Write the equation of the graph of y = cos(x) was shifted downwards by 3 units, shrink horizontally by a fourth of a unit, inverted horizontally and shifted 60° to the left. if it has an amplitude of 5 units.
​

AnswEr :

Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .

⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]

⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.

[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]

Therefore ,

When , x = 2 ,

When , x = –7 ,

Answer:

Hi,

Step-by-step explanation:

If the "is" means is equal to

Let's say a-1, a, a+1 the 3 consecutive integers.

[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]

[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]

The two sets are : (0,1,2) and (4,5,6).

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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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

Answer:

24%

Step-by-step explanation:

there are 50 numbers total

number of 4's: 7
number of 7's: 5

it's asking for the odds of a 4 or a 7 meaning that they're fine with either one. that means you can ADD the number of them up!

7 + 5 = 12

to get the odds, we need to divide!

convert that into a percent!

24%

let me know if you're still confused :))

105600

Significant figures are used in scientific fields to show precision.

Multiplication

When rounding to significant figures you need to first do the operation shown. So, before we round we need to multiply 573.06 * 184.25.

This is an important step whenever you are rounding to significant figures. If you preround, you will be left with the wrong answer.

Significant Figures

Now that we have the answer before rounding, we need to know how to determine significant figures. If there is a decimal point present, then start counting significant figures at the first non-zero digit from the left.

For example:

If the decimal point is not present, then start counting significant figures from the first non-zero digit from the right.

For example:

Rounding

Finally, we can round our answer. Firstly, there are more than 4 digits before the decimal point. This means that our rounded answer will not have a decimal point, so when counting sig figs we will start from the right. Remember, even when rounding, a number should always have the same number of digits before the decimal point, even if they are not all significant.

Since we are rounding to 4 sig figs, we need to look at the 5th digit from the left, which is 8. This means we will round up.

So, write the first 4 digits of the number, but round the last one up. Then, write the remaining digits before the decimal point as 0.

Step-by-step explanation:

an open (empty) point means the point itself is not included.

a closed (filled) point means the point itself is included.

the x values going from -3 (not included) to -1 (included) means

-3 < x <= -1

so, the second answer is correct.

The 73 customers who spend money in this store if a MOE of at most 0.075 with 80% confidence.

MOE is an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

MOE = z x s/√n

Where ,

Z = the z-score at the confidence interval

s =  the standard deviation

n = the number of samples.

We have p = 0.50 MOE = 0.075

Z = 1.282 at 80% confidence

0.075 = 1.282 x √0.50(1- 0.50)/ n

After solving,

n = (0.5)(0.5)/(0.0585)²

n = 73

Thus, the 73 customers who spend money in this store if a MOE of at most 0.075 with 80% confidence.

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Step-by-step explanation:

so, "- 1" is also part of the square root ?

sqrt(x - 1) = x - 3

it is clear that for any value x < 1 we have no solution in R (as this makes the argument of the square root negative, and there is so real number solution for the square root of negative numbers).

now square the whole equation.

x - 1 = (x - 3)² = x² - 6x + 9

x² - 7x + 10 = 0

the general solution for quadratic equations is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -7

c = 10

x = (7 ± sqrt(49 - 4×1×10))/(2×1) =

= (7 ± sqrt(49 - 40))/2 = (7 ± sqrt(9))/2

x1 = (7 + 3)/2 = 10/2 = 5

x2 = (7 - 3)/2 = 4/2 = 2

x2 is probably (given the answer options) not a valid solution for the original problem, as it represents the negative solution of sqrt(x - 1).

sqrt(2 - 1) = 2 - 3

± 1 = -1

remember, every square root has always 2 solutions : a positive and a negative one.

your teacher clearly only wanted the positive solution, which is x1 = 5.

so, yes,

C. x = 5

is the correct answer.

but please send your teacher my regards and comments. he/she has to state that only the positive solution to the square root is required/allowed.

because, formally, also x = 2 is a valid solution.

and therefore, C. AND D. are correct answers !!!!

The area of the figure is 51.4 unit²

Figure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6

See attachment for the figure

The figure can be divided into the following shapes:

The area of the trapezoid is:

Area = 0.5 * (Sum of opposite sides) * height

So, we have:

Trapezoid 1 = 0.5 * (8 + 5) * 5 = 32.5

Trapezoid 2 = 0.5 * (5 + 4.8) * 2 = 9.8

The area of the triangle is:

Area = 0.5 * Base * Height

This gives

Triangle = 0.5 * 4.8 * 4 = 9.6

Add the individual areas

Area = 32 + 9.8 + 9.6

Evaluate the sum

Area = 51.4

Hence, the area of the figure is 51.4 unit²

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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.

Why?

Notice that f(x) is positive when -2 < x < 1. In other words, f(x) is positive when x = -1 and when x = 1.

This interval of -2 < x < 1 translates directly to the interval notation of (-2, 1)

Unfortunately this interval notation looks identical to ordered pair notation. Be sure not to mix the two concepts up.

The parenthesis in interval notation tell the reader "do not include the endpoints". We cannot include x = -2 nor x = 1 because these values make f(x) zero, but we want f(x) > 0.

Something like choice D is a non-answer because the value x = 2 is in the interval (1,4), but f(2) = -8 which isn't positive. We can rule choice D out because of it. Choices A and C are similar situations.

Answer:

Yes

Step-by-step explanation:

The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36

The new sample size based on the information will be B-M, B-C, B-R, 8.

Sample size is the number of participants or observations that are included in a study. This is usually represented by n.

When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.

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Answer:

Step-by-step explanation:

B-M, B-C, B-R, 8.

[tex]\text{The base and height have to be factors of 60, since}\\\\~~~~~~~~\text{Area}= \dfrac{1}{2} \times \text{Base} \times \text{Height}\\\\\implies 30 = \dfrac 12 \times \text{Base} \times \text{Height}\\\\\implies \text{Base} \times \text{Height}= 60[/tex]

[tex]\textbf{Example 1:}\\\\\text{Height} = 6~ cm \\\\\text{Base} = 10~ cm\\\\\text{Area} = \dfrac 12 \times 6 \times 10 = 30~ cm^2\\\\\textbf{Example 2:}\\\\\text{Height} = 5~ cm\\\\\text{Base} = 12~ cm\\\\\text{Area} = \dfrac 12 \times 12 \times 5 = 30~ cm^2\\\\\textbf{Example 3:}\\\\\text{Height} =4~ cm\\\\\text{Base} = ~15 ~cm\\\\\text{Area} = \dfrac 12 \times 15 \times 4 = 30~ cm^2[/tex]

Let's see

Base be B

Height be H

So

The ppossible values are

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

Answer:

When -3v = -18 is solved, the result is:

21v

The result of this mathematical sentence is v=6

First degree equation is a mathematical sentence - having at least one unknown. Its representation is given by ax + b = 0. To calculate an equation, as it is in the expression in the statement, simply: isolate x and divide the second to the first member.

*Note: Equal signs, the result will be equated as positive.

-3v = -18

v = -18/-3

v = 6

Therefore, the correct value of this equation is v = 6.

A second-degree polynomial takes the form

[tex]f(x) = ax^2 + bx + c[/tex]

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

[tex]\dfrac{df}{dx} = 2ax + b[/tex]

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

[tex]f(x) = ax^2 + c[/tex]

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.

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:

Step-by-step explanation:

x^2 + 44^2 = 55^2

x^2 + 1936 = 3025

3025-1936 = 1089

sqrt(1089) = 33

x = 33

Answer:

X=33

Step-by-step explanation:

this is a right traingle so you can use pythagorean theorem

A^2 +B^2 =C^2

A^2 +44^2= 55^2

A^2 + 1936= 3025 subtract 1936 from both sides

A^2= 1089 now square root both sides

A=33

Answer:

3/4 cups

Step-by-step explanation:

3 1/2 divided by 2

Answer: not a triangle

Step-by-step explanation:

If this were to be a triangle, the shorter sides would be 11 and 4 and the longest side would be 16.

First, we should determine if it is a triangle.

The volume of 10 ounces of lemonade in litres is 0.295735 litres.

He needs 10 ounces of lemonade.

To know the volume in litres, we have to convert from ounces to litres.

Therefore,

1 ounces = 0.0295735 litres

10 ounces = ?

cross multiply

volume in litres = 0.0295735 × 10

volume in litres = 0.295735

Therefore, the volume of the lemonade in litres is 0.295735 litres.

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Answer:

1 - 135

2 - 45

3 - 45

4 - 135

5 - 135

6 - 45

7 - 45

8 - 135

Answer: None

Step-by-step explanation:

There is only one pair of angles and one pair of sides, which is not sufficient to prove triangle congruence.

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.

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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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:

[tex]f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=e^{3x-1}[/tex]

Replace f(x) with y:

[tex]\implies y=e^{3x-1}[/tex]

Take natural logs of both sides:

[tex]\implies \ln y = \ln e^{3x-1}[/tex]

Apply the Power Log Law   [tex]\ln x^n=n\ln x[/tex] :

[tex]\implies \ln y = (3x-1)\ln e[/tex]

As [tex]\ln e=1[/tex] then:

[tex]\implies \ln y = 3x-1[/tex]

Rearrange to make x the subject:

[tex]\implies 3x=\ln y +1[/tex]

[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]

Swap x for [tex]f^{-1}(x)[/tex]  and y for x:

[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]