Level D:

Rollie was successful in losing weight. He had a goal

weight in mind. He went on a diet for three months. Each

month, he would lose one-third of the difference between

his current weight and his goal weight and an additional

three pounds. At the end of three months, he was just 3

pounds over his goal weight. How many pounds did he

lose in those three months?

Explain how you arrived at your solution.

To find the exact values of cos(0), csc(0), and tan(0) given a point on the terminal side of 0, we can use the coordinates of the point to determine the values of the trigonometric functions.

To find the exact values of cos(0), csc(0), and tan(0) given that (-3,-2) is a point on the terminal side of 0, we can use the coordinates of the point to determine the values of the trigonometric functions.

First, we can find the value of cos(0) by dividing the x-coordinate (-3) by the distance from the origin, which is sqrt((-3)^2+(-2)^2). Therefore, cos(0) = -3 / sqrt(13).

Next, we can find the value of csc(0) by dividing 1 by the y-coordinate (-2). Therefore, csc(0) = 1 / -2 = -1/2.

Finally, we can find the value of tan(0) by dividing the y-coordinate (-2) by the x-coordinate (-3). Therefore, tan(0) = -2 / -3 = 2/3.

Answer:

The points for the given two linear equation as

[tex]x_1 , y_1[/tex] = - 2 , - 6

[tex]x_2 , y_2[/tex] = - 2 , 6

The graph so plotted as shown

Step-by-step explanation:

Given as :

The two linear equation are

y = 3 x                 ........A and

y = - x - 8             .........B

Solving equation A and B

Now, Put The value of y from eq A into eq B

So, 3 x = - x - 8

Or, 3 x + x = - 8

Or, 4 x = - 8

∴ x = [tex]\dfrac{-8}{4}[/tex]

I.e x = - 2

Now , Put the value of x into eq A

∵ y = 3 x

∴ y = 3 × (-2)

I.e y = - 6

Again, Put the value of x into eq B

∵ y = - x - 8

∴ y = - 2 - (-8)

I.e y = 6

So, for x = - 2 , y = - 6

And for x = - 2 , y = 6

Hence , The points for the given two linear equation as

[tex]x_1 , y_1[/tex] = - 2 , - 6

[tex]x_2 , y_2[/tex] = - 2 , 6

The graph so plotted as shown . Answer

Answer:

(- 3, 1 )

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation of f(x)

• if c > 0 then shift up by c units

• if c < 0 then shift down by c units

Thus for f(x) - 4

(- 3, 5 ) → (- 3, 5 - 4 ) → (- 3, 1 )

Answer:

Principal Invested in Municipal Bonds is $16,000

Principal Invested in Corporate Bonds is $15,000

Step-by-step explanation:

If;

Principal Invested in municipal bonds = a

Principal Invested in corporate bonds = b

then we have;

a + b = $31,000 --------------------------------Equation 1

0.075a + 0.085b = $2,475  ---------------Equation 2

From equation 1 we have;

a = 31,000 - b

By putting the values of a in Equation 2 we get;

0.075 (31,000 - b) + 0.085b = 2,475

2,325 - 0.075b + 0.085b = 2,475

0.01b = 150

b = $15,000

By putting the values of b in equation 1 we get;

a = $16,000

Final answer:

Reggie Means invested $16,000 in municipal bonds at 7.5% interest and $15,000 in corporate bonds at 8.5% interest to earn a total annual interest of $2,475.

Explanation:

Let the amount invested in municipal bonds be $x. Thus, the amount invested in corporate bonds will be $(31,000 - x). The municipal bonds earn 7.5% annual interest and the corporate bonds earn 8.5% interest. The total annual interest from both investments is $2,475.

To calculate the interest from municipal bonds, use the formula Interest = Principal × Rate × Time. The interest from municipal bonds is 0.075x (since 7.5% is the same as 0.075).

Similarly, for corporate bonds, the interest will be 0.085(31,000 - x). The sum of these interests equals $2,475:

0.075x + 0.085(31,000 - x) = 2,475

Solving this equation:

The measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees

Solution:

Given that exterior angle of triangle is 140 degrees

The exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

Given that adjacent angles are congruent

Let one of the non adjacent interior angles be "x"

x + x = 140

2x = 140

x = 70

So the two interior angles are 70 degrees and 70 degrees

Let us find the third interior angle

The angle sum property of a triangle states that the interior angles of a triangle always add up to 180 degrees

70 + 70 + third angle = 180

third angle = 180 - 70 - 70

third angle = 180 - 140

third angle = 40 degrees

Thus the measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees

Answer:

[tex]f(x)=4(6x)[/tex]

Step-by-step explanation:

Given:

the given expression is.

[tex]f(x)=4(3)2x[/tex]

Simplify the given expression.

[tex]f(x)=4(3)2x[/tex]

[tex]f(x)=4(3\times 2x)[/tex]

[tex]f(x)=4(6x)[/tex]

Therefore, the option [tex]f(x)=4(6x)[/tex] is an equivalent function to [tex]f(x)=4(3)2x[/tex].

Good evening ,

Answer:

Step-by-step explanation:

______________________________________________________

Note:

if f is a function then each number of the domain has an unique image.

______________________________________________________

since (regarding the table) the image of 9 is 6 then the answer A is wrong

The same apply on answers B and C .

then the right answer is D(-3,-8).

:)

Answer:

dddddddddddddddddd

Answer:

It has no slope because (x2-x1) in the formula [tex]m=\frac{y2-y1}{x2-x1}[/tex] is equal to zero, and the denominator of a fraction cannot be zero

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

the points (7, 10) and (7, 20)

substitute the values

[tex]m=\frac{20-10}{7-7}[/tex]

[tex]m=\frac{10}{0}[/tex] ----> is undefined

The line has a slope undefined ---> is a vertical line (parallel to the y-axis)

Answer:

It will be $7602.3

Step-by-step explanation:

The equation [tex] y = 10000(0.97)^{x}[/tex] gives the purchasing power of $10000 after x years.

Therefore, the sum of money $10000 will value [tex] 10000(0.97)^{x}[/tex] after x number of years.

Now, after 9 years i.e. x = 9 years, the sum value of $10000 will become [tex] y = 10000(0.97)^{9} = 10000 \times 0.76023 = 7602.3[/tex] dollars. ( Answer )

Answer: x≤-2

Step-by-step explanation: Solve for x. (NUMBER LINE ATTACHED)

Hope this helps you out.

The solution of the inequality is shown in figure.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 5x + 3 ≤ - 7

Now,

Solve the inequality as;

⇒ 5x + 3 ≤ - 7

⇒ 5x + 3 - 3 ≤ - 7 - 3

⇒ 5x  ≤ - 10

⇒ 5x/5 ≤ - 10/5

⇒ x ≤ - 2

Thus, The solution of the inequality is;

⇒ x ≤ - 2

Therefore, The solution of the inequality is shown in figure.

Learn more about the inequality visit:

https://brainly.com/question/24372553

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Answer: 7 bags

Step-by-step explanation:

Total no. of oranges rotten - 12

To buy no. of bags to get   -  at least 40 good oranges

No. of oranges in a bag       - 8

40  +  12 = 52 oranges

As each bag contains 8 oranges and 52 is not divisible by 8 we end up taking the closest divisible number that is 54.

If we divide 54 by 8 we get 7.

Hence Max needs to buy 7 bags of oranges.

Note: As they have asked at least 40 good oranges

Answer:

It would be 5.1942486

Step-by-step explanation:

Becuase the 0 is after the 6 the 6 stays as it is and there is no need to round up or down

We're starting with 5.19424860514, and we need to round to the 6th decimal. 1st, we need to identify the 6th place. In this case, that is 8. Everything before that is the same no matter what. 5.19424 is our base. We need to look at the 860514. More specifically, the 86. 6 is over 4, so the 8 becomes a 9 using basic rounding rules. Therefore, our final answer is 5.194249

Hope this helps!

Answer:14

Step-by-step explanation:

30 students total.

7 received an a in history.

13 received an a in math.

4 received an a in both courses.

how many students did not receive an a in either course.

20 total received an a in history or math.

of these, 4 received an a in history and math.

those 4 are being counted twice.

once in history and once in math.

you need to subtract 4 from the number who got an a in history or an a in math to get a total of 16 students who got an a in history or in math.

this leaves 30 - 16 = 14 students who did not get an a in either course.

here's the breakdown.

14 students did not get an a in either course.

3 students got an a in history only.

9 students got an a in math only.

4 students got an a in both history and math.

total is 30 students.

Final answer:

To find how many students did not receive an A in either math or history, subtract the sum of students with As in both subjects (after adjusting for 4 students who received an A in both) from the total class size. It is found that 14 students did not receive an A in either subject.

Explanation:

To determine how many students didn't receive an A in either math or history, we can use the principle of inclusion-exclusion. Firstly, we have 30 students in total. We're told that 7 received an A in history and 13 in math, including four students who received an A in both subjects.

To avoid double-counting those four students, we add the number of students who received an A in history to the number who received an A in math, and then subtract the number who received an A in both:

Number of students with A in either subject: 7 (history) + 13 (math) - 4 (both) = 16 students

Then, we calculate the students who did not receive an A in either subject by subtracting those who received an A in at least one subject from the total class size:

Number of students without an A in any course: 30 (total students) - 16 (A in at least one subject) = 14 students

Therefore, 14 students did not receive an A in either math or history.

Answer:

The shop can cut the cost of production per sandwich to $3.75.  The revenue function would then be defined as R(x)=9x.

Step-by-step explanation:

We want to make as big profit as possible by making as little sandwiches as possible. This means that we want the profit, which is [tex]revenue- production\: cost[/tex] to be as big as possible.

For the first choice the profit per sandwich is [tex]8.25-4=4.25[/tex] dollars.

For the second choice the profit per sandwich is [tex]9-3.75=5.25[/tex] dollars.

For the third choice the profit per sandwich is [tex]8.5-3.5=5[/tex] dollars.

We see here that for the second choice the profit is greatest, therefore this choice is most suitably correct.

Answer:

1. The lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level.

Step-by-step explanation:

The sea level is considered to be zero levels.

Now, the level +x feet means it is at x feet higher than sea level and the level -x feet means it is at x feet lower than the sea level.

Now, the lowest point of the country lies at −9 feet. The highest point of the country lies at +108 feet.

That means, the lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level. (Answer)

Answe

Step-by-step explanation:

he has drive 11 miles of his drive

if you divide 22 by 2 it equals 11

Answer:

(a). Number of protons in a chlorine atom = 17

(b). Atomic number of sodium = 11

Step-by-step explanation:

Let the number of protons in a sodium atom = x

Then, the number of protons in a chlorine atom = x + 6

Now, it is given that the atomic number of an element is equal to the number of protons per atom.

So, atomic number of sodium (Na) = x

Atomic number of chlorine (Cl) = x + 6

It is given that the atomic number of chlorine is 5 less than twice the atomic number of sodium.

∴ atomic number of chlorine (Cl) = 2 × atomic number of sodium (Na) - 5

⇒ x + 6 = 2x - 5

⇒ x - 2x = -5 - 6

⇒ -x = -11

Cancelling the minus sign from both sides, we get

x = 11

(a). Number of protons in a chlorine atom = x + 6

                                                                     = 11 + 6      (∵ x = 11)

                                                                     = 17

(b). Atomic number of sodium = x = 11

Answer:

1/4

Step-by-step explanation:

There are 7 points from 0 to 7/4. This means each point represents 1/4. Therefore A is 1/4

Answer:

1/4

Step-by-step explanation:

If you count back from the 7/4, A will be at the 1/4 point.

Hope this helps :)

[tex]E(t) = 40(0.65)^t[/tex]

Step-by-step explanation:

Given,

Current quantity of emission, P = 40 millions,

Reduction in emission per year, r = 35% = 0.35,

Thus, the quantity of emission after t years,

[tex]E(t)=P(1-r)^t[/tex]

[tex]E(t) = 40(1-0.35)^t[/tex]

[tex]\implies E(t) = 40(0.65)^t[/tex]

Which is the required function.

To represent Freedonia's carbon-dioxide emissions E(t), t years from now with a yearly reduction of 35%, use the function E(t) = 40 * (0.65)^t, where 40 million tons is the current emission and 0.65 is the remaining percentage of emissions after reduction.

The student is asking to write a function that models the carbon-dioxide emissions of Freedonia in million tons, E(t), t years from today, given that the emissions are being reduced by 35% each year. The current emission level is 40 million tons of carbon-dioxide.

To create this function, we need to take into account the exponential decay of the emissions due to the percentage reduction. The general form for exponential decay is given by the equation E(t) = E_0 × (1 - r)^t, where E_0 is the initial amount, r is the rate of reduction (as a decimal), and t is the time in years. For Freedonia, E_0 is 40 million tons, and r is 0.35. Therefore, the equation becomes E(t) = 40 × (1 - 0.35)^t.

Answer:

2.871052631578947‬

Step-by-step explanation:

this is exactly the answer.

The value of x is 10

Step-by-step explanation:

We know that the sum of internal angles of a quadrilateral is 360 degrees

So,

Given

Angle 1 = A1 = 3x+10

Angle 2 = A2 = 9x+50

Angle 3 = A3 = 4x

Angle 4 = A4 = 13x+10

So,

[tex]A_1+A_2+A_3+A_4 = 360\\(3x+10)+(9x+50)+(4x)+(13x+10) = 360\\3x+10+9x+50+4x+13x+10 = 360\\3x+9x+4x+13x+10+50+10 = 360\\29x+70 = 360[/tex]

Subtracting 70 from both sides

[tex]29x+70-70 = 360-70\\29x = 290[/tex]

Dividing both sides by 29

[tex]\frac{29x}{29} = \frac{290}{29}\\x = 10[/tex]

Hence,

The value of x is 10

Keywords: Angles, Quadrilateral

Learn more about angles at:

#LearnwithBrainly

Answer:

1500

Step-by-step explanation:

10×10=100

100×15=1500

Answer:

There are 110 children total in the sports club

Step-by-step explanation:

To get this answer, its actually easier than it seems. You might need a calculator however.

First you start with the 11 children who play both badminton and squash, then, you divide that by 0.25 (25%) to get 44.

Next you take 44 and divide it by 0.4 (40%) to get 110.

And there you go! If you want to make sure you got it right simply start with 110 and multiply it by 0.4 then multiply the number/decimal you get by 0.25. You should get 11 to confirm your answer :)

Answer:

1 positive solution

2.87.

Step-by-step explanation:

x^2 + 2x + 7 = 21

x^2 + 2x - 14 = 0

The product of its roots = c/a = -14 so it will have 1 positive solution.

x = -2 +/- sqrt (2^2 - 4*-14) / 2

x = -1 +/- sqrt60/2

= -1 +/- 3.873

GreATest solution is 2.87

Answer:

[tex] \frac{5}{16}, \: 31.25\%[/tex]

Answer:

it will cost $ 14,79,000

Step-by-step explanation:

Area of the rectangular theatre  ground=L*B= 145*85= 12,325 m²

Cost of cleaning per square metre = $ 120

Total cost of cleaning = $120* 12,325= $ 14,79,000

Answer:

30

Step-by-step explanation:

3x5=15

15x2=30

Answer:

30

Step-by-step explanation:

Multiply 3 by 5 which is 15 and them multiply by 2 which is 30

Answer:

[tex]y\leq 2x+4[/tex]

[tex]y\geq -x-6[/tex]

Step-by-step explanation:

step 1

Find the equation of the solid line with positive slope

we have the points

(0,4) and (-2,0)

Find the slope

[tex]m=(0-4)/(-2-0)=2[/tex]

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=2\\b=4[/tex]

substitute

[tex]y=2x+4[/tex]

step 2

Find the equation of the inequality with positive slope

we know that

The solution of the inequality, is the shaded area below the solid line

so

The equation of the inequality is

[tex]y\leq 2x+4[/tex] ----> inequality A

step 3

Find the equation of the line with negative slope

we have the points

(-6,0) and (-4,-2)

Find the slope

[tex]m=(-2-0)/(-4+6)=-1[/tex]

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=2\\point\ (-6,0)[/tex]

substitute

[tex]0=-(-6)+b[/tex]

solve for b

[tex]0=6+b[/tex]

[tex]b=-6[/tex]

so

The linear equation is

[tex]y=-x-6[/tex]

step 4

Find the equation of the inequality with negative slope

we know that

The solution of the inequality, is the shaded area above the solid line

so

The equation of the inequality is

[tex]y\geq -x-6[/tex] ----> inequality B

therefore

The system of inequalities is

[tex]y\leq 2x+4[/tex] ----> inequality A

[tex]y\geq -x-6[/tex] ----> inequality B

Answer:

Step-by-step explanation:

Find the equation of the line thru the points (2,1) and (3,5)

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

This is a 2 step process. First find the slope of the line thru the points.

slope, m = diffy/diffx

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

m = 4

---------

Now use y = mx + b with either point to find b, the y-intercept.

y = mx + b

5 = 4*3 + b

b = -7

-------

Answer:

Step-by-step explanation:

Formula for calculating the equation of a line is expressed as shown below;

y = mx+c OR y-y1 = m(x-x1) where

m is the slope or gradient

c is the intercept (the point where the line cuts the y axis)

m = ∆y/∆x

m = y2-y1/x2-x1

Given the points (-8,8) and (1,-10).

x1 = -8, y1 = 8, x2 = 1, y2 = -10

m = -10-8/1-(-8)

m = -18/9

m = -2

The equation of a line can also be written as a point slope:

y-y1 = m(x-x1)

Substituting the value of x1, y1 and m into the equation we have;

y-8 = -2(x-(-8))

y-8 = -2(x+8)

y-8 = -2x-16

y= -2x-16+8

y = -2x-8

The equation of the line is y = -2x-8