Pablo generates the function f(x) = 3/2 {5/2} ^ x-1 to determine the xth number in a sequence.

Answer:

see explanation

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2)

m = [tex]\frac{2+6}{0-4}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2

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Find the midpoint using the midpoint formula

M =( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

    = [tex]\frac{4+0}{2}[/tex] , [tex]\frac{-6+2}{2}[/tex] ) = (2, - 2 )

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Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

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The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{1}{2}[/tex] , thus

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (2, - 2) into the partial equation

- 2 = 1 + c ⇒ c = - 2 - 1 = - 3

y = [tex]\frac{1}{2}[/tex] x - 3 ← equation of perpendicular bisector

Answer:

Step-by-step explanation:

Points given: (4, -6) and (0, 2)

Slope intercept form of the line going through the given pints:

y= mx+b

y= -2x+b ⇒ -6= -2*4+b ⇒ b= 8-6= 2 ⇒ y= -2x+2

The slope of the perpendicular bisector is the negative reciprocal of the line segment which it is dividing:

Equation of perpendicular bisector:

It passes through the mid point: (2, -2), so

So the equation of perpendicular line:

Answer:

(5, 1/2)

Step-by-step explanation:

To find the midpoint

Take the sum of the x coordinates and divide by 2

(5+5)/2 = 10/2 = 5

Take the sum of the y coordinates and divide by 2

(4+-3)/2 = 1/2 = 1/2

The midpoint is ( 5, 1/2)

It is answer D

Its is exactly in between these to values

Answer:

The Answer is 5

Step-by-step explanation:

Divide the 5% of Spanish by 40% male:

0.05 / 0.40 = 0.125

Change to a percent by multiplying by 100:

0.125 x 100 = 12.5%

The answer is a. 12.5%

The probability of the student studying Spanish, if you know the students male will be 12.5%.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that in a certain group of students, the probability of a randomly chosen student being male is 40%, the probability of the students studying Spanish is 18%, and the probability of the student being male who studies Spanish is 5%.

The probability of the student studying Spanish, if you know the student male will be calculated as below:-

Divide the 5% of Spanish by 40% of males:

0.05 / 0.40 = 0.125

Change to a percent by multiplying by 100:

0.125 x 100 = 12.5%

Therefore, the probability of the student studying Spanish, if you know the students male will be 12.5%.

To know more about probability follow

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Answer:

0.35 is less than 0.37 because 35 < 37.

Answer:

C is the correct answer

Step-by-step explanation:

Answer:

8x^2 + 45/5x

Step-by-step explanation:

write the division as a fraction

3x+ 1/x + 8/x - 7/5x

using a=a/1, convert the expression into a fraction

3x/1 - 7/5x

calculate the product

3x/1 - 7x/5

expand the fraction to get the least common denominator

5 x 3x/ 5 x 1   -  7x/5

multiply the numbers

15x/5   -   7x/5

write all numerators above the common denominator

15x - 7x/5

collect like terms

8x/5

write the factor as a product

8/5 x + 1/x + 8/x

calculate the product

8x/5 + 5 x 1/5x + 5 x 8/5x

expand the fraction to get the least common denominator

X  x  8x/X  x  5 + 5/5x + 5 x 8/5x

multiply the numbers

X  x  8x/X  x  5 + 5/5x + 40/5x

calculate the product

8x^2/5x + 5/5x +40/5x

write all numerators above the common denominator

8x^2 + 5 + 40/5x

add the numbers and that's the answer

8x^2 + 45/5x

(that was l o n g)

Answer:

405 students

Step-by-step explanation:

1=teachers

9=students

1=45 teachers

9=y students

 y=9 x 45

 y=405 students

9514 1404 393

Answer:

Step-by-step explanation:

1. x +4y = 3.5 . . . . variables are defined in the problem statement

  2x +2y = 4

__

2. Subtract half the second equation from the first.

  (x +4y) -(1/2)(2x +2y) = (3.5) -(1/2)(4)

  3y = 1.5

  y = 0.5

  x = 2 -y = 1.5

The distance from home is 1.5 miles; the distance around the track is 0.5 miles.

__

3. 2x +6y = 2(1.5) +6(0.5) = 3+3 = 6

Avi walked 6 miles on Saturday.

__

4. 2p ≥ 2.5 . . . . variables are defined in the problem statement

  p +q < 3

__

5. No.

  2 + 1 < 3 is NOT TRUE

Answer: 3

Step-by-step explanation:

A simple way to calculate the distance between numbers on a number line is to count every number between them. A faster way is to find the distance by taking the absolute value of the difference of those numbers. We have to find PQ. TAking the difference we have 94-91= 3.

Answer:

[tex]3[/tex]

Step-by-step explanation:

You can find the length by subtracting.

[tex]Q-P[/tex]

[tex]94-91[/tex]

[tex]=3[/tex]

You can also find the length by counting the units of the distance covered between the points.

Answer:

[tex]q=\frac{1}{6}p- \frac{1}{2}r[/tex]

Step-by-step explanation:

[tex]p=3(2q+r)[/tex]

[tex]2q+r=\frac{p}{3}[/tex]

[tex]2q=\frac{p}{3} -r[/tex]

[tex]q=\frac{p}{6}- \frac{r}{2}[/tex]

Answer:

[tex] - \frac{11}{28} [/tex]

Step-by-step explanation:

[tex] \frac{2}{5} \bigg( - \frac{3}{7} \bigg) - \frac{1}{6} \times \frac{3}{2} + \frac{1}{14} \times \frac{2}{5} \\ \\

= - \frac{6}{35} - \frac{3}{12} + \frac{1}{35} \\ \\

= \frac{1 - 6}{35} - \frac{1}{4} \\ \\

= \frac{ - 5}{35} - \frac{1}{4} \\ \\

= \frac{ - 1}{7} - \frac{1}{4} \\ \\

= \frac{ - 1\times 4-1\times 7}{7\times 4} \\\\

= \frac{ - 4- 7}{28} \\\\

= -\frac{ 11}{28} \\\\

[/tex]

Answer:

B

Step-by-step explanation:

If the ratio of the length of the chalkboard to the width is 4:3, this means that the length of this one is 7* 4/3=28/3. This can be rewritten as approximately 9.33 inches, or answer choice B. Hope this helps!

Answer:

C

Step-by-step explanation:

C goes past -1 and almost reaches -2 so you know it will include some sort of fraction.

If you count the tick marks, C is on the 7th tick mark which is the one before -2. This represents 7/8 because 8/8 would be right on -2.

So, C shows -1 and 7/8

Answer:

Because the process by itself will force the numbers to be eventually reduced to an even number whose half is always another even number. For example, if you start taking the number 3, the result will be 10; then, the result of 10 will be 5; then, the result will be 16. When you get 16, the result will be 8, then 4, then 2 and finally 1.

Step-by-step explanation:

Answer:

Most definitely reciprocal

Answer:

2:52 or 1:26 (simplest form)probability.

Answer:

9.6 = BC

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opposite/ adjacent

tan 58 = BC / 6

Multiply each side by 6

6 tan 58 = BC

9.602007174 =BC

Round to the nearest tenth

9.6 = BC

Answer:

BC= 9.6

Hope it helps :)

Answer:

2x≤12

2x/2 ≤12/2

x≤6

therefore x=6

x+x

6+6=12

Answer:

No

Mean diameter = 44, which is in the 40 - 44 cm group

Step-by-step explanation:

Given the data:

Diameter (cm) - mid point(X) - frequency(F) - - FX

35-39 - - - - 37 - - - - 8 - - 296

40-44 - - - 42 - - - 10 - - - 420

45-49 - - - 47 - - - 13 - - - 611

50-54 - - - 52 - - - 3 - - - 156

55-59 - - - 57 - - - 1 - - - 57

Mean of grouped data:

Sum of (F × X) / sum of F

1540 / 35 = 44

Answer:

The distance when x = 6km is D = 498 KM

Step-by-step explanation:

Here, given the formula for the distance, we want to find the distance D given the value of x to be 6km

What we do simply here is to substitute the value 6km as x in the equation

The equation is

D = 4x^3 - 10x^2 -6

Substituting x = 6, we have

D = 4(6^3) -10(6^2) -6

D = 864-360-6

D = 498 km

Answer:

Step-by-step explanation:

A kite is a quadrilateral made up of two isosceles triangles. A kite does not have any parallel side, but has two pairs of equal adjacent sides. All four sides are not congruent, only two pairs of consecutive sides are congruent.

The vertices of a kite are right angles. The diagonals bisect each other at right angles ( that is they are perpendicular). Therefore the following are true:

1) two pairs of consecutive sides are congruent

2) The diagonals are perpendicular

3) The diagonals bisect each other.

Point A= (3,6), B = (5,0), C= (-2,-4) D = (-3,4)

[tex]AB=\sqrt{(0-6)^2+(5-3)^2}=\sqrt{40} \\AD=\sqrt{(4-2)^2+(-3-3)^2}=\sqrt{40}\\ BC=\sqrt{(-4-0)^2+(-2-5)^2}=\sqrt{65}\\ DC=\sqrt{(4-(-4)^2)+(-3-(-2))^2}=\sqrt{65}[/tex]

AB=AD, BC = BC.

This is a kite since two pairs of consecutive sides are congruent

it's true...........

Answer:

False

Step-by-step explanation:

Verified correct with test results.

Answer:

2a(5a+3b)(5a−3b)

Step-by-step explanation:

Both terms have 2a, so take out the 2a and you will get your answer.

Answer:

2a(5a - 3b)(5a + 3b)

Step-by-step explanation:

50a³ - 18ab² = 2a(25a² - 9b²) = 2a(5a - 3b)(5a + 3b)

Question:

The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour

Answer: 13 dollars per hour

Step-by-step explanation:

The rate of change (ROC) for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :

Point a = (5, 65) = (x2, y2)

Point b = (2, 26) = (x1, y1)

Calculating the gradient or slope :

Rate of change = (y2 - y1) / (x2 - x1)

Rate of change = (65 - 26) / (5 - 2)

Rate of change = 39 / 3

= 13 dollars per hour

Answer:

I think that the answer is D

Answer:

30,19

Step-by-step explanation:

let the numbers be x and y,x>y

x+y=49

x-y=11

add

2x=60

x=60/2=30

30+y=49

y=49-30=19

Answer:

x = first number = 30 and y = second number = 19

Step-by-step explanation:

let the first number be x and second number be y.

According to the given information

The sum of the two numbers is 49

Here, we get the equation.

x + y = 49

Now, Similarly second given information

the difference is 11.

Here, we get the equation.

x - y = 11

Now,

Step 1:

Name the equations

x + y = 49 ...(1)

x - y = 11 ...(2)

Step 2:

Now,

From equation (1) we get,

x = 49 - y

Substitute the value of x = 49 - y in equation (2) we get,

x - y = 11

i.e.,

49 - y - y = 11

49 - 2y = 11

-2y + 49 = 11

2y - 49 = - 11

2y = 49 - 11

2y = 38

y = 38/2

y = 19

Step 3:

Now,

Put the value of y = 19 in equation (1), we get.

x + y = 49

i.e.,

x + 19 = 49

x = 49 - 19

x = 30

Thus, The value of x = first number = 30 and y = second number = 19

30 + 19 = 49

30 - 19 = 11

Answer:

$24000

Step-by-step explanation:

Let the full advertising budget of the company be $x.

Therefore, 30% of x = $7,200

[tex]\frac{30}{100} \times x= 7200 \\\\x = \frac{100}{30} \times 7200\\\\x = 100 \times 240\\\\x = \$24000[/tex]

Hence, full advertising budget of the company is $24000.

Answer:

4^15

Step-by-step explanation:

(4^3)^5

We know a^b^c = a^(b*c)

(4^3)^5 = 4^(3*5) = 4^15

Answer:

[tex] {4}^{15} [/tex]

Answer B is correct

Step-by-step explanation:

[tex]( { {4}^{3} })^{5} \\ {4}^{3 \times 5} \\ = {4}^{15} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

$512

Step-by-step explanation:

His bank account started at a balance of $124.

He wrote a check, which decreased his balance by $147. His new balance is:

124 - 147 = -$23

Jeremy was then charged an overdraft fee, decreasing his balance by $32. That is:

-23 - 32 = -$55

He deposited a paycheck, which increased his balance by $567. His account balance will become:

-55 + 567 = $512

His account balance after those transactions is $512.