The dilation of a rectangle with a scale factor of 4 will result in each side of the rectangle being multiplied by 4, thus the perimeter will also be quadrupled.
Explanation:When a rectangle undergoes a dilation with a scale factor of 4, the lengths of all sides of the rectangle are multiplied by 4. Since perimeter is the sum of all the side lengths of a rectangle, the perimeter will also be affected by the scale factor. Therefore, if the original perimeter of the rectangle is P, the new perimeter after dilation will be 4 × P.
Using the property of dilations, the new dimensions of the rectangle will be proportional to the original dimensions. For example, if the original length l and width w of the rectangle are scaled by a factor of 4, the new dimensions will be 4l and 4w respectively. Subsequently, the new perimeter will be 2(4l + 4w) which is the same as saying 4 × (2l + 2w), proving the perimeter is scaled by the same factor of 4.
A basketball team averages 98 points in its first three games.How many points must it score in the next game in order to have 100 point average overall?
The basketball team must score 106 points in the next game to have a 100-point average overall.
To determine how many points the basketball team must score in the next game to have a 100-point average overall, we need to consider the total points scored in the first three games and the desired average.
The team has already played three games and has an average of 98 points. To find the total points scored in these three games, we multiply the average by the number of games:
Total points in the first three games = 98 points/game * 3 games = 294 points.
To have a 100-point average overall, the team needs to score a total of 100 points per game multiplied by the total number of games played, including the next game.
Let's represent the number of points needed in the next game as "x."
(294 points + x points) / (3 games + 1 game) = 100 points/game.
Simplifying the equation:
(294 + x) / 4 = 100.
Cross-multiplying and solving for "x":
294 + x = 400.
x = 400 - 294.
x = 106.
To learn more about average click on,
https://brainly.com/question/31340101
#SPJ2
HELP!!
Lily just paid off a $400 loan. She had to pay $60 in interest at a simple annual interest rate of 5%. How many years did Lily have this loan?
A. 2
B. 3
C. 4.5
D. 5
Answer: The correct option is (B) 3.
Step-by-step explanation: Given that Lily just paid off a $400 loan. She had to pay $60 in interest at a simple annual interest rate of 5%.
We are to find the number of years for which Lily had this loan.
Let n be the required number of years.
Also, P = $400, S.I. = $60 and r% = 5%.
Therefore, by the formula of simple interest, we have
[tex]S.I.=\dfrac{Prn}{100}\\\\\\\Rightarrow 60=\dfrac{400\times5\times n}{100}\\\\\\\Rightarrow n=\dfrac{60}{20}\\\\\\\Rightarrow n=3.[/tex]
Thus, the required number of years is 3.
Option (B) is CORRECT.
Which expression is equivalent to 3(x + 4y)?
6x + 16y
3x + 12y
8x + 24y
x + 4y
Which fraction shows a correct way to set up the slope formula for the line that passes through the points (3,7) and (5,7)?
The slope of a line through the points (3,7) and (5,7) is 0, indicating a horizontal line.
To calculate the slope of a line passing through two points, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the points are (3,7) and (5,7). Using the slope formula, we get:
m = (7 - 7) / (5 - 3) = 0 / 2 = 0
So, the slope of the line that passes through these points is 0, which means the line is horizontal.
A new law requires that 12% of an individual's income be invested in the stock market. Your accounts show that you need to put $420 in the stock market this year. How much did you earn this year.
A $5,040 B $350 C $504** D $3,500
The problem can be solved by setting up the equation 0.12x = $420, where 'x' stands for your total income. Dividing both sides of the equation by 0.12 gives x = $3500 which is the total annual income. Thus, you earned $3,500 this year.
Explanation:To solve this mathematical problem, you can set up an equation that represents the problem context. You know that 12% of your whole year's income equals $420. So if 'x' represents your total income, the equation becomes 0.12x = $420. To solve for 'x' (your total income), you would divide both sides of the equation by 0.12.
So, x = $420 ÷ 0.12. When you perform this calculation, you'll find that 'x' equals $3,500. Therefore, you earned $3,500 this year.
The answer to the problem is D. $3,500.
Learn more about Percentage here:https://brainly.com/question/35647344
#SPJ12
a culture contains 1500 bacteria initially and doubles every 30 mins. a) find a function that models the number of bacteria at time t. b) find the number of bacteria after 2 hours. c) after how much time will there be 4000 bacteria ...?
Is 89 prime or composite
Answer:
Prime
Step-by-step explanation:
A prime number is a number that has only one factor. A composite number is a number that has more than one factor.
-kiniwih426
logx + log(3x-13) = 1
The solutions for [tex]\log x + \log (3\cdot x - 13) = 1[/tex] are [tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex], respectively.
In this question, we are going to solve for [tex]x[/tex] with the help of Logarithm Properties, which are described in the image attached below.
[tex]\log x + \log (3\cdot x - 13) = 1[/tex]
[tex]\log [x\cdot (3\cdot x - 13)] = 1[/tex]
[tex]\log (3\cdot x^{2}-13\cdot x) = 1[/tex]
[tex]10^{\log(3\cdot x^{2}-13\cdot x)} = 10^{1}[/tex]
[tex]3\cdot x^{2}-13\cdot x = 10[/tex]
[tex]3\cdot x^{2}-13\cdot x -10 = 0[/tex]
This is a Second Order Polynomial, which can be solved by Quadratic Formula:
[tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex]
The solutions for [tex]\log x + \log (3\cdot x - 13) = 1[/tex] are [tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex], respectively.
Please see this question related to Logarithm Properties for further details:
https://brainly.com/question/12983107
A triangle has side lengths of 12 cm, 35 cm, and 37 cm. Classify it as acute, obtuse, or right.
acute
obtuse
right
Vanessa deposited money into a bank account that earned 1.25% simple interest each year. After 1/2 year, she had earned $5.00 in interest on the account. If no other money was deposited into or withdrawn from the account, how much was her initial deposit? Uhh... I was just testing...oops
so the answer is 800. I guarantee you this will be the answer I promise
Final answer:
Vanessa's initial deposit in the bank, earning 1.25% simple interest per year, was $800. This is calculated using the simple interest formula, rearranged to solve for the principal based on the $5 interest earned in half a year.
Explanation:
To find Vanessa's initial deposit, we use the simple interest formula, which is Interest = Principal × Rate × Time. Given Vanessa earned $5.00 in interest in half a year (0.5 years) at a rate of 1.25% per annum, we can rearrange the formula to solve for the principal (initial deposit).
Using the given information: $5 = Principal × 0.0125 × 0.5, we can solve for the Principal as follows:
$5 = Principal × 0.00625
Principal = $5 ÷ 0.00625
Principal = $800
Therefore, Vanessa's initial deposit was $800.
Factor -9x^2-36x-36 please.
mr. and mrs. boyce bought a house for 96000 in 1995. real estate values in their area increase approximately 4% each year. what was the value of the house in 2007?
The Boyce's house bought for $96,000 in 1995, increased approximately 4% yearly. By applying the compound interest formula, the house's value in 2007 would be approximately $139,254.09.
Explanation:We need to use the compound interest formula to calculate the value of Boyce's house in 2007 because the house price increase is compounded annually. The formula is P(1 + r/n)^(nt). Here, P is the initial amount (i.e., the original house price), r is the annual interest rate (the rate of increase in house value), and n is the number of times interest is compounded yearly. T is the number of years the money is invested.
However, as we deal with annual compounding, the formula simplifies to P(1 + r)^t. In this case, P = $96,000, r = 4% or 0.04, and t = 2007 -1995 = 12 years.
Inserting these values, we get 96000(1 + 0.04)^12 = $139,254.09 (rounded to the nearest cent).
So, according to the 4% annual increase rate, Boyce's house would be worth approximately $139,254.09 in 2007.
Learn more about Compound Interest here:https://brainly.com/question/14295570
#SPJ2
What are odd numbers 1-35?
sin10+sin20+sin40+sin50=sin70+sin80.prove it
Which of the following statements is true of chords?
A chord is a line segments.A chord connects two points on a circle.A chord can be a radius of a circle.A chord can be a diameter of a circle.A chord divides a circle into two regions
Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyrone works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint: Assume that there are 4 pay periods per month.)
$2073.60 per month
===================
To calculate Tyrone's total monthly cash inflow, we need to determine his weekly and then monthly earnings.
Calculate weekly gross income:
$18/hour * 40 hours/week = $720/weekCalculate net pay per week:
$720/week * 72% = $518.40/weekCalculate monthly cash inflow:
$518.40/week * 4 weeks/month = $2073.60/monthTyrone's total monthly cash inflow is $2073.60.
There are 132 people seated in the school auditorium for an assembly. There are 6 rows in the auditorium, each with the same number of seats. If the auditorium is completely filled, how many seats are there in each row?
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
The speed of Bicyclist A (heading north) is 16 km/h.
The speed of Bicyclist B (heading south) is 11 km/h.
Given:
- Let x be the speed of bicyclist A (heading north).
- Let y be the speed of bicyclist B (heading south).
- Bicyclist A is 5 km/h faster than Bicyclist B, so [tex]\(x = y + 5\)[/tex] (Equation 1).
- Time from 9:00 to 10:45 is 1.75 hours.
- The total distance covered by both bicyclists during this time is 47.25 km.
From the equation for time and distance, we have:
[tex]\[ x \times 1.75 + y \times 1.75 = 47.25 \][/tex]
Substituting Equation 1 into this equation:
[tex]\[ (y + 5) \times 1.75 + y \times 1.75 = 47.25 \]\[ 1.75y + 8.75 + 1.75y = 47.25 \]\[ 3.5y + 8.75 = 47.25 \]\[ 3.5y = 38.5 \]\[ y = \frac{38.5}{3.5} \]\[ y = 11 \text{ km/h} \][/tex]
Substituting the value of y back into Equation 1:
[tex]\[ x = 11 + 5 \]\[ x = 16 \text{ km/h} \][/tex]
Thus, the correct answer is:
- The speed of Bicyclist A (heading north) is 16 km/h.
- The speed of Bicyclist B (heading south) is 11 km/h.
Question :
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
Eric reflected parallelogram ABCD across the x-axis. If angle A is 125° and angle B is 55°, what is the degree measurement of angle A'?
Answer:
Angle A= Angle A' = 125°
Step-by-step explanation:
We have given that : Eric reflected parallelogram ABCD across the x-axis.
If angle A is 125° and angle B is 55°
To find : Degree measurement of angle A'
Solution :
As it is reflected parallelogram , and by property of reflection it form congruent parallelogram
since it is congruent then measures of angle remain same
by this statement the measure of angle of parallelogram ABCD
remain same or equal to parallelogram A'B'C'D'
⇒Angle A= angle A' = 125°
Which of the binomial is a factor of this trinomial x2-7x-44?
A side of the square is 4t. the area of the square is 400. what is the value of t?
The value of the variable 't' will be 5.
What is the area of the square?All the sides of a square are congruent. Let a be the side length of the square. Then the area of the square is the square of the side length of the square.
Then the area of the square will be
Area of the square = a² square units
A side of the square is 4t. the area of the square is 400. Then the value of the variable 't' will be
400 = (4t)²
(4t)² - 20² = 0
(4t - 20)(4t + 20) = 0
t = -5, 5
Thus, the value of the variable 't' will be 5.
More about the area of the square link is given below.
https://brainly.com/question/1658516
#SPJ6
A submarine's elevation changes -657 feet over a period of 6 minutes. If the submarine descended at a constant rate, what is the approximate elevation change per minute?
-130 feet
-90 feet
-120 feet
-110 feet
The approximate elevation change per minute for the submarine is -109.5 feet.
Explanation:To find the approximate elevation change per minute, we need to divide the total elevation change by the total time taken. The submarine's elevation changes by -657 feet over a period of 6 minutes. So, we divide -657 by 6 to get the approximate elevation change per minute.
-657 / 6 = -109.5 feet
Therefore, the approximate elevation change per minute is approximately -109.5 feet.
Learn more about Submarine elevation change here:https://brainly.com/question/21690476
#SPJ2
Is the number 53 a prime number or a composite number
Answer:
It's prime:)
Step-by-step explanation:
{-4y-11x=36
{20=-10x-10y
70 is 25% of what number
Wren bought a baseball card last year for $2.25. this year the price dropped to $.45. what was the percent of decrease in the price of the card?
a. 80%
b. 400%
c. 500%
d. 120%
Answer:
a. 80%
Step-by-step explanation:
The percent of decrease can be calculated as:
[tex]Percentage Decrease = \frac{Initial price - Final Price}{ Initial Price}*100 [/tex]
Then, replacing initial price for $2.25 and final price for $.45 we get:
[tex]Percentage Decrease = \frac{2.25 - 0.45}{2.25} *100[/tex]
percentage of decrease = 80%
Finally the percentage of decrease in the price of the card is 80%
Find the least residue of 7^5 mod 50 without using a calculator.
so far I have 7=7 mod 50 7^5 = 7^5 mod 50 7^2 = 49 7^3=343 since 7^2=(-1)mod50 and 7^3=(-43)mod50 it follows that 7^6=7^2 * 7^3 = (-1)(-43) = 43 feel like this is wrong though could somebody please explain where I have made an error?
What is the surface area of this design
Answer:
[tex]384\ in^{2} \\[/tex]
Step-by-step explanation:
Hello
according to the graph the figure is a cube, which has 6 square faces of 8 inches each side,the total area will be equal to the area of one of these faces multiplied by 6
Area of a square=side* side
Area of square= 8 in * 8 in
[tex]Area = 64\ in^{2} \\[/tex]
Now, the total area is
[tex]Tarea=6*64\ in^{2} \\Tarea=384\ in^{2}[/tex]
1 in= 1 inch = 2.54 cm
have a fantastic day
Simplify each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither. Explain your answers.
(a)6x + 2(2x – 3) = 24 + 9x
(b)25 – 4x = 3(5 – x) + 10 – x
(c)4(x + 2) = 2x + 7 + 2(x – 10)
what does the 2 represent in 12.789