Find the area of the shaded polygon.

A garden table and a bench cost S585 combined. The garden table costs S65 less than the bench. What is the cost of the bench?

garik1379 [7]

Answer:

Bench costs $325

Step-by-step explanation:

Try setting up an equation

x = cost of garden table

y = cost of bench

equation 1: x + y = 585

We also know that the table costs 65 dollars less than the bench.

cost of garden table = bench - 65

or

equation 2: x = y - 65

Now just substitute equation 2 into equation 1

(y-65) + y = 585

and solve for y

2y-65 = 585

2y = 585 + 65 = 650

y = 325 = cost of bench

8 0

3 years ago

Point G is on line segment FH. Given FG=5x+2,GH=3x-1, and FG=9, determine the numerical length of FG

stealth61 [152]

Given:

FG=5x+2

GH=3x-1

FG=9

Let us draw the line segment as follows,

Equating the length of FG, we get,

$\begin{gathered} 5x+2=9 \\ 5x=9-2 \\ 5x=7 \\ x=\frac{7}{5} \end{gathered}$

Substitute the value of x in the given value of GH,

$\begin{gathered} GH=3x-1 \\ =3(\frac{7}{5})-1 \\ =\frac{21}{5}-1 \\ =\frac{16}{5} \\ =3.2 \end{gathered}$

And the total length FH is,

$\begin{gathered} FH=FG+GH \\ =9+3.2 \\ =12.2 \end{gathered}$

Hence, the lengths are,

$\begin{gathered} FG=9 \\ GH=3.2 \\ FH=12.2 \end{gathered}$

8 0

1 year ago

Through (2, -1), perp. to y = -2x-3

kramer

9514 1404 393

Answer:

y = 1/2x -2

Step-by-step explanation:

The given equation is in slope-intercept form, so you recognize its slope is -2. The perpendicular line will have a slope that is the opposite reciprocal of that, so is -1/-2 = 1/2.

The y-intercept can be found from ...

b = y -mx . . . . . for line of slope m through point (x, y)

b = -1 -(1/2)(2) = -1 -1 = -2

Then the slope-intercept equation of the perpendicular line is ...

y = 1/2x -2

6 0

3 years ago

Expand (2x + 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all steps.

kari74 [83]

Answer:

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

Step-by-step explanation:

(2x + 3)⁵

₅C₀ (2x)⁵ (3)⁰ + ₅C₁ (2x)⁴ (3)¹ + ₅C₂ (2x)³ (3)² + ₅C₃ (2x)² (3)³ + ₅C₄ (2x)¹ (3)⁴ + ₅C₅ (2x)⁰ (3)⁵

Use Pascal's triangle to find nCr.

$\left\begin{array}{c}1\\1\ 1\\1\ 2\ 1\\1\ 3\ 3\ 1\\1\ 4\ 6\ 4\ 1\\1\ 5\ 10\ 10\ 5\ 1\end{array}\right$

1 (2x)⁵ (3)⁰ + 5 (2x)⁴ (3)¹ + 10 (2x)³ (3)² + 10 (2x)² (3)³ + 5 (2x)¹ (3)⁴ + 1 (2x)⁰ (3)⁵

(2x)⁵ + 15 (2x)⁴ + 90 (2x)³ + 270 (2x)² + 405 (2x)¹ + 243

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

7 0

3 years ago

Will give brainliest!!

vivado [14]

Answer:

continuous.

Step-by-step explanation:

Given function is $f(x)=5x^4-9x^3+x-7$ .

and value of a = 7.

Now we need to find if the given function $f(x)=5x^4-9x^3+x-7$ is continuous or not.

By definition of continuity, we know that a function is continuous at a given point if both left and right hand limits are equal.

Left Hand Limit = LHL

$LHL=\lim_{x\rightarrow 7^-}f(x)=5(7)^4-9(7)^3+(7)-7=8918$

Right Hand Limit = RHL

$RHL=\lim_{x\rightarrow 7^+}f(x)=5(7)^4-9(7)^3+(7)-7=8918$

Since both limits are equal at a=7 so we can say that given function is continuous at a=7

4 0

4 years ago