The system of equations are A = 8x³ and B = 2x³ and difference of the two equations is C = 6x³
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the difference of the two expressions be C
Let the first equation be represented as A
Now , the value of A = ( 2x )³
On simplifying the equation , we get
A = ( 2x )³ be equation (1)
A = ( 2 )³ ( x )³
A = 8x³
And , let the second equation be represented as B
The value of B = 2x³ be equation (2)
Now , dividing equation (1) by equation (2) , we get
A/B be equation (3)
Substituting the values in the equation , we get
A/B = 8x³/2x³
A/B = 8/2
A/B = 4
Multiply by B on both sides of the equations , we get
A = 4B
So , 8x³ = 4 ( 2x³ )
The difference between the two expressions C = 8x³ - 2x³ = 6x³
Therefore , the value of C is 6x³
Hence , the system of equations are solved
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What ratio is equivalent to 8/6
Answer:
3rd option: 32/24
Step-by-step explanation:
8/6 = 4/3
1st option: Now let's change the denominator to 24:
4/3 ==> ?/24
4/3 =
4*8 / 3*8 = 32/24, not 3/24.
2nd option: Now let's change the numerator to 24:
4/3 ==> 24/?
4/3 =
4*6 / 3*6 = 24/18, not 24/32
24/32 = 3/4, not 4/3 ==> don't get confused by this
3rd option: 32/24 is correct [Look at the explanation for 1st option]
4/3 ==> ?/24
4/3 =
4*8 / 3*8 = 32/24, not 3/24.
Hence, the 3rd option is correct.
14. What is the equation of a circle with a center at (4,−9) and a radius of 5?
A) (x+4)^2+(y−9)^2=5
B) (x+4)^2+(y−9)^2=25
C) (x−4)^2+(y+9)^2=25
The equation of a circle with a center at (4,−9) and a radius of 5 is
(x−4)^2+(y+9)^2=25. The correct Option C.
How to find equation of a circle?A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.
The equation of a circle with center (h, k) and radius r units is
(x−h)^2+(y−k)^2=r^2 .
where h = 4
k = -9
r = 5
The equation of the circle
(x−4)^2+(y−(-9))^2 = 5^2
The equation of the circle
(x−4)^2+(y+9)^2 = 25
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1. Choose the expression below that can be simplified using the product rule.
(4⁵ a⁰)(7²b⁻⁶)
(8⁵a⁻⁴)(b⁷c⁻⁵)
a⁻⁷b¹⁰ / c⁷ d¹⁴ . 15
(11²a⁻⁵)(11a⁹b⁷) / 5²
The only expression that can be solved using product rule of exponents is; (11²a⁻⁵)(11a⁹b⁷) / 5²
How to solve product rule of exponents?The Product Rule for Exponents states that to find the product of two numbers with the same base, add the exponents.
For example : a² * a³ = a²⁺³
1) We are given the exponential expression as; (4⁵ a⁰)(7²b⁻⁶)
From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.
2) We are given the exponential expression as; (8⁵a⁻⁴)(b⁷c⁻⁵)
From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.
3) We are given the exponential expression as; a⁻⁷b¹⁰ / c⁷ d¹⁴ . 15
From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.
4) We are given the exponential expression as; (11²a⁻⁵)(11a⁹b⁷) / 5²
Using product rule of exponents, we have;
(111/25) * (a⁻⁵⁺⁹) * b⁷
= (111/25)a⁴b⁷
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help PLEASE!!!!!
i need to pass math
Answer:
Step-by-step explanation:
pass it then
IF each term in the sum a1+a2+a3..._an . . . an is either 7 or 77 and the sum equals 350, which of the following could be equal to n ?
A. 38
B. 39
C. 40
D. 41
E. 42
If each term in the sum a1+a2+a3...+an is 7 and the sum equals 350, C: 40 would be equal to n.
In equation form, it is:
7s + 77t = 350
In this equation,
s represents the number of 7's
t represents the number of 77's
thus, the number of terms i.e n = s + t =?
now solving the equation,
7 (s + 11t) = 350
7 (s + 11t) = 350
s + 11t = 50
s + 11t = 50
now, if
s=39 & t =1
then
s + 11t = 50 -> 39 + 11 (1) = 50
Since the number of terms n = s + t
n = s + t
n = 39 + 1
n = 40
Hence, the if each term in the given sum is 7 which gives a total sum as 350, then number of terms in the given series is 40.
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Which choice is equivalent to the quotient below?
√32
OA.
√2
B. 4
C. 2
D. 24
SUBM
Answer:
C (2)
Step-by-step explanation:
• √32 = 4√2 ( bc √32 = √16×2 = √16×√2 = 4×√2 )
• √8 = 2√2 ( bc √8 = √4×2 = √4×√2 = 2×√2 )
So √32 ÷ √8 is equal to 4√2 ÷ 2√2
And there √2 cancels for both
So what you're left with is 4 ÷ 2
And 4÷2 = 2
48.
1. (2 x+1)⁰+67
2x+68
The measure of the value of x in the expression for the angle (2·x + 1)°, obtained using vertical angles theorem is; x = 33°
What are vertical angles?Vertical angles are angles formed when two lines intersect. Vertical angles are the angles vertically opposite each other, formed by the intersection of the two lines.
Vertical angles theorem states that the vertical angles formed by the intersection of two straight lines are congruent.
The angles (2·x + 1)° and 67° are vertical angles. therefore;
(2·x + 1)° ≅ 67° (Vertical angles theorem)
(2·x + 1)° = 67°, by the definition of congruency
(2·x)° = 67° - 1° = 66°
x = 66° ÷ 2 = 33°
The measure of x is 33°Therefore, plugging in the value of x = 33°, in the expression; (2·x + 1)° + 67°, we get;
(2·x + 1)° + 67° = (2 ×33 + 1)° + 67°
(2 ×33 + 1)° + 67° = 67° + 67° = 134°
The measure of the sum of the angles, (2 ×33 + 1)° and 67° is 134°
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Which ordered pair(s) are solutions to the system of inequalities?
2х + 3у > 2
3x + 5y > 1
(1,1)
(-2,-1)
(-2,3)
(7,-4)
the solutions to the system of inequalities are (1,1) and (-2,3).
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
2х + 3у > 2
3x + 5y > 1
for (1,1):
2+3 > 2 (true)
3+5 > 1 (true)
for (-2,-1)
-4-3 > 2 (false)
for (-2,3):
-4+9 >2 (true)
-6+15>1 (true)
for (7,-4):
14-12>2(false)
Hence, the solutions to the system of inequalities are (1,1) and (-2,3).
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when solving a system of equations, which of the following is a possible outcome? select all that apply. please help i will mark you brainliest.
When solving a system of two equations there are three possible outcomes for the solution of a system of three variables and two solutions for two variables.we can say that system of equation have infinite solutions.
What are the ways to solve system of equations?There are three methods used to solve systems of equations graphing, substitution, and elimination. To solve a system by graphing you simply graph the given equations and find the point(s) where they all intersect.Solve the linear equation for the remaining variable.
How do you find the solution to a system of equations?To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.
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What is the perform indicated operation for 1/3 × 6/7
The indicated operation 1/3 x 6/7 can be performed as 2/7.
What is multiplication operation?The concept that will be used in this operation is the multiplication operation.
One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream. By multiplying their outputs, you can multiply one function by another.
Given operation is 1/3 x 6/7
1/3 x 6/7
=[ (1 x 6)/(3 x 7) ]
= (6/21)
= 2/7
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check the correct question:
Perform the indicated operation. 1/3 x 6/7
You start at (-3, 2). You move left 1 unit and right 6 units. Where do you end?
The circumference of a circle is 9pi cm. What is the area, in square centimeters? Express answer in terms of pi.
==============================================
Work Shown:
C = 2pi*r
9pi = 2pi*r
r = (9pi)/(2pi)
r = 4.5
A = pi*r^2
A = pi*(4.5)^2
A = 20.25pi square cm
------------------
Explanation:
The first portion involves using the circumference C = 9pi to determine the radius r. The circumference is the perimeter around the circle.
Once we know that r = 4.5 cm, we then plug that into the area of a circle formula A = pi*r^2
Side notes:
4.5 = 9/220.25 = 81/4The following data points represent the number of chicken nuggets on each family member's plate. \qquad 1, 3, 0, 6, \large?1,3,0,6,?1, comma, 3, comma, 0, comma, 6, comma, question mark if the mean of the data set is 333 chicken nuggets, find the missing number of chicken nuggets. \qquad nuggets
The mean is 2, the missing data point must be 2 - 6 = -4. Therefore, the missing number of chicken nuggets is -4.
To find the mean of the data set, we need to add up all of the data points and divide by the number of data points. In this case, the sum of the data points is 1 + 3 + 0 + 6 = 10. Since there are 5 data points in total, the mean is 10 / 5 = 2.
Since the mean is 2, the missing data point must be 2 - 6 = -4. Therefore, the missing number of chicken nuggets is -4.
Mean is a type of average, which is a measure of central tendency. It is calculated by adding up a group of numbers and then dividing the sum by the number of numbers in the group. Mean is often referred to as the "arithmetic average".
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As per the given mean, the missing number of chicken nuggets is 5
The term mean in math is defined as the process of adding all numbers in the data set and then dividing by the number of values in the set.
Here we have given that the question assumes there are 5 people at the table.
And the number of nuggets are written as,
=> 1,3,0,6,and x.
Here x refers the missing number of chicken nuggets.
Then the equation is written as
=> 1 + 3 + 0 + 6 + x = 10 + x
Here we can multiply both sides by 5 to clear the denominator:
Then we have to isolate the x by subtracting 10 from both sides.
=> 10 + x - 10 = 15 - 10
Then the value of x is written as
=> x = 5
Therefore, the missing number of nuggets is 5.
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↓Read the passage and answer the question below.↓
"Around 7,000 years ago, agriculture emerged in Mesoamerica, including the domestication of maize, beans, and squash, causing major changes in the plants that people cultivated. Three sisters agriculture had spread across Mexico by 3,500 years ago, though they originated at different times."
------------------------------------------------------------------------------------------
How did the cultivation of maize affect settlement patterns in the American Southwest and present-day Mexico?
Warning: Choose 1 answer.
The cultivation of maize affected the settlement patterns in the American Southwest and present-day Mexico as B. It caused Native Americans in the area to develop permanent settlements supported by farming and irrigation system
What was the impact of the cultivation?The cultivation of maize had a significant impact on settlement patterns in the American Southwest and present-day Mexico. In the American Southwest, the cultivation of maize, along with other crops such as beans and squash, allowed for the development of more permanent settlements as people were able to rely on a stable food supply. This, in turn, led to the growth of larger, more complex societies and the development of elaborate systems of trade and exchange.
In present-day Mexico, the cultivation of maize played a central role in the development of complex societies such as the Olmec, Maya, and Aztec. These societies built sophisticated systems of agriculture, including terracing, irrigation, and crop rotation, which allowed them to support large populations and build elaborate cities. The cultivation of maize was also closely tied to the religious and cultural practices of these societies, and it played a central role in their economies and social systems.
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The original quantity is 10 and ghe new one is 13. What is the percent change?
Answer:
30%
Step-by-step explanation:
(13-10) / 10 * 100% = 30 %
Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $94 Two adults and three children must pay $66 Find the price of the adult's ticket and the price of a child's ticket
A child's ticket would cost $10 while and adult's ticket would cost $18.
What is a Linear Equation?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
For example, x² is a variable raised to the second power, but x is a variable raised to the first power.
5 is an example of a constant.
The expressions are;
3a + 4c = 94 ---- 1
2a + 3c = 66 ---- 2
Multiplying equation 1 by 2 and equation 2 by 3
6a + 8c = 188 ---- 3
6a + 9c = 198 ---- 4
--------------------------
- c = - 10
therefore;
c = 10
Substituting c in equation 3
6a + 8(10) = 188
6a + 80 = 188
6a = 188 - 80
6a = 108
a = 18
Therefore, child's ticket costs $10 while and adult's ticket cost $18.
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Need help doing this math problem the one that says AE is the one I need to do.
Check the picture below.
We are looking at rectangles where one side is of length 5.0 cm. Amongst those are some that can be cut into a square and a rectangle one of which has an area of 4,0 cm². How many such rectangles are there?
A: 1
B: 2
C: 3
D: 4
E: 5
Spoiler: According to the answer key it is D but I could only find 3 variations.
the answer is D : 4
How to calculate how many of these rectangles are there?According to the problem statement, one side of the rectangle is of length 5 cm. The other side can have any length greater than 4 cm (since the area of the rectangle should be greater than 4 cm^2).
Let's call this other side "x".
We know that the area of a rectangle is given by the formula A = l*w, where l is the length and w is the width.
Therefore, we can write the equation: 5*x = A, where A is the area of the rectangle.
We can also say that the area of the square and the rectangle is equal to 4 cm^2.
If we call the side of the square "y", then we can write the equation: y^2 = 4 cm^2.
Solving for y, we get: y = 2 cm.
Therefore, the length of the rectangle that can be cut into a square and a rectangle of area 4 cm^2 is 5 cm - y = 5 cm - 2 cm = 3 cm.
So, there are 4 possible rectangles that can be cut into a square and a rectangle of area 4 cm^2: (5,3), (3,5), (6,4), and (4,6).
So the answer is D : 4
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Translate the sentence into an equation.
Two more than the quotient of a number and 4 is 8.
Use the variable b for the unknown number.
The Equations is b/4 + 2= 8 and b = 24.
What is expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.
Mathematical statements called expressions must contain at least two phrases including numbers, variables, or both, and they must be joined by an operator.
Given Two more than the quotient of a number and 4 is 8,
Let number be b
b/4 + 2= 8
b/4 = 8 -2
b/4 = 6
b = 24
Hence, two more than the quotient of a number is 24.
Hence the equation for phrase is b/4 + 2= 8 and b = 24.
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A truck is carrying 5 cars weighing an average of 3,000 pounds each.
What is the total weight in tons of the cars on the truck?
The total weight of the cars the truck is carrying is
tons.
13 quarts of soil are used to completely fill 4 flower pots. If each pot holds the same amount of soil, how many quarts will each pot hold? Solve on paper and check your w
The number of quarts of soil in each pot will be 3.25 quarts.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
13 quarts of soil are used to completely fill 4 flower pots. If each pot holds the same amount of soil.
Then the number of quarts of soil in each pot will be given as,
⇒ 13 ÷ 4
⇒ 13 / 4
⇒ 3.25
The number of quarts of soil in each pot will be 3.25 quarts.
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Find the sum.
1. 1/3+1/5=
2. 1/8+2/6=
3. 8/9+11/12=
4. 1/7+5/8=
5. 1/4+2/4=
6. 1/2+3/9=
7. 1/10+1/4=
8. $3/11+11/12=
a. The sum of 1/3+1/5= 8/15
b. The sum of 1/8+2/6 = 3/8
c. the sum of 8/9+11/12= 1 87/108
d. the sum of 1/7+5/8= 1 7/36
e. the sum of 1/4+2/4= 3/4
f. the sum of 1/2+3/9= 5/6
g. the sum of 1/10+1/4= 7/20
h. the sum of 3/11+11/12 = 1 25/132
What is sum of fractions?Sum of fractions is the addition of fractions. This is obtained by by using the L.C.M of the denominator method.
a. 1/3 + 1/5 = (5+3)/15 = 8/15
b. 1/8+2/6 = (3+6)/24 = 9/24 = 3/8
c. 8/9 + 11/12 = (96+99)/108 = 195/108 = 1 87/108
d. 1/7+ 5/8 = (8+35)/56 = 43/36 = 1 7/36
e. 1/4+ 2/4 = (2+1)/4 = 3/4
f. 1/2 + 3/9 = (9+6)/18 = 15/18 = 5/6
g. 1/10+1/4 = (2+5)/20 = 7/20
h. 3/11+ 11/12 = (36+121)/132 = 157/132 = 1 25/132
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pls help this is confusing and i dont get it at all......
Completing the table with the appropriate percentage and decimals will be:
Fraction Decimal Percentage
1/4. 0.25. 25% of 1
1/10. 0.1. 10% of 1
3/4. 0.75. 75% of 1
1/5. 0.2. 20% of 1
3/2. 1.5. 150% of 1
7/5. 1.4. 140% of 1
How to calculate the percentage be decimal?It should be noted that based on the information, 0.1 will be 1/10. The percentage will be:
= 1/10 × 100
= 10%
0.1 to fraction will be:
= 1/10
The percentage for 1/5 will be:
= 1/5 × 100
= 20%
1/5 to decimal will be:
= 1/5
= 0.2
The decimal 1.5 will give 150%
The fraction for 1.5 will be:
= 1.5 / 1
= 15 / 10
= 3/2
Also 3/4 as percentage will be:
= 3/4 × 100
= 75%
75% to decimal will be:
= 75 / 100
= 0.75
140% to fraction will be:
= 140 / 100
= 7 / 5.
The decimal for 140% will be:
= 140 / 100
= 1.4
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Henry ran 1 5_8 miles in the morning and 9_10 miles in the afternoon. About how many miles did he run in all?
When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles
How to find the number of miles that Henry ranThe number of miles Henry ran is calculated by addition operation
The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all
The procedure involves addition of tractions and done as follows
= 1 5/8 + 9/10
= 13/8 + 9/10
adding both fractions will result to
= 101/40 miles
= 2 21/40 miles (as a mixed number)
Henry ran a sum of 2 21/40 miles
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resolve the equation:
6*(9^3x)-13*(6^3x)+6*(4^3x)=0
The solution to the equation 9(6^3x) - 13(6^3x) + 4(6^3x) = 0 is x = 0.
What is the equation?Generally, To solve the equation we try to get the values to be coherent by writing as
9(6^3x)-13*(6^3x)+4*(6^3x)=0
Therefore we solve the coefficients of the solution
To solve this equation, we can first distribute the constants in front of the parentheses:
9(6^3x) - 13(6^3x) + 4(6^3x) = 0
This simplifies to:
(9 - 13 + 4)(6^3x) = 0
Then, we can simplify the expression in the parentheses:
(0)(6^3x) = 0
This means that either (0) = 0 or (6^3x) = 0.
The second case is not possible, because the base of an exponent can't be zero. So, the only solution to this equation is x = 0.
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y varies directly with x. When x is 3, y is 15. Find y when x = 21.
Answer:
105
Step-by-step explanation:
y=kx where k is a constant
When y=15 and x=3
15=k3
k=15/3
k=5
Therefore y=5x
So, when x=21
y=21x5
=105
Please mark me brainliest
Jill is studying a strange bacterium. When she first
looks at the bacteria, there are 1000 cells in her
sample. The next day, there are 2000 cells. Intrigued,
she comes back the next day to find that there are
4000 cells!
Create a table and a graph for this situation. The
inputs (x) are the days that have passed after she
first began to study the sample, and the outputs (y)
are the number of bacteria cells.
We have prepared the table and drawn the graph.
What is a graph of a function?
A graph of a function is a visual representation of the relationship between the inputs (x-coordinates) and the outputs (y-coordinates) of a function. The inputs are typically represented on the x-axis and the outputs are represented on the y-axis.
Table:
x (days) y (number of cells)
0 1000
1 2000
2 4000
Graph:
The graph would be a line graph with x-axis showing the day passed and y-axis showing the number of bacteria cells,
The point (0,1000) would be plotted on the graph, representing the initial number of bacteria cells on the first day.
The point (1,2000) would be plotted on the graph, representing the second day and the number of bacteria cells.
The point (2,4000) would be plotted on the graph, representing the third day and the number of bacteria cells.
The graph would be a upward sloping line, representing the growth of bacteria cells.
Hence we have prepared the table and drawn the graph.
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Find the value of X. (please no spamming and do both problems) I'll make brainliest.
Answer:
13. x=4
14. x=8
Step-by-step explanation:
We know that these are both isosceles triangle because the two base angles are the same on #13, and the two sides are the congruent on #14. So all we need to do is make equations of equivalence. So #13 9x-8=28 and #14 11x-18=70. Look at the work shown in the image and follow those steps.
-Hope this helped & Happy New Year!
The relationship between pressure (P),
volume (V), and temperature (T) for
an ideal gas is stated by the Ideal Gas
Law: PV = nRT, where n is the number
of moles and R is the universal gas
constant. If n is kept constant, which of
these statements is not true according to
the equation?
A Decreased volume at constant
pressure reduces temperature.
B Decreased volume at constant
temperature increases pressure.
C Decreased temperature at constant
volume reduces pressure.
D Decreased temperature at constant
volume increases pressure.
Answer:
A
Step-by-step explanation:
For an ideal gas : PV=RT
And the internal energy of an ideal gas:
E
in
=
2
3
RT
E
in
=
2
3
PV
V
E
in
=
2
3
P
Energy density (E)=
2
3
P
P=2/3E
What value in the replacement set is a solution to this equation? 3(n+7)=48 Replacement set: {8, 9, 10} Drag the solution into the box. Put responses in the correct input to answer the question.
In the replacement set, 9 is the solution to this equation 3 (n+7) = 48.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 3 (n + 7) = 48
And, Replacement set: {8, 9, 10}
Now, We can solve the expression as;
⇒ 3 (n + 7) = 48
Divide by 3,
⇒ n + 7 = 48/3
⇒ n + 7 = 16
Subtract 7, we get;
⇒ n = 16 - 7
⇒ n = 9
Thus, The solution of the equation is, 9.
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