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3 years ago

F(x)=-5x^2+1 is translated vertically downward by 4 units

1 answer:

8 0

To move a function, f(x) up, c units, add c to the whole function, to get c+f(x)

f(x)=-5x^2+1
move up -4 units (aka move down 4 unit)
f(x)=-5x^2+1-4
f(x)=-5x^2-3

the new function is
f(x)=-5x^2-3

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Rewrite equation to solve for m 4n-6m=-2

hram777 [196]

Answer:

Step-by-step explanation:

4n - 6m = - 2 Subtract 4n from both sides.

4n-4n - 6m = -2-4n

-6m = - 2 - 4n Divide by - 6

-6m/-6= -2/-6 -4n/-6 Do the division

m = 1/3 + 2n/3

The signs change because each term has 2 minus signs. 2 minus signs make a plus. Or both minus signs cancel.

7 0

4 years ago

1+secA/sec A = sin^2 A / 1-cos A

Fofino [41]

Answer: see proof below

Step-by-step explanation:

$\dfrac{1+\sec A}{\sec A}=\dfrac{\sin^2 A}{1-\cos A}$

Use the following Identities:

sec Ф = 1/cos Ф

cos² Ф + sin² Ф = 1

Proof LHS → RHS

$\text{LHS:}\qquad \qquad \dfrac{1+\sec A}{\sec A}$

$\text{Identity:}\qquad \qquad \dfrac{1+\frac{1}{\cos A}}{\frac{1}{\cos A}}$

$\text{Simplify:}\qquad \qquad \dfrac{\frac{\cos A+1}{\cos A}}{\frac{1}{\cos A}}\\\\\\.\qquad \qquad \qquad =\dfrac{1+\cos A}{1}$

$\text{Multiply:}\qquad \qquad \dfrac{1+\cos A}{1}\cdot \bigg(\dfrac{1-\cos A}{1-\cos A}\bigg)\\\\\\.\qquad \qquad \qquad =\dfrac{1-\cos^2 A}{1-\cos A}$

$\text{Identity:}\qquad \qquad \dfrac{\sin^2 A}{1-\cos A}$

$\text{LHS = RHS:}\quad \dfrac{\sin^2 A}{1-\cos A}=\dfrac{\sin^2 A}{1-\cos A}\quad \checkmark$

3 0

4 years ago

How to solve inequaities?

bulgar [2K]

Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own.
But these things will change direction of the inequality:
Don't multiply or divide by a variable (unless you know it is always positive or always negative)

8 0

4 years ago

On a map the distance between rip and Janeiro Brazil and San Jose Costa Rica is 4 inches.the scale on the map shows that 1 inch=

Vera_Pavlovna [14]

Answer:

The way a proportion is set is as follows;

$\dfrac{1 \ inch}{200 \ miles } = \dfrac{4 \ inches}{ Distance \ from \ Rio \ de \ Janeiro \ to \ San \ Jose}$

The Distance from Rio de Janeiro and San Jose Costa Rica is then found as 800 miles

Step-by-step explanation:

The dimension of the distance between Rio de Janeiro and San Jose Costa Rica = 4 inches

The map scale = 1 inch to 200 miles

To figure out how many miles it is or the actual distance from Rio de Janeiro and San Jose Costa Rica, we have;

$\dfrac{1 \ inch}{200 \ miles } = \dfrac{4 \ inches}{ Distance \ from \ Rio \ de \ Janeiro \ to \ San \ Jose}$

Therefore, we have;

(4 inches × 200 miles)/(1 inche) = Distance from Rio de Janeiro and San Jose Costa Rica

Which gives;

Distance from Rio de Janeiro and San Jose Costa Rica = 800 miles.

4 0

3 years ago

What is 1 over 5m minus 20

mrs_skeptik [129]

I think is 18.5,.............

3 0

3 years ago