The non-real solutions are (2 + i√26)/3 and (2 - i√26)/3
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x^3 + 14x^2 - 14x + 60 = 0
From the question, we have
x = -6
This gives
So, we have
x + 6 = 0
The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0
This is represented as
3x^3 + 14x^2 - 14x + 60/x + 6
Using a graphing calculator, we have
3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10
Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3
So, we have
x = (4 ± √-104)/6
This gives
x = (4 ± 2√-26)/6
Divide
x = (2 ± √-26)/3
Rewrite as
x = (2 ± i√26)/3
Split
x = (2 + i√26)/3 and x = (2 - i√26)/3
Hence, the non-real solutions of the polynomial expression are x = (2 + i√26)/3 and x = (2 - i√26)/3
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Dean biked 88 kilometers on Thursday and 5.7 kilometers on Friday. How far did Dean bike in all on Thursday and Friday?
Dean's bike moved a total distance of 93.7 kilometers on Thursday and Friday
How to determine the total distance moved by Dean bike altogether on Thursday and Friday?From the question, we have the following parameters:
Thursday = 88 kilometers
Friday = 5.7 kilometers
The total distance moved by Dean bike altogether on Thursday and Friday is the sum of the distance moved on Thursday and on Friday
Substitute the known values in the above equation
So, we have
Total distance = Distance moved on Thursday + Distance moved on Friday
Substitute the known values in the above equation
So, we have
Total distance = 88 kilometers + 5.7 kilometers
Evaluate the sum
So, we have
Total distance = 93.7 kilometers
Hence, the total distance moved by the bike is 93.7 kilometers
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What is the missing perfect square in this list?
9, 16, ___, 36, 49
A. 22
B. 25
C. 5
D. 20
the ratio of the number of miles run to the number of miles biked is equavlent for each row in the table
When the ratio of the number of miles run to the number of miles biked is equivalent for each row in the table, the value for A is C. 2 3/4.
How to illustrate the information?It should be noted that based on the information, the table has been given and the appropriate figures have been put into it.
The constant rate will be:
7 / 3 1/2 = 2
Now we can then write the relationship and this is illustrated as:
B = 2R
where B is the distance biked
R = the distance that's run.
We want to find the missing value of A. This is illustrated as:
5 1/2 = 2 × A
2A = 5 1/2
A = 2 3/4
Therefore, based on the information given, the correct option is C.
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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table.
Complete the table for A
A 2 1/4
B 2 2/4
C 2 3/4
D 3 3/4
Please help :(((
Question 1(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Determine if the table shows a proportional relationship.
Time (hours) 0 6 12 18 24
Pay (dollars) 0 72 144 216 288
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 12 dollars per hour.
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 13 dollars per hour.
No, it is not proportional because 72 over 6 does not equal 216 over 18.
No, it is not proportional because 216 over 18 does not equal 288 over 24.
Question 2(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
The graph of a proportional relationship is shown.
graph of a line beginning at point 0 comma 0 and continuing to the right going through points 5 comma 700 and 6 comma 840 and 7 comma 980
Create a table from the graph.
x 1 2 3
y 140 280 420
x 14 28 42
y 1 2 3
x 1 2 3
y 14 28 42
x 140 280 420
y 1 2 3
Question 3(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Three different recipes each make a different number of cookies and require a different amount of flour.
Recipe 1: 2 dozen cookies; 1.5 cups of flour
Recipe 2: 3 dozen cookies; 3 cups of flour
Recipe 3: 4 dozen cookies; 4.5 cups of flour
Determine if the three recipes use a proportional amount of flour.
Yes, it is proportional because the cookies increase by 1 dozen for every 1.5 cups of flour.
Yes, it is proportional because the ratios between the number of cookies and cups of flour are all equivalent.
No, it is not proportional because the number of cookies and cups of flour could not be zero at the same time.
No, it is not proportional because the ratios between the number of cookies and cups of flour are not all equivalent.
Question 4(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Determine if the table shows a proportional relationship.
x 36.5 23.2 63.3
y 18.25 11.6 21.1
Yes, it is proportional because the ratios for y over x are all equivalent to one half.
Yes, it is proportional because the ratios for y over x are all equivalent to one third.
No, it is not proportional because 18.25 over 36.5 is not equal to 23.2 over 11.6.
No, it is not proportional because 18.25 over 36.5 is not equal to 21.1 over 63.3.
Question 5(Multiple Choice Worth 2 points)
(Proportional Relationships LC)
Determine if the graph shows a proportional relationship.
Graph with x axis labeled distance miles and y axis labeled time hours. A line begins at point 0 comma 0 and continues to the right.
No, it is not proportional because the line does not intersect with the origin.
No, it is not proportional because the x-axis and y-axis are not labeled correctly.
Yes, it is proportional because it is a line that intersects with the origin.
Yes, it is proportional because the x-axis and y-axis are labeled correctly.
Question 6(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 190 380 570
Create a description in words for the table.
The number of calories burned is dependent on the number of hours working out. For every 190-hour workout, there is 1 calorie burned, and for every 380-hour workout, there are 2 calories burned.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there are 380 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 190-hour workout, there is 1 calorie burned, and for every 380-hour workout, there are 2 calories burned.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there are 380 calories burned.
Question 7(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
A group of hikers tracked how long it took to hike a 15-mile trail. They hiked 3.5 miles in 2 hours, 8.75 miles in 5 hours, and 12.25 miles in 7 hours.
Determine if the relationship between the hikers' distance and time is proportional.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.75 miles per hour.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 0.6 miles per hour.
No, it is not proportional because 3.5 miles in 2 hours is not equivalent to 8.75 miles in 5 hours.
No, it is not proportional because 8.75 miles in 5 hours is not equivalent to 12.25 miles in 7 hours.
The relationship between the input and output variables in the given table of values are;
Question 1
Yes, it is proportional, because the ratio of Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
x; 1, 2, 3, 4, 5
y; 140, 280, 420, 560
Question 3
No it is not proportional because the ratio between the number of cookies, and the cups of flour are not equivalent
Question 4
No, it is not proportional because 18.26/36.5 ≠ 21.1/63.3
Question 5
Yes, it is a proportional relationship because it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out, 190 calories are burned, and for a two–hours work out, there are 380 calories burned
Question 7
Yes because the ratio of the miles per hour are all equivalent to 1.75
What is a proportional relationship?A proportional relationship is one in which the input and output have a constant ratio, and in which the graph passes through the origin.
Question 1
A proportional relationship is one that has the x and y –intercept as the origin, (0, 0) and in which the ratio of the values at each point, y/x is a constant
Given (0, 0) is a data point and 72/6 = 144/12 = 216/18 = 12
Therefore; Yes it is proportional because the ratio for Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
The points on the graph are;
(0, 0), (5, 700), (6, 840), (7, 980)
Therefore;
y = (5/700)•x = (1/140)•x
The table is therefore;
x; 1, 2, 3, 4
y; 140 280 420 560
Question 3;
The ratio of the dozens of cookies to cups of flour, gives;
Recipe 1; R = 2/1.5 dozen per cup of flour
Which gives;
Approximately 1.33 dozens per cup of flour
Recipe 2, R = 3/3 dozens per cup of flour
Which gives;
Recipe 3, R = 4/4.5 dozens per cup of flour
Therefore;
No it is not proportional because the ratios between the number of cookies and the cups of flour are not all equivalent
Question 4
The ratio of the terms are;
18.26/36.5 = 11.6/23.2 = 1/2 ≠ 21.1/63.3 = 1/3
Therefore;
No it is not proportional because 18.26/36.5 is not equal 21.1/63.3
Question 5
Given that the graph is a straight line that passes through the origin, it is a proportional relationship with which gives;
Yes, it is a proportional relationship because, it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out 190 calories are burnt, and for a two–hours work out there are 380 calories burned
Question 7
The relationship is proportional, given that 3.5/2 = 8.75/5 = 12 .25/7 = 1.75
Therefore; Yes, because the ratios for miles per hour, are all equivalent to 1.75
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Answer:
The relationship between the input and output variables in the given table of values are;
Question 1
Yes, it is proportional, because the ratio of Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
x; 1, 2, 3, 4, 5
y; 140, 280, 420, 560
Question 3
No it is not proportional because the ratio between the number of cookies, and the cups of flour are not equivalent
Question 4
No, it is not proportional because 18.26/36.5 ≠ 21.1/63.3
Question 5
Yes, it is a proportional relationship because it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out, 190 calories are burned, and for a two–hours work out, there are 380 calories burned
Question 7
Yes because the ratio of the miles per hour are all equivalent to 1.75
What is a proportional relationship?
A proportional relationship is one in which the input and output have a constant ratio, and in which the graph passes through the origin.
Question 1
A proportional relationship is one that has the x and y –intercept as the origin, (0, 0) and in which the ratio of the values at each point, y/x is a constant
Given (0, 0) is a data point and 72/6 = 144/12 = 216/18 = 12
Therefore; Yes it is proportional because the ratio for Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
The points on the graph are;
(0, 0), (5, 700), (6, 840), (7, 980)
Therefore;
y = (5/700)•x = (1/140)•x
The table is therefore;
x; 1, 2, 3, 4
y; 140 280 420 560
Question 3;
The ratio of the dozens of cookies to cups of flour, gives;
Recipe 1; R = 2/1.5 dozen per cup of flour
Which gives;
Approximately 1.33 dozens per cup of flour
Recipe 2, R = 3/3 dozens per cup of flour
Which gives;
Recipe 3, R = 4/4.5 dozens per cup of flour
Therefore;
No it is not proportional because the ratios between the number of cookies and the cups of flour are not all equivalent
Question 4
The ratio of the terms are;
18.26/36.5 = 11.6/23.2 = 1/2 ≠ 21.1/63.3 = 1/3
Therefore;
No it is not proportional because 18.26/36.5 is not equal 21.1/63.3
Question 5
Given that the graph is a straight line that passes through the origin, it is a proportional relationship with which gives;
Yes, it is a proportional relationship because, it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out 190 calories are burnt, and for a two–hours work out there are 380 calories burned
Question 7
The relationship is proportional, given that 3.5/2 = 8.75/5 = 12 .25/7 = 1.75
Therefore; Yes, because the ratios for miles per hour, are all equivalent to 1.75
Step-by-step explanation:
Angel placed a rectangular photograph on a page of the yearbook.
Rectangle ABCD, shown on the coordinate grid below, represents the location of
the photograph on the yearbook page.
The points plotted in the cartesian plane are:
A( - 6 , 8 )
B( -2 , 8 )
C( - 2 , 2 )
D( - 6 , 2 )
What is a cartesian plane?The intersection of two perpendicular lines forms a cartesian plane. The X-axis is the horizontal line, and the Y-axis is the vertical line.
1st Quadrant - x > 0 and y > 0. Thus, the sign = ( +, +).
2nd Quadrant - x < 0 and y > 0. Thus, the sign= ( -, +).
3rd Quadrant - x < 0 and y < 0. Thus, the sign = ( -, -).
4 th Quadrant - x > 0 and y < 0. Thus, the sign= ( +, -).
In this given question all the points lie in the second quadrant that is all the point are of the form ( - x, y)
Thus the points are A( - 6 , 8 )
B( -2 , 8 )
C( - 2 , 2 )
D( - 6 , 2 )
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pls help i will give brainliest etc
Answer:
Quotient = 58.5
Step-by-step explanation:
Long division is a method used to divide large numbers by breaking the division down into multiple steps.
Parts of long division:
The dividend is the number that is divided by the divisor.The divisor is the number that divides the dividend. The quotient is the result obtained by the division.The remainder is the number left over.The divisor is placed to the left of the parenthesis.
The dividend is placed to the right of the parenthesis.
The quotient is placed above the dividend and separated from it by a bar.
To finish the given long division, subtract 64 from 68:
⇒ 68 - 64 = 4
Now divide the result by the divisor:
⇒ 4 ÷ 8 = 0.5
Finally, add 0.5 to 58 to give the final quotient:
⇒ 58 + 0.5 = 58.5
[tex]\large \begin{array}{r}58.5\\8{\overline{\smash{\big)}\,468\phantom{))}}}\\{-~\phantom{(}\underline{40\phantom{))..}}\\68\phantom{))}\\-~\phantom{()}\underline{\phantom{)}64\phantom{))}}\\4\phantom{))}\\-~\phantom{()}\underline{\phantom{)}\phantom{)}4\phantom{))}}\\0 \phantom{))}\\\end{array}[/tex]
Therefore, from inspection of the given long division:
The dividend is 468.The divisor is 8.The quotient is 58.5.I really need help with this
The equation of the lines are:
5. y - 5 = -3(x - 1)
6. y - 3 = 2(x + 4)
7. y - 6 = -4/3(x - 1)
8. y - 8 = -12/9(x + 2)
9. y = -5x + 1
10. y + 1 = -2(x - 2)
11. y - 1 = 2/3(x - 3)
How to Write the Equation of a Line?For any given line, the equation that represents the line can be written as:
y = mx + b, in slope-intercept form, where m is the slope and b is the y-intercept of the line.y - b = m(x - a), in point-slope form, where m is the slope and (a, b) is a point on the line.5. Substitute m = -3, and (a, b) = (1, 5) into y - b = m(x - a):
y - 5 = -3(x - 1) [equation in point-slope form]
6. Substitute m = 2, and (a, b) = (-4, 3) into y - b = m(x - a):
y - 3 = 2(x - (-4))
y - 3 = 2(x + 4) [equation in point-slope form]
7. Given the points, (4, 2) and (1, 6)
Find the slope (m):
Slope (m) = change in y/change in x = (6 - 2)/(1 - 4)
Slope (m) = -4/3
Substitute m = -4/3, and (a, b) = (1, 6) into y - b = m(x - a):
y - 6 = -4/3(x - 1) [equation in point-slope form]
8. Given the points, (-2, 8) and (7, -4)
Find the slope (m):
Slope (m) = change in y/change in x = (-4 - 8)/(7 -(-2))
Slope (m) = -12/9
Substitute m = -12/9, and (a, b) = (-2, 8) into y - b = m(x - a):
y - 8 = -12/9(x - (-2))
y - 8 = -12/9(x + 2) [equation in point-slope form]
9. y - 6 = -5(x + 1)
y - 6 = -5x - 5
y - 6 + 6 = -5x - 5 + 6 [addition property of equality]
y = -5x + 1 [equation in slope-intercept form]
10. Find the slope (m):
Slope of the line (m) = rise/run = -2/1
Slope (m) = -2
Substitute m = -2, and (a, b) = (2, -1) into y - b = m(x - a):
y - (-1) = -2(x - 2)
y + 1 = -2(x - 2) [equation in point-slope form]
11. Find the slope (m):
Slope of the line (m) = rise/run = 2/3
Slope (m) = 2/3
Substitute m = 2/3, and (a, b) = (3, 1) into y - b = m(x - a):
y - 1 = 2/3(x - 3) [equation in point-slope form]
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Suppose that the functions h and g are defined as follows.
h(x) = (x+5)(x+5)
g(x) = 4x+5
h
¹(²)(-1).
(a) Find
h
(b) Find all values that are NOT in the domain of
g
If there is more than one value, separate them with commas.
For the given functions, we have that:
a) The numeric value of the division function at x = 4 is of (h/g)(4) = 81/21 = 3.86.
b) The value that is not in the domain of the division function is of x = -1.25.
Division functionIn this problem, the functions that we are given are defined as follows:
h(x) = (x + 5)(x + 5).g(x) = 4x + 5.To find the quotient function of h(x) and g(x), we just divide the function h(x) by the function g(x), that is:
h(x)/g(x) = [(x + 5)(x + 5)]/(4x + 5).
At x = 4, the numeric value is found replacing each instante of x by 4, hence:
(h/g)(4) = [(4 + 5)(4 + 5)]/(4(4) + 5)) = 81/21 = 3.86.
The denominator of a fraction cannot be zero, as division by zero does not exist, hence the value of x that is not on the domain of the division function is found as follows:
4x + 5 = 0.
4x = -5.
x = -5/4
x = -1.25.
What is the missing information?The complete problem is given by the image at the end of the answer. There are lots of instances of this problem, just with different functions, so we use the functions given in this problem and not on the image.
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Manuela is making a banner for a school dance. She makes one angle 116°. What should she make the measures of angles B and D so that the banner is a parallelogram?
64°
116°
128°
244°
Answer: 64
Step-by-step explanation:
If angle A is 116, then the angle C is also 116. As the sum of the angles of a parallelogram is 360, the sum of B and D should be 360 - 2*116 = 132. Hence, the angles B and D should be each 132/2 = 64
A straight road named Planet Drive will connect the diner and the community garden.What is the equation of the line that represents Planet Drive? Show your work
As the line intersected the y-axis at x = 4, the equation of the line which represents planet Drive to the community garden is x = 4.
How is line equation represented?The shortest distance that separates two points is represented by a line. A line can be horizontal, slanted, or straight. A equation of a line in slope-intecept form has been expressed as:
y = mx + b
where,
m is called the slope
b is the y-intercept
From the graph shown, you recognize that the planet drive line is a horizontal as well as the general equation of the a horizontal line is represented as x = a where;
'a' is indeed the x-intercept of a line, which is the point at which the line intersects the y-axis.
Because, the line intersected the y-axis at x = 4, the equation of the line which reflects planet Drive to community garden is x = 4.
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isabella bought tickets for 84 people. each ticket cost $16.22. how much did isabella spend on tickets
Aisha drew a square that had a side length of 2 inches. What is the perimeter of 's Aisha square ?
Karen and Wayne need to buy a refrigerator because theirs just broke. Unfortunately, their savings account is depleted, and they will need to borrow money in order to buy a new one. Sears offers them an installment loan at 15% ( add-on-rate). If the refrigerator at Sears costs $1,500 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 2 years, what is the monthly payment?
Sears offers them an installment loan at 15% (add-on rate) and if at Sears costs $1,500 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 2 years, the monthly payment will be $75.47 using the interest and percentage formulas.
As per the question statement, Karen and Wayne need to buy a refrigerator because theirs just broke but their savings account is depleted and they will need to borrow money in order to buy a new one. The Sears offers them an installment loan at 15% ( add-on-rate), If the refrigerator at Sears costs $1,500 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 2 years. We are supposed to find the monthly payment made by them using the interest formula and percentage formula.
5% of $1500 = $75
Total amount borrowed is 1500 + 75 = $1575.00
Sears charges 15% to borrow the money
15% of 1575 = $236.25
total amount is 1575 + 236.25 = $1811.25
There are 24 months present in 2 years so,
The monthly payment = 1811.25 / 24 = $75.47
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A sector of a circle has a central angle of 150∘. Find the area of the sector if the radius of the circle is 17 cm.
Answer:
378.3 [tex]cm^{2}[/tex]
Step-by-step explanation:
a =[tex]\pi[/tex][tex]r^{2}[/tex] for a whole circle, but we only want the area for part of a circle
a = [tex]\frac{150}{360}[/tex] [tex]\pi[/tex][tex]17^{2}[/tex]
a = 378.3 [tex]cm^{2}[/tex] rounded to the nearest tenths place
Jeremy and Justine work for a company that receives $45 for each unit of output sold. The company has a variable cost of $25 per item and a fixed cost of $1600.
Based on this information, Jeremy and Justine make some projections about potential profit.
Jeremy states that for every 100 units of output sold, the company will make $3,600 in profit.
Justine states that for every 300 units of output sold, the company will make $4,400 in profit.
Part A
Determine a function that models the profit for the company based upon the conditions for revenue and expense.
Part B
Are the claims about profit that Jeremy and Justine made true? Explain why Jeremy and Justine are each correct or incorrect and justify your reasoning.
The function for profit given the conditions for revenue and expense is P = $20a - $1,600.
The first claim is incorrect because profit is $400
The first claim is incorrect because profit is $4,400.
What is the profit?Profit is revenue less total cost. Total cost consists of fixed cost and variable cost. Fixed cost is the cost that does not change with the level of output. Variable cost is the cost that changes with output. It increases as the level of output increases. Revenue is output multiplied by price per unit.
Profit = revenue - total cost cost
Profit = (price x output) - fixed cost - variable cost
P = ($45 x a) - $1,600 - ($25 x a)
P = $45a - $1,600 - $25a
P = $20a - $1,600
Where:
P = profit
a = output
Profit when 100 units is sold:
P = (20 x 100) - $1,600
$2,000 - $1,600 = $400
Profit when 300 units are sold
P = (300 x 20) - $1600
$6,000 - $1,600 = $4,400
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Write an equation for the function graphed.
PLEASE SHOW WORK THANK YOU
Answer:
you nrriebr dhdhxbe ahowe a grap by doing your work
The yearly profits of a company is $25,000. The profits have been decreasing by 6% per year.a. What is the initial value? $ b. What is the decay factor? c. What will be the profits in 8 years? Round your answer to the nearest dollar
The initial value is the initial profits of the company, so:
Answer a: $25,000
The decay factor is the percentage in what the profits have been decreasing, so:
Answer b: 6% or 0.06
Finally, the profits every year can be calculated as:
[tex]\begin{gathered} \text{profits}=InitialValue(1-0.06)^t \\ \text{Profits}=25,000(1-0.06)^8 \\ \text{Profits}=25,000(0.609) \\ \text{Profits}=15,239 \end{gathered}[/tex]Answer c: $15,239
What is the value of y? (20 points)
{question in image}
Answer:
Step-by-step explanation:
I will use cross multiplication to answer this question.
[tex]4(2y)=3y+10\\8y=3y+10\\8y-3y=10\\5y=10\\\frac{5y}{5} =\frac{10}{5} \\y=2[/tex]
I hope this helps!!!!!!!
Use the graph to evaluate the expressions below.
f(2) = 3
f⁻¹(2) = 1
f⁻¹(0) = -1
(f⁻¹o f)(1) = 1
The graph of f(x) is given. Here, f(x) = y and f⁻¹(y) = x.
That is, f(x) are y values corresponding to the given x-values and f⁻¹(y) is the x-value corresponding to the given y-value.
From the graph, f(2) is the y value when x = 2.
So, f(2) = 3
Now f⁻¹(2) is the x-value when y = 2.
So, f⁻¹(2) = 1
Also f⁻¹(0) =-1
Since f(1) = 2,
(f⁻¹o f)(1) = f⁻¹(f(1)) = f⁻¹(2) = 1
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What are the next numbers on the ratios chart
The equivalent ratios are 14:56 and 5 : 20 .
A ratio in mathematics shows how many times one number appears in another. For instance, if there were eight oranges and six lemons on a fruit platter, the ratio of oranges to lemons would be eight to six.
By dividing each quantity by the sum of all the numbers' common components, ratios can be reduced (much like fractions are). The fraction is said to be in its simplest form when the ratio's numbers are the tiniest practical integers.
A and B are frequent names for the ratio's antecedent and consequent, respectively.
The given ratios are 2 : 8 and 7 : 28 . which when simplified given the ratio 1 : 4 .
Now we know that 1 / 4 = k which is the common ratio.
Hence 14 / x = k = 1 / 4
or , x = 56
Again 5 / y = k = 1 / 4
or , y = 20
Therefore the equivalent ratios are 14:56 and 5 : 20 .
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What type of linear equation is X +1 equals X +1?
It depicts horizontal linear equation, as the slope is 0.
The slope of horizontal lines is zero. Consequently, m = 0 in the slope-intercept equation y = mx + b. Y = b, where b is the y-coordinate of the y-intercept, results in the equation.
The y-coordinate of every point on a horizontal line is the same. The line's equation is y=b if two points share the same y coordinate, b. The point (0,b) is the y-intercept of the horizontal line y=b. Horizontal lines don't have an x -intercept other than the line y=0.
A horizontal line is a line that is perpendicular to the x-axis. Because the value of x never changes, the graph of a relation of the form x = 5 is a line parallel to the y-axis.
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Divide.
−10 ÷ −2
Drag and drop the correct number into the box to complete the sentence.
FIND THE DOMAIN AND RANGE(Algebra 1)
The function's domain and range are (-3, -3, 2, 4) and (-2, 7, 1, 6) correspondingly.
Equation domain and rangeThe value of the independent function for which the function exists is referred to as the function's domain.
The value of the dependant function, for which the function exists, is referred to as the function's range.
The values in the x-column of the provided table are the domain, and the values in the y-column are the range.
The domain are shown in the table as (-3, -3, 2, 4) and the range as R = (-2, 7, 1, 6) Visit this link to learn more about domain and range: brainly.com/question/10197594
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Help please!!!!!!!!!!!
Answer:
522 1/2 revolutions
Step-by-step explanation:
First convert 13 3/4 into improper fraction
13 3/4 = (13 x 4 + 3)/4 = 55/4
Since these many revolutions are made in 1 minute, to find total number of revolutions made in 38 minutes, simply multiply 55/4 x 38
==> 55/4 x 38 = (55 x 38)/4 = 2090/4
Divide by 2 both numerator and denominator
==> (2090 ÷ 2)/(4 ÷ 2) = 1045/2 = 522 1/2
Kim bought 0.32 pounds of ham and 0.832 pounds of turkey How many pounds did she buy altogether?
A. 1.152 pounds
B. 1.052 pounds
C. 0.864 pounds
D. 0.152 pounds
Answer: A. 1.152 pounds.
Step-by-step explanation:
Add vertically
0.320
+0.832
[tex]2+0=2[/tex]
0.320
+0.832
2
[tex]2+3=5[/tex]
0.320
+0.832
52
Since [tex]3+8=11[/tex] , the one Carries Over to the ones place.
1
0.320
+0.832
.152
[tex]1+0+0=1[/tex]
1
0.320
+0.832
1.152
Therefore, 1.152 pounds is the correct answer.
PLEASE HELP ME!!!!!!!!
Answer:
In point-slope form: y + 4 = -2(x + 1)
In slope-intercept form: y = -2x - 6
In standard form: 2x + y = -6
Step-by-step explanation:
y + 4 = -2(x + 1)
y + 4 = -2x - 2
y = -2x -6
2x + y = -6
Write an equation of a line that passes through (-1,3)and (1,4)
SOLUTION
We want to write an equation of a line that passes through (-1,3) and (1,4)
First, let us find the slope m of the line for the points (-1,3) and (1,4)
We have
[tex]\begin{gathered} m=\frac{4-3}{1-(-1)} \\ m=\frac{1}{1+1} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, equation of a line in point slope form becomes
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(-1,3) \end{gathered}[/tex]plugging in the values, we have
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=\frac{1}{2}(x-(-1) \\ y-3=\frac{1}{2}(x+1) \\ y-3=\frac{1}{2}x+\frac{1}{2} \\ y=\frac{1}{2}x+\frac{1}{2}+3 \\ y=\frac{1}{2}x+\frac{7}{2} \end{gathered}[/tex]Hence the answer becomes
[tex]y=\frac{1}{2}x+\frac{7}{2}[/tex]Given g(x)= 4x-5, find g(3)
Combine like terms, if possible. Write the result with descending powers.
6x³ + 5x³+4x5
Select the correct choice below and, fill in the answer box to complete your choice.
OA. The polynomial cannot be simplified. The polynomial written in descending powers is__
OB. The polynomial can be simplified. 6x³ + 5x³+4x5=__
B. The polynomial can be simplified. 6[tex]x[/tex]³ + 5[tex]x[/tex]³ + 4[tex]x[/tex] + 5 = 11[tex]x^3[/tex] + 4[tex]x[/tex] + 5
determine whether the side lengths form a right triangle just say yes or no
Answer:
Yes, the side lengths
Explanation:
To be able to determine if the given side lengths of the triangle will form a right triangle, we'll have to apply the Pythagorean Theorem which states, in a right-angled triangle, the square of the hypotenuse(the longest side) must be equal to the sum of squares of the other two sides.
So let's go ahead and confirm;
[tex]\begin{gathered} 14.5^2=10.5^2+10^2 \\ 210.25=110.25+100 \\ 210.25=210.25 \end{gathered}[/tex]Since the Pythagorean theorem is obeyed as we can see above, then the side lengths will form a right triangle.