In the figure below, m1=103°. Find m2.
1
2

Answer: the answer is 12

Step-by-step explanation:

2x+6 =4x-12

-2x=-18

x=9

3(9)-15

27-15

12

Answer:

The best estimate for her earnings is $1200

Step-by-step explanation:

Number of time spent babysitting each week = 21 hours = BBS

Number of time spent dog walking each week = 9 hours = DW

She earns $7.50 per hour for dog walking,

She earns $(7.50+1.50) = $9 for baby sitting,

There are 4 1/2 weeks = 9/2 weeks in July,

Now, for each week she earns 21(9) = $189 from baby sitting

and 9(7.5) = $67.5 from dog walking,

So, for the month of July, i.e. 9/2 weeks, she earns,

9/2(189) = $ 850.5 from baby sitting,

and (9/2)(67.5) = $303.75 from dog walking,

In total for the month, she earns,

850.5 + 303.75 = $1154.25

Hence the best estimate for her earnings is $1200

Answer:

The answer is

C. The mapping represents y as a function of x, because each x-value corresponds to exactly one y-value.

Step-by-step explanation:

In mathematics, mapping is used synonymously to a function, and a function is basically a relation between two values or expressions say y and x

like the difference equation relating y and x.

In a function, for every value of x plugged into the function there is always a corresponding value of y.

Example.

Given the function

y=2x+5.

find the value of y when x=0

we are going to substitute x=0 and solve

y=2(0)+5

y=5

so for x=0 y=5

In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

Note that by examining the the image if ∠EDA≅∠HCB, the two lines can never intersect even if they go a longer distance.

The reason why is that there are no parallel lines on it and as such, they cannot intercept.

Hence, In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

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According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.

Property of Equality:

The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.

That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.

Multiplicative Property of Equality:

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.

The formula for this property can be expressed as for the real numbers a, b, and c.

If a × b, then, a × c = b × c.

In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.

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trueeeeeeeeeeeeeeeee

Step-by-step explanation:

Hindi ko poh alam ✌️

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

h = 19.7 ft.

Step-by-step explanation:

Use the Pythagoras Theorem

\((Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\\\\(20)^2=(3.5)^2+(h)^2\\400=12.25+h^2\\400-12.25=h^2\\387.75=h^2\\\)

Now we take square root on both sides,

\(\sqrt{387.75} =\sqrt{h^2}\\19.69=h\\h=19.7\ ft\\\)

so the value of h equals 19.7 ft.

:-):-):-):-):-)

Step-by-step explanation:

1) 40÷10

2) 40÷2

The function \(\(f: \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}\)\) given by \(\(f(x,y) = |x||y|\)\) is not onto.To determine if a function is onto, we need to check if every element in the codomain has a preimage in the domain.

In this case, the codomain is \(\(\mathbb{Z}\)\), the set of integers. Let's consider an arbitrary integer z in \(\(\mathbb{Z}\)\). To find a preimage for z, we need to solve the equation \(\(f(x,y) = |x||y| = z\)\).

Now, let's consider two cases:

1. If z is positive or zero \((\(z \geq 0\))\), we can choose \(\(x = |z|\)\) and \(\(y = 1\)\). This gives us \(\(f(x,y) = |x||y| = |z||1| = |z| = z\)\), satisfying the equation.

2. If z is negative z < 0, we cannot find x and y such that f(x,y) = z. This is because the absolute value of a number is always non-negative, so it is not possible to obtain a negative value for f(x,y) using the function \(\(f(x,y) = |x||y|\)\).

Therefore, for any negative integer \(\(z\) in \(\mathbb{Z}\)\), there is no preimage in the domain. Hence, the function is not onto.

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Answer:

0≤x≤3

Step-by-step explanation:

The domain is just all the possible values of x

we can see that the line goes through the x values 0 through 3

which means that

0≤x≤3

It's ≤ because it's a close circle

Step-by-step explanation:

d+q =12

.25q + .10d = 1.95

d = 12-q

substitute

.25q + .10(12 -q) =1.95

.25q + 1.2 - .1q = 1.95

.15q = .75

q = 5. quarters

d + 5 = 12

d = 7 dimes

Answer:

5 quarters and 7 dimes

Step-by-step explanation:

5 quarters = $1.25

7 dimes = $0.70

7 + 5 = 12

$1.25 + 0.70 = $1.95!!

I hope this helped :)

Also, this answer was calculated by g00gle.

y=5x-6

Hope it helps.

Do comment if you have any query.

Answer: A) 1

The inequality for the possible value of the number of tacos sold in the number of burrito will be;

⇒ $3.75x + $7.75y < 430

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Cost of each taco = $3.75

Cost of each burrito = $7.75

And, Hannah Montana less than 430 of worth of tacos and burritos each day.

Now,

Let the number of taco = x

Let the number of burrito = y

So, Cost of taco = $3.75x

Cost of burrito = $7.75y

Since, Hannah Montana less than 430 of worth of tacos and burritos each day.

So, we can formulate the inequality as;

⇒ $3.75x + $7.75y < 430

Therefore,

The inequality for the possible value of the number of tacos sold in the number of burrito will be;

⇒ $3.75x + $7.75y < 430

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An example of a pyramid and a prism that have the same base and volume is a triangular pyramid and a triangular prism with congruent bases and heights.

Let's consider a triangular pyramid and a triangular prism with congruent bases and heights. Both shapes have a triangular base, meaning their base area is the same. The volume of a pyramid is given by the formula V = (1/3) * base area * height, whereas the volume of a prism is calculated as V = base area * height.

Since the bases of the pyramid and prism are congruent, their base areas are equal. In order for the pyramid and prism to have the same volume, the height of the pyramid must be three times the height of the prism. This is because the volume of a pyramid is one-third of the volume of a prism with the same base and height.

By choosing a triangular pyramid and a triangular prism with congruent bases and heights, we ensure that the base area and the height are the same for both shapes. Therefore, their volumes will also be equal.

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The distance between point P and line l is

1. Distance = 2√2

2. Distance =0

3. Distance =6

4. Distance =1

5. Distance =√10

To find the distance between a point and a line, we can use the formula for the distance between a point and a line in the coordinate plane. The formula is:

Distance = |Ax + By + C| / √(A² + B²)

1. Line & contains points (0, -3) and (7, 4). Point P has coordinates (4,3).

The equation of the line is y = x - 3. We can rewrite it as x - y + 3 = 0.

So, Distance = |4 - 3 + 3| / √(1² + (-1)²)

= |4| / √2

= 4 / √2

= 2√2

2. Line & contains points (11, -1) and (-3, -11). Point P has coordinates (-1, 1).

The equation of the line is y = -2x - 1. We can rewrite it as 2x + y + 1 = 0.

So, Distance = |2(-1) + 1 + 1| / √(2² + 1²)

= |-2 + 2| / √5

= 0 / √5

= 0

3. Line & contains points (-2, 1) and (4, 1). Point P has coordinates (5, 7).

The equation of the line is y = 1.

So, Distance = |0(5) + 7 - 1| / √(0² + 1²)

= |6| / √1

= 6

4. Line & contains points (4, -1) and (4, 9). Point P has coordinates (1, 6).

The line is vertical, and its equation is x = 4.

so, Distance = |1 - 4 + 4| / √(1² + 0²)

= |-1| / √1

= 1

5. Line & contains points (1, 5) and (4, -4). Point P has coordinates (-1, 1).

The equation of the line is y = -3x + 8.

So, Distance = |3(-1) + 1 - 8| / √(3² + 1²)

= |-3 - 7| / √10

= |-10| / √10

= 10 / √10

= 10√10 / 10

= √10

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Answer:

A. ii, iv, v

A polygon having ten angles and ten sides.

Answer:

  A.  ii, iv, v

Step-by-step explanation:

You want to know the descriptors that apply to a regular decagon from those on the list ...

A convex polygon with n sides has interior angles that total 180°×(n -2). When the number of sides is 10, the total of interior angles is ...

  180°×(10 -2) = 1440°

The prefix "deca-" signifies 10. A regular polygon has congruent sides and angles Thus, a regular decagon has 10 congruent sides and 10 congruent interior angles.

Since the total of interior angles is 1440°, the measure of each is ...

  1440°/10 = 144°

The applicable descriptors of the regular decagon are ...

a) the solution to the equation tan(x) sin(x) - sin(x) = 0 on the interval [0, 3π) is:x = {0, π/4, π, 2π, 3π}

Explanation:

a) Solve the equation ab - a = 0:ab - a = 0a(b - 1) = 0 a = 0, b - 1 = 0 b = 1

Therefore, the solution to the equation ab - a = 0 is a = 0 or b = 1.b)

Using the factoring you found in part a) along with the substitutions a = tan(x) and b = sin(x) to solve the equation tan(x) sin(x) - sin(x) = 0 on the interval [0, 3π):

Let's begin by substituting a = tan(x) and b = sin(x) in tan(x)sin(x) - sin(x) = 0 equation.

tan(x) sin(x) - sin(x) = 0sin(x)(tan(x) - 1) = 0sin(x) = 0 or tan(x) - 1 = 0tan(x) = 1

The above equation has to be solved on the interval [0, 3π) since it is given that the solution is required on this interval.

At x = 0,  π, 2π, and 3π the value of sin(x) is equal to 0.

Hence, sin(x) = 0 for x = 0, π, 2π, and 3π.And, at x = π/4, tan(x) is equal to 1.

Therefore, the solution to the equation tan(x) sin(x) - sin(x) = 0 on the interval [0, 3π) is:x = {0, π/4, π, 2π, 3π}

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The temperature of the steam is 441.7 K.

A 1-m³ tank contains 2.1085 kg of steam at 0.6 MPa.

The gas constant, critical pressure, and critical temperature of steam are

R = 0.4615 kPa.m³/kg.K,

TCr = 647.1 K, and

PCr = 22.06 MPa.

Using data from the steam tables, let's find the temperature of the steam.

According to the steam table, the specific volume of the steam is 0.194 m³/kg at 0.6 MPa and 393.71 K. Since 1 m³ tank contains 2.1085 kg of steam, the total volume of steam is:

V = m/v

= (2.1085 kg)/(0.194 m³/kg)

= 10.8665 m³

The ideal gas equation of state is:

Pv = mRTor

T = PV/mR

Substituting the values we get:

T = (0.6 MPa)(10.8665 m³)/(2.1085 kg)(0.4615 kPa.m³/kg.K)

T = 441.7 K

Therefore, the temperature of the steam is 441.7 K.

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1a) Complementary solution: y(t) = c₁ + c₂e^t + c₃e^(-t) + c₄cos(t) + c₅sin(t)

1b) Particular solutions:

(i) yp(t) = (1/2)e^t

(ii) yp(t) = (1/5)t^2 + (2/15)

(iii) yp(t) = [(3/20)t^2 + (1/4)t + C₁]cos(2t) - [(3/40)t^3 + (1/8)t^2 + C₂]sin(2t)

2) Linear differential equation: y''(x) + 4y'(x) + 5y(x) = 0

1a) To find the complementary solution of y(5) - y(3) = f(t), we need to find the homogeneous solution of the differential equation y(5) - y(3) = 0. We assume that y(t) = e^(rt) and substitute it into the differential equation to obtain the characteristic equation:

r^5 - r^3 = 0

r = 0, ±1

Since there are three distinct roots, the complementary solution is of the form:

y(t) = c₁ + c₂e^t + c₃e^(-t) + c₄cos(t) + c₅sin(t)

where c₁, c₂, c₃, c₄, and c₅ are constants.

1b) Using the method of undetermined coefficients, we can determine the particular solution of y(5) - y(3) = f(t) for each of the given functions f(t):

(i) f(t) = e^t

Assuming yp(t) = Ae^t, we obtain:

A(e^(5t) - e^(3t)) = e^t

A = 1/2

yp(t) = (1/2)e^t

(ii) f(t) = 2t^2

2A(t^5 - t^3) + 6B(t^3 - t) + 6C(t^2 - 1) = 2t^2

A = 1/5, B = 0, C = 2/15

yp(t) = (1/5)t^2 + (2/15)

(iii) f(t) = (3t+2)cos(2t)

A''(t)cos(2t) + B''(t)sin(2t) + 4A'(t)sin(2t) - 4B'(t)cos(2t) = (3t+2)cos(2t)

A(t) = (3/20)t^2 + (1/4)t + C₁

B(t) = -(3/40)t^3 + (1/8)t^2 + C₂

yp(t) = [(3/20)t^2 + (1/4)t + C₁]cos(2t) - [(3/40)t^3 + (1/8)t^2 + C₂]sin(2t)

2) The given general solution is:

y(x) = C₁e^x + C₂xe^x + C₃e^(-x)cos(2x) + C₄e^(-x)sin(2x)

y'(x) = C₁e^x + C₂(e^x + xe^x) - C₃e^(-x)sin(2x) + C₄e^(-x)cos(2x)

y''(x) = C₁e^x + C₂(2e^x + xe^x) + C₃e^(-x)cos(2x) - C₄e^(-x)sin(2x)

(C₁ + C₂ + C₃ + C₄)e^x + (2C₂ + C₂x - C₃sin(2x) + C₄cos(2x))e^x + (-C₁ + 2C₂ - C₃cos(2x) - C₄sin(2x))e^(-x) = 0

Since this equation must hold for all values of x, we obtain the following system of equations:

C₁ + C₂ + C₃ + C₄ = 0

2C₂ - C₁ - C₃cos(2x) - C₄sin(2x) = 0

C₂x - C

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Answer:

227

Step-by-step explanation:

nth term = a₁ + (n - 1)d

where a1 = first term , n = # of terms and d = common difference.

here we need to solve for the common difference so we can find the missing term, we do so by plugging in what we are given and solving for d

here we are given an nth term, 456 and we are given the first term, -2.

and from what we see there are 3 terms

So we have nth term = 456 , a1 = -2 and n = 3

==> plug these values into the formula

456 = -2 + (3-1)d

==> add 2 to both sides

458 = (3-1)d

==> subtract 1 from 3

458 = 2d

==>divide both sides by 2

d = 229

We then add the common difference to the term before the missing term to get the missing term

-2 + 229 = 227

We want to solve the proportion:

For doing so, we remember that solving a proportion equivals to find the variable x. We will multiply means and extremes:

This means that the value of x is 8, which is the solution of the proportion.

Answer:

40 miles per hour

Step-by-step explanation:

Answer:

average speed

=(Total distance/Total time)

=(480miles/12hours)

=40mile/hour

Step-by-step explanation:

Answer:

(2,10) or x=2 y=10

Step-by-step explanation:

1. Pick one of your equations and solve for a variable. I chose the first equation and solved for x.

5x-2y=-10 (Move the -2y to the other side, you need to do the opposite so you add +2y to -10)

5x=2y-10 (Divide the 5 from the x)

x=2/5y-2

2. Now take what you got for x and plug it into the x variable on the other equation.

3(2/5y-2)+6y=66 (Multiply 3 by 2/5y and -2)

6/5y-6=6y=66 (Move the -6 to the other side and add 6/5y to 6y)

36/5y=72 (Since the number on the y is a fraction, you must do the opposite to the other side)

y=72/1 x 5/36 (Flip your fraction and multiply it by the 72)

y=10

3. Now that you have one of the variables solved for, in order to get the other we must plug in what we have to the first equation.

5x-2(10)=-10 (Multiple 2 by 10)

5x-20=-10 (Move -20 to the other side, since you do the opposite add +20 to the -10)

5x=10 ( Divide 10 by 5)

x= 2

4. If needed, plug in the values of x and y to check your solution.

Hope this could help! :)