Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-\frac{4}{3}$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained in both triangles $XYZ$ and $X'Y'Z'.$ Find $\frac{A}{[XYZ]}.$
Answers
The area divided by XYZ is 16/9
i.e. [tex]\frac{A}{[XYZ]} = \frac{16}{9}[/tex]
The given parameters can be represented as:
[tex]r = -\frac{4}{3}[/tex] --- the ratio of dilation
The area of the second triangle is as follows:
[tex]A =r^2 * \triangle XYZ[/tex]
Make [tex]r^2[/tex] as subject
[tex]r^2 = \frac{A}{\triangle XYZ}[/tex]
Substitute value for [tex]r^2[/tex]
[tex](\frac{4}{3})^2 = \frac{A}{\triangle XYZ}[/tex]
[tex]\frac{16}{9} = \frac{A}{\triangle XYZ}[/tex]
Rewrite as:
[tex]\frac{A}{\triangle XYZ} = \frac{16}{9}[/tex]
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Answer:
Step-by-step explanation:
Let each side of triangle XYZ have length s. We therefore have:
s = YZ = YQ + QR + RZ = x + 2y
Since each side of triangle X1 Y2 Z2 is 3/4 the length of the corresponding side of triangle XYZ, we have:
3/4s = X1 Z1 = X1 Q + QP + P Z1 = 2x +y.
The system of equations:
x + 2y = s
2x + y = 3/4s
Multiply the second equation by 2, then subtract the first equation.
3x = 1/2s, so x = 1/6s.
Now we have y = 3/4s-2x = 5/12s.
A/[XYZ] = [XYZ] - 3[YPQ]/[XYZ]
= {[XYZ] - 3[(25)/144] * [XYZ]} / [XYZ]
={23/48* [XYZ]} / [XYZ]
= 23/48
Related Questions
Two pedestrians begin to walk toward each other at dawn, each walking at a constant speed. They meet at noon, and continue along their separate routes. The pedestrian walking from point A to point B reaches point B at 4:00 pm, and the pedestrian walking from point B to point A reaches point A at 9:00 pm. At what time was dawn?
Answers
Edit: Please mark brainliest!!!!
Answer:
6:00 am
Heeeeyyyyyy, so i had the same problem from rsm, but like anyways, here it is
Let the distance between
solve for x
5x-10>20 or 5x-10≤ -15
A.-5≤x6
B. -1≤x<6
C. x≤-5or x>6
d. x≤-1 or x>6
Answers
Answer:
D
Step-by-step explanation:
For example,
5×7-10>20
5(-3)-10<15
what is the simplification of 9^8 / 9^7?
Answers
Answer:
9
Step-by-step explanation:
We know that a^b / a^c = a^(b-c)
9^8 / 9^7
9^(8-7)
9^1
9
Rewrite the expression in the picture in the form y^n.
Answers
Step-by-step explanation:
here's the answer to your question
Answer:
y^(2/3)
Step-by-step explanation:
( y ^ ( 7/3) * y^ ( 1/3) ) ^ 1/4
Combine the terms in side the parentheses
a^b* a^c = a^(b+c)
( y ^ ( 7/3+ 1/3) ) ^ 1/4
( y^( 8/3) )^1/4
We know a^b^c = a^(b*c)
y ^(8/3*1/4)
y^(2/3)
At one sitting, a typical doughnut eater consumes 4 doughnuts containing a total of 680 calories and 40 grams of fat. The typical bagel eater consumes exactly one bagel, at 500 calories and one or two grams of fat per sitting, though the addition of spreads can raise calorie and fat content to the four-doughnut range. Thus, as far as total calorie content is concerned, there is very little difference between what a typical doughnut eater and a typical bagel eater each consumes at one sitting.
The argument depends on assuming which one of the following?
(A) The calories and fat in bagels have the same health impact on bagel eaters as the calories and fat in doughnuts have on doughnut eaters.
(B) Most bagel eaters are not fully aware of the calorie and fat content of a bagel.
(C) Eating bagels instead of eating doughnuts provides no real health benefit.
(D) The typical doughnut eater does not add to doughnuts any substances that increase the total caloric intake.
(E) Most typical doughnut eaters are not also bagel eaters.
Answers
Answer:
C. Eating bagels instead of eating doughnuts provides no real health benefits.
Step-by-step explanation:
There is no such difference in health benefit due to eating bagels or doughnuts. The bagel eaters are not necessarily doughnut eaters. The calories in bagels is 500 cal per bagel while the calories in doughnuts is 680cal for every 4 doughnuts intake.
The height and radius of a cone are each multiplied by 11. What effect does this have on the volume of the cone?
The volume of the cone is multiplied by (Blank 1).
Answers
The volume of the new cone would be 1331 times more than the volume of the original cone. Thus, The volume of the original cone is multiplied by 1331
The volume of the cone can be calculated by the given formula:
The volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
where r = radius of the cone
h = height of the cone
Solution:
The volume of the original cone= .......1
It is given that the height and radius of a cone are multiplied by 11.
then volume
= [tex]\frac{1}{3} \pi (11r)^{2} (11h)[/tex]
= [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex] .........2
The change in volume of the cone after multiplying 11 to r and h would be
dividing equation 2 by equation 1
= [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex]/[tex]\frac{1}{3} \pi r^{2} h[/tex]
= 121*11
= 1331
Thus, The volume of the original cone is multiplied by 1331
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√25x+75 +3√x-2 =2+4√x-3 +√9x-18
Answers
Answer: No solutions
Step-by-step explanation:
[tex]\large \bf \boldsymbol{ \boxed{\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b} }} \\\\\\ \sqrt{25x+75} +3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9x-18} \\\\ \sqrt{25} \cdot \sqrt{x+3}+3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9}\cdot \sqrt{x-2} \\\\5\sqrt{x+3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \ \ =2 +4\sqrt{x-3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \\\\(5\sqrt{x+3})^2 =(2+4\sqrt{x-3} )^2 \\\\ \ \ \ let \ \ t=x+3 \ \ ; \ \ \ t-6=x-3 \\\\ \big(5\sqrt{t} \ \big)^2=(2+\sqrt{t-6} )^2 \\\\[/tex] [tex]\large \boldsymbol{} \bf 25t=4+16\sqrt{t-6} +16(t-6) \\\\(9t+92)^2=(16\sqrt{t-6} )^2 \\\\81t^2+1656t+8464=256(t-6)\\\\81t^2+1400t+10000=0 \\\\ D=1400^2-324000=-128000=> \\\\D<0 \ \ no \ \ solutions[/tex]
Someone help me out please
Answers
Answer:
254.5
Step-by-step explanation:
Area = πr²
= π×9²
= 81π
= 254.5 (rounded to the nearest tenth)
Answered by GAUTHMATH
HELP ME WIT THIS QUESTION
Answers
Answer:
I (-4, -3)
J (-4,-2)
K (-2,-2)
L (0,-4)
do any of u know how to do this ?
Answers
Answer:
The correct answer is (B)
Step-by-step explanation:
remember it is (x,y) so -4 would be on the x axis, whereas the 0, is on the y axis.
A certain company sells tea in loose leaf and bagged form, and in five flavors: Darjeeling, earl grey, chamomile, peppermint, and orange pekoe. The company packages the tea in boxes that contain either 8 ounces of tea of the same flavor and the same form, or 8 ounces of tea of 4 different flavors and the same form. If the order in which the flavors are packed does not matter, how many different types of packages are possible
Answers
Answer:
- 20
Step-by-step explanation:
Given that,
Flavors of tea = 5
Types of packaging = 2
So,
No. of possibilities = 5 * 2
= 10
A.T.Q.,
4 from 5 total flavors will be included in the variety pack, the number of available choices = 5C4
= 5 choices
Since 5 choices are probable for each form, The total in two forms would be 5 * 2 = 10.
Therefore,
Total no. of different packs can be possible = 10 + 10
= 20
Which angles are supplementary to each other?
Angle 4 and Angle 2
Angle 5 and Angle 2
Angle 4 and Angle 3
Angle 2 and Angle 7
Answers
Answer:
The answer is Angle 4 and Angle 3.
Answer:
It's answer is angle 4 and angle 3
WHO CAN HELP ME !!!!!!! PLEASE FINNA CRY RN
Answers
Answer:
In the other polygon which is smaller you just half the size of the larger one like 12 became 5 and 6 became 3 so 14 will also be halved and the answer will be
7
Line A passes through points (-3,2) and (-23,54) line B is parallel to line A and passes through point (-8,0) what is the equation of line B? please help!!
Answers
Answer:
the correct answer to this question is b
Step-by-step explanation:
got it right
Find the distance between points M(-1,-10) and P(-12,-3). Round to the nearest tenth
Answers
Answer: Distance = √170
Step-by-step explanation:
Concept:
Here, we need to know the concept of the distance formula.
The distance formula is the formula, which is used to find the distance between any two points.
If you are still confused, please refer to the attachment below for a clear version of the formula.
Solve:
Find the distance between M and P, where:
M (-1, -10)P (-12, -3)[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance = \sqrt{(-3+10)^2+(-12+1)^2}[/tex]
[tex]Distance = \sqrt{(7)^2+(-11)^2}[/tex]
[tex]Distance = \sqrt{49+121}[/tex]
[tex]Distance = \sqrt{170}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Step-by-step explanation:
(x₁ , y₁) = (-1 , -10) & (x₂,y₂)=(-12,-3)
Distance = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
[tex]= \sqrt{(-12-[-1])^{2}+(-3-[-10])^{2}}\\\\= \sqrt{(-12+1)^{2}+(-3+10)^{2}}\\\\=\sqrt{(-11)^{2}+(7)^{2}}\\\\= \sqrt{121+49}\\\\=\sqrt{170}[/tex]
= 13.03
= 13
Select whether each equation has no solution, one solution, or infinitely many solutions. No Solution One Solution Infinitely Many Solutions
7x + 14 = 14 x + 7
5 x + 8 = 8 + 5 x
9x = 9 x + 5 17.
Answers
Answer:
Step-by-step explanation:
7x + 14 = 14 x + 7
-7x = -7
x = 1 (one solution)
~~~~~~~~~~~~~~~~~
5 x + 8 = 8 + 5 x
0 =0 (infinite solutions)
~~~~~~~~~~~~~~~~
9x = 9 x + 5 17
0 = 517 (no solution)
Aaron, Blaine, and Cruz are solving the equation 4 7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7 4 . Blaine started by using the distributive property to multiply 4 7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4 7 .
Answers
Answer:
D. All three chose a valid first step toward solving the equation.
Step-by-step explanation:
Aaron, Blaine, and Cruz are solving the equation 4/7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7/4 . Blaine started by using the distributive property to multiply 4/7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4/7 .
Which of the following is true?
A. Blaine and Cruz made an error in picking their first steps.
B. Cruz made an error in picking his first step.
C. All three made an error because the right side equals -1.
D. All three chose a valid first step toward solving the equation.
Given:
4/7(7 - n) = -1
Aaron:
4/7(7 - n) = -1
Multiple both sides by 7/4
4/7(7 - n) * 7/4 = -1 * 7/4
7 - n = -7/4
- n = -7/4 - 7
- n = (-7-28)/4
- n = -35/4
n = 35/4
Blaine:
4/7(7 - n) = -1
4/7(7 - n) × 7 = -1 × 7
4(7 - n) = -7
28 - 4n = -7
-4n = -7 - 28
- 4n = - 35
n = -35/-4
n = 35/4
Cruz:
4/7(7 - n) = -1
Divide both sides by 4/7
4/7(7 - n) ÷ 4/7 = -1 ÷ 4/7
4/7(7 - n) × 7/4 = -1 × 7/4
7 - n = -7/4
- n = (-7-28)/4
- n = -35/4
n = 35/4
D. All three chose a valid first step toward solving the equation.
Answer:
D-All three chose a valid first step toward solving the equation.
Step-by-step explanation:
Hope I Helped
Which is a point on the circle whose center is (0, 0) and whose radius is 5?
A. (2, 3)
B. (0, 0)
C. (3, 4)
D. (4, 5)
Answers
The equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x-a)²+(y-b)² = r²
Where (a, b) is the centre and 'r' is the radius
We have a circle with centre (0, 0) and radius of 5.
Now, Substituting these value into the equation form, we have
(x-0)²+(y-0)² = 5²
x² + y² = 25
Hence, the equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.
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Which graph represents the function f(x)= |x| -4?
Answers
Answer:
the graph will be the parent function : |x|, but shifted down by 4 units
Step-by-step explanation:
express 23/7 in decimal form
Answers
Answer:
3.285714286
Step-by-step explanation:
The step function g(x) is defined as shown.
-3, X < 0
g(x) = 2 0 < x < 4
5, 4 < x < 10
What is the range of g(x)?
0 -3 = g(x) 5
Os g(x) = 10
O {-3, 2, 5)
{0, 4, 10}
Answers
The 3rd option is correct.
The range refers to the y-values so the multiple choice answer is restricted to the 1st and 3rd options. The range of the step function is not continuous, it is only the discrete values {-3, 2, 5}.
Determine el radio vector del punto medio del segmento que se forma al unir los puntos (-8, 7) y (6, 3).
Es para hoy
Answers
Answer:
The radius vector is (-8, 7) and (-1 , 5).
Step-by-step explanation:
Determine the radius vector of the midpoint of the segment that is formed by joining the points (-8, 7) and (6, 3).
The end points are (- 8, 7) and (6, 3) .
The mid point is given by
[tex]x = \frac{x' + x''}{2}\\\\y = \frac{y' +y''}{2}\\\\x =\frac{- 8 + 6}{2}=-1\\\\y = \frac{7+3}{2} = 5[/tex]
So, the radius vector is (-8, 7) and (-1 , 5).
What is the fastest way to solve the following question:
The ratio of boys to girls in Mr. Brown's class is 2:3. If there are 30 students in the class, how many more girls than boys are in the class?
Answers
Answer:
There are 6 more girls than boys
Step-by-step explanation:
boys :girls : total
2 3 2+3 = 5
There are 30 total students
30/5 = 6
Multiply each number by 6
boys :girls : total
2*6 3*6 5*6
12 18 30
There are 18 girls and 12 boys
18-12 = 6
There are 6 more girls than boys
Answer:
Answer is 6.
Step-by-step explanation:
I will now explain the fastest way to solve this. First off, the ratio is 2:3 so the first thing I do is combine that for 5, then do 30/5 for an answer of 6. Then, I multiply 6 for the ratio, which comes out as 12:18, 12 boys and 18 girls. 18-12=6, so there are 6 more girls than boys in the class.
Could anyone please help me with this question, this is my last one?
#iamarookie
Giving away 15 points this time and I just need help on QUESTION B!
Answers
Answer:
28 = 2² x 7
Step-by-step explanation:
Factors of 28: 1, 2, 4, 7, 14, 28.
Prime factorization: 28 = 2 x 2 x 7, which can also be written 28 = 2² x 7.
simplify (2^2×4^-2)×5^8+2+3^0
Answers
I am sorry if it’s wrong
This is my best
Sorry if missed it.
what percentage of 50kg is 65 kg?
Answers
Answer:
130
Step-by-step explanation:
65/50*100= 130
hello i need help someone please!!
find the inverse of this relation
h(t) = -6t + 7
Answers
Answer:
73
Step-by-step explanation:
Answer:
[tex]h^{-1}[/tex] (t) = [tex]\frac{7-t}{6}[/tex]
Step-by-step explanation:
let y = h(t) and rearrange making t the subject
y = - 6t + 7 ( add 6t to both sides )
6t + y = 7 ( subtract y from both sides )
6t = 7 - y ( divide both sides by 6 )
t = [tex]\frac{7-y}{6}[/tex]
Change y back into terms of x with t = [tex]h^{-1}[/tex] (t)
[tex]h^{-1}[/tex] (t) = [tex]\frac{7-t}{6}[/tex]
what function equation is represented by the graph?
Answers
Answer:
maybe f(x)= -2/3 x + 1 since it goes down two times or up two times and three times to the left or right depending where you wanna go i don't know how to explain but maybe this might help
convert 100110 base two to a number in base three
Answers
Convert to base 10:
10 0110₂ = 2⁵ + 2² + 2¹ = 38
Convert to base 3:
38 = 27 + 11 = 27 + 9 + 2 = 3³ + 3² + 2×3⁰ = 1102₃
Please help, easy geometry work
Answers
Step-by-step explanation:
Find the slope of AB
: The slope is
[tex] \frac{7 - 0}{3 - 8} = - \frac{7}{5} [/tex]
Find the y intercept by plugging coordinates in
[tex]0 = - \frac{ 7}{5} (8) + b[/tex]
[tex]0 = \frac{ - 56}{5} + b[/tex]
[tex]b = \frac{56}{5} [/tex]
Find CD: We know that AB and CD are parallel to each other so this means they both have the same slope.
We can find the next point by subtracting 7 from the y coordinate of Point D, Adding 5 to the x coordinate of Point D.
Point C=(10,-2).
Find the y intercept by a plugging coordinates in
[tex] 5 = - \frac{7}{5} (5) + b[/tex]
[tex]5 = - 7 + b[/tex]
[tex]12 = b[/tex]
So the Equation of Line CD is
[tex] - \frac{7}{5} x + 12[/tex]
