The area of a rectangle is 18 m² if the length is 6 m less than five times the width then find the dimensions of the rectangle round off your answer to the nearest hundredth
Answer:
Step-by-step explanation:
width = w
L = 5w - 6
w(5w - 6) = 18
5w^2 - 6w = 18
5w^2 - 6w - 18 = 0
Using the quadratic equation formula
x = 2.58997 and
x = -1.38997 This root cannot be. (No rectangle has a minus length.
w = 2.58997
L = 5*2.58997 - 6
L = 6.94985
w = 2.59
L = 6.95
prove the difference of the squares of two successive intergers is equal to the sum of the intergers
Answer:
[tex]\displaystyle \begin{aligned} \displaystyle (n+1)^2 - n^2 &= 2n +1 \\ &= n (n+1)\end{aligned}[/tex]
Where ? = 2.
Step-by-step explanation:
We want to prove that the difference of the squares of two successive integers is equal to the sum of the integers.
In other words, we want to show that for any given integer n:
[tex]\displaystyle (n+1)^2 - n^2 = n + (n+1)[/tex]
From the original equation, expand:
[tex]\displaystyle = (n^2 + 2n + 1) - n^2[/tex]
Combine like terms:
[tex]= 2n +1[/tex]
And rewrite. Hence:
[tex]\displaystyle = n + (n + 1)[/tex]
Therefore:
[tex]\displaystyle \begin{aligned} \displaystyle (n+1)^2 - n^2 &= 2n +1 \\ &= n (n+1)\end{aligned}[/tex]
In conclusion, ? = 2.
Write the 127.5 in scientific notation please.
Find the value of x.
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Answer:
x = 6
Step-by-step explanation:
The angle bisector divides the sides proportionally.
(6x -1)/42 = (10x +5)/78
13(6x -1) = 7(10x +5) . . . . . . . multiply by 546 = LCM(42, 78)
78x -13 = 70x +35 . . . . . . . . eliminate parentheses
8x = 48 . . . . . . . . . . . . . . . . add 13-70x
x = 6 . . . . . . . . . . . . . . . . . divide by 8
a meayerologist at television station reported that a town received 0.90 inches of rain. Which fraction is equivalent to this amount of rain in inches?
Answer:
9/10
Step-by-step explanation:
0.90 = 0.9 = 90/100 = 9/10
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Write the ratio 2/3/4/5 in simplest form
Answer: The given ratio, in simplest form, is 4/7.
Step-by-step explanation:
Rewrite 2/3.5 as 4/7 by multiplying both the 2 and the 3.5 by 2. This eliminates the decimal fraction.
The given ratio, in simplest form, is 4/7.
Identify the property that justifies each step asked about in the answer area below.
Line 1:
c(bd)
Line 2:
(cb)d
Line 3:
(bc)d
Line 1 to Line 2:
Line 2 to Line 3:
The properties that justify each line is:
Line 1 to Line 2: Associative property of multiplicationLine 2 to Line 3: Associative property of multiplicationThe expressions are given as:
[tex]c(bd)[/tex]
[tex](cb)d[/tex]
[tex](bc)d[/tex]
Notice that only the positioning of the variables are changed, the operator within the variables remain the same (i.e. the multiplication)
Hence, the properties that justify the three lines is the associative property of multiplication
Read more about algebra properties at:
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Answer:
Step-by-step explanation:
KJ,BDUVLJ,B SIV.LNDFVLIK.,snV LK,BNDIRLKN
The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is ₹157. Find the sum
Answer:
The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. ... Hence, the sum is Rs. 63,100.
Step-by-step explanation:
Hopefully it is helpful....Have a nice day..
Which of the following tables represent functions? If the relation is not a function, indicate why it is not.
Step-by-step explanation:
1. the table on the left is a function, with the formula : y = x²
2. the table on the right is also a function, indicated by the values of the input are different each others
Resolva a inequação (x + 4)(x – 4) < 0.
Answer:
-4 < x < 4
Step-by-step explanation:
6.5 / (2.2 x 3.6 / 7.92)
(pls help)
Answer:
6.89
Step-by-step explanation:
Do what's in the parentheses first then the rest and I rounded. Hope this helps!
Use a number line or place value to round each number to the place of the underlined digit
you didn't put a picture in,
What type of function is represented in the table? 0 -3 1 -4 2 -11 3 -24 4 -43 5 -68 logarithmic linear exponential quadratic
Answer:
exponential quadrant
hope it helps you
The given function is of quadratic type. Therefore, the correct option is option C among all the given options.
What is mathematical function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a predictor variables (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Expressions of well-known functions can be found in many frequently used mathematical formulas. As an illustration, the formula A = r2 for both the area of either a circle plots the predictor variables A (this same area) as little more than a consequence of the regression coefficient r. (the radius).
Mathematical functions with more than two variables, often known as multivariable or multivariate functions, are frequently used; this is seen by the triangle's area formula. The given function is of quadratic type.
Therefore, the correct option is option C.
To know more about mathematical function, here:
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When 8 is subtracted from the square of a number, the result is 7times the number. Find the positive solution
Answer:
x=8 , x=-1
Step-by-step explanation:
let the number is x
According to the condition
[tex] {x}^{2} - 8 = 7x \\ {x}^{2} - 7x - 8 = 0 \\ {x}^{2} - 8x + x - 8 = 0 \\ x(x - 8) + 1(x - 8) = 0 \\ (x - 8)(x + 1) = 0 \\ x - 8 = 0 \: or \: x + 1 = 0 \\ x = 8 \: or x = - 1[/tex]
Determine the volume of
the right rectangular prism
shown.
112 cm
4 cm
24 cm
Answer:
5376
Step-by-step explanation:
V=sh
Which property is shown?
If m ZABC = m ZCBD, then mZCBD = m ZABC
reflexive property
substitution property
symmetric property
Transitive property
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Answer:
(c) symmetric property
Step-by-step explanation:
The symmetric property of equality lets you swap sides of the equal sign.
__
Reflexive: A = A
Substitution: if A=B and A=C, then C=B
Symmetric: A = B ⇔ B = A
Transitive: if A = B and B = C, then A = C.
note that the substitution and transitive properties are almost indistinguishable.
Given that BE bisects LAB Din the figure below, find the value of x.
help please!
which of this shape will tessellate?
Answer: You can consult:
Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. You can have other tessellations of regular shapes if you use more than one type of shape. You can even tessellate pentagons, but they won't be regular ones. Tessellations can be used for tile patterns or in patchwork quilts!
Step-by-step explanation:
I'm not sure but hope it helps.
The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t^4 – 9t^3 + 24t^2 – 20t, where t is the number of months since the restaurant opened. How many months after the franchise opens will it begin to show a profit?
5 months
3 months
2 months
1 month
(2 months isn’t the answer btw)
The profitability of the restaurant is when the function gives a value greater than 0. The franchise does not make a profit after 5, 3, 2 or 1 month of opening.
Given that:
[tex]P(t) = t^4 - 9t^3 + 24t^2 - 20t[/tex]
To calculate the profit, we simply substitute the values of t in the above equation.
(a) 5 months
This means [tex]t =5[/tex]
So, we have:
[tex]P(5) = 5^4 - 9\times 5^3 + 24 \times 5^2 - 20 \times 5[/tex]
[tex]P(5) = 0[/tex]
(b) 3 months
This means that [tex]t=3[/tex]
So, we have:
[tex]P(3) = 3^4 - 9 \times 3^3 + 24 \times 3^2 - 20 \times 3[/tex]
[tex]P(3) = -6[/tex]
(c) 2 months
This means that [tex]t = 2[/tex]
So, we have:
[tex]P(2) = 2^4 - 9 \times 2^3 + 24 \times 2^2 - 20 \times 2[/tex]
[tex]P(2) = 0[/tex]
(d) 1 month
This means that [tex]t = 1[/tex]
So, we have:
[tex]P(1) = 1^4 - 9 \times 1^3 + 24 \times 1^2 - 20 \times 1[/tex]
[tex]P(1) = -4[/tex]
For the restaurant to make a profit, the equation has to give a positive value. Since none of the values of t gives a positive value for P(t).
Then, we can say the franchise does not make a profit after 5, 3, 2 or 1 month of opening.
Read more about functions at:
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1.2 recognizing function worksheet
Answer: Perhaps you did a typo..?
Step-by-step explanation: I know all about functions, but there seems not to be a worksheet. Perhaps you didn't add it on, or it's just me. But anyways, I would absolutely adore and love to help when you add it on. I wish you the best of luck
Solve the triangle.
A = 46°, a = 31, b = 27
Step-by-step explanation:
a=31
b=27
A = 46 degree
now, Area of ️ABC =ab siny÷2
=31×27 sin46÷2
=301.04371 .
what is the slope -intercept of this line
Step-by-step explanation:
at x (2,-2)
y(0,4)
You can use the formula Y = MX + C
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Answer:
Hope This Helps You
Have A Great Day
Find the arc length of the partial circle. Either enter an exact answer in terms of π or use 3.14 πpi and enter your answer as a decimal
Answer:
C (circumference) = 2 pi R for circle
A (arc length) = R * theta = pi R = pi * 9 = 28.27
Phil wants to fence off his rectangular yard. If the yard is 65 feet by 80 feet, and fencing costs $6 per foot, how much will it cost Phil to fence the yard?
Answer:
Step-by-step explanation:
if Phil intents to surround the entire yard with fence then he needs
6(65)+6(80)870feet of fence >>> this is the parameter of the rectangle
and since the fence cost $6 per foot
total would 870x6= $5220
The product of 4x and 0 is:
a- 4x
b- 4
c- 0
d- none of these
Given IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15 , the proportion of people with s above 130 is:
Given the assumption of a normal distribution with a mean of 100 and a standard deviation of 15, a score of 130 represents a z-score of 2. In different mostly older handbooks of descriptive statistics you can find a ‘from z to percentile-table’. Nowadays it’s more easy to use the computer. Using R, a free and open source statistical environment (www.r-project.org), you can use the command pnorm (130, 100, 15) and it will give 0.9772. Because yo want the proportion above that score you use 1-pnorm (130, 100, 15). Another way of writing in R and with for example 3 IQ-scores:
perc = pnorm (c (70, 100, 130), 100, 15)
(1 - perc)
gives you the above-proportion of the IQ-scores of respectively 70, 100 and 130.
Qu. In a triangle ABC, side AB has length 10cm, side AC has length 5cm, and angle BAC = θ
where θ is measured in degrees. The area of triangle ABC is 15cm^2
(a) Find the two possible values of cos θ
Given that BC is the longest side of the triangle,
(b) find the exact length of BC.
Answer:
To find cosθ, use the formula for the area of a triangle i.e. AREA=1/2 x a x b x sinC.=> For this case: 15= 1/2 x 10 x 5 x sinC to find sinC.=> SinC = 3/5 thus, Arcsin(3/5)=+- 4/5 or +-0.8
To find the exact length of BC, use the cosine rule.=> c(sq)=a(sq)+b(sq)-2abCosC=> c(sq)=10(sq)+5(sq)-2(10)(5)(+-4/5)=> c(sq)= Square root of 205
Andrew is employed and paid at rate of R650 per day . Calculate his new daily rate after a 7% increase. Show all your calculations
Answer:
650 x 1.07 = 695.5.......
9.00391 to the nearest ten-thousandth
Answer:
It is 9.0039
Step-by-step explanation:
9 » ones
.0 » tenths
0 » hundredths
3 » thousandths
[tex]{ \boxed{ \bf{9} \: » \: ten - thousandths}}[/tex]
1 » hundred thousandths
Answer:
9.0039
Step-by-step explanation: