Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.
Find the slope of DE and FG.
Answers
Answer:
B. See explanation
Step-by-step explanation:
Use the distance formula between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2):[/tex]
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Find the lengths of all sides of quadrilateral DEFG:
[tex]DE=\sqrt{(-a-b-0)^2+(c-2c)^2}=\sqrt{(a+b)^2+c^2}\\ \\
EF=\sqrt{(a+-b-0)^2+(c-2c)^2}=\sqrt{(a+b)^2+c^2}\\ \\
FG=\sqrt{(a+b-0)^2+(c-0)^2}=\sqrt{(a+b)^2+c^2}\\ \\
GD=\sqrt{(-a-b-0)^2+(c-0)^2}=\sqrt{(a+b)^2+c^2}\\ \\[/tex]
All sides are of the same length. Now fond the slopes of all sides:
[tex]DE=\dfrac{2c-c}{0-(-a-b)}=\dfrac{c}{a+b}\\ \\EF=\dfrac{c-2c}{a+b-0}=-\dfrac{c}{a+b}\\ \\FG=\dfrac{c-0}{a+b-0}=\dfrac{c}{a+b}\\ \\GD=\dfrac{c-c}{-a-b-0}=-\dfrac{c}{a+b}\\ \\[/tex]
The slopes of the sides DE and FG are the same, so these sides are parallel. The slopes of the sides EF and GD are the same, so these sides are parallel.
Related Questions
In △ABC, m∠A=16°, m∠B=49°, and a=4. Find c to the nearest tenth.
Answers
Answer:
c=13.2 units
Step-by-step explanation:
step 1
Find the measure of angle C
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
so
A+B+C=180°
substitute the given values
16°+49°+C=180°
65°+C=180°
C=180°-65°=115°
step 2
Find the measure of c
Applying the law of sines
c/sin(C)=a/sin(A)
substitute the given values and solve for c
c/sin(115°)=4/sin(16°)
c=4(sin(115°))/sin(16°)
c=13.2 units
ANSWER QUICK PLEASE
Use the grouping method to factor:
Answers
(x^3 + x^2) + (5x + 5)
Factor out common factors from the binomials
x^2(x + 1) + 5(x + 1)
Now you factor out the greatest common binomial in the remaining expression
(x +1)(x^2 + 5)
Answer:
B. [tex](x^2 + 5)(x + 1)[/tex]
Step-by-step explanation:
Hello!
We can group the first two terms and the last two terms and factor each group.
Factor by Grouping[tex]x^3 + x^2 + 5x + 5[/tex][tex](x^3 + x^2)+ (5x + 5)[/tex][tex]x^2(x + 1) + 5(x + 1)[/tex]Now we can combine the like factors:
[tex](x^2 + 5)(x + 1)[/tex]The answer is Option B.
find the permiter of the polygon PLEASE help
Answers
Check the picture below.
Answer:
P = 46cmStep-by-step explanation:
If the circle inscribed in a quadrilateral, then the sums of the opposite sides of the quadrilateral are the same.
Therefore we have the equation:
AB + CD = BC + AD
Therefore the perimeter of polygon ABCD is equal to
P = 2(AB + CD)
Substitute AB = 10.5cm, CD = 12.5cm:
P = 2(10.5cm + 12.5cm) = 2(23cm) = 46cm
What is the equation of a line that passes through the point (0, -2) and has a slope of -3?
Answers
Answer: Y = -3x-2
Step-by-step explanation:
if there are two co-ordinates (x1,y1) and (x2,y2).
If the line is passing through these co-ordinates
Then Slopw of the line = (y2-y1)/(x2-x1)
We have one co-ordinate (-0,-2) let it be (X1,Y1)
Let second co-ordinate be (X,Y)
Slope = -3 = (Y-(-2)) / (X-0)
-7 = (Y+2)/(X)
Y+2 = -3 (X)
Y+2 = -3X
ADDING -2 ON BOTH SIDES OF THE EQUATION
Y+2-2 = -3X-2
Y = -3x-2
Which of the following statements best describes a linear pair
Answers
Answer:
B) A linear pairs consists of supplementary angles
Step-by-step explanation:
First let's see the definition of linear pair.
The two adjacent angles add up to 180° (supplementary) is called linear pair.
Example:
If ∠A and ∠B said to be linear pair, then they must be adjacent angles and add up to 180 degrees.
∠A + ∠B = 180°
From the definition, we can find the answer.
A) in correct because complementary angles add up to 90 degrees.
B) Correct (A linear pair consists of supplementary angles)
C) In correct because the pair consists of adjacent angles
D) In correct because vertical angles is nothing but 90°
Solve |y-2|<10
——————————
Answers
[tex]|y-2|<10\\y-2<10 \wedge y-2>-10\\y<12 \wedge y>-8\\y\in(-8,12)[/tex]
1. Which equation represents a linear function?
A. y = x - 4
B. y = x + 4
C. x = (y - 2)2
D. y = x + 7
Answers
Answer:
A, B, D are equations representing a linear function
Step-by-step explanation:
All linear functions have an equation like the following: y=mx+b, where m is the slope and b is an offset.
A. y=x-4, m=1 and b=-4
B. y=x+4, m=1 and b=4
D. y=x+7, m=1 and b=7
The third eq dont behave like a linear function since there is quadratic term on one side of the equation, this is not a linear function
What is the value of x in the equation 2(x−3)+9=3(x+1)+x?
x = −3
x = −1
x = 0
x = 3
Answers
Answer : 0
Step-by-step explanation:
2(x−3)+9=3(x+1)+x
2x-6+9=3x+3+x
3-3=4x-2x
0=2x
x=0
The value of x in the equation 2(x−3)+9=3(x+1)+x is 0 option third x = 0 is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a linear equation in one variable:
2(x−3)+9=3(x+1)+x
2x - 6 + 9 = 3x + 3 + x
Combine like terms
2x + 3 = 4x + 3
x = 0
Thus, the value of x in the equation 2(x−3)+9=3(x+1)+x is 0 option third x = 0 is correct.
Learn more about the linear equation here:
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if Q(-3,4), R(-2,-1),T(3,1),W(3,5) is a quadrilateral and Q'(-27,36) is the image of Q under a dilation centered at the origin, find W'
Answers
Answer:
W'(27,45)
Step-by-step explanation:
First we must fnd the scale factor of the dilation and then multiply the coordinates of W(3,5) by the scale factor.
Let k be the scale factor of the dilation centered at the origin.
The mapping for a dilation by a scale factor k is
[tex](x,y)\to (kx,ky)[/tex]
[tex]Q( - 3,4)\to Q'( - 3k,4k)[/tex]
But we were given the coordinates of the image, which is
Q'(-27,36)
Comparing coordinates:
[tex]4k = 36[/tex]
[tex] \implies \: k = 9[/tex]
We could compare the first coordinates too and get the same result.
The image of W(3,5) is given by:
[tex]W(3,5) \to \: W'(3 \times 9,5 \times 9)[/tex]
[tex]W(3,5) \to \: W'(27,45)[/tex]
What is the mean of 108,305,252,113,191
Answers
Answer:
193.8
Step-by-step explanation:
Mean is the average. Find the average by dividing the sum of all numbers by the amount of numbers.
108+305+252+113+191
divided by 5
108+305+252+113+191= 969
969/5= 193.8
Final answer:
The mean of 108, 305, 252, 113, and 191 is 193.8.
Explanation:
To find the mean of a set of numbers, you need to add up all the numbers in the set and then divide the sum by the total number of values.
In this case, we have the numbers 108, 305, 252, 113, and 191.
To find the sum, you add these numbers together:
108 + 305 + 252 + 113 + 191 = 969.
Next, you divide this sum by the total number of values, which is 5 in this case.
So, the mean is 969 ÷ 5 = 193.8.
This is the average value of the set of numbers provided.
A triangle contains angles of 95° and 35°. what is the measure of the third angle of the triangle ?
Answers
Answer:
50
Step-by-step explanation:
Add up the two known angle measurements:
95+35=130
Subtract this number from 180°:
180-130=50
Write down your answer
95+35+25=180
*The three angles should add up to 180° for the triangle to exist*
I hope that helped
Consider the quadratic function f(x)=8x2−7x+6. What is the constant of the function?
Answers
The 6 is the constant because it is never going to change
f(x), and others that contain x will change based on the value x
Since 6 doesn’t have the c with it it will be constant
Answer:
6 is constant of the function .
Step-by-step explanation:
Given : f(x)=8x²−7x+6.
To find : What is the constant of the function?
Solution : We have given that f(x)=8x²−7x+6.
Standard quadratic equation : ax² +bx +c = 0.
Here,
a is the coefficient of x² and b is the coefficient of x .
c = constant.
Hence on comparing with it standard quadratic equation
Here, 6 is constant.
Therefore, 6 is constant of the function .
Let f(x) = (4x^2 - 11)^3 and g(x) = 4x^2- 11.
Given that f(x) = (hºg)(x), find h(x).
Enter the correct answer.
Answers
Answer:
[tex]\large\boxed{h(x)=x^3}[/tex]
Step-by-step explanation:
[tex]f(x)=(4x^2-11)^3\\\\f(x)=(h\circ g)(x)=h\bigg(g(x)\bigg)\to\text{exchange x to}\ g(x)=4x^2-11\\\\f(x)=(\underbrace{4x^2-11}_{g(x)})^3=\bigg(g(x)\bigg)^3=h\bigg(g(x)\bigg)\\\\\text{Therefore}\ h(x)=x^3[/tex]
Answer:
the person on top is correct
Step-by-step explanation:
what is 4/2 ÷ 2 +(3^2 - 1)
Answers
Answer:
9
Step-by-step explanation:
Good ol' PEMDAS
First things first, we simplify what is in the parentheses.
4/2 ÷ 2 + (3² - 1)
4/2 ÷ 2 + (9 - 1)
4/2 ÷ 2 + 8
Next we do division. Because there are two instances of division, we work left-to-right. Note that a fraction such as 4/2 is division itself.
4/2 ÷ 2 + 8
2 ÷ 2 + 8
1 + 8
Lastly, it just solving the addition.
1 + 8 = 9
the answer would be 9
In the triangle below, what is the measure of R?
Answers
Answer:
30
Step-by-step explanation:
Solve the system of equations.
y= 6x-27
y= 4x - 17
a. (-5, 3)
b. (-3, -5)
C. (5, 3)
d. No solution
Answers
Answer:
C. (5, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=6x-27&(1)\\y=4x-17&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\6x-27=4x-17\qquad\text{add 27 to both sides}\\6x=4x+10\qquad\text{subtract}\ 4x\ \text{From both sides}\\2x=10\qquad\text{divide both sides by 2}\\x=5\\\\\text{Put it to (2):}\\\\y=4(5)-17\\y=20-17\\y=3[/tex]
What is the product?
(6r-1)(-8r3)
Answers
Answer:
[tex]\large\boxed{(6r-1)(-8r^3)=-48r^4+8r^3}[/tex]
Step-by-step explanation:
[tex](6r-1)(-8r^3)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(6r)(-8r^3)+(-1)(-8r^3)\qquad\text{use}\ (a^n)(a^m)=a^{n+m}\\\\=-48r^{1+3}+8r^3\\\\=-48r^4+8r^3[/tex]
The product of the binomials (6r-1) and (-8r-3) is obtained using the FOIL method, and the final product is -48r² - 10r + 3.
To find the product of the binomials (6r-1) and (-8r-3), we use the distributive property (also known as the FOIL method). The FOIL method stands for First, Outer, Inner, Last, which refers to the multiplication of the respective terms in each binomial.
Applying the FOIL method:
First: Multiply the first terms in each binomial: 6r * -8r = -48r²
Outer: Multiply the outer terms in each binomial: 6r * -3 = -18r
Inner: Multiply the inner terms in each binomial: -1 * -8r = 8r
Last: Multiply the last terms in each binomial: -1 * -3 = 3
Now, combine the like terms (-18r + 8r = -10r) and write the final product: -48r² - 10r + 3
An aerial camera is suspended from a blimp and positioned at D. The camera needs to cover 125 meters of ground distance. If the camera hangs 10 meters below the blimp and the blimp attachment is 20 meters in length, at what altitude from D to B should the camera be flown?
A blimp over triangle EDF with height of 10 meters and FE equals 20 meters and triangle ADC with height BD and AC equals 125 meters. Triangles share point D.
A. 31.25 m
B. 62.5 m
C. 150 m
D. 250 m
Answers
Answer:
B. 62.5 m
Step-by-step explanation:
∠EDF and ∠ADC are vertical angles, and therefore equal.
EF and AC are parallel, so ∠DEF and ∠DAC are alternate interior angles, as well as ∠DFE and ∠DCA. Therefore, each pair is equal.
From this, we can say ΔDEF and ΔDAC are similar triangles. So we can write a proportion:
10 / 20 = DB / 125
DB = 62.5
Answer:
The correct option is B.
Step-by-step explanation:
Given information: In ΔEDF, FE=20 m and height = 10 m. In ΔADC, AC=125 m.
From the given information, we conclude that AC║EF.
In ΔEDF and ΔADC,
[tex]\angle E=\angle A[/tex] (Alternate interior angles)
[tex]\angle EDF=\angle ADC[/tex] (Vertically opposite angle)
By AA rule of similarity,
[tex]\triangle EDF\sim \triangle ADC[/tex]
The corresponding sides of two similar triangles are similar. So in ΔEDF and ΔADC,
[tex]\frac{base}{height}=\frac{FE}{h}=\frac{AC}{DB}[/tex]
[tex]\frac{20}{10}=\frac{125}{DB}[/tex]
[tex]2=\frac{125}{DB}[/tex]
On cross multiplication, we get
[tex]2DB=125[/tex]
Divide both sides by 2.
[tex]\frac{2DB}{2}=\frac{125}{2}[/tex]
[tex]DB=62.5[/tex]
Therefore the correct option is B.
Complete the equation of the line through (6,-6) and (8,8).
Use exact numbers.
y=?
Answers
use slope formula so, y2 - y1 over x2 - x1 to get your m value or your slope which is 7. then plug in the slope and a random set of point so I used (6, -6). -6 = 6(7) + b, simplify.
-6 = 42 + b, subtract 42 which leaves you with b= -48. hope this helps :)
Answer:
7x-48
Step-by-step explanation:
12.03,1.2,12.3,1.203,12.301 order least to greatest
Answers
Answer:
1,2, 1,203, 12,03, 12,3, 12,301
Step-by-step explanation:
1,2 → 1,200
1,203
12,3 → 12,300
12,301
I am joyous to assist you anytime.
Ordered from least to greatest:
1.21.20312.0312.312.301Jeffrey used to be on the phone 3 1/2 times as much as his sister. His parents were angry and told him they would take his his phone away is he did not reduce his time spent on the phone. He cut down to 2/5 of the time he used to be on the phone. How many times as much as his sister is Jeffrey on the phone now?
Answers
Answer:
1 2/5 times as much as his sister
Step-by-step explanation:
3 1/2x * 2/5 = 1 2/5x
What term do you use to describe the amount of three-dimensional space
inside a solid?
A. Volume
B. Perimeter
C. Surface area
D. Lateral area
Answers
Answer:
volume
Step-by-step explanation:
volume is measured in cubic
Answer:
A. Volume
Step-by-step explanation:
IN two-dimension space we use to calculate area, perimeter but not volume.
In three-dimensional space we also find Volume, Surface area and lateral surface area only.
In volume we find what amount of substance kept inside that container/solid.
Perimeter is the length of total boundary.
Surface area is total area of each face.
And, In Lateral surface area we find the area of each face except bottom and top face.
Thus, "the amount of three-dimensional space inside a solid" is described by VOLUME.
4 middle school questions
Answers
Answer:
884. D
885. C ( changed my answer)
886. B
887.A
For number 844, the diameter if the fan is 12 inches. To find Circumference, multiply the radius by two and then pi. The radius of the fan is 6, multiplied by 2 is 12, and multiplied by pi gives 12 times pi.
885 says half of the area gives the circumference. So we can write a formula, (pi*r^2)/2=2*pi*r. If the radius were 4, this would make the equation true. So the answer is 4.
886. Circumference=2*pi*r
r=6.78
2*pi*6.78
13.56*pi
887.
3*3=9
13-3=10
10*23=230
230+9=239 units squared
Answer:
884.D
885.C
886.B
887.A
Step-by-step explanation:
I just multiplied
is 42 a multiple of 7
Answers
Answer:
yes
Step-by-step explanation:
7 * 6 = 42
7x6 is 42
the slope in decimal form ?
Answers
Answer:
2
Step-by-step explanation:
Look at two points on the graph that are easy to read.
(0, 0) and (1, 2) are on the graph and are easy to read.
slope = (y2 - y1)/(x2 - x1) = (2 - 0)/(1 - 0) = 2/1 = 2
Answer:
-2
Step-by-step explanation:
Let's get two coordinate points and plug into the slope equation.
(1,2) and (.5,1)
[tex](y_{2} - y_{1}) / (x_{2} - x_{1} )[/tex]
(1-2) / (.5 - 1)
1 / (-.5)
-2
3 units
V13 units
2 units
In this right triangle, the length of the hypotenuse, BC, is units:
Answers
Answer:
[tex]\large\boxed{BC=\sqrt{13}}[/tex]
Step-by-step explanation:
[tex]\text{If}\ a\leq b\leq c\ \text{are lengths of sides of a right triangle, then}\\\\a^2+b^2=c^2.\\\\\text{We have:}\ 2<3<\sqrt{13}\\\\\text{Substitute:}\\\\2^2+3^2=(\sqrt{13})^2\qquad\text{use}\ (\sqrt{a})^2=a\\4+9=13\\13=13\qquad\bold{CORRECT}\\\\\text{The hypotenuse is the longest side of a right triangle.}\\\text{Therefore}\ BC=\sqrt{13}[/tex]
Simplify the expression below.
3 · -8 + 5 - 4 ÷ 2
A-11.5
B-21
C-12.5
S-27
Answers
3 · -8 + 5 - 4 ÷ 2
Use PEMDAS
P=parenthesis
E=exponents
M= multiplication
A= addition
S=subtraction
-24+5- 4÷ 2
-19-2
=-21
Answer is B-21
Answer:
B. -21
Step-by-step explanation:
You have to follow PEMDAS
3*-8=-24
So, -24+5-4÷2
-4÷2=-2
So, -24+5-2
Then add and subtract from left to right
-24+5=-19
-19-2=-21
A hummingbird lives in a nest that is 3 meters high in a tree. The hummingbird flies 5 meters to get from the nest to a flower on the ground. How far is the flower from the base of the tree
Answers
Imagine a right triangle. The right angle is formed by the line from the nest to the ground, and the line from the tree to the flower. The hypotenuse is the direct distance from the nest to the flower. The hypotenuse is 5 meters, and the height of the nest is 3 meters. If the distance from the flower to the base of the tree is X, then 3^2 + x^2 = 5^2. So, x = 4.
Answer: 4 meters.
Step-by-step explanation: You need to set up the Pythagorean Theorem, which is a^2 + b^2 = c^2. The c is the hypotenuse. A is 3 because it is the height. We are trying to find b, the distance from the flower to the tree. C is 5.
Plug in the numbers.
3^2 + b^2 = 5^2.
Simplify.
9 + b^2 = 25.
Isolate b by subtracting 9 from each side.
B^2 =16.
Square root each side.
B = 4.
The flower is 4 meters away from the base of the tree.
In the next Olympics, the United States can enter four athletes in the diving competition. How many different teams of four divers can be selected from a group of nine divers?
a. 36
b. 6,561
c. 126
d. 3,024
Answers
Answer:
The correct option is C.
Step-by-step explanation:
From the given information it is clear that the total number of divers in a group is 9.
The number of selected divers is 4.
The total ways to select r items from total n item is
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Using this combination formula, the number of different teams of four divers that can be selected from a group of nine divers is
[tex]^9C_4=\frac{9!}{4!(9-4)!}[/tex]
[tex]^9C_4=\frac{9!}{4!5!}[/tex]
[tex]^9C_4=\frac{9\times 8\times 7\times 6\times 5!}{4\times 3\times 2\times 1\times 5!}[/tex]
Cancel out common factors.
[tex]^9C_4=126[/tex]
Therefore the correct option is C.
The correct answer is c. 126 different teams of four divers can be selected from a group of nine divers.
To solve this problem, we use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In this case, we want to find out how many different ways we can select 4 divers out of 9 to form a team, and the order in which we select the divers does not matter.
The formula for calculating combinations is given by:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
For our problem:
[tex]- \( n = 9 \) (the total number of divers)\\ - \( k = 4 \) (the number of divers we want to select for a team)[/tex]
Plugging these values into the formula, we get:
[tex]\[ C(9, 4) = \frac{9!}{4!(9-4)!} \] \[ C(9, 4) = \frac{9!}{4!5!} \] \[ C(9, 4) = \frac{9 \times 8 \times 7 \times 6 \times 5!}{4 \times 3 \times 2 \times 1 \times 5!} \] \[ C(9, 4) = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} \] \[ C(9, 4) = \frac{3024}{24} \] \[ C(9, 4) = 126 \][/tex]
Therefore, there are 126 different ways to select a team of four divers from a group of nine divers.
What number comes next in the series? 31, 1031, 402, 16, ____
Answers
Answer:
Another person already answered this question. Their name is writersparadise. I give all credit to him/her for this answer.
Step-by-step explanation:
There could be many answers for this question. In general, the number that comes after 16 is a number with 8 as the sum of its digits.
Explanation:
1st number 31 – Sum of digits is 3 + 1 = 4
2nd number 1031 – Sum of digits is 1 + 0 + 3 + 1 = 5
3rd number 402 – Sum of digits is 4 + 0 + 2 = 6
4th number 16 – Sum of digits is 1 + 6 = 7
Therefore, the missing number could be the single digit number 8 or any of the two-digit numbers 17, 26, 35, 44, 53, 62, 71 or 80. It could also be a bigger number with the digits of any of the given two-digit numbers and 0 for the other digits such as 260 or 7001.
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