The local gym holds three 45-minute workout sessions and two 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?

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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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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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:

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 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:5

Step-by-step explanation:

Answer:

Use the formula L(x)=f(a)+f'(a)(x−a) to find the linearization.

L(x)=2

Step-by-step explanation:

Answer:

Let y = length of side parallel to the side with no fence

x = length of each of the other two sides

Then, y+2x = 64. So, y = 64-2x

Area = A = xy = x(64-2x)

The graph of the area function is a parabola opening downward with a highest point and with x-intercepts (0,0) and (32,0).

By the symmetry of the parabola, the x-coordinate of the maximum point lies halfway between the x-intercepts.

So, the area is maximized when x = 16 ft

y = 64 - 2x = 32 ft

Maximum area = xy = (16)(32) = 512 ft2

To maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.

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?

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)

The required value of y is 10.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx,       —-- 1

Now, find k for given x = 15 and y = 25, we need to put these values in equation 1, i.e.

25 = k(15)

k = 25 / 15

k = 5 / 3

Further calculate y for given x = 6 and constant of proportion = 5/3 i.e.

y = (6)(5 / 3)

y = 10

Hence, the required value of y is 10.

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Answer:

a+b= (-1)

Step-by-step explanation:

4+(-5)=

4-5= (-1)

Answer:

-1

Step-by-step explanation:

a = 4

b = -5

4 + -5 = -1 ( +- turns to -)

Answer: 4 inches.

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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Answer:

x-int: (-12/9, 0)

y-int: (0, 6)

Step-by-step explanation:

x-int ==> on x-axis when y=0

y-int ==> on y-axis when x=0

9/4x -1/2y = -3

x-int: 9/4x -1/2(0) = -3

9/4x = -3

9x/4 = -3

9x*4/4=-3*4

9x=-12

x=-12/9 ==> x-int: (-12/9, 0)

y-int: 9/4(0) -1/2y = -3

-1/2y = -3

1/2y=3

y/2=3

y=6 ==> y-int: (0, 6)

Answer:

23

Step-by-step explanation:

Porque 23 X 8 = 184

Espero te ayude

Hope this helps

Answer:

A product of a number and 12 is increased by 23

If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.

a.  0scar sits between Morgan and Phil

First step is to calculate the total distance

Total distance=2 feet+4 feet+3 feet

Total distance=9 feet

Since Morgan is 2 feet from Phil.

Hence,

P(Oscar sits between Morgan and Phil)=2/9

b. Oscar sits between Phil and Tyreese.

First step is to calculate the  distance between Phil and Tyreese

Distance= 4 feet + 3 feet

Distance =7 feet

Hence,

P(Oscar sits between Phil and Tyreese)=7/9

Therefore If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.

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The complete question is:

Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. Morgan is 2 feet from Phil. Phil is 4 feet from Callie. Callie is 3 feet from Tyreese. Oscar joins them.

a. Find the probability that 0scar sits between Morgan and Phil.

b. Find the probability that Oscar sits between Phil and Tyreese.

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:  x-axis

Explanation:

The point (2,3) moves to (2, -3)

The x coordinate stays the same, but the y coordinate flipped from positive to negative. Therefore, the rule used is [tex](\text{x},\text{y}) \to (\text{x}, -\text{y})[/tex] which is a reflection over the horizontal x axis.

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

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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In the sample that is used number of viruses were 6000 times greater than the number of protozoa.

Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population.

Given the number of protozoa in the sample as 5 × 10⁵ and the number of viruses in the sample as 3x10⁹.

This is represented in the scientific notation.

To calculate the number of times the viruses in the sample is more than the protozoa in the sample we divide the amount of virus by the amount of protozoa.

∴ (3x10⁹) ÷ (5 × 10⁵)

= 6000

Therefore in the sample that is used number of viruses were 6000 times greater than the number of protozoa.

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Answer:

f(- 2) = 14

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = 3(- 2)² + 2 = 3(4) + 2 = 12 + 2 = 14

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:

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

Answer:

total of 50 employees

Step-by-step explanation: