Answer:
1. (-10x -5) -(-7x -4)
2. (-10x -5) -(-3x -1)
Step-by-step explanation:
The process of simplifying an expression generally involves eliminating parentheses, collecting terms, simplifying fractions, rationalizing denominators, removing appropriate factors from under radicals, and generally putting expressions into general form.
So, to accomplish what the problem is asking, you can create an expression that requires you accomplish as many or as few of these steps as you may like.
In general, you will want to both "do" and "undo" whatever operation(s) you may choose. For example, consider a couple of expressions "a" and "b". For this example, we want our final result to simplify to "a".
If we choose to add "b", we might have ...
(a+b) -b . . . . . we have both added and subtracted b, so the simplified result is "a"
If we choose to multiply by "b", we might have ...
(ab)/b . . . . . . we have both multiplied by b and divided by b, so the simplified result is again "a"
_____
We can solve both these problems at once by using ...
a = -3x -1b = -7x -4If we choose the first approach, we want an expression that is (a+b). That will be ...
a+b = (-3x -1) +(-7x -4) = -10x -5
By subtracting "b" from this expression, we get "a"--and vice versa. That is ...
(-10x -5) -(-7x -4) . . . simplifies to . . . -3x -1(-10x -5) -(-3x -1) . . . simplifies to . . . -7x -4_____
Alternate solution to 2
Suppose we choose to multiply instead. Let "b" be -3x+2. Then, using the template for multiplication above, we can write the expression
(-7x -4)(-3x +2)/(-3x +2) = (21x^2 -2x -8)/(-3x +2)
and we know this rational expression simplifies to -7x -4.
_____
Of course, we can be as elaborate as we might like in modifying the original expression. Whatever we do, we must also include the "undo" so the original expression is recovered when we simplify. To illustrate the point, we can add and subtract 2x from the above rational expression.
((21x^2 -2x -8)/(-3x +2) + 2x) - 2x = (21x^2 -2x -8 +2x(-3x +2))/(-3x +2) - 2x
= (21x^2 -2x -8 -6x^2 +4x)/(-3x +2) -2x
= (15x^2 +2x -8)/(-3x +2) -2x . . . . . . another alternate solution to #2.
If we're not careful, we can create an expression that is extremely difficult to simplify. The one we have here can be factored to be ...
(-5x -4)(-3x +2)/(-3x +2) -2x = -5x -4 -2x = -7x -4 . . . our original #2 expression
Knowing that it can be factored is a big help.
Given the equation 6/x=3/k+2, and the constraints x ≠ 0 and k ≠-2, what is x in terms of k?
A) x=2k+4
B) x=2k+12
C) x=2k-1/4
D) x=1/4+12
Answer:
A) 2k+4
Step-by-step explanation:
To solve for terms of x, we need to. she sure that x is on its own side while every other term is on the other side.
To start, we will cross multiply. If we have a/b=c/d, then ad=bc
We can perform the same calculation here,
6/x=3/(k+2)
6(k+2)=3x
Divide both sides by 3
2(k+2)=x
x=2k+4
A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?
Choose one of the best answers.
A. x² – 99 = 0
B. x² – 99x = 0
C. x² + 5x + 104 = 0
D. x² + 5x – 104 = 0
Please explain your answer?
If your answers is wrong, it's going mark your answer report and it's called "improper answer."
No need to spam answers, if your answer is spam is going to be report.
Don't copied or paste answers with someone else answers from other sites. If you copied and paste answers from other websites and it mark your answer report and it's called "plagiarism."
Thank you!
-Charlie
Answer:
D
Step-by-step explanation:
(x + 5)x = 104
Distribute:
x² + 5x = 104
Subtract 104 from both sides:
x² + 5x − 104 = 0
A woman has 14 different shirts: 10 white shirts and 4 red shirts. If she randomly chooses 2 shirts to take with her on vacation, then what is the probability that she will choose two white shirts? Show your answer in fraction and percent, round to the nearest whole percent.
Answer:
1/5; 20%
Step-by-step explanation:
If she is only choosing 2 shirts, and they both have to be white, the probability of choosing those 2 white shirts out of 10 white shirts is 2/10 or, equivalently, 1/5. In percent form, this is 20%
The probability of a woman randomly choosing two white shirts from a collection of 14 shirts (10 white and 4 red) is approximately 49%, derived through the process of combinations calculation in the field of probability.
Explanation:The question relates to the field of probability in mathematics. To calculate her probability of selecting two white shirts, we first need to understand the number of total possible outcomes when she is selecting 2 out of the 14 shirts. This is represented by the combination formula C(n, r) = n! / r!(n-r)!, where n is the total number of items to choose from and r is the number of items to choose. Using this combination formula, we find that there are C(14, 2) = 91 total possible combinations of shirts she could end up with.
Next, we need to find the number of combinations that involve her picking 2 white shirts. As there are 10 white shirts, this is represented by C(10, 2) = 45. So, the probability of her taking two white shirts is then the number of desired outcomes divided by the total number of outcomes, or 45 / 91 which simplifies to approximately 0.4945 or 49% when rounded to the nearest whole percent.
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what is the exact value of cos 90degrees as found on the unit circle?
Answer:
it is 0 because cosine is the x and sine is the y. Sin is 1 and cos is 0
Twenty-five blue and twenty-five yellow marbles are placed in a jar. Thirty-four marbles are removed from the jar and put in a second jar. What is the positive difference between the number of blue marbles in the second jar and the number of yellow marbles remaining in the first jar?
Answer:
a) Let b represent the number of blue marbles placed in the second jar. Then 34-b is the number of yellow marbles in the second jar, and 25 - (34-b) is the number of yellow marbles remaining in the first jar. That value simplifies to b-9. The positive difference between b and (b-9) is 9.
b) Let n, d, p represent the numbers of nickels, dimes, and pennies, respectively.
.. (5n + 10d + p)/(n + d + p) = 7 ... the average value of the collection is 7 cents per coin
.. (5(n-1) + 10d + (p+5))/((n-1) + d + (p+5)) = 6 ... replacing one nickel with pennies changes the average to 6 cents per coin
Multiplying by the denominator and subtracting the right side of each resulting equation gives
.. 10d + 5n + p = 7d + 7n + 7p
.. 10d + 5n + p = 6d + 6n + 6p + 24
Subtracting the second equation from the first gives
.. 0 = d + n + p - 24 ... tells us the total number of coins is 24. This tells us the total value is $1.68 = 24*$0.07.
This sum will consist of at least 3 pennies. If that is all the pennies, then the remaining 21 nickels and dimes must add to $1.65. If all were nickels, the value of the 21 coins would be $1.05. We have $0.60 more than that. For each nickel traded for a dime, we gain $.05, so 12 of the 21 nickels must be traded for dimes to raise the total coin value to $1.65.
Alternatively, you can write two equations in the two unknowns:
.. d + n = 21
.. 10d + 5n = 165
Subtracting 5 times the first equation from the second gives
.. 5d = 60 ... which gives the same answer as reasoned above.
There are 3 pennies, 9 nickels, 12 dimes. (If there are 8 pennies to start, then the number of nickels is zero, so it is impossible to trade one for 5 pennies. The solution shown is the only one.)
two lengths of a triangle are show
I can't give you the correct answer but you can guess for it, cause I can give you the the scop of the length of KL.
So, as we know this;
The sum of the two sides of a triangle is greater than the third and the difference between the two sides is less than the third.
10+5 >= KL >= 10-5
15 >= KL >= 5
based on your option, the answer should be:
9 in
Solve the 3 × 3 system shown below. Enter the values of x, y, and z. X + 2y – z = –3 (1) 2x – y + z = 5 (2) x – y + z = 4 (3)
[tex]\boxed{x=1, \y=-1, \ z=2}[/tex]
Step-by-step explanation:We will use the Gaussian elimination method to solve this problem. To do so, let's follow the following steps:
Step 1: Let's multiply first equation by −2. Next, add the result to the second equation. So:
[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}[/tex]
Step 2: Let's multiply first equation by −1. Next, add the result to the third equation. Thus:
[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&-~~~3~ y&+~~2~ z&~=~7\end{array}[/tex]
Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:
[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~\frac{ 1 }{ 5 }~ z&~=~\frac{ 2 }{ 5 }\end{array}[/tex]
Step 4: solve for z, then for y, then for x:
[tex] \frac{ 1 }{ 5 } ~ z & = \frac{ 2 }{ 5 } \\ \\ \boxed{z & = 2}[/tex]
[tex]-5y+3z &= 11\\-5y+3\cdot 2 &= 11\\ \\ \boxed{y &= -1}[/tex]
By substituting [tex]y=-1 \ and \ z=2[/tex] into the first equation, we get the [tex]x[/tex]. So:
[tex]x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}[/tex]
Answer:
X= 1, y= -1, z= 2
Step-by-step explanation:
The vertices of ABC are (2,8), B (16,2), and C (6,2). the perimeter of ABC is units, and it’s area is square units
Answer:
Perimeters is 32.44 unit and area is 30 square unit.
Fill in the blank. if necessary, use the slash mark ( / ) for a fraction bar.if cos = , then tan = _____.
Answer:
5/4
Step-by-step explanation:
The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. The amount collected can be modeled by the equation. What is the equation?
Answer:
The equation is 5x + 10y = 800
Step-by-step explanation:
* Lets explain what is the equation and how can we make one
- The equation is a mathematical statement that two things are equal.
- It consists of two expressions, one on each side of an equal sign (=).
* Lets solve the problem
- There are two types of vehicles, large one and small one
- The cost of washing the small vehicle is $5
- The cost of washing the larger vehicle is $10
- They collected from washing both is $800
- To make an equation for the amount collected let the number of the
small vehicles is x and the number of the large vehicles is y
∵ x is the number of the small vehicles were washed
∵ y is the number of the large vehicles were washed
∵ The cost of washing the small vehicle is $5
∵ The cost of washing the larger vehicle is $10
∴ The money collected from the small vehicles = 5 × x = 5x
∴ The money collected from the large vehicles = 10 × y = 10y
- find the total money collected from both
∴ The amount of money collected from both = 5x + 10y
∵ The amount of money collected is $800
- Equate the two expressions above
∴ 5x + 10y = 800
* The equation is 5x + 10y = 800
Analyze the zeros of f(x) =x^4 - 3x^3 - 2x^2 + 3x + 5.
Determine the number of possible positive real zeros and the number of possible negative real zeros
a. positive 1; negative 3 or 1
b. positive 1; negative 2 or 1
c. positive 3 or 1; negative 1
d. positive 2 or 1; negative 1
Answer:
c
Step-by-step explanation:
c. positive 3 or 1; negative 1
According to this partial W-2 form, How much money was paid in FICA taxes?
FICA taxes on a W-2 form include Social Security and Medicare taxes, summed up at a standard rate of 7.65% of gross wages. To know the total FICA taxes paid, one must multiply the gross wages by 7.65% based on the provided rates.
Explanation:The question is asking for the total FICA taxes paid, which includes both Social Security and Medicare taxes. The information provided indicates that the employee pays 6.2% for Social Security and 1.45% for Medicare, which are standard rates for FICA tax deductions. To calculate the total amount of FICA taxes, add these percentages together to get a combined rate of 7.65%. If you know the gross wages, you multiply this amount by 7.65% to find the total FICA tax contribution on your W-2 form. If the actual gross wages earned are unknown, the calculation cannot be completed without this figure.
It is important to note that your employer also matches the FICA tax contributions, and some economists argue that this employer contribution effectively reduces employees' wages, meaning that employees might bear the total cost of these taxes indirectly.
Matthew earned $325 giving haircuts. He charged $25 for each haircut. How many haircuts did he give? PLEASE ANSWER AS SOON AS POSSIBLE (nvm i got it)
Answer: 13
Step-by-step explanation:
Divide 325 by 25
Using the following triangle, what is the tangent of angle B?
Answer:
tanB=b/a
Step-by-step explanation:
A farmer wants to plant peas and carrots on no more than 200 acres of his farm. If x represents the number of acres of peas and y represents the number of acres of carrots for solution (x, y), then which is a viable solution?
A.(−50, 160)
B.(80, 160)
C.(75, −200)
D.(60, 135)
Answer:
Option D.(60, 135)
Step-by-step explanation:
Let
x -----> the number of acres of peas
y ----> the number of acres of carrots
we know that
The inequality that represent the problem is equal to
[tex]x+y\leq 200[/tex]
so
Verify each case
case A) (-50,160)
substitute the value of x and the value of y in the inequality and then compare the result
[tex]-50+160\leq 200[/tex]
[tex]110\leq 200[/tex] ----> is true
The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number
case B) (80,160)
substitute the value of x and the value of y in the inequality and then compare the result
[tex]80+160\leq 200[/tex]
[tex]240\leq 200[/tex] ----> is not true
therefore
The point is not a solution
case C) (75,-200)
substitute the value of x and the value of y in the inequality and then compare the result
[tex]75-200\leq 200[/tex]
[tex]-125\leq 200[/tex] ----> is true
The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number
case D) (60,135)
substitute the value of x and the value of y in the inequality and then compare the result
[tex]60+135\leq 200[/tex]
[tex]195\leq 200[/tex] ----> is true
therefore
The point is a viable solution
Pia printed two maps of a walking trail. The length of the trail on the first map is 8 cm. The length of the trail on the second map is 6 cm.
(a) 1 cm on the first map represents 2 km on the actual trail. What is the scale factor from the map to the actual trail? What is the length of the actual trail?
(b) A landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm. What is the scale factor from the first map to the second map? What are the side lengths of the landmark on the second map? Show your work.
Answer:
Two trail maps:
Trail on the first map is 8 cm
Trail on the second map is 6 cm
Scale on first map is 1 cm : 2 km
A. What is the scale factor from the map to the actual trail?
For the first map, the scale factor is 1 cm: 2km. Therefore the actual trail is 8 centimeters * 2 kilometers = 16 km.
The scale factor of the second map is 16 km / 6 cm = 2.67 km : 1 cm
B. The length of the actual trail is 16 kilometers.
Answer:
Given:
Two trail maps:
Trail on the first map = 8 cm
Trail on the second map = 6 cm
Scale on first map = 1 cm : 2 km
A) What is the scale factor from the map to the actual trail?
For the first map, the scale factor is 1 cm: 2km. Therefore the actual trail is 8 centimeters * 2 kilometers = 16 km.
The scale factor of the second map is 16 km / 6 cm = 2.67 km : 1 cm
B) The length of the actual trail is 16 kilometers.
Step-by-step explanation:
I
f point A is located at (–15, –7) and JKL has vertices at J(–22.5, –10.5), K(19.5, –3.0), and L(–4.5, 15.0), find the scale factor ABC to JKL of the dilation from
Answer:
1.5
Step-by-step explanation:
The coordinate values of point J are 1.5 times those of point A, so if dilation is about the origin, the scale factor is 1.5.
If the dilation is about some other point, this problem statement does not contain enough information to tell what the scale factor might be.
Gabriel is making a mixture of compost and soil to use for a special plant.He wants his final mix to be 2 parts compost to 6 parts potting soil.He wants to end up with 10 kilograms of mix.How many compost should Gabriel use?
Answer:
2.5 kg
Step-by-step explanation:
Parts of compost = 2 parts
Parts of potting soil = 6 parts
Total parts = 2 parts + 6 parts = 8 parts
from the above, we can see that 2 out of 8 parts of the total mix is compost,
i.e compost makes up [tex]\frac{2}{8}[/tex] of the total mix.
Given: total mix is 10 kg,
the amount of compost is then [tex]\frac{2}{8}[/tex] x 10 kg = 2.5 kg
Answer:Your answer is 2.5
Step-by-step explanation:
HELP ME!!!!! ......
The number –1,000 can be used to indicate a(n) A. increase in inventory of 1,000 units. B. harvest of 1,000 bushels of wheat. C. withdrawal of $1,000 from a checking account. D. receipt of $1,000.
Answer:
C. withdrawl of $1000 from a checking account
Step-by-step explanation:
When you withdraw money from a checking account, you lose the amount of money which you withdraw. In this situation, you are withdrawing $1000, which means you have -1000 dollars in your checking account
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Rosana is tracking how many customers she can serve in a morning. She listed the number of customers served per hour in the following table:
Hour (x) Number of Customers f(x)
1 3
2 5
3 7
Determine if these data represent a linear function or an exponential function, and give the common difference or ratio.
A. This is a linear function because there is a common difference of 2.
B. This is an exponential function because there is a common ratio of 2.
C. This is a linear function because there is a common difference of 3.
D. This is an exponential function because there is a common ratio of 3.
Answer:
A. This is a linear function because there is a common difference of 2
Step-by-step explanation:
Differences are ...
5 - 3 = 27 - 5 = 2The differences of 2 are common, so this is an arithmetic function.
Option: A is the correct answer.
A. This is a linear function because there is a common difference of 2.
Step-by-step explanation:Linear function--
A function is said to be linear if the rate of change is constant.
i.e. the function is increasing by a fixed constant.
Here the table is given by:
Hour (x) Number of Customers f(x)
1 3
2 5
3 7
From the table of values we observe that as the value of increasing by 1 the value of y is increasing by 2.
i.e. the rate of change is constant i.e. 2.
Also, the common difference is 2.
since,
5-3=2
and 7-5=2
Hence, the table represents a linear function.
The sum of all but one interior angle of a heptagon is 776°. The final angle must have a measure of degrees.
Answer:
The final angle is 124°
Step-by-step explanation:
1. Getting the total sum of all angles:
The general rule to get the sum of all interior angles is as follows:
sum of interior angles = (n-2)*180
where n is the number of sides
We know that a heptagon has 7 sides, therefore:
sum of interior angles of a heptagon = (7-2)*180 = 5 * 180 = 900°
2. Getting the missing angle:
We know that the total sum of all 7 angles is 900°
We also know that the sum of 6 of those angles = 776°
This means that:
measure of the last angle = 900 - 776
measure of last angle = 124°
The final angle is 124°
Hope this helps :)
Answer:
124 degrees
Step-by-step explanation:
A box has a base of 13 inches by 12 inches and a height of 30 inches. What is length of the interior diagonal of the box? Round to the nearest hundredth
The diagonal of a box is found by the formula:
Diagonal = √(length^2 + width^2 + height^2)
Diagonal = √(13^2 + 12^2 + 30^2)
Diagonal = √(169 + 144 + 900)
Diagonal = √1213
Diagonal = 34.828
Rounded to nearest hundredth = 34.83 inches.
Answer:
34.83 in
Step-by-step explanation:
See attached
In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that the test has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?
Answer:
1329
Step-by-step explanation:
A suitable calculator can tell you the minimum score is 1329.
Using the concept of z-scores and normal distributions, the lowest possible SAT score a student needs to qualify for acceptance into a top university, that requires top 5% of SAT scores, is approximately 1328.
Explanation:The subject of your question falls under Mathematics, particularly statistics. The problem involves understanding SAT scores and how they apply to scholarships. The problem also asks for the understanding of z-scores and how they apply to normal distributions.
In this case, the SAT score requirement is stated to be within the top 5% of all test-takers. In terms of z-scores, this requirement matches with a z-score of approximately 1.64, since z-scores of this value represent the cut-off for the top 5% in a normal distribution.
To calculate the corresponding SAT score, we use the formula for z-score which is Z = (X - μ) / σ, where X is the SAT score, μ is the mean and σ is the standard deviation. We rearrange the formula to find X, where X = Z * σ + μ. Since we know the mean (μ = 1000), standard deviation (σ = 200), and Z (Z = 1.64), we can substitute these values to get X = 1.64 * 200 + 1000 = 1328.
Therefore, the lowest possible score a student needs to qualify for acceptance into the university is approximately 1328.
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This week, 300 tickets were sold to the school play. This is 120 percent of the number of tickets sold last week. How many tickets were sold last week for the school play?
Answer:
250 tickets
Step-by-step explanation:
300/1.2 or 120%
= 250 tickets
Answer:
250 tickets
Step-by-step explanation:
I have a model motorcycle that is all metal parts and is 18" long. Since the size all the models online are given in a scale, What scale to an actual motorcycle do I have and where do I look to find a value?
Answer:
See below.
Step-by-step explanation:
The model may have the scale written somewhere. Try looking for it.
If you can't find it, then you can calculate this way.
Search online for the real motorcycle's length.
Then divide the scale model's length, 18 inches, by the real length. Express that as a ratio. That is the scale.
Let's say the length of a real motorcycle of this type is 90 inches.
Divide 18 inches by 90 inches.
18/90 = 1/5
The scale, then, is 1:5.
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Sum of Arithmetic Series (Sigma Notation)
Find the numerical answer to the summation given below.
(Image Shown Below)
[tex]\displaystyle\sum_{n=2}^{91}(3n+8)=\sum_{n=1}^{91}(3n+8)-a_1=(*)\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\a_1=3\cdot1+8=11\\n=91\\a_n=3n+8\\d=a_n-a_{n-1}\\a_2=3\cdot2+8=14\\d=14-11=3\\a_{91}=11+(91-1)\cdot 3=11+90\cdot3=281\\\\S_{91}=\dfrac{11+281}{2}\cdot91=146\cdot91=13286\\\\(*)=13286-11=\boxed{13275}[/tex]
Solve for x.
5(2x - 1) = 6
x = 1/10
x = 11/10
x = 1/2
Answer:
Distributive Law : x= [tex]\frac{11}{10}[/tex]
Step-by-step explanation:
5(2x - 1) = 6
Using Distributive law on right hand side we get
5*2x - 5 * 1 = 6
10x - 5 = 6
Now we add 5 on both hand sides
10x-5+5=6+5
10x= 11
Now we divide both sides by 10
[tex]\frac{10x}{10} = \frac{11}{10}[/tex]
Hence we get
x= [tex]\frac{11}{10}[/tex]
Find the area of a regular hexagon with an apothem 11.4 yards long and a side 13 yards long. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
area=6×11.4×13÷2=444.6 yd²
Final answer:
The area of a regular hexagon with an apothem of 11.4 yards and a side of 13 yards is approximately 444.6 square yards when rounded to the nearest tenth.
Explanation:
To find the area of a regular hexagon with a given apothem and side length, you can use the formula for the area of a regular polygon:
Area = (1/2) × Perimeter × Apothem
In this case, the perimeter of the hexagon can be calculated by multiplying the length of one side by 6 (since a hexagon has 6 sides). Therefore, the Perimeter = 13 yards × 6 = 78 yards.
Now, plug the values into the area formula:
Area = (1/2) × 78 yards × 11.4 yards
Area = (1/2) × 889.2 square yards
Area = 444.6 square yards
So, the area of the regular hexagon is approximately 444.6 square yards, when rounded to the nearest tenth.
How many terms are in the expression shown below?
2x3 - 10x2 +Z
2
3. 4. 5
Answer:
3 terms. All of the numbers are considered terms.
Step-by-step explanation:
If it asked for variables, it would be 2.