Q4. The diagram shows a triangle inside a rectangle.
2x
All measurements are given in centimetres.
Show that the total area, in cm², of the shaded regions is 18x - 30
3x-5
Diagram NOT
accurately drawn

The balance of the account which earns annual simple interest of $250 at 4% for 1 year is $260

Simple interest = principal × rate × time

= 250 × 4% × 1

= 250 × 0.04 × 1

= $10

Balance = Principal + Simple interest

= $250 + $10

= $260

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Answer:

14π cm

Step-by-step explanation:

Circumference of a circle given the diameter is :

πd

We simply substitute the value given in the image into our formula to find our answer:

πd = π×14 = 14π

Units will be cm as circumference is a length

This is our final answer as the question states to leave it in pi form .

Hope this helped and brainliest please

Answer:

14π cm

Step-by-step explanation:

Circumference of a circle with radius r = 2πr or 2rπ

The diameter d is twice the radius so circumference = dπ

Here d= 14 so the answer is 14π cm

The area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.

Note that:

The area of an Equilateral triangle is expressed as A = ((√3)/4)a²

Where a is the dimension of the side.

The area of an Isosceles triangle is expressed as A = (ah)/2

Where a is the dimension of the base and h is the height.

The area of a Right angled triangle is expressed as A = (ab)/2

Where a and b is the dimension of the two sides other than the hypotenuse.

For the Equilateral triangle.

Given that;

A = ((√3)/4)(5.4mm)²

A = ((√3)/4)( 29.16mm² )

A = 12.6mm²

Area of the Equilateral triangle is 12.6mm²

For the Isosceles triangle.

Given that;

The height h is the imaginary line drawn upward from the center of a.

First, we calculate the height using Pythagorean theorem

x² = y² + z²

Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h

(5.9in)² = (1.7in)² + h²

34.81in² = 2.89in² + h²

h² = 34.81in² - 2.89in²

h² = 31.92in²

h = √31.92in²

h = 5.65in

Now, the area will be;

A = (ah)/2

A = (3.4in × 5.65in )/2

A = 19.21in²/2

A = 9.61in²

Area of the Isosceles triangle is 9.61in².

For the Right angled triangle

Given that;

A = (ab)/2

A = ( 8.2yds × 4.1yds)/2

A = ( 33.62yds²)/2

A = 16.81yds²

Area of the Right angled triangle is 16.81yds²

Therefore, the area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.

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Answer:

$3.00

Step-by-step explanation:

$5.00 = 5

$2.00 = 2

5

-2

_

3

3 = $3.00

Answer:

$3.00

Step-by-step explanation:

Answer: a. -25

Step-by-step explanation:

1. Multiply the numbers

5x(−5)

Solution

−25x

The total length of the trip 190.08 miles

How you do it is to add the 44% of 132 to 132

= (132 + (132×44%))

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.

First, you have to find out how much 44% is. Change it into decimal form (0.44) and then multiply the two together.

132 × 0.44 is 58.08 miles.

Then you add that to the rest of the trip, 132 miles.

= (132 + 58/08

=190.08

The total length of the trip was 190.08 miles.

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To find the volume of a cylinder we must perform a mathematical operation that is expressed in the following formula V = Π h r².

To find the volume of a cylinder we must solve the following mathematical formula:

Our example cylinder is 10 centimeters high and 6 centimeters in diameter. What is its volume?

To find the volume we substitute the values as follows:

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The function which represents the graph is f(x) = (x + 2)(x² + 3x - 4). Then the correct option is 1.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The graph is given below.

The value of the function is zero for the values of x are -4, -2, and 1.

Let's check which function gets satisfied.

f(x) = (x + 2)(x² + 3x - 4)

The function can be written as

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

Then the values of x for which the value of the function is zero.

                       f(x) = 0

(x + 2)(x + 4)(x - 1) = 0

                         x = 1, -2, -4

Then the function will be f(x) = (x + 2)(x² + 3x - 4). Then the correct option is 1.

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Answer:

5x^5y

Step-by-step explanation:

Answer:

[tex]\dfrac 32[/tex]

Step-by-step explanation:

[tex]~~~~~~~2^{2x} = 2^3\\\\\implies \ln\left(2^{2x} \right) = \ln (2^3)\\\\\implies 2x \ln(2) = 3 \ln(2) \\\\\implies 2x = 3\\\\\implies x = \dfrac 32[/tex]

Answer:

B

Step-by-step explanation:

Answer:

1 pint is equal to 2 cups

Step-by-step explanation:

2 cups is equivalent to__1_ pint.

Hope This Helped

Answer:

answer is 1

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

f(6)=6^2-4

f(6)=36-4

f(6)=32

Answer:

f(6)=32

Step-by-step explanation:f(6)=6^2 -4

f(6)=36-4

f(6)=32

Answer:

John is 20 years old.

Step-by-step explanation:

Given the second mean is 18, it is equal to the first mean age plus John's unknown age. The sum is also divided by 2 because there are 2 values in the sum (1. John's age and 2. the mean, 16 yrs old).

Set up an equation: [tex]\frac{x+16}{2}=18[/tex]

multiply both sides by 2: [tex]x+16=36[/tex]

simplify: [tex]x=20[/tex]

In the given figure, the length of BC is 6.66 cm and the length of DC is 5.33 cm

From  the question, we are to determine the length of BC and DC

Considering the diagram,

First, we will determine the measure of angle A

Using SOH CAH TOA

We can write that

[tex]sin A = \frac{4}{5}[/tex]

sin A = 0.8

∴ A = sin⁻¹(0.8)

A = 53.13°

Now, we will determine the measure of angle C

∠A + ∠ABC + ∠C = 180° (Sum of angles in a triangle)

53.13° + 90° + ∠C = 180°

∠C = 180° - 90° - 53.13°

∠C = 36.87°

Also,

Using SOH CAH TOA

[tex]tan C = \frac{BD}{DC}[/tex]

[tex]tan36.87 ^\circ=\frac{4}{DC}[/tex]

[tex]0.7500 = \frac{4}{DC}[/tex]

[tex]DC = \frac{4}{0.75}[/tex]

DC = 5.33 cm

By the Pythagorean theorem,

/BC/² = /BD/² + /DC/²

/BC/² = 4² + 5.33²

/BC/² = 16 + 28.4089

/BC/² = 44.4089

/BC/ = √44.4089

/BC/ = 6.66 cm

Hence, the length of BC is 6.66 cm and the length of DC is 5.33 cm

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Answer:

6x - 7

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] (12x + 6x - 21 ) ← multiply each term in the parenthesis by [tex]\frac{1}{3}[/tex]

= 4x + 2x - 7 ← collect like terms

= 6x - 7

Hey there!

ORIGINAL EQUATION:

1/3(12x + 6x - 21)

COMBINE the LIKE TERMS

= 1/3(18x - 21)

DISTRIBUTE 1/3 WITHIN the PARENTHESES:

= 1/3(18x) + 1/3(-21)

SIMPLIFY:

= 6x - 7

Therefore, the answer should be:

6x - 7

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The quadrants is tan⁻¹x restricted is A. Quadrants I and IV

To answer the question, we need to know what tan⁻¹x is.

tan⁻¹x is the inverse trigonometric function of tanx, which is the value of the angle for tanx.

To find the quadrants in which tan⁻¹x is restricted, we know that tanx lies in the range

-∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°.

tan⁻¹x lies between quadrant I and IV

So, the quadrants is tan⁻¹x restricted is A. Quadrants I and IV

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Answer:

Here's your answer.

Let the number be x.

Here we have to multiply with 100 on both sides.

[tex] \implies \: 100x = 252.5252 \\ \\ \implies \: 100x = 250 \ + 2.5252... \\ \\ \implies \: 100x = 250 + x \\ \\ \implies \: 99x = 250 \\ \\ \implies \: x = \frac{250}{99} [/tex]

Therefore, sum of numerator and denominator = 25099 = 349

Answer:

349

Step-by-step explanation:

The result of evaluating 67.8046 + 8.264 - 243.5 is -167.431

The expression is given as:

67.8046 + 8.264 - 243.5

The highest number of significant figures in the expression is 6 (i.e. 67.8046)

This means that the result must be in 6 significant figures.

Next, we evaluate the expression as follows:

67.8046 + 8.264 - 243.5 = -167.4314

Approximate to 6 significant figures.

67.8046 + 8.264 - 243.5 = -167.431

Hence, the result of evaluating 67.8046 + 8.264 - 243.5 is -167.431

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The extra amount that Mary would pay for apples under a monopoly instead of perfect competition is B. $3

From the complete information,

There are images of the prices that can be gotten under a monopoly and the ones that can be gotten in a perfect competition by Mary.

The marginal cost which is graphed against the pound of apples and the price shows Mary would pay $15 and the marginal revenue shows that Mary would pay $12.

Hence, the difference between them, which is the extra amount to be paid would be $15-$12

=$3

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Answer:

B. 3$

Hope this helps!

Step-by-step explanation:

Answer:

1. c. statistical inference

19. d. statistical inference

20. b. relative frequency distribution

Answer:

a=15.7mm2,31.4

b=18.84in2,37.68

Answer:

y = 1.6x + 3.4

Step-by-step explanation:

We have to use the equation y = m x + c to find the equation of the line.

Here,

m ⇒ slope

c ⇒ y-intercept

First, let us find the slope.

For that, we can use the given two coordinates.

( -1 , 5 ) ⇒ ( x₁ , y₁ )

( 4 , -3 )  ⇒ ( x₂ , y₂ )

The formula to find the slope of a line is :

m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )

Let us solve now.

m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )

m = ( 5 - ( -3 ) ) ÷ ( -1 - 4 )

m = ( 5 + 3 ) ÷ -5

m = 8 ÷ -5

m = -1.6

Now let us find the y-intercept (c ) of the line.

For that, let us get one of the coordinates which are given in the question.

I'll get ( -1 , 5 ) from  that.

( -1 , 5 ) ⇒ ( x , y )

Let us solve now.

y = mx + c

5 = -1.6 × -1 + c

5 = 1.6 + c

5 - 1.6 = c

3.4 = c

Therefore,

m ⇒ -1.6

c ⇒ 3.4

So, the equation of the line is :

y = mx + c

y = 1.6x + 3.4

Answer:

(2+3)+4 = 2+(3+4) this is an example of associative property

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &10 \end{cases} \\\\\\ A=4000e^{0.07\cdot 10}\implies A=4000e^{0.7}\implies A\approx 8055.01[/tex]

An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called a prime polynomials.

The polynomial 6x⁴ – 8x² + 3x² + 4 needs to be factored and the steps are:

Step 1: (6x⁴ – 8x²) + (3x² + 4)

Step 2: 2x²(3x² – 4) + 1(3x² + 4)

Since they do not have any common factor.

Faelyn should realize that her work indicates that the polynomial is prime.

Prime polynomials have integer coefficients.

An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.

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The true statement about the set of quadrilaterals in the coordinate plane is B. Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

A quadrilateral is a polygon having four sides, four angles, and four vertices.

In this case, because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

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Answer:

the answer to this question is 3/40

Step-by-step explanation:

if you want my explanation you ca

Answer:

√2' = t

Step-by-step explanation:

1 1/2s = 3/5t^2 + 1/3u^2; substitute known values

1 1/2 • 28 = 3/5 • t^2 + 1/3 • -6^2; simplify

42 = 3 • t^2 ÷ 5 + 1/3 • 36

42 = 3 • t^2 ÷ 5 + 12; apply property of subtraction of equality

42 – 12 = 3t^2 ÷ 5 + 12 – 12; simplify

30 = 3t^2 ÷ 5; apply property of multiplication of equality

30 • 5 = 3t^2 ÷ 5 • 5; simplify

6 = 3t^2; apply property of division of equality

6 ÷ 3 = 3t^2 ÷ 3; simplify

2 = t^2

√2' = t

Answer:

12.5% is the answer.

Step-by-step explanation: