Answer:
a(30) = 145
Step-by-step explanation:
a(n) = a(1) + (n-1)d
d = 5
a(30) = 0 + (30-1)5
a(30) = 0 + (29)5
a(30) = 0 + 145
a(30) = 145
Using the concept of arithmetic sequence, the value of a30, which is the 30th term of the sequence is 145
The common difference, d = 35 / 7 = 5
The nth term of an arithmetic sequence is obtained using the relation :
A(n) = a1 + (n - 1)da1 = first terma1 = a2 - d = 5 - 5 = 0
Hence,
A(30) = 0 + (30 - 1)5
A(30) = 0 + 29(5)
A(30) = 145
Therefore, the value of the 30th term of the sequence is 145.
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Write the values that make the denominators zero. then solve the equation?
10/5x-5 + 1/5 = 2/x-1
Answer:
denominators are zero for x=1
there is no solution
Step-by-step explanation:
We suspect your equation is supposed to be ...
10/(5x -5) +1/5 = 2/(x -1) . . . . . parentheses are required on denominators
The denominators will be zero for x=1.
This version of the equation has no solution. It simplifies to ...
2/(x-1) + 1/5 = 2/(x -1)
1/5 = 0 . . . . . subtract 2/(x-1) from both sides
There is no value of x that will make this equation true.
_____
Alternative interpretation
The way your equation is written, it must be interpreted according to the order of operations to be ...
(10/5)x -5 +1/5 = (2/x) -1 . . . . x=0 makes the denominator zero
2x -3.8 = 2/x
2x^2 -3.8x = 2 . . . . multiply by x
2(x^2 -1.9x +.95^2) = 2 +2(0.95^2)
(x -0.95)^2 = 1.9025
x = 0.95 ± √1.9025 ≈ {-0.4293, 2.3293}
Malik is planning a 6-day summer vacation trip. He has $840 in savings, and he earns $45 per hour for tutoring. The trip will
cost him $525 for airfare, $780 for food and sightseeing, and $95 per night for the hotel. How many hours must he tutor to
have enough money to pay for the trip?
Answer:
23
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The number of hours required to tutor to have enough money to pay for the trip is 23 hours.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of days for the summer vacation = 6
Savings = $840
Earnings per hour = $45
Airfare cost = $525
Food and sightseeing = $780
Hotel cost per night = $95
Number of hours = x
We can make an expression.
525 + 780 + 6 x 95 = 840 + 95x
525 + 780 + 570 = 840 + 45x
1875 = 840 + 45x
1875 - 840 = 45x
1035 = 45x
1035/45 = x
x = 23
This means 23 hours.
Thus,
The number of hours required to tutor to have enough money to pay for the trip is 23 hours.
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Billy walks 2.5 miles every day to soccer practice and catches a ride home from his Grandma. Billy had 5 practices last week. How many miles did Billy walk last week to practice? 10 points please help
Answer:12.5 mike he walked to practice last week
Step-by-step explanation:
2.5 miles everyday
5 practices last week
2.5 miles x 5 practices
Ann invested $61,000 into two accounts. The first account pays an annual interest rate of 5% and the second account pays an annual interest rate of 7%. After one year, Ann earned $3430 in interest. How much was invested in each account? Round your answer to the nearest cent, if necessary. [For full credit, set a system of linear equations and solve the system]
Answer:
2nd Account has $19,000
1st Account has $42,000
Step-by-step explanation:
First let's split the money invested.
x is money in account 1
y is money in account 2
1st equation
$61,000=x+y
5%=0.05
7%=0.07
2nd equation
0.05*x+0.07*y=$3,430
x=61,000-y
substitute into 2nd equation
0.05(61,000-y)+0.07y=3430
Solve.
3050-0.05y+0.07y=3430
0.02y=3430-3050
0.02y=380
y=380/0.02
y=$19,000
There are 2(two) ways to solve for the 1st account, but I will do it the long way.
y=61,000-x
substitute into 2nd equation
0.07(61,000-x)+0.05x=3430
Solve.
4270-0.07x+0.05x=3430
-0.02x=3430-4270
-0.02x=-840
x=-840/-0.02
x=$42,000
The short way...
x=61,000-y
x=61,000-19,000
x=$42,000
what number gives a result of -5 when 8 is subtracted from the quotent of the number and 6
Answer:
if you do 6-8
Step-by-step explanation:
6-8 = -5 because if you subtract 8 from 6 you will still have -5
Round 35,124 nearest ten thousands
Answer:
40,000
Step-by-step explanation:
because of the 5 in the thousands place means were rounding up
A standard working day is 8 hours. If you were to work 125% of a normal day, how many total hours would you work?
Find the midpoint of segment AB A(-7,6) B(4,-2)
Answer:4,05
Step-by-step explanation:
3(-5y+2)= 21 how do i solve this problem algebraically?
Answer:
Step-by-step explanation:
1)expand out the bracket
-15y+6=21
2) get the y to one side
6=21+15y
3) solve
15=15y
1=y
Answer:
Y= -1
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(−5y+2)=21
(3)(−5y)+(3)(2)=21(Distribute)
−15y+6=21
Step 2: Subtract 6 from both sides.
−15y+6−6=21−6
−15y=15
Step 3: Divide both sides by -15.
−15y −15 = 15 −15
Y= -1
A is a 3 times 3 matrix with three pivot positions.
(a) Does the equation Ax = 0 have a nontrivial solution?
(b) Does the equation Ax = b have at least one solution for every possible b?
(a) Does the equation Ax = 0 have a nontrivial solution? No Yes
(b) Does the equation Ax = b have at least one solution for every possible b? No Yes
Answer:
The following are the answer:
In option a "No".
In option b "Yes".
Step-by-step explanation:
In choice a:
Ax = 0 has no nontrivial solution. A would be the three-pivot matrix, it may assume, that the function has no free variable, and only if the function has had at least one free factor are their nontrivial formulas for the equations of the form Ax=0.
It implies that since A is a 3x3 matrix, has no free variables so that it has no non-trivial choices, and Ax = 0.
In choice b:
we assume that every potential has at least one solution that is Ax=b . If A does have a three-pivot matrix, It will be a pivot element for each row and column, and for each possible b∈ R³, Ax = b has at least one solution.
The number of hot dogs needed for the
picnic is two for each student
How many hot dogs do we need for 150
students?
solve: 3(2x+1)-2(x+5)-5(5-2x)=16 value of x?
Step-by-step explanation:
3(2x + 1) - 2(x + 5) - 5(5 - 2x) = 16
6x + 3 - 2x - 10 - 25 + 10x = 16
6x - 2x + 10x = 16 - 3 + 10 + 25
14x = 48
x = 48/14
x = 24/7
Graph 5x + 3y = 15 on a graph
Answer:
x and y
Step-by-step explanation:
you have to put 5 on the x axes and 3 on the y axes to cordanate 15
The school athletic director had a budget of $500 to purchase 164 items
for the soccer team. She purchased vests for $2.50 each, soccer balls for
$9.25 each, and cones for $0.75 each. She purchased 40 more cones than
balls. How many of each item can purchase?
Answer: She purchased 72 cones, 32 balls, and 60 vests.
Step-by-step explanation:
The total number of items is 164.
The price of the vests is $2.50 each.
The price of the soccer balls is $9.25 each.
The price of the cones is $0.75 each.
The total budget was $500.
If V is the number of vests, B the number of balls, and C the number of cones, we have that:
V + B + C = 164.
V*$2.50 + B*$9.25 + C*$0.75 = $500.
and:
"She purchased 40 more cones than balls."
C = B + 40.
Then we have a system of 3 equations and 3 variables:
V + B + C = 164.
V*$2.50 + B*$9.25 + C*$0.75 = $500.
C = B + 40.
Here the first step is to replace the third equation into the other two, in this way we eliminate one variable and one equation:
V + B + (B + 40) = 164
V*$2.50 + B*$9.25 + (B + 40)*$0.75 = $500.
Now we want to isolate one variable in one of the equations, i will isolate V in the first equation:
V = 164 - 2*B - 40 = 124 - 2*B
Now i can replace this into the other equation:
(124 - 2*B)*$2.50 + B*$9.25 + (B + 40)*$0.75 = $500
Now let's solve this for B.
$310 - $5*B + B*$9.25 + B*$0.75 + $30 = $500
B*( $9.25 - $5 + $0.75) = $500 - $310 - $30
B*$5 = $160
B = 160/5 = 32
Now we know the value of B.
And by the equations above:
V = 124 -2*B = 124 - 2*32 = 60
C = B + 40 = 32 + 40 = 72.
Then:
She purchased 72 cones, 32 balls and 60 vests.
I need help with this question
Answer:
188 miles or 188.5 miles
Step-by-step explanation:50-17.95/17
a/b=c for b helppppp
Answer:
Step-by-step explanation:
A/b = c for b
A/b = c
A = bc
bc = A
b = A/c
Answer:
See below
Step-by-step explanation:
[tex]\frac{A}{b}=c\\\frac{A}{b} * b = c * b\\ A = c * b\\\frac{A}{c} = \frac{c*b}{c}\\\frac{A}{c} = b\\ b =\frac{A}{c}[/tex]
Part D
Describe any patterns or trends you noticed when finding the products in part
c
Answer:
The middle two terms cancel out each time, and the final product is x2 plus the product of the positive coefficients of i in the original expression. All imaginary parts either cancel out or get replaced with -1, leaving an expression that doesn’t include imaginary numbers.
Step-by-step explanation:
Between what two integers does the square root of 14 lie?
Answer:
3 and 4
Step-by-step explanation:
Ifa student wanted to design an experiment that uses sound scientific principles, which of the following
should he or she not do?
A. Start with a hypothesis
B.Test more than one variable at a time
C.Record data in a table
D. compare results with others
Answer:
the answer is B
Step-by-step explanation:
A government agency has 6000 employees. As an alternative to the traditional five day work week, employees were asked whether they preferred a four day work week (10 hours per day) or flexible hours. The employee data provides the results by age category. What is the probability that a randomly selected employee at this government agency prefers a four day work week or is under 30
The table showing the data is missing, so i have attached it.
Answer:
0.8
Step-by-step explanation:
We want to find the probability that a randomly selected employee at this government agency prefers a four day work week or is under 30.
Now, we are told that the government agency has 6000 employees. Also, from the attached table, we see that the number of people who prefer a 4 day work week are a total of:
600 + 1200 + 2100 = 3900
Thus, probability of people who prefer a 4 day work week = 3900/6000 = 39/60
Also, we see that total number of people aged under 30 = 600 + 300 = 900
Thus, probability of people aged under 30 is;
900/6000 = 3/20
Thus;
probability that a randomly selected employee at this government agency prefers a four day work week or is under 30 = 39/60 + 3/20 = 48/60 = 4/5 = 0.8
Solve for x. 9x=288
Answer:
x = 32
Step-by-step explanation:
9x=288
divde both side by 9
Complete the sentences to make true statements 6 is 100 times 0.06 is 10 times 60 is 1/100 of
Answer:
6 is 100 times 0.06
0.06 is 10 times 0.006
60 is 1/100 of 6,000
Step-by-step explanation:
Since 6/100 is equal to 0.06, we can say that 6 is the result of multiplying 0.06 by one hundred (0.06 x 100 = 6).
On the other hand, since 0.06 / 10 is equal to 0.006, it is correct to say that 0.006 x 10 is equal to 0.06 (0.006 x 10 = 0.06).
Finally, 60 is one hundredth of 6000, since multiplying 60 x 100 the result is 6,000 (6,000 / 100 = 60).
Will give brainliest answer
Answer:
-105°Step-by-step explanation:
Rotation is counterclockwise
It means the angle is negative
We can see point C of the original figure is making a vertical line with point P
If we connect P to C' it is going to make more than 90 degree angle as it is above the horizontal line passing through the point P
Therefore we can estimate the angle as -105°
I really need helpp
Answer:
C
Step-by-step explanation:
Answer: B. Sandwich Town's Dipping Sauce
Step-by-step explanation: Sandwich town has 1/2 more spoonful than Burger Barn so Sandwich Town has a stronger mustard flavor.
Hope this helps! : )
solve the equation x to the power of 2=10
Answer:
√10,−√10
Step-by-step explanation:
award brainliest
Point B lies on AC between A and C. If AB = 8 and AC = 10, find BC.
Point S is on line segment RT.Given ST = 2x, and RT = 4x, and RS = 4x – 4,
determine the numerical length of RS
Answer:
2
Step-by-step explanation:
The required measure of the numerical length of RS is 4.
Given that,
Point S is on line segment RT.
ST = 2x, and RT = 4x, and RS = 4x – 4,
To determine the numerical length of RS.
A line is a curve showing the shortest distance between 2 points.
Standard equation of the line, y = mx + c, where m is slope of the equation and c is y-intercept of the equation.
Here,
Point S is on line segment RT
The total length of RT,
RT = RS + ST
4x = 4x - 4 + 2x
4x = 6x - 4
2x = 4
x = 2
RS = 4 x - 4
RS = 4 * 2 - 4
RS = 4
Thus, the required measure of the numerical length of RS is 4.
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Could somebody help me solve this step-by-step? I'm stuck
Answer:
[1, 3]
Step-by-step explanation:
g(x) = f(2x), so g(x) is f(x) compressed horizontally by a factor of 2. Vertically, it is not changed.
Therefore, the ranges are identical.
Need helpw ith this plz
If UV = 6 and TV = 12, what is TU?
Answer:
TU = 6
Step-by-step explanation:
Using the Segment Addition Postulate, we know that TU + UV = TV, and since UV = 6 and TV = 12, we know that TU + 6 = 12, therefore, TU = 6.