Simplifying the algebraic expression [tex]( x + 4 ) ( 2 x + 9 )[/tex] will give an answer [tex]2x^{2}+17x+36[/tex].
The technique of writing an algebraic expression in the most effective and compact form without altering the original expression's value is known as simplification.
The procedure involves gathering related phrases, which calls for adding or removing terms from an expression.
According to the distributive property of algebraic expressions, each term in an expression's sum or difference must be multiplied by a number outside of the parenthesis. A number is used as the value outside of the parenthesis with the total or difference.
Here the algebraic expression is:
[tex]( x + 4 ) ( 2 x + 9 )[/tex]
Use the distributive property to simplify the expression,
⇒ [tex]( x + 4 ) ( 2 x + 9 )[/tex]
⇒ [tex](x)(2x)+(x)(9)+(4)(2x)+(4)(9)[/tex]
⇒ [tex]2x^{2} +9x+8x+36[/tex]
⇒ [tex]2x^{2} +17x+36[/tex]
Therefore, the solution will be [tex]2x^{2} +17x+36[/tex] when the algebraic expression is simplified.
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PART A: Given the rate at which the zookeeper is giving the animals hay and grain, on which day will she have the same amount of grain and hay remaining? Explain how you determined your answer
Given the rate at which the zookeeper is giving the animals hay and grain, on which day will she have the same amount of grain and hay remaining is 6 days.
Every three days, one pound of hay and one pound of feed are used.
10 pounds of grain and 8 pounds of hay are present.
There are 6 pounds of hay and 6 pounds of grain left on the sixth day.
A rate in mathematics is the comparison of two related values expressed in different units.
The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
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At a sale, dresses were sold for $76 each. If the dresses originally cost $200 each, what percentage of its original price was a dress sold for?
According to the given information 62% of its original price was a dress sold.
A percentage of what?A % is a quantity or ratio that, in mathematics, representing a portion of one hundred. A non - dimensional connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, as well as decimals. The sign "%" is frequently put after the number to indicate percentages.
Briefing:Each dress price = $76
If Original price = $200
Formula = (price difference/ original price)100
Prince deference = 200-76 = $124
In percentage :
[tex]\left(\frac{124}{200}\right) \times 100[/tex]
= 12400/200
= 62%
Thus the final answer is 62% .
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One thousand tickets are sold at $5 each. One ticket will be randomly selected and the winner will receive a color television valued at $375. What is the expected value for a person that buys one ticket?
Multiple choice:
-$4.62
-$1.00
$1.00
$4.62
Answer:
Hope this helps, Good Luck! :)
Step-by-step explanation:
EV = - + prob(win)*win
= -5 + 1/1000 * 375
= -4.62
The requried, the expected value for a person that buys one ticket is approximately -$4.62. The correct answer is option A. -$4.62.
To calculate the expected value, we need to consider the probability of winning the color television and the corresponding value of the prize. We can then subtract the cost of buying the ticket to find the expected value.
Given:
Cost of one ticket = $5
Value of the color television (prize) = $375
Number of tickets sold = 1000
The probability of winning the color television is 1 out of 1000, as only one ticket will be selected out of the total 1000 tickets sold.
Expected Value (EV) = (Probability of winning * Value of prize) - Cost of the ticket
EV = (1/1000 * $375) - $5
EV = $0.375 - $5
EV = -$4.625
Rounded to two decimal places, the expected value for a person that buys one ticket is approximately -$4.62. The correct answer is option A. -$4.62.
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According to last year's 7th grade standards test results 73% of the students and John's graduating class passed the math section. If 400 students took the test how many students did not pass the math section.
Answer:175
Step-by-step explanation:
you have ads personalization enabled for your property, but want to exclude specific events. what does this mean for the data for those events?
This mean for the data for those events is that data will only be used for measurement purposes.
Given :
You have ads personalization enabled for your property, but want to exclude specific events.
You may use digital advertising to help reach people online and drive conversions on your application and website when you enable personalization in analytics .
Example :
By activating you gain the ability to use your analytics audiences to personalize your digital , which can improve the performance of your campaigns.
You can adjust personalization for a specific event type or user property in your analytics property.
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Find the annual percentage yield (APY) for the investment. $8000 at 5.75% compounded daily
The annual percentage yield (APY) for the investment $8000 at 5.75% compounded daily is; 5.918%
How to calculate the Annual Percent Yield?
The Annual percentage yield(APY) is defined as the amount of interest you'll earn in one year from a savings account.
Annual percentage yield (APY) is calculated by the usage of the formula;
APY= (1 + r/n )ⁿ – 1
Where;'
r is the said annual interest rate
n is the variety of compounding intervals every year.
Thus, we are given;
r = 5.75% = 0.0575
n = 365 days
Thus;
APY= (1 + (0.0575/365 )³⁶⁵ – 1
APY = 5.918%
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in the simplex method, the pivot column is the column with the most negative number (to the left of the vertical bar) in the bottom row. why?
The most negative number corresponds to the variable that has the largest impact on the Value of the objective function. So, maximizing it first is most efficient.
What is pivot column in simplex method?
The Simplex method's pivot column is selected by the fundamental variable's biggest reduced cost coefficient. 4. The highest ratio of right side parameters to positive coefficients in the pivot column determines the pivot row in the Simplex approach.
A location of a leading entry in the matrix's echelon structure. A pivot is a non-zero number that is either transformed into a leading 1 and then used to make 0s, or it is utilized in a pivot position to create 0s.
The element of a matrix or array chosen first by an algorithm (such as Gaussian elimination, simplex algorithm, etc.) to do particular computations is known as the pivot or pivot element.
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The perimeter of a rectangular field is 298 yards. If the width of the field is 65 yards, what is its length?
Answer:
4.6
Step-by-step explanation:
298 divided by 65=4.58....
If 16* = find the value of x. 1 64 7
Answer:it's 16 or 4 I can't confirm
Step-by-step explanation:
A point is plotted on the number line at 3. A second point is plotted at 5.
What is the length of a line segment joining these points?
Enter your answer as a simplified mixed number in the box.
PLEASE HELP!!
Answer:
[tex]\huge{\boxed{2 \text{ units}}}[/tex]
Step-by-step explanation:
N.B. I attached an image of the number line as presented by the problem.
The absolute value of a number is its distance from zero. A simple way to say that is that the absolute value of a number is the number made positive and is denoted by "||"
i.e.
|-4| = 4
|4| = 4
|-219| = 219
The distance between two points on a number line is the absolute value of their difference. Thus, simply do:
|5 - 3|
|2|
2
OR
|3 - 5|
|-2|
2
Thus, the length of the segment is simply 2.
Hope it helps :) and let me know if you want me to elaborate.
Translate and solve the following: three more than the difference of 6s and 5s is equal to the sum of 12 and 6.
Therefore, the value of "s" that satisfies the given equation three more than the difference of 6s and 5s is equal to the sum of 12 and 6. is 15/4.
What are linear equations?A linear equation is one where the variable's maximum power is 1. To put it another way, a linear equation is one that has the form axe + b = 0, where a and b are constants and x is the variable.
The speed of an item travelling straight forward or the pace at which a population is increasing are two examples of real-world scenarios that are equal to the frequently modelled using linear equations. They are rather easy to resolve, and the answers may be obtained by applying fundamental algebraic strategies such isolating the variable and running calculations on both sides of the problem.
In several disciplines, including physics, engineering, and economics, linear equations are used extensively.
How to solve?
Let "s" be the unknown value that we are trying to find.
3 + (6s - 5s) = 12 + 6
3 + (6s - 5s) = 12 + 6
3 + 1s = 18
4s = 15
s = 15/4
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(7 × 10) + (7 × 10%) + (7 × 10²) = 700 070.07
Write down a possible set of values for x, y and z.
The equation (7 × 10) + (7 × 10%) + (7 × 10²) = 700 070.07 can be rewritten as:
7x + 0.7y + z = 700 070.07
To find a set of values for x, y, and z that satisfies this equation, we can use trial and error. One possible set of values is:
x = 100
y = 10
z = 7000
If we plug these values into the equation, we get:
(7 × 100) + (7 × 0.1) + (7 × 7000) = 700 070.07
Which simplifies to:
700 + 0.7 + 49000 = 700 070.07
This equation is true, so the values x = 100, y = 10, and z = 7000 are a solution to the original equation.
function rule to find f(10).
Answer:
[tex]f(10) = 103[/tex]
Step-by-step explanation:
f(x) = 3+10x
when x is 10, we have
3+10*10
= 103
:]
loverdale Middle School is buying new helmets for the football team. Each helmet costs $89.95. How much money does the school spend if they buy 45 of these football helmets?
Answer:
$4047.75
Step-by-step explanation:
If each helmet costs $89.95 and there are 45 of these helmets, you would multiply $89.95 x 45. Plug this into a calculator and you get $4047.75.
What is the value of x in this figure?
The value of x in the figure is 5√3.
What is the trigonometry?
Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.
What does cos 30 mean?
The trigonometric function "Cosine" is denoted by the notation "Cos." The definition of cosine is the ratio of a right-angle triangle's hypotenuse to base length (the longest and slant side). Cos (x), where x is the angle formed by the two sides, equals base/hypotenuse, or b/h.
What is the formula of Cos 30?
Cos 30° = √3/2
3/2 is the value of Cos 30°, which is a trigonometric ratio or trigonometric function of a specific angle. The exact value of cos 30 degrees is expressed as 0.8660 roughly.
Cos 30°= b/h
√3/2 = x/10
X= √3/2 × 10
X= 5√3
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Which expression is equivalent to the following complex fraction? startfraction 1 over x endfraction minus startfraction 1 over y endfraction divided by startfraction 1 over x endfraction + startfraction 1 over y endfraction startfraction y + x over y minus x endfraction startfraction (y minus x) (y + x) over x squared y squared endfraction startfraction x squared y squared over (y + x) (y + x) endfraction startfraction y minus x over y + x endfraction.
I believe that x²y²/((y+x)(y+x)) is identical to (1/x-1/y)/(1/x+1/y) based on the expression above.
What is expression?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Here,
Expression:
=(1/x-1/y)/(1/x+1/y)
Option:
=((y+x)/(y-x))
=((y-x)(y+x))/x²y²
=x²y²/((y+x)(y+x))
=(y-x)/(y+x)
From the above expression, I think x²y²/((y+x)(y+x)) is equivalent to (1/x-1/y)/(1/x+1/y).
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Answer: aka (D) edg 2023
Step-by-step explanation:
trust ^.^ hoped this helped
Kayden's math teacher said that each
question answered correctly on a test would
be worth 7 points. Answer the questions
below regarding the relationship between
the number of questions correct and the
score on the test.
Step-by-step explanation:
Kayden's math teacher said that each question answered correctly on a test would be worth 7 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
Since 00 questions correct gets you 00 points on the test, the function will have a yy-intercept of 0.0.
The rate at which points are earned is 7 points per question, so the slope of the function should be 7.7.
\text{Function Rule:}
Function Rule:
V(x)=7x
V(x)=7x
Plug x=11 Into Rule:
V(11)=7(11)=77
Correct Answer:
The independent variable, x, represents the number of questions correct, and the dependent variable is the score on the test, because the score on the test depends on the number of questions correct.
A function relating these variables is V(x) =V(x)= 7x7x.
So V(11) =V(11)= 7777, meaning 1111 questions correct will earn 7777 points on the test
4/6 x 3/5 in the simplest form.
Answer:
Step-by-step explanation:
2/5
what is the slope of the line tangent to f(x)= x-sin(x) at x= pi
The slope of the line tangent to the given function would be m= 2.
What is the slope of the function?
If the function f(x) is given then differentiation will give you the gradient or slope for the tangent at any point.
The given function is f(x) = x - sinx
Now differentiating the above function with respect to x.
f'(x) = 1 - cosx
Now put x = π, we get
Slope = 1 - cos(π)
= 1 - (-1)
= 1 + 1
Slope (m) = 2.
Hence, the slope of the line tangent to the given function would be m= 2.
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Kevin uses each of the digits 5, 7, 4 and 9, once and once only, to make
four-digit numbers.
c) What is the largest number that he can make?
d)
What is the smallest even number that he can make?
Answer:
largest number= 9754
smallest number = 4579
Step-by-step explanation:
largest number - 9754
9 is the larger number in 5,7,4,9
7 is the second largest
so you basically count it backwards
smallest number=4579
4 is the smalleat number in 5,7,4,9
so you basically count forward
2x - 7 + 3x + 10 > x - 6 + 8x - 11 PLEASE SOLVE "STEP BY STEP" AND SHOW ME THE WORK!
thank you!
Answer:
x<5
Step-by-step explanation:
2x-7+3x+10>x-6+8x-11
5x+3>9x-17
5x-9x>-17-3
-4x>-20
x<5
Answer:
x < 5
Step-by-step explanation:
step 1: simplify both sides of the inequality.
5x + 3 > 9x − 17
step 2: subtract 9x from both sides.
5x + 3 − 9x > 9x − 17 − 9x − 4x + 3 > − 17
step 3: subtract 3 from both sides.
−4x + 3 − 3 > − 17 −3 − 4x > − 20
step 4: divide both sides by -4.
-4x/-4 > -20/-4
x < 5
(4b-7)^2 find the product
Answer:
16b2-56b+49
Step-by-step explanation:
hope this helps
in order to conduct an experiment, four subjects are randomly chosen from a group of 20 people . how many differenty groups of four subjects are pssoibke
The total number different groups of four subjects are possible are 4845 ways.
Define the term combination?A combination is indeed a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.The formula for the combination is-
ⁿCr = n!/r!(n - r)!
We are wondering in how many distinct options there are to choose 4 subjects out of 20;
n = 20
r = 4.
Sequence is not important because the topics can be arranged in any order and still form the same group, hence we must use a combination:
Review the combination's definition:
²⁰C₄ = 20!/4!(20 - 4)!
²⁰C₄ = 20!/4!16!
²⁰C₄ = 4845
Thus, the total number of different groups four subject groupings is 4845.
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solve for x -12x-14=24
PLEASE HELP NOW ILL DO ANYTHING
Answer: x= 38/11
Step-by-step explanation: x-12x-14=24
-11x-14=24
Add 14 to both sides
simplfy
-11x=38
Divide both sides by the same factor
x=11-38/11
Answer:
3
Step-by-step explanation:
someone help me I need a good grade my mom gonna yell at my if i don't get it ):
The correct justification for the given steps are;
Step 1; Addition property of equality.
Step 2; Subtraction property of equality.
Step 3; Division property of equality.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
For the given condition,
⇒ 200 + 20w = - 100 + 25w
Where, 'w' is number of weeks.
Now,
Since, For the given condition,
⇒ 200 + 20w = - 100 + 25w
Where, 'w' is number of weeks.
Solve for w as;
⇒ 200 + 20w = - 100 + 25w
Apply Addition property of equality,
⇒ 200 + 20w + 100 = - 100 + 25w + 100
⇒ 300 + 20w = 25w
Apply Subtraction property of equality,
⇒ 300 + 20w - 20w = 25w - 20w
⇒ 300 = 5w
Apply Division property of equality,
⇒ 300/5 = 5w/5
⇒ 60 = w
⇒ w = 60
Thus, The correct justification for the given steps are;
Step 1; Addition property of equality.
Step 2; Subtraction property of equality.
Step 3; Division property of equality.
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The two statements below are different ways to say that the sides of these similar triangles are proportional.
Complete the equations that go with the statements.
Drop down options
1: e,f
2: q,r
3: p,q,r
4: d,e,f
Step-by-step explanation:
it is simple : it always has to be the corresponding side of the other triangle. all sides must have the same scaling factor.
d/p = e/q = f/r
d/e = p/q
e/f = q/r
f/d = r/p
The equations that go with the statements are; e/f = q/r and f/d = r/p
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inversely proportional, can be built to find the desired measures in the problem.
We want the different ways sides of similar triangles can be shown as proportional.
Corresponding sides
From shorter to longer, the corresponding sides in similar triangles are ...
Smaller ... Larger
b . . . . . . . e
a . . . . . . . d
c . . . . . . . f
d/p = e/q = f/r
d/e = p/q
e/f = q/r
f/d = r/p
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What is the standard form of the equation of the circle with the given center (-6,8) and radius r=10
Answer:
(x+6)^2 + (y-8)^2 = 10^2
or
(x+6)^2 + (y-8)^2 = 100
Step-by-step explanation:
Equation of a circle in standard form: (x-h)^2 + (y-k)^2 = r^2
(h,k) represent the center of the circle
h = -6
k = 8
r = the length of the radius
10^2 = 100
What can you divide to get 1.25
Dividing 1.25 by 1: 1.25 / 1 = 1.25
Dividing 1.25 by 5: 1.25 / 5 = 0.25
Dividing 1.25 by 8: 1.25 / 8 = 0.15625
Dividing 1.25 by 10: 1.25 / 10 = 0.125
what are three powers that have values greater than 120 and less than 130. ?
Answer: 11^2, 5^3, 2^7
Step-by-step explanation:
11^2= 121
5^3= 125
2^7= 128
Is the system of equations consistent and independent, consistent and dependent, or inconsistent?
y=−x+1
2y=−2x+2
Select the correct answer from the drop-down menu.
After solving the equations it will the infinite solutions, then it is a consistent system.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given information in the question,
The equations are,
y = -x + 1 (i) and,
2y = -2x + 2 (ii)
Divide equation (ii) by 2
y = -x + 1 (iii)
Solve equation (i) and (iii)
The value of x and y will be 0 which means that it has infinite solution, then it is a consistent system.
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