Answers
Answer:
PQRS is a parallelogram with right-angle corners
Step-by-step explanation:
We know that the midsegment of a triangle is parallel to the base.
QR is the midsegment of triangle BCD, so is parallel to BD.
SP is the midsegment of triangle DAB, so is parallel to BD.
QR and SP are both parallel to BD, so are parallel to each other.
RS is the midsegment of triangle CAD, so is parallel to AC.
PQ is the midsegment of triangle ABC, so is parallel to AC.
RS and PQ are both parallel to AC, so are parallel to each other.
__
We have shown that opposite sides of PQRS are parallel to each other, so the figure is at least a parallelogram.
__
By virtue of the congruence of corresponding angles where a transversal crosses parallel lines, each of the so-far named lines can be shown to be perpendicular to any of the lines it meets.* Hence the figure PQRS must be a parallelogram with right angles, a rectangle.
_____
* Transversal BD crosses PQ, AC, and RS at right angles. Hence, transversals RS and PQ cross QR, BD, and SP at right angles. That is, the angles at corners P, Q, R, and S of the parallelogram are right angles.
Related Questions
Consider line A which is defined by the equation:
y=5/6x-5/2
and the point P(-3,6) and then answer the following questions:
a. How would you find the line (B) that passes through point P and is perpendicular to line A? What is the equation of that line?
b. How would you find the length of the segment of line B from point P to line A?
c. How would you find the midpoint between point P and the intersection of line A and line B ?
Answers
Answer:
y = -6/5x +12/5distance from P to A: (66√61)/61 ≈ 8.4504midpoint: (-18/61, 168/61) ≈ (-0.2951, 2.7541)Step-by-step explanation:
a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...
m = -1/(5/6) = -6/5
Then the point-slope form of the desired line through (-3, 6) can be written as ...
y = m(x -h) +k . . . . . line with slope m through (h, k)
y = (-6/5)(x +3) +6
y = -6/5x +12/5 . . . equation of line B
__
b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.
When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...
d = |ax +by +c|/√(a² +b²)
The equation of line A can be written in general form as ...
y = 5/6x -5/2
6y = 5x -15
5x -6y -15 = 0
Then the distance from P to the line is ...
d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61
The length of segment PX is (66√61)/61.
__
c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...
y = 5/6x -5/2
y = -6/5x +12/5
Equating y-values gives ...
5/6x -5/2 = -6/5x +12/5
Adding 6/5x +5/2 gives ...
x(5/6+6/5) = 12/5 +5/2
x(61/30) = 49/10
x = (49/10)(30/61) = 147/61
y = 5/6(147/61) -5/2 = -30/61
Then the point of intersection of the lines is X = (147/61, -30/61).
So, the midpoint of PX is ...
M = (P +X)/2
M = ((-3, 6) +(147/61, -30/61))/2
M = (-18/61, 168/61)
Follow the process of completing the square to solve x2 = -4x + 3
Answers
Answer:
x1 = 0.64575
x2 = -4.64574
Step-by-step explanation:
Step 1: We want to rearrange the equation so all the variables are on one side
0 = -x² - 4x + 3
Step 2: We take out -1 in the first 2 terms so a = 1
0 = -(x² + 4x) + 3
Step 3: Force a square, take the 'b' value and divide it by 2 and square the result. Add it and subtract it from the inside of the brackets
b = 4
4/2 = 2
2² = 4
0 = -(x² + 4x + 4 - 4) + 3
Step 4: Move the -4 out remembering to apply the -
= -(x² + 4x + 4) + 4 + 3
Step 5: We notice is inside the brackets is a perfect square
0 = -(x + 2)² + 7
Therefore the vertex form of the equation is
y = -(x + 2)² + 7
Step 6: We want to solve the equation (find the x intercepts) so we set y to 0 and solve for x
0 = -(x + 2)² + 7
-7 = -(x + 2)²
7 = (x + 2)²
[tex] \sqrt{7 } = x + 2 [/tex]
[tex]x = \sqrt{7} - 2[/tex]
1st Solution:
x = +2.64575 - 2
x = 0.64575
2nd Solution:
x = -2.64575 - 2
x = -4.64574
multiple choice
a. 126 pie cm^3
b. 84 pie cm^3
c. 504 pie cm*3
Answers
Answer:
a. 126 pie cm^3
Step-by-step explanation:
Area of a circle = pi*r²
Volume = area*height
(pi*r²)*14
Since your answers are with Pi omit the Pi and times 3² * 14 = 126 pie cm³
Answer:
A. 126pi cm^3
Step-by-step explanation:
The volume of a cylinder can be found using the following formula.
[tex]v=\pi r^2 h[/tex]
First, we must find the radius. The radius is half of the diameter.
[tex]r=\frac{d}{2}[/tex]
The diameter of the cylinder is 6 cm.
[tex]r=\frac{6cm}{2}[/tex]
[tex]r= 3cm[/tex]
The radius is 3 cm.
Now, we can substitute values into the formula.
[tex]v=\pi r^2 h[/tex]
[tex]r= 3cm\\h=14 cm[/tex]
[tex]v=\pi (3cm)^2*14 cm[/tex]
Evaluate the exponent.
[tex](3cm)^2=3cm*3cm=9cm^2[/tex]
[tex]v=\pi*9cm^2*14cm[/tex]
Multiply 9 cm^2 and 14 cm
[tex]9 cm^2*14cm=126cm^3[/tex]
[tex]v=\pi*126cm^3[/tex]
The answer choices are in terms of pi, so we can simply rearrange our answer:
[tex]v=126\pi cm^3[/tex]
The volume of the cylinder is 126pi cubic centimeters and A is the correct answer.
How many 3-digit numbers can you write if you cannot use any other digits except 4 and 6?
Answers
Answer:
Step-by-step explanation:
4 4 4
4 4 6
4 6 6
4 6 4
6 6 6
6 6 4
6 4 4
6 4 6
If EH = 80, calculate GF.
Answers
Answer:
The length of Segment GF is 120
Step-by-step explanation:
Given that EH = 80, and AB, GF, RH, and DI are parallel lines, we have;
DC ≅ DE ≅ EF ≅ FA Given
Therefore, CI ≅ HI ≅HG ≅ GB (Triangle proportionality theorem)
From where we have;
EH/GF =CH/CG (Intercept theorem otherwise known as Thales' theorem )
CH = 2 × CI (Transitive property of equality)
Also CG = 3 × CI (Transitive property of equality)
EH/GF = 2×CI/(3×CI) = 2/3
EH/GF = 2/3
80/GF = 2/3
Therefore we have;
Segment GF = 80 × 3/2 = 120
The length of Segment GF = 120.
120 U-U
Mostly cuz i looked it up and i am not explaining it cuz i dont wanna
Max A = 15 - x^2 - x
Answers
Answer:
not exactly sure what the question is but
if it is "what is the max that 15 - x^2 - x can be
then 2x-1 = 0 solves that
x = 1/2
Step-by-step explanation:
Write down all the prime numbers between 20 and 70
Answers
Answer:
23,29,31,37,41,43,47,53,59,61 and 67.
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:
23, 29, 31, 37, 41, 43, 47, 53, 61, 67
Step-by-step explanation:
Im not entirely sure but I believe I'm correct here.
The admission fee at an amusement park is $3.50 for children and $6.80 for adults. On a certain day, 223 people entered the park, and the admission fees collected totaled 1160 dollars. How many children and how many adults were admitted?
Answers
Answer:
108 children and 115 adults were admitted
Step-by-step explanation:
Create a system of equations where c is the number of children admitted and a is the number of adults admitted:
c + a = 223
3.5c + 6.8a = 1160
Solve by elimination by multiplying the top equation by -3.5:
-3.5c - 3.5a = -780.5
3.5c + 6.8a = 1160
Add the equations together and solve for a:
3.3a = 379.5
a = 115
So, 115 adults were admitted.
Find how many children were admitted by subtracting 115 from 223, the total number of people admitted:
223 - 115
= 108
108 children and 115 adults were admitted.
-10 + (-15) =
+
what do i do first
Answers
Answer:
-15 then -10 = -25 we can only take one sign that accompanies the -10 and put in front of the brackets.
Step-by-step explanation:
-10 + (-15) = -25
just like (-15) -10 = 25
This is because ( ) is order of parenthesis Brackets first.
Answer:
-10 + (-15) is -25 and you do subtraction first.
Step-by-step explanation:
Since negative + negative is negative, you ignore the plus sign and continue with the equation. So -10 minus -15 is -25.
Solve: MXC multiplied by IV. Show your answer in standard form. Standard Roman Number Numeral 1 1 5 V 10 50 L 100 C 500 D 1,000 M X-003 O A) 4,060 OB) 4,360 OC) 4,440
Answers
Answer:
4360
Step-by-step explanation:
MXC is 1090 and a IV is 4 so 1090 x 4 is 4360
PLS HELP ASAP! 20 PTS
evaluate
Answers
Answer:
Step-by-step explanation:
Cos^-1(1/2) = 60
To get from a degree to radian, simply multiply by pi then divide by 180. So the final answer is 1/3pi or approximately 1.0472
I hope this helped! :D
HCF of algebraic expression x square minus y square and x y minus y square.
Answers
Answer:
(x-y+z)(x-y-z)
Given (x²-2xy+y²) - z²
= (x-y)² - z²
/* By algebraic identity
a²-2ab+b² = (a-b)² */
=[(x-y)+z][(x-y)-z]
/* a²-b² = (a+b)(a-b) */
= (x-y+z)(x-y-z)
Therefore,
(x²-2xy+y²)-z² =(x-y+z)(x-y-z)
Step-by-step explanation:
x
2
y
2
=x×x×y×y
xy
2
=x×y×y
h.c.f=xy
2
The value of 1.8/(0.4×0.3) is
Answers
Answer:
15
Step-by-step explanation:
1.8 over 0.4 multiply 0.3
Answer: 15
Step-by-step explanation:
1.8/(0.4×0.3)
=1.8/0.12
=15
Hope this helps!! :)
Rita bought 4 CDs that were each the same price. Including sales tax, she paid a total of $ 61.60. Of that total,$ 2.80 was tax. What was the price of each CD before tax
Answers
Answer:
The price of each CD is:
$14.70
Step-by-step explanation:
(61.6 - 2.8) /4
= 58.8/4
= $14.7
Answer:
$14.70
Step-by-step explanation:
We want to find the price of each CD before tax. Therefore, we must first subtract the tax from the total.
total -tax
The total cost was $61.60 and the tax was $2.80
$61.60 - $2.80
$58.80
The price for the 4 CDs (without tax) was $58.50.
We know that each CD costs the same price and Rita bought four CDs. Therefore, we can divide the cost without tax by 4.
cost without tax / 4
The cost without tax is $58.80
$58.80 /4
$14.70
Each CD before tax costs $14.70
Please help!
Suppose that [tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex]. If [tex]\alpha=4[/tex] when [tex]\beta=9[/tex], find [tex]\alpha[/tex] when [tex]\beta=-72[/tex]
Answers
Answer:
The answer is
[tex] \alpha = - \frac{1}{2} [/tex]Step-by-step explanation:
From the question
[tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex] is written as
[tex] \alpha = \frac{k}{ \beta } [/tex]where k is the constant of proportionality
When
[tex]\alpha[/tex] = 4[tex]\beta[/tex] = 9Substituting the values into the formula
we have
[tex]4 = \frac{k}{9} [/tex]
cross multiply
k = 4 × 9
k = 36
So the formula for the variation is
[tex] \alpha = \frac{36}{ \beta } [/tex]
when
[tex]\beta[/tex] = - 72
That's
[tex] \alpha = \frac{36}{ - 72} [/tex]
Simplify
We have the final answer as
[tex] \alpha = - \frac{ 1}{2} [/tex]Hope this helps you
Answer the question below. Type your response in the space provided. Then compare your answer to the sample answer.
Point B(-2,4) lies on a circle centered at A(1, 3). Write a paragraph proof to determine whether C(4, 2) also lies on the circle.
В І О
x x
Font Sizes
A- A
DEE
Characters used: 0/15000
Submit
Answers
Answer: see proof below
Step-by-step explanation:
The standard equation of a circle is (x - h)² + (y - k)² = r² where (h. k) is the center of the circle and r is the radius. It is given that A (h, k) = (1, 3) and point B (x, y) = (-2,4) is on the circle. Substitute the center (h, k) and point B(x, y) = (-2,4) into the standard equation of a circle to get r² = 10. To prove that C(x, y) = (4, 2) is also a point on the circle, substitute the center (h, k) and the point C(x, y) = (4, 2) into the standard equation of a circle to get r² = 10. Since the radius is the same for both point B and point C and it is given that point B is on the circle, then we must conclude that point C is also on the circle.
Answer:
I am given that the center of a circle is at A(1, 3) and that point B(-2, 4) lies on the circle. Applying the distance formula to A and B, I get the following:
AB=Square Root ( (-2 - 1 )^2 + (4 - 3 )^2 ) = Square root ( 9 + 1 )
AB = Square root (10)
Since B lies on the circle, this length is the length of the radius of the circle. Applying the distance formula to A and C(4, 2), I get the following:
AC = Square Root ( ( 4 - 1 )^2 + (2 - 3 )^2 ) = Square root ( 9 + 1 )
AC = Square root (10)
Thus, the distance to C from the center A is equal to the length of the radius of the circle. Any point whose distance from the center is equal to the length of the radius lies on the circle. Therefore, point C lies on the circle.
Step-by-step explanation:
The table shows the times that street lights come on one night and go off the next morning.In Glasgow, the lights go off later than they do in Newcastle. How much later?
Answers
Answer:
10 mns later
Step-by-step explanation:
Select the correct answer.
Solve – 93-(-103)
OA.
-13
11
OB.
Oc. 1917
D. 19 /
Answers
Answer:
1 1/7.
Step-by-step explanation:
-9 2/7 - (-10 3/7)
= -9 2/7 + 10 3/7
= - 9 + 10 - 2/7 + 3/7
= 1 + 1/7
= 1 1/7.
Answer:
[tex] \huge \boxed{ \bold{ \purple{1 \frac{1}{7} }}}[/tex]Option B is the correct option
Step-by-step explanation:
[tex] \mathsf{ - 9 \frac{2}{7} - ( - 10 \frac{3}{7}) }[/tex]
First thing we have to do is that convert the mixed number into improper fraction .
[tex] \blue{ \mathsf{how \: to \: convert \: \: the \: improper \: fraction \: to \: mixed \: number}}[/tex]
Follow the steps:
Multiply denominator by the whole number.Add the answer from step 1 to the numerator.Put step 2 answer over the denominatorNow, let's do it!
[tex] \mathsf{ - \frac{ 9 \times7 + 2 }{7} - ( - 10 \frac{3}{7} )}[/tex]
⇒[tex] \mathsf{ - \frac{65}{7} - ( - 10 \frac{3}{7} )}[/tex]
When there is a ( - ) in front of an expression in the
parentheses , change the sign of each term in the expression
⇒[tex] \mathsf{ - \frac{65}{7} + 10 \frac{3}{7} }[/tex]
Convert mixed number into improper fraction
⇒[tex] \mathsf{ - \frac{65}{7} + \frac{73}{7} }[/tex]
While performing the addition and subtraction of like fractions , you just have to add or subtract the numbers for respectively in which the denominator is retained same
⇒[tex] \mathsf{ \frac{ - 65 + 73}{7} }[/tex]
Calculate
⇒[tex] \mathsf{ \frac{8}{7} }[/tex]
Convert the improper fraction into mixed fraction.
( Since 8 is being divided by 7 , I am gonna use long division )
( See attached picture )
⇒[tex] \mathsf{1 \frac{1}{7} }[/tex]
Hope I helped!
Best regards!!
solve for x 15x + 6 = 10x + 21
Answers
Answer:
15x+6=10x+21
15x-10x=21-6
5x=15
divide by 5
5x/5=15/5
x=3
Answer:
x=3
Step-by-step explanation:
15x+6=10x+21
-10x
5x+6=21
-6
5x=15
divided by 5
x=3
Question 12
What is the value of x in the following equation?
2/3x + 2 = 4
Answers
Step by step solution-
You subtract both sides by 2,
2/3x= 2
Then divide both sides by 2/3 to isolate the x.
2/ (2/3) = 3
Therefore, x=3
Evaluate the function below at x=7. Then enter your solution rounded up to 2 decimal places. 1500•1.09^x
Answers
Answer:
Value of the function will be 2742.06
Step-by-step explanation:
Given function is,
f(x) = 1500(1.09)ˣ
By substituting the value of x we can find the value of the given function.
For x = 7,
f(7) = 1500(1.09)⁷
= 1500(1.828)
= 2742.0587
≈ 2742.06
Value of the function will be 2742.06
Divide. Write your answer as a decimal.
8.722÷(−3.56)=
Answers
Answer:
-2.45
Step-by-step explanation:
I used a calculator to find this so I hope it helps :)
please help i beg plsssssssssz
Answers
Answer:
5/2=20/8=35/14=125/50
Answer:
8, 14, 50
Step-by-step explanation:
5 x 4 = 20
2 x 4 = 8
5 x 7 = 35
2 x 7 = 14
5 x 25 = 125
2 x 25 = 50
Simplify.
Remove all perfect squares from inside the square root.
V63 =
I need the answer ASAP can anyone help?
Answers
3*sqrt(7)
3 times the square root of 7
====================================================
Explanation:
I'm assuming the V stands for square root. You can write sqrt(63).
[tex]\sqrt{63} = \sqrt{9*7}\\\\\sqrt{63} = \sqrt{9}*\sqrt{7}\\\\\sqrt{63} = 3\sqrt{7}[/tex]
The idea is to factor 63 in such a way that one factor is the largest perfect square possible, that way we can pull the root apart to simplify as shown above. The rule I used for the second step is [tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex]
Imagine that you have plotted many data points on an xy-plane. Your points seem to align into a clear best-fit line. Do you think this best-fit line can help you make predictions about future data? Explain your answer, and give one or more examples to support it.
Answers
It depends really. If you stay close to the present, then predicting future results isn't too bad. The further you go out, the more unpredictable things get. This is because the points may deviate from the line of best fit (aka regression line) as time wears on. Of course, it also depends on what kind of data we're working with. Some pairs of variables are naturally going to correlate very strongly together. An example would be temperature versus ice cream sales.
A best-fit line shows an association between two variables and can therefore be used to make predictions.
An example is a scatterplot attached below showing a best-fit line that depicts the association between the number of people that bath in a pool and daily temperature.
(see attachment below).
Recall:
A best-fit line is a line drawn on a scatterplot showing a trend or an association between two variables.A best-fit line can either show a weak association or a strong association.A best-fit line is often applied in various situations to make predictions based on current trend revealed.Therefore, a best-fit line shows an association between two variables and can therefore be used to make predictions.
An example is a scatterplot attached below showing a best-fit line that depicts the association between the number of people that bath in a pool and daily temperature.
(see attachment below).
Learn more here:
https://brainly.com/question/2396661
Which regular polygon can be used to form a tessellation?
I need help
Answers
Answer:
The regular polygon that can be used to form a regular tessellation are the equilateral triangle a square and a regular hexagon
Is it ok if you help me solve this?
Answers
Answer:
For it to be parallel the answer is B (3)
Answer:
B) 3
Explanation:
If two lines are parallel that means that their equations have the same value of slope.
PLEASE HELP ASAP! If t is a real number, what is the maximum possible value of the expression -t^2 + 8t -4?
Answers
Answer:
12
Step-by-step explanation:
Hello, as the coefficient of the leading term is negative we know that the vertex of the parabola is a maximum. So we need to find the vertex.
This expression is maximum for
[tex]t=-\dfrac{b}{2a} \text{ where the parabola equation is}\\\\ax^2+bx+c=0[/tex]
So, here, it gives t = 8/2=4, and then, the maximum is
[tex]-4^2+8*4-4=-16+32-4=32-20=12[/tex]
So the answer is 12.
Thanks
I have no idea how to solve this
Answers
Answer:
9
Step-by-step explanation:
Consider the polygon to consist of 2 rectangles, rectangle X (The bigger rectangular) and Y(the smaller rectangle), as shown in the diagram attached below.
To find DE + EF, let's find each lengths as follows:
DE = BC - FA
DE = 9 - 5 = 4
EF = AB - DC
EF = 8 - DC (we don't know DC)
Let's find out DC by considering the area of the entire polygon to derive an equation that will enable us to find DC.
Area of a rectangle = L*B
Therefore:
Area of the polygon = Area of rectangle X + Area of rectangle Y
Area of Polygon = (AB*FA) + (DE*DC)
52 = (8*5) + (4*DC)
52 = 40 + (4*DC)
Subtract 40 from both sides
52 - 40 = 4*DC
12 = 4*DC
Divide both sides by 4 to make DC the subject.
12/4 = DC
3 = DC
DC = 3
Thus,
DE + EF = (BC - FA) + (AB - DC)
= (9 - 5) + (8 - 3)
= 4 + 5
= 9
Write an absolute value equation to satisfy the given solution set shown on a number line.
Answers
Answer:
Step-by-step explanation:
|x-a|≤b
-b≤x-a≤b
add a
a-b≤x≤a+b
put a-b=-8
a+b=-4
add
2a=-12
a=-12/2=-6
-6+b=-4
b=-4+6=2
so |x+6|≤2