There are two complex roots of the polynomial equation.
What is a polynomial?They are mathematical expressions involving variables raised with nonnegative integers and coefficients and constants with only operations of addition, subtraction, multiplication, and nonnegative exponentiation of variables involved.
We have been given a polynomial expression as;
[tex]-3x^ 4-7x+17=0[/tex]
Since the Degree of a polynomial is the highest power that its terms (for multi-variables, the power of the term is the addition of the power of variables in that term).
Therefore, the highest power of the given polynomial is 4.
Thus, the Maximum possible roots are 4 but; only 2 are real and 2 are complex.
Hence, There are two complex roots of the polynomial equation.
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Can some please help me?!
The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
Which statement correctly describes whether quadrilateral DEFG is a rhombus?
Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.
Quadrilateral DEFG is not a rhombus because there is only one pair of opposite sides that are parallel.
Quadrilateral DEFG is not a rhombus because opposite sides are parallel but the four sides do not all have the same length.
Quadrilateral DEFG is not a rhombus because there are no pairs of parallel sides.
Quadrilateral DEFG is not a rhombus because the four sides do not all have the same length.
Explanation:The coordinates of the vertices of quadrilateral DEFG are D(-2, 5), E(2, 4), F(0, 0), and G(-4, 1). To determine if DEFG is a rhombus, we need to observe the properties of a rhombus. A rhombus has opposite sides that are parallel and all four sides have the same length. Using the distance formula, we calculate the lengths of the four sides of DEFG:
Side DE: √((-2 - 2)^2 + (5 - 4)^2) = 4.12Side EF: √((2 - 0)^2 + (4 - 0)^2) = 4.47Side FG: √((0 - (-4))^2 + (0 - 1)^2) = 4.12Side GD: √((-4 - (-2))^2 + (1 - 5)^2) = 4.47As we can see, the lengths of DEFG's sides are not all the same. Therefore, DEFG is not a rhombus.
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Algebra Help
Let f(x)=6x. The graph of f(x) is transformed into the graph of g(x) by a vertical compression of 1/3 and a translation of 2 units up.
What is the equation for g(x)?
Enter your answer in the box.
g(x)
The correct answers are actually : 2x+2 these are correct bc i just took the test.
Hope this helps.
The graph of f(x) after transforming into the graph of g(x) by a vertical compression of 1/3 and a translation of 2 units up is g(x) = 2x + 2.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The graph of f(x) = 6x
Vertical compression = 1/3.
Translation = 2 units up.
If there is a vertical compression of 1/3 on the graph f(x).
The graph of f(x) = 6x transformed as g(x) = 1/3 x 6x = 2x
Now,
If the graph g(x) 2x has a translation of 2 units up we get,
g(x) = 2x + 2
g(x) = 2(x + 1)
Thus,
The graph of f(x) after transforming into the graph of g(x) by a vertical compression of 1/3 and a translation of 2 units up is g(x) = 2x + 2.
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The probability of choosing a blue block out of a bag containing 4 red, 2 blue, and 4 green blocks.
4 +2 +4 = 10 blocks total
2 are blue so you have a 2/10 which reduces to 1/5 probability of picking blue
To calculate the probability of choosing a blue block from a bag, divide the number of blue blocks by the total number of blocks. In a bag with 4 red, 2 blue, and 4 green blocks, the probability is 2/10, which simplifies to a 20% chance of picking a blue block.
The question is about calculating the probability of selecting a blue block from a bag containing a mix of different colored blocks. When finding the probability of an event, the formula to use is the number of ways the event can happen divided by the total number of outcomes. In the case of the blue block, if a bag has 4 red, 2 blue, and 4 green blocks, there are
A total of 10 blocks (4 red + 2 blue + 4 green).2 favorable outcomes (the blue blocks).To calculate the probability of choosing a blue block, you divide the number of blue blocks by the total number of blocks:
Probability(Blue) = Number of Blue Blocks / Total Number of Blocks
Probability(Blue) = 2 / 10
Probability(Blue) = 0.2 or 20%
The final result is that there is a 20% chance of picking a blue block from the bag.
Which one is true? Thanks
Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles. What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning?
When a pair of lines intersect, the vertical angles are acute.
When a pair of lines intersect, the vertical angles are congruent.
When a pair of lines intersect, all of the angles formed are congruent.
When a pair of lines intersect, all of the angles formed are right angles.
What is the value of a, if a2 – 64 = 0 and a > 0? A) 0 B) 4 C) 8 D) 16
Answer:
C) 8
Step-by-step explanation:
Let's solve for:
[tex]a^2 -64=0\\\\a>0[/tex]
Add 64 to both sides:
[tex]a^2-64+64=0+64\\\\a^2=64[/tex]
Take the square root of both sides
[tex]\sqrt{a^2} = \sqrt{64} \\\\a=\pm 8[/tex]
Therefore, we got two solutions:
[tex]a=8\\\\or\\\\a=-8[/tex]
However, since:
[tex]a>0[/tex]
The only solution is:
[tex]a=8[/tex]
suppose f(x)=x-2. describe the transformation from the graph of f(x) to the graph of g(x)=x+3. Use a graphing calculator to check your answer.
Help Physics Class!!!
F = kx
k = ?
F/x
x/F
F + x
F - x
F= kx
so to get k divide both sides by x
so k = F/x
The length of a rectangle is 3 more than twice its width. the perimeter is 48 feet. find the width.
A marathon is 26 miles 385 yards long . That is about what 1.4 x10 feet how many feet long is half a marathon
I believe that the correct measurement in feet is 1.4 x 10^5 feet. You forgot to include the ^5.
So since that is the measurement of 1 marathon, therefore half a marathon would simply be also half of that, that is:
0.7 x 10^5 feet
or
7 x 10^4 feet
Final answer:
Half a marathon is 69,168 feet in length. To calculate the runner's time for a full marathon at an average speed of 9.5 mi/h, divide the distance (26.2 miles) by the speed, resulting in approximately 2.76 hours or about 2 hours and 45 minutes.
Explanation:
To find the length of half a marathon in feet, we first need to know the length of a full marathon in feet then divide that by 2. Since one marathon is approximately 26.2 miles, we first need to convert miles to feet. There are 5,280 feet in one mile. So, for a full marathon:
26.2 miles × 5,280 feet/mile = 138,336 feet for a full marathon.
Therefore, half a marathon would be:
138,336 feet ÷ 2 = 69,168 feet for half a marathon.
Next, let's look at the question about the marathon runner's time. If a runner averages 9.5 mi/h over a full marathon of 26.2 miles, we can calculate the time taken to run this distance. Time is distance divided by speed, so:
26.2 miles ÷ 9.5 mi/h = approximately 2.76 hours,
which can be converted to minutes: 2.76 hours × 60 minutes/hour = approximately 165.6 minutes or about 2 hours and 45 minutes.
What is the probability of drawing a red card, not replacing it, and then drawing another red card? there are 2 red cards and 3 blue cards
Let's analyse both scenarios: for the first pick, you have 5 cards in total, of which 2 are red. So, you have a chance of 2/5 of picking a red card.
Now, assume you picked a red card with the first pick. The new scenario will be different, now there are only 4 cards in total (since you didn't replace the first picked card), of which only 1 is red. This means that you have a chanche of 1/4 of picking a red card.
Once you figured the probabilities of both events, if you want to compute the probability of the two events happening one after the other, you simply have to multiply them, so you have
[tex] \cfrac{2}{5} \cdot \cfrac{1}{4} = \cfrac{2}{20} = \cfrac{1}{10} [/tex]
Answer:
1/10 is the answer.
Step-by-step explanation:
Every employee works 7 hours per day, Every employee works 5 days per week. Every employee works 49 weeks per year. Every employee works _ days per year, Every employee works _ hours per year. Fill in the blanks.
find the coordinates of the circumcenter of triangle ABC with vertices A(1,4) B(1,2) and C(6,2)
A. 5,2
B. 3,4
C. 2.5,1
D. 3.5,3
Answer:
D. (3.5, 3)
Step-by-step explanation:
Just something simple
The height of a building in a scale drawing is 9cm.The scale is 1:600.Explain how you would use the scale to find the actual height of the building.
The actual height of the building is 54 meters.
The actual height of the building is calculated by multiplying the scale drawing height by the scale factor.
Given that the scale is 1:600, this means that 1 centimeter on the drawing represents 600 centimeters in reality.
Therefore, to find the actual height of the building, one would multiply the height of the building on the scale drawing (9 cm) by the scale factor (600).
Using the scale, the actual height H of the building can be determined as follows:
[tex]\[ H = \text{scale drawing height} \times \text{scale factor} \] \[ H = 9 \, \text{cm} \times 600 \] \[ H = 5400 \, \text{cm} \][/tex]
To convert centimeters to meters, since there are 100 centimeters in a meter, we divide by 100:
[tex]\[ H = \frac{5400 \, \text{cm}}{100} \] \[ H = 54 \, \text{m} \][/tex]
Thus, the actual height of the building is 54 meters.
PLEASE HELP!!! What is the product in simplest form? State any restrictions on the variable. z^2/z+1 times z^2+3z+2/z^2+3z
Hence, the product is:
[tex]\dfrac{z(z+2)}{z+3}[/tex] such that: z≠ -1,0 and -3.
Step-by-step explanation:We are asked to represent the product in the simplest form along with the restrictions applied to z.
We have to evaluate the expression:
[tex]\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z^2+3z}\\\\=\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z(z+3)}[/tex]
Hence,
z≠ -1,0 and -3.
Since, otherwise the denominator will be equal to zero and hence the product will not be defined.
Now, we know that:
[tex]z^2+3z+2=z^2+2z+z+2\\\\z^2+3z+2=z(z+2)+1(z+2)\\\\z^2+3z+2=(z+1)(z+2)[/tex]
Hence,
[tex]\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z^2+3z}=\dfrac{z^2}{z+1}\times \dfrac{(z+1)(z+2)}{z(z+3)}\\\\=\dfrac{z(z+2)}{z+3}[/tex]
( since z and (z+1) term is cancelled as it was same in numerator and denominator)
Hence, the product is:
[tex]\dfrac{z(z+2)}{z+3}[/tex] such that: z≠ -1,0 and -3.
Solve for r: d = rt *
A. d = rt
B. t = d/r
C. r = d/t
D. r = t/d
d =rt
to solve for r divide both sides by t
so r = d/t
Answer is C
The data set below shows the number of cars parked in the restaurant parking lot during the lunch hour each day for two weeks: 8 7 14 10 13 27 11 10 14 7 12 9 14 9 Which of the following statements is true based on the data set? There is one outlier that indicates an unusually small number of cars were in the parking lot that day. There are two outliers that indicate an unusually small number of cars were in the parking lot those two days. There is one outlier that indicates an unusually large number of cars were in the parking lot that day. There are two outliers that indicate an unusually large number of cars were in the parking lot those two days.
Answer:
The data set for two weeks that shows the number of cars parked in the restaurant parking lot during the lunch hour each day is given as:
8 7 14 10 13 27 11 10 14 7 12 9 14 9
The statements that hold true according to the data is:
There is one outlier that indicates an unusually large number of cars were in the parking lot that day( i.e. 27 in one day which is the highest among all the days).Based on the data set, the true statement is: C. There is one outlier that indicates an unusually large number of cars were in the parking lot that day.
What is an outlier?An outlier can be defined as a data value that is either unusually small or large when compared to the overall pattern of the numerical values in a data set.
This ultimately implies that, an outlier lies outside most of the other values in a particular data set, and as such makes them different from the other numerical values.
In this scenario, there is only one outlier in this data set, which is 27 and it simply indicates an unusually large number of cars were in the parking lot that day.
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A lighthouse cast a shadow that is 36 meters long at the same time , a person who is 1.5 meter tall casts a shadow that is 4.5 meters long . Write and solve a proportion to find the height of the lighthouse
To find the height of the lighthouse, set up a proportion using the lengths of the shadows and solve for h. The height of the lighthouse is 12 meters.
Explanation:To find the height of the lighthouse, we can set up a proportion based on the lengths of the shadows. Let h be the height of the lighthouse. The proportion is:
(h / 36) = (1.5 / 4.5)
Now, we can cross multiply and solve for h:
h = (1.5 / 4.5) * 36
h = 12 meters
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What is the equation of a line that is parallel to −2x+3y=−6 and passes through the point (−2, 0) ?
A theme park charges 10 per adult 5 per kid how many tickets sold if total 548 for $3750
The length of a rectangle is 6 m longer than its width. if the perimeter of the rectangle is 48 m , find its area.
Answer:
135m²
Step-by-step explanation:
Perimeter = 2(l + w)
l = w + 6
Substituting for l, gives;
2(w+6+w)
48 = 2w + 12 +2w
48 = 4w + 12
48 - 12 = 4w
36 = 4w
w = 9
Since w = 9, then l = w +6
l = 9 + 6
l = 15
Area = l * w
Area = 15 * 9
Area = 135m²
What are the odds of picking a "g" in the word Georgia?
What is the volume of a cube that measures 5 cm on each side?
a^3+b=c^2 Solve for a and show me how you got that answer
The measures of complementary angles have a sum of 90 degrees. Angle A and angle B are complementary, and their measures have a difference of 20°. What are the measures of the angles?
thanks.
To find the measures of complementary angles A and B with a known difference of 20 degrees, we set up a system of equations and solved them to find that angle A measures 55 degrees and angle B measures 35 degrees.
The problem involves finding the measures of two complementary angles, angle A and angle B, with a known difference in their measures. By definition, complementary angles are two angles whose sum is 90 degrees. Given the difference of 20 degrees between the angles, we can set up a system of equations to solve for their measures.
Let's denote the measure of angle A as a and angle B as b. Therefore, we have the two equations based on the problem statement:
a + b = 90 (because they are complementary)
a - b = 20 (the difference in their measures)
To find the values of a and b, we can add the two equations:
a + b = 90
a - b = 20
By adding them together, we get:
2a = 110
Dividing both sides by 2, we find a:
a = 55
To find b, we substitute a back into one of the original equations:
55 + b = 90
Subtracting 55 from both sides gives us b:
b = 35
Therefore, angle A measures 55 degrees and angle B measures 35 degrees.
What is the smallest positive integer with exactly 14 positive divisors?
The smallest positive integer with exactly 14 positive divisors is 24. The number is found by considering its prime factorization and adding 1 to each exponent, then multiplying the results together. Another prime factor raised to the power of 5 can be included to have exactly 14 divisors.
Explanation:The smallest positive integer with exactly 14 positive divisors is 24.
To find this, we need to consider the prime factorization of the number. Let's express 24 as a product of prime factors: 24 = 2^3 * 3^1.
The number of divisors is found by adding 1 to each exponent in the prime factorization and multiplying them together: (3+1)(1+1) = 4 * 2 = 8. However, we need exactly 14 divisors, so we can multiply 24 by another prime factor raised to the power of 5: 24 * 5^4 = 24 * 625 = 15,000.
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The smallest positive integer with exactly 14 positive divisors is 192. We derived this by using the prime factorization method and finding suitable combinations to get exactly 14 divisors.
To find the smallest positive integer with exactly 14 positive divisors, we need to understand the number of divisors formula. For an integer n = p1e* p2e² * ... * p^ke^k, the number of divisors is given by (e1 + 1)(e² + 1) ... (e^k + 1).
To have exactly 14 divisors, we need (e1 + 1)(e² + 1) ... (e^k + 1) = 14. The factorizations of 14 are 14 = 14 * 1, 7 * 2, or 2 * 7. Let's use the smallest primes to minimize our number:
14 = 14 * 1: This means n = p113. Using the smallest prime number, we have n = 213 = 8192, which is too large.
14 = 7 * 2: This means n = p16 * p21. Using the smallest primes, we get n = 26 * 3 = 64 * 3 = 192.
14 = 2 * 7: This means n = p11 * p26. Using the smallest primes, we get n = 2 * 36 = 2 * 729 = 1458.
Comparing these solutions, the smallest positive integer is n = 192, which has exactly 14 positive divisors.
A baby weighed 7.25 lb at birth at the end of 8 months , the baby weighed 2 1/2 times its birth weight. how many pounds did the baby weigh at the end of 8 month ?
Answer:
The weight of baby at the end of 8 month is 18.125 lb.
Step-by-step explanation:
Given information:
The weight of baby at birth = 7.25 lb
At the end of 8 months, the baby weighed [tex]2\frac{1}{2}[/tex] times its birth weight.
We need to find the weight of baby at the end of 8 month.
[tex]2\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}[/tex]
The weight of baby at the end of 8 month is 5/2 times of its initial weight.
[tex]\text{Total weight}=7.25\times \frac{5}{2}[/tex]
[tex]\text{Total weight}=18.125[/tex]
Therefore the weight of baby at the end of 8 month is 18.125 lb.
Solve for x: −3|x − 3| = −6
Simplify. 1/4+4(1/2−3/4)^2 Enter your answer in the box.
The Simplest form of the expression 1/4+4(1/2−3/4)^2 is 1/2
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
Using PEMDAS
1/4+4(1/2−3/4)^2
Subtract inside parenthesis
(1/2−3/4) = -1/4
Now, Square
1/4+4(-1/4)^2
1/4+4(1/16)
Then Multiply 4 and (1/16)
1/4+(1/4)
Now Adding;
2/4 = 1/2
Hence, The Simplest form of the expression 1/4+4(1/2−3/4)^2 is 1/2
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