1. Which statement correctly describes the perpendicular bisector construction below?

The exercise target rate according to the Rate of change is 162.5.

According to the statement

We have to find that the target rate of the exercise.

So, For this purpose, we know that the

Rate of change is used to mathematically describe the percentage change in value over a defined period of time

From the given information:

Alyssas resting heart rate is 50 beats per minute. Her target exercise rate is 325% of her resting rate.

then

The exercise target rate  = 325% of 50 beats.

Then

The exercise target rate  = 325/100*50

The exercise target rate  = 3.25*50

The exercise target rate  = 162.5.

So, The exercise target rate according to the Rate of change is 162.5.

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Answer:

x = 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function:

[tex]y=\dfrac{x-3}{x^2-2x-3}[/tex]

The domain is the set of all possible input values (x-values).

Factor the denominator of the function:

[tex]\implies y=\dfrac{x-3}{(x-3)(x+1)}[/tex]

The domain of the given function is restricted as the function is undefined when the denominator equals zero, and when both the numerator and denominator equal zero.  

Therefore, the function is undefined when x = -1 and x = 3.

Therefore, the domain is (-∞, -1) ∪ (-1, 3) ∪ (3, ∞).

The range is the set of all possible output values (y-values).

As the domain is restricted, the range is also restricted.

Therefore, the range is (-∞, 0) ∪ (0, ¹/₄) ∪ (¹/₄, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Point Discontinuity (holes): When a rational function has a factor with an x that is in both the numerator and the denominator.

Therefore, there is a point discontinuity at x = 3.

Infinite Discontinuity: A vertical asymptote occurs when the denominator of a rational function is zero. This is considered an infinite discontinuity when the graph exists on both sides of the asymptote.

Therefore, there is an infinite discontinuity at x = -1.

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & =\dfrac{x-3}{x^2-2x-3}\\\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{(x^2-2x-3)(1) - (x-3)(2x-2)}{\left(x^2-2x-3\right)^2}\\\\ & = \dfrac{(x-3)(x+1)-(x-3)(2x-2)}{\left((x-3)(x+1)\right)^2}\\\\& = \dfrac{(x-3)[(x+1)-(2x-2)]}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{(x-3)(-x+3)}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{-(x-3)^2}{(x-3)^2(x+1)^2}\\\\& = \dfrac{-1}{(x+1)^2}\end{aligned}[/tex]

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{-1}{(x+1)^2} & = 0\\ -1 & \neq 0\end{aligned}[/tex]

Therefore, there are no stationary points and no minimum/maximum points.

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0\\\implies \dfrac{-1}{(x+1)^2} & > 0\\ \dfrac{1}{(x+1)^2} & < 0\\ \textsf{If $\dfrac{1}{a} < 0$ then $a < 0$}:\\(x+1)^2 & < 0\\ \textsf{As $(x+1)^2\geq 0$, no solution.}\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0\\\implies \dfrac{-1}{(x+1)^2} & < 0\\ \dfrac{1}{(x+1)^2} & > 0\\ \textsf{If $\dfrac{1}{a} > 0$ then $a > 0$}:\\(x+1)^2 & > 0\\ \end{aligned}[/tex]

[tex]\textsf{For $a^n > 0$, if $n$ is even then $a < 0$ or $a > 0$}[/tex]

[tex]\implies x+1 < 0 \implies x < -1[/tex]

[tex]\implies x+1 > 0 \implies x > -1[/tex]

Combine the intervals:

(-∞, -1) ∪ (-1, ∞)

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)

Range: [0, ∞)

Continuity: Point discontinuity (hole) at x = 3.

Infinite discontinuity (vertical asymptote) at x = -1.

None

Decreasing function: (-∞, -1) ∪ (-1, ∞)

Symmetry: Neither

Answer: -3

Step-by-step explanation:

turn mixed numbers into improper fractions, simplify, and solve- see attached

Answer:

-3

Step-by-step explanation:

to find the answer first turn both numbers into improper fractions

-1 13/14 becomes -27/14

1 5/9 becomes 14/9

now multiply them

[tex]\frac{-27}{14} * \frac{14}{9}[/tex]

you can cancel out the 14s

[tex]\frac{-27}{1} * \frac{1}{9}[/tex]

now divide 9 to the top of the first fraction and to the bottom of the second one

[tex]\frac{-3}{1} * \frac{1}{1}[/tex]

now multiply

-3/1 is your answer

that is basically -3

3√5

The distance between two points on an XY plane is calculated using the distance formula, which is employed in coordinate geometry or Euclidean geometry. The x-coordinate, often known as the abscissa, is a point's separation from the y-axis. The y-coordinate, often known as the ordinate, refers to a point's separation from the x-axis. A point on the x-axis has coordinates of the form (x, 0), and a point on the y-axis has coordinates of the form (0, y). We utilize the Pythagoras theorem in this case to determine the separation between any two points in a plane.

Distance formula = √ ( x₁ - x₂)² + ( y₁ - y₂)²

                                = √ 6² + 3²

                                =3√5

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The conversion of 100 kilometers to meters would be,

100 kilometers = 100,000 meters

The correct answer is an option (a)

In this question we need to convert the metric units of length.

We need to convert 100 kilometers to meters.

We know that, 1 kilometer = 1000 meters

Let 100 kilometers = p meters

So, we get an expression,

p × 1 = 100 × 1000

From this expression we get,

p = 100,000 meters

This means, 100 kilometers = 100,000 meters

Therefore, the conversion of 100 kilometers to meters would be,

100 kilometers = 100,000 meters

The correct answer is an option (a)

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The 34 feet perimeter and width, x, of the window which is in the shape of a rectangle surmounted by a semicircle is, A = 17•x - x²•(1/2 - π/8)

The shape of the window = A rectangle surmounted by a semicircle

Perimeter of the window, P = 34 feet

Width of the window = x

Required; The area, A, of the window as a function of x

Solution:

Diameter of the semicircle = x

Length of the semicircular arc = π•x/2

Let y represent the height of the window, we have;

P = 2•y + x + π•x/2 = 34

Therefore;

y = (34 - (x + π•x/2))/2 = 17 - x•(1 + π/2)/2

Area of the window, A = x × y + π•x²/8

Which gives;

A = x × (17 - x•(1 + π/2)/2) + π•x²/8 = 17•x - x²/2 - x²•π/8

A = 17•x - x²/2 - x²•π/8 = 17•x - x²•(1/2 - π/8)

Therefore;

Window area, A = 17•x - x²•(1/2 - π/8)

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The number of vanilla and chocolate flavoured cupcakes sold every day is 1250 and 3750, respectively.

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Answer: 8 kitkats

Step-by-step explanation:

40+24= 64

72-64=8

Answer:

Total candy bars to snickers = 72:40 or simplified 9:5

Ratio of kit kats to milky ways = 8:24 or simplified 1:3

Ratio for kit kats to total candy bars = 8:72 or simplified 1:9

Step-by-step explanation:

72 = 40 + 24 + x

x = 8

Answer:

2.5

Step-by-step explanation:

By Using s = d/ t

So t = d / s

Answer:

631

Step-by-step explanation:

This problem can be expressed as:

0.05x + 15 = 21.55
0.05x + 15 - 15 = 21.55 - 15
0.05x = 6.55
0.05x/0.05 = 6.55/0.05
x = 131

We also know that:

0.05x + 15 = x + 500

If x = 131:

x + 500
131 + 500
631

The length of one side of the square is x+6

The formula for calculating the area of a square is expressed as:

A = L^2

where

L is the side length of the square

Given the following parameters

A = x^2 + 12x + 36  square feet

A = (x+6)^2

(x+6)^2 = L^2

L = x + 6

Hence the length of one side of the square is x+6

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Answer:

the answer is

Step-by-step explanation:

A is more likely to be 12 and B could be 3

so 12/3=4

and

3/12= 0.25

Answer:

Step-by-step explanation:

hi

f(a+7)

f(x) =x²+5

by remplacing X by (a+7) :

then  f(a+7) = (a+7)²+5

                  =   a² +2*a*7 +49 +5

                  = a² +14a +54

Answer:

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

Area equation of a rectangle

Answer:

Length = 88.9 cm

Step-by-step explanation:

Formula we use,

→ A = L × W

Then the value of its length is,

→ A = L × W

→ 8712 = L × 98

→ L = 8712/98

→ L = 88.8979591837

→ [ L = 88.9 cm ]

Hence, the length is 88.9 cm.

The intervals on which the function f of x is increasing is:

(6, 0) U (2, 4) U (7, 9)

When we have the graph of a function, we can identify if it is increasing if, reading from left to right, we can see that the graph of the function goes upwards.

For the graphed function, we can see that it increases for the values:

-6 < x < 0

2 < x < 4

7 < x < 9

Writing this in interval notation, we have:

(6, 0) U (2, 4) U (7, 9)

This is the list of intervals on which the function f(x) is increasing.

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Answer:

spam

Step-by-step explanation:

spam spam spam

The original cost of the dress is $14.45

The dresses were sold for $17 each

This price was 85% of the original price

Therefore the original cost of the dress can be calculated as follows

85/100= 0.85

The first step is to calculate the original pre sale price

17= 0.85x

x= 17/0.85

= 20

The original cost of the cloth is

= 0.85 × 17

= 14.45

Hence the original cost of the cloth is $14.45

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The probability of having less than 10 vegans attending the event, given that the binomial distribution requirements are satisfied, is 9%.

The requirements of a binomial distribution include:

Probability is the likelihood of an event occurring given the possibility of many outcomes.

Probability is computed as percentages, fractions, or decimals, and it cannot be more than 1.

Expected guests = 100

Expected vegans = 5%

Less than 10 vegans = 9

The chance that 9 vegans will attend the event = 9/100 = 9%.

Thus, the probability of having less than 10 vegans attending the event is 9%.

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If a sophomore was chosen yesterday, the probability that a sophomore will be chosen again today is 3/10.

Given, number of students name put into the hat = 20

total number of freshmen in the class = 12

total number of sophomore in the class = 6

total number of juniors in the class = 2

we are asked to determine the probability that the sophomore will be selected the second day also = ?

Calculating a situation's probability allows us to determine its likelihood. Absolute certainty in forecasting is challenging in many situations. With its help, we are only able to anticipate the likelihood, or chance, that an event would occur.

from the given data,

n(s) = 20

n(A) = 6 ⇒ as the name selected in the first day is put back in the hat.

⇒ P(A) = n(A)/n(s)

P(A) = 6/20

P(A) = 3/10

hence the probability that the another day again a sophomore will be chosen is 3/10.

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Answer:

Anna is correct.

Step-by-step explanation:

Using PEMDAS, you need to add the terms in the parentheses first.

After adding, you get 8×6 = 48

Jojo made the mistake of multiplying 6 and 5 first, and then adding 3.

The answer is 27 for your math

Step-by-step explanation:

54 grams of aluminium is present in aluminium sulphate Al₂(SO₄)₃.

A substance's molecular mass is the sum of the atomic masses of all of the atoms in the molecule of a substance.

For the given question, the expression is;

aluminium sulphate Al₂(SO₄)₃

As three of aluminium is present in the aluminium sulphate.

And, molecular mass of one aluminium atom is 27 grams;

Thus, for 2 aluminium atoms = 2×27 = 54  grams.

Therefore, the compound aluminium sulphate contains 54 gram of aluminium in it.

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The additive inverse of the numbers given as -7/8 and 7/8  are 7/8 and -7/8

The numbers are given as:

-7/8 and 7/8

As a general rule, the additive inverse of a number x is -x

This means that the additive inverse of the numbers given as -7/8 and 7/8  are 7/8 and -7/8

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L = 10 and w= 5 are  the dimensions of the rectangular garden.

What is a rectangle, exactly?

Let the width of the garden be a

Length of the garden = a + 5

Area = l * w

66 = ( a+ 5 ) * a

66 =  a² + 5a

a² + 5a -66 = 0

a² + 11a - 5a - 66 = 0

a( a + 11 ) -5 ( a + 11) = 0

( a + 11 ) ( a - 5) = 0

so  a + 11 = 0 ⇒  a = -11

      a - 5 = 0 ⇒ a = 5

Width cannot be negative.

l = a + 5 = 10

w = 5

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Answer:

x is 4 and y is 1

So we put 3 x 4 + 1

if it's equal 1 (since y is 1)

but in this case it equals 13 so it's wrong

Answer:

see explanation

Step-by-step explanation:

to determine if (4, 1 ) is a solution of the equation, substitute the x and y coordinates into the equation and if both sides are equal then it is a solution.

y = 3(4) + 1 = 12 + 1 = 13 ≠ 1

since y ≠ 13 then (4, 1 ) is not a solution to the equation

[tex] \: \: \: \: \large\bf\implies \: 4.32[/tex]

[tex] \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32[/tex]

First of all we know that to do this type of question that is ↓

Answer:

1 us dollar =0.84 euros so,400 us dollar =084x400 so, she will receive 336 euros in exchange.