2x + 50 = 4x + 25
To isolate x, first subtract 50 from both sides of the equation.
2x + 50 - 50 = 4x + 25 - 50
2x = 4x - 25
Then, subtract 4x from both sides.
2x - 4x = 4x - 25 - 4x
-2x = -25
Lastly, divide both sides by -2.
x = 12.5
Check work
Substitute 12.5 for every x in the equation.
2(12.5) + 50 = 4(12.5) + 25
25 + 50 = 50 + 25
75 = 75
As you can see, the statement is true; 12.5 is correct.
Answer:x = 12.5 or x = [tex]12\frac{1}{2}[/tex]
What interest rate per annum is a fund paying its clients if the third to the last payment of a depositor became Php 1,040.40 from an initial savings payment of Php 1,000.00?
The interest rate per annum if a fund paying its clients is the third to the last payment of a depositor became Php 1,040.40 from an initial savings payment of Php 1,000.00 is 1.32%
To get the interest rate, we will use the formula for calculating the compound interest as shown:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P is the amount of investment
n is the time of compounding
t is the time
A is the amount after t years
Given the following parameters
P = 1,000.00
A = Php 1,040.40
n = 1
Substitute the parameters into the formula
[tex]1040.4=1000(1+\frac{r}{1} )^{3}\\\frac{1040.4}{1000}=(1+r)^3\\1.0404 = (1+r)^3\\ln(1.0404) = 3ln(1+r)\\ 0.0396=3ln(1+r)\\ln(1+r)=0.0132\\1+r = e^{0.0132}\\1+r =1.0132\\r=1.0132-1\\r=0.0132\\r=1.32\%[/tex]
Hence the interest rate per annum if a fund paying its clients is the third to the last payment of a depositor became Php 1,040.40 from an initial savings payment of Php 1,000.00 is 1.32%.
Learn more here: https://brainly.com/question/18442810
Final answer:
The fund is paying its clients an interest rate of 4.04% per annum.
Explanation:
To determine the interest rate per annum, we can use the formula:
Interest = Final Amount - Initial Amount
In this case, the Final Amount is Php 1,040.40 and the Initial Amount is Php 1,000.00. So, the interest is Php 40.40.
Next, we can use the formula:
Interest Rate = (Interest / Initial Amount) × 100
Substituting the values:
Interest Rate = (40.40 / 1000) × 100 = 4.04%
Therefore, the fund is paying its clients an interest rate of 4.04% per annum.
3.4 divided by 55.318
3.4/55.318= 0.06146281499
There isn't much of a way to explain this just divide it as it is stated.
If the measure of angle ABF =6x+26 and the measure of angle EBF=2x-9 and the measure of angle ABE=11x-31 find the measure of angle ABF
Best Answer: m∠ABF = (8x + 6) degrees and m∠ABE = 2(x + 11) degrees
m∠EBF = (6x - 16)
To find the measure of angle ABF, set up an equation using the given angles ABE and EBF. Simplify and solve the equation to find the value of x. Substitute the value of x back into the equation to find the measure of angle ABF.
Explanation:To find the measure of angle ABF, we need to set up an equation using the given angles ABE and EBF. We can set up the equation as follows:
ABE + EBF = ABF
Substituting the given values:
(11x - 31) + (2x - 9) = 6x + 26
Simplifying the equation:
13x - 40 = 6x + 26
Moving the variables to one side:
13x - 6x = 26 + 40
Combining like terms:
7x = 66
Dividing both sides by 7:
x = 9.4286
Substituting the value of x back into the equation:
ABF = 6(9.4286) + 26
ABF = 56.5714 + 26
ABF = 82.5714
Therefore, the measure of angle ABF is 82.5714 degrees.
Learn more about Angles here:https://brainly.com/question/13954458
#SPJ3
How do I simplify this?
Help please!
Y6z2/x4
The 6, 2, and 4 are exponents
What’s 1 1/3 as an improper fraction?
*(Answer)*= [tex]4/3[/tex]
*(Explanation)*= You multiply 3 (denominator) to 1 (whole number) then you add 1 (numerator)
. Con la finalidad de conservar el medio ambiente una de las docentes del 2do grado solicita
a los estudiantes que traigan pilas usadas para enviarlas al centro de reciclaje, puesto que
estas se acumulan en los hogares y llegan a parar a la basura. Las pilas contienen metales y
sustancias químicas tóxicas como el mercurio; una sola pila podría contaminar hasta 600
000 litros de agua.
a. Sabiendo que el aula tiene 30 estudiantes, y la razón entre los que trajeron pilas y los
que no trajeron es como 2 es a 3. ¿Cuántos estudiantes trajeron pilas?
Respuesta: 12 estudiantes trajeron pilas
Solución:
Numero total de estudiantes: 30
Sea:
x: numero de estudiantes que trajeron pilas
y: numero de estudiantes que no trajeron pilas
x+y=30 (1)
La razón entre los estudiantes que trajeron pilas y los que no trajeron es como 2 es a 3:
Razón: r=x/y=2/3 (2)
Cuantos estudiantes trajeron pilas?
x=?
Tenemos un sistema de 2 ecuaciones con 2 incógnitas:
(1) x+y=30
(2) x/y=2/3
Vamos a resolver para x. Multiplicando en cruz en la segunda ecuación:
(2) 3x=2y
Depejando y: Dividiendo ambos lados de la ecuación entre 2:
3x/2=2y/2
3x/2=y
y=3x/2
Sustituyendo y por 3x/2 en la primera ecuación:
(1) x+y=30
x+3x/2=30
Sumando los términos en el lado izquierdo de la ecuación:
(2x+3x)/2=30
5x/2=30
Despejando x:
x=30*2/5
x=60/5
x=12
Answer: Respuesta: 12 estudiantes trajeron pilas
Solución:
Numero total de estudiantes: 30
Sea:
x: numero de estudiantes que trajeron pilas
y: numero de estudiantes que no trajeron pilas
x+y=30 (1)
La razón entre los estudiantes que trajeron pilas y los que no trajeron es como 2 es a 3:
Razón: r=x/y=2/3 (2)
Cuantos estudiantes trajeron pilas?
x=?
Tenemos un sistema de 2 ecuaciones con 2 incógnitas:
(1) x+y=30
(2) x/y=2/3
Vamos a resolver para x. Multiplicando en cruz en la segunda ecuación:
(2) 3x=2y
Depejando y: Dividiendo ambos lados de la ecuación entre 2:
3x/2=2y/2
3x/2=y
y=3x/2
Sustituyendo y por 3x/2 en la primera ecuación:
(1) x+y=30
x+3x/2=30
Sumando los términos en el lado izquierdo de la ecuación:
(2x+3x)/2=30
5x/2=30
Despejando x:
x=30*2/5
x=60/5
x=12
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. There is proportional relationship between the amount of raisins, r (cups), and the amount of peanuts, p (cups), in this recipe.
proportional relationship between the amount of raisins, r (cups), and the amount of peanuts, p (cups), in this recipe is [tex]r = \frac{2}{3} p[/tex]
What is proportional relationship?
We can state that two variables are in a proportional relationship if one of them is always equal to a constant multiplied by the other (quantity).
A mathematical comparison of two numbers is called a proportion. Let's examine proportionality in greater detail.
Different sorts of proportions can be categorized based on the type of relationship that two or more amounts share. Two different proportions exist.
1.Direct Proportion relationship
2. Indirect Proportion relationship
For every 6 cups of peanuts, a trail mix recipe calls for 4 cups of raisins.
The quantity of raisins, measured in cups, and the quantity of peanuts, measured in cups, are inversely proportionate in this recipe.
Ratio of raisins to peanuts is either 4:6 or 2:3.
It would apply to all mixtures equally.
If there are p cups of peanuts and r cups of raisins, then r:p is the mixed ratio.
Therefore,
[tex]\frac{r}{p} = \frac{2}{3}[/tex]
[tex]r= \frac{2}{3}p[/tex]
Therefore, the proportional relationship between the amount of raisins, r (cups), and the amount of peanuts, p (cups), in this recipe. is
[tex]r = \frac{2}{3} p[/tex]
To learn more about click here:-
https://brainly.com/question/2859544
#SPJ2
Final answer:
In this question, the student is asking about the proportional relationship between the amount of raisins and peanuts in a trail mix recipe.
Explanation:
In this question, the subject is Mathematics and the grade level is Middle School.
The question is related to proportional relationships in a trail mix recipe. The recipe calls for 4 cups of raisins for every 6 cups of peanuts. This means that for every 6 cups of peanuts, you need to add 4 cups of raisins. The relationship between the amount of raisins and the amount of peanuts is proportional, with a ratio of 4:6 or simplified as 2:3.
To determine the amount of raisins needed for a given amount of peanuts, you can set up a proportion. For example, if you have 12 cups of peanuts, you can use the ratio 2:3 to find out how many cups of raisins you need. Cross-multiplying, you get 2x = 3x 12, where x represents the number of cups of raisins. Solving for x, you find that x = 8. Therefore, you would need 8 cups of raisins for 12 cups of peanuts.
an artist enlarged a drawing she made. the original is 3cm wide and 5cm tall .the artist set the copier zoom button to 120% . what is the longer dimension of the new drawing.
For this case we have the following data:
The original dimensions of the drawing are:
Width: 3cm Height: 5cmIf the copier zoom is at 120%, we can find the new dimensions of the drawing by making a rule of three:
Width:
3 ----------> 100%
x ----------> 120%
Where x represents the new width of the drawing:
[tex]x=\frac{(120*3)}{100}\\x=3.6cm[/tex]
Long:
5 ----------> 100%
y ----------> 120%
Where y represents the new long of the drawing:
[tex]y=\frac{(120*5)}{100}\\y=6cm[/tex]
Thus, the new dimensions are 3.6 cm wide and 6 cm long
Answer:
the longer dimension of the new drawing is 6cm
Answer:
the answer is 6 cm
Step-by-step explanation:
Here’s one way you can solve this problem.
A zoom setting of one hundred twenty percent means that the dimensions of the new copy will be one hundred twenty percent of the dimensions of the original drawing.
First, write the scale that expresses the ratio of the original percent to the copy percent, one hundred to one hundred twenty.
Then, let h represent the height of the copy and write the ratio of copy to original as five centimeters to h centimeters.
Next, write a proportion that equates the two ratios. One hundred to one hundred twenty equals five to h.
Then, cross multiply the terms of the proportion. One hundred twenty times five equals one hundred h.
Next, multiply to get six hundred equals one hundred h.
Finally, divide both sides by one hundred to find h. h equals six.
So, the longer dimension of the new drawing is six centimeters, which is one hundred twenty percent of five centimeters.
hope it helps
Jon has to pay $6.00 admission for the skating rink and $1.50 per hour to rent roller blades . How many hours can he skate for $25
12.66 or 12 2/3 hrs because 25-6 = 19, $19.00 divided by $1.50 = 12.66 cont. rounded to 12 2/3
Final answer:
After deducting the $6.00 admission fee from the $25.00, Jon has $19.00 left to spend on roller blade rentals. At $1.50 per hour, he can skate for 12 full hours with his remaining budget.
Explanation:
To calculate how many hours Jon can skate for $25, we'll first account for the fixed admission fee and then see how the remaining amount can be used for hourly rental of roller blades.
Step 1: Subtract the Admission Fee
Jon has to pay a fixed admission fee of $6.00 when he enters the skating rink.
Start with the total amount Jon is willing to spend: $25.00.
Subtract the fixed admission fee: $25.00 - $6.00 = $19.00.
Step 2: Calculate the Number of Hours
The cost per hour for renting roller blades is $1.50.
Divide the remaining amount by the hourly rental rate to find out how many hours Jon can rent the roller blades.
$19.00 / $1.50 per hour = 12.6667 hours.
Since Jon cannot skate for a fraction of an hour, we can round it down to 12 hours.
Jon can skate for 12 hours with his $25 budget after paying for the admission fee.
3(-21)/7-12/6 need the answer
You randomly draw cards from a standard deck and place them face up on the table. What is the probability that the first two cards will both be aces.
a . 1/169
b. 1/221
c. 1/2
d. 1/26
4/52 * 3/51 = 12/ 2652 = 1/221
The probability of drawing two aces consecutively from a standard deck is 1/221. This is determined by calculating the individual probabilities of drawing an Ace on each draw, and then multiplying these probabilities together.
Explanation:The question at hand is about the probability of drawing two aces consecutively from a standard deck of 52 cards. Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.
Here, the total number of aces in the deck is 4. So, the probability of drawing an Ace on the first draw is 4/52 or 1/13. After drawing one ace, there are only 3 aces left and 51 cards in total. So, the probability of drawing an Ace on the second draw is 3/51.
Since these are independent events, the probability of both events occurring is the product of their individual probabilities. Therefore, the answer is (1/13) * (3/51) = 3/663 = 1/221.
So, option b. 1/221 is the correct answer.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ2
Here is a square..
Inside the square is an equilateral triangle.
The perimiter of the triangle is 54cm.
Find the perimiter of the square.
Show your working out.
If triangle MNO is congruent to triangle PQR, which statement is not true?
A) MN ≅ QR
B) ∠N ≅ ∠Q
C) NO ≅ QR
D) ∠O ≅ ∠R
Please help???
There are 16 tables in the school lunch room. Each table can seat 22 students. How many students can be seated at lunch at one time?
16 tables x 22 students = 352 students can be in the lunch room.
Final answer:
The number of students that can be seated at lunch at one time is 352.
Explanation:
To find the number of students that can be seated at lunch at one time, we need to multiply the number of tables by the seating capacity of each table.
Given that there are 16 tables and each table can seat 22 students, we can calculate the total number of students that can be seated at one time by multiplying 16 by 22:
16 tables * 22 students/table = 352 students
Therefore, 352 students can be seated at lunch at one time.
The length of each edge of a cube is x centimeters. If x is an integer, why is the volume of the cube not equal to 15m^3?
Suppose the length of each side of the cube is x, so the volume must be:
x^3.
If the volume is 15 cm^3, so the length must be cuberoot(15) which is not integer,. So, the volume of the cube with integer side never equal with 15 cm^3
Final answer:
The volume of a cube with integer edge lengths must be a perfect cube of an integer, and since 15,000,000 (15m^3) is not a perfect cube, the cube's volume cannot be 15m^3.
Explanation:
The volume of a cube is calculated by cubing the edge length, which means multiplying the length of an edge by itself three times (x3). If the length of each edge of a cube is x centimeters and x is an integer, the volume in cubic centimeters will also be an integer because the cube of any integer is an integer. Since the question specifies a volume of 15m3, which is 15,000,000 cm3 (because 1m3 equals 1,000,000 cm3), and 15,000,000 is not a perfect cube of any integer, the edge length x cannot be an integer, thus the volume of the cube cannot be 15m3.
You are given $100 for your birthday. You put the $100 in a savings account that pays an interest rate of 2.4% compounded monthly. If you leave your money for a year, how much will you have?
After one year, by depositing $100 in a savings account with a 2.4% interest rate compounded monthly, you will have $102.43.
You are given $100 for your birthday and decide to put it in a savings account that offers a 2.4% interest rate, compounded monthly. To calculate how much money you will have after one year, we'll use the formula for compound interest, which is [tex]A = P(1 + r/n)^{(nt)[/tex], where:
P is the principal amount ($100).r is the annual interest rate (0.024).n is the number of times the interest is compounded per year (12).t is the time the money is invested for in years (1).Plugging these values into the formula, we get:
[tex]A = 100(1 + 0.024/12)^{(12*1)A = 100(1 + 0.002)^{12A = 100(1.002)^{12A = 100(1.0243)A = $102.43[/tex]
Therefore, after one year, you will have $102.43 in your savings account.
125 feet in 5 seconds what is the answer
The answer:
25 feet per 1 second
Define plasma as a form of matter
Plasma is a form of matter in which many of the electrons wander around freely among the nuclei of the atoms. Plasma has been called the fourth state of matter, the other three being solid, liquid and gas.
Normally, the electrons in a solid, liquid, or gaseous sample of matter stay with the same atomic nucleus. Some electrons can move from atom to atom if an electrical current flows in a solid or liquid, but the motion occurs as short jumps by individual electrons between adjacent nuclei. In a plasma, a significant number of electrons have such high energy levels that no nucleus can hold them.
An atom that has lost some of its electrons, thereby attaining an electric charge, is an ion. When a gas is subjected to heat or an electric field, some of its atoms become ions, and the gas is said to be ionized. An ionized gas, unlike a gas in its normal condition, can conduct electrical current to a limited extent. If the heat or electric field becomes extreme, many of the atoms become ions. The resulting super-ionized gas is a plasma, which can conduct a large and sustained electric current.
The behavior and properties of plasmas have aroused interest and creative work among scientists and engineers. Applications include electric lamps, lasers, medical devices, energy converters, water purifiers and flat-panel video displays. About 99% of the visible universe is formed of plasma.
PLEASE HELP
What are the coordinates of the image of triangle ABC after it is translated (x, y ) → (x + 2, y - 4)? ( a0, a1) ( a2, a3) ( a4, a5)
Step-by-step explanation:
(x, y) → (x + 2, y - 4 ) means add 2 to the x- coordinate of the original point and subtract 4 from the y- coordinate of the original to obtain the image
(a_{0} + 2, a_{1} - 4 )
(a_{2} + 2, a_{3} - 4 )
(a_{4} + 2, a_{5} - 4 )
The translated coordinates are (a₀ + 2, a₁ - 4 ) (a₂ + 2, a₃ - 4 ) (a₄ + 2, a₅ - 4 ).
The complete image of the question is attached with the answer below.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.(x, y) → (x + 2, y - 4 ) means add 2 to the x- coordinate of the original point and subtract 4 from the y- coordinate of the original to obtain the image
A' = (a₀ + 2, a₁ - 4 )
B' = (a₂ + 2, a₃ - 4 )
C' = (a₄ + 2, a₅ - 4 )
Therefore the translated coordinates are (a₀ + 2, a₁ - 4 ) (a₂ + 2, a₃ - 4 ) (a₄ + 2, a₅ - 4 )
To know more about Coordinate geometry follow
brainly.com/question/18269861
#SPJ2
I need answer for my homework r^2=100
the is 10 because the √100 is 10. hope this helps mark me as brainliest
Use the bacteria parable to determine what fraction of the bottle is full at 11:39.
Using the bacteria parable, at 11:39 PM the jar is 1/2048 full, calculated by determining the number of doubling intervals (minutes) from midnight when the jar is full.
Explanation:The bacteria parable is designed to illustrate exponential growth, with bacteria population doubling at predetermined intervals. In the given scenario, the population doubles every minute, and the jar is full at midnight.
Working backwards from the full point (midnight), we can determine the state of the jar at any time before midnight.
Consequently, to find what fraction of the bottle is full at 11:39 PM, we simply count backward the number of doubling intervals (minutes) from midnight.
At 11:50 PM, the jar is half full. Each minute going back cuts the fullness of the jar by half:
11:49 PM - 1/4 full11:48 PM - 1/8 full11:47 PM - 1/16 full...11:39 PM - 1/2048 full (going back 11 minutes from the halfway point)Therefore, at 11:39 PM, the jar is 1/2048 full.
I'm having a bit of trouble with this question, all it says is '2k = 26'
2k=26
To find this get k by itself and to do so get rid of the numbers on it's side.
To do so do the opposite of the symbol
Ex: when adding, subtract it from both sides.
Ex when dividing multiply both sides
Now to solve this
Divide 2 from both sides which gives the answer
K=13
When you graph a system of two linear equations, which outcome is NOT possible?
a.The lines do not intersect, so there are no solutions.
b.The lines intersect at one point, so the system has one solution.
c.The lines intersect in two different points, so the system has two solutions.
d.The graphs of the two equations are the same line, so there are infinitely many solutions.
twila glisten gets paid 5,000 for every game show appearance. if Twila made 1,230,000 last year, how many appearances did she make?
please help!!! 50 pts to accurate solver!!!! no work needed. just answers
Because G is a 90 degree angle ( right angle) the 2 angles given when added together also need to equal 90 degrees:
4x + 5x = 90
Combine like terms:
9x = 90
Divide both sides by 9:
X = 90/9
X = 10
2x and 8X are supplementary angles and need to equal 180 degrees when added together:
2x + 8x = 180
Combine like terms:
10x = 180
Divide both sides by 10:
X = 180 /10
X = 18
The inside angle where they have 32 is a vertical angle to 32 so it is also 32.
The four inside angles need to equal 360 degrees.
Subtract the 3 known angles from 360 to find x:
X = 360 - 158 - 148 - 32 = 22 degree.
9 birds land on a fence . some more come now there are 18 birds on the fence. how many birds come on the fence
Answer:
9 birds landed on the fence. 18 - 9 = 9
Why hello there!
The correct answer is 9 your equation is down below
9+x=18 we use the oppisie of adding so subracting and turn the eqation to this
9-18=x so x=9
If my answer helped please mark me as brainliest thank you and have the best day ever!
After 10 months the simple interest earned annually on an investment of $6000 was $769. Find the interest rate to the nearest tenth of a percent.
B&B inc. has ordered machine parts and recieves a charge of $15 for shipping and handeling plus $20 per part. Write an equation that represents the cost c of ordering p parts?
4k+2/k2-4 • k-2/2k+1=
What is the numerator ?
(4k+2)(k-2)/(k^2-4)(2k+1)
=2(2k+1)(k-2)/ (k^2-2^2)(2k+1)
Cancel out 2k+1
2(k-2)/(k-2)(k+2) using a^2-b^2=(a-b)(a+b)
cancel out k-2
2/k+2
Therefore numerator is 2
Algebra question: Anita rides her bike 82.4 miles each month. Which is the best estimate of the total distance Anita bikes in 6 months. A) 800 miles; B) 600 miles; C) 400 miles; D) 480 miles.
*(Answer)*= [tex]494.4[/tex]