Given :
Three roots , [tex]\sqrt{7},\ -\sqrt{7},\ -4[/tex] .
To Find :
A cubic function with the given zeros.
Solution :
Equation of polynomial of 3 zeroes is given by :
[tex](x-a_1)(x-a_2)(x-a_3)=0\\\\(x-\sqrt{7})(x+\sqrt{7})(x+4)=0\\\\( x^2-7)(x+4)=0\\\\x^3+4x^2-7x-28=0[/tex]
Therefore, the cubic function of given zeroes is [tex]x^3+4x^2-7x-28=0[/tex].
Hence, this is the required solution.
is -3 a whole number and/or a natural number?
Answer: -3 is natural and a whole number can be equivalent to the natural numbers
Step-by-step explanation:
Look at this picture this will help!
Which shows two products that both result in negative values? (–2.4)(1.8) and (–0.6)(–0.4) (–2.4)(–1.8) and (–0.6)(–0.4) (2.4)(–1.8) and (0.6)(–0.4) (2.4)(–1.8) and (–0.6)(–0.4)
Answer:
I think right answer is C
Step-by-step explanation: I hope that I am right Hope this helped
The multiplication of (2.4)(–1.8) and (0.6)(–0.4) gives negative values option third is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
As we know, by the arithmetic operation rule
Multiplication of two negative values is positive.
Multiplication of one negative and one positive value is negative.
Multiplication of two positive values is positive.
In option third:
(2.4)(-1.8) = -4.32
(0.6)(-0.4) = -0.24
Thus, the multiplication of (2.4)(–1.8) and (0.6)(–0.4) gives negative values option third is correct.
Learn more about the arithmetic operation here:
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At a high school, 85 students are enrolled in fine arts, 51 are enrolled in history, and 23 are enrolled in both subjects. How many students are taking fine arts or history?
Fine arts= 85 students
History= 51 students
Both subjects=23 students
Only Fine arts=85-23=62 students
Only History=51-23=28 students
Hope you found it helpful.
Evaluate this expression:
10x^2-5x+10 When x= -3
Step-by-step explanation:
10x² - 5x + 10
x = -3
10(-3)² -5(-3) + 10
= (10×9) + 15 + 10
= 90 + 15 + 10
= 115
A pair of jeans cost $30. There is a 6% sales tax determine the total cost of the jeans
Answer:
31.80 in total
Step-by-step explanation:
multiply 30 by 0.0 and get 1.8, then add that o 30! hope this helps!
Rashad is having a picnic for 62 guests. He plans to serve each guest at least one hamburger. If each package, p, contain eight hamburgers, write the inequality that could be used to determine how many packages of hamburgers will Rashad will need to buy
Answer: 59
Step-by-step explanation:
Which two integers is 47 between
Answer:
46 and 48
Step-by-step explanation:
On a 210-mile trip, Cameron drove at an average speed of 60 miles per hour for the first x hours. He then
completed the trip, driving at an average speed of 50 miles per hour for the remaining y hours. If x = 1,
what is the value of y?
y =
Answer:
[tex]y = 3[/tex]
Step-by-step explanation:
Given
Trip = 250 miles
Speed for first x hours = 60 miles/hour
Speed for next y hours = 50 miles/hour
x = 1
Required
Find y
To solve this question, we'll make use of:
[tex]Distance = Speed * Time[/tex]
For x hours:
[tex]Distance = 60miles/hour * x[/tex]
Substitute 1 hour for x
[tex]Distance = 60\ miles/hour * 1\hour[/tex]
[tex]Distance = 60\ mile[/tex]
For y hours:
[tex]Distance = 50\ miles/hour * y\ hours[/tex]
[tex]Distance = 50y\ miles[/tex]
Given that total distance is 210 miles;
We have that:
[tex]Total Distance = 60\ miles + 50y\ miles[/tex]
[tex]210\ miles = 60\ miles + 50y\ miles[/tex]
Solve for y
[tex]210 - 60 = 50y[/tex]
[tex]150 = 50y[/tex]
[tex]y = \frac{150}{50}[/tex]
[tex]y = 3[/tex]
Hence,
y = 3 hours
X- (9× - 10) +11=12× +3 (2x + 1/3)
change 14 % into ratio into simplest form
Answer:
7:50
Step-by-step explanation:
% means /100
14 % =
[tex]14 \% \\ \frac{14}{100} [/tex]
Cross cancel common factor : 2
[tex] = \frac{7}{50} [/tex]
Write in ratio form
[tex] \frac{7}{50} \: or \: 7:50[/tex]
☽------------❀-------------☾
Hi there!
~
[tex]14[/tex]% [tex]= \frac{5}{8}[/tex]
5/8 stays the same even if its in simplest form. Simplify 5/8 reduces the fraction 5/8 to the lowest form. You can change the numerator or denominator to simplify any other fraction.
❀Hope this helped you!❀
☽------------❀-------------☾
Apply the distributive property to create an equivalent expression 1/5(15+10k)
Answer:
3 + 2k
Step-by-step explanation:
1/5(15+10k)
distribute
1/5 * 15 + 1/5 * 10k
3 + 2k
Answer:
3 + 2k
Step-by-step explanation:
First, I am going to explain what the distributive property is. Lets say he had the expression a(b + c). We can "distribute" the a to the b and c:
a(b + c) = ab + ac
We can apply the distributive property to the expression 1/5(15 + 10k):
1/5(15 + 10k)
= (1/5)(15) + (1/5)(10k)
= 3 + 2k
By using the distributive property, we found the expression 3 + 2k.
I hope you find my answer helpful.
Solve 3(k + 8) = 21
A. 3
B. 13
C. -1
D. 7
Answer:
C
Step-by-step explanation:
3(k+8)=21
3k+24=21
3k=-3
k=-1
Answer:
Step-by-step explanation:
3k + 24 = 21
3k = -3
k = -1
answer is C
Find the solution set of the following quadratic equations using the quadratic formula.
1.) x^2 - 7x + 9 = 0
2.) 3x^2 + 10x = -3
Answer:
1) [tex]x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2[/tex] 2) [tex]x_1=-\dfrac13\,,\quad x_2=-3[/tex]Step-by-step explanation:
1)[tex]x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}2\\\\x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2[/tex]
2)[tex]3x^2 + 10x=-3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b =10\,,\ c=3\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-10\pm\sqrt{10^2-4\cdot3\cdot3}}{2\cdot3}= \dfrac{-10\pm\sqrt{100-36}}6\\\\x_1=\dfrac{-10+\sqrt{64}}6=\dfrac{-10+8}6=-\dfrac13\,,\qquad x_2=\dfrac{-10-8}6=-3[/tex]HELP PLS, 40points and brainliest!!! Find the volume of a cone with a base radius of 4 cm and a height of 12 cm.
Answer:
no
Step-by-step explanation:
why do i need the ± sign before the answer? my teacher said it needed to be there but i'm not sure why it has to be or when to use it. can someone pls explain why i need the ± sign? thank u sm
i attached the work i did for the problem, the equation was y = 2/3x^2-5 and i had to find the inverse of it
Answer:
THe reason u need the ± is so that way u know that it is both neg and positive also it helps the teacher grade the work.
Hopefully this helps u out if u need more help pls feel free to text me back
Step-by-step explanation:
5=5ax+1 please help, its due in an hour.
solve for x
Answer:
x= 4/5a
Step-by-step explanation:
5=5/ax+1
Step 1: Multiply both sides by a.
5a=a+5x
Step 2: Flip the equation.
a+5x=5a
Step 3: Add -a to both sides.
a+5x+−a=5a+−a
5x=4a
Step 4: Divide both sides by 5.
5x/5=4a/5
x= 4/5a
Hope this helps!
Simplify to a single power of 4: \frac{4^{8} }{4^{5} }
Answer:
4^3 or 64
Step-by-step explanation:
[tex]\frac{4^{8} }{4^{5} }\\\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{4^8}{4^5}=4^{8-5}\\\\4^{8-5}=64\\\\or\: 4^3[/tex]
Using compatible numbers, which is the best estimate of (28.5)(7.1)
Answer:
203
Step-by-step explanation:
estimate 28.5 = 29
estimate 7.1 = 7
there for 29 x 7 = 203
I had the same question!!!The required estimated value of the given expression is 202.
What is an estimate of the numbers?The estimate is defined as a rough view calculation that helps to predict where the product value lies.
Here,
Given expression,
= (28.5)(7.1)
Multiplying the number under the parenthesis,
Gives,
= 202.35
Now, rounding the numbers, Since the number after the decimal place is close to zero,
= 202.
Thus, the required estimated value of the given expression is 202.
Learn more about round the decimal here;
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Jerome bought a sweater that was on sale for 20 percent off. Jerome paid $25.10 for the sweater, including sales tax of 8.25 percent. Write and solve an equation that can be used to find the original price of the sweater. And How much money did jerome save by buying the sweater on sale?
Answer: The picture is attached with the answer and the explanation.
Step-by-step explanation:
need to solve by factoring!!
49x² - 36 = 0
Properties of Special Triangles:
Calculate the size of angle AEF
Answer:
90 degrees
Step-by-step explanation:
Answer:
The angle of AEF is 90°.
Step-by-step explanation:
Given that DEF is an equilateral triangle so all angles are the same which is 60° and in a regular square, all angles are 90°. Next, we have to find ∠ADE :
∠EDF = 60° / ∠CDF = 180° / ∠CDA = 90°
∠ADE = 180° - ∠EDF∠CDA
∠ADE = 180° - 60° - 90°
∠ADE = 30°
Given that ADE is an isosceles triangle so ∠ADE and ∠AED have the same angles. Lastly, we have to find ∠AEF by adding ∠AED and ∠DEF together :
∠AED = 30° / ∠DEF = 60°
∠AEF = ∠AED + ∠DEF
∠AEF = 30° + 60°
∠AEF = 90°
HELP PLS i need this right now
Answer:
16.6
Step-by-step explanation:
By the property of intersecting secants outside of a circle, we have:
[tex]5 \times (5 + x) = 6 \times (6 + 12) \\ 25 + 5x = 6 \times 18 \\ 25 + 5x = 108 \\ 5x = 108 - 25 \\ 5x = 83 \\ x = \frac{83}{5} \\ x = 16.6[/tex]
Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function?
The graph of h(x) passes the vertical line test.
The graph of the inverse of h(x) is a vertical line.
The graph of the inverse of h(x) passes the horizontal line test.
The graph of h(x) passes the horizontal line test.
Answer:
The correct option is;
The graph of h(x) passes the horizontal line test
Step-by-step explanation:
In order to determine if a function has an inverse, and also if the inverse of the function is also a function, the function can be tested by drawing an horizontal line the graph of the function and viewing to find the following conditions;
A graph of a function that is intersected at only one point in all places (vertically) by an horizontal line indicates that the function has an inverse that is also a function, while a graph of a function that is intersected at more than one point in some places (vertically) by an horizontal line indicates that the function does not have an inverse that is also a function.
Answer:
D
Step-by-step explanation:
EDGE 2020
if DE = 4x - 1, EF = 9, and DF = 9x - 22, find the value of x.
Answer: x=6
Step-by-step explanation:
Answer: x=6
Step-by-step explanation:
teacher told
what is 27,430,000 as a scientific notation
Answer:
2.743 × 10^7
Step-by-step explanation:
The reason as to why 10 is to the 7th power is because the number that you turn into scientific notation (27430000), needs to be in ones form. Which is 7 decimal places away.
F(x) = 3x3+ 8x-2
k(x) = 4x
What is the value of K(F(x))?
Answer:
[tex]k (3x^3 + 8x - 2) = 12x^3 + 32x - 8[/tex]
Step-by-step explanation:
Set up the composite result function.
k (F (x))
Evaluate k (F (x)) by substituting in the value of into.
[tex]k (3x^3 + 8x - 2) = 4 (3x^3 + 8x - 2)[/tex]
Apply the distributive property
[tex]k (3x^3 + 8x - 2) = 4 (3x^3) + 4 (8x) + 4(-2)[/tex]
Simplify
Multiply 3 by 4.
[tex]k (3x^3 + 8x - 2) = 12x^3 + 4 (8x) + 4(-2)[/tex]
Multiply 8 by 4.
[tex]k (3x^3 + 8x - 2) = 12x^3 + 32x + 4(-2)[/tex]
Multiply 4 by -2.
[tex]k (3x^3 + 8x - 2) = 12x^3 + 32x - 8[/tex]
PLEASE HELP I WILL MARK YOU BRAINLIEST THERE IS A PICTURE AT THE BOTTOM.
Answer:
72 sq. inches
Step-by-step explanation:
We are trying to find the area of the shaded part, and so we start with finding the area of the entire half that is marked (the area with measurements). The length is 8 in, as seen on the bottom, and the height is 12 in, as seen on the side. 8 * 12 = 96, so the entire portion from the shaded part to the very right is 96 sq. inches. Now we have to take out the white triangle part to find the area of the shaded part. Area of a triangle = 1/2*base * height, so we multiply 1/2 * 12 * 4, which gets us 24. Now that we know the area of the triangle, we subtract it from the previous area we got, which was the area of the shaded part plus the triangle (96). 96 - 24 = 72, so the area of the shaded portion is 72 sq. inches. Hope this helps!
Write an equation that represents the line.
Answer:
Step-by-step explanation:
(0,3) (2,6)
(6 - 3)/(2 - 0) = 3/2
y - 3 = 3/2(x - 0)
y - 3 = 3/2(x - 0)
y = 3/2x + 3
Question 10(Multiple Choice Worth 1 points)
(01.04 LC)Solve (−3) ⋅ 2.
−6 please help
−5
5
6
Answer:
A —6
Step-by-step explanation:
Oscar measured a community college and made a scale drawing. The scale he used was 5 millimeters: 3 meters. The actual length of a building at the college is 111 meters. How long is the building in the drawing?
Answer:
It is 50
Step-by-step explanation:
Answer:
32 milimeters
Step-by-step explanation:
