How to prove the vertical Angles Theorem
Answers
Answer:
see below
Step-by-step explanation:
Angles opposite each other when two lines cross. (see attached)
in the attached example, the angle a° and b° are vertical angles.
Step-by-step explanation:
[tex]
\underline{\bf{Given\::}}
Given:
\underline{\bf{To\:find\::}}
Tofind:
\underline{\bf{Explanation\::}}
Explanation:
\boxed{\bf{\frac{1}{f} =\frac{1}{v} -\frac{1}{u} }}}}
\begin{gathered}\longrightarrow\sf{\dfrac{1}{-10} =\dfrac{1}{v} -\dfrac{1}{-30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-10} +\dfrac{1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{-3+1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\cancel{\dfrac{-2}{30} }}\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-15} }\\\\\\\longrightarrow\sf{v=-15\:cm}\end{gathered}
⟶
−10
1
=
v
1
−
−30
1
⟶
v
1
=
−10
1
+
30
1
⟶
v
1
=
30
−3+1
⟶
v
1
=
30
−2
⟶
v
1
=
−15
1
⟶v=−15cm
\boxed{\bf{M \:A \:G \:N\: I \:F \:I \:C\: A\: T \:I \:O\: N :}}
MAGNIFICATION:
\begin{gathered}\mapsto\sf{m=\dfrac{Height\:of\:image\:(I)}{Height\:of\:object\:(O)} =\dfrac{Distance\:of\:image}{Distance\:of\:object} =\dfrac{v}{u} }\\\\\\\mapsto\sf{m=\cancel{\dfrac{-30}{-15}} }\\\\\\\mapsto\bf{m=2\:cm}\end{gathered}
↦m=
Heightofobject(O)
Heightofimage(I)
=
Distanceofobject
Distanceofimage
=
u
v
↦m=
−15
−30
↦m=2cm
Thus;
The magnification will be 2 cm .
[/tex]
Related Questions
What is the slope of the line y = -2?
Answers
Answer:
0
Step-by-step explanation:
There is no x, therefore there is no slope.
The distance between point (-4,5) and another point is 10. What are the possible coordinates of the other point?
Answers
Answer:
Use the distance formula;
d = SQR[(x2 - x1)^2 + (y2 - y1)^2]
d = 10 and (x2, y2) = (-4, 5)
10 = SQR[(-4 - x1)^2 + (5 - y1)^2]
Step-by-step explanation:
Write the equation of the parabola in vertex form.
Vertex: (−4,6); Point: (−2,−2)
Answers
Answer:
y = - 2(x + 4)² + 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (- 4, 6 ) , thus
y = a(x - (- 4) )² + 6 , that is
y = a(x + 4)² + 6
To find a substitute (- 2, - 2) into the equation
- 2 = a(- 2 + 4)² + 6 ( subtract 6 from both sides )
- 8 = a(2)² = 4a ( divide both sides by 4 )
- 2 = a , thus
y = - 2(x + 4)² + 6 ← equation in vertex form
*30 POINTS!*
Determine if each equation represents the graph below. Choose ALL correct equations. You will select more than one answer.
The options are:
1. y= 2x-1
2. x-2y =2
3. y= 1/2x - 1
4. y+3 = 1/2 (x+4)
5. y-2= 1/2 (x-2)
Answers
Answer:
2, 3 and 4 represent the graph in the pic
Step-by-step explanation:
When you look at the graph, you can immediately tell the gradient and the y-intercept. The gradient is 1/2 and the y-intercept is -1
Hence the graph in the picture follows the formula: y = 1/2x - 1
When you expand/rearrange the options (1-5) into the slope form you would be able to see which of these options matches with the formula of the line.
1. y= 2x-1: Isn't the same as the equation of the line in the pic
2. Rearrange:
-2y = -x + 2 (divide both sides by 2)
y = x/2 - 1 (x/2 = 1/2x, its the same thing)
3. y= 1/2x - 1 (this is the formula of the line)
4. Expand right-hand-side:
y + 3 = 1/2x + 2 (rearrange)
y = 1/2x - 1 (this is the formula of the line)
5. Expand right-hand-side
y - 2 = 1/2x - 1 (rearrange)
y = 1/2x + 1 (is not the formula of the equation)
Answer:
The officeStep-by-step explanation:
“Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.” – Michael G. Scott
Square ABCD has vertices A(-4.5, 4), B(3.5, 4),C(3.5, -4), and D(-4.5, -4). What is the area of square ABCD?
Answers
Answer:
that answer is b
Step-by-step explanation:
hope this helps
The area of square ABCD would be; 64 unit sq.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²] units.
Given that Square ABCD has vertices; A(-4.5, 4), B(3.5, 4),C(3.5, -4), and D(-4.5, -4).
To find the distance from two of the vertices of the square. The distance formula is as follows;
√[(x-p)² + (y-q)²]
A(-4.5, 4), B(3.5, 4),
D = √[(x-p)² + (y-q)²]
D = √(3.5-(-4.5))² +(4 -(4))²
D = √(3.5-(-4.5))² +(4 -(4))²
D = √(64 + 0)
D = 8
Therefore, the side of the square is 8 units.
The area of the square = side x side
= 8 x 8
= 64 unit sq.
Learn more about distance between two points here:
brainly.com/question/16410393
#SPJ2
2(b + 2) > 4(1 + 5b) -b
Answers
Answer:
b<0
Step-by-step explanation:
2(b+2)>4(1+5b)−b
Step 1: Simplify both sides of the inequality.
2b+4>19b+4
Step 2: Subtract 19b from both sides.
2b+4−19b>19b+4−19b
−17b+4>4
Step 3: Subtract 4 from both sides.
−17b+4−4>4−4
−17b>0
Step 4: Divide both sides by -17.
−17b
−17
>
0
−17
b<0
Answer:
b<0
Answer:
2(b + 2) > 4(1 + 5b) -b
2b + 4 > 4 + 20b -b
2b - 20b + b > 4 - 4
-17b > 0
b < 0/-17
b < 0
Which of the following statements are FALSE when identifying the type of slope of a line.
A Positive slope increases from left to right.
B Negative slope decreases from left to right.
C Undefined slope is when there is no vertical change.
D No or Zero slope is a horizontal line.
Answers
Answer: Choice C) Undefined slope is when there is no vertical change
If you replace "vertical" with "horizontal", then choice C would be a true statement. All vertical lines have an undefined slope.
This is because the slope formula
m = (y2-y1)/(x2-x1)
has 0 in the denominator when you subtract the x coordinates. Dividing by zero is undefined. For any single vertical line, the x coordinates of any two points are the same. For instance, the vertical line through 4 on the x axis is the equation x = 4, and every point on this line has x coordinate 4.
What is the slope line through (0,4) and (3,2)?
Answers
Answer:
The answer is -2/Trust
Step-by-step explanation:
Answer:
Its D 100%
Step-by-step explanation:
The linear function m=55-8.5b represents the amount m (in dollars) of money that you have after buying b books. Find the domain of the function. Is the domain discrete of continuous? Explain.
Answers
Answer:
The domain is (-∞ , ∞)
The domain is continuous
Step-by-step explanation:
Here, we want to identify the domain of the linear function
The domain in this case can be represented by the set of all real numbers.
When we talk of the domain of a function, we are simply referring to the the range of values between the smallest value on the x-axis and the largest number on the x-axis
Hence, mathematically, we are simply considering the smallest value of b up to the largest value of b in this case. Where b simply represents the number of books
Thus, the domain here will be (-∞ , ∞)
On if the domain is discrete or continuous, we can see that the domain is continuous.
The domain is continuous simply because, the domain we have contains all the values and not some in the set of real numbers. If it had contain only some, then it would have been discrete. But since it contains all, it is continuous
Please answer this for me it’s due tonight!
Answers
Answer:
the answers are the first one and the third one.
A's slope is y = 5.75x + 3
B's slope is y = 5.5x + 4
Pls help ASAP!
Consider this linear function:
Y= 1/2x + 1
Plot all ordered pairs for the values in the domain.
D: { -8,-4,0,2,6}
Answers
y=1/2x+1, so for this one we will replace x with -8. so y=1/2(-8)+1= -4+1=-3
so the first set of coordinates with be (-8,-3)
simplify the following expression: -4x^5y^4x x 5xy^7z^4
Answers
Answer:
[tex]-20x^{7}y^{11}z^{4}[/tex]
Step-by-step explanation:
Multiply: -4 and 5 which then equals [tex]-20x^5y^4x[/tex] X [tex]xy^7z^4[/tex]
Add Exponents: [tex]x^5+x1+x1[/tex] and then [tex]y^4+y^7[/tex]which finally equals to the answer, [tex]-20x^7y^{11} z^4[/tex]
The scatterplot shows the number of hours that several students worked to sell tickets for a concert and the number of tickets that each student sold.
A graph titled Ticket Sales has number of hours on the x-axis, and number of tickets on the y-axis. Point (1, 60) is outside of the cluster.
Which data value would cause the interpretation of the data set to be overstated?
(1, 10)
(1, 60)
(9, 85)
(10, 80)
Answers
Answer:
B 1,60
Step-by-step explanation:
Answer:
B 1,60
Step-by-step explanation:
did the test
what is the translation of the expression 5 more than twice x
Answers
Answer:
5+2x
Step-by-step explanation:
Answer:
5 + 2x
Step-by-step explanation:
What is 64^2/4 in a fraction?
Answers
Answer:
128/4 or 32
Step-by-step explanation:
A square plaza at a train station has a side length as shown. Which expression represents the area of the plaza in square meters?
2x + 6
x2 + 9
6x + 9
x2 + 6x + 9
Answers
here's the answer hope this helps :)
Answer:
D. x2 + 6x + 9
Step-by-step explanation:
For anyone who didn't understand the above answer^^
solve the inequality p + 4 ≥ -10
Answers
Answer:
p ≥ -14
Step-by-step explanation:
Subtract 4 from both sides.
-10 - 4 = -14
This could also be written as -10 + (-4)
p ≥ -14
Hope this helped :)
Please consider Brainliest :)
Helps me solve this problem please
Answers
Answer:
6Step-by-step explanation:
2x - 3x + 20 + 5x - 40 = 4 combine like terms
(2x - 3x + 5x) + (20 - 40) = 4
4x - 20 = 4 add 20 to both sides
4x = 24 divide both sides by 4
x = 6
10 is 6% of what
number?
Answers
Answer:
60
Step-by-step explanation:
10 × 6 is 60. if it asks the % of a number, you multiply the number by %
Answer:
60
Step-by-step explanation:
hope this helps
4/7 of a $42 restaurant bill = $ ?
Answers
The Answer Is:
24
-Hope this helps!
Answer:
24 Dollars
Step-by-step explanation:
In order to figure out the total, we must multiply 42 times 4/7. We get a total of 24.
A toy company manufactures sealed cubes that contain a colored liquid that glows in the dark. The liquid completely fills the cubes. If 8 cubic blocks with a side length of m are needed to find the volume of each cube, how much of the liquid can each cube hold?
Answers
Answer:
[tex]Volume = 8m^3[/tex]
Step-by-step explanation:
Given
[tex]Cubes = 8[/tex]
[tex]Length = m[/tex] for each
Required
Determine how much all cubes can hold
First, we need to determine the volume of each.
[tex]Volume = m * m * m[/tex]
[tex]Volume = m^3[/tex]
For the 8 cubes, we have:
[tex]Volume = 8 * Volume\ of\ 1[/tex]
[tex]Volume = 8 * m^3[/tex]
[tex]Volume = 8m^3[/tex]
I need a quick run down of point slope form
Answers
Answer:
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
Step-by-step explanation:
Answer:
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line.
Hope this helps you Stay happy and safe ✌️Simplify the expression.
−(−x)3 − x3
Answers
Answer:
0
Step-by-step explanation:
-(-x) ^3-x^3
x^3-x^3
=0
The length of a rectangular sandbox is
6
feet less than
3
times the width. The perimeter of the sandbox is
36
feet.
Which statement is true?
The equation
(
3
w
−
6
)
+
w
=
36
can be used to find the width of the rectangle, and the width is
6
feet.
The equation ( 3 w − 6 ) + w = 36 can be used to find the width of the rectangle, and the width is 6 feet.
The equation
(
3
w
−
6
)
+
w
=
36
can be used to find the width of the rectangle, and the width is
12
feet.
The equation ( 3 w − 6 ) + w = 36 can be used to find the width of the rectangle, and the width is 12 feet.
The equation
2
(
3
w
−
6
)
+
2
w
=
36
can be used to find the width of the rectangle, and the width is
6
feet.
The equation 2 ( 3 w − 6 ) + 2 w = 36 can be used to find the width of the rectangle, and the width is 6 feet.
The equation
2
(
3
w
−
6
)
+
2
w
=
36
can be used to find the width of the rectangle, and the width is
12
feet.
Answers
Answer:
so the correct statement is;
The equation 2 ( 3 w − 6 ) + 2 w = 36 can be used to find the width of the rectangle, and the width is 6 feet
Step-by-step explanation:
Here, we want to select the statement which is true
Let the width be w
the length is 6 ft less than 3 times the width
The length will be (3w - 6) ft
Mathematically, the perimeter of a rectangle can be calculated using the formula;
2( l + b) = P
Thus;
2(3w -6 + w) = 36
divide both sides by 2
3w -6 + w = 36/2
3w -6 + w = 18
4w -6 = 18
4w = 18 + 6
4w = 24
w = 24/4
w = 6
hello… please help What is a parabola in mathematics?
Answers
Example below:
Show me how to do this one someone help
Answers
Answer:
4
Step-by-step explanation:
Answer:
The slope of the line is y = -3x+4.
Determining the Value of the Slope from a Table
A 2-column table with 5 rows. Column 1 is labeled x with entries 1000, 1000, 1000, 1000, 1000. Column 2 is labeled y with entries 20, 23, 26, 29, 32.
What can you conclude about the slope of the values in the table? Check all that apply.
The slope is 3.
The slope is 0.
The slope is undefined.
The graph will be a horizontal line.
The graph will be a vertical line.
The graph will have a line with a positive slope.
Answers
Answer:
3 and 5
Step-by-step explanation:
Hope this helped :)
I did the same assignment and it was right!
Answer:
here is the answer
Step-by-step explanation:
7-5(x+6)= -7x-17 what value of x makes the equation true?
Answers
Answer:
x=3
Step-by-step explanation:
7-5(x+6)= -7x-17
Distribute
7 - 5x-30 = -7x-17
Combine like terms
-5x-23= -7x-17
Add 7x to each side
-5x-23+7x= -7x-17+7x
2x -23 = -17
Add 23 to each side
2x-23+23 = -17+23
2x= 6
Divide by 2
2x/2 = 6/2
x =3
Answer:
x = 3
Step-by-step explanation:
7 - 5(x + 6) = -7x - 17
~Simplify left side
7 - 5x - 30 = -7x - 17
~Combine like terms
-5x - 23 = -7x - 17
~Add 23 to both sides
-5x = -7x + 6
~Add 7x to both sides
2x = 6
~Divide 2 to both sides
x = 3
Best of Luck!
y > 3x + 1
2x + 3y 2 6
Answers
I'LL GIVE BRAINLIEST IF YOU ANSWER PLEASE I'M BEGGING
Answers
Answer:
A.
Step-by-step explanation:
Answer:
The answer is a.
Step-by-step explanation:
When you plug in 2 for n, 2 - 1 1, so we put 5 for a (because a superscript 1 = 5) and evaluate. This number then become a superscript 2.