Applying the intersecting chords theorem, the possible lengths of JM and TM could be: 16 and 7.5.
What is the Intersecting Chords Theorem?The intersecting chords theorem states that product of the divided segments of each intersectint chords are equal to each other.
Based on the intersecting chords theorem, we would have:
(EM)(RM) = (JM)(TM)
If JM and TM are 16 and 7.5 respectively, we would have:
(8)(15) = (16)(7.5)
120 = 120
The lengths of JM and TM could therefore be: 16 and 7.5.
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Answer:
16 and 7.5
Step-by-step explanation:
En un curso, el 40 % de los alumnos reprobó un examen. Si el curso tiene 45 alumnos. ¿Cuántos alumnos aprobaron
Answer:
Cantidad de aprobados= 25
Step-by-step explanation:
Dada la siguiente información:
Reproado= 45%
Aprobado= 55%
Cantidad de alumnos= 45 alumnos
Para calcular la cantidad de aprobados, debemos utiliar la siguiente formula:
Cantidad de aprobados= cantidad de alumnos*porcentaje aprobados
Cantidad de aprobados= 45*0.55
Cantidad de aprobados= 25
Find the mode of the data.
Length (inches) of fish in tank:
2, 3, 1, 4, 5, 2, 2
Mode: [?] in.
Answer:
The mode is 2
Step-by-step explanation:
Mathematically, the mode of a given data set represents the most recurring number or the number with the most count
Looking at the given dataset, we can see that the number 2 recurred 3 times
Compared with the other numbers, it has the most count
this means it is the mode of the given or displayed dataset
I need help I’m stuck
find the equation of a circle with a point at ( 10 , - 4 ) and a point at ( -2 , - 4 )
Answer:
Solution given:
letA=(10,-4)
B=(-2,-4)
centre[C](h,k)=[tex]\frac{10-2}{2},\frac{-4-4}{2}=(+4,-4)[/tex]
radius=[tex]\sqrt{(4-10)²+(-4+4)²}=6[/tex]units
we have
Equation of a circle is;
(x-h)²+(y-k)²=r²
(x-4)²+(y+4)²=36
or.
x²-8x+16+y²+8y+16=36
x²-8x+8y+y²=36-32
x²-8x+8y+y²=4
The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.
Answer:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]
Step-by-step explanation:
the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter
since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle
remember midpoint formula,
[tex] \displaystyle M = \left( \frac{x _{1} + x_{2} }{2} , \frac{ y_{2} + y_{2}}{2} \right)[/tex]
let,
[tex] \displaystyle x _{1} = 10[/tex][tex] \displaystyle x _{2} = - 2[/tex][tex] \displaystyle y _{1} = - 4[/tex][tex] \displaystyle y _{2} = -4[/tex]thus substitute:
[tex] \rm\displaystyle M = \left( \frac{10 + ( - 2)}{2} , \frac{ - 4 + ( - 4)}{2} \right)[/tex]
simplify addition:
[tex] \rm\displaystyle M = \left( \frac{8}{2} , \frac{ - 8}{2} \right)[/tex]
simplify division:
[tex] \rm\displaystyle M = \left( 4, - 4 \right)[/tex]
so the centre of the circle is (4,-4)
since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is
[tex] \displaystyle r = 4 - ( - 2)[/tex]
simplify which yields:
[tex] \displaystyle\boxed{ r =6}[/tex]
recall the equation of circle
[tex] \displaystyle (x - h) ^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
we acquire that,
h=4k=-4r=6therefore substitute:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y - ( - 4))}^{2} = {6}^{2} [/tex]
simplify:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]
and we are done!
also refer the attachment
(the graph is web resource of desmos)
What angle is Framed below
60
Answer:
is there supposed to be an image?
have a good day :)
Step-by-step explanation:
Find the value of x.
Answer:
x = 29
Step-by-step explanation:
The three angles add to 90 degrees
x+3 + x-1 + x+1 = 90
Combine like terms
3x +3 = 90
Subtract 3 from each side
3x+3-3 = 90-3
3x = 87
Divide by 3
3x/3 = 87-3
x = 29
Answer:
x = 29
Step-by-step explanation:
The 3 angles sum to 90° , that is
x + 3 + x - 1 + x + 1 = 90
3x + 3 = 90 (subtract 3 from both sides )
3x = 87 ( divide both sides by 3 )
x = 29
Solve each triangle. Round your answers to the nearest tenth.
show work If possible
∠ABC = 76°
BC = 20.1
CA = 28.0
Step-by-step explanation:Solving the triangle means finding all unknown angles and sides of the triangle.
(i) Two of the angles (∠BCA = 60° and ∠CAB = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating that the sum of angles of a triangle is equal to 180°.
Therefore, the sum of angles of the triangle ABC is 180°. i.e
∠ABC + ∠BCA + ∠CAB = 180°
=> ∠ABC + 60° + 44° = 180°
=> ∠ABC + 104° = 180°
=> ∠ABC = 180° - 104°
=> ∠ABC = 76°
(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;
=> [tex]\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}[/tex]
=> [tex]\frac{sinBCA}{BA} = \frac{sinCAB}{BC} = \frac{sinABC}{CA}[/tex]
Substitute the necessary values
[tex]\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}[/tex] ---------------------(ii)
(a) To get side BC, use the first two terms of equation (ii)
[tex]\frac{sin60}{25} = \frac{sin44}{BC}[/tex]
Cross multiply
BC x sin 60 = 25 x sin 44
BC x 0.8660 = 25 x 0.6947
0.8660 x BC = 17.3675
BC = [tex]\frac{17.3675}{0.8660}[/tex]
BC = 20.05
=> BC = 20.1 to the nearest tenth
(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;
[tex]\frac{sin60}{25} = \frac{sin76}{CA}[/tex]
Cross multiply
CA x sin 60 = 25 x sin 76
CA x 0.8660 = 25 x 0.9703
0.8660 x CA = 24.2575
CA = [tex]\frac{24.2575}{0.8660}[/tex]
CA = 28.01
=> CA = 28.0 to the nearest tenth
what is the value of X in the isosceles trapezoid below?
Answer:
11
Step-by-step explanation:
what is the correct answer
The Answer is:
A. x = 4
......................
Answer:
Value of opposite ∠2 = 120°
Step-by-step explanation:
Given question:
Quadrilateral inscribed in a circle
Value of ∠1 = 60°
Find:
Value of opposite ∠2
Computation:
In Quadrilateral inscribed in a circle, sum of opposite angle is 180
So,
Value of ∠1 + Value of ∠2 = 180°
60 + Value of ∠2 = 180
Value of ∠2 = 180 - 60
Value of ∠2 = 120
Value of opposite ∠2 = 120°
What is the ordered pair for Point T?
A. (1,5)
B. (0,5)
C. (5,0)
D. (5, 5
Answer:
B.(0,5)
Step-by-step explanation:
Ordered pairs are written as (x,y)
x value of T is 0
y value of T is 5
Ordered pair for point T is (0,5)
HELP PLEASE QUICK
Suppose the function f(x) is replaced with g(x) = f(x – 5). How does the graph of g(x) compare to the graph of f(x)?
A. The graphs are the same.
B. The graph is translated 5 units down.
C. The graph is translated 5 units to the left.
D. The graph is translated 5 units to the right.
Answer:
translated 5 units to the right
Step-by-step explanation:
Which of the following represents a constant from the expression given?
15x2 + 2x + 9
Answer:
9
Step-by-step explanation:
15x^2 + 2x + 9
A constant does not have a variable with it
15x^2 is the quadratic term
2x is the linear term
9 is a constant term
Answer:
The answer is 9.
someone already explained it lol
A rectangular field has perimeter 600 m and area 21600 m squared. Find the dimensions of the field.
Answer:
Let length be x and width be y
[tex]perimeter = 2(l + w) \\ 600 = 2(x + y) \\ x + y = 300 - - - (a) \\ \\ area = l \times w \\ 21600 = xy - - - (b) \\ from \: (a) : \\ y = 300 - x \\ \therefore21600 = x(300 - x) \\ 21600 = 300x - {x}^{2} \\ {x}^{2} - 300x + 21600 = 0 \\ (x - 180)(x - 120) = 0 \\ x = 180 \: \: or \: \: 120 \: m \\ \\ y = 120 \: \: or \: \: 180 \: m \\ \\ { \boxed{ length = 180 \: m}} \\ { \boxed{width = 120 \: m}}[/tex]
A scientist has a sample of the radioactive isotope bismuth-212. The isotope decays exponentially as shown in the table. Time (seconds) Mass (grams) 10 26.8 20 23.9 30 21.3 40 19.0 50 16.9 60 15.1 Which equation best represents the curve of best fit for this set of data? A. f(x) = 29 • 0.989x B. f(x) = 27 • 1.011x C. f(x) = 30 • 0.989x D. f(x) = 28 • 0.234x
Answer:
f(x) = 30 • 0.989x
Step-by-step explanation:
Given the data :
10 26.8
20 23.9
30 21.3
40 19
50 16.9
60 15.1
Using technology, the exponential model equation obtained by plotting the data is :
y = 30.068(0.989)^x
Based on the general exponential formula :
y = ab^x
y = predicted value
Initial value, a = 30.068
Rate = b = 0.989
The most appropriate model equation from the options given is :
f(x) = 30 • 0.989^x
A 20 ft. ladder is used against a 15 ft. wall. What is the measure of the angle made by the ladder and the ground (nearest whole degree)? How far is the ladder from the wall on the ground (to the nearest tenth)?
Step-by-step explanation:
Given that,
The length of a ladder, H = 20 feet
The height of the wall, h = 15 ft
We know that,
[tex]\sin\theta=\dfrac{h}{H}[/tex]
h is perpendicular and H is hypotenuse
So,
[tex]\sin\theta=\dfrac{15}{20}\\\\\theta=\sin^{-1}(\dfrac{15}{20})\\\\\theta=48.59^{\circ}[/tex]
Now using Pythagoras theoerm,
[tex]b=\sqrt{H^2-h^2}\\\\b=\sqrt{20^2-15^2}\\\\b=13.2\ ft[/tex]
Hence, the angle made by the ladder and the ground is 48.59° and the ladder is 13.2 feet from the wall on the ground.
examine the matrices below and use to answer questiom 12 and 13
x={3 -5} y= {6 7}
{-4 2} {-4 -3}
number 2 question
calculate x and y
A {9 12}
{0 1}
B {9 -12}
{0 -5}
c {9 -2}
{-8 -1}
D {9 2}
{-8 -1}
Answer:
d
Step-by-step explanation:
If the sum of the measures of 21 and 22 is 180°, what is the sum of the measures of 23 and 24?
Answer:
180
Step-by-step explanation:
it is a quadrilateral that has 360 degrees in total. So if 1 and 2=180 then 3 and 4=360-180=180. Hope this is right.....
The tength of a picture frame is 12 cm more than twice the width. If the perimeter is 204cm, find the
dimensions (length and width) of the frame.
Answer:
30cm x 72 cm
Step-by-step explanation:
The perimeter is the measurements of all sides added together. Let's start by dividing the perimeter by 2, so we have the sum of the length and width. This gives us 102cm. Let's call the width x, and the length y. We know y is x times 2 plus 12. (2x + 12) So, we know [x + y = x + (2x + 12)]. So let's solve.
x + y = x + (2x + 12)
102 = x + (2x + 12)
102 = 3x + 12
102 - 12 = 3x + 12 - 12
90 = 3x
90/3 = 3x/3
30 = x
The width is 30cm.
what is the algebraic expression for 12 times a number x, plus a second number y ?
Answer:
12x + y
Step-by-step explanation:
Copy and complete the statement using < or >
-7 or -8
Answer: -7
Step-by-step explanation:
Well since where going below degrees the answer would be -7 because it is closer to 1
the histogram on the left shows the number of hours students in an art class practiced drawing during one week.
Step-by-step explanation:
mmm Next no se...........
Simply
7p2 x 3p
14p4
Answer:
[tex]{ \tt{ = \frac{7 {p}^{2} \times 3p}{14 {p}^{4} } }} \\ = { \tt{ \frac{21 {p}^{3} }{14 {p}^{4} } }} \\ = { \tt{1.5 {p}^{ - 1} }}[/tex]
If you are given a parallelogram with the top right and left corners each measuring 72* and the bottom right corner measuring 108*. What is the measurement of the missing corner, the bottom left corner of the parallelogram?
Answer: [tex]108^{\circ}[/tex]
Step-by-step explanation:
Given
The top left and right corners measures [tex]72^{\circ}[/tex] and the bottom right corner measures [tex]108^{\circ}[/tex].
Suppose the missing corner measures [tex]x[/tex]
So, the sum of the four angles of parallelogram is [tex]360^{\circ}[/tex]
[tex]\therefore x+72^{\circ}+108^{\circ}+72^{\circ}=360^{\circ}\\\Rightarrow x=360^{\circ}-252^{\circ}\\\Rightarrow x=108^{\circ}[/tex]
Therefore, the missing angle is [tex]108^{\circ}[/tex].
Pls I need help with this
Answer:
third side = 4
Step-by-step explanation:
third side is hypoenuse as it is opposite to 90 degree.
using pythagoras theorem
(perpendicular)^2 + (base)^2 = (hypotenuse)^2
2^2 + (2[tex]\sqrt{3[/tex] )^2 = hypotenuse^2
4 + 4*3 = hypotenuse^2
16 = hypotenuse^2
[tex]\sqrt{16}[/tex] = hypotenuse
4 = hypotensue
What’s the answer????????????
Answer:33
Step-by-step explanation:
trust
Do the surface area plzzz and u get 25 points and if u Dk don’t answer and no links
Answer:
184
Step-by-step explanation:
A = 2(wl+hl+hw) = 2 · (6 · 2 + 10 · 2 + 10 · 6) = 184
Answer:
SA = 184 m²
Step-by-step explanation:
The opposite faces of the cuboid are congruent , then surface area (SA) is
SA = 2(2 × 6) + 2(6 × 10) + 2(2 × 10)
= 2(12) + 2(60) + 2(20)
= 24 + 120 + 40
= 184 m²
There are 1,099 souvenir paperweights that need to be packed in boxes. Each box will hold 11 paperweights. How many boxes will be needed?
Answer:
1099/11=99.9
since you can't have 99 boxes, you round to 100 boxes.
you will need 100 boxes.
ONI
Write the following ratios in their simplest form:
100 minutes: 1-hours
2
15m: 1050cm
9min : 600seconds
125
(iv)
1000
efine the following terms
Common fraction
Answer:
1. 5 min : 3 min
2. 10 cm : 7 cm
3. 9 sec : 10 sec
Step-by-step explanation:
1. Since 60 minutes = 1 hour
Thus;
100 minutes : 60 minutes
10 minutes : 6 minutes
5 minutes : 3 minutes
The simplest form = (5:3) minutes
2. 100 cm = 1 m,
⇒ 15 m = 15 x 100 cm = 1500 cm
Thus;
1500 cm : 1050 cm
150 cm : 105 cm
30 cm : 21 cm
10 cm : 7 cm
The simplest form = (10:7) cm
3. 60 seconds = 1 minute
⇒ 9 minutes = 9 x 60
= 540 seconds
Thus;
540 seconds : 600 seconds
54 seconds : 60 seconds
9 seconds : 10 seconds
The simplest form = (9:10) seconds
4. A common fraction is one that has the same value on each side of an expression or equation.
Match each vertex in ABC to its corresponding vertex in the dashed triangle.
A -> A
B -> E
C -> D
Theyre similar triangles, ABC = AED
The corresponding vertex of the similar triangles are
A ≈ A
B ≈ E
C ≈ D
The triangles ABC and AED are similar triangles
What are similar triangles?
If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ABC
Let the second triangle be represented as AED
The measure of AB = 3
The measure of AD = 8
The measure of AC = 4
The measure of AE = 6
Now , for the similar triangles , corresponding sides of similar triangles are in the same ratio
So ,
AB / AE = AC / AD
Substituting the values in the equation , we get
3/6 = 4/8
1/2 = 1/2
Therefore , the triangles are similar
Hence , the triangles ABC and AED are similar triangles
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