Which expression is equivalent to (4.3x + 4)(−1.8x)?
A. −4.14x2 + 0.08x
B. −7.74x2 − 7.2
C. −7.74x2 − 7.2x
D. −7.74x2 + 7.2x

Answer: Let's first convert Cheryl's walking speed to meters per minute. Since she takes 80 steps per minute and each step is 81 cm, her walking speed is:

80 steps/min x 81 cm/step = 6480 cm/min

To convert this to meters per minute, we can divide by 100:

6480 cm/min ÷ 100 cm/m = 64.8 m/min

Now, let's find out the distance Cheryl walks to school. Since she walks for 12 minutes at a speed of 64.8 m/min, the distance she covers is:

distance = speed x time = 64.8 m/min x 12 min = 777.6 m

Next, let's find out how many steps Diane takes per minute on average:

90 steps/min

Since each of Diane's steps is 72 cm long, her walking speed is:

90 steps/min x 72 cm/step = 6480 cm/min

To convert this to meters per minute, we can divide by 100:

6480 cm/min ÷ 100 cm/m = 64.8 m/min

So Diane's walking speed is the same as Cheryl's. To find out how long it takes Diane to walk to school, we can use the formula:

distance = speed x time

Since Diane and Cheryl walked the same distance, we can use the distance we found for Cheryl:

777.6 m = 64.8 m/min x time

Simplifying this equation, we get:

time = 12 minutes

Therefore, Diane takes 12 minutes to walk to school.

Answer:

  12 min

Step-by-step explanation:

You want to know how long it takes Diane to walk to school if she takes 90 steps of 72 cm per minute, while Cherly takes 80 steps of 81 cm per minute and traverses the distance in 12 minutes.

The speed of each girl is the product of the number of steps per minute and the length of the step:

  Cheryl: (80 step/min)(81 cm) = 6480 cm/min

  Diane: (90 step/min)(72 cm) = 6480 cm/min

Both girls travel at the same speed, so will take the same amount of time to get to school. It takes Diane 12 minutes to walk to school.

Answer:

We can calculate the slope by taking 2 points on the line. I took A(4,4) and B(-4,0), so we get m=1/2.

2. y-intercept is the point where a line crosses the y-axis which is (0,2)

3. We have f(x)=1/2x +b

By taking a particular point on the line,we get :

2=1/2(0)+b

==》 b=2

So the slope intercept form is

y=1/2x+2

Suppose that the production of plastic creates a social cost which is depicted in the graph above. Without any government regulation, about 650 units of plastic will be produced. (Option C)

This is because, when the market forces are left to play out, competition drives efficiency upwards, which enable suppliers to produce at lower price thus offering consumers more quantity demanded for lower prices.

Hence, without government intervention, the unit produced will be 650 at the price of 7.

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The savings amount balance in the account is $ 467.39

Given data ,

You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years.

Using the formula FV = PV * (1 + i)^n, where FV is the future value, PV is the present value, i is the interest rate, and n is the number of periods, we can calculate the future value of the savings account after 15 years.

PV = $300 (the initial deposit)

i = 0.03 (the interest rate per period)

n = 15 years (the number of periods)

FV = $300 (1 + 0.03)^15

FV = $300 ( 1.5579 )

FV = $467.39

Hence , after 15 years, the savings account will have a balance of $ 467.39

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Valid row operations are:

Invalid row operations are:

0R₁ → R₁ (this is equivalent to multiplying a row by zero, which is not a valid row operation)

R₃ ÷ 0 → R₃ (division by zero is undefined)

-2 ÷ R₁ → R₁ (division by a variable is not a valid row operation)

2R₁ + R₂ → R₂ (the row operation should be adding multiples of one row to another row, not a combination of multiple rows)

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Answer:

To find the value of A, we can substitute g(-3) = 2 into the given equation and solve for A.

g(q) = (2q-4) / (q-A)

2 = (2(-3)-4) / (-3-A)

Multiplying both sides by (-3-A), we get:

2(-3-A) = -10 - 2A

Expanding the left side, we get:

-6 - 2A = -10 - 2A

Adding 2A to both sides, we get:

-6 = -10

This is a contradiction, which means that there is no value of A that satisfies the given conditions. Therefore, the answer to the question is:

There is no value of A that satisfies the given conditions.

b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.  f(x-a) = (x-a)^2, where a is a constant.

9) The function f(x) = x represents a linear function with a slope of 1 and y-intercept of 0. To shift the graph vertically, we need to add or subtract a constant from the function. Thus, the function that represents a vertical shift of f(x) = x would be of the form f(x) = x + b, where b is a constant.

Out of the given options, the correct answer is b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.

10) To shift the graph of f(x) = x^2 horizontally, we need to add or subtract a constant inside the function, affecting the position of the vertex of the parabola. Thus, the function that represents a horizontal shift of f(x) = x^2 would be of the form f(x-a) = (x-a)^2, where a is a constant.

Out of the given options, the correct answer is a. f(x) = (x+2)^2, which represents a horizontal shift of 2 units to the left.

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The product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.

If two secant segments are drawn to a circle from an exterior point, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measurements of the second secant segment and its external secant segment.

So, we know that:

BE * AE = CE * DE

Now, insert the values as follows:

(x+1) * (x+12) = (x+4) * (x+5)

x² + x + 12x + 12 = x² + 4x + 5x + 20

13x + 12 = 9x + 20

4x = 8x

x= 2

Then: x = 2 units

Therefore, the product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.

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The storage can hold approximately 10.94 cubic meters of grain.

Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity expressed in another set of units. For example, converting a length from feet to meters, or converting a temperature from Celsius to Fahrenheit.  

To convert cubic yards to cubic meters, multiply the given volume in cubic yards by this conversion factor to obtain the equivalent volume in cubic meters.  

Here we have

Adam’s family maintains storage that can hold 14.3 yd³ of grain.

Given that 1 yard is approximately equal to 0.9144 meters

To convert cubic yards (yd³) to cubic meters (m³),

Use the conversion factor:

1 yd³ = (0.9144 m)³

So, we can convert 14.3 cubic yards of grain to cubic meters as follows:

14.3 yd³ x (0.9144 m/yd)³ ≈ 10.94 m³

Rounding this answer to the nearest hundredth gives us:

10.94 m³ rounded to the nearest hundredth = 10.94 m³

Therefore,

The storage can hold approximately 10.94 cubic meters of grain.

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The solution is:  the following probabilities for a normal distribution is:

a. 0.5434

b. 0.5746

c. 0.2957

d. 0.0902

Here, we have,

Explanation:

To find each probability we need to use the normal distribution table that is accumulated to the left, so each probability is equal to

P(-1.80 < z < 0.20) = P( z < 0.20) - P( z < -1.80)

P(-1.80 < z < 0.20) = 0.5793 - 0.0359

P(-1.80 < z < 0.20) = 0.5434

P(-0.40 < z < 1.40) = P( z < 1.40) - P( z < -0.40)

P(-0.40 < z < 1.40) = 0.9192 - 0.3446

P(-0.40 < z < 1.40) = 0.5746

P(0.25 < z < 1.25) = P(z < 1.25) - P(z < 0.25)

P(0.25 < z < 1.25) = 0.8944 - 0.5987

P(0.25 < z < 1.25) = 0.2957

P(-0.90 < z < -0.60) = P(z < -0.60) - P(z < -0.90)

P(-0.90 < z < -0.60) = 0.2743 - 0.1841

P(-0.90 < z < -0.60) = 0.0902

Therefore, the answers are,  the following probabilities for a normal distribution is:

a. 0.5434

b. 0.5746

c. 0.2957

d. 0.0902

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The simplified form of given expression a³/a⁶b⁻¹ is b/a³.

Hence, the correct option is C.

Exponents are a shorthand notation used in mathematics to represent repeated multiplication of a number by itself. The exponent is a small number written to the right and above a base number, and indicates how many times the base should be multiplied by itself.

In the given expression, a³/a⁶b⁻¹

We can apply the rules of exponents, and we get

= a³⁻⁶/b⁻¹

= a⁻³/b⁻¹

= b/a³

Hence, the correct option is C.

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The surface area of the shape will be 46 yards².

Surface area refers to the total area that the surface of a three-dimensional object covers. It is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), etc.

The formula for the surface area of the 2 bases is just b*h

12*8=96 yd²

Finding the lateral area:

(10*10)+(10*10)+(12*10)=

100+100+120=

320 yd²

Add the lateral surface area and the surface area of the 2 bases for the total surface area:

320+96=416 yd²

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If the side AB=12 and side A'B'=9, then the scale factor of the dilation is 3/4.

The "Scale-Factor" of a dilation is the ratio of the corresponding side lengths of the two similar figures.

In this case, we can find the scale factor by dividing the length of side A'B' by the length of the corresponding side AB:

So, scale factor = A'B'/AB,

Substituting the values,

We get,

Scale factor = 9/12,

Scale Factor = 3/4,

Therefore, the scale factor of the dilation is 3/4. This means that all corresponding side lengths of the dilated triangle A'B'C' are 3/4 of the length of the corresponding side lengths of the original triangle ABC.

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Therefore, the solution to the equation -2 - 5/4x = 13 is x = -12.

A mathematical statement proving the equality of two expressions is known as an equation. Variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division are frequently included. In addition to representing a connection between variables, an equation may also be used to find an unknown number. As they enable us to define and evaluate connections between things and make predictions about how they will behave under various circumstances, equations are a crucial tool in many domains, including mathematics, physics, engineering, and many more.

To solve for x in the equation -2 - 5/4x = 13, you can follow these steps:

Add 2 to both sides of the equation to isolate the fraction on the left side:

-2 - 5/4x + 2 = 13 + 2

-5/4x = 15

Multiply both sides of the equation by -4/5 to get x by itself:

(-4/5) * (-5/4x) = (-4/5) * 15

x = -12

Therefore, the solution to the equation -2 - 5/4x = 13 is x = -12.

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Answer:

r=1

Step-by-step explanation:

The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value r = 1 means a perfect positive correlation and the value r = -1 means a perfect negataive correlation. So, for example, you could use this test to find out whether people's height and weight are correlated (they will be - the taller people are, the heavier they're likely to be).

To move Point A(-5, -2) to Quadrant IV, we need to apply one or more transformations that result in a reflection about the x-axis and/or a rotation of 180 degrees. The following transformations would move Point A to Quadrant IV:

Reflection about the x-axis: This transformation would change the sign of the y-coordinate, making it positive. So, the image of A after this transformation would be (−5, 2).

Rotation of 180 degrees about the origin: This transformation would change the sign of both the x and y-coordinates, making them positive. So, the image of A after this transformation would be (5, 2).

Therefore, either a reflection about the x-axis or a rotation of 180 degrees would move Point A to Quadrant IV.

The value of p in the expression is 45

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

For example a+5 = 2 , by solving this we add the additive inverse of 5 to both sides. The additive inverse of 5 is -5

this means,

a+5-5 = 2-5

a = 2-5

a = -3

Similarly, p-42 = 3 is solved in the same way. we add the additive inverse of -42 which is +42 to both sides,

p-42+42 = 3+42

p = 3+42

p = 45

therefore the value of p is 45

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Based on the data displayed in the dot plot, it can be concluded there are 25 students in this class.

Dot plots represent data and trends but using dots. In these types of graphs, each individual is represented with a dot. For example, in the number 3, we can see there are 3 dots, which means three students have a first name made of three letters.

Therefore, you can get the total of students by counting all the dots. Based on this, there are 25 students in this class.

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The true statement is that the difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700. (option d).

To determine the maximum profit earned by each business, we need to find the vertex of each quadratic function. The vertex of a quadratic function of the form ax² + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the maximum value of the function.

The equations for the two functions are:

f(x) = -500x² + 9000x + 7500 g(x) = -500x² + 7500x + 4200

To find the vertex of f(x), we need to first rewrite the function in standard form:

f(x) = -500(x² - 18x - 15)

Completing the square, we get:

f(x) = -500(x - 9)² + 12000

So the vertex of f(x) is (9, 12000), which represents the maximum profit earned by the sandwich shop.

Similarly, to find the vertex of g(x), we rewrite the function in standard form:

g(x) = -500(x² - 15x - 8.4)

Completing the square, we get:

g(x) = -500(x - 7.5)² + 14100

So the vertex of g(x) is (7.5, 14100), which represents the maximum profit earned by the smoothie stand.

Finally, we can calculate the difference between the maximum profits earned by both businesses as:

12000 - 14100 = -2700

Therefore, the correct answer is option (d).

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The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

From the question, we have the following parameters that can be used in our computation:

[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]

From the above expression, we can see that the different expression in each term is

9/n

So, we introduce a variable

Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

When represented using the sigma notation, we have

[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

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Alan and his mom will each have completed 10 rows after 3 hours.

An expression is a combination of numbers, variables, and/or operations (such as addition, subtraction, multiplication, division, exponents, and roots) that are grouped together to represent a value.

Let x be the number of hours it takes for Alan and his mom to have planted the same number of rows.

Alan will have planted 4 + 2x rows of carrots, and his mom will have planted 7 + x rows of tomatoes.

Setting these two expressions equal to each other gives:

4 + 2x = 7 + x

Solving for x, we get:

x = 3

Thus, after 3 hours, Alan will have planted:

4 + 2(3) = 10 rows of carrots

And his mom will have planted:

7 + (3) = 10 rows of tomatoes

Therefore, they will each have completed 10 rows of vegetables after 3 hours.

To graph these equations, we can plot them on a coordinate plane, where the x-axis represents the number of hours and the y-axis represents the number of rows planted.

Alan's equation is y = 2x + 4, and his mom's equation is y = x + 7.

The graph of these two equations intersect at the point (3, 10), which represents the moment when they have each planted 10 rows.

Therefore, Alan and his mom will each have completed 10 rows after 3 hours

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Answer:

x = -2

Step-by-step explanation:

-4x + 3 = 11

Subtract 3 from both sides:

-4x = 8

Divide both sides by -4:

x = -2

Answer:

It can't be factor

Step-by-step explanation:

n^4 − 4n^3 − 17n^2 − 36n + 108

The GCF of this is 1, so the equation can't be factor.

Answer:

(x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25

Step-by-step explanation:

The equation of a circle can be written in the form (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Since the lines are tangent to the circle at points (0,5) and (6,5), we can use these points to find the center and radius of the circle.

First, let’s find the slope of each line. The slope of the line y = 3/4x+5 is 3/4. The slope of the line 3x + 4y = 38 can be found by rearranging it into slope-intercept form: y = (-3/4)x + 19/2. So the slope of this line is -3/4.

Since the lines are tangent to the circle, they are perpendicular to the radius at their point of tangency. This means that the center of the circle lies on the line that passes through (0,5) and has a slope of -4/3, and also on the line that passes through (6,5) and has a slope of 4/3.

Let’s find the equation of these two lines. The line passing through (0,5) with a slope of -4/3 has an equation y - 5 = (-4/3)(x - 0), or y = (-4/3)x + 5. The line passing through (6,5) with a slope of 4/3 has an equation y - 5 = (4/3)(x - 6), or y = (4/3)x - 3.

The center of the circle is at the intersection of these two lines. To find it, we can set their right-hand sides equal to each other and solve for x: (-4/3)x + 5 = (4/3)x - 3. Solving this equation gives us x = 24/5. Substituting this value into either equation for y gives us y = (4/3)(24/5) - 3 = 21/5.

So the center of the circle is at (24/5, 21/5). To find its radius, we can use either point of tangency. Let’s use (0,5). The distance between this point and the center is given by sqrt((0-24/5)^2 + (5-21/5)^2), which simplifies to sqrt(481)/5.

Therefore, the equation of the circle is (x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25.

Answer: The overall score obtained is 55.5, which is higher than the passing mark of 45. Therefore, the applicant will be accepted.

Step-by-step explanation:To determine if the applicant will be accepted, we need to calculate their overall score based on the percentage weights and passing mark given for each subject.

The overall score can be calculated as follows:

Overall score = (0.25 x English score) + (0.3 x Math score) + (0.25 x Computer score) + (0.2 x Accounting score)

Substituting the given scores, we get:

Overall score = (0.25 x 60) + (0.3 x 35) + (0.25 x 80) + (0.2 x 50)

= 15 + 10.5 + 20 + 10

= 55.5

An equation that models the eggs used by LaNiyah is 2b + 6s = 144.

An equation is a mathematical statement that shows that two or more mathematical expressions are equal or equivalent.

Equations contain the equal symbol (=), unlike mathematical expressions that combine variables with numbers, and constants using mathematical operands only.

The number of eggs used to make brownies per unit = 2

The number of eggs used to make cakes per unit = 3

The number of eggs used to make soufflés per unit = 6

The total number of eggs used = 144

Let the total number of brownies made = b

Let the total number of soufflés made = s

2b + 6s = 144

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Answer:

35

Step-by-step explanation:

Simply plug in the value of your 'x' and 'y':

x = 4.5

y = 5.2

[tex]2(4.5)+5(5.2)=9+26=35[/tex]

The calculated output value for an input value of 5 is (c) 10

From the question, we have the following parameters that can be used in our computation:

Kerrin is making an input-output table for the rule "add 5."

This means that

Output = input + 5

In this case, we have

input = 5

substitute the known values in the above equation, so, we have the following representation

Output = 5 + 5

Evaluate

Output =10

Hence, the output is 10

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