Answer:
2640mm
Step-by-step explanation:
I'm assuming you need the area of the rectangle which the circles don't take up.
First, to find the area of the whole rectangle:
length x width
to find length:
the length is 1 circle, therefore it is the diameter of the circle, which is 32 x 2 = 64mm
to find width:
the width is 3 circles, which is the radius 6 times, so 32 x 6 = 192mm
So, area of rectangle = 64 x 192 = 12288mm
Now to find the area the circles take up:
area of 1 circle =
[tex]\pi \times {r}^{2} [/tex]
=
[tex]\pi \times {32}^{2} [/tex]
=
[tex]1024\pi[/tex]
As we have 3 circles, we multiply this by 3:
[tex]1024\pi \times 3 = 3072\pi[/tex]
Finally we subtract the area of the three circles from the area of the rectangle:
[tex]12288mm - 3072\pi = 2637[/tex]
As we need to round it to 3 significant figures, the answer is 2640mm
A linear equation in one variable (the variable x) that can be transformed into an equivalent equation in which of these forms has one solution?
A.
x = x
B. x= 3
C. 1=1
D. 1 = 3
Answer:
b maybe....
Step-by-step explanation:
3x^4 + 9x^3 - 5x^2 - 14x - 7 divided by x + 3 using synthetic division
Answer:
[tex]3x^3 - 5x + 1 - \frac{10}{x + 3}[/tex]
or
3x^3 - 5x + 1
Remainder: -10
Step-by-step explanation:
Please see attached image for full explanation!
1.) Write the coefficient of each term.
2.) Beginning with 3, multiply by -3, or x + 3 = 0 (the divisor.)
3.) Add the product to the next coefficient and repeat until you get to the last number, -7.
4.) You should have the numbers 3, 0, -5, 1, and -10.
5.) Rewrite this quotient as an equation:
3x^3 - 5x + 1
Note that the highest power is 3, one less than that of the highest power in the original equation.
6.) Don't forget the remainder!
You can include this in the equation or not, depending on the instructions.
Therefore, the final answer is 3x^3 - 5x + 1 - 10/x+3 or 3x^3 - 5x + 1 R: -10.
PLS HELP!!!! Mrs Gonzalez decides to write an algorithm that her employees follow when they open her store each day. What should be the first step of Mrs. Gonzalez process?
A. Check errors
B. Write a list of steps
C. Be sure that she understands every part of the situation
D. Think about what other situations could use an algorithm
Answer:
Write a list of steps
Step-by-step explanation:
Pls mark me brainliest! Tnx
help this is due today?
Answer:
2s for the first box
6u for the second box
Step-by-step explanation:
when they say like terms, just think about how the letter parts of the expression are the same
like 1/2s and 2s both have the singular variable s
and how 6u and 9u both have the singular variable u
To solve this one you have to find the ones that are connected by variables or look the same
For example.
1x and 2x are like terms because they have the same variable X
4d and 6/2d are like terms because they have the same variable D
4 and 3 are like terms because they have no variables, and they are the same
So now that you understand what like terms are you may so it
1/2 and 2s are like terms because they share the same variable S
6u and 9u are like terms because they share the same variable U
I hope this helped and if it's wrong blame me
Ps. Brainlist would really help
A line with a slope of 1/10 passes through the point (10, 1) What is its equation in slope-intercept form?
Hello there! :)
We are given the slope of the line: 1/10.We are also given the point that the line passes through.So, with the given information, we can use Point-Slope form:y-y1=m(x-x1)y-1=1/10(x-10)y-1=1/10x-1y=1/10xTherefore, that's the equation.Hope it helps. Use the comment section to clarify any doubts.
Answered by
~A teen who adores helping others
#LetItSnow
Good luck.
the equation of line which passes through point (10, 1) and having slope 1/10 is y = x/10 + 0.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
y = mx + b
In which the coefficients are described as follows:
• The coefficient m is the slope of the function, representing the rate of change of the function.
• The coefficient b is the y-intercept of the function, representing the value of y when the function crosses the y-axis(x = 0).
Here, it is given that line passes though point (10,1) and having slope of 1/10.
Now, Let us find the equation of the line using point-slope equation of line :
(y-y₁) = m(x-x₁)
Substituting all the values in above equation to get the equation of line :
(y-1) = 1/10(x-10)
y - 1 = x/10 - 1
y = x/10 + 0
Therefore, the equation of line which passes through point (10, 1) and having slope 1/10 is y = x/10 + 0.
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Maya is using shapes to create a repeating pattern. Which rule will give Maya a repeating pattern that has a triangle as the 20th shape?
A.
triangle, square, circle, circle
B.
square, triangle, circle, circle
C.
square, circle, circle, triangle
D.
circle, circle, triangle, square
Answer:
B.
square, triangle, circle, circle
Step-by-step explanation:
Answer:
C. square, circle, circle, triangle
Step-by-step explanation:
The repeating patterns are 4 elements long. Element 20 will be the last element in the 5th repeat of the pattern. That is, the triangle must be the last element of the pattern.
The rule in choice C has the triangle last.
Give the number and type of solutions of the equation.
Answer:
B. 2 non-real solutionsStep-by-step explanation:
Compare the left and right side of the given equation in terms of the lines they represent:
x² is a parabola with non-negative value- 3x - 7 is a line with negative slope and negative y-interceptTheir intersection seems not possible. Lets graph and confirm.
See attached below.
It means there are no real solutions. Correct answer choice is B
Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l contains point S. The length of segment R S is 2 x + 8. The length of segment S Q is 8 x minus 4.
What is the length of segment SR?
Answer:
12
Step-by-step explanation:
Since RS = QS, we know 2x + 8 = 8x - 4
Subtract 2x from each side
8 = 6x - 4
Add 4 to each side
12 = 6x
Divide each side by 6
2 = x
SR is 2x + 8, so it is 2(2) + 8, so RS = 12
The length of the segment SR is 12.
What is a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
Since RS = QS, we know 2x + 8 = 8x - 4
Subtract 2x from each side
8 = 6x - 4
Add 4 to each side
12 = 6x
Divide each side by 6
2 = x
SR is 2x + 8, so it is 2(2) + 8, SR = 12
Hence, the segment SR is 12.
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The length of a metal rod is 9 3/4 feet. What is the length of 1/4 of the rod?
Answer:
2 [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
2 [tex]\frac{5}{16}[/tex] × 4 = 9 3/4
9 3/4 × 1/4 = 2 5/16
I hope this helps!
Answer:
3 1/4 feet
Step-by-step explanation:
1/4 of 9 3/4
change 9 3/4 into an improper fraction → 39/3
1/4 x 39/3 = 39/12
convert back to a mixed number by dividing 12 into 39
which goes in three times with a remainder of 3 → 3 3/12
however, 3/12 can be simplified to equal 1/4
Put these numbers in order from least to greatest.-12/40 -5 19/38
this is the answer: -5 < -12/40 < 19/38
Help ASAPPPPP ALGEBRA 2
This is cross multipication. Multiply 117 times 36 together for that you would use a calculator. You get 4221. Next step is to multiply x and 12 together that would be 12x.
4221= 12x
Divide by 12 on both sides:
x= 351
351 is # of trouts in the lake .
divide 2(1+2)
No calculator, if u use something bad, will happen to u
The answer would be 6.
The first four terms of a sequence are shown below: 9, 5, 1, â’3 Which of the following functions best defines this sequence? f(1) = 9, f(n 1) = f(n) â’ 4; for n ≥ 1 f(1) = 9, f(n 1) = f(n) 4; for n ≥ 1 f(1) = 9, f(n 1) = f(n) â’ 5; for n ≥ 1 f(1) = 9, f(n 1) = f(n) 5; for n ≥ 1.
The function that best defines this arithmetic sequence is:
[tex]f(n) = f(n - 1) - 4, f(1) = 9[/tex]What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.The recursive function that defines the sequence is:
[tex]f(n) = f(n - 1) + d[/tex]
[tex]f(1) = f_0[/tex]
In which [tex]f_0[/tex] is the first term.In this problem, the sequence is: {9, 5, 1, -3}
Each term is the previous term subtracted by 4, hence [tex]d = -4[/tex].The first term is 9, hence [tex]f_0 = 9[/tex].Hence, the function is:
[tex]f(n) = f(n - 1) - 4, f(1) = 9[/tex]You can learn more about arithmetic sequences at https://brainly.com/question/6561461
To identify the functions which best define the given sequence, we have to identify the number pattern.
The correct option is (a).
Given:
The given sequence is as follows,
[tex]9,5,1,-3[/tex]
What is an arithmetic sequence?The arithmetic sequence define as the difference between two consecutive number would be same.
If we subtract 4 form each digit we will get next digit.
[tex]9-4=5\\5-4=1\\1-4=-3[/tex]
So the function would be,
[tex]f(1) = 9, f(n + 1) = f(n) -4; \rm for \:n\geq 1[/tex]
The option (b) and (d) show the increasing function whereas we have decreasing sequence.
Thus, the correct option is (a).
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Need help fast hs geometry
= [180 - (100 + 40)]° = 40°
When two angles of a triangle are equal, then the triangle is isosceles.Here, the measure of angle A and B are equal, i.e., 40°So, ∆ABC is an isosceles triangle.Answers:
40°YesHope you could get an idea from here.
Doubt clarification - use comment section.
Write an equation in point-slope form of the line that passes through the point (−3,6) and has a slope of 5.
Answer:
Below in bold.
Step-by-step explanation:
Point slope form is y - y1 = m(x - x1)
where m = the slope of the line and (x1, y1) is a point on the line.
Here m = 5, x1 = -3 and y1 = 6.
So we have:
y - 6 = 5( x - (-3))
y - 6 = 5(x + 3) (Answer)
The price of 50 litres of petrol is £36, find the price of each litre of petrol.
Answer number 7: Only number 7 please.
Answer:
C -7, 3
Step-by-step explanation:
Answer:
A (7, 3).
Step-by-step explanation:
( -7, -3) reflected over the x axis goes to the point (-7, 3)
(-7, 3) reflected across the y axis goes to (7, 3).
M.) A typical tip in a restaurant is 15% of the
total bill. If the bill is $125, what would the
typical tip be?
How many inflection point(s) do you see ?
Answer:
7
Step-by-step explanation:
There is a point of inflection at each point where the graph crosses the line y=2. There are 7 points of inflection shown.
__
A point of inflection is where the graph changes from being concave downward to concave upward, or vice versa. For a sine function, that is everywhere the function crosses its midline.
Answer:
7 inflection points
Step-by-step explanation:
The given function [tex]f(x)=sinx+2[/tex] has a midline of y=2 where each point of the function that intersects the line is an inflection point. Inflection points are where the concavity changes, defined by when the second derivative is equal to 0 or undefined.
[tex]f(x)=sin(x)+2[/tex]
[tex]f'(x)=cos(x)[/tex]
[tex]f''(x)=-sin(x)[/tex]
[tex]0=-sin(x)[/tex]
[tex]x=\pi n[/tex] for any integer [tex]n[/tex]
From [tex][-10,10][/tex], there are 7 inflection points, which are[tex]x=-3\pi,-2\pi,-\pi,0,\pi,2\pi,3\pi[/tex]
Kennyhas$893inasavingsaccount.The interest rate is 8 1/5%, compounded annually.
To the nearest cent, how much interest will he earn in 5 years?
[tex] \sf \: I = P(1 + \frac{r}{n} {)}^{nt} - P \\ \sf = 893(1 + \frac{41}{500} ) ^{1 \times 5} - 893 \\ \sf= 893 \times ( \frac{541}{500} ) ^{5} - 893 \\ \sf= 1324.30 - 893 \\ \sf = 431.30[/tex]
Answer:
$431.30(approximate value)
Hope you could get an idea from here.
Doubt clarification - use comment section.
what is the solution to the equation 4(x - 3) - 8 = 16?
Step-by-step explanation:
4(x-3)-8=16
4x-12-8=16
4x-20=16
4x-20+20=16+20
add
4x=36
divide both
4x/4 36/4
Simplify
x = 9
Triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2).
?
Complete the following equation for a line passing through point C and perpendicular AB.?
Answer:
5y - 6x = 8 or y = 6x/5 + 8/5
Step-by-step explanation:
let M1= gradient of line AB and M2= gradient of the second line
When two lines are perpendicular, the product of their gradients is -1
i.e, M1M2= -1
M2= -1/M1
A(2,9) and B(8,4)
gradient= (y2-y1)/(x2-x1)
M1= (4-9)/(8-2)
= -5/6
M2= -1÷ -5/6
-1 × -6/5= 6/5
Equation of the line passing through C(-3,-2)
[y-(-2)]/[x-(-3)= 6/5
(y+2)/(x+3)= 6/5
5(y+2)= 6(x+3)
5y+10=6x+18
5y= 6x + 8
y= 6x/5 + 8/5
As per the slope-intercept form of a straight line, the equation of the required line is 5y = 6x + 8.
What is the slope-intercept form of a straight line?The slope-intercept form of a straight line is: y = mx + c
Here, m = slope of the line , c = y-intercept
What is the relation between the slope of a line perpendicular to another line?If the slope of a line is 'a', then the slope of the line that is perpendicular to the given line is (- 1/a).
The given coordinates of the points A, B, C are (2, 9); (8, 4); and C(- 3, - 2) respectively.
Therefore, the slope of the line AB is (m)
= (y₂ - y₁)/(x₂ - x₁)
= (4 - 9)/(8 - 2)
= (- 5)/6
Slope of the required line is perpendicular to AB.
Therefore, the slope of the required line is
= - 1/(- 5/6)
= 6/5
This line passes through point C(- 3, - 2).
- 2 = - 3(6/5) + c
⇒ c = -2 + 18/5
⇒ c = 8/5
The equation of the required line is
y = (6/5) x + (8/5)
⇒ 5y = 6x + 8
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Solve, 7x-5y=20
-8x-3y=12
Answer:
x=0 y=-4
Step-by-step explanation:
Two numbers are in a ratio 11:7. If the smaller number is 700, what is the larger number? Pls tell with steps
Answer:
The larger number is [tex]1100[/tex]
Step-by-step explanation:
Let larger number be [tex]x[/tex]
We have
[tex]\frac{x}{700} =\frac{11}{7} \\\\x=100\times11\\\\=1100[/tex]
Answer:
The larger number is 1100.
Step-by-step explanation:
Solution :
Let the,
>> Larger number be 11x. >> Smaller number be 7x.Now, According to the question :
[tex]\begin{gathered} \dashrightarrow\sf{Smaller \: number} = \tt{700} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{7x}= \tt{700} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{700 \div 7} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{ \dfrac{700}{7} } \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{\cancel{\dfrac{700}{7}}} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow \sf{x}= \tt{100} \end{gathered}[/tex]
Hence, the value of x is 100.
Now, calculating the larger number :
[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{11x} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{11 \times 100} \end{gathered}[/tex]
[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{1100} \end{gathered}[/tex]
Hence, the larger number is 1100
[tex]\rule{300}{1.5}[/tex]
Solve for C if F = 77º. 5 C = (F-32) -
Answer:
C = 25
Step-by-step explanation:
C = 5/9(77-32)
C = 5/9(45)
C = 25
Suppose line g is the line with equation y=x. Given A(6,-2), B(6,3), and C(-2,-6), what are the coordinates of the vertices of A'B'C' for the reflection?
NEED ANSWER ASAP
Rg
Answer:
A'(-2, 6)B'(3, 6)C'(-6, -2)Step-by-step explanation:
Reflection across the line y=x swaps the x and y coordinates:
(x, y) ⇒ (y, x)
The image points are ...
A(6, -2) ⇒ A'(-2, 6)
B( 6, 3) ⇒ B'(3, 6)
C(-2, -6) ⇒ C'(-6, -2)
Triangle ABC has coordinates A(−6,2), B(−3,6), and C(5,0). Find the perimeter of the triangle. Round your answer to the hundredths place (2 decimal places) I will give brainliest
Answer:
26.18 units
Step-by-step explanation:
You could use distance formula three times to calculate the length of each side. Add the three lengths to find the perimeter. However, (see image) if you look at a graph of these points, two of the sides are the hypotenuse of a right triangle that have known, integer values--Pythagorean triples. The sides are 3-4-5 and the other is 6-8-10. We use the Pythagorean theorem to find the third side. See image.
11.18 + 5 + 10
= 26.18 units
The perimeter of triangle is 26.18.
What is triangle?A triangle is 2-dimensional closed curve. which has 3 sides, 3 angles and 3 vertices.
According to the question,
Triangle ABC has coordinates A(-6,2), B(-3,6), C(5,0).
Distance formula: √(x₂-x₁)² + (y₂-y₁)².
Points A and B are (-6,2) and (-3,6)
= √(-3-(-6))² + (6-2)²
= √9+16
= √25
=5.
Thus, point A and B has distance, S₁ = 5.
Points B and C are (-3,6) and (5,0)
Distance formula: √(x₂-x₁)² + (y₂-y₁)²
= √(5-(-3))² + (0-6)²
= √(8)² + (-6)²
= √(64+36)
=√100
=10.
Thus, point B and C has distance, S₂ = 10.
Points C and A are (5,0) and (-6,2)
Distance formula: √(x₂-x₁)² + (y₂-y₁)²
= √(-6-(5))² + (2-0)²
= √((-11)² + (2)²)
=√(121+4)
=√125
=5√5
Thus, point C and A has distance, S₃= 5√5.
Perimeter of triangle = S₁ + S₂+S₃
= 5 + 10 + 5√5
=15+5√5
=15+5(2.23606)
=15+11.1803
=26.1803 ≈ 26.18
Hence, the perimeter of triangle is 26.18.
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Find the zeros of ƒ(x) = x3 + 6x2 + 8x.
A) x = 0, –2, –4
B) x = 0, 2, 4
C) x = 2, 4
D) x = –2, –4
Answer:
Option A: [tex]x=0[/tex], [tex]x=-2[/tex], and [tex]x=-4[/tex]
Step-by-step explanation:
[tex]f(x)=x^3+6x^2+8x[/tex]
[tex]0=x^3+6x^2+8x[/tex]
[tex]0=x(x^2+6x+8)[/tex]
[tex]0=x(x+2)(x+4)[/tex]
[tex]x=0[/tex], [tex]x=-2[/tex], and [tex]x=-4[/tex]
[tex]x^3+6x^2+8x = 0\\\\\implies x^3+2x^2 +4x^2+8x =0\\\\\implies x^2(x+2) +4x (x+2) =0\\\\\implies (x+2)(x^2 +4x) = 0\\\\\implies x (x+2) (x+4)=0\\\\\text{Hence,} \\\\x = 0 ,-2,-4[/tex]
The formula to convert degrees Fahrenheit to degrees Celsius is: 'C = (5/9) ('F -32). The formula to convert degrees Celsius to degrees Fahrenheit is: 'F = 1.8 ('C) + 32. Using any of these formulas, determine, for what temperature the value of it in degrees Celsius is represented by the same number as its value in degrees Fahrenheit. Show your work. HINT: use either of those two equations, use x for 'C and use x for 'F, and solve it for x. The solution will be the answer to the problem (because the temperature is the same, and its numerical value in degrees Celsius in this case is the same as its number value in degrees Fahrenheit). *
Step-by-step explanation:
5/9 × (x - 32) = 1.8 × x + 32 = 9/5 × x + 32
5×(x - 32) = 9×9/5 × x + 32×9
5×5×(x - 32) = 9×9×x + 32×9×5
25x - 32×25 = 81x + 32×45
32×(-25 - 45) = 56x
4×(-70) = 7x
x = 4×(-10) = -40
-40° is the same temperature in Celsius and in Fahrenheit.
Plc help! Factor completely 2a^3b-ab^3-1 2/3ab^3-a^3b-4 1/2a^2b-1/2a^2b
Answer:
116−−√
110−−√
14√
18√
Step-by-step explanation: