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never [62]
1 year ago
14

Fully factorise x² + 7x+6

Mathematics
2 answers:
wlad13 [49]1 year ago
6 0

just find the roots and substitute

a(x - "first root") (x - "second root")

marin [14]1 year ago
5 0

\\ {\large{\textsf{\textbf{\underline{\underline{ Question \: :}}}}}}  \\

Factorise ;

  • x² + 7x+6

\qquad\rule{120pt}{2pt}

\\ {\large{\textsf{\textbf{\underline{\underline{ Solution \: :}}}}}}  \\

\\  \sf \implies \:  {x}^{2} + 7x+6 \\

\\  \sf \implies \:  {x}^{2} + 6x + x+6 \\

\\  \sf \implies \:  x(x + 6)  +1 (x+6) \\

\\  \sf \implies \:  (x + 6)   (x+1) \\

\\  \sf \implies \:  x + 6= 0 \:\:\:\:  and\:\:\:\:  x+1=0 \\

\\  \sf \implies \:  x= 0 -6\:\:\:\:  and\:\:\:\:  x=0-1 \\

\\  \sf \implies \:  x= -6\:\:\:\:  and\:\:\:\:  x=-1 \\

\\\sf\implies\;{\underline{\boxed {\bf{ \:\:x=-6\:\: }}} }\red\bigstar \;\; \;\; \;{\underline{\boxed {\bf{ \:\:x=-1\:\: }}} }\red\bigstar \\

\\\qquad\rule{120pt}{2pt}\\

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kolbaska11 [484]
I believe it is proposition
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3 years ago
Given that P = (-7, 16) and Q = (-8, 7), find the component form and magnitude of vector QP .
Katyanochek1 [597]

Answer:

a)The component form is

\vec {QP}=\binom{ - 1}{ - 8}

b)The magnitude is √65

c) <2,14>

Step-by-step explanation:

Recall that:

\vec {QP}=\vec {OP}-\vec{OQ}

We substitute the position vectors to get:

\vec {QP}=\binom{ - 8}{7} -  \binom { - 7}{15}

We subtract the corresponding components to obtain:

\vec {QP}=\binom{ - 8 -  - 7}{7 - 15}

This gives:

\vec {QP}=\binom{ - 8  + 7}{7 - 15}

This simplifies to:

\vec {QP}=\binom{ - 1}{ - 8}

The magnitude of a vector in the component form:

\binom{x}{y}

is

\sqrt{ {x}^{2}  +  {y}^{2} }

This means:

|\vec {QP}|= \sqrt{ {( - 1)}^{2}  +  {( - 8)}^{2} }

This simplifies to:

|\vec {QP}| = \sqrt{ 1 +  64 }

|\vec {QP}| = \sqrt{ 65 }

c) We have the vectors u = <4, 8>, v = <-2, 6>.

We want to find:

u+v

This implies that:

u+v=<4,8>+<-2,6>

We add the corresponding components to get;

u+v=<4+-2,8+6>

This simplifies to:

u+v=<2,14>

7 0
3 years ago
There are two vendors at the fair sleeping snow cones for the same price. If the containers are completely filled and then level
aliya0001 [1]

Answer:

d =  787.81cm^3

Step-by-step explanation:

Given

See attachment for the containers

Required

The difference in the amount of snow cone they hold

The amount they hold is determined by calculating the volume of the containers.

The traditional snow cone has the following dimension

Shape: Cone

r=4cm --- radius

h = 13cm --- height

The volume is calculated as:

Volume = \frac{1}{3} \pi r^2h

So, we have:

V_1 = \frac{1}{3} \pi * 4^2 * 13

V_1 = \frac{208}{3} \pi

The snow cone in a cup has the following dimension

Shape: Cylinder

r=8cm --- radius

h = 5cm --- height

The volume is calculated as:

Volume =  \pi r^2h

So, we have:

V_2 =  \pi *8^2 * 5

V_2 =  \pi *320

V_2 =  320\pi

The difference (d) in the amount they hold is:

d = V_2 - V_1

d = 320\pi - \frac{208\pi}{3}

Take LCM

d =  \frac{3*320\pi -208\pi}{3}

d =  \frac{960\pi -208\pi}{3}

d =  \frac{752\pi}{3}

Take \pi = 22/7

d =  \frac{752}{3} * \frac{22}{7}

d =  \frac{752 * 22}{3*7}

d =  \frac{16544}{21}

d =  787.81cm^3

4 0
3 years ago
Four numbers have a sum of 9900. The second exceeds the first by 1/7 of the first. The third exceeds the sum of the first two by
Amanda [17]

Answer:

1050, 1200, 2550 and  5100.

Step-by-step explanation:

If the first number is x then the second is  x + 1/7x.

The third =  x + x + 1/7x + 300 and the fourth = x + x + 1/7x + x + x + 1/7x+ 300 + 300.

So our equation is:-

8x +  4 * 1/7x  + 900 = 9900

60/7 = 9000

60x = 7*9000

x = 1050.

Therefore the 4 numbers are 1050,  *1/7*1050 = 1200, 2550 and  5100.


3 0
3 years ago
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A real estate agent has sold a house for $350,000. She earns 3% commission. How much did she earn? Show your work!
inessss [21]
3% is equal to .03 so .03 times $350,000 equals $10,500
8 0
3 years ago
Read 2 more answers
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