The inequality according to the the cost of pack of paper can be written as x ≤ 14.28 and Mr. Valentino can purchase a maximum of 14 packs of paper.
What is inequality?
A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. The two most common notations for representing various forms of inequalities are as follows:
The symbol a < b indicates that a is smaller than b.
The symbol a > b indicates that a is bigger than b.
Let's assume he can buy x pack of paper.
Cost of x pack of paper will be equal to the x times cost of 1 pack of paper
i.e. Total cost = 1.75x
Now, Mr. Valentino has $25
Therefore,
1.75x ≤ 25
Inequality is ⇒ x ≤ 14.28
It tells us that Mr. Valentino can purchase only 14 packs of paper.
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pls explain with working out
Answer: 26m
Step-by-step explanation:
The area is 36m^2, the possible measurement that could've worked is 4m for width and 9m for length (4x9=36). Now just do 4+4+9+9 = 26m.
Hope this helped
help please i need it
Find the value of x that satisfies the given conditions. Then graph the line on a separate sheet of paper.
The line containing (4, -2) and (x,-6) is perpendicular to the line containing (-2, -9) and (3,-4).
The value of x will be 8.
And, Graph of the line y = -x + 2 is shown in figure.
What is Equation of line?
The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The condition is;
The line containing the points (4, -2) and (x,-6) is perpendicular to the line containing the points (-2, -9) and (3,-4).
Since, Multiplication of Slopes of perpendicular lines are -1.
That is;
m₁ m₂ = -1
Where, m₁ is slope of first perpendicular line and m₂ is slope of second perpendicular line.
Now, Find the slopes of lines as;
m₁ = (-6 - (-2)) / (x - 4)
m₁ = - 6 + 2 / x - 4
m₁ = - 4 / (x - 4)
And, Slope of second line,
m₂ = (-4 - (-9)) / (3 - (-2))
m₂ = (-4 + 9) / (3 + 2)
m₂ = 5 / 5
m₂ = 1
Hence,
m₁ m₂ = -1
Substitute all the values, we get;
- 4 / (x - 4) × 1 = -1
4 = x - 4
x = 4 + 4
x = 8
Thus, The points on the line is (4 , -2) and (8 , -6).
So, Slope (m₁) = (- 6 - (-2)) / (8 - 4)
= (-6 + 2) / 4
= - 4 / 4
= -1
Thus, The equation of line passing through the points (4 , -2) and
(8 , -6) with slope -1 is;
y - (-2) = - 1 (x - 4)
y + 2 = -x + 4
y = - x + 4 - 2
y = - x + 2
Therefore,
The value of x will be 8.
And, Graph of the line y = -x + 2 is shown in figure.
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mad elf is a holiday beer that is 11.0% abv. a 12 oz bottle of mad elf has 300 calories. the rest of the calories, other than alcohol, come from carbohydrates. approximately how many grams of carbohydrates are in mad elf?
The bottle contains 9.36 g of carbohydrates.
We have,
12 oz bottle contains 300 calories
We know, 1 oz = 23.35 g
12 oz = 12 * 23.35 g =280.2 g of bottel
Alcohol content = 11 %
So, the total number of alcohol in the bottle is [tex]\frac{11}{100} *280.2 = 30.8 g[/tex]
So, the bottle contains 30.8 g of alcohol.
1 gram of alcohol 7 cal of energy,
So, 30.8 g of alcohol = 7 * 30.8 cal of energy
= 215.7 cal of energy
So, out of a total of 300 calories of mad elf, 215.7 calories come from alcohol.
So, (300-215.7 ) = 84.3 calories come from carbohydrates.
Each gram of carbohydrate produces 9 calories of energy.
9 calories of energy from 1 gram of carbohydrate,
1 calorie of energy from 1/9 of carbohydrate.
So, 84.3 calories from [tex]\frac{1}{9}*84.3 = 9.36 g[/tex]
Hence, the bottle contains 9.36 g of carbohydrates.
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Write a polynomial function, p(x), with degree 3 that has p(7) =0
The polynomial function, p(x), with degree 3 that has p(7) = 0 is p(x) = [tex]x^{3} -7x^{2} +12x-84=0[/tex].
According to the question,
We have the following conditions to find the polynomial function, p(x):
The degree has to be 3 and the value of p(7) should be 0.
Now, we are sure that we have one term as [tex]x^{3}[/tex].
Now, when 7 has to be multiplied three times we have 343 as the result.
So, we will try to make it zero in the next term.
The next term can be[tex]-7x^{2}[/tex] because we will get -343 and the result of the first two terms will be 0.
Now, the third term can be 12x (you can take any term but we have to make sure that the end result is 0).
Now, the result will be 84 when we put 7 in place of x.
Now, we can have -84.
So, we will add these 4 terms to form the polynomial function:
p(x) = [tex]x^{3} -7x^{2} +12x-84=0[/tex]
Hence, the required polynomial function is p(x) = [tex]x^{3} -7x^{2} +12x-84=0[/tex].
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Rewrite all 3 fractions with the least common denominator between them.
Answer:
To rewrite the given fraction with the least common denominator between them
The given fractions are,
[tex]\frac{1}{3},\frac{5}{10},\frac{7}{30}[/tex]we get, LCM of 3,10,30 is 30
The equivalent fractions for the above factions as common denominator 30 is as follows,
For 1/3,
Multiply and divide by 10, we get,
[tex]=\frac{1}{3}\times\frac{10}{10}=\frac{10}{30}[/tex]Using this we get,
[tex]\frac{1}{3}=\frac{10}{30}[/tex]For 5/10,
Multiply and divide by 3, we get,
[tex]\frac{5}{10}=\frac{5}{10}\times\frac{3}{3}=\frac{15}{30}[/tex]Using this we get,
[tex]\frac{5}{10}=\frac{15}{30}[/tex]For 7/30,
Since the denominator 30, we get same fraction,
[tex]\frac{7}{30}=\frac{7}{30}[/tex]Answer is:
[tex]\frac{1}{3}=\frac{10}{30}[/tex][tex]\frac{5}{10}=\frac{15}{30}[/tex][tex]\frac{7}{30}=\frac{7}{30}[/tex]Students make 93.5 ounces of liquid soap for a craft fair they put the soap in a 8.5 ounce bottles and sell each bottle for 5.50 how much do the students earn if they sell all the bottles of liquid soap
For a craft show, students make 93.5 ounces of liquid soap. They package the soap in 8.5 ounce bottles and charge $5.50 per bottle. The students will earn $60.5.
Given that,
For a craft show, students make 93.5 ounces of liquid soap. They package the soap in 8.5 ounce bottles and charge $5.50 per bottle.
We have to find how much money will the students make if they sell all the liquid soap bottles.
Total amount of liquid soap prepared by the students for a craft fair = 93.5 ounces
Weight of each bottle in which students poured the soap = 8.5 ounces
Let us first calculate the number of bottles, each contains 8.5 ounces of soap from 93.5 ounces of soap.
So, Number of bottles = 93.5/8.5
= 11
So, 11 bottles are prepared which contains 8.5 ounces of soap from 93.5 ounces of soap.
The amount at which each bottle is sold = $5.50
The total amount earned by selling all the bottles of liquid soap = 11×5.50
= $60.5
Therefore, the students will earn $60.5 if they sell all the bottles of liquid soap.
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PLS HELP DUE NOWWWWWWWWWW
The correct statement will be:
A. The rate of change is the number of inches grown per month, and the initial value is the starting height.
We can form the following equation from the given data:
H(m) = 13 + 41m,
Where H ( Height ) is a function of the number of months ( m ).
We can see that the height changes with respect to months i.e. as the number of months increases, the height of the sunflower also increases.
The initial value or the initial height of the sunflower remains constant throughout and has less impact on its height.
So, option A will be the ultimate explanation for the data given.
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Answer:
Step-by-step explanation:
This is a linear function of time, as mentioned.
A linear function is always in the form of:
[tex]y=mx+b[/tex]
The 'sunflower's height is a linear function of time', so the [tex]x[/tex] variable represents the time (which is in terms of months here), and the [tex]y[/tex] would represent the sunflower's height after time has passed.
The initial value is when [tex]x=0[/tex].
[tex]x=0[/tex] means at the very beginning.
At the very beginning, the height would be the starting height, so the initial value would be the starting height.
The rate of change means the change in [tex]y[/tex] in respect to [tex]x[/tex].
Since [tex]y[/tex] represents the height after [tex]x[/tex] months, the rate of change would be the change in height per month.
You could also write it as the number of inches grown per month.
The initial value is the starting height, and the rate of change is the number of inches grown per month, so the correct answer is (A).
At a conference 1 car was provided for every 4 people if there were 17 cars how many people were there
Answer:
just multiply 17×4=?
and it will give u an anserew..
Answer:68 people
Step-by-step explanation:
You take the 17 cars multiplied by four people and you get 68
Which of these equations is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2)?
The equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2),
The midpoint of line joining (-4,4) and (2,-2) will be -
x[m] = (- 4 + 2)/2 = -1
y[m] = (4 - 2)/2 = 1
Coordinates of the midpoint will be M(-1, 1)
Slope of the line joining (-4,4) and (2,-2) will be -
m = (- 2 - 4)/(2 + 4)
m = -6/6
m = - 1
Then, the slope of the line perpendicular to this line will be -
m[p] = -1/-1
m[p] = 1
Assume that the equation of the perpendicular line as -
y[p] = x + c
Since it passes though (-1, 1) so -
1 = -1 + c
c = 2
Therefore, the equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.
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According to the distributive property, a(5 + b) =
Answer:
From the bit that you have given , we can say = 5a + ab = to the rest of the equation
can you take 73 devided by 17 and it be a whole number
all you need is in the photo please answer fastplease
Answer:
The cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]Explanation:
Let x and y represent the cost of a cupcake and cookie respectively.
Given that;
Five cupcakes and two cookies cost $19.75.
[tex]5x+2y=19.75-------1[/tex]Two cupcakes and four cookies cost $17.50.
[tex]2x+4y=17.50-------2[/tex]Let's solve the simultaneous equation by elimination;
multiply equation 1 by 2;
[tex]10x+4y=39.50-------3[/tex]subtract equation 2 from equation 3;
[tex]\begin{gathered} 10x-2x+4y-4y=39.50-17.50 \\ 8x=22 \\ \text{divide both sides by 8;} \\ \frac{8x}{8}=\frac{22}{8} \\ x=2.75 \end{gathered}[/tex]since we have the value of x, let substitute into equation 1 to get y;
[tex]\begin{gathered} 5x+2y=19.75 \\ 5(2.75)+2y=19.75 \\ 13.75+2y=19.75 \\ 2y=19.75-13.75 \\ 2y=6 \\ y=\frac{6}{2} \\ y=3.00 \end{gathered}[/tex]Therefore, the cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]
Two cylinders have the same volume. The first has a radius of 5cm and a height of 10 cm. The second has a radius of 10cm. The surface area of the first cylinder is and the surface area of the second i s
ANSWER
[tex]\begin{gathered} 1)150\pi \\ 2)250\pi \end{gathered}[/tex]EXPLANATION
For the first cylinder;
[tex]\begin{gathered} r=5 \\ h=10 \end{gathered}[/tex]Recall, the formula for calculating the surface area of a cylinder is;
[tex]A=2\pi rh+2\pi r^2[/tex]Now, substitute the values for the first cylinder;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times5\times10+2\times\pi\times5^2 \\ =100\pi+50\pi \\ =150\pi \end{gathered}[/tex]The volume of the first cylinder is calculated using the formula;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ \end{gathered}[/tex]Substitute the values of r and h for the first cylinder;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ =\pi\times5^2\times10 \\ =\pi\times25\times10 \\ =250\pi \end{gathered}[/tex]To get the surface area of the second cylinder, we need to calculate the height (h).
To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).
Hence;
[tex]\begin{gathered} V=250\pi \\ r=10 \\ V=\pi r^{2}h \\ 250\pi=\pi\times10^2\times h \\ h=\frac{V}{\pi \cdot \:r^2} \\ h=\frac{250\pi }{\pi 10^2} \\ =2.5 \end{gathered}[/tex]Substitute the height to calculate the surface area is calculated thus;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times10\times2.5+2\times\pi\times10^2 \\ =50\pi+200\pi \\ =250\pi \end{gathered}[/tex]Change 6.3 kg to grams pls it's urgent
Answer:
6,300 grams
Step-by-step explanation:
kg to g is multiply by 1,000
Answer:
Step-by-step explanation:
630%
Use the number line shown below. What is the location of Z between X and Y such that the length of ZY is 3 times the length of XZ.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
X = -5
Y = 4
Answer:
z is -2
Step-by-step explanation:
x = -5 y = 4
<----------------------------------------->
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Z is between x and y but is 3 times the lenght of x&z
so jumb from -5 to -3 thats one, however jumb from -2 to 0 that is 1, and form 0 to 2 that is 2, and from 2 to 4 that is 3.
Darnell and emma are college students . darnell currently has 22 credits and he plans on taking 6 credits per semester . emma has 4 credits and plans to take 12 credits per semester . after how many semesters , s will darnell and emma have the same number of credits ?
After 3 semesters Darnell and Emma have same number of credits as 40.
Given,
Current credit score of Darnell = 22
Current credit score of Emma = 4
Darnell plans to score a credit per semester = 6
Emma plans to score a credit per semester = 12
Now, we have to find that after how many semesters will Darnell and Emma have the same number of credits .
Here,
Current credit score of Darnell = 22
Current credit score of Emma = 4
After 1 semester,Credit score of Darnell = 22 + 6 = 28
Credit score of Emma = 4 + 12 = 16
After 2 semester,Credit score of Darnell = 28 + 6 = 34
Credit score of Emma = 16 + 12 = 28
After 3 semester,Credit score of Darnell = 34 + 6 = 40
Credit score of Emma = 28 + 12 = 40
That is,
After 3 semesters Darnell and Emma have same number of credits as 40
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the owner of a small deli is trying to decide whether to discontinue selling magazines. he suspects that only 8.4% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. assuming his suspicion that 8.4% of his customers buy a magazine is correct, what is the probability that exactly 3 out of the first 11 customers buy a magazine?
The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%
The proportion of customers that buy a magazine = 8.4%
If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%
Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;
probability = 8.4% × 27.27%
probability = (8.4/100) × (27.27/100)
probability = 0.084 × 0.2727
probability = 0.0223
Converting it into percentage as follows;
probability = 0.0223 × 100
probability = 2.23%
Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.
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Sara buys $30 of produce at the farmer's market. She spends $5more on green vegetables than she does on fruit. How much didSara spend on green vegetables? How much did she spend onfruit? Write and solve a system of equations.
Okay, here we have this:
Considering the provided information, we are going to write and solve the correspondinf system of equation, so we obtain the following:
According to the information given, we obtain the following system of equations, where we take x as money spent on fruit and y as money spent on green vegetables, so we have:
[tex]\begin{gathered} x+y=30 \\ x+(x+5)=30 \end{gathered}[/tex]Now let's solve for x in the second equation:
x+x+5=30
2x+5=30
2x=30-5
2x=25
x=25/2
x=12.5
Now from the value of x that we got, then we will plug it into the first equation to get the value of y:
[tex]\begin{gathered} x+y=30 \\ 12.5+y=30 \\ y=30-12.5 \\ y=17.5 \end{gathered}[/tex]Then, finally we obtain that she spend $12.5 on fruits and $17.5 on green vegetables.
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
= 6; = 2
P(5 ≤ x ≤ 9) =
The probability P(5 ≤ x ≤ 9) is 0.6847
Assume that x has a normal distribution
We have been the mean and standard deviation μ = 6; σ = 2.
To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.
z = (5 - 6)/2
= -0.5
and z = (9 - 6)/2
= 1.5
Then the probability is calculated as:
P(x ≤ 5) = 0.3085
P(x ≤ 9) = 0.9932
P(5 ≤ x ≤ 9) = 0.9932 - 0.3085
P(5 ≤ x ≤ 9) = 0.6847
Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847
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If the following fraction is reduced, what will be the exponent on the p ? -
2
5
4
3
The p has an exponent of 3 when the fraction is reduced
How to determine the exponent on p?The expression is given as
5p^5q^4/8p^2q^2
Remove all other variables, except the variable p
So, we have the following expression
p^5/p^2
Apply the law of indices in the above expression
So, we have the following equation
p^5/p^2 = p^5 - 2
Evaluate the difference
p^5/p^2 = p^3
The index on p is 3
Hence, the exponent on the p is 3
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Complete question
If the following fraction is reduced, what will be the exponent on the p? - 5p^5q^4/8p^2q^2 5 4 3 2
Please answer only if you know the answer thank you.
The equation of a line passing through the point (7, 8) with slope as -3 is option (A) 3x + y - 29 = 0 or y = -3x + 29
In the above question,
It is given that a line that passes through a point = (7 ,8)
The slope of the line = m = -3
The inclination of a line with respect to the horizontal is measured numerically is called as Slope
We know the slope intercept form of the line is
( y - y1) = m (x - x1)
where (x1 , y1 ) = ( 7 , 8)
and m = -3
Putting values in the slope intercept form of line, we get
( y - 8) = -3 ( x - 7)
y - 8 = -3x + 21
3x + y -8 - 21 = 0
3x + y - 29 = 0
y = -3x + 29
Hence, The equation of a line passing through the point (7, 8) with slope as -3 is y = -3x + 29
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If a train runs on a circular track of radius 400 meters through all four sections of the park, about how long is the part of the train track that runs through Water World?
The arc length is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]In this case the radius is 400 m and the angle is 36°, plugging these values we have:
[tex]\begin{gathered} s=2\pi(400)(\frac{36}{360}) \\ s=251.33 \end{gathered}[/tex]Therefore, the part of the train track that runs through water world is approximately 250 meters.
ILL Give one hundred points and Branly only if you do it right though
Answer:
1) -2
2) -2
3) -2
4) -3
5) -4
6) -15
7) -13
8) 3
1b) -9
2b) -2
3b) 7
4b) 17
5b) -4
6b) -9
7b) -16
8b) 0
1c) -5
2c) -3
3c) 0
4c) -2
5c) -8
6c) -11
7c) -3
8c) 15
Jeez, I hope this helps xD
Can anyone please answer this question, Ill give points.
Answer:
(0,1) and (-10.-4)
Step-by-step explanation:
To find the solutions, find the points where both the curve and line intersect and read off the coordinates
45 POINTS PLEASE HELP!!!
Decide whether inductive or deductive reasoning is used to reach the conclusion
the wolf population in a park has increased each year for the last 10 years. So, the wolf population will increase again next year
Given two terms from a geometric sequence, identify the first term and the common ratio: a10 = 1 and a12=1/25
Given:
a denotes first term and r denotes the common ratio.
[tex]a_{10}=1\colon a_{12}=\frac{1}{25}[/tex][tex]a_n=ar^{n-1}[/tex][tex]a_{10}=ar^{10-1}[/tex][tex]1=ar^9\ldots.\text{ (1) }[/tex][tex]a_{12}=ar^{12-1}[/tex][tex]\frac{1}{25}=ar^{11}\ldots.(2)[/tex]Divide the equation (2) by (1)
[tex]\frac{\frac{1}{25}}{1}=\frac{ar^{11}}{ar^9}[/tex][tex]\frac{1}{25}=r^2[/tex][tex]r=\pm\frac{1}{5}[/tex][tex]\text{If r=}\frac{1}{5}[/tex][tex]1=a(\frac{1}{5})^9[/tex][tex]a=1953125[/tex][tex]\text{If r=-}\frac{1}{5}[/tex][tex]1=a(-\frac{1}{5})^9[/tex][tex]a=-1953125[/tex][tex]a=-1953125\text{ ; r = -}\frac{1}{5}[/tex][tex]a=1953125\text{ ; r = }\frac{1}{5}[/tex]Match each number to its opposite. 1. -8 8 2. -1 -11 3. -17 17 4. 31 -31 5. 11 1
The opposite for each number is: ( -8, 8), (-1,1), (-17,17), (31,-31) and (11,-11).
Number Classification Whole Numbers - They are the numbers represented by positive real numbers where the fractions and decimal numbers are not included. Integer Numbers - They are the whole numbers. They are represented by zero, positive and negative numbers. Opposite numbers - They are numbers that the distance to 0 is equal. The numbers are classified as the opposite when the sum between them is equal to zero (0).Thus, you can conclude that the opposite number of a positive number is a negative number. And the opposite number of a negative number is a positive number.
The question gives the follow numbers
1. -8 8
2. -1 -11
3. -17 17
4. 31 -31
5. 11 1
The opposite for:
-8 is the number 8-1 is the number 1-17 is the number 1731 is the number -3111 is the number -11Read more about number classifications here:
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3 3 Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost 2 pounds less than 2 times the pounds 3 he lost the first week. The third week, he lost 1 pound more than ã of the pounds he lost the first week. 3 Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 2 times the pounds Luke lost the first 5 week. The second week, he lost 4 pounds less than 2 times the pounds Luke lost the first week. The third week, he lost 2 pound more 5 than 3 times the pounds Luke lost the first week. Assuming they both lost the same number of pounds over the three weeks, complete the following sentences. 4 pounds 6 pounds 21 4 2 pounds 13 - 40Luke started a weight loss program the first week he lost X pounds the second week he lost 3/2 pounds less than 3/2 times the pounds he lost the first week the third week he lost 1 pound more than three-fourths of the Pouncey lost the first week
We know that Luke lost x pounds the first week.
We also know that the second week 3/2 less than 3/2 times the pounds he lost the first week, this means that the secons week he lost:
[tex]\frac{3}{2}x-\frac{3}{2}[/tex]Finally the third week he lost 1 pound more than 3/4 of the pounds he lost the first week. This can be written as:
[tex]\frac{3}{4}x+1[/tex]Hence luke lost a total of:
[tex]x+\frac{3}{2}x-\frac{3}{2}+\frac{3}{4}x+1=\frac{13}{4}x-\frac{1}{2}[/tex]Therefore the expression for Luke's weight loss is:
[tex]\frac{13}{4}x-\frac{1}{2}[/tex]Liam lost the first week 1 pound less than 3/2 times the loss Luke had the first week this can be express as:
[tex]\frac{3}{2}x-1[/tex]The second week he lost 4 pounds less than 5/2 times the loss of Luke the firs week then we have:
[tex]\frac{5}{2}x-4[/tex]Finally Liam lost 1/2 pound more than 5/4 times the loss of Luke the first week, then:
[tex]\frac{5}{4}x+\frac{1}{2}[/tex]Adding this we have:
[tex]\frac{3}{2}x-1+\frac{5}{2}x-4+\frac{5}{4}x+\frac{1}{2}=\frac{21}{4}x-\frac{9}{2}[/tex]Therefore Liam's expression is:
[tex]\frac{21}{4}x-\frac{9}{2}[/tex]Now, we know that both of them lost the same weight, then we have the equation:
[tex]\frac{13}{4}x-\frac{1}{2}=\frac{21}{4}x-\frac{9}{2}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{13}{4}x-\frac{1}{2}=\frac{21}{4}x-\frac{9}{2} \\ \frac{21}{4}x-\frac{13}{4}x=\frac{9}{2}-\frac{1}{2} \\ \frac{8}{4}x=4 \\ x=\frac{4}{\frac{8}{4}} \\ x=2 \end{gathered}[/tex]Therefore Luke lost 2 pound the first week.
Finally we plug the value of x in the expression for Luke's weight loss to get the total amount over the three weeks:
[tex]\begin{gathered} \frac{13}{4}(2)-\frac{1}{2}=\frac{13}{2}-\frac{1}{2} \\ =\frac{12}{2} \\ =6 \end{gathered}[/tex]Therefore they lost 6 pounds in three weeks.
Which of the following are polynomials? Check all that apply.
The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.
What are polynomials?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
A) [tex]x^{-2}+15x-3[/tex]
Here, the exponent of x is -2. So, the expression is not a polynomial.
B) [tex]-x^3+5x^2+7\sqrt{x} -1[/tex]
Here, the power of one of the term is 1/2. So, the expression is not a polynomial.
C) [tex]\frac{3}{5}x^4-18x^2+5-\frac{10}{x^2}[/tex]
Here, the power of one of the term is -2. So, the expression is not a polynomial.
D) 5.3x²+3x-2
Here, the power of each term is positive integer. So, the expression is a polynomial.
E) [tex]4x^4-10[/tex]
Here, the power of each term is positive integer. So, the expression is a polynomial.
The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.
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