What is the solution to the system of equations graphed below?

Answer:

Step-by-step explanation:

9 1/3 is 9.33333 repeated which is 9

Answer:

25%

Step-by-step explanation:

8/32=1/4=0.25

The complete sentence with correct number is,

⇒ 8 is 25% of 32.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

To find 8 is what percent of 32.

Let 8 is x percent of 32.

Now, We can formulate;

⇒ x% of 32 = 8

Solve for x;

⇒ x/100 × 32 = 8

⇒ 32x = 8 × 100

⇒ 32x = 800

⇒ x = 800 / 32

⇒ x = 25

Thus, The complete sentence with correct number is,

⇒ 8 is 25% of 32.

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Answer:

both of the solution is B and C

Answer:

1. (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A))  = 1/8

2. θ = 30°

3. tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

from tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ) and sin²(θ) +  cos²(θ) = 1

4. tan10°·tan15°·tan75°·tan80°= 1 from;

sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]

cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]

5. x² + y² = a² + b² where x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ from;

cos²θ + sin²θ = 1

Step-by-step explanation:

1. Here we have 5·tan(A) = 5·sin(A)/cos(A) = 4

∴ 5·sin(A) = 4·cos(A)

Hence to find the value of (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) we have;

Substituting the value for 5·sin(A) = 4·cos(A) into the above equation in both the numerator and denominator we have;

(4·cos(A) - 3·cos(A)/(4·cos(A) + 4·cos(A)) = cos(A)/(8·cos(A)) = 1/8

Therefore, (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) = 1/8

2. For the equation as follows, we have

\(\frac{sin \theta}{1 + cos \theta} + \frac{1 + cos \theta}{sin \theta} = 4\) this gives

\(\frac{2sin (\theta/2) cos (\theta/2) }{2 cos^2 (\theta/2)} + \frac{2 cos^2 (\theta/2)}{2sin (\theta/2) cos (\theta/2) } = 4\)

\(tan\frac{\theta}{2} + \frac{1}{tan\frac{\theta}{2} } = 4\)

\(tan^2\frac{\theta}{2} + 1 = 4\times tan\frac{\theta}{2}\)

\(tan^2\frac{\theta}{2} - 4\cdot tan\frac{\theta}{2} + 1 = 0\)

We place;

\(tan\frac{\theta}{2} = x\)

∴ x² - 4·x + 1 = 0

Factorizing we have

(x - (2 - √3))·(x - (2 + √3))

Therefore, tan(θ/2) = (2 - √3) or (2 + √3)

Solving, we have;

θ/2 = tan⁻¹(2 - √3) or tan⁻¹(2 + √3)

Which gives, θ/2 = 15° or 75°

Hence, θ = 30° or 150°

Since 0° < θ < 90°, therefore, θ = 30°

3. We have tan(θ) - cot(θ) = tan(θ) - 1/tan(θ)

Hence, tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ)

∴  tan(θ) - 1/tan(θ) = (sin²(θ) -  cos²(θ))/(cos(θ)×sin(θ))...........(1)

From sin²(θ) +  cos²(θ) = 1, we have;

cos²(θ) = 1 - sin²(θ), substituting the value of sin²(θ) in the equation (1) above, we have;

(sin²(θ) -  (1 - sin²(θ)))/(cos(θ)×sin(θ)) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

Therefore;

tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

4. tan10°·tan15°·tan75°·tan80°= 1

Here we have since;

sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]

cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]

Then;

tan 10°·tan15°·tan75°·tan80° = tan 10°·tan80°·tan15°·tan75°

tan 10°·tan80°·tan15°·tan75° = \(\frac{sin(10^{\circ})}{cos(10^{\circ})} \times \frac{sin(80^{\circ})}{cos(80^{\circ})} \times \frac{sin(15^{\circ})}{cos(15^{\circ})} \times \frac{sin(75^{\circ})}{cos(75^{\circ})}\)

Which gives;

\(\frac{sin(10^{\circ}) \cdot sin(80^{\circ})}{cos(10^{\circ})\cdot cos(80^{\circ})} \times \frac{sin(15^{\circ}) \cdot sin(75^{\circ})}{cos(15^{\circ})\cdot cos(75^{\circ})}\)

\(=\frac{1/2[cos(80 - 10) - cos(80 + 10)]}{1/2[cos(80 - 10) + cos(80 + 10)]} \times \frac{1/2[cos(75 - 15) - cos(75 + 15)]}{1/2[cos(75 - 15) + cos(75 + 15)]}\)

\(=\frac{1/2[cos(70) - cos(90)]}{1/2[cos(70) + cos(90)]} \times \frac{1/2[cos(60) - cos(90)]}{1/2[cos(60) + cos(90)]}\)

\(=\frac{[cos(70)]}{[cos(70) ]} \times \frac{[cos(60)]}{[cos(60) ]} =1\)

5. If x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ

∴ x² + y² = (a·cosθ - b·sinθ)² + (a·sinθ + b·cosθ)²

= a²·cos²θ - 2·a·cosθ·b·sinθ +b²·sin²θ + a²·sin²θ + 2·a·sinθ·b·cosθ + b²·cos²θ

= a²·cos²θ + b²·sin²θ + a²·sin²θ + b²·cos²θ

= a²·cos²θ + b²·cos²θ + b²·sin²θ + a²·sin²θ

= (a² + b²)·cos²θ + (a² + b²)·sin²θ

= (a² + b²)·(cos²θ + sin²θ) since cos²θ + sin²θ = 1, we have

= (a² + b²)×1 = a² + b²

The value of the right Riemann sum approximation for integral ∫₀² f(x) dx is (c) 60.

The right Riemann sum approximation is obtained by dividing the interval [0, 2] into four subintervals of equal length and evaluating the function at the right endpoints of each subinterval. In this case, each subinterval has a length of (2-0)/4 = 0.5. The right endpoints of the subintervals are 0.5, 1.0, 1.5, and 2.0.

To calculate the right Riemann sum, we evaluate the function at these right endpoints and sum up the values multiplied by the subinterval length.

f(0.5) = \(9^{0.5\) = 3

f(1) = 9¹ = 9

f(1.5) = \(9^{1.5\) = 27

f(2) = 9² = 27

The right Riemann sum is then

= (0.5 * f(0.5)) + (0.5 * f(1.0)) + (0.5 * f(1.5)) + (0.5 * f(2.0))

= 0.5 * (3 + 9 + 27 + 81)

= 60.

Therefore, the value of the right Riemann sum approximation for ∫2 to 0 f(x) dx is 60, which corresponds to option (c).

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Given question is incomplete, the complete question is below

let f be the function given by f(x)= 9ˣ, if four subintervals of equal length are used, what is the value of the right riemann sum approximation for∫₀² f(x) dx. 20b. 40c. 60d. 80

The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

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Answer:

i was able to get y = 1.3x - 2

Approximately 2.51 kJ of heat is absorbed in turning 3.00 grams of ethanol from a liquid to a vapor.

To calculate the amount of heat absorbed in turning 3.00 grams of ethanol (C2H5OH) from a liquid to a vapor, we need to use the molar heat of vaporization of ethanol, which is given as 38.6 kJ/mol.

First, we need to convert the mass of ethanol to moles. The molar mass of ethanol is approximately 46.07 g/mol (12.01 g/mol for carbon, 1.01 g/mol for hydrogen, and 16.00 g/mol for oxygen).

Using the formula: moles = mass / molar mass

moles = 3.00 g / 46.07 g/mol ≈ 0.065 mol

Now, we can calculate the amount of heat absorbed using the molar heat of vaporization:

Heat absorbed = moles × molar heat of vaporization

Heat absorbed = 0.065 mol × 38.6 kJ/mol ≈ 2.51 kJ

Therefore, approximately 2.51 kJ of heat is absorbed in turning 3.00 grams of ethanol from a liquid to a vapor.

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The equation of a plane in 3-space with equation c1x + c2y + c3z + c4 = 0 can be determined by passing through three non-collinear points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). This is given by the determinant equation:

Copy code

| x  y  z  1 |

| x1 y1 z1 1 | = 0.

| x2 y2 z2 1 |

| x3 y3 z3 1 |

However, if the three distinct points are collinear, meaning they lie on the same line, then the determinant equation becomes undefined as the determinant of a 3x3 or smaller matrix with linearly dependent rows or columns is equal to zero. This means that there is no plane that passes through three collinear points as a plane requires at least three non-collinear points to be defined.

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Answer:

10

Step-by-step explanation:

lol XD are you trolling?

The normal probability plot determines a normal distribution

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the centre of the range.

Normal distributions are symmetric, uni-modal, and asymptotic, and the mean, median, and mode are all equal

A data set (when graphed) must follow a bell-shaped symmetrical curve centered around the mean

Given data ,

Let the normal distribution be represented as N

Now , the normal probability is P

A normal probability plot, also known as a "normal plot," plots sorted data against values chosen to resemble a straight line in the final image if the data are roughly normally distributed.

Divergences from normalcy are shown by deviations from a straight line.

A straight, diagonal line means that you have normally distributed data. If the line is skewed to the left or right, it means that you do not have normally distributed data.

Hence , the normal probability plot determines a normal distribution

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Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

B

Step-by-step explanation:

Ok..

15 squared - 12 squared = x

I don't know why you need help on something like this?

Please don't cheat in class.

The inner products in the given space C[0, 1] are:

⟨e^x, e^(-x)⟩ = 1

⟨x, sin(πx)⟩ = 1 / π

⟨x^2, x^3⟩ = 1 / 6

To compute the inner products in the space C[0, 1] with the given inner product defined by ⟨f, g⟩ = ∫₀¹ f(x)g(x) dx, we can calculate the following:

⟨e^x, e^(-x)⟩:

Using the inner product definition, we have:

⟨e^x, e^(-x)⟩ = ∫₀¹ e^x * e^(-x) dx

= ∫₀¹ e^(x - x) dx

= ∫₀¹ dx

= [x] from 0 to 1

= 1 - 0

= 1

⟨x, sin(πx)⟩:

Similarly, we can calculate:

⟨x, sin(πx)⟩ = ∫₀¹ x * sin(πx) dx

= -[x * (cos(πx)) / π] from 0 to 1 + ∫₀¹ (cos(πx) / π) dx

= -[(1 * (cos(π)) / π) - (0 * (cos(0)) / π)] + (1/π) * ∫₀¹ cos(πx) dx

= -[(-1 / π) - 0] + (1/π) * [(sin(πx) / π)] from 0 to 1

= (1 / π) - (1 / π) * [(sin(π) - sin(0))]

= (1 / π) - (1 / π) * 0

= 1 / π

⟨x^2, x^3⟩:

Similarly, we can calculate:

⟨x^2, x^3⟩ = ∫₀¹ x^2 * x^3 dx

= ∫₀¹ x^(2+3) dx

= ∫₀¹ x^5 dx

= [(x^(5+1)) / (5+1)] from 0 to 1

= [x^6 / 6] from 0 to 1

= (1^6 / 6) - (0^6 / 6)

= 1 / 6

Therefore, the inner products in the given space C[0, 1] are:

⟨e^x, e^(-x)⟩ = 1

⟨x, sin(πx)⟩ = 1 / π

⟨x^2, x^3⟩ = 1 / 6

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Answer:

49+2m

Step-by-step explanation:

49 is increased by twice a number m

Hope this helps!

Answer:

To find the monthly interest rate as a percentage, we need to first convert the annual interest rate from decimal to percentage, and then divide by 12 (since there are 12 months in a year).

The annual interest rate is given as 4% (1.04 in decimal form).

So, the monthly interest rate as a percentage would be:

((1.04 - 1) / 12) x 100 = 0.33%

Therefore, Robert's savings account earns a monthly interest rate of 0.33%.

Multiple regression analysis is applied when analyzing the relationship between one dependent variable and two or more independent variables. The goal is to determine the extent to which the independent variables predict the dependent variable.

Multiple regression analysis is a statistical technique used to explore and quantify the relationship between a dependent variable and multiple independent variables. It allows researchers to examine how changes in one or more independent variables impact the dependent variable, while controlling for the effects of other variables. By estimating the coefficients for each independent variable, the analysis provides insights into the strength, direction, and significance of their relationships with the dependent variable. This method is commonly employed in various fields, such as economics, social sciences, and business, to understand complex relationships and make predictions based on the interplay of multiple factors.

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Answer:

J. (2, -3)​

Step-by-step explanation:

1. Substitute y = x - 5 in for y in the other equation:

5x + 2(x - 5) = 4

2. Simplify:

5x + 2x - 10 = 4 (distributed the 2)

7x - 10 = 4

3. Isolate for x:

7x - 10+10 = 4+10

7x = 14

7x/7 = 14/7

x = 2

4. Plug the new x value into an equation and solve for y:

y = 2 - 5

y = -3

hope this helps!

Answer:

\( - 6y + 12 = - 66 \\ - 6y = - 66 - 12 \\ - 6y = - 78 \\ y = - \frac{ - 78}{ - 6} \\ y = 13\)

Answer:

y = 13

Step-by-step explanation:

i just solved this now, but I'm pretty sure it's correct :)

Answer:

Step-by-step explanation:

It would be 5 because it says in the question "5 of them are blue"

Step-by-step explanation:

angle A = angle D

angle C common angle

angle E = 180 - 63 - 52

5x = 65

x = 13deg

Topic: congruence and similarity

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

Answer:

x = 13°

Step-by-step explanation:

Because of the given congruency,

Angle A = Angle D = 63°.

Angle C = 52°

Angle B = Angle E = 5x

Now, In Triangle ABC,

Angle A + Angle B + Angle C = 180°.

63° + 5x + 52° = 180°

115° + 5x = 180

5x = 65°

x = 13°

HOPE IT HELPS!!!

Step-by-step explanation:

10x² - 5x + 10

x = -3

10(-3)² -5(-3) + 10

= (10×9) + 15 + 10

= 90 + 15 + 10

= 115

The rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

We know that,

The Base is growing at the rate of 1 cm per sec.

Height is growing at the rate of 2 cm per sec.

Area of triangle: 1/2 × b × h

The rate of change will be:

1/2 × b × h

1/2 × 4/1 × 7/2

28/4

7 cm per sec

Therefore, the rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

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Boeing takes 29,454 hours to produce the fifth 787 jet. With an 80% learning factor, the time required for the production of the eleventh 787 is approximately 66,097 hours.

To calculate the time required for the production of the eleventh 787 jet, we can use the learning curve formula:

T₂ = T₁ × (N₂/N₁)^b

Where:

T₂ is the time required for the second unit (eleventh in this case)

T₁ is the time required for the first unit (fifth in this case)

N₂ is the quantity of the second unit (11 in this case)

N₁ is the quantity of the first unit (5 in this case)

b is the learning curve exponent (log(1/LF) / log(2))

Given that T₁ = 29,454 hours and LF (learning factor) = 80% = 0.8, we can calculate b:

b = log(1/LF) / log(2)

b = log(1/0.8) / log(2)

b ≈ -0.3219 / -0.3010

b ≈ 1.0696

Now, substituting the given values into the formula:

T₂ = 29,454 × (11/5)^1.0696

Calculating this expression, we find:

T₂ ≈ 29,454 × (2.2)^1.0696

T₂ ≈ 29,454 × 2.2422

T₂ ≈ 66,096.95

Rounding the result to the nearest whole number, the time required for the production of the eleventh 787 jet is approximately 66,097 hours.

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Answer:

here is a photo

Answer:

5 units

Step-by-step explanation:

To find the distance between two points on a graph, we use the distance formula \(d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2\) where \(d\) is the distance between points \((x_1,y_1)\) and \((x_2,y_2)\).

For this problem, we will identify \((x_1,y_1)\rightarrow(-1,5)\) and \((x_2,y_2)\rightarrow(2,9)\):

\(d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\d=\sqrt{(9-5)^2+(2-(-1))^2}\\\\d=\sqrt{(4)^2+(3)^2}\\\\d=\sqrt{16+9}\\\\d=\sqrt{25}\\\\d=5\)

Therefore, the distance between \((-1,5)\) and \((2,9)\) is 5 units

Answer:

2

Step-by-step explanation:

for the x-intercep put y=0 then you solve for x

Answer:

A. C(2,-2) , D(-1,-2)

●●●●●●●●●●●●●●●●●

Answer:

C. \((4+ (-6.5)) +11.5\)

Step-by-step explanation:

Just exchange:

11.5 + (4 + ( - 6.5  ) )

⇒  (4+ (-6.5)) +11.5

After applying the property the expression would be  (4+ (-6.5)) +11.5.

Changes to the order of the addends have no effect on the sum, according to the associative feature of addition.

For example, ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) or (2 + 3) + 4

Given:

11.5+ (4+ (-6.5))

In Above case we can use the  Associative property over addition.

For this we just need to exchange the position of number along with their signs.

So, 11.5+ (4+ (-6.5))

=  (4+ (-6.5)) +11.5

Hence, after applying the property the expression would be  (4+ (-6.5)) +11.5.

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