Graph the quadratic function ƒ(x) = 2(x − 3)^2 − 2 and select all of the following which is true.

The value of the scale factor k, is 1.5

The perimeter of a shape is the sum of the side lengths of the shape

The dimensions of the triangle MNO are given as:

\(MN = 5\)

\(NO = 4\)

\(OM = 2.5\)

Calculate the perimeter of the triangle as follows:

\(MNO=5 + 4 +2.5\)

\(MNO=11.5\)

Divide 17.25 by 11.5 to calculate the scale factor (k)

\(k = \frac{17.25}{11.5}\)

\(k = 1.5\)

Hence, the scale factor is 1.5

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Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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Answer:

5^3 is 125 , 5 * 5 = 25 , 25 *5 = 125

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply 5 three time's because 5 is cubed.

5 x 5 x 5 = 125

Hope this help's.

Answer:

x=1

Step-by-step explanation:

I'm not positive, it looks like a trick question but id say x=1 bc 17 × 1 is 17 and 17 is greater than -17 but then again any number greater than 1 such as 2,3,4, or 5 could work

There are a few conditions to consider to determine if WXYZ can be a parallelogram:

1)Opposite sides

2)Opposite angles

3)Consecutive angles

To determine if quadrilateral WXYZ can be a parallelogram, we need to examine the properties and conditions that define a parallelogram. A parallelogram is a quadrilateral with two pairs of parallel sides.

There are a few conditions to consider to determine if WXYZ can be a parallelogram:

1. Opposite sides: In a parallelogram, the opposite sides are parallel. We can examine the slopes of the lines connecting the vertices of WXYZ to determine if the opposite sides are parallel. If the slopes of the lines are equal, then the opposite sides are parallel.

2. Opposite angles: In a parallelogram, the opposite angles are congruent. We can check if the measures of the opposite angles of WXYZ are equal.

3. Consecutive angles: In a parallelogram, the consecutive angles are supplementary, meaning their measures add up to 180 degrees. We can verify if the consecutive angles of WXYZ satisfy this condition.

If all these conditions are met, then quadrilateral WXYZ can be a parallelogram.

It's important to note that a thorough examination of the properties of WXYZ, such as the lengths of sides and angles, is necessary to definitively determine if it is a parallelogram. Additionally, constructing a diagram or using coordinate geometry can provide visual aid in analyzing the properties of the quadrilateral.

In summary, to determine if quadrilateral WXYZ can be a parallelogram, we must verify if its opposite sides are parallel, opposite angles are congruent, and consecutive angles are supplementary. By checking these conditions and examining the properties of WXYZ, we can determine if it qualifies as a parallelogram.

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The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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Answer and Explanation:

Given:

Let's go ahead and chose different values of x and corresponding values of y;

When x = -2;

When x = -1;

When x = 0;

When x = 1;

When x = 5;

With the above values, we can go ahead and graph the function as seen below;

The domain of a function is the set of possible input values(x-values) for which the function is defined. On a graph, it is the set of x-values from left to right.

Looking at the given graph, we can see that the domain is;

The range of a function is the set of possible output values(y-values). It is the set of y-values from the bottom to the top of the graph.

Looking at the given graph, we can see that the range is;

Answer:

C: 3/5.79=13/x

Step-by-step explanation:

Two ratios are said to be in proportion when the two ratios are equal

3 markers cost $5.79 in which the proportion price is unknown

13 markers cost x

markers / cost = markers / cost

3 / $5.79 = 13 / x

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Answer: anna worked 4.33repeating hours washing cars and 3.25 hours landscaping

Step-by-step explanation:

i personally used a guess and check method.

i multiplied 9(hourly wage for washing cars) and 4.33repeating(number of hours) = 39

i multiplied 12(hourly wage landscaping) and 3.25(number of hours) = 39

39 + 39 = $78

the total decrease in value of the machine in the second 5 years after it was bought is $35000. option B is correct.

To find the total decrease in value of the machine in the second 5 years after it was bought, we need to integrate the rate of change of value over that time period.

Given that the rate at which the value changes is 500(t - 12) dollars per year, we can integrate this expression over the interval t = 12 to t = 17 (second 5 years).

The integral of 500(t - 12) with respect to t is:

∫[0 to 10] 500(t - 12) dt

= 500 ∫[0 to 10] (t - 12) dt

= 500 [(t²/2 - 12t) | [0 to 10]

= 500 [(10²/2 - 12*10) - (0²/2 - 12*0)]

= 500 [(50 - 120) - 0]

= 500 [-70]

= - 350000

Therefore, the total decrease in value of the machine in the second 5 years after it was bought is $35000. option B is correct.

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Answer:

  8.5 years

Step-by-step explanation:

You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.

The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...

  value = (initial value) × (1 - (depreciation rate))^t

where the rate is "per year" and t is in years.

  value = 18500·(1 -0.08)^t

  9100 = 18500·0.92^t . . . . fill in the value of interest

  9100/18500 = 0.92^t . . . . divide by 18500

  log(91/185) = t·log(0.92) . . . . take logarithms

  t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509

It will be about 8.5 years until the value is $9100.

__

Additional comment

The graph shows the solution to ...

  18500·0.92^t -9100 = 0

We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.

Answer:

Q 1- 15, just multiply 5 x 2 = 15

Q 2- 36, just multiply 8 x 12 = 36

Q 3- y= -2x

Q 4- 1200

Q 5- 20

Answer:

x = 5, y = 6

Step-by-step explanation:

x + 5y = 35, поэтому 3x + 15y = 105 (уравнение 1)

Кроме того, 3x + 2y = 27 (уравнение 2)

Мы должны найти y, вычитая второе уравнение из первого

Получаем, 13 y = 78, значит y = 6

А теперь подставьте y в любое уравнение, чтобы найти x = 5

The data being skewed and indicating higher wait times above 7 minutes due to a busy park is the most suitable description based on the given line plot.

The best description of the shape of the data is that it is skewed and might mean that the wait times were higher than 7 minutes because the park was busy.

Here's the explanation:

From the line plot, we can observe that there are 6 dots above 6, 5 dots above 7, 3 dots above 5, and 2 dots above 8.

The distribution is not symmetric, as the data points are not evenly spread around a central value.

The fact that there are more dots above 7 and 8 suggests that the wait times were higher than these values for a significant number of rides. This skewness in the data indicates that there were instances of longer wait times.

Additionally, the presence of dots above 5 and 6 suggests that there were some rides with shorter wait times as well.

However, the higher concentration of dots above 7 and 8 indicates that the park was likely busy, leading to longer wait times.

The option stating that the data is skewed and might mean that the wait times were higher than 7 minutes because the park was busy best aligns with the information provided by the line plot.

It acknowledges the skewness of the data towards higher wait times, suggesting that the park experienced increased demand and longer queues during the fair.

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a. The standard error of the mean for n = 25 is 3 cm

b.  The standard error of the mean for n = 100 is 1.5 cm.

Agronomist measured the height of n corn plants. If the mean height is 220 cm and the standard deviation is 15 cm, then we can calculate the standard error of the mean for n = 25 and n = 100 as shown below -

(a) For n = 25:

    If n = 25, then the formula for calculating the standard error of the mean is as follows -

    Standard Error of the Mean = (Standard Deviation / √n)

    Given,

    Standard deviation (σ) = 15 cm

    Number of samples (n) = 25 cm

    We can calculate the standard error of the mean as follows -

    Standard Error of the Mean = (Standard Deviation / √n)

                                                   = (15 / √25)

                                                   = 3

    Hence, the standard error of the mean for n = 25 is 3 cm.

(b) For n = 100:

    If n = 100, then the formula for calculating the standard error of the mean is as follows -

    Standard Error of the Mean = (Standard Deviation / √n)

    Given,

    Standard deviation (σ) = 15 cm

    Number of samples (n) = 100 cm

    We can calculate the standard error of the mean as follows -

    Standard Error of the Mean = (Standard Deviation / √n)

                                                   = (15 / √100)

                                                   = 1.5

    Hence, the standard error of the mean for n = 100 is 1.5 cm.

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You can arrange 10 people in a circle in 362880 different ways if two arrangements are considered the same

In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.

Information about the problem:

As the table is round, the first person can take any seat, then the seat on the right can be taken by 1 of 9 people, then the next seat by 1 of 8 and so on until the 10th person has no choice of seats.

This is expressed by:

9*8*7*6*5*4*3*2

9!

362,880

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Answer:

x = 6.4

Step-by-step explanation:

Taking the sin ratio of the angle :

Answer:

∠ ABC = 90°

Step-by-step explanation:

∠ ABC is the angle on the circle subtended by the diameter AC

it is the angle in a semicircle and is 90°

Answer: (x^2+20)(x-4)

Step-by-step explanation:

See attached picture

Answer:

Where is the picture?????

The weight, in pounds, of the contents in the container is: 102

The formula for the volume of the given container which is a cuboid is:

Volume = Length * Width * Height

We are given:

Length = 12 ft

Width = 8.5 ft

Height = 4 ft

Thus:

Volume = 12 * 8.5 * 4

Volume = 408 ft³

We are told that the contents weigh 0.25 pound per cubic ft and as such:

Weight in pounds = 408 * 0.25 = 102

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Step-by-step explanation:

Hey there!

Given;

The triangle is a right angled triangle, whose one side is 26 and another side is X. It has also one angle that is 41°.

Now, taking reference angle as angle 41°. We get;

Perpendicular= 26

Base = X

and Reference angle = 41°.

We know that the ratio of tan is p/b. So, let's use this ratio.

\( \tan(41°) = \frac{26}{x} \)

\(0.869 \times x = 26\)

\(x = \frac{26}{0.869} \)

Therefore, The value of x is 29.90.

Hope it helps...

The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

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The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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The value of y = -651. To find the value of y when x = -10 and z = 20, given that y varies jointly as x and z and y = 179 when x = -5 and z = -11, follow these steps:

Step 1: Understand that "y varies jointly as x and z" means y = kxz, where k is the constant of variation.

Step 2: Use the given values (y = 179, x = -5, z = -11) to find k. Substitute these values into the equation:
179 = k(-5)(-11)

Step 3: Solve for k:
179 = 55k
k = 179 / 55
k = 3.2545 (rounded to the nearest hundredth)

Step 4: Use the found value of k (3.2545) and the new values of x (-10) and z (20) to find the new value of y:
y = (3.2545) (-10)(20)
Step 5: Calculate y:
y = -651
So, when x = -10 and z = 20, y = -651.

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Thus, the probability that a randomly selected card has a consonant is 62.5%. This means that if you were to randomly select a card from the pile of cards, there is a 62.5% chance that the card would be a consonant.

The number of consonants in the word "probable" and the total number of cards. There are 5 consonants in "probable" (p, r, b, l, and b) and a total of 8 cards.

In the word "probable," there are 5 consonants (p, r, b, b, and l) and 3 vowels (o, a, and e). To calculate the probability of choosing a consonant, divide the number of consonants by the total number of letters:

Probability = (Number of consonants) / (Total number of letters)

The probability of selecting a consonant can be calculated by dividing the number of consonants by the total number of cards:

5 consonants / 8 cards = 0.625 or 62.5%

Therefore, the probability that a randomly selected card has a consonant is 62.5%. This means that if you were to randomly select a card from the pile of cards, there is a 62.5% chance that the card would be a consonant.

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(a) A basis for the subspace { (w, x, y) ∈ R³ : 2w + x - y = 0 } is {(1, 0, 2), (0, 1, 1)}.

(b) A basis for the subspace { (x, y, z) ∈ R³ : x - 2y + z = 0, x + 2z = 0 } is {(-2, 1, 1)}.

(a) To find a basis for the subspace { (w, x, y) ∈ R³ : 2w + x - y = 0 }, we can first rewrite the equation as y = 2w + x. Then any vector (w, x, y) in the subspace can be written as (w, x, 2w + x) = w(1, 0, 2) + x(0, 1, 1). Therefore, a basis for the subspace is {(1, 0, 2), (0, 1, 1)}.

(b) To find a basis for the subspace { (x, y, z) ∈ R³ : x - 2y + z = 0, x + 2z = 0 }, we can use the equations to solve for x, y, and z in terms of a free variable. Using z as the free variable, we get x = -2z and y = z. Therefore, any vector (x, y, z) in the subspace can be written as (-2z, z, z) = z(-2, 1, 1). Since there is only one free variable, z, we have a one-dimensional subspace. Therefore, a basis for the subspace is {(-2, 1, 1)}.

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