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2 years ago

Part A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational. (2 points)

1 answer:

7 0

Part A.
7.8 is a rational number between 7.7 and 7.9.
It is rational because it can be written as a fraction of integers, such as 78/10.

Part B.
sqrt(60) = 7.75
sqrt(60) cannot be written as a fraction of integers. It is a decimal number that never ends and never repeats.

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2. Find the value of x in the triangle. Round your answer to the nearest tenth of a degree. Show your work.

yarga [219]

Answer:

$\displaystyle 61,9° ≈ x$

Step-by-step explanation:

We have to determine which trigonometric ratio to use, depending on what is displayed for us, and we will be using the cotangent [or tangent] ratio, however, aside we are solving for an angle measure, we must use the inverse:

$\displaystyle cot^{-1}\: \frac{8}{15} ≈ 61,92751306° ≈ 61,9° \\ \\ OR \\ \\ tan{-1}\: 1\frac{7}{8} ≈ 61,92751306° ≈ 61,9°$

Extended Information on Trigonometric Ratios

$\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ$

I am joyous to assist you anytime.

3 0

2 years ago

A piecewise function f(x) is defined as shown. f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x

vivado [14]

Answer:

(D)The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.

Step-by-step explanation:

The piece-wise function, f(x) is defined as follows:

$f(x)=\left\{\begin{array}{ccc}-\frac{5}{4}x+90 &0\leq x$

$f(0)=-\frac{5}{4}*0+90=90\\\\f(16)=-\frac{5}{4}*16+90=70\\\\f(40)=-\frac{3}{8}*40+75=60\\\\f(120)=-\frac{3}{8}*120+75=30\\\\f(160)=-\frac{3}{8}*160+75=15\\\\f(200)=-\frac{3}{8}*200+75=0$

Therefore, the table which could represent the function is that which satisfies the points above.

In option D

$\left|\begin{array}{c|c}x&f(x)\\--&--\\40&60\\160&15\\200&0\end{array}\right|$

The correct option is D

7 0

2 years ago

Help me plz !! need it plz

liraira [26]

Answer:

5x-15

Step-by-step explanation:

Product means multiply, so that would just make it 5x. Less than means subtract. So its 5x-15.

5 0

2 years ago

Look at this system of equations. 4x+3y=33 2x+3y=21 What is the value of x+y?

Maurinko [17]

Answer:

x = 6

y = 3

x + y = 9

Step-by-step explanation:

(Step 1)

Isolate one of the variables in one of the equations. This will allow you to solve by substitution in the following steps.

2x + 3y = 21 <----- Original equation

3y = -2x + 21 <----- Subtract 2x from both sides

y = (-2/3)x + 7 <----- Divide all terms by 3

(Step 2)

Substitute the new equation into the untouched equation and isolate the "x" variable.

4x + 3y = 33 <----- Original equation

4x + 3((-2/3)x + 7) = 33 <------ Substitute manipulated equation

4x - 2x + 21 = 33 <------ Multiply 3 by terms in parentheses

2x + 21 = 33 <------ Subtract terms with variables

2x = 12 <----- Subtract 21 from both sides

x = 6 <----- Divide both sides by 2

(Step 3)

Plug the value of "x" into one of the equations to find the value of "y".

4x + 3y = 33 <----- Original equation

4(6) + 3y = 33 <----- Plug 6 in for "x"

24 + 3y = 33 <----- Multiply

3y = 9 <----- Subtract 24 from both sides

y = 3 <----- Divide both sides by 3

(Step 4)

Since you now know the value of both variables, you can add them together to find your final answer.

x = 6

y = 3

x + y = ?

6 + 3 = ?

9 = ?

3 0

1 year ago

Please help me Solve for JL

blagie [28]

We have JM=ML due to the relation between sides and angles
Set 3x+4 = 5x-16
=> x= 28/5
Substitute back to the equation ( either one would work be cause they are equal) : 3 ( 28/5) +4 = 20.8
We have JL = JM+ML
=> JL = 20.8+20.8 = 41.6

8 0

1 year ago

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