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zlopas [31]
3 years ago
11

a rectangular picture measuring 5 in. by 7 in. is surrounding by a frame with uniform width x. Write a quadratic function in sta

ndard form to show the combined area of the picture and frame.​
Mathematics
2 answers:
9966 [12]3 years ago
8 0

Answer:

(4x² + 24x + 35) in²

Step-by-step explanation:

(5+2x)(7+2x)

35 + 14x + 10x + 4x²

4x² + 24x + 35

ale4655 [162]3 years ago
7 0

Answer: A(x) = 4x² + 24x + 35

Step-by-step explanation:

Let x represent the width of the rectangular frame.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The measurement of the rectangular picture is 5 in. by 7 in.

If the width is 5 inches, then the combined width of the picture and frame is 5 + x + x = (5 + 2x) inches

The combined length would be

7 + x + x = (7 + 2x) inches

Therefore, a quadratic function in standard form to show the combined area of the picture and frame would be

(5 + 2x)(7 + 2x)

35 + 10x + 14x + 4x²

A(x) = 4x² + 24x + 35

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8 times the difference between a number and 6 is equal to 4 times the number.
7nadin3 [17]

Answer:

The variable titled "the number" is A: 12.

Step-by-step explanation:

The problem is 8 * (x - 6) = 4 * x

Try the first number as x and rewrite the expression.

8 * (12 - 6) = 4 * 12

Following PEMDAS (the Order of Operations), you need to solve the problem inside the parenthesis.

12 - 6 = 6

Rewrite the problem.

8 * 6 = 4 * 12

8 times 6 is 48.

4 times 12 is 48.

The variable in the expression 8 * (x - 6) = 4 * x is 12.

4 0
2 years ago
The net of a triangular prism and its dimensions are shown in the diagram. what is the lateral surface area of the triangular pr
Furkat [3]

Answer: 120 sq in.

Step-by-step explanation:

5 0
3 years ago
AACB = ADCE <br>&lt;A=50°, &lt;C=45°, and &lt;D=10x <br>x=[?]​
motikmotik

Answer:

X=5

Step-by-step explanation:

Angle A is congruent to angle D.

7 0
2 years ago
Is the equation below a function? explain<br>d) y2 = x2 + 5​
RoseWind [281]

Answer:

No

Step-by-step explanation:

y^2 = x^2 + 5​

Rewriting

y^2 - x^2 = 5

This is a hyperbola

We can use the vertical line test to show that it is not a function since a vertical line passes through more than one point.

5 0
3 years ago
Use synthetic division to determine whether the number k is an upper or lower bound (as specified for the real zeros of the func
mote1985 [20]

Solution:

The given Polynomial is :

f(x) = 5x^4 + 4x^3 - 2x^2 + 2x + 4=5( x^4 + \frac{4}{5}x^3 - \frac{2}{5}x^2 + \frac{2}{5}x + \frac{4}{5})

By Rational Root theorem the  of Zeroes of the Polynopmial are:

\pm\frac{1}{5},\pm\frac{2}{5},\pm\frac{4}{5},\pm1,\pm2,\pm4

But , f(\pm\frac{1}{5},\pm\frac{2}{5},\pm\frac{4}{5},\pm1,\pm2,\pm4)\neq 0

So, no root of this polynomial is real.

Therefore, All the four roots of Polynomial are imaginary.

So, we can't say whether the number k=2, is an upper or lower bound of the polynomial f(x) = 5x^4 + 4x^3 - 2x^2 + 2x + 4=5( x^4 + \frac{4}{5}x^3 - \frac{2}{5}x^2 + \frac{2}{5}x + \frac{4}{5}).

8 0
3 years ago
Read 2 more answers
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