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3 years ago

Can someone help me please

Mathematics

1 answer:

Dimas [21]3 years ago

5 0

Answer:

$g(x)=-x^2-8x-22$

Step-by-step explanation:

Perform the multiplication and addition:

$g(x)=-(x+4)^2-6=-(x^2+8x+16)-6=-x^2-8x-16-6\\\\g(x)=-x^2-8x-22$

_____

Comment on the squaring

There are several ways you can find the square (x+4)².

Use your knowledge that (x+a)² = x²+2ax+a².
Use FOIL* to compute (x+4)(x+4) = x² +4x +4x +4² = x²+8x+16
Use the distributive property: (x+4)(x+4) = x(x+4) +4(x+4) = x² +4x +4x +4² (same as FOIL for two binomials)

* FOIL is mnemonic for {First, Outer, Inner, Last} referring to pairs of terms in the factors (x +a)(x +b). The x terms are the First terms. The Outer terms are the first x and b. The Inner terms are "a" and the second x. The Last terms are "a" and "b". You are to form the sum of those pairs of terms to find the product of the binomials.

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Read the question and help me, please.

shusha [124]

<h3>Answer: B) 6</h3>

===============================================

Explanation:

Add the equations by adding the terms straight down.

The x terms add to x+x = 2x.

The y terms add to y+(-y) = y-y = 0y = 0, so the y terms go away

The constants add to 5+7 = 12

The z terms add to -z+z = 0z = 0 and those go away as well

After all that adding, we have 2x = 12 which solves to x = 6 after dividing both sides by 2.

6 0

3 years ago

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Need help on test Angles and triangles 2

erma4kov [3.2K]

Alternate interior: <2 and <7
(They are on opposite sides of the transversal line, but inside the parallel lines.)

Corresponding: <1 and <3
(They have the same measure because they are in the same spot above the parallel line.)

Alt exterior: <1 and <8
(They are on opposite sides of the transversal, but on the outside of the parallel lines.)

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3 years ago

Find the surface area of composite figures

Aleonysh [2.5K]

Answer:

429 cm²

Step-by-step explanation:

A(blue) =

= 2×6cm×10cm + 2×6cm×8cm + 8cm×10cm + (8cm×10cm - 5cm×4cm)

= 120cm² + 96cm² + 80cm² + 60cm²

= 356 cm²

A(green) =

= 4cm×5cm + 2×5cm×5cm/2 + 4cm×7cm

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= 73 cm²

A(total) =

= A(blue) + A(green)

= 356 cm² + 73 cm²

= 429 cm²

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4 years ago

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If C is the line segment from 7 3 to 0 0 find the value of the line integral C 4y2i xj dr

saul85 [17]

Parameterize $C$ by

$\mathbf r(t)=(x(t),y(t))=(1-t)(7,3)+t(0,0)=(7-7t,3-3t)$

where $0\le t\le1$ . Then

$\mathrm d\mathbf r=(-7\,\mathbf i-3\,\mathbf j)\,\mathrm dt$

and the line integral is equivalent to

$\displaystyle\int_C(4y^2\,\mathbf i+x\,\mathbf j)\cdot\mathrm d\mathbf r=\int_0^1(4(3-3t)^2\,\mathbf i+(7-7t)\,\mathbf j)\cdot(-7\,\mathbf i-3\,\mathbf j)\,\mathrm dt$
$\displaystyle=\int_0^1(-252t^2+525t-273)\,\mathrm dt=-\dfrac{189}2$

7 0

3 years ago

Find all solutions to cosx cos3 x-sinx sine3x= 0 on the interval {0,2pi}

fomenos

$\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
\boxed{cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}})}
\\ \quad \\
cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}})\\\\
------------------------$

$\bf cos(x)cos(3x)-sin(x)sin(3x)=0\implies cos(x+3x)=0
\\\\\\
cos(4x)=0\implies cos^{-1}[cos(4x)]=cos^{-1}(0)\implies 4x=cos^{-1}(0)
\\\\\\
4x=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}\implies 
\begin{cases}
4x=\cfrac{\pi }{2}\implies &\measuredangle x=\cfrac{\pi }{8}\\\\
4x=\cfrac{3\pi }{2}\implies &\measuredangle x=\cfrac{3\pi }{8}
\end{cases}$

5 0

3 years ago