What is the slope of the line passing through the points (−1, 3) and (4, −7)?


−2

34

−43

2

Answer:10

Step-by-step explanation:

Since our assumption holds for all values between 6 and k, and we have shown it also holds for k+1, we can conclude by strong induction that it is possible to cut a square into n smaller squares for any n ≥ 6.

To prove this using strong induction, we will first establish a base case and then prove that if the statement holds true for any value k, then it also holds true for k+1.
Base Case: n = 6
Divide the square into four equal smaller squares by drawing two lines, one vertical and one horizontal, each passing through the center.

Then, divide one of these smaller squares into two equal rectangles by drawing a line parallel to the side.

We have now divided the original square into 6 smaller squares.
Inductive Step:
Assume the statement is true for all values n = 6, 7, ..., k,

where k ≥ 6.

We want to prove that the statement is true for n = k+1.
Consider a square that is divided into k smaller squares.

We will show that it is possible to divide this square into k+1 smaller squares.

Choose one of the k squares and label it S.

If S is a rectangle, divide it into two smaller squares by drawing a line parallel to the shorter side.

If S is a square, divide it into two equal rectangles by drawing a line through the center parallel to a side.
In either case, we have replaced one of the original k squares with two smaller squares, resulting in a total of k+1 squares.

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Answer:

B

Step-by-step explanation:

Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

The function with the steepest slope is \(y = 7x - 3\).

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

\(y = -8x + 5\)

Slope: -8

\(y - 9 = -2(x + 1)\)

Simplifying, we get \(y - 9 = -2x - 2\)

Rearranging, we have \(y = -2x + 7\)

Slope: -2

\(y = 7x - 3\)

Slope: 7

\(y + 2 = 6(x + 10)\)

Simplifying, we get \(y + 2 = 6x + 60\)

Rearranging, we have \(y = 6x + 58\)

Slope: 6

Therefore, the steepest slope is the \(y = 7x - 3\).

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Answer:

  LO ⊥ NM

Step-by-step explanation:

The HL theorem only applies to right triangles. The angles at O need to be shown to be right angles. You need to know that LO ⊥ NM.

y = 1/2x + 1 is the line's equation in slope-intercept form.

The equation of a line in slope intercept form is expressed as y = mx + b where:

m is the slope

b is the y-intercept

Given the following coordinate points (4, 3) and (0, 1), the slope is calculated as:

Slope = 1-3/0-4
Slope = -2/-4
Slope = 1/2

For the y-intercept, it is the point where the x-coordinate is zero, hence the y-intercept if (0, 1)

Determine the required equation
y = mx + b

y = 1/2x + 1

Hence the equation of the line in slope-intercept form is y = 1/2x +1

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A is the correct answer

X

Step-by-step explanation:

Multiply by reciprocal: \(\frac{x}{6} *\frac{6}{1} =\frac{6x}{6} =x\)

\( \Large{ \underline{\underline{ \tt{Required \: answer:}}}}\)

Here we have to simplify:

So, we know that:

Dividing a fraction by another fraction is the same as multiplying the fraction by the reciprocal (inverse) of the other.

By using this,

➝ \( \rm{ \dfrac{x}{6} \times 6}\)

➝ \( \rm{x}\)

The correct answer is Option (A)

Answer:

36.3636364%

or 36.36

Step-by-step explanation:

It will take Adrian 16 full months to save enough money for the electric keyboard.

- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.

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Answer:

it costs 12 cents per day.

Step-by-step explanation:

15 days cost $1.74

1 day then costs 1.74/15 = $0.116 ≈ $0.12

Answer:$24,000

Step-by-step explanation:12 times 2 percent of option 2 is $24,000

Answer:

of what thing we have to find probability

Answer: X =  -167/63 Y = -47/21

1/2x - 2/3y = 1/6

       +2/3y   +2/3y

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

1/2x           = 1/6 + 2/3y

(Divide both sides by 1/2)

x = 1/3 + 4/3y

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

(Now plug into other formula)

-2/5x + 3/10y = 7/18

-2/5(1/3 + 4/3y) + 3/10y = 7/18

-2/15 - 8/15y + 3/10y = 7/18

-2/15 - 7/30y = 7/18

+2/15               +2/15

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

         - 7/30y = 47/90

(Divide -7/30 on both sides)

y = -47/21

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

1/2x - 2/3(-47/21) = 1/6

1/2 x + 94/63 = 1/6

1/2x = -167/126

(Divide -167/126 on both sides)

x = -167/63

Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

Required Answers :

1. 2x + 4 = 10

\(\: :\implies \) 2x = 10 - 4

\(\: :\implies \) 2x = 6

\(\: :\implies \) x = 6/2

\(\: :\implies \) x = 3.

Hence, Option (A) x = 3 is the answer.

2. 25/5 × 7 = ?

\(\: :\implies \) 5 × 7

\(\: :\implies \) 175/5

\(\: :\implies \) 35

Hence, The required answer is 35.

3. 100 - 50 + 10 - 5 = ?

\(\: :\implies \) 50 + 5

\(\: :\implies \) 55

Hence, Option (A) 55 is the answer.

4. 24 / 6 = ?

\(\: :\implies \) 24 ÷ 6

\(\: :\implies \) 4

Hence, Option (A) 4 is the answer.

5. A triangle has base 6 inches and height 8 inches. What is the area?

Area of triangle = ½ × Base × Height

\(\: :\implies \) 1/2 × 6 × 8

\(\: :\implies \) 1/2 × 48

\(\: :\implies \) 48/2

\(\: :\implies \) 24 sq. in

Hence, Option (A) 24 sq in is the answer.

6. What is the greatest common factor of 36 and 56?

36 = 1,2,3,4,6,9,12, 18 and 36.

56 = 1,2,4,7,8,14,28 and 56.

Hence, Option (A) 4 is the answer.

7. What is the square root of 121?

\(\: :\implies \) 11 × 11

\(\: :\implies \) 121

Hence, (A) 11 is the answer

8. If 2x + 4 = 14, what is x?

\(\: :\implies \) 2x + 4 = 14

\(\: :\implies \) 2x = 14 - 4

\(\: :\implies \) 2x = 10

\(\: :\implies \) x = 10/2

\(\: :\implies \) x = 5

Hence, Option (A) 5 is the answer

9. (3x - 5) + (7x + 1) = ?

\(\: :\implies \) 3x - 5 + 7x + 1

\(\: :\implies \) 10x - 5 + 1

\(\: :\implies \) 10x - 4

Hence, Option (A) 10x - 4 is the answer.

10. What fraction is 5/12?

\(\: :\implies \) 1/2 (approximately)

Hence, Option (A) 1/2 is the answer.

Answer:

\(\pm i\sqrt{2}\text{ and } \pm i\)

Step-by-step explanation:

\(\text{let u = } x^2\) so then \(u^2=x^4\).

This gives you the equation: \(u^2+3u+2=0\).

Now factor the equation by looking for factors of 2 that add up to 3, which is just 2 and 1. Use these to rewrite the equation: \((u+2)(u+1)\). So now just set each factor equal to 0:

\(u+2=0\\u=-2\)

Now substitute x^2 back in as u

\(x^2=-2\)

Take the square root of both sides

\(x=\pm \sqrt{-2}\)

Separate the radical into sqrt(-1) * sqrt(2)

\(x=\pm \sqrt{-1}*\sqrt{2}\)

Rewrite using i

\(x=\pm i\sqrt{2}\)

Now set the other factor equal to 0

\(u+1=0\\u=-1\)

substitute x^2 back in as u

\(x^2=-1\)

Take the square root of both sides

\(x=\pm\sqrt{-1}\)

rewrite using i

\(x=\pm i\)

The average rate of change of life expectancy between the ages of 50 and 60 will be 0.88.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The graph on the right shows the remaining life expectancy, E, in years for females of age x.

Then the average rate of change is given as,

Average rate = (32.8 - 24) / (60 - 50)

Average rate = 8.8 / 10

Average rate = 0.88

The average rate of change of life expectancy between the ages of 50 and 60 will be 0.88.

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Answer:

There are 10 credits per semester.

Step-by-step explanation:

Given that: A college student takes the same number of credits each semester.

They had 8 credits when they started, and after 5 semesters, they had total 58 credits.

Now, In which rate they are earning credits per semester,

for that use the formula:

\(rate=\frac{change of credits}{total no of semeters}\)

rate=50/5

The change in credits is 58-8 = 50, since the

student earned 50 credits in 5 semesters.

So the rate at which they are earning credits per semester is:

Rate = 10 credits per semester.

Hence, there are 10 credits per semester.

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Answer:

A

Step-by-step explanation:

Becuase the proability of drawing a red marble is 10/20 or 50% and drawing a green marble is 4/20 or 20% and drawing a red marble is 6/20 or 30%

Answer: D. Up and to the right

Step-by-step explanation:

Answer:

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

Steps should be self-explanatory. Happy to explain if anything is not clear.

Answer:

Step-by-step explanation:

1) 4v + 7 = 7, for v?

→ 4v + 7 = 7

→ 4v = 7 - 7

→ v = 0/4

→ [ v = 0 ]

2) 3(u + 4) = 27, for u?

→ 3(u + 4) = 27

→ 3u + 12 = 27

→ 3u = 27 - 12

→ u = 15/3

→ [ u = 5 ]

3) -20 = 10(h + 5), for h?

→ -20 = 10(h + 5)

→ 10h + 50 = -20

→ 10h = -20 - 50

→ h = -70/10

→ [ h = -7 ]

4) -10 = (n - 52)/5, for n?

→ -10 = (n - 52)/5

→ n - 52 = -10 × 5

→ n = -50 + 52

→ [ n = 2 ]

5) (48/x) - 3 = 3, for x?

→ (48/x) - 3 = 3

→ 48/x = 3 + 3

→ 6x = 48

→ x = 48/6

→ [ x = 8 ]

6) 8r = 2r + 42, for r?

→ 8r = 2r + 42

→ 8r - 2r = 42

→ r = 42/6

→ [ r = 7 ]

These are required values.

Answer:

129 degrees

Step-by-step explanation:

When we add a right angle (90 degrees) to an acute 39 degree angle we get 129 degrees.

azb = 129 degrees

The ways to elect the candidates from the total is 462

From the question, we have

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 11 and r = 6

Substitute the known values in the above equation

Total = ¹¹C₆

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 11!/5!6!

Evaluate

Total = 462

Hence, the number of ways is 462

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Answer:

The correct option is (b).

Step-by-step explanation:

The solution of the given polynomial is :

\((-\dfrac{1}{3},4)\)

x = 1/3 and y = -4

i.e.

Sum of roots = (1/3-4) = -11/3

Product of roots = (1/3)(-4) = -4/3

The quadratic equation is as follows :

\(x^2+(\text{sum of roots})x+\text{Product of roots}=0\)

Put all the values,

\(x^2+\dfrac{-11}{3}x+\dfrac{-4}{3}=0\\\\3x^2-11x-4=0\)

So, the correct option is (b).