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The system of conics has two solutions.

(x−1)2+(y+4)2=25(x−1)225+(y+4)2100=1

What are the solutions to this system of conics?

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The solution set of the inequality 2 · x² + 5 · x - 3 > 0 is (- ∞, - 3) ∪ (1 / 2, + ∞).

Herein we find a quadratic inequality, whose solution set can be found by factoring the expression and determine the interval where the expression is greater than zero. Initially, we use the quadratic formula to determine the roots of the quadratic function:

2 · x² + 5 · x - 3 = 0

x₁₂ = [- 5 ± √[5² - 4 · 2 · (- 3)]] / (2 · 2)

x₁₂ = (- 5 ± 7) / 4

x₁ = 1 / 2, x₂ = - 3

Then, the factored form of the inequality is:

(x - 1 / 2) · (x + 3) > 0

In accordance with the law of signs, we must look for that intervals such that: (i) (x - 1 / 2) > 0, (ii) (x + 3) > 0, (ii) (x - 1 / 2) < 0, (x + 3) < 0. Then, the solution set of the quadratic inequality is:

Inequality form - x > 1 / 2 ∨ x < - 3

Interval form - (- ∞, - 3) ∪ (1 / 2, + ∞)

The solution set of the inequality is (- ∞, - 3) ∪ (1 / 2, + ∞).

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We have the following equation:

We want to rewrite it in a way 'C' is a function of 'r'. We can accomplish that, if we divide both sides by 2pi.

From this, we have our result.

Given the ordered pairs:

(-12, -16), (-3, -4), (0, 0), (9, 12)

Let's say that the first coordinate corresponds to x, and the second one corresponds to y. Then, the constant of variation k relates x and y as:

Using the ordered pairs:

We conclude that the constant of variation is:

Given that a box is 12 inches long 8 inches wide and 2 inches high, the area of wrapping paper needed to wrap the gift box​ is equal to the total surface area of the box.

The total surface area of the box can be calculated using the formula;

In this problem

we have an exponential growth function

where

a=2500 ----> initial value of the number of referrals at the start of the model

b=1.50 ---> the base of the exponential function (growth factor of the number of referrals each year

therefore

The answer Part 1 is the last option

Part 2

Find out the annual percent increase

we know that

b=1+r

b=1.50

1.50=1+r

r=1.50-1

r=0.50

therefore

r=50%

The value of (f+g)(x) from the given functions is 4x³+x²+5x+2.

The given functions are f(x)=4x²+ 5x - 3 and g(x)=4x³ - 3x² + 5.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Now, (f+g)(x)=f(x)+g(x)

= 4x²+ 5x - 3+4x³ - 3x² + 5

= 4x³+4x²- 3x²+5x+5-3

= 4x³+x²+5x+2

Therefore, the value of (f+g)(x) from the given functions is 4x³+x²+5x+2.

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Expanding the expression,

We get that:

Given:

y is inversely proportional to square of x.

The equation is written as,

Also y = 0.25 when x = 5.

So, the equation of y interms of x is,

When x increases,

Hence, the value of x increases then y decreases.

Answer:

Step-by-step explanation:

What we know:

m = 4, b = -5

y = mx + b where m is the gradient/slope and b is the y-intercept

Substitute m and b values:

y = 4x + -5 which is the same as y = 4x - 5

Substitute all x values to find y coordinate:

When x = -7, y = (4 x -7) - 5 = -33

When x = -6, y = (4 x -6) - 5 = -29

When x = -5, y = …

Continue for all x values

The given equation is-

If we multiply the equation by 6, we would have the same value for the variable x since we are multiplying the same number on each side. So, the second choice is an equivalent equation to the given one.

Let's multiply by 6.

So, the third expression is also an equivalent expression.

Then, let's subtract 4 on each side.

The last choice is also an equivalent expression.

Recall that the numbers in a die are 1,2,3,4,5,6.

Hence the number of possible outcomes is 6.

We need a number less than 3. Let A be this event.

The favorable outcome is 2.

Since there are 1,2 less than 3 in a die.

Substitute n(A)=2 and n(S)=6, we get

Hence the required probability is 0.333.

Step-by-step explanation:

we have the 2 numbers x and (x+2).

x × (x + 2) = 143

x² + 2x = 143

x² + 2x - 143 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case this is

x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =

= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =

= (-2 ± 24)/2 = (-1 ± 12)

x1 = -1 + 12 = 11

x2 = -1 - 12 = -13

so, we have 2 solutions : 11 and 13, -13 and -11

11× 13 = 143

-11×-13 = 143

Given:

Required:

We need to find the points are included in the solution

Explanation:

Recall that the solution of the system of inequalities is the intersection region of all the solutions in the system.

The points G and F lie inside the intersection.

The points in the solution are G and F.

Final answer:

Points F and G.

Answer:

x < 2 or x > -11

Step-by-step explanation:

b. 1. add 12 to both sides to get -1/3x > 33

2. multiply by -3/1 to both sides to get x > -11

a. 1) subtract 10 to both sides

2) divide by -6 to both sides

Lets call x to the number of ducks

and y the number of pigs.

Then:

Because there are 2 legs per duck and 4 legs per pig.

If the total of animals is 37, then:

Then:

And replacing on the first equation we get:

There are 12 pigs and therefore 25 ducks.

For this problem we know that y=f(x) at x=0 is 5 units above y=g(x). So then the best solution for this case it seems to be:

And solving for g(x) we got:

To determine if the equation is true we multiply the expression on the right side by the denominator on the left; if the result is the numerator on the left then the equation is true:

Since the result is the numerator on the left side we conclude that the equation is true.

Answer:

11.67 yards

Explanation:

From the above figure, we can use the Pythagorean theorem to find the width of the pool as shown below;

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given details

STEP 2: Write the formula for finding sum of arithmetic series

STEP 3: Find the sum of the series

By substitution,

Hence, the sum is 416

SOLUTION

Let us make a diagram to interpret the question

from the diagram above, we can make the right-angle triangle as follows

So we can use SOHCAHTOA to solve this. The opposite side to the angle 52 degrees is 45.5 ft, this is gotten by adding the height of the cliff to Maria's height from her feet to her eyes.

The adjacent side is d, that is the distance from the seal to the cliff, so we have

Hence the answer is 36 foot to the nearest foot

Use the slope formula to find the slope of a line that goes through two points:

Substitute the coordinates (6,-10) and (3,-13) into the slope formula:

Therefore, the slope of a line that passes through those points, is 1.

A diagram of the situation is shown below:

In order to determine the angle of elevation x, use the sine function, as follow:

sin x = opposite side/hypotenuse

the opposite side is the distance from the ground to the wi

We need to find the equation of the line which:

• crosses the y-axis at -5

• crosses the x-axis at 2

The y-axis cutting point is (0,-5)

The x-axis cutting point is (2,0)

The equation of line is:

Where m is the slope and b is the y-axis cutting point

m is given by:

Where

y_2 = 0

y_1 = -5

x_2 = 2

x_1 = 0

So, slope is:

We got m, we also know b.

The y cutting point is -5, so b = -5

The equation is:

The graph would look like:

More clear version:

Step 1

Given;

Step 2

When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).

Thus;

checking properly, the sample proportion =0.30, because

Answer; Option D

The quadratic is decreasing in the interval in which the y values decrease with the increase in x values.

In the interval, (-∞, 0), the y values decrease with increase in x values.

Hence, the quadratic is decreasing in the interval (-∞, 0),

Given

The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,

Answer:

Step-by-step explanation:

This question can be solved using a rule of three.

For each configuration, we need the perimeter and the amount of bags of mulch.

For a square of side s, the perimeter is P = 4s

If the 10 x 10 garden took 3 1/2 bags of mulch:

10x10 means that s = 10.

So the perimeter is:

P = 4*10 = 40

The number of bags of mulch is:

3 1/2 = 3 + (1/2) = 3 + 0.5 = 3.5

15 x 15 garden

15x15 means that s = 15.

The perimeter is: P = 4*s = 4*15 = 60.

The number of bags is X.

Now applying the rule of three:

With the number of bags and the perimeter.

3.5 bags - 40'

X bags - 60'

Now we apply cross multiplication:

Hello there. To find this minimum weight resistance, we need to convert the percentage value to decimals and multiply it by the weight of the person.

8% converted to decimals is equal to 0.08.

Now, multiply it by the weight of the 230 pound man

0.08 * 230 = 18.4 pounds

This is the minimum weight resistance this U gym offers to the customers.

Compound Shape

The shape of the figure attached consists on four triangles and one square.

The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:

Calculating:

The area of each triangle is 60 square cm.

Now for the square of a side length of L=12.

The area of a square of side length a, is:

Calculate the area of the square:

The total surface area is:

A = 60*4 + 144

A= 240 + 144

A = 384 square cm