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4 years ago

For the following inequality, indicate whether the boundary line should be dashed or solid. 3x ≥ y + 1

Mathematics

1 answer:

Kay [80]4 years ago

8 0

The boundary line should be solid because it have a 'great/less than or equal to' sign

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3.) Write the equation of a quadratic function that is shifted down 4 and horizontally compressed by 1/5

sashaice [31]

Answer:

$5x^2 - 4$

Step-by-step explanation:

For shifted down a function you have to follow the next structured:

$f(x) - c$

In our case is:

$x^2 - 4$

Now for compressed or shrink a graph you have to multiply by a factor in the input something like this:

$f(cx)$

In our case is:

$5x^2$

Maybe you can think, why 5 and not $\frac{1}{5}$ instead?. Well, when you multiply by $\frac{1}{5}$ this dilate or stretch the graft because the output of each value is smaller, example:

$f(x) = x^2\\g(x) = \frac{1}{5} x^2$

Then evaluate for a number, for example 5:

$f(5) = 25\\g(5) = 5$

the output of $g(x)$ is 5 steps a far from the answer of $f(x)$ this in a graph is illustrate as a stretching.

So the opposite happen when you multiply by a integer number, the graph is compressed because the output take the "faster steps".

So combine the two transformation and get $5x^2 - 4$

8 0

2 years ago

Find the surface area of the cylinder. Round your answer to the nearest tenth.

kirill [66]

Given:

Height of cylinder = 12 cm

Diameter of cylinder = 6 cm

To find:

Surface area of the cylinder

Solution:

Radius = 6 ÷ 2 = 3 cm

Surface area formula:

$SA=2\pi r^2+2 \pi rh$

Substitute the given values.

$SA=2\times3.14 \times3^2+2\times3.14 \times3 \times12$

$=56.52+226.08$

= 286.2 cm²

The surface area of the cylinder is 286.2 cm².

8 0

3 years ago

I’m really confused on this one and want to make sure. I’ll make you brainlest if you add explanation. Pls and thank you :))

Darya [45]

Answer:

$\sqrt{3}$

Step-by-step explanation:

See attachment 1. This is the formula to use.

There are two numbers, so n=2. Plugging them into the formula, you get

$\sqrt[2]{6*\frac{1}{2}} \\$

Now, putting a 2 in front just means we're finding the square root, so I'll get rid of it. Then, just do the calculation.

$\sqrt{6*\frac{1}{2}}=\sqrt{\frac{6}{2}}=\sqrt{3}$

5 0

3 years ago

Read 2 more answers

4,-4 on the coordinate plane would 4 go on the x-axis or y-axis bc im du mb :)

ANTONII [103]

4 would go on the x axis because it always starts like this (x, y)

5 0

3 years ago

Casandra finds a treasure chest packed with metallic coins. The chest has a volume of 0.25^30.25 m

Vladimir [108]

Answer:

Gold

Step-by-step explanation:

Casandra finds a treasure chest packed with metallic coins. The chest has a volume of 0.25 cubic meters. The coins have a combined mass of 4825 kg. Hoping to find gold, she calculates the density to determine the metal of the coins.

What kind of metal are the coins made of?

Bronze (8700 kg per cubic meter)

Silver (10500 kg per cubic meter)

Lead (11300 kg per cubic meter)

Gold (19300 kg per cubic meter)

Density is mass per volume:

D = M / V

D = (4825 kg) / (0.25 m³)

D = 19,300 kg/m³

The coins must be made of gold.

4 0

3 years ago