Bertrand invites 21 people to his party and wants to give each guest 3 party favors. If n is the total number of party favors he will need to order, the
equation that represents this situation is
= 3
a. If Bertrand orders 58 party favors, will he be able to give each guest 3 party favors?
That is, is 58 a solution to the equation? yes or no
I
b. If Bertrand orders 62 party favors, will he be able to give each guest 3 party favors? yes or no
c. How many party favors does Bertrand need to order?n=
party favors

Answer:

3.36 quarts of paint

Step-by-step explanation:

In this question, we're trying to find how much paint she will need to cover the night stand.

First, we need to find the area.

Solve for the area (rectangle = l * w):

42 · 28 = 1176

Now, we know that 1 quart of paint covers 350 square inches.

To find how much paint she needs, divide 1176 by 350:

1176/350 = 3.36

This means that she needs 3.36 quarts of paint to cover her whole nightstand.

the answer is 16.0 or 11.0

Answer:

the horizontal asymptote it is called when a rational function is graphed so the y=3 is an imaginary line

Given equation:

\(y = 3 \cos (\frac{24 \pi}{ 149}x)\\\\\)

To find:

height of water at 2:15 am=?

Solution:

\(y = 3 \cos (\frac{24 \pi}{ 149}x)\\\\\)

where x  is the time in hours  that is 11:00 p.m and at the of time 2:15 am the calculating value of x:

\(\to X= (3:15)\ hours = 3 \frac{1}{4} = \frac{13}{4}\\\\ \to y= 3 \cos (\frac{24 \pi}{149}\times \frac{13}{4} )\\\\\)

       \(= 3 \cos (\frac{6 \pi}{149}\times 13 )\\\\= 3 \cos (\frac{78\pi}{149} )\\\\= -0.22118\approx -0.22\\\\\)

Therefore, the height of the water at 2:15 am is 0.22 feet below the marker.

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Answer:

The Answer is A 0.22 feet

Step-by-step explanation:

The class boundaries are the lower and the upper bound of each class, hence for the sixth class they are between 310 and 319.

The notation a - b means that:

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It takes 8 hours, for Jim to rake the yard alone.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

Jim and Cara, working together, can rake the yard in 6 hours.

Working alone, Cara takes three times as long as Jim.

Let x be the amount of time it takes Jim to rake the yard alone.

His work rate is 1/x.

So, Cara takes 3x.

Cara's work rate is 1/3x.

According to the question,

1/x + 1/3x = 1/6

6 + 2 = x

x = 8.

Therefore, Jim takes 8 hours.

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The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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Answer:

339, 340, 341

Step-by-step explanation:

To find the 3 consecutive numbers, divide the sum by 3 to get the average. 1020/3=340. So the middle number is 340. That means the numbers are 339, 340, and 341.

The equation be 2x² - 3x - 5 then the value of x = -1.

Let a and b represent the coefficients of a parabola in the standard form ax² + bx +c = 0.

Part A: Let f(x) = 0 and solve for x to get the x-intercepts.

Given the function 2x²-3x - 5 = 0

Factor to get (2x - 5) (x + 1) = 0

then 2x - 5 = 0 and x = 2.5x + 1 = 0 and x = -1

These are the x-intercepts.

Part B: As the coefficient of the \($$x^2\) term exists positive, the parabola opens up, and the vertex exists at a minimum. The coordinates of the parabola exist given by -b/2a, f( -b/2a)

where a and b represent the coefficients of a parabola in the standard form ax² + bx +c = 0.

In this case a = 2, b = -3 and c = -5.

So -b/2a = 3 / 4

f(-b/2a) = \(2 * (3/4)^2 -3 * (3/4) - 5\) = -6.125.

The coordinates of the vertex exist (3/4, -6.125)

Part C: I will give them a minimum from completing the square

y = \($$2(x - 0.75)^2\) - 6.125

as x approaches + ∞, y approaches + ∞.

as x approaches - ∞, y approaches + ∞.

It's a quadratic.

The y values go to + ∞ when x goes from - ∞ to + ∞.

Part D: The graph is as follows:

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In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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Answer:

252 ft2 (squared)

Step-by-step explanation:

area= a x b

area= 12 x 21

area= 252 ft2 (squared)

Since 0 < x < π/2, we know 0 < x/2 < π/4, so that cos(x/2) is still positive.

Recall the double-angle formula,

cos²(x/2) = (1 + cos(x)) / 2

so that

cos(x/2) = √((1 + 1/4) / 2) = √(5/8)

Answer:

y = x² + 8x + 16

Step-by-step explanation:

blue square = x × x = x²

green rectangle = 4 × x = 4x

yellow square = 4 × 4 = 16

Let y = total area of the square

⇒ y = blue square + green rectangle + green rectangle + yellow square

       = x² + 4x + 4x + 16

       = x² + 8x + 16

Area:-

Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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The Length is 5 inches and the Breadth is 15 inches

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Perimeter of Rectangle = 2*(Length + Breadth)

According to the question

Breadth = 3*Length

Perimeter = 40

40 = 2*(Length + 3*Length)

20 = 4*Length

Length = 5 inch

Breadth = 15 inch

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Why?

Notice that f(x) is positive when -2 < x < 1. In other words, f(x) is positive when x = -1 and when x = 1.

This interval of -2 < x < 1 translates directly to the interval notation of (-2, 1)

Unfortunately this interval notation looks identical to ordered pair notation. Be sure not to mix the two concepts up.

The parenthesis in interval notation tell the reader "do not include the endpoints". We cannot include x = -2 nor x = 1 because these values make f(x) zero, but we want f(x) > 0.

Something like choice D is a non-answer because the value x = 2 is in the interval (1,4), but f(2) = -8 which isn't positive. We can rule choice D out because of it. Choices A and C are similar situations.

_________________

1. Line up the numbers to multiply.

     2 4

x    8 3

-----------

2. First, start with multiplying 3 by 4, which is 12. So, you would write it as shown.

     1

     2 4

x    8 3

-----------

       2

3. Then, multiply 3 by 2, which is 6. Remember to add 1, which is 7.

     1

     2 4

x    8 3

-----------

     7 2

4. Now, multiply 8 by 4, which is 32. You would write it as follows.

     3

     1

     2 4

x    8 3

-----------

     7 2

     2

5. Next, add 3 and 2, which is 5. Then multiply 5 by 8, which is 19.

  1   3

      1

      2 4

x     8 3

-----------

     7 2

 9  2

6. Then, drop down the 1 to the left of 9, and fill in the empty spaces with 0. Add the two and you have your final answer.

  1   3

      1

      2 4

x     8 3

-----------

  0 0 7 2

+  1 9 2 0

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

   1 9 9 2 ← Final Solution

___________________________________________

Hope this helps!

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.

Purple 1 is thus a redder hue of purple than Purple 2.

Purple 2 is a more blue-based purple than Purple 1.

The utilization of two or more additional numbers that compares is known as the ratio.

The ratio of red to blue in purple 1 and purple 2 will be 1:2 and 1:3, respectively. The table is given below.

Purple #1              Purple #2

Red: Blue             Red: Blue

  1      2                    1      3

 2      4                   2      6

 3      6                   3      9

For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.

Purple 1 is thus a redder hue of purple than Purple 2.

Purple 2 is a more blue-based purple than Purple 1.

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Answer:

2

Step-by-step explanation:

Answer:

Angle 2

Step-by-step explanation:

Find S and find X.

Then find U.

The angle at X connected to S and U is the angle number.

Answer:

a) A = p(1 + r)^t

b) A = 500(1 + 0.07)^2=572.45

Step-by-step explanation:

t=2 in b)

The solutions for the quadratic equation:

x^2 - 8x = -3

Are:

Here we want to solve the quadratic equation:

x^2 - 8x = -3

First we can move all the terms to the left side so we get:

x^2 - 8x + 3 = 0

Using the quadratic formula (or Bhaskara's formula) we can get the solutions for x as:

\(x = \frac{8 \pm \sqrt{(-8)^2 - 4*¨1*3} }{2*1} \\\\x = \frac{8 \pm 7.2 }{2}\)

Then the two solutions for the quadratic equation are:

x = (8 + 7.2)/2 = 7.6

x = (8 - 7.2)/2 =0.4

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Answer:

2x + 1.

Step-by-step explanation:

Average = sum of the expression / number of expressions

= [(4 - 2x) + (-7 - 3x) + (11x + 6)] / 3

= (-2x - 3x + 11x + 4 - 7 + 6) / 3

= 6x + 3 / 3

= 2x + 1

Answer:

2x+1

Step-by-step explanation:

(4-2x), (-7-3x),(11x+6)

Add the three expressions

(4-2x)+ (-7-3x)+(11x+6)

Combine like terms

-2x-3x+11x+4-7+6

6x+3

Divide by the number of expressions which was 3

(6x+3)/3

2x+1

The average is 2x+1

The value of the given function is f'(x) = -7x⁶ - 20x⁴.

What is differentiation?

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

Here, we have

f(x) = (-x² - 4)x⁵

After expanding, we get

f(x) = -x⁷ - 4x⁵

Now we differentiate w.r.t x and we get

f'(x) =  -7x⁶ - 20x⁴.

Hence, the value of the given function is f'(x) = -7x⁶ - 20x⁴.

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9x-2+52=180

That's the answer

Answer:

14.44444444444444444444444444444444444

Step-by-step explanation:

9x - 2 + 52 = 180

simplify

9x +50 = 180

9x = 130

14.4444444444

Answer:

find the slope? the slope is the number attached to the x so itd be 6

Answer:

slope- 6

Step-by-step explanation:

y=mx+b

y= outcome of the equation being done to x

m=slope

b=starting point on the you axis

x=the plug in on the x axis

y=6x+5. example: x=1

y=6 (1)+5

y=11

slope=6

Answer:

troop number and activity preference or b

Step-by-step explanation: