Given: BD is perpendicular to AC, measure DBA = 7x+6. Find x

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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Answer:

24p+ -28

Step-by-step explanation:

Answer:

SO BASICALLY

Step-by-step explanation:

-4(-6p+7)

24p-28

IG THATS ITTTT :o

you just multiply negative 4 to

-7p and posititve7 sooo likeeee for example negative times negative is positivee

-positive times negative is positive

Answer:

Probably A!

Step-by-step explanation:

Answer:

Binomial distribution

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they purchase a pair of running shoes, or they do not. Customers' purchases are made independently. This means that the probability distribution of X is the binomial probability distribution.

The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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The fraction of Polygon P's area, that is Polygon Q's area, given the scale factor, is 1 / 4.

The fact that Polygon Q is a scaled copy of Polygon P using 1 / 2 as a scale factor means that Polygon Q is half the size of Polygon P.

This means that in terms of area, Polygon Q in relation to Polygon P would be :

= 1 /2 x 1 / 2

= 1 / 4

For example, a square with sides 6 would have an area of :

= 6 x 6

= 36 units ²

The scaled shape would have sides of 3 because of the scale factor of 1 / 2 :

= 3 x 3

= 9 units ²

The fraction of the smaller shape's area is:

= 9 / 36

= 1 / 4

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The population of North Carolina will reach 12 million in the year 2028.

Population growth is defined as the increase in the number of people which is calculated using population growth rate.

Given that,

Population in 2010 = 9.5 million

Population is increasing to 1.3% per year.

Annual growth rate = 1.3% = 1.3/100 = 0.013

We have the population growth formula,

P = P₀ e^(r t)

Here, P₀ = 9.5 million = 9,500,000

and P = 12 million = 12,000,000

r = 0.013

We have to find t.

12,000,000 = 9,500,000 e^(0.013t)

120 / 95 = e^(0.013t)

Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,

㏑(12/9.5) = 0.013t × ㏑e

[㏑(12/9.5) ÷ 0.013] = t  [since ln e = 1]

t = 17.97 ≈ 18 years

The year is 2010 + 18 = 2028

Hence in the year 2028, the population will be 12 million.

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For the circular cover we have:

A) The area is 379.94 ft²

B) The length of the rope must be 68.2 ft

Remember that the area of a circle of radius R is given by the formula:

\(A = pi*R^2\)

Where pi = 3.14

In this case, the diameter of the pool is 20ft, then the radius is:

R = 20ft/2 = 10ft

And it must extend 12 inches beyond, then the radius of the cover must be:

R = 10ft + 12in

Now, we know that 1ft = 12 in, then we can rewrite the radius as:

R = 10ft +1ft = 11ft

Then the area of the cover is:

\(A = 3.14*(11ft)^2 = 379.94 ft^2\)

B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.

Remember that the circumference of a circle of radius R is:

\(C = 2*pi*R\)

Then the length of the rope will be:

\(C = 2*3.14*11ft = 68.2ft\)

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Solution

a) The result of the test for evenness is given as follows: y = 18x^7.

b) The result of the test for oddness is given as follows: y = 10x^16 + 36x^8.

The function for this problem is given as follows:

y = 9x^17 + 5x^16 + 18x^8.

For evenness, we have that:

f(-x) = 9(-x)^17 + 5(-x)^16 + 18(-x)^8.

Odd exponents are odd functions, while even exponents are even functions, thus:

f(-x) = -9x^17 + 5x^16 + 18x^8.

Then the simplified expression for evenness is of:

y = f(x) - f(-x)

y = 18x^7.

For oddness, the simplified expression is given as follows:

y = f(x) + f(-x).

y = 10x^16 + 36x^8.

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Answer:  x    =   -3

Step-by-step explanation:

3(x + 1) = -6

Divide both sides by 3:   3(x + 1) / 3 = -6 / 3

                                              x + 1 = -2

Subtract 1 from each side:   x + 1 - 1 = -2 - 1

                                                      x    =   -3

Answer:

3.5 meters

First, let us convert 300 millimeters to meters. To do this, we need to divide the length value by 1000:

Now, it is said that Dean uses 300 millimeters of yarn each day, which means that he uses 0.3 meters of yarn each day.

For 5 days, Dean used:

We will then subtract the length Dean used from the 5-meter yarn that he started with:

Therefore, Dean has 3.5 meters of yarn left.

a) The constant of proportionality is given as follows: 0.5.

b) The equation is given as follows: y = 0.5x.

c) The graph would be the graph of a linear function with slope of 0.5 and intercept of 0.

d) 9 points are awarded for 18 minutes of play.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

For every 1 minute of play, the game awards one half point, hence the constant k is given as follows:

k = 0.5.

Thus the equation is given as follows:

y = 0.5x.

Then the number of points for 18 minutes of play is given as follows:

y = 0.5(18)

y = 9.

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Answer: 18(a)-89=217

Step-by-step explanation:

If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.

Hope this helped.

Answer:217

Step-by-step explanation:

putting the value of a in the equation.

18×17-89= 217

Answer:

D, E, and F

Step-by-step explanation:

✔️Statement D is true:

Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2

✔️Statement E is true:

Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1

✔️Statement F is true:

Rationale:

m<4 is an external angle of the triangle.

m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,

m<4 = m<1 + m<2

Answer:

Area = 29.64 ft^2

Step-by-step explanation:

Area = 1/2 b * h

b = 10.4

h = 5.7

Area = 1/2 * 10.4 * 5.7

Area = 1/2 59.28

Area = 29.64

Answer:

Second and third one

Step-by-step explanation:

2 nd and third one ( are the same equation)

Angle EFG is an angle with a measure of 42 degrees is drawn below.

Given that, angle EFG= 42 degrees.

Angle EFG is an angle with a measure of 42 degrees. To draw angle EFG, first draw a line segment and mark two points on the line segment. Label the two points E and F. Then, using a protractor, measure out an angle with a measure of 42 degrees from the line segment EF, starting from point E. Finally, mark the end of the angle as point G.

Therefore, angle EFG is an angle with a measure of 42 degrees is drawn below.

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Both of the intervals given are meaningful intervals in mathematics, but they are different types of intervals.Therefore, the interval (1, -13] is meaningless because it does not contain any real numbers.

An interval is a number or range of values ​​between two endpoints. 

The endpoints can be included or excluded from the interval, and the interval can be open, closed, or half-open depending on whether the endpoints are included or excluded.

The interval (-12, 0] is a closed interval, which includes the endpoint 0, and all real numbers between -12 and 0.

The square bracket indicates that the endpoint 0 is included in the interval.

The interval (1, -13] is an empty interval, which includes no real numbers, since there is no number that is greater than 1 and less than or equal to -13. This interval is meaningless because it does not contain any numbers.

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The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

                      = 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

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\((\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{4}}} \implies \cfrac{ 2 }{ -10 } \implies - \cfrac{ 1 }{ 5 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{ 1 }{ 5 }}(x-\stackrel{x_1}{4}) \\\\\\ y-2=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}\implies y=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}+2\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 5 }x+\cfrac{14}{5} \end{array}}\)

Copying the data set into another program allows you to leverage the capabilities of that program for Statistical analysis.

The provided data set can be copied into another program, such as a spreadsheet or a statistical software program, to perform various data analysis tasks. Let's explore some common operations that can be performed using the data set.

1. Descriptive Statistics: By copying the data set into a spreadsheet or statistical software, you can calculate various descriptive statistics, such as the mean, median, mode, standard deviation, and range of the data. These statistics provide insights into the central tendency, variability, and distribution of the data.

A

1   4

2   8

3   9

4   5

5   2

6   7

7   7

8   5

9   8

2. Data Visualization: Once the data set is copied, you can create visualizations to better understand the data. This can include bar charts, histograms, line plots, or box plots, depending on the nature of the data and the insights you want to gain.

3. Data Manipulation: Copying the data set into a spreadsheet allows you to manipulate and transform the data as needed. You can perform operations like sorting, filtering, grouping, and calculating new variables based on existing ones. This enables you to extract meaningful information from the data set.

4. Statistical Analysis: If you are using statistical software, you can conduct advanced statistical analyses on the data set. This may involve regression analysis, hypothesis testing, analysis of variance (ANOVA), or clustering techniques, depending on the specific research question or objective.

5. Data Integration: If you have additional data sets or variables related to the given data set, copying it into a program allows you to merge or join different data sets, thereby enriching the analysis and providing a more comprehensive understanding of the data.

Overall, copying the data set into another program empowers you to perform a wide range of data analysis tasks, enabling you to explore, understand, and draw meaningful insights from the data.

In summary, copying the data set into another program allows you to leverage the capabilities of that program for statistical analysis, calculations, and visualizations, enabling you to gain deeper insights and draw meaningful conclusions from the data.

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The volume of the given triangular prism is 384 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the area of the base is

Area of a rectangle = 1/2 ×Base×Height

= 1/2 ×12×4

= 24 cm²

Now the volume is 24×16

= 384 cm³

Therefore, the volume of the given triangular prism is 384 cm³.

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The last option

When triangle STU is reflected across line ST, angle U coincides with angle J

ST is common to triangle SUT

ST is also common to triangle SJT

ST is a reflexive property

SU corresponds to SJ

UT corresponds to JT

Hence, the image of U and J are the same distance along the same ray from T

This is in shown in the last option as B

The expression written in the simplest scientific notation is 6. 4 × 10^4

Scientific notation can be defined as a mathematical method of presenting numbers or figures too large or small in simpler forms.

It is also termed index form or standard form

From the information given, we have that;

Now, substitute the values

8 × 10² × 3. 2 × 10^5 / 4 × 10³

Using the rule of exponent, we have;

25. 6  × 10^2 + 5/ 4 × 10³

25. 6 × 10^7/ 4 × 10³

Divide the numbers, we have

6. 4

Take the inverse power of the denominator

6. 4 × 10^ 7 - 3

6. 4 × 10^4

Thus, the expression written in the simplest scientific notation is 6. 4 × 10^4

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The sequence of transformations to change figure PQRS to figure P′Q′R′S′ will be;

⇒ Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Sequence of transformations will change figure PQRS to figure P′Q′R′S′.

Now,

Since, Sequence of transformations will change figure PQRS to figure P′Q′R′S′.

And, The coordinates of figure PQRS are,

P = (1,  2)

Q = (2, 1)

R = (3, 2)

S = (3, 3)

And, The coordinates of figure P'Q'R'S' are,

P' = (1,  -2)

Q' = (2, -1)

R' = (3, -2)

S' = (3, -3)

We know that,

The transformation rule for Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis will be,

⇒ (x , y) → (x, - y)

Thus, We get;

The sequence of transformations to change figure PQRS to figure P′Q′R′S′ is,

''Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis.''

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