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2 years ago

Three-fourths of a cake remains after a birthday party. Each serving is 1/16 of the cake. How many servings of the cake remain?

Mathematics

1 answer:

Novay_Z [31]2 years ago

6 0

Answer:

3/4 = 12/16

Step-by-step explanation:

3 x 4 = 12

4 x 4 = 16

12/16 :)

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Write the equation of the line that passes through the points (-3, -3) and (8,7).

Verizon [17]

Answer:

y + 3 = 10/11(x + 3)

Step-by-step explanation:

Given the points (-3, -3) and (8, 7), we can use these coordinates to solve for the slope of the line using the formula:

$m = \frac{y2 - y1}{x2 - x1}$

Let (x1, y1) = (-3, -3)

(x2, y2) = (8, 7)

Substitute these values into the slope formula:

$m = \frac{y2 - y1}{x2 - x1} = \frac{7 - (-3)}{8 - (-3)} = \frac{10}{11}$

Thus, slope (m) = 10/11.

Next, using the slope (m) = 10/11, and one of the given points (-3, -3), we'll substitute these values into the point-slope form:

y - y1 = m(x - x1)

Let (x1, y1) = (-3, -3)

m = 10/11

y - y1 = m(x - x1)

y - (-3) = 10/11[x - (-3)]

Simplify:

y + 3 = 10/11(x + 3) this is the point-slope form.

3 0

2 years ago

What is the result of adding these two equations?<br> 5x-y=6<br> -2x+y=8

Stells [14]

3x=14 I am pretty sure

3 0

3 years ago

Task 1: Billy is trying to download a several apps for his iPhone. His iPhone’s storage capacity is 32GB. The apps he wants

Roman55 [17]

Answer:

Billy can download 6 apps

3 0

2 years ago

Read 2 more answers

Evalute costheta if sintheta = (sqrt5)/3

torisob [31]

Answer:

$\large\boxed{\cos\theta=\pm\dfrac{2}{3}}$

Step-by-step explanation:

Use $\sin^2x+\cos^2x=1$ .

We have

$\sin\theta=\dfrac{\sqrt5}{3}$

Substitute:

$\left(\dfrac{\sqrt5}{3}\right)^2+\cos^2\theta=1\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(\sqrt5)^2}{3^2}+\cos^2\theta=1\qquad\text{use}\ (\sqrt{a})^2=a\\\\\dfrac{5}{9}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{5}{9}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{9}{9}-\dfrac{5}{9}\\\\\cos^2\theta=\dfrac{4}{9}\to \cos\theta=\pm\sqrt{\dfrac{4}{9}}\\\\\cos\theta=\pm\dfrac{\sqrt4}{\sqrt9}\\\\\cos\theta=\pm\dfrac{2}{3}$

3 0

3 years ago

Read 2 more answers

Prove that √2 +√5 is irrational

Sindrei [870]

We have to prove that $\sqrt{2}+\sqrt{5}$ is irrational. We can prove this statement by contradiction.

Let us assume that $\sqrt{2}+\sqrt{5}$ is a rational number. Therefore, we can express:

$a=\sqrt{2}+\sqrt{5}$

Let us represent this equation as:

$a-\sqrt{2}=\sqrt{5}$

Upon squaring both the sides:

$(a-\sqrt{2})^{2}=(\sqrt{5})^{2}\\a^{2}+2-2\sqrt{2}a=5\\a^{2}-2\sqrt{2}a=3\\\sqrt{2}=\frac{a^{2}-3}{2a}$

Since a has been assumed to be rational, therefore, $\frac{a^{2}-3}{2a}$ must as well be rational.

But we know that $\sqrt{2}$ is irrational, therefore, from equation $\sqrt{2}=\frac{a^{2}-3}{2a}$ the expression $\frac{a^{2}-3}{2a}$ must be irrational, which contradicts with our claim.

Therefore, by contradiction, $\sqrt{2}+\sqrt{5}$ is irrational.

4 0

3 years ago