Please hurry and help me!

Answer:

Proof below

Step-by-step explanation:

Irrational and Rational Numbers

We need to use the basic property of logarithms:

[tex]log_b\ a=x\ \ \Rightarrow b^x=a[/tex]

We are given:

[tex]log_3\ 7[/tex]

And we will prove it's an irrational number, i.e., it's not a rational number.

Recall a rational number can always be expressed as a fraction a/b, where a and b are integer numbers. Thus, if the expression was a rational number, then:

[tex]\displaystyle log_3\ 7=\frac{a}{b}[/tex]

Applying the property:

[tex]\displaystyle 3^{\frac{a}{b}}=7[/tex]

Raising to the power of b:

[tex]3^a=7^b[/tex]

It's not possible to find two integers a and b that satisfy the condition above. That contradiction comes from the assumption that [tex]log_3\ 7[/tex] is rational, thus, it's proven [tex]log_3\ 7[/tex] is irrational.

Answer:

y=3x-7

Step-by-step explanation

Subtracted 3x, then divided by -1, made the 7 negative and the 3x positive

Answer:

20%

Step-by-step explanation:

Answer:

155

Step-by-step explanation:

Since the question states that;

Maximum heart rate= 220 - athletes age

If athletes age = 26 years

Maximum heart rate= 220 - 26 = 194

Again;

athlete's target heart rate= 80% × Maximum heart rate

Athlete's target heart rate= 0.8 × 194= 155

The missing part:

Make a model of probability showing the set of outcome and the probability value of each outcome.

Answer:

Step-by-step explanation:

From the given information:

a) From the word SANTA CLAUS, outcomes are all distinct letters.

This implies that the outcomes are S, A, N, T, C, L, U, S

For  S, N, T, C, L, U, S letters, each of them is repeated once.

Thus, their respective probability = [tex]\dfrac{1}{10}[/tex]

A is repeated thrice, so probability for A = [tex]\dfrac{3}{10 }[/tex]

Using the probability distribution table; we have the following.

outcome      S        A        N        T        C        L        U        S

probability   [tex]\dfrac{1}{10}[/tex]      [tex]\dfrac{3}{10 }[/tex]        [tex]\dfrac{1}{10}[/tex]      [tex]\dfrac{1}{10}[/tex]       [tex]\dfrac{1}{10}[/tex]      [tex]\dfrac{1}{10}[/tex]       [tex]\dfrac{1}{10}[/tex]       [tex]\dfrac{1}{10}[/tex]

Answer:

you're going to get an A

Step-by-step explanation:

.............

Answer:

[tex]H = (5,1)[/tex]

Step-by-step explanation:

The attachment is not clear. However, the points of G and F are:

[tex]F = (3, 2)[/tex]

[tex]G = (4, 4)[/tex]

And the options are:

[tex]A.\ (1, 2) \\ B. (4, 2)\\ C. (5, 1) \\ D. (2, 5)[/tex]

Required

Determine the coordinates of H

This question will be solved using distance formula, D

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Since F is equidistant of G and H, the formula can be represented as:

[tex]D = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}[/tex] and

[tex]D = \sqrt{(x_1 - x)^2 + (y_1 - y)^2}[/tex]

Where:

[tex](x_1,y_1) = (4,4)[/tex]

[tex](x,y) = (3,2)[/tex]

[tex]H = (x_2,y_2)[/tex]

Substitute values for x , y , x2 and y2 in [tex]D = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}[/tex]

[tex]D = \sqrt{(x_2 - 3)^2 + (y_2 - 2)^2}[/tex]

Square both sides:

[tex]D^2 = (x_2 - 3)^2 + (y_2 - 2)^2[/tex]

Substitute values for x , y , x1 and y1 in [tex]D = \sqrt{(x_1 - x)^2 + (y_1 - y)^2}[/tex]

[tex]D = \sqrt{(4 - 3)^2 + (4 - 2)^2}[/tex]

Square both sides:

[tex]D^2 = (4 - 3)^2 + (4 - 2)^2[/tex]

[tex]D^2 = (1)^2 + (2)^2[/tex]

[tex]D^2 = 1 + 4[/tex]

[tex]D^2 = 5[/tex]

Substitute 5 for D^2 in [tex]D^2 = (x_2 - 3)^2 + (y_2 - 2)^2[/tex]

[tex]5 = (x_2 - 3)^2 + (y_2 - 2)^2[/tex]

From the list of given options, the values of x and y that satisfy the above condition is: (5,1)

This is shown below

[tex]5 = (5-3)^2 + (1-2)^2[/tex]

[tex]5 = (2)^2 + (-1)^2[/tex]

[tex]5 = 4 + 1[/tex]

[tex]5 = 5[/tex]

Other options do not satisfy this condition. Hence, the coordinates of H is:

[tex]H = (5,1)[/tex]

Answer:

y = -0.8x - 5

Step-by-step explanation:

x1 = (XA + XB) / 2 = -5

y1 = (YA + YB) / 2 = -1

m = (XA - XB) / (YA - YB) = -0

__________________________________________

(y - -1) = -0.8(x - -5)

y - -1 = -0.8x - 4

y = -0.8x - 4 + -1

y = -0.8x - 5

Answer:

The third book cost $9.03

Step-by-step explanation:

Answer:

the 3rd book is 9.03

Step-by-step explanation:

all you have to do is add 8.33 + 7.33 and thate 15.66 so 24.69 - 15.66 is 9.03

Answer:

3:5

Step-by-step explanation:

There are 3 red marbles

5 blue marbles

SO

3:5

Answer:  3:5

Step-by-step explanation:

There are 3 red marbles and 5 blues marbles so the ratio of red marbles to blue marbles will be     3:5   or  3 to 5,  or 3/5

Answer:

see explanation

Step-by-step explanation:

The area (A) of a sector is calculated as

A = area of circe × fraction of circle

   = πr² × [tex]\frac{0}{360}[/tex] ← where θ is in degrees

[ note that 360° = 2π radians ], then

A = πr² × [tex]\frac{0}{2\pi }[/tex] ← where θ is in radians

( Cancel π on numerator/ denominator )

A = [tex]\frac{1}{2}[/tex]θr²

9514 1404 393

Answer:

  top down: 2, 4, 1, 7, 6, 5, 3, 8

Step-by-step explanation:

It appears the expected order may be ...

__

Write the formula for a sector area of a circle with central angle, θ, in degrees.

  [tex]\textit{Area of a Sector}=\dfrac{\theta}{360^{\circ}}\cdot\pi r^2[/tex]

Replace 360° with 2π radians.

  [tex]\dfrac{\theta}{360^{\circ}}=\dfrac{\theta}{2\pi}[/tex]

Replace the angle ratio in degrees with the angle ratio in radians.

  [tex]\textit{Area of a Sector}=\dfrac{\theta}{2\pi}\cdot\pi r^2[/tex]

Simplify by cancelling

  [tex]\textit{Area of a Sector}=\dfrac{1}{2}\theta r^2[/tex]

Answer:

32 ounces

Step-by-step explanation:

[tex]M_{1} v_1=M_2v_2\\(0.10)80=(0.25)x\\(1/0.25) (0.10)80=(0.25)x(1 /0.25)\\\frac{(0.10)80}{0.25} =32 ounces[/tex]

Answer:

You are 8 rungs on top of the ladder

Step-by-step explanation:

0 + 3 - 5 + 10 = 8

Answer:

0, 1/13, 49/100, 1/2, 11/20, 8/9, 1

Step-by-step explanation:

You know the smallest is 0, largest is 1

the middle is 1/2

49/100 is slightly smaller than 1/2 or 50/100

11/20 is slightly larger than 1/2 or 10/20

1/13 is slightly larger than 0

8/9 is slightly smaller than 1

please give thanks :)

and brainliest :)

Answer:

D.  y = -6x + 38

Step-by-step explanation:

Equation of a sequence

We are given the following sequence of numbers corresponding to the positions x={1,2,3,4,5,...}

y={32,26,20,14,8....}

To find the equation of the sequence, we must recall the general term of a sequence is:

[tex]a_x=a_1+(x-1).r[/tex]

Where r is the common difference between two consecutive terms, an and a1 are the x-th and the first terms respectively.

We can find the value of r by subtracting any pair of consecutive terms:

r = 26-32 = 20-26 = 14-20 = -6

Now we apply the formula:

y=32+(x-1).(-6)

Operating:

y=32-6x+6

y = -6x + 38

Answer:

D.   y = -6x + 38

Answer: c

Step-by-step explanation:

Answer:

B you add 4. a negative plus a positive is a negative. -15 +4 is -11

Answer:

14

Step-by-step explanation:

Answer:

heyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Answer:

52

Step-by-step explanation:

angle R is a right angle which is 90°

if you add angle S and angle R you get angle PQS because sum of two opposite interior angle is equal to it's exterior angle

34°+90°=x+72°

124°=x+72°

x=124°-72°

x=52°

Step-by-step explanation:

850 calls

1000:100=10

1%=10

10×85=850

Discount is the reduction in value. The total number of calls not answered this is 150 calls

Given the following

Total number of calls = 1000 calls

If 15% of those calls were not answered, the total calls that were not answered is given as:

Total call not answered . = 0.15 * 1000

Total call not answered = 150 calls

Hence the total number of calls not answered this is 150 calls

Learn more on percentages here: https://brainly.com/question/24304697

#SPJ2

Answer:

m<G=60 degrees.

equilateral or equiangularTriangle

Step-by-step explanation:

triangle is 180 degrees

all these angles are congruent

means they all equal the same

180/3=60

Answer:

3) 146 degrees

4) 471 degrees

5) x = 100 and 3x = 300

Step-by-step explanation:

all three are polygons whose sum of all interior angles can be found by using the formula (n - 2)*180 where 'n' refers to the number of sides

In #3 and 5 there are 5 sides, so (5 - 2)*180 = 3(180) giving a total of 540 degrees. Add all known angles and deduct from 540.

#4 has 7 sides, so (7 - 2)*180 = 1260 degrees. Add all known angles and deduct sum from 1260.

#5 Add all integers plus 'x' + '2x' to get 240 + 3x = 540

Answer:

-90%

Step-by-step explanation:

Answer:

No the school libary doesn not have enough pace for all the books. If the least amount of books came which is 15 books in all of 42 boxes (15*42), it would be 630 books and the school libary shelf can only hold 600 books becuase 10 shelves * 60 books on each shelf is 10*60 which is 600. If the least amount of books can’t even fit then the others wold defietnly not fit.

Answer:

The answer is 11 Units

Answer:

12

Step-by-step explanation:

base*height=6*2

6*2=12

Answer:

Step-by-step explanation:

Compound inequality has been given as,

12(2x - 10) + 24 ≥ 48 Or 6x + 15 - 9x ≥ 6

By simplifying it further,

12(2x - 10) + 24 ≥ 48

[tex]\frac{12(2x - 10)}{12}+\frac{24}{12}\geq \frac{48}{12}[/tex]

(2x - 10) + 2 ≥ 4

(2x - 10) + 2 - 2 ≥ 4 - 2

2x - 10 ≥ 2

2x - 10 + 10 ≥ 2 + 10

2x ≥ 12

[tex]\frac{2x}{2}\geq \frac{12}{2}[/tex]

x ≥ 6

6x + 15 - 9x ≥ 6

(6x - 9x) + 15 ≥ 6

(-3x) + 15 ≥ 6

-3x + 15 - 15 ≥ 6 - 15

-3x ≥ -9

3x ≤ 9

x ≤ 3

We have to plot the inequality on a number line

x ≥ 6 Or x ≤ 3