According to the partial construction shown, what is the next step in constructing a line perpendicular to a point on the line?
O Place compass at point D, and draw an arc that intersects the arc above DF.
1
O Place compass at point F, and draw an arc that intersects the arc above DF-
O Place compass at point P, and draw an arc above DF
O Place compass at point P, and draw an arc below DF
Answers
The next step in constructing a line perpendicular to a point on the line is A. Place a compass at point D, and draw an arc that intersects the arc above line DF.
Calculations and Parameters
To make a perpendicular line:
Draw a line segment like DFKeep the point on D and make an arc by increasing the length of the compassKeep the point on F and make an arc like same as beforeName the point as any meeting on the drawn arcConnect it to the point with PTherefore, the next step would be to Place a compass at point D, and draw an arc that intersects the arc above line DF.
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Related Questions
prove the diagonals of a square are perpendicular
Answers
Answer:
Given :- ABCD is a square.
To proof :- AC = BD and AC ⊥ BD
Proof :- In △ ADB and △ BCA
AD = BC [ Sides of a square are equal ]
∠BAD = ∠ABC [ 90° each ]
AB = BA [ Common side ]
△ADB ≅ △BCA [ SAS congruency rule ]
⇒ AC = BD [ Corresponding parts of congruent triangles are equal ]
In △AOB and △AOD
OB = OD [ Square is also a parallelogram therefore, diagonal of parallelogram bisect each other ]
AB = AD [ Sides of a square are equal ]
AO = AO [ Common side ]
△AOB ≅ △ AOD [ SSS congruency rule ]
⇒ ∠AOB = ∠AOD [ Corresponding parts of congruent triangles are equal]
∠AOB + ∠AOD = 180° [ Linear pair ]
∠ AOB = ∠AOD = 90°
⇒ AO ⊥ BD
⇒ AC ⊥ BD
Hence proved, AC = BD and AC ⊥BD
The median house price in Pickering Region increased by 5.8% from Jan 1, 2019 to Jan 1, 2021. A home was purchased in Pickering Region on Jan 1, 2019 for $600,000.
a)Assume this trend continues, write an exponential equation that models the Resale Value of this home over time.
b) At this rate, determine the date when the resale price of the home would reach $1 million (Show your work to accurate to the nearest month)
c) Use your exponential equation to determine the expected resale value of the home on April 1, 2020.
Answers
Using an exponential function, we have that:
a) The equation is: [tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex].
b) The house will have a value of $1 million during the year of 2037.
c) The expected value on April 1, 2020, is of $621,520.
What is an exponential function?
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the parameters are given as follows:
A(0) = 600000, r = 0.058 each 2 years.
Hence the exponential function is:
[tex]A(t) = 600000(1 + 0.058)^{\frac{t}{2}}[/tex]
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
Item b:
It is the year 2019 + t, for which A(t) = 1000000, hence:
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
[tex]1000000 = 600000(1.058)^{0.5t}[/tex]
[tex](1.058)^{0.5t} = 1.6667[/tex]
[tex]\log{(1.058)^{0.5t}} = \log{1.6667}[/tex]
[tex]0.5t\log{1.058} = \log{1.6667}[/tex]
[tex]t = \frac{\log{1.6667}}{0.5\log{1.058}}[/tex]
[tex]t = 18.12[/tex]
The house will have a value of $1 million during the year of 2037.
Item c:
April 1, 2020 is one year and 3 months = 1.25 years after January 1, 2019, hence the value of the home will be given by:
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
[tex]A(1.25) = 600000(1.058)^{\frac{1.25}{2}}[/tex]
A(1.25) = $621,520.
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at first decreased by 60% now increased by 80%
Answers
Answer:
72Step-by-step explanation:
at first decreased by 60% now increased by 80%
100 - 60% = 40
40 + 80% =
40 + 40 :100 * 80 =
40 + 32 =
72
3. How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
Answers
There cannot be more than two because there are only two vowels, e and a. But it has to be 4 lettered, which limits a lot of option, so there can only be one 4-letter code.
Two cards are chosen at random from a deck of 52 cards. What is the probability of
choosing a red jack at first and then choosing a red card without replacement?
Answers
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
Which of the following represents the graph of f(x) = 3x + 1? graph of exponential rising up to the right, through the point 0, 0 graph of exponential rising up to the right, through the point 0, 1 graph of exponential rising up to the right, through the point 0, 2 graph of exponential rising up to the right, through the point 0, negative 2
Answers
Answer:
Graph of exponential rising up to the right, through the point (0, 2).
Step-by-step explanation:
I think you mean f(x) = 3^x + 1.
When x = 0, 3^x = 1, so the graph of f(x) = 3^x will rise up to the right and pass through point (0. 1)
The + 1 translates the graph up 1 unit so
The graph of f(x) = 3^x + 1 passes through the point (0, 2).
Please help!!!!!!!!! in the similarity transformation of abc to def, abc was dilated by a scale factor of ?, reflected across the , and moved through the translation. i need help with the last portion of the question.
Answers
The complete similarity transformation is: triangle abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].
What is Similarity?When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.From the figure, we have:
AB = 2 units
DE = 4 units
So, the scale factor (k) is:
k = DE/AB
k = 4/2
k = 2
Also, both shapes are on either sides of the x-axis, and they are equidistant from the x-axis.
This means that the triangle is reflected across the x-axis with no translation.
Hence, the complete similarity transformation is: abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].
So, the scale factor is 2
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Find all the zeros of the polynomial x^4+x^3-34x^2-4x+120 if two of its zeros are 2,-2
Answers
Answer:
The zeroes are 2, -2, -6, 5.
Step-by-step explanation:
If 2 of the zeroes are 2 and -2 then (x - 2)(x + 2) is factor of the polynomial.
We can now do long division.
Note (x - 2)(x + 2) = x^2 - 4, so we have:
x^2 - 4 ( x^4 + x^3 - 34x^2 - 4x + 120 ( x^2 + x - 30 <--- Quotient
x^4 - 4x^4
x^3 - 30x^2 - 4x
x^3 -4x
-30x^2 + 120
-30x^2 + 120
x^2 + x - 30 = 0
(x + 6)(x - 5) = 0
x = -6, 5.
Answer:
5 and -6
Step-by-step explanation:
So when a polynomial has zeroes at a, then one of the factors (x-a). This is because in factored form, a polynomial can be written using it's factors as such: [tex]a(x\pm b)(x\pm c)(c \pm d)...[/tex] and so on, with the number of factors depending on the degree. The sign is plus or minus because it can be either, it will depend on the sign of the zero. The reason the zeroes are factors, is because when one of the factors is zero it makes the entire thing zero because multiplying them out will always get 0, if you're multiplying by a zero. Anyways, if you have a factor, you can divide, by those factors. So let's do that.
So you have the two factors (x+2)(x-2). So let's divide by each factor. In this example I'll be using long division. So essentially what long division, is finding how many times the leading coefficient of the dividend (x^4+x^3-34x^2-4x+120) can be divided by the leading coefficient of the divisor ((x-2)(x+2)). And then whatever you get, that will be part of the quotient, then take whatever you got, and multiply it by the divisor and then subtract that product from the dividend and then continue this process until the dividend is equal to 0 or you can't divide any further./
Original equation:
[tex](x+2)\div (x^4+x^3-34x^2-4x+120)[/tex]
Divide the leading coefficients:
[tex]\frac{x^4}{x}=x^{4-1} = x^3[/tex]
The x^3 will be part of the quotient, now multiply this by the divisor
[tex]x^3(x+2) = x^{3+1} + 2x^3 = x^4 + 2x^3[/tex]
Subtract the product from the dividend
[tex](x^4+x^3-34x^2-4x+120) - (x^4+2x^3) = x^4+x^3-34x^2-4x+120 - x^4 - 2x^3[/tex]
Group like terms:
[tex](x^4 - x^4) + (x^3 - 2x^3) -34x^2-4x+120[/tex]
Simplify:
[tex]-x^3 -34x^2-4x+120[/tex]
Divide leading coefficients:
[tex]\frac{-x^3}{x} = -x^{3-1} = -x^2[/tex]
The -x^2 will be part of the quotient, now multiply this by the divisor:
[tex]-x^2(x+2) = -x^{2+1} -2x^2 = -x^3-2x^2[/tex]
Subtract this from the dividend:
[tex](-x^3 -34x^2-4x+120) - (-x^3 - 2x^2) = -x^3 -34x^2-4x+120 + x^3 + 2x^2[/tex]
Group like terms:
[tex](-x^3 + x^3) + (-34x^2 + 2x^2)-4x+120[/tex]
Simplify:
[tex]-32x^2 -4x -120[/tex]
Divide the leading coefficients:
[tex]-\frac{32x^2}{x}=-32x^{2-1} = -32x[/tex]
This will be part of the quotient, now multiply this by the divisor:
[tex]-32x(x+2) = -32x^2 - 64x[/tex]
Subtract this from the dividend
[tex](-32x^2 -4x -120) - (-32x^2-64x) = -32x^2 -4x -120 + 32x^2 + 64x[/tex]
Group like terms:
[tex](-32x^2+32x^2) + (-4x+64x) -120[/tex]
Simplify:
[tex]60x+120[/tex]
Divide the leading coefficients:
[tex]\frac{60x}{x} = 60[/tex]
This will be part of the quotient, multiply it by the divisor:
[tex]60(x+2) = 60x+ 120[/tex]
Subtract this from the dividend:
[tex](60x+120)-( 60x+120) = 0\\[/tex]
Since this comes out perfectly to zero there is no remainder, and this is expected since it's a factor. You now take all the quotients from dividing the leading terms and you get [tex]x^3-x^2-32x+60[/tex]. To keep the original equation you simply multiply it, and you get: [tex](x+2)(x^3-x^2-32x+60)[/tex]. But what we really care about is the x^3-x^2-32x+60. We now divide it by the other factor x-2 using the same process
Original equation:
[tex]x^3-x^2-32x+60[/tex]
Divide leading terms:
[tex]\frac{x^3}{x} = x^2[/tex]
This will be part of the quotient, multiply it by the divisor
[tex]x^2(x-2) = x^3-2x^2[/tex]
Subtract this from the dividend
[tex](x^3-x^2-32x+60) - (x^3 - 2x^2) = x^2-32x+60[/tex]
Dividing leading coefficients:
[tex]\frac{x^2}{x} = x[/tex]
This will be part of the quotient, multiply it by the divisor:
[tex]x(x-2) = x^2-2x[/tex]
Subtract this from the dividend:
[tex](x^2-32x+60) - (x^2-2x) = -30x+60[/tex]
Divide the leading terms:
[tex]\frac{-30x}{x} = -30[/tex]
This will be part of the quotient, now multiply it by the divisor:
[tex]-30(x-2) = -30x+60[/tex]
Subtract it from the dividend:
[tex](-30x + 60) - (-30x + 60) = 0[/tex]
Now take all the quotients of the leading terms and you get:
[tex]x^2+x-30[/tex]
Now we can factor this quadratic to get the equation in completely factored form: We're looking for factors that multiply to -30 and add to 1. So we really need to look for factors that have a difference of 1, Or in other words |a-b| = 1. The sign can be determined after we fine the two factors. The factors 5 and 6 have a difference of 1, and since it needs to add to 1, the 5 has to be negative, and the 6 has to be positive.
So we get the factors: [tex](x-5)(x+6)[/tex]. Setting each of them equal to zero gets you:
x-5 = 0
x = 5
x + 6 = 0
x = -6
So the other two zeroes are 5 and -6
In a group of 55 people 3x+5 people 3x+5 people like apple.If all the people who like apple also like banana and if 2x+15 people like at least one of fruit then find how many like (i) bananas only (ii) none of the fruits (iii) at most one fruit
Answers
i. 20 people
ii. 3 people
iii. 26 people
How to determine the valuesWe have that;
3x + 5 people likes apples
3x + 5 people likes banana
2x + 15 people likes at least one of the fruits
The total number of people = 55
Let's find the value of x
3x + 5 + 2x + 15 = 55
5x + 20 = 55
5x = 55 - 20
5x = 35
x = 35/5
x = 7
i. People that likes banana only = 3x + 5 = 3 × 5 + 5 = 15 + 5 = 20 people
ii. None of the fruits = 55 - 2x + 15 = 55 - 3x + 5 - 3x + 5 = 55 - 26 +26
= 55 - 52
= 3 people
iii. At most one fruit = 55 - 2x + 15 = 55 - 2(7) + 15 = 55 - 29 = 26 people
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There are 20 girls and 15 boys in the class. How many different five-member teams could be formed if each team should be composed of three girls and two boys?
Answers
The number of combinations which are possible according to the specifications is; 119,700.
How many combinations are there to compose 3 girls and 2 boys?It follows from the task content that the 5ember teams to be formed must contain 3 girls and 2 boys.
On this note, it follows that the combinations possible are as follows
20C(3) × 15C2 = 1140 × 105 = 119,700.
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Someone PLEASEEEEE HELP!! :(
Answers
The equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Equation of a lineFrom the question, we are to determine the equation of the line that passes through the given points
Using the formula
[tex]\frac{y-y_{1} }{x-x_{1}} =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
From the give information,
[tex]x_{1} = 1 \\y_{1} = 1\\{x_{2} =5[/tex]
[tex]y_{2} = 6\\[/tex]
Putting the parameters into the formula,
[tex]\frac{y-1 }{x-1} =\frac{6-1}{5-1}[/tex]
[tex]\frac{y-1 }{x-1} =\frac{5}{4}[/tex]
∴ [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Hence, the equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]
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Three brothers divided a prize as follows. The oldest received %, the middle brother received ½, and the youngest received the remaining $120. What was the value, in dollars, of the prize?
Answers
Answer:
1200
Step-by-step explanation:
Ok since the oldest was given 2/5, the middle was given 1/2, and the youngest was given the rest, that means the fraction that the youngest was given has to make 2/5 + 1/2 + ? = 1. So we have the equation: [tex]\frac{2}{5} + \frac{1}{2} + x = 1[/tex]. Now to add the fractions simply multiply 2/5 by 2/2 and multiply 1/2 by 5/5 To get the same denominator: [tex]\frac{4}{10} + \frac{5}{10}+x=\frac{9}{10}+x[/tex]. This means that x is 1/10 , because in adding 1/10 you get the whole 10/10. So 120 is one tenth of the entire prize. This means to get the entire prize you simply multiply by 10. This gives you the equation 120 * 10 = 1200
Find the value of x in the given
right triangle.
37%
X
10
X= [?]
Enter your answer as a decimal rounded to the
nearest tenth.
Enter
Answers
Answer:
x ≈ 8.0
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos37° = = ( multiply both sides by 10 )
10 × cos37° = x , thus
x ≈ 8.0 ( to the nearest tenth )
does this help? :D
Which ordered pair makes both inequalities true?
y > –2x + 3
y < x – 2
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (0, 3) and (1, 1). Everything to the right of the line is shaded.
(0,0)
(0,–1)
(1,1)
(3,0)
Answers
The ordered pair which makes both inequalities true is: D. (3, 0).
How to determine ordered pair?In Mathematics, an inequality can be used to show the relationship between two (2) or more integers and variables in an equation.
In order to determine ordered pair which makes both inequalities true, we would substitute the points into the inequalities as follows:
At (0, 0), we have:
y > -2x + 3
0 > -2(0) + 3
0 > 3 (false).
y < x – 2
0 < 0 - 2
0 < -2 (false)
At (0, -1), we have:
y > -2x + 3
-1 > -2(0) + 3
-1 > 3 (false).
y < x – 2
-1 < 0 - 2
-1 < -2 (false)
At (1, 1), we have:
y > -2x + 3
1 > -2(1) + 3
1 > -1 (true).
y < x – 2
1 < 1 - 2
1 < -1 (false)
At (3, 0), we have:
y > -2x + 3
0 > -2(3) + 3
0 > -3 (true).
y < x – 2
0 < 3 - 2
0 < 1 (true).
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Construct a matrix of order 3×2 whose elements are given by Cij=|−2i+3j|/2
Answers
[tex]C_{ij}[/tex] is the entry of [tex]C[/tex] in row [tex]i[/tex] and column [tex]j[/tex]. [tex]C[/tex] has 3 rows and 2 columns, so
[tex]C_{11} = \dfrac{|-2\times1+3\times1|}2 = \dfrac{|-2+3|}2 = \dfrac{|-1|}2 = \dfrac12[/tex]
[tex]C_{12} = \dfrac{|-2\times1+3\times2|}2 = \dfrac{|-2+6|}2 = \dfrac{|4|}2 = 2[/tex]
[tex]C_{21} = \dfrac{|-2\times2+3\times1|}2 = \dfrac{|-4+3|}2 = \dfrac{|-1|}2 = \dfrac12[/tex]
[tex]C_{22} = \dfrac{|-2\times2+3\times2|}2 = \dfrac{|-4+6|}2 = \dfrac{|2|}2 = 1[/tex]
[tex]C_{31} = \dfrac{|-2\times3+3\times1|}2 = \dfrac{|-6+3|}2 = \dfrac{|-3|}2 = \dfrac32[/tex]
[tex]C_{32} = \dfrac{|-2\times3+3\times2|}2 = \dfrac{|-6+6|}2 = \dfrac{|0|}2 = 0[/tex]
Then the matrix is
[tex]C = \begin{bmatrix}\dfrac12 & 2 \\\\ \dfrac12 & 1 \\\\ \dfrac32 & 0\end{bmatrix} = \dfrac12 \begin{bmatrix}1&4\\1&2\\3&0\end{bmatrix}[/tex]
36. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
36. x-intercept at (-2, 0) and y-intercept at (0, -3)
Answers
Answer:
The linear equation for the line with an x - intercept at (-2,0) and y-intercept at (0,-3) is found as [tex]$y=-\frac{3}{2} x-3$[/tex].
Step-by-step explanation:
A condition is given that a line has an x- intercept at (-2,0) and y - intercept at (0,-3).
It is asked to find a linear equation satisfying the given condition.
Step 1 of 2
Determine the slope of the line.
The points of the intercepts of the line are given as (-2,0) and (0,-3). Next, the formula for the slope is given as,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute -3&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and 0&-2 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$$\begin{aligned}m &=\frac{-3-0}{0-(-2)} \\m &=\frac{-3}{2} \\m &=-\frac{3}{2}\end{aligned}$$[/tex]
Step 2 of 2
Write the equation in the slope-intercept form.
The slope-intercept form of a line is given as follows,
y=mx+b
The coordinates at the y- intercept is (0,-3). Now, as the y- coordinate is -3, so b=-3.
So, substitute -3 for b and [tex]$-\frac{3}{2}$[/tex] for m in the equation y=mx+b, and simplify to get the equation as follows,
[tex]$$\begin{aligned}&y=-\frac{3}{2} x+(-3) \\&y=-\frac{3}{2} x-3\end{aligned}$$[/tex]
This is the required linear equation.
Here's a new question!
Which ray is the terminal side of a 6 radian angle in standard position?
a) positive x axis
b) positive y axis
c) negative x axis
d) negative y axis
Answers
Answer:
negative y axis
Step-by-step explanation:
6 radians is between 3pi/2 and 2pi radians, so it lies in tje fourth quadrant.
So, a terminal side is the negative y axis.
What type of number is −0.5/ −0.5
Choose all answers that apply:
a)Whole number
b)Integer
c)Rational
d)Irrational
Answers
Answer:
[tex] \frac{ - 0.5}{ - 0.5} = 1 \\ [/tex]
1 is a whole number, an integer, and rational.
Step-by-step explanation:
HOPE THIS HELPS.What is the slope of the line through (-1, 4) and (1, -2)?
-3 -2
3
-1
-2
-3
y
2
(1,-2)
3
4
Answers
A researcher designs a study that will investigate the effects of a new
statistical software on graduate students' understanding of statistics. The
researcher creates a survey, consisting of 10 questions. She compares two
samples, each containing 10 randomly selected students. One sample
consists of students graduating in May. The other sample consists of
students graduating the following May.
A. The sample size is too small.
B. One sample has more graduate level experience than the other
sample.
C. An exam should be used, instead.
D. Randomly selected students were used.
Answers
The statement that is true is: D. Randomly selected students were used.
What is survey?Survey can be defined as the data or information that a researcher or research analyst collected from a population so as to reach or draw a conclusion.
Based on the scenario the student were randomly selected which means that the randomly selected students were used to conduct the survey.
Therefore the correct option is D.
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In construction, the precision used to build a structure directly influences the strength of the structure. In the Rocky Mountains, many houses’ roofs are built using trusses, which are strong enough to support the heavy load from snow, but light enough to build in a stockyard and transport to the construction site. Chris works in the stockyard. He has been told he needs to build a series of trusses for a new house using the pattern below. He has also been told the pattern may be inaccurate—so he needs to check and make sure the following features are all parallel, and adjust the pattern before starting.
On this discussion board, post your answers to these questions:
1) What method(s) can Chris use to make sure the segments in the pattern are all parallel and that his new trusses are built precisely and strongly?
2) What method(s) can Chris’s boss use to verify the precision of the trusses Chris builds?
3)Identify any alternate interior angles, corresponding angles, and/or alternate exterior angles.
Answers
The method that Chris can use to make sure the segments in the pattern are all parallel is to treat AI as a single line that acts as a transversal for the lines that need to be parallel.
How to illustrate the information?Within the set of lines which need to be parallel, the acute angles must be congruent.
Both angles CDE and EDF need to be 180° minus twice the measure of one of the congruent acute angles.
The pair of the acute angles previously within each of the two sets of parallel lines are corresponding.
The fact that the transversals go through endpoints, there are no alternate angles, interior or exterior because alternate angles are on opposite sides of the transversal.
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Volume = in2
Help me please
What is the volume
Answers
Answer: 1344
Step-by-step explanation:
Using the Pythagorean theorem, if we consider the unknown leg of the base, we get that it has a length of 12.
So, the area of the base is 96.
Multiplying this by the height, we get the volume is 1344 cubic inches.
Can someone help me please?
Answers
A chord is a part of a circle that joins two points on its circumference but does not pass through the center of the circle. From the given diagram in the question, GH = HJ. Thus the measure of chord HJ is option C. 8.6 units.
A chord is one of the parts of a circle which does not pass through its center but joins two points on its circumference. So that it is not the same as the radius of the circle.
In the given question, it has been stated that: GH and HJ are congruent.
So that by the congruency property of two lines, the length of chod GH is the same as the length of chord HJ.
Therefore, the measure of chord Hj is 8.6 units. This implies option C.
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using visual cues identify each pair of angles on the diagram below
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The special angles pairs that are formed are identified below.
What are the Special Angle Pairs?Special angle pairs are formed by a transversal and the parallel lines it cuts across.
Based on the image given, the special angle pairs are given as follows:
Corresponding angles:
∠1 and ∠5
∠4 and ∠8
∠2 and ∠6
∠3 and ∠7
Alternate interior angles:
∠3 and ∠5
∠4 and ∠6
Consecutive interior angles:
∠4 and ∠5
∠3 and ∠6
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During a basketball season, a player scored a total of 650 points in 31 basketball games. What is his scoring average for the season?
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Can someone help me out on this geometry questions about SSS, SAS, ASA Postulate, I’m in hurry :(
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Answer:
11. ASA
12. SSS
13. SAS
14. SAS
15. Not congruent
16. SAS
Step-by-step explanation:
11.
12, Oppositely congruent
13. indirectly congruent
14. Indirectly congruent
15.
16. Directly congruent
Help please, I can never seem to figure these out
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The area of the shaded region = π(4²) - (4√2)² = 50.27 - 32
The area of the shaded region, to one decimal place is: 18.3 m²
What is the Area of the Shaded Region of a Circle?The area of the shaded region = area of the circle - area of the square = πr² - s².
Radius (r) of the circle = 1/2(length of diagonal of the square)
Using Pythagorean theorem, we have:
Diagonal = √[(4√2²) + (4√2²)]
Diagonal = √(32 + 32]
Diagonal = 8 m
Radius (r) = 8/2 = 4
s = 4√2
The area of the shaded region = π(4²) - (4√2)² = 50.27 - 32
The area of the shaded region = 18.3 m²
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By selling my car for sh 276000,the price was below the initial price. What is the initial price?
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The initial price in this scenario is > sh 276000 and was therefore sold at a loss.
What is Loss?This is a situation in which the selling price of goods or services is lower than the cost price.
We were told that the selling price is sh 276000 which is less than the initial(cost) price hence he ran at a loss during the business transaction.
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Please help! Most Beagles have shoulder heights between 36 and 41 centimeters. The following compound inequality relates the estimated shoulder height (in centimeters) of a dog to the internal dimension of the skull D (in cubic centimeters):
36 ≤ 1.02D – 31.2 ≤ 41
Which compound inequality represents the range for the skull size of Beagles? Answer choices are rounded to the nearest tenth.
Answers
Answer: B
Step-by-step explanation:
Given:
36=<1.02D-31.2<=41
Solve the compound inequality for D:
36+31.2<=1.02D<=41+31.2
67.2<=1.02D<=72.2
65.9<=D<=70.8
Therefore, option (b) is correct answer
A flagpole casts a shadow 22 feet long. If a man 6 feet tall cast a shadow 4.3 feet long at the same time, how tall is the flagpole? Please explain your answer.
Answers
Answer:
30.70 ft
Step-by-step explanation:
For shadow problems, we make the assumption that an object's height and its shadow length are proportional.
SetupThe proportion for the two objects is ...
height/shadow = pole/(22 ft) = (6 ft)/(4.3 ft)
SolutionMultiplying by 22 ft, we find the pole height to be ...
pole = (22 ft)(6 ft)/4.3) ≈ 30.70 ft
The flagpole is about 30.70 feet tall.