Solve the quadratic equation below by completing the square. What are the solutions?
x^2 - 16x + 50 = 21
A. X= -8+sqrt 7
B. X= 8 + sqrt 7
C. X= 8 +sqrt 35
D. X= -8+sqrt 35
By completing squares we will see that the solutions are:
[tex]x =\pm \sqrt{35} + 8[/tex]
How to complete squares?
Here we have the quadratic equation:
[tex]x^2 - 16x + 50 = 21[/tex]
We can rewrite it as:
[tex]x^2 - 2*8*x + 50 - 21 = 0\\\\x^2 - 2*8*x + 29= 0[/tex]
Then we must have a 8² term to complete squares, then we need to add and subtract 35.
[tex]x^2 - 2*8*x + 29 +35 - 35= 0\\\\(x - 8)^2 - 35 = 0\\\\(x - 8)^2 = 35[/tex]
Now we can solve this:
[tex]x =\pm \sqrt{35} + 8[/tex]
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Find the standard form for the equation of the line which
passes through the point (9,-46) and which has a
y-intercept of – 1.
Answer: Well I believe the answer is Y= x - 55
Step-by-step explanation:Hope that works :)
Write the equation of the line that passes through the points (-7,9) and (-7,1). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
It is a vertical line
Step-by-step explanation:
Find the slope using rise over run (y2 - y1) / (x2 - x1)
Plug in the points:
(y2 - y1) / (x2 - x1)
(1 - 9) / (-7 + 7)
-8/0
= undefined
Dividing by 0 gives you an undefined number. This means that the slope is undefined, and the line is a vertical line.
The equation of the line that passes through the points (-7,9) and (-7,1) is x = -7.
The point slope formula is represented below:
y - y₁ = m(x - x₁)where
m = slope
Let's find slope
(-7, 9)(-7, 1)
m = 1 -9 / -7 - (-7)
m = -8 / 0 = Undefined slope.
The slope is an undefined slope. Therefore, the line is a vertical line and cannot be written in a slope intercept or point slope form.
The equation of the line can be written as x = c.
where
c = constant
Therefore,
x = -7
The equation is x = -7
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The length between the bases on a baseball field is 90 feet. A scale drawing shows the distance between the bases are 2 1/2 inches. one inch on this drawing equals how many feet?
Answer:
36
Step-by-step explanation:
YOOOO HELP ME ASAP BRO THIS IS DUED BY TONIGHT COME ON PLEASE
EITHER ONE IS FINE
Answer:
fish food
Step-by-step explanation:
bc my moomy pappa gave me food and im so smart now and they broken now up
what percent is 52.52 million of 142 million
Answer:
37%
Step-by-step explanation:
Given parameters:
Total number = 142 million
Comparing number = 52.52 million
Unknown:
What percent is the number =?
Solution
The percentage;
= [tex]\frac{comparing number }{total number } x 100[/tex]
= [tex]\frac{52520000}{142000000}[/tex] x 100
= 37%
Answer:
dwadwdwa
Step-by-step explanation:
1/3 multiplied by -3/4
Answer:
-.25
Step-by-step explanation:
Answer:
-1/4
Step-by-step explanation:
The answer is -1/4 as 1/3x3/4 is 1/4, and as we have a negative number, the 1/4 flips to -1/4. Hope it helps!
I need help3
Find the unit rate:
150 students for 5 classes. How many students per class?
Answer:
30
Step-by-step explanation:
150 divided by 5 is 30 i hope this helps
Answer:
The unit rate would be 30 students per class.
Step-by-step explanation: One way to find the unit rate in this scenario, we could divide the total students by the number of classes. (150/5) The simplified fraction would be 30/1, or 30 students per class. Hope this helps!
2/5(5k+35) -8 =12 please helpppppppp
Answer:
k =3
Step-by-step explanation:
2/5(5k+35) -8 =12
Add 8 to each side
2/5(5k+35) -8+8 =12+8
2/5(5k+35) =20
Multiply each side by 5/2
5/2 *2/5(5k+35) =20*5/2
5k+35 = 50
Subtract 35 from each side
5k+35-35 = 50-35
5k = 15
Divide by 5
5k/5 = 15/5
k =3
See attachment for math work and answer.
Find the surface area of the prism
Answer:
SA = 5645cm²Step-by-step explanation:
We have three pairs of congruent rectangles
9cm × 4m; 9cm × 5cm and 4m × 5cm
We know 1m = 100cm, therefore 4m = 400cm
The formula of an area of a rectangle l × w:
A = l · w
Substitute:
A₁ = 9cm · 4m = 9cm · 400cm = 3600cm²
A₂ = 9cm · 5cm = 45cm²
A₃ = 4m · 5cm = 400cm · 5cm = 2000cm²
Calculate the surface area:
SA = A₁ + A₂ + A₃
SA = 3600cm² + 45cm² + 2000cm² = 5645cm²
Answer:
202cm²
Step-by-step explanation:
2×(5×9)+2(4×5)+2(9×4)
90+40+72=202cm²
How do you expect me to respect you when you don’t respect yourself
Answer:
You don't
Step-by-step explanation:
*Mind Blown*
A collar maker earns $0.27 per collar. If he sews 55 collars,
then how much will he earn?
Answer:
14.85
Step-by-step explanation:
Answer: 14.85 dollars
Step-by-step explanation:
When you multiply .27 times 55 to see how much money he will make by sewing 55 collars, you will get 14.85 dollars.
A recipe for servings of pudding calls for 2/3 cups of cream. How much cream is needed for 18 servings of
pudding?
Plz help
if tiffany drove 21 miles using 7 gallons of gas, how many miles did she drive per gallon.?
Answer: she drove 3 miles per gallon
Step-by-step explanation:
21 / 7 = 3 i hope this helps
A submarine is situated 400 feet below sea level. If it drops another 250 feet below sea level, what is the new position?
Answer:
-650ft
Step-by-step explanation:
I took a test with a question like that
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 35 pounds and each large box of paper weighs 65 pounds. There were 3 times as many small boxes shipped as large boxes shipped and the total weight of all boxes was 850 pounds.
Answer:
There were 15 small boxes shipped and 5 large boxes shipped.
Step-by-step explanation:
Let s = the number of small boxes shipped
Let l = the number of large boxes shipped
Each small box weigh 35 pounds, so (s) small boxes weigh 35s pounds. Each large box weigh 65 pounds, so (l) large boxes weigh 65l pounds. Therefore, the total weight 35s + 65l equals 850:
35s + 65l = 850
Since there were 3 times as many small boxes shipped as large boxes, there were MORE small boxes, so if we multiply 3 by the number of large boxes, we will get the number of small boxes, meaning s equals 3l
s = 3l
Write System of Equations:
35s + 65l = 850
s = 3l
Substitute value of s into the first equation:
35(3l) + 65l = 850
105l + 65l = 850
170l 850
__ = __
170 170
l = 5
Since l = 5, we know 5 large boxes were shipped.
Use l = 5 to solve for s:
s = 3l
s = 3(5)
s = 15
Since s = 15, we know 15 small boxes were shipped.
Determine if the function shows a linear relationship or an absolute value relationship. Then evaluate the
function for the indicated value of x.
A. f(x) = |x-31-2; x = -5
B. g(x) = 1.5x; x = 0.2
C. p(x) = 17 - 2x]; x = -3
how do you factor p^2-5p-36
Your answer will be:
(p - 9) (p + 4) in factored form.
Michael took an online test to get his Learner's Permit to drive. He was on question number 18 and the progress bar said he was 20%. How many questions are on this test?
im sorry i couldnt figure it out
Step-by-step explanation:
What is the range of the function shown in this table? х3 4 5 6 y4 4 2 5 A. (3, 4), (4, 4), (5, 2), {6, 5{ B. {3,4,5,6} C. {3, 4} D. {2,4,5}
The answer fam is............ D. {2,4,5}
At a local store, bananas cost 0.54 per pound , apples cost 2.19 per pound , and oranges cost 1.55 per pound . Aaron bought 3 pounds of each how much money did Aaron pay for his fruit
$0.54 x 2.6 =$1.404
$1.28 x 3.1=$3.968
$1.404 rounds to $1.40
$3.968 rounds to $4
$4 = $ 1.40 = $5.40
:)
Answer:
$12.84
Step-by-step explanation:
to solve this you will just have to multiply the given prices by the three pounds and then add up all the fruits:
0.54 x 3 = 1.62
2.19 x 3= 6.57
1.55 x 3= 4.65
1.62 + 6.57 + 4.65 = 12.84
Solve for : x
6x+34+ 8x+14
my last one please helpp
Answer:
x = 10
Step-by-step explanation:
8x + 14 = 6x + 34 (vertically opposite angles are equal)
Rearrange
2x = 20
x = 10
Answer:
x=10
Step-by-step explanation:
So we know that they are equal to each other.
so 6x+34=8x+14
-6x
34=2x+14
-14
20=2x
/2
x=10
What is (16)-(11)7 in distributed property
Answer: I think you answer is -61 if not sorry
Step-by-step explanation:
PLZ HELP ME HELP PLZ
Answer:
2000
Step-by-step explanation:
that i the answer becuase you multply
Use segment addition postulate
If k is the midpoint of JL, JK=8x+11 and KL = 14x-1, find JL
If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms. b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer.
This question is Incomplete
Complete Question
The bakery bought 4 bags of flour containing 3.5 kg each. 0.475 kg of flour is needed to make a batch of muffins, and 0.65 kg is needed to make a loaf of bread.
a. If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms.
b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer.
Answer:
a. 8.85kg of flour is left.
b. 2.95 bins
Step-by-step explanation:
The bakery bought 4 bags of flour containing 3.5 kg each.
Total kg of flour the Bakery bought : 4 × 3.5kg
= 14 kg of flour
0.475 kg of flour is needed to make a batch of muffins
1 batch of muffin = 0.475kg of flour
4 batches of muffins = ???
Cross Multiply
4 batches × 0.475kg/ 1 batch
= 1.9kg of flour was used.
0.65 kg is needed to make a loaf of bread.
1 loaf of bread = 0.65kg of flour
5 loaves of bread = ???
Cross Multiply
5 loaves × 0.65/1 loaf
= 3.25 kg of flour.
Total kg of flour used = 1.9kg + 3.25kg
= 5.15kg of flour.
The amount of flour left = 14kg - 5.15kg
= 8.85kg of flour is left.
b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour?
3 kg of flour is stored = 1 bin
8.85 kg of flour is stored = x
Cross Multiply
3kg × x = 8.85kg × 1 bin
x = 8.85 kg × 1 bin/3kg
x = 2.95 bins
A kennel has 40 dogs and 10 cats. What is the ratio of cats to ALL of
the animals?
Answer:
1:5
Step-by-step explanation:
the quotient of n and 3 is less than 5
Choole a line m that passes through point, P, and is parallel to linel.
Answer:
c
Step-by-step explanation:
How do you graph a piecewise defined function?
Answer:
hope it helps..
Step-by-step explanation:
1- Indicate on the x-axis the boundaries defined by the intervals on each piece of the domain.
2- For each piece of the domain, graph on that interval using the corresponding equation pertaining to that piece.