc of C'. We can the radius because we know the diameter of Circle C is 6. The radius is therefore 3. 3 is 75% of 4. So r/r' or 3/4=0.75. r/ must be 4.
Answer: B) 4
Step-by-step explanation:
Got this right on USA test prep
The number of calories varies directly with the massive cheese if there are 200 cal in 50 g how many calories are in 70 g of cheese
Answer:
280 calories
Step-by-step explanation:
200 / 50 = 4
1 gram = 4 calories
70 * 4 = 280
Therefore, there are 280 calories in 70 grams of cheese.
A 10 meter long ladder rests against a vertical wall so that the distance between the foot of the ladder and the wall is 2 meter. Find the angle the ladder makes with the wall and height above the ground at which the upper end of the ladder touches the wall. Round your answer to the nearest hundredth of a degree if necessary.
Answer:
1. The angle ladder makes with the wall is 11.54°
2. The height above the ground at which the upper end of the ladder touches the wall is 9.80 m
Step-by-step explanation:
∠A is what we are trying to find. Also AC is the length we are trying to find, as well.We see that the side opposite of ∠A and the hypotenuse (side opposite of 90 degree angle) of the triangle are known. The ratio that relates these two sides are SINE.
We know,
[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]
Thus we can write:
[tex]sin(A)=\frac{2}{10}\\sin(A)=\frac{1}{5}[/tex]
To find ∠A, we take the inverse sine of [tex]\frac{1}{5}[/tex]. Our answer is:
[tex]sin(A)=\frac{1}{5}\\A=sin^{-1}(\frac{1}{5})\\A=11.54[/tex]
Thus the angle ladder makes with the wall is 11.54°
Second part of the question asks for the height above the ground at which the upper end of the ladder touches the wall, this is the length of AC.
Given the angle we found, we see that the side AC is adjacent of the angle and we also know the hypotenuse. The ratio that relates these 2 sides is COSINE.
We know,
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
Thus, we can write:
[tex]cos(11.54)=\frac{AC}{10}[/tex]
Cross multiplying and solving for AC, gives us:
[tex]cos(11.54)=\frac{AC}{10}\\AC=10*cos(11.54)\\A=9.80[/tex]
Thus, the height above the ground at which the upper end of the ladder touches the wall is 9.80 m
On a piece of paper, graph y < 3/4 x+2 Then determine which answer matches the graph drew.
Step-by-step explanation:
Given inequality is [tex]y<\frac{3}{4}x+2[/tex].
To graph that inequality, first we need to graph the line [tex]y=\frac{3}{4}x+2[/tex]. Then shade it for the inequality symbol <.
Graphing line can be done using two points.
plug x=0 into [tex]y=\frac{3}{4}x+2[/tex], we get:
[tex]y=\frac{3}{4}*0+2=2[/tex]
Hence first point is (0,2)
Similarly plug any random number for x say x=4, we get:
[tex]y=\frac{3}{4}*4+2=5[/tex]
Hence first point is (4,5).
Now we just need to graph both points and join them by a dotted line. because we have < not <=.
Next part is to test for shading.
Which can be done using any test point which is not on the given line. Say (0,0)
plug x=0,y=0 into [tex]y<\frac{3}{4}x+2[/tex].
[tex]0<\frac{3}{4}*0+2[/tex]
[tex]0<0+2[/tex]
0<2
which is true, hence shading will be in direction of test point (0,0).
Hence final answer will be the choice which looks like the graph attached below;
The correct answer is 2. A dashed line with the shaded area below the line.
To graph y < 3/4 x + 2, first find the y-intercept, which is the point where the line crosses the y-axis.
This happens when x is 0, so the y-intercept is 2.
The slope of the line is 3/4, so for every 3 units you move up, you must also move 4 units to the right.
Start at the y-intercept and move 3 units up.
Then, move 4 units to the right.
Repeat this process until you have graphed a few points.
The line should continue in this direction forever.
The shaded area below the line represents the values of y that are less than 3/4 x + 2.
Here are the possible answers:
A solid line with the shaded area below the line.A dashed line with the shaded area below the line.A solid line with the shaded area above the line.A dashed line with the shaded area above the line.The correct answer is 2. A dashed line with the shaded area below the line.
The dashed line indicates that the inequality is not strict, meaning that the line is allowed to touch the shaded area.
The shaded area below the line indicates that the values of y that are less than 3/4 x + 2 are represented by the points below the line.
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Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for $1.10/lb. How many pounds of lollipops are in the mixture?
Answer:
20 lbs
Step-by-step explanation:
Plz help me thank you guys so much!!!!! oops part of my face is also in the pics just ignore that
1) All three are right A.K.A 4
4) The answer is also 4).
Help would be greatly appreciated! 20 points...
3. In picture below...
4. The equation for line m is y = 1/2x - 5 . Use this information and these descriptions to write an equation for line n, line p, and line r.
(a) Line m and line n have no solutions. Write an equation that can represent line n.
(b) Line m and line p have infinitely many solutions. Write an equation that can represent line p.
(c) Line m and line r have one solution. Write an equation that can represent line r.
5. Identify whether each statement about a system of linear equations is true or false. For each false statement, change a word to make it a true statement.
(a) A system with two linear equations may have two solutions.
(b) Lines in a system with no solutions are always parallel.
(c) The solution when a system of equations has only one solution is the ordered pair at which the equations' graphs intersect.
(d) Equations that have different slopes have no solution.
Answer:
Step-by-step explanation:
Three
3a
Two lines that have slopes where 1 is the negative of the other will intersect some where once and only once. I've included a graph for this.
3b
If you multiply the top line by 2 you get the bottom line. They are the same line. There's an infinite number of solutions.
3C
They will intersect once. On your paper just extend both lines. They intersect.
3D
If they are parallel, they never intersect. No solution.
Four
what's at the tail end of four. y = 1/2x - ???? I'll give it a value. You'll have to change the value to get it to work properly.
A
m: y = 1/2x - 4 The 4 is mine. Change it to what it says.
n: y = 1/2x - 8 Any value except - 4 will work.
B
m: y = 1/2x - 4
n : -2y = -x + 8 They are really the same equation. n = -2*m
C
m: y = 1/2 x - 4
n: y = x + 3
I'm going to let you work your way through 5. There should be enough in 3 and 4 to get five.
Five
A: False
B: This question is not true, but you probably don't have enough math to say why. Bend your right arm so it is parallel to your belt. Above that "line" bend your left arm so it is over the right arm in just one place. The left arm should be pointing towards the wall of your room. Those two are not parallel nor do they have any meeting place.
C: True
D: False
Determine the rate of change of f , f(x)= 6x-5
Answer:
6
Step-by-step explanation:
the rate of change is given by the slope of the line
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
f(x) = 6x - 5 is in this form
with slope m = 6 ← rate of change
Answer:
6
Step-by-step explanation:
We are given the function f(x) = 6x-5 for which we have to determine its rate of change.
The rate of change is given by the slope of a line.
We know that the standard form of an equation of a line is given by:
y = mx + c
where m is the slope.
If we observe the given function, we can notice that is in the form y = mx + c where the slope (m) is 6.
Therefore, the rate of change for the function f(x) = 6x - 5 is 6.
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If 5x+6=10,what is the value of 10x+3
Marisa painted 1/2 of her bedroom in 3/4 of a hour at this rate how long will it take her to paint the entire room
Answers
3/8 of an hour
8/3 of an hour
4/6 of an hour
6/4 of an hour
At the same rate, it would take Marisa 6/4 of an hour to paint the entire room. This is a ratio problem, specifically dealing with rates and proportional relationships.
Explanation:Since Marisa painted 1/2 of her room in 3/4 of an hour, to paint the entire room would take double that time. When you double 3/4, you get 6/4. Therefore, at the same rate, Marisa would need 6/4 of an hour to paint the entire room.
This problem is a basic ratio problem related to rates and proportional relationships, common topics in middle school math. The rate in this case is painting speed, half a room per 3/4 of an hour. Thus, when we double the room space to be painted (from half a room to a full room) we should also double the required time.
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