The expression will be given as -4x² + 3x. Thus, option B is correct answer.
Area may be defined as the total amount of space which is covered by an entity. The area for a square will be given by the product of its sides and the area of the rectangle will be given as the product of its length and breadth. It is given that the area of Maria's garden is 8x² - 3x and the length and breadth of Jamal's garden are 4x - 2 and 3x respectively. The area of Jamal's garden is given by A = l×b = (4x - 2) × 3x = 12x² - 6x.
Now, difference between Maria's garden and Jamal's garden is given by
(8x² - 3x) - (12x² - 6x)
= 8x² - 3x - 12x² + 6x
=> -4x² + 3x which is the required answer.
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A) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A.0 ≤ x ≤ 2
B.2 ≤ x ≤ 5
C.5 ≤ x ≤ 6
D.6 ≤ x ≤ 8
B) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height increasing?
A.0 ≤ x ≤ 2
B.40 ≤ y ≤ 70
C.5 ≤ x ≤ 8
D.40 ≤ y ≤ 10
C) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height decreasing the fastest?
A.5 ≤ x ≤ 9.5
B.8 ≤ x ≤ 9.5
C.6 ≤ x ≤ 8
D.5 ≤ x ≤ 6
D) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Justify your answer from Part C.
A.5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing.
B.8 ≤ x ≤ 9.5 is the interval where the slope is the steepest.
C.6 ≤ x ≤ 8 is the interval where the balloon's height decreases the most.
D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
Please help as fast as possible <3
From the given linear function, we have that:
A. The function is constant on the following interval: B.2 ≤ x ≤ 5.
B. The function is increasing on the following interval: A.0 ≤ x ≤ 2.
C. The function is decreasing the fastest on the following interval: D.5 ≤ x ≤ 6.
D. The justification for the previous item is: D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
When a function is constant?A function is constant when it's graph is an horizontal line, hence in this problem the function is constant for two intervals.
2 ≤ x ≤ 5.10 ≤ x ≤ ∞.Hence, in item A, option B is correct.
When a function is increasing?A function is increasing on the intervals that y is increasing while x increases, that is, the function is moving right and up.
Hence, in item B, option A is correct.
When a function is decreasing?A function is decreasing on the intervals that y is decreasing while x increases, that is, the function is moving right and down.
The decrease is faster when the division of the change in the output by the change in the input has the lower value(greater absolute negative).
Hence:
In item 3, option D is correct.In item 4, option D is correct.More can be learned about linear functions at https://brainly.com/question/24808124
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please! Is for today!! HELP!!
The given pairs of lines have been identified as parallel, perpendicular lines or neither as explained below.
How to Determine if Two Lines are Parallel or Perpendicular?Two lines are parallel if they have the same slope (m), while they are perpendicular to each other if their slopes are negative reciprocal of each other.
The slope in a given equation of a line that is in slope-intercept form, y = mx + b, is represented as "m" in the equation.
1. y = 3x - 7 and y = 3x + 1 both have the same slope (m) of 3. They are parallel lines.
2. y = -2/5x + 3 and y = 2/5x + 8 both have the different slope (m), which are not negative reciprocal to each other. They are neither parallel nor perpendicular lines.
3. The slope of y = -1/4x is -1/4. The slope of y = 4x - 5 is 4. -1/4 is the negative reciprocal of 4. Therefore, the lines are perpendicular.
4. 2x + 7y = 28 can be rewritten as y = -2/7x + 4, the slope (m) is -2/7.
7x - 2y = 4 can be rewritten as y = 7/2x - 2, the slope (m) is 7/2.
-2/7 and 7/2 are negative reciprocals.
They are perpendicular lines.
5. The slope of y = -5x + 1 is -5.
x - 5y = 30 can be rewritten as y = 1/5x - 6, the slope is 1/5.
The lines are perpendicular.
6. 3x + 2y = 8 can be rewritten as y = -3/2x + 4, the slope (m) is -3/2.
2x + 3y = -12 can be rewritten as y = -2/3x - 4, the slope (m) is -2/3.
The lines are neither.
7. The slope of y = -4x - 1 is -4.
8x + 2y = 14 can be rewritten as y = -4x + 7, the slope is -4.
They are therefore parallel lines.
8. x + y = 7 can be rewritten as y = -x + 7, the slope (m) is -1.
x - y = 9 can be rewritten as y = x - 9, the slope (m) is 1.
The lines are perpendicular.
9. They have the same slope of 1/3. They are parallel lines.
10. They have different slopes that are not negative reciprocals, therefore, they are neither.
11. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.
12. They have the same slope of 3/4. They are parallel lines.
13. They have the same slope of 1. They are parallel lines.
14. Their slopes are -5/4 and 4/5. Therefore, they are perpendicular lines.
15. Their slopes are not negative reciprocals and are not the same, therefore, they are neither.
16. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.
17. They are both vertical lines, therefore they are neither.
18. x = 1 is a vertical line while y = -8 is a horizontal line that meets perpendicularly. Therefore, the lines are perpendicular.
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the minimum distance between earth and mars is about 33,900,000 miles how can this distance be expressed in scientific notation
Answer:
3.3⁷
Step-by-step explanation:
To make a scientific notation the whole number must be more than 1 and less that 9.9 repeating. To do this, move the decimal however many times it takes to make the whole number (the number before the decimal) more than one and less that 9.9 repeating. For the number 33,900,000, the decimal must be moved 7 times, which is why I added the 7 exponent. Also when making a number into a scientific notation, be sure to add the number after the whole number, placing it after the decimal.
Write the following number in standard decimal form.
eleven and seventy-eight hundredths
Answer: 11.78
Step-by-step explanation:
1. Shelley comparó el número de robles al número de arces como parte de un estudio sobre árboles de madera dura en una arboleda. Ella contó 9 árboles de arce por cada 5 árboles de roble. Más adelante en el año hubo un problema de insectos y muchos árboles murieron. Se plantaron nuevos árboles para asegurarse de que hubiera el mismo número de árboles que antes del problema de insectos. La nueva razón del número de árboles de arce al número de árboles de roble es 3:11. Después de plantar nuevos árboles, habia 132 robles. ¿Cuántos árboles de arce más había en la arboleda antes del problema de insectos que después del problema de insectos? Explica.
Answer:
Step-by-step explanation:
855555555555fhhhhhhhhhhhhhhhhg6
Write an equation of the line that passes through point (2, −4) and has the slope m=.5. y=
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since slope is 5, equation is y = 5x + c.
Substitute (2,-4) into the equation to find c.
-4 = 5(2) + c
c = -14
Hence equation of line is y = 5x - 14
A penny is dropped from the top of a new building. Its height in feet can be modeled by the equation y = 256 - 16^{2} , where x is the time in seconds since the penny was dropped. How long does it take for the penny to reach the ground?
I would greatly appreciate help with this word problem, thanks!
≧◠ᴥ◠≦✊
Answer:
4 seconds
Step-by-step explanation:
Given equation:
[tex]y=256-16x^2[/tex]
where:
y = The height of the penny (in feet).x = The time since the penny was dropped (in seconds).The penny reaches the ground when the height is zero, so when y = 0.
Substitute y = 0 into the given equation and solve for x:
[tex]\begin{aligned}y&=256-16x^2\\y=0 \implies 0&=256-16x^2\\0+16x^2&=256-16x^2+16x^2\\16x^2&=256\\\dfrac{16x^2}{16}&=\dfrac{256}{16}\\x^2&=16\\\sqrt{x^2}&=\sqrt{16}\\x&=\pm4\end{aligned}[/tex]
As time is positive, x = 4 only.
Therefore, it takes 4 seconds for the penny to reach the ground.
what is 71.04 in expanded form
Answer:
(7 x 10) + (1 x 1) + (0/10) + (4/100)
70 + 1 + 0.04
70 + 1 + 4/100
Step-by-step explanation:
Here are all the expanded forms I can think of off the top of my head, sorry if this didn’t help much!
On a coordinate plane, a triangle has points R (negative 3, 4), T (negative 1, negative 4), and S (negative 4, negative 2).
What are the coordinates of the image of vertex R after a reflection across the y-axis?
(–4, 3)
(4, –3)
(–3, –4)
(3, 4)
Translation of negative 6 units x, negative 2 units y composition reflection across the x-axis
Reflection across the x-axis composition translation of negative 6 units x, negative 2 units y
Translation of negative 6 units x, negative 2 units y composition 90 degree rotation about point 0
90 degree rotation about point 0 translation of negative 6 units x, negative 2 units y
The reflection of the coordinate (-3, 4) over the y-axis is (3, 4).
Reflection of coordinatesThe Y-coordinates do not change when a point is reflected across the Y-axis. However, the X-coordinates are changed into their opposite signs.
Given the coordinates of the triangles RST as shown below;
R = (-3, 4)
S = (-1, -4)
T = (-4, -2)
If (x, y) for instance is reflected over the y-axis, the resulting coordinate will be (-x, y). Similarly, if the coordinate R (-3, 4) is reflected over the x-axis, the resulting coordinate point will be (3, 4)
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Which number rounds to 32.6 when rounded to the nearest tenth?
1 32.58 2 32.65 3 32.68 4 32.75
1. Passes through (6, 2) and (-3, 1)
The equation of line is found as y = 9x - 16.
What is described as the equation of the line?The "equation of a line" is an important topic in high school algebra. This is an x and y equation whose solution set is just a line in the (x,y) plane. The "slope-intercept" form is the most commonly used in algebra. y = mx + b, where, m is the slope and b is the y-intercept.For the given question;
The passing points of the line are (6, 2) and (-3, 1).
The slope of line is calculated as;
slope = m = (y₂ - y₁)/(x₂ - x₁)
Where,
(x₁, y₁) = (6, 2)
(x₂, y₂) = (-3, 1)
Put the values;
m = (-3 - 6)/(1 - 2)
m = -9/-1
m = 9
Then, the equation of line using slope intercept form is-
y - y₁ = m (x - x₁)
Put the values;
y - 2 = 9(x - 2)
Simplifying;
y -2 = 9x - 18
y = 9x - 16
Thus, the equation of line is found as y = 9x - 16.
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The complete question is -
What is the equation of the line that passes through P( 6,2) and S (- 3,1)?
Which equation reveals the minimum or maximum value of f (x) without changing the form of the equation?
)A) ƒ (x) = (x+3)(x − 4)
(B) ƒ (x) = x² - 8x +15
(C)ƒ (x) = (x + 2)² − 1
(D) f(x) =x^2 +2x -1
The function has a minimum if the x2 coefficient is positive. If it is negative, the function has reached its limit. If you have the function 2x2+3x-5, for example, the function has a minimum because the x2 coefficient, 2, is positive. Divide the x term coefficient by twice the x2 term coefficient.
What exactly is an equation?A formal statement of the equality or equivalence of two mathematical or logical expressions. : a quantitative expression representing a chemical reaction using chemical symbols.A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. After solving this equation, we obtain the value of the variable x as x = 7.An equation is made up of expressions that have the same value. A formula is a two- or more-variable equation that represents a relationship between the variables.Hence, The function has a minimum if the x2 coefficient is positive. If it is negative, the function has reached its limit. If you have the function 2x2+3x-5, for example, the function has a minimum because the x2 coefficient, 2, is positive. Divide the x term coefficient by twice the x2 term coefficient.
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Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles. She worked at a steady rate after the first day. Use an equation in point-slope form to determine how many days Lizzy took to place all of the 100 tiles needed to finish the floor.
y - y1 = m (x - x1)
It will take 11 days to place all of the 100 tiles needed to finish the floor.
What is point slope form?The slope of a line and any points it contains determine the point-slope form of the line. When a point on the line and the slope are provided, the form's objective is to represent the equation of the complete line.
Given Data
She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles.
Points are:
(1,5) (4,35)
Slope = [tex]\frac{30}{3}[/tex]
Slope = 10
y - y₁ = m(x -x₁)
y - 5 = m(x- 1)
For 100, it will need,
100 - 35 = 10(x-4)
65 = 10x - 40
105 = 10x
x = 10.5
It will take 11 days to place all of the 100 tiles needed to finish the floor.
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x² - 7x-18 = 0
What is the set of all values of x that satisfy the equation above?
A. (-9,2)
B. (-6, 3)
C. (6, 3)
D. (9,-2)
method 1.
[tex] {x}^{2} - 7x - 18 = 0[/tex]
simplify:
[tex](x - 9)(x + 2) = 0[/tex]
so the answer is (D) x =9 or x = -2
method 2.
if
[tex] {a}^{2}x+ bx + c = 0[/tex]
[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \: or \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
so
[tex]x = \frac{ - ( - 7) + \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)} or\frac{ - ( - 7) - \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)}[/tex]
[tex]x = \frac{ 7 + \sqrt{ 121 } }{2}or\frac{ 7 - \sqrt{ 121 } }{2}[/tex]
[tex]x = 9 \: \: \: \: or - 2[/tex]
We can find the remainder for the quotient using either substitution or synthetic division. Using either method, explain whether or not we can conclude that x - 5 is a factor of the polynomial f(x)=x^3-x^2-17x-15. (Your answer must include what that remainder value is and what it indicates
We may get the same conclusion using either approach, which is that x—5 is a factor of the polynomial.
This will be discussed in further detail below.
Can you explain what the polynomial is?Explain, taking into account the fact that, using either method, whether or not we can think of x-5 as a factor in the polynomial based on the given information.
Generally, the equation for the problem is mathematically given as
f(x)=x^3-x^2-17 x-15
Therefore, If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this
[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]
In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).
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can y’all help me out with this worksheet?
Value of x [tex]\frac{36}{5}[/tex]
value of m∠3 = [tex]\frac{462}{5}[/tex]
Define angles.When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolized by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees. A figure made up of two rays meeting at the vertex of the angle can be referred to as an angle.
Given Data
m∠3 = 17x - 30
m∠6 = 12x +6
Angle pair - exterior alternate angle
For the value of x,
17x - 30 = 12x + 6
17x - 12x = 6 + 30
5x = 36
x = [tex]\frac{36}{5}[/tex]
For m∠3,
17x - 30
Equating value of x,
17([tex]\frac{36}{5}[/tex]) - 30
[tex]\frac{612-150}{5}[/tex]
[tex]\frac{462}{5}[/tex]
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Please tell me the answer to this and i will mark you brainliest
Answer:
A = 2x0 = 0
B= 2x2 = 4
Similarity: they both pass the origin
Difference: They have different gradients: y=2x has a gradient of 2 and y=x has a gradient of one
Step-by-step explanation:
A = 2x0 = 0
B= 2x2 = 4
Similarity: they both pass the origin
Difference: They have different gradients: y=2x has a gradient of 2 and y=x has a gradient of one
A career counselor decides to make monthly payments of $150 on credit card debt of $3,482.46 and discontinue using that credit card. Assuming the monthly interest rate is 1.55%, it will take the counselor approximately 30 months to repay the debt. How many fewer months would it take to repay the debt if the counselor makes monthly payments of $200? (Round your answer to the nearest month.)
The $150 monthly payment on the $3,482.46 credit card loan at 1.55% monthly interest rate gives the number of fewer months it would take to repay the loan if the monthly payment is $200 as 10 months
What is a monthly interest rate?A monthly interest rate is obtained from an annual interest rate by dividing it by 12.
The monthly payment formula is presented as follows;
[tex] \displaystyle{M = \frac{P \cdot r \cdot (1 + r)^{n} }{ (1 + r)^{n} - 1}} [/tex]
Where;
M = The monthly payments = $150
P = The loan amount = $3,482.46
r = The monthly interest rate = 1.55% = 0.0155
n = The number of periods (monthly payments) = 30
When the monthly payment, M = $150, it takes the career councilor approximately 30 months for the debt to be repaid.
When the monthly payment, M = $200, we have;
[tex]\displaystyle{200 \approx \frac{3482.46 \times 0.0155 \times (1 + 0.0155)^{n} }{ (1 + 0.0155)^{n} - 1}} [/tex]
Which gives;
[tex] \displaystyle{200 \times ((1 + 0.0155)^{n} - 1)= 3482.76 \times 0.0155 \times (1 + 0.0155)^{n}} [/tex]
[tex] \displaystyle{200 \times (1.0155)^{n} - 200 = 53.98278 \times (1.0155)^{n}} [/tex]
[tex]\displaystyle{ 146.017 \times (1.0155)^{n} = 200 }[/tex]
n•ln(1.0155) ≈ ln(1.3697)
[tex] n = \frac{ln(1.3697)}{ln(1.0155)} \approx 20.45[/tex]
The number of months it will take to pay back the loan using a monthly payment of $200 is therefore approximately 20 months
The number of fewer months it takes to repay the loan is therefore;
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Please help
Solve for x. Show each step of the solution.
2.54-x+12=21-42.5x+7
The value of the variables 'x' in the equation is 0. 32
What are algebraic expressions?Algebraic expressions can be defined as expressions consisting of constants, factors, coefficients, variables as well as terms.
They are also composed of certain mathematical operations such as;
AdditionSubtractionDivisionBracketParenthesesMultiplication, etcGiven the expression;
2.54 - x + 12 = 21 - 42.5x + 7
To determine the value of x, we have to follow the following steps;
collect like terms
-x + 42. 5x = 21 + 7 - 12 - 2. 54
Add or subtract like terms
41. 5x = 13. 46
Make 'x' the subject of formula by dividing both sides by the coefficient of x
x = 13. 46/41. 5
Divide the values
x = 0. 32
Hence, the value of x is 0. 32
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What is the equation of the line that passes through (-2, 2) and (1,-4)?
Oy=-2x-4
OY=2x-2
Oy=2x+4
Oy=-2 X-2
Answer:
2x-4 ravdhzfjztjt,h,rufhfjfjfjufff,ufhfutitig
Step-by-step explanation:
xbsndnsnfnzndnzanayrURJfjgjgkgjgk gk
9 x 87 = (9 x _) + (_ x 7)
The missing numbers here are given by 9×(80+7)=(9×80)+(9×7)
What are missing numbers?
Missing numbers are the numbers that got missed in the given series of numbers with similar differences among them. The process of writing the missing numbers is termed as finding similar changes between those numbers and filling their missing values in their specific series and places.
Here, given 9×87=(9×some number)+(another number×7)
Let x and y be the missing numbers.
9×87=(9×x)+(y×7)
We can write 9×87=9×(80+7)
Using distributive property,
9×87=(9×80)+(9×7)
On comparing, we get x=80,y=9.
Hence, the missing numbers are 80, 9
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okay soo.. Vance wants to determine if an old photo frame is still rectangular. The height of the frame is 8 inches, the base is 6 inches and the diagonal is 10 inches long. Is the old photo frame still rectangular? how do you know?
We can check this using Pythagoras' theorem.
Explain Pythagoras' theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It asserts that the area of the square with the hypotenuse (the side opposite the right angle) equals the sum of the areas of the squares with the other two sides. This theorem may be expressed as an equation linking the lengths of the legs a, b, and the hypotenuse c, which is known as the Pythagorean equation: a² + b² = c²
According to Pythagoras' theorem, as we see a² + b² = c²
6² + 8² = 10², so the photo frame is still a rectangle.
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Whats x+7y=-39?
Please help me and show me how to work this whole thing out thank you so much!!!
Answer:
Step-by-step explanation:
Let's solve for x.
x+7y=−39
Step 1: Add -7y to both sides.
x+7y+−7y=−39+−7y
x=−7y−39
Let's solve for y.
x+7y=−39
Step 1: Add -x to both sides.
x+7y+−x=−39+−x
7y=−x−39
Step 2: Divide both sides by 7.
7y/7 = −x−39/7
y= −1/7x+−39/7
Robin’s favorite pound cake recipe needs 2 1/3 cups of flour. She plans to make 2 cakes for a picnic. She has 4 1/2 cups of flour in her cabinet. How much more flour does she need to make the 2 cakes
Answer: 1/6
Step-by-step explanation:
Given g(x) = 2x + 3, find g(3).
Answer:
g(3) = 9
Step-by-step explanation:
replace 3 in x
g(3) = 2(3) +3 = 6 + 3 = 9
Hope this helps
convert -5C into fehrenheit
Order from least to greatest .003 3.03 33.03 .303 .383 .030
Answer:
0.003, 0.03, 0.303, 0.383, 3.03, 33.03
Step-by-step explanation:
every tuesday joe has a beer with 2 friends. they each have a unique token and every tuesday, they each put their token in a hat and ask the bartender to draw one token out. the person whose token is drawn pays the tab. over the next 3 weeks, what is the chance that joe has to pay the tab at least once? fill in the answer as a percent carried to one decimal place, but without the percent sign.
0.384 is the chance that joe has to pay the tab at least once by probability.
What is a math illustration of probability?
The likelihood or chance of an event happening is known as probability. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.Every tuesday Joe has beer with 4 friends .
Each have unique token , and the person whose token is drawn pays the tab.
Since , there are Joe and 4 friends , so we have total of 5 persons.
Now, probability that Joe token will be drawn is = 1 / 5 { 1 (Favourable Outcome) \small / 5 (Total Outcome) }
i.e there is 1/5 = 0.20 probability that Joe token will be drawn and he will pay the tab.
Over the next 3 weeks , we need to find the change that Joe pays the tab exactly one time.
Here we have n = 3 ( weeks ) , and probability of success is p = 0.20
i.e probability that Joe will pay tab (Success) is p = 0.20 and probability that Joe will not pay tab ( failure ) is 1-p = 0.80.
So we can model it by binomial distribution , as we have only two outcome which are i) Joe pays the tab , ii) Joe do not pay tab.
X ~ B(n=3 , p =0.20)
We need to find P(X=1) , i.e exactly one time Joe pays the tab .
Since, we have approximate that X follows binomial distribution , so we have
f(x) = P(X=x) = \small \binom{n}{x}p^x(1-p)^{n-x}
Hence
P(X=1) = ( n 1 ) p¹ ( 1 - p)ⁿ⁻¹
= ( 3 1 ) 0.2¹ ( 1 - 0.2)³⁻¹
= 3 * 0.2 * 0.8²
= 0.384
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Nathan and his brother Zach love to play video games. Right now, Nathan's score is 11 less than 2 times Zach's score.-example, if Zach has 80 points, then Nathan has 149 points. Find four more possibilities for the brothers' scores and fir he table below. Then write a rule relating Nathan's score, N, to Zach's score, Z.
Zach's score, Z, and Nathan's score, N, are related by the formula
2Z-11=N.
This is further explained below.
What are algebraic expressions?Generally, Assume Nathan has a score of N and Zach has a score of Z.
Zach's score is 11 points higher than Nathan's.
It implies,
N equals twice of Z minus 11.
We may format it as follows:
2Z - 11 = N
There are now four possible outcomes for these two brothers' scores:
Zach's score will be determined using algebraic formulas if Nathan's score is 81.
2Z - 11 = 81
2Z = 92
Z = 46
Zach's score will be 61 if Nathan receives a score of 111.
Zach's score will be 121 if Nathan's score is 231 or higher.
Zach's score will be 456 if Nathan's score is 901.
The formula 2Z - 11 = Z is a rule that connects Nathan's and Zach's scores.
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Chang invested his savings in two investment funds. the $3000 that he invested in fund a returned a 2% profit. the amount that he invested in fund b returned a 7% profit. how much did he invest in fund b, if both funds together returned a 4% profit?
Using algebraic expression and equation, he invested $2000 in fund b.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Let x = amount he invested in fund b
If both funds together returned a 4% profit, then the sum of the profit in each investment is equal to 4% of the total investment.
$3000(0.02) + x(0.07) = (3000 + x)(0.04)
Solving for x,
$3000(0.02) + x(0.07) = (3000 + x)(0.04)
$60 + 0.07x = $120 + 0.04x
0.07x - 0.04x = $120 - $60
0.03x = $60
x = $2000
amount he invested in fund b = $2000
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