Answers
[tex]\displaystyle \dfrac{\dfrac{4c^2-36}{8c^2-24c}}{\dfrac{12c+36}{2c^2 -6c}}\\\\\\=\left(\dfrac{4c^2 -36}{8c^2 -24c}\right) \cdot \left(\dfrac{2c^2 -6c}{12c+36}\right)\\\\\\=\left[\dfrac{4(c^2 -9)}{8(c^2-3)}\right]\cdot\left[\dfrac{2(c^2-3)}{12(c+3)}\right]\\\\\\=\dfrac{8(c^2-3^2)}{8 \cdot 12(c+3)}\\\\\\=\dfrac{(c+3)(c-3)}{12(c+3)}\\\\\\=\dfrac{c-3}{12}[/tex]
[tex]\text{Hence the answer is d.}[/tex]
Answer:
d
Step-by-step explanation:
separate the 2 divisions and simplify each , that is
[tex]\frac{4c^2-36}{8c^2-24c}[/tex] ← factor numerator/ denominator
= [tex]\frac{4(c^2-9)}{8c(c-3)}[/tex] ← factor difference of squares on numerator
= [tex]\frac{4(c-3)(c+3)}{8c(c-3)}[/tex] ← cancel (c - 3) and 4/8 on numerator/ denominator
= [tex]\frac{c+3}{2c}[/tex]
---------------------------------------------------
[tex]\frac{12c+36}{2c^2-6c}[/tex] ← factor numerator/ denominator
= [tex]\frac{12(c+3)}{2c(c-3)}[/tex] ← cancel 12 and 2 on numerator/ denominator
= [tex]\frac{6(c+3)}{c(c-3)}[/tex]
----------------------------------------------------------
to divide the top fraction by the lower fraction
leave top fraction, change division to multiplication, turn lower fraction upside down.
[tex]\frac{c+3}{2c}[/tex] × [tex]\frac{c(c-3)}{6(c+3)}[/tex] ← cancel (c + 3) and c on numerator/ denominator
= [tex]\frac{c-3}{2(6)}[/tex]
= [tex]\frac{c-3}{12}[/tex] → d
Related Questions
PLEASE HELP IM FAILING GEOMETRY HELPPPP
Answers
Answer:
473.145 in squared
Step-by-step explanation:
Trick reminder: the top of the cylinder does not need to be calculated because it is the same as the negative part of the rectangle beneath.
20.25*3.14 = 63.585
6*28.26 = 169.56
10*10 = 100
10*3.5*4 = 140
63.585 + 169.56 + 100 + 140 = 473.145
A large cone is cut into two parts, a smaller cone and a frustum of a cone.
The height of the large cone is 20 cm.
The height of the smaller cone is 4 cm.
The radius of the base of the large cone is 6 cm.
The radius of the base of the smaller cone is 4 cm.
Workout the volume of the frustum.
Answers
radius of small cone= 4 cm
radius of large cone= 6 cm
height of small cone= 4 cm
height of large cone= 20 cm
solution:big:[tex]v = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex]v = \frac{1}{ 3} \times \pi \times {6}^{2} \times 20[/tex]
[tex]v = 753.98 \: {cm}^{3} [/tex]
small:[tex]v = \frac{1}{ 3 } \pi {r}^{2} h[/tex]
[tex]v = \frac{1}{3} \times \pi \times {4}^{2} \times 4[/tex]
[tex]v = 67.02 \: {cm}^{3} [/tex]
frustum:[tex]v = 753.98 - 67.02[/tex]
[tex]v = 686.96 \: {cm}^{3} [/tex]
volume of smaller cone:
[tex] = 67.02 {cm}^{3} [/tex]
volume of larger cone:
[tex] = 753.98 {cm}^{3} [/tex]
frustum:
[tex] = 686.96 {cm}^{3} [/tex]
Lessons are 55 mins long, a history lesson ends at 3:30 pm at what time does the lesson start
Answers
Answer:
2:35 pm
If an hour is 60 minutes, what we know is that 30 minutes is half. However, we must subtract 55 from 30 (In time)
To make this easier, subtract 55 by actual 30, and split 55 into 2 parts, the result of subtraction, and the other value, 30
[tex]55-30=25[/tex]
Now, subtract.
[tex]3:30 - 30 = 3:00[/tex]
[tex]3:00-25=35[/tex]
If this is the case, the lesson must have started at 2:35 pm
1. Given O B and marked angle measure.
Find MZADC and find the measure of AC
с
135°
D
B
А
Answers
Step-by-step explanation:
angle ADC = angle ABC / 2
= 135/2 = 67.5°
AC = 2r * sin (62.5)
AC = 1.84r
r is the radius of circle
Which results only in a horizontal compression of Y =
by a factor of 6?
1
O y = 6x
O y= 6x
6
O Y =
X
o
y = -2
6
y=-
х
Answers
Answer:
B
Step-by-step explanation:
What is the value of "a" in the following quadratic? (Make sure the equation is in
standard form: ax² + bx+c=0)
x^2 + 28 = -11x
Answers
Answer: a= - [tex]\frac{b}{x}[/tex]- [tex]\frac{c}{x2}[/tex]
Step-by-step explanation:
1. Move all terms not containing [tex]\alpha[/tex] to the right side of the equation.
[tex]\alpha[/tex][tex]x^{2}[/tex]=-bx-c
2. Divide each term in [tex]\alpha x^{2}[/tex]=-bx-c by [tex]x^{2}[/tex] and simplify.
a= - [tex]\frac{b}{x}[/tex] - [tex]\frac{c}{x^{2} }[/tex]
Example a) Name the vertex of the angle. b) Name the sides of the angle. c) Give three ways to name the angle. d) Classify the angle.
Answers
Answer:
OBtuse <
Step-by-step explanation:
Complete the factorization of 3x2 – 5x 2. which two factors can be multiplied together to make this trinomial? (x – 2) (x – 1) (x 1) (3x – 2) (3x 2)
Answers
The factorization of the given polynomial is:
p(x) = (x - 2/3)*(x - 1) = (1/3)*(3x - 2)*(x - 1)
How to factorize the polynomial?
We have:
[tex]p(x) = 3x^2 - 5x + 2[/tex]
First, we need to find the two roots for the equation, then we use Bhaskara's formula to get:
[tex]x = \frac{5 \pm \sqrt{5^2 - 4*3*2} }{2*3} \\\\x = \frac{5 \pm 1}{6}[/tex]
So the two solutions are:
x = (5 + 1)/6 = 1
x = (5 - 1)/6 = 4/6 = 2/3
Then the polynomial can be written as:
p(x) = (x - 2/3)*(x - 1)
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Answer: (3x -2) and (x-1)
Step-by-step explanation:
Just took the test
Craig is constructing weights of different sizes to use in his home gym. One such weight is a solid steel sphere with a radius of 3.5 inches. The density of steel is 0.284 pounds per cubic inch. What is the approximate
mass of the spherical weight?
A. 51 pounds
B. 77 pounds
C. 15 pounds
D. 44 pounds
Answers
The approximate mass of the spherical weight is 51 pounds
To answer the question, we need to know what the mass of the sphere is
Mass of the sphereThe mass of the sphere m = ρV where
ρ = density of steel = 0.284 lb/in³ and V = volume of sphere = 4πr³/3 where r = radius of sphere = 3.5 inSo, m = ρV
= ρ4πr³/3
Substituting the values of the variables into the equation, we have
m = ρ4πr³/3
= 0.284 lb/in³ × 4π(3.5 in)³/3
= 0.284 lb/in³ × 4π × 42.875 in³/3
= 48.706π lb/3
= 153.014 lb/3
= 51 lb
The approximate mass of the spherical weight is 51 pounds
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Sarah drives at a speed of 70 miles per hour.
How long will it take to drive 385 miles?
Answers
Answer:
5.5 Hours
or
5 Hours 30 Minutes
Step-by-step explanation:
Dirving speed = 70 mphDistance = 385 milesTo find: Time Formula relating speed, distance and time is given as: [tex]Time =\frac{Distance}{Speed}[/tex][tex]\implies Time =\frac{385}{70}[/tex][tex] \implies Time = 5.5\: hours [/tex][tex]\implies \red{\boxed{\bold{Time = 5\: hours\: 30\: minutes}}}[/tex]HELP ASAP PLEASE
WILL MARK AS BRAINLIST IF YOU SOLVE THESE TWO QUESTIONS
The picture is for question 2 not 3
Question 2
How many paths are there from A to B if you must travel along the lines moving up and right only?
Question 3
In my backyard there are chickens and cows (no other animals). Among them there is a total of 366 eyes and 558 legs. How many
chickens do I have in my backyard?
Answers
2. Answer: 35
Step-by-step explanation:
4x3 grid so 4!= 24 and 3!= 6 4+3=7 so 7! = 5040 now 7!/4!*3!=35.
Solve the following equations:
[tex]1.\sqrt{5x+4}-1=2x[/tex]
[tex]1) \ 3\sqrt{x-1 }+11=2x[/tex]
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf 1. \ \sqrt{5x+4} -1=2x \end{gathered}$}[/tex]
The root of the equation is solved first. Afterwards, both members of the equality are squared, the powers are developed and it is solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{5x+4}=2x+1 \Longrightarrow 5x+4=(2x+1)^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 0=4x^2 +4x+1-5x-4 =4x^2-x-3 \\ &= 4\left(x^2-\dfrac{1}{4}-\dfrac{3}{4} \right)\\ &=4\left(x-1\right)\left( x+\dfrac{3}{4}\right) \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x_1=1 \qquad x_2=-\dfrac{3}{4} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2. \ 3\sqrt{x-1}+11=2x \end{gathered}$}[/tex]
The root of the equation is cleared. Then, both sides of the equality are squared, the powers are developed and it is solved by the general formula.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 3\sqrt{x-1}=2x-11 \Longrightarrow 9(x-1)=(2x-11)^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 0=4x^2 -44x+121 -9x+9 =4x^2-53x+130 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x_{1,2}=\dfrac{53\pm \sqrt{(-53)^2-4(4)(130)}}{2(4)}=\dfrac{53\pm \sqrt{2809-2080}}{8}\\ &=\dfrac{53\pm \sqrt{729}}{8} = \dfrac{53\pm 27}{8}; \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} \ \ \ \ \ \ x_{1}=\dfrac{53+ 27}{8} \qquad &\ \ \ \ \ x_2=\dfrac{53 - 27}{8}\\ x_1=\dfrac{80}{8} \qquad &\ \ x_2=\dfrac{26}{8}\ \ \ \\ x_1=10 \qquad &x_2=\dfrac{13}{4} \end{matrix} \end{gathered}$}[/tex]
A tank contained 1.5 litres more water than a pail. Swee Leng transferred 300 millilitre of water from the pail to the tank. Now the tank contains 4 times as much water as the pail. How many litres of water were there in the tank at first?
Answers
Answer:
i think so 4.32 L
The sum of two numbers is 29 and their difference is 13.
Set up two equations by letting x and y be the two numbers.
Use x as the larger of the 2 numbers.
sum equation:
difference equation:
Answers
Answer:
Sum equation: x + y = 29
Difference equation: x - y = 13
Paper towel rolls are covered with a plastic wrapper. How much plastic would be needed to cover the paper towel roll shown below?
Answers
The area of a 2D form is the amount of space within its perimeter. The plastic that would be needed to cover the paper towel roll is 263.76 in².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The plastic that would be needed to cover the paper towel roll is equal to the surface area of the paper towel roll, therefore, the surface area is,
Total surface area = (2πrl) + 2(πr²)
= (2×π×3×11) + 2(π×3×3)
= 66π + 18π
= 263. 76 in²
Hence, The plastic that would be needed to cover the paper towel roll is 263.76 in².
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A quarterback throws a football with a velocity of 42 mph and a direction of 172°. The wind on the field is 13 mph with a direction of 345°. What are the true speed and direction of the football? Round the speed to the thousandths place and the direction to the nearest degree.
Answers
The true speed and direction of the football thrown by the quarterback is 39.139 mph and 7⁰ respectively.
How to find the Relative velocity of the football?The true speed and direction of the football is determined by applying the concept of relative velocity.
Vr/w = Vb - Vw
where;
Vr/w is the velocity of the football with respect to the wind
Vb is the velocity of the football
Vw is the velocity of the wind
Vr/w = 42 mph - 13 mph = 29 mph
The direction speed can be determined by a triangle
Direction of the speed, θ = (360 - 345) - (180 - 172)
θ = 15 - 8 = 7⁰
Resultant speed;
[tex]R^2 = 42^2 + 13^2 - 2(42 \times 13 \times cos7)\\\\R^2 =849.139\\R = \sqrt{849.139}\\R = 29.139 mph[/tex]
Thus, the true speed and direction of the football thrown by the quarterback is 39.139 mph and 7⁰ respectively.
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Answer:
29.140 ; 175
Step-by-step explanation:
Please help me with this it's algebra WILL GIVE BRAINLIEST and 5 points
Answers
Answer: y-2 > 1/4(x-4)
Step-by-step explanation:
use slope formula y2-y1/x2-x1 so 2-0/4-(-4) = 1/4
slope int form is y-y1 = m(x-x1)
plug in one point
y-2 = 1/4(x-4)
insert (0,0)
you find y-2 > 1/4(x-4)
which fractions are equivalent to the value of 2/10 + 20/100? drag and drop the fractions into the box.
Answers
Lets see
2/10+20/1002/10+2/102+2/104/102/5Help me this pls as soon as possible this is due today!!!
Answers
Answer:
you can find the given attachment
Alguien me ayuda? Who can help me?
Is for my litte brother
es para mi hermano pequeño
Answers
The solving of the fractions simply shows that the value of 1 2/3 + 3 1/2 is 5 1/6.
How to solve the fraction?The first fraction give is:
= 1 2/3 + 3 1/2
= 1 4/6 + 3 3/6
= 4 7/6
= 4 + 1 1/6
= 5 1/6
Also 3/4 - 5/7 will be:
= 3/4 - 5/7
= 21/28 - 20/28
= 1/8
It should be noted that when solving fractions, it's important to have a common denominator.
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Simplify the expression.
5² (5³ · 5²)
The value of the expression is
Answers
[tex]5^2(5^3 \cdot 5^2)\\\\=5^{2+3+2}\\\\=5^7\\\\=78125[/tex]
Answer:
5^7 or 78125
Step-by-step explanation:
5^2 (5^3 x 5^2)
This is the 5^2 is the same thing as 5x5 while 5^3 is the same as saying 5x5x5, when we evaluate these equations we get a new formula:
= 25 ( 125 x 25)
now we simplify.
= 25 (3125)
= 78125
what are all the factor parts of 15
Answers
Answer:
1,3,5,15
Step-by-step explanation:
find the center and radius
Answers
Answer:
centre = (0, 0 ) , radius = 2
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
x² + y² = 4 ← is in this form
with centre (0, 0 ) and r = [tex]\sqrt{4}[/tex] = 2
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
3 1/2
Step-by-step explanation:
the letter j is HALFway between four and three so it is 3 1/2
How many 1/2 cup servings are there in a3/4 cup of cereal?
Answers
Answer:
1 and a half
Step-by-step explanation:
There is one full half cup in a 3/4 cup. A half of a half is a fourth and there is still one more fourth left so 1/2 plus 1/4 is 3/4.
Azeyah wants to buy a wooden rod to install curtains on the window of his room. The area of the window is ( 4x²+2x-12 ) cm². If the window's height is ( 2x+4 ) cm, what is the length, in cm, of the wooden rod required?
Pls help ASAP
Answers
Answer:
(2x - 3) cm
Step-by-step explanation:
Area of window = height × length
Given:
Area = (4x² + 2x - 12) cm²Height = (2x + 4) cmTo find the length of the window, factor the expression for Area.
Factor [tex]4x^2+2x-12[/tex]:
Find 2 two numbers that multiply to the product of the leading coefficient and the constant (4 × -12 = -48) and sum to the coefficient of the middle term (2): -6 and 8
Rewrite the middle term as the sum of these 2 numbers:
[tex]\implies 4x^2-6x+8x-12[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2x(2x-3)+4(2x-3)[/tex]
Factor out the common term (2x - 3):
[tex]\implies (2x+4)(2x-3)[/tex]
Therefore, the length of the window is (2x - 3) cm
(2x-3)cm
Answer:
Solution given:
height =2x+4
length=?
Area of window =(4x²+2x-12)cm²
we have
length*height =Area
length*(2x+4)=4x²+2x-12......(1)
Firstly let factorize 4x²+2x-12
taking common 2(2x²+x-6)
doing middle term factorization 2(2x²+4x-3x-6)
=2(2x(x+2)-3(x+2))
=2(x+2)(2x-3)
substituting it in equation 1
length*(2x+4)=2(x+2)(2x-3)
length*2(x+2)=2(x+2)(2x-3)
length =2x-3 cm
The length of window is (2x-3)cm
From the diagram shown, find the measurement of the indicated angle.
Answers
Answer:
x = 50°
Step-by-step explanation:
The three angles of any triangle always add up to 180°. Here, we have a 40° and a right angle. Right angles are always 90°.
To find the value of x, find the sum of the two other angles.
90 + 40 = 130°
Since we know that all angles add to 180, we can conclude the following:
x + 130 = 180
x = 50°
Hope this helps
4x + 90 find the value of x
Answers
Answer:
x = -22.5
Step-by-step explanation:
Assuming 4x + 90 = 0
4x + 90 = 0
4x = -90
-90/4 = -22.5
7x+8=-5x+32 can someone tell me what x is pls
Answers
Answer:
x =12
Step-by-step explanation:
combine like terms 32+ = -8 = 24 then divide 2x on each side 24/ 2x which simipfy to 12
+5x +5x
12x+8=32
-8 -8
12x= 24
÷12 ÷12
X=2
Let A = -4k+ 3 and B = 3k +17. If A = B, then what is the value of k?
Answers
Answer:
k=-2
Step-by-step explanation:
Using substitution to find what you're missing, (in this case k) is when you plug each letter into the other equation:
-4k+3=3k+17
So now solve for k:
subtract 3 from both sides...
-4k=3k+14
subtract 3k from both sides to combine with -4k...
-7k=14
divide -7 from both sides...
k=-2
