Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.
y = (smaller slope)

y = (larger slope)

4/7

4 ÷ 7 = 4/7

fraction means division

Answer:

i think 7

Step-by-step explanation:

you cant go diagonal and count it as one unit. however doing stairs up to the second point gets you 7 units

Answer: The ∠DEF= 75°

Step-by-step explanation:

The angle subtended by circumference is half of the angle subtended at the center by the same arc.

So , ∠DEF= 75°

Answer:   6^1/3x6^1/4=6^x/y

X= ,y=

Step-by-step explanation:

Answer:

x = 7 , y = 12

edge 2023

Answer:

7/20 miles

Step-by-step explanation:

get a common denominator

subtract the numerators

then you have the fraction she biked

In general, higher confidence levels provide wider confidence intervals.

What is the concept of confidence level and confidence interval?

Confidence level:

The confidence level refers to the long term success rate of the method , that is , how often this type of interval will capture the parameter of interest.

Confidence interval:

A specific confidence interval gives a range of plausible values for the parameter of interest.

As the confidence level increases, the width of confidence interval also increases.

A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means the interval is larger.

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On solving the provided question we got to say that - 500 meters long, and 250 meter wide

Differentiation is the rate at which a function changes with regard to a variable in mathematics (in mathematics, the rate of change of a function with respect to a variable). Problems involving calculus and differential equations need the use of derivatives.

125000 square meters  of area = l X w is =  length times width

[tex]l=125000/w[/tex]

Fencing =[tex]Perimeter = P = L+2W= 125000/W +2W[/tex]

Now,

derivative set = 0

P'(X) =  2 -125000/W^2 = 0

           [tex]2W^2 = 125000\\ W^2 = 62500\\ W = 250meters wide[/tex]

          [tex]L =125000/250= 500 meters long, the side parallel to the river[/tex]

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365 sets of people born on the same day, with each set containing no more than 5 people.

Assuming everybody was born on a different day, then you could have 365 people where nobody was born on the same day. the 366 person, however, would have to have been born on the same day as somebody else in the group. therefore, the minimum number of people in the group would have to be 366 to guarantee that at least 2 people were born on the same day but you wanted to guarantee that at least 6 people were born on the same day. assuming you had 5 * 365 people together, with every 5 of them being born on the same day.

you would have a total of 365 * 5 = 1825 people, with no more than 5 people being born on the same day.

Add 1 more person and you will be guaranteed that at least 6 people were born on the same day that comes out to be 1826 people.

1825 / 5 = 365 sets of people born on the same day, with each set containing no more than 5 people.

set 1 is the number of people born on day 1.

set 2 is the number of people born on day 2 etc.

that next person had to be added to one of the sets of 5 to make it a set of 6.

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The number of points of intersection for the graphs of the equations is infinite.

Point of intersection refers to the point at which two lines intersect on a graph. The graph of the equation refers to the visual demonstration of the equation obtained by plotting all the points of an equation on a graph. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.

Simplifying the given equations:

i) x/2 + 5y = 6

x + 10y = 12

ii) 3x + 30y = 36

3(x + 10y) = 36

x + 10y = 12

As the equations are equal lines, they will intersect at infinite times.

Note: The question is incomplete. The complete question probably is: How many intersections are there of the graphs of the equations below? x/2 + 5y = 6 3x + 30y = 36 none one two infinitely many

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The expression to determine the number of bags is 2/3 x = 2 1/2 and the number of bags requited is 3 3/4 bags

Information from the problem

Maya rakes up the leaves and wants to put them into bags that hold 2\3 of a cubic yard

she rakes 2 1\2 cubic yards of leaves

one bag = 2/3 cubic yard

total leaves raked = 2 1/2 cubic yard

the number of bags required is how many 2/3 cubic yards are there in 2 1/2 cubic yard. this is solved by division

let the number of bags be x

2/3 cubic yard * x = 2 1/2 cubic yard

2/3 x = 2 1/2

x = (2 1/2) / (2/3)

x = 15/4

x = 3 3/4 bags

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The course of action that can be taken to help the economy is through the expansionary fiscal policy involving cuts to individual tax rates and increased

investments in infrastructure could be used to strengthen the economy. That is option B.

The inflation of economy of a country is defined as the sudden rise in the cost of goods and services which affects the lives of the citizens of the country.

The common causes of economic inflation include the following:

The policy that can be used to help the economy of a country is the expansionary fiscal policy.

This policy involves cutting individuals tax rates, increasing investment in infrastructure which can help strengthen the economy of the country.

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the number is 40.

In mathematics, the system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables. In this article, you will get the definition of the system of linear equations, different methods of solving these systems of linear equations and solved examples.

If the tens digit of the number is X and the ones digit is Y then the number is equal to 10*X + Y

If you reverse the digits then the number is equal to 10*Y + X

If reversing the digits decreases the number by 36 then

10*Y + X = 10*X + Y - 36

The sum of the digits is 4 so X + Y = 4  ==>  X = 4 - Y

Substitute this value of X into the 1st equation

10*Y + (4 - Y) = 10*(4 - Y) + Y - 36

9*Y + 4 = 40 - 9*Y - 36

18*Y = 0

Y = 0

So X = 4 - 0 = 4 and the number is 40

Check:  40 - 04 = 36

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The minimum value, Q1, Median, Q3 and maximum value of the data are 2, 5, 12, 14 and 16 respectively

Given the data: 2, 4, 4, 5, 8, 10, 12, 12, 12, 13, 14, 14, 15, 16

The minimum value of the data is 2. Thus, Min = 2

The maximum value of the data is 16. Thus, Max = 16

The median is the data value in the middle.

2, 4, 4, 5, 8, 10, 12, 12, 12, 13, 14, 14, 15, 16

So the median (Q2) of the data is (12+12)/2 = 12. Thus, Med = 12

Consider the values to the left of the median with one of the median numbers included (since we have numbers in the middle):

2, 4, 4, 5, 8, 10, 12

Find the median of this set of numbers. The median is 5.  Q1 = 5

Also, consider the values to the right of the median with one of the median numbers included: 12, 12, 13, 14, 14, 15, 16. The median is 5. Q3 = 14

To create a box and whiskers plot use Min, Max, Q1, Median(Q2) and   Q3 (Check the attached image)

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Answer:

option (4)

Step-by-step explanation:

y = - 2x +7 → (1)

y = 4x - 5 → (2)

substitute y = 4x - 5 into (1)

4x - 5 = - 2x + 7 ( add 2x to both sides )

6x - 5 = 7 ( add 5 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

y = 4(2) - 5 = 8 - 5 = 3

solution is (2, 3 )

[tex]\red{\boxed{ \green{\sf Option \: 4: (2 \: , 3)}}}[/tex]

[tex] \\ [/tex]

[tex] \sf First, \: we \: have \: to \: understand \: that: \\ \sf If \: \red{y} = \orange{a} \: and \: \red{y} = \blue{b}, \: then \: \orange{a} = \blue{b}.[/tex]

[tex] \\ [/tex]

[tex]\sf Let \: \orange{-2x+7} \: be \: \orange{a} \: and \: \blue{4x-5 \\ } \: be \: \blue{b}.[/tex]

[tex]\star \: \sf Solve \: the \: equation \: \orange{a} = \blue{b}. \: \star[/tex]

[tex] \\ [/tex]

[tex] \sf \orange{a} = \blue{b} \\ \Longleftrightarrow \sf \orange{ - 2x + 7} = \blue{4x - 5} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Subtract \: 4x \: from \: both \: sides. \diamond \\ \\ \Longleftrightarrow \sf - 6x + 7 = - 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Subtract \: 7 \: from \: both \: sides. \diamond \\ \\ \Longleftrightarrow \sf - 6x = - 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Divide \: both \: sides \: by \: -6. \: \diamond \\ \\ \Longleftrightarrow \sf x = \dfrac{ - 12}{ - 6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \Longleftrightarrow \boxed{\sf \purple{x = 2}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \\ [/tex]

[tex]\star \: \sf Remplace \: \purple{x} \: with \: \purple{2} \: in \: one \: of \: the \: given \: equations. \: \star[/tex]

[tex] \\ [/tex]

[tex] \sf \red{y }= - 2 \purple{x} + 7 \\ \implies \sf \red{y} = - 2 \purple{(2)} + 7 \: \: \: \: \: \: \\ \\ \implies \boxed{\sf \red{y= 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \\ [/tex]

Therefore, the point which is a solution to the system of equations is (2 , 3). This corresponds to option 4.

According to the uniform distribution, there is a 0.1= 10% chance that a worker selected at random will have an annual wage between $45,000 and $60,000.

Uniform Distribution:

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely.

An uniform distribution has two bounds, a and b.  

The probability of finding a value between c and d is:

P(c ≤ X ≤ d) = [tex]\frac{d-c}{b-a}[/tex]

given that , workers' salaries in your company are uniformly distributed between $10,000 and $60,000 per year

a = 10,000 , b= 60,000 , c = 45,000 and d = 50,000

The probability is

P(45,000 ≤ X ≤ 50,000) = [tex]\frac{50,000-45,000}{60,000-10,000}[/tex]

                                       = 0.1

0.1 = 10% probability that a randomly chosen worker earns an annual salary between $45,000 and $60,000

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 Third or upper quartile, or 75th percentile, is another name for this group. The figure at which 25% of the responses are higher and 75% of the answers are lower is known as the 75th percentile.

A suitable compromise between representing the great majority of measures and being unaffected by outliers is the 75th percentile. The 75th percentile is a suitable choice for identifying medium- to long-term trends even if it is less steady than the median. Additionally, we believe that when establishing performance budgets, the 75th percentile is the ideal figure to employ.  Although the term "percentile" is frequently used, it lacks a common definition. The most typical definition of a percentile is a number below which a predetermined proportion of scores fall. You may already be aware of your test score of 67 out of 90. But without you know the percentile you fall into, that number has no actual relevance. If you know that you scored in the 90th percentile, it signifies that you outperformed 90% of test-takers.

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Answer: 1280 Kg

Step-by-step explanation:

The weight of the object given = 128 Kg

Time 1 = 10 hr

Time 2 = 1 hr

Cancel the hours,

128×10 = 1280 Kg

The pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 75% pure fruit juice is 72 and 108 pints respectively.

Let juice A = a

60% pure fruit juice

Let juice B = b

85% pure fruit juice

We need to make 180 pints of juice from both

a + b = 180

represented in terms of pure fruit

a = 0.60; b = 0.85 ;

Our mixed fruit juice from a and b should be 75% pure fruit = 0.75

Mathematically,

0.60a+ 0.85b = 180(0.75)

0.60a + 0.85b =135

Multiply this equation by 100

60a+ 85b = 13500

Now we have two equations for two variables,

a + b = 180 and

60a+ 85b = 13500

Multiply equation 1 by 60,

we get,

60a + 60b = 10800

On solving these equations we get,

b = 108

Substitute b = 108 into the second equation

60a+ 85(108)= 13500

60a+ 9180 = 13500

a = 72

Therefore , the pints of juice A required is 72 pints and the pints of juice B required is 108 pints.

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Answer:

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of the two existing types of drink must be used to make 60 pints of a mixture that is 75% pure juice?

The new dimensions of the enclosure is length is 45 feet and the new width is 28 feet

What is Area of Rectangle?

Area of rectangle is length times of breadth.

Given that rectangular enclosure at the zoo is 35 feet long by 18 feet wide. It means length is 35 feet and width is 18 feet.

Area of Rectangle=Length × Width

=35×18

=630

The zoo wants to double the area of the enclosure by adding the same distance x to the length and width.

(35+x)×(18+x)= 2(630)

630+35x+18x+x²=1260

x²+53x+630-1260=0

x²+53x-630

Now use the quadratic formula we get

x=10.

The new length is 35+10=45

The new width is 18+10=28.

Hence the new length is 45 and the new width is 28 feet after doubling of the area of enclosure.

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Six Sigma provides a continuous improvement framework and it has two methodologies.

DMAIC - Define, Measure, Analyze, Improve and Control.

DMADV - Define, Measure, Analyze, Design and verify

What is Six Sigma ?

According to the Six Sigma philosophies, every work can be broken down into discrete processes that may be measured, evaluated, improved, and managed.

                     Processes result in outputs after requiring inputs (x) (y). You can manage the outputs if you manage the inputs. This is typically written as y = f. (x).

What is a fundamental principle of Six Sigma?

The management practice known as "six sigma" aims to reduce errors. It is based on the idea that reducing defects is essential for improving margins, that costs can be cut, and that increasing customer loyalty can help because it is expensive to harbor defects.

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After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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The equation (C) (√2x + √3)² + x² = 3x² - 5x is not a quadratic equation.

A quadratic equation, or second-order polynomial equation with a single variable, is x ax2 + bx + c = 0.

Since it is a second-order polynomial equation, which is ensured by the algebraic 's theorem, it must have at least one answer.

The solution might be simple or difficult.

(A) 2(x - 1)² = 4x² - 2x + 1

Algebraic identity:

(a - b)² = a² - 2ab + b²

2(x² + 1 - 2x) = 4x² - 2x + 1

2x² + 2 - 4x = 4x² - 2x + 1

4x² - 2x² - 2x + 4x + 1 - 2 = 0

2x² + 2x - 1 = 0

The equation has a degree of two.

As a result, the equation 2(x - 1)² = 4x² - 2x + 1 is quadratic.

(B) 2x - x² = x² + 5

x² + x² + 5 - 2x = 0

2x² - 2x + 5 = 0

The equation has a degree of two.

As a result, the equation 2x - x² = x² + 5 is quadratic.

(C) (√2x + √3)² + x² = 3x² - 5x

Algebraic identity is used:

(a + b)² = a² + 2ab + b²

2x² + 3 + 2√6x + x² = 3x² - 5x

3x² - 3x² + 2√6x + 5x + 3 = 0

5x + 2√6x + 3 = 0

The equation has a degree of 1.

As a result, the equation (√2x + √3)² + x² = 3x² - 5x  is not quadratic.

(We got our answer so we don't need to solve further)

Therefore, the equation (C) (√2x + √3)² + x² = 3x² - 5x is not a quadratic equation.

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As per area of rectangle, the dimensions of the box that yield the lowest cost is (1,1,6)

Area of rectangle:

The standard formula for area of rectangle is calculated as,

A = length x breadth

Given,

A closed rectangular box with volume 6 cubic feet is made from two different types of cardboard. the top and bottom are made with a heavy-duty cardboard that costs 30 cents per square foot. The sides are made from a light-weight cardboard that costs 5 cents per square foot.

Here find the dimensions of the box that yield the lowest cost.

Here let's consider the dimensions of the rectangular box be length l, breadth is b, and height is h.

Now, from the given information, the total cost can be derived as,

=> C=2lb×48+(2bh+2lh)×8

=> C=96lb+16bh+16lh

=> C=16(6lb+bh+lh) -----------------→(1)

Then the given volume is, V = lbh = 6 ---------------→(2) cubic feet.

Then the equation 2,

=> lbh = 6h = 6/lb

And then we have to substitute the value of h in equation 1, we get

=> C(l,b,h)=16(6lb+6/l+6/b)

Now we need to minimize the resulting function of two variables.

Therefore, we need to partially derivative the above function with respect to l,b. And set these equal to zero.

And the for l=0,b is undefined. So we can eliminate l=0.

Here we have to substitute l=1,b=112⇒1 in equation 2, we get

=> lbh=6(1)(1)h=6h=6h=6

Therefore, the critical point is, (1,1,6)

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The total price of 4 pounds of apples this week at the grocery store is $5.76

Total price of apples this week = Last week price of apples per pound × Quantity of apples

= $1.60 × 4

= $6.4

Actual price paid = Total price of apples this week - (Discount × Total price of apples this week)

= $6.4 - (10% × $6.4)

= 6.4 - (0.1 × 6.4)

= 6.4 - 0.64

= $5.76

In conclusion, 4 pounds of apples cost $5.76 this week at the grocery store.

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Answer:

f(8) = 216

Step-by-step explanation:

f(x) = (2x - 10)³

So f(8) = (2(8) - 10)³

==> f(8) = (16 - 10)³

==> f(8) = (6)³

==> f(8) = 216

Answer:

533

Step-by-step explanation:

3 hours = 180 minutes

2400 : 180 = x : 40

x = 2400 * 40 / 180

x = 2400 * 4 / 18

x = 2400 * 2 /9

x = 800 * 2 / 3

x = 1600/3

x = 533.333333

x = 533

Using Pythagoras theorem, the length of the pole is 57 feet

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

In this problem, assuming the pole runs down to the ground.

We can apply Pythagoras's theorem to find the height of the the conical roof.

Taking half the length of the the wall, i.e it's diameter = 72 /2 = 36ft

Using Pythagoras theorem;

45² = 36² + x²

x² = 45² - 36²

x² = 729

x = √729

x = 27 feet

The height of the conical roof is 27

The length of the pole = height of the conical roof + height of cylindrical wall

Length of pole = 27 + 30 = 57 ft

The length of the pole is 57ft

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Answer:

Step-by-step explanation:

Solve for x:

2 cos* (2) =

Divide both sides by 2:

cost (2) =

Take the logarithm base cos(2) of both sides:

Answer:

2inn

X=

iT+ log(-cos(2))

log(2)

i7+ log(-cos(2))

for NE Z