Look at the figure. What is the next step in this construction of a line parallel to AC passing through point B.
A. use a protractor to measure ∠BAC
B. Draw a line through point B that intersects arc 2.
C. Measure the distance between AB and AC along arc 1 with a ruler.
D. Measure the distance between AB and AC along arc 1 with a compass.
Answers
Answer:
Option A is correct
Step-by-step explanation:
In the given figure to draw the parallel line to AC passing through B we have to tell the next step.
As lines AC and AB given and we know if lines are parallel then alternate angles are equal.
Hence, if line through B parallel to AC drawn then alternate angles ∠BAC and ∠ABD equal.
∴ To draw parallel lines our next step is to use a protractor to measure ∠BAC so that the same angle through B is drawn results in equal alternate interior angles.
Hence, Option A is correct.
Related Questions
Similar question to the last, just a bit more difficult
-8x-10y=24
6x+5y=2
solve for (x.y)
no clue on this one though
Answers
12x+10y=4
4x=28
x=7
6(7)+5y=2
42+5y=2
5y=-40
y=-8
Final answer: (7,-8)
Please Help. Thank you
Answers
The graphs of functions f(x) and g(x) = f(x) + k are shown below:
graph of line f of x going through ordered pairs 0, 0 and 2, 4. Graph of line g of x going through ordered pairs 0, 2 and 1.5, 5.
The value of k is ___.
Answers
[tex] m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1} } [/tex]
gives us a slope equation of:
[tex]m= \frac{4-0}{2-0} [/tex] and the slope is 2. Using the point (0, 0) to write the equation of the line for f(x) looks like this in the slope-intercept form of the equation:
[tex]y- y_{1} =m(x- x_{1}) [/tex] where m is the sloppe of 2 that we found and [tex] y_{1} [/tex] and [tex] x_{1} [/tex] are the coordinates of one of the points. It doesn't matter which one you choose; you will get the same answer whether you use (0, 0) or (2, 4): y-0=2(x-0) Distributing that 2 into the parenthesis and simplifying gives you the equation of y = 2x, or in our function notation, f(x) = 2x. Since f(x) is the first part of g(x), so far for g(x) we have that g(x) = 2x + k. Now we will do the same thing for g(x) that we did for f(x) as far as writing its equation down; we don't need to find the slope cuz the slope of g(x) is the function f(x). The equation for g(x), using the point (0, 2) (again, you could have used either point; I just picked (0, 2) cuz the other one has a decimal in it!): y - 2 = 2(x - 0). Distributing that 2 into the parenthesis gives you this: y - 2 = 2x - 0; y = 2x + 2. So 2 is your k value!
A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even? Write a system of equations to represent the situation, then solve.
Answers
Using linear functions, it is found that the store must sell 40 bicycles each month to break even.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.A bicycle store costs $2400 per month to operate, and pays an average of $60 per bike, hence the cost function is given by:
C(x) = 2400 + 60x
The average selling price of each bicycle is $120, hence the revenue function is given by:
R(x) = 120x
It breaks even when cost equals revenue, hence:
R(x) = C(x)
120x = 2400 + 60x
60x = 2400
x = 240/6
x = 40.
The store must sell 40 bicycles each month to break even.
More can be learned about linear functions at https://brainly.com/question/24808124
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To determine the number of bicycles the store must sell each month to break even, we can set up a system of equations. The store must sell 40 bicycles each month to break even.
Explanation:To determine the number of bicycles the store must sell each month to break even, we can set up a system of equations.
Let's say the number of bicycles sold per month is x.
The monthly operating cost of the store is $2400.
The cost of producing each bike is $60, so the total cost to produce x bikes would be $60x.
The average selling price of each bike is $120, so the total revenue from selling x bikes would be $120x.
To break even, the total revenue should equal the total cost, so we can set up the equation:
$120x = $60x + $2400
Simplifying the equation, we get:
$60x = $2400
Dividing both sides by $60, we find:
x = 40
Therefore, the store must sell 40 bicycles each month to break even.
Find the area of an equilateral triangle with radius 22 cm. Round to the nearest whole number.
629 cm2
363 cm2
982 cm2
1257 cm2
Answers
This measurement of the radius is the hypotenuse of the 30°-60°-90° triangle formed with the half the measurement of the side of the equilateral triangle being opposite to the 60° and equal to the hypotenuse times (1/2)(√3)
If we let s be the side of the triangle then,
s/2 = r(1/2)(√3)
Multiplying the equation by 2,
s = r√3
Substituting,
s = (22 cm)(√3) = 22√3
The area of the equilateral triangle is computed through the equation,
A = (√3 / 4)(s²)
Substituting,
A = (√3 / 4)(22√3)² = 628.7 cm²
Therefore, the answer to this item is the first choice.
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
SAS
ASA
AAS
None
Answers
The simpliest way is to use the AAS Postulate.
AAS Postulate: If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
From the diagram you have:
1. one pair of angles with measure 40°;
2. one pair of angles with measure 60°;
3. the non-included side of one triangle is congruent to the non-included side of another triangle (their lengths are 10).
Answer: correct choice is D (AAS)
Answer:
AAS postulate :)
Step-by-step explanation:
Best explained and correct answer gets brainliest.
Answers
total = 2372* (1+0.045)^20=
2372*1.045^20=
2372 * 2.411714025= 5720.585
she will have 5720.59 in 20 years
Use synthetic division to find P(–2) for P(x) = x4 + 9x3 - 9x + 2 .
A. –2
B. –36
C. 0
D. 68
Answers
P(x) = x⁴ + 9x³ - 9x + 2
substitute -2 in x such as:
P (-2) = (-2)⁴ + 9(-2)³ - 9(-2) + 2
P(-2) = 16 - 72 + 18+ 2
P (-2) = -36
The answer is - 36 which is the letter B in the choices.
-36 is the correct answer
Leonardo da vinci's mona lisa is 21 inches wide and 30.25 inches tall. what is the area of the painting in square centimeters?
Answers
lenght =30.25×2.5=75.625cm
width = 21×2.5=52.5cm
area of painting = 75.625×52.5=3970.3125cm²
Final answer:
To find the area of the Mona Lisa in square centimeters, multiply the width and height in inches, then convert to square centimeters using the conversion factor. The area is approximately 4098.97 square centimeters.
Explanation:
To calculate the area of Leonardo da Vinci's Mona Lisa in square centimeters, we start with the given measurements in inches: the painting is 21 inches wide and 30.25 inches tall. Since the area is width multiplied by height, we perform the following calculation:
Area in square inches = width in inches × height in inches
Area in square inches = 21 × 30.25
Area in square inches = 635.25
To convert square inches to square centimeters, we use the conversion factor where 1 square inch = 6.4516 square centimeters.
Area in square centimeters = Area in square inches × 6.4516
Area in square centimeters = 635.25 × 6.4516
Area in square centimeters = 4098.97
Therefore, the area of the Mona Lisa is approximately 4098.97 square centimeters.
The bulldog soccer team wants to increase the size of its
Practice field by a scale factor of 1.5. The field is a rectangle that currently measures 30 ft by 80 ft. The measurements of the new practice field should be 45 ft by ft.
Answers
multiply 80 by 1.5
80*1.5 = 120 feet
Four graphs are shown below:
Which graph best shows the line of best fit?
Graph A
Graph B
Graph C
Graph D
Answers
Which of the following is an extraneous solution of sqrt(-3x-2)=x+2 a.-6 b.-1 c.1 d.6
Answers
for example a, x - 6 is not extraneous because
left side = sqrt (-3*-6 - 2) == sqrt16 = 4 or -4
right side = -6 + 2 = -4
so x = -6 is not extraneous
Answer:
- 6 is the extraneous solution.
Step-by-step explanation:
Given : [tex]\sqrt{-3x -2} = x + 2[/tex].
To find : Which of the following is an extraneous solution .
Solution : We have given that [tex]\sqrt{-3x -2} = x + 2[/tex].
Taking square both sides
-3x - 2 = [tex](x+2)^{2}[/tex].
On applying identity [tex](a+b)^{2}[/tex] = a² + b² + 2ab
Then ,
-3x -2 = x² + 2² + 2 * 2 *x
-3x -2 = x² + 4 + 4x.
On adding both sides by 3x
-2 = x² + 4 + 4x + 3x
-2 = x² + 4 + 7x
On adding both sides by 2
0 = x² + 4 + 7x + 2
On switching sides
x² +7x + 6 = 0
On Factoring
x² +6x + x + 6 = 0
x ( x+ 6 ) +1 (x +6 ) = 0
On grouping
( x +1) ( x +6) = 0
x = -1, -6.
Let check for x = -6
[tex]\sqrt{-3 (-6) -2} = -6 + 2[/tex].
4 = -4
An extraneous solution is a root of a transformed equation that is not a root of the original equation.
Therefore, -6 is the extraneous solution.
Jerome bought 15 videos from a department store. Some videos were new releases, x, which cost $19, and some videos were classics, y, which cost $8. He spent a total of $164 on the videos. Which system of equations is set up correctly to model this information?
Answers
Answer:
The system of equations is
[tex]x+y=15[/tex]
[tex]19x+8y=164[/tex]
Step-by-step explanation:
Let
x------> the number of videos of new releases
y-----> the number of classics videos
we know that
[tex]x+y=15[/tex] ------> equation A
[tex]19x+8y=164[/tex] ------> equation B
Using a graphing tool
Solve the system of equations
Remember that the solution of the system of equations is the intersection point both graphs
The intersection point is [tex](4,11)[/tex]
see the attached figure
therefore
the number of videos of new releases is [tex]4[/tex]
the number of classics videos is [tex]11[/tex]
Answer:
Jerome bought 15 videos from a department store. Some videos were new releases, x, which cost $19, and some videos were classics, y, which cost $8. He spent a total of $164 on the videos. Which system of equations is set up correctly to model this information?
x + y = 15. 19 x + 8 y = 164.
x + y = 15. 8 x + 19 y = 164.
x + y = 164. 19 x + 8 y = 15.
x + y = 15. 19 x minus 8 y = 164.
ANSWER IS A
The path of a ping pong ball that is hit from one end of the table can be modeled by the equation (y= -1/4 x^2 5x) where x is measured in inches and represents the horizontal distance from the edge of the table, and y represents the height of the ping pong ball in inches above the table. What is the maximum height of the ping pong ball?
A.
The ball reaches a maximum height of 30 inches above the table.
B.
The ball reaches a maximum height of 20 inches above the table.
C.
The ball reaches a maximum height of 25 inches above the table.
D.
The ball reaches a maximum height of 27 inches above the table.
Answers
To find the maximum height, you must solve this equation through differential calculus. To find the maxima or minima, you differentiate the equation y in terms of x and equate it to zero.
y' = 2(-1/4)x + 5 = -1/2*x + 5 = 0
By doing this, you would solve the value of x or the horizontal distance.
-1/2*x = -5
x =-5*-2
x = 10 inches
Finally, we substitute this x to the original equation to determine the maximum height y.
y = -1/4*10 + 5(10)
y = 25 inches
The answer is C.
The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let t = 0 be 12:00 am. Which periodic function, sine or cosine, would be a simpler model for the situation? Explain.
Answers
Answer: A cosine function would be a simpler model for the situation.
The minimum depth (low tide) occurs at
t = 0. A reflection of the cosine curve also has a minimum at t = 0.
A sine model would require a phase shift, while a cosine model does not.
Step-by-step explanation:
Using a cosine function is simpler to model the tide changes because it starts at the maximum value, aligning with the high tide occurrence.
The depth of the water at the end of a pier changes periodically due to tides. Given that low tides occur at 12:00 am and 12:30 pm with a depth of 2.5 m, and high tides occur at 6:15 am and 6:45 pm with a depth of 5.5 m, we need to model this situation with a periodic function.
Let's align this with a cosine function for simplicity. In general, the cosine function can be modeled as y = A cos(B(t - C)) + D, where:
A is the amplitude (half of the difference between high tide and low tide depth, (5.5 m - 2.5 m)/2 = 1.5 m)B determines the period (a full tide cycle is roughly 12 hours and 25 minutes or 747.5 minutes; B = 2π/747.5)C is the horizontal shift (shift corresponding to the time of the first high tide, 6.25 hours or 375 minutes, so C = 375)D is the midline of the function (average depth, (5.5 m + 2.5 m)/2 = 4 m)Therefore, the function becomes: y(t) = 1.5 cos((2π/747.5)(t - 375)) + 4. Using a cosine function is simpler because it starts at the maximum value, which corresponds to the high tide.
What is the area of the obtuse triangle given below?
Answers
A = 1/2 * 11 * 7 = 38.5
your answer is D
hope that helps :)
Answer:
Option (d) is correct.
The area of triangle is 38.5 square units
Step-by-step explanation:
Given: An obtuse triangle.
We have to find the area of this obtuse angle.
Consider the given obtuse triangle
Area of triangle = [tex]\frac{1}{2}\cdot b \cdot h[/tex]
where b = Base
h = height
Given : base = 11 units
and height = 7 units
Thus, Area of triangle = [tex]\frac{1}{2}\cdot 11 \cdot 7[/tex]
Simplify, we have,
Area of triangle = 38.5
Thus, The area of triangle is 38.5 square units
What number should be added to both sides of the equation to complete the square? x^2 â 10x = 7?
Answers
Basically, the p value should be half of b and the square root of c.
Question 1- Heather wanted to find the density of a solution with a mass of 2.234
grams and a volume of 2.131 milliliters. She uses the density formula,
density = mass/volume.
If both her mass and volume were accurately measured to the thousandths place what is an accurate value for the density measured in g/mL?
Question 2- Coleton measures the sides of a rectangular piece of plywood. One
side is 72.6 inches long, and the shorter side is 36 inches long. What is the area of
the piece of plywood, rounded appropriately using significant figures?
Question 3- When would you want to use the median over the mean for
describing the measure of center for a data set?
Answers
D = M/V
D = 2.234 grams/ 2.131 milliliters
D = 1.048 grams / milliliters or 1.048 g/mL
For Question 2, you are given a rectangular piece of plywood with one
side 72.6 inches long, and the shorter side is 36 inches long. You are asked to find the area of the piece of plywood. The area of the rectangle is A = LW where A is the area, L is the length and W is the width.
A = LW
A = 72.6 inches x 36 inches
A = 2,610 in²
What is the distance between the points (22, 27) and (2, -10)? if necessary, round your answer to two decimal places.a. 57 units?
Answers
(22,27)....x1 = 22 and y1 = 27
(2,-10)....x2 = 2 and y2 = -10
now we sub
d = sqrt (2 - 22)^2 + (-10 -27)^2)
d = sqrt (-20^2) + (-37^2)
d = sqrt (400 + 1369)
d = sqrt 1769
d = 42.06 <==
Answer:
42.06
Step-by-step explanation:
Two points (22,27) and (2,-10)
using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So, distance between (22,27) and (2,-10) is D
[tex]D=\sqrt{(22-2)^2+(27-(-10))^2}[/tex]
[tex]D=\sqrt{(20)^2+(37)^2}[/tex]
[tex]D=\sqrt{400+1369}[/tex]
[tex]D=\sqrt{1769}[/tex]
[tex]D=42.059[/tex]
Round off two decimal place.
[tex]D=42.06[/tex]
Hence, The distance between the points is 42.06
Dominique is thinking about buying a house. The table below shows the projected value of two different houses for three years.
House 1 (value in dollars) year 1: 286,000 year 2: 294,580 year 3: 303,417.40 House 2 (value in dollars) year 1: 286,000 year 2: 295,000 year 3: 304,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer.
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years.
Part C: Dominique wants to purchase a house that would have the greatest value in 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years.
Answers
The functions for House 1 and House 2 are [tex]\(f_1(x) = 5079.6x + 248900.4\)[/tex] and [tex]\(f_2(x) = 4666.\overline{66}x + 256000\)[/tex] respectively.
After 45 years, House 1 will be valued at $477,555, and House 2 will be valued at $465,000.
Here's the step-by-step solution with complete calculations for the given problem:
Part A: Identifying the Function Type
- House 1:
- Year 1 to Year 2: [tex]\(259,059.60 - 253,980 = 5,079.60\)[/tex]
- Year 2 to Year 3: [tex]\(264,240.79 - 259,059.60 = 5,181.19\)[/tex]
- House 2:
- Year 1 to Year 2: [tex]\(263,000 - 256,000 = 7,000\)[/tex]
- Year 2 to Year 3: [tex]\(270,000 - 263,000 = 7,000\)[/tex]
The functions are linear because the changes are constant for House 2 and almost constant for House 1.
Part B: Formulating the Equations
- House 1 Equation:
- Slope (m): [tex]\(5079.6\)[/tex]
- Y-intercept (c): [tex]\(248900.4\)[/tex]
- Equation: [tex]\(f_1(x) = 5079.6x + 248900.4\)[/tex]
- House 2 Equation:
- Slope (m): [tex]\(4666.\overline{66}\)[/tex]
- Y-intercept (c): [tex]\(256000\)[/tex]
- Equation: [tex]\(f_2(x) = 4666.\overline{66}x + 256000\)[/tex]
Part C: Calculating Future Values
- House 1 Value at Year 45:
[tex]- \(f_1(45) = 5079.6 \times 45 + 248900.4 = 477555\)[/tex]
- House 2 Value at Year 45:
[tex]- \(f_2(45) = 4666.\overline{66} \times 45 + 256000 = 465000\)[/tex]
These equations predict the values of the houses after 45 years based on the given data. House 1 will be valued at $477,555, and House 2 will be valued at $465,000.
Which ordered pair is a solution to the system of inequalities? y <3 and y >-x+5 ?
A. (6,1)
B. (2,1)
C. (3,0)
D. (-2,4)
PS. for the equation y>-x+5, the sign should be greater than or equal to. I just can't find the key on my phone (>)
Answers
Simplify fraction 23076923076923/10000000000000
Answers
Which are the solutions of the quadratic equation? x2 = –5x – 3 –5, 0 5, 0
Answers
The solution of the given quadratic equation will be ( -5, 0 ).
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Given equation is:-
x² = -5x
x² + 5x = 0
x ( x + 5 ) = 0
x = 0 and x = -5
Therefore the solution of the given quadratic equation will be ( -5, 0 ).
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The solutions to the quadratic equation [tex]\(x^2 = -5x - 3\)[/tex] can be calculated after modifying the quadratic equation and rewriting it to [tex]x^{2} + 5x + 3 = 0[/tex], and then this can be calculated using the quadratic formula. The solutions are x =[tex]\frac{{-5 + \sqrt{13}}}{2}[/tex]and x =[tex]\frac{{-5 - \sqrt{13}}}{2}[/tex] .
To find the solutions to the quadratic equation [tex]\(x^2 = -5x - 3\)[/tex], let's first rewrite it in the standard form:
[tex]\[x^2 + 5x + 3 = 0\][/tex]
Now, we can use the quadratic formula to find the solutions:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
Where a = 1,,b = 5, and c=3.
[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 1 \cdot 3}}}}{{2 \cdot 1}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 12}}}}{2}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{13}}}{2}\][/tex]
So, the solutions are:
x =[tex]\frac{{-5 + \sqrt{13}}}{2}[/tex] and [x = [tex]\frac{{-5 - \sqrt{13}}}{2}[/tex]
Write a variable expression for 9 more than a number s.
Answers
More than suggests addition.
What is the range of the function given in the graph in interval notation.
[-4,8]
(-4,3)U(3,8]
(-4,8]
[-4,3)U(3,8)
Answers
Now, the domain and range of a given function is basically the coverage of their x and y values that are part of the solution. If the point is along the solid lines and points, the domain or range is expressed either in [ or ], depending where it starts and ends. If the point is along the hollow lines and points, the domain or range is expressed either in ( or ), depending where it starts and ends. The ∪ symbol is added to connect domains and ranges through discontinuities.
Looking at the leftmost line, it starts from the hollow point (-7,-4) and ends on the solid point (-3,3). The range for this part is expressed as (-4,3]. Looking the rightmost line, it starts from the hollow point (-1,-3) and ends at the solid point (2,-8). The range for this part is expressed as (3,8]. Connecting the two ranges, the answer would be (-4,3)U(3,8].
Write an expression for m∠ RST
3x – 9
6x – 18
1.5x – 4.5
6x – 9
This is duplicate version of the question i forgot to add a picture to it
Answers
so mRST = 2 (3x - 9)
= 6x - 18
Final answer:
The expressions provided are different forms of similar linear expressions, which could potentially describe the measure of angle RST if related algebraically or geometrically. The expression for m∠ RST is 6x - 9
Explanation:
Calculating the measure of angle RST involves understanding that the angles around a point add up to 360°, and the angles on a straight line add up to 180°. Based on the provided expressions, we are likely looking for the expression that adheres to these geometric rules.
The expressions given are: 3x – 9, 6x – 18, 1.5x – 4.5, and 6x – 9. To determine which one correctly represents the measure of angle RST, we would need some context from the problem or a diagram. However, assuming a relationship between the expressions and angle RST using linear or angular sums, we can observe that the expressions 3x – 9 and 6x – 18 are equivalent (by factoring out a 2 from the second expression), and similarly, 1.5x – 4.5 is equivalent to 3x – 9 upon multiplying by 2. The expression 6x – 9 could also be related if RST formed a linear pair with another given angle.
Given the information below, find the coordinates of the vertices L and P such that ABCD=NLPM. A(2,0), B(2,4,), C(-2,4), D(-2,0), M(4,0), N(12,0)
Answers
From the drawing it is clear that ABCD is a square with side length 4 units.
ABCD and NLPM are similar, and the side MN is 8 units. This means that NLPM is a square of side length 8 units.
The order of the letters is important, which means, after M comes N then comes L. With this in mind, there are 2 models we can draw, as drawn in the picture:
I) L(12, 8), P(4, 8)
II) L(12, -8), P(4, -8)
Answer: L(12, 8), P(4, 8) or L(12, -8), P(4, -8)
Answer:
Its B I just took the test
The GCD(a, b) = 18, LCM(a, b) = 108. If a=36, find b.
Answers
xy is displayed by a scale factor of 1.3 with the origin as the center of dialation to create the image xy. if the slope and length of xy are m what is the slope of xy
Answers
Answer:
he XY is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the X'Y'. So the length of X'Y' is 1.3 times of origin but the slope is the same. The slope is m
Step-by-step explanation:
Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain. Type your answer below
Answers
If you had something like {(1,2),(4,5),(1,7)} then it wouldn't be a function since x = 1 repeats itself. In this example, x = 1 leads to more than one output.
{(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)}
As long as there are the same x-value does not have multiple y-value results, it will be a function. This data array doesn't contain any recurring x-values. Therefore, this is a function (in simple terms of speaking).