Drag each tile to the correct box. Not all tiles will be used.
Arrange the equations in the correct sequence to rewrite the formula for displacement, d = vot+at², to find a. In this formula, d is displacement,
Vo is initial velocity, a is acceleration, and it is time.
d+vot = at²
2 (d+vot) = at²
2 (d-vot)= at²
d-vot = at²
a=
a=
2(d+ vot)
2(d-vot)

Answer:  Choice 2. x = 5 ± i √5

Step-by-step explanation:

Use the formula

(b/2)^2

in order to create a new term. Solve for x by using this term to complete the square.

Hope this helps!

By using the distributive property, we can rewrite the expression as:

24 + 8k = 8*(3 + k)

The distributive property can be written as:

C*(A + B) = C*A + C*B

Now we have the expression:

24 + 8k

And we want to rewrite it by using the distributive property, to do so we need to identify the common factor.

We can rewrite the expression as:

24 + 8k

8*3 + 8k

Then we can take 8 as a common factor, then:

8*3 + 8k = 8*(3 + k)

That is the expression rewritten.

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The point that is marked X on the graph is the standard free energy of the reaction.

Let us note that when we talk about the standard free energy of the reaction what we mean here is the energy of the reaction that is free to be able to do work. In the case of the standard change in the free energy, we are looking at the change of the free energy of the standard states of the substance.

The graph as we have it is trying to show the reaction profile and the reaction profile would give the difference between the free energy of the products and the reactants and this is the standard change in free energy.

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Answer:

✓2^5

Step-by-step explanation:

use the concept of indixes.

so;

By the power rule;

= (2^1/2)^2 *(2^3/4)^2

=2*(2^3/2)

2^(1+3/2)

2^5/2

✓2^5.

The value of solution of the expression is,

⇒ [tex]\sqrt{2^{5} }[/tex]

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ [tex](2^{1/2} * 2^{3/4} )^{2}[/tex]

Now, We can simplify as;

⇒ [tex](2^{1/2} * 2^{3/4} )^{2}[/tex]

⇒ [tex](2^{(5/4) } )^{2}[/tex]

⇒ [tex](2^{5/2} )[/tex]

⇒ [tex]\sqrt{2^{5} }[/tex]

Thus, The value of solution of the expression is,

⇒ [tex]\sqrt{2^{5} }[/tex]

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The solution of the given inequality is x<6.5. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is x/x-6 >13.

Multiply x-6 on both the sides of an inequality, we get

x>13(x-6)

x>13x-78

Add 78 on both the sides of an inequality, we get

x+78>13x

Subtract x on both the sides of an inequality, we get

78>12x

12x<78

x<6.5

Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

This rational inequality can be used to determine the number of seconds, , that a beginning ice-skater can skate before losing his or her footing. x/x-6 >13  If Charlene has never ice-skated before, which inequality describes the number of seconds she can expect to skate before losing her footing?

A. 6>x>6.5

B. x<6

C. x<0

D. x<6.5

E. x<6

Answer:

k should equal 2 and above

Step-by-step explanation:

A product of 6 is 12 which is 6 * 2 so therefore k should equal anything above 2

A Histogram from the menu should be used.

A histogram is a bar graph-like representation of data that buckets a range of outcomes into columns along the x-axis. The y-axis represents the number count or percentage of occurrences in the data for each column and can be used to visualize data distributions.

Given data is $25,745; $26,512; $27,322; $27.750; $29,820; $32,500; $35,448; $52,020; $63,485: $87,167

We know that Histograms are graphs that are preferred to determine any probability distribution of data. So, the Median, maximum value, and lowest value can be easily demonstrated in "Histogram graphs"

Thus, Histograms should be used.

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Michelle worked for at least 11 hours.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. On the number line, size comparisons between two numbers are typically conducted.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are universal.

given,

tips per day = $15

hourly rate=$9

total earnings =#110

h is the number of hours work

The equation is 9h+15[tex]\geq[/tex]110

To find the hours worked:

9h+15[tex]\geq[/tex]110

9h[tex]\geq[/tex]110 - 15

9h[tex]\geq[/tex]95

h[tex]\geq[/tex]10.55

Therefore h must at least be 11

since  Michelle worked for at least 11 hours.

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Answer:

75 = 4w

Step-by-step explanation:

Let w = width

Let w + 5 = length

Let p = perimeter ( Perimeter is given: 70 ft. )

Write the formula to find the perimeter of a rectangle

p = 2 ( l + w )

Sub the numbers in

70 = 2 [(w+5) + (w)]

Simplify the equation

70 = 2 (2w + 5)

70 = 4w + 5

75 = 4w

Statement 1 : The graph has a domain of [tex]{x|0 < x < ∞o}[/tex]and approaches 0 as x decreases.

Statement 2 : The graph has a range of [tex]{yl-co < y < ∞o}[/tex] and decreases as x approaches 0.

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

The common logarithm, abbreviated log x, is the base-10 logarithm. The natural logarithm, abbreviated ln x, is the logarithm with base e. Positive real numbers (0, ) make up the domain of logarithmic functions with definitions of the form f(x)=logb x, whereas all real numbers (0,∞ ) make up the range (-∞, ∞).

Therefore, all positive real numbers are the domain of logx, or x ∈ (0,∞) when expressed symbolically.

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Answer:

Step-by-step explanation:

6.25 X 8 = 50.000 then add 370,000 + 50.000 = 420,000

10 pints is equal to 5 quarts.

Given that there are 10 pints.

We need to convert pints to quarts.

To convert pints to quarts, we need to keep in mind that there are 2 pints in 1 quart.

Given that we have 10 pints, we can divide this value by 2 to obtain the equivalent amount in quarts:

10 pints / 2 pints per quart

= 5 quarts

Therefore, 10 pints is equal to 5 quarts.

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We can see here that AC and BC are:

AC = 5cm

BC = 3cm

A triangle is a three-sided polygon, and it is one of the basic shapes in geometry. In a triangle, three straight lines, called sides, are connected end-to-end to form the shape. The point where two sides meet is called a vertex, and there are three vertices in a triangle.

There are several types of triangles, each with their own specific properties. The most common classification of triangles is based on their side lengths.

Using Sine Rule, we have:

[tex]\frac{a}{Sin A} = \frac{b}{Sin B}[/tex] where:

Sin A = Sin 30° = 0.5

Sin B = Sin 80° =  0.9848

a = x cm

b = 5cm

Thus, inserting the the above values into the Sine Rule equation, we have:

[tex]\frac{x}{0.5} = \frac{5}{0.9848}[/tex]

Cross-multiplying, we have:

0.9848x = 5×0.5

0.9848x = 2.5

∴ x = 2.5 ÷ 0.9848 = 2.538cm

≈ 3cm.

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A compound inequality for the given statement "a number is less than 24 or greater than 35" include the following:

x < 24.

x > 35.

In Mathematics, there are four major rules that are used for writing and interpreting an inequality or compound inequality that are plotted on a graph and these include the following:

Assuming the unknown number is represented by the variable x, the required compound inequality would be written as follows;

Number less than 24 ⇒ x < 24.

Number greater than 35 ⇒ x > 35.

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The quotient is 33x-8 and the remainder is 44.

What is quotient?

In arithmetic, a quotient is described as a quantity produced by the division of two numbers.

The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

The result of dividing 23-2-11x-8 by x+1 using synthetic division is:

23 | -2  -11x -8

x+1 | 23  21  11x

          44  33x-8

I conclusion, synthetic division is also an arithmetic method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.

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The fraction that names one part of the granola bar shared by Tiana and her 3 brothers is c. 1 / 4.

Tiana has 3 brothers and they all shared a piece of the granola bar. This means that the number of people who shared the granola bar is:

= Tiana + 3 brothers

= 4 people

With each of them getting a piece of the granola bar, it means that the fraction that names one part of the bar is:
= Number of granola bars / Number of people

= 1 / 4

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The full question is:

Tiana shares a granola bar with her 4 brothers. They each get one piece of the bar. What fraction names one part?

The fraction that is equivalent to a terminating decimal between 0.25 and 0.50 is given as follows:

C. 7/20.

A fraction is represented by the division of a term x by a term y, such as in the equation presented as follows:

Fraction = x/y.

The terms that represent x and y are listed as follows:

Hence the conversion from fraction to decimal for each item in this problem is given as follows:

This means that the correct option is given by option C.

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Answer:

[tex](2, 6)[/tex]

Step-by-step explanation:

The midpoint can be thought of as drawing a line between two points and then going half-way along that line, wherever that point is, is the midpoint. The vertical and distance will be cut in half.

I attached a diagram which I will be referring to in this explanation.

The main takeaway, is we have a formula, or at least somewhat of a formula:

[tex]\text{midpoint} = (x_1 + \frac{\text{horizontal distance}}{2}, y_1 + \frac{\text{vertical distance}}{2})[/tex]

But if you look at the graph, you'll notice, the vertical and horizontal distance are simply the difference in x and y values.

[tex]\text{horizontal distance} = x_2 - x_1\\\text{vertical distance} = y_2 - y_1[/tex]

This means we can substitute something into the equation.

[tex]\text{midpoint} = (x_1 + \frac{x_2-x_1}{2}, y_1 + \frac{y_2-y_1}{2})[/tex]

Now we could directly use this equation, but we can also simplify a bit, which we can do by rewriting the following: [tex]x_1\to \frac{2x_1}{2}, y_1 \to \frac{2y_1}{2}[/tex]

[tex]\text{midpoint} = (\frac{2x_1+x_2-x_1}{2},\frac{2y_1+y_2-y_1}{2})[/tex]

combining like values, you get:

[tex]\text{midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}})[/tex]

And now we have a convenient formula we can use for this problem, which is the midpoint formula.

Now all that's left to do, is plug in x and y values, and since we're adding values, the order does not matter.

[tex]\text{midpoint} = (\frac{2+2}{2},\frac{3+9}{2})\to (2, 6)[/tex]

so the answer is: [tex](2, 6)[/tex]

The area of the shape as shown in the diagram  is 50.24 squared unit.

Area can be defined as the region bounded by a plane shape.

To calculate the area of the shape, we use the formula below.

Formula:

Where:

From the question,

GIVEN:

Substitute these values into equation 1

Hence, the area is 50.24 squared unit.

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August surveys may not adequately represent Christmas buyers' intentions. Surveying customers on a weekday between 10 AM and 4 PM may not capture the spending intentions of all demographic groups, resulting in a skewed sample.

It's also vital to consider economic situations, customer preferences, and promotional bargains when predicting consumer spending.

Generally, It is possible that the survey results do not accurately predict the actual spending during the Christmas season. Surveying shoppers in August, several months before the Christmas season, may not accurately reflect the shopping plans of consumers closer to the holiday. Additionally, surveying shoppers during a weekday and between the hours of 10 AM and 4 PM may not capture the spending plans of all demographic groups, potentially leading to a biased sample.

Another reason why the survey estimate of $250 is so far below the previous $400 figure could be due to the fact that the survey only asked 5 questions. This may not have been enough to gather enough information about the spending habits and intentions of the shoppers surveyed.

It's also worth noting that there are many different factors that can influence consumer spending, such as economic conditions, changes in consumer preferences, and the availability of promotional deals, so it's important to consider these other factors as well when trying to predict future spending.

In conclusion, the survey results do not provide a reliable indication of the sales for the upcoming Christmas. Without more information about the survey methodology and the results, it's difficult to determine the reasons for the discrepancy between the survey estimate and the actual spending from the previous Christmas season.

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The car will cover a distance of 180 miles in three hours.

We know that,

                      s = d/ t

           or       d = s* t

Where, s = speed

            d = distance

             t = time

According to the question,

               speed of the car (s) = 60 miles/ hour

                 Time taken (t)         = 3 hours

                 Distance travelled (d) = s * t

                                                      = 60miles/ hour * 3 hours

                                                      = 180 miles

Hence, the distance traveled by car in 3 hours is 180 miles.

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Answer:

-34p-63q

Step-by-step explanation:

Simplify

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12

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2

Rearrange terms

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A. The remainder theorem states that the value of f(a) is equal to the remainder for any polynomial f(x) when divided by the binomial x-a. The factor theorem states that (x-a) is a factor of f(x) and vice versa if a is a zero of a polynomial f(x).

B. Using long division method the quotient is x^2+2x-35.

C. The polynomial x^2+2x-35 has degree 2.

D. The x-intercepts of x^3-x^2-41x+105 are (-7,0), (3,0), and (5,0).

What are polynomials?

The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases." There is no limit to the number of terms that can exist in a polynomial.

A. According to the Remainder Theorem, long polynomial division yields some polynomial q(x) when the polynomial p(x) is divided by some linear factor x-a. It can be stated as follows-

p(x)/x-a=q(x)+r(x)

A polynomial can be factored and its roots can be discovered using the factor theorem. The polynomial remainder theorem is a special instance of this one.

The factor theorem states that if f(x) is a polynomial of degree n>=1 and f(a)=0, then (x-a) is a factor of f(x). If f(x) is a polynomial and f(a)=0, where an is the root, then (x-a) is a factor of f(x).

B. Using the long division method the quotient obtained after dividing x^3-x^2-41x+105 by x-3 is x^2+2x-35.

C. The solution obtained is also a polynomial of degree 2. This is known as the highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial. The degree denotes the polynomial's highest exponential power.

D. The x-intercept(s), if they exist, are of the form (a,0) where x=a is a real solution to f(x)=0.

Plot the graph for the polynomial - x^3-x^2-41x+105.

Therefore,  x-intercepts are found to be (-7,0), (3,0), and (5,0).

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Answer:

Step-by-step explanation:

1st. 4000x73+292000

2nd. 292000+42+292042

3rd. 292042-34=292008

Answer:

Step-by-step explanation:

y=1/3x-13/3

Okay so we have the points (1,-4) and (-5,-6).

Slope = (-6+4 ) / (-5-1)

Slope = -2/-6

Slope = 1/3

y=mx+b

m=1/3

Now let's take a point from the equation, and use the slope to determine b.

-4=1/3(1)+b

b=-4 1/3

Now let's combine our elements.

y=1/3x-13/3

Answer:

C. Jamila is correct because glucose is a product, not a reactant, of photosynthesis.

Step-by-step explanation:

Photosynthesis is a process that occurs in plants and some other organisms in which energy from sunlight is used to convert carbon dioxide and water into glucose (a sugar) and oxygen. In this process, carbon dioxide and water are the reactants, and glucose and oxygen are the products. Therefore, Anton is incorrect and Jamila is correct because glucose is a product of photosynthesis, not a reactant.

Answer:

b = 4

Step-by-step explanation:

b^3=64

3√b = √64

b = 4

Answer:

b = 4

Step-by-step explanation:

The function that best shows the relationship between n and f(n) is;

f(n) = 24(0.5)ⁿ⁻¹

The function table below that shows the amount of chlorine is;

n    1        2      3     5

f(n)  24     12      6    3

Where f(n) is the amount in ounces, that was left in the pool after n weeks:

We can see that the value of f(n) is decreasing as n increases from the table.

Due to the fact that f(n) does not have common difference. Let us attempt tp see if it has a common ratio;

12/24 = 0.5

6/12 = 0.5

3/6 = 0.5

Using the formula for the nth term of a geometric progression is;

aₙ = arⁿ⁻¹

Where;

a represents the first term = 24

r represents the common ratio = 0.5

Thus, the equation of the function is;

f(n) = 24(0.5)ⁿ⁻¹

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Answer:     [tex]A = 28.26 ft^2[/tex]

Step-by-step explanation:

The formula for the area of a circle is: A = π[tex]r^2[/tex]

We need to plug in the values from the question into the formula.

[tex]A = (3.14)(3)^2[/tex]

A = (3.14)(9)

A = 28.26

Don't forget the units! Since we found the area of the circle, we need to square the units.

[tex]A = 28.26 ft^{2}[/tex]