(Picture Included) 20 points - can someone solve 11, 12, 13, and 15?

Which number has both 2 and 5 as prime factors?

musickatia [10]

Answer:

Any multiple of 10

Step-by-step explanation:

A factor is defined as "a number or quantity that when multiplied with another produces a given number or expression." For example, the factors of 20 are 1, 2, 4, 5, 10, and 20.

When we multiply 2 and 5 together, we get 10. Multiplying this by anything else besides 0 will still yield something that has 2 and 5 as factors, for example 2 times 5 times 3 is 30. As this is just the same thing as multiplying 10 by 3, the answer is any multiple of 10.

4 0

3 years ago

Write an equation of a line in slope-intercept form with a slope of -12 and a y-intercept of 3.

Mila [183]

Answer:

y = -12x + 3

Step-by-step explanation:

The slope-intercept form of an equation can be written as y = mx + b where m is the slope and b is the y-intercept. We are given both values, so we can plug them into the equation to get:

y = mx + b

y = -12x + 3

5 0

3 years ago

Read 2 more answers

Futhe Mathematics <img src="https://tex.z-dn.net/?f=%28Cos%20%7B%7D%5E%7B4%7Dt%20-Sin%20%7B%7D%5E%7B4%7Dt%20%29%20%20%5Cdiv%2

Nastasia [14]

Answer:

cos2t/cos²t

Step-by-step explanation:

Here the given trigonometric expression to us is ,

$\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t }$

We can write the numerator as ,

$\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t }$

Recall the identity ,

$\longrightarrow (a-b)(a+b)=a^2-b^2$

Using this we have ,

$\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}$

Again , as we know that ,

$\longrightarrow sin^2\phi + cos^2\phi = 1$

Therefore we can rewrite it as ,

$\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}$

Again using the first identity mentioned above ,

$\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}$

Or else we can also write it using ,

$\longrightarrow cos2\phi = cos^2\phi - sin^2\phi$

Therefore ,

$\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}$

And we are done !

$\rule{200}{4}$

Additional info :-

Derivation of cos²x - sin²x = cos2x :-

We can rewrite cos 2x as ,

$\longrightarrow cos(x + x )$

As we know that ,

$\longrightarrow cos(y + z )= cosy.cosz - siny.sinz$

So that ,

$\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x)$

On simplifying,

$\longrightarrow cos(x+x) = cos^2x - sin^2x$

Hence,

$\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }}$

$\rule{200}{4}$

7 0

2 years ago

I will like to know how to solve this

Alexxandr [17]

This is a linear equation in x.

So you need to group like terms

$1 + 4x = - 5 + 7x$
Let us group the x terms on the Right Hand Side of the equation and the constant terms on the Left Hand Side.

$1 + 5 = 7x - 4x$
We can now simplify

$6 = 3x$
Now let us divide both sides by 3.

$\frac{6}{3} = \frac{3x}{3}$

This implies that

$2 = x$
or

$x = 2$
Let us our answer

$1 + 4(2) = - 5 + 7(2)$

$1 + 8 = - 5 + 14$
$9 = 9$
Good we are right

5 0

4 years ago

Read 2 more answers

A bike rider travels 58 miles 5 hours.

Elenna [48]

If the biker is going at the same rate than in 3 hours he should go 34.8 miles

7 0

3 years ago