shape y is an enlargement of shape x by a scale factor of 4
work out lengths a and b

Answer: D. [tex]5\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\tan 30^{\circ}=\frac{x}{15}\\\\x=15 \tan 30^{\circ}\\\\x=5\sqrt{3}[/tex]

x > -2

Inequalities compare the values of 2 expressions.

Solving for x

To solve the inequality, we need to isolate x. First, add 4 to both sides.

Then, divide by 5.

Finally, divide both sides by -1. When multiplying or dividing an inequality by a negative, switch the direction of the sign.

Interpreting the Answer

Verbally, the answer is that x is greater than or equal to -2. This means that any x-value greater than -2 (including -2 itself) will make the original inequality, −5x−4 ≤ 6, true. For example, let's plug in 0.

This statement is true, which proves our answer is correct.

Kevin's solution is incorrect. He found the area of the triangle as [tex]bh[/tex], not [tex]\frac{1}{2}bh[/tex].

The correct area of the triangle is [tex]\frac{1}{2}(8)(5)=20 \text{ in}^2[/tex].

The graph of the function y = f(x + 16) is a transformation of the original function f. This transformation has shifted the graph of f to the right by 16 units on the x-axis. This means that the value of x in the original function has been increased by 16, which has an effect on the corresponding value of y in the transformed function.

For example, if the point (a, b) is on the graph of f, then the point (a + 16, b) will be on the graph of y = f(x + 16). The x-coordinate of the point has been increased by 16, and since the transformation is a horizontal shift, the y-coordinate remains unchanged.

In summary, the graph of y = f(x + 16) is a reflection of the graph of f about the vertical axis. The transformation has the effect of shifting the graph to the right, but preserving the shape and overall form of the original function.

answer is 2 because if we expand the bracket we get 2x–8y+3y which is 2x–5y but if it was 2(x+4y) it would be equal to 2x+8y+3y therefore being 2x+11y

Factorization of  6ax - 15x is 3x.(2a - 5)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given expression,

6ax - 15x

It can be written as

3×2 . a . x - 3×5 . x

Factoring out common factor

3x.(2a - 5)

Hence, 3x.(2a - 5) is the factorization of 6ax - 15x.

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Answer:The length of AC to one decimal place in the trapezium is 18.1 cm

Step-by-step explanation: Using Pythagoras theorem, we can find the length AC

Pythagoras theorem

c² = a² + b²

Therefore, draw a line from the point B to the line AD and call it line BX.

BX ║ CD

Therefore,

16² - 7² = BX²

256  - 49 = BX²

BX² = 207

BX = √207

BX = 14.3874945699

BX = 14.4 cm

Therefore,

11² + 14.4² = AC²

121 + 207.36 = AC²

AC = √328.36

AC = 18.120706388

AC = 18.1 cm

The exponential function from the table is f(x) = 2 [tex](0.5)^x[/tex].

The graph is given below.

Option D is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The exponential function is given as,

f(x) = m[tex]a^x[/tex]

Now,

From the table,

2 = m[tex]a^0[/tex]

m = 2

1 = m[tex]a^1[/tex]

m = 1/a ____(1)

0.5 = m[tex]a^2[/tex]

m = 0.5/[tex]a^2[/tex] _____(2)

Now,

From (1) and (2).

1/a = 0.5/[tex]a^2[/tex]

a = 0.5

Now,

f(x) = 2 [tex](0.5)^x[/tex]

Thus,

The exponential function is f(x) = 2 [tex](0.5)^x[/tex].

The graph is given below.

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Answer:

x intercept: (0,0)

Step-by-step explanation:

y intercept: (0,0)

x = 15/2

do u need an explanation?

The area of the given rectangle will be A = 9x² - 64 yards².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

The area of the rectangle is A = a*b

Given is l =(3x+8) yards

b = (3x-8)yards

So the area of the rectangle is A = l*b

A = (3x+8)(3x-8)

A = 3x² - 8²

A = 9x² - 64

hence the area of the given rectangle will be A = 9x² - 64 yards².

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Answer:

[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\[/tex]

[tex]a=38.5[/tex] ft

[tex]b=51[/tex] ft

[tex]c=76[/tex] ft

Step-by-step explanation:

Here is the formula for the Law of Sines.

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]`

In this example we are given

[tex]\angle A =27.2 \textdegree\\\angle C=115.5 \textdegree\\c=76.0[/tex]

Angle B

The sum of the interior angles in a triangle add up to 180º. Given 2 angles, we can evaluate the 3rd.

[tex]180\textdegree-115.5\textdegree-27.2\textdegree=37.3 \textdegree[/tex]

[tex]\angle B=37.3 \textdegree[/tex]

Side a

We can use the Law of Sines formula  [tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]  to evaluate side a.

Inserting our values into the equation gives us

[tex]\frac{a}{\sin 27.2}=\frac{76}{\sin 115.5}[/tex]

Cross multiply to evaluate side a.

[tex]76*\sin 27.2=a*\sin 115.5[/tex]

Divide both sides by [tex]\sin 115.5[/tex].

[tex]\frac{76*\sin 27.2}{\sin 115.5} =a[/tex]

[tex]38.49=a[/tex]

Side b

We can use the Law of Sines formula  [tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]  to evaluate side b.

Inserting our values into the equation gives us

[tex]\frac{b}{\sin 37.3}=\frac{76}{\sin 115.5}[/tex]

Cross multiply to evaluate side b.

[tex]76*\sin 37.3=b*\sin 115.5[/tex]

Divide both sides by [tex]\sin 115.5[/tex].

[tex]\frac{76*\sin 37.3}{\sin 115.5} =b[/tex]

[tex]51.03=b[/tex]

[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\a=38.5\\b=51\\c=76[/tex]

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sin(A) / a = sin(B) / b = sin(C) / c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

Answer:

<YTZ

Step-by-step explanation:

Vertical angles are congruent.

<VTW measures 40°.

<YTZ is vertical to angle VTW.

m<YTZ = m<VTW

m<YTZ = 40°

Answer: <YTZ

Answer:

Nope

Step-by-step explanation:

No, because if you add the angles of B and C (since they're asking for line BC), they must equal the angles of A and D (Since the other line was AD)

The sum of B and C is 90+45 which = 135

The sum of A and D is 90+135 which = 225

135 =/= 225

The difference in rainfall between the wettest and driest months is 3.97 inches.

A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are utilized to contrast and compare various data types, frequencies, or other measurements of several categories of data.

On the graph, there are two axes. The numerical data is displayed against the category data on one axis, which is used to depict the numerical values.

Given the graph which shows the rainfall of the wettest and driest months,

here red blocks are for the driest months and blue blocks show the wettest months,

From the graph, we can see that the wettest month has a rainfall height of 2.3 inches

The driest month has a rainfall of -1.67 inches

So the difference between the two will be;

2.3 - (-1.67)

=  2.3 + 1.67 = 3.97 inches

Hence the difference is 3.97 inches.

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The complete question is,

The bar graph shows the differences in a city’s rainfall from the historical average. What is the difference in rainfall between the wettest and the driest months? Write your answer as a decimal.

The difference in rainfall between the wettest and the driest months is inches.

Answer:

The length of 5 inches should be counted 1 time.

Step-by-step explanation:

The 5 inches between the triangle and rectangle is inside the shape. So, it doesn't count as perimeter.

Answer:

0.955

Step-by-step explanation:

Height= volume x pi x radius squared (h = V x pi x r^2)

Volume (V) = 243

Height (h) = ?

Pi = 3.14

Radius (r) = 9

Diameter to radius = 18/2 = 9

h = 243 x 3.14 x 9^2

=0.955

Answer:

The base is 8 and the height is 3. Multiply.

8 * 3 = 24

You will then multiply your product by 1/2.

24 * 1/2 = 12

The area is 12 inches squared.

Step-by-step explanation:

Hope it helps! =D

Answer:

[tex] {12cm}^{2} [/tex]

Step-by-step explanation:

Given

[tex]a = \frac{1}{2} bh[/tex]

b= 8in

h= 3in

8x3 = 24

24 ÷ 2 (Same as multiplying by half)

The amount invensted at 5% and 7% are 3500 and 4500 respectively.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, an amount $8000, is invested at 5% and 7%, with annual interest is $490,

For this we will establish the a system of equations,

x + y = 8000......(i)

0.05x + 0.07y = 490

Multiplying by 100,

5x + 7y = 49000.....(ii)

Multiplying eq(i) by 5,

5x + 5y = 40000

Subtract eq(i) from eq(ii)

2y = 9000

y = 4500

Put y = 4500 in eq(i)

x = 8000 - 4500

x = 3500

Hence, the amount invensted at 5% and 7% are 3500 and 4500 respectively.

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Answer: 58.5

Step-by-step explanation: 65.00 - 10% = 58.5

Answer: $58.50

Step-by-step explanation: Orignal Price: $65.00

10% discount = -$6.50

$65.00 - $6.50 = $58.50.

The area for this figure is given as follows:

38.13 cm².

The composite area of the figure is obtained by the sum of the areas of each component of the figure.

The figure is composed as follows:

The area of the rectangle is given by the multiplication of the dimensions, hence:

Ar = 6 x 4 = 24 cm².

The area of the semicircle is given by half the multiplication of π = 3.14 by the radius square, hence:

As = 0.5 x 3.14 x 3² = 14.13 cm².

Hence the total area is given as follows:

A = Ar + As

A = 24 + 14.13

A = 38.13 cm².

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The value of function relating the number of people, n, to the cost, C is,

⇒ C (n) = 7n ; if 0 < n < 15

           = 105n ; if n ≥ 15

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people.

Hence, he value of function relating the number of people, n, to the cost, C is,

⇒ C (n) = 7n ; if 0 < n < 15

           = 105n ; if n ≥ 15

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Answer:

A

Step-by-step explanation:

please memorize this formula for area of sphere

A=4π r²

so d = 22, which means r=11

so A = 4* π*11² = 4*121*π =484π = 1519.76

Answer:

Step-by-step explanation

Sort the data: 41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75, 97

Find the median (Q2): 53

Split the data set into two parts: Q1 (25th percentile) and Q3 (75th percentile)

Q1: 41, 41, 43, 43, 45, 50, 52, 53

Q3: 54, 62, 63, 63, 67, 75, 97

Find the median (Q1) of Q1 and the median (Q3) of Q3:

Q1 = 45

Q3 = 63

Finally, calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 63 - 45 = 18

So, the interquartile range of the given data set is 18. This means that 50% of the data falls within a range of 45 + 18 = 63 and 45 - 18 = 27.  

AB vector is a vector whereas AB bar is a line segment.

What is a vector ?

The vectors are described as an object containing both significance and course. Vector describes the motion of an item from one point to any other. Vector math may be geometrically picturised via the directed line segment.

The duration of the phase of the directed line is known as the value of a vector and the angle at which the vector is inclined shows the path of the vector. The start line of a vector is referred to as “Tail” and the finishing factor (having an arrow) is referred to as “Head.”

The difference is in their names itself.

AB vector is a vector whereas AB bar is a line segment.

A vector has a direction and a magnitude while a line segment ( scalar ) has only magnitude.

Therefore, AB vector is a vector whereas AB bar is a line segment.

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The required graph of the equation is given by y=x/2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: A graph proportional to the line that passes through the point.

Now one of the graph has the equation y= x/2

we can treat this line as some proportional equation with 1/2 as the constant.

And it also passes through the point (2,1)

Hence, The required graph of the equation is given by y=x/2

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The options containing the graph are attached

The difference in rainfall between the wettest and driest months is the amount of precipitation.

Precipitation refers to any form of moisture that falls from the atmosphere to the ground, including rain, snow, sleet, hail, and other forms of precipitation. Precipitation is an important aspect of the Earth's water cycle, as it provides the water that replenishes rivers, lakes, and aquifers, and sustains the growth of plants and animals.

The amount of precipitation that falls in a given area can vary widely, depending on many factors such as geography, temperature, and prevailing weather patterns. For example, areas near the equator tend to receive more rainfall than areas located closer to the poles, and areas with high elevations tend to receive more snow than areas that are closer to sea level.

The distribution of rainfall and other forms of precipitation across a region can also be affected by the prevailing winds, air masses, and topographical features. For example, mountainous areas may receive more rainfall due to the prevailing winds and the way that air masses interact with the terrain.

The difference in rainfall between the wettest and driest months is the amount of precipitation that occurs in the wettest month minus the amount of precipitation that occurs in the driest month. This difference can vary greatly depending on the location and climate of a region.

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The surface area of the pyramid, given the height and base of the triangles, and the area of the hexagonal base, is 439. 8 square inches

Let's determine the area of the six isosceles triangles using the formula;

= 6 x 1 /2 x base x height

= 6 x 1 / 2 x 10 x 6

= 180 square inches

The surface area of the pyramid is therefore;

= Area of triangles + Area of hexagonal base

= 180square inches + 259.8 square inches.

Add the values, we get;

= 439. 8 square inches

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Answer: 439.8

Step-by-step explanation: