Answer:
8 divided by p
Step-by-step explanation:
what are the solutions of 4(x+6)^2=52
ANSWER: 1.211 or 13.211
Step-by-step explanation:
STEP
1
:
1.1 Evaluate : (x-6)2 = x2-12x+36
Trying to factor by splitting the middle term
1.2 Factoring x2-12x-16
The first term is, x2 its coefficient is 1 .
The middle term is, -12x its coefficient is -12 .
The last term, "the constant", is -16
Step-1 : Multiply the coefficient of the first term by the constant 1 • -16 = -16
Step-2 : Find two factors of -16 whose sum equals the coefficient of the middle term, which is -12 .
-16 + 1 = -15
-8 + 2 = -6
-4 + 4 = 0
-2 + 8 = 6
-1 + 16 = 15
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
1
:
x2 - 12x - 16 = 0
STEP
2
:
Parabola, Finding the Vertex
2.1 Find the Vertex of y = x2-12x-16
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 6.0000
Plugging into the parabola formula 6.0000 for x we can calculate the y -coordinate :
y = 1.0 * 6.00 * 6.00 - 12.0 * 6.00 - 16.0
or y = -52.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-12x-16
Axis of Symmetry (dashed) {x}={ 6.00}
Vertex at {x,y} = { 6.00,-52.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-1.21, 0.00}
Root 2 at {x,y} = {13.21, 0.00}
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-12x-16 = 0 by Completing The Square .
Add 16 to both side of the equation :
x2-12x = 16
Now the clever bit: Take the coefficient of x , which is 12 , divide by two, giving 6 , and finally square it giving 36
Add 36 to both sides of the equation :
On the right hand side we have :
16 + 36 or, (16/1)+(36/1)
The common denominator of the two fractions is 1 Adding (16/1)+(36/1) gives 52/1
So adding to both sides we finally get :
x2-12x+36 = 52
Adding 36 has completed the left hand side into a perfect square :
x2-12x+36 =
(x-6) • (x-6) =
(x-6)2
Things which are equal to the same thing are also equal to one another. Since
x2-12x+36 = 52 and
x2-12x+36 = (x-6)2
then, according to the law of transitivity,
(x-6)2 = 52
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-6)2 is
(x-6)2/2 =
(x-6)1 =
x-6
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-6 = √ 52
Add 6 to both sides to obtain:
x = 6 + √ 52
Since a square root has two values, one positive and the other negative
x2 - 12x - 16 = 0
has two solutions:
x = 6 + √ 52
or
x = 6 - √ 52
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-12x-16 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -12
C = -16
Accordingly, B2 - 4AC =
144 - (-64) =
208
Applying the quadratic formula :
12 ± √ 208
x = ——————
2
Can √ 208 be simplified ?
Yes! The prime factorization of 208 is
2•2•2•2•13
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 208 = √ 2•2•2•2•13 =2•2•√ 13 =
± 4 • √ 13
√ 13 , rounded to 4 decimal digits, is 3.6056
So now we are looking at:
x = ( 12 ± 4 • 3.606 ) / 2
Two real solutions:
x =(12+√208)/2=6+2√ 13 = 13.211
or:
x =(12-√208)/2=6-2√ 13 = -1.211
Answer: X=root of14 -6; x = -root of14 -6
Explanation: Symbolab.com
The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?
1) The complex numbers have equal imaginary parts.
2) The complex numbers have equal real parts.
3) The complex numbers have opposite imaginary parts.
4) The complex numbers have opposite real parts.
Answer:
4
It is right on edge
Answer:
the complex numbers have opposite real parts
Step-by-step explanation:
just took it on edge;)
Which statement describes A′B′?
Answer:
1 answer to your question
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positivethat is, the probability that the bureau finds a match, given that the lead at the crime scene and the lead in the possession of the suspect are actually from two different "melts," or sources. To estimate the false positive rate, the bureau collected bullets that the agency was confident all came from different melts. Then, using its established criteria, the bureau examined every possible pair of bullets and found matches. Use this information to compute the chance of a false positive.
Answer:
The correct solution will be "32.22%".
Step-by-step explanation:
The given values are:
X = 612
n = 1899
As we know,
⇒ [tex]P=\frac{X}{n}[/tex]
On substituting the above values, we get
⇒ [tex]=\frac{612}{1899}[/tex]
⇒ [tex]=0.3222[/tex]
So that the chance of false positive will be "32.22%".
Find the x-intercept and y-intercept of the line -8x+5y=18
x intercept is -2.25 and y intercept is 3.6
If Lindsay makes $9 per hour, h, of babysitting. She made a total of $63 babysitting yesterday.
Answer:
7 hours
Step-by-step explanation:
9 x 7 = 63
i suck at geometry pls help
Answer:
A line supplementary to AOD is AOC.
A line adjacent and congruent to AOE is COE (I think)
A line supplementary to EOA is EOC
A line complimentary to EOD is DOC
DOC and AOB are vertical angles.
Step-by-step explanation:
I think all of those are correct.
please helppp need the answers
Some members of the Ruiz family are getting tickets for Fireworks Night at the ballpark. Tickets cost $5 each. 17 of the tickets they get are for children and 13 are for adults. How much will the tickets cost in all?
Answer:
$150
Step-by-step explanation:
The price does not change for children and adults. They bought 30 tickets total since 17 + 13 = 30. 30*5 = 150. So they spent $150.
[3, 17): у 2 — 5х + 2
у = -3х + 7
What’s the solution ?
Answer:
The Answer Is 4 - 5x
Step-by-step explanation:
[3, 17): у 2 — 5х + 2
у = -3х + 7
Simplify=
4 - 5x
Hope This Helps
Can someone please help me with this
Answer:
3.72 x 100000000= 372000000
1.2 x 100000 = 120000
Step-by-step explanation:
idek
Pam is making icing for a birthday cake. The ratio of milk to powdered sugar is 2
tablespoons of milk to 15 tablespoons of powdered sugar.
If Pam uses 7 tablespoons of milk, how much powdered sugar will she need?
Answer:
She will need 52.5 table spoons of sugar
Step-by-step explanation:
2:15= 1:7.5
7tbs*1=7tbs of milk
7tbs*7.5=52.5tbs of sugar
Answer:
52.5
If you multiply the tbs of milk to the tbsp of sugar, then you will get 52.7!: )
Step-by-step explanation:
HOPE THIS HELPS~ :)
BRAINLIEST?
Health insurance benefits vary by the size of the company. The sample data below show the number of companies providing health insurance for small, medium, and large companies. For purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1,000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company.
Health Insurance
Size of the Company Yes No Total
Small 36 14 50
Medium 65 10 75
Large 88 12 100
A. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p-value? Compute the value of the χ2 test statistic (to 2 decimals). Using α .05 level of significance, what is your conclusion?
B. A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number). Based on the percentages calculated above, what can you conclude?
Answer:
A) The critical value found is 5.99 which is < the test statistic value ( 6.94 ) hence we will reject the null hypothesis (H₀)
The P-value associated is : 0.031 which is < 0.05 ( level of significance )
B) from the calculation it can be sen that employees of small companies are more likely without health insurance
Step-by-step explanation:
A) To conduct a test of independence
we apply the hypothesis test
Null hypothesis (H₀) = The health insurance coverage is independent of the size of the company
Alternative hypothesis (H₁) = The health insurance coverage is not independent of the size of the company
The test statistic is calculated as attached below
also the expected values are attached below indicating the formula used
E = expected value
O = observed value
Test statistic value ( as calculated ) = 6.94
The critical value found is 5.99 which is < the test statistic value ( 6.94 ) hence we will reject the null hypothesis (H₀)
The P-value associated is : 0.031 which is < 0.05 ( level of significance )
B) percentage of employees without health insurance
Small company : 14/50 * 100 = 28%
medium company: 10/75 * 100 = 13%
large company : 12/100 * 100 = 12%
from the above calculation it can be sen that employees of small companies are more likely without health insurance
Solve for x.
3x/2 = 15
x = 10 1/2
x = 1/10
x=22 1/3
x = 10
Answer:
x = 10
Step-by-step explanation:
3x/2 = 15
cross multiply
3x = 15 × 2
3x = 30
divide both sides by the coefficient of x
3x/3 = 30/3
x = 10
ratio 5: 12 if there are 50 trucks how many cars are there
If the 50 trucks represent the 5 in the ratio 5:12, then there are 120 cars.
A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole. Note that the two triangles are proportional to one another. a = 3, b = 7, c = 28
Answer:
Step-by-step explanation:
B
These two triangles are similar then the ratio of their corresponding sides will remain constant. Then the value of h is 65.33 units.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
A man places a mirror on the ground and sees the reflection on the top of a flagpole as shown in the figure below.
The two triangles in the figure are similar.
Note that the two triangles are proportional to one another. a = 3, b = 7, c = 28
If both triangles are similar then the ratio of their corresponding sides will remain constant.
Then we have
[tex]\rm \dfrac{h}{b} = \dfrac{c}{a}\\\\h \ = b \times \dfrac{c}{a}\\\\h\ = 7 \times \dfrac{28}{3}\\\\h \ = 65.33[/tex]
More about the triangle link is given below.
https://brainly.com/question/25813512
4x - 14 + 3x= 161
Will mark brainliest
Answer:
x=25
Step-by-step explanation:
What two intergers does 7 fall into
Answer:
Step-by-step explanation:
The square of 2, -2 is 4. square of 3, -3 is 9. so square root of 7 has to be less than 3 but more than 2. therefore the integers are either 2 and 3 or -3 and -2.
Answer:
2 and 3
Step-by-step explanation:
[tex]\sqrt{7}[/tex]= 2.645....
Hope this helps. Please give me brainliest.
What can be done to the graph of y=2x2+3 to obtain the graph of y=−2x2+3?
Answer:
Reflect over the x-axis.
Step-by-step explanation:
Assuming you meant 2x^2+3, putting a negative sign in front of the x value flips the graph over the x-axis.
Use synthetic division to find the quotient.
(2x3 + 3x2 - 4x + 15) = (x + 3)
Answer:
2x3 - 3x2 - 4x + 15
———————————————————
x + 3
What is the future value (total amount due) on a $12,000 loan at 8% compounded
semiannually (twice a year) for 7 years?
Answer: $20,780.10
Step-by-step explanation:
You need the Compound Interest Formula
A = P(1 + r/n)^nt
Step 1: Create the equation.
12,000(1 + 0.08/2)¹⁴
Step 2: Solve the equation.
Follow PEMDAS (parenthesis, exponents, multiplication...)
Parenthesis: (1 + 0.08/2) = (1 + 0.04) = (1.04)
Exponents: (1.04)¹⁴ = (1.73168)
Multiplication: 12,000(1.73168) = 20,780.1
what does 5/4 divided by 10 equal????
DEADLINE TOMORROW
Answer:
0.125. sorry if it's wrong. (Disclaimer: Math is not my best subject :) )
Step-by-step explanation:
5/4÷10 on a calculator
William keeps several tanks of exotic fish at his house. He feeds them 4 containers of fish food each day. Each container of fish food cost $2.00. How much money does William spend on fish food in one week?
This is for my daughters 4th grade math class....She needs to have a “plan, estimate, solve, and number model”. This is a addition and subtraction problem its can’t be multiplied!
PLEASE HELP THIS MOM WHO IS TERRIBLE WITH THIS COMMON CORE MATH!
Answer: $56
Step-by-step explanation:
Each day he feed them 4 fish food containers. How many days is a week 7. So 7x4 is 28. All we have left over is $2.00
so we just multiply 28x2. That sums up to $56!
HELP ILL GIVE BRAINLIEST!! Andrea is planning on taking the train to go to the beach, a train travels at a constant speed. An equation relating the distance traveled in miles, m, to the number of minutes, t is t = 3m . If Andrea arrived at the beach in an hour and 15 minutes, how much distance did she travel?
Answer:
225 miles I think
Step-by-step explanation:
75x3=225
tl;dr: Andrea traveled 3 [tex]\frac{3}{4}[/tex] miles.
Hello!
To solve the problem, we need to understand what it means. The distance traveled in miles is represented with t, while the number of minutes is represented with m.
Now, first we need to fill in the equation with the information we're given.
t = 3m → t = 3(1 [tex]\frac{1}{4}[/tex])
Now, we solve for t.
t = 3(1 [tex]\frac{1}{4}[/tex]) → t = 3 [tex]\frac{3}{4}[/tex]
Andrea traveled 3 [tex]\frac{3}{4}[/tex] in an hour and 15 minutes.
Hope this was helpful. Have a great day! (★‿★)
What is the solution to 5(2n+4)=−2(4n−1) ?
Answer: n= -1
Step-by-step explanation:
simplify by distributing:
5(2n+4)=-2(4n-1)
10n+20=-8n+2
add 8n to both sides:
10n+20=-8n+2
+8n +8n
————————
18n+20=2
subtract 20 from both sides
18n+20=2
-20 -20
————————
18n=-18
divide both sides by 18:
18n/18 = -18/18
n = -1
question is complete!
w (n) = n^2-n find w (-3)
Answer:
[tex]w(-3) = 12[/tex]
Step-by-step explanation:
Plug in -3 for n in the equation:
[tex]w(n) = n^2 - n[/tex]
[tex]w(-3) = (-3)^{2} - (-3)[/tex]
Simplify. Remember to follow PEMDAS. First, solve the power:
[tex]w (-3) = (-3)^2 - (-3)\\w (-3) = (-3 * -3) - (-3)\\w (-3) = (9) - (-3)[/tex]
Next, combine like terms. Note that if there are two negative signs directly next to each other, it becomes a positive sign. Add:
[tex]w(-3) = 9 - (-3)\\w(-3) = 9 + 3\\w(-3) = 12[/tex]
Your answer: [tex]w(-3) = 12[/tex]
PLEASE HELP!!!
Give a real-life situation of angle measurement
Answer:
A clock forms an example of angles in real life.
Step-by-step explanation:
What is the slope of the graph of y = 12x – 19? What is the equation in slope-intercept form of the line that passes through the points (-4,2) and (12,6) ?
Answer:
Step-by-step explanation:
1. The slope is 12
2. (6 - 2)/(12+4)= 4/16= 1/4
y - 2 = 1/4(x + 4)
y - 2 = 1/4x + 1
y = 1/4x + 3
Write an equation in point-slope form for the line that passes through the points (3, -5) and (1, -8).
Answer:
m = y2 - y1 / x2 - x1 -8 - (-5)/1-3
-8 +5/1-3
-3/-2
slope is 1 1/2
Step-by-step explanation:
Hope this helps :)
What do you get when you add 3 1/4 and 5 3/4?
2.
What is the answer to 6 2/3 + 5 3/4?
3.
How much is 18 – 4 1/5?
Answer:
HI THERE 1. is 9 2. is 7.08 and 3. is 13.8 pls mark brainlist
Step-by-step explanation:
Answer:
#1 is 9
#2 is 12 and 5/12
#3 is 69/5 or 13.8