Answer:
100 Minutes
Step-by-step explanation:
Step 1: Break it down-
3¢ can be expressed as 0.3
Step 2: Add monthly charge-
Since there is a 10$ monthly charge: 40-10=30
Step 3: Subtract-
Now divide: 30 ÷ 0.3
Step 4: Final Answer-
Hence the amount of minutes per month= 100
Question 7 (3 points)
The graph and table below represent the constant rate for the amount of time it takes for a given
number of gallons of water to flow from a hose.
a. Find the rate of both the graph and table. Be sure to show all work.
b. Which one has the greater rate? Explain how you know.
The rate of water flow is 6 gallons per unit of time.
What is slope?
Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.
a. To find the rate, we need to calculate the amount of water that flows per unit of time.
Method 1: Using the Graph
First, we can plot the points (5,30), (7,42), and (10,60) on a graph and connect them with a line.
From the graph, we can see that the line passes through the points (5,30) and (10,60), which means that the change in y-values is 60 - 30 = 30, and the change in x-values is 10 - 5 = 5.
So, the slope of the line is:
slope = change in y-values / change in x-values
= (60 - 30) / (10 - 5)
= 6
Therefore, the rate of water flow is 6 gallons per unit of time.
Method 2: Using the Table
We can also find the rate by calculating the differences in y-values and x-values in the table.
x y Difference in y Difference in x Rate (y/x)
-------------------------------------------------------
5 30 - - -
7 42 12 2 6
10 60 18 3 6
From the table, we can see that the rate of water flow is 6 gallons per unit of time.
b. Both the graph and table have the same rate of 6 gallons per unit of time. We know this because we calculated the rate using both methods, and they gave us the same result.
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from a group of seven candidates, a committee of six people is selected. in how many different ways can the committee be selected?
According to the informations, there are 7 different ways a committee of six people can be selected from a group of seven candidates.
How can we find this number?In this case, we must use the combination formula, which is expressed by:
nCr = n! / r!(n-r)!Where n is the total number of items in the set, r is the number of items being selected, and ! denotes the factorial function, which means multiplying a number by all the positive integers less than it.
Therefore, from a group of 7 candidates, a committee of 6 people can be selected in 7 different ways using the combination formula. The formula for the combination of n objects taken r at a time is C(n,r) = n!/r!(n-r)!, where n is the total number of objects and r is the number of objects to be chosen. In this case, we have n = 7 and r = 6, so the formula gives us C(7,6) = 7!/6!(7-6)! = 7 ways.
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Find the volume of a composite solid with a radius of 6 and a height of 12
The volume of the composite solid is 452. 160 ft³
How to determine the volumeFirst, it is important to note that the formula for calculating the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters of the formula are;
V is the volumer is the radius of the cone.h is the height of the cone.From the information given,
substitute the values
Volume = 3.14 × 6² × 12/3
Divide the values
Volume = 31.4 × 36 × 4
Multiply the values
Volume = 452. 160 ft³
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34. What are the coordinates of the information
center? Explain.
Generally, coordinates are a way of specifying the position of something in space, usually using a system of latitude and longitude or x, y, and z axes.
What informs the coordinates of an information center?The coordinates of a physical location that serves as a hub for information, such as a data center or a library, then the answer will depend on the specific location you have in mind. To find the coordinates of such a place, you would need to use a mapping tool or geographic information system (GIS) to locate the facility and determine its latitude and longitude.
On the other hand, if you're asking about the "coordinates" of information in a more abstract sense, then this could refer to the ways in which information is organized or classified.
For example, a database might use a system of fields and tables to arrange information in a structured way, while a search engine might use algorithms to determine the relevance and ranking of different pieces of information based on factors like keywords, backlinks, and user behavior.
In conclusion, the coordinates of an information center is dependent on its nature in terms of its structural formation and the set goals to be accomplished by determining such coordinates.
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Claim: A majority of adults would erase all of their personal information online if they could. A software firm survey of 498 randomly selected adults showed that 62% of them would erase all of their
personal information online if they could. Complete parts (a) and (b) below.
a. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.
(Type an integer or a decimal. Do not round.)
If you open a bank account with 23,000 and its annual interest is compounded quarterly. What would the interest have to be for the amount to grow to $50,000 in 7 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 50000\\ P=\textit{original amount deposited}\dotfill &\$23000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]50000 = 23000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{4}\right)^{4\cdot 7} \implies \cfrac{50000}{23000}=\left( 1+\cfrac{r}{400} \right)^{28} \\\\\\ \cfrac{50}{23}=\left( \cfrac{400+r}{400} \right)^{28}\implies \sqrt[28]{\cfrac{50}{23}}=\cfrac{400+r}{400} \\\\\\ 400\sqrt[28]{\cfrac{50}{23}}=400+r\implies 400\sqrt[28]{\cfrac{50}{23}}-400=r\implies \stackrel{ \% }{11.25}\approx r[/tex]
Find the area of the regular polygon
Round to nearest tenth
On solving the provided question we can say that area of the polygon is 24 cm sq.
What is quadrilateral?A four-sided polygon having four edges and four corners is referred to as a quadrilateral. The word is derived from the Latin words quadri and latus, both of which imply "side". An object with a rectangle's four sides, four vertices, and four corners is a two-dimensional shape. There are essentially two sorts of concave and convex surfaces. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up the two-dimensional shape of a rectangle. There are many different shapes for quadrilaterals, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
Area of this polygon is -
A = 1/2 * 6* 8
A = 24 cm sq.
Hence, area of the polygon is 24 cm sq.
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Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
–2p – 17 = 3(p – 5) {–2}
Starting with the original equation:
-2p - 17 = 3(p - 5)
Distributing the 3 on the right side:
-2p - 17 = 3p - 15
Subtracting 3p from both sides:
-5p - 17 = -15
Adding 17 to both sides:
-5p = 2
Dividing by -5:
p = -2/5
Now, we can substitute this value of p back into the original equation and check if it is a solution:
-2(-2/5) - 17 = 3((-2/5) - 5)
4/5 - 17 = 3(-27/5)
-136/5 = -81/5
The left side does not equal the right side, so the supplied value of p = -2/5 is NOT a solution to the equation.
Hope this helps :)
Identify the line that appears tangent to circle O and includes point B.
Answer:
D. Line O
Step-by-step explanation:
We can simply tell which one it is by looking at the picture. A tangent line is a line that intersects at one point only. Line L doesn't even touch the circle. Line M and N touch the circle in more than one place. If we look at O, we can see that it is "scraping" the edge of the circle, which is what pretty much every tangent line looks like.
Therefore, the answer is D.
I need help pleaseeee
The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
Reducing matricesFrom the question, we are to perform the given row operation on the given matrix
The given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]
The operation we are to carry out is:
Add -4(row 1) to row 3
This essentially means we should multiply the first row (row 1) by -4. Then, we will add each of the elements from the results to the corresponding elements on the third row
Multiplying by -4
-4 × [ 1 2 1 | -5
-4 -8 -4 | 20
Now, we will add the result from the multiplication to the corresponding elements in row 3
4 -1 6 | -8
+ -4 -8 -4 | 20
------------------------
0 -9 2 | 12
Hence,
The resulting matrix becomes
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
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What is the area of a circle with diameter of 16 meters? Leave the answer in terms of pi
Answer:
64π
Step-by-step explanation:
Use the formula for an area of a circle
[tex]A = \pi r^2[/tex]
Half of 16 is 8.
8*8 = 64.
The area of a circle with a diameter of 16 meters is equal to 64π or 200.96 square meters.
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
[tex]\text{Area} = \pi \text{r}^2[/tex]
Where:
[tex]\text{r}[/tex] represents the radius of a circle.
[tex]\text{Note:} \ \text{Radius} = \dfrac{\text{diameter}}{2} = \dfrac{16}{2} = 8 \ \text{meters}.[/tex]
By substituting the radius into the formula for the area of a circle, we have the following;
[tex]\text{Area of circle} = \pi \times 8^2[/tex]
[tex]\bold{Area} \ \text{of circle} = 64\pi \ \text{or} \ 200.96[/tex] square meters.
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Q7: Use the image to determine the line of reflection.
An image of polygon VWYZ with vertices V at negative 9, 1, W at negative 9, negative 1, Y at negative 3, negative 1, and Z at negative 3, 1. A second polygon V prime W prime Y prime Z prime with vertices V prime at 7, 1, W prime at 7, negative 1, Y prime at 1, negative 1, and Z prime at 1, 1.
Reflection across y = 1
Reflection across x = −1
Reflection across the x-axis
Reflection across the y-axis
This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1".
How to solve the question?
The line of reflection is the line that serves as the mirror for the original polygon such that each point on the original polygon is reflected to a corresponding point on the reflected polygon such that the distance between the line of reflection and each point is the same as the distance between the line of reflection and its reflection.
In this case, we are given two polygons, one original and one reflected. We need to determine the line of reflection that maps each point of the original polygon to its corresponding point on the reflected polygon.
Looking at the two polygons, we can see that the corresponding vertices are equidistant from a line of reflection that passes through the midpoint of the line segment joining V and V prime. Therefore, the line of reflection is the line that passes through the midpoint of the line segment joining V and V prime.
This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1". The other options are incorrect because they do not pass through the midpoint of the line segment joining V and V prime and do not produce the corresponding points for the original and reflected polygons.
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A balloon filled with helium gas has a volume of 326 mL at a pressure of 1 atm. The balloon is released and reaches an altitude of 6.5 km, where the pressure is at 0.5 atm. Assuming that the temperature has remained the same, what volume does the gas occupy at the height? Answer in units of mL.
The volume of the gas at the height (i.e 6.5 Km) is 652 mL
Data obtained from the question[tex]\text{Initial volume} \ (\text{V}_1) = \text{326 mL}[/tex][tex]\text{Initial pressure} \ (\text{P}_1) = \text{1 atm}[/tex][tex]\text{Temperature = Constant}[/tex][tex]\text{Final pressure} \ (\text{P}_2) = \text{0.5 atm}[/tex][tex]\bold{Final \ volume \ (V_2) = \ ?}[/tex]The final volume of the gas can be obtained by using the Boyle's law equation as shown below:
[tex]P_1V_1 = P_2V_2[/tex]
[tex]1 \times 326 = 0.5 \times V_2[/tex]
[tex]326 = 0.5 \times V_2[/tex]
Divide both side by 0.5
[tex]V_2 = \dfrac{326}{0.5}[/tex]
[tex]\boxed{\bold{V_2 = 652 \ mL}}[/tex]
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A cylinder has a radius of 5 inches and a height of 8 inches. What is its volume rounded to the nearest tenth?
Answer:
630
Step-by-step explanation:
v= pi×radius squared×hight so its 3.14×5 sqared×8 628 and 628 rounded to the nearest tenth is 630 hope this help
4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
Answer: Vertical angles are formed by the intersection of two lines and are always equal in measure. Therefore, to find the angle that is vertical to angle ∠DEB, we need to look for another angle that has the same measure as ∠DEB.
Unfortunately, we do not know the measure of angle ∠DEB, so we cannot determine which angle is vertical to it based on the given information.
Therefore, the correct answer is: None of the angles can be determined as vertical to angle ∠DEB without additional information.
Step-by-step explanation:
Consumer Price Index, 1970-2002
Year
1970
1975
1980
1985
1990
1995
2002
Source: World Almanac 2003
CPI
116.3
161.2
248.8
322.2
391.4
456.5
535.8
Describe how the CPI is related to the year.
As the year increases, the CPI decreases and then increases.
As the year increases, the CPI increases and then decreases.
As the year increases, the CPI decreases.
d. As the year increases, the CPI increases.
C.
a.
b.
The computation of the increased in salary is $500.
Here, we have,
Explanation:
Data provided in the question
Salary for the first year = $50,000
CPI increase during the year = 4%
Overstated inflation = 1% i.e. 5%
The computation of the increased in salary is shown below:
= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year
= $50,000 × 5% - $50,000 × 4%
= $2,500 - $2,000
= $500
Hence, The computation of the increased in salary is $500.
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complete question:
Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.
Please help. (b) Suppose the measure angle 3 can be represented by (3x - 8)°. What equation can be written to solve for the value of x?
(C) What is the value of X? Show all work
Answer:
53
Step-by-step explanation:
angle 2 and 3, angle 3 and 4 are both supplementary angle, which means a2+a3=180 degree, a3+a4=180 degree.
Since you know that the angle 2 and 4 are both 29 degree,
you can write
a3+29=180, and a3 is represented as 3x-8
so
(3x-8)+29=180 (<-- answer for b)
3x+21=180
3x+21-21=180-21
3x=159
x=53
i need help on problems 5-11
A scatter plot would be an appropriate data display to show the relationship between the speed of the vehicle and the number of accidents.
Why is a scatter plot appropriate for showing the relationship between speed and accidents?A scatter plot is a graphical representation of two continuous variables, where data points are plotted on a Cartesian coordinate system. The horizontal axis can represent the speed of the vehicle, while the vertical axis can represent the number of accidents. Each data point on the scatter plot would represent a specific observation of speed and the corresponding number of accidents.
By using a scatter plot, the EMT can visually display how changes in vehicle speed are related to the number of accidents. Scatter plots are effective for identifying trends, patterns, and outliers in data, making them suitable for illustrating the relationship between two continuous variables.
Answered question "An EMT wants to use a data display to show students the relationship between the speed of the vehicle and the number of accidents. Choose an appropriate data display for the situation. Explain your reasoning"
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Find the volume?? Of the triangular prism
Answer:
216 mi^3
Step-by-step explanation:
First of all you need to find the area of the base (or top, they are the same)
It is a right-angled triangle, you can simply calculate the area of the base by
A = 6*8/2 = 24 mi^2
The volume of prism is (base area)*height
volume = 24*9 = 216 mi^3
10 is redundant anyway
Answer: the volume of the prism is 62.35 mi cube
Step-by-step explanation:
so first we will find the area of triangular base of the prism, using heron formula.
and s(semi-perimeter)= a+b+c/2= 6+8+10/2= 24/2=12
Area of triangle= A = sqrt [s(s-a)(s-b)(s-c)] = sqrt {12*(12-6)(12-8)(12-10)} = sqrt {6*4*2} = sqrt (48)= 6.92 mi square
Volume = Area x Height
V= 6.92 x 9 = 62.35 mi cube.
The unknown triangle ABC has angle A=56∘ and sides a=32 and c=34. How many solutions are there for triangle ABC?
The value of angle B and C are 63° and 61° respectively.
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Therefore;
32/sin56 = 34/sinC
32sinC = 34sin56
32sinC = 28.187
divide both sides by 32
sinC = 28.187/32
sinC = 0.88
C = sin^-1(0.88)
C = 61°( nearest degree)
The sum of angle in a triangle is 180°
therefore, B = 180-(61+56)
B = 180-(117)
B = 63°
therefore the value of angle B and C are 63° and 61°.
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A right cylinder has a radius of 4 and a height of 11. What is its surface area?
OA. 152
units²
OB. 120 units²
OC. 88 units²
O D. 60 units²
The closest option among the given options is option B: 120 units².
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.
The formula for the surface area of a right cylinder is:
SA = 2πr² + 2πrh
where r is the radius and h is the height.
Substituting the given values, we get:
SA = 2π(4)² + 2π(4)(11)
SA = 2π(16) + 2π(44)
SA = 32π + 88π
SA = 120π
Using the approximation π ≈ 3.14, we can calculate the surface area to be:
SA ≈ 120(3.14)
SA ≈ 376.8
Therefore, the closest option among the given options is option B: 120 units².
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PLEASE HELP I'LL RATE 5 STARS
What is the value of this logarithmic expression?
Answer: 2
Step-by-step explanation:
We can simplify the given logarithmic expression using the logarithmic property that states:
log a base b - log c base b = log (a/c) base b
Using this property, we can rewrite the expression as follows:
log 16 base 2 - log 4 base 2 = log (16/4) base 2
Simplifying the numerator of the logarithm, we get:
log (16/4) base 2 = log 4 base 2
Now, we can evaluate the logarithm using the definition of logarithm, which states that:
log b base a = x if and only if a = b^x
In this case, we have:
log 4 base 2 = x if and only if 2^x = 4
We know that 2 raised to what power gives 4? It is 2, because 2^2 = 4.
Therefore, we have:
log 4 base 2 = 2
Hence, the value of the given logarithmic expression is 2.
what's the answer(s) I have no idea how to do this pleaseeeeee
i need answer asap my computer about to die
The answer of the given question based on the graph coordinate is , the rule for the values in the table is: Y = 7X - 0.
What is Coordinate?In mathematics, a coordinate is a set of values that specifies the position of a point in space. Coordinates are used to locate points, lines, and other geometric objects in a plane, a three-dimensional space, or even higher dimensions.
X Y
5 35
1 7
4 28
2 14
One possible way to do this is to calculate the differences between successive pairs of X and Y values, and then see if there is a constant difference or ratio between them.
Taking the first two rows as an example, we have:
X Y
5 35
1 7
The difference between the X values is 5 - 1 = 4, and the difference between the Y values is 35 - 7 = 28. Dividing the difference in Y by the difference in X gives us:
(35 - 7) / (5 - 1) = 28 / 4 = 7
This means that for every increase of 1 in X, the corresponding increase in Y is 7. We can check this for the other pairs of values in the table and see that it holds true:
X Y
5 35
4 28 (decrease of 1 in X, decrease of 7 in Y)
2 14 (decrease of 2 in X, decrease of 14 in Y)
So the rule for the values in the table is:
Y = 7X - 0.
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Mrs. Jenkins gifts 10 cookies to her six sons if they share the cookies equally how many cookies should each son get
Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.
How to solve the question?
If Mrs. Jenkins gifts 10 cookies to her six sons, the number of cookies each son should get can be found by dividing the total number of cookies by the number of sons.
So, if we divide 10 cookies equally among six sons, we get:
10 / 6 = 1.6667
This means that each son should get approximately 1.67 cookies. However, since it is not possible to divide a cookie into fractions, the actual number of cookies each son would get may vary.
To distribute the cookies equally, Mrs. Jenkins can either give each son one cookie and then divide the remaining four cookies equally among the six sons. This would give each son one cookie and each son would get an additional 4/6 or 0.67 cookies.
Alternatively, Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.
In any case, the important thing is to ensure that each son receives an equal share of the cookies.
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YOUR COMPLETE QUESTION IS :-
Mrs. Jenkins gifts 10 cookies to her six sons if they share the cookies equally how many cookies should each son get
whats the distance between (3,4.1) and (3,1.2)
Answer:
The distance between (3, 4.1) and (3, 1.2) is approximately 2.9 units.
Step-by-step explanation:
You're welcome.
a line passes through the point (-9,-5) an has a slope of -2/3.
Write an equation in slope -intercept form for this line.
The slope-intercept form of a linear equation with given point (-9,-5) and slope -2/3 is y = (-2/3)x - 11.
What is a slope of a line?The slope of a line is a measure of its steepness or incline, represented by the ratio of the vertical change between two points, known as the rise, to the change in horizontal part between the same two points, known as the run. It describes the rate at which the line is increasing or decreasing as it moves from left to right. The slope of a line can be positive, negative, zero, or undefined, and it plays a critical role in many mathematical applications, including calculus, geometry, and physics. It is commonly denoted by the letter m and is defined as m = (y₂ - y₁)/ (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are any two points on the line.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To find the equation of a line with a given slope and a point on the line, we can substitute the values into the equation and solve for the y-intercept, b.
Given that the line passes through the point (-9, -5) and has a slope of -2/3, we can substitute these values into the equation to find the value of b:
-5 = (-2/3) × (-9) + b
-5 = 6 + b
b = -11
Now that we know the value of b, we can write the equation of the line in slope-intercept form:
y = (-2/3)x - 11
Therefore, the equation of the line in slope-intercept form is y = (-2/3)x - 11.
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The medians of Jill are jn, Jn, and lm. They meet at a single point q. Suppose qp = 11, qm= 10, and jn = 39. Find the following lengths: lm, jq, kq
The lengths we found are:
LM = 20
JQ = 26
KQ = 800 / 117
Let's call the length of the median from vertex J to the opposite side LM, and the length of the median from vertex L to the opposite side JN. We can use the fact that the centroid divides each median into two parts, with the ratio of the longer part to the shorter part being 2:1.
First, we can find LM:
LM = 2 x QM = 2 x 10 = 20
Next, we can find JQ:
JQ = 2/3 x JN = 2/3 x 39 = 26
Finally, we can find KQ:
To find KQ, we need to use the fact that the three medians of a triangle divide each other into six smaller triangles with equal areas. Let's call the length of the third median KX. We know that the area of triangle JLK is:
1/2 x LM x JN = 1/2 x 20 x 39 = 390
Similarly, the areas of triangles JNQ, LMQ, JKP, LKP, and JLP are all equal to 390. Let's call this common area A. Then we have:
1/2 x KX x LM = A
1/2 x KX x JN = A
Dividing these two equations, we get:
LM / JN = KX / LM
Substituting the values we know, we get:
20 / 39 = KX / 20
Solving for KX, we get:
KX = 20 x (20 / 39) = 400 / 39
Now we can find KQ:
KQ = 2/3 x KX = 2/3 x (400 / 39) = 800 / 117
Therefore, the lengths we found are:
LM = 20
JQ = 26
KQ = 800 / 117
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Q11: Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 18, 24, and 30 and a second triangle labeled D prime with side lengths of 6, 8, and 10
Determine the scale factor used.
Scale factor of one third
Scale factor of 3
Scale factor of 4
Scale factor of one fourth
the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.
How to solve the question?
To determine the scale factor used in the dilation of triangle D to create triangle D', we need to compare the corresponding sides of both triangles. The corresponding sides of two similar triangles are proportional, meaning that they have the same ratio.
In this case, we can see that the length of every side of triangle D' is one-third the length of the corresponding side of triangle D. For example, the length of the shortest side of triangle D is 18, while the length of the shortest side of triangle D' is 6. Similarly, the length of the longest side of triangle D is 30, while the length of the longest side of triangle D' is 10.
We can use this information to find the scale factor by dividing the length of any side of triangle D' by the length of the corresponding side of triangle D. Let's choose the shortest side for this calculation:
scale factor = length of corresponding side in D' / length of corresponding side in D
scale factor = 6 / 18
scale factor = 1/3
Therefore, the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.
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Suzy can drive 53 miles in 1 hour. How many miles can she drive in 18 hours?
The total miles drive by Suzy in 18 hours when she can drive 53 miles in 1 hour is equal to 954 miles.
If Suzy can drive 53 miles in 1 hour,
Using the formula of speed based on distance and time we have,
Speed = Distance / Time
Substitute the values in the formula we get,
⇒ Speed = 53 miles / 1 hour
⇒ Speed = 53 miles/hour
Use this information to find out how far Suzy can drive in 18 hours we get,
Now, Speed = 53 miles/hour
Time = 18 hours
Distance = Speed x Time
Substitute the value of speed and time we get,
⇒ Distance = 53 miles/hour x 18 hours
⇒ Distance = 954 miles
Therefore, Suzy can drive 954 miles in 18 hours.
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The length of a rectangle is 2 inches more than 2 times the width. If the area of the rectangle is 40
square inches, find the length and the width.
The length of the rectangle is 10 inches and the width is 4 inches.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Let's assume that the width of the rectangle is "x" inches.
From the given information, we can write an equation for the length "L" in terms of the width "x":
L = 2x + 2
We also know that the area of the rectangle is 40 square inches:
A = L * x = 40
Substituting the expression for "L" in terms of "x" into the area equation, we get:
(2x + 2) * x = 40
Expanding the left-hand side of the equation and simplifying, we get:
2x² + 2x - 40 = 0
Dividing both sides by 2, we get:
x² + x - 20 = 0
This is a quadratic equation that can be factored:
(x + 5)(x - 4) = 0
The solutions are x = -5 and x = 4. Since the width of the rectangle cannot be negative, the only valid solution is:
x = 4
Substituting this value for "x" into the equation for "L", we get:
L = 2x + 2 = 2(4) + 2 = 10
Therefore, the length of the rectangle is 10 inches and the width is 4 inches.
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