Answer:
Step-by-step explanation:
Let CE and DE be the bisectors of ∠C and ∠D respectively. Then, ∠1 = 1/2∠C and ∠2 = 1/2∠D
In △DEC, we have
→ ∠1 + ∠2 + ∠CED = 180° [Sum of angles of a triangle]
→ ∠CED = 180° - (∠1 + ∠2). .....(i)
Again, the sum od the angles of a quadrilateral is 360°.
∴ ∠A + ∠B + ∠C + ∠D = 360°
→1/2(∠A + ∠B) + 1/2∠C + 1/2∠D = 180°
→1/2(∠A + ∠B) + ∠1+ ∠2 = 180°
→1/2(∠A + ∠B) = 180° - (∠1+ ∠2)....(ii)
From (i) and (ii), we get 1/2(∠A + ∠B) = ∠CED
Hence, ∠A + ∠B = 2∠CED
Find the measure of the indicated angle to the nearest degree.
1)
A) 19°
C) 36°
B) 43°
D) 47°
Answer:
D
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan? = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{18}{17}[/tex] , then
? = [tex]tan^{-1}[/tex] ([tex]\frac{18}{17}[/tex] ) ≈ 47° ( to the nearest degree )
if x/y=(3/5)^3÷(6/5)^0'find the value of (x/y)^2
Answer:
729/15625
Step-by-step explanation:
1. Evaluate the power
( (27/125) ÷ 1 )^2
2. divide
( 27/125 )^2
evaluate the power
( 27^2 / 125^2 )
729/15625
Two square based pyramids are joined, total volume is 2700mm, perpendicular height 16mm on top pyramid and 20mm on the other, joint base has length and width of x, find x. Please help me..
Answer:
15 mm
Step-by-step explanation:
Since both pyramids are joined together, this means that the base of the pyramid which is a square have the same dimensions.
Let the length and width of the base be x, hence the dimension of the base is x mm by x mm.
For the first pyramid, the volume is:
V₁ = a²h₁/3; where a is the length of the square base, h₁ is the height.
Since the pyramid has a height of 16 mm, hence:
V₁ = 16x²/3
the second pyramid, the volume is:
V₂ = a²h₂/3; where a is the length of the square base, h₂ is the height.
Since the pyramid has a height of 20 mm, hence:
V₂ = 20x²/3
Since the total volume (V) of the pyramid is 2700 mm³, hence:
V = V₁ + V₂
V = 16x²/3 + 20x²/3
2700 = 16x²/3 + 20x²/3
2700 = 36x²/3
36x² = 8100
x² = 225
x = 15 mm
identify the volume of a sphere if it has a surface area of 465 square units
Step-by-step explanation:
S.A = 465
4πr²= 465
r². = 36.9
r. = 6.08
volume of a sphere = 4/3πr³
= 4/3π * 6.08³
= 941.8 cm³
The radius of the sphere will be 6.08 units. Then the volume of the sphere will be 942.87 cubic units.
What is the volume of the sphere?A circular solid object or its surface whose points are all equally spaced from the center.
Let r be the radius of the sphere.
Then the volume of the sphere will be
V = 4/3 πr³ cubic units
The surface area of the sphere will be 465 square units.
The surface area of the sphere is given as,
SA = 4πr²
Then the radius of the sphere will be
4πr² = 465
r² = 37
r = 6.08 units
Then the volume of the sphere will be
V = 4/3 π (6.08)³
V = 4/3 π x 225.09
V = 300 π
V = 942.87 cubic units
Thus, the volume of the sphere will be 942.87 cubic units.
More about the volume of the sphere link is given below.
https://brainly.com/question/9994313
#SPJ5
please help me !!!!!!!
Answer:
(32;29) first thing is to find the gradient of that line and form some extra equation ( bodzatu ili
Round the $40435.29 to the nearest thousand dollar
Answer:
$40000
Step-by-step explanation:
The nearest thousand dollar is rounding the thousand value from its hundred value, which in this case is 4. Since 4 is less than half of 10, the thousand value must round down to $40000.
Answer:
$40000.00
Step-by-step explanation:
Report this answer if its incorrect ^_^
Solve each system of equations by substitution. Clearly identify your solution.
Answer:
(-3, 5)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = x + 8
x + y = 2
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: x + x + 8 = 2Combine like terms: 2x + 8 = 2[Subtraction Property of Equality] Subtract 8 on both sides: 2x = -6[Division Property of Equality] Divide 2 on both sides: x = -3Step 3: Solve for y
Substitute in x [1st Equation]: y = -3 + 8Add: y = 5Answer:
x = - 3
y = 5
Step-by-step explanation:
y = x + 8 ------(I)
x + y = 2 -------------(II)
Substitute y = x + 8 in equation (II)
x + x + 8 = 2
Combine like terms
2x + 8 = 2
Subtract r from both sides
2x = 2- 8
2x = -6
Divide both sides by 2
x = -6/2
x = -3
Plug in x = -3 in equation (I)
y = -3 + 8
y = 5
pls help w this
√2x+1 = 4
In the equation above, what is the value of 2x +1?
A) 3/2
B) 2
C) 4
D) 16
Answer:
[tex]\boxed {\boxed {\sf D. \ 16}}[/tex]
Step-by-step explanation:
We are given the following equation and asked to solve for 2x+1.
[tex]\sqrt {2x+1}=4[/tex]
We want to isolate the entire expression of 2x+1. Notice that it is under the square root. If we want to isolate it, we have to perform the inverse operation. The inverse of a square root is a square, so we square both sides of the equation.
[tex](\sqrt{2x+1} )^2= (4)^2[/tex]
[tex]2x+1=(4)^2[/tex]
[tex]2x+1=16[/tex]
We could continue solving for x, then plug the answer back into the expression 2x+1. However, hopefully you notice that we already found the answer!
We only had to do one step to find the answer, but you could complete many other steps to get the same answer:
[tex]2x+1-1=16-1\\2x=15\\2x/2=15/2\\x= 7.5[/tex] (Solve for x)
[tex]2x+1\\2(7.5)+1\\15+1\\16[/tex] (Plug the answer in for x)
The value of 2x+1 is 16 and the correct answer is 16.
Which of the following represents the general form of an inequality?
Ax + By 2 C
Ax + By >
Ax + By < 0
All of the choices
Answer:
Third option:
Ax + By < 0
Step-by-step explanation:
The general form of an inequality is:
(something) (symbol) (another thing).
Where the symbols can be:
> = "larger than"
< = "smaller than"
≤ = "smaller than or equal to"
≥ = "larger than or equal to"
So, a given inequality can be:
K > M
This means that K is larger than M.
From the given options, the only one that has this general form is the third option:
Ax + By < 0
This can be read as:
"A times x, plus B times y, is smaller than zero"
Find QR
PQ= 3
QR= 2x+22
PR= x+17
2 thirds divided by 4
Let f be defined as shown. What is f^-1(-3)
Hello,
[tex]f^{-1}(-3)=-1\\[/tex]
You have just to read the arrows un reversed order:
in f we find (-1,-3) so in f^{-1} we find (-1,-3)^{-1}=(-3,-1)
What is the value of a+b?
A) 110
B) 125
C) 135
D) 145
Please help!!!!
Question below plz answer it fast!
Answer:
The answer is 49 .
Step-by-step explanation:
Do i need to explain ?
which number produces a rational number when added to 0.25
0.65 is the correct one if not up there try 0.45 other possible one
Step-by-step explanation:
A rational number is defined as any number which can be expressed in fractional p/q of two integers, where 'p' is the numerator and 'q' is the denominator. 'q' can never be zero. A rational number can also be expressed as a terminating decimal. So, when 0.25 is added in 0.45 it becomes 0.65 which is rational.
a man invested 800.00in a bank at a simple interest rate of 5% per annum .Find his total amou year
Answer:
£840
Step-by-step explanation:
800 × 1.05 = 840
(1.05 Is the decimal multiplier = (100% + 5%)/100)
Juan compró un led TV en cuotas que costó $ 76.000=. Si le falta pagar 3 cuotas y ya pagó $ 47.000, ¿Cuál es el valor de cada cuota fija?
Respuesta:
$ 9666. 67
Explicación paso a paso:
Costo de TV = $ 76,000
Número de cuotas = 3
Monto ya pagado = $ 47000
Amontof cada cuota fija = Cantidad que queda por pagar / 3
Cantidad que queda por pagar = Costo de TV - Cantidad ya pagada
Cantidad que queda por pagar = $ (76000 - 47000) = $ 29000
Monto de cada cuota fija = $ 29000/3 = $ 9666. 67
Point M is the midpoint of AB. The coordinates of point A are (-8, 3) and the coordinates of M are (-2, 1). What are the coordinates of point B?
.
.
.
May you please show me the work?
Answer:
the coordinates of point B are (-5, 2)
Step-by-step explanation:
1. use midpoint formula to find the midpoint (equation attached below)
2. plug in the numbers
[tex](\frac{-8+(-2)}{2},\frac{3+1}{2})[/tex]
3. solve
[tex](\frac{-8-2)}{2},\frac{3+1}{2})[/tex]
[tex](\frac{-10}{2},\frac{4}{2})[/tex]
[tex](-5,2})[/tex]
Please help!!!!!!!! I’ve been stuck on this
PLEASE HELP! Use the graph to solve the system of equations.
A. (-5,0)
B. (0,5)
C. (0,0)
D. (2,3)
Answer:
D
Step-by-step explanation:
Look for the intersection point of the two graphs
Another way:
You can just substitute each pair in both equations and u will find that d is the correct answer
use r = 27 and x = 3
- r 9 _ + 5x
Answer:
-228
Step-by-step explanation:
Given ACM, angle C=90º. AP=9, PM=12. Find AC, CM, AM.
Answer:
AM = 25, AC = 15, CM = 20
Step-by-step explanation:
The given parameters are;
In ΔACM, ∠C = 90°, [tex]\overline{CP}[/tex] ⊥ [tex]\overline{AM}[/tex], AP = 9, and PM = 16
[tex]\overline{AC}[/tex]² + [tex]\overline{CM}[/tex]² = [tex]\overline{AM}[/tex]²
[tex]\overline{AM}[/tex] = [tex]\overline{AP}[/tex] + PM = 9 + 16 = 25
[tex]\overline{AM}[/tex] = 25
[tex]\overline{AC}[/tex]² = [tex]\overline{AP}[/tex]² + [tex]\overline{CP}[/tex]² = 9² + [tex]\overline{CP}[/tex]²
∴ [tex]\overline{AC}[/tex]² = 9² + [tex]\overline{CP}[/tex]²
Similarly we get;
[tex]\overline{CM}[/tex]² = 16² + [tex]\overline{CP}[/tex]²
Therefore, we get;
[tex]\overline{AC}[/tex]² + [tex]\overline{CM}[/tex]² = 9² + [tex]\overline{CP}[/tex]² + 16² + [tex]\overline{CP}[/tex]² = [tex]\overline{AM}[/tex]² = 25²
2·[tex]\overline{CP}[/tex]² = 25² - (9² + 16²) = 288
[tex]\overline{CP}[/tex]² = 288/2 = 144
[tex]\overline{CP}[/tex] = √144 = 12
From [tex]\overline{AC}[/tex]² = 9² + [tex]\overline{CP}[/tex]², we get
[tex]\overline{AC}[/tex] = √(9² + 12²) = 15
[tex]\overline{AC}[/tex] = 15
From, [tex]\overline{CM}[/tex]² = 16² + [tex]\overline{CP}[/tex]², we get;
[tex]\overline{CM}[/tex] = √(16² + 12²) = 20
[tex]\overline{CM}[/tex] = 20.
Triangle PQR has been dilated to form triangle P'Q'R'. What is the least amount of information needed to determine if the two triangles are similar
Answer:
angles Q and Q' are congruent, angles R and R' are congruent
Step-by-step explanation:
For two triangles to be congruent, we need to show is two of the
1. corresponding angles are congruent,
or,
2. all three pairs of corresponding sides are proportional,
or,
3. two pairs of corresponding sides are proportional AND the included angles are congruent.
And, angles are always congruent when a figure is dilated
Therefore, angles Q and Q' are congruent, angles R and R' are congruent(satisfies the first criterion that at least two corresponding angles are congruent)
what is the answer to x^2-11=25 please
Hey there!
[tex]\mathsf{x^2 - 11 = 25}[/tex]
[tex]\large\textsf{ADD 11 to BOTH SIDES}[/tex]
[tex]\mathsf{x^2 - 11 + 11 = 25 + 11}[/tex]
[tex]\large\textsf{CANCEL out: -11 + 11 because that gives you 0}[/tex]
[tex]\large\textsf{KEEP: 25 + 11 because that helps solve for the x-value}[/tex]
[tex]\mathsf{25 + 11 = \bf 36}[/tex]
[tex]\large\textsf{NEW EQUATION: }\mathsf{x^2=36}[/tex]
[tex]\large\textsf{Take the square root of the number (36)}[/tex]
[tex]\mathsf{x = \pm \sqrt{36}}[/tex]
[tex]\mathsf{\pm = \boxed{\bf plus-or-minus}}[/tex]
[tex]\mathsf{x = \sqrt{-36}\rightarrow \bf -6}[/tex]
[tex]\large\textsf{or}[/tex]
[tex]\mathsf{x = \sqrt{36} = \bf 6}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf x = 6 or x = -6}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
x² - 11 = 25
Add 11 to both sides.
x² - 11 + 11 = 25 + 11
Cancle out the 11 because when we add -11 to 11 that gives 0. On other side add 25 and 11 we get 36.
x² = 36
Take the square root of both sides of the equation and remember to use both positive and negative roots.
√x² = ± √36
x = ± 6
Write the solutions, one with a+ sign and one with a- sign.
[tex] x_1 = 6[/tex]
[tex]x_2 = -6[/tex]
This equation has two solutions which are :-
[tex] x_1 = 6[/tex]and [tex]x_2 = -6[/tex]
Question 24 of 42
Which of the following conditions is not sufficient to show that the two
triangles are congruent?
AA
A
X Х
5-
A. AABC and Axyz have the same orientation.
B. The rise and run of the translation between each pair of
corresponding points are the same.
A
Answer:
I think A is correct
Step-by-step explanation:
I can't see D so I'm not sure, hope it's right
Find x in the kite below
Answer:
5
Step-by-step explanation:
The given is 3-4-5 special triangle so the missing side represented with x is 5
What is the slope of the line shown below?
Answer:
Hello there,
The correct answer to this question would be D 1/6
Step-by-step explanation:
I had took the test and it said it was correct.
Anyways hope this helps
if the answer is correct pls mark Brainliest
thank you, have a nice day
is y=9x proportinal?
Answer:
yeah it is
y is directly proportional to x
proportionality constant is 9
Find the domain in the given ordered pairs.
{(2, 3), (3, 5), (6, 7), (8, 9)}
Answer:
saaad
Step-by-step explanation:
Answer:
Domain = {-5,2,4,6,8,9), range = (-3,-1,0,4,6,7}
Step-by-step explanation:
{(2,4), (8,-3), (-5,-1), (4,6), (6,7), (9,0)}
The domain is the input and the range is the output
domain is { 2,8,-5,4,6,9} and the range is {4,-3,-1,6,7,0}
We put the numbers in order from smallest to largest
Domain = {-5,2,4,6,8,9), range = (-3,-1,0,4,6,7}
Round your answer to one decimal places where necessary. Please give steps.
4/3 x 3.14 x 2.25 = ?
Answer:
4/3 x 3.14 x 2.25=9.42
Hope This Helps!!!
Answer:
9.4
Step-by-step explanation:
[tex] \sf \frac{ \bold{4 }}{ 3 } × 3.14 × \underline{2.25}[/tex]
Step 1 :- Multiply decimal by the number. So, that the results equals whole number.
[tex] \sf \frac{ \underline{ 4 }}{ 3 } \\ [/tex] × 2.25 × 3.14 .
[tex] \sf \frac{9}{ 3 } \\ [/tex] × 3.14
Step 2 :- Divide the fraction.
= 3 × 3.14.Step 3 :- Multiply both .
= 9.42.Round to one decimal place :- 9.4