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morpeh [17]
3 years ago
5

If f(x)=5x+a and f-1(10)=-1, find a

Mathematics
1 answer:
zhenek [66]3 years ago
4 0

Answer:

15

Step-by-step explanation:

Given the function

f(x)=5x+a

and f^{-1} (10)=-1(f^{-1} \text{is the inverse function of f})

let f(x)=y

Substitute in f(x)

y=5x+a\\y-a=5x\\x=\frac{y-a}{5}

From the definition inverse function

if f(x)=y    ⇒   f^{-1} (y)=x

Substitute this in the above expression

f^{-1} (y)=\frac{y-a}{5}

Substitute y=10

⇒

f^{-1} (10)=\frac{10-a}{5}\\-1=\frac{10-a}{5}\\-5=10-a\\a=10+5\\a=15

Therefore a=15

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Simplify.
TiliK225 [7]

Answer:

53.8

Step-by-step explanation:

45+8= 8

then add the decimal 0.0+0.8= 0.8

53.8

4 0
2 years ago
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Please HELP!!!!! ASAP PLEASE!!
fredd [130]
Y=-10 and the second one is 13 I think
4 0
3 years ago
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-3(5x + 7) + 2x – 3 = 5.x - 8 - 13​
ratelena [41]

Answer:

x=-7

Step-by-step explanation:

Simplifying

3(x + -2) = 5x + 8

Reorder the terms:

3(-2 + x) = 5x + 8

(-2 * 3 + x * 3) = 5x + 8

(-6 + 3x) = 5x + 8

Reorder the terms:

-6 + 3x = 8 + 5x

Solving

-6 + 3x = 8 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

-6 + 3x + -5x = 8 + 5x + -5x

Combine like terms: 3x + -5x = -2x  

-6 + -2x = 8 + 5x + -5x

Combine like terms: 5x + -5x = 0

-6 + -2x = 8 + 0

-6 + -2x = 8

Add '6' to each side of the equation.

-6 + 6 + -2x = 8 + 6

Combine like terms: -6 + 6 = 0

0 + -2x = 8 + 6

-2x = 8 + 6

Combine like terms: 8 + 6 = 14

-2x = 14

Divide each side by '-2'.

x = -7

Simplifying

x = -7

8 0
3 years ago
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In the figure above, square ABCD and triangle EFG have the same areas. If AB =6 and EG =8, what is the height o triangle EFG?
lawyer [7]

Answer:

The height of triangle EFG is 9 units

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the area of a square ABCD

The area of a square is equal to

A=b^2

where

b is the length side of the square

we have

b=AB=6\ units

substitute

A=6^2=36\ units^2

step 2

Find the height of triangle EFG

The area of triangle EFG is equal to

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

where

b is the base of triangle

h is the height of triangle

we have

b=EG=8\ units

A=36\ units^2 ---> area of triangle EFG is the same that the area of square ABCD

substitute the given values in the formula

36=\frac{1}{2}(8)(h)

solve for h

36=4h\\h=9\ units

therefore

The height of triangle EFG is 9 units

3 0
3 years ago
The lines graphed below are perpendicular. The slope of the red line is 4. What is the slope of the green line?
Mashutka [201]
-1/4 the negative reciprocal of the slope of the red line
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