Answers
Answer:
The only possible value for x is 7.
Step-by-step explanation:
Recognize that we are given two different equations for the area, A:
1) A = 63 in^2, and
2) A = x^2 - 16x + 126
These two equations must be equal to each other: A = A
and therefore,
x^2 - 16x + 126 = 63, which becomes x^2 - 16x + 63 = 0 if we subtract 63 from both sides.
Let's solve this using "completing the square." Take half of the coefficient of x (which coefficient is -16), halve it (obtaining -8) and square the result (obtaining 64). Now, between -16x and +63 (see the last equation, above), we write +64 - 64, obtaining:
x^2 - 16x + 64 - 64 + 63, which can be rewritten as:
(x - 8)^2 -1 = 0. Note that this has the form (x - h)^2 + k, and that h is 8 and k is -1. Thus, the associated parabolic graph has its vertex at (h, k), or (8, -1). This graph opens up. Because the vertex is below the x-axis, we know that the graph intersects the x-axis in two places.
Let's find these x values. Rewrite (x - 8)^2 -1 = 0 as (x - 8)^2 = 1. Squaring both sides results in x - 8 = 1, which simplifies to x = 9. This x = 9 is 1 greater than the x-coordinate of the vertex (8). Knowing tht the graph is symmetrical about the vertical line x = 8, we can safely assume that x = 7 is the other solution, as it is 1 unit to the left of x = 8.
Now we must check these possible solutions {7, 9}.
Evaluate the second equation at each 7 and 9 and determine whether the area turns out to be 63 in^2, as it must.
(7)^2 - 16(7) + 126 = 49 + 126 - 112, which in turn is equal to 63. Yes, x = 7 is a possible value for x.
Next: x = 9. (9)^2 - 16(9) + 126 = 81 - 112 + 126 = 95. This does not agree with A = 63 in^2, so we must reject x = 9.
The only possible value for x is 7.
Related Questions
The population of a city has decreased by 33% since it was last measured. If the current population is 13,400, what was the previous population?
0
Х
?
Continue
Answers
Answer:
8,978 People
Step-by-step explanation:
13,400 x 0.33 = 4,422
13,400 - 4,422 = 8,978
2n+3n+4n=63
Answer and Solution
Answers
Answer:
7
2n + 3n + 4n. = 63
9n = 63
n = 63/9
n = 7
hope it helps
Answer:
n=7
Step-by-step explanation:
add 2n+3n+4n, which gives 9n =63
Divide by 9 on both sides, 9n/9 =63/9
n=7
If you need to confirm that's the right answer, just plug 7 back as n
2(7)+3(7)+4(7)=63
14+21+28 =63
63=63
what is the answer to this question1/2 divided by 6/13
Answers
Answer:
0.006410256
Step-by-step explanation:
How many years in a month
Answers
Answer: There are 12 months in one 1 year
Step-by-step explanation:
Free Brainliest
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A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tenth. Enter your answer in the box.
A rectangular prism 60 centimeters wide, 80 centimeters long, and 100 centimeters tall.
Answers
EXPLANATION: use pythagorean theorem
One month Maya rented 2 movies and 3 video games for a total of $20. The next month she rented 6 movies and 5 video games for a total of $38. Find the
rental cost for each movie and each video game.
Rental cost for each movie:
Rental cost for each video game:
Answers
Answer:
[tex]M = 1.75[/tex] --- Movies
[tex]V = 5.5[/tex] --- Video games
Step-by-step explanation:
Represent the movies with M and the video games with V.
The first month, the expression is:
[tex]2M + 3V = 20[/tex]
The next month, the expression is:
[tex]6M + 5V = 38[/tex]
Required
Find M and V
We have:
[tex]2M + 3V = 20[/tex] --- (1)
[tex]6M + 5V = 38[/tex] --- (2)
Multiply (1) by 3.
3 * [tex]2M + 3V = 20[/tex]
[tex]6M + 9V = 60[/tex] --- (3)
Subtract (1) from (3)
[tex]6M + 9V = 60[/tex]
- [tex]6M + 5V = 38[/tex]
-------------------------
[tex]6M - 6M + 9V - 5V = 60 -38[/tex]
[tex]4V = 22[/tex]
Divide by 4
[tex]V = 5.5[/tex]
Substitute 5.5 for V in (1)
[tex]2M + 3V = 20[/tex]
[tex]2M + 3 * 5,5 = 20[/tex]
[tex]2M + 16.5= 20[/tex]
Subtract 16.5 from both sides
[tex]2M = 3.5[/tex]
Divide by 2
[tex]M = 1.75[/tex]
explain how 7/10 and 70/100 are equivalent decimals
Answers
Step-by-step explanation:
7/10 in percentage form is 70%
70/100 in percentage form is 70%
Simple as that
It is proved that the given decimals are equivalent decimals.
What are equivalent fractions? What is a mathematical function, equation and expression?equivalent fractions : Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given are the fractions -
7/10 and 70/100
We have the following fractions -
A = (7/10) = 0.7
B = 70/100 = (7 x 10)/(10 x 10) = (7/10)
B = (7/10) = 0.7
It can be seen that fraction A equals to B.
Therefore, it is proved that the given decimals are equivalent decimals.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
does anyone know how to do this (algebra 2)
Answers
2 < (1.12)t
ln 2 < t ln (1.12)
0.6931 < t(0.1133)
6.117 < t
FREE BRAINLIST NEED HELP ASAP
Answers
Answer:
B
Step-by-step explanation:
HELP ME!!!!!
Which inequality is represented by this graph?
A. 0 greater-than x
B. x greater-than 0
C. 0 greater-than-or-equal-to x
D. x greater-than-or-equal-to 0
Answers
Answer:
the last one
Step-by-step explanation:
x is greater than or equal to 0. you can see the line goes from 0 and up so it can be 0, or greater. hope this helps! :)
Does anyone know what 0.4 divided by 2.4 is? I think it’s 0.6 or 6 not for sure tho!
Answers
Answer:
0.16 I think............
Answer:
0.16666666666
Alex randomly chooses a shirt and pants to wear. He will choose between a green (G), orange (O), or red (R) shirt. He will choose between black
pants (Bl), brown pants (Br). Jeans (J), or tan pants (T). The possible outfits are shown in the table.
G.BO.BIR.BI
G,Br 0,Br R, Br
GJ OJ RJ
GT O,T RT
What is the probability that Alex chooses at least one of a green shirt or black pants?
Answers
Answer:
C) 1/2
Step-by-step explanation:
6 out of 12, so 1/2
Find the distance between pair of points (0, - 5) and (7, 2) . necessary , express the answer in radical form and then round to two decimal places
Answers
Answer:
d=9.899495 or √98
Step-by-step explanation:
√(7-0)^2 + (2-(-5))^2
√(7)^2+(7)^2
√98
Help me please.........
Answers
Step-by-step explanation:
it's mathematics or what I will help you.
one peach weigh 5 ounces. bella buys 8 peaches. what is the total weight of the peach
Answers
Answer:
40 ounces
Step-by-step explanation:
well if every peach weighs 5 ounces and she buys 8, just do 8 x 5 and you get 40
A watch seller gained 20% by selling a watch for rs 1260.is) What was its cost price.ii)If he had to gain 30%,at what price should have sold it
Answers
Step-by-step explanation:
A watch seller gained 20% by selling a watch for 1260.If he had to gain 30%,at what price should have he sold it?
Dalton III
Answered December 12, 2020
I shall explain the solution to this problem using rudimentary concepts.
First, we need to determine the original price of the watch.
Convert the percentage profit to a decimal by dividing by 100. In this problem, the profit is 20%, so we would divide:
20100=0.2
Add 1 to the profit expressed as a decimal.
1+0.2=1.2
Divide the price after the profit has been added by the figure which we have calculated to find the price before the profit (we shall assume that the currency used in this problem is the pound sterling)
£12601.2=£1050
Now that we have determined the original price of the watch, we shall determine at what price should the seller sell this watch in order to obtain a 30% gain. The same formula is used for the first two steps.
Convert the intended percentage profit to a decimal by dividing by 100. In this problem, the intended profit is 30%, so we would divide:
30100=0.3
Add 1 to the intended profit expressed as a decimal.
1+0.3=1.3
Now, instead of dividing, we would want to multiply the original price with the figure 1.3
£1050⋅1.3=£1365
So, in order to gain a profit of 30%, the watch seller should sell the watch at a price of £1365
It took Marjorie 15 minutes to drive from her house to her daughter's school. If the school was 4 miles away from her house, what was her unit rate of speed?
A- 16 mph
B- 8 mph
C- 4 mph
D- 30 mph
Answers
Answer:
I think it would be 4 mph because 4x4 is 16
( 3/4 ÷ 3/100 −23 1/2 )÷1 1/2 · 2/3 +1 1/6
Answers
Answer:
-7333/4400
Step-by-step explanation:
Hope this helps :)
HELP
Find the mean, median, mode, and range of the following data set.
15, 12, 19, 15, 16, 13, 15.
Mean:
Median:
Mode:
Range
Answers
Mean is 331
Mode is 15
Range is 1903
Hope this helps
Find the coordinates of the point where the lines with equations y=x and y=-6 intersect
Answers
Answer:
(-6, -6)
Step-by-step explanation:
Find the coordinates of the point where the lines with equations y=x and y=-6 intersect.
The lines intersect at y = y
Equating the right hand side of both expressions we have;
x = -6
Since y = x, hence y = -6
The required coordinate where they intersect is at (-6, -6)
Help pls also show work if needed!
Answers
Answer:
unknown value = 800
Step-by-step explanation:
f(x) = 1333/100·x + 1/5
so if x = 60 - > (1333/100)60+1/5 = 800
Answer: 800
Step-by-step explanation: 933.3-133.3=800-133.3=666.7-133.3=533.4
Which of the following is equivalent to the radical expression below? 5^8*13
Answers
Answer:
[tex](d)[/tex] [tex]5^{8.13} = 5^{8} * 5^{\frac{1}{10}} * 5^{\frac{3}{100}}[/tex]
Step-by-step explanation:
Given
[tex]5^{8.13}[/tex]
Required
Select an equivalent expression
[tex]5^{8.13}[/tex]
Simplify the power
[tex]5^{8.13} = 5^{8 + 0.1 + 0.03}[/tex]
Apply law of indices:
[tex]5^{8.13} = 5^{8} * 5^{0.1} * 5^{0.03}[/tex]
Express decimal as fractions
[tex]5^{8.13} = 5^{8} * 5^{\frac{1}{10}} * 5^{\frac{3}{100}}[/tex]
Please help that’s all I ask just please help
Answers
Answer: 1017.88
Step-by-step explanation:
Hope it is right
HELP WILL MARK BRAINLIEST
Answers
Answer:
a) 1/9
b)1/64
c)1/16
Step-by-step explanation:
The sum of deviations of n observations about 25 is 25 and the sum of deviations of the same n observations about 35 is −25. The mean of observations.
Answers
Answer:
30Step-by-step explanation:
please refer to the attachment above
Write the equation of the line that passes through the points (-7, 7) and (-6, -5).
Please help 13 points ?
Answers
Answer:
y = -12x - 77
Step-by-step explanation:
The standard form of the equation is expressed as y = mx+b
m is the slope
Given the coordinate (-7, 7) and (-6, -5).
m = -5-7/-6+7
m = -12/1
m = -12
Get the intercept b
Substitute m= -12 and (-7 7) into y = mx+b
7 = -12(-7) + b
7 = 84 + b
b = 7 - 84
b = -77
Get the required equation
y = mx+b
y = -12x +(-77)
y = -12x - 77
This gives the required equation
what is the area of this shape?
Answers
Answer:
D) 36 cm^2
Step-by-step explanation:
(9 x 3) + (2 x 4.5)(2)(0.5) = 36 cm^2
What is 27^2/3 simplified
Answers
Answer:
3^3
Step-by-step explanation:
[27]^2/3 can also be written as,
[(3)^3]^2/3
Now we know that a^m * a^n = a^m+n, therfore,
[3]^ 3*2/3
Cut 3 and 3
Therefore, you get 3^3
Let me know if you understood. If you didnt I can try to explain it to you in another way.
Also, plz mark me as the brainliest!
help and i will mark u as a brilliant and a follow
Answers
Answer:
126 minutes
Step-by-step explanation:
17.12 - 2 = 15.12
15.12 divided by 0.12 = 126 min
Im not sure about that
Does anyone know the answer?
Answers
Answer:
15°
Step-by-step explanation:
2x+5=3x
5=3x-2x
5=x
Now we can solve the angle.
<BAD=2x+5 = 2(5)+5 = 10+5 = 15°