If she starts with £400 in her account, her balance for the next three years IS; $608.35
How to solve exponential equation?
The general formula for exponential equation is;
y = a(b)ˣ
where;
a represents an initial value or amount
b is the constant multiplier, is a growth factor or factor of decay.
We are given;
Initial value; a = £400
constant multiplier; b = an increase of 15% yearly = 1.15
Thus, her balance for the next three years is;
y(3) = 400(1.15)³
y(3) = $608.35
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Evaluate the expression (x+3)(3x^2-4x-5) ?
3x³ + 5x² - 17x - 15
Step-by-step explanation:Here are the steps for solving your problem:1. Distribute
(x + 3)(3x² - 4x - 5)
x(3x² - 4x - 5) + 3(3x² - 4x - 5)
2. Distribute
x(3x² - 4x - 5) + 3 (3x² - 4x - 5)
3x³ - 4x² - 5x + 3 (3x² -4x - 5)
3. Distribute
3x³ - 4x² - 5x + 3 (3x² -4x - 5)
3x³ - 4x² -5x + 9x² - 12x - 15
4. Combine like terms
3x³ - 4x² -5x + 9x² - 12x - 15
3x³ + 5x² - 5x - 12x - 15
5. Combine like terms
3x³ + 5x² - 5x - 12x - 15
3x³ + 5x² - 17x - 15
Solution:
3x³ + 5x² - 17x - 15
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Select all the equations that are equivalent to y-4 =2/3(x-1)
The equivalent equations of y - 4 = 2/3(x - 1) are y - 4 = 2/3x - 2/3 and y = 2/3x + 10/3
How to determine the equivalent equation?From the question, we have the following parameters that can be used in our computation:
y - 4 = 2/3(x - 1)
We start by expanding the bracket
So, we have the following representation
y - 4 = 2/3x - 2/3
Next, we add 4 to both sides of the equation
This gives
y - 4 + 4 = 2/3x - 2/3 + 4
Evaluate the like terms
So, we have the following representation
y = 2/3x + 10/3
Hence, the equivalent equation is y = 2/3x + 10/3
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Could some one please help me with this question.
In the octagon, the measurement of the largest exterior angle is 90°.
What is polygon?In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words, poly, which means numerous and gon, means sides.
The given exterior angles of the octagon are,
x°, 2x°, 3x°, 4x°, 5x°, 7x°, 8x°, and 10x°.
The sum of the exterior angle of the octagon is 360°.
Implies that,
x + 2x + 3x + 4x + 5x + 7x + 8x + 10x = 360
40x = 360
x = 9
The largest exterior angle = 10 x = 10 × 9 = 90°.
The required largest exterior angle is 90°.
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f(x)=x²-25
Find f(9)
How is a system of two linear inequalities in two variables different from a system of two linear equations in two variables?
Answer:
A system of two linear inequalities in two variables is a set of two linear inequalities that involve two variables, such as x and y. A system of two linear equations in two variables is a set of two linear equations that involve two variables, also typically x and y.
There are several key differences between a system of two linear inequalities in two variables and a system of two linear equations in two variables:
Inequalities use symbols such as "less than" or "greater than" to indicate the relationship between the variables, whereas equations use the equal sign (=).
The solution to a system of linear inequalities is a region in the coordinate plane, whereas the solution to a system of linear equations is a single point.
The solution to a system of linear inequalities is found by graphing the inequalities on the coordinate plane and finding the region where they intersect, whereas the solution to a system of linear equations is found by solving the equations for the values of the variables.
The solution to a system of linear inequalities may include an infinite number of points, whereas the solution to a system of linear equations is always a finite number of points.
Overall, the main difference between a system of two linear inequalities in two variables and a system of two linear equations in two variables is the way in which the solutions are represented and found.
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[tex]x=-2 \implies y=(1/3)^{-2}=3^{2}=9\\\\x=-1 \implies y=(1/3)^{-1}=3\\\\x=0 \implies y=(1/3)^0=1\\ \\ x=1 \implies y=1/3\\\\x=2 \implies y=(1/3)^2 =1/9[/tex]
Using these points, the correct graph is shown in option C.
(3x-2)(2x2+5x-1) what is not equivalent to the product
The only option that is not an equivalent of the product of both polynomials is; C: 6x³ + 11x² − 13x + 2
What kinds of equations are there?Equations can be classified as either identities or conditioned equations. For each quantity of the variables, an identity is true. Only specific values of the variables make a conditional equation legitimate. The equals sign ("="), which separates two expressions, is a symbol for an equation.
Here,
We are given the expression;
(3x - 2)(2x² + 5x - 1)
The result of expanding the polynomial is;
6x³ + 11x² − 13x + 2
Looking at the given options as seen online, the only one that is not an equivalent of the given product is;
Option C) : 6x³ + 11x² − 13x + 2 is correct
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Picture is the question
The months when the temperature will be 0 °C are May and August.
What is a trigonometric function?A trigonometric function is a function that has the trigonometric ratios.
What is temperature?Temperature is the degree of hotness or coldess of a body.
How to find the months in which the temperature is zero degrees?Since the average monthly temperature of a particular city is T(m) = 10cos(πm/6) + 5 where m = number of months of year and January begins at m = 0.
To find the number of months in which the temperature would be 0°C. This means T(m) = 0.
So, T(m) = 10cos(πm/6) + 5
0 = 10cos(πm/6) + 5
-10cos(πm/6) = 5
cos(πm/6) = 5/10
cos(πm/6) = -0.5
cos⁻¹cos(πm/6) = cos⁻¹(-0.5)
(πm/6) = π - π/6 or (πm/6) = 3π/2 - π/6 (since cos is negative int he second and third quadrant respectively)
πm/6 = 5π/6 or πm/6 = 8π/6
⇒ m = 5π/6 × 6/π or m = 8π/6 × 6/π
⇒ m = 5 or m = 8
Since m = 5 is May and m = 8 is August,
The months when the temperature will be 0 °C are May and August.
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Compare the triangles and determine whether they can be proven congruent, if possible by SSS, SAS, ASA, AAS, HL, or N/A (not congruent or not enough information). Select your answer.... Take your time this is a grade!O N/AO SASO SSSO AASO HL
The triangles can be proven congruent using the ASA congruence postulate.
∠ABK is congruent to ∠CBK.BK is congruent to BK (common side )∠AKB is congruent to ∠CKB.Thus, we can say that triangles ABK and CBK are congruent.
Triangles are congruent, according to the Angle Side Angle Postulate (ASA), if any two angles and their included side are equivalent in the triangle. The side between two angles is considered an included side.
Additionally, you can confirm that your two triangles are congruent by employing the Side Angle Side Postulate (SAS). In this case, we choose a side and its equivalent side on two triangles rather than two angles.
Triangles are said to be congruent according to the SAS Postulate if any pair of corresponding sides and their included angle are also congruent.
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-8y² - 1 = -8y
Quadratic equation
Answer:
y = (2 + √2)/4 ; y = (2 - √2)/4
Step-by-step explanation:
-8y² + 8y - 1 = 0
8y² - 8y + 1 = 0
discriminant = 64 - 4(8) = 64 - 32 = 32 = 2^4 * 2
y = (8 + [tex]\sqrt{2^4 * 2}[/tex])/16
(8 + 2²√2)/16
(8 + 4 √2) / 16
4(2+√2)/16
(2+√2)/4
y = (8 - [tex]\sqrt{2^4 * 2}[/tex])/16
(8 - 4√2) / 16
4(2-√2)/16
(2-√2)/4
Pls help. Writing Linear equations from key information
1. goes through the points (-6,1) and (-3,2)
2. goes through the points (-3.2) and (8,2)
3. y-intercept = -1, goes through the point (3,8)
4. goes through the points (1,11) and (1,-2)
The linear functions in this problem are given as follows:
1. y = 1/3x + 3.
2. y = 2.
3. y = 3x - 1.
4. x = 1.
How to define the linear functions?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.For item 1, the points are given as follows:
(-6, 1) and (-3,2).
When x increases by 3, increases by 1, hence the slope is given as follows:
m = 1/3.
Then:
y = 1/3x + b.
When x = -3, y = 2, then the intercept b is calculated as follows:
2 = 1/3(-3) + b
b = 3.
Thus the function is:
y = 1/3x + 3.
Then items 2 and 4 are given as follows:
2 -> horizontal line -> y = 2.4 -> vertical line -> x = 1.For item 3, we have an intercept of -1, hence:
y = mx - 1.
When x = 3, y = 8, hence the slope m is calculated as follows:
8 = 3m - 1
3m = 9
m = 3.
Hence the function is:
y = 3x - 1.
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Look at photo for problem
Just need chart filled out
6. y=(x-2)(x-4)
On solving the given equation y=(x-2)(x-4) the point on the graph are as follows:
(4,0), (2,0), (5,3), (3,-1) &(0,8)
What is a graph?
A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.
It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.
It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.
1)
let y=0
0=(x-2)(x-4)
i.e. x = 4 and 2
2)
Let x =0
y=(0-2)(0-4)
y=8
3)
Let x = 3
y=(3-2)(3-4)
y=-1
4)
Let x = 5
y=(5-2)(5-4)
y=3
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Find the area of the shaded region in the figure. Round results to the nearest uni. Use 3.14
The Area of the shaded part is 3.44 cm²
Area of circle:The formula used to find the Area of a circle is given by
Area of circle = 2πrWhere r is the radius of the circle
Area of Square:The formula used to find the Area of a Square is given by
Area of Square = Side²
Here we know
The radius of the circle = 2m
As we know Area of a Circle = 2πr
=> Area of given circle = 2(3.14)2 = 12.56 cm²
Area of circle = 12.56 cm²
As we can see the circle is inscribed in a square
Then the Length of the side square = diameter of the circle
=> Length of side = 2 × Radius of circle = 2 × 2 cm = 4 cm
Length of side = 4 cm
As we know Area of the square = side²
=> Area of given square = 4 × 4 = 16 cm²
Now using the above value we will friend the area of the shaded part
Area of shaded part = Area of the square - Area of the circle
= 16 cm² - 12.56 cm² = 3.44 cm²
Therefore,
The Area of the shaded part is 3.44 cm²
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Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below.
Negative 5 x minus 3.5 greater-than 6.5. Negative 5 x greater-than 10. x greater-than negative 50.
A number line going from negative 110 to positive 10. A closed circle is at negative 50. Everything to the right of the circle is shaded.
She should divide both sides by -5 while multiplying the other side by -5. She also did not replace the > symbol with a symbol.
What is an inequality ?An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
From given question :
-5x-3.5>6.5
-5x > 10
X > -50
Since, we have to solve for x
so, we will isolate x on anyone side
step-1:
Add both sides by 3.5
- 5x - 3.5 + 3.5 > 6.5 + 3.5
- 5x > 10
step-2:
Divide both sides by -5
we know that whenever we divide both sides by negative sign , it's inequality gets revered
so, we get
- 5x / -5 < - 50 / -5
we get
x < 10
so,
She should divide both sides by -5 while she multiplied by -5 on other side
and she also did not change the > symbol to a < symbol
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Could Someone Let me know if I checked off the correct answer? And if not explain what I did wrong.
Answer:
See below ( you have it correct !)
Step-by-step explanation:
See image below....sometimes it is easier to see these things if you extend some lines a bit:
Music Company A charges a $ 15 membership fee and $ 0.75 each to download a song. Music Company B charges $ 0.90 each to download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money? Justify your answer using mathematics.
(i) At a total of 100 Songs the Charges for Company A and Company B will be Equal.
(ii) I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
Let, Songs Downloaded be x
Total Charges of Company A = 15 + 0.75*x
Total Charges of Company B = 0.9*x
(i) Total Charges by Company A = Total Charges by Company B
15 + 0.75*x = 0.9*x
15 = 0.15*x
x = 100 songs
(ii) Charges by Company A to Download 150 Songs = 15 + 0.75 * 150
= 15 + 112.5 = $127.5
Charges by Company B to Download 150 Somgs = 0.9 * 150 = $135
I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
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What is the domain of the inverse of the function graphed below?
Write your answer as a compound inequality.
The domain of the inverse function is {5,6}. And as a compound inequality the domain is 5<x<6.
What is compound inequality?A mathematical statement that expresses the inequality between two inequalities combinedly.
from the graph, we have two inequalities, x>5 and x<6
it can be written as 5<x<6
What is inverse of a function?A function that can be obtained by reversing the primary function is termed as inverse of function. it is denoted by f⁻¹.
The graph shown is got from an inverse function whose domain is {5,6} and ranges are {-2, -4}
The graph also refers the inequalities of x>5 And x<6
compound inequalities of domain 5<x<6
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Which of the following graphs represents the equation x-5y=27
The graph that shows the straight line → x - 5y = 27 is plotted and attached.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
where -
[m] is slope of the line.
[c] is the y - intercept of the line.
Given is the equation of the line as -
x - 5y = 27
The given equation of the line is -
x - 5y = 27
Rearranging the equation, we get -
5y = x - 27
y = (1/5)x - (27/5)
y = 0.2x - 5.4
Now, refer to the graph attached. The slope [m] of the equation will be -
m = 0.2 and the [y] - intercept will be y = - 5.4.
Therefore, the graph that shows the linear relation → y = 0.2x - 5.4 is plotted and attached.
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A wood state casket labeled 6/6XX would measure in length 6 feet 6 inches and in width
Answer: 28 inches
Hope this helps!!! :)
Can a triangle be formed with side lengths 15, 7, and 6? Explain
Answer:no
Step-by-step explanation:
There is a property with triangles that the sum of two sides of a triangle should always be greater than the 3rd side.
Here if we take the two smaller sides their sum is 7 + 8 = 15 which is equal to the third side.
So it is not possible to construct a triangle with sides 7, 8, and 15 respectively.
Liam spent $5.76 on 12 pounds of potatoes. How much did he spend per pound?
Answer:
$0.48/pound
Step-by-step explanation:
$5.76 divided by 12
43. What system of inequalities is represented by the graph? (1 point)
-2 -1
2
- C
0
-1
0 1
2
Oy≤3x-2 and y2-4x+2
Oy23x-2 and y≤-4x+2
Oy≤-2x+3 and y 22x-4
Oy2-3x-2 and y ≤4x+2
3 4 question is in the photo. Please help if you can and thank you in advance.
The graph's representation of the inequality system is
y≤3x-2 and y≥-4x+2. So, option a is correct.
What is meant by inequality?One of the basic ideas of social justice theories is the existence of unequal status, rights, and opportunities. In public conversation, it might be confusing because various people often interpret it differently. There are some frequent variants, though. In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. As an illustration, suppose you wish to get a 250 new bicycle. Different types of inequality are indicated by a variety of notations, including:
A less than sign, such as a, denotes that an is greater than b.
Therefore, The system of inequalities that is represented by the graph is
y≤3x-2 and y≥-4x+2. So, option a is correct.
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10 points and brainliest.
two people need to answer or i won't be able to give brainliest
Fifteen students completed 80 puzzles. How many puzzles would 1 student complete? Round the answer to the nearest tenth.
1.6
0.2
5.3
15.0
5.3
80/15=5.3
which means each person completed 5.3 puzzles
Which of the following is equivalent to 5(x+6)-6(3x+3)=10
Answer:
B
Step-by-step explanation:
5x + 30 - 18x - 18 = 10
-13x + 12 = 10
Find the reciprocals of the following numbers.
a, if a ≠ 0
The Reciprocal of a (if a ≠ 0) is...
Reciprocal of a = [tex]\frac{1}{a}[/tex]
What is Reciprocal ?
In Mathematics , reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n.
What are real numbers ?
In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions .
According to the given information
a ≠ 0
a is a real number
By the definition of reciprocal
Reciprocal of a will be the inverse of a = [tex]\frac{1}{a}[/tex]
Reciprocal of a = [tex]\frac{1}{a}[/tex]
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A total of 627 tickets were sold for the school play. They were either adult tickets or student tickets. There were 73 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
350
Step-by-step explanation:
Let "a" represent the number of adult tickets sold and "s" represent the number of student tickets sold. We can set up the following equation to represent the information given:
a + s = 627
s = a - 73
Substituting the second equation into the first equation gives us:
a + (a - 73) = 627
2a - 73 = 627
2a = 700
a = 350
Thus, there were 350 adult tickets sold.
Find how long it takes$ 2500 to double if it is invested at 6 % interest compounded semiannually. Use the formula A=P(1+r/n ) to solve the compound interest problem.
It will take approximately ___years.
It takes 11.55 years for money to double if invested at 6% compound interest.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.Compound interest is commonly abbreviated C.I. in mathematics.Calculating the answer exactly: P⁰°⁰⁶ⁿ=A .
We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.
P⁰°⁰⁶ⁿ = 2P
We divide both sides by P
e⁰°⁰⁶ⁿ = 2
Using natural logarithm:
0.06 n = ln(2)
n = ln(2)/0.06
n = 11.55 years
Hence, It takes 11.55 years for money to double if invested at 6% compound interest.
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What is the quotient of 14 divided by 3/4
Answer:
18.6
Step-by-step explanation:
what is the average rate of change of the function on the interval from x=1 to x=2? f(x) = 10(5.5)^x
Answer: 246.7
Step-by-step explanation:
Why do you think taxes have become more complicated since 1913?
Answer:
Before 1913, federal government revenues came mainly from taxes on goods—tariffs on imported products and excise taxes on items like whiskey.
Step-by-step explanation:
What was the tax rate in 1913?
The act levied a tax of one percent on all incomes above the exemption with additional surtax rates imposed for progressively higher incomes. Those surtax rates started at one percent for those making $20,000 or more and topped out at a mere six percent on incomes in excess of $500,000.