Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14​

The domain is [tex]x \le 5[/tex] and the range of the function is [tex]f(x) \ge - 3[/tex]

The function is given as:

[tex]f(x) = \sqrt{5 - x} - 3[/tex]

The radicand must be at least 0.

So, we have:

[tex]\sqrt{5 - x} \ge 0[/tex]

Square both sides

[tex]5 - x \ge 0[/tex]

Rewrite as:

[tex]5 \ge x[/tex]

Solve for x

[tex]x \le 5[/tex]

This means that the domain is [tex]x \le 5[/tex]

For the range, we have; [tex]\sqrt{5 - x} \ge 0[/tex]

This means that:

[tex]f(x) \ge 0 - 3[/tex]

[tex]f(x) \ge - 3[/tex]

Hence, the range of the function is [tex]f(x) \ge - 3[/tex]

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Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,

sin²(x) + cos²(x) = 1

we always take the positive square root when solving for either sin(x) or cos(x).

Given that cos(α) = √11/7 and sin(β) = √11/4, we find

sin(α) = √(1 - cos²(α)) = √38/7

cos(β) = √(1 - sin²(β)) = √5/4

Now, recall the sum identity for cosine,

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

It follows that

cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28

By using the midpoint approach, the price elasticity of demand between each of the given prices are:

The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).

By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]

Price elasticity of demand = 1/-0.1818

Price elasticity of demand = 5.50.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]

Price elasticity of demand = 0.5/-0.2222

Price elasticity of demand = 2.25.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]

Price elasticity of demand = 0.33/-0.2857

Price elasticity of demand = 1.17.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]

Price elasticity of demand = 0.25/-0.4

Price elasticity of demand = 0.63.

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By solving a quadratic equation, we will see that the length is 10m and the width is 6.5m

For a rectangle of width W and length L, the area is:

A = W*L

In this case, we know that the area is 65m² and that the length is 3 meters less than 2 times the width, so:

L = 2*W - 3m

Then we can write:

65m² = (2*W - 3m)*W = 2*W² - 3m*W

This is a quadratic equation:

2*W² - 3m*W - 65m² = 0.

The solutions are given by the Bhaskara's formula:

[tex]W = \frac{3 \pm \sqrt{(-3)^2 - 4*2*(-65)} }{2*2} \\\\W = \frac{3 \pm 23 }{4}[/tex]

We only care for the positive solution, which is:

W = (3m + 23m)/4 = 26m/4 = 6.5m

Then the length is:

L = 2*6.5m - 3m = 10m

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Using proportions, it is found that the number of chaperones that the school needs is given by:

B. 8.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 2 chaperones are needed for every 25 students. How many are needed for 100 students? The rule of three is given by:

2 chaperones - 25 students

n chaperones - 100 students

Applying cross multiplication:

25n = 2 x 100

n = 200/25

n = 8.

Hence option B is correct.

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The correct function shown in the graph is,

⇒ log₁₀ (ax) = 1

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:

⇒ log₁₀ (ax) = 1

or , ax = 10¹ = 10

Thus, x  = 10/a

So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .

⇒ log (3 × 3.33) = 0.99 ≈ 1

Thus, out of the given options only Option D seems to be the most probable answer.

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Answer:

Angle1 and Angle2 are supplementary.

Step-by-step explanation:

There are at least 8 pairs and I want to say up to maybe 16 pairs if angles that are supplementary.

Supplementary angles add up to 180°. So any pair that is lying together on a straight line (that's 180°) are supplementary:

1&2

2&4

3&4

1&3

5&6

6&8

7&8

5&7

Since angles don't have to touch in order to be supplementary there are many more pairs.

The rise from the ground by the skateboard is 5.5 inches

The length of the skateboard is given as:

Length (l) = 18 inches

The angle of elevation (x) is

x = 17∘

Represent the height with h.

The value of h is calculated using the following tangent ratio:

tan(x) = h/l

Make h the subject

h = l * tan(x)

Substitute known values

h = 18 * tan(17)

Evaluate

h = 5.5

Hence, the rise from the ground by the skateboard is 5.5 inches

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Answer: 5.3

Step-by-step explanation:

S​OH-CAH-TOAsin 17=oppositehypotenuse=x18sin 17=hypotenuseopposite​=18x​sin 17=sin 17=  x1818x​sin 171=1sin 17​=  x1818x​18 sin 17=18 sin 17=  xxx=5.262690...≈5.3x=5.262690...≈5.3

−9x^4−18x^4y+27x^2y^2

Answer:

=−18x^4y−9x^4+27x^2y^2

Step-by-step explanation:

(−9x^2)(x^2+2x^2y−3y^2)

=(−9x^2)(x^2+2x^2y+−3y^2)

=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)

=−9x^4−18x^4y+27x^2y^2

=−18x^4y−9x^4+27x^2y^2

---

Hope I helped! Have a great day :)

Answer:

 Numbers are 5 , 7

Step-by-step explanation:

  Let the two consecutive odd numbers be (2x + 1) and (2x + 3)

         Their product = 35

(2x + 1)(2x + 3) = 35

Use FOIL method.

       2x*2x + 2x*3  + 1*2x + 1*3 = 35

              4x² + 6x  + 2x + 3       = 35

      Combine like terms

                            4x² + 8x  + 3    = 35

                         4x² + 8x + 3 - 35 = 0

                            4x² + 8x  - 32   = 0

 Solving:

                 4x² + 8x - 32 = 0

Divide the entire equation by 2

                [tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]

                  2x² + 4x - 16 = 0

Sum = 4

Product = -32

Factors = 8 , (-4)

When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.

Rewrite the middle term

2x² + 8x - 4x  - 16 = 0

 2x(x + 4) - 4(x + 4) = 0

   (x + 4) (2x - 4) = 0

2x - 4 = 0   {Ignore x +4 = 0  as it gives negative number}

2x = 4

   x = 4/2

   x= 2

2x + 1 = 2*2 + 1 = 5

2x + 3 = 2*2 +3 = 7

   The numbers are 5 , 7

Answer:

[tex]p = 3\\\\q= 1[/tex]

Step-by-step explanation:

[tex]x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1[/tex]

let me answer the last one first

compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.

hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.

hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.

now let's do the others

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]

Answer:

2.66666666667

Step-by-step explanation:

(1/8)^-1/3 means 1/8 to the -1/3 power, which equals 2.66666666667. So the answer is 2.66666666667.

(4)

1. 11.444 repeater

2. 0.58333 repeater

3. 6.7333 repeater

4. 27.5454 repeater (on both 5 and 4)

5. 1.482517482517 (482517 repeater)

6. 2.285714285714 (285714 repeater)

7. 7.5666 repeater

8. 60.60606060 (60 repeater)

(5)

1. 0.666 (repeater)

2. 0.3666 (repeater)

3. 1.1818181818 (18 repeater)

4. 0.418181818 (18 repeater)

Answer:

your answer is 4 my friend

Step-by-step explanation:

The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The question is: Consider the function f(x) = (-2/3)x - 24  Which conclusions can be drawn about f⁻¹(x) Select two options:

f⁻¹(x) has a slope of -2/3

f⁻¹(x) has a restricted domain.

f⁻¹(x) has a y-intercept of (0, –36).

f⁻¹(x) has an x-intercept of (–36, 0).

f⁻¹(x) has a range of all real numbers.

f(x) = (-2/3)x - 24

To find the inverse of a function:

interchange the x and y

x = (-2/3)y - 24

y = (-3/2)(x + 24)

y = (-3/2)x - 36

The slope of a function f⁻¹(x) is -3/2

From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.

Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

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Answer:

D and  E

Step-by-step explanation:

did the test

Answer:

[tex]x=5\\[/tex]

Step-by-step explanation:

First, put your equations into a system.

[tex]\left \{ {{x+7y=16} \atop {3x-7y=4}} \right.[/tex]

Next, use the method of elimination to solve the system. Elimination is when either x or y has an opposite coefficient (so in this case y has a coefficient of 7 or -7 depending on the equation). You can then add the equations, and y is eliminated as a variable. Now you can solve for x.

[tex]4x=20[/tex]

Lastly, divide by 4 on both sides to get x by itself.

[tex]x=5\\[/tex]

The arithmetic sequence that has a common difference of -5 from the options given is: A. 8, 3, -2, -7...

The common difference of an arithmetic sequence is determined as: a term - previous term.

For the sequence, 8, 3, -2, -7,.. the common difference is:

-7 - 2 = -2 - 3 = 3 - 8 = -5.

Therefore, the arithmetic sequence with a common difference of -5 is: A. 8, 3, -2, -7...

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Answer:

Step-by-step explanation:

First, label it out:

Then, we add up 12 twice (Since the length is on 2 sides):

Now, we write down a 6 in the ?:

Width = 6.

We are not done!

Now, we have to solve for area.

Answer:

The experimental probability is 4%

Step-by-step explanation:

The theorem that verifies that the two right angled triangles are similar is HA.

Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.

Analysis:

From the diagrams KL = OQ ( hypotenuse)

∠L is equal to ∠Q which are acute.

so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.

In conclusion, the HA theorem verifies that the two triangles are similar.

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The amount of Rita deposit is $2556.

The interest calculated on the principal amount or the initial investment.

It is given in the question

If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days.

P = ?

S.I. =  $63.90

Interest = 6%

T = 150days

S.I. = (P *R*T)/100

63.90 = P * 6 * 150*100 /360

63.90 * 360*100 /( 150 *6) = P

P = $2556

Therefore the amount of Rita deposit is $2556.

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Answer:

a. D. f⁻¹(x) = x - 21, for all x

b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x

Step-by-step explanation:

See attached picture.

The required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:

x = y + 21

Now, let's solve for y:

y = x - 21

Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.

b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.

First, let's calculate f(f(x)):

f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42

Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.

Now, let's calculate f¯¹(f(x)):

f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x

Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.

Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

Therefore, the required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

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Answer: C

Step-by-step explanation:

[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]

[tex]~~~~~~~\cos^2 \left(34^{\circ}\right) - \sin^2 \left( 34^{\circ} \right)=\cos A\\\\\implies \cos \left( 2 \cdot 34^{\circ} \right) = \cos A~~~~~~~~~~~~~;[\cos 2x = \cos^2 x -\sin^2 x]\\\\\implies \cos \left(68^{\circ}\right) = \cos A\\\\\implies A = 68^{\circ}[/tex]

Answer: Commutative property

The original height  of the water in a pool is 5 ft , Option B is the correct answer.

An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.

It is given in the question that

A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.

the height of the water is 4.75 feet.

The equation

4.75 = x + (negative 0.25)

can be used to find x, the original height of the water in a pool.

4.75 = x - 0.25

x = 5

Therefore the original height  of the water in a pool is 5 ft , Option B is the correct answer.

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Answer:

B

Step-by-step explanation: