==============================================
Explanation:
The term "equidistant" means "equally distant".
We want (x,y) to be the same distance to the x axis, the y axis, and the point (3,6).
Let n represent this unknown equal distance. Negative distance doesn't make sense, so we'll have n > 0.
Start at the origin and move n units to the right to arrive at (n,0). We are n units from the y axis.
Now move n units up to arrive at (n,n). This point is guaranteed to be n units away from each axis.
That is one potential point. Other potential points are:
(-n,n)(n,-n)(-n,-n)One point for each quadrant.
Let's assume that the answer is in the 1st quadrant since (3,6) is located here.
We need to find an expression that represents the distance from the point (n,n) to (3,6). We'll set that distance expression equal to n so we can solve.
Part 1 of those steps
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\n = \sqrt{(n-3)^2+(n-6)^2}\\\\n^2 = (n-3)^2+(n-6)^2\\\\n^2 = (n^2-6n+9)+(n^2-12n+36)\\\\n^2 = 2n^2-18n+45\\\\[/tex]
Part 2 of those steps
[tex]0 = 2n^2-18n+45-n^2\\\\0 = n^2-18n+45\\\\n^2-18n+45 = 0\\\\(n-3)(n-15) = 0\\\\n-3 = 0\ \text{ or } \ n-15 = 0\\\\n = 3\ \text{ or } \ n = 15\\\\[/tex]
The quadratic formula could be used as an alternative pathway.
Therefore, the mystery point could be located at (3,3) or at (15,15)
Use the distance formula to verify each answer. I'll let you do this part.
---------
Extra info:
If you were to perform similar steps with the point (-n,n), then you'll find that no real numbered solutions exist. The two solutions would be complex numbers.
The cases (n,-n) and (-n,-n) have no solutions at all.
Therefore, we have confirmed only case (n,n) would work.
The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the scale factor?
a. 0.08
b. 1.08
c. 0.92
d. 8
The scale factor after one year of depreciation is 0.92.(option-c)
The depreciation rate of 8% per year means that the car loses 8% of its value each year. To find the scale factor, we need to determine how much of the original value remains after one year of depreciation.
If the car loses 8% of its value each year, then the remaining value after one year is:
100% - 8% = 92% of the original value
We can express this as a decimal by dividing 92% by 100%, which gives:
92%/100% = 0.92
This means that the value of the car is 0.92 times its original value after one year of depreciation.
We can also check our answer by calculating the value of the car after one year:
Value after one year = 0.92 * $15,000 = $13,800
This is the expected value of the car after one year of depreciation, which confirms that our scale factor of 0.92 is correct.
Therefore, the answer is (C) .
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4=[(43-34-32)*0]+2-2+4-3+5-2
Is this True?
Answer: True
Step-by-step explanation:
to copy an angle using only a compass and a straightedge begin by marking the vertex of the new angle. then draw a ray from vertex which will be one of the legs of the new angle what is the next step in the construction?
Answer:
Set the compass to a convenient width, and draw an arc that is centered at the vertex of the original angle and intersects both legs of the original angle.
Step-by-step explanation:
Edmentum. Enjoy.. Don't get too tired yall, I love you and so does Christ Jesus.
Question 16
QUICK
Please help me find out what d is
Answer:
864
Step-by-step explanation:
d/6=144
cross multiply
d=144×6
d=864
El cuadrado de un número -17 es igual a 152 .Encuentra el número
Answer:
hajskshsjakalskksks
A store is designing the space for rows of nested shopping carts.
Each row has a starting cart that is `4` feet long, followed by the nested carts. (`0` nested carts means there's just the starting cart.)
• A row of `13` nested carts is `23.5` feet long.
• A row of `18` nested carts is `31` feet long.
Enter the appropriate label and scale for each axis, and drag the movable points to create a graph of the situation.
By creating a graph that shows the relationship between the number of carts and the space required, the store can better design the space for rows of nested shopping carts.
To design the space for rows of nested shopping carts in a store, a graph can be created that shows the relationship between the number of carts and the amount of space required.
This can be done by plotting the number of carts on the x-axis and the space required on the y-axis.The appropriate labels for each axis are "Number of Carts" for the x-axis and "Space Required" for the y-axis.
The scale for the x-axis would depend on the maximum number of carts that the store wants to accommodate, while the scale for the y-axis would depend on the amount of space that each cart takes up.
The movable points on the graph can be used to illustrate different scenarios.
For example, if the store wants to know how much space would be required for 50 carts, the movable point can be placed at 50 on the x-axis, and the corresponding space required can be read off the y-axis.
Similarly, if the store wants to know how many carts can be accommodated in a given amount of space, the movable point can be placed at the desired space on the y-axis, and the corresponding number of carts can be read off the x-axis.
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What would be the perimeter of this figure?
Answer:
40.9ft
Step-by-step explanation:
The perimeter is when you add all the sides together.
8 + 10 + 10 + 4 + 8.9 = 40.9ft
Any number or variable raised to the zeroth power is equal to what
Answer:
1
Step-by-step explanation:
Any number raised to the 0th power is 1, except for 0; 0 to the 0th power is undefined.
Answer:
[tex]\huge{\boxed{\sf{1}}}[/tex]
Step-by-step explanation:
Any number or variable raised to the 0 th power is equal to 1.
For example: If [tex]x^{0}[/tex] is an algebraic term, then [tex]x^{0}[/tex] =1. So, the value of the term having the index 0 is 1.
Hope I helped!
Best regards! :D
~TheAnimeGirl
Please help with homework! I don't understand this
Answer:
B.
Step-by-step explanation:
Basic Power Rule: f'(x) = n · xⁿ⁻¹
Step 1: Define
[tex]\frac{dy}{dx} [6x^{\frac{-2}{3} }][/tex]
Step 2: Use Basic Power Rule
[tex]f'(x)=6(\frac{-2}{3})x^{\frac{-2}{3} -1}[/tex]
[tex]f'(x)=-4x^{\frac{-5}{3}}[/tex]
Step 3: Simplify
[tex]f'(x)=\frac{-4}{x^{\frac{5}{3} }}[/tex]
[tex]f'(x)=\frac{-4}{\sqrt[3]{x^5} }[/tex]
Write the complex number in standard form. (Simplify your answer completely.) (5+ √5) (6-√-10)
To write the complex number (5+√5)(6-√-10) in standard form, we simplify the expression by multiplying the terms and then combine the real and imaginary parts. The standard form of the complex number is 30 + 5√2.
To simplify the expression (5+√5)(6-√-10), we need to multiply the terms using the distributive property.
First, let's multiply the real parts:
5 * 6 = 30.
Next, we multiply the imaginary parts:
√5 * -√-10 = -√(5 * -10) = -√(-50) = -√(50)(-1) = -√(25 * 2)(-1) = -√25 * √2 * (-1) = -5√2.
Now, let's combine the real and imaginary parts to write the complex number in standard form:
(5+√5)(6-√-10) = 30 + 5√2.
Therefore, the complex number (5+√5)(6-√-10) can be written in standard form as 30 + 5√2. In standard form, the complex number is expressed as the sum of a real part and an imaginary part. The real part is 30, and the imaginary part is 5√2.
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If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, multiply it by 3 and add 1 to the result."
Answer:
3x+1
Step-by-step explanation:
The algebraic expression is 3x+1
What is a polynomial?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is defined as an expression that is composed of variables, constants, and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here let the number be x and we multiply it by 3 and add 1 to the result then we get 3x+1
Hence, the algebraic expression is 3x+1
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A number is missing the tens digit.
The number is 51 3 6.
What could the tens digit be if the number
is divisible by 2? By 4? By 8?
Answer:
The answer is 51,338
Step-by-step explanation:
Find the midpoint of points A(-7,7) and B(-1,-3)
Answer:
( −4,2)
Step-by-step explanation:
Use the midpoint formula to find the midpoint of the line segment.
8 gallons of gasoline cost $16.80. What is the price per gallon?
Answer:
$2.10/gallon
Step-by-step explanation:
8 gallons - $16.80
1 gallon - $2.10
Hope this helps!
Answer:
$2.10 per gallon
Step-by-step explanation:
Do
16.80/8 = 2.10
CHECK
2.10*8 = 16.80
(1 point) Deshaun is a plumber who charges $40 per hour for his work. Another plumber, Silvio, charges based on the equation d = 60+ 20h, where h is the number of hours worked and d is the cost in dollars. Which statement is true? a b Deshaun's charge per hour is more expensive. Silvio's charge per hour is more expensive. Deshaun and Silvio charge the same amount. Deshaun's initial value is $20. C d
Answer:
A
Step-by-step explanation:
Deshaun charges $40 per hour.
So if Deshaun and Silvio work for 5 hours, then it would be $40(5) which would be more expensive than Silvio's with $60 + 20(5). Silvio gets $60 with $20 per hour.
Deshaun would get $200 while Silvio would get $160.
Last question ;-; i think...
10 pnts
Answer:
a) -11
b) 75
Step-by-step explanation:
a= -24-13=-11
b= 61-(-14)=75
Solve for the indicated variable
ab-ac= 2 for a
Given, the indicated variable is: ab - ac = 2, We have to solve the given equation for a. So the answer is a = 2/(b - c).
Let's do this: Factor out the a from the left-hand side of the equation.
Using the distributive property, we get: a(b - c) = 2
Now, we'll isolate a by dividing both sides by (b - c).
Thus, we get: a = 2/(b - c)
Therefore, the value of the variable a is 2 divided by the quantity of (b - c).
Let's have a look at the steps: ab - ac = 2
a(b - c) = 2
a = 2/(b - c). Hence, we have obtained the value of the variable a by solving the given equation.
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21.1w + 4.6 = 10.9w + 35.2
Answer:
25.7 = 46.1
Step-by-step explanation:
This question doesn't make sense but if it's true or false it's false
consider the function h(x)= -2cos(8x-π/4)+5. what transformation results in j(x)=-2cos(8x-π/4)-5
The transformation from h(x) that gives j(x) is 10 units translation down
How to determine the transformation?The equation of the functions are given as
h(x) = -2cos(8x - π/4) + 5
j(x) = -2cos(8x-π/4) - 5
From the above equations, we can see that only the constant term of the equations are different
This means that the function h(x) is translated vertically to get the function j(x)
So, we simply subtract j(x) from h(x) to calculate the unit of translation
This is represented as
Units = j(x) - h(x)
This gives
Units = -2cos(8x - π/4) - 5 + 2cos(8x-π/4) - 5
Evaluate the like terms
Units = - 5 - 5
Evaluate the sum
Units = -10
This means that the transformation is 10 units translation downwards
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Solve for X!!!
The equation is in the picture.
Answer:
x - 4 + 88 = 108
x + 84 = 108
x = 24
The correct answer is a.
Which of the following pairs of trigonometric ratios is/are equal?
I. sin A and cos B
II. tan A and tan B III. cosec A and sec B A. I only B. II only C. I and II only
D. III only
E. I and III only
The pair of equal trigonometric ratios among the given options is tan A and tan B.
To identify the pair of equal trigonometric ratios among the given options, we have to use the basic identities of trigonometry.
Basic identities of trigonometry:1. sin² θ + cos² θ = 1 (Pythagorean identity)2. tan θ = sin θ/cos θ3. cot θ = cos θ/sin θ4. sec θ = 1/cos θ5. cosec θ = 1/sin θ.
Now, let's check the given options,I. sin A and cos B: Not equal because sin is opposite/hypotenuse and cos is adjacent/hypotenuse in a right-angled triangle.II. tan A and tan B:
Equal because the tan is opposite/adjacent in a right-angled triangle. III. cosec A and sec B: Not equal because cosec is hypotenuse/opposite and sec is hypotenuse/adjacent in a right-angled triangle.
Therefore, the correct answer is (B) II only. Hence, the main answer is B. II only.
The pair of equal trigonometric ratios among the given options is tan A and tan B.
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Suzy is making an apple pie and her recipe calls for 40 oz of apples at the grocery store apples are sold in pounds if there are 16 ounces in a pound how many pounds of apples should Suzy buy?
Answer: 2.5 lbs
Step-by-step explanation: Divide 40 by 16 to get the weight she needs.
which ones are in scientific notation? 15 points
What is the value of y when x = 5 in the equation y = 5x?
What is the value of x in 5x - 4 = 7x + 8?
Answer:
x = -6
Step-by-step explanation:
To find the value of x in the given equation, we have to solve for x.
5x - 4 = 7x + 8
Add 4 to both sides.
5x = 7x + 12
Subtract 7x from both sides.
-2x = 12
Divide both sides by -2.
x = -6
So the value of x would be -6.
I hope this helps. Happy studying.
Q: What is the value of x in 5x-4=7x+8
A: -6
SBS: 5x-4-7x=7x+8-7x -2x-4=8 -2x -4+4 --> 8+ 4-2x=12
(DIVIDE)
-2x/-2 = 12/-2= -6
exercise 10.6. golden ticket. a student was at work at the county amphitheater, and was given the task of cleaning 1500 seats. to make the job more interesting, his boss hid a golden ticket somewhere in the seats. the ticket is equally likely to be in any of the seats. let x be the number of seats cleaned until the ticket is found. calculate the expected value of x. round your answer to 1 decimal plac
The expected value of x is 750.5, rounded to 1 decimal place.
To calculate the expected value of x, we need to determine the probability distribution of x and then calculate the weighted average of x.
The probability of finding the golden ticket in the first seat cleaned is 1/1500, as there are 1500 seats and the ticket is equally likely to be in any of them.
Similarly, the probability of finding the ticket in the second seat cleaned is (1499/1500) * (1/1499) = 1/1500. The probability of finding the ticket in the third seat cleaned is (1499/1500) * (1498/1499) * (1/1498) = 1/1500, and so on.
From this pattern, we can observe that the probability of finding the ticket in the x-th seat cleaned is 1/1500.
Now, let's calculate the expected value of x:
E(x) = (1/1500) * 1 + (1/1500) * 2 + (1/1500) * 3 + ... + (1/1500) * 1500
E(x) = (1/1500) * (1 + 2 + 3 + ... + 1500)
E(x) = (1/1500) * [(1500 * 1501) / 2]
E(x) = (1501 / 2) = 750.5
Therefore, the expected value of x is 750.5, rounded to 1 decimal place.
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3. For what value of x is the equation 224 +7 = 2" true?
A. 2
B. 4
C. 11
D. 16
E. 44
Please lmk soon
Step-by-step explanation:
I think it's TRUE but the equation is false.
I need help with this pls
Answer:
make the picture more clear its hard to see.
Step-by-step explanation:
Answer:
4. y=-1x+1
5. y=-2x+27
Step-by-step explanation:
Between which 2 whole numbers is the square root of 50?
Answer: It would be between 7 and 8
For problems 4-6, determine the outputs for the following inputs of the function: f(x) = -2x² + 12x-4 x=3 5) x=-4 6) x=0 For problems 7 & 8, write the equation of the line through the points given. 7) (-5,2) and (5,4) 8) (-3,8) and (1.-4)
For the function f(x) = -2x² + 12x - 4, we can find the outputs for specific inputs. When x = 3, the output is 14. When x = -4, the output is -84. When x = 0, the output is -4.
For finding the equation of a line passing through given points, the equation can be determined using the slope-intercept form, y = mx + b.
To determine the outputs of the function f(x) = -2x² + 12x - 4 for specific inputs, we substitute the given values of x into the function and calculate the corresponding outputs.
a) For x = 3: f(3) = -2(3)² + 12(3) - 4 = -18 + 36 - 4 = 14.
b) For x = -4: f(-4) = -2(-4)² + 12(-4) - 4 = -32 - 48 - 4 = -84.
c) For x = 0: f(0) = -2(0)² + 12(0) - 4 = 0 - 0 - 4 = -4.
Moving on to finding the equation of lines passing through given points:
7) The points given are (-5,2) and (5,4). We can calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates, we have m = (4 - 2) / (5 - (-5)) = 2 / 10 = 1/5. Using the slope-intercept form, y = mx + b, we can substitute one of the given points and the slope to solve for b. Let's use the point (5,4): 4 = (1/5)(5) + b. Simplifying, we find b = 4 - 1 = 3. Therefore, the equation of the line is y = (1/5)x + 3.
The points given are (-3,8) and (1,-4). Calculating the slope, m = (-4 - 8) / (1 - (-3)) = -12 / 4 = -3. Again, using the slope-intercept form, we substitute the point (1,-4) and the slope: -4 = (-3)(1) + b. Solving for b, we find b = -1. Hence, the equation of the line is y = -3x - 1.
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