What is the value of x in the figure below? In this diagram, AABD ~ ACAD.

Answer:

[tex] f(-4) = \dfrac{1}{9} [/tex]

Step-by-step explanation:

[tex] f(x) = 9(3)^x [/tex]

[tex] f(-4) = 9(3)^{-4} [/tex]

[tex] f(-4) = 3^2 \cdot 3^{-4} [/tex]

[tex] f(-4) = 3^{-2} [/tex]

[tex] f(-4) = \dfrac{1}{9} [/tex]

Answer:

1/9

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

Answer:

no solution

Step-by-step explanation:

| | is a notation for absolute value, which is the distance that a number is from 0.

you can think of this as the "positive version" of a number

so, |-x| will become: x

We can plug this into the equation, and solve like we would for any variable

3 + 7 = 6 - |-x|  {simplify}

3 + 7 = 6 - x   {simplify}

10 = 6 - x

Now, we can isolate x (isolate = get it alone)

10 = 6 - x

-6     - 6    {subtract 6 from both sides}

 4 = -x         {multiply both sides by -1 to get positive x}

·-1   ·-1

- 4 = x

{check solution:}

3 + 7 = 6 - | -4 |

10 = 6 - 4

10 = 2

FALSE

because this solution has been found to be false, there is no possible value for x

we write this as: no solution

[tex]3+7=6-|-x|\\10=6-|x|\\|x|=-4\\x\in\emptyset[/tex]

Answer:

141 cubic inches

Step-by-step explanation:

The candle can be modeled as a cylinder.

To find how much wax is needed to make the candle, calculate the volume of the cylinder.

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula and solve for V:

[tex]\implies \sf V=3.14 \cdot 3^2 \cdot 5[/tex]

[tex]\implies \sf V=3.14 \cdot 9 \cdot 5[/tex]

[tex]\implies \sf V=28.26 \cdot 5[/tex]

[tex]\implies \sf V=141.3\:in^3[/tex]

Therefore, the amount of wax needed to make the candle is 141 cubic inches (nearest whole cubic inch).

The domain and the range of the function is (d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}

What are the domain and range of the function f(x) = x^2 + 8x + 7/x + 1

We have the function to be

[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]

Set the denominator to 0

x + 1 = 0

Solve for x

x = -1

This means that the domain of the function is the set of all real numbers except -1

Hence, the domain of the function is {x ∊ ℝ | x ≠ -1}

We have the function to be

[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]

Factorize the numerator

[tex]f(x) = \frac{(x + 1)(x + 7)}{x + 1}[/tex]

Simplify

f(x) = x + 7

The function is undefined at x= -1.

So, we have:

f(-1) = -1 + 7

f(-1) = 6

This means that the range of the function is the set of all real numbers except 6

Hence, the range of the function is {y ∊ ℝ | y ≠ 6}

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Answer:

It is d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}

Step-by-step explanation:

I took the test

Answer:

As the x-values go to positive infinity, the function's

values go to negative infinity.

Step-by-step explanation:

upon viewing the graph you will notice that the function in blue will appear to go down (negative) as you follow the x to the right, in the positive direction.

Making your answer to be as the x goes to positive inf (right) the values of the function go to negative inf (down).

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

Answer:  [tex]\textsf{y = -1.75x - 11.75}[/tex]

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

Given:  [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution: We need to first solve for y in the equation that was provided so we can determine the slope.  Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.

Subtract 7x from both sides

Divide both sides by 4

Plug in the values

Simplify and distribute

Subtract 3 from both sides

Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75

The Equation is represented as  [tex]\rm F = \dfrac{9}{5} (K -273.15 ) +32[/tex]

Option B is the answer.

An equation is am mathematical statement formed when an algebraic expression is equated by an equal sign with another algebraic expression or a constant.

A Equation is given in the question

[tex]\rm K = \dfrac{5}{9}(F -32) +273.15[/tex]

where K denotes temperature in Kelvins and F denotes Fahrenheit .

To convert the equation in terms of K it can be rewritten as follows

[tex]\rm K = \dfrac{5}{9}(F -32) +273.15\\\\K -273.15 = \dfrac{5}{9}(F -32) \\\\\dfrac{9}{5} (K -273.15 ) = F - 32\\\\F = \dfrac{9}{5} (K -273.15 ) +32[/tex]

Therefore Option B is the right answer.

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Answer:

B. x = 3

Step-by-step explanation:

Simplifying

4 + 3x = 2(3x + -7) + 9

Reorder the terms:

4 + 3x = 2(-7 + 3x) + 9

4 + 3x = (-7 * 2 + 3x * 2) + 9

4 + 3x = (-14 + 6x) + 9

Reorder the terms:

4 + 3x = -14 + 9 + 6x

Combine like terms: -14 + 9 = -5

4 + 3x = -5 + 6x

Solving

4 + 3x = -5 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation.

4 + 3x + -6x = -5 + 6x + -6x

Combine like terms: 3x + -6x = -3x

4 + -3x = -5 + 6x + -6x

Combine like terms: 6x + -6x = 0

4 + -3x = -5 + 0

4 + -3x = -5

Add '-4' to each side of the equation.

4 + -4 + -3x = -5 + -4

Combine like terms: 4 + -4 = 0

0 + -3x = -5 + -4

-3x = -5 + -4

Combine like terms: -5 + -4 = -9

-3x = -9

Divide each side by '-3'.

x = 3

Simplifying

x = 3

Answer: [A] addition property of equality

Step-by-step explanation:

    Mitch used the addition property of equality because he added 43 to both sides of the equation.

         75r - 43 = 332

         43 + (75r - 43) = (332) + 43

         75r = 375

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If the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Thus, you're a sphere.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

Mathematically, the volume of a sphere can be calculated by using this formula:

V = 4/3 × πr³

Similarly, the volume of a cylinder can be calculated by using this formula:

V = πr²h

In this context, we can infer and logically deduce that if the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Also, multiplying the volume of a cylinder by 1/3 would produce the volume of a sphere.

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The statement that best describes a tessellation is an arrangement of repeating shapes with no spaces or overlaps between them. Option C

A tessellation can be defined as a pattern of geometric shapes that fill a two-dimensional space without gaps and overlaps

It is also known to repeat infinitely in all directions.

Thus, the statement that best describes a tessellation is an arrangement of repeating shapes with no spaces or overlaps between them. Option C

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Answer:

7

Step-by-step explanation:

for you to get the missing number just take the complete numbers and minus them then you'll get the incomplete digit needed good day.

The possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

(k - 1)x² + (4k)x + k -3 = 0

Here,

a = k - 1

b = 4k

c = k - 3

As we know for distinct real roots:

D > 0

[tex]\rm {b^2-4ac}} > 0[/tex]

(4k)² - 4(k-1)(k-3) > 0

[tex]\rm 16k^2-4\left(k-1\right)\left(k-3\right) > 0[/tex]

[tex]\rm 12k^2+16k-12 > 0[/tex]

[tex]\rm 3k^2+4k-3 > 0[/tex]

[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2-\dfrac{13}{3} > 0[/tex]

[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{3}[/tex]

[tex]\rm \left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{9}[/tex]

[tex]\rm k < \dfrac{-\sqrt{13}-2}{3}\quad \mathrm{or}\quad \:k > \dfrac{\sqrt{13}-2}{3}[/tex]

or

[tex]\rm k < -1.868 \quad \mathrm{or}\quad \:k > 0.535[/tex]

Thus, the possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.

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The monthly payment is; $104.9; The total amount paid over the term of the loan is; $31470

We are given;

Loan principal = $12,500

Interest rate = 12%

Number of payments per year = 12 payments per year.

Loan term = 25 years.

Formula for monthly payment is;

PMT = (p * APR/n)/[1 - (1 + APR/n)^(-nY)]

Where;

p is principal

APR is interest rate

n is number of payments per year

Y is loan term

Thus;

PMT = (12500 * 0.09/12)/[1 - (1 + 0.09/12)^(-12 * 25)]

PMT = 93.75/(1 - 0.106288)

PMT = $104.9

B) Total amount paid over the loan term is;

A = PMT * m * n

where;

m is number of months in a year,

n is number of years

A = 104.9 * 12 * 25

A = $31470

C) The principal as a percentage of the loan is;

P/A = 12500/31470

P/A = 39.72%

Percentage paid for interest is = 100% - 39.72% = 80.28%

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Answer:

z= 38°

Step-by-step explanation:

z= 90(from right angle)+52=142

180-142=38°

The simplified fractional equivalent of 0.25 is 1/4 .

The complete question is

What is the simplified fractional equivalent of the terminating decimal 0.25?

When a number is solved to a state where it cannot be further simplified , but can be written in a different format , the two numbers are then called the simplified equivalent of each other.

The given number is decimal 0.25

So this number is in its simplified state but can also be written as

0.25 * 1

= 0.25 * 100 /100

= 25/100

= 1/4

Therefore 1/4 is the simplified fractional equivalent of 0.25.

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Answer:

The answer is C. Hope it helps

Answer:

B

Step-by-step explanation:We know Volume = (a*b*c)

Answer:

B) 54 cubic feet

Step-by-step explanation:

The function among the given option is height of a building in feet, height of the building in inches , Option B is the correct answer.

A function is a law that relates a dependent and an independent variable.

The options mentioned below needs to be studied to determine which forms a function.

Option A , C and D doesn't really form a function ,

For two variables need to be a function then they have to be dependant on each other and have only one output for a given input.

height of a building in feet, height of the building in inches

Height of building in feet = (height of building in inches/12)

so this is a function

Therefore Option B is the right answer.

The missing options are

If the relationships below are given in the form (input, output), which pairing always describes a function?

A) (number of doors in a car, number of cup holders in the car)

B) (height of a building in feet, height of the building in inches)

C) (beverage charge on a bill, total meal charge on the bill)

D) (distance from home during a trip, time elapsed during the trip)

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Step-by-step explanation:

please mark me as brainlest

Answer:

$809.25

Step-by-step explanation:

→ Find the sum of the sales amount

2400 + 3200 + 1900 + 800 = 8300

→ Find the amount that s commission

( 9.75 × 8300 ) ÷ 100 = $809.25

The decision of purchasing a car must be taken by Frankie after considering the following points:

1. what he will be giving up if he spends $800 on the car

2. The cost to maintain and ensure the car

3. his short- and long-term financial goals

4. if an alternate mode of transportation, such as a bicycle or the bus, is sufficient for his needs.

Frankie is an individual person when he wants to purchase a car that is his long-term goal.

he must consider various things before making such a big expenditure.

The points to be noted before purchasing a car are:

what is the cost for Frankie for spending $800?

What will be the maintenance and insurance cost?

He must check his other short and long-term goals before purchasing a car.

Is the expense of the car a necessity for Frankie or he can use public transport.

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Answer:

Step-by-step explanation: thank me later

A,B,E

Answer:

Step-by-step explanation:

The expanded expressions are shown below:

Perfect square trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:

a) (x + 1)² = x² + 2 · x + 1

b) (x - 3)² = x² - 6 · x + 9

c) (x + 4)² = x² + 8 · x + 16

d) (x - 1/2)² = x² - x + 1/4

e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75

f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2

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Answer:

≈ 47.2 m

Step-by-step explanation:

let the height from the sea to the base of lighthouse be h₁

let the height from the sea to the top of the lighthouse be h₂

using the tangent ratio in the right triangle

tan55.1° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h_{1} }{610}[/tex] ( multiply both sides by 610 )

h₁ = 610 tan55.1°

tan56.5° = [tex]\frac{h_{2} }{610}[/tex] ( multiply both sides by 610 )

h₂ = 610 tan56.5°

then

height of lighthouse = h₂ - h₁        

                                  = 610 tan56.5° - 610 tan55.1°

                                  = 610(tan56.5° - tan55.1° )

                                 ≈ 47.2 m ( to the nearest tenth )

Answer:

yessss

Step-by-step explanation:

yessssssss

The condition that distinguishes organism from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction, and the power of adaptation to the environment through changes originating internally.

The probability of failure for Luis will be 0.18.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability of passing is = 0.82

We know that the maximum probability of happening any event is 1 or 100 per cent if the probability of passing of the person is 0.82 then the probability of failure will be calculated as:-

Probability of failing = 1 - probability of passing

Probability of failing = 1 - 0.82

Probability of failing = 0.18

Therefore the probability of failure for Luis will be 0.18.

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Answer:

D

Step-by-step explanation:

5x-2+2x+1

5x+2x+1-2

7x-1