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3 years ago

6.

Mathematics

1 answer:

Lena [83]3 years ago

8 0

Answer:

-1110/39 is the number

Step-by-step explanation:

We want to find the number should be added to both numerator and denominator of the ratio 29 : 36 to make it equal to 3:42

Let the number to be added be x.

Thus;

(29 + x) : (36 + x) = 3:42

The proportion symbol is essentialy a division symbol.

Thus;

(29 + x)/(36 + x) = 3/42

Cross multiply to give;

42(29 + x) = 3(36 + x)

1218 + 42x = 108 + 3x

1218 - 108 = 3x - 42x

1110 = - 39x

x = -1110/39

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Find the lengths of the missing side . Simplify all radicals !!!<br> help mee!!!!!!

larisa86 [58]

Answer:

$e = 13\sqrt{2}$

$f = 13\sqrt{2}$

Step-by-step explanation:

The ∆ given is an isosceles ∆ with a right angle measuring 90°, and two congruent angles measuring 45° each.

Using trigonometric ratio formula, we can find the lengths of the missing side as shown below:

Finding e:

$sin(\theta) = \frac{opp}{hyp}$

$sin(\theta) = sin(45) = \frac{\sqrt{2}}{2}$

hyp = 26

opp = e = ?

Plug in the values into the formula

$\frac{\sqrt{2}}{2} = \frac{e}{26}$

Multiply both sides by 26

$\frac{\sqrt{2}}{2}*26 = \frac{e}{26}*26$

$\frac{\sqrt{2}}{2}*26 = e$

$\frac{\sqrt{2}}{1}*13 = e$

$13\sqrt{2} = e$

$e = 13\sqrt{2}$

Since side e is of the same length with side f, therefore, the length of side f = $13\sqrt{2}$

3 0

3 years ago

The University of Texas at Austin has three times as many students enrolledas the University of Miami. The University of Califor

harina [27]

Answer:

University of Texas has 46,500 students, University of California has 34,000 students and University of Miami has 15,500 students.

Step-by-step explanation:

Represent Texas with T, Miami with M and California with C. With the given information, the following equations were obtained.

T = 3 × M

T – 3M = 0 ………………………….(i)

C = 3,000 + 2 × M

C – 2M = 3,000…………………..(ii)

T + C + M = 96,000…………….(iii)

By rearranging, we have:

1T + 0C – 3M = 0 ………………………….(i)

0T + 1C – 2M = 3,000…………………..(ii)

1T + 1C + 1M = 96,000………….…….(iii)

The Augmented Matrix is:

$\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]$ $\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]$

Making $\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ the subject of the formula we have:

$\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\frac{\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]}{\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]}$

Let’s say matrix A = $\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]$ , the inverse of matrix A = $\left[\begin{array}{ccc}\frac{1}{2} &-\frac{1}{2} &\frac{1}{2} \\-\frac{1}{3} &\frac{2}{3} &\frac{1}{3} \\-\frac{1}{6} &-\frac{1}{6} &\frac{1}{6} \end{array}\right]$ is determined by the formula $\frac{Adjoint(A)}{determinant(A)}$ . This can also be computed directly on a scientific calculator.

$\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\left[\begin{array}{ccc}\frac{1}{2} &-\frac{1}{2} &\frac{1}{2} \\-\frac{1}{3} &\frac{2}{3} &\frac{1}{3} \\-\frac{1}{6} &-\frac{1}{6} &\frac{1}{6} \end{array}\right]$ $\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]$

= $\left[\begin{array}{ccc}46,500\\34,000\\15,500\end{array}\right]$

T = 46,500

C = 34,000

M = 15,500

6 0

4 years ago

Read 2 more answers

Determine the equation, in vertex form, of a parabola that has been:

Dennis_Churaev [7]

Answer:

$a)\ y=-(x-5)^2;\\b)\ y=4x^2-5;\\c)\ (y-2)^2=4*(x+3).$

Good luck!

4 0

2 years ago

Here is a scenario that came up in the nationally syndicated column called "Ask Marilyn" in Parade Magazine. Suppose a certain d

goldenfox [79]

Answer:

Drug User Not a drug user Totals

Test positive 475 475 950

Test negative 25 9025 9050

Totals 500 9500 10,000

Step-by-step explanation:

Drug User Not a drug user Totals

Test positive 475 475 950

Test negative 25 9025 9050

Totals 500 9500 10,000

As we know that 5% of all people are drug users

Total drug users=5% of 10,000=0.05(10,000)=500

Total non drug users= Total people - drug users= 10,000-500=9500

or total non drug users=95% of 10,000=0.95(10,000)=9500

Test is correct for 95% of times means that 95% times drug users test results is positive and non drug users test results is negative.

Test positive for drug user= 95% of 500=0.95(500)=475

Test negative for non drug user= 95% of 500 = 0.95(9500)=9025

Test is correct for 95% of times and it means that 5% of times test is not correct. It means that 5% of times drug users test results is negative and non drug users test results is positive.

Test negative for drug user= 5% of 500=0.05(500)=25

Test positive for non drug user= 5% of 9500 = 0.05(9500)=475

4 0

3 years ago

Does anyone know the answers to A, B, C, and D?

NeTakaya

It would be b because it the best choice

3 0

3 years ago