When shopping for accessories for her action camera, Giana found an advertisement for a replacement battery. The advertisement includes
the given graph of a function to represent the charge remaining in the battery after streaming x hours of video.
Answers
Answer:
The correct options are;
The equation of the function is 2·y = -25·x + 200
The equation of the function is y = -25/2·x + 100
The x-intercept of the function is (8, 0)
Step-by-step explanation:
From the graph of the function, the y-intercept is observed at (0, 100), the x-intercept occurs at (8, 0)
Therefore, we have the slope, m given by the following relation
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where:
y₁ = 100
x₁ = 0
y₂ = 0
x₂ = 8
Which gives;
[tex]m =\dfrac{0-100}{8-0} = -12.5[/tex]
The equation in slope can be found as follows
y - 100 = -12.5×(x - 0)
y = -12.5·x + 100 = -25/2·x + 100
Multiplying by 2 gives;
2·y = -25·x + 200
25·x + 2·y = 200
Therefore, the correct options are;
The equation of the function is 2·y = -25·x + 200
The equation of the function is y = -25/2·x + 100
The x-intercept of the function is (8, 0).
Answer:
The x-intercept for the function is (8,0).
The equation of the function is 25x + 2y = 200.
The equation of the function is y =-25/2 x + 100.
Step-by-step explanation:
Related Questions
PLLLLLLLLLLLLLLLEEEEEEEEEAAAAAAAASSSSSSSE HEEEEEEEEELP As soon as a new car that costs $25,000 is driven off the lot, it begins to depreciate at a rate of 24.9% annually. About how much money is the car worth after the second year?
Answers
Answer:
The value of the car after two years is $14,100.025
Step-by-step explanation:
Here, we want to calculate the value of a car after its second year, given the depreciation percentage.
To get the value of the car year after year at the fixed percentage level, what we do is to set up an exponential equation;
V = I(1-r)^t
where V is the present value
I is the initial value = $25,000
r is the rate = 24.9% = 24.9/100 = 0.249
t is the number of years = 2 in this case
So we substitute these values in the depreciation case and have;
V = 25000(1-0.249)^2
V = 25000(0.751)^2
V = $14,100.025
Find the area of the composite figure in square mm. Round your
answer to the nearest square milimeter. (Enter only a number as
your answer.)
Answers
Answer:
521
Step-by-step explanation:
Composite figure.
Draw a straight down from C to line segment AB. This forms a triangle.
Now, the area of this figure=
Area of semicircle+area of rectangle+ area of triangle.
Rectangle area formula = l times w
Length - 20
Width =14
14 times 20 = 280
Area of rectangle = 280
Semicircle area = area of circle/2
Area of circle = π[tex]r^2[/tex]
Diameter =20= 2r
r=10
π[tex]r^2[/tex]= π 10^2 =100π
100 times 3.14 =314
314/2 = 157
Area of semicircle = 157
Area of triangle= bh/2
Triangle's base= 32-20=12
Triangles height = 14
14 times 12 = 168
168/2 = 84
Area of triangle: 84
Area of semicircle+area of rectangle+ area of triangle.
157+280+84 =521
What is the slope of the line that passes through the points (-3,2) and (6, -9)?
Answers
Answer:
-11/9 is the slope
Step-by-step explanation:
Use the formula and u will find this is the answer, hope this helped!
Y2 - Y1 / X2 - X1
(-9 - 2) / (6 - (-3))
<!> Brainliest is appreciated!
Answer:
-11/9
Step-by-step explanation:
In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]
Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:
[tex]\frac{-9-2}{6-(-3)}[/tex]
The negatives cancel out and become postive, so the denominator will then read to be 6+3:
[tex]\frac{-9-2}{6+3}[/tex]
[tex]-\frac{11}{9}[/tex]
Here’s a graph of a linear function. Write the equation that describes that function.
Express it in slope-intercept form.
Answers
Answer:
y=3/4 x+2
Step-by-step explanation:
y=mx+b
take two points from graph
(0,2) and (4,5)
find b when x=0 then y=b=2
find m : y2-y1/x2-x1=5-2/4-0
m=3/4
y=3/4 x +2
Select the correct answer.
Use the power of a product property to answer the question.
Which expression equals (
Answers
Answer:
7^1/3 * y^1/3
Step-by-step explanation:
(7y) ^ 1/3
We know that (ab) ^c = a^c * b^c
7^1/3 * y^1/3
Answer:
7^1/3 * y^1/3
Step-by-step explanation:
7^1/3 * y^1/3
Find an equation for the nth term of the sequence. -3, -12, -48, -192, ... (1 point)
Answers
a = -3
common ratio(r) = -12/(-3) = 4
nth term = a.r^(n-1)
= -3.(4)^(n-1)
A delivery company estimates that it will take 4 minutes for their drone to fly 7 km how long will it take the drone to fly 21 km
Answers
Answer: 12 minutes
Step-by-step explanation:
7 km ........ 4 minutes
21 km ...... ?
21/7 x 4= 12 minutes
Answer: 12 minutes.
Step-by-step explanation:
It is easy to put the numbers into a ratio form to work it out. So-
4 minutes for 7 km = 4 : 7
Then ? minutes for 21 km = ? : 21
You first divide the given value by the original value of that it is proportioned to (the number on the same side of the original ratio as 21). In this case divide 21 by 7 = 3. You now have to times the answer you got by the other original value which will be 4 x 3 = 12.
Therefore your answer is 12 minutes.
If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.
Answers
Answer:
0.723 seconds
Step-by-step explanation:
Let h = 0
0 = -16t² + 6t + 4
Let’s solve by completing the square.
Subtract 4 from both sides.
-4 = -16t² + 6t
Since the coefficient of -16t² is -16, divide both sides by -16.
1/4 = t² - 3/8t
The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.
Then we need to add (b/2)² = 9/256 to both sides to complete the square.
Add 9/256 to both sides.
73/256 = t² - 3/8t + 9/256
Factor right side.
73/255 = (t-3/16)²
Take the square root on both sides.
±√(73/255) = t-3/16
Add 3/16 to both sides.
3/16 ± √(73/255) = t
The answer has to be positive, not negative.
0.72254626884 = t
0.723 ≈ t
Answer:
Rounding to the nearest hundredth, it is 0.72
please solve and verify your answer 6j+7=21−j2
Answers
Answer:
j=1.75
Step-by-step explanation:
6j=21-2j-7
6j=14-2j
6j+2j=14
8j=14
[tex]\frac{8j}{8} = \frac{14}{8}[/tex]
j=1.75
4. If 30 locusts eat 420 grams of grass in a week. How many days will it
take 21 locusts to consume 420 grams of grass if they eat at the same
rate
Answers
Answer:
The amount one locust eats in a week is 420/30 = 14 grams so it eats 14/7 = 2 grams per day, therefore 21 locusts can eat 21 * 14 = 42 grams per day. 420 / 42 = 10 so the answer is 10 days or 1 week and 3 days.
If g(x) = 3x2 - 4x + 1, what is the value of g(-2)?
Answers
Answer:
21
Step-by-step explanation:
substitution
Answer:
21
Step-by-step explanation:
Plug in x as -2.
3(-2)² - 4(-2) + 1
3(4) - - 8 + 1
12 + 8 + 1
= 21
Rewrite 4 − 5 using the additive inverse and display the new expression on a number line. (5 points) 4 + 5 An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 4 − (−5) An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 5 − 4 An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 and ends at 5. Another arrow begins at 5 and ends at 1. 4 + (−5) An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Answers
Answer: 4 + (−5)
An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Step-by-step explanation: The arrow from 0 running to 4 is the graph of how the point on the line is a positive 4: Four added to 0
The "additive inverse" means start there and go in the opposite direction. The arrow is 5 units long, so they ended up at -1 . Adding -5 is the same as subtracting 5
4 + (-5) = -1 is the additive inverse of 4-5= -1
The descriptions of the number lines are well done, but difficult to sort out.
Answer:
4 + (−5)
Step-by-step explanation:
it is got it correct
There are only r red counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is Find the number of red counters and the number of green counters that were in the bag originally. ( 5 marks)
Answers
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
There are only r red counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7 The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13
Find the number of red counters and the number of green counters that were in the bag originally.
Answer:
Total number of green counters = 9
Total number of red counters = 12
Step-by-step explanation:
Recall that probability is given by
P = number of desired events/total number of events
The probability that the counter is green is 3/7
P(green) = 3/7 = 3x/7x
Where 3x is the number of green counters
7x is the total number of counters
So then red counters are
red counters = 7x - 3x = 4x
4x is the number of red counters
P(green) = 3/7 = 3x/3x + 4x
The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. The probability that the counter is green is 6/13
So after addition of 3 green and 2 red new counters,
P(green) = 6/13 = (3x + 3)/(3x + 4x + 3 + 2)
Now solve for x
6/13 = (3x + 3)/(3x + 4x + 3 + 2)
6/13 = (3x + 3)/(7x + 5)
6(7x + 5) = 13(3x + 3)
42x + 30 = 39x + 39
42x - 39x = 39 - 30
3x = 9
x = 9/3
x = 3
So total number of green counters are
green counters = 3x = 3*3 = 9
So total number of red counters are
red counters = 4x = 4*3 = 12
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. Triangle A Y X is shown. Line segment B C is drawn from side A Y to A X to form triangle A B C. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?
Answers
Explanation:
Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX 3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC/AX = AB 6. division property of equality
7. AC/AX = AB/AY 7. division property of equality
8. Corresponding sides are proportional 8. Definition of proportional
9. △ABC ~ △AYX 9. SAS similarity theorem
_____
The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.
Answer:
I think its A. ∠A ≅ ∠A; reflexive property
Step-by-step explanation:
Dale is following this recipe to make shortbread fingers. Dale uses 75 g of butter. How many shortbread fingers does he make? Recipe: Makes 20 fingers 125 g butter 55 g sugar 180 g flour
Answers
Answer:
For 75 g butter ≈ 27 fingers
Step-by-step explanation:
Using unitary method
For 20 fingers = 55 g butter
For 1 g butter = 20/55 fingers
=> For 1 g butter = 4/11 fingers (Simplified form)
Multiplying both sides by 75
=> for 75 g butter = [tex]\frac{4}{11} * 75 {fingers}[/tex]
=> For 75 g butter ≈ 27 fingers ( approximately )
please help me! Bethany incorrectly simplified the following expression: (4 x 10^11) (3 x 10^-14) + 0.000005 Which of Bethany’s steps show an error based solely on her previous step? Choose all that apply: A. Step one: (4 x 10^11) (3 x 10^-14) + (5 x 10^-5) B. Step two: (12 x 10^-3) + (5 x 10^-5) C. Step three: (120 x 10^-4) + (5 x 10^-5) D. Step four: (120 x 10^-4) + (50 x 10^-4) E. Step five: 170 x 10^-8 F. Step six: 1.7 x 10^-6
Answers
Answer:
Below.
Step-by-step explanation:
Step 1: it is 5 x 10^-6 not 5 x 10^-5.
Step 5 : the result of the addition is 170 x 10^-4 not 170 x 10^-8.
Answer: yes that is correct explanation:
Please can someone help!
Answers
Answer:
51 mph
Step-by-step explanation:
→ The first thing we need is a formula which links speed, distance and time so,
Speed = Distance ÷ Time
Speed = mph
Distance = metres/miles
Time = hours
→ Since we want to work out the average speed of the entire journey we need to first work out the total distance and total time. Using the first sentence of the paragraph, it says that the car travels at an average speed of 45 mph for 40 minutes, we can rearrange the formula to work out the distance so,
Speed = Distance ÷ Time
→ Rearrange to get distance as subject
Distance = Speed × Time
→ Substitute in the values
Distance = 45 × 40
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
40 ÷ 60 = 0.666666667
→ Substitute in the time value multiplied by the speed
Distance = 45 × 0.666666667 = 30
⇒ 30 metres/miles is overall distance for the first part of the journey
→ Now we have to work out the distance for the second part of the journey. State the distance formula.
Distance = Speed × Time
→ Substitute in the values into the distance formula
Distance = 60 × 25
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
25 ÷ 60 = 0.416666667
→ Substitute in the time value multiplied by the speed
Distance = 60 × 0.416666667 = 25
⇒ 25 metres/miles is overall distance for the second part of the journey
→ Now we have to add the distance of both the journeys together
25 + 30 = 55
→ Then we add the times of the journey together
40 minutes + 25 minutes = 65 minutes
→ Convert 65 minutes into hours
65 ÷ 60 = 1.08333 hours
→ Substitute both values into the speed = distance ÷ time formula
Speed = 55 ÷ 1.08333 = 50.76923077
→ The question says to round it to the nearest whole number so,
50.76923077 = 51 mph
The circumference of a circular field is 285.74 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
yards
x
?
Answers
Answer:
The diameter is 91.
Step-by-step explanation:
The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91
Answer:
91 yards
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
c=π * d
We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.
285.74= 3.14 *d
We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14
285.74/3.14= 3.14*d/3.14
285.74/3.14=d
Divide
91=d
d= 91 yards
The diameter of the field is 91 yards.
Use the first four terms of the binomial theorem to approximate 2.2^7
Answers
Answer:
248.96 which is approximately 249
Step-by-step explanation:
2.2^7
The coefficients are;
1,7,21,35,35,21,7,1
So the terms we want to use are 1,7,21 and 35
We can write 2.2 as 2+ 0.2
So the approximations are;
1(2)^7(0.2)^0 + 7(2)^6(0.2) + 21(2)^5(0.2)^2 + 35(2)^4(0.2)^3
= 128 + 89.6 + 26.88 + 4.48 = 248.96
D. Is no solution please help
Answers
Answer:
B
Step-by-step explanation:
I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.
Answer:
B
Step-by-step explanation:
It is too blurry BTW but B is correct
the function g(x)=-5x-6
Answers
Answer:
D. the slope of f(x) is greater than the slope of g(x)
Step-by-step explanation:
slope of f(x) =rise/run
=y2 -y1 / x2 -x1
slope of f(x)= -1-2/1-0= -3
g(x)= -5x-6
slope of g(x)= -5
-3>-5
D. the slope og f(x) is greater than the slope of g(x)
HELP NOW PLZ 20 POINTS FOR BRAINLIEST Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:
Answers
Step-by-step explanation:
Equation 1: [tex]3x^{2} +7x-6[/tex]
Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.
Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.
1. The parabola should open upwards: a> 0
2. [tex]3x^2+7x-6[/tex] (a>0), y-int is negative (0s for x's)
3(0)^2 + 7(0) -6
y= -6
Step 2:
1. Factor the original equation: (3x-2)(x+3)
x=2/3, -3
2. Strategy used (factor by grouping)
Equation 2: -[tex]x^{2}[/tex] + 3x - 6
Equation 2 should represent a parabola that opens down and has a negative y-intercept.
Parabola that opens down = a<0
Ax^2 + Bx + C
-[tex]x^{2}[/tex] + 3x - 6
Negative y-intercept: -(0)^2 +3(0) -6 = y= -6
Strategy to solve: Quadratic formula
Why? - This equation doesn't factor cleanly.
Show your work:
a= -1 b= 3 c= -6
Write the quadratic formula down ([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Show step, solve.
x= 1.5 + 1.9365i
Equation 3:
Sorry, I can't do this.
Equation 4 :[tex]x^{2} -1[/tex]
You decide.
Alright, easy parabola.
1. Does parabola open up or down. UP
2. Is there a vertical stretch or compression? NO
3. What is the y-intercept- (0,-1)
[tex]x^{2} -1[/tex]
Strategy: Simple factoring patterns (Difference of squares) -
(x+1)(x-1)
x = + 1
Show work: x^2 is square of x,
Equation 5: [tex]x^{2} -3x+15[/tex]
x^2−3x+15
a=1 b= -3 c=15
([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.
What is the solution to this equation?
4x + 2(x + 6) = 36
O A. x = 7
B. x = 5
O c. x = 4
D. x = 8
Answers
Simplifying
4x + 2(x + 6) = 36
Reorder the terms:
4x + 2(6 + x) = 36
4x + (6 * 2 + x * 2) = 36
4x + (12 + 2x) = 36
Reorder the terms:
12 + 4x + 2x = 36
Combine like terms: 4x + 2x = 6x
12 + 6x = 36
Solving
12 + 6x = 36
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 6x = 36 + -12
Combine like terms: 12 + -12 = 0
0 + 6x = 36 + -12
6x = 36 + -12
Combine like terms: 36 + -12 = 24
6x = 24
Divide each side by '6'.
x = 4
Simplifying
x = 4
Four whole numbers are rounded to the nearest 10 The sum of the four rounded numbers is 90 What is the maximum possible sum of the original four numbers
Answers
Answer:
110
Step-by-step explanation:
example:
rounded 20+20+20+30 = 90
original 25+25+25+35 = 110
Which pair of quantities is LEAST likely to be directly proportional?
1. Hours worked and money earned
2. Distance and time when speed is constant
3. Area and side length of a square
4. Total cost and the number of hats purchased
Answers
Answer:
A
Step-by-step explanation:
Hours worked, probably because of commission or bonuses (the other ones seem to be proportional)
Proofs are used to show that a mathematical statement is true. The most common form of mathematical statements are if-then statements. Give an example of a true mathematical statement and a false mathematical statement in if-then form. For the false statement, include a counterexample showing that the statement isn't true.
Answers
Answer:
See explanation
Step-by-step explanation:
True Mathematical Statement
[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{xy}=ab[/tex]
False Mathematical Statement
[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{x+y}=a+b[/tex]
To show using a counterexample that the statement isn't true.
[tex]\text{Let x}=16\\\text{Let y}=9\\\sqrt{16}=4\\\sqrt{9}=3\\\sqrt{16+9}=\sqrt{25}=5\\a+b=3+4=7\\5\neq 7[/tex]
Therefore, the mathematical statement is false.
Question 11 PLEASE HELP find the slope of the line that passes through the points (6,2) and (8,8)
Answers
Answer:
Slope would equal 3.
slope= (y2-y1)/(x2-x1)
Plug in you get (8-2)/8-6)
Simplify (6)/(2)=3
Step-by-step explanation:
Solve for x 7 x − 4 = 6 Give your answer as an improper fraction in its simplest form.
Answers
Answer:
10\7
Step-by-step explanation:
7x-4=6
7x=6+4
7x=10
7x\7=10\7
x=10\7
Answer:-13/3
Step-by-step explanation:
What is the solution of log3x − 5 16 = 2?
Answers
A square is inscribed in a circle of diameter 12 millimeters. What is the area of the shaded region? A square is inscribed in a circle with a diameter of 12 StartRoot 2 EndRoot millimeters. Everything outside of the square is shaded. Recall that in a 45 – 45 – 90 triangle, if the legs each measure x units, then the hypotenuse measures x units. (72π – 144) mm2 (72π – 72) mm2 (288π – 288) mm2 (288π – 144) mm2
Answers
Answer: A. (72π - 144) mm²
Step-by-step explanation:
[tex]A_{shaded}=A_{circle}-A_{square}\\\\\\A_{circle}=\pi \cdot r^2\\.\qquad \ =\pi \bigg(\dfrac{12\sqrt2}{2}\bigg)^2\\\\.\qquad \ =\pi (6\sqrt2)^2\\.\qquad \ =72\pi\\\\\\A_{square}=side^2\\.\qquad \quad =\dfrac{12\sqrt2}{\sqrt2}^2\\\\.\qquad \quad =12^2\\\\.\qquad \quad =144\\\\\\\large\boxed{A_{shaded}=72\pi-144}[/tex]
The area of shaded region is (72π – 144) square millimeters.
To understand more, check below explanation.
Area of shaded region:It is given that,
The diameter of circle is [tex]12\sqrt{2}[/tex] millimeters.
Since, radius = diameter/2
So that, radius of circle[tex]=12\sqrt{2}/2=6\sqrt{2}[/tex]
now, we have to find area of circle,
[tex]Area=\pi *r^{2} \\\\Area=\pi *(6\sqrt{2} )^{2} \\\\[/tex]
Area = 72π square millimeters
The side of inscribed square[tex]=12\sqrt{2} /\sqrt{2}[/tex] = 12mm
Since, area of square= (side)^2
Area of square= 12 * 12 = 144 square millimeters
To find the area of shaded region, subtract area of square from area of circle.
Area of shaded region = area of circle - area of square
Area of shaded region = (72π – 144) square millimeters.
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