what is g(x)? (apex algebra 1 semester 2 2019).

[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}-sin(\theta ) \right)~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&3\\ \theta =&\stackrel{radians}{\frac{2\pi }{3}}\\ &\stackrel{degrees}{120} \end{cases} \\\\\\ A=\cfrac{3^2}{2}\left(\cfrac{\pi (120) }{180}-sin(120^o) \right)\implies A=\cfrac{9}{2}\left(\cfrac{2\pi }{3}-\cfrac{\sqrt{3}}{2} \right) \\\\\\ A \approx \cfrac{9}{2}(1.23)\implies A\approx 5.535[/tex]

2 as what he said above

Answer:

[tex]10^{-6}=7[/tex]

Step-by-step explanation:

Remember that according to the laws of logarithms if [tex]log_ay=x[/tex], then [tex]a^x=y[/tex],

In other words to convert a logarithm to an exponential equation we just need to raise the base of the logarithm to the result and equate that to the argument of the logarithm.

Since our logarithm does not have a base, its base is 10; therefore [tex]a=10[/tex]. The argument of our logarithm is 7, so [tex]y=7[/tex]. The result of our logarithm is -6, so [tex]x=-6[/tex].

Replacing values

[tex]log_ay=x[/tex] ⇔ [tex]a^x=y[/tex]

[tex]log_{10}7=-6[/tex] ⇔ [tex]10^{-6}=7[/tex]

By the way [tex]log_{10}7=-6[/tex] is not a true equation since [tex]10^{-6}\neq 7[/tex].

Answer:

D

Step-by-step explanation:

Answer:

D.-$21

Step-by-step explanation:

Answer:

Step-by-step explanation:

7. False.  Opposite angles of a rhombus are congruent, not necessarily supplementary unless it's a square.

8. False.  Parallelograms' consecutive angles must be supplementary.  168 and 22 do not add up to 180.

9. False.  Rhombuses are not the only quadrilateral with perpendicular diagonals.  Kites also have perpendicular diagonals.

10. Area of a regular polygon is:

A = 1/2 aP

where a is the apothem and P is the perimeter.

We're given a = 24.78, but we need to find the side length.

The interior angle of a regular polygon is:

θ = (n - 2) × 180° / n

So a hexagon with 6 sides has an interior angle of:

θ = (6 - 2) × 180° / 6

θ = 120°

If we draw lines from the bottom corner to the center, we get a 30-60-90 triangle.  Therefore:

(s/2) × √3 = 24.78

s/2 = 14.307

s = 28.61

So the perimeter is:

P = 6s

P = 171.68

And the area is:

A = 1/2 aP

A = 1/2 (24.78) (171.68)

A = 2127.13 cm²

11. Area of a regular polygon is:

A = 1/2 aP

where a is the apothem and P is the perimeter.

We're given s = 11, but we need to find the apothem.

The interior angle of a regular polygon is:

θ = (n - 2) × 180° / n

So a polygon with 11 sides has an interior angle of:

θ = (11 - 2) × 180° / 11

θ = 1620/11 °

If we draw lines from the bottom corner to the center, we get a right triangle with a base angle of θ/2.  Therefore:

tan (θ/2) = a / (s/2)

a = s/2 tan(θ/2)

a = 11/2 tan(810/11 °)

a = 18.73

The perimeter is:

P = 11s

P = 121

And the area is:

A = 1/2 aP

A = 1/2 (18.73) (121)

A = 1133.24 in²

Answer:

b=3:25 and b:c=105 3:25/105

Step-by-step explanation:

{3}{25}}{105}={1}{875}=0.00114

{3}{25.105}

{3}{2625}

=1/875

Hope this helps

Answer: Peter had 48 quarters and 11 dimes.

Step-by-step explanation:

Let be "q" the number of quarters and "d" the number of dimes.

We know that $13.10 in cents is 1,310 cents. Then, we can set up the following system of equations:

[tex]\left \{ {{25q+10d=1,310} \atop {q=3d+15}} \right.[/tex]

Applying the Substitution method, we can substitute the second equation into the first one and solve for "d":

[tex]25(3d+15)+10d=1,310\\\\75d+375+10d=1,310\\\\85d=1,310-375\\\\d=\frac{935}{85}\\\\d=11[/tex]

Finally, we must substitute the value of "d" into the second equation to find the value of "q". Then:

[tex]q=3(11)+15\\\\q=33+15\\\\q=48[/tex]

Peter had 48 quarters and 11 dimes

Simultaneous Linear Equations could be solved by using several methods such as :

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

Let :

Number of quarters ( 25 cent coins ) = x

Number of dimes ( 10 cent coins ) = y

When he counted his quarters and dimes, he found they had a total value of $13.10.

The number of quarters was 15 more than 3 times the number of dimes.

If we would like to use the Substitution Method , then second equations above could be substituted into first equations.

0.25x + 0.10y = 13.10

0.25 (15 + 3y) + 0.10y = 13.10

3.75 + 0.75y + 0.10y = 13.10

0.85y = 13.10 - 3.75

0.85y = 9.35

y = 9.35 / 0.85

At last , we could find the value of x by substituting this y value into one of the two equations above :

x = 15 + 3y

x = 15 + 3(11)

x = 15 + 33

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

Answer:

the answer would be 90

Step-by-step explanation:

100 giants fills 5/8 (100/160) of the theater leaving 3/8 of the theater for the elves.

3/8 times 240 elves is 90 elves.

If there were 150 elves that would also be 5/8 filled plus the original 5/8 filled with 100 giants! Some elves might suffer!!!

Answer: x=62

Step-by-step explanation:

A triangle is 180 degrees. When you add 71 and 47, it equals 118. Then subtract 118 from 180 and you are left with 62 degrees.

Hope this helps!

Answer: x = 62°

Remember: the interior angles of a triangle add up to 180°.

47 + 71 = 118

180 - 118 = 62

As we can see on the picture we have a rectangle and half of circle.

The areas for half circle and rectangle are:

[tex]

A_{rectangle}=a\cdot b \\

A_{halfcircle}=\frac{A_{circle}}{2}=\frac{\pi r^2}{2}

[/tex]

The area of the figure is the sum of the area of half circle and rectangle. Also the height of a rectangle (6ft) is a diameter of a half circle therefore the radius of half circle is 6ft ÷ 2 = 3ft.

Now we calculate the areas.

[tex]

A_{rectangle}=10\cdot 6=\underline{60} \\

A_{halfcircle}=\frac{3.14\cdot3^2}{2}=\underline{14.13} \\

A_{total}=A_{rectangle}+A_{halfcircle} =60+14.13=\boxed{74.13\approx74}

[/tex]

The area of the figure is approximately 74ft squared.

Hope this helps.

r3t40

Answer:

B

Step-by-step explanation:

Answer:

(15 km/2 days)(5 days) = 37.5 km/week

(37.5 km/week)(4 weeks) = 150 km

The correct answer is A.

Answer: hey! sorry if very late :(

it's A).

Step-by-step explanation:

d

Answer: The answer to your question is 4 ft

Step-by-step explanation: we know that the formula to find the area of a rectangle is

A=LW

In this problem, we have:

[tex]A= 30 ft^{2}[/tex]

[tex]L= 7.5ft[/tex]

Substitute the values and solve for W

30=7.5W

Divide by 7.5 on both sides

W= 30/ 7.5= 4ft

Answer:

The width of the tablecloth is 4 ft

Answer:

Last option: 4

Step-by-step explanation:

The quadratic equation simplified: [tex]x^2-4x=-\frac{7}{2}[/tex] has the form:

[tex]ax^2+bx=c[/tex]

In this case, you can identify that "a", "b" and "c" are:

[tex]a=1\\b=-4\\c=-\frac{7}{2}[/tex]

To solve this quadratic equation  by completing the square, Carlos should add [tex](\frac{b}{2})^2[/tex] to both sides of the equation. This is:

[tex](\frac{-4}{2})^2=(-2)^2=4[/tex]

Then:

[tex]x^2-4x+4=-\frac{7}{2}+4[/tex]

Therefore you can observe that the number he should add to both sides of the equation is: 4

Answer:

823.7 m²

Step-by-step explanation:

Given the ratio of sides = 5 : 6, then

the ratio of area = 5² : 6² = 25 : 36

let x be the area of the larger prism then by proportion

[tex]\frac{25}{572}[/tex] = [tex]\frac{36}{x}[/tex] ( cross- multiply )

25x = 36 × 572 ( divide both sides by 25 )

x = [tex]\frac{36(572)}{25}[/tex] ≈ 823.7

The surface area of the larger prism is 823.7 ( nearest tenth )

Answer: 823.7

Step-by-step explanation: (5/6)^2, cross multiply with 572/SA, 572*36/25 = 823.68, rounded to the nearest tenth is 823.7

For this case we must find the value of the variable "x" of the following equation:

[tex]5x (4-2) = 20[/tex]

We solve the operation within the parenthesis:

[tex]5x (2) = 20[/tex]

We multiply the left side:

[tex]10x = 20[/tex]

We divide both sides of the equation by 10:

[tex]x = \frac {20} {10}\\x = 2[/tex]

ANswer:

[tex]x = 2[/tex]

The solution of the expression given for x is 2.

Given is an expression 5x(4-2) = 20, we need to solve for x.

To solve the expression 5x(4-2) = 20 step by step, follow these steps:

Simplify the expression inside the parentheses:

5x(4 - 2) = 20

5x(2) = 20

Multiply 5x by 2:

10x = 20

Divide both sides of the equation by 10 to isolate x:

(10x)/10 = 20/10

x = 2

Therefore, the solution for x is 2.

Learn more about expression click;

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Answer:

8 ft and 14 ft

Step-by-step explanation:

Let one diagonal be x then the other diagonal is 2x - 2

The area (A) of the rhombus is calculated using

A = [tex]\frac{1}{2}[/tex] product of the diagonals, that is

A = [tex]\frac{1}{2}[/tex] x(2x - 2) = 56

Multiply both sides by 2

x(2x - 2) = 112 ← distribute left side

2x² - 2x = 112 ( subtract 112 from both sides )

2x² - 2x - 112 = 0 ← in standard form ( divide through by 2 )

x² - x - 56 = 0

To factor the quadratic

Consider the factors of the constant term (- 56) which sum to give the coefficient of the x- term (- 1)

The factors are - 8 and + 7, since

- 8 × 7 = - 56 and - 8 + 7 = - 1, thus

(x - 8)(x + 7) = 0

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x + 7 = 0 ⇒ x = - 7

However, x > 0 ⇒ x = 8

One diagonal = 8 ft and the other = 2x - 2 = (2 × 8) - 2 = 16 - 2 = 14 ft

Answer:

Step-by-step explanation:

We have three pairs of rectangles:

4cm × 5cm

4cm × 7cm

5cm × 7cm

The formula of an area of a rectangle l × w:

A = l × w

l - length

w - width

Substitute:

A₁ = (4)(5) = 20 cm²

A₂ = (4)(7) = 28 cm²

A₃ = (5)(7) = 35 cm²

The Surface Area:

SA = 2A₁ + 2A₂ + 2A₃

Substitute:

SA = 2(20) + 2(28) + 2(35) = 40 + 56 + 70 = 166 cm²

Answer:

A. 1.2 yd

Step-by-step explanation:

We are informed that Mr.Reddrick has a 74 total yards of red and blue felt to distribute to students in his art class. Moreover, we also have the information that each of his 20 students gets 2.5 yards of blue felt for the project. This implies that the total blue felt distributed is;

20*2.5 = 50 yards

The remainder is the total red felt left for distribution;

74 - 50 = 24 yards

Since we have 20 students, each one of them receives;

24/20 = 1.2 yd

Answer:

A 1.2

Step-by-step explanation:

Answer:

The graph is included in the attached pictures

Step-by-step explanation:

The graph for y=4-|x| is shown in the attached picture, the inequality tell us that the region is located below that particular graph including the function, hence you have the second attached picture

Answer:

1249.37

Step-by-step explanation:

7850 = 2 pi r

r = 7850/(2pi) = 1249.37

ANSWER

The radius is approximately 1249 units.

EXPLANATION

The relation between the radius of a circle and its circumference is expressed in the formula:

[tex]C = 2\pi \: r[/tex]

The circumference is given as 7,850 .

This implies that

[tex]7850 = 2\pi \: r[/tex]

[tex]r = \frac{7850}{2 \: \pi} [/tex]

[tex]r = 1249.4[/tex]

to the nearest tenth.

2. First you need to know about the pythagorean theorem which is

a^2 + b^2 = c^2. Look at the first picture below for more reference.

Next you use the pythagorean theorem to find out the right triangle sides to then know the length and width of the rectangle.

a = 8

b = unknown

c = 10

Now use algebraic steps. 8^2 + b^2 = 10^2 --) 64 + b^2 = 100 --) b^2 = 36 --)

b = 6 .

Finally you know the length which is 8 + 8 = 16 and the width which is 6, so the area of the rectangle is 16 x 6 = 96. And to look apporpriate 96in.^2 .

Answer:

In a part-to-whole ratio, one ratio compares a part to a whole.

In mathematics, a fraction is an example of a ratio that compares a part to a whole. Understanding this is crucial for analyzing parts and how they conform to the whole. Another practical illustration of this concept is through a pie graph, which represents the whole and its parts.

In a fraction, one ratio compares a part to a whole. This goes along with a concept in Mathematics where it's useful to take into consideration the parts that contribute to the totality of a whole. An example of this can be seen in numbers. If we look at the relationship between a part and a whole in a ratio, for example, the mass ratio of copper and chlorine in a certain compound, we can gain significant insights.

Another approach is to use a pie graph, which is a graphical representation showing how a whole is divided into parts. The whole circle showcases the entire group, while each slice or part shows the relative size or percentage it contributes to the whole. This visualization makes it easy to understand the relationship between parts and the whole.

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Check the picture below.

so then, let's use the pythagorean theorem to find "x" and "y", and the distance is just x+y.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{9}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ x=\sqrt{9^2+5^2}\implies x=\sqrt{81+25}\implies x=\sqrt{106} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{17}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ y=\sqrt{17^2+5^2}\implies y=\sqrt{289+25}\implies y=\sqrt{314} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{total distance}}{x+y}\implies \sqrt{106}+\sqrt{314}\qquad \approx 10.296+17.72\qquad \approx 28.016[/tex]

Final answer:

To find the distance from Carson's house to Salemburg through Pueblo 'as the crow flies', we use the Pythagorean theorem. Adding together the two legs of a right triangle formed by the given distances and solving for the hypotenuse, we find it is approximately 26.48 miles.

Explanation:

To determine the distance from Carson's house to Salemburg through Pueblo 'as the crow flies', we need to create a diagram and use the Pythagorean theorem. First, we know that Salemburg is 17 miles south of Linbrooke, Linbrooke is 5 miles west of Pueblo, and Carson lives 9 miles north of Linbrooke. Therefore, the distance directly north from Carson's to Pueblo is 9 miles (since he is directly north of Linbrooke), and from Pueblo to Salemburg the direct line would consist of 5 miles west and 17 miles south, which forms a right triangle.

Using the Pythagorean theorem to find the length of the hypotenuse (direct line from Carson's past Pueblo to Salemburg), we have:

Calculate the total distance north-south by adding Carson's 9 miles north to Salemburg's 17 miles south, which gives us 26 miles.

Since we already have the west-east distance as 5 miles, we can set up the equation a^2 + b^2 = c^2, where 'a' is 5 miles, 'b' is 26 miles, and 'c' is the hypotenuse we are looking for.

Plugging in the values gives: 5^2 + 26^2 = c^2, or 25 + 676 = c^2, resulting in c^2 = 701.

Take the square root to find 'c': c ≈ 26.48 miles.

Therefore, the distance from Carson's house to Salemburg 'as the crow flies' passing through Pueblo is approximately 26.48 miles.

Answer:

87380

Step-by-step explanation:

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{16}{4}[/tex] = 4 and a = 4, hence

[tex]S_{8}[/tex] = [tex]\frac{4(4^8-1)}{4-1}[/tex] = [tex]\frac{4(65535)}{4}[/tex] = 87380

Answer:

y = -x + 4

Step-by-step explanation:

Step 1: Use the subtraction property of equality

6y = -6x + 24

Step 2: Use the division property of equality

y = -x + 4

Answer:

y = -x +4

Step-by-step explanation:

6x+6y= 24

Subtract 6x from each side

6x-6x+6y=-6x+ 24

6y = -6x+24

Divide by 6 on each side

6y/6 = -6x/6 +24/6

y = -x +4

This is the area of a triangle

Answer:

Use the formula Area=1/2bh

Step-by-step explanation:

To find the distance of objects sighted at angles of 29 degrees and 59 degrees, use the function d = 93 sec(theta). Substituting theta values, the distances are 106.87 feet and 166.39 feet, respectively.

To find the distance of an object sighted at angles of 29 degrees and 59 degrees, we can use the function given, d = 93 sec(theta). Substituting theta = 29 degrees, we get d = 93 sec(29) = 93*(1/cos(29)) = 93/0.8714 = 106.87 feet. Similarly, substituting theta = 59 degrees, we get d = 93 sec(59) = 93*(1/cos(59)) = 93/0.5588 = 166.39 feet.

Answer:

B. 2340

Step-by-step explanation:

Interior angles of a polygon is given by

(n – 2)180 where n is the number of sides

(15-2) *180

13*180

2340

B. 2340

Step-by-step explanation:

Interior angles of a polygon is given by

(n – 2)180 where n is the number of sides

(15-2) *180

13*180

2340

Answer:

Step-by-step explanation:

b) 1- scale factor from the first map to the second map:

[tex]\frac{8}{6}[/tex]  = 1.33

   2- landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm.

Side lengths of the landmark on the second map

Divide the length by scale factor:

side lengths of 3 mm:  [tex]\frac{3}{1.33}[/tex] = 2.25 mm

side lengths of 4 mm:  [tex]\frac{4}{1.33}[/tex] = 3.007 mm

side lengths of 5 mm:  [tex]\frac{5}{1.33}[/tex] = 3.75 mm

Answer:

A. Being above 180 centimeters and having black hair are independent of each other.

Step-by-step explanation:

These are instinctively two characteristics that are not related and the table data proves it.

If they were dependent, you would have only people with black hair above 180 cm, and all people with black hair would be above 180 cm.

You can be above 180 cm and have black, brown or blonde hair. The table shows a proportion of people > 180 cm about equal (around 30% of the sampling) for each hair color.

And people above 180 cm only represent 30% of the people with black hair.

Option: A is the correct answer.

     A. Being above 180 centimeters and having black hair are independent of each other.

Height :         Less than  175 cm  175-180 cm Above 180 cm     Total

Hair  Color

   Black                    38                        32                  30               100

  Brown                    27                        24                  19                70

  Blonde                    21                        33                  26                80

  Total                    86                89                  75                250

Two events A and B are said to be independent if:

     [tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

else they are dependent.

A)

Being above 180 centimeters and having black hair are independent of each other.

Let A denote Black hair

and B denote above 180 cm.

[tex]P(A)=\dfrac{100}{250}=\dfrac{10}{25}[/tex]

and [tex]P(B)=\dfrac{75}{250}=\dfrac{3}{10}[/tex]

This means that:

 [tex]P(A)\times P(B)=\dfrac{10}{25}\times \dfrac{3}{10}=\dfrac{3}{25}[/tex]

Also,

[tex]P(A\bigcap B)=\dfrac{30}{250}=\dfrac{3}{25}[/tex]

Since,

[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

Hence, events A and events B are independent.

        Hence, option: A is correct.