pls help ill give brainiest
For your trip to Austin you know you are going to travel 182 miles and your car can do that in 14 gallons. How far can your car travel on 8 gallons of gas?​

The equation could be used to solve for charles' rate if it is represented by x is 2x=54.

In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.

Bill riding a bicycle at an average rate of 9 mph.

Charles' rate is x.

So the relative rate = x−9 mph

Distance traveled by Bill in 4 hours = 9*4 =36 mph

Charles' overtook Bill in 2 hours. So

Relative Rate = Distance/Time

x−9=36/2

Multiply by 2 on both side. We get

2(x−9)=36

Simplifying

2x−18=36

Add 18 on both side, we get

2x=36+18

2x=54

Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.

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In order to calculate the slope of a line that passes through the points (-2, 6) and (8, 4), we can use the formula:

Where (x1, y1) and (x2, y2) are the points coordinates. So we have:

So the slope of the line is -1/5.

Answer:

Step-by-step explanation:

c

For this question it would have helped to have a graph but, the answer is 50. Hope this helps

Answer:

AB and DE are parallel because they have the same slope.

Step-by-step explanation:

Slope of the line AB :

\(=\frac{\text{rise} }{\text{run} } =\frac{CA}{-BC} =\frac{12}{-8} =-\frac{3}{2}\)

Slope of the line DE :

\(=\frac{\text{rise} }{\text{run} } =\frac{CE}{-DC} =\frac{9}{-6} =-\frac{3}{2}\)

Given:

A graph of bell peper patch is given as below

Find:

we have to find the Maximum possible area of bell peper patch represented by the function p corresponding to the length of the tomato patch x.

Explanation:

From the given graph of function p(x), it is observed that the function has maximum value at x = 6.

Therefore, when x = 6, we get

as the function p represents the area of the bell peper patch,

Therefore, Maximum possible area of the bell peper patch is p = 18 square feet, when the length of the zomato patch is x = 6 feet.

Answer:

19 1-dollar bills

Step-by-step explanation:

We will call the number of 1 dollar bills "a"

We will call the number of 5 dollar bills "b"

a + b = 30 (the number of 1 dollar bills + the number of 5 dollar bills = 30 bills in total)

1a + 5b = 74 ("a" 1 dollar bills are worth 1a dollars, and "b" 5 dollar bills are worth 5b dollars. In total they are worth 74 dollars)

Next, you can "solve for a variable" in the first equation to plug into the second equation

b = 30 - a (move "a" to the other side, now "b" is equal to 30 - a)

1a + 5(30-a) = 74 (substitute "b" in the second equation for the new value of "b" you found in the previous step)

1a + 150 - 5a = 74 (distribute out 5(30-a) to get 150 - 5a)

-4a = 74 - 150 (combine like terms)

-4a = -76 --> a = 19 (simplify the right side, and divide both sides by -4 to get answer)

Refer back to the first sentence of the explanation where we said the variable "a" equals the number of $1 bills there are. Therefore, there are 19 $1 bills.

Answer:

4 x 3 = 12

Step-by-step explanation:

12 x 1 = 12

6 x 2 = 12

Answer:

The cost of 1 orange is $2.05.

Step-by-step explanation:

Lisa needed to make a fruit salad. She bought 5 oranges for x dollars and 2 packs of strawberries for $5.00 each. She spent a total of $20.25.

Cost of 5 oranges = $5x

Cost of 2 packs of strawberries = 2×5 = $10

ATQ,

5x + 10 = 20.25

Subtract 10 both sides

5x + 10 -10 = 20.25-10

5x = 10.25

x = 2.05

So, the cost of 1 orange is $2.05.

Answer:

A = 628.32

Step-by-step explanation:

Area of a circle = 2\(\pi\)\(r^{2}\)

A = 2 x \(\pi\) x \(10^{2}\)

A = 628.32

Please mark brainliest, hope this helps!

Answer:

a is 16 yards hope this helps

Step-by-step explanation:

Let's label the diagram with the information provided. The diagram would look like:

This is labeled as x.

With respect to angle alpha, the side x is opposite and the antenna is the side adjacent.

Thus, we need the trig ratio tan to solve for "x". Shown below:

Answer: 58.23 feet

This is labeled as y.

With respect to angle beta, the side y is opposite and the antenna is the side adjacent.

Thus, we need the trig ratio tan to solve for "y". Shown below:

Answer: 77.97 feet

The distance between Anchor 1 and Anchor 2 is "x + y". We already found x and y. Let's do the sum:

Answer: 136.2 feet

Answer:

There are 10 two point questions and 16 five point questions.

Step-by-step explanation:

The means to study and analyze economic phenomena, formulate economic models, make predictions, and derive policy recommendations.

1. Importance of studying mathematics in economics:

a. Modeling and Analysis: Mathematics provides the tools and techniques for constructing models that represent economic phenomena.

These models help economists analyze and understand complex economic systems, predict outcomes, and make informed decisions.

b. Quantitative Analysis: Economics involves analyzing numerical data and making quantitative assessments. Mathematics equips economists with the necessary skills to handle and manipulate data, perform statistical analysis, and draw meaningful conclusions from empirical evidence.

c. Logical Reasoning and Problem Solving: Mathematics trains students to think critically, logically, and abstractly. These skills are essential in economics, where students need to formulate and solve economic problems, derive solutions, and interpret results.

2. Mathematical tools used in economics:

a. Calculus: Calculus plays a crucial role in economics by providing techniques for analyzing and optimizing economic functions and models. Concepts such as derivatives and integrals are used to study economic relationships, marginal analysis, and optimization problems.

b. Linear Algebra: Linear algebra is employed in various economic applications, such as solving systems of linear equations, representing and manipulating matrices, and analyzing input-output models.

c. Statistics and Probability: Statistics is used to analyze economic data, estimate parameters, test hypotheses, and make inferences. Probability theory is essential in modeling uncertainty and risk in economic decision-making.

d. Optimization Theory: Optimization theory, including linear programming and nonlinear optimization, is used to find optimal solutions in various economic problems, such as resource allocation, production planning, and utility maximization.

e. Game Theory: Game theory is a mathematical framework used to analyze strategic interactions and decision-making among multiple agents. It is widely applied in fields such as industrial organization, microeconomics, and international trade.

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Answer:

\(x = \sqrt{3 \frac{ - 1}{3} } \)

So, what i got was 24 and I'm not very sure if its correct. I'm very sorry if I'm wrong.

This was how I got 24:

Perimeter= 12+2+8+2= 24

Answer:

35000/1000 = 35m height

Answer: 35m

Step-by-step explanation: 35000mm -m

1m = 1000mm

therefore, 35000/1000

= 35m

HOPE IT HELPED U,

PLS MARK AS BRAINLIEST

^_^

Answer:

The second one the amount of monthly sales

Step-by-step explanation:

The 2000 is the total

Answer:

In mathematics, a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a symbol, called the imaginary unit, that satisfies the equation i² = −1. Because no real number satisfies this equation, i was called an imaginary number by René Descartes.

Step-by-step explanation:

Complex Integer

(or Gaussian integer), a number of the form a + bi, where a and b are integers. An example is 4 – 7i. Geometrically, complex integers are represented by the points of the complex plane that have integral coordinates.

Complex integers were introduced by K. Gauss in 1831 in his investigation of the theory of biquadratic residues. The advances made in such areas of number theory as the theory of higher-degree residues and Fermat’s theorem through the use of complex integers helped clarify the role of complex numbers in mathematics. The further development of the theory of complex integers led to the creation of the theory of algebraic integers.

The arithmetic of complex integers is similar to that of integers. The sum, difference, and product of complex integers are complex integers; in other words, the complex integers form a ring.

Answer:

An immediate consequence of the definition of arithmetical operations on complex numbers is that the sum, the difference, and the product of two or more complex numbers.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Have a great summer :)

The cross-section from any side in a square prism is always square.

A cross-section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections.

Cross-section of a square prism :-

The cross-section of a square prism is a square. Since a square prism has its faces shaped in square and all the edges of the square prism are equal in length.

Therefore, when we cut the cube by a plane, we get a square shape.

Hence, the cross-section from any side in a square prism is always square.

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To find the vector equation of the plane containing the two intersecting lines, we can first find the normal vector of the plane by taking the cross product of the direction vectors of the two lines. The normal vector will be orthogonal to both direction vectors and thus will be parallel to the plane.

Direction vector of the first line: (2, 4, 3)

Direction vector of the second line: (-1, -1, 3)

Taking the cross product of these two vectors, we get:

(2, 4, 3) x (-1, -1, 3) = (9, -3, -6)

This vector is orthogonal to both direction vectors and thus is parallel to the plane. To find the vector equation of the plane, we can use the point-normal form of the equation, which is:

N · (r - P) = 0

where N is the normal vector, r is a point on the plane, and P is a known point on the plane. We can choose either of the two given points on the intersecting lines as the point P.

Let's use the point (4, 7, 3) on the first line as the point P. Then the vector equation of the plane is:

(9, -3, -6) · (r - (4, 7, 3)) = 0

Expanding and simplifying, we get:

9(x - 4) - 3(y - 7) - 6(z - 3) = 0

Simplifying further, we get:

9x - 3y - 6z = 0

Dividing by 3, we get:

3x - y - 2z = 0

Therefore, the vector equation of the plane containing the two intersecting lines is:

(3, -1, -2) · (r - (4, 7, 3)) = 0

or equivalently,

3x - y - 2z = 0.

Answer:

The two numbers are 6 and -10

Step-by-step explanation:

Given

\(Product = -60\)

\(Sum =-4\)

Required

Two numbers that satisfy the above

Let the two numbers be x and y.

So:

\(x * y = -60\)

\(x + y = -4\)

Make x the subject

\(x = -4 - y\)

Substitute \(x = -4 - y\) in \(x * y = -60\)

\((-4 -y) * y = -60\)

Open bracket

\(-4y -y^2 = -60\)

Rewrite as:

\(y^2 + 4y - 60 = 0\)

Split

\(y^2 + 10y - 6y - 60 = 0\)

Factorize

\(y(y + 10) - 6(y + 10) = 0\)

Factor out y + 10

\((y - 6) (y + 10) = 0\)

Solve for y

\(y -6=0\ or\ y+10=0\)

\(y =6\ or\ y=-10\)

Recall that:

\(x = -4 - y\)

So:

\(x = -4-6= -10\)

or

\(x = -4--10= 6\)

So:

\(y =6\ or\ y=-10\)

\(x = -10\ or\ x =6\)

The two numbers are 6 and -10

write

Step-by-step explanation:

Write the difference between hardware and software

Answer:

y = x + 2

Step-by-step explanation:

change in y is 1

change in x is 1

ratio of change in y to change in x is 1

y = mx + c, where m = 1, y = 1x + c

substituting x = 1 and y = 3

in the equation y = x + c, we have c = 2.

therefore y = x + 2

Answer:

5

Step-by-step explanation:

4 7/12 + 5/12 = 4 12/12 which equals 5

Answer:

3 9/12 + (4 7/12 + 5/12) = 3 9/12 + 5

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Discrete is where its a whole number and does not continue.

There can only be a whole number of people. there cannot be half a person.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer: 6 years

Step-by-step explanation:

Formula to calculate compound amount: \(A=P(1+r)^t\), where P= Principal , r=rate of interest, t= time

Given: P = £400, r = 3% = 0.03 , A= 475

Required equation: \(400(1+0.03)^t\geq475\)

\(400(1.03)^t\geq475\\\\\Rightarrow\ (1.03)^t\geq\dfrac{475}{400}\\\\\Rightarrow\ (1.03)^t\geq1.1875\)

Taking log on both sides , we get

\(t \log 1.03\geq\log1.1875\\\\\Rightarrow\ t(0.0128372)\geq(0.0746336)\\\\\Rightarrow\ t\geq\dfrac{0.0746336}{0.0128372}=5.81385\approx6\)

Hence, he needs to invest the money for 6 years to get atleast £475.

Answer:

29%

Step-by-step explanation:

There are 4+6+2+2 = 14 male students

P( freshman given that they are male) = freshman/ male students

                                                                = 4/14

                                                                =.285714286

                                                                28.5714286

      To the nearest whole percent  = 29%