A sprinkler sprays over a distance of 40 feet and rotates through an angle of 80. Find the area watered by the sprinkler.

Answer:

11

Step-by-step explanation:

In this problem we have the following expression

[tex]a + b^2[/tex]

Note that it depends on two variables a and b

Evaluating the expression for a = 2 and b = 3 means that you must replace the variable "a" with the number 2, and you must replace the variable "b" with the number 3

So we have that:

[tex]a + b^2 = 2 + 3^2[/tex]

[tex]a + b^2 = 2 +9[/tex]

[tex]a + b^2 = 11[/tex]

Finally the answer is 11

The value of the rational expression when x is -2 or -1 is 0 and 3, respectively.

To find the value of the rational expression when x is -2 or -1, we substitute these values into the expression. Plugging in -2, we have (-2)^2 - 4/((-2)+2)((-2)+1) = 0.

Next, plugging in -1, we have (-1)^2 - 4/((-1)+2)((-1)+1) = 3.

Therefore, the value of the rational expression when x is -2 or -1 is 0 and 3, respectively.

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[tex]8 - 4 \frac{2}{5} < 3 \frac{3}{4} \\ 3 \frac{3}{5} < 3 \frac{3}{4} [/tex]

The value of larger and smaller angles are 135 and 45 degrees respectively.

Two angles are supplementary if their sum is 180 degrees.

Since, given that One angle measures three times the measure of a smaller angle.

Let us consider that one angle is 3x and other is x.

                   [tex]3x+x=180\\\\4x=180\\\\x=180/4=45[/tex]

Larger angle is, [tex]3x=3*45=135[/tex]

Smaller angle is, [tex]x=45[/tex]

Learn more about the Supplementary angle here:

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Answer:

1. Number line 2

2. Number line 1

3. Number line 4

4. Number line 3

Step-by-step explanation:

1. x – 99 ≤ -104

Solving by adding +99 on both sides

x - 99 +99 ≤ -104 +99

x ≤ -5

Number line 2 represent x ≤ -5

2. x – 51 ≤ -43

Adding +51 on both sides

x -51 +51  ≤ -43 +51

x ≤ 8

Number line 1 represent x ≤ 8

3. 150 + x ≤ 144

Adding -150 on both sides

150 + x -150 ≤ 144 -150

x ≤ -6

Number line 4 represent x ≤ -6

4. 75 < 69 – x

Adding +x on both sides

75 + x < 69 -x +x

x < 69 -75

x < -6

Number line 3 represent x < -6

The correct matches are:

[tex]\(x - 99 \leq -104\)[/tex] with the number line showing [tex]\(x \leq -5\)[/tex].

[tex]\(x - 51 \leq -43\)[/tex] with the number line showing [tex]\(x \leq 8\)[/tex].

[tex]\(150 + x \leq 14475\)[/tex] with the number line showing [tex]\(x \leq 14325\)[/tex].

[tex]\(69 - x < 14475\)[/tex]  with the number line showing [tex]\(x > -14406\)[/tex].

To solve the given inequalities and match them to their corresponding number lines, we will first solve each inequality algebraically and then represent the solution on a number line.

1. For the inequality [tex]\(x - 99 \leq -104\)[/tex], we add 99 to both sides to isolate \[tex](x\)[/tex]:

[tex]\[x \leq -104 + 99\][/tex]

[tex]\[x \leq -5\][/tex]

This means that all values of [tex]\(x\)[/tex] less than or equal to -5 satisfy the inequality.

2. For the inequality[tex]\(x - 51 \leq -43\)[/tex], we add 51 to both sides:

[tex]\[x \leq -43 + 51\][/tex]

[tex]\[x \leq 8\][/tex]

This means that all values of [tex]\(x\)[/tex] less than or equal to 8 satisfy the inequality.

3. For the inequality [tex]\(150 + x \leq 14475\)[/tex], we subtract 150 from both sides:

[tex]\[x \leq 14475 - 150\][/tex]

[tex]\[x \leq 14325\][/tex]

This means that all values of [tex]\(x\)[/tex] less than or equal to 14325 satisfy the inequality.

4. For the inequality [tex]\(69 - x < 14475\)[/tex], we subtract 69 from both sides and reverse the inequality sign because we are dividing by a negative number (-1):

[tex]\[-x < 14406\][/tex]

[tex]\[x > -14406\][/tex]

This means that all values of [tex]\(x\)[/tex] greater than -14406 satisfy the inequality.

Now, let's represent these solutions on number lines:

- For [tex]\(x \leq -5\)[/tex], the number line will have a closed circle at -5 and shading to the left of -5.

- For [tex]\(x \leq 8\)[/tex], the number line will have a closed circle at 8 and shading to the left of 8.

- For[tex]\(x \leq 14325\)[/tex], the number line will have a closed circle at 14325 and shading to the left of 14325.

- For [tex]\(x > -14406\)[/tex], the number line will have an open circle at -14406 and shading to the right of -14406.

Matching the inequalities to the number lines:

- The inequality [tex]\(x - 99 \leq -104\)[/tex] corresponds to the number line with a closed circle at -5 and shading to the left.

- The inequality [tex]\(x - 51 \leq -43\)[/tex] corresponds to the number line with a closed circle at 8 and shading to the left.

- The inequality [tex]\(150 + x \leq 14475\)[/tex] corresponds to the number line with a closed circle at 14325 and shading to the left.

- The inequality [tex]\(69 - x < 14475\)[/tex] corresponds to the number line with an open circle at -14406 and shading to the right.

Therefore, the correct matches are:

[tex]\(x - 99 \leq -104\)[/tex] with the number line showing [tex]\(x \leq -5\)[/tex].

[tex]\(x - 51 \leq -43\)[/tex] with the number line showing [tex]\(x \leq 8\)[/tex].

[tex]\(150 + x \leq 14475\)[/tex] with the number line showing [tex]\(x \leq 14325\)[/tex].

[tex]\(69 - x < 14475\)[/tex]  with the number line showing [tex]\(x > -14406\)[/tex].

Answer:

One solution; x = -[tex]\frac{6}{7}[/tex]

Step-by-step explanation:

12x + 6 = 5x

12x - 5x = -6

7x = -6

x = -[tex]\frac{6}{7}[/tex]

Answer:

The vertex is: [tex](\frac{3}{2},\ \frac{7}{2})[/tex]

The axis of symmetry is:

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

Step-by-step explanation:

For a quadratic equation of the form:

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

The vertex of the parabola will be the point: [tex](-\frac{b}{2a},\ f(-\frac{b}{2a}))[/tex]

In this case we have the following equation:

[tex]y= -2x^2+6x-1[/tex]

Note that:

[tex]a=-2\\b=6\\c=-1[/tex]

Then the x coordinate of the vertex is:

[tex]x=-\frac{b}{2a}[/tex]

[tex]x=-\frac{6}{2(-2)}[/tex]

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

Then the y coordinate of the vertex is:

[tex]y= -2(\frac{3}{2})^2+6(\frac{3}{2})-1[/tex]

[tex]y=\frac{7}{2}[/tex]

The vertex is: [tex](\frac{3}{2},\ \frac{7}{2})[/tex]

For a quadratic function the axis of symmetry is always a vertical line that passes through the vertex of the function.

Then the axis of symmetry is:

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

Answer:

Step-by-step explanation:89

Given - Length of the Rectangular Plot : 16 meters

Given - Width of the Rectangular Plot : 4 meters

We know that - Area of a Rectangle is given by : Length × Width

[tex]:\implies[/tex]  Area of the Rectangular plot = (16 × 4) m²

[tex]:\implies[/tex]  Area of the Rectangular plot = 64 m²

Given : Square plot and Rectangular plot have same Area

[tex]:\implies[/tex]  Area of Rectangular plot = Area of Square plot

[tex]:\implies[/tex]  Area of Square plot = 64 m²

We know that - Area of Square is given by : Side × Side

[tex]:\implies[/tex]  Side × Side = 64 m²

[tex]:\implies[/tex]  S² = 64 m²

[tex]:\implies[/tex]  S² = 8² m²

[tex]:\implies[/tex]  S = 8 m

Answer : One side of the Square Garden plot is 8 meter

Answer:

Side of the square plot = 8 m

Step-by-step explanation:

l = 16 m

b = 4 m

Area of the rectangular plot = l * b

                                                 = 16 * 4 = 64 m²

Area of square plot = Area of rectangular plot

          side  *  side    = 64 m²

                    side       =  √64 = 8 m

Answer:

the answer should be 1

Step-by-step explanation:

4[(-3+z)2-2(-3+z)]+1

4(-6+2z+6-2z)+1

-24+8z+24-8z+1

the 24's and 8's cancel out leaving 1

To find g(h(-3+z)), we first find h(-3+z) by substituting -3+z into h(a), it becomes z^2-8z+15. Then, substitute this into g(a) to get g(h(-3+z)), which results in 4z^2-32z+61.

In the field of Mathematics, to solve the problem g(h(-3+z)), we need to substitute h into g. It means that every 'a' in g(a) will be replaced by what h(-3+z) is equal to. To find h(-3+z), we substitute -3+z into h(a) in place of a. Therefore, h(-3+z) equals to (-3+z)^2-2(-3+z). After simplifying, it becomes z^2-6z+9+6-2z=z^2-8z+15. Next, we substitute this into g(a) to get g(h(-3+z))=4[z^2-8z+15]+1=4z^2-32z+61. Hence, the solution to the problem g(h(-3+z)) is 4z^2-32z+61.

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Answer:

The last choice.

Step-by-step explanation:

That would be the last one, with a minimum value of -4.

Answer:

IV graph

Step-by-step explanation:

Given is a picture consisting of 4 parabolas with first 3 open up and last one open down.

We are to find the minimum value vertex

Seeing the graph we can write coordinates of vertex as where they turn their direction.

Hence vertices are

Graph           Vertices        y value

I                      (0,5)               5

II                     (0,0)               0

III                    (1,2.5)             2.5

IV                   (0,-4)              -4

Of the 4 y values, IV graph has the minimum value vertex

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

3 times the square root of 2 +2 times the square root of 3 =3sqrt2+2sqrt3

We need to simplify the above expression.

In addition and subtraction, there is a rule of adding or subtracting of like terms is possible only.

But, here, √2 ad √3 are unlike term.

so, we cannot simplified it.

Hence, Option 'D' is correct.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

Step-by-step explanation:

3√2 + 2√3 is as simple an expression as you'll get for this quantity.

Final answer:

To solve probability questions, you need to understand the basic concepts and formulas.

Explanation:

To solve probability questions, you need to understand the basic concepts and formulas.

Answer:

2 sets of possible solutions:

x=3, y = 5

and

x=-1, y = -3

Step-by-step explanation:

Using the graphical method, (see attached)

you can graph both equations and find their intersection points.

From the attached plot, you can see that the graphs intersect at (3,5) and (-1,-3)

Alternatively, you can solve this numerically by solving the following system of equations. You will get the same answer.

y = 2x + 1 ------------------- eq. (1)

y = x² - 4 ------------------- eq. (2)

Answer:

D   sin 85         sin 31

    ---------- =     ----------

      b                  9.3

Step-by-step explanation:

We can use the law of sins

sin B        sin A         sin C

---------- = ----------- = ----------

b                   a            c

We do not know angle C, but we can calculate it

The angles of a triangle add to 180

A + B + C = 180

64+ 85 + C = 180

149 + C = 180

C = 180-149

C =31

sin B         sin C

---------- = ----------

b                  c

We know B =  85, C = 31, b = unknown and c = 9.3

sin 85         sin 31

---------- = ----------

b                  9.3

the correct answer would be D

The third angle would have to be either an obtuse angle or a right angle.

The third angle can either be an acute angle or obtuse angle

The sum of an interior angle of a triangle is 180 degrees

Acute angles are angles that are less than 90 degrees. If the two angles of a triangle are acute, the two angles can be 30 and 45 degrees

If the third angle is m<C

m<C = 180 - (30 + 45)

m<C = 180  - 75

m<C = 105 degrees

Since the angle is greater than 90 and less than 180, hence it is an Obtuse angle.

Similarly, if the two angles of a triangle are acute, the two angles can be 30 and 89 degrees

If the third angle is m<D

m<D = 180 - (30 + 90)

m<D = 180  - 119

m<D = 61 degrees

Since the angle is less than 90degrees, hence it is an acute angle.

This shows that the third angle can either be an acute angle or obtuse angle

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[tex]x(x-3)=x\\x^2-3x-x=0\\x^2-4x=0\\x(x-4)=0\\x=0\vee x=4[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{In order for you can do the distributive property then work from there}[/tex]

[tex]\text{x(x - 4) = x}\\\\\text{x(x)=x}^2\\\\\text{x(-3)= -3x}[/tex]

[tex]\text{Subtract by the value of x on your sides!}[/tex]

[tex]\text{Your new equation becomes: x}^2\text{- 3x = x}[/tex]

[tex]\text{Like}\downarrow[/tex]

[tex]\text{x}^2\text{- 3x - x = x - x}[/tex]

[tex]\text{x - x = 0 }[/tex]

[tex]\text{-3x + (-1x) = -4x}[/tex]

[tex]\text{Our equation becomes: x}^2\text{- 4x = 0}[/tex]

[tex]\text{Next, we have to FACTOR on the LEFT side of your equation}[/tex]

[tex]\text{x(x - 4) = 0}[/tex]

[tex]\text{Set the numbers to FACTOR out to 0}[/tex]

[tex]\text{Like: x = 0 or x - 4 = 0}\text{ (solve that and you SHOULD have the x-values)}[/tex]

[tex]\boxed{\boxed{\bf{Answer: x = 0\ or \ x =4}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirt:)}[/tex]

Answer:

reciprocals

Step-by-step explanation:

Let's actually find the slopes.  Then we can better compare them.

8x - 9y = 5 → - 9y = 5 - 8x → slope is m = (-8) / (-9), or 8/9.

9x - 8y = 1  →  - 8y = 1 - 9x  → slope is (-9) / (-8), or 9/8

These two slopes are reciprocals (but not negative reciprocals).

Answer:

reciprocals, but not negative reciprocals

Step-by-step explanation:

8x - 9y = 5

9y = 8x - 5

y = 8/9x - 5/9

m1 = 8/9

9x - 8y = 1

8y = 9x - 1

y = 9/8x - 1/8

m2 = 9/8

Answer:

x^3(2x+1)(2x-1)

Step-by-step explanation:

first take common then use formula of a^2-b^2

Answer:

The factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]16x^5-x^3[/tex]

Here the Greatest common factor in the above expression is x³.

The above expression can be written as:

[tex]x^3(16x^2-1)[/tex]

[tex]x^3((4x)^2-1^2)[/tex]

Now use the difference of the square property: [tex]a^2-b^2=(a+b)(a-b)[/tex]

By using the above property we can rewrite the provided expression as shown:

[tex]x^3(4x-1)(4x+1)[/tex]

Hence, the factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]

Answer:

D:Spring A is 3 m longer than spring B because 15 – 12 = 3.

Step-by-step explanation:

In this question, you should remember the Hooke's Law in physics.

The Hooke's Law simply explains that the extension that occurs on a spring is directly proportional to the load applied on it.

The mathematical expression for this law is

[tex]F=-kx[/tex]

where;

F= force applied on the spring

x = the extension on the spring

k= the spring constant which varies in spring.

The question will need you to calculate the extension on the springs A and B then compare the values obtained.

In spring A

Force, F=60N and spring constant ,k=4 N/m

To find the extension x apply the expression;

[tex]F=-kx\\\\60=-4*x\\\\60=-4x\\\\\frac{60}{-4} =\frac{-4x}{-4} \\\\\\-15=x[/tex]

Here the spring extension is 15 m

In spring B

Force, F=60N and spring constant , k=5N/m

To find the extension x apply the same expression

[tex]F=-kx\\\\60=-5*x\\\\60=-5x\\\\\\\frac{60}{-5} =\frac{-5x}{-5} \\\\\\-12=x[/tex]

Here the extension on the spring is 12 m

Compare

The extension on spring A is 3 m longer than that in spring B because when you subtract the value of spring B from that in spring A you get 3m

[tex]=15m-12m=3m[/tex]

Answer:

D)Spring A is 3 m longer than spring B because 15 – 12 = 3.

trust

Answer:

Option C is correct.

Step-by-step explanation:

Slope of line JK

J (1,-6) K (0,4)

slope of JK = y₂ - y₁ / x₂ - x₁

Slope of JK = 4-1/0-(-6) = 3/6 = 1/2

so slope of JK = 1/2

Slope of line LM

L (-5,-3) and M(0,3)

slope of LM = y₂ - y₁ / x₂ - x₁

slope of LM = 3-(-5)/0-(-3) = 3+5/3 = 8/3

Slope of line NO

N(-6,-5) and 0 (0,0)

slope of NO = y₂ - y₁ / x₂ - x₁

slope of NO = 0-(-6)/0-(-5) = 6/5

So, slope of line NO = 6/5

Slope of PQ

P(-5,4) Q(0,-2)

slope of PQ = y₂ - y₁ / x₂ - x₁

slope of PQ = -2-4/0-(-5) = -2/5

so slope of line PQ = -2/5

the two lines are perpendicular if slope of one line is m then slope of other line is -1/m

The slope of given line =m= -5/6

The slope of line perpendicular to the given line = -1/m = 6/5

So, line NO is perpendicular to the given line as its slope is 6/5

Option C is correct.

Answer:

A. 3,1,1/3,1/9,1/27 because you are multiplying by 1/3 every time to get new term.

C. 1,6,36,216,1296 because you are multiplying by 6 every time to get new term.

The other sequences you are not multiplying repeatedly to get new terms..

Step-by-step explanation:

The sequence is geometric sequence is 3, 1, 1/3, 1/9, and 1/27.

The sequence is a geometric sequence that is 1, 6, 36, 216, 1, 296.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

If the common ratio between the two successive terms must be constant. Then the sequence is called a geometric sequence.

The sequences are given below;

3, 1, 1/3, 1/9, 1/27

The common ratio between the terms are;

[tex]\rm \dfrac{a_2}{a_1}=\dfrac{1}{3}\\\\\dfrac{a_3}{a_2}=\dfrac{\dfrac{1}{3}}{1}= \dfrac{1}{3} \times \dfrac{1}{1}=\dfrac{1}{3}\\\\\dfrac{a_4}{a_3}=\dfrac{\dfrac{1}{9}}{\dfrac{1}{3}}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

The sequence is a geometric sequence.

The sequences are given below;

1, 6, 36, 216, 1, 296.

The common ratio between the terms are;

[tex]\rm \dfrac{a_2}{a_1}=\dfrac{6}{1}=6\\\\\dfrac{a_3}{a_2}=\dfrac{36}{6}=6\\\\ \dfrac{a_4}{a_3}=\dfrac{216}{36}=6\\[/tex]

The sequence is a geometric sequence.

More about the sequence link is given below.

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Answer:

42

Step-by-step explanation:

This means 0.84 divided by 0.02

which equals to 42

the points mean that there is a zero

if a number has been written in that format of  "point" then "number" without any number before the point, it means there is  a zero there

if you need anything else clarified please do so in the comment section i would like to help more

           Hope this helps and if it does mark as branliest answer thx

Answer:

C - AC equals AD times AB over AE

Step-by-step explanation:

If Hiro is creating a larger scaled replica of a triangular canvas, then Hiro will get two similar triangles ABE (the small one) and ACD (the large one). Similar triangles have proportional corresponding sides, so

[tex]\dfrac{AC}{AB}=\dfrac{AD}{AE}[/tex]

From this proportion:

[tex]AC=\dfrac{AD\cdot AB}{AE}[/tex]

So, option C (AC equals AD times AB over AE) is correct option

Answer:

3. B. 128

4. B. 50.24

Step-by-step explanation:

3. The Books

The numbers of the problem make it quite easy.

We can easily figure out how many books will be stacked in each dimension of the trunk.

Length:

Books: 10 inches

Trunk: 40 iinches.

How may books can you fit lengthwise in the trunk?  40 / 10 = 4

We then to the same for the width:

Books: 6 inches

Trunk: 24 inches

How many books can you stack wide-wise in the trunk?  26/4 = 4

And then the height:

Books: 2.5 inches

Trunk: 20 inches

How many books stacked in height? 20 / 2.5 = 8

So, we can saw the trunk is 4 books long, by 4 books wide by 8 books thick... so, the number of books you can fit in that trunk is:

B = 4 * 4 * 8 = 128

4. Tomato juice

First, we have to find the volume of that big can...

Since it's a cylinder, its volume is calculated by:

V = π * r² * h and we have everything we need:

V = 3.14 * 4² * 12 = 192 * 3.14 = 602.88 cu in

We know a cup of tomato juice takes 12 cu inches...

So, how many cups of juice fit in that can?

C = 602.88 cu in / 12 cu in/cup = 50.24 cups

Answer:

10

Step-by-step explanation:

f(x) = 3x + 1

f(3)= 3 * 3 + 1 + 10

Answer:h= [tex]\frac{(p/0.7-b)}{r}[/tex]

Step-by-step explanation:

1) p/0.7=rh+b

2) (p/0.7)-b=rh

3) [tex]\frac{(p/0.7-b)}{r}[/tex] =h

h= [tex]\frac{(p/0.7-b)}{r}[/tex]

The equivalent equation for isolated variable h = [tex]\frac{p-0.7b}{r}[/tex] obtained from the equation p = 0.7(rh + b).

Isolating a variable is the re-arrangement of the equation for the required variable. Even though rewriting the terms, doesn't affect the logic of the equation. It forms an equivalent equation.

The given equation is p = 0.7(rh + b)

Where,

p - home pay

h - working hours

r - the rate of dollars per hour

b - bonus received

Re-writing the equation for the variable h:

p = 0.7(rh + b)

⇒ p/0.7 = rh + b

⇒ p/0.7 - b = rh

⇒ h = p/0.7r -b/r

∴ h = [tex]\frac{p-0.7b}{r}[/tex]

Therefore, variable h is isolated and obtained an equivalent equation.

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Answer:

function

Step-by-step explanation:

hoped this helped;)

Answer:

Step-by-step explanation:

Not a function.  The number of people has little direct connection with the total number of watches owned.

Answer:

your answer would be just x

Step-by-step explanation:

you just subtract the exponents

The expression x^-8/x^-7 simplifies to 1/x. This is due to the rule for dividing exponential expressions with the same base, which involves subtracting the exponents.

To solve x^-8/x^-7, we need to understand the rule for division of expressions with exponents which is: x^a / x^b  = x^(a-b).

When you divide exponential expressions with the same base, you subtract the exponents.

In our case, x^-8 / x^-7 = x^(-8 - -7). This simplifies to x^-1 or x^-1 = 1/x. So, the result is 1/x.

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