If f(x)=⎧⎩⎨⎪⎪2x−3x2x+5ifififx≤−4−4
?


A. 25

B. 7

C. -4

D. 10

Answer:

1,200

Step-by-step explanation:

The formula is Length x Width x Height so it will be 20 x 5 x 12 and you get 1,200.

Hope this helps!

The linear inequalities in the given graph  is y ≥ x/2 -1 and  y< -1/2x -3.

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.

Here, we have,

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.

we have,

In the given graph, the area above solid line,

points, (-2 , -2) , (0 , -1)

slope = 1/2

so,  y ≥ x/2 -1

The area below dashed line ,

points, (-2 ,-2) , (0 ,-3)

slope= -1/2

so, y< -1/2x -3.

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The image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).

To rotate a point counterclockwise about the origin, we can use the following formulas:

(x', y') = (y,-x)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the rotated point

In this case, we want to rotate the point (-1, 2) by 270° counterclockwise about the origin.

So, we have

(x', y') = (2,1)

Therefore, the image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).

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The bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.

Since the ship travels at a constant speed, we can use the formula:

distance = speed × time

For the first hour, the ship travels at a bearing of S80°E, which is equivalent to a bearing of N10°E. Therefore, the ship travels 15 nautical miles in a direction N10°E. This gives us:

PA = distance = speed × time = 15 × 1 = 15 nautical miles

After the first hour, the ship turns 90° towards the North. This means that the ship is now heading due East. Therefore, for the next 2 hours, the ship travels 15 × 2 = 30 nautical miles in an easterly direction. This gives us:

AB = distance = speed × time = 15 × 2 = 30 nautical miles

Now, we can use the Pythagorean theorem to find the value of y:

y² = x² + (AB)²

y² = 15² + 30²

y² = 225 + 900

y² = 1125

y ≈ 33.54 nautical miles

To find the bearing of B from P, we can use trigonometry. The bearing is the angle between the line PA and due North. Let θ be this angle. Then we have:

tan(θ) = x / y

θ = tan^-1(x / y)

Using the values we have found, we get:

tan(θ) = 15 / 33.54

θ ≈ 24.65°

Therefore, the bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.

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Answer:

8. mArc ED = 38°

9. mArc EA = 142°

10.mArc BDC = 308°

Step-by-step explanation:

The measure of an a central angle and it's intercepted arc are equal

So if the measure of the angle for the angle that intercepts Arc ED is 38° the arc is also 38°

Same thing with Arc EA, the central angle that intercepts it is 142° so the measure of Arc EA is 142°

Arc BDC is a major arc so it is greater than 180°. It goes around the circle from point B to point C and point D is one of the points on the arc.

We could find the value of the arc two ways. We could add all the angles  the that make up the central angle it is intercept by or we could simply subtract the 52° that isn'tt a part of the arc and subtract that from 360°

360 - 52 = 308

So the central angle intercepting Arc BDC is 308° so the arc also has a measure of 308°.

Answer:

38 inches

Step-by-step explanation:

We can use the Law of Sines to solve for the length of side g:

sin(66°)/67 = sin(30°)/g

Cross-multiplying, we get:

g*sin(66°) = 67*sin(30°)

Dividing both sides by sin(66°), we get:

g = 67*sin(30°)/sin(66°) ≈ 38 inches (rounded to the nearest inch)

Therefore, the length of side g is approximately 38 inches.

The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.

Linear function: y = 3x + 1

x y

3 10

5 16

7 22

9 28

The linear function is positive, which means that the airplane's altitude is increasing as it moves towards the right on the graph. In context, this means that the airplane is ascending as it moves away from the observer towards the rainbow.

The system of equations created by the two functions is:

y = -x^2 + 19

y = 3x + 1

By substituting y in the second equation with the first equation, we get:

-x^2 + 19 = 3x + 1

Solving for x, we get:

x = -2 or x = 5

Substituting these values of x back into either of the equations, we get the corresponding values of y:

(-2, 7) and (5, 16)

These two solutions represent the points of intersection between the rainbow and the airplane's trajectory.

The domain of the rainbow is all real numbers, while the range is y ≤ 19. In context, this means that the rainbow can appear at any point in the observer's field of view, but its highest point is at y = 19.

All of the values in the domain and range make sense in this situation since they are within the physical limits of the observer's perception.

The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.

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The estimated value of the expression [tex]6/5/8 - 2/3/8[/tex] is approximately [tex]0.5082[/tex].

In Mathematics, fractions are defined as the parts of a whole. The whole can be an object or a group of objects

To estimate 6/5/8 - 2/3/8, we can convert the fractions to decimals and then perform the subtraction.

6/5/8 is equivalent to 6 ÷ 5.8, which is approximately 1.0345. 2/3/8 is equivalent to 2 ÷ 3.8, which is approximately 0.5263.

Therefore, 6/5/8 - 2/3/8 is approximately 1.0345 - 0.5263 = 0.5082.

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Answer:

64π

Step-by-step explanation:

Use the formula for an area of a circle
[tex]A = \pi r^2[/tex]
Half of 16 is 8.
8*8 = 64.

The area of a circle with a diameter of 16 meters is equal to 64π or 200.96 square meters.

Mathematically, the area of a circle can be calculated by using this formula:

[tex]\text{Area} = \pi \text{r}^2[/tex]

Where:

[tex]\text{r}[/tex] represents the radius of a circle.

[tex]\text{Note:} \ \text{Radius} = \dfrac{\text{diameter}}{2} = \dfrac{16}{2} = 8 \ \text{meters}.[/tex]

By substituting the radius into the formula for the area of a circle, we have the following;

[tex]\text{Area of circle} = \pi \times 8^2[/tex]

[tex]\bold{Area} \ \text{of circle} = 64\pi \ \text{or} \ 200.96[/tex] square meters.

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Answer: 2

Step-by-step explanation:

Answer: 195 adult tickets and 262 children tickets

Step-by-step explanation:

     Let a be adult tickets and c be children tickets.

We know there are 457 seats.

     a + c = 457

We also know the cost of the tickets and how much money was made.

     $54a + $17c = $14,984

Now, we have a system of equations we can use to solve.

     a + c = 457

     $54a + $17c = $14,984

Lastly, we will graph this system, see attached. The point of intersection, or where the lines intersect, is our answer.

     195 adult tickets and 262 children tickets.

Answer:

Chidden tickets were 262 and adult tickets were 195 tickets

Step-by-step explanation:

Let x = the number of children tickets

Let y = the number of adult tickets.

x + y = 457

17x + 54y = 14984

Use substitution

x + y = 457 Solve for y

y = 457 -x  Substitute 457 -x for y in the equation 17x + 54y = 14984

17x + 54y = 14984

17x + 54(457 -x) = 14984  Solve for x  Distributer the 54

17x + 24678 - 54x = 14984  Combine like terms

-37x = -9694   Divide both sides by -37

x = 262

The number of children tickets.

x + y = 457  Substitute 262 for x and solve for y

262 + y = 457  Subtract 262 from both sides

y = 195

The number of adult tickets.

Helping in the name of Jesus.

Answer: there is no solution

Step-by-step explanation:

The solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.

The general form of the quadratic equation is: ax² + bx + c = 0

Given that, a quadratic equation (x-5)² + 3(x-5) + 9 = 0, we need to solve it,

So, put x-5 = u

Therefore,

u² + 3u + 9 = 0

Solving using quadratic formula,

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}} {2a}[/tex]

Here a = 1, b = 3 and c = 9

Therefore,

[tex]u=\frac{-3 \pm \sqrt{3^2-4(9)}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{9-36}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{-27}} {2}[/tex]

[tex]u=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

Put u = x-5,

Therefore,

[tex]x-5=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

[tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Hence, the solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

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According to the information, the horizontal distance traveled by the ball is 443.404 feet.

We can use the kinematic equations of motion to solve for the hang time, maximum height, and horizontal distance traveled by the golf ball.

First, we need to resolve the initial velocity vector into its horizontal and vertical components. The vertical component will determine the maximum height and hang time, while the horizontal component will determine the horizontal distance traveled.

The initial velocity can be represented as:

where v0 is the initial velocity, theta is the angle of elevation, v0x is the horizontal component of the initial velocity, and v0y is the vertical component of the initial velocity.

Now we can use the kinematic equations to solve for the hang time, maximum height, and horizontal distance traveled.

Hang time (time in air):

We can use the vertical motion equation to solve for the time when the ball reaches its maximum height:

Since the ball will be in the air for twice the time it takes to reach its maximum height, the hang time is:

Maximum height:

We can use the vertical motion equation to solve for the maximum height reached by the ball:

Therefore, the maximum height of the ball is 64 feet.

Horizontal distance traveled:

We can use the horizontal motion equation to solve for the horizontal distance traveled by the ball:

x = v0x t

x = 110.851(4)

x = 443.404 ft

Therefore, the horizontal distance traveled by the ball is 443.404 feet.

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Answer:

x = 360°/8 = 45°

y = 2 × 45° = 90°

Answer:

$526.25, and your total monthly expense (including rent and maintenance fee) is $2,326.25.

Step-by-step explanation:

To calculate your average monthly expense, we need to first add up all of your annual expenses and divide by 12 (the number of months in a year) to find the monthly average.

Annual expenses:

Insurance: $325

Lost interest: $50

Utility bills: $5,940

Total annual expenses = $325 + $50 + $5,940 = $6,315

To find the average monthly expense, we divide the total annual expenses by 12:

Average monthly expense = Total annual expenses / 12

Average monthly expense = $6,315 / 12

Average monthly expense = $526.25

In addition to the annual expenses, you also pay a monthly rent of $1,700 and a monthly fee for all maintenance. Let's assume that the monthly maintenance fee is $100.

Therefore, your total monthly expense would be:

Total monthly expense = Monthly rent + Monthly maintenance fee + Average monthly expenses

Total monthly expense = $1,700 + $100 + $526.25

Total monthly expense = $2,326.25

So, your average monthly expense is $526.25, and your total monthly expense (including rent and maintenance fee) is $2,326.25.

The period of the sinusoidal equation of the graph is 4 months.

The amplitude of the sinusoidal equation of the graph is 84 degrees Celsius.

The period and amplitude are two important characteristics of a wave.

Period: The period of a wave is the time it takes for one complete cycle of the wave to occur. The period of a wave determines its frequency, which is defined as the reciprocal of the period.

Amplitude: The amplitude of a wave is the maximum displacement of the wave from its equilibrium position. In simpler terms, it represents the height or strength of the wave.

In then given graph, the period of the wave = 1 complete cycle in 4 months = 4 months/cycle = 4 months

Amplitude = 84 degrees Celsius.

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Answer:

$525

Step-by-step explanation:

To calculate the sales commission for this employee, we need to first calculate the total sales made by the employee for the week. The employee made sales of 800 on Monday, 600 on Tuesday, 1300 on Wednesday, 800 on Thursday and 800 on Friday. The total sales made by the employee for the week is:

800 + 600 + 1300 + 800 + 800 = 4500

Since the employee does not earn sales commission for the first $1000 of sales but earns a 15% sales commission on all sales made thereafter, we need to calculate the commission earned on sales above $1000.

The total sales above $1000 is:

4500 - 1000 = 3500

The commission earned on sales above $1000 is:

3500 x 15% =$525

Therefore, the employee earned a sales commission of $525 this week.

Therefore , the solution of the given problem of volume comes out to be the other leg of the right triangular pyramid's base is 3 yards long.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.

Here,

Let's use "x" yards to represent the other leg of the right triangle pyramid's base.

A pyramid's volume can be calculated using the following equation: => Volume = (1/3) * Base Area * Height

In this instance, we are informed that the pyramid has a volume of 168 cubic yards and a height of 14 yards.

=> 168 = (1/3) * 14 * base area

The base area can be estimated as (8 * x)/2 = 4x because we know that one leg of the base is 8 yards long and the other leg is designated as "x" yards.

=> 168 = (1/3) * 4x * 14

=> 168 = (4/3)x * 14

=>  168 = (4/3) * 14x

=> 168 = 56x

=> x = 168/56

=> x = 3

Therefore, the other leg of the right triangular pyramid's base is 3 yards long.

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In linear equation., both quantities are different from each other.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Taking LHS

  5 2/3 - 3 3/4= 17/3 - 15/4

  17/3 - 15/4 =  68 - 45/12  = 23/12

now solving RHS

  1+2/3+3/4  = 12 + 8 + 9/12  = 29/12

clearly, LHS≠ RHS

hence both quantities are different from each other.

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Answer:

See below!

Step-by-step explanation:

Length = 735 meters

Width = 756 meters

Area = length × width

Area = 735 × 756

Area = 555660 m²

To find the area of largest square, we first need to find the highest common factor of 735 and 756.

HCF of 735 and 756:

= 21

This means the length of largest square will be 21 m.

Now,

= length × length

= 21 × 21

No. of squares = Total area / Area of largest square

No. of squares = 555660 / 441

[tex]\rule[225]{225}{2}[/tex]

Answer: So, what are you asking?

Step-by-step explanation:

The answer on shape of house is , (1) A rectangle for the main structure of the house. (2) A triangle for the roof. (3) A rectangle for the front porch. (4) Two trapezoids for the roof of the front porch. (5) A rectangular door.

A trapezoid is a four-sided geometric shape with two parallel sides, called the bases, that are of different lengths, and two non-parallel sides that connect the bases. The non-parallel sides are also called legs, and they may or may not be equal in length.

Trapezoids are often encountered in geometry and in real-life situations, such as in construction and architecture. They can be classified as either right trapezoids or oblique trapezoids depending on whether one of the angles formed by the bases and a leg is a right angle or not.

Based on the image provided, the shapes that make up the front of the house are:

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Answer:

D) 50

Step-by-step explanation:

-100 <-45 < 20 < 50

Answer:

50

Step-by-step explanation:

any numbers approaching negative (before 0) in an increasing manner are the lowest, whereas numbers approaching positive in a increasing manner are the greatest.

The value of the mean of the temperatures for the two missing days are,

= - 6.5

We have to given that;

The temperatures, in degrees F, at 7:00 a.m. for five days during one week are shown.

-3, 4, -1, 6, 7

And, The mean temperature for all 7 days of the week was 0°F.

Now, We can assume that,

Last two days temp. are x and y.

Hence, We get;

(- 3 + 4 + (-1) + 6 + 7 + x + y) / 7 = 0

- 3 + 4 - 1 + 6 + 7 + x + y = 0

x + y = - 13

Divide both side by 2;

(x + y)/2 = - 13/2

(x + y)/2 = - 6.5

Thus, The value of the mean of the temperatures for the two missing days are,

= - 6.5

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If θ=2 rad then the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

In this problem, we are given that when the arc length is equal to the radius (S=r), the angle is 1 radian (θ = 1 rad). Now, we are asked to find the condition when the angle is 2 radians (θ = 2 rad).

If Θ=1 rad when S=r, it means that when the angle subtended by an arc of length r is 1 radian, then the radius of the circle is also r.

Now, if θ=2 rad, we can use the same proportionality to find the arc length S that corresponds to this angle. Since the angle has doubled, we can expect the arc length to double as well. Therefore, we have:

θ/Θ = S/r

2/1 = S/r

S = 2r

Thus, the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

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 [tex]1.[/tex] The answers are given below

   Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: [tex]4[/tex]

  Coefficients: [tex]6,4,10[/tex]

   Constants: [tex]-3,1[/tex]

 [tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]

    Number of terms: [tex]5[/tex]

    Coefficients: [tex]25,-2,3,-6[/tex]

    Constants: [tex]25[/tex]

  [tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]

     Number of terms: [tex]3[/tex]

     Coefficients: [tex]25,-3,5[/tex]

      Constants: [tex]100[/tex]

To break down each equation or expression and identify the number of terms, coefficients, and constants.

[tex]1.[/tex] Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: 4. There are four terms in this equation separated     by addition and subtraction operators.

Coefficients: [tex]6,4,10[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (xt, yz, a) in each term.

 Constants: [tex]-3,1[/tex]. These are the constants, which are the numerical values without any variables that are added or subtracted in the equation.

[tex]2.[/tex]  Expression:[tex]25abc -2b +3ac -6bc +25[/tex]

   Number of terms: [tex]5[/tex] There are five terms in this expression separated by addition and subtraction operators.

  Coefficients: [tex]25,-2,3,-6[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (abc, b, ac, bc) in each term.

  Constants: [tex]25[/tex]. This is the constant, which is the numerical value without any variables that is added in the expression.

[tex]3.[/tex]  Equation: [tex]25y -3xy+5x = 100[/tex]

    Number of terms:[tex]3[/tex]. There are three terms in this equation separated by addition and subtraction operators.

    Coefficients: [tex]25,-3,5[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (y, xy, x) in each term.

   Constants: [tex]100[/tex]. This is the constant, which is the numerical value without any variables on the right-hand side of the equation.

Therefore,   [tex]1.[/tex] The answers are given below

   Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: [tex]4[/tex]

   Coefficients: [tex]6,4,10[/tex]

   Constants: [tex]-3,1[/tex]

 [tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]

    Number of terms: [tex]5[/tex]

    Coefficients: [tex]25,-2,3,-6[/tex]

    Constants: [tex]25[/tex]

  [tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]

     Number of terms: [tex]3[/tex]

     Coefficients: [tex]25,-3,5[/tex]

      Constants: [tex]100[/tex]

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Where the conditions above are given with regard to the above triangle, the ratio AD:DB is 1:1.

Since D is the midpoint of AB, we have:

AD = DB

Let M and N be the midpoints of OA and OB, respectively. Then we have:

AM = MO = x/2

BN = NO = y/2

Also, from the given information, we have:

OD = 3/7x + 4/7y

Since D is the midpoint of AB, we have:

AD + DB = AB

Substituting AD = DB, we get:

2AD = AB

Therefore:

AD = AB/2

We can express AB in terms of x and y using the law of cosines:

AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos(BOA)

Since M and N are midpoints, we have:

OM = OA/2 and ON = OB/2

Therefore, using the law of cosines, we have:

MN^2 = OM^2 + ON^2 - 2(OM)(ON)cos(MON)

Substituting OM = OA/2 and ON = OB/2, we get:

MN^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

But MN = OD, so we can also express this as:

OD^2 = (3/7x + 4/7y)^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

Substituting OD^2 = (3/7x + 4/7y)^2 and simplifying, we get:

9x^2 + 16y^2 = 49(OA^2 + OB^2) - 42(OA)(OB) cos(BOA)

Substituting AB^2 = OA^2 + OB^2 - 2(OA)(OB) cos(BOA) and simplifying, we get:

9x^2 + 16y^2 = 49AB^2

Substituting AD = AB/2, we get:

9x^2 + 16y^2 = 49(2AD)^2

Simplifying, we get:

x^2 + 4y^2 = 28AD^2

We want to find the ratio AD:DB, which is the same as the ratio AD:(AB - AD). Substituting AB = 2AD, we get:

AD:(AB - AD) = AD:AD = 1:1

Therefore, the ratio AD:DB is 1:1.

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Answer:8%

Step-by-step explanation:

you divide 25 by 32 and round to nearest tenth

hope this helps :)

Answer:

[tex]tringle = \frac{1}{2} \times base \times hieght[/tex]

1/2 × 8×5

0.5×40

=20m

The length of the arc is 1 unit.

The distance that runs through the curved line of the circle making up the arc is known as the arc length.

length of an arc is expressed as;

l = tetha/360 ×2πr

the circumference of circle is expressed as ;

C = 2πr

6 = 2×3.14 × r

r = 6/6.28

r = 0.955 units

Therefore length of the arc

= 60/360 × 6

since 2πr is the circumference,

l = 360/360 = 1 unit

therefore the length of the arc is 1 unit.

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