Which of the following is a metric unit for distance?

A. centimeters
B. miles
C. feet
D. kilograms

Based on the calculations, the slope of line YZ in simplest form is equal to 2.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since points X, Y, and Z are collinear, we can deduce that the line passes through line Z at 6 units form the origin and 3 units for Y from the origin.

Substituting the parameters into the formula, we have;

[tex]Slope, m = \frac{6\;-\;0}{3\;-\;0}[/tex]

Slope, m = 6/3

Slope, m = 2.

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3x + 6 = 48 (alternate angles are equal)

- 6

3x. = 42

÷3

x = 14 degrees

180-48 - 2y + 5y-9 =180

123 + 3y = 180

-123

3y = 57

÷3

y = 19 degrees

Explanation:

To find the last angle on the top straight line, do:

180 - (the 2 given angles).

So, 180 - (3x + 16, which is 48 due to alternate angles being equal). Then, minus the 2y.

(180 - 48 - 2y) & simplify => 132 - 2y

This gives you the equation for the missing angle on our top straight line.

Thus, co-interior angles add to 180. So, we add the new equation (132 - 2y) to 5y - 9.

Simplify

=> 123 + 3y (because - 2+5 =3)

and put it equal to 180. Solve for y

Hope this helps!

Answer:

25 hours.

Step-by-step explanation:

Let the hours worked be x

2/5x = 10

2x = 50

x = 25

She has to work 25 hours to spend 10 hours doing paperwork.

Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

The parameters for this problem are given as follows:

A = 144, r = 0.06, n = (68 - 24) x 12 = 528.

Then:

r/12 = 0.06/12 = 0.005.

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}[/tex]

[tex]P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}[/tex]

P = $26,731.23.

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The formula of P(x) = -0.7 (x-2)²(x+4)

A root of a polynomial is defined as the point or value at which the overall value of the polynomial = 0

It is given that

for a polynomial of degree 3

root x=2, multiplicity 2:  (x-2)²

root x= - 4, multiplicity 1:  (x+4)                  ³ ²

P(x) = a(x-2)²(x+4)

here a is constant

y-intercept =  -11.2

P(0) = -11.2

a(0-2)²(0+4) = -11.2

a * 4 * 4  = -11.2

16a = -11.2

a = -11.2/(16)

a= -11.2/16

P(x) = -(11.2/16)(x-2)²(x+4)

P(x) = -0.7 (x-2)²(x+4)

Therefore the formula of P(x) = -0.7 (x-2)²(x+4)

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The 3-D figure and combination of shapes that Scarlett can use is A. Equilateral triangle prism with two equilateral triangles and three rectangles

This refers to the solid figure or shape that has defined dimensions of length, width, and height.

Therefore, based on the fact that a 3-D figure is made up of six equal squares, option A is the best answer because it contains a total of six squares.

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The arcs intersected by these chords are not congruent.

Given that two circles with different radii have chords AB and CD, such that AB is congruent to CD.

Let r₁ and r₂ be the radii of two different circles with centers O and O' respectively.

Assuming that the each of the ∠АОВ  and ∠CO'D is less than or equal to π.

Then, we have isosceles triangle AOB and CO'D such that,

AO = OB = r₁,

CO' = O'D = r₂,

Let us assume that r₁< r₂;

We can see that arc(AB) intersected by AB is greater than arc(CD), intersected by the chord CD;

arc(AB) > arc(CD)      .......(1)

Indeed,

arc(AB) = r₁ angle (AOB)

arc(CD) = r₂ angle (CO'D)

So, we have to prove that ;

∠AOB >∠CO'D       ......(2)

Since each angle is less than or equal to π, and so

∠AOB/2  and ∠CO'D/2 is less than or equal to π

it suffices to show that :

tan(AOB/2) >tan(CO'D/2) ......(3)

From triangle AOB :

tan(AOB/2) = AB/(2*r₁)

tan(CO'D/2) = CD/(2*r₂)

Since AB = CD and r₁ < r₂ (As obtained from the result of (3) ), therefore, arc(AB) > arc(CD).

Hence, for two circles with different radii have chords AB and CD, such that AB is congruent to CD but the arcs intersected by these chords are not congruent.

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The value of x in the equation 1/2x = -1/2x when 4 is subtracted from both sides is 0(not defined)

Subtraction of fraction

Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction

1/2x = -1/2x

1/2x - 4 = -1/2x - 4

(x-8) / 2 = (-x-8) / 2

(x - 8) / 2 = (-x-8) / 2

2(x - 8) = 2(-x - 8)

2x - 16 = -2x - 16

2x + 2x = -16 + 16

4x = 0

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Answer:c

is the answer

Step-by-step explanation:

Answer:

1,483

Step-by-step explanation:

The equation that models this set of data is y=17.2x^2-226.3x+2184.5. Since x=0 represents 6:00 a.m, x=5 represents 11:00 a.m. Substitute 5 for x in the model, and solve for y.

Based on the number of registered users who log into the social media app during weekdays and weekends, the following are true:

The given model for the users in the week is:

y = 17.2x² - 226.3x + 2,184.5

x is 5 because 11 am is 5 hours after 6 am:
= 17.2(5)² - 226.3(5) + 2,184.5

= 1,483 users

The company should post when there are the most people online and on weekdays that's 14 hours after 6 am which is:
=14 + 6

= 20:00

= 8 pm

On weekends this is 6 hours after 6 am:

= 6 + 6

= 12 pm

Missing information from question:

Model for calculating weekday users y = 17.2x² - 226.3x + 2,184.5.

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The coefficient are as follows:

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

1. 12s + 4t

Variables: s, t

Coefficient: 12, 4

2. 46rs + 10x

Variables: r, s, x

Coefficient: 46, 10

3. 12q + 14x

Variables: q, x

Coefficient: 12, 14

4. 10x + 10y

Variables: x, y

Coefficient: 10, 10

5. 17rs + 32x

Variables: r, s, x

Coefficient: 17, 32

6. 5x + 7y - 12z

Variables: x, y, z

Coefficient: 5, 7, -12

7. 36ab + 70m

Variables: a, b, m

Coefficient: 36, 70

8. 3r + 19a + 10m

Variables: r, a, m

Coefficient: 3, 19, 10

9. 7k + 16m

Variables: k, m

Coefficient: 7, 16

10. 8r + 5s

Variables: r, s

Coefficient: 8, 5

11. 9h + 120m

Variables: h, m

Coefficient: 9, 120

12. 12k + m

Variables: k, m

Coefficient: 12, 1

13. 7g + 15h + w

Variables: g, h, w

Coefficient: 7, 15 , 1

14. 4c - 8d + 12f

Variables: c, d, f

Coefficient: 4, -8, 12

15. 6t + 17r - 35j

Variables: t, r, j

Coefficient: 6, 17, -35

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Round

8724 to the nearest whole number is 8720

Answer:

199.5 ft^3

Step-by-step explanation:

to find your answer you simply multiply all the measurements together

19 * 1.5 * 7 is your equation

19 * 1.5 * 7 = 199.5

it is 199.5 ft^3

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

This question is incomplete, the complete question is;

Which equation is correct for ∆FON?

Answers:

A.) cos F= 9/18

B.) sin F 9/18

C.) sin F=18/9

D.) cos F=18/9

From the diagram, we have a right angle triangle.

Note that; sinθ = Opposite / Hypotenuse

Therefore, for angle F

sin F = Opposite / Hypotenuse

sin F = 9/18

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

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The solution of Tx" + (4t - 2)X' + (13t - 4)X = 0, If X(0) = 0 is mathematically given as

[tex]&n \times(S)=\frac{c}{\left((s+2)^{2}+9\right)^{2}}[/tex]

Generally, the equation for is mathematically given as

[tex]&t x^{\prime \prime}+(4 t-2) x^{\prime}+(13 t-4) x=0, \quad x(0)=0\\\\&\Rightarrow \quad t x^{\prime \prime}+4 t x^{\prime}-2 x^{i}+13 t x-4 x=5\\[/tex]

By taking Laplace to transform,

[tex]&L\left\{t x^{13}\right\}+L\left\{4 t x^{\prime}\right\}-L\left\{2 x^{\prime}\right\}+L\{13 t x\}-L\{4 x\}=0\\\\\\&-25 x(s)-s^{2} x^{1}(5)-4 x(s)-45 x^{\prime}(s)-25 x(s)-13 x^{\prime}(5)-4 x(s)=0\\[/tex]

[tex]&\Rightarrow \quad-\left(5^{2}+45+13\right) x^{4}(5)-4(5+2) x(5)=0\\\\\\&\Rightarrow \quad\left(s^{2}+45+13\right) x^{1}(5)+4(5+2) x(5)=0\\\\\\&\Rightarrow\left(s^{2}+4 s+13\right) x^{\prime}(s)=-4(s+2)^{x}(s)\\\\\\&\Rightarrow \frac{x^{\prime}(s)}{x(s)}=-\frac{4(s+2)}{s^{2}+4 s+13}\\\\\[/tex]

In conclusion, By integrating both sides

The solution is

[tex]&x(s)=\frac{c}{\left(s^{2}+4 s+13\right)^{2}}\\[/tex]

[tex]&n \times(S)=\frac{c}{\left((s+2)^{2}+9\right)^{2}}[/tex]

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The function which represents the annual salary for total sales of x dollars, where x is greater than $250000 is 0.025x+29750.

Given basic salary=3000 p.m. , bonus 2.5% of total sales above $250000.

We have to make a function which shows the annual salary for total sales of x dollars where x is greater than $250000.

Function is a relationship between two or more variables which have each y values corresponding to x values.

According to question

Total basic salary of whole year=3000*12=$36000

We have been given total sales be x.

Sales above $250000 is x-250000

Bonus on sales=2.5%(x-250000)

Function f(x)=36000+2.5%(x-250000)

=36000+0.025x-0.025*250000

=36000+0.025x-6250

=0.025x+29750

Hence the function which shows the annual salary for total sales of x dollars is f(x)=0.025x+29750.

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The value of this car is decreasing at a rate of 6% per year.

The function V(t) = 38000 (0.94)^t represents the value (in dollars) of a car "t" years after its purchase

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,

V(t) = 38000 (0.94)^t
Cleary, above function is an exponential function
while putting certain values in equation we have certain outcomes.
for,
V(1) = 35720;    V(2) =33576.8;      V(3) = 31562.192

Now, the rate of change is given by = [V(2)-V(1)/ V(1)] x 100
= [(33576.8-35720)/35720]*100
= 6%

now V(2) x 6% = V(3)
33576.8 x 6% = 31562.192 = V(3)

Thus, The required rate of decreasing care price is 6%.

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Answer:

4x

Step-by-step explanation:

[tex]\frac{500x^{4} }{(5x)^{3} }[/tex] = [tex]\frac{500x^{4} }{125x^{3} }[/tex] = [tex]4x[/tex]

Answer:

262 passengers can have both headphones and blankets .

Step-by-step explanation:

I hope it will help you

Answer:

Step-by-step explanation:

Solution

Interesting question.

The formula for the sum of the interior angles is

(n - 2)*180 = x

In this case, x = 1260

(n - 2)*180 = 1260                            Divide both sides by 180

(n -2 )* 180/180 = 1260/180

( n - 2) = 7                                         Remove the brackets

n - 2 = 7                                            Add 2 to both sides

n - 2 + 2 = 7 +2                                 The 2s on the left cancel

n = 9

Answer: Nonagon

The polygon with an interior angle sum of 1260° is the nonagon as per the concept of interior angles.

To find the sum of the interior angles of a polygon, we can use the formula:

Sum of interior angles = (n - 2) × 180°

where "n" is the number of sides of the polygon.

To achieve an interior angle sum of 1260°, we would need to consider a polygon with fewer sides.

For example, a nonagon (9 sides) would have an interior angle sum of 1260°:

Sum of interior angles = (9 - 2) × 180°

Sum of interior angles = 7 × 180°

Sum of interior angles = 1260°

So, a nonagon (a polygon with nine sides) has an interior angle sum of 1260°.

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Answer:

Answers are below.

Step-by-step explanation:

1) 60 centimeters

2) Perimeter = 48, Area = 144

3) Circumference = 20π, Area = 100π

4) 180 feet

5) 75 meters

6) 15 yards

Hope this helps!

Explanation:

The first step is to add up all the values given:

11.01 + 10.50 + 5.70 + 14.67 + 9.50 + 12.54 + 8.90 + 13.56 + 11.23 + 6.80 + 3.00 + 10.55 = 117.96

Then we divide this sum over n = 12 since this is the sample size given (i.e. the number of customers)

117.96/n = 117.96/12 = 9.83

Answer:

  647

Step-by-step explanation:

The divisibility rule for 9 can be used to find the unknown number.

A number is divisible by 9 if the sum of its digits is divisible by 9.

The number 3D8 will be divisible by 9 when 3 + D + 8 = <multiple of 9>. Since D is a single digit, we must have ...

  11 +D = 18

  D = 7 . . . . . . . subtract 11

The number 3D8 is 378.

Now we know that the difference is ...

  ABC -3D8 = ABC -378 = 269

  ABC = 269 +378 = 647

ABC represents the number 647.

Answer:

=======================

Use circumference formula to find the tire circumference:

Find the distance by multiplying the number of revolutions by circumference:

Convert the inches to feet, or yards, considering 12 in = 1 foot and 3 feet = 1 yard:

The solution of the graph can be located at the point of intersection of the two lines. The solution, approximated to the tenths place will be (0.4, 2.8)

The solution of a system of two linear equations can be calculated by determining the point of intersection.

Therefore, the solution = the coordinates of the point of intersection (x-coordinate, y-coordinate).

Given graph shows the system of equations in two lines:

The solution of the graph can be located at the point of intersection of the two lines, the x-coordinate against the y-coordinate.

The integers that the x-coordinate of the point of intersection is in between are 0 and 1.

The y-coordinates of the point of intersection lie between the integers 2 and 3.

The solution, approximated to the tenths place will be (0.4, 2.8)

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The volume of volume of the rectangular prism is=240cm³ while the surface area of cylinder =225.04cm²

The volume of rectangular prism

= l×w×h

= 10× 6× 4

= 240cm³

The surface area of cylinder,

= 2πrh+2πr²

= 2× 3.14× 2.8 × 10 + 2×3.14×2.8²

= 175.84 + 49.2

= 225.04cm²

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Here are the awnsers

1. D ⅔

2.C 60%

The radius of the quadrant whose perimeter is 52cm is 14.56cm.

A quadrant is 1/4th of a circle, consisting of two radii, perpendicular to each other.

So, the perimeter of a quadrant consists of two radii and an arc, which is 1/4th the perimeter of a circle.

Therefore, the perimeter of the quadrant = 2r + (1/4)*(2πr) = 2r + (πr/2).

Now, we are given the perimeter of the quadrant = 52cm and are asked to find its radius.

We suppose the radius to be r cm.

Therefore, we can say that:

52 = 2r + (πr/2).

or, 52 = (4r + πr)/2

or, 52*2 = r(4 + π)

or, r = 104/(4 + π) = 14.56.

Therefore, the radius of the quadrant whose perimeter is 52cm is 14.56cm.

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