If ƒ = {(2, -4), (2, 7) (3, 5), (4, -1), (8, 7)}, then ƒ is a function.

Answer:

x<1

Step-by-step explanation:

10x + 80 < 90

10x < 90 - 80

10x < 10

x < 1

Step-by-step explanation:

hope it helps.

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

9514 1404 393

Answer:

  20, 31, 42, 53, 64, 75, 86, 97

Step-by-step explanation:

The difference of 18 means the difference of digits is 18/9 = 2. Since the number you seek is the larger number, the 10s digit will be 2 more than the 1s digit. Possible numbers are ...

  20, 31, 42, 53, 64, 75, 86, 97

_____

If t and o are the tens and ones digits respectively, the relation you seek is ...

  (10t +o) -(10o +t) = 18

  9(t -o) = 18

  t - o = 2 . . . . as above

Since both t and o must be single digits, the minimum will be t=2, o=0, and the maximum will be t=9, o=7.

Answer:

10a+b=10b+a-18

9a+9b = -18

9(a+b) = -18

a+b = 18/9

a + b =2

Step-by-step explanation:

Answer:

The answer is 3.

Step-by-step explanation:

1/7(21)= 3

The equation of the tangent function with period 27, phase shift 7, and vertical shift - 1 is

y = A tan((2π/27) (x - 7)) - 1.

In trigonometry, the tangent function (usually abbreviated as tan) is a periodic function that relates the ratios of the lengths of two sides of a right-angled triangle. The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side of the triangle.

The general equation of the tangent function is:

y = A tan(Bx + C) + D

where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Using the given values of the period, phase shift, and vertical shift, we can write the equation of the tangent function as:

y = A tan((2π/B) (x - C)) + D

y = A tan((2π/27) (x - 7)) - 1

Since the period of the tangent function is 27, we know that:

B = 2π/27

The phase shift is 7, so:

C = 7

The vertical shift is -1, so:

D = -1

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The coordinates point of polygon A'B'C'D' are: A' (0, 0), B' (-2, 5), C' (-5, 5), and D' (-3, 0).

A polygon is a two-dimensional geometric shape that is defined by a closed path consisting of three or more straight line segments. These line segments are called sides, and the points where they meet are called vertices. Polygons can have any number of sides, although the most common polygons are those with three (triangles), four (quadrilaterals), five (pentagons), six (hexagons), and eight (octagons) sides.

To find the coordinates of A', B', C', and D', we need to apply a 180° rotation to the coordinates of A, B, C, and D.

The general formula for a 180° rotation about the origin is:

(x', y') = (-x, -y)

Using this formula, we can find the coordinates of A', B', C', and D':

A' = (-0, -0) = (0, 0)

B' = (-2, -(-5)) = (-2, 5)

C' = (-5, -(-5)) = (-5, 5)

D' = (-3, -0) = (-3, 0)

Therefore, the coordinates of polygon A'B'C'D' are:

A' (0, 0), B' (-2, 5), C' (-5, 5), and D' (-3, 0).

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Answer:

the answer is to the question is 691648

The value of r can be found as follow

We will use the relationship

Collecting like terms

Divide both sides by 6

r=3

Answer = A

Refer to the attachment for the required table:

What is the unit rate?

A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

From the table,

For 0 hours, distance = 15 miles

For 1 hour, distance = 80 miles

Difference between distances= 80-15=65 miles

Since it is given that, it is at a constant rate,  for every hour there is an increase of 65 miles in distance.

The completed table is shown in the attachment.

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Answer:

I'm not sure of the exact term in the blank, but a^3 and a^7 are both exponents with the same base meaning you can add the exponents to create one.

Step-by-step explanation:

In the quadrilateral ACDE, we can identify two congruent angles: angle CDA and angle C'EA.

In the given diagram, we have ACDE as a quadrilateral, and we know that CD is congruent to CE. To identify two congruent angles, let's examine the properties of the quadrilateral.

Since ACDE is not specified to be a particular type of quadrilateral (such as a parallelogram or rectangle), we cannot directly infer congruent angles from its properties.

However, we can make use of some general properties of quadrilaterals to identify two congruent angles. One property is that the sum of the interior angles of a quadrilateral is always 360 degrees.

Let's consider angle C as one of the angles in ACDE. Since CD is congruent to CE, we can denote angle CDE as angle C' to represent the congruent angles.

Now, using the property that the sum of the interior angles of a quadrilateral is 360 degrees, we can express the relationship between the angles of ACDE as:

∠ACD + ∠CDE + ∠DEA + ∠EAC = 360 degrees

Since CD is congruent to CE, angles CDA and CEA are also congruent (opposite angles in a quadrilateral). So, we can rewrite the equation as:

∠ACD + ∠CDA + ∠C'EA + ∠EAC = 360 degrees

Since we want to identify two congruent angles, let's focus on angles CDA and C'EA. These two angles are formed by the intersection of the congruent sides CD and CE with different adjacent sides.

Therefore, we can conclude that angles CDA and C'EA are congruent in ACDE.

In summary, in the quadrilateral ACDE, we can identify two congruent angles: angle CDA and angle C'EA.

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The measure of the angle B of the triangle is 78.15 degrees

From the question, we have the following parameters that can be used in our computation:

A = 25 degrees

a = 9.5 units

b = 22 units

Using the law of sines, the angle B is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(25)/9.5= sin(b)/22

This gives

sin(b) = 22 * sin(25)/9.5

Evaluate

sin(b) = 0.9787

Take the arc sin of both sides

b = 78.15

Hence, the measure of the angle is 78.15 degrees

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Answer:

Step-by-step explanation:

You want to know the amounts invested in stocks, bonds, and CDs when the total investment is $145000, $10000 more is invested in bonds than CDs, earnings are $6977.50, and rates of return are 6.7% for stocks, 2.5% for bonds, and 5.75% for CDs.

We can write three equations in 3 unknowns for this problem. Let s, b, c represent amounts invested in stocks, bonds, and CDs, respectively. Then the problem statement tells us the relations are ...

These equations can be solved using any of several methods. The second equation offers a nice relation between b and c, so substitution for one or the other of those will reduce the equations to two equations in two unknowns.

We prefer a calculator solution using an augmented matrix of the coefficients. That is shown in the attachment. It tells us the investment amounts are ...

__

Additional comment

Using b = c +10000, the two remaining equations are ...

<95141404393>

Answer:

c:2,4,6,8,10,12,14,16,18,20

Step-by-step explanation:

set d:4,8,13,15,20

The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.

The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?

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Work Shown:

18% = 18/100 = 0.18

18% of 24 = 0.18*24 = 4.32

The tip is $4.32

Adding this tip amount onto the original bill leads to 4.32+24 = 28.32

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

As a slight shortcut, we can use the multiplier 1.18 to get

1.18*24 = 28.32

This works because

1.18*24 = (1+0.18)*24 = 1*24 + 0.18*24 = 24 + 0.18*24

Notice the portion "24 + 0.18*24" can be found buried in the 1.18*24 expression. I applied the distributive property.

The multiplier 1.18 represents an increase of 18%

We can think of it as

100% + 18% = 1+0.18 = 1.18

Answer:

its 6000 because 300 x 20 is 6000

Calculate total weight of cement:

300 gallons x 20 lbs per gallon = 6000 pounds.

1 ton = 2000 pounds:

Weight of truck in pounds: 4 Toni x 2000 = 8,000 pounds

Total weight = 8000 + 6000 = 14,000 pounds

The answer is D.

The rock will take 5 seconds to reach to the surface to hit the water modelled by the function h = - 16 t² + 68 t + 60.

The function for the height of the rock in terms of t is given as:

h = - 16 t² + 68 t + 60

Also, we are given that the rock is thrown from a cliff that is 60 ft. high above the water.

We need to find the time taken by the rock to hit the surface of the water.

We have:

h = 0 ( as we need the stone to touch the water.)

Now, we will substitute this value in the function to find the time taken by the rock to hit the surface of the water.

So, we get that:

0 = - 16 t² + 68 t + 60

- 16 t² + 68 t + 60 = 0

- 4 t² + 17 t + 15 = 0

4 t² - 17 t - 15 = 0

By using the quadratic formula, to solve the equation, we get the value of t as:

D = b² - 4 a c

D = ( - 17 )² - 4 ( 4) (-15)

D = 289 + 240

D = 529

t = (17 ± 23) / 8

t = 5   or t = - 3 / 4

So, t = 5 seconds as time cannot be negative.

Therefore, we get that, the rock will take 5 seconds to reach to the surface to hit the water modelled by the function h = - 16 t² + 68 t + 60.

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Answer:

( 0 , 1 ) ,  ( 1 , 0 )

( − 5 , 9 ) ,  ( 3 , 0 )

( 0 , 9 ) ,  ( 8 , 6 )

Step-by-step explanation:

Answer:

A made 6 B worth 3p

S made () worth 2p

so it would be 6 baskets because the all multiply the same way. 3x2 and 2x3 they both equal to 6

Answer: a. 1

Step-by-step explanation:

There are 4 walls in total, and each wall measures 5ft high, 8ft wide

5 × 8=40 ft² for each wall

4×40=160 ft² for 4 walls

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

stated one gallon cover 160 ft²

160 ÷ 160=1 gallon

Hope this helps!! :)

Please let me know if you have any question

Answer: 14π

Step-by-step explanation: The formula for circumference is 2 * pi * the radius. However, we are looking for the terms of pi, so we will multiply 2 times pi to get 2 pi. then we get 2 pi x 7 which gives us 14pi, the answer.

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Work Shown:

Given data set of passing scores = {9,6,7,8,4,5,8,10,9,7,5,7}

Sorted data set of passing scores = {4,5,5,6,7,7,7,8,8,9,9,10}

Let x, y, and z represent the three failing scores.

The order of which doesn't matter but I'll have x < y < z.

In other words, x is the smallest, y in the middle, and z the largest of the failing scores sub-group.

Again the order of x,y,z in themselves don't matter. What does matter is that all three scores are smaller than 4. I'll assume that 4 represents the lowest passing grade possible.

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

We have this updated set of scores

{x,y,z,4,5,5,6,7,7,7,8,8,9,9,10}

We've gone from n = 12 scores to n = 12+3 = 15 scores.

n/2 = 15/2 = 7.5 which rounds to 8

The median of that updated set will be in slot 8. This trick only works when n is odd.

The score in the 8th slot is 7. More specifically, it is the first copy of "7" that is the median.

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

Another way to find the median:

Start with this set here: {x,y,z,4,5,5,6,7,7,7,8,8,9,9,10}

Erase the first and last items to get:  {y,z,4,5,5,6,7,7,7,8,8,9,9}

Repeat the last step to get:  {z,4,5,5,6,7,7,7,8,8,9}

Repeat again: {4,5,5,6,7,7,7,8,8}

Keep repeating those steps until you arrive at {6,7,7} which helps us zoom in on the middle-most item, which is the first "7" of that three element subset. We can then see that 7 must be the median of the 15 element set.

By the principle of mathematical induction, we have shown that

M(2k) = k  2k for all k ∈ N.

The principle of mathematical induction is a proof technique used to prove a statement that holds for all positive integers.

It consists of two steps:

Base case: Show that the statement is true for the smallest possible value of the positive integer, usually n = 1.

Inductive step: Assume that the statement is true for an arbitrary positive integer k, and then use this assumption to show that the statement must also be true for k + 1.

Here we have

The following recursive function computes the number of comparisons used in the worst case of merge sort.

M (1) = 0

M (2k) = 2M (2k−1) + 2k for all k > 0

To prove that M(2k) = k × 2k for all k ∈ N using mathematical induction, we will first show that the base case holds:

Base case: When k = 1,

we have M(2) = 2M(1) + 2¹ = 2(0) + 2 = 2, and k × 2k = 1 × 2¹ = 2.

Therefore, the base case holds.

Inductive hypothesis:

Assume that M(2k) = k × 2k holds for some positive integer k.

Inductive step:

We need to show that M(2k+1) = (k+1) × 2k+1.

Using the recursive definition of M, we have:

M(2k+1) = 2M(2k) + 2(2k+1)

= 2(k × 2k) + 2(2k+1) (using the inductive hypothesis)

= 2k(2k+2) + 2(2k+1)

= 2k(2(k+1)) + 2(2k+1)

= 2(k+1) × 2k + 2(2k+1)

= (k+1) × 2(2k+1)

Therefore, the inductive step holds.

Hence,

By the principle of mathematical induction, we have shown that

M(2k) = k  2k for all k ∈ N.

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Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

To solve -7y > 161, we divide both sides by -7 and we get y < -23. The inequality sign flipped because we divided both sides by a negative number.

To solve 7y > -161, we divide both sides by 7 and it leads to y > -23. The inequality sign does not flip in this case, because we are not dividing both sides by a negative number.

The similarities is that we end up with -23 on the right side, but the inequality signs are different.

To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.