If f(1) = 0, what are all the roots of the function ? use the remainder theorem.

The quadrilateral is a trapezoid. The value of x is 5 by applying midsegment theorem for trapezoids.

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

The side with length 21 units and 27 units are parallel to each other.

From the given diagram, the expression below is true:

5x-1 = (21 + 27)/2

2(5x - 1) = 21 + 27

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

x = 50/10

x = 5

Hence the value of x is 5

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The image of this question is probably this.

Answer:

Hi dear !!

area of semicircle = πr²/2

=> 3.14× 6x6 /2

3.14× 6× 3

=> 56.52 cm².

area of rectangle= l x b = 13 x 12 = 169

total area = 169 +56.52 = 225.5 cm²

The distance between the points in simplest radical form is equal to 2√10 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-2))² + (5 - 3)²]

Distance = √[6² + 2²]

Distance = √[36 + 4]

Distance = √40

Distance = 2√10 units.

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Using the formula to convert Fahrenheit to Celsius, we get that 100.8°F is 38.22°C.

To convert 100.8°F to °C, we can use the formula:

°C = (°F - 32) x 5/9

Plugging in the value of 100.8°F, we get:

°C = (100.8 - 32) x 5/9

°C = 68.8 x 5/9

°C = 38.22

Therefore, 100.8°F is equal to 38.22°C.

This formula is used to convert temperatures between the Fahrenheit and Celsius scales. It involves subtracting 32 from the Fahrenheit temperature and then multiplying by 5/9 to obtain the equivalent Celsius temperature. The resulting Celsius temperature is then rounded to the nearest tenth. It's important to note that Fahrenheit and Celsius are two different temperature scales, where 0°C is equal to 32°F, and 100°C is equal to 212°F. The Celsius scale is based on the freezing and boiling points of water, whereas the Fahrenheit scale is based on the freezing and boiling points of a solution of salt and water. Knowing how to convert between these two scales can be useful in a variety of settings, including cooking, weather reporting, and scientific research.

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$189.13

That's the correct answer On Ax

Answer:

  $189.13

Step-by-step explanation:

You want to know the interest saved if interest at 30.8% compounded monthly on a balance of $1400 is waived for 5 months.

The balance with interest compounded would be ...

  A = P(1 +r/12)^n

where P is the principal earning interest at annual rate r for n months.

The amount of interest earned in that time is ...

  I = P((1 +r/12)^n -1) = $1400(1 +0.308/12)^5 -1) ≈ $189.13

Hugo will save $189.13 in interest charges for the first 5 months.

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The missing angle measures are:

m2F = 50 degrees

m2H = 125 degrees

m2G  = 5 degrees

m2C  = 158 degrees

Since triangle ABC is similar to triangle FGH, the ratios of their corresponding angles are equal. Let's call the missing angles m2F, m2H, m2G, and m2C.

From the given information, we have:

m2F / mLA = m2H / mzB

So, we can find m2H by cross-multiplying and solving for m2H:

m2H = (mzB * m2F) / mLA

Since we don't know m2F, we can use the fact that the sum of the angles in a triangle is 180 degrees:

m2F + m2H + 75 = 180

So,

m2F + ((mzB * m2F) / mLA) + 75 = 180

Expanding and solving for m2F:

m2F + (75 * m2F / 22) + 75 = 180

(22 + 75) * m2F / 22 + 75 = 180

97 * m2F / 22 + 75 = 180

97 * m2F / 22 = 180 - 75

97 * m2F / 22 = 105

m2F = 105 * 22 / 97 = 50

So, the missing angle measures are:

m2F = 50 degrees

m2H = (75 * 50) / 22 = 125 degrees

m2G = 180 - 50 - 125 = 5 degrees

m2C = 180 - 22 = 158 degrees

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Answer: The equation y + 6 = 3/4 (x + 4) can be solved for y to find the corresponding graph:

First, isolate x by subtracting 4 from both sides:

y + 6 - 6 = 3/4 (x + 4) - 6

y = -6 + 3/4 (x + 4)

Next, isolate y by dividing both sides by 3/4:

y = -6 + 3/4 (x + 4) ÷ (3/4)

y = -6 + (x + 4)

y = x - 2 + 10

This equation represents a line with a slope of 1 and a y-intercept of 10 - 2 = 8. The graph of this line is a line that passes through the points (0, 8) and (1, 9).

Step-by-step explanation:

To have a unique outfit for each day of the week, you would need at 3 pairs of pants and 3 shirts.

To have a unique outfit for a month you would need at 6 pairs of pants and 5 shirts.

To have a unique outfit for each day of the year, you would need 26 pairs of pants and 15 pairs of shirts.

To find the unique outfits, you need to have enough clothes to have a unique outfit made from those clothes.

There are 7 days in a week. If you had 3 pairs of pants and 3 shirts, the unique outfits would be :

= 3 x 3

= 9 unique outfits

For a month :

= 6 x 5

= 30 unique outfits

For a year :

= 26 x 15

= 390 unique outfits for 365 days

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Answer:

b = - 12

Step-by-step explanation:

calculate the slope of the line passing through the 2 points and equate to [tex]\frac{1}{2}[/tex]

calculate the slope ( gradient ) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (b, 2 )

m = [tex]\frac{2-6}{b-(-4)}[/tex] = [tex]\frac{-4}{b+4}[/tex]

equating gives

[tex]\frac{-4}{b+4}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

b + 4 = - 8 ( subtract 4 from both sides )

b = - 12

The magnitude of acceleration of the car just before it reaches point C is -0.79 m/s^2.

The magnitude of acceleration of the car just before it reaches point C can be calculated using the given formula for acceleration, at= (-1/4t^1/2)m/s^2.

First, we need to determine the time it takes for the car to travel from point A to point C.

Since the speed of the car at point A is 25 m/s, and the speed at point C is 0 m/s, we can use the formula for speed, v=at, to find the time it takes for the car to travel from point A to point C.

Rearranging the formula, we get t=v/a.

Substituting the values for speed and acceleration, we get t=25/(-1/4t^1/2).

Solving for t, we get t^3/2 = -100.

Taking the square root of both sides, we get t=10 seconds.

Now, we can substitute the value of t back into the formula for acceleration to find the magnitude of acceleration just before the car reaches point C.

at= (-1/4t^1/2)m/s^2

= (-1/4)(10^1/2)m/s^2

= (-1/4)(3.16)m/s^2

= -0.79 m/s^2

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There were 65 more adults than students who bought tickets to the concert.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let the number of discounted student tickets sold be x.

Then the number of adult tickets sold is 10 more than twice x, which is 2x+10.

The total number of tickets sold is the sum of the student and adult tickets, which is x + (2x+10) = 3x+10.

We know that the total number of tickets sold is 175, so:

3x+10 = 175

Subtracting 10 from both sides gives:

3x = 165

Dividing by 3 gives:

x = 55

Thus, the number of discounted student tickets sold is 55, and the number of adult tickets sold is:

2x+10 = 2(55) + 10 = 120.

The number of adults who bought tickets is 120, and the number of students who bought tickets is 55.

difference = 120 - 55 = 65

Therefore, there were 65 more adults than students who bought tickets to the concert.

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Answer:

Step-by-step explanation:

kaboom hope this helps

The volume of concrete is required to make the cylindrical tank is approximately 14 cubic meters.

Given that, external diameter = 10 m and an internal height = 3 m.

We know that, the volume of a cylinder is πr²h.

Volume of a tank with external dimensions = 3.14×5²×3

= 3.14×25×3

= 235.5 cm³

The walls and bottom of the tank are 30 cm thick

So, internal diameter = 1000-30 (10 m =1000 cm)

= 970 cm

= 9.7 m

= 4.85 m

Volume of a tank with internal dimensions = 3.14×4.85²×3

= 3.14×23.5225×3

= 221.58195 cm³

So, volume of concrete = 235.5-221.58195

= 13.91805

≈ 14 cm³

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Answer:

483

Step-by-step explanation:

Answer:483

Step-by-step explanation:

69*7=483

Spike-and-slab regression is a method used to model the relationship between a response variable and a set of predictor variables, and nonlinear constraints can be applied to the model to specify relationships between the predictor variables, such as monotonicity or convexity.

Spike-and-slab regression is a statistical method used to model the relationship between a response variable and a set of predictor variables, where the predictor variables are partitioned into two groups: a set of important predictors (spikes) and a set of unimportant predictors (slabs). Nonlinear constraints can be applied to the model to specify relationships between the predictor variables, such as monotonicity or convexity. These constraints can be used to enforce prior knowledge or assumptions about the relationships between the predictor variables, and can help to improve the accuracy and interpretability of the model. Examples of nonlinear constraints that can be used in spike-and-slab regression include the convexity constraint and the total variation penalty.

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The probability of an event can be calculated from the odds against that event. The formula for converting odds against to probability is:

Probability = 1 / (1 + odds against)

So in this case, the odds against winning $1.00 in the lottery are 19 to 1, and the probability of winning can be calculated as follows:

Probability = 1 / (1 + 19) = 1 / 20 = 0.05

So the probability of winning $1.00 in the lottery is 0.05, or 5%.

The temperature 350°F is equivalent to 176.667°C. This is because the temperature in Fahrenheit can be converted to Celsius using the formula, °C = (°F - 32) / 1.8. Using this formula, 350°F - 32 = 318 and 318/1.8 = 176.667°C.

The relationship between Fahrenheit and Celsius scales is a linear one, meaning that for every degree increase in Fahrenheit, there is a corresponding increase of 1.8 degrees in Celsius. This means that if the temperature increases from 350°F to 351°F, then the corresponding temperature in Celsius would increase from 176.667°C to 178.472°C. The same formula can be used to convert Celsius to Fahrenheit, with the formula °F = (°C x 1.8) + 32. In this case, 176.667°C x 1.8 = 319.2 and 319.2 + 32 = 351.2°F, which is a close approximation of the original temperature of 350°F..

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For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.

Non occurrence patterns identifies the absence of events when detecting a pattern.

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The answer to this is 50/12, which is not a whole number. She would need 5 shelves (you have to round up a number because 4 shelves would only be able to fit 48 books)

Answer: 5 shelves  

Step-by-step explanation: you times 12x4 which gives you 48 but you need all 50 so you add a extra shelve so the total shelves is 5

x-intercepts of the curved line are (-2,0) and (0,0)

The points where a line or curve intersects the chart's axes are called intercepts. When a point intersects the x-axis it is called the x-intercept. When a point intersects the y-axis,  it is called the y-intercept.

A line intercept is a point where it intersects  the x-axis or the y-axis. If no axis is specified,  the y-axis is normally considered. It is usually represented by the letter 'b'.

Given,

A curved line with a minimum value of (-1 , -2)

it crosses x-axis at (-2,0) and y-axis at (0,0)

We know that, x-intercept is the point where line crosses x-axis, y-coordinate = 0

x-intercepts are (-2,0) and (0,0)

Hence,  (-2.0) and (0,0) are x-intercepts of the curved line.

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Answer: (–2, 0), (0, 0)

Step-by-step explanation:

Only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.

Neron Co. should report the gains from the fair value hedge related to instrument A in its income statement. This is because fair value hedges are used to offset changes in the fair value of a financial instrument, and any gains or losses from these hedges are recognized in income.

On the other hand, gains from the cash flow hedge related to instrument B should be reported in other comprehensive income, not in the income statement.

This is because cash flow hedges are used to offset changes in the cash flows of a financial instrument, and any gains or losses from these hedges are recognized in other comprehensive income until the hedged item affects income.

Therefore, only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.

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Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

Answer:

  A - scatter plot; it would show the relationship

Step-by-step explanation:

You want to determine if a scatter plot or line graph is a more appropriate way to represent the relationship between a manatee's weight and height.

The variables of concern in the data are weight and height. Time is not involved. (Eliminates choices B and D.)

It seems likely there may not be a functional relationship between weight and height. That is, manatees of the same weight may have different height, and vice versa. This suggests a line graph would not be a useful way to represent the relationship

A scatter plot in this case would be used to relate weight on one axis to height on the other axis. Any relationship between them would show up as grouped data points, or data points that generally fall on a line or curve.

Since the "marine biologist [is] interested in seeing the relationship between a manatee's weight and height", ...

  A scatter plot [is more appropriate] because it would show the association or relationship between the two variables.

__

Additional comment

As is often the case, the wording of the answer that matches the wording of the problem statement tells you which answer is appropriate.

Answer:A scatter plot, because it would show the association or relationship between two variables

Step-by-step explanation:

Answer: Let's call the speed of the airplane in still air "x".

Since the airplane takes 7 hours to fly 2800 kilometers against the wind, its speed against the wind is 2800/7 = 400 km/hr.

Since the return trip with the wind takes only 4 hours, the speed of the wind must be 400 - x.

The total speed of the airplane on the return trip is x + (400 - x) = 400 km/hr.

So, we have:

400 = x + (400 - x)

Expanding the right side:

400 = 400

Therefore, x = 400 km/hr, which is the speed of the airplane in still air.

Step-by-step explanation:

Answer:

W) 1/18=10/180

N) 2/15=4/30

F) 7/12= 84/144

S) 9/25= 36/100

D) 7/20=35/100

T) 9/10=36/40

M) 19/20=95/100

Step-by-step explanation:

W) is 10/180 as you need to multiply the numerator as the denominator.

N) is 4/30 as you need to multiply the numerator as the denominator.

F) is 84/144 as you need to multiply the numerator as the denominator.

S) is 36/100 as you need to multiply the numerator as the denominator.

D) is 35/100 as you need to multiply the numerator as the denominator.

T) is 36/40  as you need to multiply the denominator as the numerator.

M) is 95/100 as you need to multiply the numerator as the denominator.

The measure of the angle is 60 degrees. Option B

It is important to value of the angle, we have to take note of the following;

From the information given, we have that;

The angles 80,690 and x are on a straight line, that is, the sum of the angles is 180

This is represented as;

60 + 80 + x = 180

collect like terms

x = 180 - 140

substract the like terms

x = 60 degrees

Hence, the value is 60 degrees

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Answer:

29.68

Step-by-step explanation:

If you are rounding to the hundredth place, you take the number in the hundredth place and round it. If it is less than five, for example, if you were rounding 29.674 then it would be 29.67 because 4 is not 5 or more. With 29.675 you will round to 29.68. A saying to remember is, five or above, give it a shove.

The area of the rhombus is 384cm²

a rhombus is a type of quadrilateral. It is a special case of a parallelogram, whose all sides are equal and diagonals intersect each other at 90 degrees. This is the basic property of rhombus. The shape of a rhombus is in a diamond shape.

The area of a rhombus is given as:

PQ/2

Where and q are the diagonals of a the rhombus

A = PQ/2

But in these case the rhombus is a parallelogram, therefore the area = base × height

= 20× 19.2

= 384cm²

The area of the rhombus is 384cm²

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Answer:

106.

Step-by-step explanation:

7^2 + [ 81 - (4 x 6)]        First work out the exponential:

= 49 + (81 - (4 * 6)]         Work out the expression in the inner parentheses:

= 49 + [81 - 24]              Work out the expression in the parenthes:      

= 49 + 57                       Add:

= 106.

The equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).

The given expression is c² - 64.

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

1) The factorization of c² - 64 is as follows:

Now, factors of c² - 64 is c² - 8²=(c-8)(c+8)

2) 12y² -75 = 3 (4y²-25)

= 3((2y)²-5²)

= 3 (2y+5)(2y-5)   (∵ a²-b²=(a-b)(a + b))

3) 9y²-36 = 9(y²-4)

= 9(y²-2²)

= 9(y-2)(y+2)   (∵ a²-b²=(a-b)(a + b))

4) -x²+5x-4

= x²-5x+4

= x²-4x-x+4

= x(x-4)-1(x-4)   (∵ a²-b²=(a-b)(a + b))

= (x-4)(x-1)

5) ab²-b

=b(ab-1)

Therefore, the equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).

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