An employee at Kennedy Space Center (KSC) lives in Daytona Beach and works in the vehicle assembly building (VAB). She
carpools to work with a colleague. She drives 7 miles from her house to the park-and-ride. Then she rides with her colleague from the
park-and-ride in Daytona Beach to the KSC headquarters building, and then takes the KSC shuttle from the headquarters building to
the VAB. The drive from the park-and-ride to the headquarters building is of her total trip, and the shuttle ride is of her total trip.
How many miles does she travel from her house to the VAB on days her colleague drives?

The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

Read more on 30-60-90 triangle here: brainly.com/question/30283450

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

890 1/2 or  890.5

Step-by-step explanation:

Answer:

890.5 ft²

Step-by-step explanation:

Formula to find rectangular area

    Area = A = L × W

So put values

R 1        A 1 = 24.5 ×  18 = 441

R 2      A 2 = 14.5  × 18.5 = 268.25

R 3      A 3 = 12.5 ×  14.5 = 181.25

Add them up

441 + 268.25 + 181.25 = 890.5

Answer:

Hope my ans help you plz if u can mark me brainlist

Step-by-step explanation:

A = 43.3

The area of an equilateral triangle has a side length of 10 units is 43.3 square units.

An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle.

Given the side of an equilateral triangle  = 10 units

the area is given by,

A = √3/4 × a²

where a is the length of the side,

A = √3/4 × 10²

A = 1.732 x 100/4

A = 43.3 square units.

Therefore, the area of a triangle is 43.3 square units.

Learn more about equilateral triangle;

https://brainly.com/question/3461022

#SPJ5

Answer:

The GCF of the terms is 2c

Step-by-step explanation:

Greatest common factor:

To find the gcf of the expression, we find the gcf separately for the numbers and for the powers of c, and then multiply them.

Numbers:

8, 12 and 10.

Dividing them all by prime factors:

8 - 12 - 10|2

4 - 6 - 5

5 is not divisible by 2, so we stop there, and the gcf of the numbers is 2.

Powers of c:

Powers of c are 1, 2 and 3. The gcf of 1,2,3 is 1, as there is not a number that is divisible by all of 1,2,3 other than 1. So the gcf for the powers of c is c^1 = c.

GCF of the expression:

2*c = 2c

Answer:

it should round up to 36000

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:  \(y \ge -3\)

Explanation:

The smallest y can get is y = -3. So y can be anything larger than this, or equal to -3. We can then say the set of possible y values is \(y \ge -3\) which describes the range of this function. The range is the set of all possible y outputs.

The range of the graph is y≥-3.

The collection of all a function's outputs is its range.

Consider the function f: A: B, where f(x) = 2x and A and B each represent a "set of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range. The components of the co-domain that are mapped are known as the pictures, while the elements of the domain are known as pre-images. The set of all pictures of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.

As, seen from the graph the lowest value of y is y = -3.

So, y can be more than this or equal to -3.

Thus, The range of this function is thus described by the set of potential y values. The set of all feasible y outcomes is the range.

Hence, the range of the graph is y≥-3

Learn more about range of the graph here:

https://brainly.com/question/28754571

#SPJ2

The first equation is incorrect.

The second equation is correct.

The third equation is correct.

Let's go through each equation and determine whether it is correct or incorrect:

(b²+7b-9)+(4b-6b²) = -8b² + 14b-9

To determine if this equation is correct, we need to simplify both sides and check if they are equal.

On the left side:

(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9

On the right side:

-8b² + 14b - 9

Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.

(4a+6)-(3a²-9a+1)=-3a²+ 13a +5

Again, we need to simplify both sides of the equation and check if they are equal.

On the left side:

(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5

On the right side:

-3a² + 13a + 5

Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.

(12c-8c²)+(5c²- 10c) = -3c²+2c

Again, let's simplify both sides and compare them.

On the left side:

(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c

On the right side:

-3c² + 2c

Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.

For more such questions on equation visit:

https://brainly.com/question/17145398

#SPJ8

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define vertical line test

If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.

STEP 2: Perform the vertical line test on the graph in 12

The graph did not pass the vertical line test since there are vertical lines that pass through more than one point on the graph.

Hence, the graph does not represent a function since the line crosses the graph twice.

The pounds of raw materials that should be purchased in July is 102900.

From the information illustrated, Morganton Company makes one product and the budgeted selling price per unit is $60. Budgeted unit sales for June, July, August, and September are 8,900, 20,000, 22,000, and 23,000 units.

The raw materials to be bought will br:

= Closing Raw materials + Used in production - Opening raw materials

= 11100 + 102000 - 10200

= 102900

The raw materials is 102900.

Learn more about raw material on:

brainly.com/question/21323235

#SPJ1

Answer:

\(x=-1\)

Step-by-step explanation:

Cross multiply.

10(4x + 1) = 15(2x)

Expand brackets.

40x + 10 = 30x

Add -30x and 10 on both sides.

40x - 30x = -10

10x = -10

Divide both sides by 10.

10/10x = -10/10

x = -1

Answer: (4x200) + (4x10) + (4x3)

Step-by-step explanation:

First, break apart 213 into hundreds, tens, and ones.

Then, Multiply the hundreds by 4

Then, Multiply the tens  by 4

Then, Multiply the ones by 4

Lastly, Add it all together

Answer:

i think its 4

Step-by-step explanation:

Figure 20 would have 60 squares on the base, 60 squares height

Perimeter = 60 + 60 + 60 + 20 + 40 + 20 + 40 + 20 = 320 ==> Perimeter = 320

Area = seven times 20 by 20 = 7 (20 x 20) = 7 (400) = 2800 ==> Area = 2800

Equation: Number of squares = 7 n^2, where n is the number of the figure

Equation: Number of squares = 7 n^2

The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

Learn more about graph:
https://brainly.com/question/25184007
#SPJ1

Answer:

5 6/7

Step-by-step explanation:

how many times does 7 go onto 41?

7 x 5 = 35

remainder is 6 so;

5 6/7

Hey there!

41/7

= (5 * 7 + 6)/7

= (5 * 7)/7 + 6/7

= 5 6/7

= 5 6/7 ≈ 41/7

Therefore, your answer is: 5 6/7

Good luck on your assignment and enjoy your day’

~Amphitrite1040:)

The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

for such more question on matching expressions

https://brainly.com/question/12270624

#SPJ8

To calculate how much Naruto spends on ramen in 15 days, we need to determine the total cost of ramen per day and then multiply it by 15.

Since Naruto receives a 33.33% discount, he pays 100% - 33.33% = 66.67% of the original price.

66.67% of 45 cents is (66.67/100) * 45 = 30 cents.

So, Naruto spends 30 cents on ramen per day.

To find out how much he spends in 15 days, we multiply the daily cost by the number of days:

30 cents * 15 = 450 cents.

Therefore, Naruto spends 450 cents, which is equivalent to $4.50, on ramen in 15 days.

The value of the fraction expression -2 1/2 - (-4 3/5) is 2 1/10

From the question, we have the following parameters that can be used in our computation:

−2 /2/1 −(−4 3/5)

Express properly

So, we have the following representation

-2 1/2 - (-4 3/5)

Remove the brackets

This gives

-2 1/2 - (-4 3/5) = -2 1/2 + 4 3/5

Express the denominator as 10

So, we have

-2 1/2 - (-4 3/5) = -2 5/10 + 4 6/10

Evaluate the difference

-2 1/2 - (-4 3/5) = 2 1/10

Hence, the solution is 2 1/10

Read more about fraction at

https://brainly.com/question/1622425

#SPJ1

Answer:

32y^2-8z^2 and x^4 - 400

Step-by-step explanation:

The expressions X^4 - 400 and 32y^2 - 8z^2 can be factored using the difference of squares identity.

The difference of squares identity is shown below:

a^2 - b^2 = (a + b)(a - b)

We can factor each expression individually to determine if the identity is being used.

6x^2 - 81 = 3(2x^2 - 27)

The identity is not used.

49x - x^4 = x(49 - x^3)

The identity is not used.

x^4 - 400 = (x^2 + 20)(x^ - 20)

The identity is used.

32y^2 - 8z^2 = 2(16y^2 - 4z^2)

= 2(4y - 2z)(4y + 2z)

The identity is used.

4a^2 - 64b^5 = 4(a^2 - 16b^5)

The identity is not used.

Therefore, we have determined that the expressions x^4 - 400 and 32y^2 - 8z^2 can be factored by using the "difference of squares" identity.

Learn more about identities here: https://brainly.com/question/10041032

#SPJ2

The tree is 6 feet tall

The interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

In this question we have an expression that combines polynomic and exponential expression, whose variable x cannot be cleared by analytical approaches, but by numerical and graphical methods. Herein we decide to find the interval by graphical methods, using a graphing tool:

First, write the function in explicit form (f(x) = 3 · x - eˣ). Second, find the two points such that the function goes through the x-axis (horizontal axis). Third, define the set of possible x-values by interval notation such that y > 0.

Then, the points of the function that are on the x-axis are (x₁, y₁) = (0.6191, 0) and (x₂, y₂) = (1.5121, 0). Then, the interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

To learn more on functions: https://brainly.com/question/12431044

#SPJ1

Answer:

c=a2+b2=102+172≈19.72308

Step-by-step explanation:

a calculator bro its easy

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

To know more about equation visit:

https://brainly.com/question/10413253

#SPJ1

Answer:

a:6÷9

b:0.666% are the answers

The quadrant of the terminal side for 15) is fourth quadrant.

To change from radians to degrees, you need to the multiple the number of radians by 180/π.

Multiple the number of radians by 180/π.

15) 5 radians = 5 * (180/π)

16) 11π/6 = (11*180)/6 = 330.

19) 3.5 = 3.5*(π/180) degree.

20) 1 = 1*(π/180) degree.

therefore, terminal side for 15) is fourth quadrant.

Learn more about radians here:

https://brainly.com/question/28990400

#SPJ

the slope-intercept form of the line parallel to y = -2x-1, passing through (4,-3) is y = -2x +5.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, a linear equation y = -2x -1

Compare with the slope-intercept form of the line, we get that slope of the line m is -2.

Since. another line that is parallel to y = -2x -1 So, this equation will have the same slope.

The slope-intercept form of the equation of a line

y = mx + b,

where m is the slope

b is the y-intercept

thus, the equation of the line will be

y = -2x + b

Since the given line passes through the point (4, -3)

-3 = -2*4 + b

-3 = -8 + b

b = -3 + 8

b = 5

therefore, the equation of the line will be y = -2x +5.

Learn more about Linear equations here:

https://brainly.com/question/11897796

#SPJ1

Answer: She can select 7 workshops if more than 4 must be about anthropology in 1716 ways.

Step-by-step explanation:

Given, The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology.

If he select 7 workshops if more than 4 must be about anthropology, the possible combinations = (5 anthropology, 2 psychology), (  6 anthropology, 1 psychology), (7 anthropology, 0 psychology)

Number of possible combinations = \(^9C_5\times ^5C_2+^9C_6\times ^5C_1+^9C_7\times ^5C_0\)

\(=\dfrac{9!}{5!4!}\times\dfrac{5!}{2!3!}+\dfrac{9!}{6!3!}\times(5)+\dfrac{9!}{7!2!}\times (1)\\\\=\dfrac{9\times8\times7\times6}{4\times3\times2\times1}\times\dfrac{5\times4}{2}+\dfrac{9\times8\times7}{3\times2\times1}\times5+\dfrac{9\times8}{2}\\\\=1260+420+36\\\\=1716\)  [using formula for combinations \(^nC_r=\dfrac{n!}{r!(n-r)!}\)]

Hence, she can select 7 workshops if more than 4 must be about anthropology in 1716 ways.

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

For more such questions on direction

https://brainly.com/question/30016405

#SPJ8