Answer:
Step-by-step explanation:
SecA - TanA
= 1/CosA - SinA/CosA
= 1 - SinA/CosA
We know that Sin2A = 2SinACosA and Cos2A = Cos²A - Sin²A
Thus SinA = Sin2(A/2) = 2Sin(A/2)CosA/2
CosA = Cos2(A/2) = Cos²A/2 - Sin²A/2
Now substituting the values back,
=> 1 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
// we know that Sin²θ + Cos²θ = 1
=> Sin²(A/2) + Cos²A/2 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
//We know that numerator is of form a² + b² - 2ab which is (a - b)².
//Similarly denominator is of form a² - b² which is (a - b)(a + b)
=> [Sin(A/2) - Cos(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [ - {Cos(A/2) - Sin(A/2)}]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)] / [Cos(A/2) + Sin(A/2)]
= R.H.S
Hence proved.
help me out (geometry)
Answer:
⊥
Step-by-step explanation:
d and b meet at a 90 degree angle ( as shown by the box)
The lines are perpendicular (⊥)
I’m stuck on this one help anyone?
Answer:
just add a small amount to the 2.8 and square the result
Step-by-step explanation:
x x^2
2.8 7.84
2.81 7.8961
2.82 7.9524
2.83 8.0089
2.84 8.0656
2.85 8.1225
2.86 8.1796
2.87 8.2369
A car travelling at v kilometers per hour will need a stopping distance, d, in meters without skidding that can be modelled by the function d=0.0067v2+0.15v. Determine the speed at which a car can be travelling to be able to stop within 37m.
I’m need of serious help!
Answer:
v = 14 km/h
Step-by-step explanation:
d = 0.0067[tex]v^{2}[/tex] + 0.15v
differentiate the function with respect to v to have;
d = 0.0134v - 0.15
given that the distance without skidding = 37 m (0.037 km) , then;
0.037 = 0.0134v - 0.15
0.0134v = 0.037 + 0.15
= 0.187
v = [tex]\frac{0.187}{0.0134}[/tex]
= 13.9552
v = 14 km/h
The speed of the car travelling would be 14 km/h to be able to stop within 37m.
Let j=+5 - 5+ |-5 x 1/5
What is the value of+J?
Answer:
j=|x|
Step-by-step explanation:
3c + 2 = -22
whats c?
3c+ 2= -22
⇔3c = -22 -2
⇔3c = -24
⇔c= -24/3
⇔c=- 8
Answer:
3c= -22-2
3c= -24
c= -24/3
c= -8
Step-by-step explanation:
Lines c and d are parallel lines cut by transversal p.
Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8.
Which must be true by the corresponding angles theorem?
A. ∠1 ≅ ∠7
B. ∠2 ≅ ∠6
C. ∠3 ≅ ∠5
D. ∠5 ≅ ∠7
Answer:
Option (B).
Step-by-step explanation:
Here there are two parallel lines c and d cuts by a transversal p.
The angles are formed as shown in diagram.
Here,
[tex]\angle 1 = \angle 7 (alternate)\\\\\angle 2 = \angle 6 (corresponding)\\\\\angle 3 = \angle 5 (alternate)\\\\\angle 5 = \angle 7 (alternate)[/tex]
So, the option (B) is correct.
What expression is equal to (3 x 5) x 4
Answer:
60
Step-by-step explanation:
Step 1:
3 x 5 = 15
Step 2:
15 x 4 = 60
Answer:
well 3. x 5 is 15, then multiply by 4 to get 60.
Step-by-step explanation:
2. En una división el dividendo es 445, el divisor es 32, el cociente es 14 y el resto es 7. ¿Está bien hecha? Compruébalo de dos maneras diferentes
Respuesta:
El cálculo no está bien hecho.
el cociente es 13
El resto es 29
Explicación paso a paso:
Dividendo = 445
Divisor = 32
Cociente = 14
Resto = 7
445/32 = 13,90625
El cociente = 13
Resto = (13.90625 - 13) * 32
Resto = 0.90625 * 32
Resto = 29
Por lo tanto, el cálculo no se realiza correctamente ya que el cociente es 13 y el resto es 29
Which is a y-intercept of the continuous function in the table? х – 4 -3 -2 -1 0 1 f(x) -10 0 0 – 4 -6 0 2 O (0,6) O (-2, 0) O (6,0) 0 (0, -2)
Plz Hurry
Answer:
x:-4,-3,-2,-1,0,1
f(x):-10,0,0,-4,-6,0
from the table we can see when x=0, y=-6
Therefore the y-intercept will be (0,-6)
OAmalOHopeO
The y intercept of the continuous function in the table is given by the relation f ( 0 ) = -6
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
Let the values of x be x = { -4 , -3 , -2 , -1 , 0 }
Let the values of y be y = { -10 , 0 , 0 , -4 , -6 }
Now , the y intercept of the function is when the value of x = 0
So , when x = 0 , the value of y = -6
And , f ( 0 ) = -6
Therefore , the y intercept is ( 0 , -6 )
Hence , the y intercept of the function is ( 0 , -6 )
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simplify:-a). (-5a²)²(6ab²)(-3ab²)
A research historian is interested in finding sunken treasure in the Atlantic Ocean. She knows that her equipment is only good enough to recover items that are at a depth of 5 000 m or less. The speed of sound through the water is 1 530 m/s. While working, the sonar equipment detects a reflection that is of interest. The echo from the item takes 6.2 s to return to the sonar detector. Will she be able to retrieve this item?
Answer:
Yes, she will be able to retrieve the item
Step-by-step explanation:
The information with regards to the research historian interest in finding a sunken treasure are;
The depth from which the equipment can recover items = 5,000 m
The speed of sound through water, v = 1,530 m/s
The time it takes the echo from the item to return to the sonar detector, t = 6.2 s
Let d, represent the depth at which the item is located
Given that an echo travels from the sonar detector to the item and back to the sonar detector, the distance traveled by the sound wave which is received as an echo by the sonar detector = 2 × d
Velocity, v = Distance/time
∴ Distance = Velocity × Time
The distance traveled by the echo = 2 × d = v × t
2 × d = v × t
∴ 2 × d = 1,530 m/s × 6.2 s
d = (1,530 m/s × 6.2 s)/2 = 4,743 m
The depth at which the item is located, d = 4,743 m is less than the maximum depth the equipment can recover items, therefore, she will be able to retrieve the item.
17
x
3
8
Find the unknown side length, x. Write your answer in simplest radical form.
A 15
B. 5/10
C2/70
D. 4 37
==========================================================
Explanation:
It helps to add point labels. Let's place point A at the very top point of the triangle. Then point B will be at the 90 degree angle. Point C is the far left point. Lastly, point D is on segment BC such that DC = 3.
Since BC = 8 and CA = 17, we can use the pythagorean theorem to get...
(AB)^2 + (BC)^2 = (AC)^2
(AB)^2 + (8)^2 = (17)^2
(AB)^2 + 64 = 289
(AB)^2 = 289-64
(AB)^2 = 225
AB = sqrt(225)
AB = 15
Now focus on triangle ABD and apply the pythagorean theorem again to find side AD
(AB)^2 + (BD)^2 = (AD)^2
AD = sqrt( (AB)^2 + (BD)^2 )
AD = sqrt( (AB)^2 + (BC-CD)^2 )
AD = sqrt( (15)^2 + (8-3)^2 )
AD = sqrt(250)
AD = sqrt(25*10)
AD = sqrt(25)*sqrt(10)
AD = 5*sqrt(10) .... answer is choice B
if x=3√8, find the value of 1/x
plz its urgent
Answer:
[tex]\frac{1}{x} =\frac{1}{3\sqrt{8} } =\frac{1(\sqrt{8})}{3\sqrt{8}(\sqrt{8})} =\frac{\sqrt{8}}{3*8} =\frac{\sqrt{8}}{24} =\frac{\sqrt{(2)(2)(2)}}{24}=\frac{2\sqrt{2} }{2(12)} =\frac{\sqrt{2} }{12}[/tex]
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 - x = 25
Answer:
[tex]x1 = - 4.525[/tex]
[tex]x2 = 5.525[/tex]
Step-by-step explanation:
[tex]x1 = \frac{1 - \sqrt{101} }{2} [/tex]
[tex]x2 = \frac{1 + \sqrt{101} }{2} [/tex]
When solving a quadratic in the form a x squared + b x + c = 0 we are really finding the x–intercepts. These x–intercepts are also called roots. What is another term for roots or x-intercepts? a. exponents c. zeros b. quadratics d. variables Please select the best answer from the choices provided A B C D
Choose the correct description of the graph of the inequality X - 3 greater than or equal to 25
A. Open circle on 8, shading to the left
B. Closed circle on 8, shading to the left.
C. Open circle on 8, shading to the right.
D. Closed circle on 8, shading to the right.
I’m pretty sure it’s D
Answer:
D. Closed circle on 8, shading to the right.
Find the BD in the image below
Answer:
x = 10
The both line crosses with a little hyphen, meaning those are same
Answered by GAUTHMATH
Please help me Find PA.
plsssssssssss helppppppppp i want it right now pls
Answer:
hope this helps you
have a great day
Consider the following 8 numbers, where one labelled x
is unknown.
27, 20, 34,
x, 7, 47, 26, 41
Given that the range of the numbers is 63,
work out 2 values of x
Answer: 70 and -16
==========================================================
Explanation:
For now, we'll assume x is the largest value (aka the max)
Let's sort the values from smallest to largest.
7, 20, 26, 27, 34, 41, 47, x
We see that 7 is the smallest item, so,
range = max - min = x - 7
Set this equal to 63 and solve for x
x-7 = 63
x = 63+7
x = 70
So x could be equal to 70.
---------------------------
Next, we'll assume that x is the smallest value
That means the min is x and 47 is now the max
max - min = range
47 - x = 63
-x = 63-47
-x = 16
x = -16
So if x is the smallest value, then it must be -16
----------------------------
Finally, we'll let x be somewhere between 7 and 47
Unfortunately, we can't pin down a specific value here since we could have lots of possible values. Three such examples are x = 8, x = 9, and x = 10. There are many others.
If your teacher is looking for 2 values only, then I would refer to the previous two sections and ignore this section entirely.
The square root of 0.25 is 0.5 which is a greater number. Give another number whose square root is larger than the number and explain why.
Answer:
Another example of a number who's square root is greater than the number is [tex]\sqrt{0.49}[/tex] which is 0.7
Step-by-step explanation:
This square root is larger than the number because it is a decimal. When you multiply a decimal by a decimal, the decimal point becomes greater. For example: 0.7 multiplied by 0.7 equals 0.49 which has 2 decimal places, while 0.7 only has one.
Mr. Mancuso plants tomatoes on 1/3 acre of land, corn on 3/4 acre, and carrots on 1/2 acre. On how many acres of land total did he plant?
1 acres
1 acres
1 acres
2 acres
Answer:
1 7/12 acres of land
Step-by-step explanation:
Tomatoes = 1/3 acre of land
Corn = 3/4 acre of land
Carrots = 1/2 acre of land
Total acres of land he planted = tomatoes + corn + carrots
= 1/3 + 3/4 + 1/2
= (4+9+6) / 12
= 19/12 acres
= 1 7/12 acres of land
Or
= 1.5833333333333 acres
Total acres of land he planted = 1 7/12 acres of land
None of the given options is correct
Si un proyectil asciende verticalmente, y después de 3 segundos alcanza su altura máxima, calcule la velocidad que lleva a la mitad de su trayectoria descendente
Answer:
The speed is 20.8 m/s
Step-by-step explanation:
If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory
Let the maximum height is h and initial velocity is u.
From first equation of motion
v = u + at
0 = u - g x 3
u = 3 g.....(1)
Use third equation of motion
[tex]v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g[/tex]
Let the speed at half the height is v'.
[tex]v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s[/tex]
A bus has less than 42 seats. If 36 seats are already occupied, write an
inequality representing the possible number of passengers that can be
added to the bus.
A.) x - 36 < 42
B.) x + 36 < 42
C.) x - 36 > 42
D.) x + 36 > 57
Answer:
B
Step-by-step explanation:
A x - 36 <42 is wrong because its saying how many can be added
B x +36 < 42 this one is most likely correct because its displays x as how many can be added
C x - 36 > 42 this is wrong because the bus has less than 42 seats
D x + 36 >57 like i said cant be over 42
The inequality representing the possible number of passengers that can be added to the bus is Option(B) x + 36 < 42.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. Inequality is used most often to compare two numbers on the number line by their size. There is always a definite equation to represent it.
How to form the given inequality equation ?Let x be the number of passengers that can be added to the bus.
It is given that the bus has less than 42 seats and 36 seats are already occupied.
The sum of the remaining seats which are to be filled by the passenger and the 36 seats which are filled, must be less than the total seats that is 42.
Therefore the inequality equation becomes,
x + 36 < 42.
Thus, the inequality representing the possible number of passengers that can be added to the bus is Option(B) x + 36 < 42.
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Solve EFD. Round the answers to the nearest hundredth.
A. m F ≈ 26, m D ≈ 64.01, FD = 7,921
B. m F ≈ 26, m D ≈ 64.01, FD = 89
C. m F ≈ 64.01, m D ≈ 26, FD = 89
D. m F ≈ 64.01, m D ≈ 26, FD = 7,921
Answer:
Option B
<F = 26°
<D = 64.01°
FD = 89
Answered by GAUTHMATH
For right triangle EFD, m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89
The correct answer is an option (B)
What is hypotenuse?It is the longest side of the right triangle.
What is Pythagoras theorem?For a right triangle,
[tex]a^{2}+ b^{2} = c^{2}[/tex], where c is hypotenuse and a, b area other two sides of the right triangle
For given example,
We have been given a right triangle EFD with hypotenuse FD.
Also, EF = 80, ED = 39
Using the Pythagoras theorem,
[tex]\Rightarrow FD^{2}= EF^{2} + ED^{2}\\\\ \Rightarrow FD^{2}= 80^{2} + 39^{2}\\\\ \Rightarrow FD^2 = 6400 + 1521\\\\ \Rightarrow FD^2 = 7921\\\\\Rightarrow FD = 89[/tex]
Consider, sin(F)
[tex]\Rightarrow sin(F)=\frac{ED}{FD} \\\\\Rightarrow sin(F)=\frac{39}{89}\\\\ \Rightarrow sin(F)=0.4382\\\\\Rightarrow \angle F=sin^{-1}(0.4382)\\\\\Rightarrow \angle F=25.98^{\circ}\\\\\Rightarrow \angle F\approx 26^{\circ}[/tex]
Now, consider sin(D)
[tex]\Rightarrow sin(D)=\frac{FE}{FD}\\\\ \Rightarrow sin(D)=\frac{80}{89}\\\\ \Rightarrow \angle D = sin^{-1}(0.8988)\\\\\Rightarrow \angle D = 64.009^{\circ}\\\\\Rightarrow \angle D \approx 64.01^{\circ}[/tex]
Therefore, for right triangle EFD, m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89
The correct answer is an option (B)
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How much money invested at 3% compounded monthly for 3 years will yield $520?
$179.42
$475.30
$358.84
$148.78
Answer:
Step-by-step explanation:
Use this formula:
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex] where A(t) is the amount after the compounding is done, P is the initial investment (our unknown), r is the interest rate in decimal form, n is the number of compoundings per year, and t is the time in years. Filling in:
[tex]520=P(1+\frac{.03}{12})^{(12)(3)}[/tex] and simplifying that a bit:
[tex]520=P(1+.0025)^{36[/tex] and a bit more:
[tex]520=P(1.0025)^{36[/tex] and even bit more:
520 = P(1.094551401) and divide to get
P = $475.30
Find the line’s slope and a point on the line
Y-4=-3/4(x+5)
Answer:
The slope is -3/4 and a point on the line is (-5,4)
Step-by-step explanation:
This equation is in point slope form
y -y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
Y-4=-3/4(x+5)
Y-4=-3/4(x - -5)
The slope is -3/4 and a point on the line is (-5,4)
Find the value of x.
A. 99
B. 9
C. 90
D. 11
ILL GIVE BRAINLIEST
Answer:
B) 9
Step-by-step explanation:
Because there's a square between the 2 angles, that means these angles are complementary (angles that add up to 90°). So:
5x - 9 + 6x = 90
11x - 9 = 90
11x = 90 + 9
11x = 99
x = 9
Answer:
B.9
Step-by-step explanation:
The way to solve this is by noticing that these angles are complementary(they add up to 90 degrees). So you add the equations together and equal them to 90. 5x-9+6x=90.Then you solve to find that x=9.
In a shipment of airplane parts, 6% are known to be defective. If 42 parts are found to be defective, how many parts are in the shipment?
Answer:
700 parts
Step-by-step explanation:
To find the total amount of parts in the shipment, all we need to do is divide.
6% = 0.06
42 / 0.06 = 700
Best of Luck!
WILL MARK BRAINLIEST! Can someone please help! I don't understand some of these questions :(
Answer:
18
Step-by-step explanation:
The interior and exterior angle of a polygon is supplementary
let interior be I
let exterior be E
I + E = 180
Since the interior angle is 8 times that of an exterior angle,
8E + E = 180 [replacing I with 8E]
9E = 180
E = 20
The exterior angle is 20 degrees
I + E = 180
I + 20 = 180
I = 160
The interior angle is 160 degrees.
The equation to find the interior angle of a polygon with 'n' number of sides is:
I = ( (n − 2) × 180 ) ⁄ n
We know the interior angle, so plug it in and solve for n:
160 = ( (n − 2) × 180 ) ⁄ n
160n = (n − 2) × 180
160n = 180n − 360
-20n = -360
n = 18
