Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination.

If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen?

Differentiating each function, we have for all x, unless otherwise indicated,

[tex]h(x) = 2^x - 1 \implies h'(x) = \ln(2) \, 2^x > 0[/tex]

[tex]g(x) = -4 (2^x) \implies g'(x) = -4 \ln(2) \, 2^x < 0[/tex]

[tex]f(x) = -3x+7 \implies f'(x) = -3 < 0[/tex]

[tex]j(x) = x^2 + 8x + 1 \implies j'(x) = 2x + 8 > 0 \text{ only when } x > -4[/tex]

and only h(x) has a strictly positive derivative. (A)

Answer:

Hendecagon

Step-by-step explanation:

a hendecagon has 11 sides

Answer:

Hendecagon

Step-by-step explanation:

It has 11 sides, 11 corners, and 11 angles inside the shape that equal to 1620 degrees

Answer:

The median of the data is 12.

Step-by-step explanation:

The median is really just another word for the average. To find that, you add all of the numbers and divide that sum by the number of numbers there are.

9+15+17+18+6+20+8+5+18+18+10+5+14+12+10+7=192

There are 16 numbers in this data set. So, we will divide the sum by 16.

192÷16=12

I hope this helps!! :)

Answer: a. 720

Step-by-step explanation:

       You have 6 different sticks to choose from for the first stick. Then there are 5 for the second (6 - 1 = 5), then 4 for the third (5 - 1 = 4), etc all the way to the last stick.

       Mathematically, this can be shown with 6!. In other words, 6 factorial.

                      6 * 5 * 4 * 3 * 2 * 1 = 720

      The answer to our question is:

                      a. 720

The angle between two parallel lines is zero, we can prove it by putting the value of tanθ as 0.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

As we know, parallel lines in geometry are co-planar straight lines that do not cross at any point. Parallel planes are planes that never meet in the same three-dimensional space. Curves that do not touch or contact each other and maintain a constant minimum distance are known as parallel curves.

We know that the angle between two parallel lines is zero degrees.

[tex]\rm tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}[/tex]

tanθ = 0

m1 = m2

Thus, the angle between two parallel lines is zero we can prove it by putting the value of tanθ as 0.

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The inequality which represents this is x ≥ 22 , Option C is the right answer.

When two algebraic expressions are equated using an inequality operator, <, > etc then the expression formed is called Inequality.

IT is given in the question that

There is a number line , with points marked for eighteen, nineteen, twenty, twenty one, twenty two, twenty three.

The twenty two point is marked with an open circle pointing left

The inequality which represents this is

x ≥ 22 , Option C is the right answer.

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The area of the trapezoid is 284.31 square inches

The area of a trapezoid is:

Area = 0.5 * (Sum of parallel sides) * height

Using the given figure, we have:

Area = 0.5 * (17 + 31.6) * 11.7

Evaluate

Area = 284.31

Hence, the area of the trapezoid is 284.31 square inches

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Answer:

Right Triangles

Step-by-step explanation:

Answer:

Hi,

a=b+3

Step-by-step explanation:

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]

Thus:

c+2b+8-4a=c-a-b-1

3b-3a=-9

a=b+3

Answer:

what is your from my from is province philippines

Step-by-step explanation:

coordinates of center is 0,0 there are no hints given to find radius

The interval where |q| will fall will be[ 12√2−7√3,∞ ).

A complex number is an element of a number system that contains the real numbers and a specific element.

In this case, p and q are complex numbers such that |p|=7√3 and |p+q|=12√2. The interval where |q| will fall will be[ 12√2−7√3,∞ ).

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The function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function that has vertex at (2, 6)

The options are:

f(x) = 2|x – 2| – 6

f(x) = 2|x – 2| + 6

f(x) = 2|x + 2| + 6

f(x) = 2|x + 2| – 6

As we know the vertex form of a quadratic function is given by:

f(x) = a(x - h)² + k

Similarly, mod function  can be expressed as:

m(x) = a|x - h| + k

Here (h, k) is the vertex of a function.

In the function:

f(x) = 2|x – 2| + 6

The vertex of the function is (2, 6)

Thus, the function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.

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The question requests proof that WV = VR. See the definition of Mathematical proof and the explanation for the proof below.

Mathematical proof refers to the steps of logical arguments which are given to show that a mathematical statement is true or correct.

Reason: This is given. The image is a parallelogram.

Therefore if  ΔSVR ≅ PVW;

Then WV = VR.

QED.

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The midterm score of 45 is the 3rd decile, meaning that 42% of the Senior High School students scored below this test.

Deciles are a type of percentile that divides data into groups of 10%. That is, each decile comprises 10% of the dataset.

To determine the decile, sort the data from lowest to highest. Now, divide the result by ten. This number reflects the no. of observed values within each decile.

Sorting the data from lowest to highest, we have:

= 14/10

= 1.4

Thus, each decile contains only a 1.4 score.

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Area of sector

option B

Answer:

b

Step-by-step explanation:

The area of a sector is (the angle) over 360 multiplied by pi (radius) squared

This would be 45/360 pi (4.5) squared, resulting in option b.

Answer: 3360 ft squared

Step-by-step explanation:

Short side : 30 x 14 = 420

Long side 30 x 3 x 14 = 1260

420 + 420 + 1260 + 1260 =  3360

pls give brainliest

have a nice day

Answer:

Step-by-step explanation:

we know that

Solve for x

so

therefore

The number of pounds of apples is 4.5 and the number of pounds of grapes is 2.5

This is a means of reducing the cost of a goods or an asset over time. The value of the car after 9 years is approximately $888

This is a means of reducing the cost of a goods or an asset over time.

Mathematically, the cost of goods after a particular year is expressed as:

P(t) = P0e^-rt

Given

Substitute

P(17) = 41000r^0.17(9)
P(17) = 4100(0.21653)

P(17) = 887.79

Hence the value of the car after 9 years is approximately $888

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Answer:

C

Step-by-step explanation:

-4x+2<6

-4x<4

x<-1

because the sign doesnt have a line under it, it is an open hole

Answer:

x = 4.2

Step-by-step explanation:

14.1² + x² = 14.7²

198.81 + x² = 216.09

216.09 - 198.81 = 17.28

√17.28 = 4.15

x = 4.15

Round to nearest tenth

x = 4.2

The angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have shown a right-angle triangle in the picture.

In the right angle triangle, ABC

The angle BAC = 55 degree

Angle BAA' = 90 degree

In the figure, the angle of depression = CAA'

= BAA' - BAC

= 90 - 55

= 35 degree

Thus, the angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.

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Answer: [tex]109^{\circ}[/tex]

Step-by-step explanation:

The exterior angles of a polygon add to 360 degrees, so the sixth angle measures [tex]360-39-47-42-59-64=\boxed{109^{\circ}}[/tex]

Answer:

  g(x) = -√(x+6)

Step-by-step explanation:

The inverse of the function y = f(x) can be found by solving for y the relation x = f(y).

__

  x = f(y)

  x = y^2 -6

  x +6 = y^2 . . . . . . add 6

  -√(x +6) = y . . . . . negative square root

The negative root produces y ≤ 0, equivalent to x ≤ 0 for f(x).

The inverse of f is g(x) = -√(x +6).

_____

Additional comment

The graph of a function and its inverse are mirror images of each other across the line y=x. This is shown in the attachment for the f(x) and g(x) in this problem.

Answer:

[tex] (\frac{{m}^{2} }{4} )\pi[/tex]

Step-by-step explanation:

we can find the radius from the diameter by dividing the diameter by 2 (radius is half the diameter)

the formula for the area of a circle is r²π (with r being radius) but since we must use diameter we have to replace r with (m/2)

this gives us our new formula of (m/2)²π, which simplifies to (m²/4)π

that is the answer

- kan academy advance

Answer:#1 A, #2 B

Step-by-step explanation:

Heres the proof

Using it's formula, it is found that the value of the monthly payment for the loan to buy the drum set is of $50.32.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

In this problem, the parameters are given as follows:

P = 1800, r = 0.1525, n = 4 x 12 = 48.

Hence:

r/12 = 0.1525/12 = 0.01270833.

Hence, the monthly payments will be of:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 1800\frac{0.01270833(1 + 0.01270833)^{48}}{(1 + 0.01270833)^{48} - 1}[/tex]

A = 50.32.

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Answer:

p=Parentheses

e=Exponents

m=Multiplication

d=Division

a=Addition

s=Subtraction

its an order of solving a equation