if f(x)=6x^4-17x^3-57x^2+153x+27, and the graphing calculator tells you that x=3 and x=-3 are integer roots, algebraically determine when f(x)>0

Answer: 13

Step-by-step explanation:

Answer:

1,-4

Step-by-step explanation:

formula for rotation of 270 is (x,y) to (y,-x)

The area of the triangle FGH is equal to  13√10 unit²

Given that the vertices;

F(-5,-7), G(-2,-5), and H(-6,-2)

We have to find the area of the triangle as;

Area of triangle = 1/2bh²

Here,

Area of triangle FGH = 1/2 (GH) (FG)²

Now,

Length of FG =  √26

Length of GH =  √10

Then,

Area of triangle FGH = 1/2 (GH) (FG)²

Area of triangle = 1/2 × √10 × √26²

Area of triangle = 1/2 × √10 × 26

Area of triangle FGH = 13√10

Therefore,

The area of the triangle FGH = 13√10 unit²

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The volume of Joe chocolate box is 48in³

1. Volume of Joe chocolate box

Given the following dimensions:

length = 6in

height = 2in

width = 4in

Recall that,

Volume = length x width x height

Volume = 6 in x 4 in x 2 in

Volume = 48in³

2. Gift paper to wrap rectangular gift box

To calculate the amount of gift paper required to wrap the rectangular box, we need to find the surface area of the box.

Recall that,

Surface Area = 2(length x width) + 2(length x height) + 2(width x height)

Surface Area = 2(15 in x 10 in) + 2(15 in x 8 in) + 2(10 in x 8 in)

Surface Area = 300 in² + 240 in² + 160 in²

Surface Area = 700in²

3. Quantity of pasta served to Olivia

To find the quantity of pasta served to Olivia, we need to calculate the volume of the rectangular prism lunch box.

The volume of a rectangular prism can be calculated by multiplying its length, width, and height.

Given the dimensions of the lunch box, we have:

Volume = Length x Width x Height

Volume = 5 in x 4 in x 3 in

Volume = 60in³

Therefore, the quantity of pasta served to Olivia is 60in³

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Step-by-step explanation:

sin Φ  = 5/6 = .8333

Arcsin ( sin Φ) =  arcsin (.8333)

Φ = 56.4 degrees

Answer:

x=-17 y=-14 (-17,-14)

Step-by-step explanation:

-2(y-3)+3y=-8

-2y+6+3y=-8

combine like terms

y+6=-8

y=-14

next plug in y to find x

x=-14-3

x=-17

Answer:105.60

Step-by-step explanation:your welcome

One way Olivia might have moved ABCDE onto A"B"C"D"E" is by first reflecting ABCDE over the x-axis, and then translating it 4 units to the left and 6 units down.

1) This would map point A to A", B to B", C to C", D to D", and E to E", creating A"B"C"D"E".

2) Angelica's transformation does not result in a figure that matches A"B"C"D"E". Reflecting ABCDE over the y-axis would map point A to A", B to E", C to D", D to C", and E to B", so the shape would be flipped horizontally. Translating it up 8 units would then shift the shape up, but it would still be horizontally flipped, so it would not match A"B"C"D"E".

3) Michael's claim is not correct. Translating ABCDE diagonally 8 units up and 10 units right would move point A to point J, which is not on A"B"C"D"E". The other points would also not be in their correct positions, so the resulting shape would not match A"B"C"D"E". To get to A"B"C"D"E" with one transformation, Michael would need to use a combination of translation, rotation, and/or reflection.

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Answer:

\(C=120/2=60\)

Step by step Explanation'

To solve this problem, we will need to apply trial-and-error calculation with the binomial distribution, even though it appears like Central Limit Theorem but it's not.

For us to know the value of C , we will look for a minimum integer such that having 'n' number of high performance level of employee has the probability below 0.01.

Determine the maximum value of C, then the maximum value that C can have is 120/n

Let us represent X as the number of employees with high performance with a binomial distribution of

P =0.02( since the percentage of chance of achieving a high performance level is 2%)

n = 20 ( number of employees who achieve a high performance level)

The probability of X= 0 can be calculated

P( X= 0) = 0.98^n

\(P(X=0)=0.98^20\)

\(P(X=0)=0.668\)

\(P(X=1)=0.02*20*0.98^19\)

\(P(X=1)=0.272\)

\(P(X=2)=0.02^2*20*0.98^18\)

\(P(X=2)=0.053\)

Summation of P( X= 0)+ P( X= 1)+P( X= 2) will give us the value of 0.993 which is greater than 0.99( 1% that the fund will be inadequate to cover all payments for high performance.)

BUT the summation of P( X= 0)+ P( X= 1) will give the value of 0.94 which doesn't exceed the 0.99 value,

Therefore, the minimum value of integer in such a way that P(X >2) is less than 0.01 have n= 2

then the maximum value that C can have is 120/n

\(C=120/2=60\)

Answer:

Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day

Step-by-step explanation:

To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.

Let's calculate his average time per day:

Average time per day = Total time / Number of days

Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:

Average time per day = 6 hours / 5

Average time per day = 1.2 hours per day

To convert hours to minutes, we'll multiply the average time per day by 60:

Average time per day = 1.2 hours * 60 minutes

Average time per day = 72 minutes per day

Therefore, Clarence's average time per day is 72 minutes.

Answer:

6688

Step-by-step explanation:

I think, I hope!

The correct sequence for the numbers that are given will be:

It can be seen that from the information given, a number has been attached to each diagram. This will be used in answering the questions given.

Therefore, the correct sequence for the numbers are given will be 6408, 4608, 0846, and 8064.

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The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Answer:

87 is the answer

Hope it helps!!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

4,800 mcg × 0.5^t = 300 mcg

0.5^t = 1/16 = (1/2)⁴

t = 4

Answer:

\(4,800\left(\frac{1}{2}\right)^{t} \, = \, 300; \ 3 \ \text{hours}\)

Step-by-step explanation:

Every hour, the research assistant is removing half the mass from the original 4,800 micrograms of the bacteria culture. So, the mass remaining after t hours can be represented by an exponential expression, a(b)t, where a is the initial mass of the bacteria culture and b is the base of the exponent that represents the decay factor. Since half of the mass of bacteria is being removed every hour, half of the mass remains. So, b = \(\frac{1}{2}\). The exponential expression for this situation is \(4,800\left(\frac{1}{2}\right)^{t}\).

The research assistant will stop removing half the mass from the original bacteria culture after the original bacteria culture has a mass of 300 micrograms. Hence, set the expression for the mass remaining after t hours equal to 300.

\(4,800\left(\frac{1}{2}\right)^{t} \, = \, 300\)

In order to solve this equation for t, the base needs to be isolated. Divide both sides of the inequality by 4,800.

\(\begin{array}{rclC40C40} 4,800\left(\frac{1}{2}\right)^{t} &=& 300\\ \left(\frac{1}{2}\right)^{t} &=& \frac{1}{16} \end{array}\)

Next, rewrite the base of \(\frac{1}{16}\) as a power of \(\frac{1}{2}\). Then, set the exponents equal to each other to solve for t.

\(\begin{array}{rclC40C40C30} \left(\frac{1}{2}\right)^{t} &=& \frac{1}{16} \\ \left(\frac{1}{2}\right)^{t} &=& \left(\frac{1}{2}\right)^{4} \\ t &=& 4 \end{array}\)

So, after 4 hours the research assistant will stop removing half the mass of the bacteria culture.

The perimeter and area of the figure are 41.50mm and 18.50mm².

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

The perimeter of an enclosed space is referred to by the word. A house's property line is found on its outside.

Length of BD=√13²-2²

BD=√165

Length of DC=√36-4

=√32

Area of ABC=Area of ADB+ Area of ADC

=(1/2)(BD)(AD)+ (1/2)(DC)(AD)

=(1/2)(√165)(2)+(1/2)(√32)(2)

Area=√165+√32

=18.50

Perimeter=Perimeter of ADB+ Perimeter of ADC

=(13+2+√165)+(6+2+√32)

=23+√165+√32

=41.50

Therefore, the perimeter and area of the figure are 41.50mm and 18.50mm².

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Answer/Step-by-step explanation:

a. To construct a stem-and-leaf plot for the given sample data, 7, 13, 28, 12, 16, 23, 13, 49, 18, 11, 9, 27, 36, 18, 15, 11, 32, 22, 19, 21, first, order the data from the least to the greatest.

7, 9, 11, 11, 12, 13, 13, 15, 16, 18, 18, 19, 21, 22, 23, 27, 28, 32, 36, 49

The plot would like the one shown below:

Stem | Leaf

0 | 7, 9

1 | 1, 1, 2, 3, 3, 5, 6, 8, 8, 9

2 | 2, 3, 7, 8

3 | 2, 36

4 | 9

Key:

13 = 1 | 3

b.

i. Mean = (7 + 9 + 11 + 11 + 12 + 13 + 13 + 15 + 16 + 18 + 18 + 19 + 21 + 22 + 23 + 27 + 28 + 32 + 36 + 49)/20

Mean = 400/20

Mean = 20

ii. Median = average of the 10th and 11th data value

Median = (18 + 18)/2 = 36/2

Median = 18

iii. Range = max value - min value

Range = 49 - 7

Range = 42

iv. Standard deviation for sample data is given as \( s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} \)

Where,

\( \overline{x} = sample mean = 20 \)

\( x_i = each value of the sample data \)

N = total number of values in the sample = 20

Let's solve:

First, calculate \( (x_i - \overline{x})^2 \) for each data value:

7 => (7 - 20)² = (-13)² = 169

9 => (9 - 20)² = (-11)² = 121

11 => (11 - 20)² = (-9)² = 81

11 => (11 - 20)² = (-9)² = 81

12 => (12 - 20)² = (-8)² = 64

13 => (13 - 20)² = (-7)² = 49

13 => (13 - 20)² = (-7)² = 49

15 => (15 - 20)² = (-5)² = 25

16 => (16 - 20)² = (-4)² = 16

18 => (18 - 20)² = (-2)² = 4

18 => (18 - 20)² = (-2)² = 4

19 => (19 - 20)² = (-1)² = 1

21 => (21 - 20)² = (1)² = 1

22 => (22 - 20)² = (2)² = 4

23 => (23 - 20)² = (3)² = 9

27 => (27 - 20)² = (7)² = 49

28 => (28 - 20)² = (8)² = 64

32 => (32 - 20)² = (12)² = 144

36 => (36 - 20)² = (16)² = 256

49 => (49 - 20)² = (29)² = 841

Next, calculate \( \sum_{i=1}^N (x_i - \overline{x})^2 \) by summing all results gotten above:

= 169 + 121 + 81+ 81 + 64 + 49 + 49 + 25 + 16 + 4 + 4 + 1 + 1 + 4 + 9 + 49 + 64 + 144 + 256 + 841

= 2,032

Next, find \( \frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2 \) by dividing the result you have above by (N - 1):

\( \frac{2,032}{N - 1} = \frac{2,032}{20 - 1} \)

\( \frac{2,032}{19} = 106.947368 \)

Next, calculate \( s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} \) by finding the square root of the result you have above:

\( s = \sqrt{106.947} \)

\( s = 10.34 \) (to 2 d.p)

v. Interquartile Range (IQR) = Third Quarter (Q3) - First Quartile (Q1)

Q1 = (12 + 13)/2 = 25/2 = 12.5

Q3 = (23 + 27)/2 = 50/2 = 25

IQR = 25 - 12.5

IQR = 12.5

c. The distribution of the number of horses nominated for each race in the sample is slightly down-skewed. This indicates that most of lower number of horses nominated for each race in the sample chosen are more common. Most of the data values are below the mean value of 20. Also, the median shows the median number of horses selected to be 18, indicating a lower number.

With the distribution having a range value of 42, extreme value such as 49, seem to be an outlier, as it does not reflect the typical number of horses selected in each race, which are mostly lower.

The length in each circle is:

(a) CD = 19.5 units

(b) UZ = 12.8 units

(a) The Intersecting Secant-Tangent Theorem states that "if two secant lines intersect outside a circle, and a tangent line is drawn from the point of intersection to the circle, then the product of the lengths of the two secant segments is equal to the square of the length of the tangent segment".

Using the theorem, we have:

EC * ED = EG²

6.5 * ED = 13²

6.5ED = 169

ED = 169/6.5

ED = 26 units

ED = EC + CD

26 = 6.5 + CD

CD = 26 - 6.5

CD = 19.5 units

(b) The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

UZ * UW = UX * UY

UZ * 40 = 8 * 64

40UZ = 512

UZ = 512/40

UZ = 12.8 units

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The value of sin A is, 7/25.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle A goes through the point (−24/25,7/25) on the unit circle.

Now, By definition we get;

⇒ cos A = - 24/25

⇒ Sin A = 7/25

Thus, The value of sin A is, 7/25.

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Answer:

The 3rd option would be correct

Step-by-step explanation:

4 is the starting point (b) and 4/3 is the slope (m) hope this helps! Plzz mark brainliest

Answer:

Step-by-step explanation:

h(g(2)) = h( 2²)  = h(4) ; because g(x=2) = 2²

h(4) =  5*4+1 = 21

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Assuming that two straight lines, namely, "s" and "t" are parallel to each other, and another line "d" is perpendicular to "s", the Perpendicular Transversal Theorem can be used among the 4 options provided along with the question statement to prove that "d" is also perpendicular to "t"

As per the question, no information is provided on the conditions of the line or lines. Thus, we are assuming that, two lines, namely, "s" and "t" are parallel to each other, and another line "d" is perpendicular to "s"

We are required to determine the name of the property which we can use to prove that "d" is also perpendicular to "t", based on our above-mentioned assumptions.

Hence, assumed "s" and "t" are parallel to each other, and if another line "d" is parallel to "s", then as per the Perpendicular Transversal Theorem, "d" has to be perpendicular to "t" also.

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The area of the figure is 225 ft²

From the figure shown, we have that it is made up of a triangle and a rectangle.

Now, the formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Such that;

Substitute the values

Area = 1/2 × 10 × 15

Multiply the values

Area = 75 ft²

Area of the rectangle is;

Area = length × width

Area = 10(15)

Area = 150 ft²

Total area = 225 ft²

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Answer:

1/6

Step-by-step explanation:

There are 6 possible numbers for the spinner to land on, and only 1 of those cases will be where the spinner lands on 6.

Therefore, the answer is 1/6

Answer:

9/20

Step-by-step explanation:

0.45 = 45/100

45/100=9/20 (divide numerator and denominator by 5)

20 mph

Here you go!

Answered!

To show that the point (å, ä) is on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ), we need to demonstrate two things: that the point lies on the line segment, and that it is equidistant from the endpoints.

1. Determine the midpoint of the line segment:

  - The midpoint coordinates (\(x_{mid, y_{mid\)) can be found using the midpoint formula:

    \(x_{mid\) = (x1 + x2) / 2 and \(y_mid\) = (y1 + y2) / 2, where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

    In this case, we have (x1, y1) = (Ů, ü) and (x2, y2) = (ĝ, ġ).

2. Calculate the midpoint coordinates:

  - Substitute the values into the midpoint formula to find (x_mid, y_mid).

3. Find the slope of the line segment:

  - Use the slope formula: slope = (y2 - y1) / (x2 - x1).

    Apply the formula to the endpoints (Ů, ü) and (ĝ, ġ) to determine the slope of the line segment.

4. Determine the negative reciprocal of the line segment's slope:

  - Take the negative reciprocal of the slope calculated in the previous step. The negative reciprocal of a slope m is -1/m.

5. Write the equation of the perpendicular bisector:

  - Using the negative reciprocal slope and the midpoint coordinates (\(x_{mid\), \(y_{mid\)), write the equation of the perpendicular bisector in point-slope form: y - \(y_{mid\) = \(m_{perp\) * (x - \(x_{mid\)), where \(m_{perp\) is the negative reciprocal slope.

6. Substitute the point (å, ä) into the equation:

  - Replace x and y in the equation of the perpendicular bisector with the coordinates of the point (å, ä). Simplify the equation.

7. Verify that the equation holds true:

  - If the equation is satisfied when substituting (å, ä), then the point lies on the perpendicular bisector.

By following these steps, you can demonstrate that the point (å, ä) lies on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ).

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