Convert the equations into slope intercept form,

then identify the slope and y-intercept.


1. -x + y = 3

m=

b=

2. -4x + 2y = 6

m=

b=

3. 2x + =3

m=

b=

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &27080\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=\textit{elapsed time}\dotfill &5\\ \end{cases} \\\\\\ A=27080(1+0.03)^5\implies A=27080(1.03)^5\implies A\approx 31393\)

The user base of the new social media after 5 months will be 31,393.

Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.

It is given by the formula,

\(A = P(1+r)^n\)

where, A is the value after t period of time, and,

r is the rate of interest.

As it is given that the user of the social media site is increasing by approximately 3% per month. Therefore, the user will be compounding per month. Thus, the user base after 5 months will be,

\(\text{Number of User} = \text{(Current user base)} \times (1+r)^t\)

\(\text{Number of User} = 27,080 \times (1+0.03)^5\)

\(\text{Number of User} = 27,080 \times (1+0.03)^5 = 31,393.1419 \approx 31,393\)

Hence, the user base of the new social media after 5 months will be 31,393.

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In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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Answer:

115 feet below surface

Step-by-step explanation:

The starting depth of the submarine is 75 feet. Multiply 8ft.*5 to then get 40ft. Add 75ft to 40ft to get 115 ft.

Step-by-step explanation:

The given equation is :

2x+7y=11

We need to tell the point (-5,3) lies on the graph of the above equation of not.

Put x = -5 and y = 3 in the LHS of the above equation.

LHS = 2x+7y

= 2(-5)+7(3)

= -10 +21

= 11

It means, when we put  x = -5 and y = 3 in the above equation, we get 11. Hence, (-5,3) lies on the graph of the equation.

Answers:

8

6

1

3

Reason:

Add 5 to each value in the f(x) column.

Example: 3+5 = 8 for the first row.

This will shift each point 5 units up. This is because we're moving 5 units up the y axis.

The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

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

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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The simplest radical form of the sine of y/2 is:

sin(y/2) = ±√(2/5)

Here we know that:

cos(y) = 1/5.

We want to find  sin(y/2), so we can use the identity:

sin(y/2) = ±√( ( 1 - cos(y))/2)

Replacing cos(y) there we will get.

sin(y/2) = ±√( ( 1 - 1/5)/2)

sin(y/2) = ±√( ( 4/5/2)

sin(y/2) = ±√(2/5)

That is the simplest radical form.

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Answer:

56 units

Step-by-step explanation:

add all numbers then divide by 5

30+45+50+75+80 = 280

280/5 = 56

Answer:

-1.33333 < x

Step-by-step explanation:

subtract 5 from both sides

get -4<3x

divde 3 by both sides

-1.33< x

Hi, there!

 _______

The first step is:

» Subtract both sides by 5

\(\sf{-4 < 3x}\)

Now divide each term by 3:

\(\sf{-\dfrac{4}{3} < x}\)

We can flip it over:

\(\sf{x > -\dfrac{4}{3}}\)

Hope the answer - and explanation - made sense,

happy studying!!

The rectangle's circumference is 27+ (3/2) fee and one of its sides is a semicircle.

We can start by finding the perimeter of the rectangle, which is simply the sum of the lengths of all four sides:

Perimeter of rectangle = 2(length + width) = 2(12 + 3) = 30 feet

Next, we need to find the perimeter of the semicircle.

The diameter of the semicircle is equal to the width of the rectangle, which is 3 feet. The formula for the perimeter of a semicircle is:

Perimeter of semicircle = (π/2) x diameter + diameter

Plugging in the values, we get:

Perimeter of semicircle = (π/2) x 3 + 3 = (3/2)π + 3

Now, we can add the perimeter of the semicircle to the perimeter of the rectangle to get the total perimeter:

Total perimeter = Perimeter of rectangle + Perimeter of the semicircle- 2*diameter of the semicircle

= 30 + (3/2)π + 3 - 3*2

= 27+ (3/2)π

Therefore, the perimeter of the rectangle with a semicircle on one side is 27+ (3/2)π feet, or approximately 31.71 feet (rounded to two decimal places).

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Answer:

1105km

Step-by-step explanation:

d=s×t

=65kmh^-1×7

=1105km

Answer:

bugo.ka pag answer bobo ka bah ha wag kanang umasa dito piste ka

Both lines are parallel to each other, so it has no any intersection point.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 8x +10y =14   .. (i)

⇒ 4x + 5y = 4   .. (ii)

Now, By multiply by 2 in equation (ii), we get;

⇒ 2 (4x + 5y) = 4 × 2

⇒ 8x + 10y = 8  .. (iii)

Hence, By equation (i) and (iii), we get;

The both equations are parallel to each other and it has no solution.

Hence, It can never intersect each other at any point.

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The exact values of the sine and the cosine of the half angle are √(3 / 10) and √(7 / 10), respectively.

Herein we know the exact value of the cosine of an angle set in the first quadrant. Then, the half angle is also in the first quadrant, whose sine and cosine are, respectively:

cos 0.5Ф > 0, sin 0.5Ф > 0

sin 0.5Ф = √[(1 - cos 0.5Ф) / 2]

cos 0.5Ф = √[(1 + cos 0.5Ф) / 2]

First, replace the values of the cosine of the half angle:

sin 0.5Ф = √[(1 - 2 / 5) / 2]

cos 0.5Ф = √[(1 + 2 / 5) / 2]

Second, simplify the resulting expression:

sin 0.5Ф = √[(1 - 2 / 5) / 2]

sin 0.5Ф = √[(3 / 5) / 2]

sin 0.5Ф = √(3 / 10)

cos 0.5Ф = √[(1 + 2 / 5) / 2]

cos 0.5Ф = √[(7 / 5) / 2]

cos 0.5Ф = √(7 / 10)

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Answer:

vertically opposite angles and alternate pair

so by aa similarity they are similar

Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Answer:

1/12

Step-by-step explanation:

Answer:

Awwww ty <3

You are too nice lollllllllllllll

Step-by-step explanation:

Answer:

His son is 3 years old.

Step-by-step explanation:

33 years old ... 3 less than ....  =  36

36/12  =  3

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

The half life is the amount of time it takes a substance to decay to half of its original amount.

Since the radioactive substance has a half life of 1000 years, there will be half of it left after 1000 years.

So, the fraction that will be left after 1000 years is \(\frac{1}{2}\)

Answer:

1/2

Step-by-step explanation:

so if u do the waffalineneh times by arcimate it would equivently be the answer on top

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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Answer:

he is the number of people

Answer:

56

Step-by-step explanation:

Ration of the no. of women to men = 4 : 5

= 4x + 5x = 126

= 9x = 126 = 14

Thus no. of women = 4 × x = 4 × 14 = 56

Answer:

12

Step-by-step explanation:

P = is you add Length (L) plus Legnth (L) plus Width (W) plus Width (W)

4+4+2+2

The percentage of women with weights that are within the limits is:

60.93%

Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:

z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74

z-score for upper limit = (217 - 168.7) / 48.8 = 0.99

Next, we can use a z-table to find the corresponding probabilities for these z-scores:

Probability for lower limit = 0.2296

Probability for upper limit = 0.8389

Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093

Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.

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Answer: 1134.11

A=3.14*r^2

Step-by-step explanation:

Answer:

a ≈ 1134.11 cm2

Step-by-step explanation:

The formula:

\(a=\pi r^{2}\)

\(a=\pi (19)^{2} =361\pi\)

\(a=1134.11cm^{2}\)

Hope this helps

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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