The scale factor of triangle PQR to triangle STU is 3/2
How to find the scale factor of the two trianglesScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
Taking a point of reference say PR and SU
PR = 8
SU = 12
let the scale factor be r such that
8 * r = 12
r = 12 / 8
r = 3/2
checking with other sides
PR to UT
6 * 2/3 = 9 correct
QP to TS
10 * 3/2 = 15 correct
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CEDAR
1
SOULANICTA
ARANTEN
In the figure below, mZ1 = (x-6)° and m/2=5x°.
Find the angle measures.
2
Answer:
∠ 1 = 25° , ∠ 2 = 155°
Step-by-step explanation:
∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is
x - 6 + 5x = 180
6x - 6 = 180 ( add 6 to both sides )
6x = 186 ( divide both sides by 6 )
x = 31
Then
∠ 1 = x - 6 = 31 - 6 = 25°
∠ 2 = 5x = 5 × 31 = 155°
in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks? if necessary, round your answer to the nearest tenth.
The weight of all of the rocks to the nearest tenth is 6.085 pounds .
Given :
in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks if necessary, round your answer to the nearest tenth.
Let x be the total weight or all the weight of rocks .
3 = 49.3 % * x
3 = 49.3 * 1 / 100 * x
3 * 100 = 49.3 * x
300 = 49.3 * x
divide with 49.3 on both sides
300 / 49.3 = 1 * x
x = 300 / 49.3
= 6.085 pounds
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(*6./Sean drives from Manchester to Gretna Green.
He drives at an average speed of 50 mph for the first 3 hours of his journey.
He then has 150 miles to drive to get to Gretna Green.
Sean drives these 150 miles at an average speed of 30 mph.
Sean says,
"My average speed from Manchester to Gretna Green was 40 mph."
Is Sean right?
You must show how you get your answer.
Sean's real average speed was less than his predicted 40 mph.
What is average speed?Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time.
Student must calculate average speed, compare it to Sean's response, and determine total distance traveled and time expended. First, the formula must be stated: Average speed = Total distance traveled / Time required.We can rearrange this to determine the distance traveled.Total mileage equals time divided by average speed.We only need to compute the first leg of his travel as we already know the total distance was 150 miles. As a result, we can calculate 150 miles at 50 mph for 3 hours.We now know that the overall distance from Manchester to Greta Green was 300 miles after including the second half of the voyage.Now we have to think about how long it took overall. Rearranging the equation yields the necessary result: Time taken=distance/speed. This brings us back to the comparatively easy formula of 150 miles at 30 miles per hour equals 5 hours. This indicates that the total travel time from Manchester to Gretna Green was 8 hours, not including the initial 3 hours. We now possess all the knowledge required to calculate his average speed over the entire journey. The original equation is still used: Average speed = Total distance traveled / Time taken. After entering all the data, we get the result 300 miles in 8 hours = 37.5 miles per hour.Hence, Sean's real average speed was less than his predicted 40 mph.
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Online entertainment streaming services have gained in popularity in recent years as an alternative to traditional television. One such company has seen steady growth in each period of 3 months, called a quarter, over the past 4 years. The scatterplot shows the relationship between the number of quarters passed since January 2014 and the number of members to the streaming service. A least-squares equation that summarizes this relationship is
Based on the residual plot, is a linear model appropriate for summarizing this relationship?
A linear model is appropriate because the value of r is close to 1.
A linear model is appropriate because the residual plot is curved.
A linear model is not appropriate because the residual plot shows a clear pattern.
A linear model is not appropriate because the scatterplot relating time and subscribers shows a clear pattern.
PLS HURRY
Based on the residual plot, is a linear model is not appropriate for summarizing this relationship. Therefore, the correct answer option is: C. A linear model is not appropriate because the residual plot shows a clear pattern.
What is a residual plot?In Mathematics, a residual plot is sometimes referred to as scatter plot and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association or correlation (relationship) between the data set.
Mathematically, a linear model can be represented by this mathematical expression; y = mx + b.
Where:
m represents the slope.x and y are the points.c represents the y-intercept.By critically observing the residual plot (scatter plot) which shows a relationship between the residuals and quarters since January 2011, we can reasonably infer and logically deduce that a linear model is not appropriate because there is a clear pattern between the data points.
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can somebody please help
Step-by-step explanation:
The diagram is very helpful, so really go off of that. Coordinates are written in the form (x,y). If you look at the signs (either there's a negative sign, - , or no sign at all, meaning it's +) for each number in a coordinate pair, you can see where each coordinate should go.
If you look at the last example (3, -3), the first digit is positive + and the second digit is negative - . When you look at the diagram, coordinates in the form of (+, -) are put in quadrant 4.
mrs jones gave 1/5 of a cake to her neighbour. she then sliced the remainder into 3 pieces for her 3 children, ken, ron and david, in the ratio 1 : 3 : 4. what is the fraction of the cake was ron's pieces
The fraction of the cake that was ron's pieces is 1/5.
What is the fraction of the cake was ron's pieces?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Since Mrs Jones gave 1/5 of a cake to her neighbour, the remaining fraction will be:
= 1 - 1/5
= 4/5
The fraction of the cake that was ron's pieces will be:
= 2/(1+3+4) × 4/5
= 2/8 × 4/5
= 8/40
= 1/5
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Russel wants to buy 3 identical gift cards. He wants to make sure the total cost is no more than $2 above or below $60. Which of the following inequalities represents the situation?
Let the cost of each gift card be x.
Three of them will cost 3x.
We need the total cost be no more than $2 above or below $60.
This can be represented as:
3x ≤ 60 + 2 ⇒ 3x ≤ 62,and
3x ≥ 60 - 2⇒ 3x ≥ 58,or as combined inequality:
58 ≤ 3x ≤ 62An investor invested a total of $1,800 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $76, how much was
invested in each mutual fund?
The amount invested in the mutual fund that earned 6% was $
a) Using a system of equations, the amount invested in the mutual fund that earned 6% was $1,600.
b) The amount invested in the mutual fund that earned 4% was $200.
What is a system of equations?A system of equations is two or more equations solved concurrently.
A system of equations is also called simultaneous equations.
Total investment = $1,800
Profit from investment A = 6%
Profit from investment B = 4%
The total investment profit = $76
Let A = Investment A and B = Investment B
A + B = 1,800
A = 1,800 - B
0.06A + 0.04B = 76
0.06(1,800 - B) + 0.04B = 76
108 - 0.06B + 0.04B = 76
108 - 0.02B = 76
-0.02B = -32
B = 1,600
A = 200 (1,800 - 1,600)
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denise rode 3 kilometers on a bike.clark rode 5000 meters on a bike. how many more meters did clark ride than denise
In linear equation, Clark rode 2 kilometres more than Denise .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations whose variables have a power of one are called linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
Denise rode 3 kilometres .
Clark rode 5000 metres which is 5 kilometres .
So , Clark rode 2 kilometres more than Denise .
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Please answer both parts
the area will be fall in between 100≤ 20x ≤1000.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,A quadrilateral should be closed shape with 4 sides
All the internal angles of a quadrilateral sum up to 360°.
The area of a rectangle is A = a*b
Here in the figure the length is given 4x and the breadth is 5.
The area is given in between 100≤A≤1000
So this area will be A = 5x*4 = 20x
Now the area will be lie in between 100≤ 20x ≤1000
hence, the area will be fall in between 100≤ 20x ≤1000.
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If m is the centroid of triangle abc, am = 44, ce =54, and dm = 23, find each missing measure. fm=?
If m is the centroid of triangle abc, am = 44, ce =54, and dm = 23, then each missing measure fm=88 and ce=44.
What is the centroid ?The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.
How do you find the centroid of a triangle with 3 points?Step 1: Identify each vertex's coordinates.
Step 2: Add together and divide by three all the x values from the coordinates of the three vertices.
Step 3: Add together all the y values from the three vertices and divide the result by three.
Step 4: The centroid coordinate is determined from the values collected in stages 2 and 3.
the ratio of both segments is 2:1.
where;
am = 44 and dm = 23
the longer segment is double of shorter one:
2*23 = 46.
Therefore,
fm = 46-23
= <<23=23>>23
now finding ce:
= 2*44
= 88, so
ce measures
= 88-44
=44.
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Solve the system algebraically.
2x-y=-5
y=1-3x
Answer:
The answer is x= -2/3
Step-by-step explanation:
A stock is priced at $85 per share and pays a quarterly dividend of $2. 10 per share. What is the dividend yield per stock share per year?
The dividend yield per stock share per year is 9.88 %
What Is the Dividend Yield?
The dividend yield, expressed as a percentage, is a financial ratio (dividend/price) that shows how much a company pays out in dividends each year relative to its stock price.
Given,
The stock price per share is = $85
Quarterly dividend is = $2.10
Now, for to find Dividend yield
Dividend Yield = Annual Dividends Per Share / Price per share
Annual Dividends Per Share = 4 * $2. 10
= $8.4
Price per share = $85
Now, plug in the values
Dividend Yield = 8.4 / 85
= 0.0988
Now, in percentage is
Dividend Yield = 0.0988 * 100
= 9.88 %
Hence, the dividend yield per stock share per year is 9.88 %
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Do you think that practicing
mathematics will bring Peace
and Harmony in your life?.
Explain your thinking.
Practicing mathematics will bring Peace and Harmony in your life It provides us with a method for comprehending patterns, quantifying relationships, and making future predictions.
What do you mean by Peace?In the absence of animosity and violence, peace is the idea of communal friendship and harmony.
Critical thinking about our surroundings is referred to as analytical thinking. Our capacity for reasoning is what allows us to approach problems logically. The ability to think critically and rationally is crucial since it aids in issue solving and solution seeking.
Understanding the world through mathematics also helps us develop mental discipline. Math fosters logical reasoning, critical analysis, inventiveness, abstract or spatial thinking, problem-solving aptitude, and even good communication abilities.
Therefore, It gives us a way of understanding patterns, measuring relationships, and forecasting the future.
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Find the equation of a line perpendicular to y 7 = - 4/3x that pae through the point (-8, -1)
The equation of a line perpendicular to y 7 = - 4/3x that pass through the point (-8, -1) is 3x-4y=20 where x-intercept is 3 and y-intercept is -4.
What is an equation or line?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables.
What is equation of a straight line?The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.
Given line ;
y 7 = - 4/3x
now comparing it with y=mx+c to find the value of m and we found;
m1=-4/3
now if two lines are perpendicular then,
m1.m2=-1
m2=3/4
now finding the equation of line passing through the point (-8, -1)
x1=-8
y1=-1
(y−y1)=m(x−x1)
Y+1=(3/4)(x+8)
Y+1=(3x/4)+(24/4)
Y=(3x/4)+(6)-1
Y=(3x+20)/4
4y=3x+20
rearrange;
3x-4y=20
this is our required value.
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please help begging on knees rn.
10. if mB is two more than three times the measure of ZC, and ZB and Care
complementary angles, find each angle measure.
Step-by-step explanation:
First, you should translate everything into math. So,
"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)
"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)
Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:
(3C + 2) + C = 90
4C + 2 = 90
4C = 88
C = 22
Plugging C = 22 back into either equation (1) or (2) gives us
B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)
Thus, ∠B = 68º; ∠C = 22º
hope this helps
Sale! 75% OFF
of the original price!
If a strawberry milkshake has a sale price of $1, what was the original price?
Submit
Answer: $4
Step-by-step explanation:
75% = 3/4
If 4/4 = full price,
subtract 3/4
4/4 - 3/4 = 1/4 = 25% of the original price
25% = $1
75% = $3
$1 + $3 = $4
If f(x) = 3x² - x, find f{-3, 0, 3}
Step-by-step explanation:
so pretty much replace -3, 0 and 3 into the equation
-3 to the power of 2 is 9 and 9(3) is 27. 27-(-3) is 27+3, 30
0 squared is 0 so the 2nd one would be 0
3 squared times 3 is 27 and subtracted by 3 is 24.
Need this question answer quickly
By applying the exterior angle of a triangle theorem, m<WUV = 19°
What is an exterior angle of a triangle?
The angle created by one side of a triangle and the subsequently extended side is known as the external angle of a triangle. A triangle has three exterior angles, and the sum of those three external angles is always 360 degrees.
Here, we have
The given parameters are;
ΔUVW with side UW extended to X
m∠UVW = (x + 19)°
m∠VWX = (5x +14)°
m∠WUV = (x + 13)°
Applying the exterior angle of a triangle theorem:
m∠WUV + m∠UVW = m∠VWX
(x + 13)° + (x + 19)° = (5x +14)°
2x + 32 = 5x + 14
32 - 14 = 5x - 2x
18 = 3x
x = 6°
Now, we put the value of x in m∠WUV = (x + 13)° and we get
m∠WUV = (6+13)°
m∠WUV = 19°
Hence, by applying the exterior angle of a triangle theorem, m<WUV = 19°
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Find h(−5) when h(x) = −3|x − 1| + 4. Show every step.
The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.
How to solve function?
Algebraically evaluate and resolve functions.Analyze functions using data from a table or a graph.The supplied value should be used as the input variable in the formula.Determine the outcome.h(x) = −3|x − 1| + 4
Substitute x = -5
h(-5) = −3|(-5) − 1| + 4
= -3|-6| + 4
= -18 + 4
= -14
h(-5) = -14
Hence, The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.
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question 3 in the analyze stage of the data life cycle, what might a data analyst do? select all that apply.
In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations
The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle
The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems
The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system
Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations
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classify the series -1+2+(-4)+8+...as arithmetic or geometric. Then, determine whether the series is convergent or divergent.
Answer:
The series -1+2+(-4)+8+... is an arithmetic series because it has a common difference between consecutive terms. Specifically, the common difference is -4 - 2 = -6.
To determine whether the series is convergent or divergent, we need to find its sum. The sum of an arithmetic series is given by the formula:
sum = (n/2)(a1 + an)
where n is the number of terms in the series, a1 is the first term, and an is the nth term.
Since the series is infinite, we cannot determine its sum using this formula. However, we can determine its sum by taking the limit as n approaches infinity. Using the formula above, we find that the sum is equal to:
sum = (infinity/2)(-1 + infinity)
Since the series contains an infinite number of negative terms, it is divergent.
swhat happens to the diagonal of a rectangle when the rectangle is reflected across a line of symmetry? what does this suggest about the diagonals of rectangles?
When reflected across a line of symmetry, a shape having that line of symmetry will fall on itself. These are the actual claims:
(1) The rectangle's diagonals will line up exactly with one another.
(2) A rectangle's diagonals are symmetry lines.
We deduce from the question that the rectangle is mirrored across the symmetry line.
When done, the rectangle's half will fall directly on the other half.
This indicates that the rectangle's diagonal will line up perfectly with the opposite diagonal.
According to the aforementioned claim, a rectangle's diagonal is also its line of symmetry.
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does 2+x have an y-intercept of 2 and slope of 1
Rewrite the equation in logarithmic form.
9^5 = 59,049
Answer:
[tex]log_{9} 59,049=5[/tex]
Step-by-step explanation:
The equation in logarithmic form is ㏒₉59,049 = 5
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given is an equation, 9⁵ = 59,049, we need to convert it into logarithmic form.
So,
y = aˣ, then x = ㏒ₐY
Applying the same,
9⁵ = 59,049
㏒₉59,049 = 5
Hence, the equation in logarithmic form is ㏒₉59,049 = 5
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please help me with this math problem
Answer:
a - April
b - may
c - they neither made nor lost money that month
hope that helps :)
Step-by-step explanation:
Answer: a) - March
b) - May
c)- it neither made nor lost money that month
Step-by-step explanation:
a) - because -386 is the least out of all of them
b) - because 271 was the most out of all of them
c) - it didn't lose or make it just stayed the same as it was
What is the image of the point ( − 4 , − 1 ) (−4,−1) after a rotation of 27 0 ∘ 270 ∘ counterclockwise about the origin?
The image of the point (-4, -1) after a rotation of 270 counterclockwise about the origin will be (-4, 1).
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The point (- 4, -1) is in the fourth quadrant. After a rotation of 270 counterclockwise about the origin, then the coordinate would be in the third quadrant.
Let the coordinate of (-x, -y) be the fourth quadrant. Then the coordinate in the third quadrant will be (-y, -x)
Therefore, The image of the point (-4, -1) after a rotation of 270 counterclockwise about the origin will be (-4, 1).
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Find equivalent equations Of 3+2x-9-4 X +11+ 5x- X
The required expression is 2x + 5 that equivalent to the expression, 3 + 2x − 9 − 4x + 11 + 5x − x.
What are Equivalent Expressions?The expressions that have identical values are called to be equivalent expressions.
The expression is given in the question following as:
⇒ 3 + 2x − 9 − 4x + 11 + 5x − x
We have to determine the equivalent expression to the given expression
As per the question, we have
⇒ 3 + 2x − 9 − 4x + 11 + 5x − x
Combine the like terms together in the above expression,
⇒ 2x - 4x + 5x - x + 3 - 9 + 11
⇒ 2x + 5
Thus, the required expression is 2x + 5 that equivalent to the expression, 3 + 2x − 9 − 4x + 11 + 5x − x.
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PLEASE HELP!!!!!!!!!!! BEFORE 11:59 PM EST
Solve for n
8n+7=-4n+19
Answer: n= 1
Step-by-step explanation:
8n+7=-4n+19
First, subtract 7 from both sides
8n = 4n +12
Then add 4n from both sides
12n = 12
Then divide by 12 from both sides
n= 1
If you can please give me a Brainliest, thank you!
Answer: n = 1
Step-by-step explanation:
First, you could start off by bringing the -4n to the left side:
8n + 7 = -4n+19 → 12n + 7 = 19
Next, you take the 7 on the left side of the equals sign and subtract it from the 19:
12n + 7 = 19 → 12n = 12
Finally, you divide the 12 on the right by the 12 on the left:
12n = 12 → n = 12/12
A number over itself will always be 1, so n = 1.