can someone tell me how to solve translations please?

Step-by-step explanation:

REO=RBO=67

BOR=ERO=91

REB=REO-BE0=67-32=35

RYE=180-ERO-REB=180-91-35=54

(a) The equations of the two lines are:

Line 1: y = -3x + 5

Line 2: y = (1/2)x - (3/2)

(c) The lines intersect at the point (13/7, -4/7).

(d) The lines are neither parallel nor perpendicular.

(a) Equation of Line 1:

The equation of a line can be expressed in the form y = mx + c, where m is the slope and c is the y-intercept. For Line 1, the slope is m = -3 and the y-intercept is c = 5. Substituting these values, the equation of Line 1 is:

y = -3x + 5

Equation of Line 2:

To find the equation of Line 2, we can first calculate the slope using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (3, 0) and (5, 1) on Line 2:

m = (1 - 0) / (5 - 3) = 1/2

Now, we can use the point-slope form of the equation of a line, using the point (3, 0) and the calculated slope:

y - y1 = m(x - x1)

y - 0 = (1/2)(x - 3)

y = (1/2)x - (3/2)

Therefore, the equation of Line 2 is:

y = (1/2)x - (3/2)

(b) Graph:

To draw the lines on the same set of axes, we can plot the x and y intercepts for each line.

For Line 1:

x-intercept: Setting y = 0 in the equation, we get:

0 = -3x + 5

x = 5/3

y-intercept: Setting x = 0 in the equation, we get:

y = -3(0) + 5

y = 5

Plotting the points (5/3, 0) and (0, 5) on Line 1.

For Line 2:

x-intercept: Setting y = 0 in the equation, we get:

0 = (1/2)x - (3/2)

x = 3

y-intercept: Setting x = 0 in the equation, we get:

y = (1/2)(0) - (3/2)

y = -3/2

Plotting the points (3, 0) and (0, -3/2) on Line 2.

(c) Intersection Point:

To find the exact coordinates of the point where the lines intersect, we can solve the simultaneous equations formed by equating the two equations:

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

Multiplying through by 2 to eliminate the fraction:

-6x + 10 = x - 3

Combining like terms:

-7x = -13

Dividing by -7:

x = 13/7

Substituting x back into either equation (e.g., Line 1):

y = -3(13/7) + 5 = -4/7

Therefore, the point of intersection is (13/7, -4/7).

(d) Line Relationship:

To determine if the lines are perpendicular, parallel, or neither, we can compare their slopes. The slope of Line 1 is -3, and the slope of Line 2 is 1/2.

Since the slopes are not equal, the lines are neither parallel nor perpendicular.

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Answer:

x=2

Step-by-step explanation:

The number of children is 379 and the number of the adults is 339.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."

Let us suppose the number of children = C, and the number of adults = A.

Given that, 718 people used the public swimming pool:

C + A = 718 people

The cost for one child is 1.25 for children, then the cost for C child is: 1.25C

The cost for one adult is 2.00 for adults, then the cost for A adults is: 2A

The receipts for admission totaled 1151.75:

1.25C + 2A = 1151.75

The two equations are:

C + A = 718

1.25C + 2A = 1151.75

For the first equation we can write:

C + A = 718

C = 718 - A

Substitute the value of C in second equation:

1.25(718 - A) + 2A = 1151.75

897.5 - 1.25A + 2A = 1151.75

0.75A = 254.25

A = 339

Substituting the value of A in the first equation we have:

C + A = 718

C + 339 = 718

C = 379

Hence, the number of children is 379 and the number of the adults is 339.

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Consider the operation is \(R_2\to -3R_2\).

Given:

The augmented matrix below represents a system of equations.

\(\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right]\)

To find:

Matrix results from the operation \(R_2\to -3R_2\).

Step-by-step explanation:

We have,

\(\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right]\)

After applying \(R_2\to -3R_2\), we get

\(\left[\left.\begin{matrix}1&0&1\\-3(1)&-3(3)&-3(-1)\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-3(-9)\\-2\end{matrix}\right]\)

\(\left[\left.\begin{matrix}1&0&1\\-3&-9&3\\3&2&0\end{matrix}\right|\begin{matrix}-1\\27\\-2\end{matrix}\right]\)

Therefore, the correct option is A.

To transform the graph of g(x) = lnx into the graph of of f(x) = ln(x-4) + 3 we have to translate 4 units to the right and 3 units up.

What is graph transformation?

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

As given in the question,

Parent function  g(x)=ln x

resultant function  f(x)=ln(x-4)+3

By the translation rules :

If f(x) needs to be translated in f(x-h), it mean function shifted right by h unit

and if f(x) needs to be translated in f(x)+k it mean function shifted up by k unit.

As per these rules, graph of  g(x) = lnx function shifted right by 4 unit and function shifted up by 3 unit.

Therefore, Translate 4 units to the right and 3 units up.

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Step-by-step explanation:

I assume

SR = 2x + 23

RQ = x + 21

if that is true, then the situation is completely simple :

14 = (2x + 23) + (x + 21) = 3x + 44

3x = -30

x = -10

SR = 2×-10 + 23 = -20 + 23 = 3

RQ = -10 + 21 = 11

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \:x = -10 \)

____________________________________

\( \large \tt Solution \: : \)

\( \qquad \tt \rightarrow \: SR + RQ = SQ\)

\(\qquad \tt \rightarrow \: 2x + 23 + x + 21 = 14\)

\(\qquad \tt \rightarrow \: 3x + 44 = 14\)

\(\qquad \tt \rightarrow \: 3x = 14 - 44\)

\(\qquad \tt \rightarrow \: 3x = - 30\)

\(\qquad \tt \rightarrow \: x = - 10\)

Now,

\( \qquad \tt \rightarrow \: SR = 2x + 23 \)

\( \qquad \tt \rightarrow \: SR = 2(-10) + 23 \)

\( \qquad \tt \rightarrow \: SR =-20+ 23 \)

\( \qquad \tt \rightarrow \: SR = 3 \:\: units \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

The alternate exterior angles with angle 11 are angle 13 and angle 5.

Step-by-step explanation:

Two angles are called Alternate exterior angles if

1. They are on the exterior side of parallel lines and

2.  Lie on the opposite sides of the transversal line.

It is given that

\(r||s\) and \(t||u\)

From the figure it is noticed that the angle 13 and angle 5 are on the exterior side of parallel lines and they lie on the opposite sides of the transversal line.

Therefore alternate exterior angles with angle 11 are angle 13 and angle 5.

Answer:

1,120

Step-by-step explanation:

$1680 - $560 = 1,120 so there for band members will need to raise $1,120 to reach their goal

If particular shipment of thousands of components actually has a 7% rate of defects, there is a 54.29% probability that this whole shipment will be accepted.

According to the company's acceptance sampling plan, 25 components are randomly chosen and tested from a shipment before the entire batch is accepted if there are no more than three defects. The probability of choosing a defective component from a sample of 25 is computed as follows, assuming that the shipment genuinely has a 7% defect rate:

P(defective) = 0.07

P(non-defective) = 0.93

Using the binomial distribution, we can calculate the probability of having 0, 1, or 2 defectives in a sample of 25:

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

= (0.93)²⁵ + 25(0.07)(0.93)²⁵ + (0.07)²(0.93)²³

= 0.5429

This means that there is a 54.29% chance of having 2 or fewer defectives in a sample of 25. Since the whole shipment will be accepted if there are fewer than 3 defectives in the sample, this is the probability that the whole shipment will be accepted. Therefore, there is a 54.29% chance that the company will accept the shipment based on their acceptance sampling plan.

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Answer:

Using the cosines law

Step-by-step explanation:

So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC

Answer:

3.75

Step-by-step explanation:

25% = 0.25

3(0.25) = 0.75

3 + 0.75 = 3.75

Answer:21x-4

Step-by-step explanation:

5x*5x=25x

-9+5=-4

-2x*-2x=-4x

-4x+25x= 21x

21x=-4x

have a nice day <3

Answer:

270 is the answer

-Sumin <3

Answer:

0.25

Step-by-step explanation:

edge '22

Answer:

D - E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.

Step-by-step explanation:

Answer:

Step-by-step explanation:

6x + 2y = 26

5x - 2y = 7

11x = 33

x = 3

3(3) + y = 13

9 + y = 13

y = 4

(3,4)

Answer:

First:

11x +11 = 110°

11x = 110° -11

11x = 99°

x = 99/11

x = 9°

Second:

100° = 13x -4

13x = 100° + 4

13x = 104 °

x = 104/13

x = 8°

The statement "Linear programming can be used to find the optimal solution for profit, but cannot be used for nonprofit organizations" is False.

Linear programming can be used to find the optimal solution for profit as well as for non-profit organizations. Linear programming is a method of optimization that aids in determining the best outcome in a mathematical model where the model's requirements can be expressed as linear relationships. Linear programming can be used to solve optimization problems that require maximizing or minimizing a linear objective function, subject to a set of linear constraints.

Linear programming can be used in a variety of applications, including finance, engineering, manufacturing, transportation, and resource allocation. Linear programming is concerned with determining the values of decision variables that will maximize or minimize the objective function while meeting all of the constraints. It is used to find the optimal solution that maximizes profits for for-profit organizations or minimizes costs for non-profit organizations.

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Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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The profit-maximizing output level and the associated profit are both zero.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To find the minimum value of SRATC, we need to first find the expression for SRATC:

SRATC = SRTC/q = (200 + 109 + 2q)/q = 309/q + 2

To minimize SRATC, we need to differentiate it with respect to q and set it equal to zero:

d(SRATC)/dq = -309/q² = 0

Solving for q, we get q = √(309).

Substituting q back into the expression for SRATC, we get the minimum value of SRATC:

\(SRATC_{min}\) = 309/√(309) + 2 ≈ 17.22

Therefore, the value of q that minimizes SRATC is √(309) and the minimum cost value of SRATC is approximately $17.22.

If the market price is $90, the profit-maximizing value of q can be found by setting marginal cost equal to price:

MC = d(SRTC)/dq = 109 + 4q/3 = 90

Solving for q, we get q = (3/4)(90 - 109) = -14.25, which is not a feasible value since q has to be non-negative.

Therefore, the firm would not produce any output at a price of $90.

If we assume that the firm can produce any positive amount of output, the profit-maximizing value of q would be where marginal cost equals marginal revenue, which is also equal to price under perfect competition.

Since marginal revenue equals price for a perfectly competitive firm, we have:

MR = price = $90

Setting MR = MC, we get:

90 = 109 + 4q/3

Solving for q, we get q = (3/4)(90 - 109) = -14.25, which is not a feasible value.

Therefore, the firm would not produce any output at a price of $90, regardless of the assumption of being able to produce any positive amount of output.

Hence, the profit-maximizing output level and the associated profit are both zero.

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The flux of f across the surface s is 0.

To find the flux of f across the surface s, we can use the formula for flux:
flux = ∬(f · dS)
where f is the vector field, dS is the differential surface area vector, and the double integral is taken over the surface s.

In this case, f = j, which means the vector field is constant in the z-direction with a magnitude of 1. Therefore, the flux simplifies to:
flux = ∬(j · dS)

Now, let's calculate the flux step-by-step:
1. First, we need to parametrize the surface s. Since s is the part of the plane z=1 x y inside the cylinder x^2 + y^2 = 1, we can parametrize it as:
r(u, v) = (u, v, 1), where -1 ≤ u, v ≤ 1

2. Next, we need to find the differential surface area vector dS. Since s is a plane, the differential surface area vector is simply the cross product of the partial derivatives of r with respect to u and v:
dS = (∂r/∂u) × (∂r/∂v)

Calculating the cross product, we get:
dS = (1, 0, 0) × (0, 1, 0) = (0, 0, 1)

3. Now, let's evaluate the double integral ∬(j · dS) over the surface s. Since the magnitude of j is 1 and the dot product of j and dS is always 0, the flux is always 0.

Therefore, Flux of f across the surface s is 0.

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The functions are labelled in the appropriate categories as mentioned below :

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Answer:

Step-by-step explanation:

Below are the steps to follow to find the slope of any line.

First you need to pick two points. I chose (2,24) and (4,48). (It does not mater what points you chose.)

Now follow the equation

Slope (m) = ΔY/ΔX

ΔY = 48 – 24 = 24

ΔX = 4 – 2 = 2

24/2 = 12

Then no mater what points you chose, 12 should be your final answer

Answer:

D

Step-by-step explanation:

Since RS is parallel to PQ, gradient of RS is equal to gradient of PQ.

\(\boxed{gradient = \frac{y1 - y2}{x1 - x2} }\)

Gradient of RS

= gradient of PQ

\( = \frac{18 - 10}{ - 9 - ( - 3)} \)

\( = \frac{8}{ - 9 + 3} \)

\( = \frac{8}{ - 6} \)

\( = - \frac{4}{3} \)

y- intercept occurs at x= 0. Let the coordinates of the y-intercept of RS be (0, y).

\( \frac{y - 6}{0 - 3} = - \frac{4}{3} \)

\( \frac{y - 6}{ - 3} = - \frac{4}{3} \)

Multiply both sides by -3:

y -6= 4

y= 6 +4

y= 10

Thus, the correct option is D.

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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Answer:

-13, -7.5

Step-by-step explanation:

x = 15 cos 210 = -13

y = 15 sin 210 = -7.5

Answer:

-1, 0, 1, 2

Step-by-step explanation:

\(\sqrt{5-5} -1\\\sqrt{0} -1\\0-1\\-1\)

\(\sqrt{6-5} -1\\\sqrt{1} -1\\1-1\\0\)

\(\sqrt{9-5} -1\\\sqrt{4} -1\\2-1\\1\)

\(\sqrt{14-5} -1\\\sqrt{9} -1\\3-1\\2\)

Answer:

2867

Step-by-step explanation:

Answer: 2867

Step-by-step explanation: 1647+1748−528

3395−528 or 1647+1220 2867

Answer:

25.

Step-by-step explanation:

FGH-G = 3x5x2 - 5 = 30 -5 =25.