[tex]\boxed{\sf \dfrac{a^m}{a^n}=a^{m-n}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{16x^4-24x^3+3}{4x^2+3}[/tex]
Take 4x^2+3 common out[tex]\\ \rm\Rrightarrow 4x^2+3\left(\dfrac{4x^2-24x+1}{1}\right)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{4x^2-24x+1}{1}[/tex]
[tex]\\ \rm\Rrightarrow 4x^2-24x+1[/tex]
Answer:
4x² - 24x + 1
Step-by-step explanation:
[tex]\frac{16x^{4}-24x^{3}+3}{4x^{2}+3}[/tex]
~Factor out the denominator and apply quotient rule [ a^b / a^c = a^b-c ]
[tex]4x^{2}+3 (\frac{\frac{16}{4} x^{4-2}-24x^{3-2}+\frac{3}{3} }{1})[/tex]
[tex]\frac{4x^{2}-24x+1}{1}[/tex]
~Divide everything by 1
[tex]4x^{2} -24x+1[/tex]
Best of Luck!
17) There are 250 people at the mall and 148
have brown hair, approximately what percent
of the people have brown hair?
a) 20%
b) 60%
c) 70%
d) 100%
Like what is this and how do you do it please explain clearly and understandable
Answer:
1/4
Step-by-step explanation:
HT represent the probability of tossing a head then Tail.
There is 4 possible results and only 1 give us HT.
We call this theoretical probability. which is
[tex] \frac{x}{y} [/tex]
where x is favorable outcomes and y is total number of outcomes.
So there is a 1/4 probability of getting a head followed by a tail.
7. Using the diagram below, find the length of segment 5G
3x+1
6%
X+6
t
S
А G
w
Answer:
[tex]\huge\boxed{\sf SG = 31}[/tex]
Step-by-step explanation:
Given:
SW = 3x + 1
WA = 6x
AG = x + 6
SW = AG
Required:
Length of SG = ?
Solution:
Given that:
SW = AG
3x + 1 = x + 6
Combining like terms
3x - x = 6 - 1
2x = 5
x = 5/2
x = 2.5
Now,
SG = SW + WA + AG
SG = 3x + 1 + 6x + x + 6
SG = 3x + 6x + x + 1 + 6
SG = 10x + 6
Put x = 2.5
SG = 10(2.5) + 6
SG = 25 + 6
SG = 31
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!Find the mean medan mode
and range for the following
numbers
3.125.8.6.6
I'm not sure if this is what you meant - 3.12.5.8.6.6, but I'm operating based on that
mean - 6.7
median - 6
mode - 6
range - 9
Help anyone can help me do this question 2,I will mark brainlest.
Answer:
see explanation
Step-by-step explanation:
For the triangle to be isosceles it must have 2 equal sides.
Calculate the length of the sides using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = B (3, 5)
AB = [tex]\sqrt{(3-(-1))^2+(5-2)^2}[/tex]
= [tex]\sqrt{(3+1)^2+3^2}[/tex]
= [tex]\sqrt{4^2+9}[/tex]
= [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5
Repeat with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = C (3, - 1)
AC = [tex]\sqrt{(3+1)^2+(-1-2)^2}[/tex]
= [tex]\sqrt{4^2+(-3)^2}[/tex]
= [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5
Consider B (3, 5) and C (3, - 1)
Since both x- coordinates are 3, this is a vertical line and its length is the difference of the y- coordinates, that is
BC = | - 1 - 5 | = | - 6 | = 6
Then
AB = AC = 5 , BC = 6
Since AB = AC = 5 then the triangle is isosceles
If the cost price of 21 article is equalto the selling price of 18 articles. Find profit precent
Answer:
The selling price of 21 articles is equal to the cost price of 18 articles. Find the loss percent. Answer: answer is 100/7 %
It is midpoint please help
Step-by-step explanation:(2, -3)
[tex]thank \: you[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{5+8}{2},\dfrac{3.5+10}{2}\right)[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{13}{2},\dfrac{13.5}{2}\right)[/tex]
Which is the circumference of the circle? (Use = 3.14)
A. 376.8 cm
B. 188.4 cm
c. 113.04 cm
D. 37.68 cm
E 18.84 cm
Answer:
D 37.64
Step-by-step explanation:
C=2πr
so 2✘3.14 ✘6
The factorization of a (x + y + z) + b(x + y + z) + c(x + y + z) is
(≧▽≦)( ◜‿◝ )♡
this is symbol for no spamming so don't spam
Each term has a common factor of x + y + z, so
a (x + y + z) + b (x + y + z) + c (x + y + z) = (a + b + c) (x + y + z)
The measure of an angle is 87°. What is the measure of its supplementary angle?
Answer:
180-87 = 93
Step-by-step explanation:
supplementary angles add up to 180°
so (the other angle + 87)=180°
other angle =180-87=93°
Answer:
93 degrees
Step-by-step explanation:
Supplementary angles add up to 180 degrees. Therefore, the equation for finding the supplementary angle to 87 would be:
[tex]87 + x = 180\\x=180-87\\x=93[/tex]
Have a nice day. Feel free to ask questions. Spread the love.
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a. What is the area of the pool cover?
b. What is the length of the rope?
You must show all of your work to receive credit
Answer:
The cover has diameter of:
20 feet + 2*12 inches = 20 feet + 2 feet = 22 feeta.
Area of the pool cover:
A = πd²/4 = 3.14*22²/4 = 379.94 ft²b.
The length of the rope:
C = πd = 3.14*22 = 69.08 ftAnswer:
346.19ft65.94ftStep-by-step explanation:
Add the length of the pool and the extent the pool cover [ 12in = 1ft ] has over the pool.
20 + 2 = 22ft
Part A:
The formula for the area of a circle is πr².
To find the radius just divide by two; 22 / 2 = 11ft
= π(11)²
= 121π
≈ 379.94ft
Part B:
We can use the circumference formula [ dπ ] to find how long the rope is.
= 22(3.14)
= 69.08ft
Best of Luck!
Write this in set notation [-13; 4 )
Answer:
[tex]13\leq x<4[/tex]
Explanation:
If a side has a bracket [] then it is less than or equal to, meaning that it can reach that exact number.
However, if a side has a parentheses () then it is simply less than. It cannot be that exact number, but it can be even slightly less than that number.
Graph each set of integers on a number line
(-5, -1, 10, -9
Answer:
65÷5(18-5)
=65÷5×13
=13×13
=169
8^2 x 6{4 + 8^2(10 - 6)}^2
Answer:
25958400
Step-by-step explanation:
[tex] {8}^{2} \times 6(4 + {8}^{2} \times (10 - 6) {)}^{2} [/tex]
[tex] = 64 \times 6(4 + {2}^{6} \times 4 {)}^{2} [/tex]
[tex] = 64 \times 6(4 + {2}^{6} \times {2}^{2} {)}^{2} [/tex]
[tex] = 64 \times 6(4 + {2}^{8} {)}^{2} [/tex]
[tex] = 64 \times 6(16 + 2048 + 65536)[/tex]
[tex] = 64 \times 6 \times 67600[/tex]
[tex] = 25958400[/tex]
A computer and printer cost a total of 1152. The cost of the computer is three times the cost of the printer. Find the cost of each item.
Answer:
The cost of the printer is x=288 and cost of computer is 3x=864
Step-by-step explanation:
Let the cost of the printer be x and cost of computer be 3x
ATQ, x+3x=1152, x=288.
The cost of the printer is x=288 and cost of computer is 3x=864
in which figures is segment AB a median?
WILL RATE BRAINLIEST!!!
HELP
Answer:
B, D, H, I, J
Step-by-step explanation:
Median: A line segment that joins the vertex of a triangle to the midpoint of the opposite side.
can someone help me with this question
Answer: The guage block height is 4.98 m
The base of the right triangle that is formed is 7.3784 m
The last angle in the triangle is 56 degrees
Step-by-step explanation:
Redraw the triangle formed in the picture and use H for the hypotenuse, O for the block height, and A for the base. Now we can use trig (SOHCAHTOA) to find the answaers.
Using sine, we can first find the gauge block height, O (Opposite). Given the Hypotenuse (H) is 8.9 m, we can use the definition of the sine of an angle to find the height, O.
Sine(34) = Opposite/Hypotenuse (O/H), or O = H*Sine(34)
O = (8.9)*(0.5592)
O = 4.98 m, the height of the gauge block,
The base of the triangle, A, can be determined with cosine.
Cosine(34) = A/O, or A = Cosine(34)*O
A = (0.82904)*(8.9)
A = 7.3784 m
The sum of all angles in a triangle is 180 degrees.
180 = X + 34 + 90
X = 56 degrees
In the triangle above, the cosine of a is 0.8.What is sine of b?
Answer:
sin b = 0.8
Step-by-step explanation:
Since a and b are complementary angles , then
sin b = cos a = 0.8
The sine of angle b is 0.8
What is right triangle?"It is a triangle in which one of the angle measures 90° "
What is hypotenuse?"It is the longest side of the right triangle."
What is sine angle?"In a right triangle, sine of angle [tex]\theta[/tex] is the ratio of the opposite side of angle [tex]\theta[/tex] to the hypotenuse."
What is cosine angle?"In a right triangle, cosine of angle [tex]\theta[/tex] is the ratio of the adjacent side of angle [tex]\theta[/tex] to the hypotenuse."
What are complementary angles?"Two angles are complementary if the sum of their measures is equal to 90 degrees."
For given question,
We have been given a right triangle.
here,
∠a + ∠b = 90°
∠b = 90° - ∠a ................(i)
This means, a and b are complementary angles.
The cosine of a is 0.8
cos(a) = 0.8
We need to find the sine of angle b.
sin(b)
= sin(90 - a) .............(from (i))
= cos(a) .............(Since [tex]sin(90-\theta)=cos(\theta)[/tex])
= 0.8 ............(Given)
So, sin(b) = 0.8
Therefore, the sine of angle b is 0.8
Learn more about the sine angle here:
brainly.com/question/13256520
#SPJ2
Beverly just filled up her gas tank, which has enough gas to last her, at her usual driving rate, about 45 days. However, Beverly becomes extra busy and begins driving 66.6% more than she usually does. How many days does the tank of gas last Beverly at her new rate?
Answer:
27 Days
Step-by-step explanation
The rate of her gas consumption is inverse to the time she is driving. This means that if her time spent driving is increased by 66.66% (5/3 of the original rate), then it would inverse to create her decreased gas consumption by 3/5.
3/5 of 45 = 27
27 days
hope this helps :)
Help plz? Confusion :( mark brainiest if right
Answer:
The answer is C
Step-by-step explanation:
since the left side reads k times a, the only way to get a by itself is by dividing both sides by k
1.1x + 1.2x -5.4 =-10
Show answer
I circled the answer and put an example hope it helps
Will someone help me please?
Answer:
Ok so
Step-by-step explanation:
Yes yes yes yes its C
URGENT!!
1-84. Find the perimeter and area of each figure.
9.85 m
15 m
9 m
Answer:
total = 99m² + 39.4m²
= 148.4m²
Write -0.450 as a fraction in simplest form.
Answer:
-0.450 as a fraction is -9/20
Step-by-step explanation:
Since there 3 decimal places, divide it by 1000
-450/1000 and simplify it
A 180-inch pipe is cut into two pieces.one piece is three times the length of the other.find the length of the shorter piece.
The length of the shorter piece is 45 inches.
How to determine the length of the shorter piece.Let's represent the length of the shorter piece as "x" inches.
According to the information given, the length of the longer piece would be three times the length of the shorter piece, which means it's 3x inches.
Since the total length of the pipe is 180 inches, we can set up an equation:
x (shorter piece) + 3x (longer piece) = 180
Now solve for x:
4x = 180
x = 45
Therefore, the length of the shorter piece is 45 inches.
Learn more about length at https://brainly.com/question/26589728
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Determine the geometric mean of 8 and 12, to the nearest tenth.
A) 10.0
B) 4.5
C) 48.0
D) 9.8
Answer:
D) 9.8
Step-by-step explanation:
The geometric mean of two numbers x and y is
[tex]\sqrt{xy}[/tex]
so [tex]\sqrt{8*12}[/tex] = [tex]\sqrt{96}[/tex] [tex]\approx 9.7979[/tex]
Which, since the 9 in the hundredths place is greater than 5, we can round up to 9.8
a different way of proving the angle sum of a triangle is to use diagram
a.yes
Step-by-step explanation:
a.angle BCD =b because angle BCD is alternate angle of angle ABC
b.the two angles angle BAC and angle ACD is co-interior angle because they are inside a parallel line
Use the given graph to determine the limit, if it exists. A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1.5, a closed point at 3, 7, and a horizontal line starting at the open point 3, 2. Find limit as x approaches three from the left of f of x..
Explanation:
The given limit notation means we're approaching x = 3 from the left side. So start at say x = 0 and approach x = 3. We don't actually get to x = 3 itself, but instead just get closer and closer. Note how y gets closer to y = 1.5
Which of these are rational or irrational?
Answer:
Step-by-step explanation:
6.4 rationalwe don't know. It might repeat at some point.-2 rationalsqrt(16) = +/-4 which is rational.sqrt(12) is irrational. There's no pattern12/5 is rational 2.4we don't know. If it repeats then it is rational. The way it looks now, there's no pattern, so call it irrational.PLS HELP DUE TODAY
A polygon is regular if each of its sides has the same length. Find the perimeter of the regular polygon.
Here we go !!
Since it's a regular pentagon, all it's sides are equal so let's solve for x
[tex] \hookrightarrow \: 3(x - 1) = 5x - 6[/tex]
[tex] \hookrightarrow \: 3x - 3 = 5x - 6[/tex]
[tex] \hookrightarrow \: 3x - 5x = - 6 + 3[/tex]
[tex] \hookrightarrow \: - 2x = - 3[/tex]
[tex] \hookrightarrow \: x = \dfrac{ - 3}{ - 2} [/tex]
[tex] \boxed{\boxed{x = \dfrac{3}{2} }}[/tex]
now let's find the measure of each side, i.e
[tex] \hookrightarrow \: 5x - 6[/tex]
[tex] \hookrightarrow \: (5 \times \dfrac{3}{2}) - 6[/tex]
[tex] \hookrightarrow \: \dfrac{15}{2} - 6[/tex]
[tex] \hookrightarrow \: 7.5 - 6[/tex]
[tex] \mathrm{\hookrightarrow \: 1.5 \: units}[/tex]
perimeter = 5 × side length ( for a regular pentagon )
[tex] \hookrightarrow \: 1.5 \times 5[/tex]
[tex] \boxed{ \boxed{ \: \: \: \: \: \: \: \: 7.5 \: \: units \: \: \: \: \: \: \: }}[/tex]