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2 years ago

What are the x- and y- intercepts for the graph of 3x+y=15

1 answer:

6 0

To make the equation easier to look at change it to this:
y = 15 - 3x
To find the x intercept say y = 0.
0 = 15 - 3x
Subtract 15 from each side.
-15 = -3x
Divide each side by -3.
5 = x <–––– x-intercept
The y-intercept of the equation is 15.
Hope this helps!

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Grade 12<br>mathematics<br>(√98-√50)²

allsm [11]

Answer:

Step-by-step explanation:

Two different approaches:

<u>Method 1</u>

Apply radical rule √(ab) = √a√b to simplify the radicals:

√98 = √(49 x 2) = √49√2 = 7√2

√50 = √(25 x 2) = √25√2 = 5√2

Therefore, (√98 - √50)² = (7√2 - 5√2)²

= (2√2)²

= 4 x 2

= 8

<u>Method 2</u>

Use the perfect square formula: (a - b)² = a² - 2ab + b²

where a = √98 and b = √50

So (√98 - √50)² = (√98)² - 2√98√50 + (√50)²

= 98 - 2√98√50 + 50

= 148 - 2√98√50

Apply radical rule √(ab) = √a√b to simplify radicals:

√98 = √(49 x 2) = √49√2 = 7√2

√50 = √(25 x 2) = √25√2 = 5√2

Therefore, 148 - 2√98√50 = 148 - (2 × 7√2 × 5√2)

= 148 - 140

= 8

4 0

2 years ago

Find all values of the variable

labwork [276]

The values of x for which the rational expression is undefined are -6 and -8.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a rational function:

$\rm f(x) = \dfrac{3x+20}{x^2+14x+48}$

As we know in the rational function denominator cannot be zero:

The values of x for which the rational expression is undefined.

x² + 14x + 48 = 0

$\rm x_{1,\:2}=\dfrac{-14\pm \sqrt{14^2-4\cdot \:1\cdot \:48}}{2\cdot \:1}$

$\rm x_1=\dfrac{-14+2}{2\cdot \:1},\:x_2=\dfrac{-14-2}{2\cdot \:1}$

x = -6, -8

Thus, the values of x for which the rational expression is undefined are -6 and -8.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

6 0

1 year ago

Please help me find the area of shaded region and step by step

Bumek [7]

Answer:

Part 1) $A=60\ ft^2$

Part 2) $A=80\ cm^2$

Part 3) $A=96\ m^2$

Part 4) $A=144\ cm^2$

Part 5) $A=9\ m^2$

Part 6) $A=(49\pi -33)\ in^2$

Step-by-step explanation:

Part 1) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior rectangle

The area of rectangle is equal to

$A=bh$

where

b is the base of rectangle

h is the height of rectangle

$A=(12)(7)-(8)(3)$

$A=84-24$

$A=60\ ft^2$

Part 2) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior square

The area of square is equal to

$A=b^2$

where

b is the length side of the square

$A=(12)(8)-(4^2)$

$A=96-16$

$A=80\ cm^2$

Part 3) we know that

The area of the shaded region is equal to the area of four rectangles plus the area of one square

$A=4(4)(5)+(4^2)$

$A=80+16$

$A=96\ m^2$

Part 4) we know that

The shaded region is equal to the area of the complete square minus the area of the interior square

$A=(15^2)-(9^2)$

$A=225-81$

$A=144\ cm^2$

Part 5) we know that

The area of the shaded region is equal to the area of triangle minus the area of rectangle

The area of triangle is equal to

$A=\frac{1}{2}(b)(h)$

where

b is the base of triangle

h is the height of triangle

$A=\frac{1}{2}(6)(7)-(6)(2)$

$A=21-12$

$A=9\ m^2$

Part 6) we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

The area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

$A=\pi (7^2)-(3)(11)$

$A=(49\pi -33)\ in^2$

7 0

2 years ago

Can someone help me on this math problem PLEASE

egoroff_w [7]

Answer:

QR perpendicular to PT

PR^Q=SR^T=90°

also ANGLES (QPR= STR

7 0

2 years ago

Alexandra and Stephanie are sisters, and they're saving their money to buy a used car. Together they have more than $2,500, and

Vilka [71]

Answer:

Stephanie has more than $900

Step-by-step explanation:

Represent the unknowns: a for Alexandra and s for Stephanie.

Then a + s > $2,500, and a = s + $700.

Substituting the latter into the former equation, we get:

(s + $700) + s > $2,500, or

2s > $1800

Then s > $900; Stephanie has more than $900.

7 0

1 year ago