A rectangle off the length (x+2) cm and breadth (x)cm has an area of 15cm².find the va of x hence the perimeter of the rectangle.
Answer:
The area of a rectangle is given by the formula:
area = length * breadth
In this case, the length of the rectangle is (x+2) cm and the breadth is (x) cm, so the area is:
area = (x+2) cm * (x) cm
= x^2 + 2x cm^2
We know that the area of the rectangle is 15 cm^2, so we can set up the following equation:
x^2 + 2x cm^2 = 15 cm^2
We can solve for x by using the quadratic formula:
x = (-2 +/- sqrt(4 - 41(-15))) / (2*1)
= (-2 +/- sqrt(64)) / 2
= (-2 +/- 8) / 2
= (-4, 2)
We have two solutions for x, so we need to consider both of them to find the dimensions of the rectangle.
If x=-4, then the length of the rectangle is (x+2) cm = (-4+2) cm = (-2) cm and the breadth is (x) cm = (-4) cm. Since the length and breadth of a rectangle must both be positive, this solution is not valid.
If x=2, then the length of the rectangle is (x+2) cm = (2+2) cm = 4 cm and the breadth is (x) cm = 2 cm. These dimensions give us a valid rectangle with an area of 15 cm^2.
The perimeter of the rectangle is the sum of all four sides, so the perimeter is 2 cm + 2 cm + 4 cm + 4 cm = 12 cm.
Therefore, the value of x that gives us a rectangle with an area of 15 cm^2 and a perimeter of 12 cm is x=2.
Solve the system of equations -x-y=-2 and 5x + 7y= 28 by combining the
equations.
Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.
What is equation?The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.
Here,
Given :
=> -x-y=-2
=> 5x + 7y= 28
So ,
=>x = 2-y
thus,
=> 5(2-y) + 7y =28
=> 10 -5y + 7y =28
=> 10 -2y = 28
=> -2y = 18
=> y =-9
and
=> x = 2 - (-9)
=> x = 11
Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.
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please please help so desperate
Answer:
The objective of the PACER is to run as long as possible while keeping a specified pace. Students run back and forth across a 20-meter space at a pace that gets faster each minute. A point is scored for each 20-meter distance covered. The test is easier in the beginning but progressively gets more difficult.
Step-by-step explanation:
N-2=10n+4/2
Please explain step by step to get picked brainliest
Answer:
n = -4/9
Step-by-step explanation:
first get rid of n on left side
-2 = 9n + 2
Get rid of 2 on right side
-4 = 9n
Make 9n into n
-4/9 = n
ans: n = -4/9
hope this helps :)
What is the differences between solving an equation and solving an inequality?
The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
when we have to solve an equation, it does not has an equal sign and inequalities.
When we have to solve an inequality equations usually are exact answers.
The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.
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5. If a perp b and b//c. then
The answer to the above question is B. Multiply the first equation by -2 and add the second equation.
What is equation?A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."
Given,
[tex]2x - 2y = 24\\4x + 7y=-40\-4x +4y = -96\\4x+7y = -40\\11y = -136\\y = -136/11[/tex]
The answer to the above question is B. Multiply the first equation by -2 and add the second equation.
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Anthony's brother was 0.45
meters tall last year. He grew
another 0.5 meters this past
year. How tall is he now?
Answer:
0.95meters
Step-by-step explanation:
last year her was 0.45m tall
this past year he is 0.5m
Total = 0.45 + 0.5 = 0.95
Answer: 0.95
Step-by-step explanation: add 0.45+0.5=0.95
given: p is the midpoint of AN prove: AG=NI (direct proof)
As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.
what is triangle ?Given that it has three sides and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon because it has three sides and three corners. The points at which the three sides of the triangle converge are referred to as its corners. Three triangle angles can be multiplied to get 180 degrees.
given
p is the midpoint of GI
GP = PI , PN = AP ( as mid point )
∠APG = ∠IPN ( as vertical opp. angle )
∠A = ∠N ( given )
so by ASA congruency ΔAPG = ΔIPN
As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.
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Which of the following functions describes the graph of g(x)? (5 points)
Rational function with one piece decreasing from the left asymptotic to the line y equals 2 and going through a hole at the point negative 2 comma eight-fifths and going down through the point 2 comma 0 asymptotic to the line x equals 3 and another piece decreasing from the left asymptotic to the line x equals 3 and going through the point 5 comma 3 going up to the right asymptotic to the line y equals 2
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus 5 x plus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus 5 x plus 6 end quantity
The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that,
The function g(x).
The graph of a function never touches the x = 1 line
At x = -1 there will be a vertical asymptote.
At x = -2 there will be a horizontal asymptote.
The equation of the function g(x) will be:
g(x) = (2x + 4)/(x + 1)
The equation of rational function is g(x) = (2x + 4)/(x + 1)
Therefore, g(x) = (2x + 4)/(x + 1) is correct.
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Please help will mark Brainly
Answer:
it too far i can't see it
Step-by-step explanation:
Complete the graph
Red Paint 4, 8, 12, 16
Blue Paint 6, _, _, _
Please help
Answer:
Step-by-step explanation:
10,14,18
is 11^2 x 5^4 a factor of 11^3 x 5^4
No, 11^2 x 5^4 is not a factor of 11^3 x 5^4.
To see this, you can divide 11^3 x 5^4 by 11^2 x 5^4 and see that there is a remainder.
11^3 x 5^4 = (11 x 11 x 11) x (5 x 5 x 5 x 5)
= 121 x 625
= 75125
11^2 x 5^4 = (11 x 11) x (5 x 5 x 5 x 5)
= 121 x 625
= 75125
75125 / 75125 = 1 with a remainder of 0.
Therefore, 11^2 x 5^4 is not a factor of 11^3 x 5^4.
The volume of this sphere is 4500m³.
Find the length of the radius, r.
Answer:
[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex] meters
[tex]r=10.24[/tex] meters
Step-by-step explanation:
Here is the equation for the volume of a sphere
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Lets solve for [tex]r[/tex].
Multiply both sides of the equation by [tex]\frac{1}{\frac{4}{3}\pi}[/tex].
[tex]\frac{1}{\frac{4}{3}\pi}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Simplify the left side.
Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].
[tex]\frac{1}{\frac{4\pi }{3}}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]\frac{3}{4\pi } (\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Cancel the common factor of [tex]\pi[/tex] by factoring it out of the first term.
[tex]\frac{3}{4} (\frac{4}{3}*r^3)=\frac{1}{\frac{4}{3}\pi}V[/tex]
Combine [tex]\frac{4}{3}[/tex] and [tex]r^3[/tex].
[tex]\frac{3}{4}*\frac{4r^3}{3}=\frac{1}{\frac{4}{3}\pi}V[/tex]
Multiply the numerators on the left side of the equation. Then multiply the denominators.
[tex]\frac{12r^3}{4*3}=\frac{1}{\frac{4}{3}\pi}V[/tex]
[tex]\frac{12r^3}{12}=\frac{1}{\frac{4}{3}\pi}V[/tex]
Cancel the common factor of 12.
[tex]r^3=\frac{1}{\frac{4}{3}\pi}V[/tex]
Simplify the right side.
Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].
[tex]r^3=\frac{1}{\frac{4\pi }{3}}V[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]r^3=\frac{3V}{4\pi }[/tex]
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
[tex]r=\sqrt[3]{\frac{3V}{4\pi } }[/tex]
Now we have an equation to find the radius.
Substituting our number for volume gives us
[tex]r=\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]
Enter this into a calculator
[tex]\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]
You can leave the answer in simplest radical form or as a decimal.
[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex]
[tex]r=10.24[/tex]
A rating/review would be much appreciated. Hope this helps!
the students in Mr Marcos art class use six jars of paint for their project each student uses 2/3 jars of paint how many students were in Mr Marco's class
The number of students that were in Mr Marco's class will be 9 students
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Here, the students in Mr Marcos art class use six jars of paint for their project each student uses 2/3 jars of paint
The number of students that were in Mr Marco's class will be:
= 6 ÷ 2/3
= 6 × 3/2
= 9 students
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XYZ Company
Balance Sheet
Assets
Cash
$45,000
Inventory $41,000
Property $134,000
Total Assets:
Liabilities
Notes
Wages
Equity
Stock
$55,000
$56,000
$50,000
Investment $59,000
Total Liabilities + Equity:
Using the balance
sheet, calculate XYZ
Company's total
assets - liabilities.
Total Assets - Liabilities = $ [?]
Enter
PH
Skip
Total Liabilities + Equity = $220,000.
Total Assets = $220,000.
What is Ratio Analysis and Balance Sheet?
The relationship between the two separate components is established through ratio analysis. Utilizing figures from the income statement, balance sheet, statement of cash flows, and other financial statements, it is used to assess the company's financial performance.
One of a company's financial statements that is created at the end of the year is the balance sheet. It establishes the balance of a company's assets, liabilities, and stockholder equity at the end of the fiscal year.
Here we are given in the Question,
Assets
Cash = $45,000
Inventory = $41,000
Property = $134,000
Liabilities
Notes = $55,000
Wages = $56,000
and
Equity
Stock = $50,000
Investment = $59,000
Total Liabilities + Equity = ( Notes + wages ) + (stock + Investment)
Total Liabilities + Equity = ( $55,000 + $56,000) + ($50,000 + $59,000)
Total Liabilities + Equity = $220,000.
Total Assets = Cash + Inventory + Property
Total Assets = $45,000 + $41,000 + $134,000
Total Assets = $220,000
Therefore,
Total Liabilities + Equity = Total Assets.
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For the following data set, find Q1, Q2, Q3 and the interquartile range.
15, 12, 23, 15, 7, 8, 21, 10, 12, 14, 16, 24, 19
Answer: q1=11 q2=15 q3=20
Step-by-step explanation:
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Two equations that have the same solution as the given equation are;
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
What is Multiplication property of equality?Both sides of an equation will remain equal, when both sides are
multiplied by the same amount.
The given equation: 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p
Simplifying the above equation by collecting like terms gives;
2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4
2.3·p - 10.1 = 6.49·p - 4
Multiplying both sides of the original equation by 100 gives
100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)
230·p - 1010 = 650·p - 400 - p
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If the random variable X has the binomial, bin(n, p) distribution, does the unbiased estimator of （1/p）exist? Explain your answer clearly by providing the step-by-step solution.
The unbiased estimator of 1/p does not exist.
What is an unbiased estimator?An estimate that deviates from the genuine population value is said to be biased. If the kind and extent of the bias are known, a biased sample may still be informative. When a sample's value matches the actual value of a population parameter, that is an unbiased estimator.
Given:
If the random variable X has the binomial.
1/p = 1 /{1-(1-p)} = 1 + (1-p) + (1-p)²/2! + ....
And let an unbiased estimator of 1/p exist.
[tex]\sum^n_k_=_0T(k)(^n_k)p^k(1-p)^k[/tex] = 1 + (1-p) + (1-p)²/2! + ....
The above series is finite on the LHS and infinite power series on the RHS.
That is contradiction.
The basic idea is that an unbiased estimator of 1/p would have to have the property that its expected value as a function of p would have to tend to infinity as p tends to 0.
But since Ep[U(x)] is bounded above by some function of n that is independent of p, no such estimator can exist.
Therefore, the unbiased estimator 1/p can not exist.
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Maria Brought 3 cakes of the same size for her birthday. half of one cake was left and one-third of qther. how much cake was left over altogether?
Answer:
7/12 (seven over twelve)
Step-by-step explanation:
1/3 -1/4 =4/12- 3/12=1/12
1/2+1/12=6/12+1/12=7/12
so the answer is 7/12
hopefully this helps
Write the expression d-7 / 2 in words
Answer:
The expression "d-7 / 2" can be written in words as
Step-by-step explanation:
The expression "d-7 / 2" can be written in words as "the quotient of d minus 7, divided by 2".
This is the operation of subtracting 7 from d and then dividing the result by 2.
What is 6,789,694,976 x 9,452,569,132
*Can not use calculator
The product of the given numbers can be represented in a scientific notation form as = 6418 × 10^19 (approximately)
What is multiplication?Multiplication can be defined as the repeated addition of a given value with the purpose of arriving to an expected value.
The multiplication of two given numbers is the same thing as the products of the given number and it's represented by the sign (X)
The product of 6,789,694,976 x 9,452,569,132 = 6418 × 10^19
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Ayuda porfa doy corona
3/4 > 1/5
6/9 > 2/5
6/7 > 3/10
2/11 < 4/9
Answer:
3/4 > 1/5
6/9 > 2/5
6/7 > 3/10
2/11 < 4/9
Step-by-step explanation:
Manera facil de comparar fracciones:.
3/4 1/5
Multiplica el denominador (numero abajo) de cada fraccion por el numerador de la otra fraccion y escribe el producto arriba del numerador.
El numero mas grande esta arriba de la fraccion mas grande.
5 x 3 = 15 arriba de 3/5
4 x 1 = 4 arriba de 1/5
Como 15 > 4, 3/4 > 1/5
30 18
6/9 2/5
6/9 > 2/5
60 21
6/7 3/10
6/7 > 3/10
18 44
2/11 4/9
2/11 < 4/9
lex has $1,780.80 in his savings in his saving account that he opened 6 years ago his account has an annual interest rate of 6.8% compounded annually how much money did lex use to open his savings
Answer:
To find the principal, P we can use the same formula, A=P(1+rn)nt. We have the balance of the account, A, after 6 years, $1,780.80. The interest rate, r, is 6.8% (or 0.68 as a decimal) and is compounded annually, so n=1. The time, t, is 6, since we know he opened his account 6 years ago. Plug in the known values into the formula and solve for the missing variable, P.
Step-by-step explanation:
1,780.80 = P (1+0.0681 divided 1^(6)
1,780.80= 1.484P
1,200=P the principal amount Lex used to open his account 6 years ago
Simisola wants to compare the time take
to make yoghurt at different temperature
List the variables she should control.
Yogurt production is affected by the production technological conditions.
What is yoghurt different temperature?Yogurt production is affected by the production technological conditions. Increase in the incubation temperature (42-45ᵒC) resulted to increase in the coagulation of the milk protein present (induced by thermophilic bacteria) and viscosity. This also resulted in increased acidity of the yoghurt.The temperature must be 108°F to 112°F for yogurt bacteria to grow properly. Too high a temperature inactivates bacteria; too low a temperature prohibits growth. Inhibitor substances such as detergent from dishes. Wash and rinse dishes well before making yogurt.Making yogurt at home is a fairly straight-forward process. Heat milk to 180F (82C), cool that milk to at least 110F (43C), add live cultures, usually in the form of yogurt with said cultures, incubate, then chill.There are several variables in the process, some of which are: The fat content of the milk (I typically use whole), how long to hold the milk during the initial heat step, how long it takes to cool the milk, the temperature of the incubation step, and the length of time for incubation, to name a few.To learn more about yoghurt different temperature refers to;
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If a man works for 8 hours a day, he can finish a job in 12 days. How many hours per day must he work to complete it in 10 days?
Answer:
9.6 hours
Step-by-step explanation:
12×8 would equal the amount of hours it takes to complete the job in 12 days so you simply divide that number by 10 which will give you 9.6h
Answer:
6.67 hour per day
Step-by-step explanation:
If
=8 hours a day = 12 days
then
= ? = 10 days
= 10/12 × 8hours per
= 6.67 hours per day.
On the first day of spring, an ențire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The relationship between the elapsed time, t, in days, since the beginning of spring, and the total number of locusts, Nday (t), is modeled by the following function: Nday (t) = 300.(1.2)^t
Complete the following sentence about the weekly rate of change in the locust population.
Round your answer to two decimal places.
Every week, the number of locusts grows by a factor of
Answer:
3.58
Step-by-step explanation:
You want to know the weekly growth factor if the daily growth factor is 1.2.
7 daysThe weekly growth factor will be the growth factor over 7 days:
(1.2)^7 ≈ 3.58
Every week, the number of locusts grows by a factor of 3.58.
__
Additional comment
The exponential model is ...
number = (initial number)(growth factor)^t
The period of time associated with the growth factor is the units associated with t. Since 1 week = 7 days, the multiplier for 7 days is ...
weekly growth factor = (daily growth factor)^7
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12 Aftab wants a patio in his garden. He is going to use concrete slabs to make the patio. Each concrete slab is a square with sides of length 0.5 m. A sketch of the planned patio is shown below. 3 m Patio 3 m 2
(a) What is the area of Aftab's patio? Give units with your answer.
Aftab pays £3.10 per concrete slab. (b) How much will it cost Aftab to buy enough concrete slabs to make the patio?
Answer:
5-3=2m
3x2=6m^2
Step-by-step explanation:
I can’t explain
LETTER B I DON’T KNOW THE ANSWER
Given that X≈2 is an approximate solution to x^2+2x-2=5, use the graph to find another approximate solution round your answer to the nearest integer. X≈ ___
The nearest integer that is a solution, gotten through graphing of the quadratic function x² + 2x - 2 = 5, is x = -4
How to find the graphical solution of the functionQuadratic equations when plotted on a graph follows a parabolic path.
To plot the functions there will be table of values that is used in making the graph. The table of values is solved as follows
x² + 2x - 2 = 5 rearranging the equation will result to x² + 2x - 7 = 0
For x = -20, y = (-20)² + 2 * -20 - 7 = 353
For x = 0, y = (0)² + 2 * 0 - 7 = -7
For x = 20, y = (20)² + 2 * 20 - 7 = 433
x y
-20 353
0 -7
20 433
The graph is plotted and attached. From the graph the solution is
x = -3.828, to the nearest integer = -4
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3 2/5 divided by 2 7/8 equals
Answer:
17/5÷23/8= 1 21/115
The answer is 1 21/115
A parking lot contains only cars and motor bikes. If there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?
Answer:
7 cars
11 bikes
Step-by-step explanation:
18 cars would have 72 tires. This is 22 more tires than necessary. If we add a bike, we lose four tires (from the car) and add two (from the bike). This means we lose two tires. 22/2 is 11 so it would be 11 bikes and 7 cars.
11 bikes = 22 tires
7 cars = 28 tires
22+28=50 tires