In linear equations, x = 9.5 Paula use the division property of equality.
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.
That is, if a, b, and c are real numbers such that a = b and c ≠0, then
a/b = c/d
The equation was -6x = 57
To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below
-6x = 57 ( Divide both sides by -6)
-6x/6 = 57/-6
x = 9.5
Hence, we can conclude that the division property of equality.
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The complete question is -
Paula used these steps to solve an equation:
Step 1: -4(7 + 8) - 21 = 25
Step 2: -4r – 32 - 2x = 25
Step 3: -61 – 32 = 25
Step 4: -6x = 57
Step 5: x = -95
Between which two steps did Paula use the division property of equality?
Use an integer or a fraction to describe the slope of a perpendicular To this line.
Answer:
slope of perpendicular line = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
calculate the slope m of the given line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (3, 3) ← 2 points on the line
m = [tex]\frac{3-0}{3-1}[/tex] = [tex]\frac{3}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{2} }[/tex] = - [tex]\frac{2}{3}[/tex]
In 1787 the French scientist Jacques Charles observed that when he plotted the graph of volume of a fixed amount of air versus the temperature of the air, the points lay along a straight line. Therefore, he concluded that volume of a gas varies linearly with temperature. Suppose that at 27º C a certain amount of air occupies a volume of 500 cm3. When it is warmed to 90º C, it occupies 605 cm3.
a) Write the particular equation in slope-intercept form expressing volume in terms of temperature.
b) Predict the volume at 60º C.
c) The process of predicting a value between two data points is called “interpolation”.
What is the origin of the word?
d) Predict the volume at 300º C.
e) The process of predicting a value beyond any given data points is called
“extrapolation”. What is the origin of this word?
f) Extrapolate your mathematical model back to the point where the volume is zero.
That is, find the temperature-intercept.
g) What is the special name given to the temperature in part f)?
The relationship between the volume, V, and temperature, T, of a given mass of gas, found by the French scientist Jacques Charles, gives;
a) The slope–intercept form of the equation that expresses the volume in terms of the temperature of the gas is; [tex] \displaystyle{ V = 1. \bar 6 \cdot T + 455}[/tex]
b) The volume at 60 °C is 555 cm³
c) Interpolation originates from the verb interpolare
d) The temperature at 300 °Cis 955 cm³
e) Extrapolation originates from 'extra' (meaning outside) and the shortened form of Interpolation
f) The temperature–intercept is -273 °C
g) The special name is the absolute zero temperature
What is Charles law for gases?Charles law states that the volume of a given mass of gas is directly proportional to its temperature given in Kelvin.
Mathematically, Charles Law states that; V = K•T
Where;
V = The volume of the gas
T = The gas temperature
K = The proportionality constant
The volume occupied by the gas at 27 °C = 500 cm³
The volume occupied at 90 °C = 605 cm³
a) To write the equation in slope–intercept form, we have;
[tex] \displaystyle{ Slope = \frac{605 - 500}{90 - 27} =1. \bar{6} =1. \bar{6}}[/tex]
The equation of the line in point and slope form is therefore;
Point–slope form; [tex] \displaystyle{ V - 500 = 1. \bar{6} \times (T - 27) }[/tex]
[tex] \displaystyle{ V = 1. \bar{6} \cdot T -45 + 500 = 1. \bar{6} \cdot T + 455}[/tex]
The equation in slope–intercept form of expressing the volume, V, in terms of the temperature, T, is therefore;
Volume equation; [tex] \displaystyle{ V = 1. \bar{6} \cdot T + 455}[/tex]
b) The volume at 60 °C is given from the equation that gives the volume, V, in terms of time, T as follows;
[tex] \displaystyle{ V(T) = 1. \bar{6} \cdot T + 455}[/tex]
When T = 60 °C
[tex] \displaystyle{ V(60) = 1. \bar{6} \times 60 + 455=555}[/tex]
The volume occupied by the gas at 60 °C is 555 cm³c) The word interpolate originated from the Latin word interpolare which means to alter or refurbish
d) The volume occupied by the gas at 300 °C is given by the function for the volume, V, in terms of temperature, T, equation as follows;
When T = 300 °C
[tex] \displaystyle{ V(300) = 1. \bar{6} \times 300 + 455 = 955}[/tex]
The volume of the gas at 300 °C is 955 cm³e) Extrapolation originate from the word 'extra' which refers to the outside of an area. Extra is combined with a short form of interpolate to give the word, extrapolation
f) When the volume is zero, the volume function equation can be used to find the temperature as follows;
Volume function; [tex] \displaystyle{ V = 1. \bar{6} \cdot T + 455}[/tex]
When V = 0
[tex] \displaystyle{ V = 0 =1. \bar{6} \cdot T + 455}[/tex]
[tex] \displaystyle{ -455 = 1. \bar{6} \cdot T }[/tex]
[tex] \displaystyle{T = \frac{3 \times (-455)}{5}= -273 }[/tex]
The temperature at which the volume of the gas is zero is -273 °Cg) The special name given to -273 °C of the gas is the absolute zero temperature.
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Question 8 of 10
Which choices are equivalent to the expression below? Check all that apply.
√5 √5
●
A. √5
B. √5.5
C. 5
☐D. 10
E. 25
F. √25
expression :
[tex]\sqrt{5} \sqrt{5}[/tex] = [tex]\sqrt{5X5} = \sqrt{25} = 5[/tex].
What is a square root?In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer.The radical symbol used to denote a number's root is "[tex]\sqrt{x}[/tex]" The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.It is easy to determine a number's square. To determine the given number's square, we must multiply it by itself. [tex]x^{2}[/tex] integer is always used to denote the square term.To learn more about : Square and Root
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x-3/4+2/3=17/12 true?
1) 8
2) 6
3) 0
4) 4
The solution for the linear equation is x = 6, thus the correct option is the second one.
Which value of x makes the equation true?
Here we have the linear equation:
(x - 3)/4 + 2/3 = 17/12
To solve this we need to isolate the variable, x, in one of the sides of the equation.
(x - 3)/4 + 2/3 = 17/12
(x - 3)/4 = -2/3 + 17/12 = -8/12 + 17/12 = 9/12 = 3/4
(x - 3)/4 = 3/4
x - 3= 4*(3/4) = 3
x = 3 + 3
x = 6
The solution is x = 6, thus the correct option is the second one.
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Question content area top Part 1 In a certain chemical, the ratio of zinc to copper is 3 to 11 . A jar of the chemical contains 363 of copper. How many grams of zinc does it contain?
We need to know about ratio to solve this problem. The number of grams of zinc is 1331 grams.
Ratio in simple terms mean how many times one number contains another. In this question we know that the ratio of copper and zinc is 3 to 11 which means that in the chemical there are 3 parts of copper and 11 parts of zinc. The ratio between two things can be obtained by dividing one by the other and reducing it to the simplest fraction. We know that 363 grams of copper is present, we need to find the amount of zinc. Let us consider the amount of zinc to be x
363/x=3/11
x=363x11/3=121x11=1331
Therefore the amount of zinc present is 1331 grams.
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The diagonals of parallelogram LMNO intersect at point P. If MP = 2x + 5 and OP = 3x − 7, what is MP?
The value of MP in the parallelogram is 29 units.
How to find the diagonal of a parallelogram?A parallelogram is a quadrilateral with opposite sides equal to each other and opposite side parallel to each other.
Therefore,
The diagonals of parallelogram LMNO intersect at point P.
The diagonals of parallelogram LMNO are LN and MO.
The point P of the parallelogram divides each diagonal into exactly two equal parts.
Hence,
MP = OP
MP = 2x + 5
OP = 3x - 7
2x + 5 = 3x - 7
2x - 3x = -7 - 5
- x = - 12
x = 12
Therefore,
MP = 2(12) + 5
MP = 24 + 5
MP = 29
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The director will share out 18000 as follows
9 office workers will each get £500
The 4 managers will each get at least twice the bonus of an office worker
The directory will get at least 3 times the bonus of an office worker.
Answer:
Total = £18,000
9 Office workers = £500
4 Managers = 500 × 2 (twice the bonus of an office worker) = £1,000
Directory = 500 × 3 (3 times the bonus of an office worker) = £1,500
the circumference of a circle is 60cm what is the area
step by step explanation please
The area of a circle with a circumference of 60cm is 286. 38cm²
How to determine the area of the circleThe formula for calculating the circumference of a circle is expressed as;
Circumference = 2 πr
Where;
π has the value pie in decimal form is = 3. 14 and in fraction form is 22/7r is the radius of a circleNow, let's put and substitute the value of circumference of the circle as 60cm in the formula
We have;
60 = 2 πr
Interchange the value for π as 3.14, we have;
60 = 2× 3.14r
Multiply the values
60 = 6.28r
Make 'r' the subject of formula by dividing both sides by the coefficient of the variable 'r'
r = 60/6.28
Find the quotient
r = 9.55cm
But we have that the formula for area of a circle is expressed as;
Area = πr²
Substitute or put the value of radius into the formula
Area = 3. 14(9.55)²
Determine the square of the value
Area = 3.14(91. 20)
Find the product
Area = 286. 38cm²
Thus, the area is 286. 38cm²
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Rachel earns 52 dollars per week working part-time at a book store. She makes one dollar more for each book that she sells. The amount, A (in dollars), that
Rachel earns in a week if she sells b books is given by the following function.
A (b) = 52+b
How much does Rachel earn in a week if she sells 37 books?
dollars
X
Ś
Answer:
Step-by-step explanation:
x
how do i answer this?????
answer:
8.037m
step-by-step explanation:
the total of two or more addends is the sum of the numbers added.
your two addends are 5.89 and 2.147, so add them together.
5.89+2.147
=5.89+2.147
=8.037
the answer is 8.037m
Help solve please im struggling
Answer:
The domain should be "All Real Numbers" and the Range should be "y is greater than or equal to 0"
Given g(x) = 2x- 4, find g(2).
Answer:
0
Step-by-step explanation:
So repalce the x with 2 so now its 2(2)-4 you multiple the 2 times 2 which is 4 now 4-4is 0
What is the value of p when p = 6r² and r=3
Answer:
p = 54Step-by-step explanation:
What is the value of p when p = 6r² and r=3
p = 6r²
p = 6 * 3²
P = 6 * 9
p = 54
---------------
Adam buyed 8 new video games each costing $19.97. How can you represent the total amount that will be withdrawn from his bank account?
Answer:
8*19.97=159.76
Step-by-step explanation:
Answer:
8*19.97=159.76
Step-by-step explanation:
what is the y-intercept of 3x+5y=−30 ? responses
A. (0,−6)
B. (−6,0)
C. (0,10)
D. (10,−6)
find the slope of the line
Answer:
0.5
Step-by-step explanation:
want an explanation?
6.105 + 10.4 + 3.075 ?
[ this is middle school math, i dont get why it says highschool :/ ]
Answer:
Step-by-step explanation:
6.105 + 10.4 + 3.075 ? :19.58
Lowes carries 3 types of plants. 1/10 of the plants are fruit bearing,
1/2 of the plants are flower bearing, the rest are
vegetable bearing plants. How many are vegetable bearing plants?
This problem is asking me to determine?
Write the equation you will be using to solve.
The number of vegetable-bearing plants is 12/5.
How to find the number of vegetable-bearing plants?Lowes carries 3 types of plants.
1/10 of the plants are fruit bearing
1/2 of the plants are flower-bearing
The rest are vegetable-bearing plants.
Solution:
Let x be the no of vegetable-bearing plants.
The total number of plants = Number of plants that are fruit-bearing + Number of plants that are flower-bearing + Number of plants that are vegetable-bearing.
3 = 1/10+1/2+x
Taking L.C.M.,
3 = 1+5+10x/10
3 = 6+10x/10
30 = 6+10x
30-6 = 10x
24 = 10x
x = 12/5
Therefore, 12/5 of plants are vegetable-bearing.
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Which of the following does the Pythagorean Theorem reveal
According to the Pythagorean theorem, "in a right-angled triangle, the squares of the hypotenuse side is equivalent to the sum of squares of the other two sides," the hypotenuse side is the longest side of the triangle.
This is further explained below.
What is Pythagorean Theorem?Generally, The Pythagorean theorem is a well-known geometric theorem that states the number of squares just on the legs of a right triangle is equal to the square just on the hypotenuse (the side that is opposite the right angle).
This theorem can also be expressed in the familiar algebraic notation of a2 + b2 = c2, where a and b are the lengths of the legs of the triangle.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is an essential connection in Euclidean geometry that describes the relationships between the three sides of a right triangle.
It indicates that the total of the areas of the squares on the other two sides is equal to the area of the square whose side is the hypotenuse.
In conclusion, This means that the area of the square whose side is the hypotenuse is equal to that amount.
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CQ Not found: Answered Generally
if you were to extract 15000 mcubic from a lake each year for 15 years, how far would the lake level fall? total volume of water given as 5400000 m cubic and water depth of the lake is 4 m
Answer:
[tex]d=0.17m[/tex]Explanation: Each year a volume of 15,000 cubic meters is taken from the lake for 15 years, the lake has a surface area of 1.35 square kilometers and a depth of 4m. We have to find the fall in the depth of the river after 15 years:
The total water taken out of the lake in 15 years is:
[tex]\begin{gathered} T=(15,000m^3)\times15=225,000m^3 \\ \\ T_w=225,000m^3 \end{gathered}[/tex]Therefore the fall in height is:
[tex]\begin{gathered} A\times d=(225,000m^3) \\ \\ \\ A=1.35km^2=1,350,000m^2 \\ \\ \\ A=1,350,000m^2 \\ \\ \\ \therefore\Rightarrow \\ \\ \\ (1,350,000m^2)d=(225,000m^3) \\ \\ \\ \\ d=\frac{(225,000m3)}{(1,350,000m^2)}=0.1666666666 \\ \\ \\ \\ d\approx0.17m \\ \end{gathered}[/tex]Therefore the height of the lake will reduce by 0.17me.
Which among the given set is a function A = [(4,6), (A, B), (A, 6)]C = {(6,9), (6,6), (6,9)B = [(1, Z), ( 2, Y), (3, X)]
The set which is a function is B = [(1, Z), ( 2, Y), (3, X)]
What is a function ?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Since, we know that function does not repeat any x coordinate
Which means, the first coordinate of every pair does not repeat
Therefore the first coordinates which is repeated is not a function
Now, let's check out the given sets and check whether its a function or not
A = [(4,6), (A, B), (A, 6)], is not a function
Since, its first coordinate is repeated
C = {(6,9), (6,6), (6,9), is not a function
Since, its first coordinate is repeated
B = [(1, Z), ( 2, Y), (3, X)], is a function
Because, its first coordinate is not repeated
Hence, B = [(1, Z), ( 2, Y), (3, X)], is a function
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(URGENT!) The function g is defined by the following rule. Complete the function table. g(x)=4x-2 (The table is in the image)
Question
What numbers are a distance of 23 unit from 12 on a number line
Express the ratio below in its simplest form. 2:4
Answer:
1:2
Step-by-step explanation:
we divide both numbers by 2
I believe that the ratio written in its simplest form would be 1:2 in ratio form.
Hope this helps!
There are only green pens and blue pens in a box.
There are three more blue pens than green pens in the box.
There are more than 12 pens in the box.
Simon is going to take at random two pens from the box.
The probability that Simon will take two pens of the same colour is
27/55
Work out the number of green pens in the box.
Answer:
Green Pens : 21
Step-by-step explanation:
Let the number of
green pens = x
Three more blue pens than green pens translates to
=> number of blue pens = number of green pens + 3
=> blue pens = x + 3
Total number of pens = blues + green = x + 3 + x = 2x + 3
Probability of taking 2 green pens:
The first time a green pen is taken out, the probability
P( 1s green pen) = Number of green pens/Total number of pens
= [tex]\dfrac{x}{2x + 3}[/tex]
After the first green pen is removed, the number of green pens will be one less and so will the total number of pens
Number of green pens = x - 1
Total number of pens = 2x + 3 - 1 = 2x + 2
P(second green pen | first green pen)
[tex]=\dfrac{x-1}{2x + 2}[/tex]
P(2 green pens) = P(first green pen) x P(second green pen)
[tex]= \dfrac{x}{2x + 3} \times \dfrac{x-1}{2x + 2}\\\\=\dfrac{x(x -1)}{(2x +3)(2x+2)}[/tex] [1]
Probability of 2 blue pens
P( 1st blue pen) = number of blue pens/total number of pens
[tex]=\dfrac{x + 3}{2x + 3}[/tex]
P(second blue pen = (number of pens remaining if first was blue) ÷ total number of pens - 1
If the first pen taken was blue then there will be 2x + 3 - 1 blue pens out of a total of 2x + 3 - 1 pens
P(2nd blue pen | first blue pen)
[tex]=\dfrac{x + 2}{2x + 2}[/tex]
[tex]\text{P(2 blue pens)} =\dfrac{x + 3}{2x + 3} \times \dfrac{x + 2}{2x + 2}[/tex][tex]=\dfrac{(x + 3)(x+2)}{(2x + 3)({2x + 2})}[/tex] [2]
The probability of either 2 green pens or 2 blue pens is the sum of the two probability expressions [1] and [2]
[tex]= \dfrac{x(x -1)}{(2x +3)(2x+2)} + \dfrac{(x + 3)(x+2)}{(2x + 3)({2x + 2})}[/tex]
[tex]= \dfrac{x(x - 1)+ (x + 3) (x +2)}{(2x + 3)(2x + 2)}\\\\\\= \dfrac{2x^2+4x+6}{(2x + 3)(2x + 2)}\\\\\\\\[/tex]
Numerator: factor out 2 to get 2(x² + 2x + 3)
denominator = 4x²+10x+6 = 2 (2x² + 5x + 3)
2 of numerator and 2 of denominator cancel out to give the final expression:
[tex]\dfrac{x^2\:+\:2x\:+\:3}{2x^2+\:5x\:+\:3}[/tex]
But we are given that the probability of picking 2 pens of the same color = 27/55
This will give us:
[tex]\dfrac{x^2\:+\:2x\:+\:3}{2x^2+\:5x\:+\:3} = \dfrac{27}{55}[/tex]
Cross-multiplying we get
[tex]55\left(x^2+\:2x\:+\:3\right)=27\left(2x^2+\:5x\:+\:3\right)[/tex]
=> [tex]55x^2+110x+165 = 54x^2+135x+81[/tex]
Grouping like terms and simplifying gives
[tex]x^2-25x+84=0[/tex]
This is a quadratic equation which can be solved using a scientific calculator (as I did)
The solution set is
x = 21, x = 4
Remember x = number of green pens. We can ignore x = 4 because the total number of pens given by the expression 2x + 3 will be less than 12 and we are told there are more than 12 pens total
So the solution is x = 21 (number of green pens)
Number of blue pens = x + 3 = 21 + 3 = 24
Answer: Green Pens : 21 and Blue Pens: 24
The 43rd Term of Ap 26 Find The first tom of the progress in given that is common difference is 1/2 Two Aps have same first &last term
The first term of the arithmetic progression is 5
What is an arithmetic sequence?An arithmetic sequence can simply be defined as a sequence of numbers or terms in which the differences between successive or consecutive terms are always equal.
The formula for the nth term of an arithmetic sequence is expressed as;
Tn = a + (n-1)d
Where;
Tn is the nth term of the sequencea is the first term of the sequencen is the number of termsd is the common difference between successive termsGiven that the first term of the sequence is a, the 43rd term is 26 and the common difference is 1/2
Substitute the values into the formula
26 = a + (43 -1)1/2
expand the bracket
26 = a + (42)1/2
Multiply through
26 = a + 21
collect like terms
a = 26 - 21
a = 5
Thus, the value is 5
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Solve the following inequality for r. Write your answer in
simplest form.
5r - 5(-7r +9) ≥ −10r +9 – 6r
Step-by-step explanation:
10r 7r-1 r-9 7r-7=10 5r²2
Help ! Pleaseeeeeeee asap
The obtained decimal number is 0.155.
To solve the question [tex]\frac{3.1 * 10}{2.0 * 10^{2}}[/tex].
Canceling out 10 from the denominator and numerator
= [tex]\frac{3.1 }{2.0 * 10}[/tex]
= 3.1 / 20
Remove the decimal point from the numerator and add one zero in the denominator
= 31/ 200
As we divide the numbers using the long division method we get the decimal number as a result,
= 0.155
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In a fruit cocktail, for every 30 ml of orange
juice you need 20 ml of apple juice and 50
ml of coconut milk. What proportion of the
cocktail is apple juice?
Give your answer as a fraction in its
simplest form
Answer:
1/5
Step-by-step explanation:
If you mix 30 ml of orange juice, 20 ml of apple juice and 50 ml of coconut milk you will get a total of 30 + 20 + 50 = 100 ml of cocktail
The proportion of apple juice in the cocktail is merely the volume of apple juice added to the total volume of cocktail
= 20/100 = 1/5
. Describe and correct the error in finding the sum.
X
8 65+ (−16)
(-1)
15
30
6
+
8
15
=
13
6
+
||
11
49
30
19
= 1-
30
It’s the super long problem, sorry I couldn’t crop the other stuff out
Answer: see below
Step-by-step explanation:
I can’t see the whole problem, however 2 and 5/6 does not equal 13/6, it equals 17/6, if that helps.