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3 years ago

Can someone solve for x

Mathematics

1 answer:

Helen [10]3 years ago

6 0

bearing in mind that, whenever we have an absolute value expression, is in effect a piece-wise function with a positive and a negative version of the expression, so

$\bf |x^2-4x-5|=7\implies \begin{cases} +(x^2-4x-5)=7\\\\ -(x^2-4x-5)=7 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ +(x^2-4x-5)=7\implies x^2-4x-5=7\implies x^2-4x-12=0 \\\\\\ (x-6)(x+2)=0\implies x= \begin{cases} 6\\ -2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -(x^2-4x-5)=7\implies x^2-4x-5=-7\implies x^2-4x+2=0 \\\\\\ (x-2)(x-2)=0\implies x = 2$

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The area of a triangular flag is 132 square centimetres. Its altitude is 2 centimetres longer than twice its base. Find the leng

Anika [276]

Answer:

24 cm and 11 cm

Step-by-step explanation:

GIVEN: The area of a triangular flag is $132 \text{ cm}^2$ . Its altitude is $2\text{ cm}$ longer than twice its base.

TO FIND: lengths of the altitude and the base.

SOLUTION:

Let the altitude and the base of flag be $a$ and $b$

According to the question

$a=2+2b$

area of triangle $=\frac{1}{2}\times base \times alltitude=\frac{1}{2}a\times b$

$\implies \frac{1}{2}(2b+2)b=132 \Rightarrow 2b^2+2b-264$

Solving equation we get

$b=11$ then $a=24$

Hence the lengths of altitude and base of triangular flag is 24 cm and 11 cm respectively.

8 0

3 years ago

ralph is an electrician . he cgarges an initial fee of $16 plus $33 per hour if ralph earned $197 on a job how long did the job

KiRa [710]

x=#of hours worked
33 per hour or 33x (since 33 times every hour)
initial fee is independed of hours so
fee=33x+16

if fee=197 then solve for hours or x
197=33x+16
subtract 16 from both sides
181=33x
divide both sides by 33
5.4848484848=x
he worked 5.48 hours

8 0

3 years ago

A set of cubes, each with sides 1 cm long, is stacked 5 cubes high, 8 cubes deep and 7 cubes long.

Alchen [17]

Answer:

280 Cubes

Explanation:

This problem has to do with volume. To find the number of cubes in the set, you multiply the length, width, and height of all the cubes. This would look like 7*8*5. This equals 280 cubes.

7 0

2 years ago

Find the domain of the function. f(x)= -2x + 4

RideAnS [48]

Answer:

The domain of the function is (-∞,∞), otherwise known as all reals.

Step-by-step explanation:

3 0

3 years ago

Darina [25.2K]

1. Midpoint = (-2+12)/2 = 10/2 = 5

2. C(5, 2) E(-1, 0) D=?

$x_E= \frac{x_C+x_D}{2} \ \ \ \to \\\\ -1= \frac{5+x_D}{2} \ \ \ \to \ \ \ -2=5+x_D \ \ \to \ \ x_D=-2-5=-7
\\\\\\y_E= \frac{y_C+y_D}{2} \ \ \ \to \\\\ 0= \frac{2+y_D}{2} \ \ \ \to \ \ \ 0=2+y_D \ \ \to \ \ y_D=0-2=-2$

Answer: D(-7, -2)

3 0

3 years ago