Need help with number 13

The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

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Answer: Since he had fourteen, and he gave away six of them, he has eight left.

Step-by-step explanation:

The number sentence shows the number of apples Austin has left is 14 - 6 and equal to 8.

A way to express or represent numbers is through the number system.

The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.

As per the given,

Total number of apples = 14

Number of apples that make a pie = 6

Left = 14 - 6 = 8

Hence "The number sentence shows the number of apples Austin has left is 14 - 6 and equal to 8".

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Answer:

Step-by-step explanation:

Given function:

Set of domain is:

To find each term of the range substitute the terms of the domain in the function:

Set of range:

Correct option is A

Answer:

x = 13.56 when simplified

hope this is the answer you are looking for

Step-by-step explanation:

Answer:

1. V(12) = $ 1200

2. V(20) = $ 4800

Step-by-step explanation:

The following data were obtained from the question:

V(t) = 150 × 2ᵗ/⁴

V(12) =?

V(20) =?

1. Determination of V(12)

Time (t) = 12 years

V(12) =?

V(t) = 150 × 2ᵗ/⁴

V(12) = 150 × 2¹²/⁴

V(12) = 150 × 2³

V(12) = 150 × 8

V(12) = $ 1200

2. Determination of V(20)

Time (t) = 20 years

V(20) =?

V(t) = 150 × 2ᵗ/⁴

V(20) = 150 × 2²⁰/⁴

V(20) = 150 × 2⁵

V(20) = 150 × 32

V(20) = $ 4800

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

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Answer:

\(\boxed {\boxed {\sf y= \frac{5}{4}x+1}}\)

Step-by-step explanation:

We are given the equation of a line and asked to put it into slope-intercept form.

Slope-intercept form is:

\(y=mx+b\)

Where:

In order to put the equation into slope-intercept form, we have to isolate the variable y by performing the inverse operation.

\(5x-4y= -4\)

5x is being added to -4y. The inverse of addition is subtraction, so subtract 5x from both sides of the equation.

\(5x-5x-4y=-4-5x\)

\(-4y=-4-5x\)

The variable y is being multiplied by -4. The inverse of multiplication is division. Divide both sides of the equation by -4.

\(\frac {-4y}{-4}=\frac{-4-5x}{-4}\)

\(y= \frac{-4}{-4}+\frac{-5x}{-4}\)

\(y=1+\frac{5}{4}x\)

Rearrange the equation.

\(y= \frac{5}{4}x+1\)

The fractions are completely simplified, so this is our final answer.

The equation of the line in slope-intercept form is \(\bold {y= \frac{5}{4}x+1}}\).

The slope is 5/4 and the y-intercept is 1.

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

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The dimensions of the rectangle that will produce the largest area of the window are x = (12 - √3) / 2 and y = 3 / √3.

Let x be the length of the rectangle, and y be the width of the rectangle. The perimeter of the window is 12m, and since the triangle is equilateral, we know that all 3 sides of the triangle are equal to x.

Therefore, we can set up the following equation to represent the perimeter of the window: x + y + x = 12

The area expression is:

A = x*y + (x^2 * √3)/4

After substituting x = (12-y)/2, the area expression becomes:

A = [((12-y)/2)*y] + [(12-y)^2 * √3]/16

Which can be simplified to:

A = 6y - 3y^2 + (9-3y)√3 / 4

To find the maximum value of this expression, we can differentiate it with respect to y and set it to zero:

dA/dy = -3y + (9-3y)√3/4 = 0

and solve for y:

-3y + (9-3y)√3/4 = 0

-3y = (3y-9)√3/4

-3y = 3y-9 / 2√3

3y = 9 / 2√3

y = 3 / √3

To find x, we can substitute this value of y back into x = (12-y)/2:

x = (12 - 3 / √3) / 2 = (12 - √3) / 2

So the dimensions of the rectangle that will produce the largest area of the window are x = (12 - √3) / 2 and y = 3 / √3.

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Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.

To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.

First, let's simplify the equation:

2^x - 2 = 8^4

We know that 8 can be expressed as 2^3, so we can rewrite the equation as:

2^x - 2 = (2^3)^4

Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:

2^x - 2 = 2^(34)

Simplifying the right side of the equation:

2^x - 2 = 2^12

Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:

x = 12

Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.

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Answer:

-7

Step-by-step explanation:

-3-4=-7

:]

Answer:

-7

Step-by-step explanation:

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

36

Step-by-step explanation:

81 x (4/9) =

36

PRICES COUNTS COSTS

8 e 8e

10 420-e-t 10(420-e-t)

12 t 12t

420 3920

system%28e%2B420-e-t=5t%2C8e%2B10%28420-e-t%29%2B12t=3920%29

First equation gives highlight%28t=70%29.

Second equation simplifies to e-t=140.

Substitution gives highlight%28e=210%29.

Quantity of $10 tickets by difference, highlight%28140%29

Answer:

Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.

We can write the scale factor for the table as {K} = y/x.

Given is to determine the scale for the given table.

Therefore, we can write the scale factor for the table as {K} = y/x.

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The given expression is proved.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have.

tan∅/(1+ sec∅)

=(sin∅/cos∅)/(1+ sec∅)                  [tan∅=(sin∅/cos∅)]

=(sin∅/cos∅)/(1+1/cos∅)

=sin∅/1+cos∅

multiplying both numerator & denominator by 1-cos∅, we get,

=sin∅(1-cos∅)/ sin^2∅

=(1-cos∅)/sin∅

=cosec∅ - cot∅

Hence, The given expression is proved.

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Answer:

10.3923048454

Step-by-step explanation:

3 square root (4) x square root (3)

Answer:

YOUR WELCOME

\(\:\)

y = 3x − 1

Using the slope-intercept form, the slope is 3.

m = 3

Answer:

c- H0: p = 0.1 and Ha: p > 0.1

Step-by-step explanation:

Answer:

Personal Identification Number

Answer:

P.Personal

I .Identification

N . Number

Answer:

\( {x}^{2} + {8}^{2} = {y}^{2} ...(1) \\ {x}^{2} + {23}^{2} = {z}^{2} ...(2) \\ {y}^{2} + {z}^{2} = {(23 + 8)}^{2} \\ {y}^{2} + {z}^{2} = {(31)}^{2} ...(3) \)

You should be able to solve this simultaneously...to find x,y and z.

Answer: I believe its the one that says "each dog is fed between 1 and 3 pounds of dog food each week"

Step-by-step explanation:

To give each dog an equal amount you'd have to divide 20 by 7.

20 / 7

when you do that is doesn't come out to a whole number

20 / 7 = 2.8571428571

anything higher than 2.8 pounds would go over his limit of 20 pounds

so true statement I think would be the one that says between 1 and 3.

Answer:

Each student ran 1056 feet.

Step-by-step explanation:

A mile has 5280 feet in it so just divide that by 5 and you have your answer.

Make a bar that is supposed to represent 5280 feet or a mile and cut it up into five pieces.  

Sorry if this doesn't make sense, best way I could explain it

Answer:

1056

Step-by-step explanation:

First, lets convert 1 mile to feet

1 mile = 5280 feet

Five students ran an equal distance in the 5280 feet relay race. How many feet did each student run?

Now, we can divide 5280 by 5, we will get 1056.

Equation: 5280 ÷ 5 = 1056

Each student ran 1056 feet.

Each bar would be 1056.

Hope this helps :)

The trigonometric function on the graph is:

f(x)= -cos(x)

So the correct option is B.

Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.

Notice that:

sin(0)= 0

cos(0) = 1

So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:

f(x) = -cos(x)

That is the graphed function.

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Answer:

606 square units.

Is it right?