What is an equation of the line that passes through the point (8,-5) and is perpendicular to the line 5x+4y=24

Answer:

  220.5 square feet

Step-by-step explanation:

You want to know the area of an irregular shape.

The figure can be decomposed into a triangle and a trapezoid by extending the vertical line through the figure.

The triangle has side lengths 15 ft and 15 ft, so its area is ...

  A = 1/2bh

  A = 1/2(15 f)(15 ft) = 112.5 ft²

The trapezoid has bases of 25 ft and 29 ft, and a height of 4 ft, so its area is ...

  A = 1/2(b1 +b2)h

  A = 1/2(25 ft +29 ft)(4 ft) = 108 ft²

The area of the grass will be the total of these areas:

  grass area = triangle area + trapezoid area

  grass area = 112.5 ft² +108 ft² = 220.5 ft²

The area of the grass is 220.5 square feet.

When the slope m and a point (x₁, y₁) is given then the y-intercept (b) is given by an expression y = y₁ - mx₁

We know that the slope-intercept form of equation of line is y = mx + b

where m is the slope of the line and b is the y-intercept of the line.

We need to find the value of b i.e., y-intercept when the slope and a point is given.

We know that the equation of line with slope m and passing through point (x₁, y₁) is given by the formula

(y - y₁) = m(x - x₁)

If we simplify above equation  we get,

y - y₁ = mx - mx₁

y = mx - mx₁ + y₁

y = mx + y₁ - mx₁

y = mx + (y₁ - mx₁)

Comparing above equation with slope-intercept form we get the y-intercept ,

b = y₁ - mx₁

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Answer:

The answer is 7

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

8x - 8 = 48

8x = 56

x = 7

On solving the provided question, we can say that Cai's thinking expression will be area of the poster k = Ax Bt +Cz => K = x^2 + lb + 1/2wm

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

Cai's thinking expression will be

area of the poster k = Ax Bt +Cz

Ax = x^2

Bx = lb

Cz = 1/2wm

K = x^2 + lb + 1/2wm

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In the regrouping to use a different expression for the number in place of * is 11 thousands.

Here we have to write the regroup to express the number as 71,830 = 6 ten thousands + 11 thousands + 8 hundreds + 3 tens

What in elementary math is regrouping?

When doing mathematical operations like addition or subtraction, regrouping is the process of creating groups of ten. When dealing with double digits, this happens most frequently. Technically, though, it happens whenever you get a response that is more than 10.

Where using regrouping, you may frequently solve addition or subtraction problems, and this is when the Place Value Table comes in extremely handy.

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The ratio of the cost of the book to the dictionary to the folder is 3:4:1

The cost of the book to the cost of the dictionary is 3:8

The ratio of the cost of the dictionary to the cost of the folder is 4:1

Hence the cost of the ratio of the book to the dictionary to the folder is 3:4:1

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The ratio of the cost of the book to the dictionary to the folder is 3:4:2.

The ratio of the cost of the book to the cost of a dictionary is 3:8. This means that for every 8 dollars spent on a dictionary, 3 dollars are spent on a book.

The ratio of the cost of a dictionary to the cost of the folder is 4:1. This means that for every 1 dollar spent on a folder, 4 dollars are spent on a dictionary.

To find the ratio of the cost of the book to the dictionary to the folder, we need to combine the two ratios above. To do this, we can first find the equivalent ratio of the cost of the book to the dictionary. To do this we can multiply the ratio of the cost of the book to the dictionary with the ratio of the cost of the dictionary to the folder.

3/8 * 4/1 = 12/8 = 3/2

So, the equivalent ratio of the cost of the book to the dictionary to the folder is 3:8:1. This means that for every dollar spent on a folder, 3/2 dollars are spent on a book and 8/2 dollars are spent on a dictionary. This can be simplified to 3:4:2

The ratio is 3:4:2

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Solving the provided question, we can say If p and q are rational numbers, which equation p-q=0 is true

Any number that can be expressed as a ratio (or fraction) of two integers is said to be rational. A rational number is a fraction that has a nonzero denominator. 1/2, 1/5, and 3/4 are examples of rational numbers. Additionally a rational number, "0" may be expressed in a variety of ways, including 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, etc. The number seven is logical. When two integers are divided, the result is known as a rational number. Divide the whole number 7 by the whole number 1 to obtain the rational number 7. Since two integers may be divided to yield 7, it is known as a rational number.

If p and q are rational numbers, which equation

p-q=0 is true

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Solving a simple equation we will see that there were 96 students sampled.

We know that 7 out of every 8 children have a bike.

Then if we have a sample of N students, we can expect that the number of students with a bike will be:

N*(7/8)

And the number of students that do not have a bike is:

N*(1/8)

In this case, we know that the difference betwwen these numbers is 72, so we can write the equation:

N*(7/8) - N*(1/8) = 72

We can solve that for N.

N*(6/8) = 72

N = (8/6)*72 = 96

There are 96 students sampled.

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0.0188 is the probability of obtaining a sample of 1012 adults in which 67% or fewer say they drink the cereal milk.

The value reduced by the mean, divided by the standard deviation, is the z-score:

Z = x - μ / σ

= [tex]\frac{0.67 - 0.70}{0.0144}[/tex]

≈ - 2.08

Using table A, calculate the corresponding probability:

P(X ≤ 67 % )

= P (Z < -2.08)

=0.0188

As a result, we highlight that this is an uncommon conclusion given the extremely low chance.

The likelihood that something will happen is what is commonly referred to as probability. We can talk about the chance or likelihood of various outcomes when we don't know how such an event will turn out. Events that match a probability distribution are the subject of statistics. Potential is described by probability. This branch of mathematics examines the probability of a random event. The value's range is 0 to 1.

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You will need 6.25 lbs of the cheaper chocolate, and 1.75 lbs of the more expensive chocolate to get 8 lbs of a chocolate mix that sells for $6.90/lbs.

To find the specific amounts of each chocolate needed to make 8 lbs of a chocolate mixture that sells for $6.90/lb, we can substitute x + y = 8 into the equation (6.80x + 8.80y) / (x + y) = 6.90 and solve for x.

First, we'll substitute x + y = 8 in the equation:

(6.80x + 8.80y) / 8 = 6.90

6.80x + 8.80y = 55.20

x = (55.20 - 8.80y) / 6.80

We know that x + y = 8, so we can substitute that in for y:

x = (55.20 - 8.80(8 - x)) / 6.80

x = (55.20 - 70.40 + 8.80x) / 6.80

Now we'll solve this equation for x:

8.80x = 125.60 - 70.40

8.80x = 55.20

x = 55.20 / 8.80

x = 6.25

So, you will need 6.25 lbs of the cheaper chocolate, and

8 - 6.25 = 1.75 lbs of the more expensive chocolate.

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From 2015 to 2020, the population decrease, based on mathematical operations, was 12,800.

The population decrease from 2015 to 2020 is determined using multiplication and subtraction mathematical operations.

In 2015, the population increased by a growth factor of 1.08 of the 2010 figure.  

In 2020, the population decreased by a decline factor of 0.94 compared to 2015.

The city population in 2010 = 197,000

Percentage growth from 2010 to 2015 = 8%

Population in 2015 = 212,760 (197,000 x 1.08)

Percentage decrease from 2015 to 2020 = 6%

Population in 2020 = 199,994 (212,760 x 0.94)

Population decrease from 2015 to 2020 = 12,766 (212,760 - 199,994)

= 12,800 people

Thus, we can assert that the city's population decreased by 12,800 persons.

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The angle between the angles 0 to 2π is π / 2.

The coterminal angles are the angles that have the same initial side and the same terminal sides. We determine the coterminal angle of a given angle by adding or subtracting 360° or 2π to it. In trigonometry, the coterminal angles have the same values for the functions of sin, cos, and tan.

The coterminal angle will be calculated by subtracting the angle 2π from the angle 5π / 2.

Coterminal angle =  ( 5π / 2 ) - 2π

Coterminal angle =  π / 2

Hence, the value of the angle will be π / 2.

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which is the following exterior angles

Answer:

6,4,3,2

When a line has negative slope, it goes down and right OR up and left.

We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.

The slope of the line describes the steepness of a line.

Also,  if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ

m = tan θ

In order to graph a negative slope, we must know that a negative number in the ratio to move down along the y-axis or to the left along the x-axis.

Suppose the negative slope is of the form m = -b/a

This means, for every 'a' units change in the horizontal distance there is -b unita change of vertical distance.

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Answer:

Acute Angle

Step-by-step explanation:

Answer:

acute

Step-by-step explanation:

its less than 90

The numbers that can be expressed as a ratio of two integers are called as Rational Numbers , and one such example is [tex]\frac{2}{3}[/tex] .

What are Rational Numbers ?

The Rational Numbers are defined as the ratio of two integers where the denominator is non zero .

Mathematically , the rational numbers are the numbers that can be expressed in the form of [tex]\frac{p}{q}[/tex] , where [tex]q\neq 0[/tex] .

So , We can say that any fraction that fits under category of rational numbers, where denominator and numerator are integers and denominator is not equal to zero.

Few Examples of that can expressed as ratio of integers are :

(i)  [tex]\frac{1}{2}[/tex] , here 1 and 2 both are integers , and [tex]2\neq 0[/tex] .

(ii) [tex]\frac{5}{6}[/tex] , here 5 and 6 both are integers , and [tex]6\neq 0[/tex] .

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Side of first diagram is 6.6  and Perimeter  of first diagram is 23.6.

What is perimeter?

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.

15. to find sides of triangle using pythagoras theorem.

[tex](hypo)^2=(side)^2+(side)^2[/tex]

As, the triangle is right angles triangle so we can use pythagoras theorem,

10/2=5

Putting values,

[tex](12)^2=(10)^2+(side)^2[/tex]

[tex]144 = 100+(side)^2\\144-100=(side)^2\\side=\sqrt{44}[/tex]

side=6.6

Perimeter of triangle P= sum of all sides

                                     =6.6+12+5

                                     =23.6

Perimeter is 23.6

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The value of x for 4 + 5√x = 14 is 4.

Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.

Given 4 + 5√x = 14

5√x = 14 - 4

5√x = 10

√x = 10/5

√x = 2

square both side

(√x)² = 2²

x = 4

Hence the value of x is 4.

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The scatter plot's line is a strong line of fit because it Yes, as the line depicts a favorable association.

A scatter plot's maximum number of points and an approximately equal number of points above and below the line are the parameters that define the line of best fit. It is employed to examine the type of relationship between two variables. In general, a graph's "line of best fit" passes through the center of each scatter point.

Stronger correlations occur when points are located along the line of best fit. the sum of squares of errors for each and every conceivable line. The most accurate line is the one with the lowest total of squared errors. The correlation between the two variables is higher when the data points are drawn so that they nearly form a straight line.

Therefore the correct answer is Yes, because the line models a positive association.

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Answer:

Yes

Step-by-step explanation:

because 8/10 can 4/5 by diving by 2

To find the measure of an interior angle of a polygon, you can use the formula: (n-2) * 180 / n, where n is the number of sides in the polygon.

Sum of interior angles of a polygon

=x+(x+75)+2x+33+140

solving for x,

x+x+75+2x+33+140=540

4x+248=540

4x=540-248

4x=292

x=[tex]\frac{292}{4}[/tex]

x=73

Angle x=73

angle x+75

=73+75

=148

Angle 2x=2*73=146

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The y - intercept, based on the points of the graph, can be found to be 0

To find the y - intercept, you can use the slope - intercept equation which is:

y = mx + b

Where :

m = slope

b = y - intercept

Solve for the slope using ( 2, 8 ) and ( 14, 56 ) to be:

= ( Y2 - Y1 ) / ( X 2 - X 1 )

= ( 56 - 8 ) / ( 14 - 2 )

= 4

Given the slope as 8, and the point ( 2, 8 ), the y - intercept would be:

y = mx + b

8 = 4 ( 2 ) + b

b = 8 - 8

b = 0

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Smaller angle is (2a+33) is 73°

What is Parallelogram?

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions.

A parallelogram's adjacent angles add up to 180 degrees.\

Step by step Explaination:

Measures of two angles of parallelogram are  (2a+3) and (5a+14).

As we all know , Measure of Supplementary Angles = 180°

Therefore,

(2a + 33°) + (5a+14°) = 180°

10a + 28°+ 165a+ 462° = 180°

175a +  490°= 180

175a=180-490°

175a=-310

a=310/175

a=20°

(i) 2a + 33°

= 2*20° + 30°

= 40+33°

=73°

(ii) 5a+14°

=5*20+14°

=100+14°

=114°

Smaller angle is (2a+33) is 73°

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Answer:

First question :

a = 2

Second question :

a = 5

b = [tex]\frac{-a+5}{0}[/tex]

Their displacement , that is shortest distance is equals to 13 miles

What is Displacement ?

Displacement can be defined as the shortest path covered from one path to another.

Given,

A car travels 13 miles to the North before turning and drive 10 miles East.

From here,

they drive 5 miles South, another 2 miles East, and finally drive 3  miles South

So, the shortest distance can be called as the displacement

displacement = [tex]\sqrt{a^2+b^2}[/tex]

so,

a = 10+2

b = 13-5-3

b = 5

displacement = √(12^2 + 5^2 )

displacement = √169

displacement = 13

Hence, Their displacement , that is shortest distance is equals to 13 miles.

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Answer: I believe the answer is M= -4

Step-by-step explanation:

The approximate number caused by secondhand smoke is 35,000.

Secondhand smoke is defined as the smoke that is inhaled by someone who is not the main smoker of the cigarette and is typically present near the main smoker while he or she is smoking.

35 000 deaths from secondhand smoke and 1000 baby deaths from maternal smoking are included in the predicted 435 000 deaths from smoking in the year 2000. Environmental tobacco smoke, often known as secondhand smoke, includes more than 7000 carcinogenic and harmful compounds.

Some studies suggest that second-hand smoke poses a greater risk due to the presence of any residue from the initial smoker's lung.

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Answer:

$291.51

Step-by-step explanation:

So, as Erin earns $10 per hour, she worked 32 hours and earned $320.

32x10=320.

After taxes, (the bane of our life!) it'll be 320-28.49=

$291.51

The five number summery of the data set is minimum = 2.2, Q1 = 3.3, median = 23.3, Q4 = 69.1 and maximum = 78.8

A box plot is a visual representation of the localization, dispersion, and skewness of a collection of numerical data through its quartiles.

The center "box" denotes the group's middle 50% of points. The inter-quartile range is the range of scores from the lower to higher quartile. The interquartile range encompasses the middle 50% of the scores. 75 percent of the scores are lower than the highest quartile.

When doing descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

Arranging the data in ascending order :

2.2, 3.3, 11.3, 16.1, 18.2, 18.8, 23.3, 23.5, 37.4, 44.8, 54.9, 69.1, 78.8

Total number of data = 13

The minimum value = 2.2

The maximum value = 78.8

The median is 7th term = 23.3

The Q1 of 1st quartile = 3.3

The Q4 of 4th quartile = 69.1

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