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3 years ago

Find the value of a2 + b when a = -2 and b = 5

Mathematics

1 answer:

REY [17]3 years ago

4 0

Answer: 9

Step-by-step explanation: In this problem, we're going to evaluate a² + b knowing that a = -2 and b = 5.

So the first thing we want to do is substitute these numbers into our problem.

Since a = -2, we will replace a with a -2 and as we do that, we will put that -2 in parentheses and square it since we have a². Squaring a number just means multiplying a number by itself so (-2)² is equal to 4 since a negative multiplied by a negative gives us a positive.

Now we will replace b with 5 and now we have the following.

4 + 5 simplifies to 9.

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An architect wants to draw a rectangle with a diagonal of 15 centimeters. The length of the rectangle is to be 6 centimeters mor

S_A_V [24]

Answer:

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

Step-by-step explanation:

The diagonal of a rectangle is represented by $\sqrt{length^2+width^2}$ .
Area of rectangle is = length×width
Perimeter of a rectangle = 2(length+width).

Assume x be the width of the rectangle.

The length of the rectangle is to be 6 cm more than twice the width.

The length of the rectangle is= (2x+6) cm

Then the diagonal of the rectangle is $\sqrt{length^2+width^2}$

$=\sqrt{(2x+6)^2+x^2}$

$=\sqrt{4x^2+24x+36+x^2}$

$=\sqrt{5x^2+24x+36}$ cm

According to the problem,

$\sqrt{5x^2+24x+36}=15$

Squaring both sides

$\Rightarrow{5x^2+24x+36}=15^2$

$\Rightarrow{5x^2+24x+36}=225$

$\Rightarrow{5x^2+24x+36-225=0$

$\Rightarrow{5x^2+24x-189=0$

⇒5x²+45x-21x-189=0

⇒5x(x+9)-21(x+9)=0

⇒(x+9)(5x-21)=0

⇒x+9=0 or, 5x-21=0

$\Rightarrow x=-9, \frac{21}5$

⇒x= -9, 4.2

Since the width of a rectangle can not negative.

So, x=4.2 cm

The width of rectangle is = 4.2 cm

The length of the rectangle is =(2×4.2+6)

=14.4 cm

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

8 0

3 years ago

Marina correctly simplified the expression StartFraction negative 4 a Superscript negative 2 Baseline b Superscript 4 Baseline O

Sav [38]

Answer:

Step-by-step explanation:

We know that x^a / x^b = x^ (a-b)

b^4 / b^ -3 = b^(4 - -3) = b^ (4+3) = b^7

The exponent for b is 7

6 0

3 years ago

Find the slope of a line perpendicular to y=3×+7

polet [3.4K]

Answer:

-1/3

Step-by-step explanation:

y = 3x+7

This is in the form y = mx+b

The slope is m so it is equal to 3

Perpendicular lines have slopes that are negative reciprocals

m perpendicular = - (1/3)

7 0

3 years ago

Why are and Iby 4 and - 1 zeroes of the polynomial p(x) = 4² +3x-1?

Serggg [28]

Answer:

$- 1 = 16 + 3x - 1 \\ 3x = 16 - 1 + 1 \\ \frac{3x}{3} = \frac{16}{3} \\ x = 5.33$

7 0

3 years ago

Help me if you understand thanks sm

kumpel [21]

First, find the slope of the line using the formula for slope:

m = (y2 - y1) / (x2 - x1)

m = (4 - (-2)) / (-3 - 2) = -6/5

Then, use the point-slope formula using a point that you were given and the slope that you calculated.

y - y1 = m(x - x1)

y - 4 = (-6/5)(x + 3)

Then, simply get y alone.

y = (-6/5)x + 2/5

3 0

2 years ago