definition of theorem

Answer:

[tex]\large\boxed{x=\log_\frac{5}{3}5}[/tex]

Step-by-step explanation:

[tex]3^x=5^{x-1}\qquad\text{use}\ a^{n-m}=\dfrac{a^n}{a^m}\\\\3^x=\dfrac{5^x}{5^1}\qquad\text{multiply both sides by 5}\\\\5\cdot3^x=5^x\qquad\text{divide both sides by}\ 3^x\\\\5=\dfrac{5^x}{3^x}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\5=\left(\dfrac{5}{3}\right)^x\qquad\text{logarithm both sides}\ \log_\frac{5}{3}\\\\\log_\frac{5}{3}5=\log_\frac{5}{3}\left(\dfrac{5}{3}\right)^x\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log_\frac{5}{3}5=x\log_\frac{5}{3}\dfrac{5}{3}\qquad\text{use}\ \log_aa=1\\\\\log_\frac{5}{3}5=x[/tex]

Answer:

The last option (62 degrees)

Step-by-step explanation:

Angle F is the same measure as angle E, just like angle D is the same measure as G.

The measure of angle ∠E will be 62°. Then the correct option is D.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.

DEFG is an isosceles trapezoid.

Then the angle ∠E and ∠F will be congruent.

∠E = ∠F

∠E = 62°

Then the correct option is D.

More about the trapezium link is given below.

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Answer:

120 square centimeters

Step-by-step explanation:

The question says the formula already.

Area = bh

b = base length   b = 10

h = height length   h = 12

Area = 10 · 12

Area = 120 square centimeters

Answer: B. 120 square centimeters

Step-by-step explanation:

Given : The area of a parallelogram is found using the formula [tex]bh[/tex], where b represents the length of the base and h represents the length of the height.

Then , the area of a parallelogram that has a base of 10 centimeters and a height of 12 centimeters will be:-

[tex]\text{Area}=10\times12\\\\\Rightarrow\text{Area}=120\text{ square centimeters}[/tex]

Therefore , the area of the parallelogram = 120 square centimeters

[tex]\( 44 - 11 \)[/tex] factors to [tex]\( 33 \)[/tex] when using the greatest common factor method.

To factor the expression [tex]\( 44 - 11 \)[/tex] using the greatest common factor (GCF), we first need to find the GCF of the two numbers.

The numbers 44 and 11 have a common factor of 11.

Now, we can factor out 11 from both terms:

[tex]\( 44 - 11 = 11 \times (4 - 1) \)[/tex]

This simplifies to:

[tex]\( 44 - 11 = 11 \times 3 \)[/tex]

Finally, we calculate the product: [tex]\( 11 \times 3 = 33 \)[/tex]

So, the factored expression for [tex]\( 44 - 11 \)[/tex] using the GCF is [tex]\( 33 \)[/tex].

To summarize:

[tex]\( 44 - 11 = 11 \times (4 - 1) \)[/tex]

[tex]\( 44 - 11 = 11 \times 3 \)[/tex]

[tex]\( 44 - 11 = 33 \)[/tex]

Therefore, [tex]\( 44 - 11 \)[/tex] factors to [tex]\( 33 \)[/tex] when using the greatest common factor method.

Complete Question:

Factor the expression using the GCF. 44 - 11 = _____

The answer is 1/2.

2r = d.

Hope this helps!

A Radius Of The Circle Is Always Half The Diameter. This Means That The Radius Is Half Way Across A Circle.

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have m = -1/4 and the point (4, 5). Substitute:

[tex]y-5=-\dfrac{1}{4}(x-4)[/tex]

Answer:

The correct answer option is -7.

Step-by-step explanation:

We are asked to determine the minimum value of y on the graph of [tex]y = sin x - 6 [/tex].

[tex]y' = cos(x) = 0[/tex]

[tex]x = arccos(0) = \pm\frac{\pi }{2} +2k\pi[/tex] where 'k' is any integer.

So, [tex] y = sin ( \frac { \pi} { 2 } ) - 6 = 1 - 6 = -5 [/tex] (it is the absolute minimum value)

and [tex]y=sin(\frac{-\pi}{2}+2\pi )-6 = sin(\frac{3\pi}{2})-6 [/tex] = -7 (absolute minimum y value)

Answer:

The correct answer option is -7.

We are asked to determine the minimum value of y on the graph of . where 'k' is any integer.

So,  (it is the absolute minimum value)and  = -7 (absolute minimum y value)

Answer:

1320

Step-by-step explanation:

This is a simple permutation.

Since you start with 12 people and there are 3 winners, after every winner the number pf people available to win decrease.

First, there are 12 people, then after the first win there are 11 people, and after the 2nd win, for the third win the there are 10 people.

Thus, to find the total number of combinations, you multiply:

12*11*10=1320

Thus, there are 1320 possible combinations

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

What exactly does the question consist of

6(b+5) would be the factorization

3.25 • p = t

Or

p = t/3.25

Hope this helps!

The time it takes to print a number of photos can be shown as a proportionality relationship p = (78/24) * t, with p being the number of photos printed and t being time in seconds.

The relationship between the time (t) needed to print pictures and the number of pictures (p) printed by a photo printer can be represented by a simple proportionality relationship. This means that we can express this relationship as a rate. In this case, the printer prints 78 pictures in 24 seconds, so we can write the relationship as:

p / t =78/24

Or in other words:

p = (78/24) * t

This equation suggests that for any given unit of time t, you simply multiply t by the rate (78/24) to find the number of pictures p that can be printed in that time.

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Answer:

B. y+13=5(x+2)

Step-by-step explanation:

I personally do y=_+_(x-_) when solving these equations

Plug in -2 the x coordinate for (x- (-2) to be (x+3)

Plug in -13 for the y intercept.

5 from 5x is the slope.

Thus y=-13+5(x+3)

Then just move 13 to the other side

Answer:

(-6, -36)

Step-by-step explanation:

The vertex [tex](h,k)[/tex] of a function of the form [tex]f(x)=ax^2+bx+c[/tex] is given by the formula:

[tex]h=\frac{-b}{2a}[/tex]

[tex]k=f(h)[/tex] in other words, we find h and then evaluate function at h to find k.

We know from our function that [tex]a=1[/tex], [tex]b=12[/tex].

Replacing values

[tex]h=\frac{-12}{2(1)}[/tex]

[tex]h=-\frac{12}{2}[/tex]

[tex]h=-6[/tex]

Now we can evaluate our function at -6 to find k:

[tex]k=f(h)=f(-6)[/tex]

[tex]k=(-6)^2+12(-6)[/tex]

[tex]k=36-72[/tex]

[tex]k=-36[/tex]

We can conclude that the vertex (h, k) of our function is (-6, -36)

Answer:

(-6,-36)

Step-by-step explanation:

The given function is

[tex]f(x)=x^2+12x[/tex]

We complete the square to write this function in the vertex form.

Add and subtract the square of half the coefficient of x.

[tex]f(x)=x^2+12x+6^2-6^2[/tex]

[tex]f(x)=x^2+12x+36-36[/tex]

The first three terms is now a perfect square trionomial

[tex]f(x)=(x+6)^2-36[/tex]

Or

[tex]f(x)=(x--6)^2-36[/tex]

The function is now in the form:

[tex]f(x)=a(x-h)^2+k[/tex]

where h=-6 and k=-36

The vertex is therefore (h,k)=(-6,-36)

0.53 is 69.96 divided by132

Answer:

The answer is 0.53

ANSWER

The train is moving 82.5mi/hr

EXPLANATION

How fast the train is going is the same as the speed of the train:

The speed of the train is calculated using the formula,

[tex]Speed = \frac{distance}{time} [/tex]

[tex]Speed = \frac{330}{4} [/tex]

[tex]Speed = 82.5[/tex]

Therefore the train is moving 82.5mi/hr

The algebraic representation of the given statement is:

[tex]n^2 + (n + 1)^2 = 85[/tex]

Expanding and simplifying:

[tex]n^2 + (n^2 + 2n + 1) = 85[/tex]

[tex]2n^2 + 2n + 1 = 85[/tex]

[tex]2n^2 + 2n + 1 - 85 = 0[/tex]

[tex]2n^2 + 2n - 84 = 0[/tex]

Dividing the equation by 2 to simplify:

[tex]n^2 + n - 42 = 0[/tex]

Now, we can solve this quadratic equation using the quadratic formula:

[tex]n = [-b ± √(b^2 - 4ac)] / (2a)[/tex]

Where a = 1, b = 1, and c = -42:

n = [-(1) ± √((1)^2 - 4(1)(-42))] / (2(1))

n = [-1 ± √(1 + 168)] / 2

n = [-1 ± √169] / 2

n = [-1 ± 13] / 2

This yields two possible values for n:

n₁ = (-1 + 13) / 2 = 12 / 2 = 6

n₂ = (-1 - 13) / 2 = -14 / 2 = -7

Since n represents the smaller of the two consecutive integers, we discard the negative value.

Therefore, the smaller integer (n) is 6.

To solve this problem algebraically, we first translate the given statement into an equation. We know that the sum of the squares of two consecutive integers can be represented as[tex]n^2 + (n + 1)^2, v[/tex]where n is the smaller integer. Setting this expression equal to 85, we get the equation [tex]n^2 + (n + 1)^2 = 85.[/tex]

We then expand and simplify this equation to get a quadratic equation in standard form: [tex]2n^2 + 2n - 84 = 0.[/tex]

Next, we use the quadratic formula to solve for n, which gives us two possible values. Since we are looking for the smaller of the two consecutive integers, we discard the negative solution.

Thus, the smaller integer is n = 6.

Complete question:

The sum of the squares of two consecutive integers is 85. Using n to represent the smaller of the two consecutive integers, express this statement in algebraic form

For this case we have the following functions:

[tex]g (x) = 9 + 4x\\h (x) = \frac {x + 21} {5}[/tex]

We must find [tex](h * g) (x)[/tex]. By definition of composite functions we have to:

[tex](h * g) (x) = h (x) * g (x)[/tex]

So:

[tex](h * g) (x) = 9 + 4x * \frac {x + 21} {5}[/tex]

We apply distributive property:

[tex](h * g) (x) = \frac {9x + 9 * 21 + 4x ^ 2 + 4x * 21} {5}\\(h * g) (x) = \frac {9x + 189 + 4x ^ 2 + 84x} {5}\\(h * g) (x) = \frac {4x ^ 2 + 93x + 189} {5}\\[/tex]

Answer:

[tex](h * g) (x) = \frac {4x ^ 2 + 93x + 189} {5}[/tex]

Answer:

Do you need work shown?

Step-by-step explanation:

(I don't know where to comment here)

Answer:

(B) 132 in²

Step-by-step explanation:

Top Length = 3 + 8 + 3 = 14 in

Bottom Length = 8 in

Area of the trapezoid

= 1/2 (14 + 8) x 12

= 1/2 (22) (12)

= 132 in²

Answer:

B

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases.

here h = 12, a = AB = 8 and b = DC = 3+ 8 + 3 = 14

A = [tex]\frac{1}{2}[/tex] × 12 × (8 + 14) = 6 × 22 = 132 in² → B

Answer:

5/48

Step-by-step explanation:

Answer:

5/48

Step-by-step explanation:

Answer:

[tex]9 \cdot 10^6[/tex]

Step-by-step explanation:

A phone number contains 7 digits. How many different numbers can be made using the digits 0–9 if the first digit is not 0 and all of the digits can be repeated

In 7 digit phone number, the first number cannot be 0

So only 1  to 9 are used to get the first digit. 9 numbers can be used

other digits can use number from 0 to 9. 10 number can be used

So possible numbers can be made is

[tex]9 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10[/tex]

[tex]9 \cdot 10^6[/tex]

The correct option is C.[tex]\ 9 \times 10^6[/tex]

To solve the problem of finding how many different [tex]7[/tex]-digit phone numbers can be made using the digits [tex]0–9[/tex], with the first digit not being 0 and digits allowed to repeat, we can follow these steps:

1. First Digit Choices

The first digit has 9 possible choices ([tex]1[/tex] through [tex]9[/tex]) since it cannot be 0.

2. Remaining Digits Choices

Each of the remaining [tex]6[/tex] digits can be any of the [tex]10[/tex] digits ([tex]0[/tex] through [tex]9[/tex]).

So, the total number of different [tex]7[/tex]-digit phone numbers can be calculated by multiplying the number of choices for each digit:

[tex]\[9 \text{ choices for the first digit} \times 10 \text{ choices for each of the remaining 6 digits}\][/tex]

This can be represented mathematically as:

[tex]\[9 \times 10^6\][/tex]

Calculating [tex]\(10^6\)[/tex]

[tex]\[10^6 = 1,000,000\][/tex]

So,

[tex]\[9 \times 1,000,000 = 9,000,000\][/tex]

Multiplying two negative numbers would always give you a positive product

Example 1) -2 * -1 = 2

Example 2) -5 * -4 = 20

Example 3) -10 * -3 = 30

Simplify 6x/9 to 2x/3

2x/3(x + y)

Simplify

= 2x(x + y)/3

Answer: view image. its a proof (in red)

Step-by-step explanation:

Answer:

all real numbers

Step-by-step explanation:

first off let's convert the mixed fraction to improper fraction, and then do the division, since it was divided among all 6, he and 5 friends.

[tex]\bf \stackrel{mixed}{4\frac{4}{5}}\implies \cfrac{4\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{24}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{24}{5}\div 6\implies \cfrac{24}{5}\div \cfrac{6}{1}\implies \cfrac{24}{5}\cdot \cfrac{1}{6}\implies \cfrac{24}{6}\cdot \cfrac{1}{5}\implies \cfrac{4}{1}\cdot \cfrac{1}{5}\implies \cfrac{4}{5}[/tex]

Answer:

0.8 or 4/5

Step-by-step explanation:

4/5=.8 4.8/6=.8

3/6 because there are 6 sides and there are 3 numbers that you want to roll. They are even numbers so if you want to roll half of the numbers but not the other half well you have 3/6

Answer: $32.45

Step-by-step explanation:

Because....

55%  × 59 = $32.45

You could also write 55% as 0.55.

So it will look like this :

0.55 × 59 = 32.45.

It will still give you the same answer :)

* Hopefully tis helps:) Mark me the brainliest:)!!

Answer:

D

Step-by-step explanation:

Distribute the negative 1 in the second group.

[tex]5k^4*-1=-5k^4 \\ 5k^3*-1=-5k^3 \\ -k*-1=k[/tex]

Now add by combining like terms.

[tex]3k^4-5k^4=-2k^4 \\ -2k^3-5k^3=-7k^3 \\ k+k=2k[/tex]

[tex]-2k^4-7k^3+2k[/tex]

The answer is B. I just answered this question earlier!

Answer:

i need the ansrew too

Step-by-step explanation:

hehe