Mathematics High School

prove this trigonometric equation;

- tan^2x + sec^2x = 1,

Answers

Answer 1
Hey there :)

- tan²x + sec²x = 1    or    1 + tan²x = sec²x

sin²x + cos²x = 1 
Divide the whole by cos²x

[tex] \frac{sin^2x}{cos^2x} + \frac{cos^2x}{cos^2x} = \frac{1}{cos^2x} [/tex]

[tex] \frac{sinx}{cosx} = tanx[/tex] so [tex] \frac{sin^2x}{cos^2x} = tan^2x[/tex]
and
[tex] \frac{1}{cosx} = secx [/tex] so [tex] \frac{1}{cos^2x} = sec^2x[/tex]

Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}

1 = - tan²x = sec²x or sec²x - tanx = 1

Related Questions

What is cot theta when sin theta < 0 and cos theta = -5/13

Answers

If cos and sin are both minus, you are in quadrant III where the cot(theta) is plus.

The reason for that is that cot(theta) = cos(theta)/sin(theta) which means that the two minuses will cancel out.

Now all you have to do is calculate sin(theta).
a^2 + b^2 = c^2
cos = adjacent / hypotenuse

a = 5 The adjacent side
b = ????
c = 13 The hypotenuse
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 144
b = 12
sin(theta) = -12/13

cot(theta) = -5/13//-12/13
cot(theta) = -5/-12 = 5/12

Soon you will determine the right triangle connection the pythagorean theorem

Answers

I don't know I just need the points Lol sorry

Fill in the scale dimensions in the table to the nearest thousandth. The scale of a blueprint is 1/4 inch = 1 foot. A house has 1 bedroom measuring 10 feet 6 inches by 11 feet, a living room measuring 25 feet by 18 feet 8 inches, a kitchen measuring 13 feet 6 inches by 8 feet, and a dining room measuring 12 feet by 10 feet. Put the shortest length in the first box for each room. Give all answers to three decimal places (thousandths place).
bedroom inches by inches
living room inches by inches
kitchen inches by inches
dining room inches by inches

Answers

The scale dimensions of the rooms on the blueprint using a scale of 1/4 inch = 1 foot are calculated by converting feet to inches, then dividing by the scale ratio (0.25 inches per foot) to find each room's dimensions in inches on the blueprint.

To calculate the scale dimensions of the rooms on the blueprint, you will use the given scale of 1/4 inch = 1 foot. This means for every 1/4 inch on the blueprint, it represents 1 foot in actual size.

Step-by-Step Calculation for Each Room

Convert the scale into a ratio that can be used for calculations (1/4 inch / 1 foot or 0.25 inches / 12 inches since there are 12 inches in a foot).

Calculate the scale dimension for each room by dividing the actual dimension in inches by the scale ratio.

For each room, ensure to convert feet to inches first (1 foot = 12 inches) and then apply the scale.

Bedroom: 10 feet 6 inches is (10 * 12) + 6 = 126 inches, 11 feet is (11 * 12) = 132 inches. Scale dimensions: (126 inches / 48) by (132 inches / 48) equals 2.625 inches by 2.750 inches.Living room: 25 feet is (25 * 12) = 300 inches, 18 feet 8 inches is (18 * 12) + 8 = 224 inches. Scale dimensions: (300 inches / 48) by (224 inches / 48) equals 6.250 inches by 4.667 inches.Kitchen: 13 feet 6 inches is (13 * 12) + 6 = 162 inches, 8 feet is (8 * 12) = 96 inches. Scale dimensions: (162 inches / 48) by (96 inches / 48) equals 3.375 inches by 2.000 inches.Dining room: 12 feet is (12 * 12) = 144 inches, 10 feet is (10 * 12) = 120 inches. Scale dimensions: (144 inches / 48) by (120 inches / 48) equals 3.000 inches by 2.500 inches.

Below is the scale dimensions for each room to the nearest thousandth:

Bedroom: 2.625 inches by 2.750 inchesLiving room: 6.250 inches by 4.667 inchesKitchen: 3.375 inches by 2.000 inchesDining room: 3.000 inches by 2.500 inches

4) A mountain climber climbed up a cliff 1/4 mile at a time. he did this 5 times in one day. How many miles did he climb up? *

Answers

He climbes 1 1/4 miles.
1/4+1/4+1/4+1/4+1/4= 1 1/4.

Suppose we deposit $73,000 into a savings account which compounds daily with 5% APY and we want to know how much the account will be worth after two days.

Answers

Let
I1-------------> interest first day
I2-------------> interest second day

we know that
P0=$73000----------> initial amount

first day
I1=73000*(5%/100)*(1/365)-----------> I1=$10
P1=P0+I1------> $73000+$10-------- P1=$73010

second day
P1=$73010
I2=73010*(5%/100)*(1/365)-----------> I2=$10
P2=P1+I2------> $73010+$10-------- P2=$73020

the answer is $73020

If arc XV = 68° and ∠YUV = 36°, what is the measure of arc VY?

Answers

the complete question in the attached figure

we have
arc XV = 68°
∠YUV = 36°
 
we know that
The measure of the external angle is the semidifference of the arcs that it covers.
therefore
∠YUV =[arc VY-arc XV]/2
arc VY=[2*∠YUV]+arc XV----------> [2*36]+68---------> 140°

the answer is
the measure of arc VY is 140°

Write the percent as a decimal and as a fraction.

215% (1 point)
2.15; 2 1/20
2.15; 2 3/20
21.5; 21,1/2
21.5; 21, 3/10
Just tell me what one what it is..

I'LL GIVE A MEDAL (:,

Answers

To write 215% as a decimal you can approach the problem two ways. You can divide 215 by 100. 215/100 = 2.15 You can also move the decimal two places to the left 215.0 = 2.15 To write 2.15 as a fraction you will place 215 over 100. {215/100}. You will then want to write this fraction in it’s simplest form. The greatest common denominator is 5 so you will then divide the numerator and denominator by 5. 215/5 = 43 100/5 = 20 215/100 = 43/20 To write this fraction as a mixed fraction you would divide 43 by 20. 43 ÷ 20 = 2 with a remainder of 3 This is written as: 2 3/20

Find the 7th term of the arithmetic sequence -5x-8,-x-14,3x-20,...

Answers

a₁ = -5x-8;  a₂ = -x-14; a₇=?

d = a₂ - a₁
  = x-14 - (-5x-8)
  = -x - 14 + 5x + 8
  = 4x-6

a(n) = a₁ + (n-1)d

a₇ = -5x-8 + (7-1)(4x-6)
    = -5x-8 + 6(4x-6)
    = -5x - 8 + 24x - 36
    = 19x - 44

find the exact value of cos285 using the fact that 285=330-45

Answers

[tex]\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\ -------------------------------\\\\ cos(285^o) \\\\\\ cos(330^o-45^o)=cos(330^o)cos(45^o)+sin(330^o)sin(45^o) \\\\\\ cos(330^o-45^o)=\left( \frac{\sqrt{3}}{2} \right)\left( \frac{\sqrt{2}}{2} \right)~~+~~\left( \frac{1}{2} \right)\left( \frac{\sqrt{2}}{2} \right) \\\\\\ cos(330^o-45^o)=\cfrac{\sqrt{6}}{4}+\cfrac{\sqrt{2}}{4}\implies cos(330^o-45^o)=\cfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Find the radius of a circle with the equation 2x2+y2-6x+2y-45=0

Answers

2x²+y²-6x+2y-45=0
center:(3/2,-1)
vertex1:(3/2,-1+√202/2)
vertex2:(3/2,-1-√202/2)
focus1:(3/2,-1+√101/2)
focus2:(3/2,-1-√101/2)


I hope this helps!!!!!!!!!!

Somebody help. I can’t figure this question out. thanks

Answers

The large triangle and the smaller one are similar. Comparing long sides to short ones, we get
.. (30 mm)/(21 mm) = (14 mm +x)/(14 mm)
.. (14 mm)*10/7 = 14 mm +x
.. (14 mm)*(10/7 -1) = x
.. (14 mm)*(3/7) = x = 6 mm

The value of x is 6 mm.

[tex]21 \div 30 = 14 \div 14 + x[/tex]
[tex]30 \times 14 = 420[/tex]
[tex]21 \times 14 + x = 294 + 21x[/tex]
[tex]420 = 294 + 21x[/tex]
[tex]420 - 294 = 126[/tex]
[tex]126 = 21x[/tex]
[tex]126 \div 21 = 6[/tex]
[tex]x = 6[/tex]

what steps transform the graph of y=x^2 to y= -(x+3)^2+5

Answers

[tex]\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)= A( Bx+ C)+ D \\\\ ~~~~y= A( Bx+ C)+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \\\\ f(x)= A sin\left( B x+ C \right)+ D \\\\ --------------------[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

now, with that template in mind, let's check this one

[tex]\bf y=x^2\implies y=\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{+0})^2\stackrel{D}{+0} \\\\\\ y=-(x+3)^2+5\implies y=\stackrel{A}{-1}(\stackrel{B}{1}x\stackrel{C}{+3})^2\stackrel{D}{+5}[/tex]

A = -1, reflection over the x-axis.

B = 1, C = +3, C/B = +3/1 = +3, horizontal shift to the left of 3 units.

D = 5, vertical shift up of 5 units.

Need Help. I will give a thanks and rate you 5 stars.
2. A tree that is 10 yards tall casts a shadow 14 yards long. Find the angle of elevation from the tip of the shadow to the top of the tree. Round to the nearest degree.
A. 54
B. 36
C. 46
D. 44
3. Use the Law of Sines to find the missing side of the triangle. Find b.
A. 70.1
B. 43.8
C. 57.1
D. 31.5
4. For a triangle ABC, find the measure of AB given m A. 45.22
B. 96.68
C. 88.19
D. 81.12
5. Use the Law of Cosines to solve the problem. On a baseball field, the pitchers mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet. the path of the ball makes a 34 angle with the line connecting the pitcher and the catcher, to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?
A. 207.4 ft
B. 224.3 ft
C. 169.3 ft
D.

Answers

The angle of elevation will be given by: 
tan θ=opposite/adjacent
tan θ=10/14
θ=arctan 10/14=
θ=35.5~26°

5. c^2=a^2+b^2-2abcos C
c^2=60.5²+216²-2*60.5*216cos34
c^2=28,648.524
c=169.255~169.3 ft

What is the coefficient of the term x7y in the expansion of (x + y)^8?

a1
b8
c28
d56,

Answers

The coefficient for x^7*y is equal to 8Choose7 which is 8!/7! which is 8, or answer b. Pascal's triangle may be used to capture this as well, or use the exponent as above.

Ashley is digging for rocks at a geological site. She has 140 meters of rope and 4 stakes to mark off a rectangular area. Which set of dimensions will create a rectangle using all the rope Ashley has with her?

14 m × 10 m
70 m × 70 m
60 m × 10 m
55 m × 10 m

Answers

the answer is 60 m x 10 m

The total perimeter of the rectangle is P = 140m and the length and width of the rectangle is 60 m and 10 m respectively

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangle be represented as P

Now , the equation will be

Let the total perimeter of rectangle P = 140 m

The Perimeter P = 2 ( Length + Width )

Let the length of the rectangle L = 60m

Let the width of the rectangle be W = 10 m

So , Perimeter P = 140 m

140 = 2 ( L + W )

140 = 2 ( 60 + 10 )

140 = 2 ( 70 )

140 = 140

Therefore , the length and width is given by 60m x 10m

Hence , the perimeter of rectangle is P = 140 m

To learn more about perimeter of rectangle click :

https://brainly.com/question/15725265

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PLS HELP ME ASAP ON THIS!! THANK YOU SO MUCH!!

BRAINLIEST WILL BE GIVEN



(RANDOM ANSWERS GETS MODERATED.)

Answers

Your picture shows 3 combinations that are sufficient to tell you the price of each item.

The other two are
.. 0 fries + 1 shake + 1 burger = 4.20
.. 1 fries + 1 shake + 0 burger = 2.80

_____
Add any two orders and subtract the third to find the cost of one of the items.
For example add the two orders written above and subtract the one shown in the picture.
.. (1 fries + 2 shakes + 1 burger) - (1 fries + 1 burger) = (4.20 +2.80) -(3.40)
.. 2 shakes = 3.60
.. 1 shake = 1.80
Then the last equation tells you
.. 1 fries = 2.80 - 1 shake = 1.00
and the first equation tells you
.. 1 burger = 3.40 - 1 fries = 2.40

1 fries = $1.00
1 shake = $1.80
1 burger = $2.40

can someone help me with this?

Answers

It's C.

I did it by plugging the functions into a graphing calculator and seeing which one matched, but you could also plug in 2 or 3 values into each x position and see which one's results matched with the shown function.

Circle 1: center (8, 5) and radius 6
Circle 2: center (−2, 1) and radius 2
What transformations can be applied to Circle 1 to prove that the circles are similar?
What scale factor does the dilation from Circle 1 to Circle 2 have?
Show your work.

Answers

we have that
Circle 1: center (8, 5) and radius 6
Circle 2: center (−2, 1) and radius 2

we know that
the equation of a circle is
(x-h)²+(y-k)²=r²
for the circle 1---------> (x-8)²+(y-5)²=36
for the circle 2---------> (x+2)²+(y-1)²=4

using a graph tool 
see the attached figure

Part A)What transformations can be applied to Circle 1 to prove that the circles are similar?

we know that
r1/r2---------> 6/2------> 3

to prove that the circle 1 and circle 2 are similar, the radius of circle 1 must be divided by 3 and  translate the center of the circle 1  (10) units to the left and (4) units down  

 the answer part A) is
the radius of circle 1 must be divided by 3 and  translate the center of the circle 1  (10) units to the left and (4) units down  


Part B) What scale factor does the dilation from Circle 1 to Circle 2 have?

the answer Part B) is 
the scale factor is (3/1)

how fast is the water level rising in a rectangular fish tank whose base is 20 ft^2 if the tank is being filled at a rate of 0.5ft^3/min

Answers

V = Bh
0.5 ft^3 = (20 ft^2)h
h = (0.5 ft^3)/(20 ft^2) = 0.025 ft

The rate of change of water depth is 0.025 ft/min.

The water level is rising at a rate of 0.025 ft/min.

To determine how fast the water level is rising in the rectangular fish tank, you can use the formula for the volume of a rectangular prism:

V = base area × height

Given that the base area is 20 [tex]ft^2[/tex] and the tank is being filled at a rate of

0.5 cube ft/min, you want to find the rate at which the height (h) is changing  [tex](\frac{dh}{dt} )[/tex].

V = base area × height

[tex]\frac{d V}{d t}=\text { base area } \times \frac{d h}{d t}[/tex]

Substitute the known values:

0.5 = 20 x [tex](\frac{dh}{dt} )[/tex]

Now, solve for [tex](\frac{dh}{dt} )[/tex]

[tex]\frac{d h}{d t}=\frac{0.5}{20}[/tex] = 0.025 ft/min

Thus, the required answer is 0.025 ft/min.

Find the volume for the regular pyramid.

4 cu. units
6 cu. units
12 cu. units

Answers

4 cu units
Formula is V = lwh/3
v=volume
I=base length
w=base length
h=base height

Answer:

[tex]4\ cu.\ units[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base of the pyramid

h is the height of the pyramid

Find the area of the base

[tex]B=2^{2}=4\ units^{2}[/tex]

[tex]h=3\ units[/tex]

Find the volume

[tex]V=\frac{1}{3}(4)(3)=4\ units^{3}[/tex]

Is the answer 85.3???????

Answers

Look at the picture below.

I hope this helps!

Is the mean always a more accurate measure of center than the median

Answers

I want to say yes it is but it's been a little while since I have learned this

trevor needs to let his puppy outside every quarter (1 fourth) hour to potty train him. draw and label a number line from 0 hours to 1 hour to show every 1 fourth hour.

Answers

make a number line and make it into four parts that shows that needs to let his puppy outside every 25 min.

The base 10 logarithm is called the _____ logarithm and is often written as log x instead of log10 x.,

Answers

A common logarithm is any logarithm with base 10. Our number system is base 10; there are ten digits from 0-9, and place value is determined by groups of ten. You can remember a “common logarithm,” then, as any logarithm whose base is our “common” base, 10.

Explain what needs to happen to the inequities sign when dividing or multiplying by a negative number

Answers

Inequality symbols need to be reversed when multiplying or dividing by a negative number, because that reverses the ordering of values.
2 > 1
-2 < -1 . . . . . multiplied or divided by -1

___
A more "interesting" case is when a function is applied that has a negative slope.
0 < a < b < π
cos(0) > cos(a) > cos(b) > cos(π)

10,11, and 12 please and show work

Answers

10).  5 x 10^6            5.3 x 10^-4
        5 x 1,000,000    5.3 x 0.0001
        5,000,0000    x    0.00053 = 2,650
 
2,650

A die is tossed. Find the odds against rolling a number greater than 4.
*the probability of rolling a # greater than 4 is 1/3.
*the probability that the event doesn't occur is 2/3.

What is the ratio?

Answers

The chance of rolling a number greater than 4 (a 5 and 6) is 2/6 = 1/3 after simplification. The probability it WON'T happen is 1 - 1/3 = 2/3. 
 The ratio of against to for is 2/3:1/3
 You can further simplify this ratio by multiplying each side by 3 and yielding
 2:1.
 The chance of it not happening is twice as likely as it is to roll a number greater than 4

Factor completely: 9ab + 12ax - 6b - 8x (1 point)
1. Prime
2. (3b - 4x)(3a - 2)
3. (3b + 4x)(3a - 2)
4. (3b + 4x)(3a + 2)

Answers

3. (3b + 4x)(3a - 2) is correct.
Use FOIL to expand each factored form, only #3 will result in 9ab + 12ax - 6b - 8x
the correct answer would be C or #3

Given that the points (-3, 8), (2, 8), (2, -2), and (-3, -2) are vertices of a rectangle, what is the ratio of the rectangle's length to its width?

Answers

let
A ---> (-3, 8)
B ---> (2, 8) 
C----> (2, -2) 
D----> (-3, -2)

step 1
find the distance AB
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(8-8)²+(2+3)²]----> d=√25-----> d=5 units

step 2
find the distance BC
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(-2-8)²+(2-2)²]----> d=√100-----> d=10 units

step 3
find the ratio of the rectangle's length to its width
ratio=rectangle's length/rectangle's width
length=10 units
width=5 units
ratio=10/5-----> ratio=2

the answer is 
 the ratio of the rectangle's length to its width is 2

see the attached figure

Answer:

2:1

Step-by-step explanation:

state whether the relationship between x and y in y=4x-5 is proportional or nonproportional

Answers

The relationship is proportional because it is in standard form
Its proportional it’s a standard form
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The walking distance from the Empire State Building into sues hotel is 8 times as far The potential energy in atp is released when the terminal high-energy bond is broken by a process called which of the following is a conflict resolution skills is best for dealing with a situation which has escalate due to temper A stock had returns of 11 percent, -18 percent, -21 percent, 20 percent, and 34 percent over the past five years. what is the standard deviation of these returns?a. 18.74 percentb. 20.21 percentc. 20.68 percentd. 24.01 percente. 23.49 percent Agonistic interaction and matched submission are which type of social behavior? parental care behavior courtship behavior aggressive behavior cooperative behavior There are two people in Sophia's class of 25 named Michael. She infers that 8% of people in the U.S. are named Michael. What is wrong with Sophia's conclusion? A) Nothing is wrong with Sophia's conclusion. 2/25 = 0.08, which is 8%. 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