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2 years ago

(Subtracting rational coefficients-Mixed numbers)

Mathematics

1 answer:

OleMash [197]2 years ago

6 0

Answer:

-8 5/12

Step-by-step explanation:

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A flower show has an inventory of 60 tulips and 100 roses. If T represents tulips and R represents roses, which of the following

PilotLPTM [1.2K]

Answer: 3/5xr=t and 5/3xt=r

Step-by-step explanation:

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3 years ago

Determine algebraically whether f(x) = 3 is even or odd.

Artist 52 [7]

Answer:

f(x) is even

Step-by-step explanation:

f(x) = 3

f(-x) = 3

f(x) = f(-x)

3 0

3 years ago

#4 a and b and #5 please

Cloud [144]

The intrusions are there on the paper read it 3 times

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3 years ago

Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

3 years ago

Read 2 more answers

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respect

AysviL [449]

Answer:

<NPM + <NZM = 146°

Step-by-step explanation:

Given:

In triangle STU: M, N and P are the midpoints of the line TU, US and ST respectively.

Line UZ is the altitude of the triangle STU

<TSU =71°, <TSU = 36°, <TUS = 73°

From the diagram:

N is the midpoint of line SU and M is the mid point of line UT.

∴ Line NM is parallel to line ST

P is the mid point of line ST and M is the mid point of line UT

∴Line PM is parallel to line SU

N is the mid point of line SU and P is the mid point of line ST

∴Line NP is parallel to line UT

Δ SPN = Δ STU = 36°

<SPN + <NPM + <MPT (Sum of angles in a triangle = 180°)

<UST = <MPT = 71°

36° + <NPM + 71° = 180°

<NPM + 107° = 180°

<NPM= 180°-107°

<NPM= 73°

In ΔSNZ, line SN = line NZ

∴ side SN = side NZ

< NSZ = <NZS = 71°

<MTZ = <MZT = 36°

<NZS + <NZM <MZT = 180° (Sum of angles in a triangle = 180°)

71° + <NZM + 36° = 180°

107° + <NZM = 180°

<NZM = 180° - 107°

<NZM = 73°

<NPM + <NZM =73° + 73°

<NPM + <NZM = 146°

5 0

3 years ago