5. Your bill at a restaurant is $24.50. You tip 16%. What's
the final bill?

Answer is rational numbers

Answer:

y-intercept: -7

slope: -9

Step-by-step explanation:

The y-intercept is the constant number(s), which in this case is -7.

The slope is the one with x next to it, which is -9.

Hope This Helps! •v•

Answer:

When multiplying like bases, keep the base the same and add the exponents. When raising a base with a power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Step-by-step explanation:

i hope this helps

Answer:

(6,-8)

Step-by-step explanation:

By rotating the point (-6,-8) Counterclockwise you get the point (6,-8)

Hope it helps

The new coordinates after rotation will be - P'(8, -6)

We have a Point on a X - Y plane as P(-6, -8) which is rotated by 90° counter clockwise about the origin.

We have to determine the image of this point after the rotation.

A rotation is a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point.

According to the question, we have -

A point with coordinates → P(-6, -8)

Any point (say A[x, y]) when rotated 90° counter clockwise about the origin, then its new coordinates become A'(-y, x).

Using this rule, the coordinates of the point after rotation of point by 90° counter clockwise about the origin will be → P'(8, -6)

Hence, the new coordinates will be - P'(8, -6)

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Answer:

Step-by-step explanation:

hello : an equation is :

x²+y²=64

Answer:

29

Step-by-step explanation:

Since all triangles have to add up to 180, we can do the sum of the two angles we know minus 180. 90+61=151, 180-151=29

So your answer would be 29

The critical points are (0, 0) and (1/2, 1/8).

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

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

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Let's call the length of the pen Krista wants to build that is 3 times as big as the original one as "x". The area of the pen would be 15 feet * 4.5 feet = 67.5 square feet.

The original pen has an area of 5 feet * 4.5 feet = 22.5 square feet.

The desired pen has an area of 3 times the original pen, which is 3 * 22.5 = 67.5 square feet.

Since the desired pen has a width of 4.5 feet, we can use the equation for the area of a rectangle to solve for the length:

Area = Length * Width

67.5 = x * 4.5

Dividing both sides by 4.5:

x = 67.5 / 4.5 = 15 feet

So the length of the pen would be 15 feet if Krista could build one that size. The area of the pen would be 15 feet * 4.5 feet = 67.5 square feet.

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Connie's total bill is sum of trail mix and water will be  $9.13.

What is sum ?
In mathematics, the sum refers to the result of adding two or more numbers together. It is a basic arithmetic operation, often used in many different mathematical concepts and calculations. The symbol for addition is '+', and the sum of a set of numbers is often represented using the capital Greek letter sigma (∑).

According to the question:

Connie's total bill would be the sum of the cost of the trail mix and the cost of the water, which is:

Total bill = cost of trail mix + cost of water

Total bill = $6.98 + $2.15

Total bill = $9.13

Therefore, Connie's total bill was $9.13.

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Answer:

----------------------

Use the formula for simple interest:

where:

Substituting the given values into the formula, we get:

Therefore, the rate of interest per year is 8%.

The cost of the car in 2000 would be $17,520, which is more than four times the original cost in 1970.

To calculate the cost of the car in 2000, we need to first adjust the original cost for inflation. Inflation is the general increase in prices of goods and services over time. So, if the inflation rate is constant at 4%, the cost of the car in 2000 will be much higher than its original cost in 1970.

To calculate the cost of the car in 2000, we can use the formula:

Adjusted cost = Original cost x (1 + Inflation rate)^Number of years

In this case, the original cost of the car in 1970 was $4000, and the inflation rate is constant at 4%. The number of years between 1970 and 2000 is 30.

So, the adjusted cost of the car in 2000 can be calculated as follows:

Adjusted cost = $4000 x (1 + 0.04)^30
Adjusted cost = $4000 x (1.04)^30
Adjusted cost = $4000 x 4.38
Adjusted cost = $17,520

Therefore, the cost of the car in 2000 would be $17,520, which is more than four times the original cost in 1970. This example shows how inflation can have a significant impact on the cost of goods and services over time. It is important to consider inflation when making financial decisions, such as budgeting, saving, and investing.

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Answer: n < 3

Step-by-step explanation:

so you have n + 1.91 < 4.91

you need to move that 1.91 to the other side so that the variable n is alone

a trick I learned is that cross the imaginary line that separates both sides and then change the sign.

it may sound tricky but imagine that any equal sign or anything that separates the equation has a imaginary line

Answer:

\(n < 3\)

Step-by-step explanation:

Given inequality:

\(n+1.91 < 4.91\)

Subtract 1.91 from both sides of the inequality:

\(\implies n+1.91-1.91 < 4.91-1.91\)

\(\implies n < 3\)

Answer:

1) x = 12.2

3) x = 21.7

5) x = 17.9

7) x = 31.8

Step-by-step explanation:

Use Pythagorean Theorem (a^2 + b^2 = c^2 where a and b are bases and c is hypotenuse)

1) 10^2 + 7^2 = x^2

100 + 49 = x^2

149 = x^2

x = sqrt 149 which is about 12.2

3) 16^2 + x^2 = 27^2

256 + x^2 = 729

x^2 = 473

x = sqrt 473 which is about 21.7

5) 9^2 + x^2 = 20^2

(we know the other base is 9 because in an isosceles triangle, the altitude (the height) is the same as the median (which divides the base into half)

81 + x^2 = 400

x = sqrt 319 which is about 17.9

7) 16^2 + y^2 = 22^2 (y is the height of the triangle)

256 + y^2 = 484

x = sqrt 228

(sqrt 228)^2 + (44-16)^2 = x^2

228 + 784 = x^2

x^2 = sqrt 1012 which is about 31.8

The Reparametrized curve with respect to arc length is:

r(s) = (1/2) * sqrt(2) * e^(4t) cos(4t) i + 3 j + (1/2) * sqrt(2) * e^(4t) sin(4t) k

To reparametrize the curve with respect to arc length, we need to find the expression for the curve in terms of the arc length parameter s.

The arc length parameter s is given by the integral of the speed function |r'(t)| with respect to t:

s = ∫|r'(t)| dt

Let's calculate the speed function |r'(t)| first:

r(t) = e^(4t) cos(4t) i + 3 j + e^(4t) sin(4t) k

r'(t) = (4e^(4t) cos(4t) - 4e^(4t) sin(4t)) i + 0 j + (4e^(4t) sin(4t) + 4e^(4t) cos(4t)) k

|r'(t)| = sqrt((4e^(4t) cos(4t) - 4e^(4t) sin(4t))^2 + (4e^(4t) sin(4t) + 4e^(4t) cos(4t))^2)

= sqrt(16e^(8t) cos^2(4t) - 32e^(8t) cos(4t) sin(4t) + 16e^(8t) sin^2(4t) + 16e^(8t) sin^2(4t) + 32e^(8t) cos(4t) sin(4t) + 16e^(8t) cos^2(4t))

= sqrt(32e^(8t))

Now, we can express s in terms of t by integrating |r'(t)|:

s = ∫sqrt(32e^(8t)) dt

To find the integral, we can make a substitution u = 8t, du = 8 dt:

s = (1/8) ∫sqrt(32e^u) du

= (1/8) ∫2sqrt(2e^u) du

= (1/8) * 2 * sqrt(2) ∫e^(u/2) du

= (1/4) * sqrt(2) * ∫e^(u/2) du

= (1/4) * sqrt(2) * 2e^(u/2) + C

= (1/2) * sqrt(2) * e^(4t) + C

Therefore, the reparametrized curve with respect to arc length is:

r(s) = (1/2) * sqrt(2) * e^(4t) cos(4t) i + 3 j + (1/2) * sqrt(2) * e^(4t) sin(4t) k

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The curve reparametrized with respect to arc length is:

r(u) = e^(2u/√2) cos(2u/√2) i + 3j + e^(2u/√2) sin(2u/√2) k

We have the curve given by:

r(t) = e^(4t) cos(4t) i + 3j + e^(4t) sin(4t) k

The speed of the curve is:

|v(t)| = √( (dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 )

= √( 16e^(8t) + 16e^(8t) )

= 4e^(4t) √2

Thus, the arc length from t = 0 to t = s is:

s = ∫0s |v(t)| dt

= ∫0s 4e^(4t) √2 dt

= √2 e^(4t) |_0^s

= √2 ( e^(4s) - 1 )

Solving for s, we get:

s = (1/4) ln( (s/√2) + 1 )

Let u be the parameter with respect to arc length, then we have:

u = ∫0t |v(t)| dt

= ∫0t 4e^(4t) √2 dt

= √2 e^(4t) |_0^t

= √2 ( e^(4t) - 1 )

Solving for t, we get:

t = (1/4) ln( (u/√2) + 1 )

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Answer:

y=-2x-13

Step-by-step explanation:

y=mx+b

3=-2(-8)+b

3=16+b

3-16=b

-13=b

The correct answer is option C. At the point (2,1) on the curve x² - xy + y²= 3, the derivative dy/dx exists, and the tangent line at that point is neither horizontal nor vertical.

To determine the correct option, we need to analyze the properties of the curve x² - xy + y² = 3 at the point (2,1). First, let's find the derivative dy/dx. Taking the derivative of the given equation implicitly with respect to x, we get:

2x - y - x(dy/dx) + 2y(dy/dx) = 0

Rearranging the terms, we have:

dy/dx = (2x - y) / (x - 2y)

Now, substituting the values x = 2 and y = 1 into the expression for dy/dx, we can determine its value at the point (2,1):

dy/dx = (2(2) - 1) / (2 - 2(1)) = 3 / 0

Since the denominator is zero, dy/dx is undefined at (2,1). Therefore, option D, stating that dy/dx does not exist at (2,1) and the tangent line at that point is vertical, is incorrect.

However, we can still determine the nature of the tangent line at (2,1). Although the derivative is undefined, it is still possible for the tangent line to exist and have a defined slope. In this case, the tangent line would be neither horizontal nor vertical. Therefore, option C, which states that dy/dx exists at (2,1) and the tangent line at that point is neither horizontal nor vertical, is the correct answer.

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The product should have a 1 significant digit.

When multiplying Scientific notations, the significant figure of the final result must be approximated to the scientific notation that has the least decimal place.

From the question given, if we 4.5160 x 10^3, 2.09 x 107, and 5.8 x 10^3 are multiplied, the product should have 1 significant digits since the least decimal value that occur in question is 1dp

Hence the product should have a 1 significant digit.

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Step-by-step explanation:

inversely means

y = k/x

therefore

30 = k/4

120 = k

y = 120/10 = 12

FYI :

directly would mean

y = kx

The value of y will be 12 when x is equal to 10.

The relationship between two variables known as "inverse variation" occurs when the value of one variable increases while the value of the other variable decreases.

Given that, y varies inversely with x.

Here, y∝1/x

y=k/x

xy=k

When x is 4, y is equal to 30, we get

k=4×30

k=120

When x=10, we get

10y=120

y=12

Therefore, the value of y will be 12 when x is equal to 10.

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The Z value(atomic number) of the given atom is 8

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Answer:

2x-4(x+7)=2

Step-by-step explanation:

Peter's age:x.... twice age:2x

Phil's age:x+7...4times age:4(x+7)

Difference if ages is 2

Hence; 2x-4(x+7)=2

Answer:

Answer

4.9/5

38

loitzl9006

Ambitious

54 answers

6.5K people helped

Answer:

x=25

Step-by-step explanation:

we know that "x" is Peter's age

assume that "y" is Phil's age

In the sentence "Phil's age is 7 years more than 1/5 times than Peter's age" are two things: "Phil's age": y and "1/5 times Peter's age": 1/5 x

create equation with these two things

y = 1/5 x

including "7 years more"

many people make a lot of errors with it, they dont know: y+7 = 1/5 x or y=1/5 x + 7 ?

in order to avoid mistakes

read the sentence and point, which: y or 1/5 x is greater and smaller

"Phil's age is 7 years more than ..."

so y is greater, and 1/5 x smaller

y = 1/5 x

greater = smaller

we must add 7 to smaller number to make an equality

greater = smaller + 7

y = 1/5 x + 7

Second sentence:

"4 times Phil's age is 2 years less than twice Peter's age."

Two things: "4 times Phil's age": 4y and "twice Peter's age": 2x

4y = 2x

read the sentence once again

"4 times Phil's age is 2 years less than (...)" , so 4y - smaller, 2x - greater

4y = 2x

smaller = greater

including "2 years less" we add 2 to a smaller number

smaller + 2 = greater

4y + 2 = 2x

Substitute y=1/5 x + 7 to the equation 4y+2 = 2x

Step-by-step explanation:

Answer:

m

Step-by-step explanation:

The thickness of each cookie is 0.318 cm.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

\(V = \pi r^2 h \: \rm unit^3\)

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

We are given that;

Diameter=5cm

Volume= 100cm3

Now,

To find the thickness of each cookie, you need to follow these steps:

Plug in the values into the formula for volume and solve for height:

Volume = π × radius^2 × height

100 = π × 2.5^2 × height

100 = 19.635 × height

height = 100 / 19.635

height = 5.093 cm

Divide the height by the number of cookies to get the thickness of each cookie:

Thickness = height / number of cookies

Thickness = 5.093 / 16

Thickness = 0.318 cm

Therefore, by the volume of cylinder answer will be 0.318 cm.

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Answer:

96

Step-by-step explanation:

Because If you add all of the numbers together you will get 96.

Answer:

467 cm²

Step-by-step explanation:

First off, cut the shape so its in 3 rectangles so you can find the area. Then, however much you cut off of that side you'll subtract from the original length of that side. Then, you'll multiply the lengths of the sides together for all of them and then add.

Answer:

The last one center is (-16,-4) radius is 6

Step-by-step explanation:

Equation of a circle ( x - h )^2 + ( y - k )^2 = r^2

R is radius

H and k are (h,k)

Answer:

Step-by-step explanation:

A

Answer:

....◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉

It is to be noted that the relative frequency of a class is computed by " dividing the frequency of the class by the sample size" (Option D)

The empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of occurrences of a given event to the total number of trials in an actual experiment, not in a theoretical sample space.

The number of times a specific value for a variable (data item) has been seen to occur in proportion to the overall number of values for that variable is described by a relative frequency. The absolute frequency is divided by the total number of values for the variable to produce the relative frequency.

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Answer:

1/4

Step-by-step explanation:

Multiply 75% and 1/3

Change 75% to a fraction

75/100 reduce the numerator and denominator by 25.

75/100 = 3/4

3/4 x 1/3

3/12

reduce

1/4

Answer:

Step-by-step explanation:

Given equation:

Answer:

Simplify: