9. On a map, 2.5cm represents 1km, what is the actual distance between two towns 15cm apart on the map? ​

Answer:

[tex]b=3/11[/tex]

Step-by-step explanation:

[tex]-3b+11=8b+8 \\ \\ 11b+8=11 \\ \\ 11b=3 \\ \\ b=3/11[/tex]

Answer:

x = -11.2

Step-by-step explanation:

hope it helps

The way that they could calculate the point that is equidistant from all three gates is; By joining the entry point of all three friends to form a triangle and then finding the centroid of this triangle , they can calculate the required point.

The circumcenter of a triangle is defined as the locus of point equidistant from the three vertices of a triangle.

From the image attached showing the location of the three gates, the first step to take is to join all the three entry points of the friends in order to form a triangle.

The second step to take now, will be to find the centroid of the triangle, such that all three friends must start moving in the direction of the midpoint of the opposite side.

Finally, following that procedure, the point equidistant from all the three gates can be calculated.

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Answer:

x=16

Step-by-step explanation:

right!!

The height of the mountain is derived to be 410 m approximately to 2 significant figure using the trigonometric ratio of tangent for angles of elevation 32° and 58°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We shall represent the length from point B to the foot of the mountain with x and the height of the mountain with h so that:

the distance from a to the foot of the mountain = 400m + x

tan 32° = h/(400 + x)

h = tan 32° (400 + x) {by cross multiplication}

h = 400 × tan 32° + xtan 32°

h = 249.9477 + xtan 32°

also;

tan 58° = h/x

h = tan 58° × x {by cross multiplication}

h = xtan 58°

so;

xtan 58° = 249.9477 + xtan 32°

xtan 58° - xtan 32° = 249.9477 {collect like terms}

x(tan 58° - tan 32°) = 249.9477

x(0.9755) = 249.9477 {divide through by 0.9755}

x = 249.9477/0.9755

x = 256.2252

h = 256.2252 × tan 58°

h = 410.9460.

Therefore, the height of the mountain is 410 m approximately to 2 significant figures using the trigonometric ratio of tangent for angles of elevation 32° and 58°.

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There are 51 trees, 41 weeds, and 16 grasses that are significant pollen producers.

In the context of beekeeping, the phrase "pollen source" refers to flowering plants that provide pollen to bees and other insects. Bees gather pollen to use as a source of protein for their young.

G, W, and T should stand for the number of grasses, weeds, and trees that serve as significant pollen sources.

According to information provided, state A is home to 80 significant sources of pollen. This data can be represented as follows in an equation:

G + W + T = 108......(1)

According to what is said, there are 7 times as many weeds as there are grasses. This data can be represented as follows in an equation:

W = 3G - 7......(2)

We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:

T = 3G + 3

We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:

G + W + T = 108

G + 3G - 7 + 3G + 3 = 108

7G - 4 = 108

7G = 112

G= 112/7

G = 16

Therefore, there are 16 grasses that are major pollen sources.

Number of weeds that are major pollen sources:

W = 3G - 7  = 3(16) - 7  = 48 - 7 = 41

Therefore, there are 41 weeds that are major pollen sources.

Number of trees that are major pollen sources:

T = 3G + 3  = 3(16) + 3  = 48 + 3  = 51

Therefore, there are 51 trees that are major pollen sources.

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The area of rectangle in the simplest Form is: [tex]= 45[/tex]

What is the area of a rectangle?

The area of a rectangle of length (L) and width (W) is given by the multiplication of the dimensions, as follows:

Area of rectangle = Length (L) * Width (W)

Given:

Area of rectangle =[tex]\sqrt{15*9*5*3}[/tex]

                              ⇒[tex]\sqrt{3*5*3*3*5*3}[/tex]

                              ⇒3*5*3

                              ⇒45

Therefore, the area of rectangle in the simplest Form is: 45

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Answer:

y + y + y + y + y + y

Step-by-step explanation:

6y =

6 * y =   ==> add y 6 times

Hence, 6 * y = y + y + y + y + y + y

Answer:

x = 12

Step-by-step explanation:

3/9 = 4/x

3x = 36

x = 12

Answer:

The quadrilateral ABCD was dilated with a scale factor of 1.8

Take the value of x before the dilation (4), and multiply that by 1.8

The result should be 7.2

Hope this helps.

Based on the given set of real numbers, a list of all the rational numbers in the set include the following: B. √4, -2/3, 1, 9/8, √(9/4), 2.4. Therefore, the correct answer option is: B. square root of 4 comma space short dash 2 over 3 comma space 1 comma space 9 over 8 comma space square root of 9 over 4 end root comma space 2.4 with bar on top.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.

In this scenario, the rational numbers include all of the following:

However, -√2 and √10 would not be classified as rational numbers because they cannot be obtained when an integer is divided by another integer.

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The median distance is 5km.

The median distance, symbolized by δM, is the median value of the distance among any two node pairs. This is measured over each network's largest linked component, and takes into account pairs including of the same node.

In this case, the dots in the picture (attached) represent the number of matches.

So, if we write it all down here, the data will be:

3, 4, 4, 5, 5, 5, 5, 7, 7

Since the total of values in the data is odd number, that is 9, then the formula for the median distance will be:

Median = (n + 1) / 2

with n = 9

Thus, the median distance in this case:

= (n + 1) / 2

= (9 + 1) / 2

= 10 / 2

= 5

Hence, the median distance is 5km.

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Answer:

yes?

Step-by-step explanation:

The opposite sides are parallel to each other if diagonals of the quadrilateral bisect each other.

The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.

AC and BD bisect each other.

We know that in a quadrilateral if the diagonal of the quadrilateral bisect each other then the opposite sides are parallel to each other.

AC = BD         (Equal diagonal)

Then the side AB and CD are parallel to each other. And similarly, the sides BC and AD are also parallel to each other.

AB || CD or BC || AD

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Answer:

A)  f(x) = tan(2x - π)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.3cm}\underline{Standard form of a tangent function}\\\\$f(x)=A \tan(B(x+C))+D$\\\\where:\\\\\phantom{ww}$\bullet$ $A=$ vertical stretch\\ \\\phantom{ww}$\bullet$ $\dfrac{\pi}{|B|}=$ period\\\\\phantom{ww}$\bullet$ $C=$ horizontal shift (positive is to the left)\\\\\phantom{ww}$\bullet$ $D=$ vertical shift\\\end{minipage}}[/tex]

The parent tangent function is:

[tex]f(x)=\tan(x)[/tex]

The period of the parent tangent function is π.

A tangent function is discontinuous when cos(x) = 0, so it has vertical asymptotes whenever cos(x) = 0.

Therefore, the parent tangent function has vertical asymptotes at:

[tex]x=\dfrac{\pi}{2}+\pi n[/tex]

and so its domain is:

[tex]\left\{ x \in \mathbb{R} \;| \;x \neq \dfrac{\pi}{2}+\pi n\right\}[/tex]

If the domain of the given tangent function is:

[tex]\left\{ x \in \mathbb{R} \;| \;x \neq \dfrac{\pi}{4}+\dfrac{\pi}{2}n\right\}[/tex]

then its vertical asymptotes are when:

[tex]x =\dfrac{\pi}{4}+\dfrac{\pi}{2}n[/tex]

Therefore, its period is π/2.

[tex]\implies \dfrac{\pi}{|B|}=\dfrac{\pi}{2}[/tex]

[tex]\implies B=2[/tex]

And it has been horizontally shifted by π/2:

[tex]\implies f(x)=\tan\left(2\left(x-\dfrac{\pi}{2}\right)\right)[/tex]

[tex]\implies f(x)=\tan\left(2x-\pi\right)[/tex]

Function g(x)

[tex]g(x)=\tan(x- \pi)[/tex]

Function h(x)

[tex]h(x)=\tan \left(x-\dfrac{\pi}{2}\right)[/tex]

Function j(x)

[tex]j(x)=\tan \left(\dfrac{x}{2}- \pi \right)[/tex]

Answer:fsjcc

Step-by-step explanation:

8473274+5487643=593fdj

]

The profit the company would make over the course of its 5 years of operation, given the starting annual profit and the constant increase in the profit, is $ 998, 329.34

To find the total profit that the company would make over the first 5 years of the operation, use the future value formula :

= First profit x Future value interest factor of annuity, 27%, 5 years

First profit = $ 117, 000

Rate of increase = 27 %

Number of years = 5 years

The profit in 5 years is:

= 117, 000 x 8.53272941

= $ 998, 329.34

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The value of k  for the point on the line is 63

We can find the value of k by using the slope formula. The slope of a line can is given by:

Slope = (y2-y1)/(x2-x1)

Since the pass through the origin (0,0), (k,7) and (-81,-9). we can write:

x1 = 0, y1 = 0 and x2 = -81, y2 = -9

Slope = (-9-0)/(-81-0) = 1/9

Also, we can write:

x1 = k, y1 = 7 and x2 = -81, y2 = -9. And the slope is still the same

1/9 =  (-9-7)/(-81-k)

1/9 = -16/(-81-k)

1/9(-81-k) = -16

-9 - k/9 = -16

-k/9 = -16 + 9

-k/9 = -7

-k = -7 × 9

-k = -63

k = 63

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Answer:

-6, 19, 29

Step-by-step explanation:

Range = y

Domain = x

The equation is y = 5x + 4

we plug x into the equation:

5 (-2) + 4 = -6

5 (3) + 4 = 19

5 (5) + 4 = 29

The best step to use in getting angle ECA is the exterior angle property which gives us; Angle ECA =  154°

In a triangle geometry, we know that the exterior angle is always equal to the sum of the interior opposite angles. This property is referred to as  the exterior angle property. This tells us that any two triangles will be similar if their corresponding angles tend to be congruent and the length of their sides will be proportional.

Now, in this question, we are trying to find the measure of angle ECA which is an exterior angle given by the expression 166 - 6x.

Now, the interior opposite angles are (100x - 59) and (6x + 1). Thus;

Applying the exterior angle property, we will have the first step as;

(100x - 59) + (6x + 1) = 166 - 6x

106x - 58 = 166 - 6x

112x = 166 + 58

112x = 224

x = 224/112

x = 2

Thus;

Angle ECA = 166 - 6(2) = 154°

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The matching statements and reasons:

The given polynomial does not have x - 3 as its factor.

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The remaining factors of the polynomial can be found by dividing it by the same factor.

The polynomial is given as P(x) = 2x¹ − 5x³ - 4x² + 4.

In order to check whether x - 3 is a factor, evaluate P(3) as below,

P(3) = 2 × 3¹ - 5 × 3³ - 4 × 3² + 4

⇒ -161

Since, P(3) ≠ 0, x - 3 is not a factor of P(x).

Hence, the given expression is not a factor of P(x).

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The radius of the hemisphere with volume 3839cm³ is 11.9cm

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr3 cubic units.

The volume of a hemisphere is given as ⅔πr³

Where r is the radius

V = ⅔×3.14r³

3839 = 2/3× 3.14r³

r³ = (3839× 3)/3.14×2

r³ = 11517/6.28

r³ = 1833.9

r = cube root of 1833.9

r = 11.9cm

Therefore the radius of the hemisphere is 11.9cm

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Answer:

APR stands for Annual Percentage Rate, which is the interest charged on a loan expressed as a yearly rate. In this case, we are given the interest rate for a loan over 10 days.

To calculate the APR, we need to determine the annualized interest rate, which is the interest rate multiplied by the number of times the interest is compounded per year.

We know that the interest on the loan is $200. The loan amount is $800 and the loan period is 10 days.

First we need to calculate the daily interest rate:

Interest/Loan amount = 200/800 = 0.25

To find the annualized interest rate, we need to multiply the daily interest rate by the number of days in a year:

0.25* 365 = 91.25%

To the nearest percent the APR for this loan is 91%

To evaluate the expression 5/6 - 3/4, we need to first convert the fractions to a common denominator. The least common multiple of 6 and 4 is 12, so we can rewrite the fractions as follows:

5/6 - 3/4 = (5/6)(2/2) - (3/4)(3/3)

= 10/12 - 9/12

= 1/12

Therefore, Devon used 1/12 of a cup more sugar than flour.

1) The triangle classified according to their sides is given as follows:

a) Isosceles triangle - It has two equal sides

b) Scalene Right Angled Triangle.

c)  obtuse scalene triangle -Has an angle that is over 90 degrees, as well as three unequal sides

d) Equilateral Triangle - Three equal sides and three equal angles

e) Isosceles Right Angled Triangle - Right angle with two equal sides and two equal angles

f) Scalene Triangle - Three unequal sides and three unequal angles.

g) Equilateral Triangle - Three equal sides and three equal angles

h) Obtuse Isosceles Triangle - has two equal sides with an angle measuring above 90 degrees.

2) Note that the value of x is 6, JK is 83, KL is 83 and JL is 83.

As indicated above, an Equilateral Triangle is one whose sides are equal. Thus,

JK = KL = JL

That means 13x + 5 = 17x -19 ..............1

Simplifying 1 by collecting like terms:

17x - 13x = 19 + 5

4x = 24

x = 24/4

x = 6

We can proceed to find the sides now

JK = 13x + 5

13 x 6 + 5

= 78 + 5

= 83

JK = 83

KL = 17x - 19

= 17 x 6 - 19

= 102 - 19

= 83

KL = 83

JL= 8x + 35​

= 8 x 6 + 35

= 48 + 35

= 83

JL = 83

Therefore, the value of x is 6, JK is 83, KL is 83 and JL is 83.

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1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.

The idea of area is essential to contemporary mathematics. A two-dimensional shape, figure, or planar lamina in a plane will occupy a specific amount of space, which is denoted by the area.

The area can be simply defined as the volume of cloth, or other material with the specified thickness, required to construct a model of the shape, or as the volume of paint required to completely cover the surface of the shape in a single layer, or "coat," of paint.

It is a two-dimensional illustration of the length of a curve or the volume of a solid, where length is a one-dimensional concept and volume is a closely related concept that exists in three dimensions.

Area of national park = 9,542 miles²

14% of the area of the park is reserved for animal preservation

= 9542 × 14

= 9542 × 14/100

= 9542 × 0.14

=  1335.88 miles²

Thus, 1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.

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The equation that represent the proportional relationship is y = 11k.

Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.

Therefore, proportional relationship can be represented as follows:

y ∝ x

y = kx

where

Hence,

x = 2

y = 22

Therefore,

22 = 2k

k = 22 / 2

k = 11

Therefore, the equation is y = 11k

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on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

equation given is 3(x+2)=7x-48

value of x

[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]

value of x from the given equation comes out to be 13.5

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The total number of pears consumed by all the 6 partridges is given by the equation A = 84 pears

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of pears be represented as A

Let the number of partridges be n = 6

Now , Pete the partridge eats 4 pears in 30 minutes

So , the number of pears in 1 hour = 2 x 4

The number of pears in 1 hour = 8 pears

The number of pears in 1 hour 30 minutes = 8 + 4 pears

The number of pears in 1 hour 30 minutes = 12 pears

The number of pears in 1 hour 45 minutes = 12 + 2 pears

The number of pears in 1 hour 45 minutes = 14 pears

So ,

The total number of pears by all 6 partridges A = 6 x number of pears in 1 hour 45 minutes

Substituting the values in the equation , we get

The total number of pears by all 6 partridges A = 6 x 14

On simplifying the equation , we get

The total number of pears by all 6 partridges A = 84 partridges

Therefore , the value of A is 84 partridges

Hence , the number of partridges is 84

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X xcm 6cm 8cm is equal to 10cm if the area of the trapezium underneath is 40%2cm2.

Provide A B C D. trapezium the length of the sides excluding the base is 10,

[tex]$$\therefore \mathrm{AD}=\mathrm{DC}=\mathrm{CB}=10 \mathrm{~cm} \text {. }$$[/tex]

Draw a parallel DP & CQ on AB.

Let [tex]$\mathrm{AP}=x \mathrm{~cm}$[/tex]

In symmetry

[tex]$$\mathrm{QB}=x \mathrm{~cm}$$[/tex]

Consider area A of the trapezium. A B C D

[tex]$$\begin{aligned}& \left.A=\frac{1}{2} \text { (Sum of parallel sides }\right) \times(\text { Height }) \\& A=\frac{1}{2}(D C+A B) \times \text { DP } \quad \ldots(1)\end{aligned}$$[/tex]

Therefore, DPCQ creates a rectangle because DP & CQ are perpendicular to A B and C D were parallel to A B.

[tex]$$\therefore \mathrm{PQ}=\mathrm{DC}=10 \mathrm{~cm}$$[/tex]

Thus,

[tex]$$\begin{aligned}A B & =A P+P Q+Q B \\& =x+10+x \\& =2 x+10\end{aligned}$$[/tex]

Use the equation A r e a = h 2 (a + b) to determine a trapezium's area. The distance between a and b, which are two parallel sides, is denoted by the letter h. To put it another way, add the two parallel sides together, divide by 2, and then multiply this number by the separation between the parallel sides. The surface of a shape's surface is measured by its area. The length and width of a rectangle or square must be multiplied to determine their respective areas. A has a perimeter of x by y.

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