Therefore, the coordinates of point B are approximately (12.67, 0.67).
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. Equations are written using an equal sign (=) between the two expressions that are being compared. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. The equation is true if the LHS is equal to the RHS. Equations are used to represent various relationships and patterns in mathematics, and are an important tool in problem-solving and mathematical modeling.
Here,
(a) To calculate the length of OC, we need to find the coordinates of point O, which is the intersection of the diagonals of the parallelogram. The midpoint of AC is:
((12+5)/2, (0+5)/2) = (8.5, 2.5)
Therefore, the equation of the line passing through the midpoint of AC and perpendicular to AC is:
y - 2.5 = -(5-0)/(5-12) (x - 8.5)
Simplifying:
y - 2.5 = 5/7 (x - 8.5)
y = 5/7 x - 1
This is the equation of the line passing through O and parallel to AB. We can see that when x = 12, y = 5/7 * 12 - 1 = 7.4. Therefore, the coordinates of O are (12, 7.4).Using the distance formula, we can now calculate the length of OC:
OC = √((12-5)² + (7.4-0²) = √(109.96) ≈ 10.49
Therefore, the length of OC is approximately 10.49 units.
(b) The gradient of OC can be found using the coordinates of points O and C:
m = (y₂ - y₁)/(x₂ - x₁) = (7.4 - 5)/(12 - 5) = 0.4/1 ≈ 0.4
Therefore, the gradient of OC is approximately 0.4.
(c) The equation of line AB can be found using the coordinates of points A and B:
m = (y₂ - y₁)/(x₂ - x₁) = (y - 0)/(x - 12)
Simplifying and substituting the coordinates of point A:
0.4 = (y - 0)/(x - 12)
0.4(x - 12) = y
Therefore, the equation of line AB is y = 0.4x - 4.8.
(d) The coordinates of point B can be found by solving the system of equations formed by the equations of lines AB and OC. Equating y in both equations:
0.4x - 4.8 = 5/7 x - 1
Simplifying and solving for x:
0.3x = 3.8
x = 12.67
Substituting x in either equation:
y = 0.4(12.67) - 4.8 ≈ 0.67
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If I get paid $12.50 an hour and I worked a total of 15 hours and 35 minutes how much did I make?
Answer: $194.79
Step-by-step explanation:
It is easiest to approach this question in two parts.
First part is simple - multiply the wage per hour times the number of whole number you have worked. ($12.50)(15) = $187.50
Next you need to find how much you make in 35 minutes at a wage rate of 12.50 an hour. You can set up a ratio to find this out -
($12.50) | (60 min) - (x dollars) | (35 min)
then cross multiply and divide - (12.5 * 35) / 60 = 7.291
This means you make $7.29 for 35 minutes of work.
$187.50 + $7.29 = $194.79 for 15 hours 35 minutes of work.
(this is based on a per minute/hour scale)
Question 14
Josh used the zeros of a polynomial to sketch the following graph of the function.
based on the graph above what are the zeros of the polynomial?
help me pls D:
quiz
The zeros of the polynomial are given as follows:
Option B: (3,0) and (-2,0)
What are the zeros of the polynomial?The zeros of a polynomial function are the values of the independent variable (usually denoted by x) that make the function equal to zero. In other words, they are the values of x for which the function crosses the x-axis.
The values of x for which the graph of the polynomial crosses the x-axis are given as follows:
x = -2 and x = 3.
At these points, the y-coordinate is of zero, hence the points on the graph are given as follows:
(3,0) and (-2,0).
Meaning that the correct option is given by option B.
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A merchant mixed 12 lb of a cinnamon tea with 3 lb of spice tea. The 15-pound mixture cost $39. A second mixture included 16 lb of the cinnamon tea and 6 lb of the spice tea. The 22-pound mixture cost $58. Find the
cost per pound of the cinnamon tea and of the spice tea.
cinnamon
spice
Answer:
Step-by-step explanation:
Let x be the cost per pound of the cinnamon tea and y be the cost per pound of the spice tea.
From the first mixture, we have:
12x + 3y = 39
From the second mixture, we have:
16x + 6y = 58
We can solve this system of equations by elimination. Multiplying the first equation by 2 and subtracting it from the second equation gives:
16x + 6y = 58
(24x + 6y = 78)
-8x = -20
Dividing both sides by -8 gives:
x = 2.5
Substituting this value of x into the first equation, we get:
12(2.5) + 3y = 39
Simplifying, we get:
30 + 3y = 39
Subtracting 30 from both sides gives:
3y = 9
Dividing both sides by 3 gives:
y = 3
Therefore, the cost per pound of the cinnamon tea is $2.50 and the cost per pound of the spice tea is $3.
The perimeter of a rectangle is 34 units. Its width is 6.5 units.
Write an equation to determine the length of the rectangle
Given:
P = 34 [Perimeter]
W = 6.5 {let's use W and L to make it easy to read]
Also known:
P = W + L + W + L = 2(W+L)
Fill in values:
34 = 2(6.5+L) [NOTE: This is an equation to determine the length (L) of the rectangle."]
17 = 6.5 + L [NOTE: This is a simplified form of the above equation.]
10.5 = L [NOTE: This is the solution (the value of L)]
Cybersecurity is a field limited to only government agencies and defense contractors. true or false
Explanation:
Any company that has an online presence (eg: website) needs to take cybersecurity seriously. This is safeguard their customers against online criminals, and also keep their employees safe. Cybersecurity isn't limited to government roles or defense contractor roles only.
Help with number 4!!!
Answer:forgot the explanation
Step-by-step explanation: give me a equation to solve
Let a and b be real numbers, where Which of the following functions could represent the graph on the right? f(x) = x (x – a)(x – b)2 f(x) = (x – a)(x – b)2 f(x) = x(x – a)³(x – b) f(x) = x2(x – a) 2(x – b)2
Answer:
Without a graph provided, it's difficult to determine which of the given functions represents the graph on the right. However, we can analyze each function to see if it has any characteristics that match the shape of the graph.
f(x) = x(x – a)(x – b)2
This function has one x-intercept at x = 0 and a double root at x = b. If b > a, then the function will have a local maximum at x = a and a local minimum at x = b. This function may represent a graph with a single x-intercept, a double root, and a local maximum and minimum.
f(x) = (x – a)(x – b)2
This function has one x-intercept at x = a and a triple root at x = b. If b > a, then the function will have a local minimum at x = a and a local maximum at x = b. This function may represent a graph with a single x-intercept, a triple root, and a local minimum and maximum.
f(x) = x(x – a)³(x – b)
This function has one x-intercept at x = 0 and a triple root at x = a. If a < b, then the function will have a local minimum at x = b. This function may represent a graph with a single x-intercept, a triple root, and a local minimum.
f(x) = x²(x – a)²(x – b)²
This function has two x-intercepts at x = 0 and x = a and a double root at x = b. If b > a, then the function will have a local maximum at x = a and a local minimum at x = b. This function may represent a graph with two x-intercepts, a double root, and a local minimum and maximum.
Based on these analyses, it's unclear which function represents the graph on the right, as all four functions have characteristics that could match the shape of the graph.
Answer:
It's A
Step-by-step explanation:
2023 edge
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The figure below shows a circle with Center A, diameter IP, and tangents SL, PL, and IC. Which of the angles must be right angles?
"^ a popular shopping Centre waiting time for an ABC Ban ATM machine is found to be uniformly distributed between 1 and 5 minutes. what is the probability of waiting between 2 and 3 minutes to use the ATM
The probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur. For example, the probability of flipping a fair coin and getting heads is 1/2 or 0.5.
Since the waiting time for the ABC Ban ATM machine is uniformly distributed between 1 and 5 minutes, the probability density function is given by:
f(x) = 1/(5-1) = 1/4 for 1 ≤ x ≤ 5
To find the probability of waiting between 2 and 3 minutes, we need to find the area under the probability density function between 2 and 3. This is given by the definite integral of the probability density function over the interval [2, 3]:
P(2 ≤ x ≤ 3) = ∫2^3 f(x) dx
= ∫2^3 (1/4) dx
= (1/4) [x]2^3
= (1/4) (3-2)
= 1/4
Therefore, the probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.
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Solid metal support poles in the form of right cylinders are made out of metal with a
density of 6.6 g/cm³. This metal can be purchased for $0.38 per kilogram. Calculate
the cost of a utility pole with a diameter of 17.6 cm and a height of 790 cm. Round
your answer to the nearest cent.
The cost of the utility pole is $127.36.
2 eggs are needed to make 24 cookies. how many eggs are needed to make 60 cookies
Answer:
5 eggs.
Step-by-step explanation:
Since two eggs are needed for 24 cookies, we know by dividing both numbers by two that the rate is one egg for 12 cookies. 60/12 = 5. Multiply both numbers by 5 to get the answer. So, the answer is 5 eggs.
BONUS SECTION
This section is optional. Each correct answer will receive 2 points (12 points total)
which will be added to your test's raw score. Clearly indicate the necessary steps,
including appropriate formula substitutions, diagrams, graphs, charts, etc. For all
questions in this part, correct numerical answers without work shown or an
explanation will not receive any credit.
1. Shanika has a dilemma. She has five choices for future employment but does not
know which job opportunity to take. Calculate the annual income for each option
and let her know which job would earn her the most money.
Option 1: Keeping her present job at $15,000 per
year plus a 20% year-end bonus.
Option 2: Taking a job that pays $1,250 per month
Answer:
A
Step-by-step explanation:
The circumference of the circle is 20 pi inches. What is the arc length of the shaded sector? Express the answer in terms of Pi. A circle. The shaded sector has an angle measure of 45 degrees. Recall that StartFraction Arc length over Circumference EndFraction = StartFraction n degrees over 360 degrees EndFraction. 2.5 pi inches 5 pi inches 7.9 pi inches 10 pi inches
The provided remark indicates that option (A) is accurate for 2.5 inches.
What length of time is an example?The measurement or size of something to end to end is referred to as its length. To put it another way, it is the bigger of the upper two or three dimensions of a geometric form or object. For instance, the length and width of a parallelogram define its measurements.
Using the given equation:
Arc Length / 20π = 45/360
Cross multiply:
Arc length × 360 = 20π x 45
Arc length x 360 = 900π
Divide both sides by 360:
Arc length = 900π / 360
Arc Length = 2.5 π inches.
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Solve the following quadratic by completing the square
f(x) = x^2 + 2x-12
The quadratic equation f(x) = x² + 2x - 12 can be rewritten as f(x) = (x + 1)²- 13 using the completing square method.
What is completing squares method?Completing the square is a strategy used in algebra to solve quadratic equations of the type ax² + bx + c = 0, where a, b, and c are constants and x is the variable. By converting the quadratic equation into a perfect square trinomial, the square roots of both sides of the equation may be used to quickly solve the problem. This is the core notion behind the completion of the square. The quadratic expression becomes a perfect square when we add and subtract a specific number from it to complete the square. Half of the x-term squared coefficient is equal to the sum of the numbers we add and remove.
The given function is f(x) = x² + 2x-12.
Now, group the x terms together:
f(x) = (x² + 2x) - 12
Between the parenthesis, add and remove the square of the x-half-coefficient: term's:
f(x) = (x² + 2x + (2/2)² - (2/2)²) - 12
f(x) = (x + 1)² - 1 - 12
f(x) = (x + 1)² - 13
Hence, the quadratic equation f(x) = x² + 2x - 12 can be rewritten as f(x) = (x + 1)² - 13.
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What is the percent change from 310 to 155?
Answer: 50% decrease
Step-by-step explanation:
50% of 310 = 155
310-155=155
50% decrease :)
ANSWER: 50% decrease
SOLUTION:
50% of 310 = 155
310-155=155
So in all the answer is.......
50% decrease :)))))
-XOXOXO:)
Your take home pay is $3,210 and your federal witholding tax rate is 16%. What was your gross pay? show the math
Answer:
To find your gross pay, we can use the following formula:
Gross Pay = Take Home Pay / (1 - Federal Withholding Tax Rate)
Plugging in the given values, we get:
Gross Pay = 3,210 / (1 - 0.16)
Simplifying the denominator, we get:
Gross Pay = 3,210 / 0.84
Calculating the division, we get:
Gross Pay = 3,821.43
Therefore, your gross pay was $3,821.43.
Elijah works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commission on top of his base salary equal to 30% of his total sales for the week. How much would Elijah make in a week in which he made $775 in sales? How much would Elijah make in a week if he made
x dollars in sales?
Total earnings when selling $775:
Total earnings when selling $x:
Elijah's total earnings for the week if he made x dollars in sales would be: $500 + 0.3x.
What is sale?
A sale is an event or activity in which goods or services are sold at a reduced or discounted price.
What is discount?
A discount is a reduction in the price of an item or service. It is often offered as a promotion or incentive to encourage customers to buy or use a product or service.
According to given information:Total sales commission earned by Elijah for selling $775 worth of clothing:
30% of $775 = 0.3 x $775 = $232.50
Therefore, Elijah's total earnings for the week would be:
$500 (guaranteed salary) + $232.50 (commission) = $732.50
For selling x dollars worth of clothing, the commission earned by Elijah would be:
0.3x
Therefore, Elijah's total earnings for the week if he made x dollars in sales would be:
$500 (guaranteed salary) + 0.3x (commission) = $500 + 0.3x
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Grace The Brand Jewelry generated the following information from its financial statements:
Earnings after interest and taxes R600 000
Earnings per share R2,50 per share
Shareholder equity R1000 000
Market to book ratio 2,60
What is the company’s market price per share?
Answer:
Step-by-step explanation:
We can use the market-to-book ratio to calculate the company's market price per share.
Market-to-book ratio = Market value per share / Book value per share
Book value per share = Shareholder equity / Number of shares outstanding
We are given the market-to-book ratio as 2.60, and the shareholder equity as R1000 000. We can calculate the book value per share as follows:
Book value per share = R1000 000 / Number of shares outstanding
To calculate the number of shares outstanding, we can use the earnings per share (EPS) formula:
EPS = Earnings / Number of shares outstanding
We are given the earnings per share as R2.50, and the earnings after interest and taxes as R600 000. Substituting these values, we get:
R2.50 = R600 000 / Number of shares outstanding
Solving for Number of shares outstanding:
Number of shares outstanding = R600 000 / R2.50 = 240,000 shares
Now, we can calculate the book value per share:
Book value per share = R1000 000 / 240,000 = R4.17 per share
Finally, we can calculate the market value per share using the market-to-book ratio:
Market-to-book ratio = Market value per share / Book value per share
2.60 = Market value per share / R4.17
Market value per share = 2.60 x R4.17 = R10.83 per share
Therefore, the company's market price per share is R10.83.
The diagram below represents how rock is affected when water enters cracks in rock, freezes, and becomes ice.
Which geologic process is represented in the diagram?
Answer: Physical weathering, more specifically, ice wedging
Step-by-step explanation:
:D
Explain the difference between a) comparing, b) non-standard units of measurement and c) standardised units of measurement.
Answer:
a) Comparing: Comparing means evaluating the similarity or difference between two or more objects, values, or variables. It is a process of identifying and highlighting the similarities and differences among objects, values, or variables based on specific criteria.
b) Non-standard units of measurement: Non-standard units of measurement are those that are not part of the International System of Units (SI) and are often created for specific purposes or contexts. These units may be used to measure variables such as time, distance, weight, or volume, but they are not universally recognized or standardized.
c) Standardized units of measurement: Standardized units of measurement are those that are part of the International System of Units (SI) and are universally recognized and accepted. These units provide a standard framework for measuring variables such as time, distance, weight, or volume, making it possible to compare and communicate measurements accurately across different contexts and languages. Some examples of standardized units of measurement include seconds, meters, kilograms, and liters.
What is 7% as a decimal ?
Answer: 0.07%
Step-by-step explanation:
Answer:
0.07
Step-by-step explanation:
FACTOR BY GROUPING
SEE ATTACHED IMAGE
SOLVE 4-6 BY STEPS 1-4
Answer:
see explanation
Step-by-step explanation:
(4)
5x³ - 10x² - 3x + 6
factor out 5x² from first 2 terms and - 3 from last 2 terms
= 5x²(x - 2) - 3(x - 2) ← factor out (x - 2) from each term
= (x - 2)(5x² - 3)
----------------------------------------------------
(5)
9a³ - 45a² - 7a + 35
factor out 9a² from first 2 terms and - 7 from last 2 terms
= 9a²(a - 5) - 7(a - 5) ← factor out (a - 5) from each term
= (a - 5)(9a² - 7)
-----------------------------------------------------
(6)
5x²y - 15y - 2x² + 6
factor out 5y from the first 2 terms and - 2 from the last 2 terms
= 5y(x² - 3) - 2(x² - 3) ← factor out (x² - 3) from each term
= (x² - 3)(5y - 2)
jay eats 2/3 of a pizza but if dan eats 4 times that amount how much did dan eat
Answer:
Dan eat 2 2/3 of a pizza
Step-by-step explanation:
the answer is above
Let
x-----> amount of pizza Jay ate
y-----> amount of pizza Dan ate
we know that
----> equation A
-----> equation B
substitute equation A in the equation B and solve for y
Convert to mixed number
What’s the answer to this question? I can’t seem to find the answer.
You could try factoring.
[tex]6x^2-x-1=(2x-1)(3x+1)\\3x^2+25x+8=(x+8)(3x+1)\\x^2+4x-32=(x+8)(x-4)\\2x^2+7x-4=(x+4)(2x-1)[/tex]
So your expression becomes...[tex]\frac{(2x-1)(3x+1)}{(x+8)(3x+1)}*\frac{(x+8)(x-4)}{(x+4)(2x-1)}=\frac{x-4}{x+4}[/tex].
1pt equal how many mL
Answer:
1 American pt equals approximately 568.261 mL
OR
1 British Imperial pt is approximately 473 mL
I recommend choosing the answer that better relates to where you are from.
Step-by-step explanation:
There seem to be TWO kinds of pint sizes. A US pint is 16 ounces and an Imperial pint is 20 ounces.
How many solutions does the system of nonlinear equations graphed below
have?
A. Zero
B. Several
C. Infinite
D. One
Hence, the system with nonlinear equations may contain one of these kinds of answers, depending on the particular equations and their graph.
How do nonlinear equations work?Unable to form a straight line is a non-linear equation. With a fluctuating slope value, it resembles a graphed curve.
In general, there can be zero, one, many, or an infinite number of solutions to a system of nonlinear equations. It depends on the particular equations and how those interact with one another.
The problem has zero solutions if there are no values of the parameters that satisfy both equations, which occurs when the equations are inconsistant.
A single solution exists for the system if the equations cross at that point.
The system has multiple solutions if the equations cross more than once.
The system has an infinite number of solutions if the equations all describe the same curve.
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If Planet I is 31.1 million miles farther from the sun than Planet II, then Planet III is 24.6 million miles farther from the sun than Planet I. When the total of the distances for these three planets from the sun is 197.8
million miles, how far away from the sun is Planet II?
After solving the equations e know that Planet II is 35 million miles away from the sun.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
So, let x be the separation between planet I and the sun.
Planet II's distance from the sun is x-30.2.
Planet iii's distance from the sun is equal to x+24.8.
x + x-30.2 + x+24.8 = 190.2
Mix related phrases to find x.
3x - 5.4 = 190.2
3x = 195.6
x = 65.2
65.2 million miles separate planet I from the sun.
Planet II is 35 million miles from the sun or 65.2-30.2.
Planet iii is 90 million miles from the sun (65.2 + 24.8 = miles).
Therefore, after solving the equations e know that Planet II is 35 million miles away from the sun.
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If Planet I is 31.1 million miles farther from the sun than Planet II, then Planet III is 24.6 million miles farther from the sun than Planet I. When the total of the distances for these three planets from the sun is 197.8
million miles, how far away from the sun is Planet II?
If Marie were to paint her living room alone, it would take 3 hours. Her sister Fran could do the job in 6 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.
The time it takes them to paint the living room together is 2 hours. Expressing this as a fraction reduced to lowest terms 2 hours is 2/1.
What is time working together?Time working together refers to the amount of time that two or more people need to work together to complete a certain task. It is often used in situations where people are working collaboratively or cooperatively to achieve a common goal.
According to question:Let's denote the time it takes Marie to paint the living room alone by M and the time it takes Fran to paint the living room alone by F.
From the problem, we know that:
M = 3 hours
F = 6 hours
To determine the time it takes them to paint the living room together, we can use the following formula:
1 / (time working together) = 1 / M + 1 / F
Substituting the values we have:
1 / (time working together) = 1 / 3 + 1 / 6
Simplifying the right-hand side of the equation:
1 / (time working together) = 2 / 6 + 1 / 6
1 / (time working together) = 3 / 6
1 / (time working together) = 1 / 2
Therefore, the time it takes them to paint the living room together is 2 hours. Expressing this as a fraction reduced to lowest terms:
2 hours = 2/1
So the answer is: 1 / (time working together) = 1 / 2, or equivalently, the time working together is 2/1.
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change 3 5 to a decimal fraction
Answer:
7/20
its the answer to your question