Answer:
17 miles
By adding the miles they have traveled, you get you total distance.
21.Factorize : x² +10x+21
22.Factorize: x² -2x-35
23.Solve : 2x+28 = 9x-56
Step-by-step explanation:
21.
x²+10x+21x²+3x+7x+21x(x+3)+7(x+3)(x+3)(x+7)22.
x²-2x-35x²-5x+7x-35x(x-5)+7(x-5)(x-5)(x+7)23.
2x+28=9x-5628+56=9x-2x84=7xx=84/7x=12hope it helps
stay safe healthy and happy..Answer:
21. (x+7)(x+3)
22. (x-7)(x+3)
23. 12
Step-by-step explanation:
X^2+10x+21
(X+7)(x+3)
(We know that 7*3 is equal to 21 and that 7+3= 10)
Now try the same thing for 22.
(X-7)(X+5)
(-7*5= -35 . and -7+5=-2)
23. Use SPOE to get like terms to one side:
-7x=-84
Then use DPOE to find the value of X
x=12
7. Draw an equilateral triangle of side 6.5 cm and after locating its circumcentre. Draw its circumcircle. send it with image
Answer:
Step-by-step explanation:
A circumcircle can be referred to as a circumscribed circle to a triangle. The steps to follow is stated below:
i. Since the triangle is equilateral, draw the triangle with sides 6.5 cm
ii. Bisect any of its two sides. The two bisecting lines would intersect at center, O, of the triangle.
iii. With the center and either radius OA, OB or OC, draw a circumscribed circle to the triangle.
The construction is attached to this answer for clarifications.
The area of a rectangle is 110 square units. Its length measures 11 units. Find the
length of its diagonal. Round to the nearest tenth of a unit.
Answer:
A
=
w
l
d
=
w
2
+
l
2
Solving for
d
d
=
l
2
+
(
A
l
)
2
=
11
2
+
(
110
11
)
2
≈
14.86607
The length of the diagonal of the rectangle is 14.9 units.
What is a diagonal?A diagonal is the longest line that divides a plane shape into two halves.
To calculate the diagonal of the rectangle, we use Pythagoras theorem.
Formula:
A = lw.............. Equation 1Where:
A = Area of the rectanglel = Length of the rectanglew = width of the rectangle.make w the subject of the equation
w = A/l.............. Equation 2From the question,
Given:
A = 110 square unitsl = 11 unitsSubstitute these values into equation 2
w = 110/11w = 10 units.Finally, to calculate the diagonal of the rectangle, we use the formula below
d² = l²+w²............. Equation 3Given:
w = 10 unitsl = 11 units.Substitute these values into equation 3
d² = 10²+11²d² = 100+121d² = 221d = √221d = 14.9 units.Hence, the length of the diagonal of the rectangle is 14.9 units.
Learn more about diagonal here: https://brainly.com/question/654982
#SPJ2
Which of the following is the value of a when the function (x) - 3|xlis written in the standard form of an absolute value
function?
Answer:1
Step-by-step explanation:2
2
The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.
What is meant by an absolute function ?An absolute function is defined as a function which consists of an algebraic expression that is within absolute value symbols.
Here,
The standard form of the absolute value function is written by,
f(x) = a|x|
Given that,
f(x) = 3|x|
Comparing this with the standard form, we get,
a|x| = 3|x|
Therefore, a = 3
Hence,
The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.
To learn more about absolute function, click:
https://brainly.com/question/14364803
#SPJ7
Express the function as the sum of a power series by first using partial fractions. f(x)=x+62x2−9x−5
Answer:
[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}][/tex]
when:
[tex]|x|<\frac{1}{2}[/tex]
Step-by-step explanation:
In order to solve this problem, we must begin by splitting the function into its partial fractions, so we must first factor the denominator.
[tex]\frac{x+6}{2x^2-9x+5}=\frac{x+6}{(2x+1)(x-5)}[/tex]
Next, we can build our partial fractions, like this:
[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]
we can then add the two fraction on the right to get:
[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A(x-5)+B(2x+1)}{(2x+1)(x-5)}[/tex]
Since we need this equation to be equivalent, we can get rid of the denominators and set the numerators equal to each other, so we get:
[tex]x+6=A(x-5)+B(2x+1)[/tex]
and expand:
[tex]x+6=Ax-5A+2Bx+B[/tex]
we can now group the terms so we get:
[tex]x+6=Ax+2Bx-5A+B[/tex]
[tex]x+6=(Ax+2Bx)+(-5A+B)[/tex]
and factor:
[tex]x+6=(A+2B)x+(-5A+B)[/tex]
so we can now build a system of equations:
A+2B=1
-5A+B=6
and solve simultaneously, this one can be solved by substitution, so we get>
A=1-2B
-5(1-2B)+B=6
-5+10B+B=6
11B=11
B=1
A=1-2(1)
A=-1
So we can use these values to build our partial fractions:
[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]
[tex]\frac{x+6}{(2x+1)(x-5)}=-\frac{1}{2x+1}+\frac{1}{x-5}[/tex]
and we can now use the partial fractions to build our series. Let's start with the first fraction:
[tex]-\frac{1}{2x+1}[/tex]
We can rewrite this fraction as:
[tex]-\frac{1}{1-(-2x)}[/tex]
We can now use the following rule to build our power fraction:
[tex]\sum_{n=0}^{\infty} ar^{n} = \frac{a}{1-r}[/tex]
when |r|<1
in this case a=1 and r=-2x so:
[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2x)^n[/tex]
or
[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2)^{n} x^{n}[/tex]
for: |-2x|<1
or: [tex] |x|<\frac{1}{2} [/tex]
Next, we can work with the second fraction:
[tex]\frac{1}{x-5}[/tex]
On which we can factor a -5 out so we get:
[tex]-\frac{1}{5(1-\frac{x}{5})}[/tex]
In this case: a=-1/5 and r=x/5
so our series will look like this:
[tex]-\frac{1}{5(1-\frac{x}{5})}=-\frac{1}{5}\sum_{n=0}^{\infty} (\frac{x}{5})^n[/tex]
Which can be simplified to:
[tex]-\frac{1}{5(1-\frac{x}{5})}=-\sum_{n=0}^{\infty} \frac{x^n}{5^(n+1)}[/tex]
when:
[tex]|\frac{x}{5}|<1[/tex]
or
|x|<5
So we can now put all the series together to get:
[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}}[/tex]
when:
[tex]|x|<\frac{1}{2}[/tex]
We use the smallest interval of convergence for x since that's the one the whole series will be defined for.
The University of Montana ski team has thirteen entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the thirteen team entrants achieve first, second, and third places
Answer:
1716 ways
Step-by-step explanation:
Given that :
Number of entrants = 13
The number of ways of attaining first, second and third position :
The number of ways of attaining first ; only 1 person can be first ;
Using permutation :
nPr = n! ÷(n-r)!
13P1 = 13! ÷ 12! = 13
Second position :
We have 12 entrants left :
nPr = n! ÷(n-r)!
12P1 = 12! ÷ 11! = 12
Third position :
We have 11 entrants left :
nPr = n! ÷(n-r)!
11P1 = 11! ÷ 10! = 11
Hence, Number of ways = (13 * 12 * 11) = 1716 ways
2/3 - 10/9and5/3 and 7/9
Step-by-step explanation:
always Pythagoras with the coordinate differences as sides and the distance the Hypotenuse.
c² = (2/3 - 5/3)² + (-10/9 - -7/9)² = (-3/3)² + (-10/9 + 7/9)² =
= (-1)² + (-3/9)² = 1 + (-1/3)² = 1 + 1/9 = 10/9
c = sqrt(10)/3
Answer:
Step-by-step explanation:
Point 1 ([tex]\frac{2}{3}[/tex] , [tex]\frac{-10}{9}[/tex]) in the form (x1,y1)
Point 2 ( [tex]\frac{5}{3}[/tex] , [tex]\frac{-7}{9}[/tex]) in the form (x2,y2)
use the distance formula
dist = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]
dist = sqrt [ [tex]\frac{5}{3}[/tex] -[tex]\frac{2}{3}[/tex])^2 + ( [tex]\frac{-7}{9}[/tex] - ( [tex]\frac{-10}{9}[/tex] ) )^2 ]
dist = sqrt [ ([tex]\frac{3}{3}[/tex])^2 + ([tex]\frac{3}{9}[/tex])^2 ]
dist = sqrt [ 1 + ([tex]\frac{1}{3}[/tex])^2 ]
dist = sqrt [ [tex]\frac{9}{9}[/tex] + [tex]\frac{1}{9}[/tex] ]
dist = [tex]\sqrt{\frac{10}{9} }[/tex]
dist = [tex]\sqrt{10}[/tex] *[tex]\sqrt{\frac{1}{9} }[/tex]
dist = [tex]\sqrt{10}[/tex] * [tex]\frac{1}{3}[/tex]
dist = [tex]\frac{\sqrt{10} }{3}[/tex]
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 volt, and the manufacturer wishes to test volts against volts, using units. In your intermediate calculations, use z-scores rounded to two decimal places (e.g. 98.76).
(a) The acceptance region is_____. Find the value of a.
(b) Find the power of the test for detecting a true mean output voltage of 5.1 volts.
Answer: hello your question was poorly written but i was able to the get missing parts online which enabled me resolve your question
answer:
a) a = 0.1096
b) 1.89 watts
Step-by-step explanation:
Std of output voltage = 0.25 volt
H0 : μ = 5 volts
Ha : μ ≠ 5 volts
n = 16
a) Acceptance region = 4.9 ≤ X ≤ 5.1
Determine the value of a
value of a = 0.0548 + 0.0548
= 0.1096
attached below is the reaming solution
note : a is a type 1 error
b) power of test
True mean output voltage = 5.1 volts
P = - 1.89 watts
power cant be negative hence the power of the test = 1.89 watts
A woman had 88 goats.20 of them died.how many did he remains with.
Answer:
68 i think..........
Step-by-step explanation:
(⌒_⌒;)
1. Come up with an integer that is BIGGER than 10.
2. Come up with an integer that is SMALLER than 10.
3. Come up with an integer that is BIGGER than 0.
4. Come up with an integer that is SMALLER than 0.
I need help pleaseeee
Answer:
1) any number that is greater than ten is considered an integer bigger than ten: for example, 11, 12, 100, 1000000, etc.
2) any number that is smaller than ten is considered an integer smaller than ten: for example, 9, 8, 7, -100, -100000, etc.
3) any number that is bigger than zero is considered an integer bigger than ten: for example, 1, 2, 10, 100, 100000, etc.
4) any number that is smaller than zero is considered an integer smaller than zero: for example, -1, -2, -3, -10, -100000, etc.
Step-by-step explanation:
An integer is any whole number
Answer:
Step-by-step explanation:
integer bigger than 10 is 11
integer smaller than 10 is 9
integer greater than 0 is 1.
integer smaller than 0 is -1.
Find the least positive integer, written only by numbers 0, 1 and 2, which is divisible by 225.
9514 1404 393
Answer:
1,222,200
Step-by-step explanation:
A search using a computer program found ...
5432 × 225 = 1,222,200
__
1000 mod 225 = 100
4 × 225 = 900
This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.
three friends, akira,bruno and carmela pooled thier money to start a lemonade stand. akria contributes $25, bruno contributed $20 and carmela contributed $35. after a month, thier lemoneade stand had earned 2000, and they want to distribute this money in the same ratio as the money that was invested. how many dollars will brouno recieve
plz explian
9514 1404 393
Answer:
$500
Step-by-step explanation:
Bruno's fraction of the total contribution was ...
Bruno / Total = $20/($25 +20 +35) = 20/80 = 1/4
Then Bruno's share of the earnings is this same fraction, so is ...
(1/4) × ($2000) = $500
IN Ohio, I-75 and I-80 intersect at right angles. What type of lines do I-75 and I-80 form?
Answer:
Step-by-step explanation:
Interesting question
They form at right angles. The reason is the highways meet at right angles is that the United States does something really interesting and well thought out with its highway system.
The odd numbers run North and South
The even numbers run East and West.
So I-75 runs North and South
I-80 runs East and West.
They will, when they meet, form a right angle. This works for the interstates, but there a system for the intrastates as well.
I wish Canada would do something like that.
The number of users of a certain website (in millions) from 2004 through 2011 follows:
Year Period Users (Millions)
2004 1 1
2005 2 5
2006 3 11
2007 4 58
2008 5 145
2009 6 359
2010 7 607
2011 8 846
Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast users (in millions). (Round your numerical values to one decimal place.)
Answer:
y = 26.3x² - 116.9x + 109.6
Step-by-step explanation:
Given the data ;
Year Period Users (Millions)
2004 1 1
2005 2 5
2006 3 11
2007 4 58
2008 5 145
2009 6 359
2010 7 607
2011 8 846
A quadratic regression model can be obtained using a quadratic regression calculator ; The quadratic regression modeled obtained is in the form :
y = Ax² + Bx + C
y = 26.3x² - 116.9x + 109.6
What table represents g(x) = -2•f when f(x) = x + 4
Answer:
-2 is the answer.
Step-by-step explanation:
#CarryOnLearning
Find the values of x for which the denominator is equal to zero for y=x^2/x^2+1 .
Answer:
Step-by-step explanation:
I assume that you mean y = x²/(x²+1), not y = x²/x²+1.
x²+1 = 0
x² = -1
x = ±√(-1) = ±i
deleted: deleted by user
The area of a square is increasing at a rate of 24 centimeters squared per second. Find the rate of change of the side of the square when it is 4 centimeters. The rate of change of the side is Number cm/sec.
Answer:
3cm/s
Step-by-step explanation:
Area of a square is expressed as:
A = L²
Rate of change of area is expressed as:
dA/dt = dA/dL•dL/dt
Given that
dA/dt = 24cm²/s
L = 4cm
Required
dL/dt
Since dA/dl = 2L
dA/dl = 2(4)
dA/dl = 8cm
Subatitute the given values into the formula
24 = 8 dL/dt
dL/dt = 24/8
dL/dt = 3cm/s
PLEASE HELP!!! What is the domain of D(t) as it applies in this situation?!?!
Answer:
This Question Is From The Novel Of The Fantastic Mr.Fox
Q. Boggis , Bunce and Bean are Offering a reward for Mr.Fox , They are tired of Losing Chickens Geese and Cider , Create a Description And Drawing of Mr.Fox to allow him to be captured , use the word bank....
________________________________
Swift | Slay | Ginger | Rough | Fast
Thief. | Clever | Fur | Tail | Wife | Night
Cunning | Bushy | wiry | bush | Den | trick
________________________________
help please!!!!!!!!!!!!!!!!!!!!!:):)
Answer:
1-g
2-b
3-a
4-i
5-f
6-e
7-d
8-c
What is the area of area of 7 meters, 15 meters and 9 meters?
Answer:
10
Step-by-step explanation:
10-7 do it yourself and don't vheat
The value of Tonya's car is $21,000. The car's value depreciates at a rate of 15% per year.
Which function represents the value of the car after t years?
f(t)=0.85(21,000)t
f(t)=1.15(21,000)t
f(t)=21,000(0.85)t
f(t)=21,000(1.15)t
9514 1404 393
Answer:
(c) f(t)=21,000(0.85)^t
Step-by-step explanation:
Each year, the value is multiplied by 1-15% = 85% = 0.85. This is correctly shown in the function ...
f(t)=21,000(0.85)^t
Please help me with the question; It is attached in the image
Answer:
The function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].
Step-by-step explanation:
Firstly, we integrate the function by algebraic substitution:
[tex]\int {x^{2}\cdot e^{2\cdot x^{3}}} \, dx[/tex] (1)
If [tex]u = 2\cdot x^{3}[/tex] and [tex]du = 6\cdot x^{2} dx[/tex], then:
[tex]\int {e^{2\cdot x^{3}}\cdot x^{2}} \, dx[/tex]
[tex]\frac{1}{6}\int {e^{u}} \, du[/tex]
[tex]f(u) = \frac{1}{6}\cdot e^{u} + C[/tex]
[tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} + C[/tex]
Where [tex]C[/tex] is the integration constant.
If [tex]x = 0[/tex] and [tex]f(0) = 0[/tex], then the integration constant is:
[tex]\frac{1}{6}\cdot e^{2\cdot 0^{3}} + C= 0[/tex]
[tex]C = -\frac{1}{6}[/tex]
Hence, the function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].
Wrap your foot by plastic cover. B. Directions: Read the sentences carefully. Write TRUE if the statement is True and FALSE if not. 16. Rain and dull clouds, windy blue skies, cold snow, and sticky heat are very different conditions, yet they are all weather. 17. A weather instrument is any type of measurement device that gives information about the weather. 18. Weather is the mix of events that happen each day in our atmosphere. 19. Weather is different in different parts of the world and changes over minutes, hours, days and weeks. 20. The four letters EW, SW, NE, SN represent the four directions: East West, South West, North East, and South North.
Answer:
16. false
17. True
18. True
19. True
20. false
Step-by-step explanation:
16. all terms are expressions of weather - except for cold snow. "snowfall" would be the weather condition. "snow" itself is the accumulated mass of snowflakes on the ground.
17. that is simply true. there is nothing really to explain.
18. the same as 17. that is the definition of weather.
19. yes, that is part of the explanation of the difference between weather and climate.
20. South North is NOT a direction. it kind of contradicts itself. and what is between South and North ? East and West. so, even from that perspective it is not clear.
overall, what kind of math question is that ? that is more for geography, Earth science, or meteorology or something like this.
in the diagram below, triangle PQR is similar to triangle STU. based on the diagram, select all the equations that are true.
Answer:
ACF
Step-by-step explanation:
angles must be equal since the triangles are similar
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The statement that are correct are x=35, y = 55, and z =90.
What are Similar Figures?Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
Given the ΔPQR is similar to ΔSTU, therefore, the statements that are correct about the two triangles are,
∠P = ∠S = x = 35°
∠Q = ∠T = y
∠R = ∠U = z = 55°
Since the sum of all the angles of a triangle is equal to 180°. For ΔPQR we can write,
∠P + ∠Q + ∠R = 180°
°35 + y + 55° = 180°
y = 180° - 55° - 35°
y = 90°
Hence, the statement that are correct are x=35, y = 55, and z =90.
Learn more about Similar Figures:
https://brainly.com/question/11315705
#SPJ2
Need help on this problem
Answer:
Step-by-step explanation:
[tex]2(x-2)^2=8(7+y)\\2(x-2)^2=56+8y \Rightarrow y={1\over{8}}[2(x-2)^2-56]={1\over{4}}(x-2)^2-7\\finally\\y={1\over{4}}(x-2)^2-7\\let ~change~x~and~y\\x={1\over{4}}(y-2)^2-7\\x+7={1\over{4}}(y-2)^2\\4(x+7)=(y-2)^2\\y-2=\pm\sqrt{4(x+7)}\\\\y=2\pm\sqrt{4x+28}[/tex]
a total of 678 tickets were sold for the school play. They were either adult tickets or student tickets. there were 72 fewer student tickets sold than adult tickets. how many adult tickets were sold
Step-by-step explanation:
678-72=606/2=303+72=375
Given: f(x) = x- 7 and h(x) = 2x + 3
Write the rule for f(h(xc)).
Answer:
[tex]f(h(xc)) = 2xc-4[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 7[/tex]
[tex]h(x) = 2x + 3[/tex]
Required
[tex]f(h(xc))[/tex]
First, calculate h(xc)
If [tex]h(x) = 2x + 3[/tex]
Then
[tex]h(xc) = 2xc + 3[/tex]
Solving further:
[tex]f(x) = x - 7[/tex]
Substitute h(xc) for x
[tex]f(h(xc)) = h(xc) - 7[/tex]
Substitute [tex]h(xc) = 2xc + 3[/tex]
[tex]f(h(xc)) = 2xc + 3 - 7[/tex]
[tex]f(h(xc)) = 2xc-4[/tex]
Please help me as soon as possible
Answer:
I think the choose (B)
5x/x + 3/x
Answer:
I thinkchoose no.3
5x+3
5x+3x
if angle ACB = angle DCD, angle BAC = 3x-10, angle ECD= 45degrees, and angle EDC = 2x+10 wgat is x
Answer:
x = 20
Step-by-step explanation:
3x -10 = 2x +10
x = 20
1. 650 - 700 - 800 = ?
2. 25 - 45 + 23 ＝?
carry on learning
Answer:
- 850
3
Step-by-step explanation:
650 - 700 - 800
650 - 1500
- 850
25 - 45 + 23
- 20 + 23
3
