true or false a number that corresponds to a point is an origin

Answer:

x = 5/3

Step-by-step explanation:

=> 5x + 8 = 2x - 3

=> 5x - 2x = -3 + 8

=> 3x = 5

=> x = 5/3

Step-by-step explanation:

\( \tt{}5x+8=2x-3\)

\(\tt{}5x - 2x = - 3 - 8\)

\(\tt{}3x = - 11\)

\(\tt{} x = - \frac{11}{3} \)

\(\tt{}x = - 3 \frac{2}{3} \)

Answer:

C. s= 85m + 45

Step-by-step explanation:

Given data

She opened the account with $85

and deposited $85

The equation that best models the relationship is

s= 85m + 45

Hence option C is correct

The sporting goods store's ad is correct, but it is important to note that the actual average price is very close to $401

Yes, the sporting goods store's ad is correct. The average price of the bicycles can be calculated by adding up all the prices and then dividing by the number of bicycles. Since the ad says the average price is under $400, it may seem like it's not correct. However, the $401 average price is only slightly over $400 and can be considered as "under $400" for advertising purposes.

The total price is $2005 ($300 + $250 + $325 + $780 + $350), and there are 5 bicycles. So, the average price is $401 ($2005 ÷ 5), which is under $400 as advertised.

So, the sum of all the prices is:
$300 + $250 + $325 + $780 + $350 = $2,005
And there are five bicycles, so the average price would be:
$2,005 ÷ 5 = $401

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The formula for the exponential function is V = 5000 (2)^(−t/4).

What is an exponential function?

A function whose value is a constant raised to the power of an argument is called an exponential function.

Here, we have

The value of an item initially worth $5000 loses half its value every 5 years.

V = V₀eˣⁿ

At t = 0,V = V₀

So, V = 5000eˣⁿ

At t = 4,V = V₀/2 = 2500

Substituting these into our equation, we have

5000e^(4k) = 2500

e^(4k) = 12

4k = −ln2

k = −ln2/4

Finally, we have our equation

V = 5000e^(−tln2/4 )

V = 5000(e^ln2)^(−t/4)

V = 5000 (2)^(−t/4)

Hence, the formula for the exponential function is V = 5000 (2)^(−t/4).

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The time she rented the bike is equal to 4.5 hours.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the oceanside bike rental shop charges fourteen dollars plus eight dollars an hour for renting a bike Nancy paid 50 four dollars for renting a bike.

The time will be calculated as,

TC = 8x + 14

Here, x is the time,

50 = (8x) + 14

8x = 50 - 14

8x = 36

x = 4.5 hours

Therefore, the time she rented the bike is equal to 4.5 hours.

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A quadratic equation is a polynomial equation of degree 2, which means the highest power of the variable is 2. It is generally written in the form: ax^2 + bx + c = 0. Option (d) x = -8, x = 8 is the correct answer.

The given equation is 15x^2 - 56 = 88 - 6x^2.

We need to find the values of x that are solutions to the given equation.

Solution: We are given an equation 15x² - 56 = 88 - 6x².

Rearrange the equation to form a quadratic equation in standard form as follows: 15x² + 6x² = 88 + 56  21x² = 144  

x² = 144/21 = 48/7

Therefore x = ±sqrt(48/7) = ±(4/7)*sqrt(21).

The values of x that are solutions to the given equation are x = -4/7 sqrt(21) and x = 4/7 sqrt(21).

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The given equation is 15x² - 56 = 88 - 6x². Values of x are solutions to the equation below 15x² - 56 = 88 - 6x² are x = -2.62, 2.62 or x ≈ -2.62, 2.62.

Firstly, let's add 6x² to both sides of the equation as shown below.

15x² - 56 + 6x² = 88

15x² + 6x² - 56 = 88

Simplify as shown below.

21x² = 88 + 56

21x² = 144

Now let's divide both sides by 21 as shown below.

x² = 144/21

x² = 6.86

Now we need to solve for x.

To solve for x we need to take the square root of both sides.

Therefore, x = ±√(6.86).

Therefore, the values of x are solutions to the equation below are x = -2.62, 2.62 or x ≈ -2.62, 2.62.

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The points on the given curve where the tangent line has slope 1 are (-107/54, 19/54) and (-25/27, -91/108).

To find the points on the given curve where the tangent line has slope 1, we need to find where dy/dx = 1.
Using implicit differentiation, we get:
dx/dt = \(6t^2\)
dy/dt = 5/12 - 14t
dy/dx = (dy/dt) / (dx/dt) = (5/12 - 14t) / (\(6t^2\))
Now we set dy/dx = 1:
1 = (5/12 - 14t) / (\(6t^2\))
Simplifying, we get:
\(6t^2\) = 5/12 - 14t
Rearranging, we get a quadratic equation:
\(6t^2\) + 14t - 5/12 = 0
Using the quadratic formula, we get:
t = (-14 ± \(\sqrt{(14^2 - 4*6*(-5/12))}\)) / (2*6)
Simplifying, we get:
t = (-7 ± \(\sqrt{(157)}\))/12
Now we can find the corresponding values of x and y by plugging these values of t into the original equations:
When t = (-7 + \(\sqrt{(157)}\))/12:
x = \(2t^3\) = -107/54
y = 5/12 - 14t = 19/54
So the point is (-107/54, 19/54).
When t = (-7 - \(\sqrt{(157)}\))/12:
x = \(2t^3\) = -25/27
y = 5/12 - 14t = -91/108
So the point is (-25/27, -91/108).

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Answer:

14 is the answer if you mean 3 by that e

Elizabeth will take 9 hours and 45 minutes to catch up with Duane using the given speed-distance-time values.

The speed-distance-time relations are:

Speed = Distance/Time, Distance = Speed*Time, and Time = Distance/Speed.

The distance traveled by Duane on the bike at 14 miles per hour for 3 hours = 14*3 miles = 42 miles.

The time that Elizabeth takes to cover 42 miles jogging at 5 miles per hour = 42/5 hours = 8.4 hours.

The distance traveled by Duane in the extra time which Elizabeth took to reach his bike (8.4 - 3 = 5.4 hours) walking at 2 miles per hour = 2*5.4 = 10.8 miles.

Now, the distance between Elizabeth and Duane is 10.8 miles, before Elizabeth starts riding the bike.

Keeping the distance constant, we calculate the relative speed to calculate the time to cover this distance.

Relative speed = Elizabeth's speed - Duane's speed {As Elizabeth is moving towards Duane, that is, covering the distance but Duane is moving away from Elizabeth, that is, increasing the distance}.

or, Relative speed = 10 - 2 = 8 miles per hour.

Time taken to cover the distance = 10.8/8 = 1.35 hours.

Therefore, the total time taken by Elizabeth to catch up with Duane = 8.4 + 1.35 hours = 9.75 hours or 9 hours and 45 minutes.

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When the base of the ladder is 12 feet from the wall, the base is moving away from the wall at a rate of approximately 4.125 ft/s.

When the base of the ladder is 9 feet from the wall, the base is moving away from the wall at a rate of approximately 5.5 ft/s.

To solve this related rates problem, we can use the Pythagorean theorem to relate the lengths of the ladder, the distance of the base from the wall, and the height on the wall.

Given:

Ladder length: 15 feet

Rate of change of the ladder height:

dh/dt = -5.5 ft/s (negative because the height is decreasing)

Distance from the wall: x

We can use the Pythagorean theorem to relate the lengths:

x^2 + h^2 = 15^2

Differentiating both sides with respect to time t:

2x(dx/dt) + 2h(dh/dt) = 0

We want to find dx/dt when x = 12 ft and x = 9 ft.

When x = 12 ft:

Plugging in the values:

2(12)(dx/dt) + 2h(-5.5) = 0

24(dx/dt) - 11h = 0

To find the value of h, we can substitute the values into the Pythagorean theorem equation:

12^2 + h^2 = 15^2

h^2 = 225 - 144

h^2 = 81

h = 9 ft

Substituting h = 9 ft into the equation:

24(dx/dt) - 11(9) = 0

24(dx/dt) = 99

dx/dt = 99/24

dx/dt ≈ 4.125 ft/s

Therefore, when the base of the ladder is 12 feet from the wall, the base is moving away from the wall at a rate of approximately 4.125 ft/s.

When x = 9 ft:

Using a similar process, we find h = 12 ft.

Substituting h = 12 ft into the equation:

24(dx/dt) - 11(12) = 0

24(dx/dt) = 132

dx/dt = 132/24

dx/dt ≈ 5.5 ft/s

Therefore, when the base of the ladder is 9 feet from the wall, the base is moving away from the wall at a rate of approximately 5.5 ft/s.

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Answer:

107

Step-by-step explanation:

The pattern is +10

Your finding the 9 term to your going +10 9 times from 27. Which simplifies to +80.

27 + 90 = 107

Answer: nm(m-n)

Step-by-step explanation:

m^2n-mn^2=

n*m(m)-m*n(n)=

n*m(m-n)=nm(m-n)

Answer:

A -2

Step-by-step explanation:

the line meets up there and it would be rise divided by run and it would get you -2

Answer:

Step-by-step explanation:

You look at where the lines cross a point, which could be (-1,3) and (0,-2). By looking at the graph and using rise over run, your slope would be -5.

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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Answer: 7.75 and 6.25

Step-by-step explanation:

The volume is the area of the ground plane times the height.

The area is πr², and r is half the diameter = 4.

So area = 3.14 x 4² = 50.24 and volume = 5 x 50.24 = 251.2

Therefore, the volume of the can is 251.2 inches²

if it has a diameter of 8, that means its radius is half that, or 4.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=4\\ h=5 \end{cases}\implies V=\pi (4)^2(5)\implies V\approx 251.33~in^3\)

Answer:

Option 3

Step-by-step explanation:

4 is a factor so the answer is.. 4(3a-b-5)

Interpreting the scatterplot, it is found that the correct option is:

Springside weakens the correlation shown in the scatterplot.

Springside weakens the correlation shown in the scatterplot.

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Answer:

2,957,468

Step-by-step explanation:

Each digit to the left is worth 10 times more than the same digit one place to the right.

If 2,957,648 becomes 2,957,468, the 4 moves from the tens place to the hundreds place, and now its value is 400 instead of 40, so it's 10 times greater.

Answer:

Wassup, what do you need help on?

Step-by-step explanation:

Answer:

What's ya problem? What do you need help on? hahahah I'm sure you don't bite.

According to the question, to express the rational function for the vertical asymptote whose equation is \(x=8\) and horizontal asymptote whose equation is at \(y=0.\)

As per the question, the function 'f(x)' is vertical at \(x=8\). Therefore, the denominator be \((x-8)\)

\(f(x)=\frac{g(x)}{(x-8)}\)

The function 'g(x)' should have same degree as the denominator function has and it is defined as\(y=0\)

The rational function can be written as:

Rational function = \(\frac{y}{(X-8)}\)

What is rational function?

Rational function is a function whose numerator and denominator terms are in polynomials. Basically, it is a ratio of polynomials. The important condition for these type of function is that denominator should be of degree one.

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m = 54.8 inches

std = 4.9 inches

We can standarize the variable as:

(X - m)/std

So, the probability of a height randomly choosen is between 51.05 and 54.75 inches is:

P[ 51.05 < X < 54.75]

Standarizing those values:

(51.05 - m)/std = (51.05 - 54.8)/4.9 = -75/98...

(54.75 - m)/std = (51.05 - 54.8)/4.9 = -1/98...

So, the new probability is:

P[ -75/98 < Z < -1/98] = Phi(-1/98) - Phi(-75/98)

Where Z is the new standarized variable.

We can find these Phi values from tables of the standarized normal distributions:

Phi(-1/98) = 0.77796

Phi(-75/98) = 0.49593

So the probability is:

P[ -75/98 < Z < -1/98] = Phi(-1/98) - Phi(-75/98) = 0.77796 - 0.49593

P[ 51.05 < X < 54.75] = 0.28203 = 0.282

And that is the answer

Answer:

the answer is A because it is ap

Answer:

16-30i

Step-by-step explanation:

This is what I got :)

Answer:

16−30i

Step-by-step explanation:

Use Square of Difference: {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}(a−b)  

2

=a  

2

−2ab+b  

2

.

{5}^{2}-2\times 5\times 3\imath +{(3\imath )}^{2}

5  

2

−2×5×3+(3)  

2

2 Simplify  {5}^{2}5  

2

  to  2525.

25-2\times 5\times 3\imath +{(3\imath )}^{2}

25−2×5×3+(3)  

2

3 Use Multiplication Distributive Property: {(xy)}^{a}={x}^{a}{y}^{a}(xy)  

a

=x  

a

y  

a

.

25-2\times 5\times 3\imath +{3}^{2}{\imath }^{2}

25−2×5×3+3  

2

  

2

4 Simplify  {3}^{2}3  

2

  to  99.

25-2\times 5\times 3\imath +9{\imath }^{2}

25−2×5×3+9  

2

5 Use Square Rule: {i}^{2}=-1i  

2

=−1.

25-2\times 5\times 3\imath +9\times -1

25−2×5×3+9×−1

6 Simplify  2\times 5\times 3\imath2×5×3  to  30\imath30.

25-30\imath +9\times -1

25−30+9×−1

7 Simplify  9\times -19×−1  to  -9−9.

25-30\imath -9

25−30−9

8 Collect like terms.

(25-9)-30\imath

(25−9)−30

9 Simplify.

16-30\imath

16−30

Answer:

a) 84π b) 109.2π

Step-by-step explanation:

The formula to find this is v=πr^2h/3

r=d/2. so the radius (r) is 6 because you have to divide the diameter (12) by 2. and the height is 7. so, 6^2=36 and 36x7=252.

252/3=84

and because the question is asking for the EXACT value, you need to just put the pi symbol next to it. Final answer for a is 84π

B) you need to find 30% of 84, which is 25.2 and add it to 84, and you will get 109.2! Final answer is 109.2π.

The Answer is :

30,000

The Answer is:

30,000

Therefore, there are 53,248 different super subs that can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from at Sandwich Station.

The super sub at Sandwich Station consists of 4 different toppings and 3 different condiments. The question is asking how many different super subs can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from.

To solve this problem, we can use the multiplication principle of counting. The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

Let's use the multiplication principle to solve this problem. There are four different toppings, and we can choose any of the eight toppings for each of the four spots.

Using the multiplication principle, there are

8 x 8 x 8 x 8 = 4096

ways to choose the toppings. Similarly, there are

6 x 6 x 6 = 216

ways to choose the condiments. Lastly, there are 6 different types of homemade bread to choose from. Using the multiplication principle again, there are

4096 x 216 x 6 = 53,248,

which means there are 53,248 ways to make the super subs.

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The distance from the line x=4 to the given point (-2,5) is 6 units .

Distance formula from line to point :

The distance from the line ax+by+c=0 to the point (u,v) is given by the formula

\(distance=\frac{|au+bv+c|}{\sqrt{a^{2} +b^{2} } }\)

In the given question

the equation of the line is \(x=4\)

taking all the terms to Left side we get

\(x-4=0\)

\(1.x+0.y-4=0\)

given the points (-2,5)

From above values we the values as a=1 , b=0 , c=-4 , u=-2 , v=5 .

Substituting the values in the distance formula we get

\(d=\frac{|1*(-2)+0*(5)-4|}{\sqrt{1^{2} +0^{2} } }\)

\(=\frac{|-2+0-4|}{1} \\ \\ =|-6|\\ \\ =6\)

Therefore , the distance from the line x=4 to the given point (-2,5) is 6 units.

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