Which equation does not represent a function? Why? A) y = x2; There are two outputs for each input. B) y2 = 4x; There are two outputs for each input. C) y = x; The output value is the same as the input value. D) y = −x; The output value is the opposite of the input value.

Answer:

3 miles

Step-by-step explanation:

if she can run at a constant speed for 30 minutes, then it is 3 miles. But, if there is some reason that she cannot run at the same rate as she did for one mile, the answer is unknown.

Answer:

360 cm^2

Step-by-step explanation:

Find the area of each face of the triangular prism.

Imagine the triangular prism as its net, it is composed with 2 triangular faces (these are tye bases of the prism) and 3 rectangular faces.

Areas of the 2 triangular bases (they are similar triangles):

1/2 x 8 cm x 6 cm = 24 cm^2

24 x 2 = 48 cm^2

Area of the rectangular face:

8 x 13 = 104 cm^2

Area of another rectangular face:

6 cm x 13 cm = 78 cm^2

Area of another rectangular face:

13 cm x 10 cm = 130 cm^2

Add up all the areas of all faces:

48 + 104 + 78 + 130 = 360

So the SA is 360 cm^2

Answer:

Suppose A and B , both has initial volume, say x

120 ML is poured from B to A, then new volumes of A and B will be:

new volume of A (x-120)

new volume of B  (x+120)

Volume of B is now four times volume of A, then

(x+120)= 4(x-120)

(x+120)=4x-180

3x=600

x=200

So, the initial volume of A and B containers is 200

So, at the end, volume of container A = 200-120=80

Hence the answer is 80   :

Step-by-step explanation:

Answer:

  a) 489.77 ft from friend

  b) 470.80 ft from cliff

Step-by-step explanation:

Given a man on a 135 ft cliff sees his friend at an angle of depression of 16°, you want to know the distance of the man from his friend, and the distance of the friend from the cliff.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Tan = Opposite/Adjacent

The 135 ft height of the cliff is modeled as the side of a right triangle that is opposite the angle of elevation from the friend to the top of the cliff. (See attachment 2.) That angle is the same as the angle of depression from the top of the cliff to the friend.

The hypotenuse of the triangle is the distance between the man and his friend. The side of the triangle adjacent to the friend is the distance to the cliff.

Using the above relations, we have ...

  sin(16°) = (cliff height)/(distance to friend)

  tan(16°) = (cliff height)/(distance to cliff)

Solving for the variables of interest gives ...

  distance to friend = (cliff height)/sin(16°) = (135 ft)/sin(16°) ≈ 489.77 ft

  distance to cliff = (cliff height)/tan(16°) = (135 ft)/tan(16°) ≈ 470.80 ft

The ma is 489.77 ft from his friend; the friend is 470.80 ft from the cliff.

__

Additional comment

The distances are given to more decimal places than necessary so you can round the answer as may be required.

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There are no solutions to the given logarithmic equation that satisfy the conditions.

Let's solve the logarithmic equation step by step:

log₃(x) + 7 = 11 - log₃(x - 80)

Combine logarithms

Using the property logₐ(M) + logₐ(N) = logₐ(MN), we can combine the logarithms on the left side of the equation:

log₃(x(x - 80)) + 7 = 11

Simplify the equation

Using the property logₐ(a) = 1, we simplify the equation further:

log₃(x(x - 80)) = 11 - 7

log₃(x(x - 80)) = 4

Rewrite in exponential form

The equation logₐ(M) = N is equivalent to aᴺ = M. Applying this to our equation, we get:

3⁴ = x(x - 80)

Convert to a quadratic equation

Expanding the equation on the right side, we have:

81 = x² - 80x

Set the equation equal to 0

Rearranging the terms, we get:

x² - 80x - 81 = 0

Solve for x

To solve the quadratic equation, we can factor or use the quadratic formula. However, upon closer examination, it appears that the equation does not have any integer solutions.

Check for extraneous solutions

Since we don't have any solutions from the quadratic equation, we don't need to check for extraneous solutions in this case.

Therefore, there are no solutions to the given logarithmic equation that satisfy the conditions.

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Answer:

he uses 30 pages

Step-by-step explanation:

turn 10% into a decimal. this would be .10

.10 • 300=30

30 pages

Answer:

The grand pacer test stated that the percentage of the core would be 50%

SThe range of tep-by-step explanation:

To determine the number of ways Samantha can arrange her mathematics books and computer science books on the shelf, we can use the concept of permutations.

1. First, we'll arrange the 3 mathematics books in the first 3 positions. Since Samantha has 7 mathematics books to choose from, she can arrange them in 7P3 ways:
7P3 = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210 ways

2. Next, we'll arrange the 2 computer science books in the last 2 positions. Since Samantha has 5 computer science books to choose from, she can arrange them in 5P2 ways:
5P2 = 5! / (5-2)! = 5! / 3! = 5 x 4 = 20 ways

3. Now, we need to multiply the number of ways to arrange the mathematics books by the number of ways to arrange the computer science books since these are independent events:
Total ways = 210 (mathematics books) x 20 (computer science books) = 4200 ways

So, Samantha can arrange her 7 mathematics books and 5 computer science books in 4200 different ways, with the first 3 positions occupied by math books and the last 2 by computer science books.

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Answer:

Step-by-step explanation:

\((8,-1) = (x_1,y_1)\\\\m = -\frac{3}{2}\)

Substitute values into point-slope form

\(y-y_1=m(x-x_1)\\\\y -(-1)=-\frac{3}{2} (x -8)\\\\y+1 = -\frac{3}{2}x+12\\\\y = -\frac{3}{2}x +12-1\\\\y =-\frac{3}{2}x +11\)

The equation of line passes through the point (8, -1) will be;

⇒ y = - 3/2x + 11

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (8, - 1).

And, The slope of the line is,

⇒ m = - 3/2

Now,

Since, The equation of line passes through the point (8, -1).

And, Slope of the line is,

⇒ m = - 3/2

Thus, The equation of line with slope - 3/2 is,

⇒ y - (-1) = - 3/2 (x - 8)

⇒ y + 1 = - 3/2 (x - 8)

⇒ y + 1 = - 3/2x + 12

⇒ y = - 3/2x + 12 - 1

⇒ y = - 3/2x + 11

Therefore, The equation of line passes through the point (8, -1) with slope - 3/2 is,

⇒ y = - 3/2x + 11

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Answer:

6\(\sqrt{34}\)

Step-by-step explanation:

\(\sqrt{1224}\\\) = \(\sqrt{36*34}\) = 6\(\sqrt{34}\)

For ceiling

the area of ceiling is = 12 × 10 = 120ft²

white paint cost = 120ft²

Now the four walls cost

area of two wall = 2×{length × width}

= 2(8×10)

=2×80

=160ft²

for calculating this we need to subtract that area of 2 windows and door from the total area of door.

total area of two walls was 160ft²

area of door is 22sq²

area of two windows= 2 ×(2²) = 8ft

total = 22+8 = 30ft²

Area of two walls which have 2 windows and one door = 160- 30

= 130ft²

The margin of error for a 95% confidence interval for the mean, with a lower value of 102 and an upper value of 131, would be 14.5.

In statistics, a confidence interval provides a range of values within which the true population parameter is likely to fall. The margin of error is a measure of the uncertainty associated with estimating the population parameter.

For a 95% confidence interval, the margin of error is determined by dividing the width of the interval by 2.

Since the width of the interval is the difference between the upper and lower values, we can calculate the margin of error by subtracting the lower value (102) from the upper value (131), which gives us 29. Dividing this by 2, we find the margin of error to be 14.5. Therefore, the margin of error for this 95% confidence interval is 14.5.

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In the given word problem the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Gunnar's car travel using per gallon of gas = 22.4 miles.

According to the given question,

Gunnar's car can hold 17.82 gallons of gas. Then number of miles does Gunnar's car can travel is ,

=> 22.4 × Car's total tank has hold

=> 22.4 × 17.82

=> 399.17 miles

Hence the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

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To find the interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days, we use the simple interest formula as follows:

Simple Interest = (P × R × T)/100Where:P = Principal or amount borrowedR = Rate of interest per annumT = Time in years or fraction of a year110 days ÷ 360 days = 0.3056 (time as a fraction of a year)The rate of interest, 10(1/3)% is equal to 10 + (1/3) percent = 10.33% per annum in decimal form = 0.1033Substituting the values we have into the formula,Simple Interest = (P × R × T)/100= (3,290 × 0.1033 × 0.3056)/100= $100.68 (rounded to the nearest cent)

Therefore, the interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days is $100.68.

A credit union loan is a type of personal loan that can be used for a variety of purposes. One of the most common reasons people take out credit union loans is to purchase big-ticket items like a new computer system. When you take out a loan, you must pay back the amount borrowed plus the interest charged by the lender. The interest rate is usually expressed as a percentage of the amount borrowed and is charged for a specific period of time known as the loan term. Simple interest is a method of calculating interest that is charged only on the principal amount borrowed.

It does not take into account the interest that has already been paid. Simple interest is calculated by multiplying the principal amount borrowed by the interest rate and the length of the loan term. The answer is more than 100 words.The interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days is $100.68. Therefore, he would pay $3,290 + $100.68 = $3,390.68 in total to the credit union over the loan term. It is important to note that when rounding dollar amounts to the nearest cent, amounts that end in .50 or higher are rounded up to the next highest cent, while amounts that end in .49 or lower are rounded down to the next lowest cent. In this case, $100.6847 would be rounded up to $100.68. In conclusion, the interest charged on a loan can significantly increase the total amount that must be repaid, making it important for borrowers to understand how interest is calculated and the terms of their loan.

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Answer:

No

Step-by-step explanation:

If it was a full line, then it would represent a function.

If you realize that you've made a mistake after the fact, the first thing to do is to acknowledge it.

This means accepting responsibility for your actions and recognizing that you could have done better. Once you've done this, you can take steps to correct the mistake and prevent it from happening again in the future.

If your mistake has affected other people, it's important to apologize. Be sincere and acknowledge the impact your actions have had on others. This can help to repair any damage done to relationships and show that you're taking responsibility for your actions.

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Step-by-step explanation:

maybe this is not the full expression, as you wrote the line equation in a funny way.

I understand the following :

the line is

y = (-2/5)×x - 7

perpendicular means crossing at a right angle (90 degrees).

the slope of the original line is -2/5.

as in every line equation, the slope is the factor of x. and it expresses the ratio y/x indicating the amount of units y is changing, when x changes a certain amount of units (e.g. when going from one point on the line to another).

the perpendicular slope turns the original y/x ratio upside-down, and also flips the sign.

so, it is 5/2.

the equation for the perpendicular line looks like

y = (5/2)×x + b

now what is b ?

for this we use the specified point on the line : (4, -1)

and we put these values as x and y into the equation :

-1 = (5/2)×4 + b = 5×2 + b = 10 + b

b = -11

and so, the full equation of the perpendicular line is

y = (5/2)×x - 11

Answer:

Step-by-step explanation:

A function does not have any repeating domains (x-coordinates).

Hope it helps!

Answer:

16x25x15=6000

4+11÷2=9.5

Step-by-step explanation:

1) 16x25x15 is 16 times 25 times 15, which is 6000

2) This question requires BIDMAS/BODMAS. As you start with the multiplication (Brackets Indices Multi Divide Add Subtract) 11÷2 = 5.5, 5.5+4=9.5

Answer:

mar as briallist pls

Step-by-step explanation:

Given that,

-3X = 27

=> -3X*(-1) = 27*(-1) [ multiply by -1 in both side ]

=> 3X = -27

=> X = -27/3

=> X = -9

Answer: X = -9

The translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5). (option b)

To translate the triangle two units to the left, we need to subtract 2 from the x-coordinates of each vertex, while leaving the y-coordinates unchanged. This is because moving the triangle left means we're decreasing its x-values.

So, let's apply this transformation to each point.

The first point, (-1, -1), becomes (-1 - 2, -1), which simplifies to (-3, -1).

The second point, (-1, -5), becomes (-1 - 2, -5), or (-3, -5).

The third point, (0.5, -5), becomes (0.5 - 2, -5), or (-1.5, -5).

These new coordinates give us the vertices of the triangle after it has been translated two units to the left.

Now that we have the new vertices, we can label them A', B', and C' to distinguish them from the original vertices. So, the translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5).

This is the second option in the answer choices given.

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The distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

To find the distance between successive fourth roots of a complex number on the unit circle, we can use the concept of the angle between the roots. Let's proceed step by step:

The given complex number is √3/2 - 1/2i. This complex number lies on the unit circle because its magnitude is equal to 1.

1. Convert the given complex number to trigonometric form:

  √3/2 - 1/2i = cos(θ) + i*sin(θ)

  By comparing the real and imaginary parts, we can determine the angle θ:

  cos(θ) = √3/2

  sin(θ) = -1/2

  Using the unit circle, we can find that θ = 5π/6 (or 150 degrees). This angle represents the position of the given complex number on the unit circle.

2. Find the angle between successive fourth roots:

  Since we are interested in the fourth roots, we divide the angle θ by 4:

  θ/4 = (5π/6) / 4 = 5π/24

  This angle represents the angular distance between two successive fourth roots on the unit circle.

3. Calculate the distance between the two points:

  To find the distance, we multiply the angular distance by the radius of the unit circle (which is 1):

  Distance = (5π/24) * 1 = 5π/24

  Therefore, the distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

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It's important to note that the resulting polynomial is not in P_3, as it has a degree of 4.

The student's question involves a linear operator L acting on a polynomial p(x) in P_3, the space of polynomials of degree 3 or less. The linear operator is defined as L(p(x)) = x * p'(x) * p''(x). Let's find the result of this operation step-by-step.

1. Determine the general form of a polynomial in P_3: A polynomial in P_3 has the form p(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

2. Compute the first derivative p'(x): To find the first derivative, differentiate p(x) with respect to x. We get p'(x) = 3ax^2 + 2bx + c.

3. Compute the second derivative p''(x): Next, differentiate p'(x) with respect to x. We get p''(x) = 6ax + 2b.

4. Compute the product x * p'(x) * p''(x): Multiply the first derivative, second derivative, and x together. We have (x)(3ax^2 + 2bx + c)(6ax + 2b).

5. Simplify the expression: After multiplying and combining like terms, we get L(p(x)) = 18a^2x^4 + 12abx^3 + 4a^2x^3 + 4b^2x^2 + 12acx^2 + 6bcx + 2cx^2.

This is the resulting polynomial after applying the linear operator L to a polynomial p(x) in P_3. However, it's important to note that the resulting polynomial is not in P_3, as it has a degree of 4.

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Therefore, a maximum area the farmer can enclose with the 144 feet of fencing will be1250 square feet.

Let the length of the field =  feet

 And the width of the field =  feet

Therefore, area of the rectangular field = Length × Width

                                                             A =  x*y  square feet

Since, length of the fence = 100 feet

And the farmer has to enclose three sides of the rectangle as shown in the figure attached.

Therefore, length of the fence = length + 2(width)

                                               = (x+2y) feet

Hence,  (x+2y)=100

x=100-2y

By substituting the value of 'x' in the expression for the area of the rectangular field.

A=(100-2y)y

A=-2y^2+144y

Find the derivative of the expression with respect to y ,

A'= -4y+100

A'=0

4y=100

y=25

A=-2*625+2500

A=2500-1250

A=1250 square feet

Therefore, maximum area the farmer can enclose with the 144 feet of fencing will be1250 square feet.

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a. The projectile will be at a height of 576 ft above the ground after 1.43 seconds and after 5.56 seconds.

b. The projectile will crash on the ground after 9.84 seconds.

The solution has been obtained by solving the equation.

What is an equation?

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.

We are given an equation as h = -16t² + v₀t + 448

Also v₀ is given as 112.

a. In order to find the time (t) the projectile will be at a height of 576 ft above the ground, we need to substitute h = 576 and v₀ = 112.

On substitution, we get

⇒h = -16t² + v₀t + 448

⇒576 = -16t² + 112t + 448

⇒36 = -t² + 7t + 28                (On dividing both sides by 16)

⇒0 = -t² + 7t - 8  

⇒t² - 7t + 8 = 0  

On solving the equation using the quadratic equation formula, we get

t = (7 ± √49 - 32)/2

t = 1.43 or 5.56

So, it will be at height 576 ft after 1.43 seconds and after 5.56 seconds.

b. Similarly, now we will put h = 0 and v₀ = 112.

Now, we get

⇒0 = -16t² + 112t + 448

⇒t² - 7t - 28 = 0                (On dividing both sides by 16)

On solving the equation using the quadratic equation formula, we get

t = (7 ± √49 + 112)/2

t = 9.84 or -2.84

Since, time cannot be negative, so it will crash after 9.84 seconds.

Hence, the projectile will be at 576 ft after 1.43 seconds and after 5.56 seconds and will crash on the ground after 9.84 seconds.

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The set of expressions that is NOT an example of the associative property is B. (8 - 2) + 3 and 8 + (-2 + 3).

The associative property states that the way you group numbers when adding or multiplying does not change the result. For example, (8 + 2) + 3 is the same as 8 + (2 + 3). However, the associative property does not apply to subtraction or division. Therefore, (8 - 2) + 3 is not the same as 8 + (-2 + 3).

Besides associative property, there are 3 other mathematical properties that only works on adding and multiplying. They are:

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Answer: B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

2((18)(12) + (12)(10) + (18)(10)) = 2(516)

= 1,032 in.²

Answer:

n^3 + 1.

Step-by-step explanation:

Each term is 1 more than a perfect cube.

2 = 1^3 + 1

9 = 2^3 + 1

28 = 3^3 + 1

65 =  4^3 + 1

126 = 5^3 + 1

So the explicit formula is n^3 + 1.

The explicit formula that generates the given sequence is indeed aₙ = n³+1.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The nth term of the sequence can be obtained by substituting n = 1, 2, 3, ... into the expression n³+1:

a₁ = 1³+1 = 2

a₂ = 2³+1 = 9

a₃ = 3³+1 = 28

a₄ = 4³+1 = 65

a₅ = 5³+1 = 126

Hence, the explicit formula that generates the given sequence is indeed aₙ = n³+1.

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