Step-by-step explanation:
Hey there!
To solve this type of question, you must take square of variable"X" to right side making it ±squareroot. As it is a quadratic equation it will have two values (±).
Given;
[tex] {x}^{2} = 16[/tex]
Taking (square) to right side. It becomes ± square root.
[tex]x = + - \sqrt{16} [/tex]
[tex]x = + - \sqrt{ {4}^{2} } [/tex]
Cancel square and square root.
[tex]x = + - 4[/tex]
Therefore, X = ±4
Hope it helps...
Answer:
There are two I results found which is x=4 and x=-4
Step-by-step explanation:
Step by Step Solution:
More Icon
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2-(16)=0
Step by step solution :
STEP
1 :
Trying to factor as a Difference of Squares:
1.1 Factoring: x2-16
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (x + 4) • (x - 4)
Equation at the end of step
1 :
(x + 4) • (x - 4) = 0
STEP
2 :
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Solving a Single Variable Equation:
2.3 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4 and/or x=-4
A state forest service is conducting a study of the people who use state-operated camping facilities. The state has two camping areas, one located in the mountains and one located along the coast. The forest service wishes to estimate the average number of people per campsite during a popular weekend when all sites are expected to be used. There are 50 campsites in the mountains and 100 along the coast. From experience, the forest service knows that most sites in the mountains contain from 1-6 people and most sites along the coast contain from 1-10 people. Suppose the forest service can afford to conduct 20 interviews (e.g. they can select 20 campsites) (because they are asking many other questions in addition to number of people using the campsite and they want to do the interviews in person).
Using Neyman allocation, how would you suggest they allocate the 20 interviews among these 2 strata to minimize the standard error of the estimate of the overall average number of people per campsite?
Answer:
Allocation: 4 samples should be from the mountain and 16 from along the coast.
Step-by-step explanation:
Neyman allocation is technique of sample allocation used in cases of stratified sampling.
The formula to compute the best sample size of each stratum is:
[tex]n_{h}=n\times \frac{(N_{h}\times SD_{h})}{\sum\limits^{k}_{i=1}(N_{i}\times SD_{i})}[/tex]
The information provided is:
[tex]N_{m}=50\\N_{c}=100\\n=20\\[/tex]
Compute the range for the number of people at the mountain campsite as follows:
[tex]R_{m}=6-1=5[/tex]
Then the standard deviation for the number of people at the mountain campsite will be:
[tex]SD_{m}=\frac{R_{m}}{4}=\frac{5}{4}[/tex]
Compute the range for the number of people along the coast campsite as follows:
[tex]R_{c}=10-1=9[/tex]
Then the standard deviation for the number of people along the coast campsite will be:
[tex]SD_{c}=\frac{R_{c}}{4}=\frac{9}{4}[/tex]
Compute the sample size for the mountain campsite as follows:
[tex]n_{m}=n\times \frac{(N_{m}\times SD_{m})}{(N_{m}\times SD_{m})+(N_{c}\times SD_{c})}[/tex]
[tex]=20\times \frac{(50\times (5/4))}{(50\times (5/4))+(100\times (9/4))}\\\\=20\times 0.2174\\\\=4.348\\\\\approx 4[/tex]
Compute the sample size for along the coast campsite as follows:
[tex]n_{c}=n-n_{m}=20-4=16[/tex]
Thus, 4 samples should be from the mountain and 16 from along the coast.
What is the domain and range of the function?
Answer: input values for the function.
Step-by-step explanation:
find the distance between (5,2) and (−1,9)
Answer:
[tex]d=9.21954[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in the 2 coordinates into the distance formula to find distance d:
[tex]d=\sqrt{(-1-5)^2+(9-2)^2}[/tex]
[tex]d=\sqrt{(-6)^2+(7)^2}[/tex]
[tex]d=\sqrt{36+49}[/tex]
[tex]d=\sqrt{85}[/tex]
[tex]d=9.21954[/tex]
Find the perimeter and area of a rectangle of cardboard measuring 15.9 cm by 11.7cm
2
1
3
4
The statement “Angle 2 is congruent
to angle 4" is justified by the
a
b
Alternate Interior Angles Theorem
Definition of Linear Pair
Vertical Angles Theorem
Definition Corresponding Angles.
The statement “Angle 2 is congruent to angle 4" is justified by the Vertical Angles Theorem. Option C is correct.
A mathematical proposition or assertion that has been proven to be true is known as a theorem.
According to this theorem, when two straight lines cross, they create two sets of linear pairs with matching angles. The adjacent angles created by the junction of these two lines are likewise said to be supplementary, or equivalent to 180 degrees.
It is given that,
∠2=∠4
From the diagram, it is observed that two straight lines cross, and they create two sets of linear pairs with matching angles as a result of the Vertical Angles Theorem angle 2 is congruent to angle 4.
Thus, the statement “Angle 2 is congruent to angle 4" is justified by the Vertical Angles Theorem. Option C is correct.
Learn more about the Theorem here:
brainly.com/question/12642646
#SPJ5
HELPP!!
if f(x)= 5x - 12 what is f(-4)
Answer:
-32
Step-by-step explanation
f(-4)= 5(-4) - 12
f(-4)= -20 -12
f(-4)= -32
what is the opposite of 1/2
Answer:
The opposite of 1/2 is -2/1, which can also be written as -2.
Identify the slope and intercept of the following linear equation.
y=3/7x-5
A. Slope: 3/7; intercept: 5
B. Slope: 3/7; intercept: -5
C. Slope: 5; intercept: 3/7
D. Slope: -5; intercept: 3/7
Answer:
3/7 is the slope and -5 is the y intercept
Step-by-step explanation:
y=3/7x-5
The equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
3/7 is the slope and -5 is the y intercept
Answer:
B
Step-by-step explanation:
The slope is always the coefficient of the x value in the linear equation. And the y intercept is the constant in the equation.
Which model is 85% Shaded
Answer:
cant tell
Step-by-step explanation:
need more explanation
I WILL GIVE BRAINLIEST TO WHOEVER HELPS ME!!
Answer:
it changes by -4 pounds each month
Step-by-step explanation:
20 pounds in 5 months
20/5 is 4 pounds per month
the elephant loses 4 pounds a month
2 ton of rocks cost $2,920.00. What is the price per pound?
Answer:
$0.73 per pound
Step-by-step explanation:
2920 divided by 4000 (2 tons is 4000 pounds) equals 0.73
tan theta equals 8 / 15 find sine theta + cos theta / cos theta (1 - cos theta)
I guess you have to find
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}[/tex]
given that [tex]\tan\theta=\frac8{15}[/tex].
We can immediately solve for [tex]\sec\theta[/tex]:
[tex]\sec^2\theta=1+\tan^2\theta\implies\sec\theta=\pm\dfrac{17}{15}[/tex]
(without knowing anything else about [tex]\theta[/tex], we cannot determine the sign)
Then we get [tex]\cos\theta[/tex] for free:
[tex]\cos\theta=\dfrac1{\sec\theta}=\pm\dfrac{15}{17}[/tex]
and we can now solve for [tex]\sin\theta[/tex]:
[tex]\sin^2\theta+\cos^2\theta=1\implies \sin\theta=\pm\dfrac8{17}[/tex]
Notice that we have 2*2 = 4 possible choices of sign for either sin or cos.
• If both are positive, then
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{391}{90}[/tex]
• If both are negative, then
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{391}{480}[/tex]
• If sin is positive and cos is negative, then
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{119}{480}[/tex]
• If cos is positive and sin is negative, then
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{119}{30}[/tex]
Factor the expression 1/4x + 11/4
Answer:
1 /4 ( x+11 )
Step-by-step explanation:
Factor 1 /4 out of each term.
(3x+2)/5 =31 PLEASE HELP FAST
Answer:
x = 51
Step-by-step explanation:
3 x 51 = 153, 153 + 2 = 155, 155 / 5 = 31
Answer:
x=51
Step-by-step explanation:
3x+2=155
3x+2-2=155-2
3x=153
3x/3 = 153/3
x=51
It is known that
solve for the value of x algebraically,
Here’s a picture too for the other ones I need help with please
Step-by-step explanation:
Complementary Angles add up to 90 degrees since both m∠BAM and m∠CTX are known to be complementary, they must add up to 90 degrees. So....
[tex]m∠BAM + m∠CTX = 90 \\ (2x +4) + (x + 11) = 90 \\ 3x +15 = 90 \\ -15 + 3x +15 = 90 -15 \\ 3x = 75 \\ \frac{3x}{3} = \frac{75}{3} \\ x = 25[/tex]
Answer:[tex]x = 25[/tex]
what is the nineteenth term in the sequence 7, 10, 13, 16,...? A 64 B 61 C 57 D 19
Answer:
B. 61
Step-by-step explanation:
7, 10, 13, 16...
ok so were starting with 7 and adding 3 every time
im going to do 3 times 19 like as if we started with 3 then im going to add 4
3 x 19 = 57
57 + 4 = 61
the 19th term is 61
Answer:
B: 61
Step-by-step explanation:
Hope this helps :)
What’s the domain of (2x-9)/(3-x)
Answer:
The domain in interval notation would be (−∞,3)∪(3,∞) In set builder notation it would be {x|x≠3}
5,5,3 Is this a triangle? Explain.
8,8,8,Is this a triangle? Explain.
7,8,15 Is this a triangle? Explain.
5,6,10 Is this a triangle? Explain.
No clown answers or you'll get reported please help me I have until 3:00 am desperate please solve
Answer:
None of these points form a right triangle.
Step-by-step explanation:
IF YOU'RE TRYING TO FIND IF THE POINTS FORM A RIGHT TRIANGLE, THIS SHOULD WORK.
5,5,3 Explantation: To first start things off, we know our hypotenuse is the longest side of the right triangle. Using this information, we know that 5*2( 5 squared) is 25 and that 3 squared is 9. Now we add these two points and we get 34. (Don't forget to square the other side.) Now we have 34=25 which is not true sooo we know the points given do not form a RIGHT triangle.
The same goes with the other points. Once you solve them, neither of them form a right triangle. (Don't forget that we use a*2 + b*2=c*2) (The c should be the biggest point given!)
Hope this helps, if you have any questions please feel free to ask! :)
2/3 plus 6 1/5
pls also thank you if you do and you get brainlist
Confused PLEZZZZZ HELLLPPPP
Answer:B
Step-by-step explanation:
Answer:
believe it is the last one because the room is decreasing at 4 per minute so it would be -4x. Then the room is a 300 capacity so you would minus the -4x from the 300 leaving the formula as p(x)=300-4x
can you guys help me?
Answer:
I am doing this for the gram say hi
Step-by-step explanation:
Evaluate 3x-4 when x=7
Answer:
17
Step-by-step explanation:
We plag the var in first
3(7)-4
21-4
17
Answer:
17
Step-by-step explanation:
3(7) - 4
21 - 4
17
Hope this helps!
what is the total of 87,326;17 and 60
Answer: 490
Step-by-step explanation: 87+17+60+326 = 490
Simplify the fraction -24/6 then add -2
Answer:
-6
Step-by-step explanation:
-24 divided by 6 is -4, so the fraction would be simplified to -4/1, then change to a whole number and subtract 2, which equals -6.
What are the two values on a number line that are a
distance of 5 from 0?
Answer:
the two values that are a distance of 5 from 0 are -5 and 5.
Step-by-step explanation:
if you look at a number line, you will see that the number 0 is in the middle. if you count 5 from each side, it's -5 and 5. any other number would have a greater distance than 5 from 0. hope this helps.
Carlos earns $7.50 per hour cutting grass on the weekends with his dad. Last Saturday, he worked 5 and 1 over 2 hours. On Sunday he worked 8.5 hours. How much money did Carlos earn last weekend?
Answer:
$105
Step-by-step explanation:
5.5+8.5=14
14 * 7.5=105
d = rt, for r
Someone please help me out?
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
All you have to do is divide the t on both sides and you'll get...
[tex]r=\frac{d}{t}[/tex]
The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 10% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of eight adult friends, what is the probability of the following? (Round your answers to three decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
(a) no one has done a one-time fling
(b) at least one person has done an one time fling
(c) no more than two people have done a one time fling
Answer:
..
Step-by-step explanation:
(2x+4) + (3x-9) simplify
A scientist measured the water pressure at different depths. She made a table showing her findings. The x-values represent the depth, in meters. The y-values represent the pressure in atmospheres (atm).
x
y
0
0
15
3
30
6
Assuming there is a proportional relationship, which additional set of values could be included in the table?
Answer:
100,70 is the answer I took the test
Answer:
The answer is A ppl
Step-by-step explanation:
