The focal length of the lens is 40cm.
What is the focal length?The distance between the center of a lens or curved mirror and its focus.
A plane convex lens is made of glass ( n = 1. 5) with one flat surface and the other having a radius of 20 cm.
The focal length of the lens is given by the following formula;
[tex]\rm \dfrac{1}{f}=(n-1) \left ( \dfrac{1}{r_1}-\dfrac{1}{r_2} \right)\\\\Where; \ r_1 =\infty , \ r_2=20, \ and \ n = 1.5[/tex]
Substitute all the values in the formula;
[tex]\rm \dfrac{1}{f}=(n-1) \left ( \dfrac{1}{r_1}-\dfrac{1}{r_2} \right)\\\\\rm \dfrac{1}{f}=(1.5-1) \left ( \dfrac{1}{\infty}-\dfrac{1}{20} \right)\\\\ \rm \dfrac{1}{f}=(0.5) \left ( 0-\dfrac{1}{20} \right)\\\\ \dfrac{1}{f} = \dfrac{-0.5}{20}\\\\\dfrac{1}{f}=-0.025\\\\f = \dfrac{-1}{0.025}\\\\f=-40[/tex]
Hence, the focal length of the lens is 40cm.
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The diameter of a circle is 12 centimeters. What is the circle's area?
BEST ANSWER :
CIRCLE
solve for area
A = 113.1 cm^2
d diameter = 12 cm.
Answer:
Area of circle = π r^2
Step-by-step explanation:
Diameter = 12
Radius = 12/2
= 6
Area = π x 6^2
= π x 36
= 113.04
therefore the area of the circle is 113.04
Mamadou surveyed 500 of his students in his school about their favorite color students could choose between blue and red 390 students said their favorite color was red what percentage of the surveyed students said they favorite color was red
Answer:
78%
Step-by-step explanation:
a percentage is equivalent to a number over 100.
43% is 43/100
72% is 72/100
87% is 87/100
etc.
to find the percentage of students who said their favorite color is red, we need to set up a cross-multiplication equation
390/500 = ?/100
390 times 100 is 39000
39000/500 = 78
78% of the students said their favorite color is red
give brainliest please!
hope this helps :)
Geometry help I NEED ASAP ( see picture).
8π is the circumference
Based on probability and if it is appropriate for a decision to be left up to chance, choose every situation that is both statistically fair and morally fair.
The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5
How to categorize the situations?For a situation to be fair, the probability of every outcome must be equal.
Using the above definition, we can now analyze each option
Situation 1
Letters = 26
P(Vowel) = 5/26
P(Consonant) = 21/26
Both probabilities are not equal.
Hence, this situation is not fair
Situation 2
Participants = 4
P(Each) = 1/4
All probabilities are equal in the above scenario i.e. 1/4
Hence, this situation is fair
Situation 3
Cousins = 5
P(Each) = 1/5
All probabilities are equal in the above scenario i.e. 1/5
Hence, this situation is fair
Situation 4
Numbers = 5 i.e. 2 to 6
P(Prime) = 3/5
P(Composite) = 4/6
Both probabilities are not equal.
Hence, this situation is not fair
Situation 5
Roommates = 5
Cards = 5
Aces = 4
P(Each) = 1/5
All probabilities are equal in the above scenario i.e. 1/5
Hence, this situation is fair
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Need help!
Y=-2x^2-4x+6
Answer: (1, 0) , (-3, 0)
Step-by-step explanation:
I used an app. T-e-e-h-e-e
Review the steps of the proof of the identity
At which step was an error made?
sin (A-3) - COSA.
= A.
step 1
step 2
3п
sin
step 3
step 4
Step 1: = sinAcos
3 п
2
-
COSAsin
n ()
Step 2: = (sinA)(0) + COSA( - 1)
Step 3: = (sinA)(0) + (1) (COSA)
Step 4: = 0 + COSA
Step 5: Cos A
Answer:
step 2
and then step 3 : the error neutralized the error of step 2
Step-by-step explanation:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
and because
sin(-b) = -sin(b)
cos(-b) = cos(b)
we have
sin(a - b) = sin(a)cos(-b) + cos(a)sin(-b) =
= sin(a)cos(b) - cos(a)sin(b)
3pi/2 = 270° or -90°.
sin(3pi/2) = sin(270) = sin(-90) = -1
that means, it is the full radius straight down from the center of the circle.
cos(3pi/2) = cos(270) = cos(-90) = cos(90) = 0
so, step 1 is correct :
sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2) =
= sin(A)×0 - cos(A)×(-1) (correct step 2)
but as we see, the provided step 2 is incorrect.
it should have been the indicated
sin(A)×0 - cos(A)×(-1)
and NOT the provided
sin(A)×0 + cos(A)×(-1)
step 3 based on the erroneous step 2 should then have been
sin(A)×0 - (1)cos(A)
but instead another error with the sign was made that neutralized the error of step 2 and we got after this second mistake by pure chance the overall correct step 3
sin(A)×0 + (1)cos(A)
so, again, the first error was made in step 2.
but technically, there was also a consecutive error made in step 3 to bring everything back to the correct approach.
if a shoelace drawer is 12.49 inches and a paperclip drawer is 4.579 inches about how many inches wider is the shoelace drawer than the paperclip drawer
The shoelace drawer is 7.911 inches wider than the paperclip drawer.
Measurement difference between two drawersThe height of shoelace drawer is = 12.49 inches
The height of paperclip drawer is = 4.579 inches
Therefore the measurement difference between the two drawer is = 12.49 inches - 4.579 inches
= 7.911 inches
Therefore, the shoelace drawer is 7.911 inches wider than the paperclip drawer.
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whats the answer for this? 0.5x=24
The answer for the expression 0.5x=24 will be x=48
What is a linear equation?The linear equation is defined as the equation having a degree of one or the power of the variable will be one. Linear equation shows the staright line on the graph.
here the given equation is:-
0.5x=24
We can write 0.5 in fraction as 1/2
1/2x=24
x=48
Hence the answer for the expression 0.5x=24 will be x=48
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Question
Consider the diagram.
A triangle with interior angles labeled w degrees, x degrees, and y degrees. A ray extends to the left on the top side of the triangle to create an exterior angle labeled z degrees.
Which equations are true? Select all true equations.
Answer: 1, 2, 5
Step-by-step explanation:
The first equation is true because angles in a triangle add to 180 degrees.
The second equation is true because both sides equal 180 degrees (left hand side is a straight angle, right hand side is the sum of angles in a triangle)
The third equation is not true because z = 180 - y, and 180-y+w+z is not 180.
The fourth equation is not true because z=180-y, and 180-y=w+y is not always true.
The fifth equation is true by the exterior angle theorem.
I need help with writing the number as a decimal.
The question is
Two hundred thirty eight and forty-nine thousandths
Answer: 0.23849
Step-by-step explanation:
0.23849
2 is tenth
3 is hundredth
8 is thousandth
4 is ten thousandth
9 is hundred thousandth
Graph the two sides of the equation 2* – 2.5 = 2x +0.7. Zoom in a few times for added accuracy, and use the pointer tool to approximate the intersection. Then, find the value of x at the point (or points) of intersection.
By graphing both functions, we will see that there are two intersections at (-1.41, -2.12) and (3.28, 7.27).
How to solve the equation graphically?
Here we must solve:
[tex]2^x - 2.5 = 2x + 0.7[/tex]
To do it, we can graph the functions:
[tex]y = 2^x - 2.5\\\\y = 2x + 0.7[/tex]
And see where do the curves intersect.
The graph can be seen below, in there we can see two intersections.
One at (-1.41, -2.12) and (3.28, 7.27).
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1/2 2/4 4/8 are mixed numbers
Which of the following fall between 12 and 13?
least to greatest:
1.11, 1 1/10, the square root of 3, 1.73, 1 2/5
Answer:
least to greatest:
1 1/10, 1.11, 1 2/5, 1.73, the square root of 3
Step-by-step explanation:
1 1/10 = 1.10
1.11 = 1.11
1 2/5 = 1.4
1.73 = 1.73
the square root of 3 is approximately 1.732
please help me solve this !
The equation of a function f(x) = x² -4x -12 in the vertex form is f(x) = (x -2)² -16 and the value of the a = 1, h = 2, and k = -16
What is a quadratic equation ?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
We have a quadratic equation:
f(x) = x² -4x -12
f(x) = x² -4x -12 + 4 -4
f(x) = (x -2)² -16
Here a = 1, h = 2, and k = -16
Thus, the equation of a function f(x) = x² -4x -12 in the vertex form is f(x) = (x -2)² -16 and the value of the a = 1, h = 2, and k = -16
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A rectangular stained glass window is made up of identical triangular parts as pictured below. 24 triangles are connected to have a height of 36 inches and a width of 48 inches. every 2 triangles combine to form a rectangle. what is the area of the shaded triangular section? 18 square inches 36 square inches 72 square inches 144 square inches
The area of the shaded triangular section of the stained glass window is 72 square inches.
What is the area of the shaded triangular section?
The first step is to determine the dimensions of each rectangle that makes up the stained glass window.
Length of one rectangle = length of the window / number of rectangles along the length
36/4 = 9 inches
Width of one rectangle = width of the window / number of rectangles along the width
48/3 = 16 inches
Area of the shaded triangular section = 1/2 x area of one rectangle
1/2 ( length x width)
1/2 x (16 x 9) = 72 square inches.
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Answer:
144
Step-by-step explanation:
i took the test
5,200,000×(8.3×10^2)−(3.1×10^8) in scientific notation, need it quick
Step-by-step explanation:
5,200,000 = 5.2 × 10⁶
so, we have
(5.2 × 10⁶) × (8.3 × 10²) - (3.1 × 10⁸)
(5.2 × 8.3 × 10⁸) - (3.1 × 10⁸)
(43.16 × 10⁸) - (3.1 × 10⁸) = 40.06 × 10⁸ = 4.006 × 10⁹
In the figure above, the shaded triangle is bounded by the y-axis, the line y=6, and the line y=2/3x. What is the area, in square units, of the shaded triangle?
Answer:
84.9
Step-by-step explanation:
Julianna is making a rectangular garden in her backyard. She has plotted three of the corners on the coordinate plane.
Determine the identity. Show all steps.
Step-by-step explanation:
[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}=1-\frac{1}{\csc \left(x\right)}[/tex]
[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}[/tex]
[tex]=1-\sin \left(x\right)[/tex]
⇒ [tex]\sin \left(x\right)=\frac{1}{\csc \left(x\right)}[/tex]
[tex]=1-\frac{1}{\csc \left(x\right)}[/tex]
• A. All real numbers
• B. All real numbers except 2
• C. All real numbers except -6
• D. All real numbers except -6 and 2
Answer:
Option C
Step-by-step explanation:
you cancel the whole parentheses.
So you know, x+6 can't equal to 0.
that's why there is a choice that is all real numbers but not -6.
Answer:
A. All real numbers
Step-by-step explanation:
Given
(x - 2)(x + 6)/7(x + 6) = (x - 2)/7On cross multiplying,
(x - 2)(x + 6)(7) = (x - 2)(x + 6)(7)LHS = RHSThis means on applying any value for x, both sides will be equalHence, the correct option is ACan you please help me with 12 please? I will give an brainlist
Answer:
[tex]x+(\frac{1}{2} x + 12) =[/tex] number of postcards Simone has now
Step-by-step explanation:
x = the number of postcards in Simone's collection
Simone bought 12 more than half the number of postcards in her collection.
So Simone bought half her collection ( [tex]\frac{1}{2} *x = \frac{1}{2} x[/tex] ) plus 12 more postcards.
[tex](\frac{1}{2}x +12)[/tex] = number of postcards Simone bought
Write an expression to show how many pstcards she has now.
[tex]x+(\frac{1}{2} x + 12) =[/tex] number of postcards Simone has now
Let she has p no of postcards before .
She bought 12 more than the half of p
p/2+12Currently she has
p+p/2+123p/2+12(3p+24)/2 postcardssolve the equation 3x^2-x-3=0 to the nearest tenth
Answer:
You use the quadartic foruala for this problem your fanial anwers is
x=1 + or - radical 37 / 6.
1+ radical 37 over 6 =1.180460422
To the nearest tenth =1.2
1-radical 37 over 6= -0.8471270884
To the nearest tenth=-0.8
This figure is divided into triangles. What fraction of the figure is each triangle?
Answer:
a) 1/8
Step-by-step explanation:
There are 8 triangle in that shape. So, the fraction will be 1/8. Hence, option (a) is the correct answer.
write the ratio in the simplest form 40kg : 480g
Answer: 1kg : 12g
Step-by-step explanation: Ratio in the simplest form is to divide both numbers by the greatest factor.
40 divided by 40 is 1
480 divided by 40 is 12
The answer is 1 kg : 12g
does anyone live in the concord, NC area? I need to get out of this place TwT
that's tuff you live in NC
2x+4 (2x+7)= 3(2x+4)
solve x
[tex]2x + 4(2 x + 7) = 3(2x + 4)[/tex]
to find:solve the ( x ).
solution:[tex]2x + 4(2x + 7) = 3(2x + 4)[/tex]
[tex]2x + 8x + 28 = 6x + 12[/tex]
[tex]10x + 28 = 6x + 12[/tex]
[tex]4x + 28 = 12[/tex]
[tex]4x = - 16[/tex]
[tex]x = - 4[/tex]
2x+4(2x+7)= 3(2x+4)
2x+8x+28=6x + 12
10x+28=6x + 12
4x+28=12
4x= -16
x=-4
Samin can run 5 kilometers in 30 minutes. Assuming she keeps a constant pace, how many kilometers can she run in 45 minutes
Answer:
7.5 kilometres
Step-by-step explanation:
In 30 minutes she ran 5 kilometres.
We know that 30 + 15 = 45, so we can divide the minutes and kilometres by 2.
So 30 divided by 2= 15 minutes.
And 5 kilometres divided by 2= 2.5 kilometres.
Now we just add the two distances, as we know that the minutes make 45.
2.5 + 5 = 7.5.
I hope this helps, have a lovely day.
The speed is the distance covered by an object at a particular time. The distance covered by Saima in 45 minutes is 7.5 km.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given Samin can run 5 kilometres in 30 minutes. Therefore, the speed of Samin will be,
Speed = 5km/30min = 5/30 km per minute
The distance covered by Saima in 45 minutes will be equal to
Distance = 5/30 × 45 = 7.5 km
Hence, The distance covered by Saima in 45 minutes is 7.5 km.
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how much larger is 8 x 10^8 than 2 x 10^5
Answer:
799800000 larger
Step-by-step explanation:
8 × (10 × 8) = 8000000002 × (10 × 5) = 200000
So . . Subtract
800000000 - 200000 = 799800000
Answer: 799800000
Step-by-step explanation: For 8 x 10^8, do 10 x 10 x 10 10 x 10 x 10 10 x 10 to get 100,000,000 and x 8 is 800,000,000
For 2 x 10^5 do 10^5 ( 10 x 10 x 10 x 10 x 10) which is 100,000 and then x 2 is 200,000
Then subtract.
800,000,000 - 200,000 is 799800000
A scale drawing of a rectangular park had a scale of 1 cm = 100 m. What is the actual area of the park in meters squared?
Explanation:
5.1 cm on paper corresponds to 5.1*100 = 510 meters in real life due to the scale 1 cm = 100 m.
11.9 cm on paper corresponds to 11.9*100 = 1190 meters in real life.
The 5.1 cm by 11.9 cm rectangle on paper corresponds to the real life counterpart of 510 meters by 1190 meters.
The actual area of the real life park is length*width = 510*1190 = 606,900 square meters
