x = milliliters of 40% alcohol
y = milliliters of 20% alcohol
so just alcohol alone in each quantity will just be "x" * (40/100) = 0.4x and "y" * (20/100) = 0.2y, whilst trying to get 1000 mL of 36% alcohol only.
[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ \textit{40\% solution}&x&0.4&0.4x\\ \textit{20\% solution}&y&0.2&0.2y\\ \cline{2-4}&\\ mixture&1000&0.36&360 \end{array}~\hfill \begin{cases} x+y=1000\\\\ 0.4x+0.2y=360 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=1000\implies }x=1000-y ~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.4(1000-y)+0.2y=360} \\\\\\ 400-0.4y+0.2y=360\implies 40-0.4y+0.2y=0\implies 40-0.2y=0 \\\\\\ 40=0.2y\implies \cfrac{40}{0.2}=y\implies \boxed{\stackrel{mL}{200}=y} ~\hfill \boxed{\underset{mL}{\stackrel{1000~~ - ~~200}{x=800}}}[/tex]
Which answer would be a sufficient counter example to the statement below? “Two angles that are supplementary are always different measures”
The counter example to the statement “Two angles that are supplementary are always different measures” is 90° and 90°.
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees
In other words, two Angles are Supplementary when they add up to 180 degrees.
For example 130 degrees and 50 degrees are supplementary angles.
The statement says "two angles that are supplementary are always
different measures".
Therefore, the counter example to this statement is 90 degrees and 90 degrees. This is because they are the same and it still sum to 180 degrees.
In other words, the angles are supplementary and the same which is counter example to the statement.
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Select all the lines that are perpendicular to 3x – y = 10. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36) E. y = 13x + 2
From the list given, the line that is perpendicular to 3x – y = 10 is x + 3y = 27. (Option C)
What is a perpendicular line?It is to be noted that lines that intersect at a right angle (90 degrees) are considered perpendicular lines.
To justify the above results, we recall that when two lines are perpendicular then the product of their slope is -1.
The slope is given by y = mx + c where m is the slope.
Hence, the slope of the given equation 3x -y = 10 is arrived at by re-writing the expression as follows:
Y = 3x -10 where
slope m₁ = 3
given Lets attempt to derive the slope of the options given:
1) y = 3x + 5
m₂ = 3
The product of the slopes are:
= m₁ x m₂
= 3 x 3
⇒ 9 ≠ -1
Therefore, this is not a perpendicular line.
2) y = -13x + 17 our new m₂ = -13
m₁ x m₂
⇒ 3 x -13
⇒ -39 ≠ -1
Again, this is not the required line.
3) x + 3y = 27 [divide all sides by 3]
y = -1/3(x) + 9
The new m₂ = -1/3
Compute for slope:
= 3 x - (1/3)
= -3/3
= -1
Hence, x + 3y = 27 is the perpendicular line.
4) y -2 = 13(3x + 36)
y = 39x + 468 +2
y = 39x + 470
New Slope (m₂) = 39
Solving to check the slope, we have:
m₁ x m₂ = 3 x 39
⇒ 117 ≠ -1.
Thus, we have our final answer as option C.
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The required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.
What is the slope perpendicular line?
The slope of the perpendicular lines is equal to the inverse and of the opposite sign.
Here,
Standard equation of the line,
y = mx + c
The property of the perpendicular line states that the product of their slopes is equal to -1.
So the slope of the given line is m = 3,
Let the slope of the perpendicular line that we have to determine, be x
According to the property,
The slope of line × slope of perpendicular line = -1
3 × x = -1
x = -1/3
So looking forward to the option, the line that has a slope of -1/3 is x + 3y = 27. because
x + 3y = 23
Transform the above equation to standard form,
y = -1/3x + 23
From the above equation, the slope of the above line is m = -1/3,
Thus, the required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.
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whats the anwser to 8ab - 5ab I want to know
Answer:
3ab
Step-by-step explanation:
i hope you don't want to know how i did this :)
Solve the equation for x. −0.24x − 16.4 = 1.48 x = −62.2 x = 62.2 x = −74.5 x = 74.5
hurry pls
The solution of the given linear equation is x = -9.53
How to solve the equation for x?Here we have the linear equation:
-0.24*x - 16.4 = 1.48*x
To solve this, first we need to move all the terms with x to the left and the terms without x to the right.
-0.24*x - 1.48*x = 16.4
(-0.24 - 1.48)*x = 16.4
-1.72*x = 16.4
Now we can divide both sides by -1.72 to get:
x = 16.4/-1.72 = -9.53
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Answer: c) (is it c?)
Step-by-step explanation: c) x= - 74.5
0.24x+16.4=-1.48 step 1- subtract: -1.48- 16.4
0.24x= -17.88 (divide)
x= −74.5
there
i hope this helps!!
Translate this phrase into an algebraic expression. Seven more than the product of 17 and Julie's savings Use the variable j to represent Julie's savings.
17j+7 is the algebraic expression for Seven more than the product of 17 and Julie's savings.
What is Expression?Expression is a combination of variables, operators and numbers.
The given phrase is
"Seven more than the product of 17 and Julie's savings"
and j is variable to represent Julie's savings.
In the phrase we have Seven more than, it means we are adding 7 to something.
According to problem we are adding 7 to "product of 17 and Julie's savings"
Product means multiplying a number with another factor. Here the factor is julies saving j.
17j+7 is the translated algebraic expression.
Hence 17j+7 is the translation of Seven more than the product of 17 and Julie's savings.
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the long division method to find the result when 12x^{3}+5x^{2}-27x+1312x
3
+5x
2
−27x+13 is divided by 3x-13x−1. If there is a remainder, express the result in the form q(x)+\frac{r(x)}{b(x)}q(x)+
b(x)
r(x)
(hope it makes sense)
The solution of the polynomial division 12x³ + 5x² - 27x + 13 is divided by 3x - 1 is; 4x² + 3x - 8 + (5/(3x - 1))
How to carry out Polynomial Long Division?
We want to use long division method to solve the polynomial division when 12x³ + 5x² - 27x + 13 is divided by 3x - 1.
4x² + 3x - 8
-------------------------
3x - 1 | 12x³ + 5x² - 27x + 13
- 12x³ - 4x²
-----------------------------
9x² - 27x
- 9x² - 3x
-----------------------------
-24x + 13
- -2x + 8
-----------------------------
5
-----------------------------
Expressing the solution of the polynomial division in the given quotient and remainder form gives us; 4x² + 3x - 8 + (5/(3x - 1))
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6.0 x 10^4 ÷ 4.0 x 10^8
Scientific Notation Please
Answer:
1.5x10^12
1500000000000
Step-by-step explanation:
Simplify the expression.
F(11/10) if f(x) = 2x -7
PLUG IN
[tex] \frac{11}{10} [/tex]
in the place of x in the function and simplify.
[tex]f( \frac{11}{10} ) = 2( \frac{11}{10} ) - 7 \\ f( \frac{11}{10} ) = \frac{22}{10} - 7 \\ f( \frac{11}{10} ) = \frac{ - 48}{10} \\ f( \frac{11}{10} ) = \frac{ - 24}{5} [/tex]
ATTACHED IS THE SOLUTION
Hello!
To solve for f(11/10)
==> must simply plug '11/10' into x's position in the equation
[tex]f(\dfrac{11}{10} )=2(\dfrac{11}{10} )-7=\dfrac{11}{5} -7=\dfrac{11}{5} -\dfrac{35}{5} =-\dfrac{24}{5}[/tex]
Hope that helps!
Select the pair that could be a reasonable approximation for the diameter and
circumference of a circle.
5 meters and 22 meters
19 inches and 60 inches
33 centimeters and 80 centimeters
Explain your reasoning.
Your answer
We know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.So, let 'D' be the diameter and 'C' be the circumference.
Calculate C as:
C = πD (π = 3.14)(A) D = 5 m and C = 22 m
C = πD C = 3.14 × 5C = 15.7 mSo, C = 15.7 m does not approximate 22 m.
(B) D = 19 in and C = 60 in
C = πD C = 3.14 × 19C = 59.66 inSo, C = 59.66 approximates 60 in.
(C) D = 33 cm and D = 80 cm
C = πD C = 3.14 × 33C = 103.62cmSo, C = 103.62cm does not approximate 80cm.
Therefore, we know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.
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The correct question is given below:
Select all the pairs that could be reasonable approximations for the diameter and circumference of a circle. * 1 point A. 5 meters and 22 meters. B. 19 inches and 60 inches. C. 33 centimeters and 80 centimeters.
find equations of the lines that passe through the given point and are parallel to and perpendicular to the given line Y +4 =0 (-6,3)
Answer:
y = 3 and x = - 6
Step-by-step explanation:
y + 4 = 0 ( subtract 4 from both sides )
y = - 4
this is the equation of a horizontal line, parallel to the x- axis.
a parallel line will also be horizontal with equation
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (- 6, 3 ) with y- coordinate 3 , then
y = 3 ← equation of parallel line
a line perpendicular to the given line will be a vertical line with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (- 6, 3 ) with x- coordinate - 6 , then
x = - 6 ← equation of perpendicular line
At a butcher shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat. Express the number of pounds of pork he bought using a decimal.
The number of pounds of pork he bought in decimal is 12.21 lb
Decimal:
A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
For example 12.34 is a decimal.
Given,
At a butcher shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat.
Here we need to find the number of pounds of pork he bought using a decimal.
First, we have to convert the given fractions into decimal then we get,
Amount of beef = 2 7/20
Which is equal to,
=> 2 + 7/20
=> 2 + 0.35 = 2.35 lb
Similarly, total amount of meat = 14 14/25
=> 14 + 14/25
=> 14 + 0.56 = 14.56
Therefore, the amount of pork is,
=> total amount of meat - the amount of beef
=> 14.56 - 2.35
=> 12.21.
Therefore, the the number pounds of pork in decimal is 12.21 lb.
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What is the slope of the line that passes through the points (-10, 9)
and (-10, 18)? Write your answer in simplest form.
Hello!
What is the equation for the slope:
[tex]\hookrightarrow \text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁,y₁): a random point on the line ⇒ (-10,9) (x₂,y₂): another random point on the line ⇒ (-10,18)[tex]Slope =\dfrac{18-9}{-10-(-10)} =\dfrac{9}{0} \\[/tex]
Thus the slope is undefined:
Hope that helps!
Which of the following shows the values of −0.5, −2.8, 1.9, 0.9, and −1.7 plotted on a number line?
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.9, negative 2, negative 0.6, 0.9, and 1.7 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 3, negative 1.9, negative 0.7, 0.8, and 1.9 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.9, negative 2, negative 0.6, 0.9, and 1.9 are plotted.
The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7,negative 0.5,0.9 and 1.9 are plotted."
Here the values are
-0.5,-2.8,1.9,0.9 and -1.7
The number line a graphical representation that a line on which numbers are marked at intervals, used to represents the simple numerical operations.
Here there are three negative numbers -0.5,-2.8 and -1.7
The positive numbers are 1.9 and 0.9
The statement "A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5,0.9 and 1.9 are plotted" is suited of all the given conditions
Hence, The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted."
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Elizabeth is posting 12 flyers for the science club and 20 for the music club. She wants to make all the locations identical, with the same combination of science club flyers and music club flyers. In addition, she wants to make sure that no flyers are left over. What is the greatest number of locations that Elizabeth can post at?
we have the following:
in this case we must find the largest divisor between the numbers 12 and 20, this number is 4:
[tex]\begin{gathered} \frac{12}{4}=3 \\ \frac{20}{4}=5 \end{gathered}[/tex]Therefore 3 flyers for the science club and 5 flyers for the music club. And it would be 4 places
Use the information given to enter an equation in standard form.
Slope is 2, and (3, 5) is on the line.
Standard form of equation is 3x + 5y = 2.
Define equation.Ax+ By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful. A linear equation has the conventional form Ax+ By=C. A slope-intercept form equation (y=mx+ b) must have the x and y on the same side of the equal sign and the constant on the opposite side in order to be converted to standard form. To relocate terms, use inverse operations.
Slope = 2
Points = (3, 5 )
Standard form of equation,
Ax + By = C
Equating,
3x + 5y = 2
Standard form of equation is 3x + 5y = 2.
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I'll send you the question
We know that
< means smaller than
≤ means smaller or equal to
> means greater than
≥ means greater or equal to
We want to find a number (let's call it x), greater than -34
Since, > means greater than, we use this symbol:
y > -34
Answer: D13. Sofia's car can travel 228 miles on 6 gallons of gas.
a. Write an equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
The most appropriate choice for unitary method will be given by-
y =38x is the equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
What is unitary method?
Unitary method is the method in which the value of single unit can be calculated from the value of multiple unit and value of multiple unit can be calculated from the value of single unit.
Sometimes value of single unit is more than value of multiple unit
For example - Relationship between price of a commodity and quantity of a commodity
Sometimes value of single unit is less than value of multiple unit
For example - Relationship between number of men and number of days taken by those men to do a work
Here,
Let y be the distance travelled by Sofia's car in miles and let Sofia's
car can travel on x gallons of gas.
On 6 gallons of gas, Sofia's gas can travel 228 miles
On 1 gallon of gas, Sofia's car can travel [tex]\frac{228}{6}[/tex] miles
On 1 gallon of gas, Sofia's car can travel 38 miles
On x gallons of gas, Sofia's car can travel 38x miles
By the problem,
y = 38x
This is the equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
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Amy got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 19 cents per yard. If after that purchase there was $16.77 left on the card, how many yards of ribbon did Amy buy? pls answer this!
Answer:
price for one ribbon =19 cents
she got $20
20- 16.77 the rest from the money = 3.23
so she spends 3.23 from buying the ribbon
how much ribbon does she buy
3.23 ÷ 0.19= 17 ribbons
Geometry Question on Foundations, Need Help.
Answer:
Plane RAT
Step-by-step explanation:
:]
x+y-7
-2x - 2y = -14
What’s y and x ?
Answer:
Step by step solution of a set of 2, 3 or 4 Linear Equations using the Substitution Method x-y=7;2x-2y=14 Tiger Algebra Solver.
Step-by-step explanation:
Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 60 centimeters by 20 centimeters and uses the scale 1 cm : 1.5 m.
A new Snack Shack is being constructed at Sandy Island Beach which dimensions are 90 centimeters by 30 centimeters.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object
Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 60 centimeters by 20 centimeters which are given in the question
Here the scale 1 cm : 1.5 m
As per the given scale, the dimensions would be as
60 centimeters :
⇒ 60 × 1.5 = 90
20 centimeters :
⇒ 20 × 1.5 = 30
Therefore, a new Snack Shack is being constructed at Sandy Island Beach which dimensions are 90 by 30 cm.
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The nth term of a sequence is 2n - 6
a) Work out the first three terms of the sequence.
b) Work out the tenth term of the sequence.
Answer:
a) do the first three terms
Answer: a) -4, -2, 0 b) 14
Step-by-step explanation:
To find any term, we plug the number into the equation for n.
a)
1st term => 2(1) - 6 = 2 - 6 = -4
2nd term => 2(2) - 6 = 4 - 6 = -2
3rd term => 2(3) - 6 = 6 - 6 = 0
b)
10th term => 2(10) - 6 = 20 - 6 = 14
A scale drawing of a field is shown below.8 in.10 in.6 in.The drawing uses a scale of 1 in. = 14 ft. What is the area of the actual field?
We can multiply each side by 14ft yo find the value on feet and late calculate the area
[tex]\begin{gathered} 8\times14=112ft \\ 10\times14=140ft \\ 6\times14=84ft \end{gathered}[/tex]tha area formula is
[tex]A=\frac{b\times h}{2}[/tex]where b=84ft and h=112ft
[tex]\begin{gathered} A=\frac{84\times112}{2} \\ A=4704 \end{gathered}[/tex]the area is 4,704ft2
What is the slope of the line that passes through the points (-8, -1)(−8,−1) and (-8, -11)(−8,−11)? Write your answer in simplest form.
Answer:
Undefined slope
Step-by-step explanation:
Slope , m is equal to rise/run Or ( y1-y2) / ( x1 -x2)
This line is a vertical line at x = -8 And thus has undefined slope
(Because you cannot divide by zero)
Answer:
Undefined
Step-by-step explanation:
Hey! Let's help you with your question here! I am unsure if the points are correct cause you've written each one down twice. If it does change, I will change my answer accordingly.
We're looking for a slope of the line that passes through 2 points I see! Alright, so as you would recall, most equations of a linear line are described in the form of slope-intercept form. And that being this:
[tex]y=mx+b[/tex]
When we're finding for slope of the line, we're essentially just look for m. But how can we find m with only just 2 points? Well, we can! Using a formula that helps us find the slope using exactly 2 points! And that is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, all we have to do is plug in the values as such and solve:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-11-(-1)}{-8-(-8)}[/tex]
From here, we come to a problem. If we were to solve this equation to find the slope, we will get an undefined value mainly because the denominator will equal 0 and we can't have it equal 0. So therefore, it is undefined.
need asap pleaseeeeeeee
Answer:
c) f = 28
Step-by-step explanation:
Given problem,
→ f³ = 21952
Now the value of f will be,
→ f³ = 21952
→ f = ³√21952
→ [ f = 28 ]
Let's check the following,
→ 28³
→ (28 × 28) × 28
→ 784 × 28 = 21952
Hence, option (c) is correct.
A line through (-1,b) and (c,8) is parallel to a line through (-6,3) and (0,12). Find values of b and c that make the above statement true.
Answer:[tex]b=4, c=-7[/tex]
Step-by-step explanation:
Parallel lines have the same slope.
The slopes of the lines are [tex]\frac{8-b}{c+1}[/tex] and [tex]-\frac{3}{2}[/tex].
Therefore, [tex]\frac{8+b}{c+1}=-\frac{3}{2}[/tex], and one possible pair is [tex]b=4, c=-7[/tex].
Please tell me what −7 7/8+3.7−(−15.9) is...
A local builder estimated that each year 57 homes are built in the surrounding area. In 2002 there was 43,800 homes. Find the number of homes in 2011.
The number of homes in 2011 is 44,313
Explanation:Given that 57 homes are built each year, in 2002, there were 43,800 homes, then the next years have the number of homes as follows:
2003: 43,800 + 57
2004: 43,800 + 57 + 57
2005: 43,800 + 57 + 57 + 57
This goes on until 43,800 + 57n
where n is the number of years after 2002.
2011 is 9 years after 2002, so the number of homes will be:
43,800 + 57(9)
= 43,800 + 513
= 44,313
The average cost of producing x game disks for a computer is given by the function C(x)=2.6+5460/x. Find the number of game disks that must be produced for the average cost to be $4.70.
The number of game disks that must be produced for the average cost to be $4.70 is 2600.
Given:
The average cost of producing x game disks for a computer is given by the function C(x) = 2.6+5460/x
To determine the number of game disks that must be produced for the average cost to be $4.70.
Substitute the average cost in the equation and solve to find the value of x i.e. number of disks,
4.70 = 2.6 + 5460/x
4.70 - 2.6 = 5460/x
2.1x = 5460
x = 5460/2.1
x = 2600
Therefore, the number of game disks that must be produced for the average cost to be $4.70 is 2600.
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Please help!! Name the reciprocals for the equations
In picture
1. 3
_ x = 9
4
4
2. -4 — x
7
If n is a real number, then its reciprocal will be 1/n.
1. If the equations be [tex]$\left(\frac{3}{4}\right) x=9$$[/tex] then the value of x = 12.
2. If the equations be [tex]$-4=\left(\frac{4}{7}\right) x$$[/tex] then the value of x = -7.
What is meant by reciprocals?The inverse of a value or a number is the definition of reciprocal in mathematics. If n is a real number, then its reciprocal will be 1/n. Reciprocals are used to convert division to multiplication when dividing fractions, which simplifies the division process.
1. Let the equations be [tex]$\left(\frac{3}{4}\right) x=9$$[/tex]
Multiply both sides by 4
[tex]$4 \cdot \frac{3}{4} x=9 \cdot 4$$[/tex]
Simplifying the above equation, we get
3x = 36
Divide both sides by 3
[tex]$\frac{3 x}{3}=\frac{36}{3}$$[/tex]
Simplify
Therefore, the value of x = 12.
2. Let the equations be [tex]$-4=\left(\frac{4}{7}\right) x$$[/tex]
Switch sides
[tex]$\left(\frac{4}{7}\right) x=-4$$[/tex]
Multiply both sides by 7
[tex]$7 \cdot \frac{4}{7} x=7(-4)$[/tex]
Simplifying the above equation, we get
4x = -28
Divide both sides by 4
[tex]$\frac{4 x}{4}=\frac{-28}{4}$$[/tex]
Therefore, the value of x = -7.
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