Tony used a photocopier to dilate the design for a monorail track system. The figure below shows the design and its photocopy:The ratio of CD:GH is 2:3. What is the length, in meters, of side EH on the photocopied image?
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Solution
The length of EH is;
[tex]\begin{gathered} \frac{2}{3}=\frac{8}{EH} \\ \\ \Rightarrow EH=\frac{3}{2}\times8=12 \\ \\ \Rightarrow EH=12 \end{gathered}[/tex]Related Questions
Question 12 of 15 What is the midpoint of a line segment with endpoints at (-1,-1) and (3, 3)?
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To find the midpoint, we will use the formula;
(Xm, Ym) = [ x₁+x₂ /2 , y₁+y₂ /2]
x₁=-1 y₁=-1 x₂=3 y₂=3
substitute the values into the formula
(Xm , Ym) = [ -1+3 /2 , -1+3 /2]
(Xm , Ym) = (1, 1)
The midpoint is : (1, 1)
Write two fractions where the denominator of one is a multiple of the denominator of other
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The two fractions are; 1/3 and 1/9.
What is a fraction?A fraction has two parts: Numerator and Denominator.
It is in the form of a Numerator / Denominator. A fraction is a numerator divided by the denominator.
We need to write two fractions where the denominator of one is a multiple of the denominator of the other.
Let's consider the first fraction as;
1/3
Then other fraction must be multiple of the denominator of the other.
So, it can be 1/9
We can see that "the denominator of one is a multiple of the denominator of other".
Thus the two fractions are; 1/3 and 1/9.
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Find an ordered pair (x, y) that is a solution to the equation.
4x-y=5
(x,y) = ( , )
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Ordered pair for the equation 4x-y=5 which is a solution of a given equation is (0,-5).
An ordered pair refers to a pair of two numbers or variables written inside the bracket and separated by comma.
To find an ordered pair of a equation we just need to find the values of x and y which will satisfy the given equation.
Here given equation is 4x-y=5
So we will put x=0 and y=-5
⇒ 4(0)-(-5)=5
Therefore (0.-5) satisfy given equation.
Hence (0.-5) is an ordered pair of 4x-y=5.
Note:- There are many ordered pairs that satisfy the given equation.
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Find the conjugate of the following binomial ^15t-^5
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The conjugate is formed by changing the sign between the terms of the binomial:
[tex]\begin{gathered} \sqrt{15}t-\sqrt{5} \\ \uparrow\downarrow conjugate \\ \sqrt{15}t+\sqrt{5} \end{gathered}[/tex]In this case, the sign is negative, then the sign of its conjugate is positive.
Answer: [tex]\sqrt{15}t+\sqrt{5}[/tex]Ten yards of a particular kind of wire cost $15.30 . What is the cost of the wire per foot?
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Given:
Length of wire = 10 yards
Total cost of wire = $15.30
To be able to determine the cost of wire per foot, let's first convert the unit of measure of the wire's length from yards to feet.
Recall: 1 yard = 3 feet
Step 1: Convert the measure of the wire length from yards to feet.
[tex]\text{ 10 (yards) x }\frac{\text{ 3 feet}}{\text{ 1 (yard)}}\text{ = }\frac{\text{10 x 3}}{\text{ 1}}\text{ feet}[/tex][tex]\text{ = 30 feet}[/tex]Therefore, 10 yards is equivalent to 30 feet.
Step 2: Divide the total cost by the total length of wire in feet.
[tex]\text{ Cost of wire per foot = }\frac{\text{ Total cost of wire}}{\text{ Total length of wire}}[/tex][tex]\text{ = }\frac{\text{ \$15.30}}{\text{ 30 feet}}[/tex][tex]=\text{ \$0.51 per foot}[/tex]Therefore, the cost of the wire per foot is $0.51
(-2,-7);y=-2 the equation is
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Answer: -2= 5/2x -2
Step-by-step explanation:
I need help with this problem. My math teacher mentioned it not exactly being a arithmetic sequence.
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The freezing point of water is 0 °C. Imanis refrigerator is set at 4°C and her freezer is set at -19°C. which change in temperature would bring imanis refrigerator or her freezer to the same temperature as the freezing point of water?A: +23°CB: +15°CC: -19°CD: -4°C
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The freezing point of water is 0 °C
The tempreature of Imanis refrigerator = 4degree C
and the freezer is -19 degreeC
So, the net tenpreature of refrigerator is 4+(-19)
The net tempreature = (-15) degreeC
We want
Question 4 The graph of f(x) is shown. For what values of x does f(x) = 0 ? Select all that apply. MU 0 2 3
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Question 4 The graph of f(x) is shown. For what values of x does f(x) = 0 ? Select all that apply. MU 0 2 3
___________________________________
Can you see the updates?
Give me two minutes to point out the points on your graph
__________________________________
Answer
x= 2, -1, -3
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Do you have any questions regarding the solution?
Given the following figure is a parallelogram, solve for x.
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The given figure is a parallelogram. The opposite angles of a parallelogram are congruent.
From the information given,
angle E and angle G are opposite
Thus,
94 = 11x + 6
11x = 94 - 6 = 88
x = 88/11
x = 8
all of the following are names of spheres shown except
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SOLUTION
Consider the image given,
From the image above,
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center.
Hence
[tex]\begin{gathered} \text{ Point T has equal distance from the center} \\ \text{Also} \\ \text{ Point S has equal distance from the center} \end{gathered}[/tex]But
[tex]\text{ Point A is at the circumference }[/tex]
Answer:
a
Step-by-step explanation:
Expand and simplify (a^2+b)^8
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For this exercise, we must use the binomial theorem. The formula of this theorem is described as follows
[tex](a+b)^n=\sum_{i\mathop{=}0}^nnCi(a^{n-i})(b^i)[/tex]Where nCi represents the combinatory of n between i. For our case,
[tex]a=a^2\text{ y }b=b[/tex]Replacing the values you have in the formula
[tex]\begin{gathered} (a^2+b)^8=\sum_{i\mathop{=}0}^88Ci(a^2)^{8-i}(b^i) \\ =\frac{8!}{0!(8-0)!}(a^2)^{8-0}b^0+\frac{8!}{1!(8-1)!}(a^2)^{8-1}b^1+\frac{8!}{2!(8-2)!}(a^2)^{8-2}b^2+....+\frac{8!}{8!(8-8)!}(a^2)^{8-8}b^8 \\ =\frac{8!}{8!}(a^2)^8+\frac{8!}{1(7)!}(a^2)^7b^1+\frac{8!}{2(6)!}(a^2)^6b^2+....+\frac{8!}{8!}(a^2)^5b^8 \\ =a^{16}+8a^{14}b+28a^{12}b^2+56a^{10}b^3+70a^8b^4+56a^6b^5+28a^4b^6+8a^2b^7+b^8 \end{gathered}[/tex]Thus,the expansion and simplification is as follows
[tex](a^2+b)^8=\placeholder{⬚}+8a^{14}b+28a^{12}b^2+56a^{10}b^3+70a^8b^4+56a^6b^5+28a^4b^6+8a^2b^7+b^8[/tex]The finishing time for a runner completing the 200-meter dash is affected by the tail-wind speed, s. The change, t, in a runner's performance is modeled by the function shown below:t = 0.0119s^2 - 0.308s - 0.0003Predict the change in a runner's finishing time with a wind speed of 5 meters/second. Note: A negative answer means the runner finishes with a lower time. Round to the nearest hundredth.
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The change, t, in a runner's performance is modeled by:
[tex]t=0.0119s^2-0.308s-0.0003[/tex]Here s is the tall-wind speed.
It's required to find the change in a runner's finishing time with a wind speed of s = 5 m/s.
Substitute in the equation:
[tex]t=0.0119(5)^2-0.308(5)-0.0003[/tex]Operating:
[tex]\begin{gathered} t=0.0119(25)-1.44-0.0003 \\ \\ t=0.2975-1.44-0.0003 \end{gathered}[/tex]Calculating:
t = -1.24
A teacher asks students to determine the accuracy of this statement.A reflection over the x-axis and then over the y-axis results in the same transformation as a 180° rotation about the originof the original figure.Kwame's explanation of the accuracy of the statement is shown below.Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3).Step 2: Reflect the pre-image over the x-axis: (1, -2), (1, -4), (2, -3).Step 3: Reflect the figure from step 2 over the y-axis: (-1,2), (-1, 4), (-2, 3).Step 4: Rotate the pre-image 180°:(-1, -2), (-1,-4), (-2, -3).Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore thestatement made by the teacher is inaccurate.Which best explains Kwame's solution?
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(Reminder: To find the reflection over the x-axis, we just need to switch the signal of the y-coordinate of the points.
To find the reflection over the y-axis, we just need to switch the signal of the x-coordinate of the points)
Kwame's solution has a mistake in step 3:
The figure from step 2 is:
(1, -2), (1, -4), (2, -3).
Then, when reflecting these points over the y-axis, the result is:
(-1, -2), (-1, -4), (-2, -3)
At this point Kwame wrote (-1,2), (-1, 4), (-2, 3), which is incorrect.
Step 4 is correct, then when comparing the images in step 5, the vertices will be located in the same place, therefore the statement made by the teacher is accurate.
A dresser and nightstand costs $900. If the dresser costs $150 more than the nightstand, what does each piece cost separately?
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We will solve this problem using a system of linear equations.
[tex]\text{Let D=dresser's cost and N=nightstand's cost}[/tex]We are given the following relationship between the variables
[tex]\begin{gathered} D+N=900,\text{ (1)} \\ D=N+150,\text{ (2)} \end{gathered}[/tex]Replacing the value of D from equation (2) in equation (1)
[tex]N+150+N=900[/tex]Solving for N
[tex]\begin{gathered} 2N+150=900 \\ 2N=900-150 \\ 2N=750 \\ N=\frac{750}{2}=375 \end{gathered}[/tex]Replacing the value of N in equation (2)
[tex]\begin{gathered} D=375+150 \\ D=525 \end{gathered}[/tex]The answer is the nightstand costs $375 and the Dresser costs $525
Use the approximate half-life formula for the case described below. Discuss whether the formula is valid for the case described.Urban encroachment is causing the area of a forest to decline at the rate of 5% per year. What is the half-life of the forest? What fraction of the forest will remain in 30 years?(Type an integer or decimal rounded to the nearest hundredth as needed.)
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ANSWER:
EXPLANATION:
Give the rate of decline as 5% per year, we'll go ahead and use the below formula to determine the half-life of the forest;
[tex][/tex]Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.)5x^2 + x = −5
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5x^2 + x = -5
Equal to zero:
5x^2 + x + 5 = 0
General form:
ax^2 + bx + c
Where:
a= 5
b= 1
c= 5
Apply the quadratic formula:
[tex]\frac{-b\pm\sqrt{b^2-4\times a\times c}}{2\times a}[/tex]Replacing:
[tex]\frac{-1\pm\sqrt{1^2-4\times5\times5}}{2\times5}[/tex][tex]\frac{-1\pm\sqrt{-99}}{10}[/tex][tex]\frac{-1\pm\sqrt[\placeholder{⬚}]{-1}\times\sqrt{99}}{10}[/tex][tex]\frac{-1\pm3\sqrt[\placeholder{⬚}]{11}\text{ i}}{10}[/tex]Positive:
[tex]\frac{-1+3i\sqrt[\placeholder{⬚}]{11}}{10}[/tex]Negative
[tex]\frac{-1-3i\sqrt[\placeholder{⬚}]{11}}{10}[/tex]Find the area of the circle if the square has an area of 900 in.² to give your answer in terms of
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Diameter of circle = length of each side of the square
The formula for calculating the area of a square is
Area = l^2
where l is the length of each side
From the information given,
Area = 900
900 = l^2
l = √900
l = 30
diameter = 30
radius = diameter/2 = 30/2
radius = 15
The formula for calculating the area of a circle is
Area = πr^2 = π * 15^2
Area of circle = 225π in^2
Marcus para sailing in Florida. The angle of depression from his line of sight to the boat is 41 °. if the cable attaching Mark to the boat is 500 ft long how many feet is Mark above the water
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As you can see, a right triangle is formed in the situation that the statement describes. So to solve the exercise you can use the trigonometric ratio sin(θ):
[tex]\sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}[/tex]Graphically
So, in this case, you have
[tex]\begin{gathered} \theta=41\text{\degree} \\ \text{Opposite side = Mark's height above water } \\ \text{Hypotenuse = 500 ft} \\ \sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}} \\ \sin (41\text{\degree})=\frac{\text{Mark's height above water }}{500ft} \\ \text{Multiply by 500ft from both sides of the equation} \\ \sin (41\text{\degree})\cdot500ft=\frac{\text{Mark's height above water }}{500ft}\cdot500ft \\ \sin (41\text{\degree})\cdot500ft=\text{Mark's height above water } \\ 328.03ft=\text{Mark's height above water } \end{gathered}[/tex]Therefore, Mark is 328.03 feet above the water.
Your favorite music artist is inside Best Buy signing autographs. If you are at the back of a single fileline that is 2 miles out the door, how many people are ahead of you? Each person takes up 18 inches.
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there are 7372 people ahead of you
The first thing we will do is state the parameters we are given:
Your location is 2miles from the door.
Each person takes 18inches.
To know the number of people ahead, we will find how many inches make up a mile.
1 mile = 66360inches
[tex]\begin{gathered} 2\text{ miles = 2}\times66360\text{ } \\ =\text{ 132720 inches} \end{gathered}[/tex]Since 1 person = 18inches, the number of persons on that line would be:
[tex]\begin{gathered} =\text{ }\frac{132720}{18} \\ =\text{ 7373 approxi}mately \end{gathered}[/tex]There are 7373 people on the line.
The number of people ahead of you = 7373-1 = 7372
But, there are 7372 people ahead of you
What is the scale factor of XYZ to UVW?y836075V83"1556°4156X9018W410A. 5B.14OOC.011aD. 4
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In order to solve this exercise, it is important to remember that when two figures are similar the corresponding angles are congruent (this means that they have equal measure) and the ratios of the lengths of their corresponding sides are equal.
In this case, you know that the triangle XYZ and the triangle UVW are similar triangles. Let be "k" the scale factor of XYZ to UVW.
Based on the explained above, you can set up the following:
[tex]k=\frac{UV}{XY}[/tex]You can identify that:
[tex]\begin{gathered} UV=12 \\ XY=60 \end{gathered}[/tex]Then, substituting values into the equation, you get that:
[tex]k=\frac{12}{60}=\frac{1}{5}[/tex]The answer
In a survey, 315people said they drivetheir car to work. Thisrepresents 90% of thepeople surveyed.How many peoplewere surveyed?
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We know that 90% is equivalent to 315 people and we want to know how many people are equivalent to 100%. So, using the rule of three, we get:
90% ------------------- 315
100% ------------------ X
Where X is the number of people surveyed.
Solving for X, we get:
[tex]X=\frac{100\cdot315}{90}=350[/tex]Therefore, 350 people were surveyed.
Answer: 350 people
Put following list in descending order 64/100
60%
0.66
6%
0.066
13/20
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Answer:
0.66 , 13/20 , 64/100 , 60% , 0.066 , 6%
Step-by-step explanation:
Put following list in descending order:
64/100 = 0.64
60% = 0.6
0.66 = 0.66
6% = 0.06
0.066 = 0.066
13/20 = 0.65
descending:
0.66 , 13/20 , 64/100 , 60% , 0.066 , 6%
HeLPPP quick
This is very important :’)
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Answer:
A
Step-by-step explanation:
im smart :)
also 153/225 is .68 then multiply by 100 and you get 68% aka im a genius aka give me brainliest lol
Can you please help me out with a question
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In the figure, the value of angle inscribed, m[tex]\text{Inscribed angle=}\frac{1}{2}\times Intercepted\text{ arc}[/tex]In the figure, Hence,
[tex]\begin{gathered} mTherefore, m ZWX= 230º.please choose all answers that best matches the question provided thank you
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ANSWER
• Quadrilateral
EXPLANATION
In a parallelogram, opposite sides are parallel and congruent - they have the same length.
A rectangle is like a parallelogram, but all interior angles are right angles.
A square has four congruent sides, as well as a rhombus.
If a trapezoid is isosceles, then the non-parallel legs are congruent. If it is not isosceles, then all sides have different lengths and two opposite sides are parallel.
We know that this is a quadrilateral because it has 4 sides.
What is the area of this parallelogram? (HINT: Use Pythagorean Theorem) 28 in 17 in lih 15 in X. 238in? b. 224in? < 112in? 210 in?
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using pythagorean theorem we can get h
[tex]17^2=15^2+h[/tex][tex]h=\sqrt[]{64}\text{ =8}[/tex]so we get h as 8.
A=bxh
h=8 b= 28
so,A=224in
The difference between eight times a number and three is equal to negative nineteen. What is the number?-22-33
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Given:
The difference between eight times a number and three is equal to negative nineteen.
Required:
We want to find that number
Explanation:
Take the unknown number x
Now,
The difference between eight times a number and three is equal to negative nineteen means
[tex]\begin{gathered} 8x-3=-19 \\ 8x=-19+3 \\ 8x=-16 \\ x=-2 \end{gathered}[/tex]Final answer:
-2
in how many ways can six players be assigned to six positions on a baseball team assuring there any player can play any position
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Imagine htat each position is a box numbered from 1 to 6. You have the following
We will first find all posibilitied by simply calculating all possibilities for each box if we fill them in order.
For the first box, since we haven't chosen any player, we have 6 possibilities.
For the second box, since we have already filled box 1, we have 5 possibilites.
In the same manner, for box 3 we have 4 possibilites.
For box 4 we have 3 possibilities
For box 5 we have 2 possibilites.
Finally, for box 6 we will have only 1 possibility
So, the total number of possibilites is simply the product of all possibilites for each box
That is
[tex]6\cdot5\cdot4\cdot3\cdot2\cdot1=6!=720[/tex]so there are 720 possiblilites.
Would 2(3 + X) - 2x make 4x?
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Given that,
2(3 + X) - 2x, we have to verify whether the solution results in 4x. For that, solve the equation
2(3+x) - 2x
=> 6 + 2x - 2x
=> 6
Hence, it does not make 4x.