the value of x is one quarter of z. the sum of x, y, and z is equal to 26. if the value of y is twice the value of z, what is the largest factor of the sum of y and z?
Answers
The largest factor of the sum of y and z is 24.
What is the benefit of using substitution method?The replacement approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.
What is substitution method?When using the "by substitution" method, you must first solve one of the equations provided (you must choose which one) for one of the variables (you must choose which one), after which you must plug this value back into the other equation provided (you must "substitute" for the chosen variable and solve for the other value). The first equation is then used to back-solve for the first variable. The many procedures required in using the replacement approach to solve problems have been described in full above. Use those to discover the solution to a given system of linear equations.
We are given with three equations having three unknowns:
x = z/4
x + y + z = 26
y = 2z
Using the method of substitution, we can now solve for each of the three unknowns.
Since the first equation, x = z/4, is an equation for x in terms of z, and the third equation, y = 2z, is an equation for y in terms of z, we can replace x and y in the second equation by their equivalent expressions as follows:
x + y + z = (z/4) + (2z) + z = 26
We are left with an equation with just one unknown z. We can now solve for z:
(z/4) + (2z) + z = 26
z/4 + 8z/4 + 4z/4 = 13z/4 = 26
z/4 = 2
z = 8
Now that we know z, we can easily solve for y, then compute y + z (note: we can also solve for x, but since we are not interested in the value of x there is no need to do so):
y = 2z = 2(8) = 16
y + z = 16 + 8 = 24
Since the largest factor of any number is the number itself, the largest factor of the sum of y and z is 24.
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Related Questions
y + 1 = y + 2 need help asap pls !!!
Answers
Answer:
Alright
Ignore the 20, We have 5(x-2)
Brackets mean Multiplication
So, Multiply 5 with x and multiply 5 with 2
=> 20 = 5x - 10
Transpose the 20 to the other side
the twenty being transposed to the other side becomes Minus because it is in plus
And bring 5x in front of the =
=> 5x = 20 - 10
=> 5x = 10
So now we have 5x but we need x so transpose the 5 to the other side
by transposing the five becomes division because its in positive so
=> x = 10 ÷ 5
=> x = 2
Kaboom, All done!
List five tasks that a layer can perform. is it possible that one (or more) of these tasks could be performed by two (or more) layers?
Answers
Error control, flow control, segmentation and reassembly, multiplexing, and connection setup are five tasks that a layer can perform.
Flow control: It is the efficient management of data flow between two or more devices like computers or nodes of a network.
Error control: The identification and correction of errors that occur during the transmission of data is called error control.
Segmentation and reassembly: Data to be transmitted is divided into small parts or chunks for convenience. This process is called segmentation. The combining of these chunks to reform the original data is called reassembling.
Multiplexing: The process of combination of digital data streams in one signal over a shared medium is known as multiplexing.
Connection setup: Establishing a connection between two devices that are connected to the same network is called connection setup.
All these tasks can be duplicated at different layers.
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is 1/5 a rational or irrational number (20 points pls help)
Answers
Answer:
rational
Step-by-step explanation:
Answer:
it's Rational Number
Step-by-step explanation:
since each integer can't be written in the fraction form or for this example it would be thus 5 so it would be a rational number
In the context of the information research process, the second step of determining a research problem involves _____.
A) redefining the initial problem into research questions
B) confirming the value of the information sought
C) identifying variables that are pertinent to the problem
D) specifying the research objectives
Answers
In the context of the information research process, the second step of determining a research problem involves specifying the research objectives. The correct option is D) specifying the research objectives
Research is the methodical investigation into a subject to discover and interpret facts, data, and theories. Research often involves both inductive and deductive approaches. Researchers use the research process to design, plan, execute, and interpret their findings in a structured way. They are trying to discover something new, expand our knowledge, and demonstrate their discoveries to others.
The research process consists of five primary phases:
The objectives of research are a statement of what the researcher intends to do in the research. On the other hand, the research problem is a question or statement that addresses the issue or topic that the research project seeks to address. The first step in the research process is to identify and clearly define the problem.The second stage in the research process is to specify the research objectives. The third step is to develop the research plan.The fourth stage is to collect data and conduct research, and The fifth stage is to interpret the data and prepare the final report or thesis.The correct option is D) specifying the research objectives
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The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n?
Answers
The relationship between the values of m and n is that m is greater than n.
In the factored form (x + m)(x - n), the coefficient of x in the middle term of the trinomial is determined by the sum of the values of m and n. The coefficient of x is given by (m - n).
Since b is positive, the coefficient of x is positive as well.
This means that (m - n) is positive.
Therefore, the relationship between the values of m and n is that m is greater than n.
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Chris mixes 4 cups of cereal 3 cups of pecans and 2 cups of raisins. What are three ways to write the ratio of cups of cereal to cups of pecans?
Answers
Answer:
cereal : pecans : raisins = 2 : 1.5 : 1
Step-by-step explanation:
Given:
The amount of cereal in snack mix = 4 cups
The amount of pecans in snack mix = 3 cups
The amount of raisins in snack mix = 2 cups
Therefore,
The total amount of snack = 4 cups + 3 cups + 2 cups = 9 cups
Now,
The ratio is given as:
=
therefore,
Ratio of cereal in snack mix =
and,
Ratio of pecans in snack mix =
Ratio of raisins in snack mix =
Now,
we have ratio as:
4 : 3 : 2
i.e cereal : pecans : raisins
taking 2 common
we get
2 : 1.5 : 1
therefore,
the maximum amount
Step-by-step explanation:
What is the result of 1.58/3.793 written with the correct number of significant figures?
A.) 0.41656
B.) 0.4166
C.) 0.417
D.) 0.42
E.) 0.4
Answers
Answer:C
Step-by-step explanation:
Please help me!!!!!Q!!!!!!!
Answers
-x = .6
x = -0.6
answer: C
We are given the equation:
\({:\implies \quad \sf -2.1-\underline{?}=-1\dfrac12}\)
Let assume the unknown value be x, so that:
\({:\implies \quad \sf -2.1-x=-\dfrac32}\)
\({:\implies \quad \sf x-1.5=-2.1}\)
\({:\implies \quad \sf x=1.5-2.1=\boxed{\bf -0.6}}\)
Hence, Option c) is correct
Which of the following are true statements?
If a * b = c, and a is not equal to zero, then b = c / a
If a * b = c, and b is not equal to zero, then a = c / b
If m / n = p, then m = p * n
All of these statements are true.
Answers
Answer:
(d) All of these statements are true.
Step-by-step explanation:
You want to know which statements relating multiplication and division are true.
Multiplicative inverseThe multiplicative inverse of (non-zero) 'a' is 1/a. The product of these is 1 (by definition).
Multiplicative identity1 is the multiplicative identity element, so 1·a = a.
Multiplication property of equalityStarting with a·b = c, we can multiply both sides of the equation by 1/a without altering its truthfulness.
(1/a)(a)(b) = (1/a)(c)
(a/a)(b) = c/a . . . . . . . for a ≠ 0
b = c/a
Using the other factor, we have ...
a = c/b . . . . . . . from (1/b)(a)(b) = (1/b)(c)
Substitution propertyWe can always substitute equals for each other. Then for c=m, a=n, b=p, the first of these equations is ...
p = m/n
m/n = p . . . . symmetric property of equality
Effectively, all of the multiplication and division relations shown are true:
ab = c ⇔ b = c/a . . . . . . . a ≠ 0ab = c ⇔ a = c/b . . . . . . . b ≠ 0m/n = p ⇔ m = pn . . . . . n ≠ 0__
Additional comment
In the first two cases, we included the caveat that the divisor could not be zero. This is also true of the last case (m/n=p). However, in this case, we assume that p is defined, which automatically means that n ≠ 0.
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All of the statements provided are true. If two numbers, a and b, have a product of c, then dividing c by a will yield the value of b, as long as a is not equal to zero. All options are true.
In the first statement, if a * b = c and a is not equal to zero, then dividing both sides of the equation by a gives us (a * b) / a = c / a. The term (a * b) / a simplifies to b, so we have b = c / a, which confirms the truth of the statement.
Similarly, in the second statement, if a * b = c and b is not equal to zero, dividing both sides of the equation by b results in (a * b) / b = c / b. The term (a * b) / b simplifies to a, so we have a = c / b, validating the statement.
Finally, in the third statement, if m / n = p, multiplying both sides of the equation by n gives us (m / n) * n = p * n. The term (m / n) * n simplifies to m, so we have m = p * n, confirming the truth of the statement.
In summary, all of the given statements hold true, as they follow logical mathematical operations and principles.
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I'm ready to appreciate. Please describe every detail please
Show that Let measure of ACR be 0. Then measure of the set {x²: EA} be 0 Every detail as possible and would appreciate
Answers
This can be proven by properties of measure theory and applying them .By establishing the relationship between the measures of ACR and {x²: x∈A}, it becomes clear that if ACR has a measure of 0, then the measure of {x²: x∈A} is also 0.
In measure theory, the measure of a set represents its "size" or "extent" in some sense. It provides a way to quantify the notion of size for various types of sets. In this case, we are interested in the measure of two sets: ACR and {x²: x∈A}.Given that the measure of set ACR is 0, we aim to demonstrate that the measure of the set {x²: x∈A} is also 0. Intuitively, this means that the set of squared values obtained by taking each element x from set A, denoted as x², has a measure of 0 as well.
One key property is that if two sets have a containment relationship (i.e., one set is a subset of the other), then the measure of the subset cannot exceed the measure of the superset. In other words, if ACR has a measure of 0, then any subset of ACR, including {x²: x∈A}, must also have a measure of 0 or less. Since {x²: x∈A} is a subset of ACR, it follows that its measure must be 0 or less.
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2 ÷ 2 × 2 ÷ 2 plz anwers for point
Answers
PLS HELP (algebra 1)
solve -6 + 8(16 - 19z)
Answers
Answer:
122-152z
Step-by-step explanation:
-6+ 8(16 - 19z)
= -6 + 128 - 152z
= 122 - 152z
I hope this helps!
An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 2 small baskets and 4 large baskets, using a total of 60 pieces of fruit. Using wire baskets, the employee assembled 2 small baskets and 10 large baskets, using a total of 132 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?
The small baskets each include______pieces and the large ones each include_____pieces.
Answers
Answer:12 and 15
Step-by-step explanation:
someone help I don't know this trig question
Answers
Answer:
Bill is 9.80 km apart from Concert
Step-by-step explanation:
It's given in the question,
m∠B = 75°
m∠C = 45°
By triangle sum theorem,
m∠A + m∠B + m∠C = 180°
m∠A + 75° + 45° = 180°
m∠A = 180° - 120°
m∠A = 60°
By sine rule,
\(\frac{\text{sin}(\angle A)}{BC}=\frac{\text{sin}(\angle C)}{AB}\)
\(\frac{\text{sin}(60)}{BC}=\frac{\text{sin}(45)}{8}\)
BC = \(\frac{8\text{sin}(60)}{\text{sin}(45)}\)
= 9.80 km
Therefore, Bill is 9.80 km apart from Concert.
Jennifer has a checking account deficit. Her balance is -$21.41. How much must she add to her account to have a balance of $0?
Answers
Answer:
21.41
Step-by-step explanation:
Answer:
Add 21.41 to ur negative number and it will be zero
Step-by-step explanation:
Use the diagram to find the measures of all the angles, given that m∠2=159∘
PLEASE HELP!!!
Answers
Answer:
Angle 1 = 21
Angle 3 = 21
Angle 4 = 159
Step-by-step explanation:
the angle of elevation to an airplane viewed from the control tower at an airport is 7. the tower is 200 feet high and the pilot reports that the altitude is 5200 feet. how far away from the control tower on a straight line is an airplane?
Answers
The distance between control room to airplane is 41027.5 feet.
What is trigonometric function?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here This distance (d) from tower will be the hypotenuse of a right triangle.
The altitude is the side opposite the angle at the tower
The tower is 200' high, therefore, the altitude above the tower.
=> 5200 - 200 = 5000 feet.
Now using sine ratio then,
=> Sin 7° = AC/BC
=> BC = AC/sin 7°
=> BC = 5000/sin 7°
=> BC = d = 41027.5 feet.
Hence the distance between control room to airplane is 41027.5 feet.
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4/5 and -4/5 are same or not
Answers
Answer:
not
Step-by-step explanation:
Answer:
4/5 and -4/5 are not same because
4/5=
The sample space for a roll of two number cubes is shown in the table. A 6 by 6 table of ordered pairs is shown. • A single ordered pair appears in each cell of the table. In row one, the first element of each ordered pair is 1. This pattern continues through row 6, where the first element in each ordered pair is 6. • In column one, the second element in each ordered pair is 1. This pattern continues through column 6, where the second element in each ordered pair is 6. What is the probability that the roll will result in both numbers being the same? A. start fraction 1 over 6 end fraction B. one-third C. start fraction 7 over 18 end fraction D. Start Fraction 2 over 3 End Fraction
Answers
Explanation :
m/4 = 77°, m/8 = 4x + 57
Answers
f(x) = 2x2 - 1 What is f(x) when x=2 ?
Answers
Answer:
7
Step-by-step explanation:
To evaluate, substitute x = 2 into f(x), that is
f(2)= 2(2)² - 1 = 2(4) - 1 = 8 - 1 = 7
asapppp help me someone please
Answers
Answer:
3/5
Step-by-step explanation:
P ( walks or takes the bus) = walks or takes the bus/ total
walks = 10
takes the bus = 25+ 20+5 = 50
There is no overlap
P ( walks or takes the bus) = walks or takes the bus/ total
= (10+ 50)/ 100
= 60/100
=3/5
Answer:3/5
Step-by-step explanation:
Just put the answer in and it’s right
How do you do this? I am really confused
Answers
Answer:
Step-by-step explanation:
ok, so this is an infinitly repeating function, so you can write it as:
sqrt(12-x)
Although, x is also equal to sqrt(12-x), so
x = sqrt(12-x), and
x^2 = 12-x
x^2-12+x = 0
now just apply the quadratic formula and you're good
hope i helped :D
The triangle above has the follow measures.
q= 8in
m
find the length of side r.
Round to the nearest tenth and include correct units.
Answers
The measure of the side r is 13.29 in
How to determine the valueTo determine the value of the side of the triangle:
We need to take note of the six trigonometric identities. These identities are;
sinecosinecotangentcosecantsecanttangentFrom the information shown in the diagram, we have that;
side q is the opposite side of angle Q
r is the hypotenuse side
s is the adjacent side
Using the sine identity, we have;
sin 37 = 8/r
cross multiply the values, we have;
r = 13. 29 in
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the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. ure that your work includes a sketch of the region and calculations to find the limits/paramelers of integration for the 3) The region bounded by y=4x−x 2
and y=x about the y-axis You may use any one of the formulae V=∫ a
b
π[f(x)] 2
dx
V=∫ a
b
π[f(x) 2
−g(x) 2
]dx
V=∫ a
b
2π×[f(x)−g(x)]dx
Answers
The volume of the solid generated by revolving the region bounded by \(y=4x−x²\) and\(y=x\) about the y-axis is 128π cubic units.
The region bounded by \(y=4x−x² and y=x\) about the y-axis will look like this:
Now we can see that the region is symmetric with respect to the y-axis.
Hence we can use the washer method to find the volume of the solid generated by revolving the region about the y-axis.
The washer method formula is given by:
V = π [R² - r²] dx
Where, R = Outer radius of the washer = distance from the y-axis to the curve \(y=4x-x²R = 4x-x²r =\) Inner radius of the washer = distance from the y-axis to the curve y=xr = x
Also, the limits of integration for x are from x=0 to x=4.
Let's write the integral expression for volume and solve it:
\(V = π ∫ 0 [R² - r²] dxV = π ∫ 0 [(4x-x²)² - x²] dxV = π ∫ 0 [16x² - 8x³ + x⁴ - x²] dxV = π ∫ 0 [x⁴ - 8x³ + 15x²] dxV = π [x⁵/5 - 2x⁴ + 5x³] | 0V = π [ (4⁵/5 - 2(4⁴) + 5(4³)) - 0]V = 128π cubic units\\\)
Therefore, the volume of the solid generated by revolving the region bounded by\(y=4x−x²\) and \(y=x\) about the y-axis is 128π cubic units.
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pls help
Lcm of 4 and 15?
least common multiple
Answers
=================================================
Explanation:
Multiply the two values to get 4*15 = 60
Then divide by the GCF 1 to get 60/1 = 60. The GCF being 1 means the result hasn't changed.
------
Another example would be: "Find the LCM of 6 and 8". We would first do 6*8 = 48, then divide by the GCF 2 to get 48/2 = 24. The LCM of 6 and 8 is 24.
Answer:
60
Step-by-step explanation:
I NEED HELP ASAP! SO EASY
Answers
Answer:
165 hope this helps
Step-by-step explanation:
\(--------------------------------------------\)
Answer:
159
\(--------------------------------------------\)
Step-by-step explanation:
-4 + 91=87
87 + 72=159
\(--------------------------------------------\)
SIMPLE
6y=24−3x i need what x is and what y is but i cant seem to get it right
Answers
Step-by-step explanation:
6y=24-3x
6y/6=24-3x/6
y= 4-1/2x
x= -2y+8
Answer:
Please see below
Step-by-step explanation:
There are two variables so you can't really solve for both of them
Here's x:
3x = 24 - 6y
x = 8 - 2y
Here's y:
6y = 24 - 3x
y = 4 - x/2
Hope this helps :)
(Please let me know if I've gotten anything wrong!)
find the quotient of 67.98÷28 round your answer to the hundredths place
Answers
Answer:
2.43
Step-by-step explanation:
The quotient is the answer to a division problem.
67.98/28 = ~2.42785714286
To round to the nearest hundredth, leave 2 decimal digits remaining. If the thousandth place (3rd decimal digit) is greater they or equal to 5, add 1 to the hundredths digits.
7 \(\geq\) 5
2.42+0.01
2.43
I need this asapppppppp
Answers
The measure of the smaller angle is 45°.
How to find the measure of the smallest angle?An heptagon is a figure with 7 sides, and the sum of the interior angles is equal to 900°.
Then here we can write a linear equation that depens on x, where we add all the given angles and we know that it must be equal to 900.
2x + 3x + 4x + 5x + 7x + 9x + 10x = 900
Solving that linaer equation for x:
(2 + 3 + 4 +5 + 7 + 9 + 10)*x = 900
40x = 900
x = 900/40 = 22.5
The measure of the smaller angle is:
(2x)°
replacing the value of x that we just got we will get:
2*22.5° = 45°
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