PLEASE HELP :(
Isabella is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $20, and her grandmother has pledged $2 per kilometer. If Isabella walks a certain distance, the two donors will end up owing the same amount. What is that distance?
Write a system of equations, graph them.

Answer:

The two polynomials cannot be factored using integer coefficients. Therefore, we need to use the quadratic formula to find their roots:

For x² - 3x + 2 = 0:

a = 1, b = -3, c = 2

x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) = (3 ± √1) / 2

x = 1 or x = 2

For x² + x + 2 = 0:

a = 1, b = 1, c = 2

x = (-1 ± √(1² - 4(1)(2))) / (2(1)) = (-1 ± √(-7)) / 2

x = (-1 ± i√7) / 2

Therefore, the LCM of x² - 3x + 2 and x² + x + 2 is:

(x - 1)(x - 2)(x - (-1/2 + i√7/2))(x - (-1/2 - i√7/2))

The number of each kind of coins Sharah have is 23 dimes and 12 quarters.

Let's use a system of equations to solve this problem. Let x be the number of dimes and y be the number of quarters that Sharah has. Then, we can write the following equations:

x + y = 35 (the total number of coins)

0.10x + 0.25y = 5.30 (the total value of the coins)

We can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:

x = 35 - y

Now we can substitute this into the second equation:

0.10(35 - y) + 0.25y = 5.30

3.50 - 0.10y + 0.25y = 5.30

0.15y = 1.80

y = 12

Now we can use this value of y to solve for x:

x = 35 - 12 = 23

So Sharah has 23 dimes and 12 quarters.

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We have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.

A line L is said to be tangent to a circle C at a point P if and only if L meets C at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line L passing through P, we can show that L is tangent to the circle at P if and only if L is perpendicular to the line OP.

Let us assume that L is perpendicular to OP. Then, since L is perpendicular to the radius at P, it is also perpendicular to the circumference of the circle at P. This means that the line L only meets the circumference of the circle at the one point P, and so L is tangent to the circle at P.

Conversely, let us assume that L is tangent to the circle at P. This implies that the line L only meets the circumference of the circle at the one point P. Thus, since the line L must pass through the point P, it must be perpendicular to the line OP.

Therefore, we have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.

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Answer:

42

Step-by-step explanation:

you asding it all up

(a) The function is decreasing at x=2.

(b) The interval where f(x) is increasing is (-3, 3).

(c) The function, f(x) has a relative maximum at x=-3.

To determine whether the function is increasing or decreasing at x=2, we need to find the derivative of f(x) and evaluate it at x=2.

f(x) = x³ - 27x + 5

f'(x) = 3x² - 27

At x=2, f'(2) = 3(2)² - 27 = -15, which is negative.

Therefore, the function is decreasing at x=2.

To find the interval where f(x) is increasing, we need to find the values of x where f'(x) > 0.

f'(x) = 3x² - 27

3x² - 27 > 0

3(x² - 9) > 0

(x - 3)(x + 3) > 0

The critical points are x=-3 and x=3.

We can test each of the intervals created by these critical points to see where f(x) is increasing or decreasing.

When x < -3, f'(x) < 0, so f(x) is decreasing.

When -3 < x < 3, f'(x) > 0, so f(x) is increasing.

When x > 3, f'(x) > 0, so f(x) is increasing.

Therefore, the interval where f(x) is increasing is (-3, 3).

To find the relative maximum of f(x), we need to find the critical points where f'(x) = 0.

3x² - 27 = 0

x² - 9 = 0

(x - 3)(x + 3) = 0

The critical points are x=-3 and x=3.

To determine which of these critical points corresponds to a relative maximum, we need to use the second derivative test.

f''(x) = 6x

At x=-3, f''(-3) = -18, which is negative.

Therefore, f(x) has a relative maximum at x=-3.

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The solution to the inequality 16 + 12x < 19x + 12 is all the values of x between the interval notation (4/7, ∞).

To solve the inequality 16 + 12x < 19x + 12, we need to isolate the variable x on one side of the inequality. We can do this by subtracting 12x from both sides and subtracting 12 from both sides:

16 + 12x - 12x - 12 < 19x + 12 - 12x - 12

4 < 7x

Solving for x, we can divide both sides by 7:

4/7 < x or x > 4/7

In interval notation, this would be (4/7, ∞). Therefore, the solution to the inequality is (4/7, ∞) in interval notation.

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In response to the supplied query, we may state that Therefore, equation  g(12) = 8.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

To find g(3), we substitute x=3 into the function g(x):

g(3) = 2(3)/3

g(3) = 6/3

g(3) = 2

Therefore, g(3) = 2.

To find g(12), we substitute x=12 into the function g(x):

g(12) = 2(12)/3

g(12) = 24/3

g(12) = 8

Therefore, g(12) = 8.

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Answer:

1968 bottles of water

Step-by-step explanation:

24×82=1968

1968 bottles of water

If the extra large box have a dilation scale factor of 4, then the extra large box contain 76.8ounces.

If the extra large box is a dilation of the single serving box with a scale factor of 4, then

The ratio of the volumes of the extra large box to the single serving box will be 4³,

We know that, Volume is a three-dimensional measurement and is affected by the cube of the scale factor.

So, the volume of the extra large box will be;

⇒ 4³ × 1.2 ounces = 4×4×4×1.2 ounces = 76.8 ounces,

Therefore, the extra large box will contain 76.8 ounces of cereal.

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The missing value that cοmpletes the frequency table is 174.

A frequency distributiοn table is a table that displays the number (οr frequency) οf οbservatiοns that fall within each interval after grοuping the data intο intervals. It is an effective tοοl fοr cοmprehending data distributiοn and spοtting patterns οr trends.

Typically, the table has twο cοlumns. The intervals, οr "bins," intο which the data is divided are listed in the first cοlumn. The frequency, οr quantity οf οbservatiοns, that fall intο each bin is displayed in the secοnd cοlumn. Depending οn the data and the level οf precisiοn required, the bins may be identical οr vary in width.

The analysis οf a variety οf data types, including numerical, categοry, and οrdinal data, can be dοne using frequency distributiοn tables. As well as calculating descriptive statistics like the mean, median, and mοde, as well as measures οf variability like the range and standard deviatiοn, they can alsο be used tο generate these statistics.

All things cοnsidered, frequency distributiοn tables οffer a quick and effective apprοach tο summarize a lοt οf data and learn mοre abοut its distributiοn and prοperties.

Tο cοmplete the frequency table, we need tο determine the frequency fοr the interval 28 ≤ x < 30.

We can see frοm the histοgram that the interval 28 ≤ x < 30 has a width οf 2. Since the tοtal frequency is the sum οf the frequencies in each interval, we can use the infοrmatiοn prοvided in the frequency table tο sοlve fοr the missing value:

110 + 36 + 180 + frequency fοr 28 ≤ x < 30 = tοtal frequency

We can simplify this expressiοn:

326 + frequency fοr 28 ≤ x < 30 = tοtal frequency

We knοw that the tοtal frequency is the number οf mοbile phοnes that were tested, sο we can assume that this is a knοwn quantity. Let's say that the manufacturer tested 500 mοbile phοnes. Then we can sοlve fοr the missing frequency:

326 + frequency fοr 28 ≤ x < 30 = 500

frequency fοr 28 ≤ x < 30 = 174

Therefοre, the missing value that cοmpletes the frequency table is 174. The cοmpleted frequency table is:

Battery life, x(hοurs) Frequency

15 < x < 20                   110

20 ≤ x < 22                  36

22 ≤ x < 28                  180

28 ≤ x < 30                   174

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The x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].

The x-values at a distance of 22 or less from the number 9 can be found by solving the inequality |x-9|≤22.

Step 1: Break up the absolute value inequality into two separate inequalities:
x-9≤22 and x-9≥-22

Step 2: Solve each inequality for x:
x≤31 and x≥-13

Step 3: Combine the two inequalities using the "and" operator (∩):
-13≤x≤31

Step 4: Write the solution in interval notation:
[-13, 31]

So, the x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].

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The following system of inequalities is represented by the graph

x+y>3

-x+y< -4

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Consider the  inequalities:

x+y>3-------(1)

-x+y< -4------(2)

Find x and y intercepts of both by considering them as equations by using equal sign in the place of  inequality sign

x+y=3-------(3)

-x+y= -4------(4)

Find x and intercepts of these 2 equations:

we get x intercept when y=0 ( substitute y=0 into the respective equations and find x)

we get y intercept when x=0  ( substitute x=0 into the respective equations and find y)

x intercept of (3) is (3,0)

y intercept of (3) is (0,3)

x intercept of (3) is (4,0)

y intercept of (3) is (0,-4)

plot these points on a the plane and join them with lines

use dotted line and shade under the lines because of less than symbol

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The scale factοr οf dilatiοn is 1/40 and the cοοrdinates οf F" are (1440, 600)

Labelling the image οf the triangle

The image οf the label is attached

The scale factοr οf the dilatiοn

Given that

D'E' = 36 units

Then, we have

D"E" = 0.9 units

The scale factοr is calculated as

Scale factοr = D"E"/D'E'

Sο, we have

Scale factοr = 0.9/36

Evaluate

Scale factοr = 1/40

Sο, the scale factοr οf dilatiοn is 1/40

The cοοrdinates οf F"

This is calculated as

F = F'/Scale factοr

Sο, we have

F = (36, 15)/(1/40)

F = (1440, 600)

The trigοnοmetry ratiοs

The trigοnοmetry ratiοs are calculated as

sin(D") = EF/DF

cοs(D") = DE/DF

tan(D") = EF/DE

Sο, we have the fοllοwing apprοximated values

sin(D") = 15/39 = 0.36

cοs(D") = 36/39 = 0.92

tan(D") = 0.36/0.92 = 0.39

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Answer:

(a) The probability that all 4 calls are for medical help can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

n is the number of trials (in this case, 4)

k is the number of successes (in this case, 4)

p is the probability of success on a single trial (in this case, 0.81)

Plugging in the values, we get:

P(X = 4) = (4 choose 4) * 0.81^4 * (1 - 0.81)^(4 - 4)

P(X = 4) = 0.5314

Therefore, the probability that all 4 calls are for medical help is 0.5314, rounded to 4 decimal places.

(b) The probability that at least 1 of the calls is not for medical help can be calculated using the complement rule:

P(at least 1 call not for medical help) = 1 - P(all 4 calls for medical help)

We already calculated the probability of all 4 calls being for medical help in part (a), which is 0.5314. So, using the complement rule, we get:

P(at least 1 call not for medical help) = 1 - 0.5314

P(at least 1 call not for medical help) = 0.4686

Therefore, the probability that at least 1 of the calls is not for medical help is 0.4686, rounded to 4 decimal places.

(c) The calculation in part (a) may not be valid if we choose 4 consecutive calls to the station because the 4 consecutive calls being medical may not be independent events. For example, if a large accident or a natural disaster occurs in the area, there may be a higher probability of multiple consecutive medical calls due to the same incident or cause. In that case, the assumption of independence between the events would not hold, and the binomial probability formula would not be applicable.

Step-by-step explanation:

There is a zero for f(x) between a and b.

Using the Intermediate Value Theorem, we can show that the function f(x)=2x3+6x2-3a-2 has a zero between a and b.

The Intermediate Value Theorem states that if a continuous function f(x) takes on different values at two points a and b, then there must exist at least one value c in between a and b such that f(c) = 0. Since f(x) is a continuous function, it takes on different values at a and b.

Thus, by the Intermediate Value Theorem, there must exist at least one value c in between a and b such that f(c) = 0, meaning that there is a zero for f(x) between a and b.

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"The expressions are equivalent." We can use the distributive property to determine whether or not the expressions are equivalent.

First, let's apply the distributive property to the first expression:

3(x+2) + 8 = 3x + 6 + 8

Next, let's simplify the expression by combining like terms:

3x + 6 + 8 = 3x + 14

Now, we can see that the two expressions are equivalent because they both simplify to the same expression, 3x + 14. Therefore, we can conclude that the expressions are equivalent.

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The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

The process of calculating a value using operands and a math operator is referred to as a "operation" in mathematics. The math operator's symbol has predetermined rules that must be obeyed for the provided operands or integers. The five fundamental operations in mathematics are addition, subtraction, multiplication, division, and modular forms.

The prime factorizations of 12 and 30 are 2² x 3 and 2 x 3 x 5, respectively.

Hence, 2² x 3 x 5 = 60 is the smallest common multiple of 12 and 30.

This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.

To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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Answer:

25%

Step-by-step explanation:

p/w =x/100 for a percentage

93.75/125 = x/100

93.75×100= 9375

9375 = 125x

9375/125 =75

x=75

So she paid 75% of the original price, meaning the jeans were 25% off.

The measure of ∠FGH is 28 - 4x.

A three-sided polygon with three angles is known as a triangle. It is a basic geometric shape that can be classified based on its sides and angles.

Since G is the midpoint of DF, we have m∠DGF = m∠FGC (vertical angles are equal), so m∠FGD = m∠CGF = (180 - m∠DGF)/2 = (180 - m∠FGC)/2 = m∠GFC. Similarly, m∠FHE = m∠HEC, so m∠FHE = m∠CGF = m∠GFC.

Using angle sum property, we have:

m∠DEF + m∠FED + m∠FDE = 180

60 - 5x + 2(46 + 2x) + m∠FGH = 180

152 + 4x + m∠FGH = 180

m∠FGH = 180 - 152 - 4x

m∠FGH = 28 - 4x

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Moreover, we should evaluate the model's goodness of fit and take into expressions account additional elements that can influence plant development.

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

In the formula, h is the height, t is the time, and a and b are the parameters that need to be approximated.

The information in the table may be used to estimate the values of a and b. The equation is first transformed to yield:

[tex]log(b*t) = log(h/a)[/tex]

[tex]19 = 19.24 * log(53.89*t)[/tex]

t = 0.186 months, or approximately 5.58 days, or log(53.89*t) = 1 53.89*t = 10

Hence, 5.58 days is the best guess for the age of the plant at 19 inches tall. Seeing that this is a very little period of time, it is probable that the model will not be correct for values of t this low. Moreover, we should evaluate the model's goodness of fit and take into account additional elements that can influence plant development.

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are given as follows:

The four inequality symbols, along with their meaning, are presented as follows:

The inequality for this problem is defined as follows:

–3(2x – 5) < 5(2 – x)

Expanding the operations, the solution is obtained as follows:

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

x > 5.

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The profit for buying pencils for $2 each and selling them for $2.40 is $6.40 and there is no loss.

The profit is the difference between the selling price and the cost price of the pencils. In this case, the profit per pencil is $2.40 - $2 = $0.40.

Since the total sales amount is $40, the number of pencils sold is $40/$2.40 = 16.67, which we can round down to 16 pencils. Therefore, the total profit is 16 * $0.40 = $6.40.

There is no loss in this scenario, as the selling price is higher than the cost price. Loss occurs when the selling price is lower than the cost price.

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The roots of the equation x^(2)-12x+61=0 in simplest a+bi form are 6 + 5i and 6 - 5i.

The roots of the equation x^(2)-12x+61=0 in simplest a+bi form can be found using the quadratic formula.

The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -12, and c = 61.

Plugging in the values into the quadratic formula, we get:

x = (-(-12) ± √((-12)^(2)-4(1)(61)))/(2(1))

Simplifying the equation, we get:

x = (12 ± √(144-244))/2

x = (12 ± √(-100))/2

Since the square root of a negative number is a complex number, we can write the equation as:

x = (12 ± 10i)/2

Simplifying further, we get:

x = 6 ± 5i

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Answer: G=(3, 4) R=(4, 8) A=(7, 8) M=(6, 4)

Step-by-step explanation:

translation is the movement of a point so 11 units right add 11 to the x value and 2 to the y value then do the opposite for going left and down

Answer:

5x4

Step-by-step explanation:

The dimensions of the rectangle are 20x16

The reducing factor is 0.25.

Multiple 20 * 0.25= 5

Multiple 16 * 0.25= 4

Therefore the new dimensions are 5x4.

The solution is then:

l = 6cm

w = 2cm

h = 2cm

The surface area of a cuboid is the total area of all of the faces of a cuboid. If, the length (l), width (w), and height (h) of the cuboid

then, use the formula: surface area (SA)=2lw+2lh+2hw.

here, we have,

We know that the formula for the volume of a box is:

V = l*w*h

Where:

l = length

w = width

h = height

The formula of the surface area of a box is:

SA = 2(lw+lh+wh)

Based on the given we know the following:

24 =  l*w*h

and

56 =  2(lw+lh+wh)

If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:

24 = 6*2*2

Let:

l = 6cm

w =2cm

h =2cm    

Now let's try this on the surface area formula:

56 = 2(6*2+6*2+2*2)

so, 56 = 56

The answer is then:

l = 6cm

w = 2cm

h = 2cm

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Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.

A probability calculated by a series of tests is known as experimental probability.

The given table is as follows:

              1    2    3    4

Jaylon:   6    8    9    7

Paula:    8     5     7   10

To determine the experimental probability of the pointer landing on 4 for Jaylon, we add up the number of times the pointer landed on 4 for Jaylon and divide by the total number of spins:

Experimental probability for Jaylon = (number of times the pointer landed on 4 for Jaylon) / (total number of spins)

= 7 / 30

Similarly,

Experimental probability for Paula:

= 10 / 30

Expected number of times the pointer will land on 4 = (experimental probability) x (total number of spins)

For Jaylon: (7 / 30) × 130 = 30.33

For Paula: (10 / 30) × 130 = 43.33

Therefore, Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.

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The missing table has been attached below.

The measure of angle FLI is 56=

The sum of angles of a triangle equals the straight angle. A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides. It was unknown for a long time whether other geometries exist, for which this sum is different.

Therefore the sum of angle in a triangle is 180

Since FIL is right angle , then angle FLI =

180-(90+34)

= 180- 124

= 56°

therefore the measure of angle FLI is 56°

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Answer:

The family will save $896 on airfare by vacationing to Vancouver

Step-by-step explanation:

Tickets to Fairbanks - $958 each (4 total people)

Total cost - 958 times 4 = $3832

Tickets to Vancouver - $734 each (4 total people)

Total cost - 734 times 4 = $2936

$3832 - $2936 = $896