sovle this this an hard one

The graph of the function g(x) = 7cosx after the shift of 5/3 is shown by the second graph.

A right-angled triangle's relationship between its angle and sides is represented by a series of functions known as trigonometric functions.

What is Cosine (Cos) Function?

The ratio of the neighbouring side to the hypotenuse is known as the cos function (cosine function) in a triangle.

The range of cosine function lies between -1 to 1.

Calculation for the range of given function:

The given function is, g(x) = 7cosx  

Consider x = 0, put in the function.

g(x) = 7cos0

g(x) = 7×1

g(x) = 7

As, for the domain of x = 0 range is 7. the graph will shift upward with 7 units from origin.

Now, according to question, there is a shift of  5/3 of the graph, which means this 7 shift upward will move to  5/3 .

This condition is satisfied by the second graph.

Therefore, the shift for the function g(x) = 7cosx is shown correctly by the second graph.

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Answer:

B

Step-by-step explanation:

I took the test and graph B was the correct one

The Lindsey should save around $28,000 for the down payment. If she wants to expedite her savings, she can look into cutting down expenses or increasing her income.

Congratulations to Lindsey for being debt-free and having a fully funded emergency fund! As for her question, the down payment for a house usually ranges from 3% to 20% of the home's purchase price.

Based on Lindsey's desired home worth $140,000, the down payment can range from $4,200 (3%) to $28,000 (20%).

However, it's recommended to aim for a 20% down payment to avoid private mortgage insurance (PMI) and to lower monthly payments. Best of luck to Lindsey on her journey towards homeownership

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Hello !

125 * $0.29 * 6 = $217.50

Gradient is another word for slope.

Slope = rise/run = (y2-y1)/(x2-x1)

So pick 2 points.

Let's do line A first.

(1,1) and (2,4)

slope = (1-4)/(1-2)

= -3/-1 = 3

The slope (aka gradient) of line A = 3.

Line B.

(0,5) and (1,1)

slope = (5-1)/(0-1)

= 4/-1

= -4

The slope (aka gradient) of line B = -4.

Answer:

y = kxz. y = 10.8

Step-by-step explanation:

y = kxz, where k is a constant.

12 = k(4)(5) = 20k

k = 12/20 = 0.6.

y = kxz

= (0.6) (6) (3)

= 10.8

The coordinates of the point of intersection of the tangent and the secant are;

T(a, b) = (9/5, -14/5)

C = (0, -1)

A tangent is a line or segment that touches a circle only once.

The equation of the line AN is; y - 2 = ((-2 - 2)/(2 - 3)) × (x - 3)

y = 4·x - 12 + 2 = 4·x - 10

y = 4·x - 10

The coordinates of the center of the circle is; ((-5 + 3)/2, (4 + 2)/2) = (-1, 3)

The radius of the circle is; √((3 - (-1))² + (2 - 3)²) = √(17)

The equation of the circle is; (x + 1)² + (y - 3)² = 17

The point C indicates;

(0 + 1)² + (y - 3)² = 17

(y - 3)² = 17 - 1 = 16

y - 3 = √(16) = ±4

y = 4 + 3 = 7, and y = -4 + 3 = -1

The coordinates of the point C is; (0, -1)

The slope of AC = (2 - (-1))/(3 - 0) = 1

AC is perpendicular to BC

The slope of BC = -1

The equation of BC is therefore; y - 4 = -(x - (-5)) = -x - 5

y = -x - 1

The equation of the segment AN is; y - 2 = ((2 - (-2))/(3 - 2))×(x - 3)

y - 2 = 4·(x - 3)

y = 4·x - 12 + 2 = 4·x - 10

-x - 1 = 4·x - 10

x-coordinate of T = 9/5

The y-coordinate of T = -9/5 - 1  = -14/5

Therefore, at the point T, we get; (9/5, -14/5)

a = 9/5, b = -14/5, C = (0, -1)

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Answer:

B and C

Step-by-step explanation:

We can determine which three sides will form a right triangle using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

A:  

5^2 + (√8)^2 = 33^2

25 + 8 = 1089

33 ≠ 1089

Because 33 is not equal to 1089, these three lengths do not form a right triangle.

B:  

8^2 + 15^2 = 17^2

64 + 225 = 289

289 = 289

Thus, these three side lengths form a right triangle.

C:

(√2)^2 + (√2)^2 = 2^2

2 + 2 = 4

4 = 4

Thus, these three side lengths also form a right triangle.

Answer:

translation

Step-by-step explanation:

The distance between line and the point P(4,1) is,

⇒ d = 4.47

We have to given that;

Line contains points (- 4,0) and (0, - 2).

Since, The equation of line in point-slope form passing through the points  (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Hence, The equation of line is,

⇒ y - 0 = (- 2 - 0) / (0 - (- 4)) (x - (- 4))

⇒ y = - 2/4 (x + 4)

⇒ y = - 1/2 (x + 4)

⇒ y = - 1/2x - 2

⇒ 2y = - x - 4

⇒ 2y + x + 4 = 0

So, The distance between the line 2y + x + 4 = 0 and the point P(4, 1) is:

⇒ d = (2 × 1 + 4 + 4) / √(2² + 1)

⇒ d = 10 / √5

⇒ d = 2√5

⇒ d = 2 x 2.23

⇒ d = 4.47

Thus, The distance between line and the point P(4,1) is,

⇒ d = 4.47

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The image you provided is a mathematical expression written in a non-standard format. To simplify it and obtain the result of 3, we can break it down step by step.

The expression can be written as follows:

(8c8) * (8x83)

Let's simplify each part separately:

(8c8):

The term "8c8" represents the combination or binomial coefficient. In general, the combination "nCr" is calculated as n! / (r! * (n-r)!), where "!" denotes factorial. When r = n (as is the case here with 8c8), the combination simplifies to 1. Therefore, 8c8 equals 1.

(8x83):

The term "8x83" represents multiplication between the numbers 8 and 83, which equals 664.

Now, let's put it all together:

(8c8) * (8x83) = 1 * 664 = 664

According to the given expression, the simplified result is 664, not 3. Please double-check the expression or provide further clarification if needed.

The proposition x − y = y − x is true.

We are given that;

The equation x − y = y − x

Now,

X − y = -(y - X)

-(y - X) + 2X - 2X = y - X + X - y = y - x.

Similarly, y - x = -(x - y)

-(x - y) + 2y - 2y = x - y + y - x = X - y.

Both sides of the equation are equal.

Therefore, by the given function answer will be true.

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Answer:

Part A:

122.5 cubic inches

Part B:

No

Step-by-step explanation:

Part A:

The volume of a rectangular prism is the product of its length, width, and height. Volume = 5 x 3.5 x 7 = 122.5 cubic inches Since the volume of the box is less than 22 cubic inches.

Part B:

Answer:

The original price of the television was $3620.00.

Answer:

$3620.00

Step-by-step explanation:

5% = 181

1% = 36.2

100% = 3620

Answer:

Step-by-step explanation:

We know that,

sum of three side of triangle is 180°

So,

x + 72° + 90° = 180°

x + 162° = 180°

x = 180° - 162°

x = 18°

[tex]\underline{\rule{190pt}{4pt}}[/tex]

The value of x in the triangle is 18 degrees.

The given triangle is a right angled triangle.

We have to find the value of x.

As the triangle is a right angle one angle is 90 degrees.

And the other angle is 72 degrees.

The missing angle is x which we have to find.

By angle sum property we know that the sum of three angles is 180 degrees in a triangle.

72+90+x=180

Combine the like terms:

162+x=180

Subtract 162 from both sides:

x=180-162

When one hundred sixty two is subtracted from one hundred eighty, we get 18.

x=18 degrees

Hence, 18 degrees is the value of x in the triangle.

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The number of professionals in the office, given that 8 professionals is 20 % would be 40 professionals.

To calculate the total number of staff in the office, use the following formula :

Total staff = ( Professionals / Percentage ) x 100

Professionals = 8 professionals

Percentage = 20 %

Plugging in the values, we get :

Total staff = ( 8 / 20 ) x 100

Total staff = 0. 40 x 100

Total staff = 40 professionals

In conclusion, the office would have a total of 40 professionals if 8 professionals are 20 % of staff.

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Full question is:

en una oficina trabajan 8 profesionales haciendo un porcentaje de 20%. calcular el numero del personal de tal oficina

Translated is:

8 professionals work in an office making a percentage of 20%. Calculate the number of staff in such an office.

The function f(x) = (x+2)²(x-1)(x-5)² has-2 is a zero with multiplicity 2

5 is a zero with multiplicity 1 and the graph is tangent to x-axis at x = 1

For the function f(x) = (x+2)²(x-1)(x-5)²

-2 is a zero with multiplicity 2

This is represented by the factor (x+2)², indicating that -2 is a zero that appears twice in the function.

5 is a zero with multiplicity 1
This is represented by the factor (x-5), indicating that 5 is a zero that appears once in the function.

The graph is tangent to the x-axis at x = 1:

This is represented by the factor (x-1), indicating that the graph touches the x-axis at x = 1.

Therefore, the function f(x) = (x+2)²(x-1)(x-5)² has all the specified attributes.

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Answer:

Let’s use x to represent the number of goats and y to represent the number of chickens. We know that there are 62 animals in total, so x + y = 62. We also know that there are 148 legs in total, so 4x + 2y = 148 (since goats have four legs and chickens have two).

We can solve for x and y by using substitution or elimination method. Let’s use substitution method here. From x + y = 62, we can get x = 62 - y. Substituting this into 4x + 2y = 148 gives us:

4(62 - y) + 2y = 148 248 - 4y + 2y = 148 248 - 2y = 148 100 = 2y y = 50

So there are 50 chickens on the farmyard. Substituting this into x + y = 62 gives us:

x + 50 = 62 x = 12

So there are 12 goats in the farmyard.

Therefore, there are 12 goats and 50 chickens on the farmyard.

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The opening balance is 100.00 A. Its placement on the credit side implies funds deposited before the statement period. The specific impact on Gloria's finances and the value of B are not provided.

Based on the provided information, let's address each question:

3.2.1 The opening balance is 100.00 A (currency is not specified). This amount represents the initial balance in the bank account before any transactions occur.

3.2.2 When the opening balance is on the credit side of the bank statement, it indicates that there were funds deposited or credited to the account before the statement period. In this case, the opening balance of 100.00 A suggests that there were funds deposited or credited into the account before the statement period began.

3.2.3 If Gloria decides to withdraw money at Capital Bank ATM, her account balance will decrease by the amount of the withdrawal. The specific amount of the withdrawal is not mentioned in the provided information, so we cannot determine the exact impact on her finances. However, it's important to note that ATM withdrawals may also incur transaction fees, which could further reduce her account balance.

3.2.4 Based on the information given, the value of B is not explicitly provided. It seems to be missing or not specified in the provided data. Without knowing the value of B, it is not possible to calculate it.

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In the given diagram, we have a triangle with two angles labeled as (3x + 10)° and (5x - 30)°. We need to solve for the value of x.

According to the properties of triangles, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the following equation:

(3x + 10) + (5x - 30) + 90 = 180

Let's simplify the equation:

3x + 10 + 5x - 30 + 90 = 180

8x + 70 = 180

Next, we'll isolate the variable term by subtracting 70 from both sides of the equation:

8x = 180 - 70

8x = 110

To solve for x, we'll divide both sides of the equation by 8:

x = 110 / 8

Now, let's calculate the value of x:

x ≈ 13.75

Therefore, the value of x is approximately 13.75.

Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.

The correct representation of the function g(x) as a translation 2 units right and 5 units up of f(x) = -√√x is:

g(x) = -√√(x - 2) + 5.

To perform a translation 2 units right, the x-coordinate needs to be replaced with (x - 2). This shift moves the entire graph horizontally to the right by 2 units.

Additionally, to shift the graph 5 units up, we add 5 to the function. Thus, the function g(x) is obtained by taking the negative square root of the square root of (x - 2) and then adding 5 to the result.

Among the given options, g(x) = -√√(x - 2) + 5 accurately represents the translation described, while the other options either have incorrect sign placement, incorrect order of operations, or an incorrect translation direction.

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The probability of selecting a large or green marble is 0.7333.

The probability of selecting a large marble is 19/30 (19 large marbles out of 30 total marbles). The probability of selecting a green marble is 3/30 (3 green marbles out of 30 total marbles).

To find the probability of selecting a large or green marble, you need to find the probability of selecting a marble that is either large or green. This is known as the union of two events. The union of two events is found by adding the individual probabilities of each event together.

The probability of selecting a large or green marble is 19/30 + 3/30 = 22/30 = 0.7333.

Therefore, the probability of selecting a large or green marble is 0.7333.

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Answer:

A.  -0.693147

Step-by-step explanation:

Replace f(x) with y in the given function:

[tex]y=\left(\dfrac{1}{2}\right)^x[/tex]

Take natural logs of both sides of the equation:

[tex]\ln y=\ln \left(\dfrac{1}{2}\right)^x[/tex]

[tex]\textsf{Apply the log power law:} \quad \ln a^n=n \ln a[/tex]

[tex]\ln y=x\ln \left(\dfrac{1}{2}\right)[/tex]

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

[tex]\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln \left(\dfrac{1}{2}\right)[/tex]

Differentiate with respect to x:

[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=\ln \left(\dfrac{1}{2}\right)[/tex]

[tex]\textsf{Apply the log quotient law:} \quad \ln \left(\dfrac{a}{b}\right) = \ln a - \ln b[/tex]

[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=\ln(1)-\ln(2)[/tex]

[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=0-\ln(2)[/tex]

[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=-\ln(2)[/tex]

Multiply both sides by y:

[tex]\dfrac{\text{d}y}{\text{d}x}=-y\ln (2)[/tex]

Substitute back in the expression for y:

[tex]\dfrac{\text{d}y}{\text{d}x}=-\left(\dfrac{1}{2}\right)^x\ln (2)[/tex]

Therefore, the differentiated function is:

[tex]f'(x)=-\ln(2)\left(\dfrac{1}{2}\right)^x[/tex]

To find f'(0), substitute x = 0 into the differentiated function:

[tex]\begin{aligned}x=0 \implies f'(0)&=-\ln(2) \left(\dfrac{1}{2}\right)^0\\&=-\ln(2) \cdot 1\\&=-\ln(2) \\&=-0.693147\; \sf (6\;d.p.)\end{aligned}[/tex]

Answer :

From the figure XY and WZ are opposite sides and XW and YZ are the opposite sides.

XY = WZ

3a - 4 = a + 2

3a - a = 2 + 4

2a = 6

a = 6/2

a = 3

Now put the value of a in XY

XY = 3a - 4

XY = 3(3) - 4

XY = 9 - 4

Similarly,

XW = YZ

2b = b + 1

2b - b = 1

1b = 1

b = 1

Now put the value of b in YZ

YZ = 2b

YZ = 2 × 1

Answer :

Step-by-step explanation :

As We Know that Opposite sides of the Parallelogram are equal.

SO,

(i) YZ = XW (opposite sides)

→ 2b = b + 1

→ 2b - b = 1

→ b = 1

Since, YZ = 2b

→ YZ = 2 × 1

→ YZ = 2.

Also,

(ii) XY = WZ (opposite sides)

→ 3a - 4 = a + 2

→ 3a - a = 2 + 4

→ 2a = 6

→ a = 6/2

→ a = 3 .

Since, XY = 3a - 4

putting the value of a = 3.

=> 3(3) - 4

→ 9 - 4

→ 5

XY = 5.

Therefore, Option D is the required answer.

Answer:

e^1.4 = 4.05519

to 3dp = 4.055

Step-by-step explanation:

3dp meaning 3 decimal places counting according to the value of 5

Answer:

The temperature change from noon to midnight is 50 degrees. The temperature at noon was 40 degrees and at midnight it was -10 degrees. Therefore, the change in temperature is 40 - (-10) = 50 degrees.

This study uses a repeated measures design, random sampling, and a control group.

Repeated measures design is used because each child experiences all treatments over time. Random sampling is present as children were randomly selected.

The control group is the group with no screen time. Blocking isn't used as participants aren't grouped based on shared characteristics affecting the response. Blinding isn't used as it's not mentioned that participants or researchers are unaware of the treatment given, which would prevent bias.

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