Write each equation in slope-intercept form. Then find the slope and y -intercept of each line. 5 x+y=4

Answer: x=18

Step-by-step explanation:

2x+8x=180 ==> angles CDE(8x) and ABC(2x) are opposite supplementary angles meaning that they add up to 180 degrees.

10x=180

10x/10=180/10

x=180/10

x=18

Ms.Nishino can drive using Zipcar  for 4 hours

How is the total cost of of car rental modelled?

The total cost of car rental can be viewed using a straight-line equation, such total cost comprises of the fixed monthly charge and the total cost of hours based on the fact that hourly fee is $12.50 of car rental

y=a+bx

y=total cost=$75.00

a=fixed charge per month for car rental=$25.00

b=hourly charge=$12.50

x=number of hours spent driving in a month=unknown

75=25+12.50x

75-25=12.50x

50=12.50x

x=50/12.50

x=4

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Concluding part of the question:

How many  can she drive the rental car to get it in her budget?

The value of x is -14.

Rewriting the equation mentioned in question to solve for the value of x -

4(x + 2) -2 (x - 10) = 0

Performing multiplication with brackets on Left Hand Side of the equation

4x + 8 - 2x + 20 = 0

Performing addition and subtraction on Left Hand Side of the equation

2x + 28 = 0

Shifting 28 to other side of equation

2x = - 28

Shifting 2 to other side of equation as denominator

x = - 28/2

Performing division to find the value of x

x = -14

Hence, the value of x is -14.

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The required minimum distance she will run is 600 km.

Given that,
Magdalena runs 5 days per week. Her goal is to run a minimum of 60 km each week. If she runs 50 days, what is the minimum distance she will run is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
In 5 days she ran 60 km
In one day she ran = 60 / 5 = 12
Let the number of km run be x

for 50 days minimum run would be,
= 50 * 12
= 600 km

Thus, the required minimum distance she will run is 600 km.

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Answer:

300 widgets

Step-by-step explanation:

Each time the widgets sold goes up by 100, the profits goes up by 400. This shows a ratio/slope of 4 if we were to graph this. To find out when they break even you need to subtract $400 from the first row to get to zero and the equivalent amount of widgets. If each widget is $4 then subtract 100 from 400 to get 300 widgets

well, we know the table has linear relationship, so let's use it to get the Profit function then, to get the equation of any straight line, we simply need two points off of it, so let's use those two points in the picture below.

[tex](\stackrel{x_1}{500}~,~\stackrel{y_1}{800})\qquad (\stackrel{x_2}{700}~,~\stackrel{y_2}{1600}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1600}-\stackrel{y1}{800}}}{\underset{run} {\underset{x_2}{700}-\underset{x_1}{500}}} \implies \cfrac{1600 -800}{700 -500} \implies \cfrac{ 800 }{ 200 }\implies 4[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{800}=\stackrel{m}{4}(x-\stackrel{x_1}{500}) \\\\\\ y-800=4x-2000\implies y=4x-1200[/tex]

how many bucks will they lose by selling "0" items?

well, let's find out by setting x = 0.

[tex]\stackrel{profit}{y}=4(0)-1200\implies y=-1200~\hfill \stackrel{\textit{they'd be losing}}{\text{\LARGE 1200}}[/tex]

how many will they need to sell to break-even?

well, to break-even that means no loses, no profits but no loses either, so-called breaking-even, you simply sell enough to cover costs, at that point the profit = y = 0, so

[tex]\stackrel{profit}{0}=4x-1200\implies 1200=4x\implies \cfrac{1200}{4}=x\implies \text{\LARGE 300}=x[/tex]

Step-by-step explanation:

If theres 168 frames in six seconds, to find out how many there are per second, we simply need to divide 168 by 6. This equals 28. If you know how many there are for 6, and you want to find out how many for 1, you know you're dividing 6 by 6. So you have to do the same to the amount of frames.

Answer:

Step-by-step explanation:

−4−(−7)=

The opposite of −7 is 7.

−4+7

Add −4 and 7 to get 3.

3

Answer:

3

Step-by-step explanation:

Think of -4-(-7) as -4+7

just remove the negative and add instead

your answer is 3

The angle which is complementary to angle BAC is ∠ACB which is option (a) .

From the figure we can see that ΔABC is right angled triangle at B .

∠BAC and ∠ACB on adding gives the right angle ∠CBA .

Hence , on adding ∠ACB  to ∠BAC  , we get the sum 90° so , ∠ACB is the complementary to angle BAC .

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The catcher at home plate had to throw the ball 60 cm to reach the 2nd baseman at second base.

The hypotenuse of a right triangle is formed by the line from home plate to 2nd base. The triangle's two sides are each 60 feet long.

We can calculate the length of the hypotenuse using the Pythagorean theorem:

Diagonal² = side² + side²

Side= 60 feet

Diagonal = √s² + s²

Put the value in formula;

(√s² + s²)² = 60² + 60²

2s² = 2 ×60²

Further simplify;

s² = 60²

Taking root on both sides;

s = 60 feet.

Thus, the side of the square field is 60 feet.

Therefore, a catcher at home plate ought to throw the ball 60 cm to reach the 2nd baseman at second base.

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Basically you are correct its C , ut go with your gut!

The explicit formula has the benefit of making it simple to locate any term in the sequence. The recursive formula only includes one addition or multiplication operation, hence this formula's drawback is that it has more operations overall.

We discovered that a recursive rule is a rule that repeatedly alters a prior number in order to reach a subsequent number. As an illustration, our formula for counting numbers is recursive since each number is equal to the preceding number plus 1.

A recursive function is one that generates a series of phrases by repeating or using its own prior term as input.

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Answer:

total of 50 employees

Step-by-step explanation:

Addition of two fractions which are both less than (1/2) must result in a fraction which is always less than 1.

A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Given data

The fractions can be represented as follows;

x < ½   and y < ½

The sum of both of the inequalities is;

x + y < ([tex]\frac{1}{4}[/tex]) + ([tex]\frac{1}{4}[/tex])

x + y < ½

Examples are-

[tex]\frac{1}{5}[/tex]+ [tex]\frac{2}{3}[/tex] =[tex]\frac{13}{15}[/tex]

¼ + ½ = ¾

[tex]\frac{1}{2}[/tex] +[tex]\frac{1}{3}[/tex] = [tex]\frac{5}{6}[/tex]

Therefore, Addition of two fractions which are both less than (1/2) must result in a fraction which is always less than 1.

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Value of s is 1.8.

The midpoint of a line is a point that bisects the line into equal parts. It is equidistant from both end points of the line.

As B is the midpoint of AC,

2AB = AC

∴ 2(10s + 2) = 40

∴ 20s + 4 = 40

∴ 20s = 36

∴ x = 1.8.

Now, AB = 10s + 2

Substituting the value of s,

∴ AB = 10(1.8) + 2

∴ AB = 20 units

Thus, the value of s is 1.8 and the length of AB is 20 units.

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Answer:

2 laps

Step-by-step explanation:

The equation for circumference of a circle is 2πr.

We can use this equation to find how many ft are in a lap, then determine with the circumference how many laps need to be completed.

This is simple algebra

2πr

2π(50)

2(3.14)(50)

314.

One lap is 314 feet, so Sammy needs to walk 2 laps.

Answer: 2 laps

Step-by-step explanation:

Length of a circular path is 2πR (R=50ft)

Length of a circular path is:

2*3.14*50=

314 ft

628:314=

2 laps

If sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².

As given in the question,

In triangle ABC,

AB = Perpendicular side

BC = Base

AC = Hypotenuse

sinx = 0.6

AB = 12

sinx = AB / AC

⇒0.6 = 12/AC

⇒AC = 12 /0.6

⇒ AC = 20

Using Pythagoras theorem,

AB² + BC² = AC²

⇒ BC² = 20² -12²

⇒BC = 16

Area of ΔABC = (1/2)× AB×BC

                       = (1/2)×12×16

                       = 96 units²

Therefore, if sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².

The complete question is:

If sin x = 0.6 and AB = 12 as shown in the diagram , what is the area of ΔABC ?

a. 96 units²

b. 28.8 units²

c. 31.2 units²

d. 34.6 units²

e. 42.3 units²

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Answer:

A product of a number and 12 is increased by 23

Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30

Step-by-step explanation:

To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"

First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15

Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30

Now we can set up our equation,

center (c) = 15

tolerance (t) = 30

|t - 15| ≤ 30

Now that we have our equation, we can set up the inequality

|x - c| ≤ t = -t ≤ x - c ≤ t

so,

-30 ≤ t - 15 ≤ 30

Hope this helps!

(sorry it was so long)

Answer:

The lines are the same, they are just in a different position.

A reflection is a type of rigid transformation. Rigid transformations do not

change the size nor the length of the pre-image.

In other words, the pre-image and the image in a rigid transformation are congruent.

Step-by-step explanation:

Hope this helps.  

The triangle with vertices J(5 , 0), K(5 , -8), and L(0 , 0) has its circumcenter located at Point (5/2 , -4).

Circumcenter of a triangle refers to the point inside a triangle at which the perpendicular bisectors of the sides of a triangle intersect. This point is also equidistant from the three vertices.

Given the location of the three vertices, there are different methods that can be used to locate the circumcenter of the triangle.

One method is to calculate the intersection point of any two perpendicular bisectors.

First is to find the midpoint of the two sides given the formula:

midpoint = M(xm ,ym) = [(x1 + x2)/2 , (y1 + y2)/2]

Consider side JK and side KL.

JK : midpoint = [(5 + 5)/2 , (0 + -8)/2] = (5 , -4)

KL : midpoint = [(5 + 0)/2 , (-8 + 0)/2] = (5/2 , -4)

Next, solve for the slope of each side and slope of its perpendicular bisector (-1/m).

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

JK : m = (-8 - 0)/(5 - 5) = -8/0 = 0/8 = 0

KL : m = (0 - -8)/(0 - 5) = 8/-5 = 5/8

Using the midpoint and the slope of the perpendicular bisector, set up its equation using the point-slope form.

(y - ym) = -1/m(x - xm)

JK : (y - -4) = 0(x - 5)

y + 4 = 0

y = -4

KL : (y - -4) = 5/8(x - 5/2)

y + 4 = 5/8 x - 25/16

y = 5/8 x - 89/16

Find the intersection (circumcenter of the triangle) of these two perpendicular bisectors.

Since from the equation 1, y = -4, input this value to the 2nd equation.

y = 5/8 x - 89/16

-4 = 5/8 x - 89/16

5/8 x = 25/16

x = 5/2

y = -4

Hence, the circumcenter is at Point (5/2 , -4).

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Distance between the points [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex] is [tex]a[/tex]. (Option D)

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by [tex]d= \sqrt{(x^{2}-x) ^{2}+(y^{2}-y) ^{2} }[/tex]. This formula is used to find the distance between any two points on a coordinate plane or x-y plane. This formula is called distance formula.

Let A= [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and B= [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex].

Putting values in above formula:

AB=[tex]\sqrt{a^{2}[cos(0+\frac{\pi }{3})-cos(0+\frac{2\pi }{3})]^{2}+a^{2}[sin(0+\frac{\pi }{3})-sin(0+\frac{2\pi }{3})]^{2} }[/tex]

AB= [tex]a\sqrt{cos^{2}(0+\frac{\pi }{3})+sin^{2}(0+\frac{\pi }{3})+cos^{2}(0+\frac{2\pi }{3})+sin^{2}(0+\frac{2\pi }{3})}[/tex]

AB= [tex]a\sqrt{cos(0+\frac{\pi }{3})cos(0+\frac{2\pi }{3})sin(0+\frac{\pi }{3})sin(0+\frac{2\pi }{3})}[/tex]

AB=[tex]a\sqrt{1+1-2cos(0+\frac{2\pi }{3}-0-\frac{\pi }{3}) }[/tex]

AB= [tex]a\sqrt{2-2cos\frac{\pi }{3} }[/tex]

AB= [tex]a\sqrt{2-2\frac{1}{2} }[/tex]

AB= [tex]a\sqrt{2-1} =a[/tex]

Hence, the distance between the two given points is [tex]a[/tex].

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Answer:

9 multiple choice questions and 2 short answer questions

===========================================================

Explanation:

x = number of multiple choice

y = number of short answers

The statement "It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question" means it takes 2x+6y minutes to answer x multiple choice and y short answer questions. We want this total to be 30 minutes or less.

Therefore, [tex]2x+6y \le 30[/tex] is one constraint.

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

Another constraint is that [tex]0 \le x \le 9[/tex] since the most multiple choice questions you can answer is 9.

Because there are 3 short answer questions, this means another constraint is [tex]0 \le y \le 3[/tex]

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

The list of constraints is:

[tex]\begin{cases}2x+6y \le 30\\0 \le x \le 9\\0 \le y \le 3\\\end{cases}[/tex]

If you were to graph and shade these regions on the xy grid, then you should get a pentagon with the following corner points

A = (0, 0)

B = (0, 3)

C = (6, 3)

D = (9, 2)

E = (9, 0)

We'll plug the coordinates of each vertex into the objective function P(x,y) = 3x+5y which will compute the number of points total after answering x multiple choice and y short answer questions. This computes the maximum points possible.

Plug in the coordinates of point A to get P(0,0) = 0

Repeat for point B to get P(0,3) = 15

Now move onto point C to get P(6,3) = 33

Then point D is P(9,2) = 37 and point E gets us P(9,0) = 27

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

Summary:

P(0,0) = 0

P(0,3) = 15

P(6,3) = 33

P(9,2) = 37

P(9,0) = 27

We see that x = 9 and y = 2 produce the largest P(x,y) value of 37

Therefore, you should answer 9 multiple choice questions and 2 short answer questions. This will yield 37 points if you were to get all of those questions correct. In other words, the most points possible are 37 when given 30 minutes.

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

Side note:

If you had unlimited time, then the most points possible are 9*3+3*5 = 27+15 = 42 which is the total number of points on the exam.

Getting a 37 out of 42 is a grade of about 37/42 = 0.881 = 88.1%

The maximum score is achieved at the corner point (9, 0), where the student answers 9 multiple-choice questions and 0 short-answer questions. The score at this point is 27, which is the maximum score the student can achieve in the given time.

To maximize the student's score in the given 30 minutes, we need to create an objective function and constraints based on the time available and the number of questions.

Let:

x = Number of multiple-choice questions to answer

y = Number of short-answer questions to answer

Objective Function (Score):

The score can be calculated as the sum of points obtained from multiple-choice questions and short-answer questions:

Score (S) = 3x (for multiple-choice questions) + 5y (for short-answer questions)

Constraints:

1. Time Constraint: The total time taken to answer all the questions should not exceed 30 minutes:

Time for multiple-choice questions + Time for short-answer questions ≤ 30

2. Number of Questions Constraint: The student can't answer more questions than available:

Number of multiple-choice questions (x) ≤ 9 (total number of multiple-choice questions available)

Number of short-answer questions (y) ≤ 3 (total number of short-answer questions available)

Now, let's consider the time taken to answer each type of question:

- Time for multiple-choice questions: 2 minutes per question

- Time for short-answer questions: 6 minutes per question

Based on the above information, the time constraint can be written as an equation: 2x + 6y ≤ 30

Now, we need to maximize the score (S) by selecting the values of x and y that satisfy the above constraints. This is a linear programming problem that can be solved using various optimization techniques, such as the graphical method, simplex method, or linear programming software.

Since this is a simple problem with a small number of variables and constraints, we can use the graphical method to find the maximum score. We will graph the feasible region defined by the constraints and find the corner points of the feasible region. Then, we will calculate the score (S) at each corner point and select the one with the highest score.

The feasible region will be bounded by the lines:

2x + 6y ≤ 30 (Time constraint)

x ≤ 9 (Number of multiple-choice questions constraint)

y ≤ 3 (Number of short-answer questions constraint)

The corner points of the feasible region are the intersection points of these lines.

Now, calculate the score (S) at each corner point:

For (0, 0): S = 3(0) + 5(0) = 0

For (0, 3): S = 3(0) + 5(3) = 15

For (9, 0): S = 3(9) + 5(0) = 27

The maximum score is achieved at the corner point (9, 0), where the student answers 9 multiple-choice questions and 0 short-answer questions. The score at this point is 27, which is the maximum score the student can achieve in the given time.

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Part (a)

We need to consider

[tex]x=\frac{1}{k\pi}, k \in \mathbb{Z}[/tex]

[tex]f\left(\frac{1}{k\pi} \right)=\tan (k\pi)

[/tex]

tan(x) has a period of pi, so this is equal to tan(0)=0.

Part (b)

We need to consider

[tex]x=\frac{4}{(4n+1)\pi}, n \in \mathbb{Z} \\ \\ f \left(\frac{4}{(4n+1)\pi} \right)=\tan \left(\frac{(4n+1)\pi}{4} \right) \\ \\ =\tan \left(\pi n+\frac{\pi}{4} \right) \\ \\ =1[/tex]

Part (c)

We see that 1/x approaches infinity, and hence the limit does not exist.

The chord of a circle is defined as the line segment connecting any two points on its circumference.

VU is not a radius it is a chord.

The chord of a circle is defined as the line segment connecting any two points on its circumference. It should be noted that the diameter of a circle is the longest chord passing through its center.

A circle chord is a straight line with both ends on a circular arc. A secant line, or simply secant, is the infinite line extension of a chord. A chord is a segment of a line that connects two points on a curve, such as an ellipse.

A radius is a segment with ends at the center and circumference of a circle. VU, on the other hand, is a chord because it has both endpoints on the circle.

Therefore, VU is not a radius it is a chord.

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The RHS congruency criterion showed ABD ≅ DCA.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

The diameters of a circle with an O-centered center are AOC and BOD.

To Locate:

By RHS, ABD and DCA are congruent.

Solution:

The fact that AOC and BOD are a circle's diameters is a given.

BD = CA (circle circumferences)

"BAD = CDA" [90° angles in semicircle]

AD = AD (shared by both triangles)

[Using RHS congruence criterion] ABD ≅ DCA

As a result, the RHS congruency criterion showed ABD ≅ DCA.

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Answer:

23

Step-by-step explanation:

Porque 23 X 8 = 184

Espero te ayude

Hope this helps

The sum of the given arithmetic series (-3)+(-6)+(-9)+. . . . . . +(-30) is  -165

The given series is:

     (-3)+(-6)+(-9)+. . . . . . +(-30)

First, we need to find how many terms in that arithmetic series.

Recall, the formula for the nth term of an arithmetic sequence is:

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

From the given series we know that:

the first term : a(1) = -3

the last term: a(n) = -30

the common difference: d = -6 - (-3) = -3

Substitute these parameters into the formula:

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

-30 = -3 + (n-1) . (-3)

-30 = -3n

n = 10

So there 10 terms in the series.

Use the sum formula:

S(n) = n/2 [a(1) + a(n)]

S(10) = 10/2 [-3 + (-30)]

S(10) = -330/2 = -165

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Answer: 4 inches.

Step-by-step explanation: