Consider the line y=5/7x+7. Find the equation for the line that is parallel to the line and passes through the point (-5,-2). Find the equation for the line that is perpendicular to the line and passes through the point (-5,-2).

Therefore, the distance across the river is approximately 283 feet (rounded to the nearest foot).

An equation is a mathematical statement that uses symbols, such as letters and numbers, to show that two expressions are equal. It typically consists of two sides separated by an equals sign. The expressions on both sides can contain variables, constants, functions, and operators, and the goal is often to solve for the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and many other fields to model real-world phenomena, make predictions, and solve problems.

Here,

Without a diagram, it is difficult to determine the exact location and orientation of the points and lines. However, based on the information provided, we can use the Law of Sines to find the length of PR.

In triangle ROC, we have:

sin(CEO) = RO/OC

sin(CEO) = 165/330

sin(CEO) = 0.5

CEO = sin⁻¹(0.5)

CEO = 30 degrees

In triangle REO, we have:

sin(ERO) = RO/RE

sin(ERO) = 165/210

sin(ERO) = 0.7857

ERO = sin⁻¹(0.7857)

ERO = 51.06 degrees

Now, in triangle PER, we have:

sin(PER) / 210 = sin(ERO) / PR

Therefore, we can solve for PR:

PR = 210 * sin(ERO) / sin(PER)

PR = 210 * sin(51.06) / sin(180 - CEO - ERO)

Plugging in the values, we get:

PR = 210 * sin(51.06) / sin(99.94)

PR ≈ 283.2 feet

To know more about equation,

https://brainly.com/question/28243079

#SPJ1

Answer: The question requires an understanding of how to compose and decompose multi digit numbers. The expanded form 70,000 + 4,000 + 70 + 2 corresponds to the number 74,072, which is the population of Davidson County.

(sorry if i'm wrong)

:(

Answer:

Step-by-step explanation:

U={x|x∈N and x<10}

or U={1,2,3,4,5,6,7,8,9}

B={x|x∈N and x is even and x<10}

or

B={2,4,6,8}

C={x|x∈N and x<10}

or

C={1,2,3,4,5,6,7,8,9}

(B∩C)={2,4,6,8}

(B∩C)'={1,3,5,7,9}

1/17 is  the probability that his GPA .

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                      Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

If a student has a GPA 3.0 or higher , she has a chance 0.8 getting in a preferable major with a GPA lower than 3.0, the chance will drop to 0.2 . Suppose 20% of the students have their GPA's> 3.0" .

If frank fails to get in this perferable major , then the probability that his GPA is 3.0 or higher is equal to 4/5, 5/18, 1/5 , 1/17

              GPA ≥ 3

        P(P/G) = 0.8

        P(P/Gc ) = 0.2

               P(G) = 0.2

                   = { 1 - 0.8 } 0.2/ { 1 - 0.8 } 0.2 + { 1 - 0.2 } { 1 - 0.2 }

                       = 1/17

Learn more about probability

brainly.com/question/11234923

#SPJ4

Answer:

if this is ur question, then ur answer is 53

Answer:1/4 + 1/4 = 1/2 = 0.5

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

Answer:

top row would be 5 and 8 and the bottom row would be 42 and 60

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

Learn more about congruent angles here: https://brainly.com/question/28262429

#SPJ1

Answer:

Sarah has to invest $502,958.58 today.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

\(E = P*I*t\)

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

\(T = E + P\)

In this question:

\(t = 35, I = 0.07, T = 1700000\)

She has to invest P today.

\(T = E + P\)

\(1700000 = E + P\)

\(E = 1700000 - P\)

So

\(E = P*I*t\)

\(1700000 - P = P*0.07*34\)

\(3.38P = 1700000\)

\(P = \frac{1700000}{3.38}\)

\(P = 502958.58\)

Sarah has to invest $502,958.58 today.

Answer:

q=200+13×5=200+65=265

Answer: bc its numbers

Step-by-step explanation:

Answer:

Because the sum of two even numbers is even.

Hope this helps! :)

An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).

The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.

In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.

Learn more on functions:https://brainly.com/question/11624077

#SPJ1

Answer:

10

Step-by-step explanation:

Answer:

The rock hits the ground at t = 4.68 seconds.

Step-by-step explanation:

The height of the rock after t seconds is given by the following equation:

\(h(t) = -16t^{2} + v(0)t + h(0)\)

In which v(0) is the initial speed and h(0) is the initial height.

An rock is thrown downward from a platform that is 163 feet above ground at 40 feet per second.

This means that \(v(0) = 40, h(0) = 163\)

So

\(h(t) = -16t^{2} + 40t + 163\)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

When the rock hits the ground?

When h(t) = 0. So

\(h(t) = -16t^{2} + 40t + 163\)

\(-16t^{2} + 40t + 163 = 0\)

So

\(a = -16, b = 40, c = 163\)

Then

\(\bigtriangleup = (40)^{2} - 4*(-16)*163 = 12032\)

\(t_{1} = \frac{-40 + \sqrt{12032}}{2*(-16)} = -2.18\)

\(t_{2} = \frac{-40 - \sqrt{12032}}{2*(-16)} = 4.68\)

Time is a positive measure, then:

The rock hits the ground at t = 4.68 seconds.

Answer:

(-1,1)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

equation form:
x=-1, y=1

have a great day and thx for your inquiry :)

By substituting each of the provided options into the given system of linear equations, it is revealed that the ordered pair (-1, 1) is a valid solution for both the equations.

The correct answer is (-1, 1)

In mathematics, a system of linear equations consists of multiple linear equations with the same variables. These equations describe various relationships among these variables, typically representing lines in a multi-dimensional space. Solving such systems involves finding values for the variables that satisfy all equations simultaneously. Methods like substitution, elimination, or matrix algebra can be used to solve these systems. These systems are fundamental in fields like physics, engineering, economics, and computer science for modeling and solving real-world problems involving multiple interconnected variables.

We can solve this problem by substituting values from the given options into the equations and checking for which option both equations are valid. The system of linear equations is: x + 4y = 3 and y = -4x - 3.

Therefore, the ordered pair that is a solution to the system of linear equations is (-1, 1).

Learn more about System of Linear Equations here:

https://brainly.com/question/33609849

#SPJ2

Choice D is correct

Every point on circle is equidistant from the point at its centre and that fixed distance = radius of that circle.

So on solving the provided question, we can say that the mathematical expression will be as follows, z-12, 17xy, 4x+75.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +. In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

x - 6 + z  = 9-6+5 = 8

5*(x+y) = 5*(9 + 10 ) = 95

2x + z = 2*9 + 5 = 23

To know more about expression visit:-

brainly.com/question/14083225

#SPJ1

Answer:

0.5

Step-by-step explanation:

We have to find a  number which is greater than the absolute value of -3/8.

Absolute value of -3/8 = 3/8

3/8=0.375

Now, we have to find a number which is greater than 0.375

1/4=0.25

0.25 is smaller than 0.375

0.5 is greater than 0.375

also -5/8 and -1/8 are less than 0.375

Hence, the only number which is greater than the absolute value of -3/8 is:

0.5

Step-by-step explanation:

The dimensions of the area covered by flowers are 9 ft and 6 ft.

The area of Rectangle is length times of width.

The given garden is a rectangle

Since the garden is a rectangle, its area is A = LW where

L = length = 12 ft and

W = width = 9 ft

So, A = Length×Width

= 12×9

= 108 ft²

As flowers are planted on the remaining side of the garden with a path of width x on on side, we have that the dimensions of the area covered by flowers is

length, L' = 12 - x and

width, W' = 9 - x

Since the planted part is rectangle, its area is A' = L'W' where L' 12 - x and W'= 9 - x

So, A' = L'W'

= (12 - x)(9 - x)

Since it is given that he part covered by flowers is half of the entire enclosed area, we have that

A' = A/2

(12 - x)(9 - x) = 108 ft²/2

(12 - x)(9 - x) = 54

Expanding the brackets, we have

108 - 21x + x² = 54

x² - 21x + 108 - 54 = 0

x² - 21x + 54 = 0

By using quadratic formula, we find value of x

We get x=18 or x=3

Since x cannot be greater than the greatest dimension, we choose x = 3. length, L' = 12 - x = 12 - 3 = 9 ft and the width W' = 9 - x = 9 - 3 = 6 ft

Hence, the dimensions of the area covered by flowers are 9 ft and 6 ft.

To learn more on Rectangles click:

https://brainly.com/question/20693059

#SPJ1

Answer:

6/5 x 5/3 is 2

if that's what you need help with

step-by-step explanation

Answer: 20

Step-by-step explanation:

= 1/5 (10)^2

= 1/5 * 100

= 20

Answer: 20

Step-by-step explanation:

To solve this problem, we need to use the order of operations.

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

\(\frac{1}{5}(6+3+1)^2\)             [parenthesis]

\(\frac{1}{5}(10)^2\)                        [exponent]

\(\frac{1}{5}(100)\)                       [multiply]

\(20\)

Now, we know the answer is 20.

The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

for such more question on inequality

https://brainly.com/question/17448505

#SPJ11