Hi there!
Answer:
[tex]\huge\boxed{x = 5}[/tex]
4x + 5 = 25
Subtract 5 from both sides:
4x + 5 - 5 = 25 - 5
4x = 20
Divide both sides by 4:
4x/4 = 20/4
x = 5.
what is the answer to "sin2x=sinx" ?
Answer:
Think of the double angle formula for
sin
2
x
Explanation:
sin
2
x
=
sin
x
2
sin
x
cos
x
=
sin
x
2
sin
x
cos
x
−
sin
x
=
0
sin
x
(
2
cos
x
−
1
)
=
0
Solution A:
sin
x
=
0
⇒
x
=
k
π
,
k
∈
Z
Solution B:
2
cos
x
=
1
⇒
cos
x
=
1
2
,
x
=
±
π
3
+
2
k
π
=
π
3
(
6
k
±
1
)
,
k
∈
Z
∴
x
=
k
π
or
x
=
π
3
(
6
k
±
1
)
,
k
∈
Z
Step-by-step explanation:
Answer:
[tex]\bold{x=\frac\pi3+2k\pi\quad \vee\quad x=\frac{5\pi}3+2k\pi\quad \vee\quad x=k\pi\ ,\quad k\in\mathbb Z}[/tex]
Step-by-step explanation:
[tex]\sin 2x=\sin x\\\\\sin2x - \sin x=0\\\\2\sin x\cos x-\sin x=0\\\\(2\cos x-1)\sin x=0\\\\2\cos x-1=0\qquad\qquad\qquad\qquad or\qquad \sin x=0\\\\2\cos x=1\quad\qquad\qquad\qquad\qquad\ or\qquad \sin x=0\\\\\cos x=\frac12\qquad\qquad\qquad\qquad\qquad or\qquad \sin x=0\\\\x=\frac\pi3+2k\pi\quad \vee\ \ x=\frac{5\pi}3+2k\pi\quad\ \ \vee\ \ x=0+k\pi\ ,\quad k\in\mathbb Z[/tex]
A biased coin is tossed 4 times. The probability of heads on any toss is 0.4. Let X denote the number of heads that come up. Calculate: (i) ( ≤ 2) (ii) (1 ≤ ≤ 3)
Answer:
0.8208 ; 0.8448
Step-by-step explanation:
Given the following :
Number of tosses = 4
Probability of head on any toss :
P(head) = 0.4
Therefore ;
(1 - p(head)) = (1 - 0.4) = 0.6
Binomial probability :
P(X) = nCx * P^x * (1 - P) ^(n-x)
Where:
n = number of trials ; x = number of success ; P = probability of success.
P(X≤2) = P(0) + P(1) + p(2)
using binomial probability calculator to ensure faster computation:
P(X≤2) = 0.1296 + 0.3456 + 0. 3456
= 0.8208
B)
P(1 ≤ X ≤ 3) = P(1) + P(2) + P(3)
P(1 ≤ X ≤ 3) = 0.3456 + 0.3456 + 0.1536
= 0.8448
Write standard form, expanded form and word form at the top of the page write five numbers that are at least 8 digits long
Answer:
See Explanation
Step-by-step explanation:
1.
Standard Form: 2 * 10^8
The number is expanded as follows:
[tex]10^8 = 100,000,000[/tex]
So: [tex]2 * 10^8 = 2 * 100,000,000[/tex]
[tex]Expanded\ Form: 200,000,000[/tex]
Word Form: Two hundred million
2.
Standard Form: 3.5 * 10^7
The number is expanded as follows:
[tex]10^7 = 10,000,000[/tex]
So: [tex]3.5 * 10^7 = 3.5 * 10,000,000[/tex]
[tex]Expanded\ Form: 35,000,000[/tex]
Word Form: Thirty five million
3.
Standard Form: 9 * 10^9
The number is expanded as follows:
[tex]10^9 = 1000,000,000[/tex]
So: [tex]9 * 10^9 = 9 * 1000,000,000[/tex]
[tex]Expanded\ Form: 9,000,000,000[/tex]
Word Form: Nine billion
4.
Standard Form: 5.5 * 10^7
[tex]10^7 = 10,000,000[/tex]
So:
[tex]5.5 * 10^7 = 5.5 * 10,000,000[/tex]
[tex]Expanded\ Form: 55,000,000[/tex]
Word Form: Fifty five million
5.
Standard Form: 4.3 * 10^7
[tex]10^7 = 10,000,000[/tex]
So:
[tex]4.3 * 10^7 = 4.3 * 10,000,000[/tex]
[tex]Expanded\ Form: 43,000,000[/tex]
Word Form: Forty Three million
What type of graph is this?
not a regular graph
a regular graph
Please solve. 6(3 + 8) - 4/5
G'Day mate! Here's the answer:
53 1/3
1. 6(3 + 6) - 4/5
2. 6 x 3 is 18, and 6 x 8 is 48
3. 18 plus 48 is 66
4. 66 - 4/5 = 266/5
5. 266/5 as mixed number is 53 1/5
Answer:
[tex]\Large \boxed{\frac{326}{5}}[/tex]
Step-by-step explanation:
[tex]\displaystyle 6(3 + 8) - \frac{4}{5}[/tex]
Solving brackets.
[tex]\displaystyle 6(11) - \frac{4}{5}[/tex]
[tex]\displaystyle 66 - \frac{4}{5}[/tex]
Subtract.
[tex]\displaystyle \frac{66}{1} - \frac{4}{5}[/tex]
[tex]\displaystyle \frac{66 \times 5}{1 \times 5} - \frac{4}{5}[/tex]
[tex]\displaystyle \frac{330}{5} - \frac{4}{5}[/tex]
[tex]\displaystyle \frac{330-4}{5}[/tex]
[tex]\displaystyle \frac{326}{5}[/tex]
please help :) Write the number shown in standard notation. 5.002 x 10 to the 7 power A. 5,002,000,000 B. 50,020,000 C. 5,002,000 D. 50,020,000,000
Answer:
Hey there!
That would be 50,020,000, and choice B would be correct.
Let me know if this helps :)
Find the value of y
(PlZ help me). :)
Answer:
[tex]\huge \boxed{y=\sqrt{30} }[/tex]
Step-by-step explanation:
We can use ratios to solve for the problem.
y/5 = 6/y
Cross multiply.
y × y = 5 × 6
y² = 30
Take the square root of both sides.
y = [tex]\sqrt{30}[/tex]
You Walked around a circle which has diameter of hundred metre how far you worked
Answer:
314.16 metres
Step-by-step explanation:
The answer to this problem is essentially just the circumference of the circle.
The circumference, or perimeter, is denoted by C = 2πr = πd, where r is the radius (and half the diameter) and d is the diameter.
Here, the diameter is 100 metres, so plug this in for d:
C = πd
C = π * 100 ≈ 314.16 metres
The answer is about 314.16 metres.
~ an aesthetics lover
7/10 +2/15 = 2 3/3+ 3 1/2= 15/16 - 11/12 = 11/15 - 7/20
Answer:
Addition and Subtraction of Fractions · 1. Add: (i) 7/ 10 + 2/15 (ii) 2²/₃ + 3¹/₂ · 2. Simplify: (i) 15/16 – 11/12 (ii) 11/15 – 7/20 · 3. Simplify: 4⁵/₆ – 2³/₈ + .
Answer:
7/10 + 2/15= 5/6
2 3/3 + 3 1/2= 6 1/2
15/16 - 11/12= 1/48
11/15 - 7/20= 23/60
Step-by-step explanation:
When adding or subtracting fraction with different denominators, we must find there LCM to be their new denominators. Then divide the new denominator by the old denominator, do for both fractions, then multiply the answer with the numerator, do for both fractions to get their new numerators. Then add or subtract the fractions. Then simplify the answer if needed.
Ex 1:
The LCM of 10 and 15 is 30
7/10 + 2/15
(30 ÷ 10=3, 3 × 7= 21)(30 ÷ 15= 2, 2 × 2=4)
=21/30 + 4/30= 25/30 or 5/6
With whole numbers, add the two whole numbers together. Then n add the fractions. Lastly add both of the answers together.
Ex:
The LCM of 3 and 2 is 6
2 3/3 + 3 1/2
=2 + 3= 5
= 3/3 + 1/2= 9/6 or 1 3/6 or 1 1/2
= 5 + 1 1/2
= 6 1/2
Always remember to simplify if possible or necessary.
I hope this helps! I'm sorry if it's wrong or too complicated.
There are 10 cups of coffee in each coffee pot and 12 donuts per box, how many cups of coffee and how many donuts will be available if I make two pots of coffee and 3 boxes of donuts?
Answer:
There are 20 cups of coffee in two pots of coffee and 36 donuts in 3 boxes of donuts
Step-by-step explanation:
The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other), the direct rule of three must be applied as follow:
a ⇒ b
c ⇒ x
So [tex]x=\frac{c*b}{a}[/tex]
In this case, the rule of three can be applied as follows:
if in 1 coffee pot there are 10 cups of coffee, in 2 pots of coffee how many cups of coffee are there?[tex]amount of cups of coffe=\frac{2coffe pots*10 cups of coffee}{1 coffe pot}[/tex]
amount of cups of coffe= 20
If there are 12 donuts in 1 box, how many donuts are there in 3 boxes?[tex]amount of donuts=\frac{3 boxes*12 donuts}{1 box}[/tex]
amount of donuts= 36
There are 20 cups of coffee in two pots of coffee and 36 donuts in 3 boxes of donuts
Please solve this, will rate 5 stars and mark as STAR!
Answer:
[tex]\boxed{5 \cdot \sqrt{2} \cdot \sqrt[6]{5} }[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }[/tex]
[tex]\sqrt{\sqrt[3]{10} } \implies (10^\frac{1}{3} )^\frac{1}{2} =10^\frac{1}{6} =\sqrt[6]{10}[/tex]
[tex]\therefore \sqrt{\sqrt[3]{10} }=\sqrt[6]{10}[/tex]
[tex]\text{Solving }\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }[/tex]
[tex]250=2 \cdot 5^3[/tex]
[tex]\sqrt[3]{250}=\sqrt[3]{2\cdot 5^3}=5 \sqrt[3]{2}[/tex]
Once
[tex]\sqrt[6]{2} \cdot \sqrt[6]{5} = \sqrt[6]{10}[/tex]
We have
[tex]5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5}[/tex]
We can proceed considering the common base of exponentials
[tex]\sqrt[3]{2} \cdot \sqrt[6]{2} = 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} }=\sqrt{2}[/tex]
Therefore,
[tex]5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5} = 5 \cdot \sqrt{2} \cdot \sqrt[6]{5}[/tex]
What is the area of a rectangle with side lengths of 5/12 foot and
2/3 foot?
Answer:
5/18
Step-by-step explanation:
Lets write an equation:
5/12*2/3=5*2/12*3.
5*2=10,
12*3=36.
10/36=5/18
The answer is 5/18.
Hope this helps!
simplify (2xy)3x2 will give brainliest.
Answer:
6x³y
Step-by-step explanation:
(2xy) * 3x²
We know that 2 * 3 = 6 and x * x² = x¹ * x² = x⁽¹⁺²) = x³ so the final answer is 6x³y.
At a meeting of 3 representatives from each of 6 different companies, each person shook hands once with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place
Answer:
135
Step-by-step explanation:
From the given information:
The total number of handshakes can be represented by the combination of 18 combination 2, which can be mathematically expressed as:
[tex]\mathbf{^{18}C_2}[/tex] .
where;
[tex]\mathbf{^{18}C_2}[/tex] is the number of ways two people can shake themselves from a total of 28 people without much regard about the order of arrangement of the handshakes.
[tex]\mathbf{^{18}C_2 = \dfrac{18!}{2!(18-2)!}}[/tex]
[tex]\mathbf{= \dfrac{18!}{2!(16)!}}[/tex]
= 153
From these 6 companies, the possibility that there will be handshakes from within the company is [tex]\mathbf{^3 C_2}[/tex]
[tex]\mathbf{^3 C_2} = \dfrac{3!}{2!(3-2)!}[/tex]
[tex]= \mathbf{ \dfrac{3 \times 2!}{2!(1)!}}[/tex]
= 3
However, number of companies = 6
∴ the number of handshakes within companies = 3 × 6 = 18
But we are being told that :
If the representatives did not shake hands with people from their own company, how many handshakes took place
Therefore, the number of handshakes that took place in regard to the given criteria = 153 - 18
= 135
a bus is leaving the bus station at 5:45 p.m. and it takes 2 days 6 hours 30 minutes to reach a destination if the bus leaves on Friday what will be the day and time when it arrive it destination?
Answer:
Monday, at 12:15 AM
Step-by-step explanation:
Do this question in parts. First, add 2 days to Friday to get Sunday at 5:45 PM. Then, add 6 hours to 5:45 to get 11:45 PM. Finally, add 30 minutes to 11:45 PM. That takes you to 12:15, and since you passed midnight, Sunday is now Monday. That means the bus arrives Monday, at 12:15 AM.
Define square root. Give an example.
Answer:
A square root of a number is a value that, when multiplied by itself, gives the number.
Example: 4 × 4 = 16, so a square root of 16 is 4.
The symbol for a square root is √ which always means the positive square root.
Example: √36 = 6 (because 6 x 6 = 36)
Katherine bought 7 yards of streamers, 25 balloons, and five spools of ribbon to use for party decorations. Each spool contained 500 feet of ribbon. What was the total length of the streamers and ribbon Katherine bought?
George said that 6 x 10 to the 3 power is 180. do your Agree of Disagree? if you disagree explain the mistake he made and the correct answer. (HELP)
Answer:
The correct answer is 6000
Step-by-step explanation:
I disagree because 10 to the 3rd power = 1000 x 6 = 6000
The mistake he made was that George multiplied all of the number so, 6 x 10 x 3 = 60 x 3 = 180.
What is the solution to the equation
X/6 = 4/12
X=1
x= 2
x=4
x = 6
Answer:
x = 2
because we have the same question and i got it right its hard to explain but trust me its x = 2
The solution to the given equation is 2. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is x/6 = 4/12.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, x/6 = 4/12
By cross multiplication, we get
12x=24
⇒ x=2
The solution to the given equation is 2. Therefore, option B is the correct answer.
To learn more about the solution of an equation visit:
https://brainly.com/question/14506845.
#SPJ2
what transformation(s) is taking place i’ll mark u the brainliest if u help
Answer:
Reflection, Translation, and possibly Rotation
Parvin often cleans the dishes with her mother she can clean 17 plates in 10 minutes how many plays country clean in different amounts of time
Point B lies between points A and C on Line segment A C . Let x represent the length of segment AB in inches.
Answer:
5,5,15
Step-by-step explanation:
Two trains leave stations 342 miles apart at the same time and travel toward each other. One train travels at 105 miles per hour while the other travels at 85 miles per hour. How long will it take for the two trains to meet?Do not do any rounding.
Answer:
1.8 hours.
Step-by-step explanation:
It is important to note that:
Speed = Distance ÷ Time
We have two trains.
Step 1
We have to find the distance that each train travelled.
Since Speed = Distance ÷ Time
Distance = Speed × Time
First train
It travels at 105 miles per hour
Distance travelled by first train =
105 × x hours
= 105x miles
Second Train
It travels at 85 miles per hour
Distance travelled by the second train = 85 miles × x hours
= 85x miles
We are told that: the two trains leave stations 342 miles apart at the same time and travel toward each other
Hence, the time it would take each train to meet each other is calculated as:
105x + 85x = 342 miles
190x = 342 miles
x = 342/190
x = 1.8 hours.
Simplify. 1/2−3(1/2+1)^2
Answer:
-6.25
Step-by-step explanation:
The answer is -6.25.
Write an expression to represent:
Eight more than the product of two and a number
x
xx.
Answer:
2x+8
Step-by-step explanation:
The mathematical expression will be;
⇒ 2x + 8
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
⇒ '' Eight more than the product of two and a number x''.
Now,
Since, The algebraic expression is,
⇒ '' Eight more than the product of two and a number x''.
Hence, We get the mathematical expression as;
⇒ Product of 2 and number x = 2x
And, 8 more than 2x = 2x + 8
Thus, We get the mathematical expression as;
⇒ 2x + 8
Learn more about the mathematical expression visit:
brainly.com/question/1859113
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Simplify the following expression: a + 2c − 5b − c + a − b 2a − 6b + 2c 2a − 6b + c a − 6b + c a − 5b + 2c
Answer:
=−ab2+2ac2+2ac+2a−28b+3c
Step-by-step explanation:
a+2c−5b−c+a−b2a−6b+2c2a−6b+ca−6b+ca−5b+2c
=a+2c+−5b+−c+a+−ab2+−6b+2ac2+−6b+ac+−6b+ac+−5b+2c
Combine Like Terms:
=a+2c+−5b+−c+a+−ab2+−6b+2ac2+−6b+ac+−6b+ac+−5b+2c
=(−ab2)+(2ac2)+(ac+ac)+(a+a)+(−5b+−6b+−6b+−6b+−5b)+(2c+−c+2c)
=−ab2+2ac2+2ac+2a+−28b+3c
Answer:
=−ab2+2ac2+2ac+2a−28b+3c
Answer:
B. 2a − 6b + c
Step-by-step explanation:
Took the test :)
14. If EF bisects CD, CG = 5x - 1, GD = 7x - 13, EF = 6x - 4, and GF = 13, find EG.
3. EF = 6-a. and Cr -13, cihad ES
Greetings from Brasil....
As stated in the statement of the question, EF is a bisector of CD, so point G is the median point of CD, so CG = GD
5X - 1 = 7X - 13
X = 6
EF = EG + GF
6X - 4 = EG + 13 x = 6, so
6·6 - 4 = EG + 13
EG = 19(see attachment)
in each question,first make an inequality, then solve the inequality
1) A rectangle is 8cm long and b cm broad.find the range of values of b if the perimeter of the rectangle is not greater than 50 cm and not less than 18cm
2) the sides of a triangle are x cm,x+3 cm, find the lowest value of x.
Answer:
a) The perimeter of a rectangle is written as:
P = 2*L + 2*W
where L is the length amd W is the width (broad in this case).
here we have:
L = 8cm and W = b
then the perimeter is:
P = 2*8cm + 2*b
And we know that:
18cm ≤ P ≤ 50cm
where ≤ is used because there is written "not more" and "not less", so the equalities are allowed
now we can replace P by the above equation:
18cm ≤ 16cm + 2*b ≤ 50cm
now we can subtract 16cm in each side and get:
18cm - 16cm ≤ 2*b ≤ 50cm - 16cm
2cm ≤ 2*b ≤ 34cm
Now we can divide each side by 2.
1cm ≤ b ≤ 34cm/2 = 17cm
1cm ≤ b ≤ 17cm.
b) Here we have missing information, so this can not be answered.
(only knowing that one side length is x, and another side length is x + 3cm, we can know that x > 0cm, so the minimum value of x is really close to 0cm)
given that is a = 3 , b = -4 and c = -2 evaluate 3a - b / 2c + 3a - c / c - b
Answer:
5.2
Step-by-step explanation:
= 3a - b / 2c + 3a - c / c - b
= 3(3) - (-4) / 2(-2) + 3(3) / -2 -(-4)
= 9 + 4 / -4 + 9 / -2+4
= 13 / 5 / 2
= 13 / 5 * 2
= 2.6 * 2
= 5.2
Answer:
Step-by-step explanation:
[tex]\frac{3a -b}{2c}+\frac{3a-c}{c-b}=\frac{3*3-[-4]}{2*(-2)}+\frac{3*3-[-2]}{-2-[-4]}\\\\=\frac{9+4}{-4}+\frac{9+2}{-2+4}\\\\=\frac{13}{-4}+\frac{11}{2}\\\\=\frac{-13}{4}+\frac{11*2}{2*2}\\\\=\frac{-13}{4}+\frac{22}{4}\\\\=\frac{-13+22}{4}\\\\=\frac{9}{4}\\\\=2\frac{1}{4}[/tex]
5(7x+8y) simplified
Answer:
35x+40y
Step-by-step explanation:
1. expand the terms by multiplying 5 by what's inside the parenthesis, so multiply by 7x and 8y and add them. So you get 35x+40y
Answer:
35x +40y
Step-by-step explanation:
5(7x+8y)
Distribute
5*7x + 5*8y
35x +40y