9
)
14+(−9)+(−9)14, plus, left parenthesis, minus, 9, right parenthesis, plus, left parenthesis, minus, 9, right parenthesis.

Answer:

3x² - 4x - 5

Step-by-step explanation:

Definitions:

Long Division Method of dividing polynomials:

Given:

Rearrange the dividend in descending order of the exponents:

6x³ - 17x² + 2x  + 15

Now use the method of long division to divide (6x³ - 17x² + 2x  + 15) by (2x - 3):

\(\large \begin{array}{r}3x^2-4x-5\phantom{)}\\2x-3{\overline{\smash{\big)}\,6x^3-17x^2+2x+15\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-9x^2)\phantom{-b)))))))).)}}\\-8x^2+2x+15\phantom{)}\\-~\phantom{()}\underline{(-8x^2+12x)\phantom{)))..}}\\-10x+15\phantom{)}\\-~\phantom{()}\underline{(-10x+15)\phantom{}}\\0\phantom{)}\\\end{array}\)

Therefore, the quotient is:

\(\boxed{\boxed{3x^2-4x-5}}\)

Answer:

The length of the third side is approximately ≈ 14.79 inches

Step-by-step explanation:

A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Use the law of cosines to find the length of the missing side.

Let C be the third side.

A = 18

B = 23

Angle C = 40^∘

c^2  =  a^2  +  b^2 - 2ab  cos C

c =  √a^2 + b^2 - 2ab cos C

c =  √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘

c = √583 - 828 cos40^∘

≈ 14.79

Thus, The length of the third side is approximately  14.79 inches.

Hope this helps!

Answer:

£1,049

Step-by-step explanation:

The computation of the amount after 5 years is shown below:

Here we have to determined the future value

As we know that

Future value = Present value × (1 + rate of interest)^number of years

=  £950 × (1 + 0.02)^5

=  £950 × 1.02^5

=  £950 × 1.1040808032

= £1,049

Answer:

x= 21/4

Step-by-step explanation:

1- Convert the expressions

5 ( x - 3 3/4 ) = 7 1/2

2- Remove the parentheses

5 ( x - 15/4 ) = 15/2

3- Move the constant to the right

5x - 75/4 = 15/2

4- Calculate the sum

5x = 15/2 + 75/4

5- Divide both sides

5x = 15/2 + 75/4

When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

5a³ - 40

Step-by-step:

The algebraic expression is:

5a³ - 40

Answer:

r=1

Step-by-step explanation:

\(-11r+8-8=10r-13-8\\\\-11r=10r-21\\-11r-10r=10r-21-10r\\-21r=-21\\\frac{-21r}{-21}=\frac{-21}{-21}\\r=1\)

Answer: Reflection in the y -axis:

Explanation: The rule for a reflection over the y -axis is (x,y)→(−x,y) .\

Answer:

See below

Step-by-step explanation:

Dilation of 4

Z (0, -1) Z' (0, -4)

X (1, -1) X' (4, -4)

Area of rectangle is,

A = 45 units²

And, Perimeter of rectangle is,

⇒ P = 28 units

We have to given that;

Vertices of rectangle are,

⇒ (- 4, - 5)  

⇒ (-4, 0)

⇒ (5, 0)

⇒ (5, - 5)

Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, Length of rectangle is distance between (- 4, - 5) and (- 4, 0).

Which is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (- 4 + 4)² + (0 + 5)²

⇒ d = √ 25

⇒ d = 5

And,  Width of rectangle is distance between (- 4, 0) and (5, 0).

Which is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (- 4 - 5)² + (0 - 0)²

⇒ d = √ 81

⇒ d = 9

Thus, Area of rectangle is,

A = L x W

A = 5 x 9

A = 45 units²

And, Perimeter of rectangle is,

⇒ P = 2 (L + W)

⇒ P = 2 (5 + 9)

⇒ P = 2 × 14

⇒ P = 28 units

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The slant height \(l = 29 \: mm\).

A cone is a three-dimensional geometric shape with a smooth transition from a flat, usually circular base to the apex or vertex, which forms an axis to the base's center.

As per the given data:

Height = 21 mm

Volume = 8792 mm

Radius = 20 mm

For slant height of the one (\(l\)):

\(l = \sqrt{r^2 + h^2}\) {using Pythagoras theorem}

\(l = \sqrt{(20)^2 + (21)^2}\)

\(l = \sqrt{(20)^2 + (21)^2}\)

\(l = \sqrt{400 + 441}\)

\(l = 29 \: mm\)

Hence, the slant height \(l = 29 \: mm\).

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The side length of the the rectangular garden are 20 feet by 5 feet.

Let

s = side length of the square garden

l = length of the rectangular garden

w = width of the rectangular garden

From the problem statement,

area of the square garden = area of the rectangular garden

Since the area of a square is just the side length squared, we can write:

s² = l * w

We also know that the length of the rectangular garden is 10 feet longer than the side of the square garden, and that the width of the rectangular garden is 5 feet shorter than the side of the square garden. We can express them as:

l = s + 10

w = s - 5

Now we can substitute these expressions for l and w into our first equation:

s² = (s + 10) * (s - 5)

Expanding the right-hand side, we get:

s² = s² + 5s - 50

0 = 5s - 50

5s = 50

Dividing both sides by 5, we get:

s = 10

Since the side length of the square garden is 10 feet.

We can use this to find the dimensions of the rectangular garden:

l = s + 10 = 10 + 10 = 20

w = s - 5 = 10 - 5 = 5

So the dimensions of the rectangular garden are 20 feet by 5 feet.

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Answer: 13.60 gallons divide 355 by 17 to get the base miles per gallon then use that and divide it 284 by 20.88

Step-by-step explanation:

Step-by-step explanation:

17g = 335miles

1g = 335÷17

= 19.70588235

284miles = (284÷19.70588235) × 1

284miles = 14.4119403

Answers:

284miles = 14.41gallons (2.dp)

OR

284miles = 15gallons (nearest whole number)

Answer:

The regular cost of each ticket is $30

Step-by-step explanation:

Hi,

You and three friends means there was a total of 4 people. Your equation is...

4x - 20 = 100

Remember to add the -20 since there was a coupon that saved you $20.

Now solve...

4x - 20 = 100

+ 20 on both sides

4x = 120

Divide by 4 on both sides

x = 30

The regular cost of each ticket is $30

Hope this helps :)

Answer:

e it's  really first question re  want to make this

each ticket would be $25  a regular

Step-by-step explanation:

Answer:

10 root 2

Step-by-step explanation:

root 200 = root 2 × root 100 = 10 root 2

To answer this question we will transform the given times to the 24 hour format.

We know that:

Then Tom traveled for

Answer: Last option.

Hi student, let me help you out!

.........................................................................................................................

--------------------------------------------------

First of all, let the number be z.

Now, since the question says "4 times a number", we should multiply 4 times the number z: \(\mathsf{4z}\).

Now, this little expression equals 84 less than 6 times the number (which is z). The phrase "84 less than" tells us to subtract 84 from 6 times z: \(\mathsf{6z-84}\).

Put this together and obtain ✨ \(\bigstar\underline{\boxed{\mathrm{4z=6z-84}}}\).

--------------------------------------------

Now let's solve the equation for z by following several steps, which are:

Step 1. Subtract 6z from both sides: \(\mathsf{4z-6z=6z-6z-84}\).

Upon simplifying, we obtain \(\mathsf{-2z=-84}\)

Step 2. Solve for z by dividing both sides by -2: \(\mathsf{-2z\div(-2)=-84\div(-2)}\).

Upon simplifying, we obtain ✨ \(\bigstar\underline{\boxed{\mathrm{z=42}}}\).

Hope this helped you out, ask in comments if any queries arise.

\(\overline{\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}\)

The number which is Four times a number is 84 less than 6 times the number will be 42.

When trying to set up or construct a linear equation to fit a real-world application, identify the known quantities and treat the unknown quantity as a variable.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let the number be x

Four times = 4x

84 less than  6 times the number = 6x - 84

Both are equal according to the question

4x = 6x - 84

4x - 6x = -84

-2x = - 84

x = 84/2  = 42 hence, that number will be 42.

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Solution

Given that Plane A departs at a 41° angle from the runway while plane B departs at a 43° angle from the runway.

h stands for the height of the planes above the ground

x stands for the distance of plane A away from the airport.

y stands for the distance of plane A away from the airport.

When h = 5, we shall calculate their respective x

From the above calculation, we can see that Plane A what 7.62 miles away from the airport while Plane B was 7.33 miles away from the airport.

Since 7.62 > 7.33;

Therefore, Plane A was farther away from the airport when it was 5 miles from the ground.

The correct answer is Graph 1: y = cos(x/4)Graph 2: y = cos(x/2)

Based on the given descriptions of the graphs and the patterns they follow, the correct pairs are:

Graph 1: y = cos(x/4) ⟶ This graph has a period of 8 units and matches the pattern described.Graph 2: y = cos(x/2) ⟶ This graph has a period of 4 units and matches the pattern described.

Graph 3: y = cos(x) ⟶ This graph has a period of 2π (or approximately 6.28 units) and matches the pattern described.

Graph 4: (Not used)

Graph 5: (Not used)

Please note that without visual representation, it's difficult to provide a definitive answer. The pairs are based on the descriptions provided and may vary depending on the actual shapes of the graphs.

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Answer: x =21

Step-by-step explanation:

x +2 = 3x -40  They both have the same angle measures so they have to equal each other to solve for x

x + 2 = 3x -40

-x         -x  

   2 = 2x -40

 +40        +40

42 = 2x

x = 21

The value of the composite function (f o g)(x) is 8x - 17

The definition of the functions are given as

f(x) = 4x - 1

g(x) = 2x - 4

The composite function definition is given as

(f o g)(x)

This composite function is calculated using the following composite function formula

(f o g)(x)= f(g(x))

Substitute the known values in the above equation

So, we have the following equation

(f o g)(x) = 4(g(x)) - 1

So, we have the following equation

(f o g)(x) = 4(2x - 4) - 1

Open the brackets

(f o g)(x) = 8x - 16 - 1

Evaluate

(f o g)(x) = 8x - 17

Hence, the composite function is (f o g)(x) = 8x - 17

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Answer:

The dimensions are 45 feet by 40 feet.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

\(\displaystyle A=w\ell\)

Where w is the width and l is the length.

The length is five feet longer than the width. Thus, we can write that:

\(\ell = w+5\)

The total area is 1800 square feet. Substitute:

\(1800=w(w+5)\)

Solve for w. Distribute:

\(w^2+5w=1800\)

Subtract 1800 from both sides:

\(w^2+5w-1800=0\)

Factor. We can use 45 and -40. Hence:

\(\displaystyle (w+45)(w-40)=0\)

Zero Product Property:

\(w+45=0\text{ or } w-40=0\)

Solve for each case:

\(\displaystyle w=-45\text{ or } w=40\)

Since the width cannot be negative, we can ignore the first solution.

So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.

The dimensions are 45 feet by 40 feet.

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Answer:

2.113

Step-by-step explanation:

               \(3.600\\1.487 \ -\\\overline{2.113}\)

Answer:

2000 meters

Step-by-step explanation:

400 * 5

Answer:

it's really hard to see the numbers.. but I can explain how to do it. the 5 is on the x axis and the 0 is on the y axis. if you from 0 to 5 on the x axis and the line crosses through that point then it is true.

Answer:

-7/3

Step-by-step explanation:

Rise/Run = -4-3/1--2

= -7/3

9514 1404 393

Answer:

  45.6°

Step-by-step explanation:

The attached result was found by typing "arccos(7/10) in degrees" into a web browser search box.

Your calculator can give you the same result. The inverse cosine function often shares a key with the cosine function. It is often marked as cos⁻¹. Be sure that the angle mode is set to degrees, not radians.

Answer:

I think it is p= $60