what is the mesaure of angle a

Answer:

There were 5 phones sold and 10 accessories sold.

Step-by-step explanation:

Answer:

\(2x + 15 = \frac{x}{2} - 3\)

Move the variable

\(4x + 30 = x - 6\)

\(4x - x + 30 = - 6\)

Collect like terms

\(4x - x = - 6 - 30\)

\(3x = - 6 - 30\)

\(3x = - 36\)

Divide both sides by three

\(x = - 12\)

Answer:

The area is 13 feet squared.

Step-by-step explanation:

To find the area, first separate the composite figure into two shapes: a rectangle and a triangle.

Find the area of each shape separately, and then add the areas together.

First, the rectangle:

length= 4.5 feet

width = 2 feet

\(2*4.5=9 ft^{2}\)

The area of the rectangle is 9 feet squared.

Next, the triangle:

The base is 2 feet + 1 foot + 1 foot = 4 feet

The height is 6.5 feet - 4.5 feet = 2 feet

The formula to find the area of a triangle is \(\frac{h*b}{2}\) (height times base over two)

\(\frac{2*4}{2}=4ft^{2}\)

the area of the triangle is 4 feet squared.

Add the two areas together to find the total area of the composite figure:

\(9ft^{2} +4ft^{2}=13ft^{2}\)

The area is 13 feet squared.

The slope and the y-intercept of the line y = 4x + 5 are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is given as follows:

y = 4x + 5.

Hence the slope and the intercept are given as follows:

The problem asks for the slope and the intercept of y = 4x + 5.

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Answer:

C

Step-by-step explanation:

Answer:

Answer is B

Step-by-step explanation:

7y+21=5y+8

2y=-13

y= -6.5

Answer:

mx+b+a= x-12x=0.88x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Your equation makes no sense.

I will ASSUME you mean

y = -x² - 2x + 3

which can be factored

y = (x + 3)(-x + 1)

x intercepts occur when y = 0

0 = (x + 3)(-x + 1)

which means either

x + 3 = 0

x = -3

or

-x + 1 = 0

x = 1

x intercepts are (-3, 0) and (1, 0)

The vertex will occur halfway between these point

x = (-3 + 1) / 2 = -1

so vertex = y = -(-1)² - 2(-1) + 3 = 4

(-1, 4)

The range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

The range of function g depends on the range of the function f.

Let's start by assuming that we know the range of f.

If the range of f is Rf, then the range of -2f is the set {-2y | y ∈ Rf}, which is just the set of all numbers that can be obtained by multiplying an element of Rf by -2.

Finally, we add 1 to each of these values to get the range of g. Therefore, the range of g is:

Rg = {1 - 2y | y ∈ Rf}

In other words, the range of g is obtained by taking the range of f, multiplying each element by -2, and adding 1 to each result.

If we don't know the range of f, we can still say something about the range of g. Specifically, we know that g(x) can never be greater than 1 (since the largest value that -2f(x) can take is 0, and adding 1 to 0 gives us 1), and g(x) can never be less than 1 - 2M, where M is the largest possible value that f(x) can take on. In other words, the range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

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Answer:

C

Step-by-step explanation:

5 x -6=-30

-30 x -2=60

Answer:

2

Step-by-step explanation:

6 shelves x 8 books = 48 books

Answer:

y = | x | - 2

Explanation:

If we have a function g(x) = f(x) + c, we can say that g(x) is a translation of c units up or down of f(x)

If c is negative, the translation is c units down.

Therefore, the translation of 2 units down of the graph y = | x | is:

y = | x | - 2

Answer:

\((a)\ V = \{(N,30),(R,37),(S,17)\}\)

\((b)\)

\(Domain = \{N,R,S\}\)

\(Range = \{37,30,17\}\)

Step-by-step explanation:

Given

\(V(R) = 37,\ V(N) = 30,\ V(S) = 17\)

Solving (a): Set of ordered pair

A function y = f(x) is represented as (x,y)

So, the ordered pair of V is:

\(V = \{(R,37),(N,30),(S,17)\}\)

Order the alphabets in increasing order

\(V = \{(N,30),(R,37),(S,17)\}\)

Solving (b): The domain and the range

In a function \(\{(x_1,y_1),...,(x_n,y_n)\}\)

The domain and the range are represented as:

\(Domain = \{x_1,x_2....x_n\}\)

\(Range = \{y_1,y_2....y_n\}\)

So, we have:

\(Domain = \{N,R,S\}\)

\(Range = \{37,30,17\}\)

Answer:

C. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

hope i helped

Answer:

Look down

Step-by-step explanation:

Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.

Answer:

x< -12

Step-by-step explanation:

-1/2x>6
x-2.   x-2

x>-12

Since we multiply by we negative we flip the sign

x< -12

Hopes this helps

Answer:

The graph has a y- intercept at(0,1) and is decreasing over the interval -infinity <x< infinity

Step-by-step explanation:

Trust me

To graph the function f(x) = -3x + 2, we can plot some points and then connect them to form a straight line.

Here are a few points you can use to plot the graph:

1. When x = 0, f(0) = -3(0) + 2 = 2. So, the point (0, 2) is on the graph.

2. When x = 1, f(1) = -3(1) + 2 = -1. So, the point (1, -1) is on the graph.

3. When x = -1, f(-1) = -3(-1) + 2 = 5. So, the point (-1, 5) is on the graph.

Plot these points on a coordinate plane and then draw a straight line passing through them. The graph should be a straight line sloping downwards from left to right.

Key features of the graph:

1. Slope: The slope of the line is -3, which means it goes down 3 units for every 1 unit it moves to the right.

2. Y-intercept: The y-intercept is the point where the graph crosses the y-axis. In this case, the y-intercept is 2, as the graph passes through the point (0, 2).

3. X-intercept: The x-intercept is the point where the graph crosses the x-axis. To find the x-intercept, set f(x) = 0 and solve for x:

0 = -3x + 2

3x = 2

x = 2/3. So, the x-intercept is approximately (2/3, 0).

4. Linearity: The graph is a straight line, indicating that the function is a linear function.

5. Decreasing: The graph decreases as you move from left to right, indicating that the function is a decreasing function.

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Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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Answer:

-0.756

Step-by-step explanation:

N1 = 9

N2 = 9

Sd1 = 1.5 hours

Sd2 = 1.3 hours

X1 = 5 hours

X2 = 5.5 hours

Hypothesis

H0: mu1 - mu2 = 0

H1 : mu1 - mu2 not equal to 0

Test statistic

t = (x1 - x2)/SE

SE is the standard error, which is unknown

SE = √sd1²/n1 + sd2²/n2

= √1.5²/9 + 1.3²/9

= √0.25+0.1878

= √0.4378

= 0.66166

t statistics = (5-5.5)/0.66166

= -0.5/0.66166

= -0.756

The value of x in the similar triangle is 6 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the similarity ratio to find the value of x in the similar triangle as follows:

Hence,

5 / 40 = x / 48

48 × 5 = 40x

240 = 40x

divide both sides by 40

x = 240 / 40

x = 6

Therefore,

x = 6

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Answer:

Step-by-step explanation:

Let's use a system of equations to solve for the cost of each type of dinner.

Let x be the cost of ribeye steak dinners and y be the cost of grilled salmon dinners.

From the first day's sales, we can write:

13x + 12y = 592.87

And from the second day's sales, we can write:

18x + 6y = 580.21

We now have two equations with two variables. We can solve for one variable in terms of the other in either equation, and then substitute that expression into the other equation to solve for the remaining variable.

Solving the first equation for y, we get:

y = (592.87 - 13x) / 12

Substituting this expression into the second equation, we get:

18x + 6[(592.87 - 13x) / 12] = 580.21

Simplifying and solving for x, we get:

x = 28.95

Substituting this value of x back into the first equation to solve for y, we get:

y = 23.56

Therefore, the cost of ribeye steak dinners is $28.95 and the cost of grilled salmon dinners is $23.56.

The temperature drops by \(31\°C\) from day to night in this city.

To calculate the temperature drop from day to night in \(\°C\), we subtract the average nightly low temperature from the average daily high temperature.

Given:

Average nightly low temperature: \(-40\°C\)

Average daily high temperature: \(-9\°C\)

The temperature drop can be calculated as:

Temperature drop = Average daily high temperature - Average nightly low temperature

Substituting the given values:

Temperature drop = \(-9\°C - (-40\°C)\)

Simplifying the equation:

Temperature drop = \(-9\°C + 40\°C\)

Temperature drop = \(31\°C\)

The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.

Therefore, the temperature drops by \(31\°C\) from day to night in this city.

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===================================================

Explanations:

Use a marker/pen of a different color to highlight angle ABC so its easier to see. Check out the diagram below. The only ray in the interior of this angle is ray BD.  The bisector must always be in the interior. The angle markers for angle ABD and DBC are the same indicating they are the same measure; therefore, ray BD bisects angle ABC.

------------------------

Segments IG and GH are the same length because they share the same single tickmark. Their lengths are shown as 3x and 5x-10. Set the algebraic expressions equal to one another. Solve for x. Then use this x value to find GH

IG = GH

3x = 5x-10

3x-5x = -10

-2x = -10

x = -10/(-2)

x = 5

GH = 5x-10

GH = 5*5-10

GH = 25-10

GH = 15

note that IG = 3x = 3*5 = 15 as well

ANSWER:

The total surface area is 450 mm^2

STEP-BY-STEP EXPLANATION:

We have a pyramid with a triangular base, which the formula to calculate the total surface area is the following

Replacing:

The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.

To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.

Algorithm/Abstract Strategy:

Start with the numerator, which is 3.

Identify the denominator, which is 5.

Interpret the fraction as a ratio or comparison between the numerator and denominator.

Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).

Perform the division: 3 ÷ 5.

Simplify the division to its simplest form, if necessary.

The result of the division, in this case, is the decimal representation of the fraction.

If required, convert the decimal representation to a percentage or any other desired form.

For example, if we perform the division 3 ÷ 5, the result is 0.6.

So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.

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The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.

The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.

By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.

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Answer:

0.721

Step-by-step explanation:

the last digit (the number '1') must be in the thousandths place; then work backward so the '2' would be in the hundredths and the '7' would be in the 'tenths'

Answer:

y = 1/2x - 4

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = -2x + 8. Its slope is -2. A line perpendicular to this one will  have a slope of 1/2.

Plug this value (1/2) into your standard point-slope equation of y = mx + b.

y = 1/2x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (4, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 1/2(4) + b

To find b, multiply the slope and the input of x (4)

-2 = 2 + b

Now, subtract 2 from both sides to isolate b.

-4 = b

Plug this into your standard equation.

y = 1/2x - 4

This equation is perpendicular to your given equation (y = -2x + 8) and contains point (4, -2)

Hope this helps!

9514 1404 393

Answer:

  y = 1/2x -4

Step-by-step explanation:

We presume the given line is ...

  y = -2x +8

This is in slope-intercept form, which allows us to determine easily that the slope of this line is -2.

A perpendicular line will have a slope that is the opposite reciprocal of -2:

  m = -1/(-2) = 1/2

The y-intercept of the desired line can be found from the point (x, y) = (4, -2) using the equation ...

  b = y - mx

  b = -2 -(1/2)(4) = -4

Now, we know the slope and y-intercept of the desired perpendicular line through (4, -2), so we can write its equation as ...

  y = 1/2x -4

__

Additional comment

"Slope-intercept form" is ...

  y = mx + b . . . . . . where m is the slope and b is the y-intercept

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Answer:

Step-by-step explanation:

Confidence coefficient is also the confidence level. A confidence coefficient of 0.95 is the same as a confidence level of 95%.

Confidence level is used to express how confident we are that the population mean lies within the calculated confidence interval. It expresses the possibility of getting the same result if tests are repeated. Since the study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95, then the true statement is

G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.