After 22 months, Jed and Esther have the same amount of money in their accounts.
How to balance the equations?Simplify both sides of the equation as much as possible using the order of operations (distribute, combine like terms, etc.)
Given: Jed has £48 in his bank account and from then on, at the end of each month he put £40 into his account and
Esther had £180 in her bank account and from then on, at the end of each month she put £34 into her account.
Now, let us consider after 't' months they have same amount of money in their accounts
⇒ £48 + £40t = £180 + £34t
⇒ £40t - £34t = £180 - £48
⇒ 6t = 132
⇒ t = 22.
Therefore, after 22 months, Jed and Esther have the same amount of money in their accounts.
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8. K is the midpoint of JL. If JL = 13x – 9 and JK = 28, find the value of x.
The value of x is 5 when the line is JL and the midpoint of the JL is K.
Given that,
The line is JL and the midpoint of the JL is K.
JL= 13x-9 and JK= 28.
We have to find the value of x.
The midpoint is the point on a line that connects two points that is exactly in the middle of the line.
We know that,
JL= JK+ JK
JL=2JK
13x-9 = 2×28
13x-9= 56
13x= 56+9
13x= 65
x=65/13
x=5
Therefore, The value of x is 5 when the line is JL and the midpoint of the JL is K.
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What is the equation of a line that is perpendicular to the line y = 1/2x + 2 and passes through the point (–4, 1)?
The equation of line that is perpendicular to the line y = 1/2x + 2 is y = -2x - 7
Equation of Perpendicular LineA perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the prerequisite to finding out the perpendicular line.
The equation of perpendicular line is given as
(y - y₁) = m(x - x₁)
m = slope of the line.
But the slope of a perpendicular line is given as
m₁m₂ = -1
m₁ = 1/2, m₂ = ?
1/2m₂ = -1
m₂ = -2
The new slope is -2.
Substituting the values into the equation above,
(y - y₁) = m(x - x₁)
y - 1 = -2(x - (-4))
y - 1 = -2x - 8
y = -2x - 7
The new equation is y = -2x - 7
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I need the correct answer to this question
During the progressive era many state and local governments adopted initiative referendum and recall together these procedures gave citizens a more direct voice in government.
At the progressive era the citizens was given by a more direct voice in government because of the three principles they are initiative ,referendum and recall.
Initiative:
Proposed law with backing can be put on the ballot at election,in that case the petitions must be approved with valid signatures.
Referendum:
plebiscite is a kind of referendum in which meaning decree of the people it depends on nature of advisory called as referendum.
Recall:
Recall defines that voters may remove a public official from office that must be before the expiration.
Therefore During the progressive era many state and local governments adopted initiative referendum and recall together these procedures gave citizens a more direct voice in government.
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The Problem
The school band is making a large banner for its annual fall concert. After the
band members worked for one hour, the band director entered the room and
asked how many feet long the completed banner would be. The trombone
section leader replied, "We're not sure. The trombone section and the
clarinet section work at different rates, but we are sure that the length of the
banner will be 40 feet and 1/2 the total banner's length."
How long will the banner be?
Answer:20
Step-by-step explanation:
PLS HELP IF U ARE GOOD AT MATH
Game Station 2: Amazing Race- Each team has to match 9 of the 20 banners with the word “Hello” in different languages with the 9 countries that speak that language
A. Determine the number of ways of selecting and matching nine banners with a country.
B. Determine the number of ways of selecting nine banners without having to match them with a country.
combinations problem btw
The number of ways to select the banners is given as follows:
a. Matching with the country: 362,880.
b. Not matching with the country: 60,949,324,800
How to select the banners matching the country?To select the banners matching the country, only the nine countries are chosen, and then the specific banner regarding the country is chosen, thus the arrangements formula is used.
The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
Hence for item a the total number of outcomes is the factorial of nine, which is the number of countries, is given as follows:
Total = 9! = 362,880.
If the country does not have to be matchedThen just nine banners are taken at random from a set of 20. The order is important, hence the permutation formula is used.
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 9 banners are selected from a set of 20, hence the number of ways is:
N = 20!/(20 - 9)! = 20!/11! = 60,949,324,800.
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Find the area of the shaded region in the figure below, if the radius of the outer circle is 12 and the radius of the inner circle is 2. Keep your answer in terms of π.
A football player makes an annual salary of 2,100,000.
A charitable organization states that for $120 it can send 1 child to school in a developing country for 1 year. The football player decides to donate 10% of his annual salary to this organization.
Calculating it would be 210,000
About how many children could his donation send to school for 1 year?
For a year, 1750 students were able to donate to the school.
What is meant by percentage?A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it by % lacks dimensions and has no associated unit of measurement.
The Latin word per centum, which means "hundred" or "by the hundred," is where the word "percent" originates. The % calculator computes a variety of percentage-based numbers, such as the percentage difference between two provided values.
Given,
The annual salary of a football player is 210000
1 student ----------$120
x ------------$210000$
x=(210000/120)
x=1750 students
1750 students could send their donation to the school for 1 year.
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what is the value of 36x - 8y² when x = 3 and y = -6
can you add the explanation?
Answer:
-180
Step-by-step explanation:
You would plug in x=3 and y=-6 into the equation
So, the first part would be 36x when x=3, 36(3)=108
The second part would ne -8y^2 when y=-6 (-6 squared is 36), -8(36)=-288
Putting these together, you get 108-288 which is -180
Answer: -180
hops this helps
have a good day
Step-by-step explanation:
A bike wheel has a diameter of 42 inches. If a rider is traveling 110 feet per minute,how many revolutions does the bike wheel make in 1 minute
The bicycle wheel performs 10 revolutions every minute
What is a revolution?A revolution in math is a full rotation, or a complete, 360-degree turn. In a 360-degree rotation, the object starts and ends in the same position. A mathematical revolution can be visualized when a top spins.
The bicycle wheel makes 1 complete revolution which is equal to the circumference of the wheel = πD
but D = diameter = 42 inches, converting inches to feet
12inches is 1 foot, then 42 inches = 42/12 = 7/2 inches
Also circumference = 22/7 x 7/2 = 11 feet/rev
Also if the rider travelled 110 feet per minute.
Then the wheel's revolution per minute = 110/11
= 10 rev/minute
In conclusion the bicycle wheel revolves 10 times every minute
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3. A pool has 25 inches of water in it when it begins to rain. The rain falls at 4 inches per hour
Write an equation for the height of the water h as a function of the hours rained, t
A) h = 4t - 25
B) h = 25t + 4
C) h = 4t + 25
D) h = 25t + 4
Answer:
The Answer is C.
Step-by-step explanation:
It's important to know how the standard form of an equation works.
Remember that y = mx + b, where y is the output value, m is the slope of the equation, and b is the y-intercept (the initial value) of the equation. We know that the pool starts with 25 inches of water in it, so the initial value, or y-intercept is 25, because the pool starts with 25 inches of water after 0 hours. We know that the pool fills up 4 inches per hour, meaning as each hour progresses, the equation will increase by 4. This is the slope. y has been replaced with h in this equation. So, your answer would be h = 4t + 25.
someone help please ty
The percentage reduction of the jacket is 20 percent.
How to find the percentage reduction of the jacket?Percentage decrease or reduction means subtracting a given percentage of a value from the original value.
Therefore, the jacket cost 80 dollars and it is reduced to 64 dollars.
The percentage reduction of the jacket can be calculated as follows:
% reduction = (Decreased Value / Original Value) × 100
Decreased value = 80 - 64 = 16
Original Value = 80
% reduction = 16 / 80 × 100
% reduction = 1600 / 80
% reduction = 20%
Therefore, the percentage reduction is 20%.
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Question 2(Multiple Choice Worth 1 points)
(03.01 MC)
Simplity √10•√8•
O√18
04√5
O√80
08√10
The simplified form of the expression √10•√8 is 4√5.
Expression:
Expression refers the mathematical statements that have two terms at least that contain variables, numbers, or both.
Given,
Here we have the expression √10•√8.
Now we have to find the simplified form of these expression.
Now, we have to multiply the values inside the square root then we get,
=> √10 x √8 = √(10 x 8)
After the multiplication we can get,
=> √80
Now, we have to expand this as the following,
=> √16 x 5
We know that √16 is equivalent for 4²,
So, it can be written as,
=> √4² x 5
Now, we have to simplify this as,
=> 4√5
Therefore, the simplified expression is 4√5
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GENETICS AND HEREDITY
CHECKPOINT
Using a standard 52-card
deck, what is the probability
of being dealt an ace and then another ace?
The probability of being dealt an ace=4/52
The probability of being dealt another ace = 3/51
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
The probability of drawing one of the four aces from a typical 52-card deck is 4/52; but, the probability of drawing a second ace is merely 3/51 since, after the first ace was drawn, there were only three more aces remaining in the remaining 51 cards.
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A number, n, is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value
of n?
O 3n-15+n= 101
O 3n+15+ n = 101
O 3n-15-n=101
O 3n+15-n=101
Mark this and return
Save and Exit
Next
Submit
The correct expression will be;
⇒ 3n - 15 - n = 101
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.
Given that;
The algebraic expression is;
''A number, n, is added to 15 less than 3 times itself. The result is 101.''
Now,
Since, The algebraic expression is;
''A number, n, is added to 15 less than 3 times itself. The result is 101.''
So, We can formulate;
⇒ 3n - (15 + n) = 101
⇒ 3n - 15 - n = 101
Thus, The correct expression will be;
⇒ 3n - 15 - n = 101
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Use the digits -9 to 9 (each only once) to create a real solution between 30 and 80
(a+bi)(c+di)
According to the imaginary number, the real solution between 30 and 80 is 60
Imaginary number
An imaginary number refers a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.
Given,
Here we have to use the digits -9 to 9 (each only once) to create a real solution between 30 and 80 (a+bi)(c+di).
We know that the digits from -9 to 9 are listed as follows:
(-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9)
Now, we have to choose the digits -9 to 9, as the value of a, b, c and d,
For that we have to choose the value of a = 3, b = -9, c = 2 and d = 6,
Now, we have to apply these value on the given imaginary equation, then we get,
(a + bi) (c + di) = (3 + -9i) (2 + 6i)
When we simplify this one then we get,
=> 6 + 18i + (-18i) – 54i²
We know that value of i² = -1, then the equation is written as,
=> 6 - 54(-1)
=> 6 + 54
=> 60
Therefore, 60 is a real solution between 30 and 80.
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(Multiplying and Dividing with Scientific Notation MC)
How many times larger is 7 x 105 than 2 x 10³?
Answer:
1,265
Step-by-step explanation:
10^3=1000*2=2000
105*7=735
2000-735
There are 500 sheets of paper in one ream. The counter on a copier says that 23,500 copies have been made. How many reams of paper were used?
Answer:
All you simply do is divide 23,500 by 500....that is equal to 47. So 47 is the answer
Step-by-step explanation:To find out how many reams were used, all we have to do is divide 23,500 by 500.
This gives us: 47 reams
pls help ill give brainliest if right
Answer:
Step-by-step explanation:
{x,y}={0,-3}
Consider the ways the function , the cost of the shoes using the coupon, and the function , the cost of the shoes using the discount, can be combined to answer the following question. Which function could be used to represent the total cost of the shoes by applying the $15 coupon first and the 20% member discount second for original cost ?
The function that could be used to represent the total cost of the shoes by applying the $15 coupon first and the 20% member discount second for original cost, using proportions, is of:
C(x) = 0.8(x - 15).
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially division and multiplication, to find the desired amounts in whichever context of the problem.
The value of shoe is given as follows:
x.
The discounts are given as follows:
$15 off coupon: x - 15.20% member discount: 0.8(x - 15) -> as the discount of 20% means that 80% of the original price will be paid.Hence the function that gives the total cost paid is presented as follows:
C(x) = 0.8(x - 15).
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a) What are the coordinates of A?
b) What are the coordinates of B?
Answer:
Coordinates of A are (-2.5, -1.5)
Coordinates of B are (4.5, -3.5)
Write a number to represent the coldest temperature.
Answer: -15 degrees
Step-by-step explanation:
Nicholas started a canned-food drive at school. The equation representing this is y = 235x + 15, where x is the number of days, and y is the number of cans collected. Explain how to determine how many days it would take to collect 2600 cans.
The number of days it would take to collect 2600 cans is; 11 days
How to change the subject of the formula?We are given the equation that represents the number of cans that Nicholas collected as; y = 235x + 15
where;
x represents the number of days.
y represents the number of cans collected.
Now, we want to make x the subject of the formula;
y = 235x + 15
Subtract 15 from both sides to get;
y - 15 = 235x
divide through by 235 to get;
(y - 15)/235 = x
When y = 2600;
x = (2600 - 15)/235
x = 11 days
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Select all that apply. If 2x²-6x=0, then 2x = 0 x + 1 = 0 x - 3 = 0 x - 6 = 0
Answer:
x-3
Step-by-step explanation:
2x²-6x=0
divide both sides by x
2x²/x -6x/x=0
2x-6=0
2x=6
x=6/2
x=3
or (x-3)
Consider the following system of two linear equations:
4y + 3x = 0
4y - x = 16
What is the point of intersection?
Answer: The two lines intersect at (-4,3)
Step-by-step explanation:
So our first step would be to turn both of these into standard slope-intercept form.
1.)
4y + 3x = 0
4y = -3x
y = -3/4x
2.)
4y - x = 16
4y = x + 16
y = 1/4x + 4
Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)
Ming was planning a trip to Western Samoa Before going, She did some research and learned that the exchange rate is 6 Tala for $2. How many tala would get if she exchanged $6
If she did some research and learned that the exchange rate is 6 Tala for $2. The number of tala she get if she exchanged $6 is 18 tala.
How to find the number of tala?Given data:
Exchange rate = 6 Tala for $2
Let x represent the tala Ming will get if she exchange $6
$2/6 = $6/X
Cross multiply
2x = 6× $6
2x = 36
Divide both side by 2x
x = 36/2
x = 18 tala
Therefore she would get 18 tala.
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Determine whether the relation represents y as a function of x.
y = x^2
The relation y = x² represents y as a function of x because every x-value returns a unique y-value.
Is the relation a function?Using the definition of a function, y=x² is a function because you will only get one unique y-value for each x-value in your domain.
The vertical line test is a quick check you can perform. The function y=x² is a parabola, and if you draw vertical lines anywhere on it, they will only cross the parabola once.
As a result, it is a function. A circle is not an example of a function because a vertical line drawn on a circle crosses at two different points.
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Angles W and X are complementary. Determine the degree measure of ∠W if m∠X = 53.4°.
36.6°
63.3°
90°
126.6°
Answer:
∠W = 36.6°
Step-by-step explanation:
Hello!
If angles are complementary, it means that they add up to 90°.
Since the measure of Angle X is 53.4, we can find measure of Angle W by subtracting 53.4 from 90.
Solve for WW = 90° - XW = 90° - 53.4°W = 36.6°The value of W is 36.6°.
Which equations are equivalent to Negative one-fourth (x) + three-fourths = 12 Select all that apply. (StartFraction negative 4 x over 1 EndFraction + three-fourths = 12 Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12 StartFraction negative x + 3 over 4 EndFraction = 12 One-fourth (x + 3) = 12 (StartFraction negative x over 4 EndFraction + three-fourths = 12
Answer:
negative x over 4 + three-fourths = 12
Answer:
Step-by-step explanation:
(StartFraction negative x over 4 EndFraction + three-fourths = 12
Find the distance between the two points. Write your answer as a decimal rounded to the hundredths place if needed.
(-8,-2) and (12,10)
HELP!!!!!
The distance between the points, (-8, -2) and (12, 10), is 23.3
Calculating the distance between two pointsFrom the question, we are to determine the distance between the two given points.
From the given information,
The points are (-8, -2) and (12, 10)
The distance between two points in given by the formula
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where d is the d is the distance between the points
Thus,
d = √[(12 - (-8))² + (10 - (-2))²]
d = √[(12 + 8)² + (10 + 2)²]
d = √[(20)² + (12)²]
d = √[400 + 144]
d = √[544]
d = 23.3
Hence, the distance is 23.3
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Please help. The question is in the attached image
∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.
In the given question we have to prove ∆GHJ congrurnce ∆KLM.
Given that: ∠G≅∠K, ∠J≅∠M, [tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex].
As given that;
∠G≅∠K
∠J≅∠M
[tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex]
So from the angle sum property of triangle
∠G+∠H+∠J=180................(1)
∠K+∠L+∠M=180.................(2)
Now equation equation 1 and 2
∠G+∠H+∠J=∠K+∠L+∠M
As we know that ∠G=∠K, ∠J=∠M
So now the expression is
∠G+∠H+∠J=∠G+∠L+∠J
After solving ∠H=∠L (3rd Angle Theorem)
Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,
∆GHJ≅∆KLM
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