Solve this 2 step equation b/9 -34

The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

3 years ago

Tara has two standard, six-sided dice. If she rolls them 36 times, how many times should she expect a sum less than 5 to show up

andreyandreev [35.5K]

There are six sides on each die. For each possible score on Die 1, there are six possible scores on Die 2. So the number of possible combinations is 6*6 = 36.
It follows that if the dice are thrown 36 times, you would expect each combination to come up once. 

We therefore simply need to know how many combinations add up to less than 5. (I've interpreted this as not including a total of 5 itself). 
These combinations are: 1 and 1, 2 and 1, 1 and 2, 2 and 2, 3 and 1, and 1 and 3 ---> six combinations out of 36. 

So you'd expect a sum less than 5 six times.

8 0

3 years ago

Please help thanks!!!

lora16 [44]

$probablity \: of \: \: six = 29 : 150$

<h2>hope it helps you ❣❣ </h2>

<h2>Mark me as brainliest</h2>

in fraction=29/150

3 0

3 years ago

Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with t

Maru [420]

Answer:

See explanation

Step-by-step explanation:

First plot points A, B, C and D on the coordinate plane and connect them to get quadrilateral ABCD. Then plot the vertices E, F, G, H of the quadrilateral EFGH in each case.

For each of these cases there are attached diagrams

1 case - reflection acraoss the x-axis

2 case - translation 5 units down

3 case - reflection across the y-axis

4 case - translation 7 units right

3 0

3 years ago

An elephant at the zoo maintains her weight by eating 2.5% of her body weight in food each day. If she maintains a constant weig

Lelu [443]

Answer:

2100

Step-by-step explanation:

Multiply the rate by the time and the weight to find the amount per week.

(2.5%/day)(6 tons)(2000 lb/ton)(7 days/week) = 2100 lb/week

7 0

3 years ago

Solve this 2 step equation b/9 -34 < -36