Answer:
400 + 5x = 582 - 8x
14 weeks
Step-by-step explanation:
Set them both up in an equation ---> x = weeks
400 + 5x = 582 - 8x
Solve
13x = 182
x = 14
To determine how many weeks it will take for Chris and Ben to have the same amount in their bank accounts, we can set up and solve an equation based on their weekly deposits and withdrawals. After setting their equations equal to each other and solving for 'x', we find that it will take 14 weeks.
Explanation:To determine how many weeks it will take for Chris and Ben to have the same amount in their bank accounts, we can set up an equation based on their weekly deposits and withdrawals. Let's represent the number of weeks as 'x'.
Chris's bank account balance can be represented by the equation: 400 + 5x
Ben's bank account balance can be represented by the equation: 582 - 8x
To find the number of weeks it takes for their balances to be equal, we can set their equations equal to each other and solve for 'x':
400 + 5x = 582 - 8x
Combining like terms and isolating 'x', we get:
13x = 182
Dividing both sides by 13, we find that x = 14.
Thus, it will take 14 weeks for Chris and Ben to have the same amount in their bank accounts.
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an electrician charges $322 for 7 hours of work. how much does the electrician charge per hour?
Answer:
The electrician charges $46 per hour
Step-by-step explanation:
we know that
An electrician charges $322 for 7 hours of work
so
using proportion
Find out how much does the electrician charge per hour
Let
x ----> the charge per hour
[tex]\frac{322}{7}\frac{\$}{h}=\frac{x}{1}\frac{\$}{h}\\\\x=322/7\\\\x=\$46[/tex]
therefore
The electrician charges $46 per hour
The electrician charges $46 per hour.
The total charge is $322, and the total number of hours worked is 7.
To find the charge per hour, use the formula:
Charge per hour = Total charge / Number of hours
Substitute the given values into the formula:
Charge per hour = 322 / 7
Perform the division:
322 divided by 7 equals 46. Therefore, the electrician charges $46 per hour.
So, the calculation is:
Charge per hour = 46
Which equation has the solutions x = 1 plus-or-minus StartRoot 5
For this case we have the following solutions:
[tex]x_ {1} = 1 + \sqrt {5}\\x_ {2} = 1- \sqrt {5}[/tex]
Then, the factorized equation is of the form:
[tex](x- (1+ \sqrt {5})) (x- (1- \sqrt {5})) = 0\\(x-a) (x-b) = 0[/tex]
We apply distributive property:
[tex]x ^ 2-bx-ax + ab = 0\\x ^ 2- (1- \sqrt {5}) x- (1+ \sqrt {5}) x + (1+ \sqrt {5}) (1- \sqrt {5}) = 0\\x ^ 2-x + \sqrt {5} x-x- \sqrt {5} x + (1 ^ 2- \sqrt {5} + \sqrt {5} - (\sqrt {5}) ^ 2) = 0\\x ^ 2-2x + (1-5) = 0\\x ^ 2-2x-4 = 0[/tex]
ANswer:
The equation is [tex]x ^ 2-2x-4[/tex]
IF A SUBSCRIPTION IS $499 PLUS 8% TAX FOR 30 DAYS, BUT IS BEING PRORATED FOR 7 DAYS, PLUS THERE IS A $10 OFF COUPON, WHAT'S THE FINAL COST?
Answer:
$528.92
Step-by-step explanation:
The subscription given is $499 plus 8% tax
Add tax
108/100 * $499 = $538.92
$538.92 for 30 days.
If its being promoted for 7 days there is a $10 off coupon, this will be;
$538.92-$10 = $528.92
Final cost = $528.92
Which number sentence is TRUE?
A. 3 ÷ 1 < 0 ÷ 3
B. 0 ÷ 3 > 3 ÷ 3
C. 3 ÷ 1 > 3 ÷ 3
D. 3 ÷ 3 < 4 ÷ 4
The correct option is C. 3 ÷ 1 > 3 ÷ 3.
To solve this problem, we need to evaluate each of the given number sentences to determine which one is true.
A. 3 ÷ 1 < 0 ÷ 3
First, we perform the divisions:
3 ÷ 1 = 3
0 ÷ 3 = 0
Now we compare the results:
3 < 0
This statement is false because 3 is not less than 0.
B. 0 ÷ 3 > 3 ÷ 3
Again, we perform the divisions:
0 ÷ 3 = 0
3 ÷ 3 = 1
Now we compare the results:
0 > 1
This statement is false because 0 is not greater than 1.
C. 3 ÷ 1 > 3 ÷ 3
We perform the divisions:
3 ÷ 1 = 3
3 ÷ 3 = 1
Now we compare the results:
3 > 1
This statement is true because 3 is greater than 1.
D. 3 ÷ 3 < 4 ÷ 4
We perform the divisions:
3 ÷ 3 = 1
4 ÷ 4 = 1
Now we compare the results:
1 < 1
This statement is false because 1 is not less than 1; they are equal.
Therefore, the only true statement is C. 3 ÷ 1 > 3 ÷ 3.
Tell which property you used 64+58=58+64
Answer:Communitive Property
Step-by-step explanation: You can only do this property with addition and multiplication because you are able to switch the places and still get the same answer
Which are correct statements regarding proofs? Select three options.
1. In a paragraph proof, statements and their justifications are written in sentences in a logical order.
2. A two-column proof consists of a list statements and the reasons the statements are true.
3. A flowchart proof gives a visual representation of the sequence of steps without justifications.
4. A paragraph proof is a two-column proof in sentence form.
5. A two-column proof lists only the given information and what is to be proven.
Answer:
In a paragraph proof, statements and their justifications are written in sentences in a logical order.
A two-column proof consists of a list statements and the reasons the statements are true.
A paragraph proof is a two-column proof in sentence form.
Step-by-step explanation:
In a paragraph proof, statements and their justifications are written in sentences in a logical order.A two-column proof consists of a list statements and the reasons the statements are true.A paragraph proof is a two-column proof in sentence form.A paragraph proof is only a two-column proof written in sentences. However, since it is easier to leave steps out when writing a paragraph proof.
A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column
The statements regarding proofs are,
(1)In a paragraph proof, statements and their justifications are written in sentences in a logical order.
2. A two-column proof consists of a list of statements and the reasons the statements are true and
(4) A paragraph proof is a two-column proof in sentence form.
We have given that the statement is,In a paragraph proof, statements and their justifications are written in sentences in a logical order.
A two-column proof consists of a list of statements and the reasons the statements are true.
A flowchart proof gives a visual representation of the sequence of steps without justifications.
A paragraph proof is a two-column proof in sentence form.
A flowchart proof gives a visual representation of the sequence of steps without justifications.
A paragraph proof is a two-column proof in sentence form.
A two-column proof lists only the given information and what is to be proven.
What is the meaning of logical order?Logical order is when all of the messages and segments within a group are in their logical sequence.
So we have the correct statements are
In a first, statements in paragraph proof,and their justifications are written in sentences in a logical order.A two-column proof consists of a list of statements and the reasons the statements are true.A paragraph proof is a two-column proof in sentence form.A paragraph proof is only a two-column proof written in sentences. However, since it is easy to leave steps out when writing a paragraph proof.
A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true.
The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column
Therefore the statement 1. 2 and 4 are true.
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Which exponential function goes through the points 1,8 and 4,64
Answer: the correct answer is B
Classify the expression: 5x + 2x - 3
A. Quadratic expression
B. Linear expression
C. Cubic expression
D. Exponential expression
The expression [tex]\(5x + 2x - 3\)[/tex] is a linear expression.
The expression [tex]\(5x + 2x - 3\)[/tex] represents a linear expression because it consists of terms involving only the variable \(x\) raised to the power of 1. In other words, each term is a linear term.
Linear expressions depict relationships that are straight lines when graphed on a Cartesian plane. In this case, \(5x\) and \(2x\) are both linear terms since they involve the variable \(x\) raised to the first power, while the constant term \(-3\) does not involve \(x\) at all.
The expression simplifies to [tex]\(7x - 3\),[/tex] maintaining its linear form. Linear expressions are fundamental in algebra and represent relationships with constant rates of change.
Choose all the statements that are true about this sequence.
60, 66, 72, 78
The value of the first term is 1.
This is an arithmetic sequence.
The value of the third term is 72
The sequence starts at 60 and adds 4 repeatedly.
The sequence starts at 66 and adds 6 repeatedly.
There are four terms in this sequence.
The sequence starts at 60 and adds 6 repeatedly.
This is an arithmetic sequence
The value of the 3rd term is 72
There are 4 terms in this sequence
The sequence starts at 60 and adds 6 repeatedly
Answer:
b, c, f, g
Step-by-step explanation:
What percent of 208 is 114.4
Answer:
55%
Step-by-step explanation:
all you have to do is divide 114.4 by 208 to get 0.55, then turn that into a percentage by moving the decimal 2 times to the right.
Answer:
55%Step-by-step explanation:
[tex]\bold{METHOD\ 1}\\\\\begin{array}{ccc}208&-&100\%\\\\114.4&-&p\%\end{array}\qquad\text{cross multiply}\\\\208p=(100)(114.4)\\\\208p=11440\qquad\text{divide both sides by 208}\\\\p=\dfrac{11440}{208}\\\\p=55[/tex]
[tex]\bold{METHOD\ 2}\\\\\text{Calculate the quotient of given numbers and convert it to the percent:}\\\\\dfrac{114.4}{208}=0.55\\\\0.55\cdot100\%=55\%[/tex]
During the flu epidemic, 98 of 392 middle school students we
hool students were absent on a
single day. What percent of the students were absent?
Answer:
25% of the students were absent.
Step-by-step explanation:
100/392=0.26*98=25
To check 25%=1/4
so, 98*4=392
which makes sense.
Round 503.782 to the nearest tenth
The value 503.782 to the nearest tenth is 503.8
Rounding up to the nearest tenth means we want only a digit to be placed after the decimal point.
Given the value 503.782, this value to the nearest tenth will be 503.8.
Note that 1 was added to the value "7" after the decimal point. This was because the adjacent value "8" is more than 4.
Hence the value 503.782 to the nearest tenth is 503.8
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Final answer:
To round 503.782 to the nearest tenth, the digit in the hundredths place is 8, which is greater than or equal to 5. Therefore, the rounded number is 503.8.
Explanation:
To adjust 503.782 to the closest 10th, we really want to take a gander at the digit in the hundredths place, which is the second digit after the decimal point. It is 7 in this instance.
Since 7 is more prominent than or equivalent to 5, we gather together the digit in the tenths place, which is the primary digit after the decimal point. For this situation, it is 8.
Therefore, 503.8 is obtained by rounding 503.782 to the nearest tenth.
To round 503.782 to the nearest tenth, we look at the digit in the hundredths place, which is 8. Since 8 is greater than or equal to 5, we round up. Therefore, the rounded number is 503.8.
f(x)=x^2+1
g(x)=2x-5
Find f(x)-g(x)
Answer:
[tex]\large\boxed{f(x)-g(x)=x^2+2x+6}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2+1\\\\g(x)=2x-5\\\\f(x)-g(x)=(x^2+1)-(2x-5)\\\\f(x)-g(x)=x^2+1-2x-(-5)\\\\f(x)-g(x)=x^2+1-2x+5\qquad\text{combine like terms}\\\\f(x)-g(x)=x^2+2x+(1+5)\\\\f(x)-g(x)=x^2+2x+6[/tex]
test the continuity of f(x)=1÷(x-3) at x doesnot equal to 3
Good evening ,
____________________
Step-by-step explanation:
it’s a rational function then it’s continue at all real numbers except when x=3
[tex]\frac{1}{x-3}[/tex] ; x≠3.
:)
A manufacturing company produced 1,800 vehicle.of those 30% were trucks 25% were sports cars, and 10% were vans. How many of the vehicle were not trucks,sports cars, or vans ?
Answer:
630
Step-by-step explanation:
if you add the percentages of the trucks, sport cars and vans you get:
30% + 25% + 10% = 65%. So to find the percentage of vehicles that aren't in this categories you substract this percentage from 100%.
100% - 65% = 35%
This means that 35% of the vehicles aren't in those categories, so to find the amount you just multiply the total of vehicles with the percentage an then divide by 100
(1,800*35)/100 = 630 vehicles
What is the solution for x in the equation 0.5x+4+0.9x=x+5
Answer:
2.5
Step-by-step explanation:
Use the given functions to set up and simplify
D
.
x
=
0.5
x
+
4
+
0.9
x
=
x
+
5
=
x
=
2.5
A
=
x
=
2.5
x
=
2.4
=
x
=
2.5
B
=
x
=
2.5
x
=
0.42
=
x
=
2.5
C
=
x
=
2.5
x
=
0.4
=
x
=
2.5
D
=
x
=
2.5
x
=
2.5
=
x
=
2.5
The solution for x in the equation 0.5x + 4 + 0.9x = x + 5 is 2.5.
Given that:
0.5x + 4 + 0.9x = x + 5
It is required to find the value of x.
In order to find the value of x, first operate the like terms together and then solve it to find the value of x.
Consider,
0.5x + 4 + 0.9x = x + 5
1.4x + 4 = x + 5
Subtract both sides by x.
0.4x + 4 = 5
Subtract both sides by 4.
0.4x = 5 - 4
0.4x = 1
Now, divide both sides by 0.4.
x = 1 / 0.4
x = 2.5
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Arun scores 36 marks in English 44 marks in Hindi and 75 marks in maths and X in Science if average score is 50 find the value of x
Answer:
x = 45
Step-by-step explanation:
The average is calculated as
average = [tex]\frac{score}{count}[/tex]
here the average = 50 , thus
[tex]\frac{36+44+75+x}{4}[/tex] = 50
Multiply both sides by 4
36 + 44 + 75 + x = 200
155 + x = 200 ( subtract 155 from both sides )
x = 45
Write 10^15 in standard form
In order to get the answer to this question you will have to multiply the whole number as many times as it's exponent so in this case you will have to multiply 10, 15 times.
[tex]10^{15}[/tex]
[tex]10^{15} = 10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10[/tex]
[tex]10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10 = 1000000000000000[/tex]
[tex]= 1000000000000000[/tex]
Therefore your answer is "1,000,000,000,000,000."
Hope this helps.
Consider the cubic function f(x) = x^3 + ax^2 + bx + 4 where (a) and (b) are constants. When f(x) is divided by x-3, the remainder is 10. When f (x) is divided by x+1, the remainder is 6.
Show that a = -1 and b = -4
Answer:
see explanation
Step-by-step explanation:
Using the Remainder theorem
If f(x) is divided by (x - h) then f(h) = remainder, thus
f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is
27 + 9a + 3b + 4 = 10
9a + 3b + 31 = 10 ( subtract 31 from both sides )
9a + 3b = - 21 → (1)
f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is
- 1 + a - b + 4 = 6
a - b + 3 = 6 ( subtract 3 from both sides )
a - b = 3 → (2)
Rearrange (2) expressing a in terms of b
a = 3 + b → (3)
Substitute a = 3 + b into (1)
9(3 + b) + 3b = - 21 ← distribute and simplify left side
27 + 9b + 3b = - 21
12b + 27 = - 21 ( subtract 27 from both sides )
12b = - 48 ( divide both sides by 12 )
b = - 4
Substitute b = - 4 into (3)
a = 3 - 4 = - 1
Hence a = - 1 and b = - 4
If the trip takes 3 hours for a total distance of 350 km, travelling at x hours at 120km/h and remaining time at 60 km/h
Answer:
x = 2.8 hours
Explanation
Total distance = 350 km
Time period = 3 hrs
Hence we need to formulate an equation...,
Distance = Speed × Time
; Distance covered travelling at 120 = 120x Since the total time period was 3hrs...then the remaining time is (3 - x)
;Distance covered travelling at 60 = 60(3- x)
The equation is going to be...,
; 120x + 60(3 - x) = 350...since total distance is 350 km
; 120x + 180 - 60x = 350
; 60x = 170....divide both sides by 60
Hence..., x = 2.8 hours
Todd and Agnes are making desserts. Todd buys
peaches and a carton of vanilla yogurt. Agnes
buys apples and a jar of honey. They bought
the same number of pieces of fruit. Is there a
situation in which they pay the same amount for
their purchases? Explain.
apples
peaches=
$1.25 ea. For peaches
$1 ea. For the apples
YOGUR
HONEY=
$4 for yogurt
$6 for honey
Answer:
If the number of fruits is 8, then Todd and Agnes will pay the same amount for their purchases
Step-by-step explanation:
Let
x ----> the number of pieces of fruit
y ----> the total pay for the purchase
we know that
Todd
[tex]y=1.25x+4[/tex] ----> equation A (peaches plus a carton of vanilla yogurt)
Agnes
[tex]y=1.00x+6[/tex] ----> equation B (apples plus a jar of honey)
Equate equation A and equation B and solve for x
[tex]1.25x+4=1.00x+6[/tex]
[tex]1.25x-1.00=6-4[/tex]
[tex]0.25x=2[/tex]
[tex]x=8\ pieces\ of\ fruits[/tex]
therefore
If the number of fruits is 8, then Todd and Agnes will pay the same amount for their purchases
The price per share of a stock changed by -$4.50 on each of 5 consecutive days. If the starting price per share was $67.50, what was the ending price?
Answer:
$45
Step-by-step explanation:
Multiply 4.5 by 5 to give you the total amount lost over 5 days,which is 22.5. If you lost 22.5 and started with 67.5, subtract the two to get your answer
Miss smith’s pay is directly proportional to the number of hours she work at the airport. Her pay for 22 hours is $297.How much should she earn in a 40 hour week
Answer:
She should earn $540 in a 40 hour week
Step-by-step explanation:
we know that
Her pay for 22 hours is $297
so
using proportion
Find out how much should she earn in a 40 hours week
[tex]\frac{22}{297}=\frac{40}{x}\\\\x=297*40/22\\\\x= \$540[/tex]
0.08 os ten times great as ...
0.5 is ten times great as
Answer:
Part 1) The number is 0.008
Part 2) The number is 0.05
Step-by-step explanation:
Part 1) we have
0.08 is ten times great as ...
That means----> 10 times a number is equal to 0.08
Let
x -----> the number
To find the number divide 0,08 by ten
so
0.08=10x
x=0.08/10
x=0.008
Part 2) we have
0.5 is ten times great as...
That means----> 10 times a number is equal to 0.5
Let
x -----> the number
To find the number divide 0,5 by ten
so
0.5=10x
x=0.5/10
x=0.05
Write the equation of a function whose parent function, f(x) = x + 5, is shifted 3 units to the right.
a) g(x) = x + 3
b) g(x) = x + 8
c) g(x) = x − 8
d_ g(x) = x + 2
Answer:
[tex]g(x) = x + 2[/tex]
Step-by-step explanation:
Parent function [tex]f(x) = x + 5[/tex], is shifted 3 units to the right.
If f(x) is shifted 'a' units to the right then f(x) becomes f(x-a)
If f(x) is shifted 'a' units to the left then f(x) becomes f(x+a)
[tex]f(x) = x + 5[/tex], is shifted 3 units to the right.
Then we subtract 3 from x
So , [tex]f(x) = x + 5[/tex] becomes [tex]f(x-3) = x-3 + 5=x+2[/tex]
[tex]g(x) = x + 2[/tex]
The equation of function will be;
g (x) = x + 2
Option d is true.
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
Parent function, f(x) = x + 5 is shifted 3 units to the right.
Since, If a function f(x) is shifted 'a' units to the right then function f(x) becomes f(x-a).
So, The equation of function will be calculated as;
The parent function is shifted 3 units to the right.
Then, we subtract 3 as;
g (x) = x + 5 - 3
g (x) = x + 2
Thus, The equation of function will be;
g (x) = x + 2
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Complete the place value chart for the following number.Write its number name and tell the value of the underlined digit.
6.325 the underlined digit is 2
Answer:
two hundredths
Step-by-step explanation:
6 is in the ones place. 3 is in the tenths place. 2 is in the hundredths place
5 is in the thousandths place.
Answer:
two hundredths
Step-by-step explanation:
its two places after the decimal point
Simplify: -24w^2+ (-4w^2)
Enter the original expression if it cannot be
simplified.
Enter the correct answer.
The answer is [tex]-28w^2[/tex]
5.241 divided by 3 please help me
The required, 5.241 divided by 3 equals approximately 1.747.
To divide 5.241 by 3, we can perform the division as follows:
1.747
------------
3 | 5.241
To start, we divide the whole number part, 5, by 3. The result is 1, which becomes the whole number part of the quotient.
Next, we bring down the decimal point and consider the decimal part of the dividend, which is 0.241. We can continue the division process by adding a decimal point to the quotient and placing a 0 to the right of the decimal point.
1.747
3 | 5.241
- 3
-----
24
Now, we divide 24 by 3, which gives us 8. We bring down the next decimal digit, which is 1, and continue the division:
1.747
3 | 5.241
- 3
-----
24
- 24
-----
1
Since there are no more decimal digits to bring down, we have finished the division. The final quotient is 1.747, rounded to three decimal places.
Therefore, 5.241 divided by 3 equals approximately 1.747.
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Mrs. Alvarez asked her class how many hours of TV they watched per day (to the nearest half hour) The results were shown: 0 - 1 hours = 1/6 : 1 1/2 - 2 hours = 5/12 : 2 1/2 - 3 = 1/4 : 3 hours & over = 1/6. What fraction of students watch between 0 and 2 hours of TV a day.
Answer: 7/12
Step-by-step explanation:
Answer:
7/12
Step-by-step explanation:
The problem is asking us to find what fraction of students watch between 0 and 2 hours of TV a day:
The information we have is:
0 - 1 hours = 1/6
1 1/2 - 2 hours = 5/12
We only need this information because it is asking us for 0 to 2 hours.
Now we have to add the fraction of students that watch TV 0-1 hours and the fraction of students watch TV 1 1/2 - 2 hours:
1/6 + 5/12
To be able to solve this we have to have the same denominator and to do it we have to multiply the first fraction by 2:
(1/6) *2 = 2/12
Now we can add:
2/12 + 5/12 = 7/12
We add the numerators and the denominator stays the same.
This is the answer to a problem or an equation
Answer:solution
Step-by-step explanation:
I got it right