In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearest
tenth of a cm, how long is that leg?

Hi there! :)

Answer:

4/7 times 35, minus 8.5 is no more than 11.5

The number is : 35

Step-by-step explanation:

Let's replace "a number" by the letter "x" because that's what we are looking for.

4/7 × x = 4/7x

4/7x MINUS 8.5 = 4/7x - 8.5

The expression "no more than" is represented by this sign: ≤

"No more than" can also be "less than or equal to".

The final inequality should look like this:

4/7x - 8.5 ≤ 11.5

Now all you need to do is solve the inequality by isolating "x":

4/7x - 8.5 ≤ 11.5

Add 8.5 to each side of the inequality → 11.5 + 8.5 = 20

4/7x ≤ 20

Divide each side of the inequality by "4/7" → 20 ÷ 4/7 = 35

x ≤ 35

There you go! I really hope this helped if there's anything just let me know! :)

Answer:

1. A. 66 cubic inches.

2. A. 151,410,000

Step-by-step explanation:

For number one: Multiply 3 x 4 and that will give you 12 then multiply that by 11 and that will also give you 132. Lastly, divide 132 by 2 and it will get you 66 cubic inches.

For Number two: Multiply 420 by 721,000 and that will give you 302,820,000.

Once you have that, divide it by 2 and will give you 151,410,000.

Answer:

See below

Step-by-step explanation:

Since you didn't give an actual quadratic equation and just the standard form equation, I will reduce ax^2+bx+c=0:

(ax+p)(x+q) where p+q=b and pq=c

Answer:

c

Step-by-step explanation:

Answer:

A and D

That is the answer.

Answer:

[tex]y = \frac{1}{100} \times 10{}^{x} [/tex]

Step-by-step explanation:

Use coordinates (2,1) and 3,10

The exponential equation is

[tex]y = a \times b {}^{x} [/tex]

Plug in the x and y values.xfor both functions of coordinates.

[tex]1 = a \times b {}^{2} [/tex]

[tex]10 = a \times b {}^{3} [/tex]

Divide the equation with the larger exponet by the other equation.

[tex]10 = b[/tex]

Substitute that in for one of the equations.

[tex]10 = a \times 10 {}^{3} [/tex]

Solve for a.

[tex]10 = a \times 1000[/tex]

[tex] \frac{1}{100} = a[/tex]

So our exponetial equation is

[tex]y = \frac{1}{100} \times 10 {}^{x} [/tex]

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Answer:

私は人間の前に神の弓です

翻訳してください

Step-by-step explanation:

Answer:

Yes, one inch is a twlefth of a ft which is a porportion of a feet

Step-by-step explanation:

Answer:

Drip is the only answer

Step-by-step explanation:

Answer: i dont have the answer key but i did answer them for you

Step-by-step explanation:

Answer:

....

Step-by-step explanation:

1.weights

2.coach

3.Olympics

4.stadium

5.finish line

6.gold medal

7.swimming pool

8.team

9.first place

21.starting line

11.score

12.medal

13.athlete

14.trophies

Answer:

109

Step-by-step explanation:

Hope this helped :)

Answer: The answer is 48 degrees hope this helped

Step-by-step explanation:

Answer:

a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]

b)

The balance after 1 year is of $10,768.644

The balance after 2 years is of $11,500.91

The balance after 5 years is of $14,010.25.

The balance after 10 years is of $19,467.15

c)

The doubling time is of 10.54 years.

Step-by-step explanation:

Continuously compounded interest:

The amount of money earning after t years, with interest compounded continuously, is given by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.

a) Find the exponential function that describes the amount in the account after time t, in years.

Suppose that $10,083 is invested at an interest rate of 6.8% per year

This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]

So

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 10083(1+0.068)^t[/tex]

[tex]A(t) = 10083(1.068)^t[/tex]

b) What is the balance after 1 year? 2 years? 5 years? 10 years?

After 1 year:

[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]

The balance after 1 year is of $10,768.644

After 2 years:

[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]

The balance after 2 years is of $11,500.91.

After 5 years:

[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]

The balance after 5 years is of $14,010.25.

After 10 years:

[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]

The balance after 10 years is of $19,467.15.

c) What is the doubling time?

This is t for which [tex]A(t) = 2A(0)[/tex]. So

[tex]A(t) = A(0)(1.068)^t[/tex]

[tex](1.068)^t = 2[/tex]

[tex]\log{(1.068)^t} = \log{2}[/tex]

[tex]t\log{1.068} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]

[tex]t = 10.54[/tex]

The doubling time is of 10.54 years.

Answer:

8.0

Step-by-step explanation:

Answer:

50m

Step-by-step explanation:

The triangles are similar, so their sides are in ratio:

BC/BE=AD/ED

j/46=25/23

j=(25/23)(46)=50

Answer:

x  = 5.

Step-by-step explanation:

The area of a rectangle can be determined by the following formula.

A = l ⋅ w  

l  stands for length or the longer side.

w  stands for width or the shorter side.

Now, we can plug the values we are given into the equation.

A = ( x − 2 ) ⋅ ( x + 8 )

The easiest way to multiply is to follow the acronym FOIL , which stands for First Outside Inside Last, and dictates the order in which you multiply these terms.

A = x 2 + 8 x − 2 x −16 = x 2 + 6 x − 16

Now, we can plug in the given value for the area.

39 = x 2 + 6 x − 16  

Next, we simplify by moving all terms to one side and factor the equation.

0 = x 2 + 6 x − 55

Finally, we factor the equation. This means we reverse-FOIL, trying to determine the two things that we multiplied together.

0= ( x − 5 ) ⋅ ( x + 11 )

If the equation ultimately equals zero, either  ( x − 5 )  or  ( x + 11 )  or both equal zero. Therefore, we set each equal to zero to find the value of  

x .

x − 5 = 0 x = 5 x + 11 = 0

x = − 11

Since  x  is a length, we know it cannot be negative. Thus, we can conclude that it equals 5.

Answer:

Mean = 1

Step-by-step explanation:

[tex]mean = \frac{ - 1 + 9 - 4 - 6 + 5 + 3}{6} \\ \\ mean = \frac{6}{6} \\ \\ mean = 1[/tex]

I hope that is useful for you :)

Answer:

1

Step-by-step explanation:

Hello, if you ever heard the hey diddle diddle song, it would say that you add and divide for the mean. So lets try that! First, add all the numbers together like this:

-1+9+(-4)+(-6)+5+3=6

Then, you take the number and divide it by the number of numbers in that set. In this case, it would be 6.

6/6=1

That means that the mean of the low temperatures is 1.

(4,-8)

Step-by-step explanation:

from -5 to -1 you would have to count from 1 to 4. and do the same for -8 to -16

Answer:

B, C, F

Step-by-step explanation:

7x + 4 - (2x - 5) = 7x - 2x + 4 + 5 or 5x + 9

The solution is, B: 7x + 4 - 2x + 5, C: 7x + 4 + (-2x) - (-5), F: 5x + 9, are the expressions that are equivalent to 7x + 4 - (2x - 5).

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

the expression is :

7x + 4 - (2x - 5)

now, we have to simplify this to get the equivalent expressions.

so, we have,

7x + 4 - (2x - 5)

= 7x + 4 - 2x + 5

(Removing the brackets)

=7x + 4+ (-2x) - (-5)

= 7x + (-2x) +4 - (-5)

=5x +4 + 5

= 5x + 9

so, the equivalent expressions are, B,C,F.

Hence, The solution is, B: 7x + 4 - 2x + 5, C: 7x + 4 + (-2x) - (-5), F: 5x + 9, are the expressions that are equivalent to 7x + 4 - (2x - 5).

To learn more on simplification click:

brainly.com/question/28996879

#SPJ3

Answer:

4th number line (the one of the bottom right)

Step-by-step explanation:

First, solve the inequality, then choose the number line that mathes the solution.

3x ≤ -6

Only step: Divide by 3.

x ≤ -6/3

x ≤ -2

But which number line matches the solution?

We know this is going left, so #1 & #3 are out. This also has a closed circle (because of ≤ (less than/equal to)), so #2 is also out.

Number line #4 matches the solution (x ≤ -2), so it is the answer.

Answer: =7/12

Step-by-step explanation:

Answer:

30[tex]\sqrt{5}[/tex]

Step-by-step explanation:

3[tex]\sqrt{500}[/tex] = 3[tex]\sqrt{100}[/tex] [tex]\sqrt{5}[/tex] = 3(10)[tex]\sqrt{5}[/tex]

Answer:

none of the above

30√5

Step-by-step explanation:

3 √500

3√25x4x5

3x5x2√5

30√5

Answer:

Y = 28

Step-by-step explanation:

Y=16 + 12 = 24

Therefore the y scored 24 points

Answer:

Options (1), (2), (3) and (4)

Step-by-step explanation:

By applying the sine and cosine rules in the given triangle,

sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

cos(30°) = [tex]\frac{AC}{AB}[/tex]

              = [tex]\frac{11\sqrt{3} }{22}[/tex]

              = [tex]\frac{\sqrt{3}}{2}[/tex]

sin(30°) = [tex]\frac{BC}{AB}[/tex]

             = [tex]\frac{11}{22}[/tex]

             = [tex]\frac{1}{2}[/tex]

cos(60°) = [tex]\frac{BC}{AB}[/tex]

              = [tex]\frac{11}{22}[/tex]

              = [tex]\frac{1}{2}[/tex]

sin(60°) = = [tex]\frac{AC}{AB}[/tex]

              = [tex]\frac{11\sqrt{3} }{22}[/tex]

              = [tex]\frac{\sqrt{3}}{2}[/tex]

Options (1), (2), (3) and (4) are the correct options.