The secant of circle is SU and RT.
What is Secant of the Circle?A straight line that intersects a circle in two points is called a secant line.
From the given diagram,
The line which intersects the circle at two points or an extended chord is SU and RT.
Hence, secant is SU and RT.
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1. ABCD is a square with side length 12 cm.
a) Find the exact area of the shaded
[2 MARKS]
b) Find the area, correct to 2 decimal places. Use =3.142. [1 MARK]
region. [Leave your answer in terms of #]
NOT
A
6
с
I
Answer:
Exact Area of shaded region = 141.39cm²
Step-by-step explanation:
Quadrant of a circle - Quadrant refers to the four quarters in the coordinate plane system. Each of the four sections is called a quadrant. When it comes to circle, the quarter of a circle is called a quadrant, which is a sector of 90°.
area of circle =πr²
area of quadrant of a circle = πr²/4
where r is the radius of the circle.
In the given figure there are 2 types of quadrants of circle are present
one with radius AB (bigger )
another with radius AB/2 (smaller)
Now area of quadrant having radius = AB
⇒ π(AB) ²/4
here AB is the side of square
so AB = 12cm
substituting this in the area of quadrant formula
area of bigger quadrant = π(12²)/4
area₁ = 144×π/4
area₁ = 144×3.142/4
area₁ = 113.112cm²
now area of smaller quadrant = π(AB/2) ²/4
area ₂ = π(6) ²/4
area ₂ = 36π/4
area ₂ = 9×π
area ₂ = 28.278cm²
Now it is clear from the given figure,
area of shaded region is = area₁ - area₂ +2×area₂
= 113.112cm² - 28.278cm² + 2× 28.278cm²
= 113.112cm² + 28.278cm²
= 141.39cm² (answer)
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Five siblings decide to buy their father a birthday present that costs b dollars, splitting the cost evenly amongst themselves. In terms of B, how much money does each sibling save by buying the gift as a group rather than alone?
A = b/25
B = b/5
C = 4b/5
D = 4b
Answer: b/5
Step-by-step explanation:
They divide the total by 5 to get the cost each person has to pay
Find the equation of the line passing through the points -2x+1 (8,2)
The line that passes through (-2, 1) and (8, 2) is:
y = (1/10)*x + 12/10
How to find the equation of the line?I assume you want to find the equation of the line that passes through (-2, 1) and (8, 2).
A general linear equation is written as:
y = a*x + b
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that it passes through (-2, 1) and (8, 2), then:
[tex]a = \frac{2 - 1}{8 - (-2)} = 1/10[/tex]
Then the line is:
y = (1/10)*x + b
To find the value of b, we use one of the given points, for example if we use (8, 2), it means that when x = 8, we must have y = 2.
2 = (1/10)*8 + b
2 - 8/10 = b
20/10 - 8/10 = b
12/10 = b
Then the linear equation is:
y = (1/10)*x + 12/10
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Square measures 8 m on each side if each side is written by 1/4 of eight originally the premiere of the new square will be blank meters and its area blank square meters
Step-by-step explanation:
so, if I understand this correctly, the original square had a side length of 8 m.
now we transform this square into one with side length 1/4×8 = 8/4 = 2 m.
and the questions are what are the perimeter and the area of that new (smaller) square ?
the perimeter of a square is
4× side length = 4×2 = 8 m
the area of a square is
side length ² = 2² = 4 m²
PLEASE HELP! I WILL MARK BRAINLIEST! Which type of lines is shown in the illustration above?
A. parallel lines
B. perpendicular lines
C. skew lines
D. intersecting lines
Answer:
D. Intersecting lines.
Step-by-step explanation:
The lines are intersecting each other.
The reason it is not perpendicular lines is because perpendicular lines have 90° angles.
Hope this helps!
If not, I am sorry.
You are riding along a straight river from east to the west at speed of 160m/m. At a given time, you will see the bearing of a church on the other parallel road is N 70 degrees W, and 4 minutes later the bearing is N 56 degrees W. What is the width of the river? (Round your answer to two decimal points)
Using the given information, the width of the river is 505.96 m
Bearing and DistancesFrom the question, we are to determine the width of the river
Consider the given diagram,
Let F be the first position of the biker
S be the second position
and C be the position of the church
First, we will determine the distance covered from F to S
Speed = 160m/min
Time = 4 minutes
Using the formula,
Distance = Speed × Time
Distance covered = 160 × 4
Distance covered = 640 m
That is, /FS/ = 640 m
Now, consider ΔFSC
∠F = 90° - 70° = 20°
∠S = 90° + 56° = 146°
and ∠C = 180° - 20° - 146° = 14°
By the Law of Sines
[tex]\frac{/FC/}{sin\ S}= \frac{/FS/}{sin\ C}[/tex]
∴ [tex]\frac{/FC/}{sin\ 146^\circ}= \frac{640}{sin\ 14^\circ}[/tex]
[tex]/FC/ =\frac{640 \times sin \ 146^\circ}{sin \ 14^\circ}[/tex]
/FC/ = 1479.33 m
Now,
By SOH CAH TOA
[tex]cos \ 70^\circ = \frac{d}{/FC/}[/tex]
NOTE: d is the width of the river
∴ d = /FC/ × cos70°
d = 1479.33 × cos70°
d = 505.96 m
Hence, the width of the river is 505.96 m
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In January, Bangkok is hotter than Cape Town while Cape Town is hotter than Moscow. Which inequality correctly compares the temperatures of the three cities?
Which Answer-
A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature
B.
Bangkok's temperature < Moscow's temperature < Cape Town's temperature
C.
Bangkok's temperature > Moscow's temperature > Cape Town's temperature
D.
Bangkok's temperature > Cape Town's temperature > Moscow's temperature
The correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given that:-
In January, Bangkok is hotter than Cape Town while Cape Town is hotter than Moscow.We have the data from the question that the temperature of Bangkok is hotter than cape town.
Bangkok > Cape town
And the temperature of Cape town is hotter than Moscow.
Cape town > Moscow
Now for both the statements, the inequality will be given as:-
Bangkok's temperature < Cape Town's temperature < Moscow's temperature.
Therefore the correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.
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The graph below represents which system of inequalities
Y≤-2×+3
Y≤x+3
y≥-2x+3
2 ≥x+3
Y ≤3x+2
Y ≤-x+2
Y >2x+3
Y >x+3
Answer:
a
Step-by-step explanation:
HELP WITH THIS PLSSS ITS CYLINDERRR
Answer:
6) B
7) D
Step-by-step explanation:
6)
The surface area of a cylinder is 2 * pi * r * (r + h)
SA = 2 * 3.14 * 3.6 * (3.6 + 8.5) = 2 * 3.14 * 3.6 * 12.1 = 273.6 cm^2
7)
The volume of a cylinder is pi * r^2 * h
V = 3.14 * (3.6)^2 * 8.5 = 345.9 cm^3
Answer:
6. surface area= 2πrh
where r=radius of the base
h=height of the cylinder
π=pie
π=22/7, r=3.6, h=8.5
2×22/7×3.6×8.5= 192.3cm²
square root of 192.3 is 13.9, the one whose square root is closest to that of 192.3 in the options is 178 whose square root is 13.3. A
7. volume=product of the height and its base area
volume=πr²h
22/7×3.6²×8.5 = 346.2. D
Henry leads a team of hikers for a full-day hike that takes 8 hours. Every hour, the hikers gain 250 feet in elevation. • The independent variable is ____, ________ in ________. • The dependent variable is _____, increased elevation in feet, or __________. A possible verbal description is “____ equals 250 times ____.” The equation ______ = ___________ corresponds to this relationship.
The missing blanks have been filled.
What is a Function ?A function is a mathematical statement used to relate a dependent and an independent variable.
It is given that
Total time taken to hike is 8 hours
Let the time taken in hours is represented by t
and the elevation is represented by h
Every hour, the hikers gain 250 feet in elevation.
The independent variable is t , time taken to hike , in hours .
The dependent variable is h , increased elevation in feet or elevation the hikers have gained .
A possible verbal description is Elevation at any given time equals 250 times the time taken to hike.
The equation h = 250 t corresponds to the relationship.
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A line with slope 2 passes through the point (2, -4). Find the coordinates of another point on the line.
Answer:
(3, -2)
Step-by-step explanation:
We can view slope as: [tex]\frac{rise}{run}[/tex] (rise / run)
"rise" is the change in y from one point to another
"run" is the difference in x from one point to another
So, if the slope of a line is 2, it rises 2 every time it runs 1 (2 = 2/1)
So, we can find another point on the line by adding 2 to the y-value, and adding 1 to the x-value.
(x, y)
(2, -4)
+ 1 + 2
(3, -2)
So, another point on this graph is (3, -2)
PLEASE HELP ASAP
(Picture shown)
Answer:
first blank: 3
second blank: 4
Step-by-step explanation:
The completed equation should say:
y = -3x + 4
This is slope-intercept form of the equation. It's a fill-in-the-blank equation. You put the slope in the first blank and the y-intercept in the second blank. Your math program put the negative sign in and it does need to be there. To find the slope, look at the points on the line. To get from one point to the next you go DOWN3 and over 1. DOWN3 and OVER1 is the slope -3/1, which is -3. This number goes beside (in front of) the x. The line crosses the y-axis at 4, fill that in at the end of the equation (the second blank).
The equation for the line is
y = -3x + 4
Find p and q if, √3 −1 /√3 +1 = p + q√3
Answer: p=2, q=-1
Step-by-step explanation:
[tex]\frac{\sqrt{3}-1}{\sqrt{3}+1} \left(\frac{\sqrt{3}-1}{\sqrt{3}-1} \right)=\frac{3+1-2\sqrt{3}}{2}=\frac{4-2\sqrt{3}}{2}=2-\sqrt{3}\\\\\therefore p=2, q=-1[/tex]
Which is the graph of g(x) = 2x-1+3?
O
-12
-8
-4
8-
4
-8
-12+
8
X
Answer:
See below
Step-by-step explanation:
The question is garbled. I don't see a graph nor can I interpret the list of numbers.
g(x) = 2x-1+3 can be simplified to:
g(x) = 2x+2
This line is shown in the attached graph. It has a slope of 2 and a y-intercept of 2.
Determine the Angle Measures
The angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.
For the given figures we need to find the unknown angles.
In the first figure to find angle p first apply the angle sum property to the triangle.
That is, 82°+31°+p=180° (∵ Sum of interior angles of a triangle is 180°)
⇒p=67°.
p=67° is a vertically opposite angle to the other triangle.
To find q:
67°+98°+q=180°
⇒q=15°.
In the second figure to find angles x and y apply the angle sum property to the triangle.
That is, 28°+(53°+x)+17°=180°
⇒98°+x=180°
⇒x=82°.
To find y:
x+y+17°=180°
⇒82°+y+17°=180°
⇒y=81°
In the third figure to find angles x and y apply the angle sum property to the triangle.
That is, 100-x+30+4x+7x=180°
⇒10x=80°⇒x=10°.
Now the angles of the triangle are 100-10=90°, 30+4x=70°
y=90°+70°=160° (∵Exterior angle is equal to the sum of two opposite interior angles).
In the 4th figure, to find angle 's' use the isosceles triangle concept.
That is, s+76°+76°=180° (∵In isosceles triangle base angles are equal)
⇒s=28°
In the 5th figure, to find angle 'm' use the isosceles triangle concept.
That is, 35°+m+m=180° (∵In isosceles triangle base angles are equal)
⇒2m=145°
⇒m=72.5°
Hence, the angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.
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) How long does he travel at 30 km/h, if he travels 1.2 h at 20 km/h?
Step-by-step explanation:
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A contractor is purchasing some stone tiles for a new patio, each tile costs $3 and he wants to spend less than $1000 the size of each tile is 1 square foot, write and inequality that represents the number of tiles he can purchase with a $1000 limit, and the figure out how large the stone patio can be
Answer:
333.333 Tiles and 333.333 Square Foot
Step-by-step explanation:
3X <= 1000
X <= 1000/3
X <= 333.333 Tiles
Then
333.333* 1sqt2 = 333.333 Square Foot
Select two ratios that are equivalent to 2 : 9.
Choose 2 answers:
9:2
1881
12:54
18:4
20:45
someone help me with rest please asap!!
Answer:
3. Definition of Midpoint
4. VAT, Vertical Angles Theorem
5. ASA, Angle-Side-Angle Theorem
Venn diagrams ! 3rd times a charm….
Answer:
1. 85 people were surveyed
When 7/11 is written as a decimal, what is the sum of the first 20 digits after the decimal point? Pls Help
There's a neat trick to finding the rational form of a repeating decimal number. Take for instance [tex]x=0.123123123\ldots[/tex]. Then
[tex]x = 0.123123123\ldots \\\\ \implies 1000x = 123.123123\ldots \\\\ \implies 1000x - x = 123.123123\ldots - 0.123123\ldots \\\\ \implies 999x = 123 \\\\ \implies x = \dfrac{123}{999}[/tex]
It's easy to reverse this method to find the repeating decimal form of [tex]\frac7{11}[/tex]. Let
[tex]x = \dfrac7{11}[/tex]
Multiply the numerator and denominator by 9,
[tex]x = \dfrac{63}{99}[/tex]
It follows that
[tex]x = \dfrac{63}{99} \\\\ \implies 99x = 63 \\\\ 100x - x = 63.6363\ldots - 0.6363\ldots \\\\ \implies x = 0.636363\ldots[/tex]
The first 20 digits after the decimal are made up of 10 each of 3 and 6, so the sum is 10 × (3 + 6) = 90.
Answer:
90
Step-by-step explanation:
Using long division, we find that Every group of two digits after the decimal point has a sum of 9 so the sum of the first 20 digits after the decimal point is 10*9=90
Avani has a loyalty card good for a discount at her local hardware store. The item she wants to buy is priced at $17, before discount and tax. After the discount, and before tax, the price is $15.64. Find the percent discount.
The percentage discount on the item will be equal to 8%.
What is the percentage?
The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
Price of the item before tax and discount = $17After discount and before tax price is = $15.64The percentage of the discount will be calculated as:-
Percentage discount = ( 17 - 16.64 ) / ( 17 )
Percentage discount= ( 1.36 ) / ( 17 )
Percentage discount = 0.08 x 100 = 8%
Therefore the percentage discount on the item will be equal to 8%.
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On Thursday, the amount of snowfall was 1/8 cm. On Wednesday, the amount of snowfall was 4 1/4 cm. What was the amount of snowfall on the two days combined?
The total amount of snowfall on the two days combined is 4 3/8 cm
Addition of fractionsFrom the question, we are to determine the amount of snowfall on the two days combined
From the given information,
the amount of snowfall was 1/8 cm on Thursday
The amount of snowfall was 4 1/4 cm on Wednesday
Then,
The total amount of snowfall on the two days combined will be
[tex]\frac{1}{8}+4\frac{1}{4}[/tex] cm
= [tex]\frac{1}{8}+\frac{17}{4}[/tex]
= [tex]\frac{1+34}{8}[/tex]
= [tex]\frac{35}{8}[/tex]
= [tex]4\frac{3}{8} \ cm[/tex]
Hence, the total amount of snowfall on the two days combined is 4 3/8 cm
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The line with equation y = mx + 3 intersects the line with equation 3x + 4y + 12 = 0 at the point (1, −15/4) Find the value of m.
The value of m will be; m = (-∞ , - 15/4) ∪ ( 1 , ∞ ).
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given: line y = mx + 3 intersects the line 3x + 4y + 12 = 0 at two distinct points.
To find the set of values of m.
The system of equations are;
y = mx + 3
3x + 4y + 12 = 0
The intersection point are (1, −15/4)
So, the value of m will be
m = (-∞ , - 15/4) ∪ ( 1 , ∞ )
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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
The value of angle x is 67 degree.
What is a Right Angled Triangle ?A right angled Triangle is a triangle with one angle as 90 degree.
It is given that the for the angle x , the base of the triangle is 28 ft.
The hypotenuse = 72ft.
The trigonometric ratios can be used to find the value of x
cos x = 28 /72
x = cos⁻¹ (28/72)
x = 67 degree (Rounded off to nearest tenth)
Therefore the value of angle x is 67 degree.
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The cost of the toy is expressed by the function y = 3x + 5, where x is the number of toys. If Peter bought 8 toys, find the cost of the toys.
Answer: If Peter bought 8 toys, the cost of the toys will be 29.
From the equation, y = 3x + 5, they have given the value of x as eight. So if we put eight in the equation and solve it, we will get the value of y. I believe there are some errors in the question as it doesn't specify that y is the cost. Also cost requires some sort of unit, which is not given in the context. I can't really tell if it is dollars or rubles or pounds etc. So I just gave it as the way it is. Since no other clues are given, this is most likely it.
y = 3x + 5
y = 3(8) + 5
y = 24 + 5
y = 29
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
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The length of a rectangle is units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?
A.
2(w) + w
B.
w + w
C.
3w +
D.
6w + 5
The expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.
Given that, the length of the rectangle is [tex]\frac{5}{2}[/tex] units greater than twice its width.
We need to determine the expression that gives the perimeter of the rectangle in terms of w.
Given, width = w units, then length= 2w + [tex]\frac{5}{2}[/tex] units.
What is the perimeter of the rectangle?The perimeter of the rectangle is the sum of all the sides of the rectangle.
That is, perimeter of a rectangle = 2 (length+width).
Now, perimeter of a rectangle = 2 (2w + [tex]\frac{5}{2}[/tex]+w)=6w+5 units.
Hence, the expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.
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3. Find x 75° (4x 25)°
If two lines intersect, then their opposite angles are equal. Then the value of x is 25°.
The missing graph is given below.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Then the value of x will be
75° = (4x - 25)°
100° = 4x
x = 25°
Then the value of x is 25°.
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If the set U = {all positive integers} and set A = {x|x ∈ U and x is an odd positive integer}, which describes the complement of set A, Ac?
Ac = {x|x ∈ U and is a negative integer}
Ac = {x|x ∈ U and is zero}
Ac = {x|x ∈ U and is not an integer}
Ac = {x|x ∈ U and is an even positive integer}
Answer: Choice D) set of even integers
=======================================================
Explanation:
U = universal set = {all positive integers} = {1, 2, 3, 4, 5, ...}
A = {stuff in set U that is odd} = {1, 3, 5, 7, 9, ...}
[tex]A^c[/tex] = {stuff in set U but NOT from set A} = {2, 4, 6, 8, ...}
[tex]A^c[/tex] = {set of even numbers from set U}
In set theory, the complement is simply the complete opposite. If the number 7 is found in set A for instance, then 7 is not going to live in the complement [tex]A^c[/tex]
The opposite of the odd numbers is the set of even numbers.
Therefore, we go for choice D as our final answer.
Side note: if we union set A with its complement [tex]A^c[/tex] then we get the universal set as a result. [tex]A \cup A^c = \text{universal set} = \text{set of all positive integers}[/tex]
The solution is Option D.
Ac = {x|x ∈ U and is an even positive integer} where Ac represents the complement of set A
What is union and intersection of sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set U be = {all positive integers}
So , the values of set U = { 1 , 2 , 3 , 4 , 5 .. }
And , let the set A = {x|x ∈ U and x is an odd positive integer}
So , the value of set A = { 1 , 3 , 5 , 7 , ... }
And , the complement of set A is Ac
The value of set Ac is all the even positive odd integers
So , the value of set Ac = { 2 , 4 , 6 , 8 .. }
Therefore , the value of set Ac = { 2 , 4 , 6 , 8 .. }
Hence , the set Ac = {x|x ∈ U and is an even positive integer}
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Can somebody help me and tell me if i’m right or not because I don’t know how to do this
Find the value of y.
Answer:
y = 5
Step-by-step explanation:
Since the lines are parallel, same side interior angles are supplementary.
That allows us to solve for x.
7x + 17 + 5x - 5 = 180
12x = 168
x = 14
The angles 23yand 5x - 5 are supplementary, so the sum of the measures equals 180°.
23y + 5x - 5 = 180
We already know that x = 14.
23y + 5(14) - 5 = 180
23y = 115
y = 5