Step-by-step explanation:
in a dilation all the angles stay the same. only the lengths of lines (like sides or heights) change - and all with the same scale factor (which makes the original and the dilated result similar objects).
angle EDC = 117°.
therefore angle E'D'C' = 117°.
AB = 1.8 in
A'B' = 4.5 in
the scale factor r is
r = 4.5 / 1.8 = 2.5
every segment of A'B'C'D'E'F' is parallel to its original counterpart in ABCDEF.
like
AB to A'B'
as well as
BC to B'C'
CD to C'D'
DE to D'E'
EF to E'F'
that is the reason why projections work (even at an inclined angle of the projection screen the picture might seem strangely stretched, but the angles are still all the same, parallel lines remain parallel, perpendicular lines remain perpendicular, ... - and the viewer still recognizes the pictures).
(Attached imagine) PLEASE HELP!! Simplifying complex numbers
Answer:
6i-4
Step-by-step explanation:
To simplify the expression 4i+(8-3i) - 12+√-25, you can start by combining like terms.
First, you can combine the terms 4i and -3i to get 1i. You can also combine the constants 8 and -12 to get -4.
So, the expression becomes 1i - 4 + √-25.
Next, you can simplify the square root. √-25 is the same as √(-25) which is the same as √(5*-5), which is the same as 5√(-1). √(-1) is equal to i, so 5√(-1) is equal to 5i.
Therefore, the final simplified form of the expression is 1i - 4 + 5i, which is equal to 6i - 4.
find the exact length of the curve.x = 1/3 √y (y - 3), 16 ≤ y ≤ 25
The length of the curve x = 1/3 √y (y − 3) is 64/3.
What is arc length?The distance between two point along a segment of a curve is known as the arc length.
The equation of the curve is given by:
x = 1/3 √y (y − 3), 16 ≤ y ≤ 25
Length of the curve y = f(x) between point x =a to x = b is given by:
[tex]\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx[/tex]
√1 + [f′(x)]2 dx.
x = 1/3 √y (y − 3)
x = 1/3 * [tex]y^\frac{3}{2}[/tex] - [tex]y^\frac{1}{2}[/tex]
Let's find the first derivative of x.
dx/dy = 1/3. 3/2. [tex]y^\frac{1}{2}[/tex]- 1/2 . [tex]y^\frac{1}{2}[/tex]
dx/ dy = 1/2 ( [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])
(dx/dy)^2= 1/4 ( [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])^2
= 1/4(y + [tex]y^-^1[/tex]-2)
1 + {f′(x)}2 = 1 + 1/4(y +[tex]y^-^1[/tex]-2)
= 1/4 y + 1/4[tex]y^-^1[/tex]+ 1/2
1 + {f′(x)}2= 1/4 (y + [tex]y^-^1[/tex] + 2)
√[1 + {f′(x)}2] = 1/2 ( [tex]y^\frac{1}{2}[/tex] + [tex]y^\frac{-1}{2}[/tex])
Length of curve is given by:
25
∫ [tex]\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }[/tex] dy
16
= [tex]\left \{ {{y=25} \atop {x=16}} \right.[/tex] [[tex]y^\frac{3}{2}[/tex]/3 + √y]
= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]
= [125/3 + 5] - [64/3 + 4]
= 140/3 - 76/3
= (140 - 76)/3
= 64/3
So the length of the curve is 64/3
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What is the slope of the line through (-9, 6) and (3,-9)?l
Answer:
-5/4
Step-by-step explanation:
the main answer is -5/4
Bo went to the grocery tore and bought ome bottle of oda and bottle of juice. Each bottle of juice ha 25 gram of ugar. Bo purchaed a total of 7 bottle of juice and oda which collectively contain 250 gram of ugar. Determine the number of bottle of oda and juice purchaed. Someone tell me how to write out the equation, I know the anwer I jut need the written out equation
The two simultaneous equations are 50x + 25y = 250 and x + y = 7
What are simultaneous equations?Simultaneous equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations
How to make simultaneous equations from given information?Assuming the bottle of soda has 50 grams of sugar in each bottle (since this information is not given). Let the bottles of soda bought be x and bottles of juice bought be y. Two equations will be formed so that we can solve them simultaneously.
50x = total amount of sugar in soda bottles
25y = total amount of sugar in juice bottles
50x + 25y = 250 (total amount of sugar in all bottles)
x + y = 7 (total number of bottles)
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Select all the correct answers.
Michael is graphing the parabola represented by this equation.
y = -(x - 3)² - 1
Which features should he include in his graph?
The features that Michael should include on the graph of the parabola are given as follows:
Focus at (3, -3/2).Vertex at (3,-1).How to graph the parabola?The parabola for this problem is defined as follows:
y = -0.5(x - 3)² - 1.
Comparing to the vertex form definition, the coordinates of the vertex are given as follows:
(3, -1).
The equation can also be written as follows:
-0.5(x - 3)² = y + 1
(x - 3)² = -2(y + 1).
Then the coefficient p is obtained as follows:
4p = -2
p = -0.5
Then the coordinates of the focus are given as follows:
(3, -1 - 0.5) = (3, -3/2),
The equation of the directrix is then given as follows:
y = 1 - 0.5
y = 1/2.
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How much work is done on a car if you push with 100 Newtons of force but it does not move?
Answer:
0 Joules (No work)
Step-by-step explanation:
The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the car is 100 newtons, but the car does not move, so the distance over which the force is applied is 0 meters.
Therefore, the amount of work done on the car is 100 newtons * 0 meters = 0 joules. This means that no energy has been transferred to or from the car as a result of the force applied to it.
three hearts are dissected from individuals with unknown histories. two of the three hearts are enlarged. what is a possible reason why the two hearts may be enlarged
they belong to high-performance athletes
It may be a sign of a family history of early heart disease. If one of your close relatives, such as a parent or sibling, has experienced a heart attack, a stroke, or was previously diagnosed with heart disease before the age of 60. Thus, option B, C is correct.
What individuals with a history of heart disease?The CDC's Response to the Risk Factors in the Country. Leading causes of heart disease and stroke risk factors include high blood pressure, high levels of low-density lipoprotein (LDL) cholesterol, diabetes, smoking, exposure to second-hand smoke, obesity, a poor diet, and inactivity.
People who are aware of their situation make wiser decisions, live longer, and experience greater well-being. Even if you have heart failure, it is still possible to lead a regular life. The secret to success is realizing heart failure and taking charge of it.
Therefore, They are from well-trained professional athletes, and They are from individuals with a history of heart disease.
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The question is incomplete, complete question with option given below:
Three hearts are dissected from individuals with unknown histories. Two of the three hearts are enlarged. Select all of the possible reasons the two hearts may be enlarged.
A. They are from individuals who had low blood pressure histories.
B. They are from well-trained professional athletes.
C. They are from individuals with a history of heart disease.
D. They are from individuals who had arthritis issues.
gerardo is 9 feet away from his car when he begins walking directly away from his car at a constant speed of 3 feet per second. if gerardo is 24 feet from his car, how many seconds have elapsed since he started walking away from his car?
The time that has elapsed since Gerardo started walking away from car will be equal to 5 seconds.
We solve this problem by converting it into a linear equation that has three variables in it. Since we have distance, time and speed the three variables will be d, t and s respectively. The expression which shows the distance of Gerardo will be expressed as
d = (s×t) + 9; we have the constant as 9 because Gerardo was 9 feet away from his car.
Now, we have the distance as d = 24 feet and the speed is constant that is equal to 3 feet per second and we need time which will be
24 = (3×t) + 9
15 = 3×t
=> t = 15/3
=> t = 5 seconds
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sketch the region enclosed by the given curves. y = 4/x, y = 16x, y = 1 4 x, x > 0
In order to plot the region enclosed by the given graphs we have to find the intersection points of all the 3 graphs taking 2 at a time
so finding intersection point of the y=4/x and y=16x
4/x=16x
=> = 1/4
=> x = 1/2 as x>0
and y=16x
=> y =8
now finding intersection point of y=4/x and y=1/16x
=> 4/x =x/16
=> = 64
=> x = 8 as x>0
and y= 4/x
=> y=1/2
now finding intersection point of y=16x and y=1/16x
the intersection point of both line is x=0
so y=16x
=> y=0
so we will get the intersection point of all the lines now after plotting all the points below we will get the graph as attached below.
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A beverage distributor conducts regular surveys of consumer spending on its products. The average weekly household spending (in dollars) on cow milk and almond milk for each of 12 states was recorded. A scatterplot of spending on cow milk versus almond milk is shown. Which of the following statements is true?
Select one:
a. Point (1, 12) is an outlier.
b. There is clear evidence of a positive association between spending on cow milk and almond milk.
c. The equation of the least-squares regression line for this plot is approximately ŷ = x + 12.
d. The correlation for these data is r = −1.
e. The observation in the upper right corner of the plot is influential for the least-squares regression line.
Answer:
The observation in the upper right corner of the plot is influential for the least-squares regression line.
Step-by-step explanation:
Find the average rate of change
Answer:
[tex]\frac{3}{5\pi}[/tex]
Step-by-step explanation:
[tex]\frac{f(5\pi/6)-f(0)}{5\pi/6}=\frac{3}{5\pi}[/tex]
how i can do this? (7-i)(7+i)
please help it’s for tomorrow..
one segment measures 161 cm. Calculate its multiple according to the number 3 and its submultiple according to the number 7
Answer:
78
Step-by-step explanation:
The answer is 78 or 87 dear friend its a mystery
9. Triangles CDE and NOP are similar. The lengths of CD and NO are 53 in and 212in, respectively. DE
is 106 inches long and NP is 318 inches (draw a diagram and then answer the questions below)
a) Find OP and CE.
b) What is the perimeter of NOP?
c) What is the perimeter of CDE?
d) What is the ratio between the two perimeters?
Answer:
op
Step-by-step explanation:
I only require the explanation, not the answer.
The children in a class state how many children there are in their family.
The numbers they state are given below: 1, 2, 1, 3, 2, 1, 2, 4, 2, 2, 1, 3, 1, 2, 2, 2, 1, 1, 7, 3, 1, 2, 1, 2, 2, 1, 2, 3
So the question that I do not understand is:
Which is the most sensible average to use in the case.
The person with the most through explanation will get brainliest and will get awarded 75 points!
The most sensible average to use in this case would be the mode, which is the value that appears most frequently in the data set. In this case, the mode is 2, which appears 9 times in the data set. This means that the most common number of children in a family in the class is 2.
In this case, the most sensible average to use would be the mode, which is the number that appears most frequently in the data set. This is because the mode represents the most common number of children in the families of the children in the class, which is likely to be a more accurate representation of the typical family size in the class than the mean or median.
To find the mode, we first need to count how many times each number appears in the data set. In this case, the numbers 1, 2, 3, and 4 appear in the data set as follows:
1: 7 times
2: 11 times
3: 3 times
4: 1 time
We can see that the number 2 appears most frequently, with a count of 11. Therefore, the mode in this case is 2, and this is the most sensible average to use in this situation.
a study found an association between preferred warm beverage and stress level. it showed tea drinkers have lower stress levels than coffee drinkers. tea drinkers are known to have a higher proportion of yoga practitioners than coffee drinkers, and they exercise on average two hours per week more than their coffee-drinking counterparts. what is the term used to describe these additional factors that might have an effect on the stress levels of tea drinkers? responses categorical variables categorical variables cause-and-effect variables cause-and-effect variables confounding variables confounding variables quantitative variables quantitative variables response variables
Confounding variables is the term used to describe these additional factors that might have an effect on the stress levels of tea drinkers.
What is confounding variables?Confounding variables are those that have an effect on other factors in such a way that misleading or distorted relationships between two variables result. They misinterpret the "real" relationship between two variables. Confounding variable illustration You track sunburns and ice cream consumption. You discover that eating more ice cream increases your chances of becoming sunburned. To establish if a particular risk factor produced confounding, compare the estimated measure of association before and after controlling for confounding. To put it another way, compute the measure of association before and after correcting for a potential confounding factor.
Here,
Confounding variables are the terms used to explain these other elements that may have an influence on tea users' stress levels.
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to divide data with a high value of h and a low value of l into k classes, the class interval must be:
The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.
The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.
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help pls i don’t understand this cause my teacher can’t teach
Answer:
3/5
Step-by-step explanation:
AB = AC · cos A
18 = 30 · cos A
cos A = 18/30
cos A = 3/5
Brianne's annual contribution to her union dues is $200. If her salary is $38,500, approximately what is her percentage
rate contribution?
0.05%
0.5%
O 1%
5%
NEXT QUESTION
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Approximately, Brianne percentage rate of contribution is 0.5%.
How to find the percentage rate contribution?Brianne's annual contribution to her union dues is $200. Her salary is $38,500.
Approximately, her percentage rate of contribution can be calculated as follows:
percentage rate of contribution = union dues / salary × 100
union dues = 200 dollars
salary = 38500
percentage rate of contribution = 200 / 38500 × 100
percentage rate of contribution = 20000 / 38500
percentage rate of contribution = 0.51948051948
Therefore,
percentage rate of contribution ≈ 0.5%
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1.) Graph the system of equations on the grid below.
4x +2y=-12
3x-5y = -35
Answer:
first equation = red line
second equation = blue line
Step-by-step explanation:
First, we solve for y for both equations
4x + 2y = -12
2y = -12 - 4x
2y = -4x -12
y = -2x - 6
3x - 5y = -35
-5y = -35 - 3x
-5y = -3x - 35
y = (-3/5)x + 7
Given the equation 14.25y = 99.75, determine the value of y.
114.00
85.50
7.00
1421.44
The value of y in the equation 14.25y = 99.75 is C. 7.00.
How for determine the value of y?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, the equation is given as:
14.25y = 99.75
Divide through by 14.25
y = 99.75 / 14.25
y = 7
The value of y is 7.
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the residents of a city voted on whether to raise property taxes. the ratio of yes votes to no votes was 8 to 5. if there were 4955 no votes, what was the total number of votes?
A city's citizens cast ballots on whether or not to increase property taxes. There were 8 yes votes and 5 nay votes, in that order. if there were 4955 no votes,The total number of votes was 6,940.
The ratio of yes votes to no votes was 8 to 5, meaning for every 8 yes votes there were 5 no votes.
This ratio can be expressed as a fraction: 8/5.
To calculate the total number of votes, we need to know only the number of no votes, which we know is 4955.
We can then multiply this number by the fraction 8/5. This gives us a total of 6,940 votes.
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Which systems have infinite solutions? check all that apply. y = 0.5x 2.75 and 2y = x 2.75 y = 0.5x 2.75 and y – 0.5x = 2.75 y = 0.5x 2.75 and 0.5x y = 2.75 y = 0.5x 2.75 and y = 0.5(x 5.5) y = 0.5x 2.75 and y = –2(–0.25x ) 2.75
Both equations y = 0.5x + 2.75 and y – 0.5x = 2.75 are equal. Hence, these systems will have infinite solutions. Hence, Option a is the most suitable answer to this question.
The system of equations having an infinite number of solutions must be the same.
In option a -
we have, y = 0.5x + 2.75 and 2y = x + 2.75
Rewriting the second equation 2y = x + 2.75 in slope-intercept form, we get,
2y = x + 2.75
y = x/2 + 2.75/2
y = 0.5x + 1.375
Both equations are not similar.
Hence this option is not the right choice.
Similarly, we will check for option b -
we have, y = 0.5x + 2.75 and y – 0.5x = 2.75
From the second equation y - 0.5x = 2.75, this can be expressed as y = 0.5x + 2.75 in the slope-intercept form.
Here, we get both equations equal.
Thus, y = 0.5x + 2.75 and y – 0.5x = 2.75 will have infinite solutions.
Similarly, checking for other options, we do not get any similar equations.
Hence, option b is the correct answer to this question.
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The complete question is -
Which systems have infinite solutions? Check all that apply.
a) y = 0.5x + 2.75 and 2y = x + 2.75
b) y = 0.5x + 2.75 and y – 0.5x = 2.75
c) y = 0.5x + 2.75 and 0.5x + y = 2.75
d) y = 0.5x + 2.75 and y = 0.5(x + 5.5)
e) y = 0.5x + 2.75 and y = –2(–0.25x )+ 2.75
Answer: look at the screenshot below I hope it helps you, my friend
have a lovely day :3 :) :D
UWU
Step-by-step explanation:
a 10-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 125-ft shadow. how tall is the cell phone tower?
Answer:
750 ft
Step-by-step explanation:
the 2 situations are similar ( both right triangles ) with corresponding sides being in proportion.
let h be the height of the cell phone tower
We require the dimensions to be the same, using the conversion
1 foot = 12 inches , then
10 ft = 10 × 12 = 120 in
125 ft = 125 × 12 = 1500 in
then we obtain
[tex]\frac{h}{1500}[/tex] = [tex]\frac{120}{20}[/tex] = 6 ( multiply both sides by 1500 to clear the fraction )
h = 1500 × 6 = 9000 in ( divide by 12 to convert to ft )
h = 9000 in ÷ 12 = 750 ft
that is the cell phone tower is 750 ft tall.
I do everything correctly, and it still says that it's wrong! I do it the exact way my teacher taught me!
[tex]-\cfrac{5}{7}(-42k-56)\implies -\cfrac{5}{7}(-42k)\left[ -\cfrac{5}{7}(-56) \right]\implies +\cfrac{5}{7}(42k)+\left[ \cfrac{5}{7}(56) \right] \\\\\\ \cfrac{5(42k)}{7}+ \cfrac{5(56)}{7}\implies 5\cdot \cfrac{42}{7}k + 5\cdot\cfrac{56}{7}\implies 5\cdot 6k+5\cdot 8\implies {\Large \begin{array}{llll} 30k+40 \end{array}}[/tex]
Find the slope of the line:
Which of the following expressions will have a product greater than 4? four times ninety-nine hundredths four times eight-eighths three-fourths times four one hundred and one-one hundredths times four
The correct expression that has a product greater than 4 is one hundred and one hundredths times four.
What is an expression?A mathematical expression is a sentence with at least two numbers or variables and at least one mathematical operation. Math operations include addition, subtraction, multiplication, and division.The most common type of algebraic expression is a monomial expression. A binomial expression. A polynomial expression.There are four expressions given as
(a) four hundredths of a percent
= 4 × 99/100
= 4 × 0.99
= 3.96
(b) four times the eighth
= 4 × 8/8
= 4 × 1
= 4
(c) four times three-fourths
= 3/4 × 4
= 3
(d) one hundred and one hundredths multiplied by four
= 1.01 × 4
= 4.04
As a result, the expression with a product greater than four is one hundred and one hundredths times four.
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the beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in.
the beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in is[tex]487.5lb .[/tex]
Calculate the moment of inertia by using following expression,
\begin{aligned}
[tex]I & =\frac{1}{12} b d^3 \\& =\frac{1}{12} \times 6 \times(4)^3 \\& =32 \mathrm{in}^4\end{aligned}\\[/tex]
The centroid at center is,
[tex]\begin{aligned}Q & =\bar{y}_1 A \\& =1 \times 6 \times 2 \\& =12 \mathrm{in}^3\end{aligned}$$[/tex][tex]\begin{aligned}q & =\frac{V Q}{I} \\& =\frac{650 \times 12}{32} \\& =243.75 \mathrm{lb} / \mathrm{in}\end{aligned}$$[/tex]
The shear flow is,
[tex]\begin{aligned}q & =\frac{V Q}{I} \\& =\frac{650 \times 12}{32} \\& =243.75 \mathrm{lb} / \mathrm{in}\end{aligned}[/tex]
Since, there is 3 rows of nails so the shear force resisted by each nail is,
[tex]\begin{aligned}\tau & =\frac{1}{3} q s \\& =\frac{1}{3} \times 243.75 \times 6 \\& =487.5 \mathrm{lb}\end{aligned}$$[/tex]
Therefore, the shear force resisted by each nail is 487.5
[tex]487.5lb .[/tex]
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points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. t or f
The given statement is true that the points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.
A line that splits another line segment into two equal halves by intersecting it perpendicularly is known as a perpendicular bisector. A rule, compass, and pencil can be used to create a perpendicular bisector.
When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized parts is known as a bisector. A line segment's perpendicular bisector suggests that it meets the segment at a 90-degree angle and splits it into two equal halves.
Perpendicular bisector theorem"Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints".
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There is a line that includes the point (9,1) and has a slope of -1/6. What is its equation in point-slope form?
It's equation in point-slope from is -1/6x+5/2.
What is equation?An equation is a formula that is express the equality of two equation.
Based on the given condition the formula
M= -1/6
Substitute {m -1/6
{ X= 9
{Y = 1
(Into y= mx+b)
1=-1/6×9+b
Reduce the expression into the Lowest term
1=-1/2×3+b
Write as a single fraction
1=-3/2+b
Rearrange variables to the left side of the equation.
-b= -3/2-1
Now we have to find the denominator and write the numerators above common denominator
-b=-3-2/2
Calculate the sum or difference
-b=-5/2
b=5/2
Substitute {m=-1/6 b=5/2 into y mx+b
Y=-1/6x+5/2
Rewrite the equation of the line
Y= -1/6x+5/2 in point-slope
Y-1 = -x-9/6
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