variables y = 1.5, x = 5, hence, the value of y is 9 when x is 30
How are linear equations solved?Two variables, such as x and y, are proportional to one another and their ratio is constant when they vary directly. In other words, if y and x vary directly, their relationship can be written as y = kx, where k is the proportionality constant. With the knowledge that y = 1.5 when x = 5 as provided, we can utilise this information to find the value of y when x equals 30:
1.5 = k(5) \sk = 1.5/5 \sk = 0.3
We can use the equation y = kx to get the value of y for x = 30 now that we know the value of k:
y = 0.3(30) \sy = 9
Hence, the value of y is 9 when x is 30.
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What are the solutions to the equation x2−4x−5=0
?
Answer:
I think the answer is x= 5, -1
Answer:
i got x= 5,-1
Step-by-step explanation:
i hope this helps and have a good day
The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor. This is an example of
a. Nominal data
b. Ordinal data
c. Interval data
d. Quantitative data
The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor is an example of Ordinal data.
Ordinal data is a type of data that is used to rank or order objects or individuals. It is a type of categorical data that can be ranked or ordered, but cannot be measured numerically. In this case, the machines are ranked based on their design quality, which is an example of ordinal data. Other examples of ordinal data include movie ratings, letter grades, and customer satisfaction ratings.
Therefore, the correct answer is option b. Ordinal data.
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Find all values of c that will make the polynomial a perfect square trinomial. 225r^(2)-120r+c
The value of c that will make the polynomial a perfect square trinomial is 16.
To find the values of c that will make the polynomial a perfect square trinomial, we need to use the formula for a perfect square trinomial, which is:
[tex](a+b)^(2) = a^(2)+2ab+b^(2)[/tex]
In this case, we have:
[tex]225r^(2)-120r+c = (15r+b)^(2)[/tex]
Expanding the right side of the equation, we get:
[tex]225r^(2)-120r+c = 225r^(2)+30rb+b^(2)[/tex]
Comparing the coefficients of the terms, we can see that:
-120r = 30rb
b = -4
Now, substituting b back into the equation, we get:
[tex]c = b^(2) = (-4)^(2) = 16[/tex]
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Help please answer 7 and 8
Algebra 2
Answer:
Step-by-step explanation:
At a local coffee shop,a bagel cost 1$ore than a cup of coffee. You buy 4 cups of coffee and 6 bagels for a total of $31. Set up a system of equations to determine the price of each item.
Answer: A cup of coffee costs $2.50 and a bagel costs $3.50.
Step-by-step explanation: Let's use the following variables to represent the price of each item:
c: price of a cup of coffee (in dollars)
b: price of a bagel (in dollars)
From the problem statement, we know that:
b = c + 1 (a bagel costs $1 more than a cup of coffee)
We also know that you bought 4 cups of coffee and 6 bagels for a total of $31. This can be expressed as:
4c + 6b = 31
Now we can substitute the first equation into the second equation to eliminate b:
4c + 6(c + 1) = 31
Simplifying this equation, we get:
10c + 6 = 31
Subtracting 6 from both sides, we get:
10c = 25
Dividing both sides by 10, we get:
c = 2.5
Now we can use the first equation to find the value of b:
b = c + 1 = 2.5 + 1 = 3.5
Therefore, a cup of coffee costs $2.50 and a bagel costs $3.50.
Find Key Features of an Ellipse from Conic Form Feb 21, 10:24:52 AM Find the foci of the ellipse defined by the equation ((x+4)^(2))/(4)+((y+3)^(2))/(9)=1. If necessary round to the nearest tenth.
The required foci of the ellipse are also at (-4, -3).
To find the foci of the ellipse defined by the equation:
[tex]\dfrac{(x+4)^2}{4}+\dfrac{(y+3)^2}{9}=1[/tex]
We need to identify the values of 'a' and 'b' from the equation, where 'a' is the semi-major axis, and 'b' is the semi-minor axis of the ellipse.
The general equation of an ellipse centered at (h, k) is given by:
[tex]\dfrac{(x - h)^2}{ a^2} + \dfrac{(y - k)^2}{ b^2} = 1[/tex]
Comparing this with the given equation, we can see that the center of the ellipse is at (-4, -3), so (h, k) = (-4, -3).
Next, we find 'a' and 'b':
For the x-term: a² = 4
a = √4
a = 2
For the y-term: b² = 9
b = √9
b = 3
So, the semi-major axis 'a' is 2 units, and the semi-minor axis 'b' is 3 units.
Now, the distance from the center of the ellipse to the foci is given by:
[tex]c = \sqrt{(a^2 - b^2)[/tex]
[tex]c = \sqrt{(2^2 - 3^2)[/tex]
[tex]c=\sqrt{-5[/tex]
The distance is imaginary, which means the foci are not real, and the ellipse is degenerate. A degenerate ellipse is essentially a circle. Since we have a degenerate ellipse, the foci coincide with the center of the ellipse.
Therefore, the foci of the ellipse are also at (-4, -3).
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HOW DO YOU SEE IT? Write expressions for the tangent of each acute angle in the right triangle.
A right-angled triangle B C A, with angle C marked right angle. Side B C is labeled a, C A is labeled b, and A B is labeled c.
$\tan A=$tanA=
$\tan B=$tanB=
Question 2
Explain how the tangent of one acute angle is related to the tangent of the other acute angle. What kind of angle pair is angle cap A$\angle A$∠A and angle cap b$\angle B$∠B ?
Check the picture below.
How many ways are there to choose 4 books from a collection of 11 books? Hint... does order matter? Type your answer...
There are 330 ways to choose 4 books from a collection of 11 books.
To solve this problem, we need to use the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items, r is the number of items to choose, and ! means factorial (the product of all positive integers up to that number).
In this case, we have n = 11 (the total number of books) and r = 4 (the number of books to choose). Plugging these values into the formula, we get:
C(11, 4) = 11! / (4! * (11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8 * 7!)/ (4! * 7!)
= (11 * 10 * 9 * 8)/ (4 * 3 * 2 * 1)
= 330
So there are 330 ways to choose 4 books from a collection of 11 books.
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Suppose you have a coin with P[H] = p. You toss it n times and get
a sequence x1, . . . , xn. Write down the likelihood as a function of p.
Give the max-likelihood estimate for p.
use the notation that 1 denotes H and 0 denotes T
The likelihood function for a sequence of coin tosses x1, . . . , xn with P[H] = p is given by:
L(p) = P(x1, . . . , xn | p) = P(x1 | p) * P(x2 | p) * . . . * P(xn | p)
Using the notation that 1 denotes H and 0 denotes T, we can write the likelihood function as:
L(p) = p^k * (1-p)^(n-k)
where k is the number of heads in the sequence and n-k is the number of tails.
To find the maximum likelihood estimate for p, we need to take the derivative of L(p) with respect to p and set it equal to zero:
dL(p)/dp = k*p^(k-1)*(1-p)^(n-k) - (n-k)*p^k*(1-p)^(n-k-1) = 0
Solving for p, we get:
p = k/n
Therefore, the maximum likelihood estimate for p is the number of heads in the sequence divided by the total number of tosses.
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a) Determine whether the following set of vectors inR4is linearly independent or linearly dependent.S={(1,0,−1,0),(1,1,0,2),(0,3,1,−2),(0,1,−1,2)}b) Write the vectoru=(10,1,4)as a linear combination of the vectorsv1=(2,3,5),v2=(1,2,4) and v3=(−2,2,3)
The given set of vectors in R4 is linearly independent and the vector u as a linear combination of the vectors v1, v2, and v3 can be written as u = (7,12,22)
a) To determine if the set of vectors in R4 is linearly independent or linearly dependent, we can use the rank of the matrix formed by these vectors. If the rank of the matrix is equal to the number of vectors, then the set is linearly independent. Otherwise, it is linearly dependent.
First, let's form the matrix using the vectors:
| 1 0 -1 0 |
| 1 1 0 2 |
| 0 3 1 -2 |
| 0 1 -1 2 |
Next, let's find the rank of the matrix. We can do this by using Gaussian elimination to reduce the matrix to row echelon form:
| 1 0 -1 0 |
| 0 1 1 -2 |
| 0 0 4 -6 |
| 0 0 0 4 |
The rank of the matrix is 4, which is equal to the number of vectors. Therefore, the set of vectors is linearly independent.
b) To write the vector u as a linear combination of the vectors v1, v2, and v3, we need to find the scalars a, b, and c such that:
u = av1 + bv2 + cv3
This gives us the following system of equations:
10 = 2a + b - 2c
1 = 3a + 2b + 2c
4 = 5a + 4b + 3c
We can use Gaussian elimination to solve this system of equations:
| 2 1 -2 | | a | = | 10 |
| 3 2 2 | | b | = | 1 |
| 5 4 3 | | c | = | 4 |
After reducing the matrix to row echelon form, we get:
| 1 0 1 | | a | = | 2 |
| 0 1 -2 | | b | = | 3 |
| 0 0 0 | | c | = | 0 |
From the third equation, we can see that c can be any value. Let's choose c = 0. Then, from the first two equations, we get:
a = 2
b = 3
Therefore, the vector u can be written as a linear combination of the vectors v1, v2, and v3 as follows:
u = 2v1 + 3v2 + 0v3
u = (2)(2,3,5) + (3)(1,2,4) + (0)(-2,2,3)
u = (4,6,10) + (3,6,12) + (0,0,0)
u = (7,12,22)
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Overproduction of uric acid in the body can be an indication of
cell breakdown. This may be an advance indication of illness such
as gout, leukemia, or lymphoma.† Over a period of months, an adult
m
Overproduction of uric acid in the body is a condition known as hyperuricemia. It occurs when the body produces more uric acid than it can excrete. Uric acid is a waste product that is formed when the body breaks down purines, which are found in certain foods and drinks. If the body is unable to get rid of the excess uric acid, it can build up and form crystals in the joints, causing a painful form of arthritis known as gout.
Hyperuricemia can also be an indication of other health conditions, such as leukemia and lymphoma. These are types of cancer that affect the blood cells and the immune system, respectively. When cells in the body break down, they release uric acid into the bloodstream. If there is an overproduction of cells, as in the case of leukemia and lymphoma, this can lead to an excess of uric acid in the body.
It is important to monitor the levels of uric acid in the body, as it can be an early indication of these serious health conditions. A healthcare professional can conduct tests to measure the levels of uric acid in the body and determine the cause of the overproduction.
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Correct question is" Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advanced indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eleven blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.75 mg/dl. (a) Find a 95 % confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) (b) Find the sample size necessary for a 95 % confidence level with a maximal margin of error E = 1.02 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)"
Math question 4 help
Answer:
-1 and 0
Step-by-step explanation:
This is a set of simultaneous equations. To solve them, you need to substitute one into the other. The easiest way to do this would be to rearrange x - y = -6 to make x the subject:
x = -6 + y
x = y - 6
Now we can substitute this equation into y = -x^2 + 5x + 6:
y = -(y - 6)^2 + 5(y - 6) + 6
Now simplify this equation, and rearrange to make it equal to 0:
y = -y^2 + 12y - 36 + 6
y = -y^2 + 12y - 30
0 = -y^2 + 12y - y - 30
-y^2 + 11y - 30 = 0
Now solve this quadratic equation to obtain two solutions:
y = 5, y = 6
Now substitute these values back into one of the starting equations to find the respective values for x:
When y = 5:
x - 5 = -6
x = -1
When y = 6
x - 6 = -6
x = 0
Therefore, the x solutions are -1 and 0.
The scale factor of two similar cylinders is 5:2.
The volume of the smaller cylinder is 28 m3.
What is the volume of the larger cylinder?
Question 8 options:
175 m3
350 m3
437.5 m3
70 m3
700 m3
Answer:
70m3
Step-by-step explanation:
5:2
The 2 represents the smaller cylinder. The smaller cylinder=28
To find out how much 1 is we can divide 28 by 2 and that =14. So in the ratio 1=14 and as seen on the left side we have 5 1's. So 14 times 5= 70
Have a nice day :-)
the expression a[(9b-c)+z] is equivalent to
Answer:
The expression a[(9b-c)+z] can be simplified using the distributive property of multiplication. The distributive property states that:
a(b + c) = ab + ac
Using this property, we can distribute the a to the terms inside the brackets:
a[(9b-c)+z] = a(9b-c) + az
Now, we can distribute the a again to get:
a(9b-c) + az = 9ab - ac + az
Therefore, the expression a[(9b-c)+z] is equivalent to 9ab - ac + az.
Answer:
Step-by-step explanation: Equivalent to 9ab - ac + az.
Determine which numbers in the set are solutions of the equation. n-7=12;{17,19,21}
The number 19 is the solution of the equation n-7=12.
How do we find the solution?The equation given is n-7=12. To find the solution, we need to isolate the variable n on one side of the equation. We can do this by adding 7 to both sides of the equation. This gives us:
n-7+7=12+7
Simplifying the equation gives us:
n=19
Now, we can check which numbers in the set {17,19,21} are solutions of the equation. The only number that satisfies the equation is 19. Therefore, the solution of the equation is 19.
Answer: The number 19 is the solution of the equation n-7=12.
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7th garde math question pt 2 pls answer a s a p i ready grade f level
Answer:
45
Step-by-step explanation:
3² · (12-2) ÷ 2
= 9 · (10) ÷ 2
= 90 ÷ 2
= 45
So, the answer is 45
Answer: 135
Step-by-step explanation: use a calculator/online calculator
Step 3. Calculate the sample variance and the sample standard deviation. Provide your sample standard deviation answer precise to one decimal place. Sample variance sample standard deviation
The value of the sample variance and the sample standard deviation for the given data is equal to 47.4 and 6.9 respectively.
Data values are,
23, 12, 5, 9,8
Number of observations 'n' = 5
Mean = ( sum of all the observations ) / ( number of observations)
= (23 + 12 + 5 + 9 + 8) / 5
= 57 /5
= 11.4
Deviations of each data point from the mean,
(23 - 11.4) = 11.6
(12 - 11.4) = 0.6
(5 - 11.4) = -6.4
(9 - 11.4) = -2.4
(8 - 11.4) = -3.4
Square each deviation is equal to,
11.6² = 134.56
0.6² = 0.36
(-6.4)² = 40.96
(-2.4)² = 5.76
(-3.4)² = 11.56
Sample Variance = ( Sum of squared deviation )/ ( n - 1)
⇒Sample Variance = (134.56 + 0.36 + 40.96 + 5.76 + 11.56) / (5-1)
⇒Sample Variance = 47.35
⇒Sample Variance = 47.4(rounded to one decimal place)
Now,
Standard deviation = √variance
Substitute the value we get,
⇒ Standard Deviation = √(47.35)
⇒ Standard Deviation = 6.9 (rounded to one decimal place)
Therefore, the sample variance is 47.4 and the sample standard deviation is 6.9.
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The above question is incomplete, the complete question is:
Calculate the sample variance and the sample standard deviation for the given data. Provide your sample standard deviation answer precise to one decimal place.
23, 12, 5, 9,8
Find each quotient. Write all final answers in simplest form. (28x^(5)-8x^(4)+40x^(2))/(4x^(3))
The final answer in simplest form is 7[tex]x^{2}[/tex] - 2x + 10/x.
To find the quotient of (28[tex]x^{5}[/tex]-8[tex]x^{4}[/tex]+40[tex]x^{(2)[/tex])/(4[tex]x^{3}[/tex]), we need to divide each term in the numerator by the denominator.
First, we divide 28[tex]x^{5}[/tex] by 4[tex]x^{3}[/tex]:
(28[tex]x^{5}[/tex])/(4[tex]x^{3}[/tex]) = (28/4)[tex]x^{(5-3)[/tex] = 7[tex]x^{2}[/tex]
Next, we divide -8[tex]x^{4}[/tex] by 4[tex]x^{3}[/tex]:
(-8[tex]x^{4}[/tex])/(4[tex]x^{3}[/tex]) = (-8/4)[tex]x^{(4-3)[/tex] = -2x
Finally, we divide 40[tex]x^{2}[/tex] by 4[tex]x^{3}[/tex]:
(40[tex]x^{2}[/tex])/(4[tex]x^{3}[/tex]) = (40/4)[tex]x^{(2-3)[/tex] = 10[tex]x^{(-1)[/tex] = 10/x
Putting it all together, we get:
(28[tex]x^{5}[/tex] - 8[tex]x^{4}[/tex] + 40[tex]x^{2}[/tex])/(4[tex]x^{3}[/tex]) = 7[tex]x^{2}[/tex] - 2x + 10/x
Therefore, the final answer in simplest form is 7[tex]x^{2}[/tex] - 2x + 10/x.
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You afe choosing between two health clubs. Club A offers membership for a fee of$18plus a monthly fee of$15. Club B offers membership for a fee of$11plus a monthly lee of$16. After how many months will the totat cost of each health club be the same? What will be the fotal cost for each club? In months the total cost of each health dub will be the same.
Tthe total cost for each club after 7 months will be $123.
To find out when the total cost of each health club will be the same, we can use the equation:
Club A total cost = Club B total cost
18 + 15x = 11 + 16x
Where x is the number of months. We can rearrange the equation to solve for x:
15x - 16x = 11 - 18
-x = -7
x = 7
So the total cost of each health club will be the same after 7 months. To find the total cost for each club, we can plug x = 7 back into the equation:
Club A total cost = 18 + 15(7) = $123
Club B total cost = 11 + 16(7) = $123
So, the total cost for each club after 7 months will be $123.
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16. Arden surveyed the 6th grade to see what there favorite colors were.
If 48
students chose yellow, how many students
were surveyed in all?"
How
students chose blue?
many
red?
How many chose purple, green& other?
Answer:
in all 240
60 chose blue
72 chose red
36 chose orange
7 chose purple
10 chose green
7 chose other
Step-by-step explanation:
48 x 5 = 240
48 = 20%
20% x 5 = 100%
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The probability of rolling a dice less than 3 times is 17/100.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The total no of times rolling = 200
The probability of rolling 1 = 17 times
And, The probability of rolling 2 = 17 times
So, the probability of rollng a dice less than 3 times is
17+17/200
34/200
17/100
Hence, the probability of rolling a dice less than 3 times is 17/100.
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Company C had 60 defective batteries out of 10,800. If Company C also manufactures 15,000 new batteries next month, how does this company compare to the others? Explain.
The expected number of defective batteries out of 15,000 batteries is of:
83.3.
Then this expected amount is compared to the number of different batteries of the other companies.
How to obtain the number of defective batteries?The number of defective batteries is obtained applying the proportions in the context of the problem.
Company C had 60 defective batteries out of 10,800, hence the proportion of defective batteries is of:
60/10,800.
Out of 15,000 batteries, the expected number of defective batteries is of:
60/10,800 x 15,000 = 83.3.
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Which of the following options would be considered a liability? Select all that apply
mortgage payment
investments
student loan
money you owe your parents
car payment
retirement funds
Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.
What is liability ?
Liability refers to an obligation or debt that an individual, company, or organization owes to another party. In accounting and finance, liabilities are generally classified as current or long-term and can include items such as loans, mortgages, accounts payable, taxes owed, and salaries payable.
The following options would be considered a liability:
Student loan
Money you owe your parents
Mortgage payment
Car payment
Investments and retirement funds would not be considered liabilities as they are assets.
Therefore, Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.
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If BE CD, which pair of triangles is similar ?
Triangle ABC and ADC are similar if BE is parallel to CD.
What does a triangle similarity mean?
Two triangles are comparable if the measurements of their corresponding sides are proportionate. The same is true if the lengths of two sides in one triangle are proportional to the lengths of the corresponding sides in another triangle and the included angles are congruent.
What is the triangle Theorem's similarity?
According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.
We are given that BE is parallel to CD.
As per the theorem of similarity, the two triangles are similar when the a line segment of the triangle is parallel to that of another triangle.
So, from this we get that the Triangle ABC and ADC are similar.
Hence, Triangle ABC and ADC are similar.
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the area of a rectangular picture frame is given by the trinomial 3x^2-13x-30
Answer:
(3x + 5) and (x - 6).
Step-by-step explanation:
HELPHELPHELPHELP!!!!!!!!!!!
The Dart Frog is a brightly colored frog. These bright colors could mean that this frog is poisonous,
warning predators to stay away. Plants in the rainforest are normally crowded and have very little
space. The big leaves of a Hosta Plant allow the plant to receive as much sunlight as possible when
the sun is out.
What type of adaptations are these? Compare and contrast the adaptations of the Dart Frog and the
Hosta Plant. Your answer should be 3–4 sentences long.
Answer:
Answer:
Most poison dart frogs are brightly colored, displaying aposematic patterns to warn potential predators. Their bright coloration is associated with their toxicity and levels of alkaloids. ... Poison dart frogs are an example of an aposematic organism.
Hostas for Full Sun
In general, yellow or gold hostas tolerate partially sunny location without losing their vibrant yellow color. About two hours of daily sun exposure will keep these yellow or golden beauties looking their best. Aim for morning sun to avoid burned leaves.
hope this helps
Step-by-step explanation:
Hope this is the right answer Have a good day!
have a good day
Help pls due today
I’m stressing out
Answer:
If the relationship is proportional, we can use the proportionality constant, k, to relate the cost and number of climbs. The equation would be:
t = kc
We can find the value of k by using the given information that 5 climbs cost $52.50:
52.50 = k(5)
Solving for k, we get:
k = 10.50
Therefore, the equation that represents the total cost, t, of c climbs is:
t = 10.50c
is 90 rational please help
Answer:
Step-by-step explanation:
I'm assuming you mean is the number 90 a rational number. The answer is that yes, it is a rational number.
Let me explain:
Under all the possible numbers, there is a taxonomy to organize these types of numbers. It goes down a list from:
- all numbers, which is divided into two groups; complex and real
Under real numbers, there's rational and irrational:
Under rational, there's integers and fractions
Under integers, there's whole numbers and negative
Under whole numbers, there's natural numbers and 0 (yes, zero).
90 falls under natural numbers, which means it is also a rational number. Hope this helps!
Please solve this for me
Answer:
55%
Step-by-step explanation:
When you have a question that asks you about a percentage and it gives you a fraction, most of the time you just have to divide the numbers. In this case you will do 11/20=0.55 and you will change the decimal to a percentage. Which will be 55%.
what expression is equivalent to 8x+4
The expression that is equivalent to the given expression, 8x + 4, is 4(2x +1)
Determining the expression that is equivalent to the given expressionFrom the question, we are to determine the expression that is equivalent to the given expression.
The given expression is:
8x + 4
To determine the expression that is equivalent to the given expression, we will factorize the given expression.
First, we will determine the Greatest common factor (GCF) of the terms in the expression.
The terms in the expression are 8x and 4
The GCF of 8x and 4 is 4
Thus,
We can factor the expression as shown below:
8x + 4
4(2x + 1)
Hence, the expression is 4(2x + 1)
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