Answers
Answer:
1. x² - 16x = -12
2. x² - 16x + 64 = -12 + 64
3. (x - 8)² = 52
4. x - 8 = ± √52
5. x = 8 ± √52
6. x = 8 ± 2√13
Step-by-step explanation:
1. Move the constant to the other side of the equation:
x² - 16x +12-12 = 0-12
x² - 16x = -12
2. Find the new value of c by using the formula [tex](\frac{b}{2} )^{2}[/tex]
[tex](\frac{-16}{2} )^{2}\\\\(-8)^{2} \\\\c =64[/tex]
3. Plug the new value of c into the equation. Make sure to add it to both sides of the equation, because if you do something to one side, you must do it to the other:
x² - 16x + 64 = -12 + 64
x² - 16x + 64 = 52
4. Form a perfect sqaure by factoring -16 and 64 by figuring out two numbers that have a sum of -16 and a product of 64:
-8 + (-8) = -16
-8 · (-8) = 64
(x - 8)²
Plugging this into the equation:
(x - 8)² = 52
5. Take the square root of both sides:
√(x - 8)² = √52
x - 8 = √52
6. Isolate x:
x - 8+8 = 2√52+8
x = 8 ± 2√52
52 can be squared, so:
x = 8 ± 2√13
hope this helps!
Related Questions
everday at 9:15 am jessie takes his for a walk for 30 min he takes the next 2 hours to work on his computer before he eats lunch what time does he eat lunch
Answers
Answer:
11:45 AM
Step-by-step explanation:
9:15 +30 mins is 9:45
9:45 +2 hours is 11:45
Hope this helps!
equation of circle: mastery test HELPPPP PLS !!
Answers
PQ is the diameter so the midpoint of PQ is the center of the circle. if we suppose the center point of the circle called o then ;
[tex]o = \frac{pq}{2} \\ [/tex]
[tex]pq = \sqrt{ { (- 10 - 6})^{2} + ({10 - ( - 2)})^{2} } [/tex]
[tex]o = \frac{( -10 ,10) + (6 , - 2) }{2} \\ [/tex]
[tex]o = \frac{( - 10 +6 ,10 - 2)}{2} \\ [/tex]
[tex]o = ( \frac{ - 4}{2} , \frac{8}{2} ) \\ [/tex]
[tex]o = ( - 2,4)[/tex]
For the second step we need to find the radius of the circle which has the half the PQ distance measure, so we have to find the the PQ distance and divide it by 2 :
_____________________________________________
As u know the distance between 2 point is going to find by following formula :
[tex]pq = \sqrt{ {(x(p) - x(q)})^{2} + {(y(p) - y(q)})^{2} } \\ [/tex]
[tex]pq = \sqrt{ ({ - 10 - 6})^{2} + ({10 - ( - 2)})^{2} } [/tex]
[tex]pq = \sqrt{ ({ - 16})^{2} + ({12})^{2} } [/tex]
[tex]pq = \sqrt{256 + 144} [/tex]
[tex]pq = \sqrt{400} [/tex]
[tex]pq = 20[/tex]
Thus :
[tex]radius = \frac{pq}{2} \\ [/tex]
[tex]radius = \frac{20}{2} \\ [/tex]
[tex]radius = 10[/tex]
_____________________________________________
Ok we're almost done cuz we have what we needed:
If we suppose that the first coordinate of the center is a and the second coordinate of the center is b and the radius shown by r then :
[tex] ({x -a})^{2} + ( {y - b})^{2} = {r}^{2} [/tex]
Is the equation of the circle in the standar form thus :
[tex] ({x - ( - 2)})^{2} + ({y - 4})^{2} = {10}^{2} \\ [/tex]
[tex] ({x + 2})^{2} + ({y - 4})^{2} = 100[/tex]
As u can see option B is the correct answer.
And we're done ...
Have a great day ♡♡♡♡♡Which set of three side lengths will not from a triangle
A 17, 12, 6 C 36, 14, 27
B 25, 38, 13 D 39, 44, 6
Answers
Answer:
5tv. 9. v. 9. 9. o. o. o o. o. 9.
Dividing by 1/2 means you are finding how many halves are in the dividend
Answers
to multiply it by 2 because two is the dividend and that is closest to 1
Lane loads his stuck with 3 tons of bricks. How many pounds of bricks does he have
Answers
2000 pounds in a ton
Solve the following equation using distribution. 1 2 (4x − 12) = 5 ( 1 2 ) (4x) − ( 1 2 ) (12) = 5 2x − 6 = 5 +6 +6 2x = 11 What is the value of x? 5.5 9 11.5 13
Answers
Answer:
5.5
Step-by-step explanation:
Answer: IT IS 5.5I DID THE TEST
Step-by-step explanation:
Algebra II | Progressions
It’d be very much appreciated if someone could a.) solve this for me, and b.) kindfully explain how to get the correct answer in simple terms. It looks easy, but the lesson isn’t making it make sense. Thank you! :)
Answers
Answer:
Option 1
Step-by-step explanation:
Substiute the value of n with 1 to 6 and find each term.
When n = 1 ,
[tex]\sf First \ term = \dfrac{1}{2*1+1}=\dfrac{1}{2+1}=\dfrac{1}{3}\\\\[/tex]
[tex]\sf When n = 2,\\\\Second \ term = \dfrac{2}{2*2+1}=\dfrac{2}{4+1}=\dfrac{2}{5}\\\\[/tex]
When n = 3 ,
[tex]\sf Third \ term = \dfrac{3}{2*3+1}=\dfrac{3}{6+1}=\dfrac{3}{7}[/tex]
When n = 4,
[tex]\sf Fourth \ term =\dfrac{4}{2*4+1}=\dfrac{4}{8+1}=\dfrac{4}{9}\\[/tex]
When n = 5 ,
[tex]\sf Fifth \ term = \dfrac{5}{2*5+1}=\dfrac{5}{10+1}=\dfrac{5}{11}\\\\When \ n = 6,\\\\ \: Sixth \ term =\dfrac{6}{6*2+1}=\dfrac{6}{12+1}=\dfrac{6}{13}[/tex]
[tex]Answer: \dfrac{1}{3}+\dfrac{2}{5}+\dfrac{3}{7}+\dfrac{4}{9}+\dfrac{5}{11}+\dfrac{6}{13}[/tex]
A right cylinder with a diameter of 8 ft and a height of 15 ft. Help!!
Answers
Given :-
Diameter = 8ft , radius = 4ft.Height = 15ftWe can find Total Surface Area , Lateral Surface Area and Volume of Cylinder by given values.
Volume of Cylinder = πr²h
putting the known values ,Volume = 3.14×4²×15 cubic feet
Volume = 753.6 cubic feet
Total Surface Area of Cylinder = 2πr(r+h)
TSA = 2×3.14×4(4+15) square feet
TSA = 477.28 square feet
Lateral Surface Area Of Cylinder = 2πrh
CSA = 2×3.14×4×15
CSA = 376.8 square feet
can anyone solve this?
Answers
Answer:
The answer is 14/50
Step-by-step explanation:
sin=opp/hyp
sin=14/50
A market research company wants to collect opinions on the comfort and performance of a new type of sneaker by brand x. which group of individuals would be the best choice for a random sample? ask every fourth person on the street ask every fourth person who is wearing that brand of sneaker ask every fourth employee from the brand x flagship store ask every fourth person who is wearing shoes
Answers
The group of individuals would be the best choice for a random sample is to ask every fourth person who is wearing that brand of sneaker.
We have,
A market research company wants to collect opinions on the comfort and performance of a new type of sneaker by brand x.
We have to determine which group of individuals would be the best choice for a random sample.
What is the simple random sampling?
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen
One of the best methods in random sampling is called quartering.
In quartering, the population is divided into 4 quadrants and the
the sample is obtained on one of the quadrants obtained.
In this case, the procedure to do is:
To ask every fourth person who is wearing that brand of sneaker.
Therefore option A is correct.
To learn more about the sampling visit:
https://brainly.com/question/12892403
Answer:
It's b
Step-by-step explanation:
Took it on edge 2022
What are three ratios that are equivalent to 16:12.
Answers
Answer:
4:3 = 8:6 = 12:9 = 16:12 = 20:15 = 24:18 = 28:21 = 32:24 = 36:27 = 40:30
Step-by-step explanation:
Answer:
8:4, 32:24, 48:36
Step-by-step explanation:
16 ÷3=8
12÷3=4
↓
8:4
----------------------
16 ×2=32
12×2=24
↓
32:24
-----------------------
16×3=48
12×3=36
↓
48:36
Hope this helps! Have a good day! : )
What is the value of χ2 for the two-way table?
A B C D
X 5 10 15 20
Y 7 13 17 21
(2 points)
0.5320
0.0801
1.08
0.2830
0.9632
Answers
Answer:
0.2830
Step-by-step explanation:
Observed Values
Add totals for the rows and columns to the two-way table (see attachment 1).
Expected Values
Create an "Expected Values" table by multiplying each row total by each column total and dividing by the overall total (see attachment 2).
Chi-square test statistic
[tex]\sf \dfrac{(observed-expected)^2}{expected}[/tex]
Create a third table by using the formula to calculate the chi-square test statistic for each cell of the table (see attachments 3 and 4)
Chi-square
Add the values from the table in attachment 4.
[tex]\sf X^2=0.05556+0.03945+0.002315+0.05465+0.04789+0.03401+0.001996+0.04711[/tex] [tex]\implies \sf X^2=0.2830 \:(4 \:sf)[/tex]
help i need help and this is due soon
Answers
Answer:
8π or 35.133 (3 d.p.)
Step-by-step explanation:
Volume of cone is [tex]V=\pi r^{2}\frac{h}{3}[/tex], where V is the volume, r is the radius, and h is the vertical heightSubstitute in the values[tex]V=\pi\times 2^{2}\times\frac{3}{3}[/tex][tex]V=4\pi\times 1[/tex][tex]V=4\pi[/tex]There are 2 cones, so times by 2This gives 8πfind the absolute value of -5/8
Answers
Answer:
5/8
Step-by-step explanation:
To find the absolute value you simply remove the negative symbol
Suzie paid a total of \$324$324dollar sign, 324 for xxx tickets to a rock festival.
How much did each ticket cost?
Write your answer as an expression
Answers
Answer:
324/x
khan let me know
Find the area of the figure
Answers
Step-by-step explanation:
there is one central rectangle :
from (-4, 2) to (2, -2).
that means it dimensions are 6×4 (for x from -4 to +3, for y from +2 to -2).
and then there are 3 additional triangles
(2, -4) (2, 2) (6, 2)
(-4, -2) (2, -2) (2, -4)
(-6, 2) (-4, 2) (-4, -2)
with the leg lengths
(2, -4) to (2, 2) = 6, and (2, 2) to (6, 2) = 4
(-4, -2) to (2, -2) = 6, and (2, -2) to 2, -4) = 2
(-6, 2) to (-4, 2) = 2, and (-4, 2) to (-4, -2) = 4
the area of the rectangle is
6×4 = 24 square units
the area of the first triangle is
6×4/2 = 3×4 = 12 square units
the area of the second triangle is
6×2/2 = 6 square units
the area of the third triangle is
2×4 = 8 square units.
so, the total area is
24 + 12 + 6 + 8 = 50 square units.
Can someone pleas help???????
Answers
Answer:
written all the angles below:
m<1 = 35°
m<2 = 77°
m<3 = 49°
m<4 = 77°
m <5 = 62°
m<6 = 28°
hope that helps...
4-5 practice proving right triangles congruent worksheet 1-7
Answers
Step-by-step explanation:
1. mzoGE = M2GOE
1. Given
2. GE = OE
2.
3. E is the midpoint of AT
3. Given
4. AE ET
4. Definition of the midpoint of a line segment.
5. AE = ET
5. Congruent segments have equal length.
6. MLAEG > MZTEO
6. Given
7. AG > TO
check if 5/11 and 7/6 are rational numbers.
Answers
Answer:
they are rational numbers
Step-by-step explanation:
Any fraction with integers in numerator and denominator is a rational number.
__
5, 6, 7, 11 are integers, so the fractions 5/11 and 7/6 are rational numbers.
What is the value of the expression 16 + 56/n when n = 8?
Answers
Answer:
23
Step-by-step explanation:
[tex]16 + \frac{56}{n} [/tex]
[tex]where \: n = 8[/tex]
[tex]16 + \frac{56}{8} [/tex]
[tex]23[/tex]
[tex]56 / 8 = 7[/tex]
Add second[tex]7 + 16 = 23[/tex]
With that information, your answer is twenty-three.
100 Points!! 0_0
Solve and check for extraneous solutions.
5(3x+1)^1/2=10
Please SHow Steps!!! WIll give the brainiest!!
Answers
[tex]5\sqrt{3x+1} = 10\\\\\implies \sqrt{3x+1} = \dfrac{10}5 \\\\\implies \sqrt{3x+1} = 2 \\\\\implies 3x +1 = 4\\\\\implies 3x = 4-1 \\\\\implies 3x = 3\\\\\implies x =1[/tex]
Answer:
x = 1
Step-by-step explanation:
Given equation:
[tex]\dfrac{5(3x+1)^1}{2} =10[/tex]
If a term has "1" as it's exponent, it means that it's the number itself. Therefore, we can remove the "exponent".
[tex]:\implies\dfrac{5(3x+1)}{2} =10[/tex]
Simplify the distributive property:
[tex]:\implies\dfrac{15x+5}{2} =10[/tex]
Using cross multiplication:
[tex]:\implies15x+5} =10 \times 2[/tex]
Simplify the R.H.S:
[tex]:\implies15x+5} =20[/tex]
Subtract 5 both sides:
[tex]:\implies15x+5 - 5} =20 - 5[/tex]
Simplify both sides:
[tex]:\implies15x} =15[/tex]
Divide 15 both sides:
[tex]:\implies\dfrac{15x}{15} } =\dfrac{15}{15}[/tex]
Simplify both sides:
[tex]:\implies x= 1[/tex]
What is the exact circumference of a circle with a radius of 17 mm?
•
8.5T mm
O
177 mm
O 347 mm
O
687 mm
Answers
Answer:
[tex]34\pi[/tex]
Step-by-step explanation:
Given,
r = 17 mm
→ Circumference =
[tex]2\pi \: r[/tex]
→ 2x3.14x17
→ 34x3.14 =
[tex]34\pi[/tex]
↓
c = 106.76 mm
What is the value of the expression below if C = 5 and d = 7? A. 65 B.315 c. 15 d. -7
Answers
Answer:
Step-by-step explanation:
=2(5)^2 - 5(7)
= 2(25) - 35
= 50 - 35
= 15
100 Points!!! WILL MARK BRAINLIEST!!!
Daisy is a botanist who works for a garden that many tourists visit. The function f(s) = 3s + 35 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 15w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks. (4 points)
Part B: What are the units of measurement for the composite function in Part A? (2 points)
Part C: Evaluate the composite function in Part A for 36 weeks. (4 points)
Answers
Answer:
A) [tex]f(w)=45w+35[/tex]
B) f(w) is the total number of flowers that bloomed
w is the number of weeks
C) 1655 flowers
Step-by-step explanation:
Part A
[tex]f(s) = 3s + 35[/tex]
[tex]s(w) = 15w[/tex]
To create the composite function, replace the variable [tex]s[/tex] in the function f(s) with function s(w):
[tex]\implies f(w)=3(15w)+35[/tex]
[tex]\implies f(w)=45w+35[/tex]
Part B
f(w) is the total number of flowers that bloomedw is the number of weeksPart C
Substitute w = 36 into the compositie function and solve:
[tex]\implies f(36)=45(36)+35=1655[/tex]
please teach me how to do this
Answers
Answer:
16.4
Step-by-step explanation:
x = radius
x = 8.7 + 7.7
x = 16.4
PLEASE HELP I WILL GIVE YOU 5 STARS
Answers
Answer:
3/4 lbs.
Step-by-step explanation:
In order to find how much more the heavier boxes weigh than the lighter boxes, we have to subtract the lighter box weight from the largest box weight.
Lighter box weight = 4 1/2
Heavier box weight = 5 1/4
Now we can find their difference:
The heavier box weight - lighter box weight = 5 1/4 - 4 1/2 = 21/4 - 9/2 = 21/4 - 18/4 = 3/4.
The heavier boxes weigh 3/4 lbs. more than the lighter boxes.
Answer:
3/4 lbs
Step-by-step explanation:
The heavier box weight - lighter box weight = 5 1/4 - 4 1/2 = 21/4 - 9/2 = 21/4 - 18/4 = 3/4.
The difference is:
The heavier boxes weigh 3/4 lbs. more than the lighter boxes.
Please may I have brainliest
The function H(n) describes the total amount of money a movie theater receives for n ticket sold.
which domain is appropriate for this function.
all integers
all real numbers
all positive integers and zero
or
all positive real numbers and zero
Answers
The domain which is appropriate for the function, H(n) is; all positive integers and zero.
Domain of functionsFrom the task content;
We are required to identify the domain which is most appropriate for the function.On this note, we are required to determine the possible values for the number of tickets bought, n.
Ultimately, since tickets are whole, it follows that the appropriate domain for this function is; all positive integers and zero.
Read more on domain of functions;
https://brainly.com/question/1369616
The table of ordered pairs gives an exponential function.
Write an equation for the function. NEED ASAP!!!
Answers
Answer:
12+34+67+12
Step-by-step explanation:
im in 12th grade with straight as trust me
help me please please
Answers
Answer:
5 units down, two to the left. Therefore, x+-2, y+-5
Step-by-step explanation:
All the dimensions of a pentagon were multiplied by the same factor, and the area of the figure changed by a factor of 25. By what factor were the dimensions of the pentagon multiplied?
12. 5
625
5
50
Answers
Answer:
625
Step-by-step explanation:
I just did this question