Class work help Algebra 2

The measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

Parallel lines are those straight lines that are always the same distance apart from each other.

Given that, two lines RS and TU are parallel, and ∠ 7 = 3x-10 and ∠ 3 = 2x+5,

We need to find ∠ 1

Since, ∠ 7 and ∠ 3 are corresponding angles between two parallel lines therefore, both are congruent,

Therefore,

3x-10 = 2x+5

x = 15

Now, ∠ 1 = ∠ 3 as they are vertically opposite angles,

Therefore,

∠ 1 = 2(15)+5

∠ 1 = 35°

Hence, the measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

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The figure was not given so the figure is attached.

The answer is  is 30.59

Answer:

about 75.4

Step-by-step explanation:

V=πr^2h/3

radius is half of diameter

so the radius is 6

Based on the information given ,it should be noted that the area of the real kite will be 1615.548 cm²

The given coordinates are:

(1, 5) -> (10 cm, 50 cm)

(3, 6) -> (30 cm, 60 cm)

(5, 5) -> (50 cm, 50 cm)

(3, 0) -> (30 cm, 0 cm)

Base = Distance between (10 cm, 50 cm) and (30 cm, 0 cm)

= ✓((30 cm - 10 cm)² + (0 cm - 50 cm)²)

= ✓(400 + 2500)

= ✓(2900) cm

Height = Distance between (30 cm, 60 cm) and (30 cm, 0 cm)

= 60 cm - 0 cm

= 60 cm

Area of Triangle 1 = (1/2) * Base * Height

= (1/2) * ✓(2900) cm * 60 cm

= 1615.548 cm²

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The angle  of EBF is  6w -28°.

It is required to find the angle  of EBF.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given:

ABF = 8w - 6

ABE = 2(w + 11)

According to given question we have,

Angle EBF = ABF - ABE

Angle EBF = 8w - 6 - [2(w + 11)]

Angle EBF = 8w - 6 - [2w + 22]

Angle EBF = 8w - 6 - 2w - 22

Angle EBF = 6w -28°

Therefore, the angle  of EBF is  6w -28°.

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Answer:24200

Step-by-step explanation:

I=PxRxT

20000x.07x3=4200

20000+4200=24200

(2, 2), (3, 1), (4, 2) are ordered pairs are in the solution set of the system of linear inequalities.

What are linear inequalities, exactly?

A mathematical expression that compares two expressions using the inequality symbol is known as a linear inequality. The expression may be either a numerical or an algebraic expression, or it may be both.

                               x - 5 > 3x - 10 is an illustration of a linear inequality. Since greater than is utilized in this inequality, the LHS is indubitably greater than the RHS. The inequality is represented by the formula 2x 5 x (5/2).

y >-1/3x+2

y < 2x + 3

The answer is "None" of the given choices satisfy the linear inequality. Each choice has a point (2,2) which dissatisfy the equation.

(2, 2), (3, 1), (4, 2)

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Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

According to the information in the table, the histogram would be as shown in the attached image.

To graph the information in the table we must take into account the relationship of the data. On the one hand we have the frequency, which is the data that varies, and the different variations of time.

In accordance with the above, what we want to demonstrate with this table are the different frequencies of time that students take to do their math homework. Additionally, most students take between 10 and 25 minutes to do their math homework.

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Number of customers who purchased exactly two types of books

= 36 - 5Number of customers who purchased exactly two types of books = 31Therefore, a total of 31 customers purchased exactly two types of books.

Only 19 customers purchased only mysteries. Explanation:

Customers who purchased only mysteries = Total number of customers who purchased mysteries - (Number of customers who purchased mysteries and science fiction + Number of customers who purchased mysteries and romance novels + Number of customers who purchased all three types of books)Customers who purchased only mysteries = 34 - (15 + 12 + 5)

Number of customers who purchased exactly two types of books =

(Number of customers who purchased mysteries and science fiction) +

(Number of customers who purchased mysteries and romance novels)

+ (Number of customers who purchased science fiction and romance novels)Customers who purchased exactly two types of books = (15) +

(12) + (9)Customers who purchased exactly two types of books = 36However, we have to subtract the number of customers who purchased all three types of books because they were counted twice.

Number of customers who purchased exactly two types of books = 36 - 5Number of customers who purchased exactly two types of books = 31Therefore, a total of 31 customers purchased exactly two types of books.

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The critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

To find the critical value zₐ/₂, we need to determine the value that leaves an area of (1 - α)/2 in the tails of the standard normal distribution. In this case, α is the complement of the confidence level, which is 1 - 0.83 = 0.17. Dividing this value by 2 gives us 0.17/2 = 0.085.

To find the z-value that corresponds to an area of 0.085 in the tails of the standard normal distribution, we can use a standard normal distribution table or a statistical calculator. The corresponding z-value is approximately 1.381.

Therefore, the critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

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Answer:

\(2x^2+7x+6=0\\\\2(x^2+\frac72x+3)=0\\\\2[x^2+2\cdot x\cdot\frac74+(\frac74)^2-(\frac74)^2+3]=0\\\\2[x^2+2\cdot x\cdot\frac74+(\frac74)^2]-2(\frac74)^2+6=0 \\\\2(x+\frac74)^2-2\cdot\frac{49}{16}+6=0\\\\2(x+\frac74)^2-\frac{49}8+\frac{48}8=0\\\\2(x+\frac74)^2-\frac18=0\)

Answer:

(x+7/4)^2=1/16

Step-by-step explanation:

The correct option from the given options is (a) a lower bound on how many donuts he can eat in one sitting.

A lower bound is a value which is equal to or greater than the minimum value of a set. In this given scenario, eight donuts are a lower bound on how many donuts a teenager can eat in one sitting. He might be able to eat more than eight donuts in one sitting but he cannot eat less than eight donuts in one sitting because it's a lower limit.

A lower limit or a lower bound is an absolute minimum. It is the minimum number of donuts that the teenager can consume in one sitting. In this scenario, there is a possibility that the teenager might eat more than eight donuts, but the lower limit is eight.

Therefore, the correct option is (a) a lower bound on how many donuts he can eat in one sitting.

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If the explanatory variables explained more than 20% of the variation in the response variables, it would mean that the coefficient of determination is above 0.2.

The coefficient of determination, also known as R-squared, is a statistical measure that represents the proportion of the variation in the dependent variable that is explained by the independent variables in a regression model. It ranges from 0 to 1, with 1 indicating that all the variation in the dependent variable is explained by the independent variables and 0 indicating that none of the variation is explained.

Therefore, if the explanatory variables explain more than 20% of the variation in the response variables, it means that the coefficient of determination is greater than 0.2. This is a good indicator that the regression model is a good fit for the data and that the independent variables are significant predictors of the dependent variable.

It is important to note that the question does not mention anything about there being two response variables or two explanatory variables. Therefore, we cannot conclude anything about the number of variables based on the given information.

However, we can conclude that the explanatory variables are significant in explaining the variation in the response variable.

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The volume of a hemisphere with a radius of 44.9 m, rounded to the nearest tenth of a cubic meter, is approximately 222,232.7 cubic meters.

To calculate the volume of a hemisphere, we use the formula V = (2/3)πr³, where V represents the volume and r is the radius. In this case, the radius is 44.9 m. Plugging in the values, we get V = (2/3)π(44.9)³. Evaluating the expression, we find V ≈ 222,232.728 cubic meters. Rounding to the nearest tenth, the volume becomes 222,232.7 cubic meters.

The explanation of this calculation lies in the concept of a hemisphere. A hemisphere is a three-dimensional shape that is half of a sphere. The formula used to find its volume is derived from the formula for the volume of a sphere, but with a factor of 2/3 to account for its half-spherical nature. By substituting the given radius into the formula, we can find the volume. Rounding to the nearest tenth is done to provide a more precise and manageable value.

Therefore, the volume of a hemisphere with a radius of 44.9 m is approximately 222,232.7 cubic meters.

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The quantity theory of money is an economic theory that suggests a direct relationship between the money supply (M) and the price level (P) in an economy

According to this theory, the equation MV = PY holds, where V represents the income velocity of money and Y represents real output. This equation states that the total value of money spent in an economy (MV) is equal to the total value of goods and services produced (PY).

The quantity theory of money assumes that the velocity of money (V) and real output (Y) are relatively stable over time and that changes in the money supply (M) primarily affect changes in the price level (P). It implies that an increase in the money supply will lead to inflation, as there is more money chasing the same amount of goods and services.

Therefore, the correct answer is "static quantity theory of money," which refers to the idea that the relationship between money, velocity, price level, and real output is static and can be represented by the equation MV = PY.

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The marginal profit if you sell 150 pieces of pie is $1.20 per piece.E. The marginal profit if you sell 150 pieces of pie is the additional profit made by selling one more unit of a good.

Given,The cost to make x servings of apple pie is C(x) = 300+ 0.1x +0.003x².

The price to sell one piece of pie is $4.00.So, the revenue function, R(x) can be written asR(x) = price per unit × number of units soldR(x) = 4x.

The profit function, P(x) is given by the difference between the revenue function and cost function i.e.,P(x) = R(x) - C(x)

Substituting R(x) = 4x and C(x) = 300 + 0.1x + 0.003x² in P(x), we haveP(x) = 4x - (300 + 0.1x + 0.003x²)

P(x) = 4x - 300 - 0.1x - 0.003x²

P(x) = - 0.003x² + 3.9x - 300.

The marginal profit function is given by P'(x) = R'(x) - C'(x).Let's find R'(x) and C'(x).Differentiating R(x) = 4x with respect to x, we getR'(x) = 4Differentiating C(x) = 300 + 0.1x + 0.003x² with respect to x, we getC'(x) = 0.1 + 0.006x.

Substituting R'(x) = 4 and C'(x) = 0.1 + 0.006x in P'(x), we getP'(x) = 4 - (0.1 + 0.006x)P'(x) = 3.9 - 0.006x.

Now, let's find the marginal profit if we sell 150 pieces of pie.

Substituting x = 150 in P'(x), we getP'(150) = 3.9 - 0.006 × 150P'(150) = $1.20 per piece.

The marginal profit if we sell 150 pieces of pie is $1.20 per piece.

The marginal profit is the additional profit made by selling one more unit of a good.So, if we sell one more piece of pie, the profit will increase by $1.20.

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Answer:

\(y-7=-\dfrac{1}{2}(x+3)\)

Step-by-step explanation:

The point-slope formula is:

\(y-y_1=m(x-x_1)\)

where:

The equation of the original line in point-slope form is:

\(y-25=2(x-10)\)

Therefore, the slope of the line is m = 2.

As the slope of a perpendicular line is the negative reciprocal of the slope of the original line, the slope of the perpendicular line is m = -1/2.

To find the point-slope equation of the line that is perpendicular to the given line and passes through point (-3, 7), substitute m = -1/2 and point (-3, 7) into the point-slope formula:

\(\implies y-7=-\dfrac{1}{2}(x-(-3)\)

\(\implies y-7=-\dfrac{1}{2}(x+3)\)

Therefore, the point-slope equation of the line that is perpendicular to y - 25 = 2(x - 10) and passes through (-3, 7) is:

\(\boxed{y-7=-\dfrac{1}{2}(x+3)}\)

Answer:

\( y -7= \dfrac{-1}{2} (x+3)\)

Step-by-step explanation:

The given equation of the line is ,

\(\implies y - 25 = 2(x-10) \\\)

Simplify the RHS by opening the brackets,

\(\implies y - 25 = 2x - 20\\\)

\(\implies y = 2x + 25 - 20 \\\)

\(\implies y = 2x + 5 \\\)

On comparing it with the the slope intercept form of the line, namely y = mx + c , where m is the slope, we have;

\(\implies m = 2\\\)

Again as we know that the product of slopes of two perpendicular lines is -1 , Hence,

\( \implies m\cdot m_{\perp} = 2 \\ \)

\(\implies m_{\perp} =\dfrac{-1}{2} \\\)

Now the point given to us is (-3,7) , the point slope form of the line is ,

\(\implies y - y_1 = m(x-x_1) \\\)

where ,

On substituting the respective values, we have;

\(\implies y - 7 = \dfrac{-1}{2} \{ x -(-3)\}\\\)

Simplify,

\(\implies \underline{\underline{ y - 7 =\dfrac{-1}{2}(x+3)}}\\\)

This is the required answer in point slope form .

Answer:

7/4

Step-by-step explanation:

i am sooo sure that  the answer is 1.75

The critical points of the function f(x) are found where f'(x) = 0 or f'(x) is undefined. At these points, the function may have local maxima or minima.

To find the critical points of a function f(x), we need to find where the derivative f'(x) equals zero or is undefined. These points are potential candidates for local maxima or minima. At a critical point, the derivative either changes sign or is zero.

To determine if it is a maximum or minimum, we can use the second derivative test or analyze the behavior of the function around the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, further analysis is needed.

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The statement ' if this model suffers from heteroskedasticity, then the usual OLS t statistics no longer have a t distribution and the f statistics no longer have an f distribution' is true because a model suffering from heteroskedasticity will not be accurate.

If a model suffers from heteroskedasticity, which is the condition where the variance of the errors is not constant across observations, then the usual OLS t statistics and F statistics no longer have t or F distributions, respectively. In other words, the standard errors of the coefficients and the overall fit of the model cannot be accurately estimated using the usual assumptions of OLS regression.

Specifically, when heteroskedasticity exists, the OLS estimator remains unbiased, consistent, and asymptotically normal, but its estimated standard errors are biased and inconsistent, leading to invalid inference. This means that t-tests for individual coefficients and F-tests for overall model significance based on these standard errors may be unreliable.

Instead, alternative methods such as robust standard errors or weighted least squares should be used to correct for heteroskedasticity.

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Answer:

y = 60°

Step-by-step explanation:

The tangent- chord angle y is half the measure of its intercepted arc , then

y = \(\frac{1}{2}\) × 120° = 60°

The value of y is 60 °

Given , the angle is 120°

Now apply the  tangent- chord angle theorem, " a chord meeting at the point of tangency is half the measure of the intercepted "

y = 1/2 × 120°

y = 1/2 × 120° = 60°

Therefore, the value of angle y is 60°.

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The general equation of a given circle is \(x^{2} +y^{2} +2x+6y+9=0\)

Given a plot of the circle in the X-Y plane, The center of circle has the coordinates  ( -1, -1) and the circle is passing through (-1 ,-4) and (-1 ,-2)  and  (-1 ,-4)  , (-1 ,-2)   are coordinates of diametrically opposite ends of circle

If there are two points on a circle (x₁, y₁) and (x₂, y₂) that are at opposite ends of the same diameter, then the circle's equation can be written as

(x-x₁)(x-x₂)+(y-y₁)(y-y₂)=0

Given x₁= -1 , x₂ = -1  ,  y₁= -4 , y₂= -2

The circle's equation can be written as ( x+1)(x+1) + (y+4)(y+2)

⇒\(x^{2} +1+2x+y^{2} +6y+8=0\)

⇒\(x^{2} +y^{2} +2x+6y+9=0\)

Therefore, \(x^{2} +y^{2} +2x+6y+9=0\) is the general equation of circle.

Hence,The general equation of a given circle is \(x^{2} +y^{2} +2x+6y+9=0\)

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Answer:

34

Step-by-step explanation:

Substitute the values.

s = 3 and t = -2

8s-5t

8 (3) - 5(-2)

( 8 x 3 ) - ( 5 x -2 )

24 + 10 [ - x - = + ]

= 34

Answer:

I put in a screenshot on what the graph would look like (i used desmos)

Step-by-step explanation:

Ok, you have the equation y=3-4x. This can be broken down into the y=mx+b format. -4 would be the m, and since m is the slope -4 would be the slope of your line. 3 would be your b- your y-intercept. Basically at (0,3) your line crosses the y-axis.

I hope this helps :)

5 yellow tiles should be removed.

The original ratio of red tiles to yellow tiles as per the question :Ratio = 6:15. Now, after removal of red tiles, the numerator of ratio will become = 6 - 2. The numerator of new ratio will be 4. For yellow tiles, let the number of yellow tiles removed be x. So, the denominator or new number of yellow tiles will be 15 - x.

Now, relating the two ratio -

6:15 = 4:(15 - x)

Performing cross-multiplication to find the value of x.

6 × (15 - x) = 4 × 15

Performing multiplication on both the Left Hand Side and Right Hand Side

90 - 6x = 60

6x = 90 - 60

Performing subtraction to find the value of x

6x = 30

x = \(\frac{30}{6}\)

Performing division to find the value of x

x = 5

So, the number of yellow tiles to be removed is 5.

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The complete question is -

A bag contains 6 red tiles and 15 yellow tiles. Lilia removes 2 red tiles. How many yellow tiles should she remove so that the ratio of red tiles to yellow tiles in the bag stays equivalent to 6 : 15?

Answer:

1/6 yards

Step-by-step explanation:

Pipes available = 4/6 yards

Pipes used = 1/2 yards

Pipes left = total pipes bought - she doesn't suit that way

Pipes left = Total pipes available - pipes used

= 4/6 yards - 1/2 Yards

= 4-3/6

= 1/6 yards

Pipes left = 1/6 yards

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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Answer:       Look down bellow

Step-by-step explanation:

Hope that helped