Find the solution of the system of equations.

5x+y=-19

5x-4y=-24

The exponential function is given by \(y = 210000(1.125)^t \\\)

An exponential function is in the form:

\(y=ab^x\)

Where a is the initial value of y and b is the multiplier factor

Let y represent the population after t years.

Given an initial population of 210000, hence:

The population increases by 12.5% each year, hence:

The exponential function is given by \(y = 210000(1.125)^t \\\)

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Answer: 53.33

Step-by-step explanation:

60 + 9x =540

540-60 = 480

480 = 9x

53.33 = x

Answer:

Volume V ≈ 1481.3269 cubic inches

Step-by-step explanation:

Volume V of a cylinder is given by the formula

V = πr²h  where r = radius of the base of the cylinder and h the height

Here we are given the diameter, d = 5.9375 inches

Radius r = d/2 = 5.9375/2 = 2.96875 in

Height h = 53.5 in

V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches

Answer V ≈ 1481.3269 cubic inches

Given:

Principal, P = $5000

Interest rate, R = 8% = 0.08

Time, T = 2 years

Let's fnd the toatal amount of interest.

To find the interest, apply the simle interest formula:

Hence, we have:

Therefore, the total amount of interest is $800.

ANSWER:

$800

Answer: CHAA

Step-by-step explanation:

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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The length of QT is given as follows:

b. 12.

A bisection means that the larger angle is divided into two smaller angles of equal measure, and the side lengths of relative to the angle are equal.

The bisection segment for this problem is given as follows:

RT.

Hence the congruent segments are:

QT and TS = 12.

Thus the length of QT is given as follows:

QT = 12.

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The possible value of the side length of the plot of land that Abby owns, which is between 2200 and 2400 square meters is A. 48 meters.

The length is the quantitative measurement of a distance from one point to another position.

Length can also refer to the size of an object that has width or/and height.

The square of 2,200m² = 46.9 meters (√2,200)

The square of 2,400m² = 48.99 meters (√2,400)

The square of the median value of 2,200m² and 2,400m², which is 2,300m² is 48 meters approximateluy.

Thus, the possible value of the side length of the plot of land is A. 48 meters.

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A. 48 meters

B. 46 meters

C. 44 meters

D. 50 meters

Answer:

\(\fbox{\begin{minipage}{5em}A = 18.3\end{minipage}}\)

Step-by-step explanation:

Given:

Dan was thinking of a number.

Dan adds 10 to it, then doubles it and gets an answer of 56.6.

Solve for:

Dan's original number

Step 1: Clarify the problem:

Denote Dan's original number as A

Dan adds 10 to A => 10 + A, then

Dan doubles this sum => 2 x (10 + A), then

Dan gets an answer of 56.6 => 2 x (10 + A) = 56.6

Step 2: Solve for the defined equation:

2 x (10 + A) = 56.6

Let's divide both sides of equation by 2:

2 x (10 + A)/2 = 56.6/2

We simplify both sides after division:

10 + A = 28.3

Let's transfer all numbers to the right side, except A (the sign of 10 is changed from + to -)

A = 28.3 - 10

Let's perform the subtraction to get A:

A = 18.3

Hope this helps!

:)

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Answer:

Step-by-step explanation:

I assume you want to simplify this expression.

First take away the parenthesis.

-5x+4+-1x+1

Now combine like terms.

-5x+-1x=-5x-1x=-6x.

4+1=5

So -6x+5 is your answer.

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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The absolute value is a non negative value. Since - 5 is a negative number, thereis no number whose absolute value would be - 5. Thus, the answer is

None

Answer:

-12

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

because if you do negative 3 times 6 it will give you -12

Answer:

quarterly

Step-by-step explanation:

i just took the unit exam i got it right, its quarterly.

Answer:

1.46%

Step-by-step explanation:

Pretend you have a number as a test dummy. We'll go with 100 for simplicity. A 14% increase to 100 would be 114. Then we can decrease 114 by 11%. We can find 11% of 114 with an equation like so: x/114 = 11/100. We can then cross multiply to get this" 100x = 1254, which can be simplified to x=12.54. Now, we can subtract 12.54 from 114, which will get us 101.46. Because percentage is based on 100, we can simply subtract 100 from 101.46, which gives us 1.46. So, the answer is 1.46%.

(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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Answer:

Answer is option  D

Step-by-step explanation:

Hope this helps:)

Answer:

113.6 feet

Step-by-step explanation:

set up a proportion of height of structure over height of shadow

let t = height of tree

t = 125

5      5.5

cross-multiply:  5.5t = 625

                             t = 625 / 5.5

Answer:

it would be 3025

Step-by-step explanation:

605

x. 5

3025

Answer:

15125

Step-by-step explanation:

   605

   x25

   ------

   3025

+1210

-----------

  15125     

The cosine value is given as follows:

\(\cos{\theta} = \frac{4\sqrt{23}}{23}\)

The tangent value is given as follows:

\(\tan{\theta} = -\frac{\sqrt{7}}{4}\)

First we must obtain the secant value, according to the identity presented as follows:

\(\sec^2{\theta} = 1 + \tan^{2}{\theta}\)

Replacing the tangent into the expression, we have that:

\(\sec^2{\theta} = 1 + \frac{7}{16}\)

\(\sec^2{\theta} = \frac{23}{16}\)

\(\sec{\theta} = \frac{\sqrt{23}}{4}\)

The secant is positive, as the angle is in the fourth quadrant, where the cosine is positive.

The cosine is then given as follows:

\(\cos{\theta} = \frac{1}{\sec{\theta}}\)

\(\cos{\theta} = \frac{4}{\sqrt{23}} \times \frac{\sqrt{23}}{\sqrt{23}}\)

\(\cos{\theta} = \frac{4\sqrt{23}}{23}\)

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Answer:

the z score of 105 is 1.03

Step-by-step explanation:

Given that

the mean is 102

And, the standard deviation is 2.9

We need to find the z score of 105

As we know that

Z score = (Observed value - mean) ÷ standard deviation

= (105 - 102) ÷ 2.9

= 1.03

Hence, the z score of 105 is 1.03

The same would be considered and relevant

Answer:B.

Step-by-step explanation: it is better to have empty seats than toforce people to give up their seats.

Answer:

the cost of an apple is 12p i.e. 12x

And, the cost of an orange is 20p i.e. 20y

Step-by-step explanation:

Let us assume the apple be x

And, the orange be y

Now the cost of an apple is 12p i.e. 12x

And, the cost of an orange is 20p i.e. 20y

So the above represents an expression

Answer:

I think its 400

Step-by-step explanation:

8 seats per table, if there are 10 tables, means 80 seats in total. 80 times 5 gives you the amount of silverware: 400

If there are 10 tables (t) with 8 seats (s), there will be a total of 80 people needing silverware. So the equation is 5·10·8=400

There will be 400 pieces of silverware.

Answer:

A. down

Step-by-step explanation:

The parent graph is

f(x)=x

If this graph is transformed to obtain

g(x)=f(x)−4

The subtracttion means the graph will shift downward vertically

The graph of g(x) is obtained by shifting f(x) down by 4 unit.

Therefore the direction is down.

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The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7

From the question, we have the following parameters that can be used in our computation:

(x + 1) (x - 5) = 16

The above expression is the product of two factors

(x + 1) and (x - 5)

And the result is 16

Express 16 as 8 * 2

So, we have

(x + 1) (x - 5) = 8 * 2

By comparison, we have

x + 1 = 8 and x - 5 = 2

When evaluated, we have

x = 7 and x = 7

This means that the value of x in the equation is 7

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The value that would help Charlie find out how long it takes his basketball to reach the highest point is "x at the vertex". The correct option is A.

When the basketball reaches the highest point, its vertical velocity is zero. The time taken to reach this point can be found using the equation:

t = -b / (2a)

where a is the acceleration due to gravity (-9.8 m/s²) and b is the initial vertical velocity of the basketball.

The vertex of the parabolic path that the basketball follows is the point where the basketball reaches its maximum height. This point occurs at the halfway point of the ball's total flight time. The horizontal distance the basketball travels during this time is called "Ox at the vertex".

Therefore, by finding the "x at the vertex", Charlie can calculate the total flight time of the basketball, and then use the equation above to find the time it takes to reach the highest point.

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Answer:

2.25

Step-by-step explanation:

We can write a ratio to solve

1.69           x

------     = ---------------

3/4 lb              1 lb

Using cross products

1.69 * 1 = 3/4 *x

1.69 = 3/4 x

Multiply by 4/3

1.69 * 4/3  = x

x=2.25333

Rounding to the nearest cent