Answer:
area of entire circle = 84 in²
Explanation:
[tex]\sf \dfrac{\theta}{360} *\pi *r^2 = Area \ of \ sector[/tex]
===========
[tex]\sf \rightarrow \dfrac{60}{360} *\pi *r^2 = 14[/tex]
[tex]\sf \rightarrow \dfrac{1}{6}\pi *r^2 = 14[/tex]
[tex]\sf \rightarrow r^2 = \dfrac{14*6}{ \pi}[/tex]
[tex]\sf \rightarrow r = \sqrt{\dfrac{84}{ \pi} }[/tex]
[tex]\sf \rightarrow r = 5.17\ in[/tex]
Area of circle:
[tex]\sf \pi r^2[/tex]
=====
[tex]\hookrightarrow \sf \pi (5.17)^2[/tex]
[tex]\hookrightarrow \sf 84\ in^2[/tex]
Eliminate the parameter.
x = 5t, y = t + 8 (2 points)
Answer: y = [tex]\frac{1}{5}[/tex]x + 8
Step-by-step explanation:
This is asking us to remove the parameter. In other words, we want an equation with only the relation between x and y, so we need to remove the t. There are a few ways to do this, but I am going to set one equation equal to t and then plug it into the next one.
Given:
x = 5t
Divide both sides of the equation by 5:
t = [tex]\frac{1}{5}[/tex]x
-
Given:
y = t + 8
Plug in:
y = ([tex]\frac{1}{5}[/tex]x) + 8
Answer:
y = [tex]\frac{1}{5}[/tex]x + 8
Find the missing side of the right triangle.
options:
6.5 ft
7 ft
5.5 ft
6 ft
Answer:
6ft, the missing side is the base(b), 10ft is the hypotenuse(h) and 8ft is the perpendicular(p). The formula for base is root over h²-p² and root over 10²-8² equals 6.
what is an equation of the line that passes through the points (6,3) and (-6,1)
Answer: y = [tex]\frac{1}{6}[/tex]x + 2
Step-by-step explanation:
[1] First, we will graph the points given. See the attachment with [1] in the corner.
[2] Next, we will find the slope.
(2a) Using rise over run. See the attachment with [2] in the corner.
(2b) Use the slope equation:
[tex]\displaystyle \frac{1-3}{-6-6}= \frac{-2}{-12} =\frac{1}{6}[/tex]
[3] Find the y-intercept. Look to the graph. See the attachment with [3] in the corner.
This gives us a final answer of y = [tex]\frac{1}{6}[/tex]x + 2
Translate this phrase into an algebraic expression.
One less than the product of 18 and a number
Use the variable n to represent the unknown number.
one less than the 18 and a number
18 × n = (product) - 1
simplify (-3x)^2
please I need to know this answer
Answer:
9x²
Step-by-step explanation:
(- 3x)²
= - 3x × - 3x
= - 3 × - 3 × x × x
= 9 × x²
= 9x²
what is pi and why do we need it
Answer:
Pi is the number you get from dividing the circumfrence by the diameter of a perfect circle. It is important because without this, we wouldnt have perfect circles and even wheels could be disformed and cause crashes.
Answer:
Pi is an infinite number. We need it to find the area and circumference of a circle.
Step-by-step explanation:
Opposite of 3 less than 10
Answer:
-13
Step-by-step explanation:
Answer:
-13
Step-by-step explanation:
Becuase 13's opposite is -13.
(If you still dont understand you can search up negative and positive number lines up to 20!)
The hypotenuse of a right triangle ensures 17cm and one of its legs measures 13cm
Answer:
sqrt (120)
Step-by-step explanation:
Use pythag theorem
Leg1 ^2 + Leg2^2 = Hypot ^2
13^2 + Leg2^2 = 17^2
Leg2^2 = 17^2 - 13^2
Leg2 = sqrt (120)
23). figure b is a scale image of figure a enter the scale factor applied.
24). to figure A to produce fiber B
Answer:
9
Step-by-step explanation:
The scale factor is the ratio of a Figure B dimension to the corresponding Figure A dimension.
__
The ratio of left-side dimensions is ...
scale factor = fig B/fig A = 81/9 = 9
The scale factor is 9.
Answer:9
Step-by-step explanation:
A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and
2 plastic containers contain 6p quarts of water in all
how much water can the plastic container hold? give your answer is terms of p.
Answer:
12
Step-by-step explanation:
collect the like terms and divide
(p+6)2×2=64p+24=6p1) Water in a plastic container, p'= 10 - 3 p
2) Water in a glass container = 27 quarts
Water in a plastic container = 1 quarts
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.
Now,
Let j represents water in one glass jag while p' represents the water in one plastic container,
Hence, According to the question,
⇒ j - p' = 6p+8 --------(1)
And, 2j+2p'=56p --------(2)
2 × equation (1)
⇒ 2 j - 2 p' = 12p + 16 ---------(3)
Equation (2) + equation (3)
We get, 4 j = 12 p + 72
⇒ j = 3 p + 18
Putting this value in equation (1),
We get, 3p+18-p'=6p+8
p' = -3p + 10 = 10 - 3p
Thus, water in a plastic container, p'= 10 - 3 p
b) If p=3
Water in a glass container = 3 × 3 + 18 = 27 quarts
Water in a plastic container = 10 - 3 × 3 = 1 quarts
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
What’s the area of the circle?
Answer:
153.86
Step-by-step explanation:
The area of a circle is π[tex]r^2[/tex].
Since the radius of that circle, and we are using 3.14 for π, we get:
[tex]3.14 * 7^2 = 153.86[/tex]
Answer:
Technically you should get :153.94
But for your answer choice its the 2nd one.
Step-by-step explanation:
area=πr^2
Which means that you would plug in 7 for r.
Which means it would look like this: area=π7^2
Next you would square 7 which comes out to 49
Lastly multiply 49 time π (3.14)
HELPPPP PLEASEEE!!!!!!!!!!!!!!!!!!!!
Answer:
I can't see the full question but as far as I can tell
by the picture
x=100
What is the perimeter of the figure?
Answer:
68.7
Step-by-step explanation:
Lets say this triangle is represented as ABC.
AB = BC
So:
23+23+22.7 = p
p = 68.7
help me find m and n please
Answer:
n is 68 and m is 44
Step-by-step explanation:
Factor 15x ^2 −42xy+24y^2
please help me with this slope intercept form
Answer:
5x+3=8
Step-by-step explanation:
this is the answer
Write an equation in slope-intercept form that is perpendicular to 4x - 5y = 1 and passes through (-3, 4).
Answer:
y=[tex]\frac{-5}{4}[/tex]x + [tex]\frac{-1}{ 4}[/tex]
Step-by-step explanation:
4x-1=5y
4/5 is the original slope and negative [tex]\frac{5}{4}[/tex] is the perpendicular slope.
Using that to put (-3,4) and the slope into point-slope form:
y-4=[tex]\frac{-5}{4}[/tex](x+3)
distribute and isolate y
y=[tex]\frac{-5}{4}[/tex]x + [tex]\frac{-1}{4}[/tex]
Answer:
y = -5/4x + 1/4
Step-by-step explanation:
*Pependicular line have negative reciprocal slopes*
Rewrite your equation to slope-intercept form: y = mx + b
y = mx + b
m = slopeb = y-intercept (when x = 0)4x - 5y = 1 <== subtract 4x from both sides
-4x -4x
-5y = -4x + 1 <== divide both sides by -5
/-5 /-5
y = 4/5x - 1/5
Find the Negative reciprocal of the line:
Steps:
1. Take your original slope (4/5)
2. Flip it (5/4)
3. Change the sign (-5/4)
The slope of the perpendicular line would be: -5/4 (y = -5/4x + b)
We need to find the y-intercept (b) for the perpendicular line using (-3, 4):
y = -5/4x + b <== substitue -3 for x and 4 for y
4 = -5/4(-3) + b
4 = 15/4 + b <== multiplify both sides by 4
4(4 = 15/4 + b)
16 = 15 + 4b <== subtract 15 from both sides
-15 -15
1 = 4b <== divide both sides by 4
/4 /4
1/4 = b
y = -5/4x + b changes to y = -5/4x + 1/4
Hope this helps!
What is the fourth term of the geometric sequence whose first term is 7 and has a common ratio of -2
Answer:
-56
Step-by-step explanation:
It is often easiest to find terms of a sequence by simply writing each one based on the previous one. Here, the common ratio of -2 tells you that each term is -2 times the previous term.
The first four terms are ...
7, -14, 28, -56
The fourth term is -56.
factor the equation y=9x²-18x+9
Answer:
9(x-1)(x-1) or 9(x-1)²
Step-by-step explanation:
9x² - 18x + 9
factor out a 9
9(x² - 2x + 1)
use middle term factorization to factor x² - 2x + 1
9(x-1)(x-1) or 9(x-1)²
Middle term factorization explained:
For x² - 2x + 1, you want to find 2 numbers that multiply to +1 and add to -2. You then split x² to x and x and add the 2 numbers individually to x.
It should look something like (x+1st number)(x+2nd number)
the two numbers that multiply to get to 1 and add to get to -2 are -1 and -1
( -1 × -1 = 1 and -1 + -1 = 2 )
so we then add the number to the split x² to get (x-1)(x-1) which is the same as (x-1)², the 9 is then added to the factored form to get 9(x-1)(x-1) or 9(x-1)²
!!!!????????!!!!!??????
Answer:
h = 19 mm
Step-by-step explanation:
the volume (V) of the prism is calculated as
V = Ah ( A is the area of the base and h the height )
the base is a regular pentagon whose area (A) is calculated as
A = [tex]\frac{1}{2}[/tex] pa ( p is the perimeter and a the apothem )
p = 5 × 12 = 60 mm and a = 5 mm , then
A = [tex]\frac{1}{2}[/tex] × 60 × 5 = 30 × 5 = 150 mm²
given V = 2850 , then
150h = 2850 ( divide both sides by 150 )
h = 19 mm
Helppppp pls
I don’t understand I’ll give brainliest
Answer:
m∠5 = 75°
Step-by-step explanation:
Angle 2 and Angle 4 are the same as they are alternate interior angles.
Since m∠2 = 45°
We then have m∠4 = 45°
We are given m∠3 = 60°
Now, we just have to find 7∠5.
The sum of the angle of a triangle adds up to 180°.
So, m∠3 + m∠4 + m∠5 = 180°.
60° + 45° + m∠5 = 180°.
Solving for ∠5
m∠5 = 180° - (60° + 45°)
m∠5 = 180° - (105°)
m∠5 = 75°
hi guys I need this ASAP please answer ty
Answer:
6. 30% 7. -30%
Step-by-step explanation:
6. The total comment after the song released =5000
Then, the next day comment add up by 1500
Thus, (1500/5000) × 100
=30% of increase
7. 15.5-10.75 =4.75
(4.75/15.5 )×100= 30%
So, the decrease is -30%( If its about increase then its a positive number, but if its decrease just add a '-')
Answer:
See below ↓↓
Step-by-step explanation:
6.
% increase = Total - Original / Original5000 + 1500 - 5000 / 50001500 / 50000.330% increase8.
% decrease = | New - Original | / Original10.75 - 15.50 / 10.754.25 / 10.750.39539.5% decreasechris took a spelling quiz last week.she got 12 out of 16 problems correct.what percentage did chris get correct
Answer:
Chris got 75% correct.
Step-by-step explanation:
[tex]\frac{12}{16}[/tex] x 100 = 75
So, the percentage chris got correct is 75%
Answer:
He got 75% correct
Step-by-step explanation:
you can do it like this:
[tex]\frac{12}{16}[/tex] × 100 = 3× 25= 75%
Hope you understood and it helped!!
- Select the equivalent expressions. 71-9y and (7x - y) (9) 5 (3t - 6) and 15 - 30 4 (6a +86) and 10a + 126 16 + 72n and (2 + 9n) (8)
Answer:
D. 16 + 72n and (2 + 9n) (8)
Step-by-step explanation:
Select the equivalent expressions.
71 - 9y and (7x - y) (9) 5(3t - 6) and 15 - 30 4(6a +86) and 10a + 126 16 + 72n and (2 + 9n) (8)Distribute to find the equivalent expressions:
A.
71 - 9y and (7x - y) (9)
71 - 9y = 9(7x) + 9(-y)
71 - 9y = 63x - 9y
Not equivalent
B.
5(3t - 6) and 15 - 30
5(3t) + 5(-6) = 15 - 30
15t - 30
Not equivalent (it's missing the variable - t)
C.
4(6a + 86) and 10a + 126
4(6a) + 4(86) = 10a + 126
24a + 344 = 10a + 126
Not equivalent
D.
16 + 72n and (2 + 9n) (8)
16 + 72n = 8(2) + 8(9n)
16 + 32n = 16 + 72n
Equivalent
Therefore the correct answer is D
Hope this helps!
A train museum has a toy train that goes around the entire museum. the train goes around 10 times in 2 hours.
A student calculated the amount of times it takes for the train to go around 1 time. the work is shown.
2 hours ÷ 10 = 0.2 hour
0.2 is the same as 0.20, so it takes 20 minutes for the train to go around 1 time
the student's work is incorrect.
explain any error in the student's work
explain how to correct the student's work and find the amount of time it took for the train to go around the museum 1 time
Answer:
See below
Step-by-step explanation:
.2 of an hour is .2 * 60 min = 12 min
120 min / 10 times = 12 min per trip
The train takes 12 minutes to go around the museum once.
What is multiplication?A mathematical arithmetic operation is multiplication. Moreover, it is the practice of repeatedly adding the same expression kinds.
Example: 2 x 3 means that 2 is multiplied by 3 or that 3 is multiplied by 2 times.
A toy train that travels the length of a train museum is present. In two hours, the train travels roughly ten times.
The error in the student's work is converting 0.2 hours to 20 minutes. 0.2 hours is equal to 12 minutes, not 20 minutes.
To correct the student's work, we can multiply 0.2 by 60 to convert it to minutes:
0.2 hours × 60 minutes/hour = 12 minutes
Therefore, it takes 12 minutes for the train to go around the museum 1 time.
To learn more about multiplication;
https://brainly.com/question/19634536
#SPJ1
32,000 is what fraction of 106,000
Step-by-step explanation:
I hope this helps, you can ask any questions for clarification
One side of a rectangle is 7 inches longer than another side. If the longer side of this rectangle decreases by 3 inches, and the shorter side increases by 2 inches, the area of the new rectangle equals the area of the original rectangle. Find the dimensions of the original rectangle.
Answer:
Length = 8+7 = 15
Width = 8
Step-by-step explanation:
New
Length = x+7 , x+4
Width = x ,x+2
(x+7) x = (x+4)( x+2)
expand and simplify x =8
The length of the shorter side length of original rectangle is 8 inches and of original rectangle longer side length is 15 inches.
Area of rectangleLet l is the length and b is the breadth of the rectangle.
then the area of the rectangle is ab.
How to find the dimensions of the original rectangle?Given One side of a rectangle is 7 inches longer than another side.
then shorter side length is x and the large side length is 7+x.
then the area of the original rectangle is x(x+7)
Now calculate the sides of the new rectangle.
longer side of this rectangle decreases by 3 then new side is 7+x -3= 4+x
The shorter side increases by 2 inches then x+2.
So new rectangle area is (x+4)(x+2)
Both rectangle area is equal then
(x+4)(x+2) = x(x+7)
x² +2x+4x+8 = x²+7x
x²+6x+8 = x²+7x
x²-x²+7x-6x = 8
x = 8
Since a shorter side length is 8 inches and a longer side length is 8+7 =15 inches.
Learn more about rectangle here: https://brainly.com/question/15019502
#SPJ2
What expression can be used to subtract 2/3 - 4/9
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
1. [tex]\frac{2}{3} -\frac{4}{9}[/tex]
2. Multiply [tex]\frac{2}{3}[/tex] by [tex]\frac{3}{3}[/tex] to get a denominator equal to [tex]\frac{4}{9}[/tex]
3. [tex]\frac{2}{3} *\frac{3}{3} =\frac{6}{9}[/tex]
4. [tex]\frac{6}{9}-\frac{4}{9} =\frac{2}{9}[/tex]
The expression is: [tex]\frac{2}{3}*\frac{3}{3} -\frac{4}{9}[/tex]
Answer:
6/9-4/9
Step-by-step explanation:
ez pls mark branliest
Solve the equation and show your work.
A . 17x + 12 = 54 - 4x
B . 5x - 10 + 2x = 6(x + 1) - x
Answer:
A. x= 2
B. x= 8
Step-by-step explanation:
Solving an equation refers to finding the value of the variable in the equation.
A. 17x +12= 54 -4x
Bring all x terms to one side, constant to the other:
17x +4x= 54 -12
21x= 42
x= 42 ÷21
x= 2
B. 5x -10 +2x= 6(x +1) -x
7x -10= 6x +6 -x
7x -10= 5x +6
Bring all x terms to one side, constant to the other:
7x -5x= 10 +6
2x= 16
Divide both sides by 2:
x= 16 ÷2
x= 8
Hey ! there
Answer:
Value of x in equation A is 2 .Value of x in equation B is 8 .Step-by-step explanation:
In this question we are provided with two equations that are 17x + 12 = 54 - 4x and 5x - 10 + 2x = 6(x + 1) - x . And we are asked to solve the equation that means we have to find the value of x for both the equations .
Solution : -
A)[tex] \longmapsto \qquad \: 17x + 12 = 54 - 4x[/tex]
Step 1 : Subtracting 12 on both sides :
[tex] \longmapsto \qquad \: 17x + \cancel{ 12} - \cancel{12} = \bold{54} - 4x - \bold{ 12}[/tex]
Simplifying it ,
[tex] \longmapsto \qquad \: 17x = 42 - 4x[/tex]
Step 2 : Adding 4x on both sides :
[tex] \longmapsto \qquad \: 17x + 4x = 42 - \cancel{4x} + \cancel{4x}[/tex]
On further calculations, we get :
[tex] \longmapsto \qquad \: 21x = 42[/tex]
Step 3 : Dividing with 21 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{21}x}{ \cancel{21} } = \cancel{ \dfrac{42}{21} }[/tex]
We get :
[tex] \longmapsto \qquad \: \red{\underline{\boxed{ \frak{x = 2}}}} \quad \bigstar[/tex]
Henceforth , value of x is 2 .Verifying : -
Now , we are verifying our answer by substituting value of x as 2 in the given equation . So ,
17x + 12 = 54 - 4x 17 ( 2 ) + 12 = 54 - 4 ( 2 )34 + 12 = 54 - 846 = 46L.H.S = R.HSHence , Verified .Therefore , our solution is correct .
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
B)[tex] \longmapsto \qquad \: 5x - 10 + 2x = 6(x + 1) - x[/tex]
Step 1 : Adding like terms on left side :
[tex] \longmapsto \qquad \: 7x - 10 = 6(x + 1) - x[/tex]
Step 2 : Solving parenthesis on right side by using distributive property . ( Multiplying 6 with x and 1 both ) :
[tex] \longmapsto \qquad \: 7x - 10 = \bold{6x} + 6 - \bold{x}[/tex]
Step 3 : Solving like terms on right side :
[tex] \longmapsto \qquad \: 7x - 10 = 5x + 6[/tex]
Step 4 : Adding 10 on both sides :
[tex] \longmapsto \qquad \: 7x - \cancel{10} + \cancel{ 10} = 5x + 6 + 10[/tex]
Simplifying it ,
[tex] \longmapsto \qquad \: 7x = 5x + 16[/tex]
Step 5 : Subtracting 5x on both sides :
[tex] \longmapsto \qquad \: 7x - 5x = \cancel{5x }+ 16 - \cancel{5x}[/tex]
On further calculations , we get :
[tex] \longmapsto \qquad \: 2x = 16[/tex]
Step 6 : Dividing with 2 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{2}x}{ \cancel{2}} = \cancel{\dfrac{16}{2} }[/tex]
We get :
[tex] \longmapsto \qquad \: \red{\underline{\boxed{ \frak{x = 8}}} } \quad \bigstar[/tex]
Henceforth , value of x is 8 .Verifying : -
Now , we are verifying our answer by substituting value of x as 8 in the given equation . So ,
5x - 10 + 2x = 6(x + 1) - x5 ( 8 ) - 10 + 2( 8 ) = 6 ( 8 + 1 ) - 840 ( - 10 ) + 16 = 6 ( 9 ) - 856 - 10 = 54 - 846 = 46L.H.S = R.H.SHence , Verified .Therefore , our solution is correct.
#Keep LearningWhat is the greatest common denominator of 24 and 25
Answer:
1
Step-by-step explanation:
The only number 24 and 25 can both have is 1