The dimension of rectangle : 6 and 12 units
square= 9 units
What is Perimeter ?Perimeter is the distance around the edge of a shape.
Given:
let the width of rectangle be x.
length= 2x
let the side of square is y units.
Perimeter of rectangle = Perimeter of square
and, Area of square= Area of rectangle + 9
First, Perimeter of square= 4* side
= 4y units
Perimeter of rectangle,
=2(l+b)
=2(2x+x)
=6x units
Since, Perimeter of rectangle = Perimeter of square
6x=4y
3x=2y
Now, Area of square= Area of rectangle +9
y²= x*2x+9
y²= 2x²+9
y²= 2(2y/3)²+9
y²= 8y²/9+9
1/9 y²= 9
y²=81
y=±9
So, x=2y/3= 2*9/3
x= 6
Hence, dimension of rectangle is 6 and 12.
dimension of square is 9 units.
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A weather forecast predicts that the temperature in antarctica will decrease 8 degrees fahrenheit each hour for the next 6 hours. write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36 degrees fahrenheit
It will take at least 5 hours for the temperature to drop by 36 degrees Fahrenheit.
To determine how many hours it will take for the temperature in Antarctica to drop at least 36 degrees Fahrenheit, you can set up an inequality. Let's call the number of hours it takes for the temperature to drop x.
Given that the temperature decreases 8 degrees Fahrenheit each hour, you can represent the temperature drop as:
8x
Now, you want this temperature drop to be at least 36 degrees Fahrenheit, so you can write the inequality:
8x ≥ 36
To solve for x, divide both sides of the inequality by 8:
x ≥ 36 / 8
x ≥ 4.5
So, it will take at least 4.5 hours for the temperature in Antarctica to drop by at least 36 degrees Fahrenheit.
Since time is typically measured in whole hours, it will take at least 5 hours for the temperature to drop by 36 degrees Fahrenheit.
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It will take at least 4.5 hours for the temperature in Antarctica to drop at least 36 degrees Fahrenheit.
Explanation:To determine how many hours it will take for the temperature in Antarctica to drop at least 36 degrees Fahrenheit, we can write and solve an inequality:
Let x be the number of hours it takes for the temperature to drop.
The temperature decreases 8 degrees Fahrenheit each hour for the next 6 hours:
8x ≥ 36
Divide both sides of the inequality by 8:
x ≥ 4.5
Therefore, it will take at least 4.5 hours for the temperature to drop at least 36 degrees Fahrenheit.
Curt just drank a cup of coffee to help him stay awake. The coffee had 130 milligrams of caffeine in it. If his body processes 7% of the caffeine every hour, how much will be left in 4 hours?
93
94
98
91
Answer:
After 4 hours, there will 91.31 miligrams of caffeine within his body.Step-by-step explanation:
Givens
Curt drank 130 miligrams of caffeine.His body processes 7% of caffeine everyhour.If Curt's body processes 7% every hour, we just need to that 7% after each hour. Also, we know that 7% equals 0.07.
First hour.
[tex]0.07(130)=9.1ml[/tex]
The first hour, his body processed 9.1 miligrams, so it remains
[tex]130-9.1=120.9ml[/tex]
There's still 120.9 miligrams in his body.
Second hour.
[tex]0.07(120.9)=8.46ml[/tex]
[tex]120.9-8.46=112.44ml[/tex]
Third hour.
[tex]0.07(112.44)=7.87ml[/tex]
[tex]112.44-7.81=104.63ml[/tex]
Fourth hout.
[tex]0.07(104.63)=7.32ml[/tex]
[tex]104.63-7.32=97.31ml[/tex]
Therefore, after 4 hours, there will 91.31 miligrams of caffeine within his body.
|2y+10|=-4 solve for y
This diagram of airport runway intersections shows two parallel runways. A taxi way crosses both runways. How are 6 and 2 related?
a)corresponding angles
b) alternate interior angles
c)same side interior angles
d) none of these
Find the Domain and Range (show work)
see attached picture for solutions:
Find four consecutive even integers such that if the sum of the first and the third is multiplied by 5 the result is 12 less than 9 times the fourth
Whether or not a measurement gives the same results when it is repeated under the same conditions is an indication of the measurement’s _____
Analyze the function’s graph to determine which statement is true.
Over the interval [–2.5, 0.5], the local maximum is 2.
As the x-values go to positive infinity, the function’s values go to negative infinity. The function is decreasing over the interval (–1, 0.75).
The function is negative for the interval [–2, 0]
The truth of the statements in the question can be verified by analyzing the function's graph over the stipulated intervals. Understanding concepts such as local maxima, the behavior of functions at infinity, an interval of decrease, and intervals where a function remains negative or positive are essential in this process.
Explanation:To determine which statement in the question is true, we need to analyze the function's graph. The statements included talk about specific behaviors of the function in different intervals of the x-axis.
The first statement mentions a local maximum of 2 over the interval [–2.5, 0.5]. You will need to locate this interval on the x-axis and see if 2 is indeed the highest y-value within this range. If there is a point on the function where the y-value is 2 and it is higher than all neighboring points, then this statement is true.
The second statement states that as the x-values go to positive infinity, the function's values go to negative infinity. This implies that as the function continues towards the positive direction on the x-axis, the y-values continuously decrease towards negative infinity. If the graph shows this, then this statement is true.
The third statement says the function is decreasing over the interval (–1, 0.75). This would mean that as x goes from –1 to 0.75, the y-values decrease. If you observe this on the graph, this statement is true.
The last statement asserts the function is negative for the interval [–2, 0]. If, for all x-values from –2 to 0, the corresponding y-values are below the x-axis (negative), then this statement is valid.
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Which expression is the factored form of 2/3x+4 ?
A 2/3(x+6)
B 2/3(x+12)
C 2/3(x+4)
D 1/3(2x+6)
The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.
Shaylee is determining if 6 is the solution to the equation.
42 ÷ w = 7 for w = 6
First, Shaylee must substitute ( ) for ( ).
To simplify, Shaylee must divide ( ) by ( ) .
First, Shaylee must substitute (6) for (w)
To simplify,Shaylee must divide (42) by(6)
:)
6 is the solution of the equation 42 ÷ w = 7.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Shaylee is determining if 6 is the solution to the equation
42 ÷ w = 7 for w = 6
Forty two divided by w equal to seven for w equal to six.
First, Shaylee must substitute 6 for w.
To simplify, Shaylee must divide 42 by 6
42/6=7
So 6 is the solution of the equation.
Hence, 6 is the solution of the equation 42 ÷ w = 7.
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Loretta invested $1000 in a simple interest account yielding 5% paid annually. In 2 years, she will have $1100 in her account. From this example, we can conclude that 5% represents the:
Final answer:
The 5% represents the annual interest rate on Loretta's investment in a simple interest account.
Explanation:
The 5% represents the annual interest rate on Loretta's investment. In simple interest, the interest is calculated as a percentage of the initial investment. So, if Loretta invested $1000, and after 2 years her account has grown to $1100, the interest earned would be $100 (1100 - 1000).
To find the interest rate, we can use the formula:
Interest = Principal * Rate * Time
Using the given information, we can plug in the values and solve for the rate:
100 = 1000 * Rate * 2
Simplifying the equation, we get:
Rate = 100 / (1000 * 2) = 0.05 or 5%
Therefore, the 5% represents the annual interest rate in this scenario.
Chords AC and BD intersect at the center of circle ABCD. If the length of CP = 8, which is the length of PB?
Evaluate 4x^3 + 2 for x
Need Answer ASAP!!!!!!!Solve the equation using the zero product property. -n(5n-4)=0
Answer:
[tex]n=0\text{ or }n=\frac{4}{5}[/tex]
Step-by-step explanation:
We have been given an equation [tex]-n(5n-4)=0[/tex]. We are asked to solve our given equation using zero product property.
Zero product property states that the product of two expressions are zero, if and only if, one of them is zero.
Using zero product property, we will set each factor of our equation to zero as:
[tex]-n=0\text{ or }(5n-4)=0[/tex]
[tex]n=0\text{ or }5n-4=0[/tex]
[tex]n=0\text{ or }5n-4+4=0+4[/tex]
[tex]n=0\text{ or }5n=4[/tex]
[tex]n=0\text{ or }\frac{5n}{5}=\frac{4}{5}[/tex]
[tex]n=0\text{ or }n=\frac{4}{5}[/tex]
Therefore, the solutions for our given equation are [tex]n=0\text{ or }n=\frac{4}{5}[/tex].
If a data set has an even number of data, is it true or false that the median is never equal to a value in the data set? explain.
The median is never equal to a value in the data set when the data set has an even number of data points.
The statement is true - if a data set has an even number of data points, the median will never be equal to a value in the data set. The median is the middle value in an ordered set of data. When there is an even number of points, there are two middle values, so the median is the average of those two values.
For example, if we have the data set (2, 4, 6, 8), the median would be (4 + 6)/2 = 5. As you can see, the median is not equal to any of the values in the data set.
In conclusion, the median is never equal to a value in the data set when the data set has an even number of data points.
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The expression 53 ( 1 − x) gives the discounted price of a pair of shoes, where x is the percent of the discount written in decimal form.
What does 1 − x represent in the expression?
A. percent of original price being paid
B. discount price of the shoe
C. percent of discount
D. original price of shoe
Compare 4:10 and 12:20 using fractions. Which ratio is smaller? How do you know?
Answer:
4:10 is smaller because when put into fraction form and making the denominators even, 12:20 comes out to be 6/10
Step-by-step explanation:
Jorge is 1 year younger than his brother. The sum of their ages is no less than 25 years. Enter the youngest age Jorge's brother can be. Question 10 options:
12
13
14
15
The youngest age Jorge's brother can be is 13. This is derived from the given condition that the sum of their ages is no less than 25, by assigning Jorge's brother's age as an unknown 'x' and using algebraic principles.
Explanation:The subject question is a simple algebraic problem. Let's denote Jorge's brother's age as x, so Jorge's age would be x-1. The problem states that the sum of their ages is no less than 25, which would translate algebraically into x + (x-1) ≥ 25.
Then we simplify the equation by combining like terms, it turns into 2x - 1 ≥ 25. To isolate x, you first add 1 to both sides of the equation, which gives you 2x ≥ 26, and then divide both sides by 2, resulting in x ≥ 13.
Therefore, the youngest age Jorge's brother can be is 13.
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Solve 4/5m = -15 show you’re work please ;)
If 6 cats can kill 6 rats in 6 minutes, how many cats will it take to kill 100 rats in 50 minutes? previous next
5x + 2y = 8
x + y = 4
If you want to solve the system of equations by addition, which of the following could you do?
(A.) Multiply the second equation by 5 and add.
(B.) Multiply the second equation by 2 and add.
(C.) Multiply the second equation by -2 and add.
Answer: C. Multiply the second equation by -2 and add
Step-by-step explanation:
Answer:
Step-by-step explanation:
The solution is C
5x + 2y = 8
-2x -2y= -8
3x = 0
x = 0
2y = 8
y = 4
(0,4)
A 10-pound weight in a 2-pound weight are dropped from the same height at the same time which weight will hit the ground first
they would drop at the same time
Answer:
explained below
Step-by-step explanation:
when two object one of 10 pound weight and another of 2 pound is dropped from same height
condition 1 : when body fall In vaccum
When body fall in vaccum then there will be no effect of weight.
Both the body will hit the ground at the same time.
Condition 2 : when body falls in normal condition
When body falls in normal condition then in this condition the heavy weight object will fall first as the light weight object will have more air resistance than the heavy one.
How to find an equation in slope intercept form given two points?
The information below represents the cost of Cody's home ownership. What is his average monthly expenditure related to his home?
mortgage $1,255 per month
● taxes $2,881 per year
● insurance $156 per month
● HOA fees $320 per year
● utilities $475 per month
Answer:
Cody's average monthly expenditure related to his home is $2,152.75
Step-by-step explanation:
Since the question is asked for monthly expenditure. Thus our first work is to convert all given expenditure for per monthly.
Mortgage = $1,255
Taxes = $240.08
Insurance = $156
HOA fees = $26.67
Utilities = $475
Thus, Cody's average monthly expenditure related to his home is: 1,255 + 240.08 + 156 + 26.67 + 475 = $2,152.75
Point M is the midpoint of AB. What are the coordinates of B if A is (-8, 3) and if M is (-4, 2).
What is the product written in scientific notation? (5.91×10^−3)⋅(8.7×10^10)
a) 14.61 × 10^−30
b) 5.1417 × 10^8
c) 14.61 × 10^7
d) 5.1417 × 10^7
The product written in scientific notation will be; 5.1417 × 10^8
How do scientific notations work?Scientific notations have some of the profits as Better readability due to compact representation. Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.
We have been given that (5.91 × [tex]10^{-3}[/tex])⋅(8.7 × [tex]10^{10}[/tex])
Required to find the product written in scientific notation;
(5.91 × [tex]10^{-3}[/tex])⋅(8.7 × [tex]10^{10}[/tex])
(5.91 x 8.7) ( [tex]10^{-3}[/tex]× [tex]10^{10}[/tex])
51.417 × [tex]10^7[/tex]
which is the same as; 5.1417 × [tex]10^8[/tex]
Hence, the product written in scientific notation will be; 5.1417 × [tex]10^8[/tex]
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John and Mary Billings own a condominium with an acid value of 110000 if the tax rate is 25 meals per dollar off the valuation how much tax do they pay
A segment has an endpoint (14,-8) and (4,12) what are the coordinates of its midpoint
The coordinates of the midpoint of the segment that has endpoints as (14,-8) and (4,12) are (9,2).
What are the coordinates of the midpoint of the line segment AB?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
Suppose we've two endpoints of a line segment:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = (p+m) / 2
and
y = (q+n) / 2
Given that a segment has an endpoint (14,-8) and (4,12). Therefore, The coordinates of the midpoint of the segment can be written as,
X- coordinate = (14+ 4)/2
= 18/2
= 9
Y- coordinate = (-8+12)/2
= 4/2
= 2
Hence, the coordinate of the midpoint of the segment that has endpoints as (14,-8) and (4,12) is (9,2).
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Find the point-slope form of the equation of the line passing through the points (–1, –3) and (4, 1).