Solve and choose the correct graph

Answer:

A. 122

Step-by-step explanation:

in right-angle triangle,

AB² + AC² = BC²

22²+120² = BC²

2²×11² + 2⁶×5²×3²= 2²(121+16×25×9)

4(121+3600) = 14884

BC=√14884 = 122

Answer:

independent variable/ variables

Step-by-step explanation:

100

Step-by-step explanation:

So, you are essentailly finding the mean (the average of a set of numbers).

1. Add up all the numbers (should get 400)

2. Divide by the amount of numbers presented in the set. (Here there are 4)

3. Solve :  400/4 = 100

Answer: The amount budgeted for Auto Expenses is $18,200

Step-by-step explanation:

13 Percent of $140,000 is $18,200

0.13 times 140,000 :-)

The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

Based on the statement we construct the geometric diagram, by definition of tangent we have expressions for the initial and final angles ([tex]\theta_{1}[/tex], [tex]\theta_{2}[/tex]), in radians, of the figure:

Initial triangle

[tex]\tan \theta_{1} = \frac{y_{1}}{x_{1}}[/tex] (1)

Final triangle

[tex]\tan \theta_{2} = \frac{y_{2}}{x_{2}}[/tex] (2)

By using (2), the equivalence [tex]\theta_{2} = \theta_{1}+\Delta \theta[/tex] and trigonometric identities we have the following expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\tan \theta_{1}+\tan \theta_{2}}{1-\tan \theta_{1}\cdot \tan \theta_{2}}[/tex] (3)

By (1), we simplify the expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}} + \tan \Delta \theta}{1-\frac{y_{1}}{x_{1}}\cdot \tan \Delta \theta}[/tex] (3b)

If [tex]0 \le \Delta \theta \le \frac{\pi}{6}[/tex], then we can use the following approximation:

[tex]\tan \Delta\theta \approx \Delta \theta[/tex] (4)

Then, we reduce (3b) into an entirely algebraic expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}}+\Delta \theta }{1-\frac{y_{1}}{x_{1}}\cdot \Delta \theta }[/tex] (3c)

Where [tex]y_{2} = \sqrt{r^{2}-x_{2}^{2}}[/tex].

Now we clear [tex]\Delta \theta[/tex] within the formula:

[tex]\Delta \theta = \frac{\frac{y_{2}}{x_{2}}-\frac{y_{1}}{x_{1}}}{\frac{y_{1}}{x_{1}}\cdot \left(1+\frac{y_{2}}{x_{2}} \right) }[/tex]  (5)

If we know that [tex]x_{1} = y_{1} = 0.5[/tex], [tex]r = 0.707[/tex] and [tex]x_{2} = 0.45[/tex], then we estimate the angle change:

[tex]y_{2} = \sqrt{0.707^{2}-0.45^{2}}[/tex]

[tex]y_{2} \approx 0.545[/tex]

[tex]\Delta \theta = \frac{\frac{0.545}{0.45}-1 }{1\cdot \left(1+\frac{0.545}{0.45} \right)}[/tex]

[tex]\Delta \theta = 0.095[/tex]

As [tex]\Delta \theta < \frac{\pi}{6}[/tex], then the result seems to be reasonable. The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845

Answer:

Girls are   4/5 of the students.

Step-by-step explanation:

boys + girls = 100% of students.

If 20% of the students are boys then 80% are girls

80% = 80/100 =  4/5

Answer:

1,000

Step-by-step explanation:

10 x 10 x 10 = 1,000

1000

Step-by-step explanation:

10³

=10×10×10

1000

Answer:

3,168 cal= 2lbs of Ice Cream

Step-by-step explanation:

I need to fin how many calories are in two pounds of that ceratin ice cream.

594cal/6=99cal

99cal=1 oz

16oz x 2 = 32oz

99 x 32 = 3,168 cal

There is 3,168 cal in two pounds of ceratin ice cream.

Answer:

3.525 gal/person

Step-by-step explanation:

My class would consume 52.875 gallons

Answer:

B) 5,900 pounds

Step-by-step explanation:

1,900 pounds + 2 tons = 5,900

Step-by-step explanation:

10y - 3(y + 2) > 2y + 4

10y - 3y - 6 > 2y + 4

(10 - 3 - 2)y > 4 + 6

5y > 10

y > 10/5

y > 2

[tex] \: [/tex]

Solution → y > 2

Interval Notation → [tex] \lang 2 , \infty\rang[/tex]

The solution in interval notation is: (2, ∞)

To solve the inequality 10y - 3(y + 2) > 2y + 4, follow these steps:

Step 1: Distribute the -3 on the left side of the inequality:

10y - 3y - 6 > 2y + 4

Step 2: Combine like terms:

(10y - 3y) - 6 > 2y + 4

7y - 6 > 2y + 4

Step 3: Get all the y terms on one side by subtracting 2y from both sides of the inequality:

7y - 2y - 6 > 2y - 2y + 4

5y - 6 > 4

Step 4: Get the constant term on the other side by adding 6 to both sides of the inequality:

5y - 6 + 6 > 4 + 6

5y > 10

Step 5: Finally, solve for y by dividing both sides by 5:

y > 10/5

y > 2

The solution to the inequality is y > 2. Now, let's write it in interval notation.

To know more about interval:

https://brainly.com/question/29126055

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Answer:

[tex]f(-9)=\frac{131}{2}[/tex]

Step-by-step explanation:

In order to evaluate a function at a given x-value, plug in that value into the actual function

[tex]f(x)=-\frac{x}{2} -7x-2\\\\f(-9)=-\frac{9}{2} -7(-9)-2\\\\f(-9) = \frac{131}{2}[/tex]

Answer:

35

Step-by-step explanation:

Hope it helps.

Do comment if you have any query.

Answer:

-17 degrees F

Step-by-step explanation:

Assuming that the temperature in the chart is the temperature before noon, all we need to do to find the temperature at noon is to add 16 degrees Fahrenheit to the table value (since "risen by 16 degrees F" means to increase by 16 degrees, aka to add 16 degrees).

So,

-33 + 16 = -17

Answer:

I would assume it is c. 1, because of rounding, but I'm only 70% sure.

Answer:

x>2

Step-by-step explanation:

1) 6x+3 > 15

2) 6x > 15-3

3) 6x > 12

4) x > 12÷6

5) x > 2

Answer:

k=0.023

Step-by-step explanation:

[tex]r \alpha {t }^{2} \\ r = k {t}^{2} \\ 144 = k \times {72 }^{2} \\ k = \frac{144}{ {72 }^{2} } \\ k = 0.023 \\ the \: eqn \: is \: therefore \\ r = 0.023 \times {t}^{2} [/tex]

The equation that expresses the relationship between the variables is r=kt and the variation constant k=2.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Given that, the variable r is directly proportional to the square of t

Now, r∝t

r=kt

Here, r =144 when t =72

Thus, 144=k×72

k=2

Therefore, the equation that expresses the relationship between the variables is r=kt and the variation constant k=2.

To learn more about the proportional relationship visit:

brainly.com/question/12917806.

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Answer:

1/8

Step-by-step explanation:

9514 1404 393

Answer:

  $1.50 per pint

Step-by-step explanation:

1 pint = 2 cups, so the cost of it is ...

  x/(2 cups) = $12/(16 cups)

  x = (2)($12/16) = $1.50 . . . . . . multiply by 2 cups

The price per pint is $1.50.

Answer:

35%

Step-by-step explanation:

100% - 65% = 35%

Hope this helps!

Answer:

35%

Step-by-step explanation:

65% of 40 is 29.25

40-29.25=15.75

15.75 over 45 × 100 = 0.35

0.35 is also written as 35%

This is just a longer method if it requires more steps:)

Answer:

Ans: 1/-2 , -1/3 , 3/10 , 3/4

Step-by-step explanation:

The LCM of 2, 3, 4 and 10 is 60.

Let's make denominator equal,

→ 3/4 , -1/3 , 1/-2 , 3/10

→ 3×15/4×15 , -1×20/3×20 , -1×30/2×30 , 3×6/10×6

→ 45/60 , -20/60 , -30/60 , 18/60

Now we can order in ascending,

→ -30/60 , -20/60 , 18/60 , 45/60

→ 1/-2 , -1/3 , 3/10 , 3/4 {final answer}

9514 1404 393

Answer:

  4.82 m

Step-by-step explanation:

The mirror reflects light at the same angle the light hits it, so the triangles formed by the line of sight, the ground, and the objects involved are similar. This means corresponding lengths are proportional.

  height/mirror distance = T/12.15 = 1.35/3.4

Multiplying by 12.15, we find the top of the goalpost to have a height of ...

  T = 12.15(1.35/3.4) ≈ 4.82 . . . meters

The goalpost is about 4.82 meters high.

Answer:

1.5 songs/minutes

Step-by-step explanation:

30÷20 = 1.5

Step-by-step explanation:

100% = 730

1% = 100%/100 = 730/100 = 7.3

30% = 1% × 30 = 7.3 × 30 = 219

so, they finished 219 of their 730 orders.

that leaves 730 - 219 = 511 orders still to be finished.