What is the intermediate step in the form (x + a)? = b as a result of completing the
square for the following equation?
x2 + 18x + 57 = 12
Answer:
(x + 9)² = 36
Step-by-step explanation:
Given
x² + 18x + 57 = 12 ( subtract 57 from both sides )
x² + 18x = - 45
To complete the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(9)x + 81 = - 45 + 81
(x + 9)² = 36
You had $1.65. After a friend returned the money you had loaned her, you
had $3.50. How much did she give you? _____
Answer:
$1.85
Step-by-step explanation:
Simple Subtraction!
$3.50 - $1.65 = $1.85
$1.85
Anthony earned $131 in tips last night while working at the restaurant. If his tips
consisted of $1 bills and $5 bills only and he counted 47 bills in total, then how
many $5 bills did Anthony receive?
Given:
Total income form tips = $131
His tips consisted of $1 bills and $5 bills only.
Total number of bills = 47
To find:
The number of $5 bills.
Solution:
Let x be the number of $1 bills and y be the number of $5 bills.
Total bills : [tex]x+y=47[/tex] ...(i)
Total income : [tex]x+5y=131[/tex] ...(ii)
Subtract (ii) from (i), we get
[tex]x+5y-(x+y)=131-47[/tex]
[tex]x+5y-x-y=84[/tex]
[tex]4y=84[/tex]
[tex]y=21[/tex]
Therefore, the number of $5 bills is 21.
Elina is gathering up change she has saved. She has a total of $2.60. All of her change is in either nickles, dimes, or quarters. She has twice as many dimes as quarters and two less quarters than nickles. Is it possible that she has eight dimes, four quarters, and six nickels? Explain.
Answer:
sadsadwsd
Step-by-step explanation:
log(x+1)−log(x−8)=log(10)
How do i solve this?
9514 1404 393
Answer:
x = 9
Step-by-step explanation:
The applicable rule of logarithms is ...
log(a) -log(b) = log(a/b)
__
Use the rules of logarithms to simplify the left side to a single log, then take the antilogs and solve the resulting equation.
log(x+1) -log(x-8) = log(10)
log((x+1)/(x-8)) = log(10)
(x +1)/(x -8) = 10 . . . . . . . take antilogs
x +1 = 10(x -8) . . . . multiply by x-8
81 = 9x . . . . . . . add 81-x, simplify
9 = x . . . . . . . . . divide by 9
_____
When the equation is rewritten to the form f(x) = 0, the x-intercept is the solution.
Piper is at the grocery store and plans on buying cans of soup and frozen dinners, but
is concerned about their sodium content. Each can of soup has 150 mg of sodium and peach frozen dinner has 450 mg of sodium.
How many milligrams of sodium are there in 4 cans of soup and 2 frozen dinners?
How many milligrams of sodium are there in c cans of soup and f frozen dinners?
Answer:
1,500 mg
150c + 450f
Step-by-step explanation:
Each can of soup has 150 mg of sodium and each peach frozen has 450 mg of sodium.
Piper plans to buy some of each product and wants to know how many milligrams of sodium are there in 4 cans of soup and 2 frozen dinners.
Since each can of soup has 150 mg of sodium, 4 cans have 4*150 = 600 mg of sodium.
Each frozen dinner has 450 mg of sodium, thus 2 of them have 2*450 = 900 mg of sodium.
There are 600 + 900 = 1,500 mg of sodium in this combination.
If Piper buys c cans of soup and f frozen dinners, they will have 150c + 450f milligrams of sodium.
what is 2x + 27 = -3 (x+5) + 7
Answer:
The answer is x = -7
Answer:
2^x = 16
Step-by-step explanation:
Estimate by rounding the largest number to hundreds and then divide.
869 ÷ 6 is approximately
Answer:
150
Step-by-step explanation:
Round: 869 → 900900 ÷ 6 = 150I hope this helps!
A recipe says to use 3 cups of flour to make 48 cookies. How many cups of
flour are needed for 80 cookies?
Certain species of fish costs $4.49 each. You spend at most $35. How many of this type of fish can you buy for your aquarium?
Also how do you give the brainlyest answer to someone?
Answer:
7 fish
Step-by-step explanation:
1. 4.49x ≤ 35
2. Divide both sides by 4.49 so it cancels out the multiplication. x ≤ 7.79510022272
3. You can't split fish, so you can buy 7 fish.
Not sure how to give Brainliest, though.
Answer:
Do 4.49 times 8 it'll get your answer
Step-by-step explantion
NO it's 8 he can buy 8 Of them fishes
Find an equation for the line below in y=mx+b
Answer:
y = -1/2x - 11/2
Step-by-step explanation:
Using slope intercept form y = mx + b, to determine the equation, first count the rise(vertical or change in y), and run(horizontal or change in x) of the line.
m is the slope, b is the y-intercept which will remain when x is 0 as this will cancel out the m.
Be careful when determining the slope, and pay attention to the steps(count) of the x, and y axis.
As this graph measures a line with a negative slope passing through the y axis at -5 1/2 → -11/2, with a step of 1, we can count the squares normally to determine the slope.
So since we know that this line has two obvious points (-5,-3) and (1,-6) we can use the equation for slope to measure it's steepness.
m = y2-y1/x2-x1
with (x1,y1) being the first point, and (x2,y2) being the second point.
So: (negative minus a negative makes a positive)
m = -6-(-3)/1-(-5) = -6 + 3/ 1 + 5 = -3/6 = -1/2.
Since m = -1/2, and b = -11/2, the line must be y = -1/2x - 11/2.
1/3 cups of butter?
(Hint:use a calculator to figure out how many tablespoons a 1/3 of a cup is,your answer will not be a whole number)
Answer:
Around 5 tablespoons or to be exact: 5.333333333333333
Please help! Drag the tiles to the correct boxes to complete the pairs...
A loon is a bird that dives in the ocean for its food. It can dive to a depth of 12ft in 8 seconds. How many feet does it dive per second? (Write your answer as a decimal) *
Answer: 1.5ft/seconds
Step-by-step explanation:
From the question, we are informed that a loon is a bird that dives in the ocean for its food and that it can dive to a depth of 12ft in 8 seconds.
The amount of feet it dive per second will be gotten by dividing 12ft by 8 seconds. This will be:
= 12ft / 8sec
= 1.5ft/seconds
Five cubic meters of copper has a mass of 44,800 kilograms. What is the density of copper?
Answer:
i thin it is 8960
Step-by-step explanation:
44800 divided by five = 8960
which of the following is the equation logx4=-2 written in exponential form
1. The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] will be;
⇒ x⁻² = 4
2. The value of √e⁷/e⁵ will be;
⇒ e
3. The equivalent expression of 3 will be;
⇒ ln e³
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
1. The expression is the equation [tex]log_{x} 4 = - 2[/tex].
2. The equation is √e⁷/e⁵.
3. The number is 3.
Now,
The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] is calculated as;
[tex]log_{x} 4 = - 2[/tex]
By the definition of logarithmic, we get;
4 = x⁻²
Hence, The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] will be;
⇒ x⁻² = 4
2. The equation is √e⁷/e⁵.
Solve as;
√e⁷/e⁵ = √ e ⁷ ⁻ ⁵
= √ e²
= e
Thus, The value of √e⁷/e⁵ will be;
⇒ e
3. Since, by the definition of logarithmic;
[tex]ln_{e} e = 1[/tex]
So, By option 1;
[tex]ln_{e} e^3[/tex] = [tex]1 * 3[/tex] = [tex]3[/tex]
Thus, The equivalent expression of 3 will be;
⇒ ln e³
Learn more about the expression visit:
https://brainly.com/question/1859113
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What is the LCD of 49:63
Answer:
21
Step-by-step explanation:
Answer:
411
Step-by-step explanation:
how do u find the sum of (5x-2) + (4x+6)
[tex] \: \: \: \: \: \: \: \: (5x - 2) + (4x + 6) \\ \\ = > 5x - 2 + 4x + 6 \\ \\ = > 5x + 4x - 2 + 6 \\ \\ = > \green{\boxed { 9x + 4}}[/tex]
Answer:
9x+4
Step-by-step explanation:
First, remove the unnecessary parentheses from (5x-2)+(4x+6) making it 5x-2+4x+6 because when there is a + in front of an expression in parentheses, the expression remains the same.
Next, collect like terms, turning 5x-2+4x+6 into 9x-2+6.
Now, calculate the sum and you should get 9x+4.
What is a pre-image?
Answer:
an image before the image your seeing
Step-by-step explanation:
Solve equation Y=9x-70 and y=2x-32
Step-by-step explanation:
y = 9x - 70 ...1
y = 2x - 32 ...2
...1 - ...2
0 = 7x -38 ...3
7x - 38 = 0
7x = 38
x = 38/7
The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 56 and a standard deviation of 10. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 36 and 86?
Answer:
97.35%
Step-by-step explanation:
Empirical rule formula states:
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
From the question, we have the mean of :
Mean of 56 and a standard deviation of 10.
For 36
36 = μ - xσ
36 = 56 - 10x
56 - 36 = 10x
20 = 10x
x = 20/10
x = 2
Hence, the data falls within 2 standard deviation of the mean
Hence, since it is one side,
= 95%
= 47.5%
For 86
86 = μ - xσ
86 = 56 - 10x
56 - 86 = 10x
-30 = 10x
x = -30/10
x = -3
Hence, the data falls within 3 standard deviation of the mean
Hence, since it is 99.7% one side,
= 99.7%
= 49.85%
Hence, we add up
= 47.5% + 49.85%
= 97.35%
The approximate percentage of 1-mile long roadways with potholes numbering between 36 and 86 is 97.35%
a cone has a volume of 33 cubic inches. of a cylinder has the same height and radius as the cone, what is the volume of the cylinder
Answer: 40 cubic inch
Step-by-step explanation:
Rico wants to buy the new Madden NFL game. It costs $60.00. He has $24.78 in his bank account. He will also get $20 for mowing his neighbors lawns. Create a number line to represent the situation. ALSO how much more does he need in order to buy the game? *
Answer:
$15.22
Step-by-step explanation:
Given that :
Cost of NFL game = $60
Amount Rico has in bank account = $24.78
Amount earned for mowing lawn = $20
Amount needed more to buy the game :
Total amount Rico has :
Cost of NFL game - (Amount in bank + amount earned for mowing)
$60 - ($24.78 + $20)
$60 - $44.78
= $15.22
Amount needed more to purchase the game = $15.22
use patterns blocks to help fidn each of the fractions
Answer:1/2?
atleast that what i thought it was
Uniforms are sold in packages of 8. The store's 137 employees will each be given 4 uniforms. How many uniforms will the store need to order all together?
Answer:
552 uniforms (69 packages)
Step-by-step explanation:
since each employee will be given 4 uniforms and each package contains 8 uniforms, you need 1 package of uniforms for every 2 employees.
Total number of employees = 137
total number of uniform packages = 137 / 2 = 68.5 packages which must be rounded up since you need to have enough uniforms for everyone = 69 packages
69 packages x 8 uniforms per package = 552 uniforms
Calculate the area of the triangle:
A=
(-2, 6)
(-2, 0)
(7,-5)
Helppp ASAP
Answer:
I got 27 as an answer
Step-by-step explanation:
Answer:
I hope this may help you ...
question in the picture!!
looking for the answer of 1) , 2) and 3)
show your work using numbers!!
Answer:
1. 24%
2. 30%
3. 30%
Step-by-step explanation:
1. 100%/25= 4% 4%*6=24%
2. 100%/50= 2% 2%*15=30%
3. 100%/40=2.5% 2.5%*12= 30%
A scale model of a building is 6in tall. The scale of the model is 1in. :50ft. How tall is the actual building?
Answer:
300 ft
Step-by-step explanation:
4.5/w = 3
what is the W?
Answer:
w=1.5 or w=13.5
Step-by-step explanation:
this is one answer:
multiply w on both sides to leave u with
4.5=3w
divide both sides by 3
[tex]\frac{4.5}{3}=\frac{3w}{3}[/tex]
1.5=w
_____________________
this is the second one if the first one is wrong:
multiply 4.5 on both sides so that the 4.5/w would leave u with just only w alone.
then 3*4.5=13.5
w=13.5
hope dis helps if not then im not dat smart enough ;?
The points (-1, r) and (2, 1) lie on a line with slope 2. Find the missing coordinate r
Please help!!!
Answer:
r = -5
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
(-1, r)
(2, 1)
r - 1/-1 - 2 = r - 1/-3
Slope = 2
-3 x 2 = -6
-6 -(-1) = -5
-5 - 1 = -6
-6/-3 = 2
So:
r = -5
Hope this helps!
9514 1404 393
Answer:
r = -5
Step-by-step explanation:
The x-coordinate of the partially-defined point is 3 units less than the x-coordinate of the given point. The slope of 2 tells you the y-coordinate of the partial point (r) will be 2·3 = 6 units less than the y-coordinate of the given point. That is ...
r = 1 - 2·3
r = -5
__
You are given the slope of the line and a point on it, so you can write the point-slope equation of the line:
y -y1 = m(x -x1) . . . . . . . line with slope m through point (x1, y1).
For the given point and slope, this is ...
y -1 = 2(x -2)
For an x-value of -1, the corresponding y-value will be ...
r = 2(-1-2) +1 = -6 +1
r = -5