Answers
Answer:
[tex]x = \frac{5}{3}[/tex]
Step-by-step explanation:
The expression under the square root is [tex]\sqrt{4x^2 - 20x + 25}[/tex]
This is equivalent of [tex](2x-5)^2[/tex]
We can check this by using the formula
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]
where [tex]\\a = 2x so a^2 = (2x)^2 = 4x^2\\\\b = -5 so b^2 = (-5)^2 = 25\\\\2ab = (2)(2x)(-5) = -20x\\[/tex]
So
[tex]\sqrt{4x^2 - 20x + 25} = \sqrt{(2x-5)^2}[/tex] which is [tex](2x-5)[/tex]
(The square root of the square of an expression is the expression itself)
So that gives us
[tex]2x - 5 = 5-2x\\[/tex]
Collecting like terms on each side gives us
[tex]2x + 2x = 5 -(-5)\\\\4x = 10\\\\x = 10/4 = 5/3[/tex]
Related Questions
The figure below is a square with dimensions given.
Part A: What is the perimeter of the square in terms of x?
2x - 1 in
Perimeter = ________
Part B: If the length of each side of the square is doubled, what would be the perimeter of this new square, in terms of x?
Perimeter = ________
Part C: If x = 5, what would be the ratio of the area of the original square to the area of the new square?
Answer: ____________________
Answers
Answer:
A: 8x-4
B: 16x-8
C: 1:2
Step-by-step explanation:
Simplify y ^2 over 6y^5.
Answers
Answer:
1/6y^3
Step-by-step explanation:
Answer:
1/6y^3
Step-by-step explanation:
cancel the common factor of y^2 and y^5
Can I get some help on this
Answers
Answer:
the first one, 2.5x
Step-by-step explanation:
Hope this helps!
write the number seventeen thousand and forty-eight in figures
Answers
Answer:
17 048
hi lets be freinds pleeease
Step-by-step explanation:
Fourth eight is 48 (2 figures)
add them up 17,000+48 = 17048
Keith buys 6 pencils for 90p how much would 11 pencils cost
Answers
Answer:
keith buy 11 pencils at the cost of 165 paise
Step-by-step explanation:
6 pencils cost = 90 paise
so 1 pencil cost = 15 paise
4. If 4 bananas weigh 4 4/5 kilograms , how
many kilograms would you expect 3
bananas to weigh?
A.
//
C. 3
B. 1
}
D. D.8
Answers
Answer:
It's the same process, change 4 4/5 to an improper fraction = 24/5 then set up a proportion
4 bananas/(24/5) kg = 3 bananas/x kg take cross products
4x = 3 (24/5) = 72/5 divide by 4 (this is the same as multiplying by 1/4)
x = 72/20, change this to a mixed number = 3 12/20 = 3 3/5 kg
Step-by-step explanation:
witch expression represents a number 5 times the difference of 6 and 2
Answers
Answer:
i think it is 20
Step-by-step explanation:
6-2=4
4×5=20
Question 4
0/20 pts
PLEASE HELP!!!: The slope of a line is –3 and the
y-intercept is (0,4). What is the
equation of the line in slope-intercept
form?
Answers
9514 1404 393
Answer:
D. y = -3x +4
Step-by-step explanation:
The slope-intercept form is ...
y = mx + b
where m is the slope (-3) and b is the y-intercept (4). Putting these values into the form gives ...
y = -3x +4 . . . . . matches choice D
The two trapezoids below are similar. What is the length of EF
Answers
Answer:
answer is 6
Step-by-step explanation:
i know answer is 2 weeks late
HELP! Below is the graph of a polynomial. Which statement about this graph is true?
A. The point (-2,1) is a maximum
B. The point (5,0) is an extreme
C. The point (2,-1.12) is a minimum
D. The point (2,-1.12) is a maximum
Answers
if you can help please do :)
Answers
Step-by-step explanation:
A
[tex]180 - 60 - 70 = 50 \\x = 180 - 50 = 130 \\ x = 130[/tex]
Tania Ramirez purchases 25 hanging file folders for $6.99. What is the price
per folder?
Answers
Write an equation in slope-intercept form for the table.
Answers
Answer:
y=4x+3
Step-by-step explanation:
y=mx+c where m is the slope and c is the intercept.
To find m, get two points and plug them into the formula (y2-y1)/(x2-x1):
(0,3) and (2,11)
m=(11-3)/(2-0)
=8/2
=4
y=4x+c
To find c, plug in one of the points, eg. (3,15)
15=4(3)+c
15=12+c
c=3
y=4x+3
One batch of cookies makes 18. How many
batches will you need to make to be sure you
have at least 100
Answers
Answer:
6
Step-by-step explanation:
100/18=5 1/2
18*6=108
Answer : 18x5=90 18x6=108
Step-by-step explanation:
What is the slope of the line that passes through the points
10, -8) and
(-8, -16)? Write your answer in simplest form.
Answers
Step-by-step explanation:
(10, -8) (-8, -16)
(-16+8)/(-8-10) = -8/-18= 4/9 is the slope
if I use the bathroom 17 times then I use the bathroom 5 more times how many times have I gone to the bathroom
Answers
Answer:
22
Step-by-step explanation:
17+5
Answer:
you have a whiz problem LOL
Step-by-step explanation:
What would be 82% of 50
Answers
80% = 40
2% = 1
82% = 41
41
Answer:
82% of 50 is 41
Step-by-step explanation:
✧brainliest appreciated✧
Using the rational root theorem, identify all the possible rational roots of the equation x^4+25x^3-14x^2-19x+30
Answers
Answer: D on Edg
Step-by-step explanation:
Which equation is a linear function
Answers
Answer:
the fourth one
Step-by-step explanation:
Answer: y= x/2 - 5
Step-by-step explanation: the first is not linear the second is not linear the third is not linear the forth one IS linear
A linear equation is an equation of a straight line, which means that the degree of a linear equation must be
0
or
1
for each of its variables.
a bird bath that is 3 ft talk casts a shadow that is 2 ft long.Find the height of a tent that casts a 6 ft shadow.
Answers
Answer:
is it 5ft
Step-by-step explanation:
if the bird bath had a foot taken off in the shadow then wouldn't a foot be taken off for the tent as well
A mathematical phrase represented by numbers, variables, and operations is a(n)
pls help:)
Answers
Answer:
Expression
Step-by-step explanation:
Answer: Expression
Got this right!!!
Hope this helps!!!
Alyssa's cat weighs 12 pounds, which is 3/8 of the weight of her dog. Use the equation 3/8d=12 to find the weight of Alyssa's dog.
Answers
Answer:
0.5 pounds!
Step-by-step explanation:
12/0.375=32
Her dog is 32 pounds
If you pay $1.49 a pound for chicken and 2/3 of the weight is bone. How much are you paying per pound of meat?
Answers
9514 1404 393
Answer:
$4.47 per pound
Step-by-step explanation:
Your cost is ...
$1.49/(1/3 lb) = $1.49×(3/1)/lb = $4.47/lb
John has two different sugar syrups. Syrup A is 2 parts of sugar and 8 parts of water, and Syrup B is 3 parts of sugar and 5 parts of water. How much of each should john mix together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
Answers
Answer:
Volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts .
Step-by-step explanation:
Syrup A : 2 parts sugar , 8 parts of water .
Total = 10 parts
Syrup B : 3 parts sugar , 5 parts of water .
Total = 8 parts .
Mixture required 280 quarts , 3 parts sugar , 7 parts water
In 280 quarts , sugar = 280 x 3 / ( 3 + 7 )
sugar = 84 parts
Let volume of syrup A be x , volume of syrup B = 280 - x
sugar A = 2 x / 10 = 0.2 x
sugar B = 3 ( 280 - x ) / 8 = .375 ( 280 - x )
Total sugar = .2 x + .375 ( 280 - x ) = 84 .
.2 x + 105 - .375 x = 84
105 - 84 = .375 x - .2 x = .175 x
.175 x = 21
x = 21 / .175 = 120
Volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts .
John mixes 120 quarts of syrup A and 160 quarts of syrup of B together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
Given that,
John has two different sugar syrups.
Syrup A is 2 parts of sugar and 8 parts of water, and Syrup B is 3 parts of sugar and 5 parts of water.
We have to determine,
How much of each should john mix together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
According to the question,
Syrup A: 2 parts sugar, 8 parts of water.
Total number of parts = 10 parts
Syrup B : 3 parts sugar, 5 parts of water.
The total number of parts = 8 parts.
The mixture required 280 quarts, 3 parts sugar, 7 parts water,
In 280 quarts, parts of sugar are,
[tex]= \dfrac{280 \times 3 }{ ( 3 + 7 )}\\\\= \dfrac{280 \times 3}{10}\\\\= 84[/tex]
Let the volume of syrup A be x,
And the volume of syrup B be 280 - x
[tex]Sugar\ A = \dfrac{2x}{10} \\\\Sugar \ A = 0.2 x[/tex]
[tex]Sugar \ B = \dfrac{3 ( 280 - x ) }{8 }\\\\Sugar \ B= .375 ( 280 - x )[/tex]
The total amount of sugar is,
[tex]0.2 x + 0.375 ( 280 - x ) = 84 \\\\0.2 x + 105 -0 .375 x = 84\\\\105 - 84 = 0.375 x - 0.2 x = 0.175 x\\\\ 0.175 x = 21\\\\x = \dfrac{21}{0.175}\\\\x = 120[/tex]
Therefore,
The volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts
Hence, John mixes 120 quarts of syrup A and 160 quarts of syrup of B together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
For more details, refer to the link.
https://brainly.com/question/11921451
An object weighs 1 pound on earth weighs about 1/15 pounds on Pluto. If a man weighs 240 pounds on earth how many pounds would he weigh on Pluto?
Answers
Answer:
16 I believe. 240 divided by 15 is 16.
write 56
as the product of prime factors
Answers
[tex]56 = 28 \times 2 \\ 56 = (14 \times 2) \times 2 \\ 56 = (7 \times 2) \times 2 \times 2[/tex]
If a man is driving at a rate of 80 km per hour, how many kilometers will he travel in 30 minutes? A. 30 km B. 40 km C. 60 km D. 240 km
Answers
Explanation
i guss d is the answer of it
Write an equation for the description.
A number x increased by 17 is 112.
Answers
Answer:
x+17 = 112
Step-by-step explanation:
Vocabulary:
Increased = Addition
Is = Equal Sign
x+17 = 112
What would the slope of a line be to line perpendicular to the following: Y = 2x - 2
Answers
Answer:
-1/2x
Step-by-step explanation: negative reciprical
Solve the Equation
P + 75 = 100.
Answers
Answer:
P= 25 so
25+75= 100
Step-by-step explanation:
100-75
Answer:
P=25
Step-by-step explanation:
P+75=100
-75 -75
_________
P=25