Answer:
The closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]
Step-by-step explanation:
Given that the first term [tex]a_{1}=0.3[/tex] and [tex]a_{n+1}=a_{n}+0.75[/tex]
To find the closed linear form for the given sequence
The formula for arithmetic sequence is
[tex]a_{n}=a_{1}+(n - 1)d[/tex] (where d is the common difference)
The above equation is of the given form [tex]a_{n+1}=a_{n}+0.75[/tex]
Comparing this we get d=0.75
With [tex]a_{1}=0.3[/tex] and d=0.75
We can substitute these values in [tex]a_{n}=a_{1}+(n - 1)d[/tex]
[tex]a_{n}=a_{1}+(n - 1)d[/tex]
[tex]=0.3+(n-1)(0.75)[/tex]
[tex]=0.3+0.75n-0.75[/tex]
[tex]=-0.45+0.75n[/tex]
Rewritting as below
[tex]=0.75n-0.45[/tex]
Therefore [tex]a_{n}=0.75n-0.45[/tex]
Therefore the closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]
Which of the following systems of inequalities has Point C as a solution?
A:
[tex]f(x)\leq 3x+4\\g(x)\leq -\frac{1}{2} x-5\\[/tex]
B:
[tex]f(x)\geq 3x+4\\g(x)\leq -\frac{1}{2} x-5[/tex]
C:
f(x) ≤ 3x + 4
[tex]g(x)\geq -\frac{1}{2}x-5[/tex]
D:
f(x) ≥ 3x + 4
[tex]g(x)\geq -\frac{1}{2} x-5[/tex]
Answer:
Option A.
[tex]f(x)\leq 3x+4[/tex]
[tex]g(x) \leq-\frac{1}{2}x-5[/tex]
Step-by-step explanation:
we know that
If point C is a solution of the system of inequalities, then point C must satisfy both inequalities
Point C is located below the solid line f(x) and below the solid line g(x)
so
The shaded region of the solution set of the system must be below of the inequality f(x) and must be below of the inequality g(x)
therefore
The system is
[tex]f(x)\leq 3x+4[/tex]
[tex]g(x) \leq-\frac{1}{2}x-5[/tex]
Answer:
B
Step-by-step explanation:
Please answer the 3 questions above. SHOW YOUR WORK
If you don’t show your word or reply with stuff like “aldbaldbs” or “Idk the answer” I’ll report your account!
Answer:
1. A
2. (6, 0.7)
3.
[tex]10.99D \leq 90.01[/tex]
and
[tex]10.99D + 9.99 \leq 100[/tex]
Step-by-step explanation:
1.
The equation to solve is:
[tex]Ax+4Ax=51+2Ax[/tex]
The variable is "x", so we take all the terms with x's and take the number to one side. Then we add up the like terms of x's and solve for x. Shown below:
[tex]Ax+4Ax=51+2Ax\\Ax+4Ax-2Ax=51\\x(A+4A-2A)=51\\x(3A)=51\\x=\frac{51}{3A}\\x=\frac{17}{A}[/tex]
x = 17/A
Correct answer is A
2.
The equation is:
[tex]10y=3x-11[/tex]
The point that would lie on the graph is the point when put, makes the equation true. So we check each point and see if the equation holds:
[tex]10y=3x-11\\10(0.5)=3(2)-11\\5\neq -5[/tex]
first point doesn't lie on the graph.
[tex]10y=3x-11\\10(1)=3(4)-11\\10 \neq 1[/tex]
second point doesn't lie on the graph.
[tex]10y=3x-11\\10(0.7)=3(6)-11\\7=7[/tex]
This point lies on the graph. So, this is the answer.
Correct answer is (6, 0.7)
3.
Let Miguel buy D DVDs. Each costing 10.99, that would make the cost:
10.99D
Shipping cost entire order is 9.99, so this would be added to DVD cost. Total cost:
10.99D + 9.99
This total cost can be NO MORE THAN 100, so this expression would be equal to or less than 100, so we can write:
[tex]10.99D + 9.99 \leq 100[/tex]
If we take 9.99 to the right side and subtract, it becomes:
[tex]10.99D \leq 90.01[/tex]
First choice is correct.
Second choice, clearly, isn't correct.
Third choice, similarly, isn't correct as well.
Fourth choice, because of "+" sign on right side (of 9.99) is also incorrect.
Fifth choice is what we initially got, so this is correct.
First and Fifth Choice is right.
What is the answer???
Answer:
20
-
3
Step-by-step explanation:
Out of 1,000 tickets in a raffle, one ticket will win a $710 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?
A flower shop has 11 red roses seven pink roses nine white roses and three yellow roses in stock one type of roses Ramsey selected for a flower arrangement what Is the probability that the selected rose is red or yellow
Answer:
11/147
Step-by-step explanation:
11 + 7 + 3 = 21
chances of red = 11/21
and chances of yellow = 3/21
3/21 = 1/7
11/21 x 1/7 = 11/147
Answer:
14:30
Step-by-step explanation:
Okay so your looking for the probability of red or yellow roses so you would combine the numbers of red and yellow roses then add all the roses up together, all the red and yellow are 14 and there are 30 roses in the shop so the answer would be 14:30
5) Linda picked a basket of apples. She gave half of the apples to a neighbor, then 10 apples to her mother, then half of the remaining apples to her best friend, and she kept the remaining 3 apples for herself. How many apples did she start with in the basket?
I need help this is due this Wednesday on my college math class! ASAP!!! This needs to be shown full work for full credit!!
Answer:
is it 8 apples to her mother or 10 since I had this exact problem?
Step-by-step explanation:
Ashe started with 32 apples in the basket initially.
How to find half of something ?To find the half of something just multiply 1/2 with the given value.
According to the given question Linda picked a basket of apples.
Assuming she had x apples initially.
She gave half of the apples to the neighbour,Therefore she now has (x - 1/2x) apples which is = 1/2x apples.
Then she gave 10 to her mother,So the remaining apples she has now is
= ( 1/2x - 10 ) apples
= (x - 20)/2.
Then she gave half of the apples to her best friend so the no. of apples she has now is (x - 20)/2×1/2 which is = (x - 20)/4 and she kept the remaining 3.
∴ (x - 20)/4 = 3
x - 20 = 12
x =32.
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Find x, y and z for the following triangle.
Please show the steps with details, Thanks!
Answer:
x = 100°
y = 125°
z = 55°
Step-by-step explanation:
A straight line is 180°
A triangle is 180°
Solve in this order:
X: 180 - 80 = 100
Z: 180 - 80 - 45 = 55
Y: 180 - 55 = 125
A square has an area of 44.89 inches squared. How do I get the length of the diagonal?
Answer:
6.7√2 in ≈ 9.48 in
Step-by-step explanation:
First, use the area of the square to find the side length.
A = s²
44.89 in² = s²
s = 6.7 in
The diagonal of a square divides it into 45-45-90 triangles. You can use Pythagorean theorem to find the length of the diagonal.
c² = a² + b²
c² = (6.7 in)² + (6.7 in)²
c = 6.7√2 in
c ≈ 9.48 in
Answer: 6.7√2
Step-by-step explanation: Let's start this problem by drawing a picture of a square with a diagonal of length x.
Now to find the length of the diagonal, let's first find the length of a side of the square. To find the length of a side, remember that the formula for the area of a square is S² and since we know that the area of the given square is 44.89 inches, we can set up the equation 44.89 = S².
Square rooting both sides, we have 6.7 = S so we can give the side of our square a length of 6.7. Now to find the value of x, it's important to understand that the diagonal of a square creates 45° 45° 90° triangles and in a 45° 45° 90° triangle, the hypotenuse = √2 × leg.
So we have x = 6.7√2.
So the length of the diagonal of the square is 6.7√2 inches.
Image provided.
MAT
8. The development budget, C, for a computer game company is described by the equation
C = $50,000t + $10,000, where t is the number of years since the company's creation.
Which statement is true?
A. Each year development expenses increase by $50,000.
B. Each year development expenses increase by $60,000.
C. Each year development expenses are $50,000.X
D. Each year development expenses are $60,000.
Answer:
B
Step-by-step explanation:
B. Each year development expenses increase by $60,000.
Answer:
B. Each year development expenses increase by $60,000.
Step-by-step explanation:
Savannah can ride her skateboard 2 miles in 10 minutes. How many miles can she ride her skateboard in 1.5 hours?
Answer:
18 miles in 1.5 hours
Step-by-step explanation:
2 miles = 10 minutes
90 minutes (1.5 hours) / 10 minutes = 9
Multiply
2 miles (9) = 10 minutes (9)
18 miles = 90 minutes
18 miles in 1.5 hours
Hope this helps :)
Factor the polynomial by its greatest common monomial factor.
44k^5-66k^4+77k^3
Answer:
11k^3 (4k^2 - 6k +7)
Step-by-step explanation:
Take out the obvious GCF of 11
11 (4k^5 - 6k^4 + 7k^3)
Take out the GCF of k^3 (from the terms in the parentheses)
11k^3 (4k^2 - 6k + 7)
.
Factor the polynomial by its greatest common monomial factor of 44k^5-66k^4+77k^3 is:
Take out the obvious GCF of 11
11 (4k^5 - 6k^4 + 7k^3)
Take out the GCF of k^3 (from the terms in the parentheses)
11k^3 (4k^2 - 6k + 7)
How do you find a monomial factor?
To find the greatest common factor (GCF) among monomials, take each monomial and write it as high factorization. Then, identify the factors commonplace to each monomial and multiply the commonplace elements collectively.
Steps to Factoring a Monomial from a Polynomial
determine the GCF of all terms within the polynomial.Write each term because of the product of the GCF and some other factor.Use the distributive property to issue out the GCF.Conclusion: factoring trivial factors greatest common factor high polynomials whole factorization big concept common monomial factoring is the procedure of writing a polynomial as a made from two polynomials, considered one of that's a monomial that elements each term of the polynomial.
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What do the following two equations represent? 4x-2y=-5 and -2x+3y=-3
Choose 1 answer:
A) equal lines
B) parallel lines
C) perpendicular lines
D) none of the above
*40 points*
Answer:
Step-by-step explanation:
4x - 2y = -5
-2y = -4x - 5
y = 2x + 5/2.....slope here is 2
-2x + 3y = -3
3y = 2x - 3
y = 2/3x - 1.....slope here is 2/3
NONE OF THE ABOVE.....they are not the same line....they are not parallel because they dont have the same slope....they are not perpendicular because they do not have negative reciprocal slopes
Answer:
this would be none of the above.
Step-by-step explanation:
its not equal because when solving, x and y isnt the same for both equations.
i cant explain the rest, my apologies but if u use a website called *desmos* you can put up equations and itll graph them for you. :3
f(x) = x2 + 3x + 4. Is it quadratic, linear, or neither
Answer:
Linear
Explanation:
The first image attached below is the problem graphed. That is a linear line.
The second image is an example of a quadratic line.
This is how you can tell the line is linear.
Find the variable x.
Answer:
x = 5
Step-by-step explanation:
7x is a secant- secant angle and has measure equal to half the difference of the intercepted arcs, that is
7x = 0.5(22x + 10 - 50)
7x = 0.5(22x - 40) ← distribute
7x = 11x - 20 ( subtract 11x from both sides )
- 4x = - 20 ( divide both sides by - 4 )
x = 5
What is the remainder of 428/19. I know it equals 22, but what’s the remainder
Answer:
the remainder is 10
Step-by-step explanation:
Answer:
R=10
Step-by-step explanation:
1. 428/19=22
2. R=10
Steps for checking your work:
1. Multiply the divisor by the answer (aka quotient)
2. After that, add the remainder to the answer you got from doing step 1 for checking your work (aka proudct, since you multiplied)
The solution to a system of linear equations is (-3,-3). Which system of linear equations has this point as its solution?
x-5y = -12 and 3x+2y = -15
OX-5y=-12 and 3x+2y = 15
x-5y = 12 and 3x+2y = - 15
X-5y = 12 and 3x + 2y = 15
Answer:
Option c) is correct.
That is x-5y=12 and 3x+2y=-15 are the system of linear equations satisfies the point (-3,3) so this is the solution.
Step-by-step explanation:
To verify that which system of linear equations having the solution (-3,-3)
Let [tex]x-5y=12\hfill (1)[/tex]
and [tex]3x+2y=-15\hfill (2)[/tex]
To solve it we have to use elimination method
First multiply the equation(1) into 3 we get
[tex]3x-15y=36\hfill (3)[/tex]
Now subtracting the equations (2)and (3) the signs may vary in the second equation we get
[tex]3x-15y=36[/tex]
[tex]-3x-2y=+15[/tex]
________________
[tex]-17y=51[/tex]
_______________
[tex]y=-\frac{51}{17}[/tex]
[tex]y=-3[/tex]
Now substitue the value y=-3 in equation (1) we get
[tex]x-5y=12[/tex]
[tex]x-5(-3)=12[/tex]
[tex]x=12-15[/tex]
Therefore x=-3
Therefore the solution is (-3,-3)
Therefore Option c) is correct.
That is x-5y=12 and 3x+2y=-15 are the system of linear equations satisfies the point (-3,3) so the solution is (-3,-3).
A truck carries apples, grapes, and blackberries in the ratio of 4:3:4 if the apple weighs 160 pounds how much does the truckload of fruit weigh in total
Answer:
160/x = 4/3
x = (160/4)(3) = 40(3) = 120
Apples: 160 pounds
Grapes: 120 pounds
Blackberries: 160 pounds
The total weight of this truckload of fruit is 160 + 120 + 160 = 440 pounds.
To find the total weight of the truckload of fruit with apples weighing 160 pounds in a ratio of 4:3:4, calculate the total ratio parts and apply it to the weight of apples. The total weight of the fruit is 440 pounds.
Explanation:The truck carries apples, grapes, and blackberries in the ratio of 4:3:4.
To find the total weight, you need to calculate the total ratio parts, which is 4 + 3 + 4 = 11 parts. Then, for apples alone, 4 parts represent 160 pounds, so each part is 160/4 = 40 pounds. The total weight of the truckload of fruit would be 11 parts * 40 pounds = 440 pounds.
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Which ordered pair is a solution of the equation?
-2 – 4y = -10
Choose 1 answer:
@
Only (3,2)
®
Only (–3, 3)
©
Both (3, 2) and (-3,3)
Neither
Answer: Neither
Step-by-step explanation:
Sally is solving the linear equation 13+4x-9=7x+7-3x. Her final two steps are 4+4x=4x+7 ,4=7 select the statement that correctly interprets Sally’s solution A: The solution is x=0 B: The solution is ordered pair (4.7). C: There is no solution since 4=7 is a false statement D: There are infinitely many solutions since 4=7 is a false statement
Answer:
C. there is no solution since 4=7 is a false statement
Linear equations are equations with a leading degree of 1. This shows that there is no solution since 4 =7 is a false statement
Solving linear equationLinear equations are equations with a leading degree of 1. Given the linear equation
Given
13+4x-9=7x+7-3x
Simplify
4 + 4x = 4x + 7
Collect the like terms
4x - 4x = 7 - 4
0x = 3
This shows that there is no solution since 4 =7 is a false statement
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team tool bella canoed 15 3/4 miles in 5/4 hours. What was their average rate of speed in mph
Average speed is 12.6 miles per hour
Solution:
Given that team tool bella canoed [tex]15\frac{3}{4}[/tex] miles in [tex]\frac{5}{4}[/tex] hours
To find: average rate of speed in miles per hour
From given information,
[tex]distance = 15\frac{3}{4} \text{ miles } = \frac{15 \times 4+3}{4} = \frac{63}{4} \text{ miles}[/tex]
[tex]time = \frac{5}{4} \text{ hours}[/tex]
To find the speed we use the below formula,
[tex]speed = \frac{distance}{time}[/tex]
Substituting the given values we get,
[tex]speed = \frac{\frac{63}{4}}{\frac{5}{4}}\\\\speed = \frac{63}{4} \times \frac{4}{5} = \frac{63}{5} = 12.6[/tex]
Thus average speed is 12.6 miles per hour
The sum of Ava’s and Grace’s age is 35. Ava is one year less than three times Grace’s age. How old is Grace?
Grace is 9 years old. We found this by setting up a system of equations with the information given and solving for Grace's age.
Explanation:We are given two pieces of information about Ava and Grace's ages:
The sum of Ava’s and Grace’s age is 35.Ava is one year less than three times Grace’s age.To find Grace’s age, we can set up a system of equations based on the information provided:
Let G represent Grace’s age.Let A represent Ava’s age.The first equation can be written as:
A + G = 35
From the second piece of information, we can write:
A = 3G - 1
Now, we can substitute the expression for A into the first equation:
3G - 1 + G = 35
Combine like terms:
4G - 1 = 35
Add 1 to both sides:
4G = 36
Divide by 4:
G = 9
So, Grace is 9 years old.
What is the domain of the given function?
{(3, -2), (6, 1), (-1, 4), (5, 9). (-4,0}}
{x|x = -4,-1, 3, 5, 6}
{yl y = -2,0, 1, 4, 9)
{x | x = -4,-2,-1, 0, 1, 3, 4, 5, 6, 9}
{yly= -4,-2,-1, 0, 1, 3, 4, 5, 6, 9)
Answer:
-4,-1,3,5,6
Step-by-step explanation:
The first set because domain is the set of elements giving values of x
At the start of the month, Jodie had sold 885 copies of her new book. At the end of the month, she had sold 1,364 copies of her book. If each book profits $13.97, approximately how much did the book profit in the entire month?
Approximately $ 31419 profit is earned from selling books in entire month
Solution:
Given that Jodie had sold 885 copies of her new book
At the end of the month, she had sold 1,364 copies of her book
We have to determine the profit earned in the entire month
From given information,
Start of month sale = 885 copies
End of month sale = 1364 copies
Total copies of books sold = Start of month sold + end of month sold
Total copies of books sold = 885 + 1364 = 2249
Also given that each book profit is $ 13.97
Profit of 1 book = $ 13.97
Therefore for 2249 books, profit earned is given as:
Profit of 2249 books = $ 13.97 x 2249 = 31418.53
Therefore approximately $ 31419 profit is earned from selling books in entire month
Simplify the expression $416.48÷4= $104.12 please
Answer:
Step-by-step explanation:
Just do the long division and you'll find out.
Raise the fraction to the highest term 1/5 to 15ths=
Final answer:
To raise the fraction 1/5 to 15ths, multiply both the numerator and the denominator by 3 to get the equivalent fraction 3/15.
Explanation:
To raise the fraction 1/5 to 15ths, we need to find an equivalent fraction that has a denominator of 15. To do this, we need to find a number that we can multiply both the numerator and the denominator of 1/5 by to get a new fraction with a denominator of 15. Since 5 multiplied by 3 equals 15, we multiply both the numerator and the denominator of 1/5 by 3.
Thus, we have:
1/5 × 3/3 = 3/15
To raise the fraction 1/5 to 15ths, multiply both the numerator and the denominator by 3 to get the equivalent fraction 3/15.
The fraction 1/5 is equivalent to 3/15 when raised to 15ths.
Which of the ordered pairs in the form X, Y is a solution of this equation
Answer:
The first is a solution, but the second is not
Step-by-step explanation:
we know that
If a ordered pair is a solution of a linear equation, then the ordered pair must satisfy the linear equation (makes the equation true)
we have
[tex]5x-\frac{y}{3}=13[/tex]
Verify the first ordered pair
Part a) we have (2,-9)
For x=2, y=-9
substitute in the linear equation
[tex]5(2)-\frac{(-9)}{3}=13[/tex]
[tex]10-(-3)=13[/tex]
[tex]10+3=13[/tex]
[tex]13=13[/tex] ----> is true
so
The ordered pair satisfy the equation
The ordered pair is a solution of the equation
Verify the second ordered pair
Part b) we have (3,-6)
For x=3, y=-6
substitute in the linear equation
[tex]5(3)-\frac{(-6)}{3}=13[/tex]
[tex]15-(-2)=13[/tex]
[tex]15+2=13[/tex]
[tex]17=13[/tex] ----> is not true
so
The ordered pair not satisfy the equation
The ordered pair is not a solution of the equation
Abby bought two slices of pizza and two bottles of water for $7.25 Cameron bought four slices of pizza and one bottle of water for $8.25 what is the solutionm
The solution is price of 1 slice of pizza is $ 1.542 and price of 1 bottle of water is $ 2.083
Solution:
Let "p" be the price of 1 slice of pizza
Let "b" be the price of 1 bottle of water
Given that Abby bought two slices of pizza and two bottles of water for $7.25
So we can frame a equation as:
two slices of pizza x price of 1 slice of pizza + two bottles of water x price of 1 bottle of water = $ 7.25
[tex]2 \times p + 2 \times b = 7.25[/tex]
2p + 2b = 7.25 ---- eqn 1
Also given that Cameron bought four slices of pizza and one bottle of water for $8.25
So we can frame a equation as:
four slices of pizza x price of 1 slice of pizza + one bottles of water x price of 1 bottle of water = $ 8.25
[tex]4 \times p + 1 \times b = 8.25[/tex]
4p + b = 8.25 ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "p" and "b"
Multiply eqn 2 by 2
8p + 2b = 16.5 --- eqn 3
Subtract eqn 1 from eqn 3
8p + 2b = 16.5
2p + 2b = 7.25
(-) ----------------------
6p = 9.25
p = 1.542From eqn 1,
2p + 2b = 7.25
2(1.542) + 2b = 7.25
2b = 4.166
b = 2.083Thus price of 1 slice of pizza is $ 1.542 and price of 1 bottle of water is $ 2.083
solve the equation -t = 9(t-10)−t=9(t−10)
Answer:
Infinitely many solutions.
Step-by-step explanation:
-t=9(t-10)-t=9(t-10)
-t=9t-90-t=9t-90
-t=8t-90=9t-90
8t-(-t)-90=9t-90
8t+t-90=9t-90
9t-90=9t-90
Answer:
If you mean −t=9(t−10), then the answer is 9, if you mean −t=9(t−10)−t=9(t−10) then infinite solutions.
Step-by-step explanation:
Here is the answer if you mean −t=9(t−10):
−t = 9 (t−10)
Simplify the equation.
-t = (9)(t) + (9)(-10)
-t = 9t + -90 (Add the opposite)
-t = 9t - 90
Subtract -9t
-t -9t = 9t - 90 - 9t
-10t = - 90
Divide -10 on both sides to make sure the equation is balanced on both sides. And to isolate t to get the final answer.
-10t = -90
-10t = -10
Therefore,
t = 9Is the final answer.
I Hope this helps! Have a great rest of your morning, afternoon, or evening! :D
Brook rode her bike 7 miles in 30 minutes. Joshua rode his bike 25 miles in 2 hours. which one is faster. HEEEEEEELLLLLLLLLLLLLLPPPPPPPPP
Answer:
Brook is faster.
Step-by-step explanation:
1 hour=60 minutes
2 hours=2*60=120 minutes
-------------
7 miles in 30 minutes vs 25 miles in 120 minutes
7/30=0.233...mile per minute
25/120=0.20833...mile per minute
Brook is faster than Joshua.
Explanation:To determine which person is faster, we can compare their average speeds.
Average speed is calculated by dividing the total distance traveled by the total time taken.
For Brook, she traveled 7 miles in 30 minutes, so her average speed is:
7 miles ÷ 30 minutes = 0.2333 miles per minute.
For Joshua, he traveled 25 miles in 2 hours, which is equivalent to 120 minutes. So his average speed is:
25 miles ÷ 120 minutes = 0.2083 miles per minute.
Therefore, Brook is faster than Joshua as her average speed is higher.
The audience thinks %30 percent of Brandon's jokes are funny.
What fraction of Brandon's jokes does the audience think are funny?
Answer:
Fraction of jokes of Brandon that are funny = [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
We are given that, 30% of the Brandon's jokes are funny.
Now, to convert percent into fraction, we will multiply it by [tex]\frac{1}{100}[/tex]
Now,
[tex]30\%=30\times\frac{1}{100}=\frac{30}{100} = \frac{3}{10}[/tex]
∴ [tex]\frac{3}{10}[/tex] of the Brandon's jokes were funny.