Answer:
Real zeros: x = 2All zeros: x = 2, x = -4i and x = 4iStep-by-step explanation:
[tex]f(x)=x^3-2x^2+16x-32\\\\\text{The zeros:}\\\\f(x)=0\Rightarrow x^3-2x^2+16x-32=0\\\\x^2(x-2)+16(x-2)=0\\\\(x-2)(x^2+16)=0\iff x-2=0\ \vee\ x^2+16=0\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}\\\\x^2+16=0\qquad\text{subtract 16 from both sides}\\x^2=-16<0\qquad\text{no real solutions}\\\\\text{In the set of the complex numbers}\\x^2=-16\to x=\pm\sqrt{-16}\\\boxed{x=-4i\ \vee\ x=4i}[/tex]
What is the median of the data set?
Answer:
8.5
Step-by-step explanation:
5 , 8 , 8 , 8 , 8 , 9 , 9 , 9 , 10 , 10
Cross one from the left and then one from the right
5 , 8 , 8 , 8 , 8 , 9 , 9 , 9 , 10 , 10
8 , 8 , 8 , 8 , 9 , 9 , 9 , 10 , 10
8 , 8 , 8 , 8 , 9 , 9 , 9 , 10
8 , 8 , 8 , 9 , 9 , 9 , 10
8 , 8 , 8 , 9 , 9 , 9
8 , 8 , 9 , 9 , 9
8 , 8 , 9 , 9
8 , 9 , 9
8 , 9
Since you have 2 numbers left, find the number right inbetween the two
Answer is provided in image attached.
The price x of apples varies from 20 cents to 32 cents a pound. Write an inequality that represents this situation.
The inequality is 20¢ ≤ x ≤ 32¢
Simplify the expression square root of 6 times the square root of 33 plus 7
Answer:
3√(22) + 7
Step-by-step explanation:
The way this is worded can be interpreted two different ways so just to cover the bases, I'll do both. I'm confident they are asking for way 1 though because it wants you to simplify the expression, not evaluate. Way 2 gives you a solution rather than an exact equation.
Number 1
√(6) x √(33) + 7
= √(6 x 33) + 7
= √(198) + 7
= √(9 x 22) + 7
= 3√(22) + 7
Number 2
√(6) x √(33 + 7)
= √(6) x √(40)
= √(6) x (4√(10))
= 4√(60)
= 8√(15)
The simplified expression for [tex]\sqrt{6} \times \sqrt{33} + 7[/tex] is [tex]3\sqrt{22} + 7[/tex]
To simplify square root of 6 times the square root of 33 plus 7 we need to first write it mathematically. We get:
[tex]\sqrt6 \times \sqrt{33}+7[/tex]
Using BODMAS, we first multiply the roots. This will give us:
[tex]\sqrt{6} \times \sqrt{33} + 7 = \sqrt{6 \times 33} +7[/tex]
Now we need to expand the digits in square by expressing them as a product of their prime factors so that common pairs can be taken out of the root. This can be done as follows:
[tex]\sqrt{6 \times 33} +7 = \sqrt{(3 \times 2)\times (3\times11)} +7[/tex]
We can see that there are two pairs of 3. Thus we extract 3 times 3 as it is a perfect square for 9 and we get:
[tex]3\sqrt{( 2\times 11)} +7 = 3\sqrt{2}+7[/tex]
Thus, the simplified expression for [tex]\sqrt{6} \times \sqrt{33} + 7[/tex] is [tex]3\sqrt{22} + 7[/tex]
Ok I don't have time to do this i got to study for a history test so can some one simplify these real fast pls
5(2z-1)
(4-2k)8
(15-4a)5
6(n+1.2)
(n-8.2)5
And can u do these
6(n+4)=42. -6(x+8)=0. 3(-4+2r)=-24. 8(-7y-6)=-160
(2a+1.75)2=7.5 (2.3-6n) 1/5=3.14
Thx pals
1. 10z - 5
2. -16k + 32
3. -20a + 75
4. 6n + 7.2
5. 5n - 41
6. n = 3
7. x = -8
8. r = -2
9. y = 2
10. a = 1
11. n = -2.23333333 ( this is the only problem im unsure of answer )
Plz help me i need it
Answer: [tex]\bold{d)\quad f^{-1}(x)=\dfrac{e^x}{5}}[/tex]
Step-by-step explanation:
To find the inverse, swap the x's and y's and solve for y. Note: f(x) is y
[tex]y = ln(5x)\\\\\text{Swap the x's and y's:}\\x=ln(5y)\\\\\text{Apply e to both sides:}\\e^x=e^{ln(5y)}\\\\e^{ln}\ \text{cancels out:}\\e^x=5y\\\\\text{Divide both sides by 5:}\\\dfrac{e^x}{5}=y\\\\\large \boxed{f^{-1}(x)=\dfrac{e^x}{5}}[/tex]
WILL MARK BRAINLIEST!! Complete the statements to find the measurements of ∠a and ∠b .
Answer:
angles b and a both equal 60 degrees
Step-by-step explanation:
a and b are both equal to 60 degrees. A flat angle is 180 and you have the one that’s 120 so that one is 60 and then the last side must be 60 as well because when you add them then subtract it from 180 you get 60
according to the graph of F(x), which of the statements below are true? check all that apply
Answer:
B, E and F
Step-by-step explanation:
This graph is a log which has an asymptote. This means the function does not cross it and does not have in its domain certain numbers. The asymptote is at -2. This means the domain is greater than -2.
The range is the y-values. With no restrictions here, the function includes all numbers.
This means B, E, and F are true.
avery prepares 2 equal size oranges for the bats at the zoo. one dish has 3/8 of an orange. Another dish has 2/8 of an orange. which dish has more orange? show your work.
Answer:
3/8
Step-by-step explanation:
it is greater than 2/8
Find the population of beetles a week later by first finding 6% of 350 and adding it to the original population
Step-by-step explanation:
6 percent of 350 is 21. 21 plus 350 is 371, therefore the answer is 371.
Brainliest? :)
The population of beetles a week later is 371.
The calculation is as follows:= 6% of 350 + 350
= 21 + 350
= 371
Learn more: https://brainly.com/question/9122916?referrer=searchResults
What is the volume of this right rectangular prism? Enter your answer in the box. ft³ 3.5 is the H, 2 is the L and 7 is the W
Answer: 49 feet to the third power
Step-by-step explanation:
1. 3.5 x 2= 7
2. 7 x 7= 49
Answer: [tex]49\ ft^3[/tex]
Step-by-step explanation:
The volume of rectangular prism is given by :-
[tex]\text{Volume}=l*w*h[/tex], hwre l is the length , w is width and h is height of prism.
The given dimensions of rectangular prism :
Length : 2 ft
Width : 7 ft.
Height : 3.5 ft.
Now, the volume of rectangular prism is given by :-
[tex]\text{Volume}=7\times2\times3.5\\\\\Rightarrow\text{Volume}=49\ ft^3[/tex]
Hence, the volume of this right rectangular prism = [tex]49\ ft^3[/tex]
Which solids have the same type of vertical cross sections through the base?
A. A rectangular prism and a cylinder
B. A rectangular prism and a cone
C. A cylinder and a cone
D. A cylinder and a pyramid
Option A. A rectangular prism and a cylinder is the correct option.
Explanation:
First option is true as the vertical cross sections of both rectangular prism and cylinder are rectangles.
Second option is false (The vertical cross section through the base of a rectangular prism is a rectangle)
Third option is false (The vertical cross section through the base of a cone is a triangle)
Fourth option is false (The vertical cross section through the base of a pyramid is a triangle)
A, prism and cylinder is correct.
a packer puts 50 vitamin capsules into a bottle. How many bottles are needed to pack 100 dozen capsules?
Odpowiedź
24
100. 12=1200
1200:50=24
please help the answer i put idk if its correct (brianlest if correct)
Answer:
9,5
Step-by-step explanation:
It's it reflection on the opposite side, so you get (9,5) as they were also given to you.
What is the likelihood that a fair coin will land heads or tails?
which would it be?
0.5
1
0
0.25
Answer:
I believe it is 0.5
Step-by-step explanation:
If you flip a normal coin (called a “fair” coin in probability parlance), you normally have no way to predict whether it will come up heads or tails. Both outcomes are equally likely. There is one bit of uncertainty; the probability of a head, written p(h), is 0.5 and the probability of a tail (p(t)) is 0.5. The sum of the probabilities of all the possible outcomes adds up to 1.0, the number of bits of uncertainty we had about the outcome before the flip. Since exactly one of the four outcomes has to happen, the sum of the probabilities for the four possibilities has to be 1.0. To relate this to information theory, this is like saying there is one bit of uncertainty about which of the four outcomes will happen before each pair of coin flips. And since each combination is equally likely, the probability of each outcome is 1/4 = 0.25. Assuming the coin is fair (has the same probability of heads and tails), the chance of guessing correctly is 50%, so you'd expect half the guesses to be correct and half to be wrong. So, if we ask the subject to guess heads or tails for each of 100 coin flips, we'd expect about 50 of the guesses to be correct. Suppose a new subject walks into the lab and manages to guess heads or tails correctly for 60 out of 100 tosses. Evidence of precognition, or perhaps the subject's possessing a telekinetic power which causes the coin to land with the guessed face up? Well,…no. In all likelihood, we've observed nothing more than good luck. The probability of 60 correct guesses out of 100 is about 2.8%, which means that if we do a large number of experiments flipping 100 coins, about every 35 experiments we can expect a score of 60 or better, purely due to chance.
Answer:
The correct answer option is 0.5.
Step-by-step explanation:
If we have a fair coin then it means that it has a 50 % chance of landing heads up and a 50% chance of landing tails up.
A fair coin is one which has two sides: head and tail.
Since their are two sides to each fair coin, so the probability of landing for each of the side should add up to 1 (which is the total probability).
Therefore, likelihood that a fair coin will land heads or tails is 0.5.
80% of the days in April were sunny, how many days were sunny?
Answer:
24 days
Step-by-step explanation:
April = 30 days
100% = 1.0
80% = 0.8
If 1 x 30 = 30
then 0.8 x 30 = 24
Answer:
24
Step-by-step explanation:
0.8 x 30 = 24
80% = 0.8
April = 30 days
HOPE THIS HELPED!!!!! XD
Can I have brain? please
Find the height of the given pyramid.
2.3m
4.5m
6m
7m
Answer:
The height is 7 m.
Step-by-step explanation:
Volume = 1/3 * area of the base * height, so
28 = 1/3 * 3 * 4 * h
4h = 28
h = 7.
What is the sum of the polynomials?
(–x2 + 9) + (–3x2 – 11x + 4)
–4x2 – 2x + 4
–4x2 – 11x + 13
2x2 + 20x + 4
2x2 + 11x + 5
[tex] - {x}^{2} + 9 - 3 {x}^{2} - 11x + 4 \\ = - 4 {x}^{2} - 11x + 13[/tex]
2nd answer
Answer:
Option B. -4x² - 11x + 13
Step-by-step explanation:
Given polynomials are ( -x² + 9 ) and ( -3x² - 11x + 4 )
We have to add them.
( -x² + 9 ) + -3x² - 11x + 4 )
-x² + 9 - 3x² - 11x + 4
Now we will collect similar terms
( -x² - 3x² ) - 11x + ( 9 + 4 )
-4x² - 11x + 13
Therefore, option B is the answer.
How to do whole number between
ANSWER:
2 and 1/4
Step-by-step explanation:
The area of the surface of a sphere is described by the formula S=4(3.14)r^2. The earth has a radius of 3960 miles and dry land forms 29.2% of the earth’s surface. What is the area of the dry land on earth?
Answer: [tex]57,512,581.63miles^2[/tex]
Step-by-step explanation:
Substitute the value of the radius of the Earth into the formula given in the problem, where r is the radius, to obtain the surface area of the Earth:
[tex]S=4(3.14)r^2\\S=4(3.14)(3,960miles)^2\\S=196,960,896miles^2[/tex]
The problem says that the dry land forms 29.2% of the Earth’s surface, therefore, multiply the surface area by [tex]\frac{29.2}{100}=0.292[/tex]
Threfore, the area of dry land is the following:
[tex]S_{land}=(0.292)(196,960,896miles^2)=57,512,581.63miles^2[/tex]
Final answer:
To find the area of the dry land on Earth, first, calculate the Earth's total surface area with the formula S=4(3.14)r². Given a radius of 3960 miles, this results in about 197,920,640 square miles for the total surface. Multiplying this by 29.2% (or 0.292) gives approximately 57,780,666.88 square miles of dry land.
Explanation:
The question asks for the area of the dry land on Earth, given Earth's radius and the percentage of its surface that is dry land. To find this, first calculate the total surface area of the Earth using the formula S = 4(3.14)r², where r is the radius of the Earth (3960 miles). The formula accounts for the surface area of a sphere. After calculating the total surface area, we then calculate 29.2% of this area to find the dry land's surface area.
Step-by-Step Calculation:
Calculate the total surface area of the Earth: S = 4(3.14)(3960)²
Find the area of the dry land by multiplying the total surface area by 29.2% (or 0.292).
Using the steps above:
S = 4(3.14)(3960)² = 197,920,640 square miles (approx.) as the total surface area.
Area of dry land = 197,920,640 * 0.292 = 57,780,666.88 square miles (approx.).
Explicit formula for the sequence -3,-14,-25,-36
ANSWER
[tex]a_{n}=a_{n-1} - 11 \: \: ,a_1 = - 3[/tex]
EXPLANATION
The given sequence is
[tex]-3,-14,-25,-36,...[/tex]
The first term of the sequence is
[tex]a_1=-3[/tex]
The common difference is
[tex]d = - 14 - - 3[/tex]
[tex]d = - 11[/tex]
The recursive formula is
[tex]a_{n}=a_{n-1} - 11 \: \: ,a_1 = - 3[/tex]
Answer:
aₙ = aₙ₋₁ -11
Step-by-step explanation:
We have given the sequence:
-3,-14,-25,-36
We have to find the explicit formula.
The first term in this sequence is:
a₁ = -3
The common difference is:
a₂-a₁= -14-(-3) = -11
a₃-a₂ = -25-(-14) = -11
a₄-a₃ = -36-(-25)= -11
Common difference d = -11
The general formula is :
aₙ = aₙ₋₁ +d
Here d = -11 so,
aₙ = aₙ₋₁ -11 is the explicit formula.
Choose the graph which represents the solution to the inequality:
-x - 3 < 0
Answer:the answer is B
Step-by-step explanation:
The graph shows how the inequality was resolved: Option B is -X-3 >
What is inequality of a graph?The collection of dots that represents each inequality solution can be found on the graph of a two-variable inequality. The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half.Inequality is the relationship between two expressions or values that are not equal to one another.Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are deemed to be equal. The symbols >,,, or indicate that the two expressions in an inequality are not necessarily equal.To learn more about inequality refer to:
https://brainly.com/question/24372553
#SPJ2
The sum of eighty five and five times a number is equal to twenty. Find the number
Answer:
4.5
Step-by-step explanation:
20= 85+5÷x
85+5=90
20=90÷x
Divide 90 by 20 and you end up with 4.5.
The function f(x) is shown in this graph
Answer:
The correct statement is:
The slope of f(x) is same as the slope of g(x)Step-by-step explanation:
We see that the graph of the function f(x) is a line that passes through (0,2) and (1,-1)Hence, the equation of the function f(x) is calculated by a two-point formula as:
[tex]y-2=\dfrac{-1-2}{1-0}\times (x-0)\\\\y-2=\dfrac{-3}{1}\times x\\\\y-2=-3x\\\\y=-3x+2[/tex]
( On comparing the equation of f(x) with slope intercept form.
i.e. y=mx+c
where m is the slope and c is the y-intercept)
We get slope of f(x)= -3
and y-intercept= 2
The function g(x) is given by:[tex]g(x)=-3x-6[/tex]
Hence, slope of g(x) = -3
and y-intercept= -6
Hence, we get that the slope of f(x) and g(x) is same.
( i.e. -3)
The average snow base at Heavenly Ski Resort is 2 feet in the month of December. In the month of January, the average base is 3 feet. If the snow base increases at about the same rate through the month of March, which is the best estimate for the snow base in the month of March?
A. 2 ft
B. 3 ft.
C. 4 ft.
D. 5 ft.
A point located at (3, -2) is translated right 3 units and down 4 units. What are the coordinates of the image? (0, -2) (6, -6) (6, 2) (0, -6)
Answer:
(6,-6)
Step-by-step explanation:
Because if you move to the right 3 units you add 3 to the x-axis number or in this case 3, so 3+3=6, and if you move down 4 units its the same as subtracting 4 from the y-axis number or in this case -2 so, -2-4=-6. Which gives you (6,-6).
Answer:
(6, -6)
Step-by-step explanation:
Which of the following are solution to the inequality below -4w - 2 < -38
Answer:
w > 9
Step-by-step explanation:
Solve the inequality by using inverse operations.
-4w - 2 < -38
-4w < -36
w > 9
Like solving equations, inequalities should be solved using inverse operations. However, unlike equations, when you divide or multiply by a negative the sign changes.
Use the net below to determine the surface area of the cylinder.
The correct answer should be :
Option 3 : [tex]753.6cm^{2}[/tex]
Hope this helps,
Davinia.
PLZ HELP ME IM STRUGGLING
$15 dollars per adult
$9 per child
We have 4 adults and 5 children.
Adults: 15 x 4 = $60
Children: 9 x 5 = $45
$60 + $45 = $105
Answer: $105
Helppppp please. .........
Answer: 12 feet
Step-by-step explanation: look at the bottom length of the rectangle, it is 10 feet, the missing length of the rectangle should be 10 ft as well. we already know that two of the sides are 3 so we can do 3+3+x=10, x=4. the base of the triangle is 4. We can now use the formula for area of the triangle, 1/2 base*height so 1/2 *6*4= 12 feet, Hope this helps!
full-time job usually means you will work how many hours per week? A. 20 B. 35 C. 40 D. 55 Please select the best answer from the choices provided A B C D
Answer:
C. 40 or B. 35
Step-by-step explanation:
Full time jobs are typically jobs that vary from 35-40 hours a week.
Hope this helps :)
Answer:
C) 40 hours
Step-by-step explanation:
Usually, a full-time job employee works 8 hours per day. There are 7 days in a week where most of employees work 5 days a week, remaining 2 days week off.
Therefore, the number of hours per week = 5 days * 8 hours per day
= 40 hours
Hence, the answer is C) 40