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4 years ago

- 5x+6=-12x+62 Simplify your answer as much as possible.

Mathematics

2 answers:

S_A_V [24]4 years ago

7 0

Answer:

x=8

Step-by-step explanation:

-5x+6=-12x+62

-5x+12x=62-6

7x=56

x=8

Nataly [62]4 years ago

3 0

The answer is x=8
Hope that helps

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10<br> c T is 4 units high. It is enlarged with a<br> scale factor of 4.<br> How high is the image?

masya89 [10]

Answer:

it is 14 pls make me brainliest pls

Step-by-step explanation:

6 0

3 years ago

Jackson Elementary School ordered 25 pizzas for an awards ceremony. At the end of the day, the principal found 8 1/4 pepperoni p

seraphim [82]

Answer: 9 pizzas

Step-by-step explanation:

From the question, we are informed that Jackson Elementary School ordered 25 pizzas for an awards ceremony and at the end of the day, the principal found 8 1/4 pepperoni pizzas and 7 3/4 sausage pizzas left over.

A reasonable estimate for the number of pizzas the students ate at the awards ceremony will be:

= 25 - (8 1/4 + 7 3/4)

= 25 - 16

= 9 pizzas

7 0

4 years ago

find the orthogonal projection of v= [19,12,14,-17] onto the subspace W spanned by [ [ -4,-1,-1,3] ,[ 1,-4,4,3] ] proj w (v) = [

12345 [234]

<h2>Answer:</h2>

Hence, we have:

$proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]$

<h2>Step-by-step explanation:</h2>

By the orthogonal decomposition theorem we have:

The orthogonal projection of a vector v onto the subspace W=span{w,w'} is given by:

$proj_W(v)=(\dfrac{v\cdot w}{w\cdot w})w+(\dfrac{v\cdot w'}{w'\cdot w'})w'$

Here we have:

$v=[19,12,14,-17]\\\\w=[-4,-1,-1,3]\\\\w'=[1,-4,4,3]$

Now,

$v\cdot w=[19,12,14,-17]\cdot [-4,-1,-1,3]\\\\i.e.\\\\v\cdot w=19\times -4+12\times -1+14\times -1+-17\times 3\\\\i.e.\\\\v\cdot w=-76-12-14-51=-153$

$w\cdot w=[-4,-1,-1,3]\cdot [-4,-1,-1,3]\\\\i.e.\\\\w\cdot w=(-4)^2+(-1)^2+(-1)^2+3^2\\\\i.e.\\\\w\cdot w=16+1+1+9\\\\i.e.\\\\w\cdot w=27$

and

$v\cdot w'=[19,12,14,-17]\cdot [1,-4,4,3]\\\\i.e.\\\\v\cdot w'=19\times 1+12\times (-4)+14\times 4+(-17)\times 3\\\\i.e.\\\\v\cdot w'=19-48+56-51\\\\i.e.\\\\v\cdot w'=-24$

$w'\cdot w'=[1,-4,4,3]\cdot [1,-4,4,3]\\\\i.e.\\\\w'\cdot w'=(1)^2+(-4)^2+(4)^2+(3)^2\\\\i.e.\\\\w'\cdot w'=1+16+16+9\\\\i.e.\\\\w'\cdot w'=42$

Hence, we have:

$proj_W(v)=(\dfrac{-153}{27})[-4,-1,-1,3]+(\dfrac{-24}{42})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=\dfrac{-17}{3}[-4,-1,-1,3]+(\dfrac{-4}{7})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=[\dfrac{68}{3},\dfrac{17}{3},\dfrac{17}{3},-17]+[\dfrac{-4}{7},\dfrac{16}{7},\dfrac{-16}{7},\dfrac{-12}{7}]\\\\i.e.\\\\proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]$

6 0

3 years ago

Solve for b.<br> ab +c=d

pshichka [43]

Answer:

Option 1 is correct.

ab + c = d

b = (d-c) / a

7 0

3 years ago

Read 2 more answers

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 42% chan

Iteru [2.4K]

Complete Question

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 42% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 12%. There is only a 52% chance that she will find a tutor at such short notice

a What is the probability that Christine fails the course

b Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability

Answer:

$P(F) = 0.264$

$P(T | F ) = 0.23636$

Step-by-step explanation:

From the question we are told that

The probability that Christine will fail the course if she does not have a tutor is $P(F| T') = 0.42$

The probability that Christine will fail the course if she has a tutor is $P(F| T) = 0.12$

The probability that she will find a tutor is $P(T) = 0.52$

Generally the probability that she will not find a tutor is

$P(T') = 1 - 0.52$

=> $P(T') = 0.48$

Generally the probability of failing the course is

$P(F) = P(F \ n \ T) + P(F \ n \ T')$

=> $P(F) = P(F| T) * P(T) + P(A | T') * P(T')$

=> $P(F) = 0.12 * 0.52 + 0.42* 0.48$

=> $P(F) = 0.264$

Generally if Christine ends up failing the course the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability is mathematically represented as

$P(T | F ) = \frac{ P(F | T) * P(T)}{ P(F)}$

=> $P(T | F ) = \frac{ 0.12 * 0.52}{ 0.264}$

=> $P(T | F ) = 0.23636$

5 0

3 years ago