Find the first five terms of the sequence defined below:

Answer:

The dimensions of the lid are 8mm by 19mm.

w = 8

l = 19

Step-by-step explanation:

[tex]l=w+11\\l\times w=152[/tex]

where l is length and w is width. This can be solved as a system of equations.

[tex]l\times w=152\\(w+11)\times w=152\\w(w+11)=152\\w^2+11w=152\\w^2+11w-152=0[/tex]

At this point, it gets a little tough. I might be unnecessarily overcomplicating things, but this is the only way I see to solve the problem.

=================== Skip down below if you don't care about factoring

You need to factor the newly created trinomial.

[tex]ax^2+bx+c[/tex]

With a trinomial in this form, you need to find 2 numbers that add together to make b and multiply together to make ac.

Here, we need 2 numbers that add to 11 and multiply to -152. First, factor 152:

1, 152

2, 76

4, 38

8, 19

Then the reverse of all of those is true too, of course:

19, 8

38, 4

etc

In our case, we're looking for -152, so one of our factors will be negative. We're also looking for factors that add up to 11. Looking at these factors, you can see that 19 - 8 = 11, so our factors are 19 and -8.

Finally, you can use those to factor our trinomial. Split up the middle number (11w) into two:

[tex]w^2+11w-152=0\\w^2-8w+19w-152=0[/tex]

And now, you can factor by grouping:

[tex]w^2-8w+19w-152=0\\w(w-8)+19(w-8)=0\\(w+19)(w-8)=0[/tex]

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

Now that the number is factored, you can finally find w:

[tex](w+19)(w-8)=0[/tex]

Here, you can see that the equation will be true when w = -19 or w = 8. Those are our solutions, but we can't have a negative distance, so it's just

[tex]w=8[/tex]

Going all the way back to the top, now you can use the width to find the length.

[tex]l=w+11\\l=8+11\\l=19[/tex]

That one was much easier.

The dimensions of the lid are 8mm by 19mm.

Finally, check that with both of the original equations to make sure it's correct.

[tex]l=w+11\\19=8+11\\19=19\\\\l\times w=152\\19\times8=152\\152=152[/tex]

Answer:

The first one

Step-by-step explanation:

A and B are similar because the proportions are the same.

A is congruent to C but none of the answers ask that.

Answer:

5^40

Step-by-step explanation:

Step 1: Multiply the exponents within the parentheses with the exponent outside of the parentheses.

Step 2: Based on the laws of exponents, add the exponents together.

Therefore, the answer is 5^40.

Answer:

[tex]f(1) = {(1)}^{3} + 3 {(1)}^{2} - 9(1) + 5 \\ (x - 1) = 0 \rightarrow \: x = 1 \\\frac{{x}^{3 } + {3x}^{2} - 9x + 5}{x - 1} = {x}^{2} + 4x - 5 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1 \\ \color{red}\boxed{x_{1} = 1} \\\color{yellow} \boxed {x_{2} = 1} \\ \color{green}\boxed{x_{3} = - 5} [/tex]

The answer would be C and F

Answer: 1 & -5

Step-by-step explanation

4 3/4 = 19/4

133/(19/4) = 133(4/19) = 1197/19 = 63 mph

Answer:

H=2  r=1

Step-by-step explanation:

P= 2h+4r + πr = π+8

h= π+8- πr -4r/2

(pls give brainliest if helps!)

Answer:

w = 5

Step-by-step explanation:

Step 1: Use the Distributive property to get 6w + 30.

Step 2: Divide 6w by 6 and cancel out both 6s.

Step 3: Divide 30 by 6 to get 5, and you have the answer.

Answer:

The height of cuboid is 50 cm.

Step-by-step explanation:

Given :

To Find :

Using Formulas :

[tex]\star\small{\underline{\boxed{\sf \pink{SA_{(Cuboid)} = 2(lb + bh + lh)}}}}[/tex]

Solution :

Substituting all the given values in the formula to find height of cuboid :

[tex]{\longrightarrow{\sf{SA_{(Cuboid)} = 2(lb + bh + lh)}}}[/tex]

[tex]{\longrightarrow{\sf{14800= 2(60 \times 40 + 40 \times h + 60 \times h)}}}[/tex]

[tex]{\longrightarrow{\sf{14800= 2(2400 + 40h + 60h)}}}[/tex]

[tex]{\longrightarrow{\sf{14800= 2(2400 + 100h)}}}[/tex]

[tex]{\longrightarrow{\sf{14800= 4800 + 200h}}}[/tex]

[tex]{\longrightarrow{\sf{200h = 14800 - 4800}}}[/tex]

[tex]{\longrightarrow{\sf{200h = 10000}}}[/tex]

[tex]{\longrightarrow{\sf{h = \dfrac{10000}{200}}}}[/tex]

[tex]{\longrightarrow{\sf{h = \cancel{\dfrac{10000}{200}}}}}[/tex]

[tex]{\longrightarrow{\sf{\underline{\underline{\red{h = 50 \: cm}}}}}}[/tex]

Hence, the height of cuboid is 50 cm.

[tex]\underline{\rule{220pt}{3.5pt}}[/tex]

Answer:

Answer: The answer is 8.91.

Answer : 8.91

Step - by - step explanation :

Sometimes if a question is to big for you - it's best to start off small . . .

4.60 + 3.28 = 7.88

7.88 + 1.03 = 8.91

Answer:

(0,-2)

Step-by-step explanation:

Answer:

0.4

Step-by-step explanation:

2/5 converted into hundredths is 40/100.

40/100 as a decimal is 0.40, or 0.4

-hope it helps

The solutions are:

(a) Standard error is 957.04. (b) The probability is 50%. (c)The probability is 0.8491. (d) The probability is 0.8617.

To calculate the values, use the standard error formula for the sample mean:

(a)

The standard error is given by:

[tex]Standard\ error =\dfrac{ Population \ standard \ deviation}{\sqrt{sample\ size}}\\Standard\ error=\dfrac {\$ 7,400 }{ \sqrt60}\\Standard\ error =\ $957.04[/tex]

(b)

To find the probability that the sample mean will be more than $27,175, convert it into a z-score and then find the area under the normal distribution curve:

z = (sample mean - population mean) / standard error

z = ($27,175 - $27,175) / $957.04

z = 0

Since the z-score is 0, the area under the curve to the right of this point is 0.5 or 50%.

c. To find the probability that the sample mean will be within $1,000 of the population mean, we need to find the area between the range of $(27,175 - $1,000) and $(27,175 + $1,000).

Lower limit: $27,175 - $1,000 = $26,175

Upper limit: $27,175 + $1,000 = $28,175

Now, we calculate the z-scores for both limits:

lower = ($26,175 - $27,175) / $957.04 ≈ -1.045

upper = ($28,175 - $27,175) / $957.04 ≈ 1.045

Using a standard normal distribution table or calculator, the probability of a z-score being between -1.045 and 1.045 is approximately 0.8491.

(d)

If the sample size were increased to 100.

[tex]Standard error = \dfrac{ \$7,400}{ \sqrt{100}} \\Standard error = \$740[/tex]

Find the probability that the sample mean will be within $1,000 of the population mean, did in part c:

Lower limit: $27,175 - $1,000 = $26,175

Upper limit: $27,175 + $1,000 = $28,175

lower = ($26,175 - $27,175) / $740

lower ≈ -1.351

upper = ($28,175 - $27,175) / $740

upper ≈ 1.351

Using a standard normal distribution table or calculator, the probability of a z-score being between -1.351 and 1.351 is approximately 0.8617.

Hence,

Learn more about Probability here:

https://brainly.com/question/32117953

#SPJ12

Step-by-step explanation:

→ 8 + 4 = 2(x -1)

→ 12 = 2x - 2

→ 2x - 2 = 12

→ 2x = 12 + 2 = 14

→ x = 14/2 = 7

→ x = 7

hence, option D (7) is correct.

Hope this answer helps you dear ! take care

Answer:

7/12 or 8/12 are both good options

Step-by-step explanation:

nvr mind, its 7/12 only

Answer:

360J/s

Step-by-step explanation:

power=work done/ time

power=600×6/10

=3600/10

=360

Keep the denominators the same and subtract the numerators. So for example in your example:

7/8 - 3/8

Leave the 8 alone. Subtract 3 from 7.

7 - 3 = 4

So answer is:

4/8

Sometimes they may have to simplify the answer, and in this case, 4/8 could be simplified to 1/2

Answer:

C. 9

Step-by-step explanation:

K(3)=3*3=9........................

Answer:

75 m, 96 m

Step-by-step explanation:

a. Area = length x width

7050 = 94 x width

7050/94 = w

75 m is width

b. perimeter = 2L + 2W

356 = 2L + 2(82)

356 = 2L + 164

192 = 2L

96 m = L

Answer:

1/4

Step-by-step explanation:

Sample space = 12

Prob of sum = 8 is:

[2,6], [3,5]. [4,4]

That is 3/12 = 1/4

Answer:

3y

Step-by-step explanation:

(-9x+7y)-(-9x+5y)

Distribute the negative(-)

-9x+7y+9x-5y

-9 and 9 cancel each other

3y

The simplest terms of the given expression  (-9x + 7y) - (-9x + 5y) will be 2y.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given expression,

(-9x + 7y) - (-9x + 5y)

Open the bracket

-9x + 7y + 9x - 5y

Combined likely terms together

-9x + 9x + 7y - 5y

0 + 2y = 2y

Hence "The formula (-9x + 7y) - (-9x + 5y) will have 2y as its simplest terms".

To learn more about expression,

https://brainly.com/question/14083225

#SPJ2

Answer: [tex]y=-\frac{1}{2}x-7[/tex]

Ok done. Thank to me :>

Answer: 384

Step-by-step explanation:

Here is ur answer of your question

[tex] = {8}^{3} \: \: cm ^{3} \\ = 512 \: \: {cm}^{3} [/tex]

Answer:

The volume is 512 cube centimetres.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

angle 1 130°

angle 2 50°

angle 3 130°

Step-by-step explanation:

180°-50°=130°, use one of the road as the straight line,

which is 180° so angle 1 is 130°

which means angle 2 is also 50° because 180°-130° is 50°

and angle 3 is 130° because 180°-50°=130°

Hope this helps :)

Using the exponential function, it is found that:

The exponential function is:

[tex]y(x) = 30078(1.003)^x[/tex]

Hence, considering today as an starting point, the function is:

[tex]y(x) = 30078(1.003)^{x + 260}[/tex]

One week from now, we have y(1), hence:

[tex]y(1) = 30078(1.003)^{1 + 260} = 65734.37[/tex]

One week from today, the stock is predicted to close at $65,734.37.

One month from now, we have y(4), hence:

[tex]y(4) = 30078(1.003)^{4 + 260} = 66327.75[/tex]

One month from today, the stock is predicted to close at $66,327.75.

One year from now, we have y(52), hence:

[tex]y(52) = 30078(1.003)^{52 + 260} = 76584.35[/tex]

One year from today, the stock is predicted to close at $76,584.35.

To learn more about exponential functions, you can take a look at https://brainly.com/question/25958656

Answer:

One week from today, the stock is predicted to close at $65,734.37.

One month from today, the stock is predicted to close at $66,327.75.

One year from today, the stock is predicted to close at $76,584.35.

Step-by-step explanation:

Answer: 4y3(1x1 - 12)

3x4y3 – 48y3

4y3(1x1 - 12)

Answer:

0

the answer is 0........