What is the area of the triangle with
vertices (2, 7), (8, 7), and (20, 9)?
A. 6 sq. units
B. 8 sq. units
c. 12 sq. units
D. 15 sq. units

Answer:

74%

Step-by-step explanation:

74 divided by 100 is 0.74, and 0.74 =

74%

Using a proportional relationship, it is found that:

Dillon recommends that the amount of time college students spend studying each week should be about the amount twice the time spent in class.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the rule presented as follows:

y = kx

For this problem, the variables are presented as follows:

From the table, the constant is calculated as follows:

k = 24/12 = 18/9 = 12/6 = 2.

Meaning that the amount of study should be twice the time spent in class.

The table relating the variables is given at the end of the answer.

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The subtraction is shown below:

The answer is:

75 - 26.5731 = 48.4269

By using all the values of the data set ,

(a) The range for the given set is 9 .

(b) The variance is 6.2045 .

(c) Standard Deviation is 2.49083 .

In the question,

it is given that 12 students gave an arithmetic test , the time (in min) is given as

10, 9, 12, 11, 8,15, 9, 7, 8, 6, 12, 10 .

Arranging the data set in ascending order , we get

6,7,8,8,9,9,10,10,11,12,12,15

Part(a)

the range is calculated by using the formula

Range = highest value - lowest value

Range = 15-6 = 9

Part(b)

calculating , the mean

mean = (6+7+8+8+9+9+10+10+11+12+12+15)/12

= 117/12

= 9.75

Variance can be calculated using the formula

Variance = [tex]\frac{\sum(\(x_i-\bar{x})^{2} }{n-1}[/tex],

where [tex]x_i[/tex] represents the different terms , and

[tex]\bar{x}[/tex] represents the mean .

Substituting the values from the data given ,  we get

Variance = [(6-9.75)²+(7-9.75)²+(8-9.75)²+(8-9.75)²+(9-9.75)²+(9-9.75)²+(10-9.75)²+(10-9.75)²+(11-9.75)²+(12-9.75)²+(12-9.75)²+(15.9.75)²] / (12-1)

On further simplifying , we get

= 68.25/11

= 6.2045

Part(c)

Standard Deviation = √Variance

Substituting the value of variance from above

we get ,

standard deviation = √6.2045 = 2.49083

Therefore , By using all the values of the data set ,

(a) the range is 9.

(b) Variance is 6.2045

(c) Standard Deviation is 2.49083

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The total cost of 5 friends is $55.

What is multiplication?

Multiplication is a basic arithmetic function in which occurs when we add a number a particular number of times.

We are given that if group of five pays $6.75 each they get the snack for $4.25.

To find the total cost we first find the cost of one

The cost of one can be given as [tex]6.75+4.25=11[/tex]

To find the cost of 5 we multiply this amount by 5

We get,

[tex]5[/tex]·[tex]11=55[/tex]

Hence the total cost is $55.

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The expression (m³n⁵)¹/⁴ can be wriiten as ⁴√m³ .  ⁴√n⁵.

To solve the expression (m³n⁵)¹/⁴ without using rational exponents

(m)ᵃ/ᵇ = ᵇ√mᵃ

The given algebric expression is (m³n⁵)¹/⁴

As per the Power distribution Formula :

(mᵃnᵃ)ᵇ = mᵃᵇ nᵃᵇ

(m³n⁵)¹/⁴ = m³ ˣ ¹/⁴ x n⁵ ˣ ¹/⁴

We know that

fraction formula : a¹/ⁿ = ⁿ√a

(m)ᵃ/ᵇ = ᵇ√mᵃ

(m³n⁵)¹/⁴ = m³ ˣ ¹/⁴ x n⁵ ˣ ¹/⁴

⁴√m³ x ⁴√n⁵

⁴√m³ .  ⁴√n⁵

The expression (m³n⁵)¹/⁴ can be wriiten as ⁴√m³ .  ⁴√n⁵.

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Answer: 16 times longer

Step-by-step explanation: 6.4 divided by 0.4 is equal to 16.

The graph of  y = -f(x) + 3 is a graph that has a negative slope and is attached.

A graph is a representation of data using the coordinate system. There are different types of graph each defining the required data.

The graph of equation of a straight line is one of the types of graphs. The graph of the form y = mx + c represents the equation of a straight line. The terms are defined as follows

The slope is a function of x and from the question it is negative.

The graph is plotted and attached

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-3.5 number can be written as the ratio -7:2.

We have,

To write -3.5 as the ratio of two integers, we can multiply both the numerator and denominator by 10 to get rid of the decimal point.

This gives us:

-3.5 = -35/10

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 5.

This gives us:

-3.5 = -7/2

Therefore,

-3.5 number can be written as the ratio -7:2.

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The results for the given function are as follows:

1. p(x) = 14(x + 7)² + 1, The direction is upward by 1 unit.

2. q(x) = –5(x + 10)² – 1, The direction is downward by 1 unit.

3. s(x) = –(x – 1)² + 0.5, The direction is upward by 0.5 unit.

4. g(x) = 2x² + 10x – 35 = (x+5/2)² - 23.75, The direction is downward by 23.75 unit.

5. t(x) = –2x² – 4x – 3 = -(x + 1)² - 0.5, The direction is downward by 0.5 unit.

What is the function?

In mathematics, the function is an expression or rule, or law which defines the relationship between dependent and independent variable. Functions are ubiquitous  and are essential for designing physical relationships.

According to the question, the given function expression as well as transformation results are as follows:

p(x) = 14(x + 7)² + 1, The direction is upward by 1 unit.

q(x) = –5(x + 10)² – 1, The direction is downward by 1 unit.

s(x) = –(x – 1)² + 0.5, The direction is upward by 0.5 unit.

g(x) = 2x² + 10x – 35 = (x+5/2)² - 23.75, The direction is downward by 23.75 unit.

t(x) = –2x² – 4x – 3 = -(x + 1)² - 0.5, The direction is downward by 0.5 unit.

By using property of the function which states that if a constant value is added to the function it will go upward, similarly, If we subtract a constant then it will go downward.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]3x+2y=8\implies 2y=-3x+8\implies y=\cfrac{-3x+8}{2} \\\\\\ y=\cfrac{-3x}{2}+\cfrac{8}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The consecutive even numbers are 12 and 14.

Even numbers can be divided into two equal groups or pairs and are exactly divisible by two. For instance, 2, 4, 6, 8, and so on. These numbers can be divided into equal groups. Consecutive numbers are numbers that follow each other in descending order from smallest to greatest. Consecutive even numbers are even integers that are separated by a factor of two.

Let the consecutive even numbers be x and x+2.

The sum of the numbers is 340. This will be illustrated as:

x² + (x + 2)² = 340

x² + (x + 2)(x + 2) = 340

x² + x² + 4x + 4 = 340

Collect like terms

2x² + 4x + 4 - 340 = 0.

2x² + 4x - 336 = 0

Divide through by 2

x² + 2x - 168 = 0

x² - 14x + 12x -168 = 0

x(x - 14) + 12(x - 14) = 0.

(x + 12)(x - 14) = 0

This shows that the numbers are 12 and 14

Check: 12² + 14² = 144 + 196 = 340.

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The dividend in the division problem is 54

The mathematical statement is given as

54 divided by 6 equals 9

The above statement is a quotient expression or quotient statement

A quotient statement is represented as

Dividend divided by Divisor equals Quotient

By comparing the quotient statement with the given mathematical statement, we have the following

This implies that the dividend is 54

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Answer:

13

Step-by-step explanation:

In the scatter plot, the person with 3 e-mail accounts have 1 credit card.

Typically, the relationship between variables is observed and visually displayed using a scatter plot, a type of chart. Dots are used to indicate the variable values. Scatter plots employ Cartesian coordinates to show the values of the variables in a data set because the placement of the dots on the vertical and horizontal axes will reveal the value of each individual data point. Other names for scatter plots are scattergram, scatter graphs, and scatter charts.

The association between two numerical variables measured for the same individuals is displayed in a scatterplot. The values of one variable are plotted on the horizontal axis, and the values of the other variable are plotted on the vertical axis. On the graph, each individual in the data is represented by a point.

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Answer:

39/98=90 so its 90

Step-by-step explanation:

you have to add the angles and to make sure to look at each corners  of the angles for the answer

The given function is y=9500+55x, where x is in hours driven and y is in miles.

Therefore, the slope of the function is

If the hypotenuse of PQR triangle is 5 and perpendicular is [tex]\sqrt{2}[/tex],then value of sin²R is 2/25.

Given that the hypotenuse is 5 and perpendicular is [tex]\sqrt{2}[/tex].

We are required to find the value of sin²R.

Trigonometric ratios are basically the ratios of the sides of the right angled triangle.

Sin is the ratio of perpendicular and hypotenuse of the right angled triangle. We can easily find the value of sin²R with the help of ratio of perpendicular and hypotenuse.

sin R=PQ/PR

sin R=[tex]\sqrt{2}[/tex]/5

Squaring both sides,

sin² R=[tex](\sqrt{2} )^{2}[/tex]/[tex](5)^{2}[/tex]

sin²R=2/25

Hence if the hypotenuse is 5 and perpendicular is [tex]\sqrt{2}[/tex],then value of sin²R is 2/25.

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Step-by-step explanation:

Time taken by hose B to fill the vat alone = 9 hours

Let 'x' be the capacity of the vat filled in an hour.

Hose A can fill the vat in 3 hours. i.e., 3x quantity is filled in the vat.

After 2 hours of pumping, 2x/3x = 2/3 of the vat is filled.

The remaining to be filled is x/3x = 1/3 capacity of the vat.

It takes 3 hours for hose B to fill the remaining 1/3 capacity of the vat alone.

Let t be the time taken by hose B to fill the whole vat .i.e., 3/3 = 1 capacity of the vat.

In ratio form, 3 : t = 1/3 : 1.

Thus Time taken by hose B to fill the vat alone = 3 ÷ 1/3

                                                                              = 3 x 3

                                                                              = 9 hours

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Answer:

1914

Step-by-step explanation:

interest for one year = 33

interest of 8 years = 264

1650+264 will be in the account in 8 years.

Let's begin by listing out the information given to us:

We will caculate fºg thus:

Hence, option B is correct

Using Pythagoras's theorem we can calculate that the bucket must reach57.134 feet .

We know from the Pythagoras theorem of aright angled triangle , the sum of squares of the two legs of a right triangle is equal to the square of the hypotenuse of the same triangle.

From the question we can ascertain that the height at which the cat is stuck is 40.4 feet.

Now it is given that the rescue ladder came in at 45 ° . So the length of the legs are equal.

Therefore length of ladder which is the hypotenuse = √(2×40.4²)

Length = 57.134... feet

length ≈ 57.13 feet

Therefore the bucket must reach 57.13 feet which is the height at which the cat is stuck on the tree of length 40.4 feet.

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a) If function be [tex]$f(x)=\frac{x^2+(17-4 x)}{9 x}$[/tex] then the value of f(5) = 22/45.

b) If function be g(x) = 3 x² - 6x + 9 then the value of g(x + 3) = 3x² + 12x + 18.

c)  If the function be [tex]$h(y)=\frac{y^3-5}{7 y}$[/tex] then the value of [tex]$h(2x) =\frac{8 x^3-5}{14 x}$$[/tex].

a) Let the function be [tex]$f(x)=\frac{x^2+(17-4 x)}{9 x}$[/tex]

substitute the value of x = 5, then

[tex]$f(5) = \frac{5^2+(17-4 \cdot 5)}{9 \cdot 5}$$[/tex]

simplifying the above equation, we get

[tex]$=\frac{22}{45}$$[/tex]

Therefore, the correct answer is 22/45.

b) Let the function be g(x) = 3 x² - 6x + 9

substitute the value of g(x) = g(x + 3), then we get

To estimate the value of g(x + 3) = 3(x + 3)² - 6(x + 3) + 9

= 3x² + 18x + 27 - 6(x + 3) + 9

simplifying the above equation, we get

=3x² + 18x + 27 - 6x - 18 + 9

Group like terms, we get

= 3x² + 18x - 6x + 27 - 18 + 9

=3x² + 12x + 27 - 18 + 9

= 3x² + 12x + 18

Therefore, the value of g(x + 3) = 3x² + 12x + 18.

b) Let the function be [tex]$h(y)=\frac{y^3-5}{7 y}$[/tex]

substitute the value of y = 2x, then we get

[tex]$h(2x)=\frac{(2x)^3-5}{7 (2x)}$[/tex]

simplifying the above equation, we get

[tex]$=\frac{8 x^3-5}{7 \cdot 2 x}$$[/tex]

[tex]$=\frac{8 x^3-5}{14 x}$$[/tex]

Therefore, the value of [tex]$h(2x) =\frac{8 x^3-5}{14 x}$$[/tex].

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Given data:

The given principal is P=$20,000.

The given rate of interest is r=6%.

The given time is t=20 years.

The expression for the interest is,

Substitute the given values in the above expression.

Thus, the interest earned after 20 years is $44,142.71, so (C) option is correct.

In order to find how much stronger was the first gust than the second, we just need to subtract their values.

So we have that:

So the strongest wind gust was 4 miles per hour stronger than the second strongest wind gust.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The rectangle's longer side is its length, while its shorter side is its breadth.

A laptop has four sides, with the opposite sides being parallel to one another and having equal lengths. As a result, a laptop stands out as a common example of a rectangle-shaped device in everyday life. The keyboard and a monitor's screen are both rectangular objects in a similar way.

Note that the following are the measurements for a rectangle's perimeter:

(Length Plus Width) = 2

= 2(25x + 12) + 2(7x + 18)

= 50x + 24 + 14x + 46

= 64x + 70

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The graph of the line y=-2/3x-1 can be given as follows,

What is a equation of ?

The general equation of straight line is y=mx+c where m is the slope and c is the y-intercept.

every point on the line satisfies its equation.

We are given a point (6,-5) and slope -2/3.

we first need to find the equation of the line

y=mx+c

[tex]y=\frac{-2}{3}x+c[/tex]

The point (6,-5) satisfies the equation.

[tex]-5=\frac{-2}{3}(6)+c[/tex]

[tex]-5=-4+c\\c=-1[/tex]

Substituting the value of c in the equation

we get,

[tex]y=\frac{-2}{3}x-1[/tex]

Now we plot the graph of the equation,

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