3 years ago

Which expression is equivalent to the expression shown ? 2 (x + 5) +3 (x2 - 5x +13)

1 answer:

3 0

$\text{Use the distributive property:}\\\\a(b+c)=ab+ac$

$2(x+5)+3(x^2-5x+13)=(2)(x)+(2)(5)+(3)(x^2)-(3)(5x)+(3)(13)\\\\=2x+10+3x^2-15x+39=3x^2-13x+49$

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The graph shows which inequality? The equation of the boundary line is y = –x + 4. y –x + 4 y ≥ –x + 4

DaniilM [7]

Answer:

y≤-x+4

Step-by-step explanation:

x intercept =4

y intercept=4

the shaded area under the solid line because it is greater than or equal

8 0

3 years ago

Graph the inverse circular function by hand, given f(x) = 3sin(2x) ;-pi/4 ≤ ≤pi/4

nasty-shy [4]

Part a)

a) The given function is

$f(x) = 3 \sin(2x)$

We let

$y = 3 \sin(2x)$

Interchange x and y.

$x= 3 \sin(2y)$

Solve for y;

$\frac{x}{3} = \sin(2y)$

$y = \frac{1}{2} { \sin}^{ - 1}( \frac{x}{3} )$

${f}^{ - 1}(x) = \frac{1}{2} { \sin}^{ - 1}( \frac{x}{3} )$

Part b) The range of f(x) refers to y-values for which f(x) exists.

The range of f(x) is

$- 3 \leqslant y \leqslant 3$

This is because the function is within y=-3 and y=3.

c) The range of

${f}^{ - 1} (x)$

$- \frac{ \pi}{4} \leqslant y \leqslant \frac{\pi}{4}$

The domain is -3≤x≤3

This is because the domain and range of a function and its inverse swaps.

Part d) The graph is shown in the attachment.

3 0

3 years ago

X + 24 + 4 + 63 = 180

Helen [10]

Answer:

x=89

Step-by-step explanation:

180-91=89

4 0

3 years ago

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Gail ran 4610 miles on Saturday and 6810 miles on Sunday. How many miles did Gail run over the weekend?

VMariaS [17]

Answer:

He ran 11,420 miles on the weekend.

Step-by-step explanation:

It's simple: add 4610 and 6810 to get 11,420

hope this helped!

8 0

3 years ago

A game normally cost $53.00, but Isabel used a coupon and got the game for $37.10. The coupon was for what percent off.

Artist 52 [7]

We could use the numbers and the difference of the original cost - the end price in a equation.

53 × x/100 = 15.9

Cross multiply 100 × 15.9.

53x=1590

Divide both sides by 53.

x=30

The coupon was 30%

5 0

3 years ago

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