Triangle side splitter theorem question

From the graph provided, it can be seen that:

There is a maximum at (6,1)

Therefore, the answer is the following:

The function has a relative maximum of 1 at x = 6

Answer: 2 million is 2,000 thousands.

Step-by-step explanation:

2,000,000 = 2 million

1,000 = 1 thousand

2,000 thousands = 2 million

The net cost equivalent is the price the customer pays after deducting all the discounts. To find the net cost equivalent given an amount n of discounts, we use the following formula

Where d is the discount written as a decimal.

In our problem, we have a series discount of 20/10/10/20, therefore, the net cost equivalent is

The measure of each angle are 36° and 144°

What is Supplementary angle?

Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. In the following image, 3 and 4 are supplementary since their sums equal 180 degrees.

Let the provided angle be x, the supplementary angle be y.

y = x + 108 since x has 108° greater than y.

The total of the additional angles is 180°.

x + y = 180,

x + x + 108 = 180,

and x = 180 - 108.

2x = 72

x = 72/2

x = 36

Then,

y = x + 108

y = 36 + 108

y = 144

Consequently, the angles are 36° and 144°.

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Answer: 4/5 × 10/16 = 1/2

Step-by-step explanation:

Multiply the numerators and then multiply the denominators to get: 4/5 * 10/16 = 40/80

Simplify with the GCF (40): 40/80 / 40/40 = 1/2

And that's your simplified answer :)

Statistics can be misleading by faulty sampling and inaccurate graphs

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

Given Data

Statistics can be misleading.

Statistics is quite powerful. So much so that some of the most significant decisions made by individuals and organizations were based on statistics. The adage that "statistics don't lie" may actually be true. However, statistics can occasionally be deceptive, and depending on how they are used, the same type of data can demonstrate the opposite tendency.

Sometimes inaccurate information is purposefully supplied in order to influence individuals and forward a goal. Similarly, it can also occur as a result of negligence or just failing to comprehend the data.

Knowing the various ways statistics can be abused will help you spot them and avoid making decisions based on skewed or inaccurate information.

1)Faulty sampling

The info can due to the sampling strategy employed to gather the data, be deceptive. For instance, the size and kind of the sample used in any statistics has a big impact. Since many surveys and polls are directed at specific groups of people who give particular answers, the sample sizes tend to be tiny and skewed.

2)Inaccurate graphs

Data manipulation can be done in a variety of ways, not just by using descriptive statistics incorrectly. You can identify them if you are aware of them.

3)Chooser Data Display

This type of data visualization might be perplexing and exaggerate differences. If you look at the data and consider how much variety there is in the numbers, you can spot false graphs in the media.

4)Absence of Baseline

Checking to see if the start-at-zero criteria has been adhered to is another approach to spot a deceptive graph. In a graph, The New York Times demonstrated that its sales are double those of The Daily Telegraph. However, if you look at the scale, you can see that the sales difference is just about 10%.

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The cost of a t-shirt is $25, the cap costs $20 and the stuffed animal costs $15

Let t-shirts be represented by x, the cap is represented by y and stuffed animals are represented by z

Items purchased by family:

4 t-shirts + 1 cap + 1 stuffed animal

The total cost of the items was = $135

Equation: 4x+y+z=135--------(1)

Items purchased by couple 1:

2 t-shirts + 1 cap + 3 stuffed animals

The total cost of the items was = $115

Equation: 2x+y+3z=115------(2)

Items purchased by couple 2:

2 t-shirts + 1 cap + 1 stuffed animals = $85

Equation: 2x+y+z=85------(3)

Subtracting equation (3) from (2) we get:

2z = 30

z = 15

Substituting the value of z=15 in equations (1) and (3) we get the following equations:

4x+y+15=135

4x+y=120------(4)

And, 2x+y+15=85

2x+y=70-------(5)

Multiplying equation (5) with 2 and subtracting equation (4) we get:

4x+2y=140

4x+y=120

y = 20

So, x = 25

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Answer:

(-2,-7)

Step-by-step explanation:

Rewrite in vertex form and use this form to find the vertex (h,k).

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-15}x^2\stackrel{\stackrel{b}{\downarrow }}{-60}x\stackrel{\stackrel{c}{\downarrow }}{-67} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -60}{2(-15)}~~~~ ,~~~~ -67-\cfrac{ (-60)^2}{4(-15)}\right) \implies \left( - \cfrac{ -60 }{ -30 }~~,~~-67 - \cfrac{ 3600 }{ -60 } \right) \\\\\\ (-2~~,~~-67+60)\implies {\Large \begin{array}{llll} (-2~~,~~-7) \end{array}}[/tex]

(8x-3)/12

Step-by-step explanation:

Answer:

[tex]n_{i+1} = -5n_i - 1[/tex]

Step-by-step explanation:

-5*2 - 1 = -11

-5*-11 - 1 = 54

Because the prisms are stacked onto one another, they have a total volume of 320 cubic units

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following parameters

The volume of a prism is the prodict of its dimensions

This means that

Cube = Length^2

Cuboid = Base area * Height

So, we have the following equations

Shape 1 = a^3

Shape 2 =a^2b

Shape 3 =a^2c

Substitute the known values in the above equation

So, we have

Shape 1 = a^3 = 4^3 = 64

Shape 2 =a^2b = 4^2 * 6 = 96

Shape 3 =a^2c = 4^2 * 10 = 160

Add the above values

Prism volume =64 + 96 + 160

Evaluate the sum

So, we have

Prism volume = 320

Hence, the volume of the three prisms is 320 cubic units

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The most appropriate choice for tabular data will be given by-

Specimen B is the longest and its size is 0.011 cm. So Monroe's teacher wants each student to draw the sketch of Specimen B

What is tabular data?

Data given in the form of rows and columns is known as tabular data.

Here,

Size of specimen A = 0.008 cm

Size of specimen B = 0.011 cm

Size of specimen C = 0.0025 cm

Size of specimen D = 0.004 cm

Size of the longest specimen = 0.011 cm

Specimen B is the longest and its size is 0.011 cm. So Monroe's teacher wants each student to draw the sketch of Specimen B

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Complete Question

The table has been attached

Specimen    Actual length(cm)     Size seen under microscope (cm)

A                          0.008

B                          0.011

C                          0 .0025

D                          0.0040

Given the following expression:

Making a comparison statement out of this will be: 27 is 3 times more than 9.

Answer:

9

Step-by-step explanation:

→ Multiply by every value to see

735 - ( 24.99 × 9 ) = 510.09

∴ He has to add money in the 9th month otherwise he will be charged

Answer:

9

Step-by-step explanation:

24.99 x 9 = 224.91

735 - 224.91 = 510.09

Answer:

Tom is currently 5 and Bill is currently 11

Step-by-step explanation:

Let b = Bill's current age

Let t = Tom's current age

We have 2 unknowns so we need to equations to solve for this.

b = t + 6  

(b-3) = 4(t-3)  We have to subtract 3 from both Tom and Bill's current age

b- 3 = 4t - 12  Distribute the 4 and then substitute in t + 6 for b.

t + 6 -3 = 4t -12  Combine like terms

t + 3 = 4t -12  Subtract t from both sides of the equation

3 = 3t - 12  Add 12 to both sides of the equation

15 = 3t  Divide both sides by 3

5 = t  Tom is 5.  Since Bill is 6 years old, her is 11.

Check:

11 = 5+ 6

Three years ago, Tom would have been 2 and Bill would have been 8.  Bill is four times older than Tom.  2x4 = 8.

The Range of the given function graph is gotten as; Option D: (-4, -1, 0, 1, 2)

The range of a function is defined as a set of all possible output values for which a function is said to hold.

Now, when it comes to a function graph, we can easily say that the range of the function of the graph will be the set of possible values along the y-axis. That is all possible y-values.

Now, in the given graph, we are given 5 coordinates and the y values at each of these coordinates would represent the range of the graph. Thus;

Range = (-4, -1, 0, 1, 2)

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Answer: maturity value = $17816.67

Explanation:

The formula for calculating simple interest is expressed as

I = PRT

where

I is the interest

P is the principal or initial amount

R is the interest rate

T is the time in years

From the information given,

P = 17104

R = 12.5% = 12.5/100 = 0.125

We would convert 4 months to years. Recall

12 months = 1 year

4 months = 4/12 = 1/3

Thus, the interest is calculated as follows

I = 17104 x 0.125 x 1/3 = 712.67

maturity value = principal + interest

maturity value = 17104 + 712.67

maturity value = $17816.67

Answer:

The answer would be 36.

Step-by-step explanation:

I linked the steps I used to get this answer in the image, I hope this helps :)

The number of mosquitoes will be increased by 5 inches of rain.

Maximum mosquito population = 25000

We are given the following in the question:

M(x) = 10x - x²

where M(x) denotes the number of mosquitos in millions and x denotes the amount of rainfall in inches.

To begin, we differentiate M(x) with respect to x, yielding

d(M(x)) /dx = d(10x - x²) /dx = 10 -2x

When we set the first derivative to zero, we get

d(M(x)) /dx = 0

10 - 2x = 0

x = 5

We get the same result when we differentiate M(x) with respect to x:

d²(M(x)) / dx² = -2

d²(M(x)) / dx² < 0

As a result of the double differentiation test, the maxima for M(x) occur at x = 5.

when the rainfall is 5 inches, the most mosquitoes are present.

Maximum mosquito population:

M(5) = 10(5) - (5)² = 25

As a result, the maximum number of mosquitos is 25000.

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The factored expression of the expression given as 12b - 30 is 6(2b - 5)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

12b - 30

Factor out the common factor from the expression

So, we have

12b - 30 = 3 * 4b - 3 * 10

Factor out 3 from the expression

So, we have

12b - 30 = 3(4b - 10)

Factor out 3 from the expression

So, we have

12b - 30 = 6(2b - 5)

The expression above cannot be further simplified

This means that the expression has been completely factored and cannot be further factored

Hence, the equivalent expression of the expression given as 12b - 30 when it is factored by grouping is 6(2b - 5)

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The number of breakfast Greg can eat from a box of cereal if he eats 1 1/2 servings for breakfast everyday is 8 breakfast.

Number of breakfast Greg can eat in a regular-sized box = A regular-sized box of cereal / servings of breakfast eaten everyday

= 12 ÷ 1 1/2

= 12 ÷ 3/2

= 12 × 2/3

= 24/3

= 8 breakfast

Cost of regular-sized box of cereal = $4.29.

Cost of one breakfast from a regular-sized box of cereal = Cost of regular-sized box of cereal ÷ Number of breakfast Greg can eat in a box

= $4.29 / 8

= 0.53625

Approximately,

$0.54 per breakfast

Number of breakfast Greg can eat in a family-sized box = A family-sized box of cereal / servings of breakfast eaten everyday

= 18 servings / 1 1/2

= 18 ÷ 3/2

= 18 × 2/3

= 36/3

= 12 servings

Therefore, the number of more servings of breakfasts Greg could eat from 1 family-sized box

= Number of breakfast Greg can eat in a family-sized box - Number of breakfast Greg can eat in a regular-sized box

= 12 servings - 8 servings

= 4 servings

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Answer:

= 4 servings

Step-by-step explanation:

The linear equation in slope intercept form is y = 200x + 200

where y represents the amount in the savings account of Jacalyn at the end of x months beginning from May.

In the slope intercept form, slope (the numerical coefficient of variable x) is having a numerical value of 200 and vertical intercept is the constant of term of the equation i.e. 200. The positive value of slope indicates that the gradient of straight line representing this linear equation is positive. Positive value of vertical intercept indicates that the linear equation's graph plot shall not pass through the origin but will intercept the y-axis at 200.

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The choice that can be used to find the expression (three times the number increased by six is twenty-four) is (C) 3m + 6 = 24.

So,  three times the number increased by six is twenty-four:

Therefore, the choice that can be used to find the expression (three times the number increased by six is twenty-four) is (C) 3m + 6 = 24.

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The correct question is given below:

Grace is thinking of a number. She states that three times the number increased by six is twenty-four. Which choice can be used to find

(A) 3(2-6) = 24

(B)3-6=24

(C) 3m + 6 = 24

(D) 9x2=18+6=2

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

y < 6x + 9 eq. 1

Step 02:

systems of inequalities

y > 6x + 7 eq. 1

<9

Graph

y = 6x + 9 eq. 2

Unlimited/Infinite solutions

The answer is:

(-4 , 32)

(3 , 25)

The point of intersection of the system of equations is (3, 4) and this is plotted in the graph shown below.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In conclusion, the coordinate (3, 4) is the point of intersection of the given system of equations.

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Answer:

In ten year you will be 10 years older than you are now and so will your brother. The 6 years difference will remain if no one dies.

Step-by-step explanation:

You are z years old

Your brother is 6 years younger than z years; z - 6 years

In 10 years time, you will be z + 10 years

Your brother will be z - 6 years + 10 years = z + 4 years

OR

In 10 years time, you will be z + 10 years

You brother is still 6 years younger than you, so is z + 10 years - 6 years = z + 4 years

Answer:

$82.50

Step-by-step explanation:

82.5 times 0.7 = 57.75

doing 57.75 + 30% wouldn't work, so you have to increase the number (original price) being discounted until you get 57.75

also, the '0.7' is 70% which also means '30% off' because you took 30% away from the original price that was 100%

math calculator saves the day? dont use paper or it would take a long time (unless it was a test or teacher said no)

The dimensions of the rectangular poster are:

Width = 3 inches.

Length = 9 inches.

A rectangle usually has a long side called the length, and a shorter side called the width.

The area of the rectangle is calculated by multiplying the length and the width together. Therefore, formula for the area of a rectangle is:

Area = (length)(width).

The rectangular poster has the following parameters:

Let x represent the width of the rectangular poster.

Width of the rectangular poster = x

Length of the rectangular poster = 3x

Area of the rectangular poster = 27 in.².

Plug in the values

(x)(3x) = 27

3x² = 27

Divide both sides by 3

3x²/3 = 27/3 [division property of equality]

x² = 9

Take the square root of both sides

√x² = √9

x = 3

Width of the rectangular poster = x = 3 inches.

Length of the rectangular poster = 3x = 3(3) = 9 inches.

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