An indexed set of vectors {v1, v2, . . . , vp} in Rn is said to be linearly independent if the vector equation x1v1 + x2v2 + · · · + xpvp = 0 has only the trivial solution. The set {v1, v2, . . . , vp} is said to be linearly dependent if there exist weights c1, . . . , cp, not all zero, such that c1v1 + c2v2 + · · · + cpvp = 0, is a definition of______

Applying the Angle of Intersecting Chords Theorem, the value of x is calculated as: x = 16.

Recall the Angle of Intersecting Chords Theorem which states that, when two chords intersect within a circle, the angle they create is equal to half the sum of the measures of the intercepted arcs and the vertical angle.

Applying the theorem, we will have the equation below:

7x + 3 = 1/2(78 + 152) [based on the Angle of Intersecting Chords Theorem]

7x + 3 = 115

7x = 115 - 3 [subtraction property of equality]

7x = 112

x = 112/7 [division property]

x = 16

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Step-by-step explanation:

when we put gasoline in a car that will depend on how much it will cost us, also for example if we are going to buy popcorn depending on how many we buy will be the price

True. The statement "cin >> x;" is used in C++ to read input from the user and store it in a variable called "x". The variable "x" can be of any data type (such as int, float, char, etc.) and can also be an expression.

For example, if "x" is an integer, the user can input a single integer value, or they can input an expression that evaluates to an integer value.
For instance, if we have an expression like "cin >> x + 5;", the user will input a value that will be added to 5, and the result will be stored in "x". Similarly, if "x" is a character array, the user can input a string of characters that will be stored in "x".
Therefore, "cin >> x;" is a versatile statement that can be used to read input of any data type and can even handle complex expressions as input. It is important to note that the input must be compatible with the data type of the variable or expression used with the "cin" statement. Otherwise, errors can occur during the input process.

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Considering their slopes, these two lines, Line 1 and Line 2, are perpendicular.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, the slopes are given as follows:

The multiplication is given by:

3 x -1/3 = -1.

Hence they are perpendicular.

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The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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1,081,620

2 x 2 is 4

9 x 30045 is 270,405

so 4 x 270,405 is 1,081,620

Answer:

Step-by-step explanation:

Hope this helps u!!

Mrs. Rosenblatt's class has an average grade of 87. After realizing she left out Joe's score of 65, the new mean will be lower than 87.

Explanation:

To find the new mean, we need to calculate the sum of all the grades in the class, including Joe's score of 65, and divide it by the total number of students in the class. Let's assume there are n students in the class.

The sum of all the grades in the class, including Joe's score, will be (87 * n) + 65, since the average grade before Joe's score was added was 87. Therefore, the new mean will be:

[(87 * n) + 65] / (n + 1)

Expanding this expression, we get:

(87n + 65) / (n + 1)

Simplifying this expression, we get:

(87n / (n + 1)) + (65 / (n + 1))

Since n is a positive integer, the value of (87n / (n + 1)) will be slightly less than 87. Therefore, the new mean will be slightly less than 87, reflecting the lower score added to the class average.

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If Lola uses only ³/₄ gallons of fruit juice, proportionately, she will need the following quantities of the other ingredients:

Proportion is the ratio or relative relationship of one value against another.

Proportion is used to show the quantity of a number contained in another.

Proportions are depicted using fractions, decimals, or percentages.

Available Ingredients for a Punch Recipe:

Bottles of ginger ale = 2 liters

Gallons of fruit juice = 1 gallon

Gallons of sherbet = ¹/₂ gallons

The proportion of fruit juice used = ³/₄ gallons

The proportion of ginger ale to be used = 1¹/₂ liters (2 x ³/₄)

The proportion of sherbet to be used = ³/₈ gallons (¹/₂ x ³/₄)

Thus, in proportion, Lola will use 1¹/₂ liters of ginger ale and ³/₈ gallons of sherbet if she cuts the recipe by using ³/₄ gallons of fruit juice.

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Answer:

Point-slope form:

\(y-4=\displaystyle\frac{1}{3}(x+4)\)

\(y-8=m(x-8)\)

Slope-intercept form:

\(y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}\)

Standard form:

\(-x+3y=16\)

Step-by-step explanation:

Hi there!

1) Point-slope form

Point-slope form: \(y-y_1=m(x-x_1)\) where \((x_1,y_1)\) is a point on the line and m is the slope

First, determine the slope:

\(m=\displaystyle\frac{y_2-y_1}{x_2-x_1}\) where two points on the line are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the points (-4,4) and (8,8):

\(m=\displaystyle\frac{8-4}{8-(-4)}\\\\m=\displaystyle\frac{8-4}{8+4}\\\\m=\displaystyle\frac{4}{12}\\\\m=\displaystyle\frac{1}{3}\)

Therefore, the slope of the line is \(\displaystyle\frac{1}{3}\). Plug this into  \(y-y_1=m(x-x_1)\):

\(y-y_1=\displaystyle\frac{1}{3}(x-x_1)\)

Now, for \((x_1,y_1)\), we can either plug in (-4,4) or (8,8):

\(y-4=\displaystyle\frac{1}{3}(x-(-4))\\\\y-4=\displaystyle\frac{1}{3}(x+4)\)

or

\(y-8=m(x-8)\)

2) Slope-intercept form

Slope-intercept form: \(y=mx+b\) where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

\(y=mx+b\)

Plug in the slope

\(y=\displaystyle\frac{1}{3}x+b\)

Now, to determine the y-intercept, plug in one of the points (-4,4) or (8,8) and solve for b:

\(8=\displaystyle\frac{1}{3}(8)+b\\\\8=\displaystyle\frac{8}{3}+b\\\\8-\displaystyle\frac{8}{3}=b\\\\b=\frac{16}{3}\)

Therefore, the y-intercept is \(\displaystyle\frac{16}{3}\). Plug this back into \(y=\displaystyle\frac{1}{3}x+b\):

\(y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}\)

3) Standard form

Standard form:

\(Ax+By=C\) where A, B, and C are numbers which are typically integers

\(y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}\)

Organize this into standard form:

\(-\displaystyle\frac{1}{3}x+y=\displaystyle\frac{16}{3}\)

Multiply both sides by 3 so A, B, and C are integers:

\(-x+3y=16\)

I hope this helps!

The solution to the inequality \(x + 5 < -2\) is \(x < -7\)

Inequalities are used to represent unequal expressions

Number lines are used to relate numbers at a constant interval

The inequality is given as:

\(x + 5 < -2\)

Subtract 5 from both sides of the inequality

\(x + 5 -5< -2-5\)

Evaluate like terms

\(x < -7\)

See attachment for the graph of the inequality

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Let a(n) denote the n-th term in the sequence. Because the terms are in arithmetic progression, there is a fixed number d that separates consecutive terms, so that starting with a(1) = a, the next few terms are

a(2) = a(1) + d = a + d

a(3) = a(2) + d = a + 2d

a(4) = a(3) + d = a + 3d

and so on, up to

a(n) = a + (n - 1) d

We're given that the 30th term is 98, so

a(30) = a + 29d = 98

The sum of the first 30 terms is 1635, so that

\(\displaystyle \sum_{n=1}^{30}a(n) = \sum_{n=1}^{30}(a+(n-1)d) \\\\ 1635 = a\sum_{n=1}^{30}1 + d\sum_{n=1}^{30}(n-1) \\\\ 1635 = 30a + d\sum_{n=0}^{29}n \\\\ 1635 = 30a + d\sum_{n=1}^{29}n \\\\ 1635 = 30a + \frac{d\times29\times30}2\)

so that

30a + 435d = 1635

Solve the equations in boldface for a and d. I'll eliminate a and solve for d first.

-30 (a + 29d) + (30a + 435d) = -30 (98) + 1635

-30a - 870d + 30a + 435d = -2940 + 1635

-435d = -1305

d = 3

Then

a + 29 (3) = 98

a + 87 = 98

a = 11

Answer: Bianca runs a fruit store. She started Thursday with 14 pears in stock. During the day, she sold 11 pears and got a shipment containing 4 times as many pears as she started the day with. This means that Bianca received a shipment of 14 * 4 = 56 pears. By the end of the day, Bianca had 14 - 11 + 56 = 59 pears in stock

Answer:

Below

Step-by-step explanation:

48 ft /  4.5 ft/piece = 10 2/3 =     ~ 10    pieces with   2/3 ft left over

Answer:

$14,362

Step-by-step explanation:

The computation of the minimum unit cost is shown below:

Given that

0.6x^2 - 108x + 19,222

And as we know that the quadratic equation form is

ax^2 + bx + c

where

a = 0.6

b = -108

c = 19,222

Now for determining the minimal cost we applied the following formula which is

\(= \frac{-b}{2a} \\\\ = \frac{-(-108)}{2\times 0.6} \\\\ = \frac{108}{1.2}\)

= 90

Now put these values to the above equation

\(= 0.6\times 90^{2} - 108 \times 90 + 19,222\)

= 14,362

radii...................

Answer:

RADI

Step-by-step explanation:

Answer:

(x + 1)(x + 2) is divisible by 3.

Step-by-step explanation:

Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.

Case 1: r = 1

If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)

= (3k + 2)(3k + 3)

= 3(3k^2 + 5k + 2)

We can see that (x + 1)(x + 2) is divisible by 3.

Case 2: r = 2

If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)

= (3k + 3)(3k + 4)

= 3(3k^2 + 7k + 4)

We can see that (x + 1)(x + 2) is divisible by 3.

Hence, the statement is proven.

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Answer:

B.21

Step-by-step explanation:

If having 71 seeds is 50 more than needed that would mean that She was gonna grow 21 sunflowers because 71 - 50 = 21

Answer:

21 sunflowers

Step-by-step explanation:

x= number needed

x+50 = 71

x 71-50

x= 21

sin θ cos C

Step-by-step explanation:

Suppose,  θ=30°

Suppose,

     sin θ cos θ=1

 ⇒sin30°cos30°=1

 ⇒\(\frac{1}{2}\)×\(\frac{\sqrt{3\\} }{2}\)=1

 ⇒\(\frac{\sqrt{3} }{4}\)≠1

Since triangle PQR is similar to triangle PTS

1) Side PQ is similar to side PT

2) Side QR is similar to side TS

3) side PR is similar to side PS

Answer:D

Step-by-step explanation:

Answer:

its 2,713

Step-by-step explanation:

i did test

The 12 months past and the fruit turned into sonic the hedge hog #PERIODAHHPERIODUHH

Answer:

128 is the answer

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

The average rate of change is found by

f(4) - f(2)

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

4-2

32 - 56

----------

4-2

-24

------

2

-12

Answer:

your answer would be A

Step-by-step explanation:

The given vector-valued function is\(r(t) = f(t) × g(t)\), where \(f(t) = t^3i − tj − tk\) and\(g(t) = 3ti + t^2j − (t + 8)k.\)

To find the domain of the vector-valued function, we need to determine the values of t for which both f(t) and g(t) are defined.

For f(t), there are no restrictions on the domain since it is defined for all real values of t.

For g(t), we need to consider the denominator (t + 8) in the k-component. To avoid division by zero, we set t + 8 ≠ 0 and solve for t: t ≠ -8.

Therefore, the domain of the vector-valued function r(t) is all real numbers except t = -8.

Main answer: The domain of the vector-valued function

\(r(t) = f(t) × g(t) is (-∞, -8) U (-8, ∞).\)

The domain of the vector-valued function \(r(t) = f(t) × g(t)\)can be found by determining the values of t for which both f(t) and g(t) are defined. The function\(f(t) = t^3i − tj − tk\)is defined for all real values of t since there are no restrictions on its domain.

However, for the function \(g(t) = 3ti + t^2j − (t + 8)k\),

we need to consider the denominator (t + 8) in the k-component. To avoid division by zero, we set t + 8 ≠ 0 and solve for t: t ≠ -8. Therefore, the domain of g(t) is all real numbers except t = -8. Finally, to find the domain of r(t), we need to consider the intersection of the domains of f(t) and g(t), which is (-∞, -8) U (-8, ∞).

The domain of the vector-valued function \(r(t) = f(t) × g(t) is (-∞, -8) U (-8, ∞).\)

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Answer:

correct answer is 110x + 29y = 333

Step-by-step explanation:

The warning approach is an example of Detection of error type prevention.

Error is a conscious or unconscious departure from a standard of conduct. A bug is a mistake in computer data. A software bug is an error, flaw, failure, or fault that results in an unwanted behavior from a computer program or system or leads it to deliver an inaccurate or unexpected outcome. Errors caused by bugs may have repercussions. The majority of defects are caused by faults and blunders in a program's source code, in its design, or in the parts and operating systems that these programs rely on.

After pressing submit or a PAR or KC quiz, D2Lprovides a warning if you have not saved your answers to one or more questions before grading your assignment. Since you are still permitted submit a quiz with unanswered questions, using a warning approach is an example of Detection type of error prevention

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Answer:

B, 15 pencils

Step-by-step explanation:

Our equation: (5 x 42)/14

42 x 5 = 210

210/14= 15