Answer:
Step-by-step explanation:
I am using trig identities and the formula for the difference of the cos of 2 angles to solve this. I'll do the steps one at a time. It's super tricky. First I'm just going to work on simplifying the sec² part and then I'll introduce the sin²(x) - sin⁴(x) when I need it. Beginning with the identity for the difference of the cos of 2 angles, knowing that sec²(x) = [tex]\frac{1}{cos^2(x)}[/tex]:
[tex]sec^2(\frac{\pi}{2}-x)=\frac{1}{cos^2(\frac{\pi}{2}-x )}[/tex] and expand that using the formula for the difference:
[tex]\frac{1}{cos(\frac{\pi}{2}-x)cos(\frac{\pi}{2}-x) }=[/tex] [tex]\frac{1}{(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x))(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x)) }[/tex] and all of that simplifies down to
[tex]\frac{1}{(0cos(x)+1sin(x))(0cos(x)+1sin(x))}[/tex] which simplifies further to
[tex]\frac{1}{(sin(x))(sin(x))}=\frac{1}{sin^2(x)}[/tex] Now we'll bring in the other term. This is what we have now:
[tex]\frac{1}{sin^2(x)}(\frac{sin^2(x)-sin^4(x)}{1})[/tex] and distribute in to get:
[tex]\frac{sin^2(x)}{sin^2(x)}-\frac{sin^4(x)}{sin^2(x)}[/tex] which simplifies to
[tex]1-sin^2(x)[/tex] and that, finally, simplifies down to a simple
[tex]cos^2(x)[/tex]
Are these relations a function? Yes or no.
{(–1,5), (2, -1),(4,3), (9,-4), (11, 1)}
Function is a set of ordered pairs where there cannot be same x-values or repetitive domain in a set.
For example below below:
{(1,1),(2,3),(3,3),(4,5)}The following relation is a function since there are no same x-values in a set.
{(1,1),(1,2),(2,2),(4,8)}The following relation is not a function since there are same two x-values which is D = {1} or (1,1) and (1,2) both have same domain. Thus, not making the relation a function.
From the question, the relation is a function because in a set of ordered pairs, there aren't any same x-values.
Answer
Yes, the following relation is a function.what are the 3 basic steps to writing equations
Answer:
Putting things in the right place
Reading the question
Using the correct symbol
Step-by-step explanation:
Putting things in the right place is very important
Example: 2+2=4
If I accidently did 2+4=2 then the answer would be incorrect.
Reading the question
You could read a question wrong in an exam so you may answer incorrectly, so if you finished the exam then always check your answers
Using the correct symbol is important because you could know the answer but write the wrong symbol and not get the mark
I hoped this helped!
Pick the geometric term that matches the real-world object. rectangular prism sphere cylinder triangular prism cube
Answer:
Assuming this is the book one the answer is rectangular prism.
Which relation is a function?
O A. {(7, 8)(5,0)(-3, 1)(-5, 0)(-3, 2)}
B. {(0, 0)(1, 1)(4, 2)(9, 3)(16,4)}
O C. {(-4, 1)(-2, 2.5)(0, 4)(-4, -1)(-2, -2.5)}
OD. {(1, 0)(2, 1)(3, 2)(1, 3)(2, 4)}
Can I get some help?
Answer:
ok for this what we need to do is just do the equation
y=2x+3
with the x inserted
y=2*-2+3
y=-1
y=2*0+3
y=3
y=2*1+3
y=5
y=2*3+3
y=9
this is the answer from left to right
y=-1,y=3,y=5,y=9
Here is a pattern made from sticks:
a)
How many sticks would be in pattern number 6?
b)
How many sticks would be in pattern number n?
Help needed I can’t figure this out.
Answer:
maybe like 12
Step-by-step explanation:
I would think 12 because because it is 2 of the square so I think 6 + 6 correct me of I'm wrong.
Which value of x satisfy the following equation 24x - 18 - 18x - 30 = 96
Answer:
(24x-18x)( -18-30)
6x-48
A girl meets a lion and unicorn in the forest. The lion lies every Monday, Tuesday and Wednesday and the other days he speaks the truth. The unicorn lies on Thursdays, Fridays and Saturdays, and the other days of the week he speaks the truth. "Yesterday I was lying," the lion told the girl. "So was I," said the unicorn. What day is it?
The linear scale factor of two similar shapes is in ratio 3:4 if the area of the smaller shape is 72cm, find the area of the bigger shape
Answer:
128 cm²
Step-by-step explanation:
Given linear scale factor of 2 similar shapes = a : b , then
ratio of areas = a² : b²
Here linear scale factor = 3 : 4 , then
ratio of areas = 3² : 4² = 9 : 16
let x be the area of the larger shape then by proportion
[tex]\frac{9}{72}[/tex] = [tex]\frac{16}{x}[/tex] ( cross- multiply )
9x = 1152 ( divide both sides by 9 )
x = 128
That is area of larger shape is 128 cm²
In ΔXYZ, x = 71 cm, y = 91 cm and z=71 cm. Find the area of ΔXYZ to the nearest square centimeter.
Answer:
2479.95
Step-by-step explanation:
i worked out that guys problem who wouldnt work it out for you.
PLEASE PLEASE HELP ME WITH THIS GEOMETRY QUESTION!!!
Step-by-step explanation:
Objective: Circle Theorems
The arcs add up to 360 and they are in proportion so
[tex]3x + 3x + 4x + 5x = 360[/tex]
[tex]15x = 360[/tex]
[tex]x = 24[/tex]
So this means that Arc AB and BC measure is 72 each. Arc CD measure is 96 and Arc DA measures is 120.
Angle 1 measure is a inscribed angle of Arc CD.
So it measures
[tex] \frac{96}{2} = 48[/tex]
Angle 2 is a inscribed angle of Arc AB so it measures
[tex] \frac{72}{2} = 36[/tex]
Angle 3 is a inscribed angle of Arc DA.
[tex] \frac{120}{2} = 60[/tex]
Angle 4 is a inscribed angle of Arc BC so it measures
[tex] \frac{72}{2} = 36[/tex]
Angle 5 is formed by tangent line ED. Since D lies on the circumference, it also is tangent to point e so it also measures 90 degrees.
Angle 4 measures 32 so Angle 5 is it complement to Angle 4.
[tex]32 + x = 90[/tex]
[tex]x = 58[/tex]
Angle 6 is formed by two intersecting chrods
so it measures
[tex] \frac{1}{2} (120+ 72) = 96[/tex]
A penny-farthing is a bicycle with a very large front wheel and a much smaller back wheel. Penny-farthings were popular in the 1800s and were available in different sizes. Suppose the diameter of one particular penny-farthing's front wheel is inches and the ratio of the diameter of the front wheel to the diameter of the back wheel is :1. What is the circumference of the back wheel? Use 3.14 for. The circumference of the back wheel is nothing inches.
Answer:
The circumference of the back wheel is 2.62 inches
Step-by-step explanation:
Given
[tex]d_1 = 5in[/tex] --- diameter of front wheel
[tex]d_1 : d_2 = 3:1[/tex] --- ratio of the diameters
Required
The circumference of the back wheel
First, we calculate the diameter of the back wheel.
We have:
[tex]d_1 : d_2 = 3:1[/tex]
Substitute: [tex]d_1 = 5in[/tex]
[tex]5in: d_2 = 3 : 1[/tex]
Express as fraction
[tex]\frac{d_2}{5in} = \frac{1}{3}[/tex]
Make [tex]d_2[/tex] the subject
[tex]d_2 =5in * \frac{1}{3}[/tex]
[tex]d_2 = \frac{5}{3}\ in[/tex]
So, the circumference (C) of the back wheel is:
[tex]C =\pi d[/tex]
[tex]C = 3.14 * \frac{5}{6}\ in[/tex]
[tex]C = \frac{3.14 * 5}{6}\ in[/tex]
[tex]C = \frac{15.7}{6}\ in[/tex]
[tex]C = 2.62\ in[/tex]
The length and width of a rectangular box
are represented by 2x+3 and 3x + 1 respectively.
What is the area of the box expressed as a polynomial
in standard form?
Answer:
[tex]6x^2+11x+3[/tex]
Step-by-step explanation:
Area of a rectangle = length x width
[tex](2x+3)(3x+1) = ?[/tex]
[tex]6x^2+2x+9x+3[/tex]
In a theater group of 36 people. 20 can sing and 12 can play instruments. If 5 can play n sing. How many can niether play nor sing
Answer:
9
Step-by-step explanation:
Draw a Venn diagram.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ \ / / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
The Venn diagram is set up as above. The two circles insiode the rectangle look like two hexagons and they overlap.
The overlap is labele B, for people who both play and sing. The left circle is P for people who play, and the right circle is S for people who sing.
Now we begin to fill it in.
5 people both play and sing, so we place a 5 in the overlap section.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ \ 5 / / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
20 people sing. Subtract the 5 who both sing and play, and you have 15 who can only sing.
12 people play. Subtract the 5 who both sing and play, and you have 7 who only sing.
Place the numbers 15 and 7 in the correct places.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ 7 \ 5 / 15 / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
Now add all the people already placed.
15 + 5 + 7 = 27
Subtract that number form the total.
36 - 27 = 9
Place the 9 in the correct area.
+------------------------------------------------------------+
| N 9 |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ 7 \ 5 / 15 / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
Answer: 9
A more normal looking Venn diagram looks like this:
Encik Basra’s age is four times his child’s age. 4 years ago, Encik Basri’s age is six times his child age. Find the age of Encik Basri’s child now.
Answer:
4 + 6 = 10 * 4 =40
Step-by-step explanation:
sana makatulong
His child is 10 years old.
What is algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
Given
Assume now his child's age is x
4x-4 = 6(x-4)
4x-4 = 6x - 24
-4+24 = 6x-4x
20 = 2x
x=10
His child is 10 years old.
To learn more about algebraic expressions refer to:
https://brainly.com/question/19864285
#SPJ2
A regular pentagon has a perimeter of 60 cm.
A regular pentagon has a perimeter of 60 centimeters and center point B. Radii B A and B D are drawn to form triangle A B D. Apothem B C is drawn to split the triangle into 2 right triangles.
What is the measure of angle CBD?
°
What is the length of segment CD?
cm
Which trigonometric ratio can be used to compare BC to CD using angle CBD?
What is the approximate length of BC?
cm
What is the approximate length of BD?
cm
Answer:
36˚
6 cm
tangent
8.3 cm
10.2 cm
Step-by-step explanation:
The side lengths of the regular pentagons are congruent
What is the measure of angle CBD?A pentagon has 5 sides, and the central angle is 360°.
Calculate the measure of ABD using:
ABD = 360°/5
ABD = 72
The measure of CBD is half the measure of ABD.
So, we have:
CBD = 0.5 * 72
CBD = 36
Hence, the measure of CBD is 36 degrees
What is the length of segment CD?A pentagon has 5 sides, and the given perimeter is 60 cm
Calculate the length of AD using:
AD = 60cm/5
AD = 12
The length of CD is half the length of ABD.
So, we have:
CD = 0.5 * 12
CD = 2
Hence, the length of CD is 6 cm
cm
Which trigonometric ratio can be used to compare BC to CD using angle CBD?Using the angle CBD, the trigonometric ratio can be used to compare BC to CD is the tangent ratio
What is the approximate length of BC?We have:
tan(CBD) = CD/BC
Make BC the subject
BC = CD/tan(CBD)
Substitute known values
BC = 6/tan(36)
Evaluate
BC = 8.3 cm
Hence, the approximate length of BC is 8.3 cm
What is the approximate length of BD?By Pythagoras theorem, we have:
BD^2 = BC^2 + CD^2
This gives
BD^2 = 8.3^2 + 6^2
Take the square root of both sides
BD = 10.2 cm
Hence, the approximate length of BD is 10.2 cm
Read more about regular pentagons at:
https://brainly.com/question/14961220
. In an enlargement with scale factor 2, which of the following statements is not true?
A. Each length is multiplied by 2
B. Each angle remains the same
C. The shape of the figure does not change.
D. The size of the figure does not change
Answer:
option B , C , D
Step-by-step explanation:
Enlargemet is a rule which transfers an object into an object of the same form by enlarging its size in a given ration.
Remember
If k > 1 , the given object is enlarged. Since the scale fator (k) is 2 and it is greater than 1 the size of the figure enlarges . So according to this definition option B , c and d are incorrect.
only option A satisfies . So out of all these statements only option A is true.
formula :
(x , y) = (kx , ky) ( k means scale factor)
here scale factor is multiplied to the coordinate x and y.
since the scale factor is 2 it means that the length or the value of both x and y coordinate is multiplied by 2.So, it is true . And rest are not true.
Can some one help me with the rest of this chapter! I’ll pay them as-well!
Answers:
a = 475r = -0.5f(3) = 59.4=======================================================
Explanation:
Any exponential function is of the form y = a*b^x
Comparing that to y = 475*(0.5)^x, we see that a = 475 and b = 0.5
Set b equal to 1+r and solve for r
1+r = 0.5
r = 0.5-1
r = -0.5
The negative r value tells us that the growth rate is -50%, in other words, we have a 50% decay rate. The amount drops by 50% each time x goes up by 1. This is the same as saying the amount cuts in half each time x goes up by 1.
-----------------------
Lastly, plug in x = 3 to find f(3)
f(x) = 475(0.5)^x
f(3) = 475(0.5)^3
f(3) = 59.375
f(3) = 59.4
A cyclist travels 8 km from home to the park. She leaves home at 10:15 and arrives at the park at 10:30. What is her average speed in km/h?
Answer:
speed = 32km/hr
Step-by-step explanation:
Time
10:15 to 10:30 = 1/4 hr
speed = distance/time
speed = 8 / (1/4)
speed = 32km/hr
The volume of a cylinder is 1280pi cm cubed. The radius is 8cm. Find the missing length.
Which of the following is most likely the next step in the series?
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The shape starts with 2 dots, then to 3 dots, and then to 4 dots. This means that the next step must have 5 dots, which option D has.
Can you ride a bike 5 miles?
Answer:
yes you physically can
Step-by-step explanation:
What is the perimeter of the shape?
2 yd
3 yd
5 yd
4 yd
2 yd
6 yd
Answer:
22 yards
Step-by-step explanation:
P = 5+2+3+4+2+6
P = 22
What is the product?
(6 r- 1)(- 8 r- 3)
Answer:
-48[tex]r^{2}[/tex] - 10r + 3
Step-by-step explanation:
FOIL method
First : (6r) · (- 8r) = - 48[tex]r^{2}[/tex]
Outer : (6r) · (-3) = -18r
Inner : (-1) · (-8r) = 8r
Last : (-1) · (-3) = +3
combine like terms
someone PLSSS HELP fast !! pls give rightt answer :( PLS
Answer:
the first one, 64(-1/2)^(n-1)
Step-by-step explanation:
To go from one number to the next, we first start with 64, so everything is multiplied by that. Next, 64 turns into -32, and (-32)/64 = -1/2. Similarly, 16/-32 is -1/2, and -8/16 is -1/2 as well. Therefore, we have to multiply each number by -1/2 a number of times. For example, to get from 64 to 16, we have to multiply 64 by negative one half 2 times. The only option with -1/2 in the multiplier is the first one, making that our answer
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
Answer:
I=70*.03*2.5
I=70*.075
I=$5.25 is the interest.
Step-by-step explanation:
Find the value of BC B 4x - 10 C A D 3x + 5
Answer:
BC = 50
Step-by-step explanation:
BC = AD in a parallelogram
4x-10 = 3x+5
Subtract 3x from each side
4x-3x-10 = 3x-3x+5
x-10 = 5
Add 10 to each side
x-10+10 = 5+10
x = 15
BC = 4x-10 = 4*15-10 = 60-10 = 50
Answer:
BC = 50
Step-by-step explanation:
BC = AD
4x - 10 = 3x + 5
4x - 3x = 5 + 10
x = 15
for BC
4x - 10
4*15 - 10
60 - 10
50
Factors of polynomial 3xsquare +x-4
Answer:
(3x + 4)(x - 1)
Step-by-step explanation:
3x^2 + x - 4
use middle term break method
we need two number which gives 12 when multiplied and 1 when subtracted
3x^2 + (4 - 3)x - 4
3x^2 + 4x - 3x - 4
x(3x + 4) -1(3x + 4)
(3x + 4)(x - 1)
Answer:
(x - 1)(3x + 4)
Step-by-step explanation:
Given
3x² + x - 4
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 4 = -12 and sum = + 1
The factors are - 3 and + 4
Use these factors to split the x- term
3x² - 3x + 4x - 4 ( factor the first/second and third/fourth terms )
= 3x(x - 1) + 4(x - 1) ← factor out (x - 1) from each term
= (x - 1)(3x + 4) ← in factored form
!$P¡D£R €ŁÆŃ!!$P¡D£R €ŁÆŃ!
Answer:
A is correct because there are only 2 sides to flip to, giving it a probability of 0.50, or 1/2 that they will lands heads up.
Answer:
I would go with D
Step-by-step explanation:
Because there are 4 possibilities.
1) they both land heads up
2) they both land tails up
3) one lands heads up and the other tails up
4) one lands tails up and the other heads up
Hope this helps!
Sendo =e y = x+2. O resultado da soma x + y, é
A) 2
B) 4
C)3
D)6
Answer:
b)4Step-by-step explanation: