All categories

3 years ago

If f(x) = 6 – 5x and g(x) = 4x – 1, evaluate f(x) – g(x) for x = –2.

Mathematics

1 answer:

alisha [4.7K]3 years ago

6 0

$f(-2)=6-5(-2)=6-(-10)=16$ , and $g(x)=4(-2)-1=-9$ .

So, the difference of them is $16-(-9)=25$ .

You might be interested in

SOLVE APPLICATION USING ALGEBRA. TYPE THE EQUATION OR INEQUALITY AND PLEASE SHOW WORK. a) A rectangle with perimeter 18 cm has l

alekssr [168]

Answer:

$w=2\\l=7$

Step-by-step explanation:

$l+l+w+w=18\\\\2w+3=l\\\\2w+3+2w+3+w+w=18\\6w+6=18\\6w=12\\w=2\\\\2w+3=l\\2*2+3=l\\4+3=l\\l=7$

4 0

3 years ago

Read 2 more answers

Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. Find the area bounded by $f(x)$ and $g(x).$

Anna [14]

Answer:

$\large\boxed{1\dfrac{1}{3}\ u^2}$

Step-by-step explanation:

Let's sketch graphs of functions f(x) and g(x) on one coordinate system (attachment).

Let's calculate the common points:

$x^2=\sqrt{x}\qquad\text{square of both sides}\\\\(x^2)^2=\left(\sqrt{x}\right)^2\\\\x^4=x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x^4-x=0\qquad\text{distribute}\\\\x(x^3-1)=0\iff x=0\ \vee\ x^3-1=0\\\\x^3-1=0\qquad\text{add 1 to both sides}\\\\x^3=1\to x=\sqrt[3]1\to x=1$

The area to be calculated is the area in the interval [0, 1] bounded by the graph g(x) and the axis x minus the area bounded by the graph f(x) and the axis x.

We have integrals:

$\int\limits_{0}^1(\sqrt{x})dx-\int\limits_{0}^1(x^2)dx=(*)\\\\\int(\sqrt{x})dx=\int\left(x^\frac{1}{2}\right)dx=\dfrac{2}{3}x^\frac{3}{2}=\dfrac{2x\sqrt{x}}{3}\\\\\int(x^2)dx=\dfrac{1}{3}x^3\\\\(*)=\left(\dfrac{2x\sqrt{x}}{2}\right]^1_0-\left(\dfrac{1}{3}x^3\right]^1_0=\dfrac{2(1)\sqrt{1}}{2}-\dfrac{2(0)\sqrt{0}}{2}-\left(\dfrac{1}{3}(1)^3-\dfrac{1}{3}(0)^3\right)\\\\=\dfrac{2(1)(1)}{2}-\dfrac{2(0)(0)}{2}-\dfrac{1}{3}(1)}+\dfrac{1}{3}(0)=2-0-\dfrac{1}{3}+0=1\dfrac{1}{3}$

6 0

3 years ago

Stephanie has a homeowners insurance policy for her $355,000 home with an annual premium of $0.42 per $100 of value and a deduct

frosja888 [35]

Answer:

$0.28 per 100 of value (B)

Step-by-step explanation:

Stephanie has a homeowner insurance policy of $355,000

Annual premium = $0.42 per 100

There is a deductible of $500

Stephanie has an annual out of pocket expense of

[($355,000/100) x $0.42] + $500 = $1,991

From the question, Stephanie now wants a new deductible amount of 1000.

Let X be the new annual premium

[(355,000X) / 100] + 1000 = 1991

3550X + 1000 = 1991

3550X = 1991 -1000

3550X = 991

X = 991/3550

X = 0.2791

X = 0.28 ( approximately)

The new annual premium is $0.28 per 100 of value

5 0

3 years ago

Toni paints a wall that is 9 feet tall and 13 feet wide.What is the area of the wall?

aksik [14]

Answer:

117 feet squared

Step-by-step explanation:

Multiply the height (9 feet) by the width (13 feet).

9 x 13 = 117

117 feet squared

Note: squared is added when describing area (it's used as an exponent in numbers)

6 0

2 years ago

The number of dogs in a shelter is equal to 4 less than 2 times the number of cats. If there are 20 dogs in the shelter how many

poizon [28]

D=number of dogs
c=cats

d equals 4 less than 2 times c
d=-4+2c
20 dogs
d=20
subsitute
20=-4+2c
add 4
24=2c
divide 2
12=c
12 cats

5 0

3 years ago