Answers
Answer:
Step-by-step explanation:
#1.
2x² + 24x + 10 = 0
2(x² + 12x + 5) = 0
2[ x² + 2(6)x + 6² - 6² + 5 ] = 0
2[(x + 6)² - 31] = 0
2( x + 6 - √31 )( x + 6 + √31 ) = 0
[tex]x_{1}[/tex] = - 6 + √31
[tex]x_{2}[/tex] = - 6 - √31
#2.
f(x) = 3x² - 36x - 12
f(x) = 3( x² - 12x - 4 )
f(x) = 3 [ x² - 2(6)x + 6² - 6² - 4 ]
f(x) = 3 [( x - 6 )² - 40 ]
f(x) = 3( x - 6 )² - 120
Related Questions
the length of the diagonal of a square is 15 square root of 2 what is the perimeter
Answers
Solution:
Given:
Diagonal of square: 15√2Perimeter of square: 4sSolving using Pythagoras theorem~
(15√2)² = s² + s²=> 225 x 2 = 2s² => 225 = s² => s = 15 unitsNow, solve for perimeter by substituting into the term '4s'.
4(15)=> 60 unitsHence, the perimeter of the square is 60 units.
Type the integer that makes the following addition sentence true:
Answers
Answer:
93
Step-by-step explanation:
Add 36 to both sides of the equation:
36 -36 + ___ = 36 +57
0 + ___ = 93
___ = 93
The integer 93 goes in the blank.
What is the product of 25.785 and 0.27?
Answers
Answer:
6.96195
Step-by-step explanation:
Solve by multiplying
25.785
0.270
------------
6.96195
If you made 30$ every 5 minutes, how much would you have in 10 hours?
Answers
as how 5 minutes = $30 so 5x 12 to represent 1 hour so 12x 30 for $360 then 360 x 10 for the ten hours
Pls help I don’t understand
Answers
It appears the graph goes through (0,3) and (5,6)
If so, then you have the correct slope and y intercept.
The formula is [tex]C = \frac{3}{5}n+3[/tex] which is the same as writing C = (3/5)n+3
Don't forget about the parenthesis around the 3/5.
We can verify this by plugging in n = 0 and you should get C = 3.
Also, if n = 5 then it leads to C = 6.
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answers
Answer:
An example would be... slope intercept form is y=mx+b m being the slope b equal the y-intercept. so an equation would be y=3x+7 3 is the slope and 7 in the y-intercept. I am giving you this way because i do not know what points the graph are going through. And do not know what the graph looks like.
If anyone can answer this question i would greatly appreciate it!! <3
An apartment rents for $665/month. To start renting, you need the first and last
month's rent, and a $650 security deposit. You also have upfront costs of $126 for
a year of tenant insurance, $95 hookup fee for phone and internet, and $80 TV
hookup fee. What is the total amount you need to begin renting the apartment?
Answers
$665 first month
$665 last month
$650 security dep
$126 tenant insurance
$95 phone and internet
$80 tv
______
$2281
You need $2281 to rent the appointment
The total amount need to begin renting the apartment is $2281.
What is rent?An agreement where a fee is paid for the temporary use of a good, service, or property owned by another is known as renting, sometimes known as hiring, or letting.
We have,
An apartment rents for $665/month.
$95 hookup fee for phone and internet, and $80 TV hookup fee.
So, the total amount
= 665 + 665 + 650 + 126 + 95 + 80
= $2281
Thus, the total amount for rent is $2281.
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Which of the following statements about variables is false? a. Mathematical operations can be performed on a variable. b. The variable will always be the letter x. c. A mathematical statement can include more than one variable. d. A variable is a letter used to represent an unknown quantity.
Answers
Answer:
b. The variable will always be the letter x (false)
Step-by-step explanation:
Variables can be any letter or symbol. The letter x is often used as a variable, but that is not the only choice. Many formulas, for example, make use of variables that have letters reminding you what they stand for.
For example, the formula ...
A = 1/2(b1 +b2)h
uses the variables A, b1, b2, and h to represent area, base-1, base-2, and height, respectively. The letter x is not used at all.
Pleaseeeee hellppppdosbshsb I NEED TO KNOW!!!
Answers
Answer: [tex]y = 3\sin\left(\frac{x}{3}\right)\right)+2\\\\[/tex]
This is the same as writing y = 3sin(x/3) + 2
=====================================================
Explanation:
The template for a sine function is
[tex]y = A\sin\left(B\left(x-C\right)\right)+D\\\\[/tex]
where,
A = deals with the amplitudeB = deals with the periodC = phase shiftD = midline---------------
The highest point is at y = 5 and lowest is at y = -1. This is a gap of 6 units, which cuts in half to 3. The amplitude is 3 meaning that A = 3.
---------------
One peak or highest point occurs when x = 3pi/2
The next peak over is at x = 15pi/2
This is a gap of (15pi/2) - (3pi/2) = 12pi/2 = 6pi units
The period is T = 6pi which leads to B = 2pi/T = 2pi/6pi = 1/3
In short, B = 1/3
---------------
We don't have to worry about the phase shift, so C = 0.
---------------
The midline is the average of the highest and lowest y values.
D = (5+(-1))/2 = 4/2 = 2
This means D = 2.
---------------
In the previous sections, we found the following
A = 3B = 1/3C = 0D = 2This means we go from
[tex]y = A\sin\left(B\left(x-C\right)\right)+D\\\\[/tex]
to
[tex]y = 3\sin\left(\frac{1}{3}\left(x-0\right)\right)+2\\\\y = 3\sin\left(\frac{x}{3}\right)\right)+2\\\\[/tex]
which is the final answer.
---------------
Extra info:
If you wanted, you could use a cosine function. This is because any cosine function is a phase shift of a sine function. But that greatly complicates things and sine is better suited here.
1. Angle BAC = 35° and angle BCA = 20°. What is the measure of angle BAD?
2. What is the measure of angle ABC?
Answers
Check the picture below.
Surface area help I am struggling
Answers
Answer:
Total Surface Area: 65.97 cm²
Lateral Surface Area: 37.70 cm²
Step-by-step explanation:
You can solve for the surface area without the height or you can solve for the height and then find the surface are, either way is easy.
Lets first solve without the height. We will solve the surface area with the radius and slant height.
Total Surface area of cone formula: πr (r + s)
Curved surface are formula: πrs
Substitute the values in the picture with the formula
Slant height: 4
Radius: 3
πr (r + s)
π(3)(3 + 4)
(3.141593)(3)(3 + 4)
=9.424778(3 + 4)
=(9.424778)(7)
=65.973446
65.973446 rounded to the nearest hundredth is 65.97
TSA = Total Surface Area
TSA = 65.97 cm²
Now to find the curved surface area or some people call it the Lateral Surface Area
Formula: πrs
Radius: 3
Slant Height: 4
π(3)(4)
(3.141593)(3)(4)
=(9.424778)(4)
=37.699112
37.699112 to the nearest hundredth is 37.70
CSA = Curved Surface Area
CSA = 37.70 cm²
If you choose to compute the height (h) the you have to know both the radius (r) and the slant height (s):
Formula: height (h) = √s² - r²
Slant height = s = 4
Radius = r = 3
Height = h = ?
Now substitute the values into the formula
h = √s² - r²
h = √4² - 3²
h = √16 - 9
h = √7
h = 2.64575131
Height: 2.64575131 cm
Now it's time to find the surface area and curved surface area, now that you have the height:
Surface area formula given height and radius: πr(r + √(r² + h²))
Substitute the values
Height: 2.64575131
Radius: 3
πr(r + √(r² + h²))
π(3)(3 + √(3² + 2.64575131²))
TSA = (3.141593)(3)(3 + √(3² + 2.64575131²)
TSA = 9.424778(3 + √(3² + 2.64575131²)
TSA = 9.424778(3 + √(9 + 7)
TSA = 9.424778(3 + √(16)
TSA = 9.424778(3 + 4)
TSA = 9.424778(7)
TSA = 65.973446
TSA = 65.97
Next, time to find the Curved surface area:
Formula: CSA = πr√(r² + h²)
CSA = πr√(r² + h²)
Substitute the values into the formula
Radius: 3
Height: 2.64575131
Slant Height: 4
CSA = πr√(r² + h²)
CSA = π(3)√(3² + 2.64575131²)
CSA = 9.424778√(3² + 2.64575131²)
CSA = 9.424778√(9 + 7)
CSA = 9.424778√(16)
CSA = 9.424778(4)
CSA = 37.699112
CSA = 37.70
So, we can conclude that the Total Surface Area is 65.97 and the Lateral Surface Area is 37.70.
Liz has turtles that triple every month. and Steven has turtles that double every month. If Liz has 7 turtles at the same time that Steven has 5 turtles. then in how many turtles after 6 months do they have in total?
Answers
The number of turtles they will have after 6 months is =1,893 turtles
Calculation of total turtleNumber of turtles owned by Liz every month =
first month = 7
second month= 7×3 = 21
third month = 21× 3 = 63
fourth month = 63 × 3 = 189
Fifth month = 189 × 3 = 567
Sixth month = 567 × 3 = 1701 turtles
Number of turtles owned by Steven every month =
first month = 6
second month = 6 × 2 = 12
third month = 12× 2 = 24
Fourth month = 24 × 2 = 48
Fifth month = 48 × 2 = 96
Sixth month = 192 turtles
Therefore total turtle owned by both Liz and Steven=
1701 + 192 = 1,893 turtles
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT. Find The area of the rhombus.
The area of the rhombus is_______
Answers
[tex] \\ [/tex]
Diagonal 1 = 19 ft[tex] \\ [/tex]
Diagonal 2 = 29 ft[tex] \\ [/tex]
To find:[tex] \\ [/tex]
Area of figure (rhombus)[tex] \\ [/tex]
Solution:-[tex] \\ [/tex]
Ad we know Area of rhombus has two Formulas:-
[tex] \\ [/tex]
First :-
Area = (Diagonal 1 × Diagonal 2)/2
[tex] \\ [/tex]
Second:-
Area = B × h
[tex] \\ [/tex]
As we know in this case base and height aren't given, so we will use first formula to find rhombus.
[tex] \\ [/tex]
We know:-
[tex] \\ [/tex]
[tex] \dashrightarrow \sf{}Area \: of \: rhombus = \dfrac{diagonal_1 \times diagonal_2}{2} \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow \sf{}Area \: of \: rhombus = \dfrac{19 \times 29}{2} \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow \sf{}Area \: of \: rhombus = \dfrac{551}{2} \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow \bf{}Area \: of \: rhombus = 275.5 \: {ft}^{2} \\ [/tex]
[tex] \\ [/tex]
know more :-
[tex] \\ [/tex]
[tex]\small\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf \small{Formulas\:of\:Areas:-}}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}[/tex]
Given the functions f(x) = 2x 5 and g(x) = x2 8, which of the following functions represents f[g(x)] correctly? f[g(x)] = 4x2 20x 32 f[g(x)] = 4x2 20x 25 f[g(x)] = 2x2 16 f[g(x)] = 2x2 21.
Answers
Functions of functions are evaluated by taking first's output as second's input. The representation of [tex]f[g(x)][/tex] is: Option D: [tex]f[g(x)] = 2x^2 + 21[/tex]
What are composite functions?Functions which are formed by composing two or more functions in a way that one's output is another's input are called composite functions. They are also called function of functions.
The given functions are
[tex]f(x) = 2x + 5[/tex][tex]g(x) = x^2 + 8[/tex]Then [tex]f[g(x)][/tex] will be evaluated as output of g(x) taken as input for f(x).
Thus,
[tex]f[g(x)] = 2[g(x)] + 5 = 2[x^2 + 8] + 5\\\\f[g(x)] = 2x^2 + 21[/tex]
[tex]f[g(x)] = 2[g(x)] + 5 = 2[x^2 + 8] + 5\\\\f[g(x)] = 2x^2 + 21[/tex]
Thus,
The representation of [tex]f[g(x)][/tex] is: Option D: [tex]f[g(x)] = 2x^2 + 21[/tex]
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a system of linear equations as represented by the two tables below what is the solution to the system table 1 x = -5, -2, 0, 3 y = 6, 3, 1, -2, table 2 x = 0, 1, 2, 3 y = -7 -4, -1, -2
Answers
Answer:
(3, - 2 )
Step-by-step explanation:
In Table 1 when x = 3 , y = - 2
In Table 2 when x = 3 , y = 2
Then the solution to the system is (3, - 2 )
plz help help plz plz plz plz
Answers
Answer:a=70
c=110
b=110
Step-by-step explanation:
The solution is in the attached file filatache
Answer:
A = 70
B = 110
C = 110
Step-by-step explanation:
A is opposite of the 70 degree angle, and vertical angles are equal, so it is also 70 degrees.
A straight line is 180 degrees, so 70 + B = 180, making B = 110 degrees.
Both of these rules apply for C, making it also 110 degrees.
The simple interest on an investment of $7540 over 8 years is $1749.28.
If the annual interest rate is R, find R as a percentage to the nearest one decimal place.
Enter each line of working as an equation.
Answers
Answer:
41.38%
Step-by-step explanation:
A= P(1+in)
7540 = 1749.28 + 13994.25i
5790.72= 13994.25i
i=0.41379×100
i=41. 38%
What is half of 1 1/2 teaspoons
Answers
Answer:
The half of 1 1/2 tps would be 3/4 tsp.
Step-by-step explanation:
Hope This Helps
Have a Great Day
Answer:
3/4 tsp
Step-by-step explanation:
give guy above brainliest ig lolz
Please help me on this question i would appreciate it
Answers
Answer: x = 120 y = 25 z = 35
Step-by-step explanation:
z = 35 because of the Z rule
y = 25 because y + 35 = 60
x = 120 because of the C rule
Sorry if you don't understand, I don't know how to explain the reason to the answers
Find the domain of the graphed function.
Answers
Answer:
the domingo of a grapa consiste of all the input vales show on the x-axis the rango is the set of posible output vales which are show on the y-axis
Write in slope intercept form. 2x + y = 2
Answers
Answer:
y= -2x+2
Step-by-step explanation:
Slope intercept form is y=mx+b.
To write this equation in slope-intercept form, we must isolate y.
2x+y=2
Subtract 2x from both sides
y= -2x+2
The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $250 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following.
c=6500+250n
1.If the total cost is $12,250, how many tons is the company transporting?
2.What is the total cost of transporting 14 tons?
Answers
Answer:
An equation that relates cost to the amount of sugar S C = 6500 + 250s the total cost is $1120 The total cost of transporting 19 tons of sugar at 250 each C = total cost C =6500 + 250(19) total cost = 6500 + 4750 = 11250
Step-by-step explanation:
Find the measures of the numbered angles in the rhombus.
Answers
Answer:
Step-by-step explanation:
Angle 1 is 90 - 34 = 46 deg.
angle 2 is 90 deg.
angle 3 is 34 deg.
angle 4 is also 46 deg.
What type of angle is angle M?
L
M
P
O A. acute
B. straight
C. obtuse
D. right
Answers
Answer:
Although it would be great to see the picture of your problem, Acute angles are usually smaller than a right angle. A right angle is half of a straight line. A straight line is exactly how it sounds. An obsute angle is bigger than a right angle, so it has a higher degree.
When solving by substitution; you first must
A- get the numbers by themselves
B-decide if you are substitution
C-start solving the problem as you would an equation
Answers
B because thd mbajdidiidid
Two similar triangles have a pair of corresponding sides of length 12 meters and 8 meters.
The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the
perimeter and area of the smaller triangle.
Answers
Answer:
32 m, 80 m^2
Step-by-step explanation:
Ratio of their sides = 12 : 8 = 3 : 2
Ratio of their perimeter = 3 : 2
so 48 : perimeter of smaller triangle = 3 : 2
Perimeter of smaller triangle = 48 * 2 / 3 = 32 m
Ratio of their areas = 3^2 : 2^2 = 9 : 4
so 180 : area of smaller triangle = 9 : 4
Area of smaller triangle = 180 * 4 / 9 = 80 m^2
a room to be carpeted measures 16 feet in length and 12 feet in width the carpet costs 30 per square yard what is the total cost
Answers
A room area
Lenght × Width = 16 × 12
= 192 square feet
1 square yard = 9 square feet
so 1 square feet = 1/9 square yard
192 square feet = 192 × 1/9 square yard
= 64/3 square yard
Total cost
$30 × 64/3 = $640
-
16. Convert 100 meters per hour to inches per
second. (1 meter = 3.3 feet, 1 ft = 12 in, 1
hour = 60 minutes, 1 minute = 60 seconds)
(1.1 inch per second)
Answers
Answer:
0.106
Step-by-step explanation:
100 meters= 382 feet (per hour)
60 minutes in an hour
60 seconds in a minute
382/60=6.34 inches per minute (rounded to nearest tenth)
1 minute = 6.34 inches
6.34 / 60 = 0.106 (rounded to nearest thousandth)
The orchard's owner plots the table's data on the coordinate plane. Which other coordinate pair is appropriate for the situation to plot on the same plane? A) (40, 60) B) (125, 50) C) (100, 60) D) (70, 140)
Answers
Answer: B:2.5
Step-by-step explanation: divide the two numbers to find the answers
Answer:
B is the answer 125,50
Step-by-step explanation:
Please mark brainlyist
Un cuadrado mide de lado 15 cm. ¿Cuál es el área? *
Answers
Answer:
225 no estoy segura pero creo que es eso