Find the domain and range verbally, given the context of the situation

a) Javier bough a used car for $7000. The car’s value decreases at a constant rate each year. After 8 years, the value decreased to $3000. Find a function to model the car’s value (in dollars). Let the independent variable be the number of years since the car was purchased.

b) Find the x and y-intercept

c) What is the domain of the function in this context?

d) What is the range of the function in this context?

The complete proof that ΔUWX ≅ ΔWUV is explained below.

Congruent triangles are set of given triangles which have equal values of corresponding properties. Thus the triangles have equal dimensions and measure of internal angles.

The two column complete proof required are given below:

              STATEMENT                             REASONS

1. WX ║ UV                                               Given

2. < V ≅ <X                                               Given

3. <VUW ≅ <UWX                                    Definition of alternate angles.

4. UW ≅ UW                                             Reflexive property of congruence

5. ΔUWX ≅ ΔWUV                                   Angle-Side-Angle (AAS) property

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Answer:

95m

Step-by-step explanation:

So to work this out you times 84 by 2 which is 168 (84×2) and then take away 168 from 358 which is 190 (358-168). Then divide 190 by 2 which is 95 (which is the the length/Answer)

(84+84+95+95=358)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Number of toys = 377
Number of bags she wants to put in the toys = 12

Step 1 - divide 377/12
= 31 and 5 as the remainder
So 31 toys in each bag and 5 toys to her brother

A singleton set has only one element, and the number of proper subsets it has is 0.

A proper subset of a set A is a subset that is not equal to A itself. In other words, a proper subset is a subset that contains at least one element less than A. Since a singleton set has only one element, it is not possible to form a subset that has fewer elements than the original set. Therefore, the number of proper subsets of a singleton set is zero.

For example, if we have a singleton set containing the element {1}, then the only subset of this set is the set {1} itself, which is not a proper subset. Therefore, the singleton set {1} has zero proper subsets.

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It is unlikely that the handwritten word will be correctly interpreted. , Option B is the answer

The missing statements are

It is impossible that the handwritten word will be correctly interpreted.

It is unlikely that the handwritten word will be correctly interpreted.

It is likely that the handwritten word will be correctly interpreted.

It is certain that the handwritten word will be correctly interpreted.

Probability can be defined as the likelihood of an event to occur , It has a range of 0 to 1 , where 0 means uncertain and 1 interprets certainty.

In the given question

A researcher finds that the probability that a word recognition app correctly interprets a handwritten word is 1/6 .

As it can be interpreted from the probability that out of 6 chances the app identified in only 1 chance so

It is unlikely that the handwritten word will be correctly interpreted.

Option B is the answer

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To find the side length of the bare canvas, we need to subtract the width of the frame from the dimensions of the framed painting. The side length of the bare canvas is option C) 21 centimeters.

The frame is 4 centimeters wide on each side, so the total width and length of the framed painting would be (side length of bare canvas + 4) centimeters.

We know that the area of the framed painting is 625 square centimeters, so we can set up the equation:

(side length of bare canvas + 4) * (side length of bare canvas + 4) = 625

Expanding and simplifying the equation, we have:

(side length of bare canvas)^2 + 8(side length of bare canvas) + 16 = 625

Now, let's solve for the side length of the bare canvas. Rearranging the equation, we have:

(side length of bare canvas)^2 + 8(side length of bare canvas) - 609 = 0

Using the quadratic formula, we can find the side length of the bare canvas:

(side length of bare canvas) = (-8 ± √(8^2 - 4(1)(-609))) / 2(1)
Calculating the square root, we have:

(side length of bare canvas) = (-8 ± √(64 + 2436)) / 2

(side length of bare canvas) = (-8 ± √(2500)) / 2

(side length of bare canvas) = (-8 ± 50) / 2

This gives us two solutions:

(side length of bare canvas) = (-8 + 50) / 2 = 42 / 2 = 21

(side length of bare canvas) = (-8 - 50) / 2 = -58 / 2 = -29

Since we are looking for a positive side length, the correct option is c. 21 centimeters.

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Answer:

10

Step-by-step explanation:

acellus

The period of the given graph is 10.

Use the concept of a period of function defined as:

One full wave is set up in a medium for the length of time it takes a particle of that medium to complete one vibration or one wave period.

In the given wave,

X-axis represents time

The Y- axis represents the amplitude of the curve

As we can see,

The first peak of this graph is located at x = 1 and the second peak is at,

x = 13

Since the period is the time interval between two consecutive peaks in a graph.

In this case, the time interval is 10.

Hence,

The period of the given graph is 10.

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Answer:

Slope = 46.000/2.000 = 23.000

x-intercept = 6/23 = 0.26087

y-intercept = -6/1 = -6.00000

Answer:

m<5 = 104°

Step-by-step explanation:

<5 and the 104° angle are alternate interior angles of parallel lines cut by a transversal, so they are congruent.

m<5 = 104°

Answer:

104 degrees

Step-by-step explanation:

I am pretty sure that it’s 104 degrees because 104 and angle 8 are same-side interior angles. Angle 8 is a vertical angle to angle 5, so if angle 8 is 104 so is angle 5.

Answer:

ASA

Step-by-step explanation:

the probability that the student is over 26 years old is 0.1587.

Mean = 23

Standard deviation = 3 years

The random variable X represents the age of a statistics student at ELAC.The distribution of the random variable X is normal with the given mean and standard deviation. We have,Mean = μ = 23 Standard deviation = σ = 3 We need to find the probability that the student is over 26 years old. That is, we need to find P(X > 26).The Z-score of 26 is given by;

Z = (X - μ) / σZ = (26 - 23) / 3Z = 3 / 3Z = 1

So, P(X > 26) = P(Z > 1)

We can find this probability using the standard normal table or calculator as;

P(Z > 1) = 0.1587

Therefore, the probability that the student is over 26 years old is 0.1587.

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The correct answer is option D. No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal.Researchers investigated whether there is a difference between two headache medications, R and S.

Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication.To construct a confidence interval, we require that some conditions are satisfied. The assumptions that should be met for inference with a confidence interval for the difference in population means are as follows:The data is independent;The data in each group should be roughly normally distributed;Both groups have the same variance, and each group should have a large enough sample size so that the central limit theorem (CLT) holds. The CLT holds for the difference in the sample means since both samples are taken from a population that is normally distributed. We can also assume that the sample size is large enough to use the t-distribution since each sample has more than 30 observations. As a result, all of the conditions have been met. As a result, we may employ a t-distribution to make inferences about the population difference between the two headache medications.

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Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

Answer:

(9 × 16) + (9 × 10) = f

Step-by-step explanation:

Lina made 9 flower necklaces.

We are told that :

Each necklace had 16 carnations and 10 hibiscus flowers.

Hence,

1 flower neck lace = 16 carnations + 10 hibiscus flowers

The total number of flowers used to make 9 flower necklaces is :

f = 9( 16 + 10)

f = (9 × 16) + (9 + 10)

f = 144 + 90

f = 234 flowers

Therefore, equation could be used to calculate the total number of flowers used for the flower necklaces is:

(9 × 16) + (9 × 10) = f

Answer:

A. Imaginary Square is 1 so ye ignore

Answer:

C = 100p + 200

Step-by-step explanation:

Because C is the total cost per day, 200 is the y-intercept because it's paid daily.

The 100 is the slope since "he pays a cost of $100 per phone produced)".

The required expression for the total cost of producing p phones is C = 200 + 100P.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

As mentioned in the quesiton,
Let the number of phones manufactured in the given day be P and the total cost of manufacturing be C,
As mentioned in the quesiton, He pays a cost of $100 per phone produced for materials and labor and also must pay a daily fixed cost of $200 to rent the building and equipment.
So,
Equation models of the situation is given as
C = 200 + 100P

Thus, the required equation is C = 200 + 100P

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Answer:

29 ft

Step-by-step explanation:

the screens have 90 degree angles so they form right triangles with the diagonal, so use Pythagorean theorem to solve for the diagonal

diagonal² = 21² +20² , square and square root both sides of the equation

diagonal = √441+400, add

diagonal = √841, square root

diagonal = 29ft

Answer:

The second choice

Step-by-step explanation:

Answer: Felipe's work!

Step-by-step explanation:

Answer:

I got 226.08

Step-by-step explanation:

I don't know if your trying to find the nearest whole number

Answer: 35

Step-by-step explanation:

height x base, then divide by 2.

7 x 10= 70

70/2=35

Answer:

the area (A) of the triangle is 35

A= HbB/2 = 7x10/2 = 35

Answer:

5 units

Step-by-step explanation:

here;

perpendicular (p)= 3

base (b) = 4

hypotenuse (h) = c= ?

By Pythagorean relationship;

h²=p²+b²

or, h= √(p²+b²)

or, c= √(3²+9²)

or, c= √25

hence, c=5

The equations that show the properties of the exponenets are a, c and d

We know that there are certain properties that are common to the numbers that appear in the exponential form. We shall look at some of those properties.

1) when we have;

(ab)^x, it is the same as a^x b^x

2) When we have b^2 * b^x, it is the same as b^2 + x

3) When we have; x^-2, it is the same as 1/x^2

These are the basics of the properties of the exponents as we can see in the question and these obey the properties of the exponents.

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Answer:

A) 4x4 – 3x3y + 8x2y2 – 7xy3

Step-by-step explanation:

The polynomial written in standard form is: 4x4 + 8x2y2 - 3x3y - 7xy3. Option C

In standard form, a polynomial is written with the highest exponents first and positive numbers in front of each term.

This means that the term with the greatest power comes first, followed by the terms in decreasing order of powers.

The polynomial is organized in option C like this.

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Answer:

7 m

Step-by-step explanation:

Use the pythagorean theorem.

a^2+b^2=c^2

7.5 is your hypotenuse and 3 is one of your legs.

7.5^2 - 3^2 = 47.25

the sqrt of 47.25 is 6.873863542, therefore the nearest meter it reaches is 7.

Answer:

Statement A describes all possible solutions where x = 2. April will purchase 2 bottles of orange juice and 4 bottles of apple juice.

Answer:

2

Step-by-step explanation:

Subtract -7--5=-2, there can not be a length on a rectangle of -2 so it would just be 2.

Answer:

2

Step-by-step explanation:

The true statements about the synthetic division are

The synthetic division is given as:

3)2 -2 -12

       6 12

    2 4 0

In the above representation of the synthetic division, we have:

Because the remainder is 0, then

(2x^2 - 2x - 12) ÷ (x - 3) = (2x + 4) --- option C

Set the divisor to 0

x - 3 = 0

Solve for x

x = 3

This means that 3 is a root of 2x^2 - 2x - 12 --- option (D) and x - 3 is a factor of 2x^2 - 2x - 12 --- option (E)

Hence, the true statements are (C), (D) and (E)

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Answer: Step 3 is incorrect because it shows an incorrect ratio for the slope.

Answer:

Step 3 is incorrect because it shows an incorrect ratio for the slope.

Step-by-step explanation:

The correct question is:

Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use:

Step 1: Choose a point on the line, such as (2, 5).

Step 2: Choose another point on the line, such as (1, 3).

Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is .

Step 4: Substitute those values into the point-slope form.

y – y1 = m(x – x1)

y – 3 = (x – 1)

Which of Talia’s steps is incorrect?

Step 1 is incorrect because it uses a point that is not on the line.

Step 2 is incorrect because it uses a point that is not on the line.

Step 3 is incorrect because it shows an incorrect ratio for the slope.

Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.

Answer:

Step 1 is correct because from the graph, points (1,3) and (2,5) lies on the line so the points can be used to find the slope.

Step 2 is also correct.

Step 3 is incorrect. Slope of a graph is the ratio of vertical change to horizontal change. The vertical change is the rise while the horizontal change is the run, hence slope is the ratio of rise to run.

Since the line runs 1 unit to the right and rises 2 units up, so the slope is 2/1 = 2

Therefore the correct point-slope form is:

y – y1 = m(x – x1)

y – 3 = 2(x – 1)

Step 4 is correct, because i t shows an incorrect substitution of (1, 3) into the point-slope form.