Determine the value of x so that line ℓ will be parallel to line m.

Answer:

Step-by-step explanation:

Answer:

The width is 3cm, and the length is 7cm.

Step-by-step explanation:

Let's call the length of the rectangle [tex]l[/tex], the width of the rectangle [tex]w[/tex], and the area of the rectangle [tex]A[/tex], and write down everything we know about them.

The length of the rectangle is 11 centimetres less than six times its width, so we know that [tex]l = 6w - 11[/tex].

We also know that [tex]A = 21[/tex]. But what exactly is the area of a rectangle? Well, it's the product of its length and width, i.e. [tex]A = l\times w[/tex].

Then we have two equations involving [tex]l[/tex] and [tex]w[/tex]:

[tex]l = 6w - 11[/tex], and [tex]l\times w = 21[/tex].

So how do we find [tex]l[/tex] and [tex]w[/tex]? Let's substitute our first equation into our second, like so:

[tex]l \times w = (6w - 11) \times w\\{}\hspace{0.8cm}= 6w^2 - 11w\\{}\hspace{0.8cm}= 21[/tex]

We can rearrange this new equation to get everything on the same side, so that we have a standard quadratic equation, like this:

[tex]6w^2 - 11w - 21 = 0[/tex].

We can use the quadratic formula for this. You should have seen this before:

[tex]w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex],

where [tex]a,b,c[/tex] are the coefficients of our quadratic equation. Plugging the values in, we see

[tex]w = \frac{11\pm\sqrt{121+504}}{12}\\\\{}\hspace{0.25cm}=\frac{11\pm\sqrt{625}}{12}\\\\{}\hspace{0.25cm}=\frac{11\pm25}{12}[/tex].

With a little further cancellation, we can find our two possible values of [tex]w[/tex] are

[tex]w = \frac{36}{12} = 3[/tex]  and [tex]w = \frac{-14}{12}[/tex].

Since [tex]w[/tex] is a width of a rectangle, it can't possibly be negative, and so it must be 3.

We can now plug in this value into our equation from earlier, namely [tex]l = 6w - 11[/tex]. We can see that

[tex]l = 6\times 3 - 11 = 18 - 11 = 7[/tex],

and so we get our answer, [tex]w = 3[/tex]cm, [tex]l = 7[/tex]cm.

We can prove that this is right by multiply 3 and 7 together, and seeing that we get 21, the area we expect.

Answer:

-x-8

Step-by-step explanation:

hope this helps

Answer:

if it is -8 subtracted from -x then

-x-(-8)

if it is 8 subtracted from x then

x-8

Answer:

y = 2/3x

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

12n

Step-by-step explanation:

Answer:

3 - x =-9

3+ 9 =x

x = 12

so, correct answer

x =12

Answer:

C

Step-by-step explanation:

By tracing the figure, we see that we go around a semicricle twice and go in a straight path twice. So the perimeter of this figure consists of two semicircles and two line segments, hence the answer is C.

Answer:

why do the delete my answer

Answer:

Step-by-step explanation:

y = 2√(x-8)

y² = 4(x-8) = 4x-32

4x = y²+32

x = 0.25y² +8

Answer:

x = 23

Step-by-step explanation:

60°=x+14

60+14=84=X

Answer:

it's a scalene triangle whose all sides are different

Answer:

No solution

Step-by-step explanation:

Please write this as 3 sqrt x + 8 = -4.  

Note that if we try to isolate 3 sqrt x by subtracting 8 from both sides, we get 3 sqrt x = -12.  There is no real solution; sqrt x can never be negative.

Answer:

1/4 = 5/20

Step-by-step explanation:

1/4 = 5/20

Answer:

Step-by-step explanation:

1/4 is equivalent only to B (5/20).  To check this, try dividing 20 into 5 with a calculator; you should get 0.25 = 5/20

Answer:

A. 5.34

Step-by-step explanation:

Reference angle = 24°

Opposite = x

Adjacent = 12

Thus, applying trigonometric ratio, we have:

tan (24) = x/12

Multiply both besides by 12

12*tan (24) = x

x = 5.34 (nearest hundredth)

Answer:

See explanations below

Step-by-step explanation:

Given the functions

f(x) = 12x - 12

g(x) = x/12 - 1

To show they are inverses, we, must show that f(g(x)) = g(f(x))

f(g(x)) = f(x/12 - 1)

Replace x with x/12 - 1 into f(x)

f(g(x)) =12((x-12)/12) - 11

f(g(x)) =  x-1 - 1

f(g(x)) =x - 2

Similarly for g(f(x))

g(f(x)) = g(12x-12)

g(f(x)) =(12x-12)/12 - 1

12(x-1)/12 - 1

x-1 - 1

x - 2

Since f(g(x)) = g(f(x)) = x -2, hence they are inverses of each other

Answer:

49 = 7m

m = 7

Step-by-step explanation:

200 - 151 = 49

There are 49 M&M's left

m = M&M's per day

7(7) = 49

Answer:

49 ÷ 7 = 7

Step-by-step explanation:

200 - 151 is 49 so 7 beacuase 49 divided by 7 is 7

Answer:

42

Step-by-step explanation:

hope this helps!;)

Answer:

105.7143%

Step-by-step explanation:

pls make me brainliest

Answer:

C

Step-by-step explanation:

SU/UR = ST/QT

10/7=10/x

70=10x

7=x

A=7

Have a nice day :)

Answer:

Mean is 83.7%

And, the standard deviation is 0.033

Step-by-step explanation:

The computation of the mean and the standard deviation is as follows:

Let us assume the P be the sample proportion

Mean is 83.7%

And, the standard deviation is

[tex]= \sqrt{\frac{p(1-p)}{n} } \\\\=\sqrt{\frac{0.837(1-0.837)}{125} }[/tex]

= 0.033

Answer:

C: 55

Step-by-step explanation:

Rearrange the bracketed terms to:

(10 + 0) + (10 + 1) + (10 + 2) + ... + (10 + 10)

There are 11 brackets so we have (11 * 10) + (0 + 1 + 2 + ... + 10) =

(11 * 10) + 55

Answer:

shiiiii i dont no Nlgga

Step-by-step explanation:

Answer:

option 3

Step-by-step explanation:

u can eliminate option 1 and 4 because the circles are empty and this problem has an equal to sign. the greatest number x can be is -2 because that would make the left side of the equation equal to three. Therefore x must be less than or equal to -2 to make the equation true(as graphed)

Answer:

Zach time of reading every weekend forms a sequence with these terms: 10, 20, 40, 80. On the other hand, that of Victoria forms a sequence with terms: 35, 50, 65, 80. By keenly observing the sequences, Zach's sequence is a geometric sequence with a common ratio equal to 2 and Victoria's sequence is an arithmetic or linear sequence with a common difference of 15. Thus, the answer is letter B.

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

A coin has two faces (H, T)

n(S) = 2 (sample space)

If it is tossed and a rail is gotten,

n(E) = 1 (event)

Probability of tossing a tail = n(E)/n(S)) = 1/2

If a dice is rolled, the sample space S = {1, 2, 3, 4, 5, 6}

n(S) = 6

Number greater than 1 are the evens E = {2, 3, 4, 5, 6}

n(E) = 5

pr(rolling a number greater than 1) = 5/6

Hence  the probability of tossing a tail and then rolling a number greater than 1 = 1/2 * 5/6

= 5/12

B) is Your answer

11.76

Step-by-step explanation:

[tex]19.98 + 64.93 = 84.93[/tex]

[tex]84.93 - 73.17 = 11.76[/tex]

is Your perfect answer

Answer:

D

Because you have to find out what they could all equal up to

Answer:

d

Step-by-step explanation:

Answer:

0.5234 = 52.34% probability that at least three of these students are in favor of the proposal to change the dress code.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they are in favor, or they are not. Students are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

18% of the students are in favor of changing the dress code.

This means that [tex]p = 0.18[/tex]

You randomly select 15 students

This means that [tex]n = 15[/tex]

What is the probability that at least three of these students are in favor of the proposal to change the dress code?

This is

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{15,0}.(0.18)^{0}.(0.82)^{15} = 0.051[/tex]

[tex]P(X = 1) = C_{15,1}.(0.18)^{1}.(0.82)^{14} = 0.1678[/tex]

[tex]P(X = 2) = C_{15,2}.(0.18)^{2}.(0.82)^{13} = 0.2578[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.051 + 0.1678 + 0.2578 = 0.4766[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.4766 = 0.5234[/tex]

0.5234 = 52.34% probability that at least three of these students are in favor of the proposal to change the dress code.