Swine Flu is attacking Springfield. The function below determines how many people have swine where t=time in days and S=the number of people in thousands.

The largest number of the wooden Els with it's total surface area that can be packed in the 2cm×4cm×6cm box is 2 wooden Els.

In finding the total surface area of a solid cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) and use the formula, SA=2(lw+lh+hw), to find the surface area.

For the box, l=2cm, w=4cm and h=6cm

total surface area of box=2(2×6+2×4+6×4) cm square units

total surface area of box=2(44) cm square units

total surface area of box=88cm square units

For the top cuboid of the wooden El, l=3cm, w=1cm and h=2cm

total surface area of top El cuboid=22cm square units

For the bottom cuboid of the wooden El, l=1cm, w=1cm and h=2cm

total surface area of bottom El cuboid=10cm square units

total surface area of the El=32cm square units

(88cm²/32cm²)=2.75

This implies that only two(2) whole Els with total surface area of 32cm² can be packed in the box.

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The given functions are,

Fog can be determined as,

The value of fog(-1) can be determined as,

Thus, the requried value is 7.

Explanation

Step 1

we have two triangles

ACE and BCD

if the triangles are similar, then the ratio of the sides must be the same:

Step 2

solve for x

rounded

I hope this helps you

Mrs.Smith took : her 3 kids + 3 of their friends = 3 + ( 3x 3 ) = 12 kids

Answer:

There are 3 kids, and 3 friends.

3 + 3 = 6

there are a total of 6 kids.

To verify that something is a function, we use the horizontal line rule. That is, if the horizontal line passes through two points, then the graph is not a function, like this:

Then the circles and the ellipses are not functions. Then the functions in the problem would be:

1, 3 and 6.

∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

Angles 1,2,7 are the interior angles of a triangle and we know that the sum of all interior angles inside a triangle is 180°.

Therefore, ∠1 + ∠2 + ∠7 = 180°

Given, ∠1  = 70° and  ∠2  = 65°

∠7 = 180° - (70 + 65) = 45°

Now, ∠8 = 180 - ∠7 ⇒ ∠8 = 135°

Now, ∠7 = ∠6 (vertical opposite angle) so ∠6 = 45°

∠6 = ∠5 (alternative interior angle) so ∠5 = 45°

Hence "∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°".

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c = 15

The perimter, P = 37

The side lengths of the triangle are:

a = 10, b = 12, c = ?

The perimeter of the triangle is given by the formula:

P = a + b + c

Substitute a = 10, b = 12, and P = 37 into the formula P = a + b + c and solve for c

37 = 10 + 12 + c

37 = 22 + c

c = 37 - 22

c = 15

Given points (1,-3) and (5,-1).

Since the slope of the line passing through two points

The slope of the equation is

Therefore, the slope of the line is 1/2.

Now, use the slope and the point (1,-3) to find the y-intercept.

Write the equation in slope-intercept form as

The values of the functions evaluated are:

a. (f + g)(x) = 9x + 1

b. (f + g)(x) = -7x + 1

c. (f * g)(x) = 8x² - 55x - 72

d. (f/g)(x) = (x - 8)/(8x + 9)

To evaluate a function expression, we are to input the given value of x and solve by combining like terms and simplifying to find the value of the given function expression.

Given the functions:

f(x) = x - 8

g(x) = 8x + 9

a. Find (f + g)(x): This implies that we are to add the two functions f(x) and g(x) together.

(f + g)(x) = x - 8 + 8x + 9

(f + g)(x) = 9x + 1

b. Find (f - g)(x): This implies that we are to subtract g(x) from f(x).

(f - g)(x) = x - 8 - 8x + 9

(f + g)(x) = -7x + 1

c. Find (f * g)(x): This implies that we are to multiply the functions, g(x) and f(x) together.

(f * g)(x) = (x - 8) * (8x + 9)

(f * g)(x) = 8x² - 55x - 72

d. Find (f/g)(x): This implies that we are to find the quotient of the functions, f(x) and g(x).

(f/g)(x) = (x - 8)/(8x + 9)

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This problem is about functions.

In this case, we don't have function j(x) defined in order to find its ordered pairs.

However, assuming that function j(x) is a function of f(x), we can deduct that points C is

The expression (xy)z can be simplified as;

The correct answer is option C

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient is -6 with the following factors (possible values for p):

The leading coefficient is 1, with factors:

Therefore, all the possible values of p/q are:

Simplifying, the possible rational roots are:

Next, we have to check if they are roots of the polynomials by synthetic division, in which the remainder should be equal to 0.

0. Dividing ,f (x), by ,x−1,. Remainder = ,-8, ,+1, is ,NOT ,a root.

1. Dividing ,f (x), by x+,1,. Remainder = 0, ,-1, ,IS ,a root.

2. Dividing ,f (x), by x-2. Remainder = 0, ,+2, ,IS ,a root.

3. Dividing ,f (x), by ,x+2,. Remainder = ,4, ,-2, is ,NOT ,a root.

4. Dividing ,f (x), by ,x−3,. Remainder = 24,, ,+3, is ,NOT ,a root.

5. Dividing ,f (x), by ,x+3,. Remainder = 0,, ,-3, IS ,a root.

6. Dividing ,f (x), by ,x−6,. Remainder = 252,, ,+6, is ,NOT ,a root.

7. Dividing ,f (x), by ,x+6,. Remainder = -120,, ,-6, is ,NOT ,a root.

Actual rational roots: A. -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)

Distance = Speed x time

For the run; speed = 5 mi/hr, time = t

For the walk: speed= 2 mi/hr, time = t + 1

Since he walked on a straight line and he returned following the same path

Distance travelled for the run = distance travelled for the walk

Distance for run: 5 x t = 5t

Distance for walk : 2 (t + 1) =2t + 2

Thus , 5t = 2t + 2

5t - 2t = 2

3t = 2

t = 2/3 hour = 2/3 x 60 minutes = 2x 20 = 40 minutes

He took him 40 minutes to run

EXPLANATION

Let's call t to the number of tickets and c to the total cost, the appropiate relationship would be:

c = 2.5t + 10

The variable in the expression represents the number of tickets.

Given to solve the expression:

step 1: Expand the bracket by multiplying each term by the factor outside

step 2: Simplify the expression obtained in step 1

Given

5x+2y=16 ---(1)

7.5x+3y=24 ----(2)

Find

1) value of x and y

2) Type of system

Explanation

From equation (1)

Putting this value of x in equation 2

From here we cannot find the values of x and y as 3y and -3y will cancel each other. Hence there is not a particular solution

Checking the type of system

From these equations we get

Therefore the lines are coincident to each other

Therefore the lines have infinte solutions

Final Answer

Therefore the lines have infinte solutions

The lines are coincident to each other

The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.

Now that we have two points, we can solve for slope m

Now that we have both m and b. Substitute these values to the slope intercept form

We use the equation: h = 100(n + 2), so:

For n = 1:

For n = 3:

We can see that this is the correct equation. Therefore, given h we find n:

For h = 700

For h = 900

Answer:

(n): 1 3 5 7

(h): 300 500 700 900

Correct equation: h = 100(n + 2)

Given:

The odds in favour of Pablo chosing a re marble is 1 : 8

The given curve is parabola and its last point is on the x axis at x = 2

So, the equation of curve is :

In the equation of line,

The line start from x = 2 so, x ≥ 2

So, Equation of line is : -x + 4, x ≥ 2

Answer : B)

Solution

- The number given to us can be rewritten as follows:

- Thus, we already know what is in the whole number bracket; 92.

- The fraction representation of 0.698 is what will occupy the fraction brackets.

- 0.698 can be rewritten as:

- Let us simplify this fraction as follows:

- Thus, the answer is

Answer:

157.5°

Explanation:

To convert from radians to degrees, multiply the angle in radians by 180/π.

Therefore, 7π/8 radians in degrees will be:

In this problem, we want to determine tangent of 62 degrees.

Recall the identity of tangent:

We are given the triangle:

Since we are referencing 62 degrees, the arrow pointing away from the 62 degrees is headed toward the opposite side. Therefore, the opposite side is 15, and the adjacent side is 8.

Tangent of 62 degrees is 15/8.

The solution of the equation is s=2.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+1. Where:

m= the slope. It can be calculated for Δy/Δx .

b= the constant term that represents the y-intercept.

For the given example: m=7and b=1.

For solving this question you should replace x for the given values ( −1, 0, 1, 2) in the equation 4s − 14 = −6. If you obtain -6, the value of s is a solution.

For s= -1 -> 4*(-1)-14= -4 -14= -20. Therefore, s=-1 is not the solution.

For s= 0 -> 4*(0)-14= 0 -14= -14. Therefore, s=0 is not the solution.

For s= 1 -> 4*(1)-14= 4 -14= -10. Therefore, s= 1 is not the solution.

For s= 2 -> 4*(2)-14= 8 -14= -6. Therefore, s=2 is the  solution.

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We have to write as inequality the following

"4 units away from x" means four units plus x. So, the expression would be

Where x represents real numbers.

This expression is referring to all real numbers more than 4 units and less than -4 units because according to the property of absolute values for inequalities, we have

This is represented in the following graph to see it better

For x=1

Both results are true.

To find this absolute value inequality we used the following property

Where the absolute value inequality has "more than" we rewrite the expression in two inequalities.

To transform a function about the y axis

f(x) becomes f(-x)

y = sqrt( x) +2

To transform replace x with -x

y = sqrt(-x) +2

The 2 is a vertical translation up 2

Answer:

Step-by-step explanation:

To start your equation is in the format y=mx+b.

For a line to be parallel it must have the same slope (m) so we know 4 must remain the same. x & y will not change since they represent the variables. y=4x (so far) then the point (0,7) as stated is the y intercept. 0 is the x value and 7 is the y we need to add 7 to our equation.

final equation y=4x+7

Given: An AP whose first term is -20 and a common difference of 3.

Required: To determine the 119th term of the AP.

Explanation: An AP with the first term, a, and with a common difference, d, is of the form-

where n is the number of terms in the AP.

The following formula gives the nth term of the AP-

Here it is given that-

Substituting these values into the formula for nth terms as-

Further solving-

Final Answer: The 19th term of the AP is 34.

m∠FCE =25º

1) Since the measure of ∠DCF = 115º and ∠DCE = 90º then by the Angle Addition postulate we can state that

∠DCF = ∠DCE +∠FCE Plugging into that the given values

115º = 90º + ∠FCE Subtracting 90º from both sides

115-90=∠FCE

25º =∠FCE

2) Then the measure of ∠FCE is 25º

We have the following estimations:

1, 5, 5, 6, 7, 8, 10, 12

The absolute value between each estimate and the answer is calculated as:

Estimate Absolute

Answer value

1 |1-7| = |-6| = 6

5 |5-7| = |-2| = 2

5 |5-7| = |-2| = 2

6 |6-7| = |-1| = 1

7 |7-7| = |0| = 0

8 |8-7| = |1| = 1

10 |10-7| = |3| = 3

12 |12-7| = |5| = 5

So, the estimated answer that was off by the most is 1.