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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Tabatha and Horatio each leave their separate houses and drive to a restaurant to meet for dinner. Tabatha lives 15 miles from the restaurant, and she drives at a rate of 3 miles every 2 minutes. The graph represents Horatio’s distance, in miles, y, from the restaurant after driving for x minutes.
Tabatha drives 1/12 mile more per minute than Horatio drives.
Tabatha drives 1/6 mile more per minute than Horatio drives
Tabatha drives 3 miles more per minute than Horatio drives.
Tabatha drives 9 miles more per minute than Horatio drives.
Answer:
Tabatha drives 1/6 mile more per minute than Horatio drives
Step-by-step explanation:
Last winter, a store sold 408 coats in
3 months. This winter, the store plans to sell
coats for 4 months. Based on the average
number of coats sold each month last winter,
how many total coats should the store plan to
sell this winter?
Total coats should the store plan to sell this winter is 952.
Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.
What is sell?
Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.
3month = 408 coats
1 month = 408/3 =136 coats
Then, 4 months = 136*4 = 544 coats
Total coats should the store plan to sell this winter = 544+408 = 952.
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What is the radius of the circumscribed circle of ABC?
Answer:
Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle
Step-by-step explanation:
:]
for what values of x and y are the triangles congruent by HL?
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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Simplify 4x - 7 + 12x - 3.
Answer:2(8x-5)
Hope this helps!
What i cot of tiling a rectangular plot of land 500m long and 200m wide at the rate r 8 per q m
The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
Area of rectangle = length × breadth
Area of rectangular plot = 500× 200 = 1,00,000 sq m
Cost of tilling 1 sq m of land = Rs. 8
Cost of tilling 1,00,000 sq m of land = 8 × 1,00,000 = Rs. 8,00,000
Thus, The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
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What is an equation of a line that passes through the points (1, 4) and (2, 9) in
5)
point-slope form? Analyze the steps and fill in the blanks. (4pts)
First, use the two given points to find the slope.
m=
Уг-У1
Use the slope and one point to write an equation of the line in
point-slope form.
Point-slope form of a linear equation.
Substitute
The equation of line in point-slope form of the line, is y = 5x - 1.
What is point - slope form of the line?
The general form of a linear equation is y - y1 = m(x - x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Given:
The line passes through the points (1, 4) and (2, 9).
We have to find the equation of line in point - slope form.
First to find the slope from the given points.
Since,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]
So, [tex]m = \frac{9-4}{2-1} = 5[/tex]
Now consider, the point slope form of the line
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]
⇒
[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]
Hence, the equation of line in point-slope form of the line, is y = 5x - 1.
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If Santa Claus ate two cookies from every child on Earth, how many cookies would he eat over one Christmas Eve?
Answer:
three billion eight hundred million
Step-by-step explanation:
Fatimah ate f cookies. Satvinder ate six fewer than two times the number that Fatimah ate. If Satvinder ate 4 cookies, write and solve an equation to find f, the number of cookies Fatimah ate.
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.
Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,
s = 2f - 6
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,
4 = 2f - 6
2f = 10
f = 5
On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.
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21. Is the following ordered pair (3, 6) a solution of the linear inequality y < -5x + 1?
The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
What is linear inequality?
A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
y < -5x + 1
Substitute the points and see if they are true
(3, 6)
6 < -5*(3) + 1
6 < -15 + 1
6 < -14
Not true not a solution
Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
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Solve for c.
4(c + 17) = 16
C =
Please help
Deposited (dollars)
12,500
10,000
7,500
$5,000
rate of change=
2,500 initial value=
Time (years)
y
dollars per year
dollars
The rate of change is $2500 per year.
The initial amount is $5000.
What is slope?The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
In the given graph,
The initial value that deposited at x = 0 is $5000.
To find the rate of change in amount per year,
Find slope of the line, because rate of change will be equal to slope.
Let two points are (0, 5000) and (1, 7500)
The slope = (7500 - 5000 / 1 - 0) = 2500
The rate of change is $2500 per year.
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Justin is going to invest $90,000 and leave it in an account for 19 years. Assuming
the interest is compounded quarterly, what interest rate, to the nearest hundredth of
a percent, would be required in order for Justin to end up with $216,000?
Answer:
4.63%
Step-by-step explanation:
You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.
Compound interestThe formula for the balance of an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
ApplicationFilling in the given values, we can solve for r:
216000 = 90000(1 +r/4)^(4·19)
2.4 = (1 + r/4)^76 . . . . . divide by 90,000
2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root
(2.4^(1/76) -1) = r/4 . . . . . . subtract 1
r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%
The required interest rate is about 4.63%.
7x+14y=21,-7x+7y=7 using elimation
Answer:(x,y)=(1/3 , 4/3)
Step-by-step explanation:
suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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x^4-2x^2-16x-15=0 find the zeros with work please
ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)
steps
find the zeros JUST MEANS SOLVE FOR X
x⁴-2x²-16x-15=0
break it up
let u = x²
x⁴ = (x²)² = u²
-16x+u²-2u-15=0
hold off on -16x
u²-2u-15=0
what 2 numbers when multiplied give you -15 & when added give you -2?
-5 and 3
(u-5) (u+3)
-16x + (u-5) (u+3) = 0
go back x
-16x + (x²-5) (x²+3) = 0
factor -1 out
( looks horrible so far lol )
-1 ((- x²+ 5) (x²+3) + 16x) = 0
multiply (- x²+ 5) with ( x² + 3 )
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0
-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0
One of the tallest ferris wheels in the world is in las vegas. It has a diameter, , of 520 feet. The circumference of the ferris wheel represents the distance traveled by a passenger after one full rotation. The circumference can be determined using the expression. What is the distance traveled, in feet, by passengers on each rotation of the ferris wheel? record your answer to the nearest tenth of a foot.
Answer:
Below
Step-by-step explanation:
Circumference of a circle = pi * diameter
circumference of ferris wheel = 3.14159 * 520=1633.6 ft
3. The vertices for A LML are L(-4,0), M(-2,0) and N(-3,-3). Its image is L'(1,1), M'(3,1) and
N'(2,-2). What is the translation rule that maps the preimage to the image?
The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)
How to determine the translation rule of the transformationFrom the question, we have the following parameters that can be used in our computation:
Pre-image: L(-4,0), M(-2,0) and N(-3,-3)
Image: L'(1,1), M'(3,1) and N'(2,-2)
The translation rule is calculated as
(x, y) = L' - L
Substitute the known values in the above equation, so, we have the following representation
(x, y) ⇒ (x + 1 + 4, y + 1 - 0)
Evaluate
(x, y) ⇒ (x + 5, y + 1)
Hence, the translation is (x, y) ⇒ (x + 5, y + 1)
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If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value. 17. f[g(–2)]
a. 7 b. 10 c. 30 d. 100
Answer:
d.) 100
Step-by-step explanation:
To solve, first find the value of g(-2):
[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]
Next, use this value to find f(-10):
[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]
Which equation, when paired with y = 2x 5, creates an inconsistent system? 2x y = 5 y = 2x 5 2x – 4y = 10 2y – 4x = –10
The equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:
2y - 4x = -10.
What is an inconsistent system?A system of equations is called inconsistent when the number of equations of the system is of zero.
The system in this problem is composed by linear equations, which have the following format:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For inconsistent system, we have that the equations:
Have the same slope.Have different intercepts.The function in this problem is given as follows:
y = 2x + 5.
Hence the inconsistent system is formed with:
2y - 4x = -10.
Which is simplified by 2 as follows:
y - 2x = -5.
y = 2x - 5.
Having the same slope of 2, but a different intercept.
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Answer: 2y – 4x = –10
Step-by-step explanation: trust.
read the picture plsss
Answer:
Step-by-step explanation:
2. How many points of inflection will f(x) = 3x5+2x4 - 5x - 12 have?
5
3
2
4
2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.
What is Inflection points definition?
An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.
If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.
[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]
Show Steps
Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]
Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]
(0,-12)
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a study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. one hundred participants are recruited to participate, and half are randomly assigned to participate in the intervention while the others serve as a control group. what study design is being used?
A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).
What is a randomized controlled trial?Generally, In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.
In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.
The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.
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What is the value of 24 + x ÷ 12 when x = −180?
17
9
−13
−178
If you don't know the answer please do not type random stuff or you'll see what ima do
The value of the expression 24 + x ÷ 12 when x = −180 is (b) 9
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?From the question, we have the following parameters that can be used in our computation:
24 + x ÷ 12
Also, we have the value of the variable to be
x = −180
Substitute the known values in the above equation, so, we have the following representation
24 - 180 ÷ 12
Evaluate the quotient in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 24 - 15
Evaluate the difference in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 9
Hence, the value of the expression is (b) 9
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Explain how to solve 2^(x + 1) = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth
The solution of the given expression is equal to 2.17.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,
[tex]2^{x+1}=9[/tex]
Take logs on both sides,
(x+1) ln(2) = ln(9)
(x+1) = ln(9) / ln(2)
x + 1 = 3.17
x = 2.17
Hence, the expression will be solved by taking log on both sides.
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Find the y intercept y = – 17 x + 12.
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
12. What is the maximum value of a periodic
function with amplitude 6.5 and minimum
value 7?
The maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.
What is a periodic function?
The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.
The maximum value of a periodic function with amplitude 6.5 and minimum value 7 is equal to the sum of the amplitude and the minimum value.
The amplitude of a periodic function is defined as the maximum distance that the function deviates from its centerline. In this case, the amplitude of the function is 6.5.
The minimum value of a function is the lowest value that the function takes on over a given period. In this case, the minimum value of the function is 7.
To find the maximum value of the function, we need to add the amplitude and the minimum value. The maximum value is equal to 6.5 + 7 = 13.5.
Hence, the maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.
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The formula for the volume of a cylinder is V=\pi r^2 h,V=πr
2
h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V / π r².
What is volume?An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.
Given:
V = π r² h
Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.
Take the remaining term of the right side to the left as shown below,
V / π r² = h
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Which is equal to 1/58^8 ? a.58^-8 b.-1/58^-8 c.58^8 d.1/(58)^-8
a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.
How to evaluate this expression ?To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.
Applying this rule to the expression 1/58^8, we get:
1/58^8 = 1/(58^8) = 58^-8
Therefore, the correct answer is 58^-8.
It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:
1/58^8 = (1/58)^8 = 58^-8
This simplification shows that the correct answer is still 58^-8.
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a vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a
A vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a two factor chi Square test.
The Pearson chi-square (χ²) test, often simply called the chi-square test, is one of the most common non-parametric tests. Nonparametric tests are used for data that do not follow the assumptions of parametric tests, especially the assumption of normal distribution.
To test hypotheses about the distribution of a categorical variable, you should use the chi-square test or another non-parametric test. Categorical variables can be nominal or ordinal and represent groups such as species or nationality. They can only have a small number of specific values, so they cannot have a normal distribution.
Bidirectional chi-square is one of several tests of goodness of fit between the actual values of two nominal or ordinal variables and the values expected if the variables were unrelated or independent. Chi-square is also known as Pearson Chi-square and Chi-square test of independence. The symbol for the chi-square test is the lowercase Greek letter chi (χ) with a superscript 2, such as χ2. χ2 is a test of significance and should be accompanied by an appropriate test of strength. The strength test should be chosen based on the number of rows and columns in the table of observations. In particular, one of the most commonly used strength tests is the π coefficient.
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