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bekas [8.4K]
3 years ago
5

Lauren solved the equation $|x-5| = 2$. meanwhile jane solved an equation of the form $x^2+ bx + c = 0$ that had the same two so

lutions for $x$ as lauren's equation. what is the ordered pair $(b, c)$?

Mathematics
1 answer:
noname [10]3 years ago
4 0
You must first solve the equation with absolute value, which has two possible solutions that in this case are x = 7 and x = 3. The equation is solved by applying the definition of absolute value. Then, you must solve the second-degree polynomial by applying the resolver and matching both solutions to the absolute value solutions.The result will be (b, c) = (- 10,21). I attach the correct solution.

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Write the slope-intercept form of the line that passes through (-10,17) and (5,-4)
RideAnS [48]

Answer:

y = - \frac{7}{5} x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 10, 17) and (x₂, y₂ ) = (5, - 4)

m = \frac{-4-17}{5+10} = \frac{-21}{15} = - \frac{7}{5}

y = - \frac{7}{5} x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, - 4), then

- 4 = - 7 + c ⇒ c = - 4 + 7 = 3

y = - \frac{7}{5} x + 3 ← in slope-intercept form


3 0
4 years ago
If a hat that costs $30 is discounted by 15%, what’s the sale price?
Amiraneli [1.4K]
The sale price would then be 25.5 dollars
8 0
3 years ago
Prove that tan 10+tan 70'+taniou = tanio tanfo'tam 1oo.​
Galina-37 [17]

Question:

Prove that:

tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)

Answer:

Proved

Step-by-step explanation:

Given

tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)

Required

Prove

tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)

Subtract tan(10) from both sides

- tan(10)+tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100) - tan(10)

tan(70) + tan(100) = tan(10). tan(70). tan(100) - tan(10)

Factorize the right hand size

tan(70) + tan(100) = -tan(10)(-tan(70). tan(100) + 1)

Rewrite as:

tan(70) + tan(100) = -tan(10)(1-tan(70). tan(100))

Divide both sides by 1-tan(70). tan(100)

\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = \frac{-tan(10)(1-tan(70). tan(100))}{1-tan(70). tan(100))}

\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = -tan(10)

In trigonometry:

tan(A + B) = \frac{tan(A) + tan(B)}{1 - tan(A)tan(B)}

So:

\frac{tan(70) + tan(100)}{1 - tan(70)tan(100)} can be expressed as: tan(70 + 100)

\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = -tan(10) gives

tan(70 + 100) = -tan(10)

tan(170) = -tan(10)

In trigonometry:

tan(180 - \theta) = -tan(\theta)

So:

tan(180 - 10) = -tan(10)

Because RHS = LHS

Then:

tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100) has been proven

6 0
3 years ago
Can somebody help me find the mean,median, and mode
andrey2020 [161]

Answer:

so for the mean u add all the numbers on there and then divide it by 5 since there are 5 numbers on there so 78+84+100+78+81=421 now we divide 421 by 5 so 421÷5= 84!

now the median would be 100? and the mode is 78 since 78 is the number that showed the most!

3 0
3 years ago
Read 2 more answers
20 POINTS BE QUICK!!!What is the solution set for x-3>3? Please explain your answer!
Montano1993 [528]

Answer:

{x:x>6}

Step-by-step explanation:

x-3>3

Add 3 to each side

x-3+3>3+3

x>6

{x:x>6}

3 0
3 years ago
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