a) To find k for parallel lines, equate slopes to get k = -10/3. b) For perpendicular lines, use negative reciprocal slopes to find k = 3/10.
To determine the conditions for parallelism and perpendicularity, we need the slope of each line. The slope-intercept form of a line is y = mx + b where m is the slope.
To find the slope of the first line, we rearrange 3x-5y=9 to the form of y = mx + b, resulting in y = (3/5)x - (9/5). Therefore, the slope is 3/5. For the second line, rearranging 2x+ky=11 gives us y = (-2/k)x + (11/k). The slope of the second line is -2/k.
For the lines to be parallel, their slopes must be equal, so 3/5 = -2/k. Solving for k, we get k = -10/3. For the lines to be perpendicular, the product of their slopes must be -1 (since perpendicular lines have negative reciprocal slopes). This gives us (3/5)(-2/k) = -1, and solving for k yields k = 3/10.
Deon rented a truck for one day. there was a base fee of $16.95, and there was an additional charge of 75 cents for each mile driven. Deon had to pay $220.20 when he returned the truck. For how many miles did he drive the truck?
An item is regularly priced at $75. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?
Jackson's football team lost 6 yards from their starring position and then lost another 5 yards. What number represents a loss of 6 yards? A loss of 5 yards?
On the next play, the team gains 12 yards. Will the team ne at their original starting position? Explain
A loss of 6 yards is represented by -6, and a loss of 5 yards by -5. After losses of 6 and 5 yards, and a gain of 12 yards, the team will be 1 yard past their original starting position, not exactly back to the original position.
Explanation:A loss of 6 yards can be represented by the number -6, and a loss of 5 yards can be represented by the number -5.
When the football team on the next play gains 12 yards, we add this value to their previous position, which results from adding -6 and -5. To determine if the team returns to their original starting position, we calculate -6 + -5 + 12. The sum of -6 and -5 is -11, then adding 12 gives 1, which means the team advances 1 yard past the original starting position, not just back to it.
Therefore, the team will not be at their original starting position after gaining 12 yards, they will be 1 yard ahead.
228% of what number is 33.06
Find the balance in the account. $4,100 principal earning 4%, compounded monthly, after 10 years
$4100*(1+0.04/12)^(12*10)
4100*1.490832682=
$6112.41
HELP PLEASE!!1!
Part A
First, take a look at Preston’s sequence. How does a 180-degree rotation about the origin change the coordinates of a shape?
How does a translation 7 units up change the coordinates of a shape?
Now look at Chanel’s sequence. How does a reflection across the x-axis change the coordinates of a shape?
please, help me
180° rotation about the origin change the coordinates from (x,y) to (-x,-y). In this exercise:
A = (-4, 5) -> (4, -5)
B = (-3, 1) -> (3, -1)
C = (-5, 2) -> (5, -2)
Translation 7 units up change the coordinates from (x, y) to (x, y+7). Continuing with the exercise:
(4, -5) -> (4, 2)
(3, -1) -> (3, 6)
(5, -2) -> (5, 5)
Which are not the coordinates of triangle DEF.
Reflection across the x-axis change the coordinates from (x, y) to (x, -y). In this exercise:
A = (-4, 5) -> (-4, -5)
B = (-3, 1) -> (-3, -1)
C = (-5, 2) -> (-5, -2)
In 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across x-axis (x, y) becomes (x, -y).
180° rotation about the origin change the coordinates from (x,y) to (-x,-y). It means if an object having coordinates (3,4) then it will be (-3,-4).
Translation 7 units up change the coordinates from (x, y) to (x, y+7). It means if an object having coordinates (3,4) then it will be (3,4+7).
Reflection across the x-axis change the coordinates from (x, y) to (x, -y). It means if an object having coordinates (3,4) then it will be (3,-4).
Hence we can summarize the above phenomenon as in 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across x-axis (x, y) becomes (x, -y).
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The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function mc002-1.jpg. Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall?
Answer:
the answer on edge is D) h(3)-h (0)/3
And, the answer to the equation is 156.
The total charge on 6 particles is -48 units. All the particles have the same charge.
What is the charge on each particle?
Which of these is the algebraic expression for "eight less than some number?"
8 − b
b − 8
Fraction 8 over b
Fraction b over 8
best answer gets brainl;iest
The game stop is having a sale and all games are reduced by 55%. If a game is now $29.99, what was the original price? Round your answer to the nearest cent
Please help
Thanks in advance
what would be the value of 150 after eight years if you earn 12 percent interest per year
Answer:
$371.3944
Step-by-step explanation:
Principal = 150
Time = 8 years
Rate of interest = 12% = 0.12
No. of compounds per year = n = 1
Formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A is the amount
P is the principal
r is the rate of interest in decimals
t = time in years
n = no. of compounds per year
Substitute the values in the formula :
[tex]A=150(1+\frac{0.12}{1})^{8}[/tex]
[tex]A=371.3944[/tex]
Hence the value of 150 after eight years if you earn 12 percent interest per year is $371.3944
Jean has 1/3 cup of walnuts for each serving of salad she makes. She has 2 cups of walnuts. How many serving can she make?
Find the volume of a cylinder with a diameter of 10 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest tenth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank)
The volume of the cylinder is 1177.5 cubic inches.
Given that the diameter of the cylinder is 10 inches, the radius r is half of that, so [tex]\( r = \frac{10}{2} = 5 \)[/tex] inches.
The height h is three times the radius, so [tex]\( h = 3r = 3 \times 5 = 15 \)[/tex] inches.
Now, we can substitute these values into the formula for the volume of a cylinder:
[tex]\( V = \pi r^2 h \)\\ \( V = 3.14 \times (5)^2 \times 15 \)\\ \( V = 3.14 \times 25 \times 15 \)\\ \( V = 3.14 \times 375 \)\\ \( V = 1177.5 \) cubic inches.[/tex]
Rounded to the nearest tenth.
Gideon made two errors in the proof. Identify and correct the errors
Answer:
Identify: Step 6 and step 7
Correction:
I think step 6 is just not necessary and should be removed.
And step 7 should be the transitive property of equality not the Substitution Property of Equality
You are selling items from a catalog for a school fundraiser.Write and solve two inequalities to find the range of sales that will earn you between $40 and $50. Earn $5 for every $50 in sales!
To find the range of sales that will earn you between $40 and $50, you can set up two inequalities and solve them to find the minimum and maximum sales required.
Explanation:To find the range of sales that will earn you between $40 and $50, we can set up two inequalities.
First, let's find the minimum sales required to earn $40. We can use the inequality 5x >= 40, where x represents the sales. This inequality represents the condition that earning $5 for every $50 in sales should be greater than or equal to $40.
Next, let's find the maximum sales required to earn $50. We can use the inequality 5x <= 50, where x represents the sales. This inequality represents the condition that earning $5 for every $50 in sales should be less than or equal to $50.
To solve these inequalities:
For the first inequality, divide both sides by 5, giving us x >= 8. This means the minimum sales required to earn $40 is $8.
For the second inequality, divide both sides by 5, giving us x <= 10. This means the maximum sales required to earn $50 is $10.
Therefore, the range of sales that will earn you between $40 and $50 is $8 to $10.
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Can you please help me
Let set A = {1, 3, 5, 7} and set B = {1, 2, 3, 4, 5, 6, 7, 8}
Which notation shows the relationship between set A and set B?
Answer:
A ⊆ B
Step-by-step explanation:
If sin Θ = negative square root 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ?
Answer: The values are
[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]
Step-by-step explanation: For an angle [tex]\theta[/tex],
[tex]\sin \theta=-\dfrac{\sqrt3}{2},~\pi<\theta<\dfrac{3\pi}{2}.[/tex]
We are given to find the values of [tex]\cos\theta[/tex] and [tex]\tan \theta[/tex].
Given that
[tex]\pi<\theta<\dfrac{3\pi}{2}\\\\\\\Rightarrow \theta~\textup{lies in Quadrant III}.[/tex]
We will be using the following trigonometric properties:
[tex](i)~\cos \theta=\pm\sqrt{1-\sin^2\theta},\\\\(ii)~\tan\theta=\dfrac{\sin\theta}{\cos\theta}.[/tex]
The calculations are as follows:
We have
[tex]\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(-\dfrac{\sqrt3}{2}\right)^2}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{\left(\dfrac{1}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\dfrac{1}{2}.[/tex]
Since [tex]\theta[/tex] is in Quadrant III, and the value of cosine is negative in that quadrant, so
[tex]\cos\theta=-\dfrac{1}{2}.[/tex]
Now, we have
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac{\sqrt3}{2}}{-\frac{1}{2}}=\sqrt3.[/tex]
Thus, the values are
[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]
Since the given theta lies in third quadrant, then you can use the fact that only tangent and cotangent are positive in third quadrant, rest are negative.
The value of cos and tan for given theta is:
[tex]cos(\theta) = -\dfrac{1}{2}\\\\ tan( \theta) = \sqrt{3}[/tex]
How to find if the angle given lies in third quadrant?If angle lies between 0 to half of pi, then it is int first quadrant.
If angle lies between half of pi to a pi, then it is in second quadrant.
When the angle lies between [tex]\pi[/tex] and [tex]\dfrac{3\pi}{2}[/tex], then that angle lies in 3rd quadrant.
And when it lies from [tex]\dfrac{3\pi}{2}[/tex] and 0 degrees, then the angle is in fourth quadrant.
Which trigonometric functions are positive in third quadrant?Only tangent function and cotangent functions.
In first quadrant, all six trigonometric functions are positive.
In second quadrant, only sin and cosec are positive.
In fourth, only cos and sec are positive.
We can continue as follows:
[tex]sin(\theta) = -\dfrac{\sqrt{3}}{2}\\ sin(\theta) = sin(\pi + 60^\circ)\\ \theta = \pi + 60^\circ[/tex]
Thus, evaluating cos and tan at obtained theta:
[tex]cos(\pi + 60^\circ) = -cos(60) = -\dfrac{1}{2}\\ tan( \pi + 60^\circ) = tan(60) = \sqrt{3}[/tex]
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How do I solve this problem: -2(7-y)+4=-4?
Which expression is equivalent to radical of 10 over ^4 and the radical of 8.
what is the ratio of x to y (simplest form)
x= 2 y=6
x=5 y=15
x=8 y=24
A savings account earns 6% (APR) interest calculated monthly, paid into the account at the end of 6 months. Travis deposits $100 into the account at the beginning of the first month. At the end of each month, he deposits an additional $100 into the account. How much interest will Travis have earned after 6 months?
How do you do 8.75 Times 38
Find the value of a and z: (x^8)^3=ax^z
Ron is half as old as Sam, who is three times as old as Ted. The sum of their ages is 55. How old is Ron?
To find Ron's age, we set up equations based on their age relations and the total sum of their ages. After solving the system of equations, we determine that Ron is 15 years old.
The question deals with a basic age-related algebra problem. To solve for how old Ron is, we can set up a system of equations based on the information provided:
Let R represent Ron's age.
Let S represent Sam's age.
Let T represent Ted's age.
From the information:
Ron is half as old as Sam, so R = 1/2 * S
Sam is three times as old as Ted, so S = 3 * T
The sum of their ages is 55, so R + S + T = 55
Substituting the expressions for R and S in terms of T into the third equation gives:
1/2 * (3 * T) + 3 * T + T = 55
Simplifying and solving for T, we find that:
1.5T + 3T + T = 55
5.5T = 55
T = 10
Now we can find Sam's age:
S = 3 * 10 = 30
And Ron's age:
R = 1/2 * 30 = 15
Therefore, Ron is 15 years old.
Find the area.
Square
A = s^2
s - side.
area = S^2
side = 12 miles
12^2 = 144
area = 144 miles
The diagonals of rhombus FGHJ intersect at point K. If side GH is equal to x + 9 and side JH is equal to 5x – 2, find x.
Answer:
x = 2.75
Step-by-step explanation:
5x - 2 = x + 9
5x = x + 11
4x = 11
9 1/4 - 6 2/3
Write answer as mixed number with fractional part in lowest terms.
To subtract the mixed numbers 9 1/4 and 6 2/3, first convert them to improper fractions, find a common denominator, and then perform the subtraction. The result is expressed as the mixed number 2 7/12 with the fractional part in lowest terms.
Explanation:Subtracting Mixed Numbers
The question involves subtracting mixed numbers, specifically 9 1/4 (nine and one quarter) from 6 2/3 (six and two thirds). First, we need to convert these mixed numbers into improper fractions for easier subtraction.
Convert 9 1/4 to an improper fraction: (9 × 4) + 1 = 36 + 1 = 37/4.Convert 6 2/3 to an improper fraction: (6 × 3) + 2 = 18 + 2 = 20/3.To subtract, we need a common denominator. Multiplying the denominators 4 and 3 gives us 12, the LCD.Adjust the fractions: 37/4 becomes 111/12 (since 37 × 3 = 111) and 20/3 becomes 80/12 (since 20 × 4 = 80).Now subtract the numerators: 111 - 80 = 31. So, the difference is 31/12.Finally, convert 31/12 back into a mixed number, which is 2 7/12 (since 31 divided by 12 is 2 with a remainder of 7).The answer is 2 7/12.
To subtract mixed numbers, find a common denominator. Subtract the fractional part by subtracting the numerators. Subtract the whole numbers as usual. The answer is 8 7/12.
Explanation:To subtract mixed numbers, we first need to find a common denominator. In this case, the common denominator is 12. Then, we can subtract the fractions by subtracting the numerators and leaving the denominator the same.
For the whole numbers, we simply subtract them as usual.
So, 9 1/4 - 6 2/3 = 8 7/12.
A quadratic equation is shown below: 9x2 − 16x + 60 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)