Which statement is true regarding the graphed functions?

On a coordinate plane, a red curved line with an upward arc, labeled g of x, crosses the x-axis at (negative 2, 0), and the y-axis at (0, 4). A blue curved line with an upward arc, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).

Answer:149 - 8b -2a

Step-by-step explanation:you put it in oder by 104 + 45 - 8b - 2a add 104 and 45 and you shoud get 149 then you put your problom together and get

149 - 8b -2a

sorry if it is not right i have not done this in a long time :(

Answer:

2

Step-by-step explanation:

The constant of proportionality k is given by k=y/x

y=2, x=1,

k=2

a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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Answer:

c

Step-by-step explanation:

your welcome! :) ❤❤❤❤❤❤❤❤❤❤❤❤

The option (b) set y equal to a constant other than zero to get the curve of points where the slope is that constant.

A slope field is a visual representation of the slopes of a function's derivative at different points on the xy-plane. The slope at a particular point in the xy-plane is given by the derivative of the function at that point.

To match the given equations with their corresponding slope fields, you need to analyze the behavior of the slopes and isoclines. An isocline is a curve in the plane along which the slope of a function is constant. Isoclines are useful in constructing slope fields by hand, as they help in determining the slope at different points.

To start with, set y equal to zero and observe how the derivative behaves along the x-axis. Similarly, set x equal to zero and observe the behavior of the derivative along the y-axis. These observations will give you an idea of the direction and magnitude of the slope at different points in the xy-plane.

Next, consider the curve in the plane defined by setting y' = 0. This curve represents the points in the picture where the slope is zero. These points are known as critical points or equilibrium points. They are essential in analyzing the stability and behavior of a system.

These curves are called isoclines and can be used to construct the slope field picture by hand.

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Match the following equations with their slope field. Clicking on each picture will give you an enlarged view. While you can probably sove this problem by guessing, it is useful to try to predict characteristics of the slope field and then match them to the picture Here are some handy characteristics to start with- you will develop more as you practice. Set y equal to zero and look at how the derivatiwe behaves along the x axis. Do the same for the y axis by setting x equal to 0. Consider the curve in the plane defined by setting y' = 0-this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slepe is that constant. These are called isoclines, and can be used to construct the slope field picture by hand.

Answer:

The person above me is correct.

Q1 − 1.5 ∙ IQR  (C) is your answer.

ED2021

For upper boundary its Q3 + 1.5 ∙ IQR (B). [This is the one right after]

The outlier rule for the lower boundary; Q1 − 1.5 ∙ IQR  (C) is your answer.

IQR(inter quartile range)  is the difference between third and first quartile.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.

Similarly, second quartile (also called median) is approximately in mid of the data.

Third quartile (also called upper quartile)  has approx 75% in its left partition, and on its right lies approx 25% of the data.

Given; An outlier is a data value that differs greatly from other values in a data set.

For upper boundary its Q3 + 1.5 ∙ IQR.

Therefore, the outlier rule for the lower boundary; Q1 − 1.5 ∙ IQR  (C) is your answer.

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Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

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Answer:

C. 21 pennants

Step-by-step explanation:

35-28=7

7 divided by 1/3= 21/1 or 21

The number of pennants that can be made is given by equation A = 49 pennants

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the number of pennants required be represented as A

The amount of fabric bought by students = 28 yards

The amount of fabric required by each pennant = 1/3 yards

The total number of pennants made by students = 35 pennants

So , the number of pennants that can be made is N

N ( 1 / 3 ) = 28 be equation (1)

Multiply by 3 on both sides , we get

N = 84 pennants

So , the remaining number of pennants A = N - number of pennants made by students

On simplifying the equation , we get

The remaining number of pennants A = 84 - 45

The remaining number of pennants A = 49 pennants

Hence , the number of pennants is 49

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Answer:

Option 1

Step-by-step explanation:

(3)(-17.25) = -51.75, he withdrew $51.75.

3 because he withdrew a total of 3 times.

-17.25 because he was taking out money.

Answer:(3)(-17.25)= -51.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

Answer:

100 grams

Step-by-step explanation:

Formala: multiply the mass value by 100

Answer:

1,000g

Step-by-step explanation:

1kg is equal to 1,000 grams, so just convert it.

1 times 1,000 = 1,000

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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The linear speed of the wheel is 150 m/min

The given parameters;

radius of the wheel, r = 50 cm = 0.5 m

angular speed, ω = 5 rad/s

The linear speed of the wheel in meter per second is calculated as follows;

\(v = \omega r\)

where;

v is the linear speed of the wheel

Substitute the given values and solve for v;

v = 0.5 x 5

v = 2.5 m/s

The linear speed in meter per minutes is calculated as;

\(v = 2.5 \frac{m}{s} \times \frac{60 \ s}{ 1 \min} = 150 \ m/min\)

Thus, the linear speed of the wheel is 150 m/min

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Answer:

SA = 240

Step-by-step explanation:

SA = (10*10) + (8*10) + (6*10)

SA = 240

Mrs. Manny needs 5.2 hours to grade her students' assignments. It would take Lexi 6.4 hours to grade the assignments alone.

In one hour, Mrs. Manny completes 1 / 5.2 = 0.1923 of the work.

In one hour, Lexi completes 1 / 6.4 = 0.15625 of the work

Together, they complete 0.1923 + 0.15625 = 0.34856 of the work.

The full work would take them 1 / 0.34856 = 2.87 hours.

It would take 2.87 hours for them to finish the task together.

The solutions to the exponential equation \(12^{x^2 + 5x - 4} = 12^{2x + 6}\) are given as follows:

x = 2 and x = -5.

The exponential equation for this problem is defined as follows:

\(12^{x^2 + 5x - 4} = 12^{2x + 6}\)

The n^x function is an injective function, which means that if they are equal, and have the same base, than their exponents are equal.

Thus the equation can be simplified as follows:

x² + 5x - 4 = 2x + 6.

x² + 3x - 10 = 0.

The coefficients of the quadratic function are given as follows:

a = 1, b = 3, c = -10.

Hence the discriminant is given as follows:

D = 3² - 4(1)(-10)

D = 49.

The first solution is given as follows:

x = (-3 + 7)/2 = 2.

The second solution is given as follows:

x = (-3 - 7)/2 = -5.

Meaning that the third option is the correct option in the context of this problem.

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Answer:

c

Step-by-step explanation:

Answer: see below...

Step-by-step explanation:

1. Reflection across the y axis.

2. Translation by a vector (0, -6): 0 units to the right/left, 6 units down.

Answer:

Step 1 is a reflection across the y- axis.

Step 2 is a translation 6 units down.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

perimeter (P) is calculated as

P = 2(l + b) ← l is the length and b the breadth

given l = x and P = 20 , then

2(x + b) = 20 ( divide both sides by 2 )

x + b = 10 ( subtract x from both sides )

b = 10 - x

Using Pythagoras' identity in the right triangle

x² + (10 - x)² = 8²

x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )

2x² - 20x + 36 = 0 ( divide through by 2 )

x² - 10x + 18 = 0 ← as required

(b)

solve using the method of completing the square

x² - 10x + 18 = 0 ( subtract 18 from both sides )

x² - 10x = - 18

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 5)x + 25 = - 18 + 25

(x - 5)² = 7 ( take square root of both sides )

x - 5 = ± \(\sqrt{7}\) ( add 5 to both sides )

x = 5 ± \(\sqrt{7}\)

Then

x = 5 - \(\sqrt{7}\) ≈ 2.35 ( to 3 significant figures )

x = 5 + \(\sqrt{7}\) ≈ 7.65 ( to 3 significant figures )

Answer: \(C. \frac{125}{7}\)

Step-by-step explanation:

1. Find the sum of the infinite geometric sequence:

\(S = \frac{125}{7}\)

2. Find the correct option:

C

Answer:

2621440

Step-by-step explanation:

The 9th term of the geometric sequence 10, 40, 160, .........  will be 655,360.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The sequence is given below.

10, 40, 160, .........

The first term is 10 and the common ratio of the sequence will be given as,

r = 40 / 10

r = 4

Then the equation of the geometric sequence is given as,

aₙ = 10 · (4)ⁿ⁻¹

The 9th term of the geometric sequence will be given as,

a₉ = 10 · (4)⁹⁻¹

a₉ = 10 · 65,536

a₉ = 655,360

The 9th term of the geometric sequence 10, 40, 160, .........  will be 655,360.

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The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

We have,

To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.

Now,

Prevalence of coronavirus in California: 3 out of 1000

False positive rate of the antigen test: 0.05 (5 out of 100)

Let's calculate the probability of a positive test result.

The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):

True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)

The probability of a positive test result can be calculated using Bayes' theorem:

P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)

P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)

P(Positive test) = 0.0024 + 0.04985

P(Positive test) = 0.05225

Therefore,

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

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Answer:

$1.22 per pair

The error is the contractor didnt take into account that there are 5 dozen gloves not 5 pairs of gloves. He calculated $73.20/5, which gave him $14.64.

Step-by-step explanation:

1 dozen = 12

5 dozen = 12 * 5 = 60

Therefore, you have 60 pairs of gloves.

He purchased all 60 pairs of gloves for $73.20.

73.20/60 = $1.22

This is how much one pair of gloves cost.

Hello!

y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

\(\hrulefill\)

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

\(\hrulefill\)

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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Step-by-step explanation:

There are two area of circle the dog can created

1. ¾ circle with radius 9-foot

2. ¼ circle with radius (9-6) foot.

so the exact area is

A = A1 + A2

A = π. 9² . ¾ + π . 3² . ¼ = 63π ft² ≈ 197.82 ft²

the perimeter also can be compute as

P = P1 + P2

P = ¾ . 2π . 9 + ¼ . 2π . 3

P = 15π ft ≈ 47.1 ft

The area above x axis is 12.6 sq units while the area under the y-axis is 42.443 sq units. The change in the average phone bill is 29.843 units.

a) Here we see that the graph is in the shape of a right-angled triangle above the x-axis

The area of a triangle = 1/2 X Base X Height

Here the base will be the measure of the distance of co-ordinates on the x-axis

The height is the distance between the coordinates on the axis for that triangle

= 1/2 X (16 - 8) X (3.15 - 0)

= 1/2 X 8 X 3.15

= 12.60 sq units

b)

Below the x-axis, the graph is a rectangle and a triangle

The area of the rectangle = length X width

Here length is the distance of the co-ordinates of the y-axis and width is the distance between the coordinates for the x-axis

Hence we get

(0 - (-5.14))(8 - 0)

= 5.14 X 8

= 41.12 sq units for the rectangle.

The area of the triangle will be

1/2 X (18 - 15.48) X (0 - (-1.05))

1/2 X 2.52 X 1.05

= 1.323 sq unit

Hence, the total area is

41.12 + 1.323

= 42.443 sq unit

c)

Since the area under the graph represents change,

Here we see that the change in the average cell phone bill will be

42.443 + 12.6

= 55.043

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