Answer:
$98
Step-by-step explanation:
x+6(120-x)=230
x+720-6x=230
-5x=-490
x-98
x represented how much money Hannah had.
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
A ________ is a letter that takes place of a number.
Example: 5+n=9,n=4
Answer:
Variable.
Step-by-step explanation:
A letter that takes the place of a number is called a variable.
Answer:
variable
Step-by-step explanation:
A variable is a letter that represents a number. It can also be solved for.
Hope this helps
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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
This is the answer to a problem or an equation
Answer:solution
Step-by-step explanation:
I got it right
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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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.
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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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]
how do you graph a quadratic with (a) in front of the x
Answer:
Remember PEMDAS? That comes into play here. Just multiply your x value with 1/3 and then square. After that just add the 4.
Step-by-step explanation:
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]
3/41 40/97 1/6 in least to greatest?
Answer:
3/41; 1/6 40/97
Step-by-step explanation:
Rachel spends 1/4 of her money
on chocolate, 1/8 on pizza.
She has $40 remaining.
How much did she have
at the beginning?
Step-by-step explanation:
Let's start by defining our term:
How much she had at the beginning = B
Now let's edit that value like the problem says
B - B/4 - B/8 = 40
Let's multiply everything by 8 to get rid of any denominators
8B - 2B - B = 320
5B = 320
B = 64
Answer:
Rachel had $64 at the beginning.
someonle plzz help me with this simple vector question
Answer:
6 AO
Step-by-step explanation:
If you compare the vector formed with AO it is 6 AO.
You can do it mathematically too converting each point in coordinates (x, y). But since it didnt say how to do it, the simplest is just drawing an hexagon and summing the vectors
Find the exact solution of x.
x2 = 16
•x = 4
•x = -4
•x = ±4
•No Solution
Answer:
x=+-4
Step-by-step explanation:
Please help with this math question
Answer:
it's the third one
Step-by-step explanation:
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]
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
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.
Write each fraction as a decimal 8/1000
Answer:
0.008.
Step-by-step explanation:
8 / 1000
= 0.008.
The 3rd position after the decimal point is the thousandth's.
The fraction 8/1000 in to a decimal gives 0.008.
Converting the Fraction 8/1000 to a Decimal:
To convert the fraction 8/1000 to a decimal, you need to divide the numerator by the denominator. In this case, divide 8 by 1000:
8 ÷ 1000 = 0.008Thus, the fraction 8/1000 as a decimal is 0.008.
What is the first step in which the student made an error
Final answer:
To identify where an error might have occurred, students should be aware of common mistakes, review personal feedback, and reflect on their thought processes. This helps in understanding and correcting errors, leading to improvement in critical and reflective thinking.
Explanation:
The first step in identifying an error in a student's work is to be cognizant of common mistakes that students make. By reviewing a common errors list and reflecting upon feedback from instructors, a student can pinpoint problem areas in his or her academic practice. Starting with the prediction and diagnosis of one's own learning process is essential. This may include recognizing patterns in mistakes, understanding why an error was made, or consulting with a teacher for further clarification. Once the source of the error is identified, the student can work on corrective measures to avoid similar issues in the future. Frequently, errors in thinking or application are not due to a lack of intelligence, but rather to the way our minds are wired, leading to characteristic mistakes that can be anticipated and mitigated with practice and reflection.
A game's parking costs $18 per vehicle and a ticket for the game is $33. If your family gave you $200 for your birthday and the use of the minivan, how many friends (including yourself) can go to the game?
Answer:
you and 4 other people can go to the game
Step-by-step explanation:
18 for parking
33 for you
33 for 4 other people
= 184 and you cant add another 33 to it cause it will go over 200
Answer:
5
Step-by-step explanation:
A game's packing cost is $18
A ticket for the game is $33
Your family gave you $200 + minivan
Let's say the number of friends (including yourself) you go with to the game is f.
Equating this expression;
$18 + $33f ≤ $200
$33f ≤ $200 - $18
$33f ≤ $182
f ≤ [tex]\frac{182}{33}[/tex]
f ≤ 5.515151515
Since we cannot have 0.515151515 friends, the number of friends (including yourself attending the game must be 5).
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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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.
What is the 30th term of the linear sequence below?
-4, -1,2,5,8,...
Answer:
The 30th term is 83
Step-by-step explanation:
we know that
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant called the common difference d
in this problem
[tex]a_1=-4\\a_2=-1\\a_3=2\\a_4=5\\a_5=8[/tex]
so
[tex]a_2-a_1=-1-(-4)=3\\a_3-a_2=-2-(-1)=3\\a_4-a_3=-5-2=3\\a_5-a_4=-8-5=3[/tex]
The common difference d is 3
We can write an Arithmetic Sequence as a rule:
[tex]a_n=a_1+d(n-1)[/tex]
Find out the 30th term
we have
[tex]n=30\\d=3\\a_1=-4[/tex]
substitute
[tex]a_n=-4+(3)(30-1)[/tex]
[tex]a_n=-4+(3)(29)[/tex]
[tex]a_n=83[/tex]
Final answer:
The 30th term of the linear sequence is 83, found using the formula for the nth term of a linear sequence an = a1 + (n - 1)d, with a common difference of 3.
Explanation:
To find the 30th term of the linear sequence given by -4, -1, 2, 5, 8,..., first identify the common difference between consecutive terms. In this sequence, each term increases by 3. So, the common difference (d) is 3.
To find the nth term of a linear sequence, use the formula:
an = a1 + (n - 1)d, where
an is the nth term,
a1 is the first term, and
d is the common difference.
For our sequence:
a1 = -4 (the first term),
d = 3,
n = 30 (since we are finding the 30th term).
Plugging into the formula gives:
a30 = -4 + (30 - 1) × 3
a30 = -4 + 29 × 3
a30 = -4 + 87
a30 = 83
Therefore, the 30th term of the sequence is 83.
41 = 32 - r solve each equation linear equations
Solve 25x^2-30=0
Round the answer to the nearest hundredth
x=-1.10 and x=1.10
x=-26.15 and x=1.15
x=0
x=-0.83 and x=0.83
Answer:
x = - 1.10 and x = 1.10
Step-by-step explanation:
Given
25x² - 30 = 0 ( add 30 to both sides )
25x² = 30 ( divide both sides by 25 )
x² = [tex]\frac{30}{25}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{30}{25} }[/tex]
x = - 1.10 and x = 1.10 ( to the nearest hundredth )
The correct answer is a. x = -1.10 and x = 1.10 .
To solve the quadratic equation [tex]\( 25x^2 - 30 = 0 \)[/tex], we first add 30 to both sides of the equation to isolate the quadratic term:
[tex]\[ 25x^2 = 30 \][/tex]
Next, we divide both sides by 25 to solve for [tex]\( x^2 \)[/tex]:
[tex]\[ x^2 = \frac{30}{25} \] \[ x^2 = 1.2 \][/tex]
Now, we take the square root of both sides to solve for x. Remember that when taking the square root of a number, we must consider both the positive and negative square roots:
[tex]\[ x = \pm\sqrt{1.2} \][/tex]
Using a calculator, we find the square root of 1.2 and round to the nearest hundredth:
[tex]\[ x = \pm1.095445115... \][/tex]
Rounded to the nearest hundredth, the solutions are:
[tex]\[ x = -1.10 \] \[ x = 1.10 \][/tex]
Therefore, the correct options are x = -1.10 and x = 1.10 . The other options provided [tex](\( x = -26.15 \)[/tex] and x = 1.15 , x = 0 , x = -0.83 and x = 0.83 are incorrect and do not satisfy the original equation.
The complete question is- Solve [tex]25x^2-30=0[/tex]
Round the answer to the nearest hundredth
a. x=-1.10 and x=1.10
b. x=-26.15 and x=1.15
c. x=0
d. x=-0.83 and x=0.83
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]
What is the solution to this equation?
X- 13 = -4
O
A. x = 17
o
O
B. x= -17
o
OC. x = 9
O
D
. = -9
Answer:
9. This is because you have to add 13 to -4, which gives you positive 9. Hope this helped!
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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Bryan took a taxi home from the opera. The taxi fare was $2.50 per mile, and he gave the driver a tip of $3. Bryan paid a total of $35.50. The equation 2.50x + 3 = 35.5 can be used to find the distance in miles (x) between the opera house and Bryan's home.
How many miles is it between the opera house and Bryan's home?
Answer:
There are 13 miles between the opera house and Bryan's home.
Step-by-step explanation:
The equation [tex]2.50x+3=35.5[/tex] can be used to find the distance in miles (x) between the opera house and Bryan's home.
We will solve this to get the value of x.
[tex]2.50x+3=35.5[/tex]
=> [tex]2.50x=35.5-3[/tex]
=> [tex]2.50x=32.50[/tex]
we get x = 13
Hence, there are 13 miles between the opera house and Bryan's home.