Answer:
25
Step-by-step explanation:
Given the expression x^2 - 10x + 8 = 0.
According to completing the square method
Subtract 8 from both sides
x^2 - 10x + 8 - 8 = 0 - 8
x^2 - 10x = -8
Complete the square
Add the square of half of coefficient of x to both sides
Coefficient of x = -10
Half of Coefficient of x = -10/2
Half of Coefficient of x = -5
Square of Half of Coefficient of x = (-5)^2
Square of Half of Coefficient of x = 25
Add (-5)^2 to both sides
x^2 - 10x + (-5)^2 = -8 + (-5)^2
(x-5)^2 = -8 + 25
(x-5)^2 = 17
Hence the required constant that was added is 25
Let f be a function having derivatives of all orders for allreal numbers. The third-degree Taylor polynomial for f about x=2 isgiven by
T(x) = 7-9(x-2)2-3(x-2)3
a. find f(2) and f '' (2).
b. Is there enough information given to determine wheather fhas a critical point at x = 2?
If not, explain why not.
If so, determine whether f(2) is a relative maximum, arelative minimum, or neither, and justify your answer.
c. Use T(x) to find an approximation for f(0). Is there enoughinformation given to determine whether f has a critical point atx=0?
If not, explain why not.
If so, determine whether f (0) is a relative maximum, arelative minimum, or neither, and justify your answer.
d. The fourth derivative of f satisfies the inequality for all x in the closed interval [0,2]. Use thelagrange error bound on the approximation to f (0) found in part(c) to explain why f (0) is negative.
Solution :
Given : [tex]$T(x)=7-9(x-2)^2-3(x-2)^3$[/tex]
a). f(2) = T(2) = 7
[tex]$\frac{f""(2)}{2!} =-9$[/tex] , so f''(2) = [tex]$-18$[/tex]
b). Yes, since f'(2) = T'(2) [tex]$=$[/tex] 0, [tex]$f$[/tex] does have the critical point at [tex]$x=2.$[/tex]
Since f''(2) = [tex]$-18$[/tex] < 0, [tex]$f(2)$[/tex] is relative maximum value.
c). [tex]$f(0)=T(0)=-5$[/tex]
It is also not possible for determining if [tex]$f$[/tex] has a critical point at x = 0 because [tex]$T(x)$[/tex] gives exact information only at [tex]$x=2.$[/tex]
d). The Lagrange [tex]$\text{error}$[/tex] bound [tex]$=\frac{6}{4!}|0-2|^4= 4$[/tex]
[tex]$f(0) \leq T(0)+4 = -1$[/tex]
Therefore, [tex]$f(0)$[/tex] is negative.
there are 24 marbles in a bag: 2/16 of the marbles are red, 1/8 of the marbles are blue, 1/4 of the marbles are yellow, 1/3 of the marbles are black, 1/6 of the marbles are silver. how many of each type of marble is there?
Answer: 3 red marbles, 3 blue marbles, 6 yellow marbles, 8 black marbles, 4 silver marbles
Step-by-step explanation:
I know these are the correct number of marbles because I set up these numbers as fractions and solved for x.
For examples, 2/16 of the marbles are red. 2/16=x/24
You would do this because we are trying to find the number of marbles that are red out of the 24 marbles.
Next, we would do 24 divided by 16= 1.5 Then 1.5 times 2=3
You would follow this rule for each fraction of marbles in order to find the true number of marbles out of 24.
30 in.
10 in.
10 in.
30 in.
20 in.
Find the area of the arrow above.
square inches
Answer: 45
Step-by-step explanation:
Write a real world problem that can be represented by 10x-40=100
Answer:
10x - 40 = 100, x = 14
Step-by-step explanation:
At a flower shop, there are 10 bouquets with the same amount of flowers in each of them. In total, 40 flowers were purchased. Now, there are 100 flowers left in the shop. How many flowers are in a bouquet?
This situation can be represented by
10x
(the number represents the bouquets, while the variable x represents the amount of flowers in a bouquet)- 40
(this represents the flowers that were purchased)= 100
(this represents the flowers remaining)Solve the system of equations graphically: x – y = 1 and 3x = 3y + 3
Answer:
x=y+1,y=y
Step-by-step explanation:
A trap to catch fruit flies uses a cone in a jar. The cone is shown with a height of 10 centimeters (cm) and a radius of 6 centimeters (cm.)
a. What is the volume of the cone? Write your answer in terms of pi.
b. Explain why an answer in terms of pi is more accurate than an answer that uses 3.14 for pi.
Answer:
120 pi
Step-by-step explanation:
a. 1/3pi(6)^2(10)
just plug them into the calculator using pi.
b. pi is more accurate because you aren't round to 3.14. If you use 3.14 your answer will be rounded and not an exact number.
The volume of the cone is 120π.
Because 3.14 is an approximation to π which is accurate to about one twentieth of a percent.
What is the volume of the cone?The volume of the cone is;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\Where \ r= radius , \ h = height[/tex]
A trap to catch fruit flies uses a cone in a jar.
The cone is shown with a height of 10 centimeters (cm) and a radius of 6 centimeters (cm.)
1. The volume of the cone is;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\ Volume \ of \ cone=\dfrac{1}{3}\times \pi \times 6^2\times 10\\\\ Volume \ of \ cone=\dfrac{1}{3}\times \pi \times 36\times 10\\\\ Volume \ of \ cone=120\pi \\\\[/tex]
The volume of the cone is 120π.
2. Because 3.14 is an approximation to π which is accurate to about one twentieth of a percent.
If you are dealing with everyday physical measurements, this accuracy for π will likely exceed the accuracy of your measurement (such as your height to within a millimetre or four hundredths of an inch!). Hence a calculated answer would not be more accurate than if you simply used 3.14 or, just to be sure, 3.142.
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Evaluate the expression when b=4 and x=-2 .
b-4x
Answer:
12
Step-by-step explanation:
b-4x
Plug in 4 as b and -2 as x
= (4)-4(-2)
Multiply 4 and 2
= 4-(-8)
Two negatives make a positive
= 4+8
= 12
I hope this helps!
The circle radius is 12 cm. Then the circle content is
PLEASE HEEEELP
3x + 2y = 4
X + 2y = -4
Notice the equations are NOT in slope-intercept form.
Rewrite them in slope intercept form y = mx + b.
(+6) ÷ (+2) =
answer choices
+12
+8
+4
+3
-3
Answer:
+3
Step-by-step explanation:
(+6) ÷ (+2)
=6/2
Divide the numbers; 6/2=3
=3
Hope this helped!!!
solve graphically this linear system of equations[tex]\left \{ {{x=3} \atop {y+1=0}} \right.[/tex]
Answer:
(3,-1)
Step-by-step explanation:
The given equations are :
x = 3 ..(1)
y+1 = 0 ....(2)
We need to solve the equations graphically. x = 3 means draw a line parallel to y axis.
For y+1=0
y = -1
Draw a line parallel to the negative x axis. The attached figure shows the graph for the given equations. The solution is (3,-1).
Which expression represents the area of the shaded region?
Given:
A circle of radius r inscribed in a square.
To find:
The expression for the area of the shaded region.
Solution:
Area of a circle is:
[tex]A_1=\pi r^2[/tex]
Where, r is the radius of the circle.
Area of a square is:
[tex]Area=a^2[/tex]
Where, a is the side of the square.
A circle of radius r inscribed in a square. So, diameter of the circle is equal to the side of the square.
[tex]a=2a[/tex]
So, the area of the square is:
[tex]A_2=(2r)^2[/tex]
[tex]A_2=4r^2[/tex]
Now, the area of the shaded region is the difference between the area of the square and the area of the circle.
[tex]A=A_2-A_1[/tex]
[tex]A=4r^2-\pi r^2[/tex]
[tex]A=4r^2-\pi r^2[/tex]
[tex]A=r^2(4-\pi )[/tex]
Therefore, the correct option is (a).
Please help, i need it done by today,
Answer:
x= 28
do i have to explain
Step-by-step explanation:
a cone has a height of 7ft and a radius 4ft. Which equation can find the volume of the cone?
PLEASE I ACTUALLY NEED HELP
Answer:
B
Step-by-step explanation:
equation for volume of a cone = [tex]V=\frac{1}{3}\pi r^2h[/tex]
plug in - [tex]V=\frac{1}{3} \pi (4)^2(7)[/tex]
Answer:
we have
volume of cone =1/3 πr²h=1/3×π×4²×7ft³
so
v=1/3 π(4²)(7)ft³
Andrew is saving up money for a down payment on a car. He currently has $3355, but knows he can get a loan at a lower interest rate if he can put down $4045. If he invests the $3355 in an account that earns 3.7% annually, compounded monthly, how long will it take Andrew to accumulate the $4045? Round your answer to two decimal places, if necessary.
Answer:
5.06 years or 60.75 months
Step-by-step explanation:
Compound interest formula:
[tex]AV=PV(1+\frac{i}{n})^{n*t}\\4045=3355(1+\frac{.037}{12})^{12t}\\1.025=(1.003)^{12t}\\log1.025_{1.003}=12t\\60.75=12t\\5.062[/tex]
5.06 years or 60.75 months
It will take Andrew 5 years to accumulate $4045 by investing $3355 in an account that earns 3.7% annually, compounded monthly.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We can use the formula for compound interest to solve this problem:
[tex]A = P(1 + r/n)^(^n^t^)[/tex]
where:
A is the amount of money at the end of the investment period
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time (in years) of the investment period
In this case, we want to solve for t. We know that:
P = $3355
r = 0.037 (3.7% as a decimal)
n = 12 (compounded monthly)
A = $4045
Substituting these values into the formula, we get:
[tex]4045 = $3355(1 + 0.037/12)^(^1^2^t^)[/tex]
ln(1.206) = 12t ln(1 + 0.037/12)
ln(1.206) = 12t ln(1 + 0.0031)
ln(1.206) = 12t ln(1.0031)
0.187=12t 0.0031
0.187=0.0372t
t=5.02
Therefore, it will take Andrew approximately 5 years to accumulate $4045 by investing $3355 in an account that earns 3.7% annually, compounded monthly.
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How to find volume of a cylinder by using the same dimensions of a cone but only knowing the volume of the cone
Answer:
Multiply the volume of the cone by 3
Step-by-step explanation:
Required
Volume of a cylinder from a cone of the same dimension
The volume of a cone is:
[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
The volume of a cylinder is:
[tex]V_2 = \pi r^2h[/tex]
Recall that:
[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
Split:
[tex]V_1 = \frac{1}{3}*[\pi r^2h][/tex]
Substitute: [tex]V_2 = \pi r^2h[/tex]
[tex]V_1 = \frac{1}{3}*V_2[/tex]
Make V2 the subject
[tex]V_2 =3V_1[/tex]
This implies that, we simply multiply the volume of the cone by 3
What is the value of 9x^2 + 13x – 15, if x = 2
Step-by-step explanation:
Given,
[tex]9 {x}^{2} + 13x - 15[/tex]
and
[tex]x = 2[/tex]
Substitute x = 2 into expression.
[tex]9 {x}^{2} + 13x - 15 = 9( {2}^{2} ) + 13(2) - 15 \\ = 9(4) + 26 - 15 \\ = 36 + 26 - 15 \\ = 62 - 15 \\ = 47[/tex]
Answer:
9(2)×2+13(2)-15
18×2+26-15
36+11
47 is your answer ☺️☺️☺️
In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If students participated in the poll, how many chose Orange?
Answer:
1666.70
Step-by-step explanation: 10,000/6=1666.70
The math teachers decided to throw a party. One teacher bought 7 cookies and 2 ice cream bars for $10.95. Another teacher bought 4 cookies and 3 ice cream bars for $10.25 . How much did one cookie and one ice cream bar cost, individually?
Answer:
0.95, 2.15
Step-by-step explanation:
cookie-x
ice bar-y
7x+2y=10.95 (*3)
4x+3y=10.25 (*2)
21x+6y=32.85
8x+6y=20.5
21x-8x=32.85-20.5=12.35
13x=12.35
x=0.95
2y=10.95-7*0.95=4.3
y=2.15
Arthur wrote that 15 – 14.7 = 3.
Use the drop-down menus to explain why 3 is incorrect.
the point is supposed to be in front of the three
.3
Answer:
the answer is 0.3
Step-by-step explanation:
I hoped this helped
If the longest side of a triangle is 12 inches, what must be true about the lengths of the remaining sides?
SOMEONE HELP ME ILL GIVE YOU 50 POINTS I AM DESPERATE I AM IN A MATHS TEST!
Answer:
12:2
4:24
6:1
Step-by-step explanation:
those 3 are the correct ones
2. A cow gives 24litre milk each day. If the milkman sells 75% of the milk, how many
liters of milk is left with him?
Answer: 6 liters
Step-by-step explanation:
24 liters
He sells 75%
24 x 0.75 = 18 liters
24 - 18 = 6
He still has 6 liters left
What does 5/9 + 1/3 equal to?
Answer:
= 5/9 + 1/3
=5/9 + 3/9
= 5+3/9
=8/9
HELP ASAP!!! find the lines of symmetry. Select all that apply
Answer:
B. and D.
Step-by-step explanation:
If you folded that shape along the lines o and m, it would match up.
There are two lines of symmetry m and o. Options B and D are correct.
From the given figure we have to determine the axes of symmetries.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
As of the given figure,
There are 2 axes of symmetry first line m and the other is line o.
Line l and line n are not symmetrical lines because the reflection of one portion will not be superimposed with the other.
Thus, there are two lines of symmetry m and o. Options B and D are correct.
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Can you give me the answer to this
Answer:
C. a translation of 1 unit right and 2 units up, followed by a dilation by a factor of 3
Step-by-step explanation:
Ariana has 99 oranges. She has to pack 9 boxes with an equal number of oranges. How many oranges should she pack in each box?
Answer:
11 oranges in each box
Step-by-step explanation:
99/9=11
Answer: 11 oranges in each box.
Step-by-step explanation:
Division is used to evenly separate totals into groups (total/#of groups= Quotient per group).
In this case, we divide the total, 99 oranges, by the amount of groups we want, which is 9 boxes, in order to find an even amount for each box from the total oranges.
So, 99/9= 11 oranges per box
1. A cooler is in the shape of a rectangular
prism. What is the volume of the cooler?
Round to the nearest tenth if necessary.
I
Answer:
what is the answerrrrrrrrrrrrrrrrr
Step-by-step explanation:
The volume of the cooler is 2772 in³
What is a volume?Volume is the amount of space taken up by an object
What is the volume of a rectangle?The formula for calculating the volume of a rectangular prism is volume = length × width × height.
According to the question
Length= 22in.
breadth= 12 in.
width= 10 1/2 in. or 21/2 in.
So, the volume= 22× 12× (21/2)
=2772 in³
Thus the volume of a rectangular prism is 2772 in³
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What is the answer when you simplify it?[tex]7^{2} +2(\sqrt{81} +\sqrt{49} )[/tex]
Help PLEASEE!!!!!!!!!!
I think it’s the third one. Hope that helps!
Answer:
the answers are B or C x>4/19