Find the 2 two-digit numbers that divide 179 with a remainder of 4.

Measure of exterior angle = 139°

Exterior angles are angles that are parallel to the inner angles of a polygon but lie on the outside of it. The measure of an exterior angle is equal to the sum of the two internal opposite angles.

Given,

In the figure

Measure of exterior angle = 15x + 34

Measure of opposite interior angle = 12x + 26 and 29°

But, measure of exterior angle is equal to sum of opposite two angles

⇒ 15x + 34 = 12x + 26 + 29

⇒ 15x - 12x = -34 + 26 + 29

⇒ 3x = 21

⇒ x = 21/3

⇒ x = 7

Measure of exterior angle = 15x + 34

                                            = 15(7°) + 34°

                                            = 105° + 34°

                                            = 139°

Hence, 139° is the measure of exterior angle.

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The value of the given expression at the given points is 52.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.

An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Consider, the given expression  

y + (x^2 - 2)/2

We have to find the value of expression at x = 10 and y = 3

Plug x = 10 and y = 2 in the above equation.

3 + (10^2 - 2)/2

3 + (100 - 2)/2

3 + 98/2

3 + 49

52

Hence, the value of the given expression at the given points is 52.

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Answer:

  m∠D = m∠E = 80°

Step-by-step explanation:

You want the measures of the angle of elevation (∠E) from A to B and the angle of depression (∠D) from B to A when they are described by the expressions 7x-4 and 4(x+8), respectively.

The angle of elevation and the angle of depression between the same two points have the same measures.

  m∠E = m∠D

  7x -4 = 4(x +8)

  7x -4 = 4x +32

  3x = 36 . . . . . . . . add 4-4x to both sides

  x = 12 . . . . . . . . divide by 3

  4(x +8) = 4(20) = 80 . . . . . . . . find the angle measures

Each of the angles has a measure of 80°.

19(360) + 18(400) + 8(480) + 5(600) /  19 + 18 + 8 + 5 this expression

represents the average wages a company pays per employee each week

Correct option is: E

An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) It is possible to compare expressions to phrases.

Mathematical expressions consist of at least two integers or parameters, at least one arithmetic operation, as well as a statement. Any one of the following mathematical operations can be used i.e multiply, divide, add, or subtract. The form of an expression is as follows: (Math Operator, Number/Variable, Expression)

From the table we get this -

Wages the company pays to employees each week:

= 19(360) + 18(400) + 8(480) + 5(600)

Total number of employees:

= 19 + 18 + 8 + 5

Thus,

the average wages a company pays per employee each week:

= Wages the company pays to employees each week / Total number of employees

= 19(360) + 18(400) + 8(480) + 5(600) /  19 + 18 + 8 + 5

Correct option is: E

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The perimeter of the triangle DEF is equal to 73 considering the segments tangent to circle J

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

DG = FG = 11

DF = 2 × 11

DF = 22

DH = FI = 9.5

and

EH = EI = 16

so!

ED = 9.5 + 16

ED = 25.5

EI = 16 + 9.5

EI = 25.5

perimeter of triangle DEF = DF + ED + EF

perimeter of triangle DEF = 22 + 25.5 + 25.5

perimeter of triangle DEF = 73

Therefore, 73 is the perimeter of the triangle DEF considering the segments tangent to the circle J.

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Answer:4

Step-by-step explanation:

First you need to find how many cups of milk is in one serving. So, you take 2 1/2 and divide it by 5 to get 1/2 then you multiply 1/2 by eight to get 8/2. Simplify to get your answer which is 4.

The slope of the line that passes through the points (0, -6) and (0, -5)is undefined.

Slope is line's inclination with regard to the horizontal is quantified numerically. In analytical geometry, a line, ray, or line segment's slope is the ratio of the vertical to horizontal distance between any two points on the line, ray, or line segment ("slope equals rise over run").

In differential calculus, the derivative of a function yields the slope of a line tangent to its graph, which represents the function's instantaneous rate of change with respect to changes in the independent variable.

Ok so slope is the change in y over change in x.

Your why changed from 6 to -5 so you can write this as -5 - 6

Your x didn’t change it went from 0 to 0

You can write this as 0-0

Now -11/0 is what you end up with as a slope.

Any number divided by 0 is undefined so your slope is undefined.

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The value of x and y is 0 and 5.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation.

Here, we have

Given: Equations y=2x+5, y=3x+5

We have to solve these equations by substitution.

y = 2x+5...(1)

y = 3x+5...(2)

From equation (1) we get

y = 2x+5

Now, we put the value of y in equation(2) and we get

2x+ 5 = 3x+5

x = 0

Now, we put the value of x in equation(1) and we get

y = 2(0) + 5

y = 5

Hence, the value of x and y is 0 and 5.

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Yes, the given relation is proportional and has a constant of proportionality = 0.3 or ratio of proportionality 3/10, thus option (A) is correct.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As  given,

A 12-ounce cup costs $3.60.

The ratio of cost to ounce = 3.60/12 = 0.3

A 16-ounce cup costs $4.80.

The ratio of cost to ounce = 4.80/16 = 0.3

So constant of proportionality is 3/10.

Hence "Yes, the given relation is proportional with a constant of proportionality is 0.3".

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The population of the cells after 7 days is 12800 cells.

The population will first exceed 60000 cells after 9.2 days.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Initial population = 100 cells

The number of population after x days is given by.

f(x) = 100 x [tex]2^x[/tex]

Now,

The population after 7 days.

f(7) = 100 x [tex]2^7[/tex]

f(7) = 100 x 8 x 8 x 2

f(7) = 100 x 2 x 64

f(7) = 200 x 64

f(7) = 12800

The population after 9 days.

= 100 x 512

= 51,200

The population after 9.23 days.

= 100 x 600.49

= 60049

The population after 10 days.

= 100 x 1024

= 102,400

This means,

The population will exceed 60,000 after 9.23 days

Thus,

The population after 7 days is 12800.

The population will exceed 60,000 population after 9.2 days.

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Answer:

Step-by-step explanation:

46

Answer:4

Step-by-step explanation: you would just plug the one in for every x there is so 8(1)-4=8-4=4

The denominator is equal to zero when u = 11/12, then for that value the expression is undefined.

The expression is undefined if we have an undefined operation, like a logarithm of a negative number or a division by zero.

Here we have a rational expression, which is:

(-9u + 8)/(-12u + 11)

Notice that we have the variable on the denominator, then the values for which the expression is undefined are the values of u such that the denominator becomes equal to zero:

-12u + 11 = 0

11 = 12u

11/12 = u

The expression is undefined for u = 11/12.

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Step-by-step explanation:

The distance between the two points (1, 2) and (-1, -7) is the square root of ((1 + 1)^2 + (2 + 7)^2), which is approximately 11.8. Rounding to the nearest tenth, the distance is 11.8.

Answer:

9.2

Step-by-step explanation:

In a two-dimensional plane, the distance between any two points (x₁, y₁) and (x₂, y₂) is given by the formula::

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

For:

(x₁, y₁) = (1, 2)
(x₂, y₂) = (-1, -7)

[tex]d = \sqrt {(-1 - 1)^2 + (-7 - 2)^2}[/tex]

==> [tex]d = \sqrt {(-2)^2 + (-9)^2}[/tex]

==>  [tex]d = \sqrt {{4} + {81}}[/tex]

[tex]d = \sqrt {85}[/tex]

[tex]d = 9.2195[/tex]

[tex]d = 9.2\;\; \textrm{rounded to the nearest thenth(one decimal place)}[/tex]

The value for which the rational expression is undefined is a = -9

A rational expression is an expression that is the ratio of two polynomials. It is also known as a fraction in which the numerator and denominator are both polynomials.

To determine the values for which a rational expression is undefined, you need to find the values that make the denominator of the expression equal to zero.

Since we have (9a-11)/(-a-9), equate the denominator to 0 and solve for a. That is:

-a-9 = 0

-a = 9

a = -9

Thus, a = -9 is the value for which the rational expression is undefined.

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The values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ are 9/√97, -4/√97, 9/√97, -4/√97, -√97/4 and √97/9.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to find the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ in standard position on the coordinate plane with the point (−4,9) on its terminal side.

r = √(16 + 81) = √97

sinθ = y/r = 9/√97

cosθ = x/r = -4/√97

tanθ = y/x = 9/√97

cotθ = x/y = -4/√97

secθ = r/x = -√97/4

cscθ = r/y = √97/9

Hence, the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ are 9/√97, -4/√97, 9/√97, -4/√97, -√97/4 and √97/9.

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Susan needs to buy 24 packages of hotdog buns to have one bun for each hot dog.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Susan buys 16 packages of hot dogs and each package contains 12 hot dogs.

Therefore, The total number of hotdogs is,

= (16×12).

= 192 hotdogs.

Also given dog buns are sold in packages of 8.

Therefore, The number of packages of hotdog buns needed are,

(192/8).

= 24 packages of hotdog buns.

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Using percentage error, the measured weight is 0.5% less than the expected weight.

The percentage error serves as a gauge for how closely a computed or experimental result matches the true or accepted value. It is determined as the true or accepted value multiplied by 100% times the absolute difference between the experimental or calculated value and the true or acceptable value.

The formula for percentage error is:

Percentage Error = (|experimental value - true value| / true value) x 100%

The weight of the distilled water can be calculated by subtracting the weight of the graduate from the combined weight of the graduate and water:

weight of water = 100.28 g - 85.49 g = 14.79 g

To calculate the percentage error, you can use the formula:

(measured weight - actual weight) / actual weight * 100%

The actual weight of 15 mL of distilled water is 15 g, so the percentage error is:

(14.79 g - 15 g) / 15 g * 100% = -0.5%

So, the deviation from the expected weight of 5 g is -0.5%, which means the measured weight of the distilled water is 0.5% less than the expected weight.

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On solving the provided question, we can say that by equation we have = x*(x-9) = x^2 - 9x

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

let the 1st number be x

2ndd be x-9

then by equation we have = x*(x-9) = x^2 - 9x

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The differentiation of [tex]e\x^{x}[/tex] is [tex]e\x^{x}[/tex] proved using the first law of differentiation or limit law.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.

[tex]\frac{d}{dx}e\x^{x}[/tex] using first order or limits to differentiate we get

for [tex]\lim_{h \to0} \frac{f(x+h) - f(x)}{h} = \frac{d}{dx}f(x)[/tex]

therefore,

[tex]\lim_{h \to 0} \frac{e\x^{(x +h)}- e\x^{x} }{h} \\[/tex] = [tex]\lim_{h \to 0} \frac{e\x^{x}(e\x^{h}-1 ) }{h}[/tex] = [tex]\lim_{h \to 0} \frac{e\x^{x}*e\x^{h} }{1} \\[/tex] ( using L-Hospital)

[tex]\lim_{h \to 0} e\x^{x} * e\x^{h} = e\x^{x} (proved)[/tex]

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The distance of coast from the nearest foot of the island is, 1300 feet

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

A helicopter hovers 1300 feet above a small island

The angle of depression from the helicopter to point P = 45°

How far is cost from the nearest foot = ?

So, here we can use methods of height and distance

here, we have height = 1300 feet

α = 45°

x = ?

tanα = h/x

tan45° = 1300/x

1 = 1300/x

x = 1300

Hence, the nearest foot is at a distance of 1300 feet

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Therefore , the solution of the given problem of equation comes out to be s = 9/4 *t is the best equation.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation

y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

s represents the number of hours sick leave

and number of weeks be represented by t.

So,

4 weeks and 9 hours of sick leave .

To find the best equation which satisfies the problem:

=> s = 9/4 *t

Putting s = 9

and t =4

=> 9 = 9/4 * 4

=> 9 =9

Therefore , the solution of the given problem of equation comes out to be s = 9/4 *t is the best equation.

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The relationship between the number of hours and cost shows a proportional relationship.

A proportion is an equation that sets two ratios at the same value. A proportion is an equation that sets two ratios at the same value. One variable in a proportional relationship is always a constant value multiplied by the other.

In this case, mechanic charges a very reasonable price per hour to work on cars. This was illustrated as the relationship between the number of hours and cost was given

For 1 hour, cost is $40, for 2 hours, the cost is $80. In this case, there's a proportional relationship. The cost per hour will be:

= $20 / 1

= $20

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Complete question

mechanic charges a very reasonable $ 40 $ 40 per hour to work on cars. For a particular repair, $ 120 $ 120 worth of parts are required. Let x x represent the number of hours that the mechanic works on the car, and let y y represent the total cost of the repair: 1 2 3 4 5 6 7 8 -1 -2 40 80 120 160 200 240 280 320 360 -40. Is the relationship proportional?

Answer:

To calculate the involuntary withholdings in all, you need to add up the amounts withheld for federal taxes, state taxes, and FICA.

First, calculate the amount withheld for federal taxes. To do this, multiply your gross pay of $1,375 by 12%, which is the percentage withheld for federal taxes:

$1,375 x 12% = $165

Next, calculate the amount withheld for state taxes. To do this, multiply your gross pay of $1,375 by 7%, which is the percentage withheld for state taxes:

$1,375 x 7% = $96.25

Next, calculate the amount withheld for FICA. To do this, multiply your gross pay of $1,375 by 8%, which is the percentage withheld for FICA:

$1,375 x 8% = $110

Now add the three amounts withheld for federal taxes, state taxes, and FICA

$165 + $96.25 + $110 = $371.25

So, the involuntary withholdings in all if your gross pay was $1,375 is $371.25

The value after the multiplication of the given expression gives 1.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given expression is (m y⁻⁴) (m⁻¹ y⁴).

We have to multiply this.

We have some of the rule of exponents that,

xᵃ . xᵇ = xᵃ⁺ᵇ and x⁰ = 1

(m y⁻⁴) (m⁻¹ y⁴) = (m m⁻¹) (y⁻⁴ y⁴)

                        = (m¹⁺⁽⁻¹⁾) (y⁽⁻⁴⁾⁺⁴)

                        = m⁰ y⁰

                        = 1

Hence the value is 1.

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Congruent angles are frequently used in the world of architecture, construction, design, and art.

Alternate Interior Angles are congruent if a transversal cuts two parallel lines. Alternate Exterior Angles are congruent if a transversal cuts two parallel lines. When a transversal cuts two parallel lines, the resulting angles are congruent.

Angle measure is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees. The angles of a regular polygon will always be congruent, regardless of its size or scale.

Are situated on opposite sides of the transversal, but between the two parallel lines. The corresponding alternate internal angles for this example would be 2 and 6, and 7 and 3. 

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The probability of choosing the city is 3/7.

What is probability ?

probability can be defined as the ratio of favourable outcomes and total number of outcomes.

Given , Sample space  = {india , chicago ,tokyo ,peru ,miami ,canada ,mexigo }

Given if we chosen randomly the city.

so the favourable = { chicado,tokyo,miami }

So, the probability of choosing the city is = x/s

where x is favourable outcomes

s is sample space

x = 3

s = 7

probability = 3/7

Hence, The probability of choosing the city is 3/7.

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Answer:

Step-by-step explanation:

Given:

The complete data is,

Team                   Pies        Hours

Crusty                   28            8

Pie Peace             27            6

Fab bakers           20            4

Yum                      26            5

To find:

The team that made pies at a rate of 4.5 per hour.

Solution:

From given table, we have,

Team Crusty made 28 pies in 8 hours.

Team Pie Peace made 27 pies in 6 hours.

Team Crusty made 20 pies in 4 hours.

Team Crusty made 26 pies in 5 hours.

In order to calculate the pies made per rate, we need to divide the number of pies made by total time taken.

So, we get,

Team Crusty = 28 pies / 8 hours = 3.5 pies per hour.

Team Pie Peace = 27 pies / 6 hours = 4.5 pies per hour.

Team Crusty = 20 pies / 4 hours = 5 pies per hour.

Team Crusty = 26 pies / 5 hours = 5.2 pies per hour.

Therefore, team Pie Peace made pies at a rate of 4.5 per hour