Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart, how far has the eastbound airplane traveled?

The numeric value of the function f(x) = 2x² - x + 3 at x = x + 1 is given as follows:

f(x + 1) = 2x² + 3x + 4.

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, the function is defined as follows:

f(x) = 2x² - x + 3.

The point at which the numeric value is calculated as given by:

x = x + 1.

Hence the numeric value is obtaining replacing the two instances of x in the function by x + 1, as follows:

f(x + 1) = 2(x + 1)² - (x + 1) + 3

f(x + 1) = 2(x² + 2x + 1) - x - 1 + 3

f(x + 1) = 2x² + 4x + 2 - x - 1 + 3

f(x + 1) = 2x² + 3x + 4.

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The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

According to the question,

We have the following information,

The given verbal phrase is one-half times a number m plus twenty-five.

Now, we will solve it step by step.

Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:

m/2

Now, adding 25 to this term, we have the following final expression:

m/2+25

Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

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The interest earned on a [tex]$\$ 50,000$[/tex] deposited for 6 years at [tex]$4\frac{1}{8 }\%$[/tex] in compounded continuously is [tex]$\$ 14040.97$[/tex].

Continuous compounding is the mathematical limit of the number of periods across which compound interest can be calculated and reinvested into the account balance. Although it is impractical, the concept of endlessly compounded interest is important in finance. This is an extreme example of compounding because most interest is compounded on a monthly, quarterly, or semiannual basis.

The given amount is [tex]$\$ 50,000$[/tex].

It will be deposited for 6 years.

With [tex]$4\frac{1}{8 }\%$[/tex] interest,

The formula for compounded continuously is

[tex]$$\begin{aligned}&A=P e^{r t} \\&P=50000 \\&r=4 \frac{1}{8}=\frac{33}{8}\end{aligned}$$[/tex]

[tex]$$\begin{aligned}r &=0.04125 \\t &=6\end{aligned}$$[/tex]

Substitute all the values

[tex]$$\begin{aligned}&A=50000 e^{0.04125 \times6} \\&A=50000 e^{0.2475} \\&A=50000\times 1.28081\\&A=64040.96811\end{aligned}$$[/tex]

[tex]$\mathrm{I}=\mathrm{A}-\mathrm{P}$[/tex]

Interest [tex]$=64040.96811-50000=14040.9681$[/tex]

Hence, Interest [tex]$=\$ 14040.97$[/tex]

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Answer:

No solutions

Step-by-step explanation:

-5y+7/2y=-5-3/2y-4

+3/2y.           +3/2y

-5y+3/2y+7/2y=-5-4

-5y+10/2y=-9

-5y+5y=-9

0=-9

No solutions

Hopes this helps please mark brainliest

The solution of the exponential equation is x = -1

We want to solve the exponential equation:

2^(3x + 1) = 1/4

If we apply the natural logarithm in both sides of that equation, we will get:

ln( 2^(3x + 1) ) = ln( 1/4)

(3x + 1)*ln(2) = ln(1/4)

3x*ln(2) = ln(1/4) - ln(2)

x = (ln(1/4) - ln(2))/(3*ln(2)) = -1

The value of x is -1

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Answer: divide the area value by 1e+6

Step-by-step explanation:

2x²+12x=0 , x²-2x=4 and 9x²+6x-3=0 are Quadratic equation

Quadratic equations are polynomial equations whose degree is of 2 in one of the variable.

The standard form of quadratic equation is ax²+bx+c = d where a, b and c are  real numbers and a ≠ 0.

In general form of quadratic equation , "a" is known as leading coefficient and "c" is known as absolute term of function.

In the given question,

Equation whose max. degree will be 2 will be quadratic .

2x²+12x=0 , equation is quadratic as degree of equation is 2

x²-2x=4 , equation is quadratic as degree of equation is 2

x³-6x²+8=0 , Degree of equation is 3

Therefore , equation is not quadratic

5x-3=0 , Degree of equation is 1

Therefore , equation is not quadratic

5x-1=3x+8 , Degree of equation is 1

Therefore , equation is not quadratic

9x²+6x-3=0 , Degree of equation is 2

It is quadratic equation.

Hence , 2x²+12x=0 , x²-2x=4 and 9x²+6x-3=0 are quadratic equation

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The area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.

First, let us understand the area under the curve:

A definite integral between two points is used to calculate the area under a curve between them. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a and x = b. This area can be estimated by integrating with specified limitations.

We are given:

y = x^2 - 3x

We need to find the area between the curve y = x^2 - 3x for x between 1 and 8.

Now,

Integrate the given function:

Integration y = Integration  x^2 - Integration 3x

y = [x^(2 + 1) / (2 + 1)] ^ 8 _1 - [3x^(1 + 1) / (1 + 1)] ^ 8 _1

y = [x^3 / 3] ^ 8 _1 - [3x^2 / 2] ^ 8 _1

y = [8^3 / 3 - 1^3 / 3] - [3 * 8^2 / 2 - 1 * 8^2 / 2]

y = [512 / 3 - 1 / 3] - [96 - 32]

y = 1535 / 3 - 64

y = 1535 - 192 / 3

y =  1343 / 3 square units.

So, the area is 1343 / 3 square units.

Thus, the area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.

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The most appropriate interpretation for the slope of the data given is the height of water in the pool increases by 2 inches per minute. Option (1) is correct.

The slope of a line, also known as its gradient, is the value of the steepness or direction of a line in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.

Given that

Time                       Height

2                                 8

4                                12

6                                16

8                                20

10                              24

The slope of the line = 2

A line's slope is also known as its gradient or rate of change.

The slope can be positive or negative; positive slope values indicate an increase in x as y increases and vice versa.

A negative slope indicates that one variable decreases as the other increases.

Because the slope value given here is positive, we can conclude that the height of the water increases over time.

As a result, the height of the water rises by 2 inches per minute.

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Answer:

-35

Step-by-step explanation:

Answer:

[tex]157^{\circ}[/tex]

Step-by-step explanation:

Using the exterior angle theorem,

[tex]m\angle K=m\angle J+m\angle L=157^{\circ}[/tex]

Answer:

14.5 gallons will be gone in 1 minute

Step-by-step explanation:

just divide 58 by 4 and thats how much water will be gone in 1 minute

Dana owns      [tex]\frac{3}{14}[/tex] fraction of the business

How to calculate the fractions?

*Identify a fraction: When writing fractions, one number is placed above the dividing line and one number is written underneath it.

*Find the numerator: The numerator—the number at the top—indicates the number of elements that make up the fraction.

*find the denominator: The denominator is the figure at the bottom. This number reveals how many components there are in the total number.

Let us take the fraction shared by Dana and Randi as x

So the equation becomes

[tex]\frac{2}{7} +\frac{2}{7} +x+x=1[/tex]

⇒ [tex]\frac{4}{7}+2x=1[/tex]

⇒2x=1-[tex]\frac{4}{7}[/tex]

⇒[tex]2x=\frac{7-4}{7}[/tex]

⇒[tex]2x=\frac{3}{7}[/tex]

⇒[tex]x=\frac{3}{7*2}[/tex]

⇒[tex]x=\frac{3}{14}[/tex]

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The total price of the toaster oven, including tax is $51.36.

Given that the toaster oven usually sells for $60 and the toaster oven is 20% off, the new price will be;

= Normal price - Discount

= $60 - (20% × $60)

= $60 - $12

= $48

Also, sales tax is 7%, therefore the new price will be:

= $48 + (7% × $48)

= $48 + $3.36

= $51.36

The price is $51.36.

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Answer:

1=180 2=90

Step-by-step explanation:

1=∠1 and ∠2 are supplementary, so m∠2 = 180° - x°. ∠2 and ∠6 are corresponding angles. So, m∠6 = 180° - x°.

2=Their measures are equal, so m∠4 = 90 . When two lines intersect to form one right angle, they form four right angles.

Answer:

∠4 = 55°

∠6 = 35°

Step-by-step explanation:

    In ΔABC,

         35 + 90 + ∠4 = 180° {Sum of all angles of triangle}

                  125 +∠4 = 180

                           ∠4 = 180 - 125

                             ∠4 = 55°

Linear pair: If in two adjacent angles, the  non-common arms form a straight line, then the two angles are called linear pair and they add up to 180.

∠7 + ∠8 = 180°  {linear pair}

   90 + ∠7  = 180°

            ∠7 = 180 - 90

                 ∠7 = 90°

In ΔACD,

         ∠6 + ∠4+ ∠7 = 180  {Sum of all angles of triangle}

           ∠6 + 55 + 90 = 180

                   ∠6 + 145 = 180

                             ∠6 = 180 - 145

                   ∠6 = 35°

The end behavior of the given graph is as x → -∞, f(x) → ∞ and as x → ∞ f(x) = ∞.

End behavior of graph

End behavior of the graph refers the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. And the degree and the leading coefficient of a polynomial function will determine the end behavior of the graph.

Given,

Here we have the graph with some function as y = f(x).

Here we have to find the end behavior of the graph.

Here we can see that the value of x goes to the positive side (the right side of the graph), the graph increases upwards, and this is shown with the arrow pointing up.

So, which means that the value of x goes to ∞,  then the value of y will also go to ∞.

Similarly, we can see the exact same behavior for the negative side of x (the left side of the graph), then as x goes to -∞, y will go to ∞.

Therefore, the correct option will be the second option, counting from the top.

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Answer:

Step-by-step explanation:

abcdefgh

On that date, 110.66 euro was worth 160.38 dollars.

On that date, 77.65 dollars was worth 53.58 euro.

Given that one U.S. dollar was worth 0.69 euro, the dollar that was 110.66 euro worth will be:

= Amount of euro / Rate

= 110.66 / 0.69

= 160.38 dollars

The euro that 77.65 dollars was worth will be:

= 77.65 × 0.69

= 53.58 euro

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The number line which represents the number of exams Ms. Filer had left to grade is "number line with an open circle on number 15 and line shaded left". option B

five eighths plus h equals eleven over eight, determine the value of h.

5/8 + h = 11/8

substract 5/8 from both sides

h = 11/8 - 5/8

h = 6/8

h = 3/4

Water boils at a minimum temperature of 100 degrees Celsius.

The inequality:

100 ≥ b

Mario total goal for the month = Number of miles Mario has left to run this month to reach her goal + number of miles Mario has run so far

150 = m + 75

substract 75 from both sides

150 - 75 = m

75 = m

The equation f + 24 = −3, solve for f.

f + 24 = -3

substract 24 from both sides

f = -3 - 24

f = -27

Number of gifts each family donates = 4

Number of families = 12

Total gifts donated = g

The equation:

g / 12 = 4

cross product

g = 12 × 4

g = 48

The equation 17 equals y over -3, solve for y.

17 = y / -3

cross product

17 × -3 = y

-51 = y

Number of cookies Bella is baking = 42

Number of cookies she has baked = 29

Number of cookies left for Bella to bake = x

The equation:

42 = x + 29

substract 29 from both sides

42 - 29 = x

13 = x

The inequality:

6(n − 5) < 3(n + 4)

open parenthesis

6n - 30 = 3n + 12

6n - 3n = 12 + 30

3n = 42

divide both sides by 3

n = 42/3

n = 14

The equation 5.24w = 16.506, solve for w.

5.24w = 16.506

divide both sides by 5.24

w = 16.506 / 5.24

w = 3.15

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The rocket splashes down after 39.164 seconds. The rocket reach its peak height 19.081 seconds after launch. The rocket peaks at 1976.13 meters above sea level.

The function of height is given by,

h(t) = -4.9t² + 187t + 192

Once the rocket will be splashed down in sea, means the height of the rocket will be zero. Means

x h(t) = 0

-4.9t² + 187t + 192 = 0

Solving the quadratic equation with quadratic formula, we have two values of t

t = 39.164 and t = -1.001

We will consider the positive value of the time

So the answer is 39.164 seconds.

For getting the maximum value, we should differentiate the function of height and make it equal to zero.

 [tex]\frac{dh(t)}{dt} = \frac{d}{dt} (-4.9t^2 + 187 t + 192)[/tex]

For maximum value of h, [tex]\frac{dh (t)}{dt} = 0[/tex]

0 = -4.9 × (2t) + 187

t = 19.081 seconds

At this time, the height of rocket will be maximum.

So putting the vaiue in the given function.

h = -4.9 × (19.081)² + 187 (19.081) + 192

h = 1976.13 meters

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Answer: 25 questions

Step-by-step explanation:

The equation that represent the given situation is y = 15x + 70

When she plants 3 stalks, each plant yields 115 ounces of beans

The first point = (3, 115)

When she plants 8 stalks, each plant yields 190 ounces of beans

The second point = (8, 190)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line m = (190-115) / (8-3)

= 75/5

= 15

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Choose one point and substitute the values in the equation

y - 115 = 15(x - 3)

y - 115 = 15x - 45

y = 15x - 45 + 115

y = 15x + 70

Hence, the equation that represent the given situation is y = 15x + 70

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The solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.

In the given question we have to solve the system using the Cramer's rule.

The given equations are

-4x-5y+6z = 5

-3x+6y-2z = 4

5x+9y-3z = 1

From the Cramer's rule

[tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]

Here,

A = [tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right][/tex]

X= [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]

Now D=|A|

D= [tex]\left|\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right|[/tex]

D= [tex]-4\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]

D= -4[6×(-3)-(-2)×9]+5[(-3)×(-3)-(-2)×5]+6[(-3)×9-5×6]

D= -4[-18+18]+5[9+10]+6[-27-30]

D= -4×0+5×19+6×(-57)

D= 0+95-342

D= -247

[tex]D_{x}=\left[\begin{array}{ccc}5&-5&6\\4&6&-2\\1&9&-3\end{array}\right][/tex]

Simplifying the matrix

[tex]D_{x}=5\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|+6\left|\begin{array}{ccc}4&6\\1&9\end{array}\right|[/tex]

[tex]D_{x}[/tex] = 5[6×(-3)-(-2)×9]+5[4×(-3)-(-2)×1]+6[4×9-1×6]

[tex]D_{x}[/tex] = 5[-18+18]+5[-12+2]+6[36-6]

[tex]D_{x}[/tex] = 5×0+5×(-10)+6×30

[tex]D_{x}[/tex] = 0-50+180

[tex]D_{x}[/tex] = 130

[tex]D_{y}=\left[\begin{array}{ccc}-4&5&6\\-3&4&-2\\5&1&-3\end{array}\right][/tex]

Simplifying the matrix

[tex]D_{y}= -4\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|-5\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|[/tex]

[tex]D_{y}[/tex] = -4[4×(-3)-(-2)×1]-5[(-3)×(-3)-(-2)×5]+6[(-3)×1-4×5]

[tex]D_{y}[/tex] = -4[-12+2]-5[9+10]+6[-3-20]

[tex]D_{y}[/tex] = (-4)×(-10)-5×19+6×(-23)

[tex]D_{y}[/tex] = 40-95-138

[tex]D_{y}[/tex] = -193

[tex]D_{z}=\left[\begin{array}{ccc}-4&-5&5\\-3&6&4\\5&9&1\end{array}\right][/tex]

Simplifying the matrix

[tex]D_{z}=-4\left|\begin{array}{ccc}6&4\\9&1\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|+5\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]

[tex]D_{z}[/tex] = -4[6×1-4×9]+5[1×(-3)-4×5]+5[(-3)×9-5×6]

[tex]D_{z}[/tex] = -4[6-36]+5[-3-20]+5[-27-30]

[tex]D_{z}[/tex] = (-4)×(-30)+5×(-23)+5×(-57)

[tex]D_{z}[/tex] = 120-115-285

[tex]D_{z}[/tex] = -280

As we know that;  x=Dx/D, y=Dy/D, z=Dz/D

x=130/(-247)

x= -0.53

y=(-193)/(-247)

y=0.78

z=(-280)/(-247)

z=1.13

Hence, the solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.

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Answer:587

Step-by-step explanation: multiply 5 by 7 and 6,thatll give you 30+35=65

then 65 multiplied by 9 is 585 then add2 is 587

The limit Lim x→1 (sinx - sin1)/(x - 1) = cos1

The limit of a function f(x) as x tends to a is the value of the function f(x) as x tends to a. It is written as [tex]\lim_{x \to a} f(x) = L[/tex]

GIven that we require the limit given as  [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1}[/tex]

So, substituting the value of x = 1 into the given equation, we have that

[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{sin1 - sin1}{1 - 1} \\= \frac{0}{0}[/tex]

Since 0/0 is one of the inderterminate forms, we use the L'hopital's rule to find the limit of the given function.

L'hopital's rule states that if [tex]\lim_{x \to a} f(x) = \lim_{x \to a} g(x) = 0[/tex] and f'(x) and g'(x) exist then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]

Let the variables be

So, since we know that

[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{0}{0}[/tex],

So,  [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]

So, we differentiate both the numerator and denominator and find the limit.

So,

[tex]\lim_{x \to 1} \frac{f'(x)}{g'(x)} = \lim_{x \to 1} \frac{\frac{d(sinx - sin1)}{dx} }{\frac{d(x - 1)}{dx} } \\= \lim_{x \to 1} \frac{cosx - 0}{1 - 0} \\= \lim_{x \to 1}cosx \\= cos1[/tex]

So, [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = cos1[/tex]

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Answer:

×= -7½

Step-by-step explanation:

2x<15

2x<15=0

2x= -15

x= -15/2

x= -7½

Answer:

30

Step-by-step explanation:

Supplementary angles add to 180°.

[tex]4x+30+2x-30=180 \\ \\ 6x=180 \\ \\ x=30[/tex]

The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86

What is a probability?

The probability of an event in an experiment is calculated by the division of the number of desired outcomes by the number of total outcomes in the experiment.

From the tree diagram, there are two ways to obtain the promotion:

0.41 of 0.68 (hit the quota).

0.14 of 0.32 (did not hit the quota).

Hence the probability of getting a promotion is:

P(A) = 0.41 x 0.68 + 0.14 x 0.32 = 0.3236.

The probability of both getting a promotion and hitting the quota is:

P(A and B) = 0.41 x 0.68 = 0.2788.

Hence the conditional probability is:

P(B|A) = P(A and B)/P(A) = 0.2788/0.3236 = 0.86. (approximately).

The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86

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The relationship which has a zero slope is a two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3, and the second column, y, has the entries, 2, 2, 2, 2. Option A is correct.

We know that a line has a zero slope is when the line is parallel to the x-axis.

The slope of a line is given by;

m = (y₂ - y₁) / (x₂ - x₁)

where (x₂, y₂) and (x₁, y₁) are the coordinates of any two points on the line of slope.

For option A:

The given coordinates are;

(-3, 2), (-1, 2), (1, 2), (3, 2)

Choose any two points to calculate the slope of the line.

We will choose the first two points and put the values in the above formula, we will get;

m = (2 - 2) / (-1 (-3)) = 0 / 2 = 0

So, the slope of the line is 0.

Thus, the relationship which has a zero slope is a two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3, and the second column, y, has the entries, 2, 2, 2, 2. Option A is correct.

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