A lock has 60 digits, and the combination involves turning right to the first number, turning left to the second number, and turning right to the third number. How many possible combinations are there?

Answer:

The answer to this question is the first option:

Line segment TU is parallel to line segment RS because 32/36=40/45

Answer:

The correct option is 1.

Step-by-step explanation:

From the given figure it is clear that QT=32, TR=36, QU=40 and US=45.

The converse of side splitter theorem states that if a line divides two sides proportionally, then that line is parallel to the third side.

The ratio in which TU divides the two sides is

[tex]\frac{QT}{TR}=\frac{32}{36}=\frac{8}{9}[/tex]

[tex]\frac{QU}{US}=\frac{40}{45}=\frac{8}{9}[/tex]

[tex]\frac{QT}{TR}=\frac{QU}{US}=\frac{8}{9}[/tex]

It means the line TU divides two sides proportionally.

Using converse of side splitter theorem, Line segment TU is parallel to line segment RS because

[tex]\frac{32}{36}=\frac{40}{45}[/tex]

Therefore the correct option is 1.

Answer:

Step-by-step explanation:

Please use " ^ " to indicate exponentation:   y= x^2 + 11x + 24.  Thanks.

Because x^2 is positive, the graph of this parabola opens up.

We can find the vertex and roots (zeros) as follows, using the quadratic formula:

With a = 1, b = 11 and c = 24,

       -11  ± √ [ (11^2-4(1)(24) ]       -11 ± √25

x = ------------------------------------ = --------------- = -3    and   x = -8

              2(1)                                     2

This tells us that the x-intercepts are at (-3, 0) and (-8, 0).  The minimum value is at x = -b / (2a), which here is x = -11 / [2] = -5 1/2 (which is halfway between the zeros).

The vertex (and thus, the minimum) is at (-5 1/2, f(-5 1/2) ).

Answer: a on edge 2021

Step-by-step explanation:

Answer:

y = -1

Step-by-step explanation:

Details have been given in the question, we need to break them apart and create our equations accordingly.

"the sum of two times x and 3 times y is 5"

2x + 3y = 5

"the sum of two times x and 3 times y is 5"

x - y = 5

So, our two equations are:

2x + 3y = 5

x - y = 5

Solve using substitution method, by moving y to the other side.

x = y + 5

2(y + 5) + 3y = 5

2y + 10 + 3y = 5

Combine like terms

5y + 10 = 5

Subtract 10 from both sides

5y = -5

y = -1

Answer:

The Answer is 1111

Step-by-step explanation:

15 = 2(7)+1

7=2(3)+1

3=2(1)+1

1=2(0)+1

look the remainder of division by 2 : 1111 in binary system​

verify : 15 = 1(2^0)+ 1(2^1)+ 1(2^2)+ 1(2^3 = 1+2+4+8=15 .....right

Answer:

[tex]h = \frac{3V}{\pi r^2}[/tex]

Step-by-step explanation:

Divide left and right by 1/3 π r²...

Answer:

B because u will have to first open the bracket according to BODMAS: bracket of division multiplication addition and subtract trust me before solving something like this use this BODMAS

Answer:

f(x)  = ax + b;

f(0) = -5;

a·0 + b = -5;

b = -5;

f(1) = -3;

a·1 + (-5) = -3;

a - 5 = -3;

a = 5 - 3;

a = 2;

f(x) = 2x - 5;

Step-by-step explanation:

The linear function with the values f(0)=−5 and f(1)=−3 is f(x) = 2x - 5

The linear function can be represented as follows:

y = mx + b

where

m = slope

b = y-intercept

The y-intercept is the value of y when x = 0

Since,

f(0) = -5

Therefore,

b = -5

The equation will be as follows

f(x) = mx - 5

lets find the slope(m) using the f(1)=−3

-3 = m - 5

m = -3 + 5

m = 2

Therefore,

f(x) = 2x - 5

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Answer:

70

Step-by-step explanation:

70 combinations of four books can be made from eight different books.

Answer:

The answer is A. (3,5,8)

Answer:

20°

Step-by-step explanation:

They are Vertically Opposite angles and hence are equal.

So, x + 40 = 3x.

Answer:

a. 20

Step-by-step explanation:

You are solving vertical angles. Put the measurements equal to each other:

x + 40 = 3x

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x from both sides.

x (-x) + 40 = 3x (-x)

40 = 3x - x

40 = 2x

Isolate the variable x. Divide 2 from both sides:

(2x)/2 = (40)/2

x = 40/2

x = 20

a. 20 is your answer.

~

Answer:

[tex]a=(9-10c)/b[/tex]

Step-by-step explanation:

we have

[tex]ab+10c=9[/tex]

Solve for the variable a

That means----> isolate the variable a

Subtract 10c both sides

[tex]ab+10c-10c=9-10c[/tex]

[tex]ab=9-10c[/tex]

Divide by b both sides

[tex]ab/b=(9-10c)/b[/tex]

[tex]a=(9-10c)/b[/tex]

Answer:

Step-by-step explanation:

Uploaded a pic of the answer. It’s correct

Given: We have the expression [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]

Step-1: [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]

Step-2: [tex]\left ( 875\times x^{5} \times y^{}\right )^{1/3}[/tex]                              [break the cuberoot as power [tex]1/3[/tex]]

Step-3: [tex]\left ( 125.7 \right )^{1/3}\times x^{5/3}\times y^{9/3}[/tex]                    [break [tex]875=125\times 7[/tex]]

Step-4: [tex]\left ( 5^{3} \right )^{1/3}\times 7^{1/3}\times x^{\left ( 1+2/3 \right )}\times y^{9/3}[/tex]       [ [tex]125=5^{3} \\\frac{5}{3} =1+\frac{2}{3}[/tex]]

Step-5: [tex]5^{1}\times 7^{1/3}\times x^{1}\times x^{2/3}\times y^{3}[/tex]                [break the power of [tex]x[/tex]] 

Step-6: [tex]5\times x\times y^{3}\left ( 7^{1/3}\times x^{2/3} \right )[/tex]

Step-7: [tex]5xy^{3}\left ( 7x^{2} \right )^{1/3}[/tex]

Step-8: [tex]5xy^{3}\sqrt[3]{7x^{2}}[/tex]

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Answer: [tex]x=2[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

We know that the slope of this line is:

[tex]m=-\frac{3}{2}[/tex]

And the y-intercept is:

[tex]b=3[/tex]

Since the line intersects the x-axis when [tex]y=0[/tex],  we can substitute values into  [tex]y=mx+b[/tex]:

 [tex]0=-\frac{3}{2}x+3[/tex]

The final step is to solve for "x", then:

[tex]-3=-\frac{3}{2}x\\\\(-3)(-2)=3x\\\\6=3x\\\\x=\frac{6}{3}\\\\x=2[/tex]

The x-intercept of the line is 2.

We must figure out the value of x when the y-coordinate is 0, in order to identify the x-intercept of a line.

We can express the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept,

Given that the slope of the line is -3/2 and the y-intercept is 3.

Substituting the given values into the equation, we have y = (-3/2)x + 3.

To find the x-intercept, we set y = 0 and solve for x:

0 = (-3/2)x + 3

Subtracting 3 from both sides:

(-3/2)x = -3

To isolate x, we multiply both sides by -2/3:

x = (-3)(-2/3)

x = 2

Therefore, the x-intercept of the line is 2.

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Answer:

12 cm.

Step-by-step explanation:

The distance between the opposite sides is a perpendicular line so we can form a right angled triangle by drawing a perpendicular line from one corner of the parallelogram  to the opposite 24 cm side.

So  one angle of the parallelogram will have a sine of 8/16 = 1/2 so this angle =  30 degrees.

In a similar way to the above we form a right angled triangle  from the same corner by drawing a perpendicular line to the opposite 16 cm side.

This has an angle of 30 degrees (  opposite angles in a parallelogram are congruent).

So sine 30 = x / 24

1/2 = x /24

x = 12 feet.

Another way to do this is by noting that the 2 triangles are similar (because  2 corresponding angles are equal).

So  8/ 16 = x/24

16x = 192

x = 12 feet.

Final answer:

The distance between the 16 cm sides of the parallelogram is 12 cm, determined by calculating the area of the parallelogram and then using it to find the missing dimension.

Explanation:

The student in the question is dealing with a geometrical problem involving the calculation of the distance between sides of a parallelogram. To solve the problem, we must understand that the opposite sides of a parallelogram are equal in length, and the area can be calculated as the product of the base and the height (the distance between the parallel sides). The question is analogous to finding the height of a parallelogram when the area and the base are known and can be approached in a similar way to finding dimensions of scaled geometric figures.

Therefore, the distance between the 16 cm sides of the parallelogram is 12 cm.

Answer: y = -x + 9

Step-by-step explanation:

First, to find the slope of the line we will use: (y₂-y₁)/(x₂-x₁)

Using the two points, we get: (8-1)/(1-8)

Simplify it: 7/-7

Finally, the slope is -1

We can now write: y = -x + b

Next we will plug in a point into the equation we have:

(8,1)  -->   1 = -8 + b          Then solve algebraically

b = 9

Then finish the equation:

y = -x + 9

The equation in slope-intercept form for the line passing through the points (8,1) and (1,8) is y = -x + 9, calculated by first finding the slope and then using it to determine the y-intercept.

To write an equation in slope-intercept form of the line passing through the points (8,1) and (1,8), we first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points gives us m = (8 - 1) / (1 - 8) = 7 / -7 = -1. With the slope and one of the points, we can then find the y-intercept (b) by rearranging the slope-intercept equation y = mx + b to b = y - mx, using one of the given points, for example, (8,1), which gives us b = 1 - (-1)(8) = 1 + 8 = 9. Therefore, the equation of the line in slope-intercept form is y = -x + 9.

Answer:

17x(1 - 2y)

Step-by-step explanation:

Given

17x - 34xy ← factor out 17x from each term

= 17x(1 - 2y) ← in factored form

Answer:

17x(1 - 2y)

Step-by-step explanation:

Answer:

360 degrees

Step-by-step explanation:

we know that

The sum of the n exterior angles for any convex polygon with n sides is always 360 degrees

Example

An equilateral triangle has three equal interior angles measures 60 degrees

Each exterior angle measures 120 degrees

The sum of the exterior angles is equal to  120+120+120=360

Answer:

[tex](x-6)(x+1)[/tex]

Step-by-step explanation:

Factoring is usually just a bit of guess and check.  [tex]x^2-5x-6[/tex] is written in the form [tex]a^2+b+c[/tex], where [tex]a=1[/tex], [tex]b=-5[/tex], and [tex]c=-6[/tex].

You need to find the two numbers that multiply together to equal [tex]-6[/tex] and can be added together to get [tex]-5[/tex].  These are [tex]-6[/tex] and [tex]1[/tex] in this case.

Now, put them together in the form [tex](x-6)(x+1)[/tex].  We will now check this answer using the FOIL method.

First term in each parentheses: [tex]x * x = x^2[/tex]

Outside terms: [tex]x * 1 = x[/tex]

Inside terms: [tex]-6 * x = -6x[/tex]

Last term in each parentheses: [tex]-6 * 1 = -6[/tex]

Now, add these together: [tex]x^2 + x - 6x - 6 = x^2 - 5x - 6[/tex]

Since we get the original expression, this is correct.

Answer:

8.75 hours

Step-by-step explanation:

We can use ratios to solve.  Put the pages over the time and set them equal.

4 pages       7 pages

------------- = ---------------

5 hours        x hours

Using cross products

4 * x = 5 *7

4x =35

Divide by 4 on each side

4x/4 = 35/4

x =8.75 hours

The algebraic expression that represents the phrase 'the difference of the number of roses and 18 lilies' is 'r - 18'. The term 'difference' in math denotes subtraction operation.

In algebra, the phrase 'the difference of the number of roses and 18 lilies' is represented as a subtraction operation between two variables or a variable and a number. In this case, the expression can be represented as r - 18, where 'r' represents the number of roses and '18' represents the number of lilies. However, in this scenario, the type of the flower doesn't really matter, it's just about the quantity which is represented by the term '18'. The key term difference denotes subtraction in mathematical terms.

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Answer:

Answers: 46, 23, and 111

Step-by-step explanation:

To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:

x=2y

z=y+88

x+y+z=180

Substituting, z = 1/2(x)+88, now plug z into the third equation:

x+1/2(x)+1/2(x)+88=180

this simplifies to 2x+88=180

subtracting 88 from both sides leaves 2x=92

x=46

plug this in to the first equation: 46 = 2y, so y = 23

plug this into the third one leaves z = 111

Hope this helps!

Answer:

your answer should be 45

Step-by-step explanation:

Answer:

15 to the third power would be 3375

Step-by-step explanation:

You start by multiplying

15 X 15 X 15

First you would get

225 X 15

Then you do the final multiplication

3375

Hello There!

I attached an image below which explains everything and gives some examples.

Final answer:

The product rule for exponents allows you to add the exponents when multiplying two terms with the same base, simplifying the calculation. Examples include multiplying powers of the same number, or dealing with terms in scientific notation.

Explanation:

Understanding the Product Rule for Exponents

The product rule for exponents states that when you multiply two expressions with the same base, you can simply add the exponents. This rule simplifies the multiplication of exponentiated quantities.

Examples of Using the Product Rule

For instance, if you have 53 multiplied by 54, the product rule allows you to add the exponents: 53+4 = 57. Another example involves numbers in scientific notation. When you multiply 3.2 x 103 by 2 x 102, the result is 6.4 x 103+2 = 6.4 x 105.

If both terms have exponents, multiply the digit terms as usual and then add the exponents of the exponential terms. This concept also applies to logarithms, where the logarithm of a product of two numbers equals the sum of their individual logarithms.

Answer:

C.

Step-by-step explanation:

The answer is C because when you add the absolute values (distance to zero) of the two numbers, you get the number 8. Divide this by 2, and you will get 4.  Then, you add four to the lower number, -6, and you get -2.

Answer: C. -2

Step-by-step explanation:

Check the picture below.

let's notice the "white" ∡1 is an inscribed angle with an intercepted arc of (x-32), and the "green" ∡5 is also an inscribed angle with an intercepted arc of (2x).

the ∡6 and ∡2 are both external angles, however they intercepted two arcs, a "far arc" and a "near arc", thus we'll use the far arc - near arc formula, as you see in the picture, and we'll use the inscribed angle theorem for the other two.

[tex]\bf \measuredangle 1=\cfrac{x-32}{2}\implies \measuredangle 1 =\cfrac{32}{2}\implies \measuredangle 1 = 16 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 5 =\cfrac{2x}{2}\implies \measuredangle 5 = x\implies \measuredangle 5 = 64 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \measuredangle 2 = \cfrac{(2x+8)~~-~~(x-32)}{2}\implies \measuredangle 2=\cfrac{2x+8-x+32}{2} \\\\\\ \measuredangle 2=\cfrac{x+40}{2}\implies \measuredangle 2=\cfrac{104}{2}\implies \measuredangle 2=52 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 6=\cfrac{[(2x+8)+(x)]~~-~~(2x)}{2}\implies \measuredangle 6=\cfrac{3x+8-2x}{2}\implies \measuredangle 6=\cfrac{x+8}{2} \\\\\\ \measuredangle 6=\cfrac{72}{2}\implies \measuredangle 6=36[/tex]

Hello There!

The answer would be "B"

We have to move the decimal place over for each one depending on what the power of the number is.

Answer:

your answer would be B. :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

"The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is false as it now stands.

If we combine -3x^2 and 3x^2, we get 0, so:

"The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is equivalent to

"The sum of (expression) and 7x^2 is 10x^2".

Subtracting 7x^2 from both sides yields (expression) = 3x^2.

So:  Although "The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is false,

"The sum of 3x^2 and 7x^2 is 10x^2" is true, and the formerly missing term is 3x^2.

Answer:

[tex]\large\boxed{x^4+\dfrac{8}{7}x^3+6x+1}[/tex]

Step-by-step explanation:

In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest.

We have:

[tex]\dfrac{8}{7}x^3+x^4+6x+1[/tex]

Look at the degrees for each term in the expression:

[tex]\dfrac{8}{7}x^3[/tex] has a degree of 3

[tex]x^4[/tex] has a degree of 4

[tex]6x[/tex] has a degree of 1

[tex]1[/tex] has a degree of 0

Write this trinomial in order by degree, highest to lowest

[tex]x^4+\dfrac{8}{7}x^3+6x+1[/tex]

The standard form of given equation is 8/7x^3 + x^4 + 6x + 1 is 7x^4 + 8 x^3 + 4 x + 7 = 0.

To write the equation 8/7x^3 + x^4 + 6x + 1 in standard form, you need to rearrange the terms in descending order of exponents.

Standard form for a polynomial is where the terms are written from the highest power to the lowest power of the variable.

So,  8/7x^3 + x^4 + 6x + 1 = 0

7x^4 + 8 x^3 + 4 x + 7 = 0.

Answer:

The mass of each cereal box is 500 grams

Step-by-step explanation:

Remember that

1 K=1,000 g

we know that

The total mass of 8 cereal boxes is 4 kilograms

4 k=4*1,000=4,000 g

therefore

The total mass of 8 cereal boxes is 4,000 grams

To find the mass of each box, divide the total mass by eight

so

[tex]\frac{4,000}{8}=500\ g[/tex]