A number cube has 6 faces, numbered from 1 to 6. If the cube
is rolled six times, what is the probability that a face with a 6
comes up exactly once?​

If an image of a triangle is congruent to the pre-image, the scale factor of the dilation is 1

From the question, we understand that the images are congruent

This means that, the shape is not dilated.

Instead, the shape is translated, reflected or rotated.

When a shape is not dilated, the scale factor is 1

Hence, the scale factor of the dilation is 1

Read more about dilation at:

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Answer:

Step-by-step explanation:

The question is to evaluate the natural logarithm of 5. Natural logarithms are logarithms with base e.

e is the irrational number equal to 2.71828182845904523536028747 ... (being irrational the decimals do not end and do not have a repetition period).

Logarithms are evaluated using tables or scientific calculators.

ln (5) = 1.6094379... it is also an irrational number, so it has infinite decimals with no repetition period.

So, rounding to two decimal numbers, ln (5) = 1.61, which is the option C).

Answer:c

Step-by-step explanation:test

Answer:

The correct answer to this problem is the final option, angle BTA is congruent to angle ATC.

Step-by-step explanation:

To solve this problem, we first have to unpack the meaning of the given information.  First, let's remember that CPCTC means that corresponding parts of congruent triangles are congruent.  This means that the same parts of two different triangles that are stated to be congruent (the same) are thus also congruent (the same).

In this case, triangle BAT and triangle CAT are stated to be congruent. This means that line segment BA and CA are congruent, angles BAT and CAT are congruent, and more because of CPCTC (explained above).

The correct answer to this problem is the final option, angle BTA is congruent to angle ATC. We can figure this out simply by looking at the triangle names.  Angle ATC is the same as angle CTA (the letters are just in reverse order).  From the congruence statement, we can tell that BTA and CTA are congruent angles due to the fact that triangle BAT and CAT are congruent using CPCTC.  Looking at the figure, this makes sense because these two angles appear to be the same measure.

Also, we can eliminate the other answer choices, since they are not corresponding parts of the two triangles (the line segments and angles do not represent two congruent pieces of the triangle - they are not matched up correctly).

Hope this helps!

Answer:

-6

Step-by-step explanation:

To find the slope, plug any two of your points into the slope formula.

I'll use your first two; (-2, 8) and (-1, 2).

[tex]\frac{y2-y1}{x2-x1}[/tex]

Your y1 term is 8, your y2 term is 2.

Your x1 term is -2, your x2 term is -1.

[tex]\frac{2-8}{-1-(-2)} \\\\\frac{-6}{-1+2} \\\\\frac{-6}{1} \\\\-6[/tex]

Your slope is -6.

Answer:

The slope is [tex]\huge \boxed{-6}[/tex].

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\displaystyle \frac{2-8}{(-1)-(-2)}=\frac{-6}{1}=-6[/tex]

Therefore, the slope is -6, and the correct answer is -6.

first off, let's notice something, the graph seems a bit misleading, since the height of the nut is 0.5 cm, whilst the side of the base is 0.6 cm, however in the picture 0.5 appears longer.  That said

1)

the volume of the nut itself is simply the volume of a hexagonal prism, which will just be the product of the area of the hexagon and the height.

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ \cline{1-1} a=0.5\\ p=\stackrel{0.6\times 6}{3.6} \end{cases}\implies A=\cfrac{(0.5)(3.6)}{2}\implies A=0.9 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the hexagonal prism}}{\stackrel{\textit{hexagon's area}}{(0.9)}~~\stackrel{\textit{height}}{(0.5)}\implies 0.45}[/tex]

2)

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=0.4\\ h=0.5 \end{cases}\implies V=\pi (0.4)^2(0.5)\implies V\approx 0.25[/tex]

3)

well, the composite figure is just a hexagonal nut with a cylindrical hole, so if we simply get the volume of the prism and subtract the volume of the cylindrical hole, what's leftover, is the volume of the nut alone without the hole.

[tex]\bf \stackrel{\textit{from 1)}}{0.45}~~-~~\stackrel{\textit{from 2)}}{0.25}\implies 0.20[/tex]

4)

in short, dividing the mass of 3.03 by our result from 3)

3.03 ÷ 0.2 = 1.515.

Answer:

True.

Step-by-step explanation:

Let's use the picture I made.

I used degrees instead...

tan(90-x)= b/a   .  I did opposite over adjacent for the angle labeled 90-x which is that angle's measurement.

cot(x)=b/a    .  I did adjacent over opposite for the angle labeled 90 which is that angle's measurement.

Now this is also known as a co-function identity.

[tex]\tan(\frac{\pi}{2}-x)[/tex]

Rewrite using quotient identity for tangent

[tex]\frac{\sin(\frac{\pi}{2}-x)}{\cos(\frac{\pi}{2}-x)}[/tex]

Rewrite using difference identities for sine and cosine

[tex]\frac{\sin(\frac{\pi}{2})\cos(x)-\sin(x)\cos(\frac{\pi}{2})}{\cos(\frac{\pi}{2})\cos(x)+\sin(\frac{\pi}{2})\sin(x)}[/tex]

sin(pi/2)=1 while cos(pi/2)=0

[tex]\frac{1 \cdot \cos(x)-\sin(x) \cdot 0}{0 \cdot \cos(x)+1 \cdot \sin(x)}[/tex]

Do a little basic algebra

[tex]\frac{\cos(x)-0}{0+\sin(x)}[/tex]

More simplification

[tex]\frac{\cos(x)}{\sin(x)}[/tex]

This is quotient identity for cotangent

[tex]\cot(x)[/tex]

Answer:

True

Step-by-step explanation:

tan( pi/2 -x)

We know that tan (a-b) = sin (a-b) / cos (a-b)

tan (pi/2 -x) = sin (pi/2 -x)

                       --------------

                      cos (pi/2 -x)

We know that

sin (a-b) = sin(a) cos(b) - cos(a) sin(b)

and cos (a-b) = sin(a) sin(b) + cos(a) cos(b)

tan (pi/2 -x) = sin (pi/2) cos (x) - cos (pi/2) sin (x)

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

                      sin(pi/2) sin(x) + cos(pi/2) cos(x)

We know sin (pi/2)=1

                cos (pi/2) = 0

tan (pi/2 -x) = 1 cos (x) - 0 sin (x)

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

                      1 sin(x) +0 cos(x)

tan (pi/2 -x) =  cos (x)

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

                      1 sin(x)

We know cos(x)/ sin (x) = cot(x)

tan (pi/2 -x) = cot(x)

Answer: D. 0.8125

Step-by-step explanation: His expenses is $975, and his salary is $1200. Divide the expenses by the salary to find the debt-to-income ratio.

975/1200 = 0.8125

The debt-to-income ratio is 0.8125.

Answer:

d) 0.8125

Step-by-step explanation:

Malcolm’s debt-to-income ratio is 0.8125 if his monthly expenses are $975 and his monthly salary is $1200.

All you have to do is divide monthly expenses by the monthly salary.

975 ÷ 1200 = 0.8125

Let the length = x and the width = y

For the length of fence we have x +x + y = 48 = 2x +y = 48

Rewrite as y = 48 - 2x

For the area we have x * y  = 254

Replace y in the are equation:

x * 48 -2x = 254

Simplify the left side:

48x - 2x^2 = 254

Subtract 254 from both sides:

48x - 2x^2 - 254 = 0

Using the quadratic formula solve for x:

a = -2, b = 48 and c = -254

x = -48 + 4√17/-4

x = 16.123 m.

The length = x = 16.123 meters.

The width = 48 - (16.123*2) = 15.754 meters

Rounding to the nearest centimeter:

Length = 16.1 ( 16 meters and 1 cm)

Width = 15.8 ( 15 meters and 8 cm)

Answer:

$1.80

Step-by-step explanation:

Based on the ratio shown in the double number line, the cost for 1 pound of avocados is $1.80.

5 pounds = 9$

9 divided by 5 = 1.8$/pound

Answer:

$1.80

Step-by-step explanation:

Note this:

5 lbs of avocado/$9

So, how much for 1 lb?

Remember units!!! They REALLY are important!!

1_lb_ x $9____ = (1 x 9)/5 = 1.8

5 lbs

**where are the numbers in our conversion coming from? Our notes!

We must now convert our answer to $'s, so $1.80 is our answer!

Answer:

[tex]4x^5\sqrt[3]{3x}[/tex]

Step-by-step explanation:

The product will be written as:

[tex]\sqrt[3]{16x^7}*\sqrt[3]{12x^9}[/tex]

As both the radicals have same root 3 so,

[tex]= \sqrt[3]{16x^7 * 12x^9}[/tex]

The powers of x will be added as the base is same

[tex]=\sqrt[3]{16*12 * x^{(7+9)}}\\=\sqrt[3]{192x^{16}}\\[/tex]

We have to break the terms so that the powers can be written as a multiple of 3

[tex]=\sqrt[3]{64*3*x^{15}*x}\\ =\sqrt[3]{(4^3)*3*(x^{3*5})*x}\\ Applying\ cube\ root\\= 4x^5\sqrt[3]{3x}[/tex]

Answer:

x = 6, x = -5, x = 9

if f(x)=(x-6)(x+5)(x-9)

Step-by-step explanation:

The zeros of a polynomial in factored form can be found by setting the polynomial equal to zero and then realizing if a product is zero, then at least one of it's factors is zero.

So we have the zero's are the x's that satisfy

(x-6)(x+5)(x-9)=0.

We just need to solve three equations:

x-6=0

           This can be solved by adding 6 on both sides:  x=6

x+5=0

         This can be solved by subtracting 5 on both sides: x=-5

x-9=0

         This can be solved by adding 9 on both sides: x=9

The solutions are in { 6,-5,9 }.

Answer:

x = 6, x = -5, x = 9

Step-by-step explanation:

If the polynomial f(x) is written in factored form, f(x) = (x − 6)(x + 5)(x − 9), the zeros of the polynomial function are x = 6, x = -5, x = 9.

x-6=0  x = 6

x+5=0  x = -5

x-9=0  x = 9

Therefore, x = 6, x = -5, x = 9 would be the correct answer.

Answer:

The measure of arc c is 86°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

86°=(1/2)[arc c+arc a]

see the attached figure with letters to better understand the problem

In this problem

Triangles ABO and CDO are congruent by SSS postulate theorem

∠AOB=∠COD

∠AOB=arc a -----> by central angle

∠COD=arc c -----> by central angle

therefore

The measure of arc a is congruent with the measure of arc c

arc a=arc c

so

86°=(1/2)[2arc c]

86°=[arc c]

arc c=86°

Answer:

[-∞, 3)

Step-by-step explanation:

We are given the following inequality which we are to express as a set using the interval notation:

[tex] - 2 x + 3 0 > 4 x + 1 2 [/tex]

Rearranging the inequality by adding the like terms together to get:

[tex] - 2 x - 4 x < 1 2 - 3 0 [/tex]

[tex] - 6 x < - 1 8 [/tex]

[tex]x<\frac{-18}{-6}[/tex]

[tex]x<3[/tex]

Since the values of [tex]x[/tex] are lesser than [tex]3[/tex] so we can express this in interval notation as:

[-∞, 3)

Answer:

A

Step-by-step explanation:

3x-5≥19

Add 5 to each side

3x-5+5≥19+5

3x ≥ 24

Divide each side by 3

3x/3 ≥24/3

x ≥8

Since this is greater than or equal to there is a closed circle at 8

greater than means the line goes to the right

Answer:

B

Step-by-step explanation:

If C is the correct answer and if the final result is multiplied out, where does the minus sign in a^4 - b^4 come from? All pluses don't make a minus. A is incorrect.

If D is correct, then a^2 - b^2 should be further factored producing a different kind of answer, like (a + b)^2(c-d)^2 which is not the same as a^4 - b^4. So D is not correct.

The first step in factoring a^4 - b^4 is (a^2 + b^2)(a^2 - b^2) A doesn't lead you anywhere. A is incorrect. The answer must be B.

a^4 - b^4 = (a^2 -  b^2)(a^2 + b^2)  The first term factors.

a4 - b^4 = (a + b)(a - b) (a^2 +b^2)

Answer:

Step-by-step explanation: THE ANSWER IS B

Answer: C

Step-by-step explanation:

plug in y=8 to

x+y=3

x+8=3

x=-5

There is no need to look at the other answer choices since they do not have x equaling to -5.

So,

[tex]x+y=3\Rightarrow y=3-x[/tex]

Then,

[tex]8=3-x\Rightarrow x=-5[/tex]

The ordered pair is therefore,

[tex]C(-5,8)[/tex]

Hope this helps.

r3t40

Answer:

x^2y^2 +9xy^2-xy-27y-6

Step-by-step explanation:

(xy+9y+2) (xy-3)

Each term of second bracket will be multiplied with the terms of first bracket

= xy(xy+9y+2) -3(xy+9y+2)

= x^2y^2+9xy^2+2xy-3xy-27y-6

=x^2y^2+9xy^2-xy-27y-6

Answer:

(23,-4):[tex]\sqrt{545}[/tex] units

Step-by-step explanation:

We are given that M(-19,4)and P(4,0)

We have to find the ordered pair that represents MP and find the magnitude of MP.

MP=P-M

MP=(4,0)-(-19,4)=(4+19,0-4)

MP=(23,-4)

Magnitude of MP=[tex]\sqrt{(23)^2+(-4)^2}[/tex]

Magnitude of MP=[tex]\sqrt{529+16}[/tex]

Magnitude of MP=[tex]\sqrt{545}[/tex] units

Hence, .option c is true.

Answer:c.(23,-4):[tex]\sqrt{545}[/tex] units

Answer:

A 2021

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

D.  (4, -4).

Step-by-step explanation:

y = -x is a line that has a negative slope of  -1 ( rising to the left)  and passing through the origin. It makes an angle of 45 degrees with the x-axis.

So, for example the point ( 0,1 )will map onto( -1 , 0).

Any point which maps on to itself across this line will have to lie on the line.

If x = 4 y = -x = -4.

Answer:

x = 8

Step-by-step explanation:

Angle bisector splits an angle into two equal angles

4x + 1 = 33

4x = 33 - 1

4x = 32

x = 32/4

x = 8

Answer:

x=8

Step-by-step explanation:

If AB is a bisector, that means  angles CAB and BAD are equal

<CAB = <BAD

33 = 4x+1

Subtract 1 from each side

33-1 = 4x+1-1

32 = 4x

Divide each side by 4

32/4 = 4x/4

8 =x

Answer:

-6

Step-by-step explanation:

f(g(-1)) means we need to find g(-1) and then plug that result into f(x).

So let's start:

g(-1) means to replace the input variable in g(x)=x^2 with -1.

So we replace x with -1.  

g(-1)=(-1)^2

g(-1)=1

Now that we have g(-1) can be replaced with 1, we can further evaluate f(g(-1)).

So let's do that:

f(g(-1))

f(1)=1-7   ; I replaced the x in f(x)=x-7 with 1 to find f(1).

f(1)=-6

----

Putting altogether

f(g(-1))=f((-1)^2)=f(1)=1-7=-6.

Answer:

f(g(-1)) = -6

Step-by-step explanation:

* Lets explain how to solve the problem

- The problem is about the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted into

 another function.

- Ex: f(g(x)) is the composite function that is formed when g(x) is

 substituted for x in f(x)

* lets solve the problem

∵ f(x) = x - 7

∵ g(x) = x²

- We want to find f(g(-1))

* At first lets find g(-1) by substitute x in the function g(x) by -1

∵ g(x) = x²

∵ x = -1

∴ g(-1) = (-1)² = 1

* Now we want to find f(g(-1)), then we will substitute x in f(x) by

 the value of g(-1)

∵ g(-1) = 1

∵ f(x) = x - 7

∴ f(g(-1)) = f(1)

∵ f(1) = 1 - 7 = -6

∴ f(g(-1)) = -6

Answer:

2.45 or 2 9/20

Step-by-step explanation

Answer:

193.8

Step-by-step explanation:

The 'mean' of a set is the set's average.

To find the average, add the terms together and divide by the number of terms.

[tex]108+305+252+113+191\\413+252+113+191\\665+113+191\\778+191\\969[/tex]

Divide by your number of terms (5).

[tex]\frac{969}{5} =193.8[/tex]

Answer:

193.8

Step-by-step explanation:

You add up all of the numers and get 969. Then you have to divide by the amount of numbers there are so divide by 5 and get 193.8

Step-by-step explanation:

i have answered ur question

The Perimeter of the given polygon can be calculated using the distance formula for each of its sides. The calculated distances are added to give a total perimeter of approximately 18.5 units.

The Perimeter of a polygon is calculated by adding the lengths of all its sides. Here, we need to calculate the distance between each pair of points, which gives the length of the sides of the polygon.

The distance between two points (x1, y1) and (x2, y2) is given by the formula sqrt((x2-x1)² + (y2-y1)²) .

To find the Perimeter of the polygon, we calculate the distances between each pair of vertices and then add them up:

Adding these distances, we get a perimeter of approximately 5 + 4.1 + 3.2 + 4.2 + 2 = 18.5 units, rounded to the nearest tenth of a unit.

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Answer:

Answer is

b = (8)tan(30°) - first choice

Step-by-step explanation:

Steps:

tan 30=b/8

b= 8tan30°

Option (a) is correct,  b = (8)tan(30°) is the equation which can be used to solve for b

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles

In a  right angle triangle the three sides are represented by the letters a, b and c .

a represents the side adjacent with given angle .

b represents the side opposite to the given angle.

c represents the hypotenuse of the triangle .

Check the attached image for clear picture of the right angle triangle with angle 30 degrees .

Using the trigonometric ratio we can write the ratio as

b/a = tan 30

Multiplying both sides by a , we get

b= a tan 30

since a=8 so

b =8 tan (30)

Hence, b = (8)tan(30°) is the equation which can be used to solve for b

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Answer:

Divide and express 2.7/1.1 to the nearest tenth.

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

If there are 12 sections and Lia paints 8, then Kira paints 4.

The fraction that represents how much Kira has painted of the wall is

4/12.

4/12 can be reduced.

4 and 12 have a common factor of 4 so we will divide top and bottom of 4/12 by 4 giving us 1/3.

The answer to the question is A

Answer:

[tex]x \geq\frac{2}{3}[/tex]

Step-by-step explanation:

The question is  [tex]3x+5 \geq 7[/tex]

We simply take the numbers to one side and variables to one side and solve via algebra (shown below):

[tex]3x+5 \geq 7\\3x \geq 7-5\\3x \geq 2\\x \geq\frac{2}{3}[/tex]

This range of values is the solutions of the inequality.