What is the value of 7(x+4)²- 3x=2

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

Answer:

\(Var = 1.9\)

Step-by-step explanation:

Given

\(p = \frac{1}{20}\)  i.e. 1 per 20cc of water

\(n = 40\) -- sample size

Required

The variance

This is calculated using:

\(Var = np(1 - p)\)

So, we have:

\(Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})\)

\(Var = 40 * \frac{1}{20} * \frac{19}{20}\)

\(Var = 2 * \frac{19}{20}\)

\(Var = \frac{38}{20}\)

\(Var = 1.9\)

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

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

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Formula of force,

F = ma

Given that,

A man pulled a cart filled with stones that had a total mass of 60 kg

He increased the amount of force used to pull the cart from 60 N to 90 N

New acceleration of cart = ?

F  = ma

Old acceleration,

60  = 60a

a   =  1 m/s²

New acceleration,

90 = 60a

a   = 90/60

a   =  3/2

a   =  1.5 m/s²

Hence, the new acceleration is 1.5 m/s²

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The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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Answer:

-20

Step-by-step explanation:

the stock decreased $4 every day for five consecutive days

so -4 × 5= -20

Answer:

8a+4b-6

Step-by-step explanation:

Hope this helps you!!!!

Combine like terms 5a -2b - 6 + 3a + 6b

8a + 4b - 6

The Area of the two circle is 14.13 cm square. and  area of the blue section is 14.13 cm square.

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the shape is the sum of the area of the two smaller circle.

The circles have diameter of 3 unit.

Area of a circle = πr²

where: π = 3.14 = pi

D = diameter

r = radius

1. Radius = 3 cm

Now the area of the big circle =  πr²

Area = 3.14 x 3² = 28.26 cm square

2. Radius = 3/2

Area = 3.14 x 3/2² = 7.06 cm square

Area of the two circle = 7.06 + 7.06 = 14.13 cm square

3.  the area of the blue section = the area of the big circle - Area of the two circle

= 28.26  - 14.13

= 14.13

Therefore, the area of the blue section is 14.13 cm square.

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Answer:

The passenger train is traveling at 45 mph, and the freight train is traveling at 27 mph.

Step-by-step explanation:

Let's assume the speed of the passenger train is represented by x mph.

According to the given information, the freight train leaves the depot 2 hours before the passenger train. Therefore, when the passenger train starts, the freight train has already been traveling for 2 hours.

Let's represent the speed of the freight train as (x - 18) mph, which is 18 mph slower than the passenger train.

Now, we know that the passenger train overtakes the freight train in 3 hours. This means that the passenger train traveled for 3 hours, while the freight train traveled for 3 + 2 = 5 hours.

Since speed = distance/time, we can set up the following equation based on the distances covered by each train:

Distance covered by passenger train = Distance covered by freight train

Using the formula, distance = speed × time, we get:

x × 3 = (x - 18) × 5

Simplifying the equation:

3x = 5x - 90

90 = 5x - 3x

90 = 2x

Dividing both sides by 2:

45 = x

So, the speed of the passenger train is 45 mph.

The speed of the freight train is 45 - 18 = 27 mph.

We are given that a coin is toseed with two possible outcomes (head or tails) and a ball from a ball with balls of three different colors is picked.

We have that the possible outcomes are all possible combinations of the faces of the coin and the color of one of the balls.

Therfore, if:

The possible combinations are:

Therefore, the right answer is C.

Answer:

A. 2

Step-by-step explanation:

The common ratio between the terms listed is 2. Each term is being multiplied by 2, so to find the first term, you have to divide the first term listed by 2.

4/2 = 2

Answer:

2

Step-by-step explanation:

The common ratio is

8/4 = 2

Take the second term and divide by the common ratio to get the first term

Take 4 /2 = 2

The first term is 2

Based on the graph, the point that is a solution to the system of inequalities is C(1,2).

What is inequality ?

An inequality is a mathematical statement that describes a relationship between two values or expressions that are not necessarily equal. Inequalities use symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) to compare the values or expressions.

The graph shows a system of linear inequalities. The shaded region represents the solution set of the system.

Therefore, Based on the graph, the point that is a solution to the system of inequalities is C(1,2).

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Answer:

4x - 3 - 2x + 5 = 6 - 3x + 2 + 5x

2x + 2 = 2x + 8

2 ≠ 8, so this equation has no solutions.

Answer:

No solution

Step-by-step explanation:

Given:

\(4x-3-2x+5=6-3x+2+5x\)

rearrange terms so like terms are together

\(4x-2x-3+5=6+2-3x+5x\)

combine like terms

\(2x+2=8+2x\)

subtract 2x to both sides

\(2\neq 8\)

2 doesn't equal 8, meaning that there are 0 solutions to this problem.

Hope this helps! :)

The value of tea changes with time in weeks since being placed on display. Therefore, the function rule for each of them would be as follows;

Point d is at (5, -5), which is five units to the right of the origin on the x-axis and five units below the origin on the y-axis. Similarly, point e is at (7, 3), point f is at (-1, 5), and point G is at (-3, -3).

The given points, d (5, -5), e (7, 3), f (-1, 5), and G (-3, -3) form quadrilateral DEFG. To plot these points, we can first draw the x and y axes on a graph paper.

Then, we can plot each point by locating its x-coordinate on the x-axis and its y-coordinate on the y-axis.

After plotting the points, we can click on the "Graph Quadrilateral" button to see the quadrilateral DEFG. It should be a closed shape with four sides, connecting the four points in the given order.

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the equivalent expression of 5^-4 is 1/625

Index forms are defined as mathematical forms that are used in the representation of numbers or variables that are too large or too small.

They are also called scientific notation or standard forms.

They are represented as a number or variable that is raised to an exponent.

Examples of index forms are;

a³, c²

5², 6³

From the information given, we have;

5^-4

Note that equivalent expressions are described as expressions that have the same solution but different arrangement of values

Then, we have;

1/5⁴

Find the fourth root

1/625

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Answer:

Step-by-step explanation:

17.

18.

f(x)=6x^2+7x-4

(a)

f(3)=6(3)^2+7(3)-4

=54+21-4

=71

(b)

f(m)=6m^2+7m-4

(c)

f(x+1)=6(x+1)²+7(x+1)-4

=6(x²+2x+1)+7x+7-4

=12x²+12x+6+7x+7-4

=12x²+19x+9

19.

(fg)(x)=f(g(x)=f(2x²+3)=2x²+3+5=2x²+8

20.

(a)

f(x)=x²+3x+4

domain:all real values

(b)

domain:all real values≥-2

(c)f(x)=log(x+7)

Domain:x≥-7

21.

x²+6x+y²-7=0

(x²+6x+6/2)²)-(6/2)²+y²=7

(x+3)²+y²=7+9

(x+3)²+y²=4²

center=(-3,0)

radius=4

22.

(x-3)²+(y-5)²=3²

or

x²-6x+9+y²-10y+25=9

x²+y²-6x-10y+25=0

Graph is for 17th question.

Answer:

.77

Step-by-step explanation:

the 7 is repeating so you can put a dash above the second 7

A=5 and 0=5A is there answer

Answer:

C. 101°

Step-by-step explanation:

We have :

m∠KMN + m∠KML = 180  (supplementary angles)

On the other hand ,

4x + 81 + m∠KML = 180  (The interior angles of a triangle add up to 180°)

Therefore

m∠KMN + m∠KML = 4x + 81 + m∠KML

Then

m∠KMN = 4x + 81

Then

13x + 36 = 4x + 81

Then

13x - 4x = 81 - 36

Then

9x = 45

Then

x = 5

…………………………………

Conclusion:

m∠KMN = 13x + 36

              = 13(5) + 36

              = 65 + 36

              = 101

THE WIDTH=67.5 feet & LENGTH=67.5+15=82.5 feet

Perimeter of a rectangle (A) is the 2× sum of of its length (l) and width (w).

A=2(l+ w)

Here, given that,

Perimeter=150 feet

Let, width be x

then, length be x +15

ATQ

x+x+15=150

2x+15=150

2x=150-15

2x=135

x=135/2

x=67.5 feet

Then:

WIDTH=67.5 feet

LENGTH=67.5+15

             =82.5 feet

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Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

Answer:

y = 5.25x + 80

Step-by-step explanation:

total income = 5.25 * phones + 80 salary

Answer:

y = 5.25x + 80

Step-by-step explanation:

Answer:

24% of the U.S. states have names that start with vowels

Step-by-step explanation:

12 ÷ 50 = 0.24

0.24 × 100 = 24%

Answer:

24 % of the U.S. states' names start with a vowel

Step-by-step explanation:

12 out of 50 vcan be written in math terms as;

12 / 50 which equals the decimal form of a percent as shown;

12 / 50 = 0.24

which in percent form is: 24 %

After answering the provided question, we can conclude that So the total  equation amount of time Sarah spent on these three activities is determined by how much time she spent reading.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "\(2x + 3 = 9\)" asserts that the statement "\(2x + 3\)" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "\(x^2 + 2x - 3 = 0\)," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Let's call Sarah's reading time "r" in minutes.

We can deduce from the problem:

Sarah painted for 5 minutes.

Because she spent twice as much time reading as she did painting,\(r = 2*5 = 10.\)

She hiked for 35 minutes longer than she read, so \(h = r + 35.\)

To calculate Sarah's total time spent on these three activities, simply add the times:

Time spent painting + time spent reading + time spent hiking = total time

Time total =\(5 + 10 + (r + 35)\)

Time total = \(50 + r\)

So the total amount of time Sarah spent on these three activities is determined by how much time she spent reading.

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Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

C

Step-by-step explanation:

The equation of tangent plane to the given parametric surface \(r(u,v) = u.cos(v)i + u.sin(v)j + vk\) is \(\frac{\sqrt3}{2}x - \frac{5}{2}y + 5z = \frac{5\pi}{3}\) .

The given parametric surface is

\(r(u,v) = u.cos(v)i + u.sin(v)j + vk\)

The tangent vectors are

⇒ \(r_u = \frac{dx}{du} i+ \frac{dy}{du}j + \frac{dz}{du}k\)

⇒ \(r_u =\) \(r(u,v) = cos(v)i + sin(v)j + 0k\)

⇒ \(r_v = \frac{dx}{dv} i+ \frac{dy}{dv} j+ \frac{dz}{dv} k\)

⇒ \(r_v =\)  \(r(u,v) = -u.sin(v)i + u.cos(v)j + 1k\)

The normal vector to the tangent plane is

\(r_u r_v = \left[\begin{array}{ccc}i&j&k\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right]\)

⇒ \(r_u r_v =\) \(sin(v)i - cos(v)j + u.k\)

When u = 5, v = \(\frac{\pi }{3}\), the normal vector becomes

⇒  \(sin(\frac{\pi}{3})i - cos( \frac{\pi}{3})j + k\)

⇒ \(\frac{\sqrt{3} }{2}i - \frac{1}{2} j + k\)

The point on the surface corresponding to the u = 5 & v= \(\frac{\pi}{3}\) is

\(r(5, \frac{\pi}{3}) = (5)cos(\frac{\pi}{3})i + (5)sin(\frac{\pi}{3})j + (\frac{\pi}{3})k\\r(5, \frac{\pi}{3}) = \frac{5}{2}i + \frac{5\sqrt3}{2}j + \frac{\pi}{3}k\)

If a is the position vector of a point on the plane & n is a vector normal to the plane, then the equation of the plane is

⇒ (r - a).n = 0

⇒ \((x - \frac{5}{2}) . ( \frac{5\sqrt3}{2}) + (y - \frac{5\sqrt3}{2}).(- \frac{5}{2}) + (z - \frac{\pi}{3}).(5) = 0\)

⇒  \(\frac{\sqrt3}{2}x - \frac{5}{2}y + 5z = \frac{5\pi}{3}\)

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Answer:

-5 degrees per hour

Step-by-step explanation:

In 10 hours, the temperature dropped -50 degrees (38 + 12, and make it negative because the temperature went down, not up).

So divide -50 by 10

-50/10 = -5

Answer:

-24.35, -7.96, 11.20

Answer:

-24.35, -7.96, 11.20

Step-by-step explanation: