Its only factors are 1 and itself
Explanation:
There's not much more to mention since choice D perfectly describes what it means to be prime.
The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, ...
There are infinitely many prime numbers.
I need help with question 4
Answer:
12/2
Step-by-step explanation:
12 halves equal 6 but 2 twelves equal 0.17 (rounded)
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
Martin spent $68 on a new drone that he had been saving for. Now, he has $41 left in his savings jar.How many dollars did Martin have saved before he bought the drone?
Answer:109
Step-by-step explanation:41+68=109
109-68=41
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 θcan someone plz help me i’m fr lost
A is the statement that is true
Find the line's slope and a point on the line.
PLEASE SOME1 ANSWER ASAP
Question in picture.
Answer:
0.6 percent
Step-by-step explanation:
I did division that why
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.
-5/8 + 8 3/8
Options:
•7 3/4
•8 3/4
•3 3/8
•8-1/4
Step-by-step explanation:
Least common multiple of 66 and 88 is 2424. Convert -\frac{5}{6}−
6
5
and \frac{83}{8}
8
83
to fractions with denominator 2424.
-\frac{20}{24}+\frac{249}{24}−
24
20
+
24
249
Step 2
Since -\frac{20}{24}−
24
20
and \frac{249}{24}
24
249
have the same denominator, add them by adding their numerators.
\frac{-20+249}{24}
24
−20+249
Step 3
Add -20−20 and 249249 to get 229229.
\frac{229}{24}
24
229
answer:222/24 = 9.5419999967
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)
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?
A bucket contains 5 green tennis balls, 7 yellow tennis balls, and 1 red tennis
balls. Tony removes 2 tennis balls, without replacement, from the bucket.
What is the probability that Tony removes 1 yellow, and then 1 green tennis
balls?
Write your answer as a fraction. Ex: 1/2
========================================================
Work Shown:
A = probability of getting a yellow ball
A = (number of yellow)/(number total)
A = 7/(5+7+1)
A = 7/13
B = probability of getting a green ball after event A happens, no replacement
B = (number of green)/(number left after the yellow is picked)
B = 5/(13-1)
B = 5/12
A*B = probability of getting yellow followed by green, no replacement
A*B = (7/13)*(5/12)
A*B = (7*5)/(13*12)
A*B = 35/156
What is the value of x in the equation 2x 3y = 36, when y = 6? 8 9 27 36.
Step-by-step explanation:
2x*3y=36
2x*3(6)=36
2x*18=36
2x=36/18
2x=2
x=1
hope this was helpful
remember if you have any question ask me in the comment section
PLEASE HELP! Matrix elements
Answer:
29
Step-by-step explanation:
The first one is a row and the second one is a column. 1st row and 5th column.
Answer:29
Step-by-step explanation:
The temperature dropped - 16.8 degrees over the course of 5 days. What was
the average daily temperature change?
Add an explanation to this if possible, <3
Answer:
The average change would be -3.36 degrees.
Step-by-step explanation:
We take the overall temperature change which is -16.8 and we would just simply divide that by 5. That's all to get the temperature.
Another example would be if the temperature change was 16 over the course of 4 days. In this case we would take the overall (16) and divide that by the number of days. There would be an average of 4 degree temperature change.
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.
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.
BRAINLIEST FOR CORRECT ANSWER If you can answer this, you are smart. What is A+B?
Answer:
C
Step-by-step explanation:
Pythagorean theorem
Answer: 3
Step-by-step explanation: A=1 and B=2 its like adding 1 and 2 it is 3
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
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
In order for the data in the table to represent a linear function with a rate of change of 8, what must be the value of a? 10 27 11 a 12 11 O a 2 O a 3 Oa 19 Oa- 35
Answer:
19 or c
Step-by-step explanation:
Hi I just took the test as you can see on the chart by the x axis it goes from 10 to 11 and on the y axis it goes from 27 to a so really it’s just simple subtraction
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
What is the domain of this function?
O {x|x>0}
O {x|x <8)
O {x|0 < x <8]
O {x|x < 0x8}
Answer:
x > 0
Step-by-step explanation:
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
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.
A 168-inch board is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece. The shorter piece is inches long.
Answer:
The shortest piece is 42
Step-by-step explanation:
168 ÷ 4 = 42 ( Shortest Piece )
42 × 3 = 126 ( Longest Piece )
168 - 126 = 42
Find sin Y, cos Y, and tan Y. Write each answer as a fraction and as a decimal rounded to the nearest hundredth.
Can someone please help me asap?!?! I’ll mark brainlist!
Answer:
$16.49
Step-by-step explanation:
Find 45% of 29.99: 45% × 29.99 = $13.4929.99 - 13.49 = $16.50The closest option to $16.50 is $16.49, so that is the answer. I hope this helps!
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
(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