Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.
[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]
[tex] \sf8 : 2 :: x : 6[/tex]
Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:
[tex]\boxed{\: x = \frac{8 \times6}{2} = \frac{48}{2} = 24 }[/tex]
Therefore, the resulting geometric proportion would be:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{8 : 24 :: 6}[/tex]
Question 3
Hint: see problem #3 on 3-6
Rollie has a credit Card limit of $4,000. He made the following purchases: $425.36, $358.33,
$377.11, and $90.20.
What is the total amount of purchases?
$
What is Rollie's available credit?
$
LA
N
The total amount of purchases of Rollie is $1,251. Rollie's available credit card limit after spending $1,251 from $4,000 is $2,749.
We are given:
Rollie has a credit card limit of $4,000.
He made the following purchases: $425.36, $358.33, $377.11, and $90.20.
We need to find the total amount of purchases and Rollie's available credit card limit.
To find the total amount of purchases, we need to perform the addition that is add all the expenses:
The total amount of purchases
= addition of all purchases
= $425.36 + $358.33 + $377.11 + $90.20
= $1251
We need to subtract the total amount of purchases from the credit card limit to get Rollie's available credit card limit.
So,
Rollie's available credit card limit
= credit card limit - the total amount of purchases
= $4000 - $1251
= $2749
Thus, the total amount of purchases of Rollie is $1,251. Rollie's available credit card limit after spending $1,251 from $4,000 is $2,749.
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Hey can someone please help me out and explain the problem? Look below. Thank you! I’ll give brainly
Tan 5 pi / 9- tan 7 pi / 18 / 1+tan 5pi/ 9 tan 7pi/18
The Mathematical Final Answer:
0
Find the next 3 numbers in the sequence: 2, 9, 11, 18, 20, 27, ___, ___, ___
Answer: 29, 36, 38
Step-by-step explanation:
The sequence starts with 2 and proceeds to go to 9, which is a difference of 7.
After 9 it is 11, and the difference is 2.
After 11 it is 18 which is a difference of 7 again.
The pattern is difference of 7, difference of 2.
Since there was a difference of 7 between 20 and 27, the next difference will be 2, which is 29.
So, the pattern is +2, +7, +2 . . .
Therefore, your next three numbers will be 29, 36, 38
Question 5 (1 point) O O The angles that are marked the same are congruent. One mark congruent to one mark; two marks congruent to two marks; three marks congruent to three marks For the image shown, which of these statements is true? O O TH a HA If vertical angles are congruent, then the lines are parallel. If alternate interior angles are congruent, then the lines are perpendicular. If corresponding angles are supplementary, then the lines are parallel. d If corresponding angles are congruent, then the lines are parallel. b
Answer:
d. If corresponding angles are congruent, then the lines are parallel
Step-by-step explanation:
This is an example of two lines intersected by a transversal. If corresponding angles on both lines are equal, then the lines must be parallel! Think about it! If both of the two-mark angles were 30 degrees, both lines would be pointing in the exact same direction - parallel!
If corresponding angles are congruent, then the lines are parallel thus option (d) is correct.
What are parallel lines?Two lines in the same plane that are equally spaced apart and never cross each other are said two lines in the same plane that are equally spaced apart and never cross each other to be parallel lines.
As per the given two parallel lines and one transversal.
The angle with a single mark is collectively known as the corresponding angle.
If the corresponding angle is the same insure that both lines which intersect at single lines will be parallel.
Hence "If corresponding angles are congruent, then the lines are parallel".
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What is the equation in standard form 0f the line y=1/9x+5
Answer:
The equation in standard form of the line y=1/9x+5 is y-5=1/9(x-0)
In the past, Jessica got paid $197,980 annually. Since switching to a new career, she has been making 35% more. How much does Jessica make now?
$
thanks if you answer!!!! :")
Answer: $267,273
Step-by-step explanation:
$197,980 × 0.35 (35%) = $69,293
$197,980 + $69,293 = $267,273
Jessica now makes $267,273 annually.
Kyra is participating in
i fundraiser walk-a-thon. She walks| 2 miles in 30 minutes. If she continues to walk at the same rate, determine how
many minutes it will take her to walk 7 miles.
Kyra takes 105 minutes to cover a distance of 7 miles if she walks at a speed of 1/15 miles per minute.
Given,
Kyra is participating in a fundraiser walk-a-thon.
She walks 2 miles in 30 minutes
We have to find the time taken by Kyra to cover 7 miles if she continues the same rate of speed;
Here,
2 miles in 30 minutes
Then,
Speed = distance / time
Speed = 2 / 30
Speed = 1/15 miles per minute
Now,
The time taken to cover 7 miles;
Speed = distance / time
1/15 = 7 / t
t = 7 x 15
t = 105 minutes
That is,
Kyra takes 105 minutes to cover a distance of 7 miles if she walks at a speed of 1/15 miles per minute.
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It takes a word processor 30 minutes to word process and spell check 4 pages. Find how long it takes her to word process and spell check 22 pages.
It will take the word processor 165 minutes to check 22 pages
How to determine the time to check the pages?The given parameters in the question are:
Speed = 30 minuter per 4 pages
Number of pages = 22 pages
The number of hours to check the pages can be calculated using the following equation
Time = Speed * Number of pages
Substitute the known values in the above equation So, we have the following equation
Time = 30/4 * 22
There is no unit to convert
So, we have
Time = 30/4 * 22
Evaluate
Time = 165
Hence, the time is 165 minutes
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PLEASE URGENT PLEASE
The equation of the line in slope-intercept form is y = 5x-22.
What is slope-intercept form of an equation?The slope-intercept form of a straight line is one of the most common forms used to represent the equation of a line.
The slope-intercept form of an equation is given as
Formula:
y₂-y₁/x₂-x₁ = y-y₁/x-x₁........... Equation 1Where:
y₂ = 4y₁ = 3x₂ = 10x₁ = 5Substitute these values into equation 1
(4-3)/(10-5) = (y-3)/(x-5)1/5 = (y-3)/(x-5) (y-3) = 5(x-5)y-3 = 5x-25y = 5x-25+3y = 5x-22Hence, the equation in slope-intercept form is y = 5x-22.
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The technician at the store worked on the computer for 4.25 hours and charged him $141 for parts. The total was $332.25. Write and solve an equation which can be used to determine x the cost of the labor per hour.
The cost of the labor per hour is $ 45
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The total cost of the parts is = $ 141
The total number of hours worked by the technician = 4.25 hours
The total cost of repair = $ 332.25
Let the cost of the labor be = y
The total cost of labor =
Cost of the labor per hour x Number of hours worked by the technician
The total cost of labor = 4.25y
Now ,
The total cost of repairing the computer =
Total cost of labor + Total cost of the parts
The total cost of repairing the computer = 141 + 4.25y
332.25 = 141 + 4.25y
Subtracting 141 on both sides , we get
4.25 y = 191.25
Divide by 4.25 on both sides , we get
y = $ 45
Therefore cost of labor per hour y = $ 45
Hence , the total cost of labor per hour is $ 45
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Determine an nth degree polynomial that satisfies the aforementioned conditions.
The nth-degree polynomial that satisfies the aforementioned conditions is the polynomial p (x) = -3 (x + 9) (x - 1 - 6i) (x - 1 + 6i).
Given that:
p is of degree 3.
1 + 6i and -9 are zeros of p.
Since 1 + 6i is an imaginary number equal to zero so 1 - 6i must also be the one equal to zero.
So, p (x) = A (x + 9) (x - (1 + 6i)) (x- (1-6i))
p (x) = A (x + 9) (x - 1 - 6i) (x - 1 + 6i) ........ (Z)
Using formula:
(a-b) (a+b) = a² - b²
(a-b)² = a² - 2ab + b²
Assume, x - 1 = a, 6i = b
p (x) = A (x + 9) (x² - 2x + 1 + 36)
As i² = -1
p (x) = A (x + 9) (x² - 2x + 37)
Solving this equation we get,
p (x) = A (x³ - 2x² + 37x + 9x² - 18x + 333)
p (x) = A (x³ + 7x² + 19x + 333) ....... (1)
Given that:
p(2) = -1221
Putting the value of x = 2 and p(2) = -1221 in equation (1).
p(2) = A (2³ + 7(2²) + 19(2) + 333)
=> -1221 = A (8 + 28 + 38 + 333)
=> A = -1221/407
=> A = -3
Putting the value of A = -3 in equation (Z).
Hence, the polynomial p (x) = -3 (x + 9) (x - 1 - 6i) (x - 1 + 6i).
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which of these statements below are true? Select all that apply
Answer:
Step-by-step explanation:
the answer is D i'm pretty sure
Consider the following linear equation.
y=−43x+2
Step 1 of 2 : Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.
Slope: -1/9
Y-Intercept: 2
On a January evening in upstate New York, 8 inches of snow was on the ground. At 11pm, it began snowing 1/4 inch per hour and snowed consistently for 14 straight hours.
The slope of the linear function that models this situation is given as follows:
m = 0.25.
How to obtain the parameters of a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
Hence the coefficients of the function and their meaning are obtained as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the amount represented by the function, i.e., the numeric value of the function when the input variable x assumes a value of 0.In this problem, these parameters are defined as follows:
Intercept of 8, as it was the initial amount of snow on the ground.Slope of 1/4 = 0.25 inches, as it is the amount by which the amount of snow on the ground increases each hour.Hence the linear function modelling the situation is:
y = 8 + 0.25x.
Missing InformationThe problem asks for what is the slope of this situation.
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Find the eigenvalues and eigenvectors
Answer:
Step-by-step explanation:
Yoga pants are on sale for 1/3 off the original price. If a pair of yoga pants normally costs $60, what is sales price?
The sales price of the yoga pants is $20.
How to calculate the price?It should be noted that from the information illustrated, the Yoga pants are on sale for 1/3 off the original price and a pair of yoga pants normally costs $60.
The sales price will be:
= Fraction given × Original price
= 1/3 × $60
= $20
The price is $20.
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6. Use the data below to make a scatter plot in Desmos and find the
exponential regression equation. Round to the nearest hundredth if
necessary. Do not type spaces.
Time (years)
7. Using your equation from #6, find out how much the Fire Dragons
comic book would be worth in 55 years.
Your answer
Answer:
I hope that the picture below helps.
Step-by-step explanation:
The number of days worked is inversely proportional to the number of people. If it takes 15 people to collect and pile sand for the construction of a classroom in five days, how many days would it take 20 men to complete the task?
15/4 days take 20 men to complete the task.
Given,
In the question:
The number of days worked is inversely proportional to the number of people.
If it takes 15 people to collect and pile sand for the construction of a classroom in five days.
To find the how many days take it 20 men to complete the task?
Now, According to the question:
Based on the given condition:
Formulate:
5 x 15 ÷ 20
Calculate :
5x 15/ 20
Cross out the common factor:
=15/4
Hence, 15/4 days take 20 men to complete the task.
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Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 6 liters of synthetic oil. In order to make 836 liters of Petrolyn oil, how many liters of synthetic oil are needed?
The liters of synthetic oil that are needed is 456 liters.
How to calculate the liters?From the information, petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 6 liters of synthetic oil.
To make 836 liters of oil, the liters of synthetic oil will be:
= 6 / (6+5) × 836
= 6/11 × 836
= 456
Therefore, 456 liters are needed.
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This number line models the division problem 14÷5 .
What is the quotient?
Enter your answer as a fraction in simplest form by filling in the boxes.
$$
The simplest form of fraction (1/4)/5 is 1/20.
What is quotient?A quotient is the simplest or resultant value of division of two numbers. In two numbers, one number is dividend and another number is divisor,
quotient=dividend/divisor
The simplest form for fraction (1/4)/5,
(1/4)/5=1/(4×5)
= 1/20
So, the simplest form of (1/4)/5 is 1/20.
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132.16 kg of beef was placed into 16 packages of equal weight. what is the weight of one package beef?
The weight of one package beef is 8.26kg
What is division of numbers?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
For example, if 10 students are to share 100 oranges, if they are to share it equal, then each students will receive 100/10= 10 oranges
Similarly 132.16kg was placed into 16packages of equal weight.
Therefore the weight of each package beef will be 132.16/16= 8.26kg
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A hoyel has 124 pillows.The hotel gets more pillows in 5 styles wiyh 8 pillows of each syyle.Write and solve an equation to find out how many pillows the hotel has in all
Answer:
164 pillows
Step-by-step explanation:
Equation: 124 + 5(8)
What happens to a parabola when you change certain elements of the equation?
Supoose a<1 compared to the parent function then parabola is wider than the parent function.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Direction the parabola opens the value of p as positive, the parabola opens up.
The focus and vertex both have the same x position, so the distance would be in terms of the y-coordinates only.
Supoose a<1 compared to the parent function then parabola is wider than the parent function
If "a" is a fraction less than one, therefore the parabola becomes wider.
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Suppose that the functions and are defined as follows.
Find the following.
The expression we get from the given functions r and s defined for all real numbers x.
r( s(-3))= -38
Given that,
All real numbers x are defined by the functions r and s.
r(x) =2x+1
s(x) =-2x²-2
We have to find the expression
r( s(-3))
Take the functions,
r(x) =2x+1
s(x) =-2x²-2
Now, Take
r( s(-3))
Substitute s function first
r(-2(-3)²-2)
r(-2(9)-2)
r(-18-2)
r(-20)
Now substitute r function
2(-20)+2
-40+2
-38
Therefore, The expression we get from the given functions r and s defined for all real numbers x.
r( s(-3))=-38
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A combination padlock in which a sequence of numbers is used as the "key" to open
the lock. Suppose a combination padlock has 10 digits to choose from for each of the
four sections of the lock.
Does the "key" for a combination padlock involve permutations or combinations?
A. Permutation
B. Combination
The "key" for a combination padlock involves a 210 combination.
What is a combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Here, we have
A combination padlock has 10 digits to choose from for each of the
four sections of the lock.
so, we apply a combination
¹⁰C₄ = 10! / (6! × 4!)
= (10 × 9 × 8 × 7 × 6!) / (6! × 4!)
= (10 × 9 × 8 × 7)/ 4!
= (10 × 9 × 8 × 7)/ (4 × 3 × 2 × 1)
= 210
Hence, the "key" for a combination padlock involves a 210 combination.
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A freight train and a passenger train leave Portland at the same time on parallel tracks heading for Springfield. The passenger train goes 30 mi/hr faster than the freight train, and in 6 hr the passenger train travels three times farther. What is the speed of each train?
The passenger train traveling at 30 mi/hr faster than the freight train and traveling 3 times the distance traveled by the freight train, through the kinematic equations, indicates that the speed of the freight train is 15 mi/hr and the speed of the passenger train is 45 mi/hr.
What is kinematics?Kinematics is the study of the motion of an object without reference to the force that causes the motion.
The speed of the passenger train = 30 + The speed of the freight train
Distance traveled by the passenger train in 6 hours = 3 × The distance traveled by the freight train
Let v represent the speed of the freight train and let d represent the distance traveled by the freight train in 6 hours
From kinematic equations, we get;
Speed of the passenger train = 30 + v
Distance traveled by the passenger train in 6 hours = 3 × d
(30 + v) × 6 = 3•d
6•v = d
Which gives; (30 + v) × 6 = 3 × 6•v
180 + 6•v = 18•v
12•v = 180
v = 180 ÷ 12 = 15
The speed of the freight train is v = 15 mi/hr
The speed of the passenger train = 30 + v
The speed of the passenger train is (30 + 15) mi/hr = 45 mi/hr
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Pleaseee help me
a +3> 14 or a -5 ≤3
Answer:
a>11
[tex]a\leq 8[/tex]
Step-by-step explanation:
a+3>14
-3. -3
a>11
a-5<=3
+5. +5
a<=8
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A regular polygon has 18 sides. If one of its angles measures (4h − 25)°, what is the value of h?
Answer: h = 46.25
Step-by-step explanation:
You can use the formula below to calculate the value of its interior angle:
n = number of sides = 18[tex]\frac{(n-2)*180}{n} =\frac{(18-2)*180}{18} =\frac{16*180}{18} =160[/tex]
So, each one of its interior angles is equal to 160°. Set that equal to the given angle measure and solve:
[tex]160=4h-25\\\\4h=160+25=185\\\\h=46.25[/tex]
Present value interest rate? You expect to receive $10000 as a bonus after 5years on the job. You have calculated the parent value of this bonus and the answer is $8000 what discount rate did you use in your calculation
The discount rate used in calculator wound be 4.56%.
Given that,
You anticipate getting a bonus of $10000 after five years on the job.
We have the result of your calculation for the parent value of this bonus is $8000. what percentage of a discount rate did you use.
We know that to find the present value of a future sum of money .
PV= FV/(1+r)ⁿ
Here,
PV is present value = $8000
FV is future value = $10000
r is discount rate we have to find
n is time = 5 years
Substitute in the formula,
$8000=$10000/(1+r)⁵
(1+r)⁵=$10000/$8000
(1+r)⁵=1.25
1+r=[tex]1.25^{1/5}[/tex]
1+r=1.0456
r=1.0456-1
r=0.0456
r=4.56%
Therefore, The discount rate used in calculator wound be 4.56%.
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