3.4/feet
5 feet
Find the area of the triangle pictured above.
h
square feet
Area =

Step-by-step explanation:

try this option, all the details are in the attachment.

Complementary Angles- When the sum of two angles is equal to 90 degrees, they are called complementary angles. (For example, 30 degrees and 60 degrees are complementary angles)

Supplementary Angles-Supplementary angles are those angles that sum up to 180 degrees. (For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.)

Congruence Postulate- to be congruent if two angles and the side between these two angles of one triangle are congruent to corresponding angles and the included side (side between two angles) of the other triangle

Linear Pairs of Angles-A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

The average rate of change in the fuel economy in the interval of speed [60,80] is 0.1

The given function F(x) = −0.005x 2 + 0.8x + 12 models the relationship between a certain vehicle’s speed and the fuel economy

where F(x)= fuel economy in kmpl

               x =speed of the vehicle in km/h

we need  to find  the average rate of change in the fuel economy in the interval of speed [60,80].

At speed 60 km/h

the fuel economy = - 0.005(60²) + 0.8(60) +12

                                      = - 18 + 48 + 12

                                      = 42 kmpl

At speed 80 km/h

the fuel economy = - 0.005(80²) + 0.8(80) +12

                                      = - 32 + 64 + 12

                                      = 44 kmpl

the average rate of change is given by the formula = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

By substituting the values we get= [tex]\frac{44- 42}{80-60}[/tex]

                                                   = 2/ 20

                                                   = 0.1

Hence, The average rate of change in the fuel economy in the interval of speed [60,80] is 0.1 which reflects that for increase in every one kilometer there is increase in fuel economy by 0.1

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Answer:

f(3) = 3 - 3   -->  f(3) = 0

f(x) = 12,  x = 15  (because 15 - 3 would equal 12)

g(-3) = 2  (because in the chart for g(x), an x of -3 is 2)

g(x) = -3,  x = 5  (because in the chart for g(x), a g(x) of -3 is an x of 5)

For the graph questions, p(0)=  means that the 0 is the x integer and you must find the y when x=0

p(0) = 3

p(-4) = 5

p(1) = 3

p(x) = 1,  x = 2

For the graph questions, p(x)=0 means that the 0 is the y integer and you must find the x when y=0

p(x) = 0,  x = 2.5

p(x) = 5,  x = -4

p(3) = -1

p(x) = 2,  x = 1.5

The number of teaspoons of pepper required for beef is ( 3 / 4).

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that the recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes the number of teaspoons required for 9 potatoes will be calculated as below:-

3 potatoes = ( 1 / 4 ) teaspoon

1 potato = ( 1 / 12 ) teaspoon

9 potatoes = 9 / 12 teaspoon

9 potatoes = 3 / 4 teaspoon

Therefore, the number of teaspoons of pepper required for beef is ( 3 / 4).

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The amount of times that the the bacterial cell is smaller than the amoeba cell is; 150 times

Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base.

We are given;

Length of a bacterial cell = 3 * 10⁻⁶ m

Length of an amoeba cell = 4.5 * 10⁻⁴ m

Thus, to get the amount of times that the bacterial cell is smaller than the amoeba cell, we need to convert the Length of a bacterial cell to have same exponent as that of the Length of an amoeba cell before dividing.

Thus;

Length of a bacterial cell = 3 * 10⁻⁶ m

Length of an amoeba cell = 450 * 10⁻⁶ m

Thus, the amount of times that the the bacterial cell is smaller than the amoeba cell is;

(450 * 10⁻⁶)/(3 * 10⁻⁶) = 150 times

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Answer:

Hello,

Step-by-step explanation:

P(n)=ax²+bx+c (quadratic sequence)

with a=1,b=1,c=13

[tex]\\\boxed{u_n=n^2+n+13}\\[/tex]

Answer:

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

Given sequence:

We can see this not AP or GP as the difference or ratio of consecutive terms is not common.

But we can see the difference between terms has common difference of 2:

and

It means the sequence is of the second degree, in other words it is quadratic.

In general it is of the form:

Use the terms of the given sequence to work out unknown coefficients.

t₀ = 15 - (4 - 2) = 15 - 2 = 13

It gave us the value of c.

t₁ = 15

t₂ = 19

Compare the last two equations and solve for a and b:

Then

So we know the coefficients:

The nth term equation is:

The garden store was able to sell a total of 1,960 bags of potting soil on Saturday and Sunday.

What is distributive property of multiplication over addition ?

If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.

In order to find the number of bags of potting soil sold over those two days, the first step is find out the number of pallets store sold there potting soil :

= 17( on Saturday) + 23 (Sunday)

= 40 palettes

Each palettes has 7 flats so the total number of flats sold is:

= 40 x 7

= 280 flats

Each flat then contains 7 bags so the total number of bags sold is:

= Number of flats sold x 7

= 280 x 7

= 1960 bags

In conclusion 1,960 bags of potting soil were sold.

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The linear equation that has a y-intercept of -4 and a x-intercept of -5 s y = -4/5x - 4

The equation of a line in slope intercept form is expressed y = mx + b

where

m is the slope

b is the y-intercept

Given the coordinate points (0, -4) and (-5, 0), the slope is calculated as:

Slope = y₂-y₁/x₂-x₁

Slope = 4/-5

Slope = -4/5

Determine the equation

y = -4/5x + (-4)

y = -4/5x - 4

Hence the linear equation that has a y-intercept of -4 and a x-intercept of -5 s y = -4/5x - 4

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The measure of angles X if Angle Z and Angle X on intersecting lines are vertical angles is 63 degrees

Vertical angles are a pair of opposite angles formed by intersecting lines. In vertical angles, the angles meet at point X.

Given the following parameters

angle Z = 63degrees

If the angleZ and angle X are vertical angles, hence <X = <Z

Therefore;

<X = 63 degrees

Hence the measure of angles X if Angle Z and Angle X on intersecting lines are vertical angles is 63 degrees

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Step-by-step explanation:

[tex]{ \purple{ \tt{(X₁ + X₂)²}}}[/tex]

This above problem is in the form of

[tex]{ \blue{ \tt{ {(a + b)}^{2}}}}[/tex]

where the expanded form of

[tex]{ \blue{ \tt {(a + b)}^{2}}} = { \green{ \bold{ {a}^{2} + {b}^{2} + 2ab}}} [/tex]

then the (X₁ + X₂)² answer will be

[tex]{ \purple{ \tt{(X₁ + X₂)²}}} = { \purple{ \tt{ {X₁}^{2} + {X₂}^{2} + 2X₁X₂}}}[/tex]

Answer:

c, 400

Step-by-step explanation:

64 square in. = 412.902 square cm

412.902 rounded equals 400

hope that helps <3

Someone who is earning $39,000 a year, would pay $1,638 towards social security out of their gross wages

Employees in 2012 paid 4.2% of their gross wages towards social security tax.

As the gross yearly wages of an employee is $39,000 and he have to pay the 4.2% of his gross wages towards social security or FICA tax.

Percentage means division by 100 and to know the contribution of the employee we need to multiply the percentage with the gross wages of the employee

He paid towards social security = 4.2% of 39000

                                                    = 4.2/100×39000                                            

                                                    = 0.042 × 39000

                                                    = $1,638.00

He would pay $1,638 towards social security tax out of their wages.

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The equivalent expression is negative eleven sixths times n minus one twelfth. Option C

Algebraic expressions are expressions that comprises of variables, terms, constants, coefficients and factors.

They are also made up of arithmetic operations such as division, multiplication, addition, subtraction, bracket, etc.

Equivalent expressions are expressions with the same solution but different arrangement of elements.

Given the expression

{ -3 1/3n + 1/6} + { 1 3/6n - 3/12 }

expand the bracket

-3 1/3n + 1/6 + 1 3/6n - 3/12

collect like terms

-10/3n + 1/6 + 9/6n - 3/12

-10/3n + 9/6n + 1/6 - 3/12

find the lowest common multiple

-20n + 9n/6 + 2 - 3 /12

-11n/6 - 1/12

Thus, the equivalent expression is negative eleven sixths times n minus one twelfth. Option C

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The area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1) coordinates is 6 square units

We first need to plot all the given points A  (2,-2), B (2,1), C (4,2), D (6,2)and E (4,-1) which is coordinate geometry

After joining the Points which is a pentagon and it can be divided in two shapes one is triangle CDE and a quadrilateral ABCE

Using the distance formula

BC = [tex]\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }[/tex] = [tex]\sqrt{(2-1)^{2} + (4-2^{2} }[/tex] = √5

Since BC = AE and BC ll AE , we can say ABCE is a parallelogram

area of a parallelogram = base × Altitude

                                      = 2 × 2= 4

Area of triangle CDE where CD is perpendicular and CE is the base

                        = 1/2 ( 2×2)

                        = 1/2 (4)

                         = 2 square units

So the area of ABCDE = Area of ABCE + area of CDE

                                     = 4 square units + 2 square units

                                      = 6 square units

Hence, the area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1)coordinates is 6 square units

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The answer option which is not an example of an experiment is to: C. pick the team that won last year's World Series.

An experiment can be defined as a scientific investigation which typically involves the process of manipulating an independent variable (the cause), so as to determine or measure the dependent variable (the effect).

In this scenario, some examples of an experiment include the following:

In conclusion, "picking the team that won last year's World Series" is not an example of an experiment because it does not connote a scientific investigation or observation

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Answer:

Nope. 5x3=15 +5=20 20+10=30 so no he didn't.

Step-by-step explanation:

Bye bye license

The point that represents an INEFFICIENT point of production is point A.

The correct answer is an option (a)

In this question we have been given a graph of Skateboards vs. Bikes.

We need to find the point that represents an INEFFICIENT point of production.

Inefficient production means the economy can be producing more goods without using any additional resources.

In given production possibility curve, an INEFFICIENT point of production is point A.

Therefore, the point that represents an INEFFICIENT point of production is point A.

The correct answer is an option (a)

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Attached is the Correct Answer Please verify yours.

[tex](x + 2 {y}^{2} )( {x}^{2} - 2x {y}^{2} + 4 {y}^{4} )[/tex]

Answer:

none of them

Step-by-step explanation:

During the experiment the temperature changes slightly. Hence

the percentage increase in the temperature of the mixture is 27.35%.

Given, the temperature of the mixture changes from 12 1/4°F to 15 3/5°F

we are asked to determine the percentage of increase in the temperature of the mixture.

Initial temperature = 12 1/4°F

convert it into proper fraction.

= 48+1/4

= 49/4°F

Final temperature = 15 3/5°F

convert it into proper fraction.

= 75+3/5

= 78/5

Therefore, percentage increase:

= Final temp - Initial temp/Initial temp × 100

% Increase = (78/5 - 49/4)/49/4 × 100

% Increase = (78×4 - 49×5/5×4)/49/4 × 100

% Increase = 312-245/5×49 × 100

as 4 gets cancelled from numerator and denominator.

% Increase = 67×100/249

% Increase = 6700/249

% Increase = 27.346%

we need to round it off to the nearest hundredth.

% Increase = 27.35%

Hence the percentage increase in the temperature is  27.35%.

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Answer:

b

Step-by-step explanation:

Answer:

A translation 4 units right and 5 units down followed by a rotation of 90 degrees clockwise about the top left vertex of triangle 2

It will cost $350.00 to buy enough carpet for the living room.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of the three-dimensional object.

Now it is given that,

Length of room,l =

Width of room, w =

So, area of the room =  l*w = 7*5

⇒ area of the room = 35 square meter

Since, indigo carpet costs $10.00 per square meter

Thus, total cost to install the carpet =  area of the room*carpet costs

⇒ total cost to install the carpet = 35*10

⇒ total cost to install the carpet = $350

Thus, It will cost $350.00 to buy enough carpet for the living room.

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The value of x in the inequality is: D. -6 < x < 9

Given the inequality,  −7 < x − 1 < 8, solve for the possible values of x as shown below:

−7 < x − 1

Add 1 to both sides

-7 + 1 < x - 1 + 1

-6 < x

or

x − 1 < 8

Add 1 to both sides

x - 1 + 1 < 8 + 1

x < 9

Combining both inequalities together, the value of x is: D. -6 < x < 9

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Answer:

98 Glass pitchers.

Step-by-step explanation:

You can determine this is the answer due to multiplying the sum and the product together, making the final answer 98 Glass pitchers. Hope this helped! :D

Answer:

1)   A - B = {2, 4, 6}

2)   B - A = {9}

3)   (A ∪ B) - C​ = {1, 3, 5, 7, 9}

Step-by-step explanation:

Set Notation

[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]

Given sets:

Question 1

[tex]\begin{aligned}\sf A-B & =\sf \{ 1, 2, 3, 4, 5, 6, 7 \} - \{1, 3, 5, 7, 9 \}\\& =\sf \{ 2, 4, 6 \}\end{aligned}[/tex]

Question 2

[tex]\begin{aligned}\sf B-A & =\sf \{1, 3, 5, 7, 9 \} - \{ 1, 2, 3, 4, 5, 6, 7 \}\\& =\sf \{9 \}\end{aligned}[/tex]

Question 3

[tex]\begin{aligned}\sf (A \cup B)-C & =\sf \left(\{ 1, 2, 3, 4, 5, 6, 7 \} \cup \{1, 3, 5, 7, 9 \} \right) - \{0, 2, 4, 6, 10 \}\\& =\sf \{ 1, 2, 3, 4, 5, 6, 7, 9 \} - \{0, 2, 4, 6, 10 \}\\& = \sf \{ 1, 3, 5, 7, 9 \}\end{aligned}[/tex]

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Answer:

g=93 h=87 k=122 m=58

Step-by-step explanation:

Answer:  √20

Step-by-step explanation:

The square root of 20 is 4.47213595 which is a decimal and not a whole number.