Answer:
A = 3x² - x - 10
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × width , then
A = (3x + 5)(x - 2)
each term in the second factor is multiplied by each term in the first factor.
A = 3x(x - 2) + 5(x - 2) ← distribute parenthesis
= 3x² - 6x + 5x - 10 ← collect like terms
= 3x² - x - 10
Answer:
A = 3x² - x - 10
Step-by-step explanation:
A = length × width
A = (3x + 5)(x - 2)
A = 3x(x - 2) + 5(x - 2)
A = 3x² - 6x + 5x - 10
A = 3x² - x - 10
all expressions for 10x-30
Which of the following polynomials has solutions that are not real numbers?
x2 - 6x +3
x2 + 4x +3
-X2 - 9x - 10
x2 + 2x + 3
Answer:
4
Step-by-step explanation:
Answer:
Option 4 is correct.
Step-by-step explanation:
To find: Polynomial whose solution are not real numbers.
Given Polynomials are Quadratic Polynomial.
So, we can check if solution of quadratic polynomial by find & checking value of discriminant.
Standard form of Quadratic polynomial is given by
ax² + bx + c
then Discriminant, D = b² - 4ac
If, D > 0 ⇒ Solutions are distinct real numbers
if, D = 0 ⇒ Solutions are equal real numbers
if, D < 0 ⇒ Solutions are not real numbers (They are complex conjugates)
Option A:
By comparing with standard form
a = 1 , b = -6 , c = 3
D = (-6)² - 4 × 1 × 3 = 36 - 12 = 24 > 0
Thus, Solutions are Real numbers.
Option B:
By comparing with standard form
a = 1 , b = 4 , c = 3
D = (4)² - 4 × 1 × 3 = 16 - 12 = 4 > 0
Thus, Solutions are Real numbers.
Option C:
By comparing with standard form
a = -1 , b = -9 , c =-10
D = (-9)² - 4 × (-1) × (-10) = 81 - 40 = 41 > 0
Thus, Solutions are Real numbers.
Option D:
By comparing with standard form
a = 1 , b = 2 , c = 3
D = (2)² - 4 × 1 × 3 = 4 - 12 = -8 < 0
Thus, Solutions are not Real numbers.
Therefore, Option 4 is correct.
gina wilson unit 8 right triangles&trignometry homework 2 help
Answer:
huh
Step-by-step explanation:
Which set of steps can be used to prove the sine sum identity, sin(x y) = sin(x)cos(y) cos(x)sin(y)?
The trigonometry identity sin(x + y) = sinx cosy + cosx siny.
What is sin(x + y) identity in trigonometry?sin(x + y) is one of the identities in trigonometry for compound angles.
The angle (x + y) represents the compound angles.
sin(x + y) = sinx cosy + cosx siny
To prove sin(x + y) = sinx cosy + cosx siny
Consider OX as a rotating line anti-clockwise. Let angle XOY = a
the making of an acute angle b the rotation in the same direction is
angleYOZ = b , angle XOZ = a + b
From triangle PTR,
∠TPR = 90 - ∠PRT , ∠ROX = a
From the right-angled triangle PQO
sin(a + b) = PQ/OP
= (PT + TQ) / OP
= PT/OP + TQ/OP
= PT/PR × PR/OP + RS/OR × OR/OP
= cos (∠TPR ) sinb + sina cosb
= sina cosb + cosa sinb
if we replace a=x and b=y
Therefore, sin(x + y) = sinx cosy + cosx siny.
Learn more about trigonometry identity;
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help pls
tysm in advance
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-We have given some information in the above table To Find :-We have to find the mean, median and mode of the given data. Let's Begin :-For completion of table you should know the basics formulas :-
For calculating x( mid point)[tex]\sf{=}{\sf{\dfrac{Sum \:of\: class \:interval }{ 2}}}[/tex]
That is,
[tex]\sf{=}{\sf{\dfrac{ = 18 + 25}{2}}}[/tex]
[tex]\sf{=}{\sf{\dfrac{ = 43}{2}}}[/tex]
[tex]\sf{= 21.5 }[/tex]
[ For more calculation ,Please refer the attachment ]
For calculating fx Multiply frequency and midpoint[tex]\sf{ fx = frequency {\times} midpoint }[/tex]
[tex]\sf{ fx = 8 {\times} 21.5 }[/tex]
[tex]\sf{ fx = 172 }[/tex]
[ For more calculation please refer the attachment ]
Now,We have to calculate mean, median and mode of the given data
For meanWe know that the,
Mean = Sum of all observation / no. of observation
That is
[tex]\sf{ Mean = }{\sf{\dfrac{ {\sigma}fx}{{\sigma}x}}}[/tex]
Subsitute the required values,
[tex]\sf{ Mean = }{\sf{\dfrac{ 1811 }{ 187.5}}}[/tex]
[tex]\sf{ Mean = 9.65}[/tex]
Hence, The mean of the given data is 9.65
For MedianWe know that, For odd numbers
[tex]\sf{ Median = l + }{\sf{\dfrac{ (n/2 - c)}{ f}}}{\sf{ h }}[/tex]
Here,
[tex]\sf{ n = }{\sf{\dfrac{ 50 + 1}{ 2}}}[/tex]
[tex]\sf{ n = }{\sf{\dfrac{ 50 }{ 2}}}[/tex]
[tex]\sf{ n = 25 }[/tex]
Lower limit = 34c = 20f = 14h = 41 - 34 = 7Subsitute the required values in the above formula :-
[tex]\sf{ Median = 34 + }{\sf{\dfrac{ (25-20)}{ 14}}}{\sf{ 7 }}[/tex]
[tex]\sf{ = 34 + }{\sf{\dfrac{ 5}{ 14}}}{\sf{ {\times}7 }}[/tex]
[tex]\sf{ = 34 + }{\sf{\dfrac{ 35}{ 14}}}[/tex]
[tex]\sf{ = 34 + 2.5}[/tex]
[tex]\sf{ = 36.5 }[/tex]
Hence, The median of the given data is 36.5 .
For ModeWe know that,
[tex]\sf{ M= l }{\sf{\dfrac{ (f1 - fo)}{ 2f1 - fo - f2 }}}{\sf{ {\times} h }}[/tex]
lower limit = 34 f1 = 14fo = 12f2 = 12H = 7Subsitute the required values,
[tex]\sf{ M= 34 }{\sf{\dfrac{ (14 - 12)}{ 2(14)- 12 - 12 }}}{\sf{ {\times} 7 }}[/tex]
[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 28 - 24 }}}{\sf{ {\times} 7 }}[/tex]
[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 4 }}}{\sf{ {\times} 7 }}[/tex]
[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 1}{ 2 }}}{\sf{ {\times} 7 }}[/tex]
[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 7}{ 2 }}}[/tex]
[tex]\sf{ M= 34 + 3.5 }[/tex]
[tex]\sf{ M= 37.5 }[/tex]
So,
Mode = 37.5Hence ,The mode of the given data is 37.5 .
Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answer:
-4, 10.
Step-by-step explanation:
(x – 3)^2 = 49
x - 3 = ±√49
x = 3 ± 7
= -4, 10.
11. What is the solution of this equation
3(2-x)=-(4+3x)
A
-
5
3
В.
5
3
C 2
D. The equation has no solution.
Answer:
D I think
Step-by-step explanation:
if you do the multiplying you get 6-3x= -4 + (-3x) and then the -3x would cross out leaving 6=-4 which isnt true so D
Answer D
it is 6-3x = -4 -3x then when you add 3 x to both sides so you can move the variables to either side it cancels out on both sides so 6 = -4 meaning there is no solution
The radius of a circle is 2 feet. What is the
circle's circumference?
r=2 ft
Given -
the radius of a circle is 2 feet. ie. r = 2ftps - use 3.14 for π
To find -
the circle's circumferenceSolution -
We know to find the circumference of a circle we use the formula C=2πr.
Doing the same,
C = 2 × 3.14 × 2
C = 12.56 feet
[tex]\sf\large\underline{Given:-}[/tex]
[tex]\rightarrow[/tex] Radius(r) of the circle = 2 ft.
[tex]\rightarrow[/tex] Value of Pie(π) = 3.14
[tex]\sf\large\underline{To\: Find:-}[/tex]
[tex]\rightarrow[/tex] Circumference of the circle.
[tex]\sf\large\underline{Formula \: Used:-}[/tex]
[tex]\rightarrow[/tex] Circumference of circle = [tex]\sf{2πr}[/tex]
[tex]\sf\large\underline{Solution:-}[/tex]
[tex]\rightarrow[/tex] Circumference of circle = [tex]\sf{2πr}[/tex](putting the value of π and r from the above given)
[tex]\rightarrow[/tex] [tex]\sf{=2×3.14×2}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=12.56\: ft.}[/tex]
Therefore, circumference of the given circle = [tex]\sf{12.56\: ft.}[/tex]
_____________________________
Hope it helps you:)
A family uses 12,986. 64 Swiss francs per year to pay a mortgage that requires US dollars. Approximately how much, in US dollars, does the family spend per month on the mortgage? 1 US dollar = 0. 9019 Swiss francs 1 Swiss franc = 1. 11 US dollar $975 $1,080 $1,200 $1,440.
Unit conversion is a way of converting some common units into another without changing their real value. The amount that is paid by the family in mortgage per month is equal to $1200.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
As it is given to us that the family uses 12,986.64 Swiss francs per year to pay a mortgage. Therefore, the amount that is paid by the family in mortgage per month can be written as,
[tex]\text{Mortgage for a month} = \dfrac{\text{Mortgage of the family for a complete year}}{\text{Number of Months}}\\\\\\\text{Mortgage for a month} = \dfrac{\rm 12,986.64\ Swiss\ francs}{12} = 1082.22\rm \ Swiss\ francs[/tex]
Thus, the family needs to pay 1082.22 swiss francs every month in the mortgage.
Now, it is mentioned in the problem that 1 Swiss franc = 1.11 US dollars, therefore, 1082.22 swiss francs when converted to US dollars will be equal to,
[tex]\rm 1\ Swiss\ francs = \$1.11 \\\\1082.22\ Swiss\ francs = 1082.22 \times 1.11 = \$1,201.26 \approx \$1,200[/tex]
Hence, the amount that is paid by the family in mortgage per month is equal to $1200.
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A ball is thrown from a height of 44 meters with an initial downward velocity of 6 m/s . The ball's height h (in meters) after t seconds is given by the following.
h= 44 - 6t - 5t squared 2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answer:
Step-by-step explanation:
h = -5t^2 - 6t + 44
I'll assume 0 meters is the ground height. That would mean we want to know the time, t, for h to be = 0 meters:
h = -5t^2 - 6t + 44
0 = -5t^2 - 6t + 44
5t^2 + 6t -44 = 0
Solve using the quadratic equation: 2.43 and - 3.63 seconds. We'll use the positive value: 2.43 seconds for the ball to reach the ground. Save the -3.63 value for the Klingons.
We can also solve by graphing the function, as per the attached image. Note that the starting time of 0 seconds, the ball is at 44 feet. It reaches the x axis at 2.43 seconds (where x = 0, the ground).
Answer:
t = 2.43 s (nearest hundredth)
Step-by-step explanation:
Given equation: [tex]h=44-6t-5t^2[/tex]
where:
h = height (in meters)t = time (in seconds)When the ball hits the ground, h = 0
[tex]\implies 44-6t-5t^2=0[/tex]
[tex]\implies 5t^2+6t-44=0[/tex]
Using the quadratic formula when [tex]ax^2+bx+c=0[/tex] and where:
a = 5b = 6c = -44x = t[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]=\dfrac{-(6)\pm\sqrt{(6)^2-4(5)(-44)}}{2(5)}[/tex]
[tex]=\dfrac{-6\pm\sqrt{916}}{10}[/tex]
[tex]=\dfrac{-6\pm2\sqrt{229}}{10}[/tex]
[tex]=\dfrac{-3\pm\sqrt{229}}{5}[/tex]
[tex]=2.43, -3.63 \ \textsf{(nearest hundredth)}[/tex]
As time is positive, t = 2.43 s (nearest hundredth)
The ratio of red candy to green candy in a bag is 3 to 4
If there were 36 pieces of green candy in the bag, how many pieces of candy in the bag were red?
Answer:
27
Step-by-step explanation:
we know that 4 multiplied with something is 36
=> 4x = 36
=> x = 36/4
=> x = 9
so we have to multiply 3 with 9
=> 3*9 = 27
work out [tex]\frac{1}{5}[/tex] of 80
Answer:
Here we will explain how to calculate one half of 80.
One half of 80 is simply one half times 80, which can be written as follows:
One/half x 80
Furthermore, you can convert "one" to "1" and "half" to "2" and then the equation and answer is:
1/2 x 80 = 40.00
Step-by-step explanation:
Hey there!
In order to find 1/5 of 80, we can just multiply 80 times 1/5:
[tex]\bold{\displaystyle\frac{1}{5} *80}[/tex]
80 can be written as follows:
[tex]\bold{\displaystyle\frac{1}{5} *\frac{80}{1}}[/tex]
In order to multiply fractions, just multiply the top of one fraction times the top of the other fraction; same with the bottom (also called the denominator)
[tex]\bold{\displaystyle\frac{80}{5}}[/tex]
Guess what? Now we can use mental maths to solve it :)
Hence, the answer is
[tex]\boxed{\boxed{\bold{16}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#ILoveLearning
:-)
What does (2x−2)(3x+5) equal?
Answer:
6x² + 4x + 10
Step-by-step explanation:
(2x - 2)(3x + 5)
2x(3x + 5) - 2(3x + 5)
6x² + 10x - 6x + 10
6x² + 4x + 10 ans.
hope this helps you !
Which could be the area of one lateral face of the triangular prism? A triangular prism. The rectangular sides are 8 feet by 2. 5 feet, 8 feet by 6 feet, and 8 feet by 6. 5 feet. The triangular sides have a base of 2. 5 feet and height of 6 feet. [Not drawn to scale] 7. 5 ft2 15 ft2 20 ft2 39 ft2.
The area of one lateral face of the triangular prism could be 20 ft².
What is a prism?a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first base, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.
Since the base of the prism is triangular so there will be three lateral faces.
Dimensions of rectangular lateral faces are:
1)8 feet by 2.5 feet
2)8 feet by 6 feet
3) 8 feet by 6. 5 feet
Area of the lateral face with dimension 8 feet by 2.5 feet = 8*2.5 =20 ft²
Area of the lateral face with dimension 8 feet by 6 feet = 8*6 =48 ft²
Area of the lateral face with dimension 8 feet by 6.5 feet = 8*6.5 =51 ft²
Therefore, the area of one lateral face of the triangular prism could be 20 ft².
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Line of best fit has a y intercept of 6 and goes through the point(4,22) what is the slope of the line
Answer:
0.7
Step-by-step explanation:
you have a slope of 6 and it goes through 4,22 so slope = rise over run so you would divide them
for each pair of lines, determine whether they are parallel, perpendicular, or neither
please someone help i will give brianliest
Answer:
the answer is 16
Step-by-step explanation:
look at the photo
How much would you have after 4 years if you invested $1250 with a quarterly compounding interest rate of 5%?
Using compound interest, it is found that you would have $1524.86.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem, we have that the values of the parameters are given by: P = 1250, r = 0.05, n = 4, t = 4. Hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(4) = 1250\left(1 + \frac{0.05}{4}\right)^{4 \times 4} = 1524.86[/tex]
Tou would have $1524.86.
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Help on this pleases.
Answer: ASA
Step-by-step explanation:
Please help I am not understanding
Answer:
12.39cm
Step-by-step explanation:
cos 25°=AB/12.5
AB=12.5 cos 25°
cos 25°=0.9912
AB=12.5×0.9912
=12.39cm
Which of the following is an expression
A. 7x = 4
B. 7 = x = 4
C. 7 - x
D. 7n - 3 = 32
Answer:
D. 7n - 3 = 32 Because is contains the neccesary amount of variables needed to be considered as an expression.
Step-by-step explanation:
Hope this helps you! :D
If x and y intercepts of the line are 3/2 and 5/4 respectively then the equation of the line is
Answer:
10x + 12y -15 =0
Step-by-step explanation
In a survey of 3,000 people who owned a certain type of car, 1,050 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
35 percent
Step-by-step explanation:
1050 / 3000 as a percent
1050 / 3000 = 105 / 300
Divide both sides by 3:
300 / 3 = 100
105 / 3 = 35
35 / 100 = 35 percent
34%
This is because when you divide 1,050 by 3,000 you get 0.34 then turn that into a percent then there you go
Rewrite each equation without using absolute value for the given conditions.
y=|x-3|+|x+2|-|x-5| if x>5
Answer:
x>5, so
let x=6
6-3=3
+
6+2=8
-
6-5=1
3+8-1=10
answer=10
help help i need it can you?
What is the product of (7 x 10^-5) x (5 x 10^-8)
(7 x 10^-5) x (5 x 10^-8) = ? x 10^?
Answer:
[tex]3.5\times10^-^1^2[/tex]
Step-by-step explanation:
[tex](7 \times 10^-5) \times (5 \times 10^-8)[/tex]
Evaluate
[tex](7 \times 5)\times(10^-^5\times10^-^8)[/tex]
[tex]35\times10^-^5^-^8[/tex]
[tex]35\times10^-^1^3[/tex]
[tex]35\times10^1\times10^-^1^3[/tex]
[tex]3.5\times10^1^-^1^3[/tex]
[tex]3.5\times10^-^1^2[/tex]
Thus, the answer is [tex]3.5\times10^-^1^2[/tex]
~Lenvy~
I need help please!!!!!
Answer:
330 ft^2
Step-by-step explanation:
See attached image
Find the value of x that makes m || n
x=
Anthony's sink is shaped like a half-sphere, and it has a volume of 512π cubic inches. It is completely full of water, and he has two different cylindrical cups he can use to scoop it out.
The blue cup has a diameter of 4 in. and a height of 8 in., and the green cup has a diameter of 8 in. and a height of 8 in.. How many cupfuls of water will it take for him to empty his sink using each cup?
In your answer, give the number of cupfuls it will take to empty the sink using each cup, and then explain how you calculated it.
By taking the quotient between the volumes, we conclude that he must use the blue cup 16 times or the green cup 4 times.
How many times do he need to use each cup?The volume of the sink is 512π in^3.
The blue cup is a cylinder of diameter = 4 in and a height = 8 in, then its volume is:
V = π*(4in/2)^2*8in = 32π in^3
The number of times that he needs to use this cup is given by:
N = (512π in^3)/(32π in^3) = 512/32 = 16
He needs to use 16 times the blue cup.
The green cup has a diameter = 8in and a height = 8in, then its volume is:
V' =π*(8in/2)^2*8in = 128π in^3
The number of times that he must use this cup is:
N' = (512π in^3/ 128π in^3) = 512/128 = 4
He needs to use 4 times the green cup.
If you want to learn more about volumes, you can read:
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Matthew bought 12 roses for his mother. Exactly 1 of the roses were white. How many of the roses were white?
2
3
4
5
What is [tex]\sf{\displaystyle\frac{1}{4}}[/tex] of 12?
In order to find it, we should divide 12 by 4:-
3
Now, solve our word problem:-
Matthew bought 12 roses. [tex]\sf{\displaystyle\frac{1}{4} }[/tex] of these roses were white.
And we already know how to solve this problem :)
Hence,
[tex]\bigstar{\boxed{\pmb{3~of~the~roses~were~white}}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)