Answer:
0/6
Step-by-step explanation:
Hope this helps I'm just typing rn bc it says it needs to be longer
PLEASE HELP WITH MATHS
Answer:
No biscuits.
Step-by-step explanation:
We know that there is a total of 100 biscuits.
Let's assign variables.
X=Icing
Y=Hundreds and Thousands
Z=Cherries
X appears every 5 biscuits, y appears every 8 biscuits, and z appears every 9 biscuits. Let's start solving by finding their multiples that are less than or equal to 100.
X: 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100
Y: 8,16,24,32,40,48,56,64,72,80,88,96
Z: 9,18,27,36,45,54,63,72,81,90,99
The multiples need to be a multiple of 5,8, and 9.
The numbers that have both x and y are: 40 and 80
The numbers that have both x and z are: 45 and 90.
Seeing as the numbers never overlap, there are no biscuits that have x,y, and z.
Note: If you like my answer, please rate it a 5 and click thanks! (It helps with my leveling. If you want to be extra nice, you can also give me brainliest if you want!) If you think there is something wrong with my answer or that there is something I should improve on, please leave it in the comments.
if sec theta + tan theta equals to X then prove that sin theta equals to x square minus x whole divided by X square + 1
Correct Question :-
If sec[tex]\theta[/tex] + tan[tex]\theta[/tex]= x , then prove that ,
[tex]\implies\sf sin\theta =\dfrac{x^2-1}{x^2+1}[/tex]
Proof :-
Here we are given that ,
[tex]\longrightarrow \sec\theta + tan\theta = x[/tex]
Firstly write everything in terms of sine and cosine .
[tex]\longrightarrow \dfrac{1}{\cos\theta}+\dfrac{\sin\theta}{\cos\theta}=x [/tex]
Add ,
[tex]\longrightarrow \dfrac{1+\sin\theta}{\cos\theta}=x [/tex]
On squaring both sides , we have ;
[tex]\longrightarrow \dfrac{(\sin\theta+1)^2}{(\cos\theta)^2}=x^2[/tex]
Simplify using identity sin²x + cos²x = 1 ,
[tex]\longrightarrow \dfrac{(1+\sin\theta)^2}{1-\sin^2\theta}=x^2 [/tex]
Simplify using identity (a+b)(a-b)=a²-b² ,
[tex]\longrightarrow \dfrac{(1+\sin\theta)^2}{(1+\sin\theta)(1-\sin\theta)}=x^2 [/tex]
Simplify,
[tex]\longrightarrow \dfrac{1+\sin\theta}{1-\sin\theta}=x^2 [/tex]
On using Componendo and Dividendo , we have ;
[tex]\longrightarrow \dfrac{1+\sin\theta+1-\sin\theta}{1+\sin\theta-1+\sin\theta}=\dfrac{x^2+1}{x^2-1}[/tex]
[tex]\longrightarrow \dfrac{2}{2\sin\theta}=\dfrac{x^2+1}{x^2-1}[/tex]
Simplify,
[tex]\longrightarrow \dfrac{1}{\sin\theta}=\dfrac{x^2+1}{x^2-1}\\[/tex]
Divide both the sides by 1 ,
[tex]\longrightarrow \underline{\underline{\sin\theta =\dfrac{x^2-1}{x^2+1}}} [/tex]
Hence proved .
And we are done !
[tex]\rule{200}4[/tex]
More to Know :-1) Trigonometric table :-
[tex]\small{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} $ \sin $ & 0 & $\dfrac{1}{2 }$ & $\dfrac{1}{ \sqrt{2} }$ & $\dfrac{ \sqrt{3}}{2}$ & 1 \\ \cline{1-6} $ \cos $ & 1 & $ \dfrac{ \sqrt{ 3 }}{2} } $ & $ \dfrac{1}{ \sqrt{2} } $ & $ \dfrac{ 1 }{ 2 } $ & 0 \\ \cline{1-6} $ \tan $ & 0 & $ \dfrac{1}{ \sqrt{3} } $ & 1 & $ \sqrt{3} $ & $ \infty $ \\ \cline{1-6} \cot & $ \infty $ &$ \sqrt{3} $ & 1 & $ \dfrac{1}{ \sqrt{3} } $ &0 \\ \cline{1 - 6} \sec & 1 & $ \dfrac{2}{ \sqrt{3}} $ & $ \sqrt{2} $ & 2 & $ \infty $ \\ \cline{1-6} \csc & $ \infty $ & 2 & $ \sqrt{2 } $ & $ \dfrac{ 2 }{ \sqrt{ 3 } } $ & 1 \\ \cline{1 - 6}\end{tabular}}[/tex]
[tex]\rule{200}4[/tex]
2) Important identities :-
[tex]\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ $\: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1$\end{minipage}}[/tex]
[tex]\rule{200}4[/tex]
If sec theta + tan theta equals to x then prove that:-
[tex]\longrightarrow \: sin \theta = \frac{ {x}^{2} - { \bold{1}} }{ {x}^{2} + 1 } [/tex]
Solution:Given that:
[tex]\longrightarrow \: sec \: \theta + tan \: \theta =x \: \: ..(i) [/tex]
We have to prove:
[tex]\longrightarrow \: sin \: \theta = \frac{ {x}^{2} - 1 }{ {x}^{2} + 1} [/tex]
We know that:
[tex]\longrightarrow \: { \sec}^{2} \theta \: - \: { \tan}^{2} \theta = 1[/tex]
[tex] \longrightarrow ( \sec \: \theta \: + \: \tan \: \theta)( \sec \: \theta - \tan \: \theta )[/tex]
[tex] \longrightarrow x( \sec \: \theta - \tan \: \theta) \: = 1[/tex]
[tex] \longrightarrow \: \sec \theta - \tan \: \theta = \frac{1}{x} \ ..(ii)[/tex]
Adding equation (i) and (ii), we get:
[tex] \longrightarrow \: 2\sec \theta = x + \frac{1}{x} [/tex]
[tex] \longrightarrow \: 2 \sec \: \theta = \frac{ {x}^{2} + 1}{x} [/tex]
[tex] \longrightarrow \: \sec \: \theta = \frac{ {x}^{2} + 1}{2x} [/tex]
[tex] \longrightarrow \: \cos \: \theta = \frac{2x}{ {x}^{2} + 1 } [/tex]
Now, we know that:
[tex] \longrightarrow \: { \sin}^{2} \theta + { \cos }^{2} \: \theta = 1[/tex]
Therefore,
[tex] \longrightarrow \: \sin \theta \: = \sqrt{1 - { \cos }^{2} } \: \theta[/tex]
[tex] \longrightarrow \: \sin \: \theta = {\sqrt{1 - ( \frac{2x}{ {x}^{2} + 1} } )}^{2} [/tex]
[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {({x}^{2} + 1)}^{2} - {(2x)}^{2} }{( {x}^{2} + 1)} } [/tex]
[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {x}^{4} \: + 2 {x}^{2} + 1 - \: 4 {x}^{2} }{( {x}^{2} { + 1)}^{2} } } [/tex]
[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {x}^{4} - {2x}^{2} + 1 }{( {x}^{2} { + 1)}^{2} } } [/tex]
[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{( {x}^{2} { - 1)}^{2} }{ {(x}^{2} + {1)}^{2} } } [/tex]
[tex] \longrightarrow \: \sin \: \theta = \frac{ {x}^{2} - 1 }{ {x}^{2} + 1} [/tex]
Hence Proved..!![tex] \: [/tex]
Learn More:1. Relationship between sides and T-Ratios.sin θ = Height/Hypotenusecos θ = Base/Hypotenusetan θ = Height/Basecot θ = Base/Heightsec θ = Hypotenuse/Basecosec θ = Hypotenuse/Height2. Square formulae.sin²θ + cos²θ = 1cosec²θ - cot²θ = 1sec²θ - tan²θ = 13. Reciprocal Relationship.sin θ = 1/cosec θcos θ = 1/sec θ tan θ = 1/cot θcosec θ = 1/sin θsec θ = 1/cos θtan θ = 1/cot θ4. Cofunction identities.sin(90° - θ) = cos θcos(90° - θ) = sin θcosec(90° - θ) = sec θsec(90° - θ) = cosec θtan(90° - θ) = cot θcot(90° - θ) = tan θ5. Even odd identities.sin -θ = -sin θcos -θ = cos θtan -θ = -tan θ3) Alex drove for 3 hours at an
average speed of 60 miles per
hour and for 2 hours at 45
miles per hour. What is his
average speed for the whole
journey?
average speed= total distance/total time taken
60+45= 105miles
1 mile= 1.609
105×1.609= 168.945km
168.945/4
Hence answer = 33.79 km/hr
Answer:
To find Alex's average speed for the whole journey, we can use the formula:
Average Speed = Total Distance / Total Time
Let's calculate the total distance traveled first:
Distance1 = 60 miles/hour * 3 hours = 180 miles
Distance2 = 45 miles/hour * 2 hours = 90 miles
Total Distance = Distance1 + Distance2 = 180 miles + 90 miles = 270 miles
Next, let's calculate the total time taken for the whole journey:
Total Time = 3 hours + 2 hours = 5 hours
Now, we can find the average speed:
Average Speed = 270 miles / 5 hours = 54 miles per hour
So, Alex's average speed for the whole journey is 54 miles per hour.
Please mark as Brainliest
can someone please help me?
Answer:
a
Step-by-step explanation:
PLS HELP 30 points
Which point represents the outlier in the scatter plot?
(A) (2,4)
(B) (5,10)
(C) (9,10)
(D) (10,9)
Answer:
The answer is D : (10,9)
Step-by-step explanation:
As you can see... the cordinate (10,9) is far away from the other points, therefore it is clearly the outlier of the data set
write step by step pls
1/2r−3=3(4−3/2r)
Answer:
r = 3
Step-by-step explanation:
[tex]\dfrac{r}{2} - 3 = 3(4 - \dfrac{3r}{2} )[/tex]
The first step to solve for "r" is to simplify the distributive property on the RHS. To simplify the distributive property, we need to multiply the term outside the parenthesis with the terms inside the parenthesis.
[tex]\rightarrow \dfrac{r}{2} - 3 = 12 - \dfrac{9r}{2}[/tex]
Now, add 9r/2 and 3 both sides to isolate the constants and variables.
[tex]\rightarrow \dfrac{r}{2} + \dfrac{9r}{2} = 12 + 3[/tex]
Simplify both sides.
[tex]\rightarrow \dfrac{10r}{2}= 12 + 3[/tex]
[tex]\rightarrow 5r = 15[/tex]
Divide 5 both sides.
[tex]\rightarrow \boxed{r = \frac{15}{5} = 3}[/tex]
(2x² - 5x-3)/ (x-3)
DIvide the polynomials
Answer:
2x + 1
Step-by-step explanation:
[tex] \frac{(2x² - 5x-3)}{(x - 3)} [/tex]
Factor out 2x² - 5x-3
[tex] \frac{(2x + 1)(x - 3)}{x - 3} [/tex]
divide x - 3 by x - 3
=> 2x + 1
Or another step
Step by Step Solution
STEP
1
:
Equation at the end of step 1
STEP
2
:
2x² - 5x - 3/ x - 3
Trying to factor by splitting the middle term
2.1 Factoring 2x² - 5x - 3
The first term is, 2x² its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .
-6 + 1 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1
2x² - 6x + 1x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-3)
Add up the last 2 terms, pulling out common factors :
1 • (x-3)
Step-5 : Add up the four terms of step 4 :
(2x+1) • (x-3)
Which is the desired factorization
Canceling Out :
2.2 Cancel out (x-3) which appears on both sides of the fraction line.
Final result :
2x + 1
Please help asap……..
Answer:
1. 96
2. 84
Step-by-step explanation:
I used the Circle theorems:
For 1 you use the alternate segment theory
For 2 you use the theory that opposite angles in a cyclic quadrilateral add up to 180.
I can't be asked to explain it properly I'm sorry but if no one else does it properly you can give me brainliest?
Which of the following is an integer?
1
8.666...
-5
10
3
Answer:
1,-5,10,3 are integers.
Step-by-step explanation:
1 is a natural number which is an integer. 8.666 is a repeating decimal which isnt an integer. -5 is a negative number and integer. 10 is a natural number which is an integer. 3 is a natural number which is an integer.
Hope this helped and have a great day!
(Please brainliest)
guys please help me i need this done NOW
Answer:
see down
Step-by-step explanation:
10. a one to one function means only one input goes to the same output,
this one is not a one to one function, because there is 2 out put for each input except vertx
Match each equation to its equivalent equation.
-6x - 2y = 10
2x + 5y = 18
-4x + 3y = 20
12x - 9y = -60
-24x - 8y = 40
4x + 10y = 36
Answer:
-6x - 2y = 10 and -24x - 8y = 40
-4x + 3y = 20 and 12x - 9y = -60
2x + 5y = 18 and 4x + 10y = 36
Step-by-step explanation:
first equation with second row second equation
third equation with second row first equation
second equation with second row third equation
Can you please help me with this question it is due at 11:59 pm
Answer:
its 11:09 pm......
Step-by-step explanation:
are u on pc?
Question in picture.
Answer:
0.6 percent
Step-by-step explanation:
I did division that why
Which statement explains why the value of [2.4] is 2 but the value of [-2.4] is –3? because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4 because 2.4 rounds to 2, and –2.4 rounds to –3 because 2.4 is positive, and –2.4 is negative because 2 is the least integer greater than 2.4, and –3 is the least integer greater than –2.4
Using the definition of the floor function, it is found that the correct statement is:
Because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4.
What is the floor function?Modeled by [x], it is the value of the greatest integer that is not greater than x.
Hence, in this problem:
[2.4] = 2, as 2 < 2.4 < 3.[-2.4] = -3, as -3 < -2.4 < -2.Hence, the correct statement is:
Because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4.
More can be learned about the floor function at https://brainly.com/question/15457745
Answer:
a
Step-by-step explanation:
on edge
I need help with question 4
Answer:
12/2
Step-by-step explanation:
12 halves equal 6 but 2 twelves equal 0.17 (rounded)
4. Trials until First Success
On the average, how many times must a die be thrown until one gets a 6?
Answer:
6
Step-by-step explanation:
There are 6 faces on a die so on average, one has to roll a fair die 6 times in order to get number 6 to show.
On average it's 6 as 6 sides a die has
But
There is equal probability for each number while rolling a die .i.e
There is 1/6 chances getting any number
Evaluate for a = 2, b = 3, and c = 4.
ab + c
Answer:
10
Step-by-step explanation:
Given;
a = 2
b = 3
c =4
ab+c
Solve;
Since a = 2, b = 3, and c = 4
Substitute
(2)(3)+4
6 +4
= 10
Answer = 10
~Learn with lenvy~
Answer:
10
Step-by-step explanation:
Given the following question:
[tex]a=2[/tex]
[tex]b=3[/tex]
[tex]c=4[/tex]
[tex]ab+c[/tex]
To find the answer we need to substitute the values in for the variables and then solve using PEMDAS.
[tex]ab+c[/tex]
[tex]2\times3+4[/tex]
[tex]2\times3=6[/tex]
[tex]6+4[/tex]
[tex]6+4=10[/tex]
[tex]=10[/tex]
Your answer is "10."
Hope this helps.
Find the line's slope and a point on the line.
PLEASE SOME1 ANSWER ASAP
Which system of equations represents the graph?
for the line that goes up - it cuts the y-axis at - 5 (p = -5)
when we take 2 points we go from one to the other by going to the right of 1 unit and going up of 3 units (slope m : 3/1)
=> y = 3x - 5
and
for the line which goes down - it cuts the y-axis in +2 (p=2)
when we take 2 points we go from one to the other by going to the right of 2 units and going down of 1 unit (slope m : -1/2)
=> y = -1/2x + 2
=> y + 1/2x = 2
2x + 4y = 8
=> B
Which sequence: an=-2(an-1),a1=4
Happy Birthday is having a party this weekend. The ratio of community friends to school friends attending the party is 8 to 14. Find an equivalent ratio of school friends to community friends.
Group of answer choices
24 to 18
28 to 16
16:28
18:24
Answer:
16: 28 is the answer for the above question
A square corner of 16 square centimeters is removed from a square paper with an area of 9x2 square centimeters. A square. Most of the square is shaded blue. In the bottom right of the square is a smaller square, outlined in a dashed line, and not shaded. Which expression represents the area of the remaining paper shape in square centimeters? (x – 7)(x – 9) (3x – 2)(3x – 8) (3x – 4)(3x + 4) (9x – 1)(x + 16)
Given:
A square corner of 16 square centimeters is removed from a square paper with an area of 9x² square centimeters.
To find:
The area of the remaining paper shape in square centimeters.
Solution:
Initial area of the square paper = 9x² sq. cm
Area of square which is removed from the initial square paper = 16 sq. cm
Subtract area of removed square from the initial area, to find the area of the remaining paper shape.
[tex]9x^2-16=(3x)^2-4^2[/tex]
[tex]9x^2-16=(3x-4)(3x+4)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
Therefore, the area of the remaining paper shape is (3x-4)(3x+4) sq. cm.
Hence, the correct option is C.
Find sin Y, cos Y, and tan Y. Write each answer as a fraction and as a decimal rounded to the nearest hundredth.
(Help ASAP will give 20 points for 2 questions)
Answer:
1.x,y is the answer to first question
2.y=2x+5
What is the value of y?
isosceles triangle so angle Q = angle R
and sum of the angles of a triangle = 180
so
y + y + 84 = 180
2y = 96
y = 48
Which expression has the same meaning as 4 9/2?
Answer:
8 1/2
or 8.5
Step-by-step explanation:
Answer:
The second one, √4^9
Sorry lol i posted the answer in the questions section by accident
can someone plz help me i’m fr lost
A is the statement that is true
A football team won 67% of their matches and drew 24% of them. What percentage of the matches did they lose?
Answer:
9%
Step-by-step explanation:
67 + 24 = 91%
100- 91 = 9%
This means they lost 9% of their games.
The requried football team lost 9% of their matches.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Since the football team won 67% of their matches and drew 24% of them, the percentage of matches they lost can be found by subtracting the percentage of matches they won and the percentage of matches they drew from 100%:
Percentage of matches lost = 100% - 67% - 24%
Percentage of matches lost = 9%
Therefore, the football team lost 9% of their matches.
Learn more about percentages here:
brainly.com/question/13450942
#SPJ3
Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units? x2 y2 4x 6y – 51 = 0 x² y² – 4x – 6y – 51 = 0 x2 y2 4x 6y – 3 = 0 x2 y2 – 4x – 6y – 3 = 0.
The equation represents the general form a circle with a center at
(–2, –3) and a diameter of 8 units is,
[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]
Given that,circle with a center at (–2, –3)
diameter of circle is 8 units
To find
the equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Radius of the Circle is,
The diameter of the circle is 8 units. therefore,
[tex]radius=\frac{d}{2}=\frac{8}{2} =4[/tex]
Equation of a circle
The equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units.
What is the general form of equation of circle?[tex](x-h)^{2} +(y-k)^{2} =R^{2}[/tex]
Substituting the values,
[tex](x-(-2))^{2} + (y-(-3))^{2} =4^{2}[/tex]
[tex](x+2)^{2} + (y+3)^{2} =4^{2}\\[/tex]
[tex]x^{2} +4x+4+y^{2} +6y+9=0[/tex]
[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]
Therefore, the option C is correct.
The equation represents the general form a circle with a center at
(–2, –3) and a diameter of 8 units is
[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]
To learn more about the general form of circle visit:
https://brainly.com/question/3612143
Lesson 7.1 Extra Practice Find the area of the parallelogram. 1. 8 m 5 m
Answer:
9m
Step-by-step explanation:
A parallelogram you have listed has the following side lengths:
1.8m and 5m.
First, we need to understand the formula and simply comprehend it.
In this case, we're dealing with an area of a quadrilateral which is a four-sided shape.
The area is base times height.
You will simply need to do 1.8 x 5 = m
That is pretty simple. You need to setup a question like this:
1.8
x 5
____
9.0
Remember you need to move the decimal point when you're done mulitplying. This case 9.0 is simply 9 by itself.