if m2 = 125, m12= 37 and m18 = 102, find the measure of each angle

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

2(y + 4) = 4y

Distribute

2y + 8 = 4y

Step 2 is incorrect because the added instead of multiplied

Continuing on to correct the problem

Subtract 2y from each side

2y+8-2y = 4y-2y

8 = 2y

Divide by 2

8/2 = 2y/2

4 =y

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

Step 2 is wrong.

2(y + 4) = 4y

The step to solve is to expand brackets or distribute 2, not divide both sides by 2.

2y + 8 = 4y

Subtract both sides by 2y.

8 = 2y

Divide both sides by 2.

4 = y

Answer:

C

Step-by-step explanation:

Using the angle of elevation we calculate the height of the smaller building to be approximately 8.99 meters.

Let the height of the smaller building be x.

Distance between the two buildings = 18.5 meters.

Angle of elevation = 18°

From the properties of trigonometric ratios we know that:

tan 18° = (15 - x) / 18.5 as tan is the ratio of perpendicular and base of a triangle.

solving we get :

15 - x = 6.011 m

or, x = 8.99 m

The shorter building is approximately 8.99 meters tall.

The angle of elevation is described as "the angle formed between the horizontal line and the line of sight when an observer looks upwards" in mathematics. It is always higher and at a greater angle than the observer.

An angle of depression is produced when someone looks down, which is the opposite of an angle of elevation.

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Answer:

4 3/8+6 5/8=x and x÷1/4=number of gallons

Answer:

4 3/8+6 5/8=x and x÷1/4=number of gallons

Step-by-step explanation:

Answer:

1. Trinomial 2. Trinomial 3. Monomial 4. Binomial 5. Binomial

Step-by-step explanation:

The numbers with variables attached are called terms, and how many there are defines the equation. It doesn't matter how many variables or exponents are attached, there could be none or 15 each to the power of 6 but it's still one term. "Mono" means one, so there's only one term, "Bi" means two, so there are two terms, and "Tri" means three, so there are three terms. "Poly" applies to everything above three, though unused words for the bigger terms do exist.

Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Answer:

z = 39

Step-by-step explanation:

Given

z - 18 = 21 ( isolate z by adding 18 to both sides )

z = 39

Answer:

z = 39

Step-by-step explanation:

z - 18 = 21​

Add 18 to both sides;

z - 18 + 18 = 21 + 18

21 + 18 = 39

Hence,

z = 39

Answer:

49°

Step-by-step explanation:

Right angled triangle:

This is a type of triangle with one of the angle as 90°

Sum of angles in a Right angled triangle is 90°

Therefore,

y + 41° = 90°

collecting like terms

y = 90 - 41 = 49°

Therefore,

y = 49°

Answer:

-1

Step-by-step explanation:

\(\frac{10-8}{-7- - 5}\) =\(\frac{2}{-7+5}\) = \(\frac{2}{-2}\) = -1

Ordered pairs are written (x,y)  The first number is the x coordinate and the second number is the y coordinate.

(-5,8)  and (-7,10)  You take the y's and subtract them that is your numerator.  Take the x's and subtract them.  That is your denominator.

We have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

To solve the given equations for the equilibrium values of C, NX, CF, r, and ε, let's go step by step.

First, we'll substitute equations (2), (3), (4), (5), (6), (7), (8), and (9) into equation (2) to eliminate the variables C, I, G, NX, CF, and T.

Equation (2) becomes:
Y = (1/2)(Y - T) + (2,000 - 100r) + 1,500 + (500 - 500ε)

Next, let's simplify the equation:

Y = (1/2)(Y - 1,000) + 2,000 - 100r + 1,500 + 500 - 500ε

Distribute (1/2) to the terms inside the parentheses:

Y = (1/2)Y - 500 + 2,000 - 100r + 1,500 + 500 - 500ε

Combine like terms:

Y = (1/2)Y + 3,500 - 100r - 500ε

Now, let's isolate Y by subtracting (1/2)Y from both sides:

(1/2)Y = 3,500 - 100r - 500ε

Multiply both sides by 2 to get rid of the fraction:

Y = 7,000 - 200r - 1,000ε

We now have one equation (10) in terms of Y, r, and ε.

Next, let's substitute equation (1) into equation (10) to solve for Y:

5,000 = 7,000 - 200r - 1,000ε

Subtract 7,000 from both sides:

-2,000 = -200r - 1,000ε

Divide both sides by -200:

10 = r + 5ε

This gives us equation (11) in terms of r and ε.

Now, let's substitute equation (11) into equation (5) to solve for NX:

NX = 500 - 500ε

Substitute r + 5ε for ε:

NX = 500 - 500(r + 5ε)

Simplify:

NX = 500 - 500r - 2,500ε

This gives us equation (12) in terms of NX, r, and ε.

Finally, let's substitute equation (12) into equation (6) to solve for CF:

CF = -100r

Substitute 500 - 500r - 2,500ε for NX:

CF = -100(500 - 500r - 2,500ε)

Simplify:

CF = -50,000 + 50,000r + 250,000ε

This gives us equation (13) in terms of CF, r, and ε.

To summarize, we have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

These equations represent the equilibrium values of Y, r, ε, NX, and CF in the given open economy.

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The system of equations with no solutions is the second one:

3x - 7y = 22

4.5x - 10.5y = 44

When we have a system of linear equations, the only case where the system has no solutions is when both of the lines are parallel lines (thus, the lines never intercept).

So we need to identify the system of linear equations where the lines are parallel.

If you look at the second system of equations, we have:

3x - 7y = 22

4.5x - 10.5y = 44

We can multiply the first equation by 1.5 to get:

1.5*(3x - 7y) = 1.5*22

4.5x - 10.5y = 33

Then the system is:

4.5x - 10.5y = 33

4.5x - 10.5y = 44

We can see that these lines are parallel,and thus, this system has no solutions.

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Answer:

2.45 sec

Explanation:

use the equation:

a = (Vfy-Viy) / t a=-10m/sec sq

Viy = 30.1 Sin 24 = +12.24

Vfy = - Viy = -12.24

-10 = (-12.24-12.24)/t

t = 24.48/10= 2.45 sec

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Answer:

x=144

Step-by-step explanation:

x/12-5=7

x-60=84

x=84+60

x=144

The given expression's quotient is \(-\frac{m^{12}n^6}{2}\).

Exponential expressions are simply a shorthand way of writing powers. The exponent indicates how many times that base has been used as a factor to multiply. So, in the case of 32, it is 2x2x2x2x2x2 = \(2^5\), where 2 is the "base" and 5 is the "exponent." This expression is translated as "two to the fifth power." In general, an=axaxax...xa(n times), where 'a' is the base and 'n' is the exponent, will be read as "a to the nth power."

Given that the exponential expression is \(\frac{2m^9n^4}{-4m^{-3}n^{-2}}\)

The given expression's quotient is

\(=\frac{2m^9n^4}{-4m^{-3}n^{-2}}\\\\\frac{1}{a^x}=a^{-x}\\\\=\frac{m^9n^4m^{3}n^{2}}{-2}\\\\=\frac{m^{9+3}n^{4+2}}{-2}\\\\=\frac{m^{12}n^6}{-2}\\\\=-\frac{m^{12}n^6}{2}\)

As a result, the given expression's quotient is\(-\frac{m^{12}n^6}{2}\).

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If you draw all diagonals of a regular hexagon you have 5⋅6=30 possible triangles, but 5 of those are the same (the equilateral triangles) so we have 30−5=25 possible triangles.

In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. A hexagon has six angles and six vertices. Hexa and gonio both denote the number six. A hexagon can be found in the shapes of a honeycomb, a football, a pencil face, and floor tiles. a standard hexagonal 2D geometric polygon with six equal-length sides and six equal-sized angles. All of the lines are closed, and there are no curving edges. A regular hexagon has 720 degrees of internal angles. Additionally, these shapes have six rotating and six reflective symmetries.

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Answer:

Step-by-step explanation:

P =$ 1300

R = 5% = 0.05

T = 6 years

I = P * R *T

 = 1300 * 0.05 * 6

 = $ 390

Answer:7

Step-by-step explanation:

Answer:

[see below]

Step-by-step explanation:

\(\frac{7}{52}\) is a proper fraction. Therefore, it cannot be written as a mixed number.

7 can go into 52 7 times with 3 'parts' remaining.

This means that 7 is the whole number and the fraction is 3/7.

\(\frac{52}{7}=7\frac{3}{7}\)

Hope this helps.

Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

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Answer:

Step-by-step explanation:

let the number be x

so according to the question ur equation is

4x=5<x^2

4x-5=x^2

4-5=x^2/x

-1=x

Answer:

{-1, 0, 1, 3}

Step-by-step explanation:

A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.

The 95% confidence interval for the population proportion is (0.88, 0.98).

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally employed. The confidence interval is the range of values within which you expect your estimate to fall a given proportion of the time if you repeat your experiment or re-sample the population in the same manner.

Here,

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.93.

The standard error of the proportion is:

σ=√(p(1-p)/n)

=√((0.93*7)/100)

=0.0255

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

=1.96*0.0255

=0.05

Then, the lower and upper bounds of the confidence interval are:

LL=0.93-0.05

=0.88

UL=0.93+0.05

=0.98

The population proportion's 95% confidence interval is (0.88, 0.98).

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Answer:

7*3=21

8-5=3

21+3-24

Step-by-step explanation:

Answer:

4.189 radians

Step-by-step explanation:

Given data

θ=240 degrees

Let us convert from  degrees to radians

Angle in Radian= Angle in degree* π/180

Substitute

Angle in Radian= 240* π/180

Angle in Radian= 4* π/3

Angle in Radian= 4* 3.142/3

Angle in Radian=12.568/3

Angle in Radian=4.189 radians

Answer:

1.77865216

Step-by-step explanation:

Answer:

About 198.6 feet

Step-by-step explanation:

This situation essentially forms a sideways triangle with height 80 feet. It can be divided into two right triangles, which you can each find the base length for, and then add them together to find the total height of the building.

Let's start with the lower base (with the angle measure of 56 degrees), which we'll call b. The tangent of an angle in a right triangle is the length of the opposite side divided by the length of the adjacent side, meaning that:

\(\tan 56=\dfrac{b}{80} \\\\b=80 \cdot \tan 56\approx 118.6\)

Now, let's do it for the upper part, which we'll call y:

\(\tan 45=\dfrac{y}{80} \\\\y=\tan 45 \cdot 80=1 \cdot 80 =80\)

Adding these together, you get a height of approximately 198.6 feet. Hope this helps!

Answer:

answer is 198.6

Step-by-step explanation:

Answer:

X= 1/2 y= -2/5. X+2y= -1/5.

The equation of the line passing through the point with coordinates (1/2, -2/5) and having slope -1/2 is:

y = -1/2x + b.

Substituting coordinates of the point in the equation, we get:

-2/5 = -1/2(1/2) + b => b = 1/5.

Therefore, the equation of the line is:

y = -1/2x + 1/5.

Step-by-step explanation: