The function f(x) represents the number of texts sent this week, and g(x) represents the number of texts sent last week. Given f(x) = 7x + 5 and g(x) = 6x − 8, find (f − g)(x) to find how many more texts were sent this week than last week.

(f − g)(x) = x + 13
(f − g)(x) = x − 13
(f − g)(x) = 13x + 13
(f − g)(x) = 13x −13

Answer: (a) To find the position vector of point D, we need to find the midpoint of the line segment AB. We can do this by taking the average of the position vectors of points A and B:

D = (A + B) / 2 = ((2i + 3j - 4k) + (4i - 2j + 3k)) / 2 = (3i + 0.5j - 0.5k)

So, the position vector of point D is (3i + 0.5j - 0.5k).

(b) To find the value of a, we use the fact that the distance between points A and C is 4. We can find the distance between two points by finding the magnitude of the difference between their position vectors. The position vector of point C is (ai + 5j – 2k), so the difference between the position vectors of points A and C is (ai + 5j – 2k) - (2i + 3j - 4k) = (a-2)i + 2j - (-2k).

The magnitude of this difference is given by:

|(ai + 5j - 2k) - (2i + 3j - 4k)| = √((a-2)^2 + 2^2 + 2^2) = 4

So, we have:

√((a-2)^2 + 2^2 + 2^2) = 4

(a-2)^2 + 2^2 + 2^2 = 16

(a-2)^2 = 16 - 4 - 4

(a-2)^2 = 8

a-2 = ±2√2

Since a < 0, we have:

a = 2 - 2√2

So, the value of a is 2 - 2√2.

Step-by-step explanation:

The length of the segment AB is 3.5 cm  

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

We have segments ratio as shown:

BC/AB = CD/ED

=> (AC - AB)/AB = (EC - ED)/ED

=> (14-AB)/AB = (84-21)/21 = 3

    Let AB=x

=>  (14-x)/x = 3

=> 14-x = 3x

=> 14 = 3x+x = 4x

=> 14/4 = x

=> x=3.5 cm

AB=x = 3.5 cm  

The length of the segment AB is 3.5 cm  

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the answer is 40780

I would show you my calculations  but I don't know how to add pictures to your answer .sorry

I hope that helped

The measure of the smaller acute angle is 26 degrees, and the measure of the larger acute angle is 64 degrees.

Let's call one acute angle x and the other acute angle y.

Since they are both acute angles of a right triangle, we know that their sum is 90 degrees:

x + y = 90

We also know that one angle is 2 times the other angle plus 6:

x = 2(y + 6)

Now we can substitute the second equation into the first equation and solve for y:

x + y = 90

2(y + 6) + y = 90

3y + 12 = 90

3y = 78

y = 26

Now that we have the value of y, we can use the second equation to solve for x:

x = 2(y + 6)

x = 2(26 + 6)

x = 64

Therefore, the measure of the smaller acute angle is y = 26 degrees, and the measure of the larger acute angle is x = 64 degrees.

Correct Question :

In a right triangle, the measure of one acute angle is 2 times the sum of the measure of the other acute angle and 6. find the measure of each acute angle.

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Answer:

y <= 40

Step-by-step explanation:

Let's call the number of people traveling by van "x", and the number of people buying train tickets "y". We know that the total number of people in the group is 40, so we can write the equation:

x + y = 40

And we also know that the van can hold up to 12 people, so we can write the inequality:

0 <= x <= 12

Now, to find the number of train tickets, we just need to substitute

x = 40 - y into the second inequality:

0 <= 40 - y <= 12

Expanding and solving for y, we get:

0 <= 40 - y <= 12

-40 <= -y <= -28

y >= 28

y <= 40

So the number of train tickets needed (y) is equal to or greater than 28 and equal to or less than 40.

Answer:

Inequality:    12 + x ≤ 40

Solution:   x ≤ 28

Step-by-step explanation:

Let x be the number of train tickets that the group will need.

As the van holds 12 people and the rest will buy train tickets, an expression for the total number of people is:

If the group is up to 40 people then 12 + x will be less than or equal to 40:

Therefore, the inequality that can be used to find the number of train tickets that the group will need is:

To solve the inequality, subtract 12 from both sides:

⇒ 12 + x - 12 ≤ 40 - 12

⇒ x ≤ 28

Therefore the number of train tickets that the group will need is less than or equal to 28 tickets.

Answer:[tex]\sqrt{6}[/tex]

Step-by-step explanation:

The distance between 2 points is given by:

[tex]\sqrt{(x2-x1)+(y2-y1)}[/tex]

Let (6,3) be (x1, y1) and (8,7) (x2,y2).

=[tex]\sqrt{(8-6)+(7-3)}[/tex]

=[tex]\sqrt{2+4}[/tex]

=[tex]\sqrt{6}[/tex]

Hope this helps :)

[tex]\sqrt{p^1^2-16p^6+80}[/tex]

A pic down below is given:

The two points that would lie on the graph of function g are (-2,-12) and (1,30). The solution has been obtained by using functions.

What is a function?

An association between a number of inputs and a single output for each input is known as a function. A function is often written as f(x), where x stands for the input. A function is typically expressed as y = f(x).

We are given that f(x) passes through the points (-2,-4) and (1,10).

So, it means that

For x = -2,  f(-2) = -4

Similarly,

For x = 1, f(1) = 10

We are given g(x) = 3f(x)

So, on substituting the obtained values of f(x) in the g(x) function, we get

For x = -2,

⇒g(-2) = 3f(-2)

⇒g(-2) = 3(-4)

⇒g(-2) = -12

Similarly,

For x = 1,  

⇒g(1) = 3f(1)

⇒g(1) = 3(10)

⇒g(1) = 30

Hence, the two points that would lie on the graph are (-2,-12) and (1,30).

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Question: An exponential function, f, passes through the points (-2,-4) and (1,10). Which two points would lie on the graph of function g if g(x)=3f(x)?

The statement "The margin of error is a key component of a confidence interval, as it reflects the uncertainty in the estimate due to sampling error." is true

A confidence interval is a range of values that likely contains the true value of a population parameter, such as the mean or proportion. It is created by taking a sample from the population and calculating a point estimate, such as the sample mean or proportion.

To account for this uncertainty, we use the concept of a margin of error, which represents the maximum amount by which the point estimate could be off from the true parameter.

The sample size refers to the number of observations in the sample. The larger the sample size, the more precise the estimate is likely to be, since there is less variability and sampling error.

The level of confidence refers to the degree of certainty that the true parameter lies within the confidence interval. A higher level of confidence means a wider interval, since we need to be more certain that the true parameter is included.

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In the given right angle triangle the measure of tanL, sinL, and cosL is 73.74°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

Given, A right-angled triangle has side lengths 7, 24, and 25.

Here, Hypotenuse is 25, Adjacent is 7 and opposite is 24.

Now, tan = opposite/adjacent.

tanL = 24/7.

L = tan⁻¹(24/7).

L = 73.74°.

Similarly,

sinL = 24/25.

L = sin⁻¹(24/25).

L = 73.74°.

And,

cosL = 7/25.

L = cos⁻¹(7/25).

L = 73.74°.

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yes. the hikers will ever be the same elevation.6+1=7  the same elevation.

Y = 6x + 1

FIll the value of y in this equation

3x + 4​= 6x + 1

3x=4-1

x=3/3=1

Y = 6x + 1

FIll the value of x in this equation

6+1=7. The height above or below a specified reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. In most cases, elevation is used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface. Elevation should not be confused with the angular separation from the Earth's center. The summits of Mount Everest and Chimborazo have the highest elevation and greatest geocentric distance, respectively, because of the equatorial bulge.

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A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, we can be multiply two polynomials step by step.

Distribute each term of the first polynomial to every term of the second polynomial.

Combine like terms by adding the coefficients of the terms that have the same variables raised to the same powers.

Simplify the result by arranging the terms in descending order of the exponent of the variable.

For example, let's say you want to multiply (2x + 3) and (x - 4):

(2x + 3) * (x - 4) = 2x * x - 2x * 4 + 3 * x - 3 * 4

Simplify the terms: 2x^2 - 8x + 3x - 12

Combine like terms: 2x^2 - 5x - 12

Therefore, the product of (2x + 3) and (x - 4) is 2x^2 - 5x - 12.

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A 5-card poker hand is dealt from a standard deck of cards and the number of distinct ways are there to form a hand with two pairs are 1326 ways.

To solve this problem, we got to use permutations and the combinations. Given that a 5-card poker hand is dealt from a standard deck of cards  and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.

Here 4 suits with 13 different kinds for each and every suit , so number of total outcomes are 13*4 = 52

Here we use combinations, and given that a 5-card poker hand is dealt from a standard deck of cards  and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.

The number of distinct ways are there to form a hand with two pairs are given by, C(52,2)

(52 * 51) / 2

(26 * 51)

1326 ways

Therefore, the  number of distinct ways are there to form a hand with two pairs are 1326 ways.

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The probability that a specific vulnerability within an organization will be attacked by a threat is known as potential.

Potential refers to the likelihood that a specific vulnerability in an organization's security will be exploited by a threat actor or attacker. In the field of information security, the concept of potential is used to assess the risk associated with a particular vulnerability.

This risk assessment helps organizations to prioritize their security efforts and allocate resources where they are most needed. Determinism is a philosophical and scientific concept that refers to the idea that events are determined by prior causes, rather than by random chance.

Externality is an economic term that refers to the impact of an economic activity on parties not directly involved in the activity. For example, pollution from a factory may have externalities that affect the health and well-being of people who live near the factory.

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Heyy! Johnny Sins back with another answer for yall!

Lets see here....

The perimeter of a rectangle can be found by adding the lengths of all four sides. If the length of the rectangle is three times its width, we can write the expression for the length as 3w. Therefore, the expression for the perimeter would be:

P = 2(width) + 2(length)

P = 2w + 2(3w)

P = 2w + 6w

P = 8w

So the perimeter of the rectangle can be represented by the expression 8w.

___________________________________________________________

Pretty easy huh? Well no worries just give me 5 stars and a thanks. 2 buttons. So simple huh?

Love, Johnny Sins :)

Answer:

Step-by-step explanation:x=28

The sine, cosine, cosecant, and secant functions have a period 2π;

the tangent and cotangent functions have period π.

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.

If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. The period is the interval between two occurrences of the wave.

The complete question is-

The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.

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This error message typically occurs when Microsoft Excel is unable to perform a calculation due to running out of memory or system resources.

This can happen when a spreadsheet is extremely large, has many complex formulas or when a large number of calculations are performed simultaneously. To resolve the issue, you can try closing other programs and processes running on your computer, increasing the amount of memory allocated to Excel, breaking down a large spreadsheet into smaller spreadsheets, or simplifying the formulas in your spreadsheet. If these steps do not work, you may need to seek assistance from a technical support expert. This error message typically occurs when Microsoft Excel is unable to perform a calculation due to running out of memory or system resources.

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Answer:

[tex]g^6[/tex]

Step-by-step explanation:

When multiplying exponents, for example

[tex]x^2 * x^5[/tex]

Their power values are added together to get

[tex]x^2 * x^5 = x * x * x* x* x* x* x = x^7[/tex]

Answer:

[tex]g^6[/tex]

Step-by-step explanation:

because, [tex]g^3*g^3[/tex] is basically [tex]g^(^3^+^3^)[/tex] which is [tex]g^(^6^)[/tex] = [tex]g^6[/tex]

Answer: Jack made $898.25 in commission

Step-by-step explanation:

Jack made $898.25 in commission. ($2,000 x 15%) + ($3,975 x 5%) = $898.25

[tex]5975-2000=3975[/tex] this is the amount jack earns 5% commission on

Ratio of the base of two triangles is 16:9 , if ratio of heights of two triangles is 3:4 and area 4:3.

It is given that the ratio of heights of two triangles is 3:4 and the ratio of area of two triangles is 4:3

We have to find the ratio of their base

The basic formula for the area of a triangle is equal to half the product of its base and height or  [tex]\frac{1}{2} \times base \times height[/tex]

Let b₁ , b₂ are the base of two triangles respectively

So, ratio of areas of triangles : [tex]\frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]

[tex]\frac{4}{3} = \frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]

[tex]\frac{b{1}}{b_{2}} =\frac{16}{9}[/tex]

So, ratio of the base of two triangles is 16:9

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In order to achieve an 80% gross margin, the store would need to sell the battery chargers for $50 each - A

The gross margin is the difference between the selling price and the cost of the item, expressed as a percentage of the selling price. To achieve an 80% gross margin, we need to set the selling price such that 80% of it represents the profit on the item.

Let's call the selling price of the battery charger S. The profit on the item is S - $10, since that is the cost of the item. So, to achieve an 80% gross margin, we want:

(S - $10) / S = 0.80

Expanding and solving for S:

S - $10 = 0.80S

0.20S = $10

S = $50

So, in order to achieve an 80% gross margin, the store would need to sell the battery chargers for $50 each. That would be the sticker price for the chargers.

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The statements are A. ∠x and ∠y are supplementary angles, B. ∠w and ∠z are a linear pair.

Angle is the void between two surfaces or lines that meet. The angle is also expressed in degrees. The angle is 360 degrees for a full rotation.

Supplementary angle: When two angles add up to 180 degrees, they are considered to be supplementary angles.

Corresponding angle: The third line if two lines are parallel. Equal angles are formed by the matching angles.

Angles that are vertically opposed to one another are equal when two lines intersect.

Alternate angle: When two lines are parallel, a third line forms a z-angle, which is an equal angle to the parallel lines.

Complementary angle - When two angles add up to 90 degrees, they are considered to be complementary angles.

Angle x and angle y are supplementary angles. True.

Angle w and angle z are a linear pair. True.

Angle w and angle y are adjacent angles. False.

Angle x and Angle z are vertical angles. False.

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Answer: C

Step-by-step explanation: An "undo" function is called an inverse and has the notation h¹(a). Note that the -1 is not a negative exponent. It is the

mathematical symbol that indicates the inverse function of h(x). Write an equation for h ¹(x), the "undo" function machine.

Answer:

y = (4/3)x - 2

Step-by-step explanation:

y intercept is (0, -2)

slope is 4/3

Check the picture below.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad P(\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 2 +8}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies (2~~,~~5)[/tex]

The function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Consider the equation :

y = 30.5(0.7)ˣ

Plug in x=0,

y= 30.5(0.7)⁰ = 30.5 *1 = 30.5

The point is (0,30.5)

Similarly, when we plug in x=1 and x=2, we get y=21.35 and y=14.95 respectively

The other 2 points in (x, y) form are (1,21.35) and (2, 14.95)

These points are matching with the points on the graph

So, the function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

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Answer:

Step-by-step explanation:

1/4 is one bow.

1/4 *4 is 1 yard.

mel can make 4 bows.

The scaled dimensions of the kitchen, given the scale and the measurements, is 1. 26 cm x 0. 96 cm

1 meter on the scaled drawing would be 500 meters of the actual kitchen. This means that the scaled length would be:

= 6. 3 / 500

= 0. 0126 meters

The scaled width would be:

= 4. 8 / 500

= 0. 0096 meters

This can be converted to centimeters :

= 0. 0126 x 100 cm per meter

= 1. 26 cm

= 0. 0096 x 100

= 0. 96 cm

The scale dimensions would be:

1. 26 cm x 0. 96 cm

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Answer: 1/3

Step-by-step explanation: The ratio of multiplication problems to total problems is 12:36, which can be simplified to 1:3.

Answer:

A

Step-by-step explanation:

Hi there.
We know this math exam has 12 multiplication and 24 division problems, making the overall exam questions 36 problems. (12+24=36)

The ratio is the fraction equivalent comparison between two variables. In this case, it's multiplication problems over total problems.

We know multiplication problems as 12, and we calculated the total, which is 36.

The answer would be 12/36; but it's divisible by 12 and can be further simplified to 1/3.