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2 years ago

How do I solve this? What do they mean

Mathematics

1 answer:

adell [148]2 years ago

8 0

Complimentary angles add to equal 90°. Write two equations to solve for two variable.
J + K = 90
J = K - 18

use substitution or elimination to solve
I will use substitution. substitute (K - 18) for J in the first equation to combine equations into one in only variable K.

(K - 18) + K = 90
2K - 18 = 90
2K = 90 + 18
2K = 108
K = 108/2
K = 54°

J and K are complimentary.
J + 54° = 90°
J = 36°

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A piece of green jade has a mass of 23.401 g.if the sample of jade displaces 50.0 ml of water to 56.5 ml in a 100 ml graduated c

OleMash [197]

we know that

The density is equal to the formula

$Density=\frac{mass}{volume}$

in this problem we have

$mass=23.401\ gr$

Find the volume of a piece of green jade

$Volume=56.5\ ml-50.0\ ml=6.5\ ml$

Substitute the values in the formula of density

$Density=\frac{23.401}{6.5}$

$Density=3.60\frac{gr}{ml}$

therefore

the answer is

$Density=3.60\frac{gr}{ml}$

3 0

3 years ago

1.) The graph of g(x) = ax? opens downward and is narrower than the graph of f(x) = x? Which of the following

laila [671]

Answer:

C. -5

Step-by-step explanation:

for g(x) =ax and f(x) = x, both are linear function. There is nothing to be upward or downward and both are lines nothing to compare its narrowness.

If g(x) = ax² vs f(x) = x²

Then a = -5 is the answer (-: downward and 5: vertical stretch)

8 0

2 years ago

What is the largest possible integral value in the domain of the real-valued function

kotegsom [21]

Answer:

Max Value: x = 400

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

Antiderivatives
Integral Property: $\int {cf(x)} \, dx = c\int {f(x)} \, dx$
Integration Method: U-Substitution
[Integration] Reverse Power Rule: $\int {x^n} \, dx = \frac{x^{n+1}}{n+1} + C$

Step-by-step explanation:

Step 1: Define

$f(x) = \frac{1}{\sqrt{800-2x} }$

Step 2: Identify Variables

Using U-Substitution, we set variables in order to integrate.

$u = 800-2x\\du = -2dx$

Step 3: Integrate

Define: $\int {f(x)} \, dx$
Substitute: $\int {\frac{1}{\sqrt{800-2x} } } \, dx$
[Integral] Int Property: $-\frac{1}{2} \int {\frac{-2}{\sqrt{800-2x} } } \, dx$
[Integral] U-Sub: $-\frac{1}{2} \int {\frac{1}{\sqrt{u} } } \, du$
[Integral] Rewrite: $-\frac{1}{2} \int {u^{-\frac{1}{2} }} \, du$
[Integral - Evaluate] Reverse Power Rule: $-\frac{1}{2}(2\sqrt{u}) + C$
Simplify: $-\sqrt{u} + C$
Back-Substitute: $-\sqrt{800-2x} + C$
Factor: $-\sqrt{-2(x - 400)} + C$

Step 4: Identify Domain

We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.

Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.

7 0

3 years ago

What are the side lengths of the equilateral triangle?

Alchen [17]

$5x + (6x - 5) + (3x + 10) = 360$

$5x + 6x - 5 + 3x + 10 = 360$

$11x - 5 + 3x + 10 = 360$

$14x + 5 = 360$

$14x = 360 - 5$

$14x = 355$

$x = 25.36$

$x = 25.36$

$5x = 5 \times 25.36 = 126.8$

$6x - 5 = 6 \times 25.36 - 5 = 147.16$

$3x + 10 = 3 \times 25.36 + 10 = 86.08$

4 0

3 years ago

Simplify [view attached image]

pav-90 [236]

Given:

The given expression is $(\sqrt{5})( \sqrt[3]{5})$

We need to simplify the given expression.

Simplification:

Let us simplify the given expression.

Rewriting the given expression, we have;

$5^{\frac{1}{2}} \cdot 5^{\frac{1}{3}}$

Let us apply the exponent rule $\:a^b\cdot \:a^c=a^{b+c}$ , we get;

$5^{\frac{1}{2}+\frac{1}{3}}$

Taking LCM, we have;

$5^{\frac{3+2}{6}}$

Simplifying, we get;

$5^{\frac{5}{6}}$

Thus, the simplified value of the given expression is $5^{\frac{5}{6}}$

Hence, Option a is the correct answer.

6 0

3 years ago