Fatima was driving home from work. She was 3/7 of the way home when she
was pulled over for speeding. Not wanting to get another ticket, she then drove
under the speed limit for half the remaining distance but had to stop again when
she got a flat tire. Giving up on driving, she walked the remaining 4 miles home.
How far away from work does Fatima live?

the solutions to the quadratic equation 1 = 2x^2 + 7x are:

\(x= \frac{(-7+\sqrt{51} )}{4}\) and \(x= \frac{(-7-\sqrt{51})}{4}\)

ToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToTo solve this quadratic equation by completing the square, we need to rewrite the equation in the form of (x + p)^2 + q = 0, where p and q are constants. This will allow us to solve for x.

First, we can factor out the coefficient of the x^2 term, which is 2:

\(2x^2 + 7x - 1 = 0\)

Next, we can isolate the x^2 and x terms on one side of the equation by subtracting 1 from both sides:

\(2x^2 + 7x = 1\)

Now, we need to add and subtract a constant term inside the parentheses to create a perfect square trinomial. To determine this constant term, we take half of the coefficient of the x term (which is 7/2) and square it:

\((\frac{7}{2} )^{2} = \frac{49}{4}\)

So we add and subtract 49/4 inside the parentheses:

\(2x^2 + 7x + \frac{49}{4} - \frac{49}{4} = 1\)

We can simplify the left side by factoring the perfect square trinomial:

\(2(x + \frac{7}{4} )^2 - \frac{51}{8} = 0\)

Now, we can solve for x by isolating the perfect square term and taking the square root of both sides:

\(2(x + \frac{7}{4} )^2 = \frac{51}{8}\)

\((x + \frac{7}{4} )^2 = \frac{51}{16}\)

\(x + \frac{7}{4}=±\sqrt{\frac{51}{16} }\)

\(x = -\frac{7}{4} ± \sqrt{\frac{51}{16} } /2\)

Simplifying this expression, we get:

\(x = (-7 ±\sqrt{51} )/4\)

Therefore, the solutions to the quadratic equation 1 = 2x^2 + 7x are:

\(x = (-7 + \sqrt{51} )/4 and x = (-7 -\sqrt{51} )/4.\)

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Answer:

W = -2

Step-by-step explanation:

8W + 20 = 4

=> 8W = 4 - 20

=> 8W = -16

=> W = -16 / 8

=> W = -2

Hope it helps :)

Please mark my answer as the brainliest

Answer:

729

Step-by-step explanation:

9x9x9

Answer:

9*9*9 = 729

Step-by-step explanation:

This can also be expressed by 9^3 (Nine cubed)

9 times 9 is equal to 81. 81 times 9 is equal to 729

There you go!

PS: Give school a chance, I know it's hard during this special time, but once this fades away, you might enjoy it a bit more. :D

The predicted population in the year 2030 is 10 people

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

Population function, P(t)= 15е⁻⁰.⁰¹²⁺

Also from the question, we have

The variable t represents the number of years since 2020

This means that the value of t in 2030 is

t = 2030 - 2020

t = 10

So, we have

P(10)= 15е⁻⁰.⁰¹² ˣ ¹⁰

Evaluate the above products

P(10)= 15е⁻⁰.¹²

Evaluate the exponents

P(10)= 13.30

Approximate the above expression

P(10) = 13

This means that the number of people is 13

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Based on equation these figures, Factory 2 has the lowest cost for producing 15,000 units. As a result, we should submit Order A to Factory 2 to be filled.

In mathematics, an equation is a statement stating the equality or two expressions. An equation consists of two sides split by an algebraic equation (=). For illustration, the argument "2x + 3 = 9" argues that the statement "2x + 3" is equal to the value "9". The goal of equation solving is to find the value or values of the variable(s) to make the equation true. Simple or complex equations, regular or nonlinear, and including one or more factors are all possible. For example, the equation "x2 + 2x - 3 = 0" has the variable x raised to the second power. Lines are used in many fields of mathematics, including algebra, calculus, or geometry.

We have a single order A for 15,000 units due on Monday. To decide which manufacturer to send the order to, we must compute the cost per unit for each plant if they were to complete the entire order.

Assume that the cost of production for each factory for 15,000 units is as follows:

Factory 1 costs $240,000.

Factory 2 costs $225,000.

Factory 3 costs $247,500.

Based on these figures, Factory 2 has the lowest cost for producing 15,000 units. As a result, we should submit Order A to Factory 2 to be filled.

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Answer:

\(Total \approx 20ft^3\)

Step-by-step explanation:

Given

\(h = 12ft\) --- height of the cylinder

\(d =1ft\) --- the diameter of the hemispheres at both end and the cylinder

See attachment for pontoon

Required

Determine the volume

First, calculate the radius (r)

\(r = \frac{1}{2} * d\)

\(r = \frac{1}{2} * 1ft\)

\(r = 0.5ft\)

Next, the volume of the cylinder

\(V_1 = \pi r^2h\)

\(V_1 = 3.14 * 0.5^2 * 12\)

\(V_1 = 9.42ft^3\)

Two hemispheres make up a sphere. So, we simply calculate the volume of a sphere.

\(V_2 = \frac{4}{3}\pi r^3\)

\(V_2 = \frac{4}{3} * 3.14* 0.5^3\)

\(V_2 = 0.52ft^3\)

So, the volume of 1 pontoon is:

\(V_3 = V_1 + V_2\)

\(V_3 = 9.42ft^3 + 0.52ft^3\)

\(V_3 = 9.94ft^3\)

The volume of both is:

\(Total = 2 * V_3\)

\(Total = 2 * 9.94ft^3\)

\(Total = 19.88ft^3\)

\(Total \approx 20ft^3\)

Answer:

1629

Step-by-step explanation:

10 to the second power = 100

100 x 16.29 = 1629

Answer: -3,-6

hope this helps

-39 is the furthers away from 0

this is because if you draw a number line -16 would be 16 away from 0, 12 would be 12 away from zero and 7 would be 7 away from 0...

| - - - - - - - - - - - - - - - |- - - - - - | - - - - |

16 0 7 12

and -39 would be 39 digits away from 0, therefore its the furthest away from 0

Hope this helped you- have a good day bro cya)

Answer:

-39, or the absolute value of 39 is farthest from 0.

Step-by-step explanation:

-16 is 16 units from 0.

-39 is 39 units from 0.

7 is 7 units from 0.

12 is 12 units from 0.

39 > 16

39 > 7

39 > 12

Hope this helps!

1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

Using a system of equations, the number of children and adults who attended the movies is as follows:

A system of equations is two or more equations solved concurrently.

A system of equations is also known as simultaneous equations.

The total number of people who went to the movies = 100

The unit cost of adult tickets = $4

The unit cost of children tickets = $2

The total sales = $276

Let the number of children who attended the movies = x

Let the number of adults who attended the movies = y

x + y = 100 ... Equation 1

2x + 4y = 276 ... Equation 2

Multiply Equation 1 by 2:

2x + 2y = 200 ... Equation 3

Subtraction Equation 3 from Equation 2:

2x + 4y = 276

-

2x + 2y = 200

2y = 76

y = 38

Substitute y = 19 in equation 1:

x + y = 100

x + 38 = 100

x = 62

Check in Equation 2:

2x + 4y = 276

2(62) + 4(38) = 276

124 + 152 = 276

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The y and x intercepts on the graph are x = 1 and y = -5

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

y = 4 + 5x - 9

By definition

The y-intercept is when x = 0

So, we have

y = 4 + 5(0) - 9

y = -5

The x-intercept is when y = 0

So, we have

0 = 4 + 5x - 9

5x = 5

x = 1

Hence, the intercepts are x = 1 and y = -5

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Answer:

Step-by-step explanation:

x - 12 = 13

x = 25

y = 12

Answer:

x=25

Step-by-step explanation:

y=x-12....eq1

y=13.... eq2

Substituting eq2 in 1:-

13=x-12

x=12+13=25

Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Answer:

403.3 feet per second

Step-by-step explanation:

please mark brainlest

Theoretical Probability of rolling a 2= 1/20

Experimental Probability of rolling a 2 =  1/20

Theoretical probability of rolling a 2:

The theoretical probability of an event is the ratio of the number of favourable outcomes to the total number of possible outcomes. Since there are 8 sides to the cube, the total number of possible outcomes is 8. Since the number 2 appeared 200 times out of 4000 rolls, the number of favorable outcomes is 200. Therefore, the theoretical probability of rolling a 2 is:

Theoretical Probability of rolling a 2 = Number of favourable outcomes / Total number of possible outcomes = 200/4000 = 1/20

Experimental probability of rolling a 2:

The experimental probability of an event is the ratio of the number of times the event occurred to the total number of trials. In this case, the  event is rolling a 2, which occurred 200 times out of 4000 rolls.    

Therefore, the experimental probability of rolling a 2 is:

Experimental Probability of rolling a 2 = Number of times the event occurred / Total number of trials = 200/4000 = 1/20

Comparing theoretical and experimental probability:

If the cube is fair, we would expect the theoretical probability and the experimental probability to be similar. In this case, both probabilities are 1/20, which means that the cube appears to be fair. However, we would need to conduct more trials to be more confident in our conclusion.

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the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35

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Answer:

\(3 \frac{3}{4}\\\)  /  3.75

Step-by-step explanation:

Step 1: Make all the mixed numbers, improper fractions:

\(5 \frac{1}{3} = \frac{16}{3}\)

\(7\frac{5}{6} = \frac{47}{6}\)

\(6\frac{1}{4} =\frac{25}{4}\)

In order to add/subtract fractions, they must all have a common denominator, the smallest common denominator for all these fractions is 12. And so in order to make 12 the denominator, we must now multiply all the fractions by their multiple.

\(\frac{16}{3} = \frac{64}{12}\)

\(\frac{47}{6} = \frac{94}{12}\)

\(\frac{25}{4} = \frac{75}{12}\)

Time to solve:

\(\frac{64}{12} -\frac{94}{12} + \frac{75}{12} =\)

\(\frac{-30}{12} + \frac{75}{12} =\)

\(\frac{45}{12}\)

Simplify:

\(\frac{45}{12} = \frac{15}{4}\)

Convert to a mixed number:

\(3 \frac{3}{4}\)

Hope this helps!

Answer:

A) \(f(t) = 2 - \frac{8}{5}\cdot t\), B) \(f(-5) = 10\), C) \(t = -15\) for \(f(t) = 26\)

Step-by-step explanation:

A) Let be \(f(t) = r\) and \(5\cdot r + 8\cdot t = 10\), the latter expression is a function in implicit form and we need to turn it into its explicit form, where \(t\) is the independent variable.

\(5\cdot r = 10 - 8\cdot t\)

\(r = 2 -\frac{8}{5}\cdot t\)

\(f(t) = 2 - \frac{8}{5}\cdot t\)

B) If we know that \(t = -5\). then \(f(-5)\) is:

\(f(-5) = 2 - \frac{8}{5}\cdot (-5)\)

\(f(-5) = 10\)

C) If we know that \(f(t) = 26\), then we solve for \(t\):

\(2 - \frac{8}{5}\cdot t = 26\)

\(\frac{8}{5}\cdot t = -24\)

\(t = -15\)

The Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.

Volume can be defined as the total quantity of a substance that a container can hold at a given period of time. Also, the volume of a container is measured in:

Based on the information provided in the table above, we can infer and logically deduce that the Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.

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The length of the two segments, written as radicals, are:

AB = √117

PQ = √244

Remember that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the length of the segment is:

L = √( (x₂ - x₁)² + (y₂ - y₁)²)

First, for the segment AB the endpoints are:

A = (-4,  -4)

B = (2, 5)

Then the length is:

L =  √( (-4 - 2)² + (-4 - 5)²)

L = √117

For the segment PQ the endpoints are:

P = (-6, 8)

Q = (6, -2)

The length is:

L =  √( (-6 - 6)² + (8 + 2)²)

L = √244

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Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

Answer: D

Step-by-step explanation:

Hope it helps

Answer:

3.875 pizzas

Step-by-step explanation:

31/8=3.875

Answer:

12

Step-by-step explanation:

Answer:

y = -3x + 7

Step-by-step explanation:

Points on the graph: (0, 7) and (3, -2)

Slope:

m=(y2-y1)/(x2-x1)

m=(-2-7)/(3-0)

m=(-9)/3

m = -3

Slope-intercept:

y - y1 = m(x - x1)

y - 7 = -3(x - 0)

y - 7 = -3x

y = -3x + 7