Answer: The length of the rectangle is 35 in.
The width of the rectangle is 28 in.
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Explanation:
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The formula for the area, "A", of a rectangle:
Area (A) = length (L) * width (w) ;
that is: " A = L * w " ;
A = 980 in² (given);
ratio of the length to the width is: " 5 : 4 " (given);
→ Find the length (L) and the width (w).
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→ 980 in² = (5x) * (4x) ;
in which: " 980 in² " is the area of the triangle;
" 5x" = the length (L) of the rectangle, for which we shall solve;
" 4x" = the width (w) of the rectangle, for which we shall solve.
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If we find solve for "x" ; we can solve for "5x" and "4x" (the "length" and the "width", respectively); by plugging in the solved value for "x" ;
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→ 980 in² = (5x) * (4x) ;
↔ (5x) * (4x) = 980 in² ;
→ (5x) * (4x) = (5) * (4) * (x) * (x) = 20 * x² = 20x² ;
→ 20x² = 980 ;
Divide each side by "10" ; by canceling out a "0" on each side of the equation:
→ 2x² = 98 ;
Now, divide each side of the equation by "2" ;
→ 2x² / 2 = 98 / 2 ;
to get:
→ x² = 49 ;
Now, take the "positive square root" of each side of the equation; (since a "length or width" cannot be a "negative value") ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ ⁺√(x²) = √49 ;
to get:
→ x = 7 ;
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Now, we can solve for the "length" and the "width" ;
→ The length is: "5x" ;
5x = 5(7) = " 35 in " ;
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→ The width is: "4x" ;
4x = 4(7) = "28 in."
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Let us check our answer:
→ A = L * w ;
→ 980 in² = ? 35 in. * 28 in. ?? ;
Using a calculator: "35 * 28 = 980" . Yes! ;
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{ Also note: " in * in = in² " ? Yes! } .
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0.9 x 10^4
Let’s break this down into steps.
So to start off with, you need to do 4.5/5 which = 0.9.
Now we can deal with the indices. 10^-3 / 10^-7 means we have to subtract them. Therefore, -3 - -7 = 4. Altogether, we have 0.9 x 10^4
The question states we should leave our answer in standard form.
So our answer is 0.9 x 10^4.
Answer:
F(x) and g(x) are not inverse functions.
Step-by-step explanation:
In order to calculate the inverse function of a function, we have to isolate X and after that, we change the variables.
As our function f(x) is a exponentian function, we can apply logarithm with base 10 (log) in both sides in order to isolate X. Remember that log10=1.
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Now we change the variables.
F(x) and g(x) are not inverse functions.
Answer:
JL
Step-by-step explanation:
given by the way the triangles were originally written, the logical answer would be JL because it is in the same order that EG is written in the order of the triangle.
Answer:
A = 80 S =70
Step-by-step explanation:
#Adults tickets = A
#Students tickets = S
A + S = 150
5A (means the price is $5 times the number of Adult tickets) equals the total amount for all of the Adult tickets altogether
3S (means the price is $3 times the number of Student tickets) equals the total amount for all of the students tickets altogether
5A + 3S = 610 (Means adding the total of all the student tickets plus adult tickets will equal $610 for all tickets sold)
Using both equations now, you can use substitution or elimination to solve for one of the variables. Then you can use the variable to substitute to solve the remaining one.
A + S = 150
5A + 3S = 610
Substitution:
A = 150 - S (Rearrange the first equation by moving S to the other side)
Substitute into the other equation
5 (150 - S) + 3S = 610
750 - 5S + 3S = 610 Combine like terms : -2S = -140
Solve for S = 70
Substitute into A + S = 150 A + (70) = 150
A = 80
