[tex]\tt (1 - sin ^2x)\times(1+tan^2x) = 1[/tex]
L.H.S
[tex]\tt cos^2x \times sec^2x[/tex]
[tex]\tt cos^2x \times \frac{1}{cos^2x}[/tex]
[tex]\tt \cancel{ cos^2x} \times\cancel{ \frac{1}{cos^2x}}[/tex]
[tex]\tt 1[/tex]
R.H.S
Hence proved
Step-by-step explanation:
[tex]{ \tt{ \blue{(1 - { \sin}^{2}x )(1 + { \tan }^{2}x) = 1 }}}[/tex]
• Remember → 1 + tan²x = sec²x
[tex] = { \tt{ \blue{(1 - { \sin }^{2}x)( { \sec}^{2}x) }}}[/tex]
• But sec²x → 1/cos²x
[tex] = { \tt{ \blue{(1 - { \sin}^{2} x)( \frac{1}{ \cos {}^{2} x} )}} }\\ \\ = { \blue {\tt{ \frac{1 - { \sin }^{2}x }{ { \cos }^{2}x } }}}[/tex]
• Remember from the first identity of trignometry;
[ cos²x + sin²x = 1 ].
• Therefore: [ cos²x = 1 - sin²x ]
[tex] = { \blue{\rm{ \frac{1 - { \sin}^{2}x }{1 - { \sin }^{2}x } }}} \\ \\ { \rm{ \blue{= 1 \: }}}[/tex]
Hence proved.
5y+4x=10.51 8y+3x=10.39
Answer:
(x, y) = (1.89, 0.59)
Step-by-step explanation:
Written in general form, the equations are ...
4x +5y -10.51 = 0
3x +8y -10.39 = 0
These can be solved using the cross-multiplication method to find ...
∆1 = (4)(8) -(3)(5) = 17
∆2 = (5)(-10.39) -(8)(-10.51) = 32.13
∆3 = (-10.51)(3) -(-10.39)(4) = 10.03
Then the values of the variables are ...
x = ∆2/∆1 = 32.13/17 = 1.89
y = ∆3/∆1 = 10.03/17 = 0.59
The solution is (x, y) = (1.89, 0.59).
4(3q + 10) = 6( 2q - 9 )
Your piggy bank has $85 and each day you take out $3. You want to have at least $22 left in your piggy
bank. How many days did you take money from your piggy bank?
HELLPPPPPPP
please help
Answer:
i think that's A
I'm just guess
i need help on this assignment
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answer:
It is too garlicky.
Step-by-step explanation:
lol, uhm, this is a little bit of a strange question ngl, but I guess it's testing you on measurements and units, right?
Well, 12 gloves of garlic for every 900 mL of sauce in comparison to 8 cloves of garlic for every 500 mL of sauce is quite a difference to be honest, might even be too much in her opinion. 8 cloves for every 500 mL is more than 12 cloves for every 900 mL, so I'd say she'll think it's too garlicy.
I apologize, in advance, if I am incorrect.
What is the equation on the graph?
Please help!!!
Answer:
y = -1/4x + 2
Step-by-step explanation:
using the slope-intercept form (y=mx+b) m is the slope of the line which is -1/4 because it is decreasing and b is the y-intercept of the line which is 2
Someone please help!!! Can’t find this one anywhere!!! please and thank you!!!!!!!
[tex]\dfrac{ 2+ 2i}{5+4i}\\\\\\=\dfrac{(2+2i)(5-4i)}{(5+4i)(5-4i)}\\\\\\=\dfrac{10-8i + 10i -8i^2}{5^2 -(4i)^2}\\\\\\=\dfrac{10+2i +8}{25+16}~~~~;[i^2 =-1]\\\\\\=\dfrac{18+2i}{41}\\\\\\=\dfrac{18}{41} + \dfrac{2}{41}i[/tex]
if 21 and 35 are two members of a pythagorean triple, what is the third member?
Answer:
28
Step-by-step explanation:
21^2+28^2=35^2
The third number of the Pythagorean triplet as c = 40.82.
What is Pythagorean triplet? What is a mathematical function, equation and expression? Pythagorean triplet : A Pythagorean triplet consists of three positive integers a, b, and c, such that a² + b² = c².function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that 21 and 35 are two members of a Pythagorean triplet.
We can write the Pythagorean triplet as -
a² + b² = c²
c² = a² + b²
c² = (21 x 21) + (35 x 35)
c² = 441 + 1225
c² = 1666
c = √1666
c = 40.82
Therefore, the third number of the Pythagorean triplet as c = 40.82.
To solve more questions on functions, expressions and polynomials, visit the link below -
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Please help me with this question!
Answer:
a) 45/4
b) 3
c) 12
d) 24
e) no; rate of change varies
Step-by-step explanation:
The average rate of change on interval [a, b] is given by ...
m = (f(b) -f(a))/(b -a)
The function values are read from the table.
__
a) m = (f(4) -f(0))/(4 -0) = (48 -3)/(4 -0) = 45/4
b) m = (f(1) -f(0))/(1 -0) = (6 -3)/(1 -0) = 3
c) m = (f(3) -f(2))/(3 -2) = (24 -12)/(3 -2) = 12
d) m = (f(4) -f(3))/(4 -3) = (48 -24)/(4 -3) = 24
e) Not a linear function. The rate of change is not constant.
A system of linear equations includes the line that is created by the equation Y = 0.5x-1 and the line through the
points (3, 1) and (-5, -7), shown below.
What is the solution to the system of equations?
A. (-6, -4)
B. (0, -1)
C. (0, -2)
D. (2, 0)
Step-by-step explanation:
the answer I think D should be
Answer:
The answer is (2,0)
Step-by-step explanation:
We know one equation [tex]y =0.5x - 1[/tex] and the other points (3, 1) and (-5, -7).
For the first step, we need to graph the equation we know, since the points already plotted, and therefore have its own line.
As we can tell it crosses over points (2,0) making this equation having exactly one solution.
Making the correct awnser D; (2,0)
: If 10 less than 5 times a number is two more than 3 times the number, then the number is
Answer:
x = 1Step-by-step explanation:
If 10 less than 5 times a number is two more than 3 times the number, then the number is
10 - 5x = 2 + 3x
10 - 2 - 5x - 3x = 0
8 - 8x = 0
x = 1
---------------
check
10 - 5 * 1 = 2 + 3 * 1
5 = 5
the answer is good
Could some please help and explain?
Answer:
x = 7
Step-by-step explanation:
A rhombus is a parallelogram where all sides are equal. Therefore, as we know two sides are equal to 7x+8 and 9x-6, we can say that
7x+8 = 9x - 6
subtract 7x from both sides to put the variable on one side
2x - 6 = 8
add 6 to both sides to isolate the variable and its coefficient
2x = 14
divide both sides by 2 to isolate x
x = 7
PLEASEEE HELPPPP ASAPPPP
[tex]\cos 27^{\circ} = \dfrac{KL}x\\\\\implies \cos 27^{\circ} = \dfrac{6.3}x\\\\\implies x = \dfrac{6.3}{\cos 27^{\circ}}=7.1~ \text{units.}[/tex]
9_9_9_9=111
what are the signs?
Answer:
Step-by-step explanation:
im not sure and what do u mean by signs
Answer:
multiplie maybe i dont know what you mean-
Step-by-step explanation:
Can someone Please help me on this easy math problem
Step-by-step explanation:
Equation of a straight line
y = mx + c, m is the slope, and c the intercept
points (3,7) x = 3, y = 7, c = 1
7 = m × 3 + 1
7 = 3m + 1
3m = 7 - 1
3m = 6
m = 6/3
m = 2
Grayson is flying a kite, holding his hands a distance of 2.75 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 26
∘
∘
. If the string from the kite to his hand is 145 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
The position of the kite with the point directly beneath the kite at the same
level with the hand and the hand for a right triangle.
The height of the kite above the is approximately 66.314 feet.Reasons:
The height of his hands above the ground, h = 2.75 feet
Angle of elevation of the string (above the horizontal), θ = 26°
Length of the string, l = 145 feet
Required:
The height of the kite above the ground.
Solution:
The height of the kite above the ground is given by trigonometric ratios as follows;
[tex]\displaystyle Height \ of \ kite, \, k_h = \mathbf{h + l \times sin(\theta)}[/tex]
Therefore;
[tex]\displaystyle Height \ of \ kite, \, k_h = 2.75 + 145 \times sin(26^{\circ}) \approx \mathbf{66.314}[/tex]
The height of the kite above the, [tex]k_h[/tex] ≈ 66.314 feet
Learn more about trigonometric ratios here:
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9. Which of the following is an example of the Commutative Property of Addition? (1 point)
O 12 + 4 = 4 + 12
O 12 + (3 + 2) = (12 + 3) + 2
O 2 + 7 + 0 = 2 +7
O 17+ (-17) = 0
V
10. If p = 8, evaluate 42+p:3. (1 point)
02.
03
06
08
Finish
Cancel
Answer:
9. the first one ( 12 + 4 = 4 + 12 )
Step-by-step explanation:
the commutative property of addition means that you can change the order of the numbers you add and the sum will still be the same. this is shown in the 12 + 4 = 4 + 12 because the order is switched, but they are still equal.
The example of the commutative property of addition is 12 + 4 = 4 + 12, the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The four options
Now,
The commutative property of addition states that changing the order of the addends does not change the sum.
This is the only option that shows the same sum with different orders of addends.
Therefore, by algebra the answer will be 12 + 4 = 4 + 12.
More about the Algebra link is given below.
brainly.com/question/953809
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When a basketball player makes a trip to the free throw line, he takes two consecutive shots. It is often
wondered whether these two shots are independent or dependent does the probability of making the
second free throw depend on whether a player makes the first free throw?
After analyzing data for Lebron James, statisticians determined that his first and second free throws are
entirely independent events. The frequency table below shows the data that analysts used to determine this
independence.
Fill in the missing values from the frequency table.
Answer:
Step-by-step explanation:
Help me with this please!!!
Write the function for the graph!?!??
The y intercept is the y value when x is 0 which is shown on the graph as (0,4) making the y intercept is 4
The next point given is (1,8) which shows for every 1 increase in x (1-0 = 1) the y value increases by a multiple of 2 (4 x2 = 8)
The equation would be f(x) = 4 * (2)^x
The answer is B
Which choice is similar to the figure shown?
Answer:
The parallelogram whose sides are 5 and 20 is similar
Step-by-step explanation:
The parallelogram whose sides are 5 and 20 is similar to the given parallelogram whose sides are 2 and 8 because the figures are the same shade and corresponding sides are proportional.
[tex]\frac{2}{5} = \frac{8}{20}[/tex] [tex]\frac{2}{4} \neq \frac{8}{18}[/tex]
[tex]\frac{2}{5} =\frac{2}{5}[/tex] [tex]\frac{2}{4} \neq \frac{8}{4}[/tex]
can somebody help me/tell me how to do these?
Hi! I'll try to help
It gives you two equations, one for "x" and one for "y"
All you have to do is replace the variable "y" with its value in the second equation. Might be kind of confusing so let's do one.
y=4x
3x-y=1
Since we know that "y" is the same as 4x, you can rewrite the equation as
3x-4x=1
Next, all you have to do is combine like terms as solve "3x-4x" which is -x
Let's rewrite the equation, then:
-x=1
You can simplify it to
x=-1
by dividing both sides by negative one, in other words swapping the negative sign so that "x" is positive
HELP PLEASE IS IMPORTANT!
Solve the equation by using the Quadratic Formula.
2x 92-5
See attachment for answer and math work.
A number cube labeled 1 through 6 is rolled 5 times. What is the probability of landing on 5 each time?
Answer:
1/6
Step-by-step explanation:
can i get brainliest pls
A triangle has side lengths 7, 17, and x. Fill in the inequality for the possible
lengths of x below.
Answer:
9 < x < 25
Step-by-step explanation:
Solve the literal equation for the variable t:
Answer:
t=y÷x+3
Step-by-step explanation:
you have to isolate t
(I may have put the equation in the wrong order but I'm like 70% sure i got it)
At a local amusement park, 70% of the rides are made for kids who are 48 inches and taller. If there are 80 rides in total, how many are made for kids who are 48 inches and taller?
Answer:
56
Step-by-step explanation:
Basically you want to find out what is 70% of 80.
first you have to set up your problem
[tex]\frac{n}{80}[/tex] = [tex]\frac{70}{100}[/tex]
the first fraction would be the percent (70) over 100. (you always use 100)
The fraction to the left would be n over 80. the denominator (the number on the bottom) would be the whole amount. n would be the unknown number
To solve you would use the butterfly method. 80 x 70 and 100 x n. 80 x 70 is 5600 and 100 x n is 100n.
The final step is dividing. 5600 divided by 100 giving you 56
What is the slope?
x: -3, -5, -9
y: 1, 5, 13
Ms. Vescelius wants to divide her class into cooperative learn-
ing groups. If there are 28 students in the class and she wants
all the groups to have the same number of students, how
many students should she put in each group?
What is the slope of the line containing (-2, 5) and (4, -4)?
Answer:
B. - 3 / 2
Step-by-step explanation:
Let,
( x1, y1 ) = ( - 2, 5 )
So,
x1 = - 2
y1 = 5
( x2, y2 ) = ( 4, - 4 )
So,
x2 = 4
y2 = - 4
Formula : -
Slope = ( y2 - y1 ) / ( x2 - x1 )
Slope = ( - 4 - 5 ) / ( 4 - ( - 2 ) )
= - 9 / ( 4 + 2 )
= - 9 / 6
Slope = - 3 / 2
Answer:
B
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (4, - 4 )
m = [tex]\frac{-4-5}{4-(-2)}[/tex] = [tex]\frac{-9}{4+2}[/tex] = [tex]\frac{-9}{6}[/tex] = - [tex]\frac{3}{2}[/tex] → B