Please hurry and answer

Answer:

m∠ABD=116°

m∠DBC=64°

Step-by-step explanation:

The sum of the two angles given equals 180°.  To find the two angle measures, use the following equation:

m∠ABD+m∠DBC=180°

For this problem, m∠ABD=(7x+67)° and m∠DBC=(8x+8)°.  So,

(7x+67)°+(8x+8)°=180°

15x+75=180

15x=105

x=7

Next, substitute x=7 into the original expressions for the angle measures.

m∠ABD=(7(7)+67)°

m∠ABD=(49+67)°

m∠ABD=116°

and

m∠DBC=(8(7)+8)°

m∠DBC=(56+8)°

m∠DBC=64°

The relationship between the interior and exterior angles of a polygon is they are supplementary.

What is a regular polygon?

If a polygon has equal sides and angles, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.

Here,

we have to show how the interior and exterior angles of a polygon relate to each other.

A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees.

As a result, the interior angles of a regular polygon are all equal to 180 degrees minus the measure of the exterior angle(s).

Hence, the relationship between the interior and exterior angles of a polygon is they are supplementary.

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The solution to the equation cosh(t) = t does not exist

The equation is given as

cosh(t) = t

To solve the equation cosh(t) = t, we can start by expressing the equation in terms of e^t and e^-t.

So, we have"

cosh(t) = (e^t + e^-t)/2 = t.

Rewrite the above equation as

e^t + e^-t = 2t.

Using a graphing calculator, the curve of e^t + e^-t and the line of 2t do not intersect

Hence, the equation has no solution

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Answer:

I) 5575

ii) 312.50

b) 345

Step-by-step explanation:

I)11.15(500)=5575

ii) 1.25(250)=312.50

b) 407.10/1.18 = 345

Answer:

No

y = –3

Step-by-step explanation:

solution

–8 = 2y – 2

–8 + 2 = 2y

– 6 = 2y

[tex] \frac{ \\ - 6}{2 } = \frac{2y}{2} [/tex]

–3 = y

y = –3

The expression that is equal to 89.7 ÷ 10 is 897.5/100

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that an expression 89.7 ÷ 10

89.7 ÷ 10 = 8.97

1. 897.5/100

= 8.97

2. 8.975/100

= 0.08975

3. 8.975/1

= 8.975

4. 8.975/1000

= 0.008975

5. 89.750/1000

= 0.08975

Hence, the expression that is equal to 89.7 ÷ 10 is 897.5/100

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Using the concept of arithmetic progression , We have t(n) = a +(n-1)d formula, The answer is 3.

A number sequence is a series of numbers that are listed in a particular order. The numbers in a sequence may follow a specific pattern or rule. Examples of number sequences include the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, etc.), the Fibonacci sequence (1, 2, 4, 8, 16, 32, etc.), and the triangular number sequence (1, 3, 6, 10, 15, etc.). Number sequences are often studied in mathematics and have many applications in fields such as computer science, engineering, and physics.

An arithmetic progression (AP) is a type of number sequence in which the difference between any two consecutive terms is always the same. This common difference is known as the "common ratio" of the sequence. For example, the sequence 2, 5, 8, 11, 14 is an arithmetic progression because the common difference is 3.

t(n) =  a + (n-1)d

n=5

t(5)=17

a=5

17 = 5 +(5-1)d

12=4d

d=12/4 = 3

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A graph of paired points that form a proportional relationship is a straight line that can be drawn through all the points, and the line passes through

the point where, x, = 0 and, y, = 0.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The equation of a line on a graph that forms a straight line and forms a proportional relationship will have to pass through the origin.

origin = (x, y) = (0, 0)

Thus,

The graph of paired points that form a proportional relationship is a straight line that can be drawn through all the points, and the line passes through the origin.

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The slope of the line is -5/6 in the graph.

The slope of a line is how steep it is going from LEFT to RIGHT. Slope is the proportion of a line's rise, or vertical change, to its run, or horizontal change.

No matter which two points you choose for the line's starting and ending points, the slope is always constant (it never changes).

From the given picture we can verify that

x₁ and y₁ is (-4, 6) and x₂ and y₂ is (2, 1).

We know the slope formula is y₂ - y₁ = m(x₂ - x₁)

Substituting the given details in formula we get

1 - 6 = m(2 - (-4))

-5 = m(6)

m = -5/6

Thus, the slope of the line is -5/6.

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Answer:

(-3, -2)

Step-by-step explanation:

-3x -4y = 17

x -y = -1  Can be rewritten x = y - 1

Substitute y -1  for x into the first equation

-3(y - 1) - 4y = 17  Distribute the -3

-3y + 3 -4y = 17   Combine like terms

-7y + 3 = 17  Subtract 3 from both sides

-7y = 14  Divide both sides by -7

y = -2

Substitute -2 for y in x = y -1 to solve for x

x = -2 -1

x = -3

Check

-3x -4y = 17

-3(-3) - 4(-2) = 17

9 + 8 = 17

17 = 17  checks

x -y = -1

-3 -(-2) = -1

-3 + 2 = -1

-1 = -1  checks

Answer:

Step-by-step explanation:

uhh

45000 tiles we need to fill a room with area 1080 m²

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

Area of floor =1080m²

Base of parallelogram shaped tile (b) =24 cm

and corresponding height (h)=10 cm

Area of one tile=b×h

=24×10

=240 cm²

=240/10000=24/1000 m²

Number of tiles required=1080/(24/1000)

=1080×1000/24

=45000 tiles

Hence, 45000 tiles we need to fill a room with area 1080 m²

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Answer:

(3, −1)

Step-by-step explanation:

I did the test

Answer:

14. x = 9.7 cos(17) = 9.28

15. x = cos^-1 (10/16) = 51.32

16. x = 41/tan(35) = 58.55

Answer:

16 boys and 8 girls

Step-by-step:

24 / 3 = 8

so 8 girls

24 - 8 = 16

and 16 boys

The quadratic equation with solutions of (4 + i) and (4- i) is,

⇒ x² - 8x + 17 = 0

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The solutions of the quadratic equation are,

⇒ (4 + i) and (4- i)

Now, We know that;

A quadratic equation with roots a and b is,

⇒ x² -  (a + b)x + a × b = 0

Hence,  A quadratic equation with roots (4 + i) and (4 - i) is,

⇒ x² - (4 + i + 4 - i)x + (4 + i) (4 - i) = 0

⇒ x² - 8x + (4² - i²) = 0

⇒ x² - 8x + 16 + 1 = 0

⇒ x² - 8x + 17 = 0

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We can rewrite one side of the given equation using distributive property.

What is distributive property?

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

A, B, and C are the operands in the formula for the distributive property, which is written as a (b + c) = (a b) + (a c). Here, each term enclosed in a bracket multiplies the number outside of it, and the results are added.

The given equation is: 3(x + 2) = 18

Simplifying this,

3*x + 3*2 = 18

3x + 6 = 18

Hence, we can rewrite one side of the given equation using distributive property.

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An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

Give nonfiction books an x-factor.

Since there are three times as many fiction books as nonfiction books, we have a 3x/5 ratio, according to the question.

Due to the fact that they initially only sold two of these sorts and the fact that there were 240 volumes overall,

Due to this, the equation will be framed.

3x/5+x=240

So 8x/5=240

x=150 ( Number of non fiction books) ( no of non fiction books)

90 novels are so required.

Right at the start, this was a number.

Allow the number of books sold to increase.

In light of this, the equation is

Since there were 5:9 books in each category (fiction and nonfiction),

(90-y)/(150-y)=5/9

y=15

Therefore, the answer is 15.

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Therefore , the solution of given problem of equation comes out to be

P is equal to 12 pounds per square foot.

Comparable to a balance scale, an equation. The equation (or scale) is out of balance if we add or subtract variable from one side. We also Must keep the "scale" (or equation) balanced while solving math equations such that both parts are always equal as expression are equal.

Here,

P= p = 12 + 4/9d is the equation that describes the relationship between the pressure,

p, of sea water in some deep ocean regions and the depth, d, below the surface.

Where

In pounds per square foot, p.

in feet is d

1) At a depth, seawater has a pressure of 85 pounds per square foot.

85 = 12 + 4/9d

4.9d/9 = 85 - 12 = 73

By xing it out, it becomes

4.9d = 73 × 9 = 657

d = 657/4.9

d = 134.1 feet

2) At 85 feet just below water's surface, the pressure of saltwater is

p = 12 + 4/9 × 85 = 12 + 4/765

P is equal to 12 pounds per square foot.

Therefore , the solution of given problem of equation comes out to be

P is equal to 12 pounds per square foot.

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Answer:

Step-by-step explanation:

-672 would be your answer

Solving the triangle we found the distance between the gazebo and the dock is: 69.34 meters. The answer is explained below:

The first thing to know is that to solve any triangle you must know at least one side and two other elements that can be sides or angles, that is, at least three elements of the six that make up a triangle.

Now, in the problem we know the value of one side (90 m) and 3 angles (see attached image), therefore the calculation of the distance (one side) is very easy if we apply the law of sines:

According to the Law of Sines, the ratio of the length of the sides of a triangle (not a rectangle) and their respective opposite angle sines, is the same value. Then:

d / sen (46°) = 90 m / sen (69 °)  

After, we pass  sen (46°) to the second term of the equation.

d= sen(46°)*90 m / sen (69°)

d = 0,7193*90/ 0,9335

d = 69,34 m

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Based on the information given the correct option is option E.) Michael has an absolute and comparative advantage in changing the oil.

Absolute advantage refers to the ability of a country or firm to produce a good or service at a lower cost than another country or firm. It is a concept in international trade and economic theory.

A country or firm has an absolute advantage in a good or service if it can produce that good or service more efficiently than another country or firm.

An individual has a comparative advantage in production if it produces at a lower opportunity cost when compared with other individuals.

The opportunity cost of Michael in the changing of oil = 10/ 8 = 1.25

Opportunity cost of Michael in changing tyres = 8 / 10 = 0.8

The opportunity cost of Martha in the changing of oil = 14 / 7 = 2

The opportunity cost of Martha in the changing of tyres = 7 / 14 = 0.5

Michael has an opportunity cost in changing of oil and Martha has an opportunity cost in changing of tyres.

Absolute advantage is when an individual produces more quantity of a good or service when compared to others.

So, Michael changes more oil (8) than Martha (7). Martha changes more tyres (14) than Michael (7)

Therefore, Based on the information given the correct option is option E.) Michael has an absolute and comparative advantage in changing the oil.

The complete question is:

Michael and Martha run a mechanic shop. In one hour Michael can perform eight oil changes or change ten tires. In one hour Martha can perform seven oil changes or change fourteen tires. Given this information which of the following is true?

A) Martha has a comparative advantage in changing oil.

B) Martha has an absolute advantage in changing oil.

C) Michael has a comparative advantage in changing tires.

D)Michael has an absolute advantage in changing tires.

E.) Michael has an absolute and a comparative advantage in changing oil

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On solving the question we can say that  slope intercept form of the equation is y = -1/4x +1/2

One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.

Any location that is not on the line will not fulfill the coordinates.

This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.

The line passes through (-2,1)

slope = -1/4

The equation of the line

y = mx + c

here m is the slope and c is the intercept.

putting the point and slope in the equation

1 = -1/4 *(-2) + c

⇒ c = 1/2

So the slope intercept form of the equation is

y = -1/4x +1/2

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Consider units digit as u and tens digit as t, so t=1/2 u is the right equation.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

given : t + u=9

1/2u+u=9 by substituting the value of t

3u=18

u=6.

t=1/2*6=3.

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Answer: it is not a function

Step-by-step explanation: occurs when there was an attempt to call a value from a function, but the value is not actually a function.

The explicit formula for this geometric sequence 3, 15, 75, 375... is aₙ = 3(5)ⁿ⁻¹.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Note: The nth term of a geometric sequence is equal to the explicit formula for the geometric sequence.

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = 15/3

Common ratio, r = 5.

Now, we can calculate the nth term (explicit formula) of this geometric sequence as follows:

aₙ = a₁rⁿ⁻¹

aₙ = 3(5)ⁿ⁻¹

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Complete Question:

Find an explicit formula for the geometric sequence 3, 15, 75, 375...

(1-0.2)C expression represents the cost after the discount

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Answer:m/s

Step-by-step explanation:

Answer:

To find the average speed of the passenger jet, we need to divide the distance traveled by the time it took to travel that distance.

Average speed = distance / time

In this case, the distance is 1,213 miles and the time is 2.7 h.

Average speed = 1213 miles / 2.7 h = 449.6 miles/h

So the average speed of the passenger jet is 449.6 miles per hour.

Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15

The value of the car is solved by using the formula for depreciation which is  y = A(1 – r)t

definition of variables

where

y = current value, = ?

A = original cost, = $24,000

r = rate of depreciation, = 15% and

t = time, in years. = 4 years

substituting the variables

current value, y = A(1 – r)t

current value, y = 24000 * (1 - 0.15)⁴

current value, y = 12528.15

the depreciation is $12528.15

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Answer: B

Step-by-step explanation:

b is 64 because exterior angles are congruent