Hello, I could use some help understanding this question please.

To find the magnitude of a vector we use the following equation

This comes from taking the value of the hypotenuse by Pythagoras, graphically it can be seen in the following image:

In the case of your exercise, the values would be

a. The actual distance from Dallas to Houston is 0.058 mi. b. The actual distance from Dallas to San Antonio is 0.064 mi

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

Given that the actual distance from San Antonio to Houston is approximately 192 ​miles.

The scale factor from the map to the real world is;

 (actual)/( map) = (192mi)/(3 in) = 64 mi/in

Then the actual distance from Dallas to Houston will be;

 (3.75 in)(64 mi/in) = 0.058 mi

And from Dallas to San Antonio, the distance will be;

 (4.125 in)(64 mi/in) = 0.064 mi

Learn more about distance here:

https://brainly.com/question/24388592

#SPJ1

The complex expression (2+5) - (-6 +bi) in the form a + bi is 13 - bi

The expression is given as

(2+5) - (-6 +bi)

The above expression is a complex expression

So, we have the following expression

(2+5) - (-6 +bi)

Remove the brackets in the above expression

So, we have the following expression

(2+5) - (-6 +bi) = 2 + 5 + 6 - bi

Evaluate the like terms in the above equation

So, we have the following expression

(2+5) - (-6 +bi) = 13 - bi

Hence, the solution to the complex expression is 13 - bi

Read more about complex expression at

https://brainly.com/question/11245197

#SPJ1

The maximum displacement of this cosine wave function is equal to 8 inches.

The frequency of this cosine wave function is equal to 1/8 Hertz.

The time (t) required for one cycle is equal to 8 seconds.

Mathematically, a cosine wave simply refers to an equation of simple harmonic motion (SHM) and it is modelled by this mathematical expression:

y = asinωt = asin2πft     ......equation 1.

Where:

From the information provided, the equation for this simple harmonic motion (SHM) is given by:

d = -8cos(π/4)t           ......equation 2.

By comparing equation 1 and equation 2, we have the following parameters:

Maximum displacement or amplitude, a = |-8|

Taking the absolute value of a, we have:

Maximum displacement or amplitude, a = 8

For the frequency, we have:

Angular velocity, ω = 2πf

Making frequency (f) the subject of formula, we have:

Frequency (f) = ω/2π

Frequency (f) = (π/4)/2π

Frequency (f) = π/8π

Frequency (f) = 1/8 Hertz.

Finally, we would calculate the amount of time (t) required for one cycle as follows:

Time (t) = 1/f

Time (t) = 1/(1/8)

Time (t) = 8 seconds.

Read more on maximum displacement here: https://brainly.com/question/12969776

#SPJ1

Complete Question:

An object moves in simple harmonic motion described by the equation d = -8cos(π/4)t, where t is measured in seconds and d in inches. Find the following:

maximum displacement

the frequency

the time required for one cycle.

The system of inequalities is x + y ≤ 300, 11x + 15y ≥ 3630, x ≥ 0 and y ≥ 0 while the three points are (70, 200), (150, 140) and (140, 150)

From the question, we have the following parameters that can be used to determine system of inequalities

Represent the adult with y and the students with x

So, we have the following representations

x + y ≤ 300 ---- the ticket holders cannot exceed the capacity

11x + 15y ≥ 3630 --- the total sales cannot be less than $3630

x ≥ 0 -- the number of students cannot be negative

y ≥ 0 -- the number of students cannot be negative

Write out the inequalities

x + y ≤ 300

11x + 15y ≥ 3630

x ≥ 0

y ≥ 0

Next, we represent the inequalities on a graph

See attachment for the graph of the inequalities

To get the combination, we make use of the coordinate points that are in the shaded region of the graph

Using the above as a guide, we have

(70, 200), (150, 140) and (140, 150)

There are other points too

Read more about inequalities at:

https://brainly.com/question/25275758

#SPJ1

Answer:

$7,000

Explanation:

To find the simple interest on any principal, we use the formula:

From the given question:

• Principal = $50,000

• Rate= 7%

• Time = 2 years

Therefore:

The simple interest is $7,000.

[tex]9y - 2y + 3 = 5y - 10 + 2 \\ 7y + 3 = 5y - 8 \\ 7y - 5y = - 8 - 3 \\ 2y = - 11 \\ \frac{2y}{2} = \frac{ - 11}{2} \\ y = \frac{ - 11}{2} [/tex]

ATTACHED IS THE SOLUTION OF Y

BE AWARE THERE IS A SOLUTION FOR THE PROBLEM.

Answer:

slope would be 4/1

Step-by-step explanation:

its rise over run, so up 4 and out 1

have a good day!

Answer:

x = 0 and 2pi/3

Explanation

Given the expression

cos(2x)=cos(x)

In trigonometry expression;

cos2x = 2xos^2x - 1

Substituting into the equation given;

cos(2x)=cos(x)

2xos^2x - 1 = cos x

Rearrange

2xos^2x - 1 - cosx - 1 = 0

Let P = cosx

2P^2 - P - 1 = 0

Factorize

2P^2 - 2P+P-1 = 0

2P(P-1)+1(P-1) = 0

2P+1 = 0 and P-1 = 0

P = -1/2 and 1

Recall that P = cosx

-1/2 = cosx

x = cos^-1(-1/2)

x = 120 degrees = 2pi/3

If P = 1

cosx = 1

x = cos^-1(1)

x = 0

Hence the value of x that satisfies the equation is 0 ad 2pi/3

Answer:

The anser is

Step-by-step explanation:

DO IT YOURSELF BRO GO LEARN AND STOP USING BRAINLY PU_$$y

We are given the following information

Slope of the line = m = -3

The line passes through the point (5, -7)

Recall that the equation of a line in the point-slope form is given by

Where m is the slope and (x₁, y₁) is a point on the line.

Let us substitute the given values into the above equation

Therefore, the equation of the line in slope-intercept form is

Given:

To find:

The roots.

Explanation:

Here,

Using the quadratic formula,

On substitution we get,

Therefore, the solutions are,

Final answer:

The solutions are,

The linear function that passes through the points (-3, 18) and (2, -7) is defined by the rule:

y = -5*x + 3

We can find a general linear function in the slope-intercept form as:

y = m*x + k

Where m is the slope and k is the intercept of the y-axis.

If we know that the line passes through the points (a, b) and (c, d) then the slope of the function is:

m = (d - b)/(c - a)

In this case the line passes through the points (-3, 18) and (2, -7), then the slope is:

m = (-7 - 18)/(2 + 3) = -5

So the line is something like:

y = -5*x + k

To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:

-7 = -5*2 + k

-7 = -10 + k

-7 + 10 = k

3 = k

So the linear function is:

y = -5*x + 3

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

hmmph..

(32, 31)

(33,30)

(34, 29)

(35, 28)

(36,27)

(37, 26)

Step-by-step explanation:

That all I got....

ANSWER:

The value of x is 16

STEP-BY-STEP EXPLANATION:

With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.

Thanks to this we can make the following equality:

Solving for x:

Answer:

16 is the answer

f(10) is a multiple of 12 because f(x) has a linear factor of x+2 and x+2 = 12, when x = 10

f(10) multiple of 12 is given as:

The first-degree equations that make up a polynomial's linear factors serve as the foundation stone for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. When paired with other linear factors, each linear factor represents a separate line, resulting in several sorts of functions with progressively more intricate graphical representations.

f(10) = (10+2)(100+20+2)

= (12)(122)

= 1220+244

= 1464

Hence, f(10) is a multiple of 12

Learn more about linear factors:

https://brainly.com/question/2510777

#SPJ1

To complete the square, we want a number such that:

because in this way we can writte the square as follows:

Hence the answer is the last option:

we have that

Two times the sum of a number and 7 -----> 2(w+7)

Two times the sum of a number and 7 equals 6 ----> 2(w+7)=6

the answer is

There will not be enough T-shirts for all the students

From the question, the given parameters are:

Number of T-shirt = 1437

From the question, we understand that the principal approximates the number of T-shirts to the nearest hundred

When the number of T-shirts is approximated to the nearest hundred, we have

Approximation = 1400

By comparison, 1400  is less than 1437

This means that the T-shirts will not be enough

Read more about approximation at

https://brainly.com/question/13221614

#SPJ1

Using the t-distribution, the 95% confidence interval estimate of the population mean rating for Miami is of:

(4.29, 7.71).

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the meaning of the parameters are:

Using a calculator from the 50 observations given in this problem, the values of the parameters are as follows:

[tex]\overline{x} = 6, s = 2.86, n = 50[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Hence the lower bound of the interval is given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6 - 2.0096\frac{6}{\sqrt{50}} = 4.29[/tex]

The upper bound of the interval is given by:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6 + 2.0096\frac{6}{\sqrt{50}} = 7.71[/tex]

More can be learned about the t-distribution at https://brainly.com/question/16162795

#SPJ1

the probability of getting a 2 tree times is

The space sample is the total quantity of possible results

for each toss there are 3 possible results

so the total results are 2x 3 = 6

The only option with 6 elements is B

so the answer is B.

The length of the diagonal of the napkin is 11 inches.

Here, we are given that a square napkin has a side of length 8 inches.

All the sides of a square are equal and the measure of angle formed by any two adjacent sides is also equal and 90°.

Thus, by using Pythagoras theorem, we can form the following equation-

[tex]side^{2} + side^{2} = diagonal^{2}[/tex]

Let the diagonal of the square be d. Then, we have-

[tex]8^{2} +8^{2} =d^{2}[/tex]

64 + 64 = [tex]d^{2}[/tex]

128 = [tex]d^{2}[/tex]

[tex]d^{2}[/tex] = 128

d = [tex]\sqrt{128}[/tex]

d = [tex]8\sqrt{2}[/tex]

the value of [tex]\sqrt{2}[/tex] is approximately 1.41. Thus,

d = 8 × 1.41

= 11.28

Thus, the length of the diagonal of the napkin to the nearest inch comes out to be 11.

Learn more about squares here-

https://brainly.com/question/25092270

#SPJ1

Area of the cricket pitch is 660 square feet

Given

1 chain is equal to 10 feet

There are 3 feet in a yard

And 22 yards in a chain

Hence it is evident that

One chain is equal to 22 x 3

1 chain = 66 Feet

Area of a rectangle is Length x Width

Length = 66

Width =  10

Hence Area = 66 x 10

Area = 660 Square feet

Hence area of the cricket pitch is 660 square feet.

Learn more about Area at

https://brainly.com/question/27683633?referrer=searchResults

#SPJ1

Answer:

Step-by-step explanation:

$220=$10x+$50

x= hours

subtract $50 from both sides making sure to cancel the right side

$220-$50=$10x

$170=$10x

Divide both sides by $10 to leaving x by itself on the right side

$170/$10=x

17hrs=x

The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Cost of new pair of shoes = $220

In order to earn money for this, Keandre babysits his neighbor for $10 an hour.

And, He also has saved up his monthly allowance which totals $50.

Now,

Let number of minimum hours = x hour

So, We can formulate;

⇒ $10x + $50 = $220

Solve for x as;

⇒ $10x + $50 = $220

Subtract 50 both side, we get;

⇒ $10x + $50 - $50 = $220 - $50

⇒ $10x = $170

Divide by 10 both side, we get;

⇒x = 17

Thus, The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.

Learn more about the expression visit:

https://brainly.com/question/4344214

#SPJ2

Roots are x = - 6 + √20/8 and x = - 6 - √20/8 of polynomial.

What in mathematics is a polynomial?

4x² - 6x+1 = 0

x = -b ± √b² - 4ac/2a

x = - (6) ± √(-6)² - 4 * 4 * 1/2 * 4

x = -( 6) ± √36 - 16/8

x = - 6 ± √20/8

So, roots are x = - 6 + √20/8 and x = - 6 - √20/8

Learn more about polynomial

brainly.com/question/11536910

#SPJ13