The amount of calories you consume after eating x pieces of candy is represented by the function y=150x. Find the domain of the function and determine whether it is discrete or continuous.

Answer:

[tex]7 < x < 37[/tex] -- Triangle 1

[tex]6.5 < x < 19.9[/tex] -- Triangle 2

[tex]22 < x < 46[/tex] -- Triangle 3

[tex]21 < x < 67[/tex] -- Triangle 4

Step-by-Step Explanation:

Given

2 sides of a triangle

1. 22 and 15

2. 13.2 and 6.7

3. 34 and 12

4. 23 and 44

Required

Determine the range of the third side in the above triangles

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]22 + x > 15[/tex]

[tex]22 + 15 > x[/tex]

[tex]15 + x > 22[/tex]

Solving

[tex]22 + x > 15[/tex]

Make x the subject of formula

[tex]x > 15 - 22[/tex]

[tex]x > -7[/tex]

Solving

[tex]22 + 15 > x[/tex]

[tex]37 > x[/tex]

Solving

[tex]15 + x > 22[/tex]

Make x the subject of formula

[tex]x > 22 - 15[/tex]

[tex]x > 7[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]37 > x[/tex] and [tex]x > 7[/tex]

Rewrite both inequalities

[tex]x < 37[/tex] and [tex]7 < x[/tex]

Combine the two inequalities

[tex]7 < x < 37[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]13.2 + x > 6.7[/tex]

[tex]13.2 + 6.7 > x[/tex]

[tex]6.7 + x > 13.2[/tex]

Solving

[tex]13.2 + x > 6.7[/tex]

Make x the subject of formula

[tex]x > 6.7 - 13.2[/tex]

[tex]x > -6.5[/tex]

Solving

[tex]13.2 + 6.7 > x[/tex]

[tex]19.9 > x[/tex]

Solving

[tex]6.7 + x > 13.2[/tex]

Make x the subject of formula

[tex]x > 13.2 - 6.7[/tex]

[tex]x > 6.5[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]19.9 > x[/tex] and [tex]x > 6.5[/tex]

Rewrite both inequalities

[tex]x < 19.9[/tex] and [tex]6.5 < x[/tex]

Combine the two inequalities

[tex]6.5 < x < 19.9[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]34 + x > 12[/tex]

[tex]34 + 12 > x[/tex]

[tex]12 + x > 34[/tex]

Solving

[tex]34 + x > 12[/tex]

Make x the subject of formula

[tex]x > 12 - 34[/tex]

[tex]x > -22[/tex]

Solving

[tex]34 + 12 > x[/tex]

[tex]46 > x[/tex]

Solving

[tex]12 + x > 34[/tex]

Make x the subject of formula

[tex]x > 34 - 12[/tex]

[tex]x > 22[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]46 > x[/tex] and [tex]x > 22[/tex]

Rewrite both inequalities

[tex]x < 46[/tex] and [tex]22 < x[/tex]

Combine the two inequalities

[tex]22 < x < 46[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]23 + x > 44[/tex]

[tex]23 + 44 > x[/tex]

[tex]23 + x > 44[/tex]

Solving

[tex]23 + x > 44[/tex]

Make x the subject of formula

[tex]x > 23 - 44[/tex]

[tex]x > -21[/tex]

Solving

[tex]23 + 44 > x[/tex]

[tex]67 > x[/tex]

Solving

[tex]23 + x > 44[/tex]

Make x the subject of formula

[tex]x > 44 - 23[/tex]

[tex]x > 21[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]67 > x[/tex] and [tex]x > 21[/tex]

Rewrite both inequalities

[tex]x < 67[/tex] and [tex]21 < x[/tex]

Combine the two inequalities

[tex]21 < x < 67[/tex]

Answer:

Hey there!

Discrete Data is the number of friends you invited to your last birthday party.

Hope this helps :)

Answer:

a) The number of friends you invited to your last party.

Step-by-step explanation:

Let’s take a step back what is discrete, and what continuous?

Discrete

This is the type of data with certain whole numbers not 2.36 only 2 or 3.

Continuous

This is the data being specific like 1.373.

So a)

The is discrete because you can only have like 5 friends not 7.49 friends.

b)

This is continuous because height can be 5.26 feet.

c)

Time is continuous because there can be 4.3739 minutes.

d)

Weight is also continuous it can be 6339.373 pounds.

Answer:

454

Step-by-step explanation:

set up a system of equation

let y be the number of students

let x be the number of adults

because there are twice the amount of students attended as adults, we can use y=2x as one equation

the other equation will be 6.5y+9x=4972 because this represents the total amount of money

plug 2x for y : 6.5(2x)+9x=4972 : x=226

plug 226 in for the first equation : y=2(226) : y=452

Answer:

(-1, -2)

Step-by-step explanation:

Look up each point in the choices on the graph. If it is on the line or in the shaded area it is a solution.

Answer: (-1, -2)

Answer:

First & Last

Step-by-step explanation:

See what is in the red portion(Shaded or line), that is what can work to the inequality.

(-1, -2) -- In the red(works)

(-1, 2) -- Out of the red(Nope)

(0, 5.2) -- Out of the red(Nope)

(-2, -1) -- In the red(works)

Answer:

Money in her purse is Rs. 500.

Step-by-step explanation:

Let the money in her purse = Rs. [tex]x\\[/tex]

Let the money in her Money box = Rs. [tex]y[/tex]

As per question statement,

[tex]2x+y=1700[/tex]  ........ (1)

[tex]3x+y=2200[/tex] ....... (2)

To find: Money in her purse = ? i.e. [tex]x=?[/tex]

Let us solve for [tex]x[/tex] using the two linear equations.

We can use substitution method here i.e. find value of one variable from one equation and then substitute that value in other equation.

Using equation (1), we get the value of [tex]y[/tex] as follows:

[tex]y=1700-2x[/tex]

Now, let us put this value of y in equation (2) to find the value of [tex]x[/tex]:

[tex]3x+1700-2x=2200\\\Rightarrow x+1700 = 2200\\\Rightarrow x=2200-1700\\\Rightarrow x = Rs.\ 500[/tex]

Money in her purse is Rs. 500.

Answer:

The parts are 24 and 16

Step-by-step explanation:

Let's call the two parts x and y. We can write the following system:

x + y = 40 -- Equation 1

1/4x = 3/8y -- Equation 2

2x = 3y -- Equation 3 (Multiply Equation 2 by 8 to get rid of denominators)

2x + 2y = 80 -- Equation 4 (Multiply Equation 1 by 2)

3y + 2y = 80 -- (Substitute 2x = 3y into Equation 4)

5y = 80 -- (3y + 2y = 5y)

y = 16 -- (Divide by 5)

x + 16 = 40 -- (Substitute y = 16 into Equation 1)

x = 24 -- (Subtract 16)

Answer:

B and D

Step-by-step explanation:

B: 14x and 14x cancel out, so there would be no x left.

D: 14 x and 14x cancel out, as well as -23 and -23, therefore leading to no solution.

Hope this is helpful! :)

Answer:

The answer is B

Step-by-step explanation:

I got this answer on Khan Academy.

Hope this helps! :)

Answer:

(-3, -11)

i needed to put more characters so here

Answer:

x=-15/2 and x=1

x=6 and x=3/4

Step-by-step explanation:

You have the following equations:

[tex]\frac{4x-3}{x+2}=\frac{2x}{x+5}[/tex]

[tex]\frac{2}{x-2}+\frac{3}{x}-\frac{9}{x+3}[/tex]

To solve both equations you can first multiply by the m.c.m of the denominators, and then solve for x, just as follow:

first equation:

[tex][\frac{4x-3}{x+2}=\frac{2x}{x+5}](x+2)(x+5)\\\\(4x-3)(x+5)=2x(x+2)\\\\4x(x)+4x(5)-3(x)-3(5)=2x(x)+2x(2)\\\\4x^2+20x-3x-15=2x^2+4x\\\\4x^2-2x^2+20x-3x-4x-15=0\\\\2x^2+13x-15=0[/tex]

In this case you use the quadratic formula:

[tex]x_{1,2}=\frac{-13\pm \sqrt{(13)^2-4(2)(-15)}}{2(2)}\\\\x_{1,2}=\frac{-13 \pm 17}{4}\\\\x_1=-\frac{15}{2}\\\\x_2=1[/tex]

Then, for the first equation the solutions are x=-15/2 and x=1

second equation:

[tex][\frac{2}{x-2}+\frac{3}{x}=\frac{9}{x+3}]x(x-2)(x+3)\\\\2x(x+3)+3(x-2)(x+3)=9x(x-2)\\\\2x^2+6x+3(x^2+3x-2x-6)=9x^2-18x\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\2x^2+6x+3x^2+3x-18-9x^2+18x=0\\\\-4x^2+27x-18=0[/tex]

Again, you use the quadratic formula:

[tex]x_{1,2}=\frac{-27\pm \sqrt{(27)^2-4(-4)(-18)}}{2(-4)}\\\\x_{1,2}=\frac{-27\pm 21}{-8}\\\\x_1=6\\\\x_2=\frac{3}{4}[/tex]

Then, the solutions for the second equation are x=6 and x=3/4

Answer:

Step-by-step explanation:

Since the area pollute sis assumed to be a circle, we will be using the formula for calculating the area of a circle to solve the problem.

Area of a circle A = πr²

r is the radius of the circle

The rate at which the area is increasing is expressed as dA/dt. According to chain rule, dA/dt = dA/dr*dr/dt where;

dr/dt is the rate at which the area is increasing.

If dA/dr = 2πr (by mere differentiation)

dA/dt = 2πr * dr/dt

Given dr/dt = 3ft/sec and r = 30feet

dA/dt = 2π(30) * 3

dA/dt = 180π ft/sec

Hence, the area is increasing at the rate of 180π ft/sec

Answer:

Step-by-step explanation:

Please write this as x^2 + 5.  

Roots are ±i√5.

The corresponding factors of x^2 + 5 are (x + i√5) and (x - i√5)

Answer:

(5^2)(11^2)

Step-by-step explanation:

Taking all the factors in the left hand side of the factor tree, we have

5,5,11,11

5 twice

5^2=25

11 twice

11^2=121

The factor of 3,025=(5^2)(11^2)

Alternatively

3025÷5=605

605÷5=121

121÷11=11

11÷11=1

We have prime number 5 as divider twice and prime number 11 as a divider twice

Therefore,

5^2*11^2=3,025

Check

(5^2)(11^2)

=(25)(121)

=3,025

Answer:

c

Step-by-step explanation:

Answer:

this is som A sorry if you can't read it

Answer:

-5-2c

Step-by-step explanation:

The additive inverse of a term must be the opposite of it.

●-(5+2c)

●-5-2c

Answer:

Step-by-step explanation:

The additive inverse is just the opposite of the binomial in terms of the signs. The additive inverse of 5 + 2C is -(5 + 2C) which is, without parenthesis,        -5 - 2C.

Answer:

2x -5

Step-by-step explanation:

-3 + 2(x - 1)

Distribute

-3 +2x -2

Combine like terms

2x -5

Answer:

5x -2

Step-by-step explanation:

Answer:

175 balls

Step-by-step explanation:

If 12.5 percent of the balls had defects, then [tex]100-12.5=87.5[/tex]% of balls didn't have defects.

We can find 87.5 percent of 200 by converting 87.5 to a decimal.

87.5% as a decimal is 0.875.

Now we multiply this decimal by 200.

[tex]200\cdot0.875 = 175[/tex]

So, 175 balls didn't have defects.

Hope this helped!

The homework completed by Eric will be equal to 13/21.

The fraction is defined as the division of the whole part into an equal number of parts.

To add fractions, you first have to set the denominators equal to each other. To do this, you find the LCD (least common denominator) of the two fractions until you find a shared number.

To do this, list out the multiples of each number (3x1=3,3x2=6,3x3=9, and so on. Do this also with 7) The LCD for 3 and 7 is 21. 3x7=21, and 7x3=21. You want to set each fraction’s denominator equal to 21.

You want to multiply each side of 1/3 by 7. 1/3 would become 7/21. You’d do this because 3x7=21, and if you multiply the bottom by you need to multiply the top by. 7x3=21 so you multiply both sides by 3 to get 6/21.

Now you have 7/21 and 6/21 and can add them. Now that they are equal, you can ignore the denominator and just add the numerators. 7+6=13 so Eric completed 13/21 of his homework.

To know more about fractions follow

https://brainly.com/question/78672

#SPJ2

Answer:

19008

Step-by-step explanation:

550 is equal to 11 multiplied by 50.

1. Solve for multiples of 11 between 550 and 850

11 · 51 = 561

11 · 52 = 572

11 · 53 = 583

11 · 54 = 594

11 · 55 = 605

11 · 56 = 616

11 · 57 = 627

11 · 58 = 638

11 · 59 = 649

11 · 60 = 660

11 · 61 = 671

11 · 62 = 682

11 · 63 = 693

11 · 64 = 704

11 · 65 = 715

11 · 66 = 726

11 · 67 = 737

11 · 68 = 748

11 · 69 = 759

11 · 70 = 770

11 · 71 = 781

11 · 72 = 792

11 · 73 = 803

11 · 74 = 814

11 · 75 = 825

11 · 76 = 836

11 · 77 = 847

2. Add the products together

= 19008

Answer:

-3

Step-by-step explanation:

You have get a graphing calculator and press y=.

Then you would type in the equation.

Then click second, graph after you type the equation.

Then scan through the t graph for the value that causes the equation to be 0

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

Explanation:

The radius of the circle is r, which doubles to 2r to get the diameter. The diameter of the circle is also the diagonal of the square. Consequently, this means we have two right triangles in which they have the same hypotenuse of 2r.

Let x be the side length of the square. Use the pythagorean theorem to isolate x

a^2 + b^2 = c^2

x^2 + x^2 = (2r)^2

2x^2 = 4r^2

x^2 = 2r^2 ... divide both sides by 2

x = sqrt(2r^2) ... apply the square root to both sides; keep in mind that x > 0

x = sqrt(r^2*2)

x = sqrt(r^2)*sqrt(2)

x = r*sqrt(2)

The side length of the square is r*sqrt(2)

Therefore, the area of the square is

Area = (side)*(side)

Area = ( r*sqrt(2) )*( r*sqrt(2) )

Area = r*r * sqrt(2)*sqrt(2)

Area = r^2 * sqrt(2*2)

Area = r^2 * sqrt(4)

Area = r^2 * 2

Area = 2r^2

Answer:

They donated 7/10 of their profits. This cannot be simplified any further.

mark me BRAINLIEST

Tysmm!!

Answer:

Step-by-step explanation:

2/10 and 1/10 are easily addable fractions so all you have to do is add the numerator to get, 3/10. After that you need to convert 2/5 into tenths so that you can continue to add it correctly. If you multiply the numerator and the denominator of 2/5 to convert it, you will get 4/10 to add.

Answer: 7/10

Answer:

Interquartile Range: 21.549999999999997 = 21.55

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply $9500 by .05 (5%) to get 475. That is 5% of $9500. Now subtract 475 from 9500 to get 9025. That is your answer!  

The value of car in month of January is, [tex]\$ 9975[/tex]

It is given that, At the end of any year a car is worth 5% less than what it was worth at the beginning of the year.

Since, car was worth $9 500 in December 2016.

Then, the value of car in month of January is, 105 % of value of car in moth of December.

So that, value of car in month of January is,

                                     [tex]=9500*\frac{105}{100}\\ \\=9500*1.05=9975[/tex]

The value of car in month of January is, [tex]\$ 9975[/tex]

Learn more about percentage here:

https://brainly.com/question/24304697

Answer:

A,C,D

Step-by-step explanation:

When b=0, there is a proportional relationship.

The slope in y=mx+b is the value next to x.

Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.

Answer:

Step-by-step explanation:

Let, Radius = r units

Height ( h ) = 3r units

Volume ( V ) = 24π units³

Now,

Let's find the height of the cylinder:

[tex]\pi {r}^{2} h \: = 24\pi[/tex]

[tex] {r}^{2} (3r) = 24[/tex]

Calculate the product

[tex]3 {r}^{3} = 24[/tex]

Divide both sides of equation by 3

[tex] \frac{3 {r}^{ 3} }{3} = \frac{24}{3} [/tex]

Calculate

[tex] {r}^{3} = 8[/tex]

Write the number in the exponential form with an exponent of 3

[tex] {r}^{3} = {2}^{3} [/tex]

Take the root of both sides of the equation

[tex]r = 2[/tex]

Replacing value,

Height = 3r

[tex] = 3 \times 2[/tex]

Calculate

[tex] = 6 \: units[/tex]

Hope this helps..

Best regards!!

Answer:

[tex]\boxed{6 \: \mathrm{units}}[/tex]

Step-by-step explanation:

The formula for volume of cylinder is:

[tex]V=\pi r^2 h\\V:volume\\r:radius\\h:height[/tex]

[tex]V=24\pi\\h=3r[/tex]

Solve for r.

[tex]24\pi =\pi r^2 (3r)[/tex]

Cancel [tex]\pi[/tex] on both sides.

[tex]24=3r^3[/tex]

Divide 3 on both sides.

[tex]8=r^3[/tex]

Cube root on both sides.

[tex]2=r[/tex]

The radius of the base is 2 units.

Solve for h.

[tex]24\pi =\pi (2)^2 h[/tex]

Cancel [tex]\pi[/tex] on both sides.

[tex]24=4h[/tex]

Divide both sides by 4.

[tex]6=h[/tex]

Answer: The number of points added for r right answers is 12r. The number of points taken away for w wrong answers is 4w, so Olga's total points will be

... 12r -4w

To win, she needs this number to be more than 400. Your inequality is ...

... 12r -4w > 400

Answer:12r -4w > 400

Step-by-step explanation:

Answer:

mRT = 4√13 ≈ 14.42

mST = 10√2 ≈ 14.14

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

Since we have right triangles, in order to find the missing side, we use Pythagorean Theorem:

mTR:

12² + 8² = c²

144 + 64 = c²

c² = 208

c = √208 = 4√13

mST:

15² = 5² + b²

225 - 25 = b²

b² = 200

b = √200 = 10√2

To get your decimals, simply evaluate the square roots:

4√13 = 14.4222

10√2 = 14.1421

Answer:

6. 56.3 degrees.

7. 70.5 degrees.

Step-by-step explanation:

6. We are given the opposite and adjacent side lengths, so we can use tangent to solve this (TOA = Tangent; Opposite over Adjacent).

tan(R) = 12 / 8

tan(R) = 3 / 2

R = cotan(3/2)

R = 56.309932474020213

So, the measure of angle R is about 56.3 degrees.

7. We are given the adjacent and the hypotenuse, so we can use cosine to solve this (CAH = Cosine; Adjacent over Hypotenuse).

cos(R) = 5 / 15

cos(R) = 1/3

R = sec(1/3)

R = 70.528779365509

So, the measure of angle R is about 70.5 degrees.

Hope this helps!

Answer:

The surface area of the pyramid is 80.9 cm²

Step-by-step explanation:

The side length, s of the cube is given as 5 cm

Therefore, the largest pyramid that can fit into the cube will have a base side length, s = The side length of the cube = 5 cm

The height, h of the largest pyramid = The height of the cube = 5 cm.

The surface area of a pyramid =  Area of base, A + 1/2 × Perimeter of base, P × Slant height, S

The slant height of the pyramid = √(h² + (s/2)²) = √(5² + (5/2)²) = (5/2)×√5

The perimeter of the base = 4×5 = 20 cm

The area of the base = 5×5 = 25 cm²

The surface area of a pyramid = 25 + 1/2×20×(5/2)×√5 = 80.9 cm².

The surface area of a pyramid =  80.9 cm².

Answer:

a. x² + 6x + 9 = -22 + 9

Step-by-step explanation:

they moved the 22 to the right by subtracting it. this leaves a binomial on the left side, which if what you want to solve it.

then they completed the square by dividing b (6) by 2 = 3. then squaring 3 to get 9.

if you added 9 to the left, then you have to add 9 to the right, therefore resulting in -22 + 9.

Answer:

In TTM/Imagine Math it is top left or a.

Step-by-step explanation:

Answer:

see derivation below

Step-by-step explanation:

Show that:

( sec(t) - cosec(t) ) ( 1 + tan(t) + cot(t) ) =

sec(t) tan(t) - cosec(t) cot(t)

Some trigonometric definitions used:

tan(t) = sin(t)/cos(t)

cot(t) = cos(t)/sin(t)

sec(t) = 1/cos(t)

csc(t) = 1/sin(t)

some trigonometric identities used:

sin^2(t) + cos^2(t) = 1 ......................(1)

rewrite left-hand side in terms of sine and cosine

(1/cos(t) - 1/sin(t) ) ( 1 + sin(t)/cos(t) + cos(t)/sin(t) )

Simplify using common denominator sin(t)cos(t)

= ( (sin(t) - cos(t))/(sin(t)*cos(t)) ) * ( ( sin(t)cos(t) + sin^2(t) + cos^2(t)) / ( sin(t)cos(t) ) )

= ( sin(t) -cos(t) ) * (1 + sin(t)cos(t) ) / ( sin^2(t) cos^2(t) )   ...... using (1)

Expand by multiplication

= ( sin(t) -cos(t) + sin^2(t)cos(t) - sin(t)cos^2(t) ) / ( sin^2(t) cos^2(t) )

Rearrange by factoring out sin(t) and cos(t) in numerator

= ( sin(t) (1-cos^2(t) - cos(t)(1-sin^2(t) )  / ( sin^2(t) cos^2(t) )

= ( sin^3(t) - cos^3(t) ) /( sin^2(t) cos^2(t) )   .........................using (1)

Cancel common factors

= sin(t)/(cos^2(t)) - cos(t)/(sin^2(t))

Rewrite using trigonometric definitions

= sec(t)tan(t) - csc(t)cot(t)   as in Right-Hand Side