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4 years ago

Write an equation of a line perpendicular to y = x + 4 in slope-intercept form that passes through the point (-2, 6)

1 answer:

5 0

$k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\ if\ m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\---------------------\\k:y=x+4;\ l:y=m_2x+b_2\\\\m_1=1\to m_2=-\dfrac{1}{1}=-1\\\\k\ \perp\ l\to l:y=-x+b_2\\\\The\ line\ "l"\ passes\ throught\ the\ point\ (-2;\ 6).\\Subtitute\ x=-2\ and\ y=6\ to\ the\ equation\ of\ the\ line\ "l":\\\\6=-(-2)+b_2\\6=2+b_2\ \ \ |subtract\ 2\ from\ both\ sides\\b_2=4\\\\Answer:\boxed{y=-x+4}$

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Find the radius of a sphere with a surface area of 804 cm^2.

Elanso [62]

Surface area of sphere equals its four radii squared multiplied by the number π.
We have then:
A = 4 * π * R ^ 2
Substituting:
804 = 4 * π * R ^ 2
Clearing the value of R we have:
R = root (804 / (4 * π))
R = 7.99876785 cm
Nearest whole number:
R = 8 cm
Answer:
The radius of a sphere is:
B. 8cm

3 0

3 years ago

How do you get -11.9 from -6.7+(-5.2)<br><br>and explain in words how

ioda

If you just type that exact equation into a calculator it gives you the same answer as well

4 0

3 years ago

Read 2 more answers

Does anyone know the answer??

Viktor [21]

Answer:

175°

Step-by-step explanation:

If angle x = 058° and angle y = 127° then the bearing A from point O is 360 minus angle x plus angle y.

Solution:

360° - (058° + 127°) = 175°

This is because the complete turn from north to north is 360°.

6 0

3 years ago

Use the distributive property to find an expression equivalent to 24 + 64.

LUCKY_DIMON [66]

Answer:

8(3+8)

Step-by-step explanation:

The distributive property of multiplication states that

A(B+C) = A* B + A* C

Here, we can say that

8(3+8) = 8*3 + 8* 8 = 24 + 64. This seems correc,t but we can check the other options to make sure

6(4 + 8) = 6 * 4 + 6*8 = 24 + 48. This is incorrect

24 + (8)(8) . The 24 and 8 are not in the same parenthesis, so we cannot multiply them. Using PEMDAS, we multiply first, so 24+(8)(8) = 24 + 8*8 = 24 + 64. If there are multiple solutions, this can work. If not, this does not use the distributive property as we are not adding anything in the parenthesis.

Similarly, for (2)(12) + (8)(8), we are not adding anything in the parenthesis, but we can use PEMDAS to get 2*12 + 8*8 = 24 + 64, so this would also work but does not use the distributive property.

4 0

3 years ago

Since at t=0, n(t)=n0, and at t=[infinity], n(t)=0, there must be some time between zero and infinity at which exactly half of t

Ostrovityanka [42]

An expression for this timet-half will be given as ln(2) / λ ≈ 0.693 / λ

<h3>What is an expression?</h3>

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The complete question is:

Suppose a radioactive sample initially contains N0unstable nuclei. These nuclei will decay into stable nuclei, and as they do, the number of unstable nuclei that remain, N(t), will decrease with time. Although there is no way for us to predict exactly when any one nucleus will decay, we can write down an expression for the total number of unstable nuclei that remain after a time t:

N(t)=No e−λt,

where λ is known as the decay constant. Note that at t=0, N(t)=No, the original number of unstable nuclei. N(t) decreases exponentially with time, and as t approaches infinity, the number of unstable nuclei that remain approaches zero.

Part (A) Since at t=0, N(t)=No, and at t=∞, N(t)=0, there must be some time between zero and infinity at which exactly half of the original number of nuclei remain. Find an expression for this time, t half.

Express your answer in terms of N0 and/or λ.

1) Equation given:

← I used α instead of λ just for editing facility..

Where No is the initial number of nuclei.

2) Half of the initial number of nuclei: N (t-half) = No / 2

So, replace in the given equation:

$N9t) = Ne^{-\lambda t}$