Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
(See picture attached below)
Answer Choices:
A. x2 + 15x − 2 = 0
B. x2 + 15x + 58 = 0
C. 4x2 + 30x − 2 = 0
D. 4x2 + 30x + 58 = 0
Answers
(8 + 2x)(7 + 2x) = 58
Expanding the equation,
56 + 30x + 4x^2 = 58
Combining like terms and arranging the equation, we have:
4x^2 + 30x - 2 = 0
Therefore, the answer is
C. 4x2 + 30x − 2 = 0
Answer:
C
Step-by-step explanation:
took the test
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Answers
The height of the demonstration calculator is 504 millimeters.
To find the height of the demonstration calculator, we can use the ratio of the key widths between the student calculators and the demonstration calculator.
Let's first convert all measurements to the same unit for consistency. Since we need to find the height of the demonstration calculator, let's convert the width of the keys on the demonstration calculator to millimeters, which is the unit used for the height of the student calculator.
1 centimeter (cm) = 10 millimeters (mm)
Width of the key on the demonstration calculator =
= 2.8 cm x 10 mm/cm
= 28 mm
Now, we know the width of each key on the demonstration calculator is 28 millimeters.
We can use this information to find the height of the demonstration calculator.
The ratio of the width of the keys on the demonstration calculator to the width of the keys on the student calculator is:
= 28 mm (demonstration calculator) / 14 mm (student calculator)
Now, let's set up a proportion to find the height of the demonstration calculator (Hd):
Hd (demonstration calculator) / 252 mm (student calculator)
= 28 mm (demonstration calculator) / 14 mm (student calculator)
Hd / 252 = 28 / 14
Hd / 252 = 2
Hd = 2 x 252
Hd = 504 millimeters
So, the height of the demonstration calculator is 504 millimeters.
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Final answer:
The height of the large demonstration calculator is 50.4 cm, determined by converting measurements to the same units and using the scale factor between the student and demonstration calculators.
Explanation:
The question involves scale factor and unit conversion in mathematics. The scale factor between the student calculator buttons and the large demonstration calculator buttons is 2.8 cm (button size of large calculator) divided by 1.4 cm (button size of student calculator, which equates to 14 mm). Therefore, the scale factor is 2.
To find the height of the large calculator, we multiple the height of the student's calculator (252 mm or 25.2 cm) by the scale factor 2. Therefore, the height of the large demonstration calculator is 50.4 cm.
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Answers
1) if the equation is
y=1/4 * x-12 then x=1/4 y-12==>1/4y=x+12==>y=x/4+3
2) if the equation is
y=1/(4x-12) then x=1/(4y-12)==>4y-12=1/x==>4y=1/x+12==>y=1/(4x)+3
Answers
A^2 + B^2=C^2 Pythagorean’s Theorem
(3a)^2 + (4a)^2 = C^2
9a^2 + 16a^2 = C^2
a^2(9+16) = C^2
a^2(25) = C^2
sqrt ((a^2(25)) = sqrt (C^2)
5a=C=|PR|
shortcut would have been to recognize a 3-4-5 triangle
Answers
abc=acb=bac=bca=cab=cba
multiplicatoin can move
some possible ones
(13)(7)(21)=(13)(21)(7)=(21)(7)(13)=(21)(13)(7)=(7)(13)(21)=(7)(21)(13)
any of those work
Answers
6/13×reciprocal of 6/12=
6/13×12/6=
6 will get cancelled and so remaining...12/13=0.92307 or. 92
Answers
The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we can plug in the values given in the question to find the final amount earned after 10 years. The principal is $500, the annual interest rate is 4%, which is divided by 4 to get 1% per quarter, the number of times compounded per year is 4, and the time in years is 10. Plugging in these values, we get A = 500(1 + 0.01)^(4*10) = $740.60. Therefore, the final amount earned after 10 years is $740.60.
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