Answers
ANSWER
A. x = 2, √11, -√11
EXPLANATION
To find the zeros of f, which is a 3rd-degree polynomial, we can try some common values to see if any of them is a zero: 1, 2, -1, -2. In this case 2 is a zero of the function:
\(\begin{gathered} f(2)=2\cdot2^3-4\cdot2^2-22\cdot2+44 \\ f(2)=2\cdot8-4\cdot4-44+44 \\ f(2)=16\cdot16 \\ f(2)=0 \end{gathered}\)Now we can reduce our polynomial by dividing it by the factor (x - 2) and obtain a 2nd-degree polynomial, whose zeros are easier to find:
So we can rewrite f(x) as:
\(f(x)=(x-2)(2x^2-22)\)To find the other two zeros we have to solve:
\(2x^2-22=0\)Add 22 to both sides of the equation:
\(\begin{gathered} 2x^2-22+22=0+22 \\ 2x^2=22 \end{gathered}\)Divide both sides by 2:
\(\begin{gathered} \frac{2x^2}{2}=\frac{22}{2} \\ x^2=11 \end{gathered}\)And take square root. Remember that the square root has a positive and a negative result:
\(\begin{gathered} \sqrt[]{x^2}=\pm\sqrt[]{11} \\ x=\pm\sqrt[]{11} \end{gathered}\)So the other two zeros are √11 and -√11.
The three real zeros of f are 2, √11 and -√11
Related Questions
Mina has 462 flowers if she wants to put nine flowers in each phase how many for vases will she have how many flowers will she have left over
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I really need help with this question
Answers
The length of each side of the wood is 5 centimetres.
How to use quadratic equation to find the length of each side of the wood?Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².
Hence, using quadratic equation let's find the length of each side of the wood.
Therefore,
8s² = 200
Hence,
8s² = 200
divide both sides of the equation by 8
s² = 200 / 8
s² = 25
s = √25
s = 5 centimetres
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Mr. Unitech decides to set up a quality candidate poster printing service. It uses the following charging rules for a candidate poster printing: For printing 250 posters or less, a standard cost of K400 is charged. For every poster printed after the first 250 copies, K5 is charged plus the maintenance fee of K50. (a) Write the multiple charging functions for the candidate poster printing service. (b) From your solution to (a), answer the following questions: (i) Calculate the charge for printing 1250 candidate posters. (ii) Calculate the charge for printing 250 candidate posters. (iii) How many candidate posters can be supplied at the cost of K2500? (iv) How many candidate posters can be supplied at the cost of K400?
Answers
By answering the presented question, we may conclude that As a result, expression up to 250 candidate posters may be made for K400.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
(a) For 0 x 250, f(x) = K400.
f(x) = K400 + (x-250)*(K5 + K50) = K400 + K5x + K50 for 250 x (x-250)
(b) I f(1250-250) = K400 + K5(1250-250) = K400 + K6250 + K50000 = K56450
As a result, the cost of producing 1250 candidate posters is K56450.
(ii) We utilise the first charge function to print 250 candidate posters:
f(250) = K400
As a result, the cost of producing 250 candidate posters is K400.
K400 + K5x + K50(x-250) = K2500
Simplifying, K55x = K13750 x = 250
Hence, at a cost of K2500, the maximum number of candidate posters that may be delivered is 250.
(iv)K400 = K400
As a result, up to 250 candidate posters may be made for K400.
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30 POINTS FOR THE GENUIS WHO CAN ANSWER THIS!!
Answers
Answer:
Answers are below in bold
Step-by-step explanation:
1) A = 1/2bh Use this equation to find the area of each triangular base
A = 1/2(8)(6) Multiply
A = 1/2(48) Multiply
A = 12cm² Area of each triangular base
2) A = L x W Use this equation to find the area of the bottom rectangular face
A = 20 x 8 Multiply
A = 160 cm² Area of the bottom rectangular face
3) A = L x W Use this equation to find the area of the back rectangular face
A = 20 x 6 Multiply
A = 120 cm² Area of the back rectangular face
4) A = L x W Use this equation to find the area of the sloped rectangular face
A = 20 x 10 Multiply
A = 200 cm² Area of the sloped rectangular face
5) To find the total surface area of the triangular prism, add together all of the numbers.
A = 12 + 12 + 160 + 120 + 200 Add
A = 504 cm² Total area of the triangular prism
3x3 + 3 x 1 = 3 x (3 +O)
Answers
Answer:
9+3=9
12 is not equal to 9
express as a ordinary numerals
(a)2×7
(b)4×10
Answers
a. 14
b. 40
Work out 5^-2 x cube root of 8
Answer in decimal form please.
Answers
Answer:
0.08
Step-by-step explanation:
\( {5}^{ - 2} \times \sqrt[3]{8} \\ \\ = {5}^{ - 2} \times \sqrt[3]{ {2}^{3} } \\ \\ = \frac{1}{ {5}^{2} } \times 2 \\ \\ = \frac{1}{25} \times 2 \\ \\ = \frac{2}{25} \\ \\ =0.08\)
Select the correct answer from each drop-down menu.
A candy company designs a package to hold chocolates. The height of the container is 13 inches and the diameter of its bottom is 9 inches.
9 in i
13 in
Which shape best models the package, and what is the approximate surface area of the package?
The best model for the package is a
The approximate surface area is
square inches.
Answers
The approximate surface area of the package is approximately 245.05 square inches.
The best model for the package is a cylinder.
To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.
The lateral surface area of a cylinder can be calculated using the formula:
Lateral Surface Area = 2πrh
where r is the radius of the base and h is the height.
The area of the circular base can be calculated using the formula:
Area of Base = \(πr^2\)
Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.
Using the given height of 13 inches, we can now calculate the surface area:
Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches
Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches
To find the total surface area, we add the lateral surface area and the area of the base:
Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches
Therefore, the approximate surface area of the package is approximately 245.05 square inches.
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The factor tree below provides the factors of 18.
18
N.
2
9
3
3
What is the prime factorization of 18?
2 x 3
2 x 9
2 x 3x3
02x3x9
Answers
Answer: it is (c)
i hope this helped :)
Jayda is older than her 12-year-old sister. Write an inequality for j, Jayda's age.
Answers
The inequality states that Jayda's age (j) is greater than 12 i.e., j > 12.
Let j represent Jayda's age.
Since Jayda is older than her 12-year-old sister, we can write the inequality:
j > 12
Thus, the inequality states that Jayda's age (j) is greater than 12.
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One thousand six hundred fifty tickets
were sold at Friday night's football
game. Each adult ticket cost $3.50,
and each student ticket cost $2.00. The
total revenue for ticket sales was
$4,650. Write the pair of equations that
represent the number of a (adult)
tickets and s (student) tickets.
Answers
Answer:
a+s=1650, 3.5a+2s=4650
Step-by-step explanation:
a=adult, s=student
a+s=1650 equation 1
3.5a+2s=4650 equation 2
Simplify the algebraic expression -30y+(-15y)+70
Answers
Answer:
\(-45y + 70\)
Step-by-step explanation:
Step 1: Combine like terms
\(-30y + (-15y) + 70\)
\(-30y - 15y + 70\)
\(-45y + 70\)
Answer: \(-45y + 70\)
-30y+(-15y)+70 is the same as
-30y-15y+70
Combine like terms-45y+70
That's the ans.hope helpful ~
A basket had 15 mangoes. A monkey came and took
away two-fifths of the mangoes. How many mangoes
were left in the basket
Answers
Answer: There are 9 mangoes left in the basket.
Step-by-step explanation:
(2/5) * 15 = 6.
15 - 6 = 9.
formula for density
formula for density
Answers
Answer:
The formula for density (ρ) is:
Density (ρ) = Mass (m) / Volume (V)
Step-by-step explanation:
Where:
Density is measured in units such as kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).Mass is the amount of matter in an object and is typically measured in kilograms (kg) or grams (g).Volume is the amount of space occupied by an object and is typically measured in cubic meters (m³) or cubic centimeters (cm³).please help please please llaodoeoe
Answers
Answer:
(a) 83°
Step-by-step explanation:
You want the measure of angle 5, given that the adjacent angle 6 has a measure of 97° where the lines cross.
Linear pairThe two angles, 5 and 6, are a linear pair, so are supplementary.
∠5 = 180° -∠6
∠5 = 180° -97°
∠5 = 83°
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Urgent 80-90 points if completed!
Complete the table (information you can use and table in images.)
Answers
The required cost function is c(b) = 35b + 475, and the completed table is shown.
What is a function?A function is a relation where every input is connected to only one possible output from a set of available inputs.
Given that, the cost of the plane ticket is $475 and the cost per checked bag is $35.
The cost of b checked bags is $35b.
Therefore, the total cost is:
c(b) = 35b + 475
The completed table is:
Number of bags(b) Total cost c(b)
0 475
1 510
2 542
3 580
4 615
6 685
8 755
Hence, the required cost function is c(b) = 35b + 475.
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the surface area of the sphere is 105 square inches what is the volume of the sphere use 3.14 for pi
Answers
Answer:
The volume of the sphere is \(V\approx101.212 \:in^3\).
Step-by-step explanation:
A sphere is a 3-D figure in which all of the points in a plane are the same distance from a given point, the center of the sphere.
A sphere with radius r has a volume of
\(V=\frac{4}{3} \pi r^3\)
and a surface area of
\(S=4\pi r^2\)
To find the volume of the sphere we use the fact that the surface area of the sphere is 105 \(in^2\) and we use it to find the radius.
\(105=4\pi r^2\\\\4\left(\pi \right)r^2=105\\\\r^2=\frac{105}{4\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{105}{4\pi }},\:r=-\sqrt{\frac{105}{4\pi }}\)
The radius cannot be negative. Therefore,
\(r=\sqrt{\frac{105}{4\pi }}=\frac{\sqrt{105}\sqrt{\pi }}{2\pi }\approx 2.891 \:in\)
Now, that we know the radius we can find the volume
\(V=\frac{4}{3} \pi (2.891)^3=\frac{96.65053\dots \pi }{3}=\frac{303.63661\dots }{3}\approx101.212 \:in^3\)
Suppose that the readings on the thermometers are normally distributed with a mean of 0∘ and a standard deviation of 1.00∘C.
If 12% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
Answers
The reading that separates the rejected thermometers from the others is given as follows:
1.175 ºC.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
\(\mu = 0, \sigma = 1\)
The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.
Hence:
1.175 = X/1
X = 1.175 ºC.
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How can you interpret the inequality?-4x<8-4 times x is less than 8-4 times x is less than or equal to 8-4 times x is greater than or equal to 8-4 times x is greater than 8
Answers
Okay, here we have this:
Considering the provided inequality we are going to interpret it, so we obtain the following:
We can see that the symbol of the inequality is only the smallest, so it means that what is on the left side of the symbol is less than what is on the right side, obtaining the following:
-4 times x is less than 8
A table has an area of x² + 12x + 35. Find the possible dimensions of the table.
Answers
Answer:
x + 7 and x + 5 are possible dimensions
Step-by-step explanation:
x² + 12x + 35 ← factor the quadratic
consider the product of the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)
the factors are + 7 and + 5 , since
7 × 5 = + 35 and 7 + 5 = + 12 , then
x² + 12x + 35 = (x + 7)(x + 5) ← in factored form
now the area A = length × breadth , that is
A = x² + 12x + 35 = (x + 7)(x + 5) , then
length = x + 7 or x + 5
breadth = x + 5 or x + 7
This morning, Jina's car had 24.14 gallons of fuel. Now, 2.7 gallons are left. How much fuel did Jina use?
Answers
24.14 gallons - 2.7 gallons = 21.44 gallons
Therefore, Jina used 21.44 gallons of fuel.
if you know how to do math 30 probability please help answer this question
three events, A, B, C are all equally. If there are no other possible events which of the following statements is true?
a) P(A) = 0
b) P(B) = 1
c) P(C) = 1/3
d) P(D) = 1/2
Answers
Answer: c) P(C) = 1/3
Step-by-step explanation:
P(A) + P(B) + P(C) = 1 (100%)
P(A) = P(B) =P(C)
Using substitution:
P(C) + P(C) + P(C) = 1
3 P(C) = 1
P(C) = 1/3
A straw is placed inside a rectangular box that is 3 inches by 2 inches by 9 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answers
The diagonal of the rectangular box will be 9.7 inches.
Given that:
Length, L = 3 inches
Width, W = 2 inches
Height, H = 9 inches
The diagonal of the rectangular prism is given as,
d² = L² + W² + H²
The diagonal of the rectangular box will be calculated as,
d² = 3² + 2² + 9²
d² = 9 + 4 + 81
d² = 94
d = √94
d = 9.7 inches
The diagonal of the rectangular box will be 9.7 inches.
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Expand -11(5-p) can someone answer that please
Answers
Answer:
-55 +11p
Step-by-step explanation:
-11(5-p)
Distribute
-11*5 -11*(-p)
-55 +11p
Suppose you draw two cards from a standard 52-card deck. Find the probability, when both cards are drawn without replacement, that the first card is a spade and the second card has a different suit.
Answers
There are 4 suits in a standard deck and each hold 13 cards from ace to king. The probability of drawing a spade will be 25% because there is a 1/4 chance. To first draw a spade and then drawing a card that is not a spade is about 75% so if you multiply 0.25 and 0.75 together you get 0.1875 which equals 18.75%
Question 23 options:
The sum of the measures of the exterior angles of a 105-gon is ___ degrees.
Answers
Answer:
360°
Step-by-step explanation:
The sum of the exterior angles of any n-gon is 360°
Does side lengths 4, 8 and 12 form a right triangle?
Answers
Answer:
No it does not form a triangle.
Step-by-step explanation:
If the lengths satisfy the Pythagorean Theorem (a2+b2=c2) then it is a right triangle.
Can someone help please
ASAP
Answers
Answer:
see explanation
Step-by-step explanation:
using the tangent ratio in the right triangle
tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then
∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )
tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then
∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )
AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )
Michael drove 638 miles in 11 hours.
At the same rate, how many miles would he drive in 8 hours?
Answers
she will drive 754 miles in 13 hrs.
A special drill is used at a construction site to dig holes. A hole is dug to a depth of 2.75 feet when the drill hits rock. The progress slows to 5/6 feet per hour of digging. The depth of the hole must be at least 10 1/2 feet by the end of the day to stay on schedule. What is the minimum amount of time the drill must continue at its present rate to complete the hole on schedule? Select from the drop-down menus to correctly complete the statement.
Answers
Answer:
9.3 hrs to finish
Step-by-step explanation:
(10.5 - 2.75)ft / (5/6 ft/hr) = 9.3 hrs to go