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ANSWER
The hexagons are similar because the side lengths of ABCDEF are reduced by the same scale factor to form hexagon GHIJKL
EXPLANATION
Two polygons are similar if they have congruent corresponding angles, and the ratio between corresponding sides is constant. This ratio is called the scale factor.
In this case, we know that each side length of hexagon ABCDEF is divided by 2 to form hexagon GHIJKL. In other words, hexagon ABCDEF is scaled to form hexagon GHIJKL by a scale factor of 1/2. Therefore, these two hexagons are similar.
Hence, the hexagons are similar because the side lengths of ABCDEF are reduced by the same scale factor to form hexagon GHIJKL.
Related Questions
In the U.K.), ortransportation (used in the U.S.), is the movement ofhumans, animals and goods from one location toanother. In other words, the action of transport isdefined as a particular movement of an organism orthing from a point A (a place in space) to a point B.sport include air, land (rail and road), water, cable, pipelinehe field can be divided into infrastructure, vehicles andransport enables trade between people, which is essential forent of
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Answer:
Step-by-step explanation:
Solving a quadratic equation:
ax² + bx + c = 0
The solution is given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this question:
2x² - 4x - 12 = 0
Dividing everything by x
x² - 2x - 6 = 0
So a = 1, b = -2, c = -6
[tex]x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\ast1\ast6}}{2}=\frac{4\pm\sqrt[]{28}}{2}=\frac{4\pm\sqrt[]{4\ast7}}{2}=\frac{4\pm2\sqrt[]{7}}{2}[/tex][tex]\frac{4\pm2\sqrt[]{7}}{2}=2\pm\sqrt[]{7}[/tex]In EFG, E(-2,7), F(7,-8) and G(-6,-3). Is EFG a right triangle. provide proof of your yes/no answer.
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Proof of a Right-Angled Triangle.
The correct answer is triangle EFG is not a right-angled triangle.
Step1: Find the distances: |EF| , |FG| and |GE| by using the formula below:
[tex]\text{Distance =}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} E(-2,7)\Rightarrow x_1=-2;y_1=7 \\ F(7,-8)\Rightarrow x_2=7;y_2=-8 \end{gathered}[/tex][tex]\begin{gathered} |EF|^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ |EF|^2=(7--2)^2+(-8-7)^2=9^2+(-15)^2=306 \end{gathered}[/tex][tex]\begin{gathered} F(7,-8)\Rightarrow x_1=7;y_1=-8 \\ G(-6,-3)\Rightarrow x_2=-6;y_2=-3 \end{gathered}[/tex][tex]\begin{gathered} |FG|^2=(-6-7)^2+(-3--8)^2 \\ |FG|^2=(-13)^2+5^2=169+25=194 \end{gathered}[/tex][tex]\begin{gathered} G(-6,-3)\Rightarrow x_1=-6;y_1=-3 \\ E(-2,7)\Rightarrow x_2=-2;y_2=7 \end{gathered}[/tex][tex]\begin{gathered} |GE|^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ |GE|^2=(-2--6)^2+(7--3)^2=4^2+10^2 \\ |GE|^2=16+100=116 \end{gathered}[/tex]Step2: By Pythagoras Theorem, if
[tex]\begin{gathered} |FG|^2+|GE|^2=|EF|^2\ldots eqn(1) \\ \text{If the above expression labeled eqn(1) is true, then we conclude that triangle EFG is a } \\ \text{right}-\text{angled triangle, otherwise, it is not a right-angled triangle.} \end{gathered}[/tex][tex]\begin{gathered} |FG|^2+|GE|^2=|EF|^2 \\ 194+116=|EF|^2 \\ 310=|EF|^2,but|EF|^2=306 \\ \text{Clearly, }310\ne306,\text{ we conclude that triangle EFG is not a right-angled triangle.} \end{gathered}[/tex]Hence, the correct answer is triangle EFG is not a right-angled triangle.
What are the 5 steps for solving linear inequalities
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If we had to break down an inequality into 5 steps to solve it, those would be the following:
1. Interpreting the inequality sign:
An inequality is just like an equation, but instead of having the sign "=" and inequality will have a ">" (greater than) or a "<" (less than). We have to take a good look and see which sign our inequality uses.
2. Simplifying: An inequailty can be solved much like an equation. You may have to combine like terms or apply any other algebraic principle to simplify both sides of the inequality.
3. Put the variable in one side of the inequality:
Using algebraic principles, move the variable to one side of the inequailty.
4. Isolate the variable:
To solve the inequality, the variable has to be in one side of the inequality, without constants or coefficients.
5. Interpret the resulting inequality as a set:
In this last step, you have to take the inequality from the previous step and write it down as a set of values that solve the inequality.
Simplify the expression: 7(8f + 1)
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Answer:
7(8f) + 7(1)
7 x 8 x f + 7 x 1
56f + 7
A recipe requires 1 1/4 cups of milk for every 1 2/3 cups of flour. How many cups of milk are needed for each cup of flour?
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Answer:
The amount of milk that will be needed for each cup of flour is:
[tex]\frac{3}{4}\text{ cups of milk}[/tex]Explanation:
Given that;
A recipe requires 1 1/4 cups of milk for every 1 2/3 cups of flour.
[tex]1\frac{1}{4}\text{ cups of milk }\rightarrow1\frac{2}{3}\text{ cups of flour}[/tex]we want to find the amount of milk that will be requires for each cup of flour.
we can get that by dividing both sides by 1 1/3;
[tex]\begin{gathered} \frac{1\frac{1}{4}\text{ }}{1\frac{2}{3}}\text{cups of milk }\rightarrow\frac{1\frac{2}{3}\text{ }}{1\frac{2}{3}}\text{cups of flour} \\ \frac{\frac{5}{4}\text{ }}{\frac{5}{3}}\text{cups of milk }\rightarrow1\text{ cups of flour} \\ \frac{5}{4}\text{ }\times\frac{3}{5}\text{cups of milk }\rightarrow1\text{ cups of flour} \\ \frac{3}{4}\text{ cups of milk }\rightarrow1\text{ cups of flour} \end{gathered}[/tex]Therefore, the amount of milk that will be needed for each cup of flour is;
[tex]\frac{3}{4}\text{ cups of milk}[/tex]Please help me I can’t seem to solve the red outlined questions
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SOLUTION
a. From the graph;
[tex]g(8)=2.0[/tex]b.
[tex]g(-4)=-1.0[/tex]c. For how many values of x does g(x) = 0.02, the answer is
[tex]3[/tex]d. For what values is g = 0; the answers are;
[tex]-3,0,3[/tex]help please. I'm not sure how to do this and there's no material in my book that explains how to do it either
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We know that
• BD bisects the angle ABC.
Remember that a bisector divides the angle in two equal parts, that means
[tex]m\angle ABD=m\angle DBC[/tex]Where,
[tex]m\angle ABD=8x+35,m\angle DBC=11x+23[/tex]Replacing these expressions we have
[tex]8x+35=11x+23[/tex]Now, we solve for x, first, we subtract -11x on each side
[tex]\begin{gathered} 8x+35-11x=11x+23-11x \\ -3x+35=23 \end{gathered}[/tex]Then, we subtract 35 on each side
[tex]\begin{gathered} -3x+35-35=23-35 \\ -3x=-12 \end{gathered}[/tex]At last, we divide the equation by -3
[tex]\begin{gathered} \frac{-3x}{-3}=\frac{-12}{-3} \\ x=4 \end{gathered}[/tex]We use this value to find each angle.
[tex]undefined[/tex]Determine the Y intercept for the following equation 4X +2Y=-12
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Answer:
b=-6
Explanation:
Given the equation
[tex]4x+2y=-12[/tex]To determine the y-intercept, we first express it in the slope-intercept form (y=mx+b).
[tex]\begin{gathered} 4x+2y=-12 \\ 2y=-4x-12 \\ \text{Divide all through by 2} \\ y=-\frac{4x}{2}-\frac{12}{2} \\ y=-2x-6 \end{gathered}[/tex]We can see that the y-intercept of the line, b= -6.
What kind of sequence is this? 1, 10, 100, 1.000,
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hello, this is a geometric progression.
To find the next number of this sequence, we have to know the reason of it. So, we divide the second by the first.
10 divided by 1 = 10.
next
Bernie bought a refrigerator at a special sale. The refrigerator regularly sold for $986. No down payment was required. Bernie has to pay $69 per month for 12 years. What is the average amount Bernie pays in interest each month?
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What’s the correct answer answer asap for brainlist please somebody
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Answer:
The answer is A. laying off employees
Step-by-step explanation:
this is due to the market crash happening and investment in those factories and business being low.
Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. P(x ≥ 5); μ = 18; σ = 5Multiple choice:a. 0.995b. 0.495c. 0.005d. 0.248e. 0.002
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Find out the value of z
Remember that
z =(x - μ)/σ
we have
μ=18
σ=5
For x=5
substitute
z=(5-18)/5
z=-2.6
Using a z-scores table
we have that
P(x ≥ 5)=0.99534
therefore
the answer is option AHow to calculate volume of a bucket that's cut from a cone?
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Given: A frustum of a cone.
Required: To determine the formula for the frustum of a cone.
Explanation: When a cone is divided into two parts, the upper part remains in the shape of a cone, and the lower part makes the frustum.
The formula gives the volume of a cone-
[tex]V=\frac{1}{3}\pi r^2h[/tex]The general formula gives the volume of the frustum as-
[tex]V=\frac{h}{3}(S_1+S_2+\sqrt{S_1S_2}[/tex]where h denotes the height, S1 and S2 are the base surface areas. Here we have-
[tex]\begin{gathered} S_1=\pi R^2 \\ S_2=\pi r^2 \end{gathered}[/tex]Here, R and r are the radius of the base at the bottom and top of the frustum, respectively.
Substituting the values into the formula for frustum as-
[tex]V=\frac{h}{3}(\pi R^2+\pi r^2+\sqrt{(\pi R^2)(\pi r^2)}[/tex]Further solving-
[tex]V=\frac{\pi h}{3}(R^2+r^2+Rr)[/tex]Final Answer: The volume of the frustum is-
[tex]V=\frac{\pi h(R^2+r^2+Rr)}{3}[/tex]AOC=96° BOC=8x-67° AOB=9x-75° find BOC
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Given data:
The given figure.
The expression for the angle AOC is,
[tex]\angle AOC=\angle\text{AOB}+\angle BOC[/tex]Substitute the given values in the abbove expression.
[tex]\begin{gathered} 96^{\circ}=(9x-75^{\circ})+(8x-67^{\circ}) \\ 238^{\circ}=17x \\ x=14 \end{gathered}[/tex]Substitute 14 for x in the angle BOC.
[tex]\begin{gathered} \angle BOC=(8(14)-67)^{\circ} \\ =45^{\circ} \end{gathered}[/tex]Solve for p:p + 5p-2p + 4p = -40
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p + 5p-2p + 4p = -40
Solving for p:
6p - 2p + 4p = -40
4p + 4p = -40
8p = -40
p = -40/8
p = -5
Answer:
p = -5
Determine whether the following points satisfy y=2x+3, y>2x+3 or y<2x-3 without drawing a grapha) (0,1)
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The expressions are given as,
[tex]\begin{gathered} y=2x+3 \\ y>2x+3 \\ y<2x-3 \end{gathered}[/tex]It is asked to check whether the point (0,1) satisfy all the above relationships.
Substitute the coordinate in the first equation,
[tex]\begin{gathered} 1=2(0)+3 \\ 1=0+3 \\ 1=3 \end{gathered}[/tex]Clearly, the result is not true. So it can be concluded that the point (0,1) does not satisfy the first relationship.
Substitute the coordinate in the second inequation,
[tex]\begin{gathered} 1>2(0)+3 \\ 1>0+3 \\ 1>3 \end{gathered}[/tex]Again, the result is not true. So it can be concluded that the point (0,1) does not satisfy the second relationship.
Substitute the coordinate in the third inequation,
[tex]\begin{gathered} 1<2(0)-3 \\ 1<0-3 \\ 1<-3 \end{gathered}[/tex]This result obtained is true. So it can be concluded that the point (0,1) satisfies the third relationship.
Thus, the given point satisfies the third relationship only.
Determine the mid points for ca the coordinates c and a are -4 and 7
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we have the folloing:
[tex]m=\frac{7-4}{2}=\frac{3}{2}=1.5[/tex]therefore, the mid point is 1.5 or 3/2
Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle.
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sec θ = -4 / 3
cot θ > 0
Step 02:
sec θ = 1 / cos θ
-4/3 = 1 / cos θ
[tex]\begin{gathered} \frac{-4}{3}\text{ = }\frac{1}{\text{cos }\theta} \\ \cos \text{ }\theta\text{ = -}\frac{3}{4} \end{gathered}[/tex]cot θ = 1 / tan θ > 0
How many different combinations can be formed by taking four digits 3, 4, 7, 5, 8, 1?
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Solution
We are given 6 numbers, we want to find how many four digits different number that can be formed
Note: All the six numbers are available to occupy the first space of the 4 digit number. There would just be 5 numbers availabe for the second space and 4 numbers for the third and 3 for the last.
Therefore, the number of different combinations is
[tex]6\times5\times4\times3=360[/tex]The answer is
[tex]360[/tex]1. Which of the following correctly gives the center and radius of the circle defined by the equation(x-7)2 + (x-2)2 = 10?
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The general equation of the circle with centre (h,k) and radius r is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Simplify the given equation to obtain the equation in general equation.
[tex]\begin{gathered} (x-7)^2+(y-2)^2=10 \\ (x-7)^2+(y-2)^2=(\sqrt[]{10})^2 \end{gathered}[/tex]On compare the equation with general equation the centre and radius is,
[tex](h,k)=(7,2)[/tex]And
[tex]r=\sqrt[]{10}[/tex]So centre is (7,2) and radius is
[tex]\sqrt[]{10}[/tex]Option B is correct answer.
Write the function y=|x| but shifter to the left 3 units.
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In this problem, we have the function
y=|x| -----> vertex is at (0,0)
The rule of the translation is given by
(x,y) -----> (x-3,y)
so
the translation is 3 units at the left
the new vertex is at (-3,0)
therefore
the new function is
y=|x+3|How to convert 9.4 degrees into ft and inches
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Step 1;
0.25 inch (1/4" or 6mm) of total rear toe-in is equal to 0.58º
Step 2:
Next, convert 9.4 degrees to inches
[tex]\begin{gathered} \text{0.25 inches = 0.58 degr}ees \\ x\text{ inches = 9.4 degre}es \\ \text{ x = }\frac{0.25\times9.4\text{ }}{0.58}\text{ } \\ \text{x = 4.05 inches} \end{gathered}[/tex]Step 3
12 inches = 1 feet
[tex]\begin{gathered} 12\text{ inches = 1 f}eet \\ 4.05\text{ inches = }\frac{4.05\text{ }\times\text{ 1}}{12}\text{ fe}et \\ \text{= 0.3376 fe}et \end{gathered}[/tex]George has a sports card collection of 250 cards.Of those, 50 cards are football cards. What percentof the cards are football?
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Solution:
Consider the following diagram:
now, by cross-multiplication, this is equivalent to:
[tex]x\text{ (250 cards)=100\%(50cards)}[/tex]solving for x, we obtain:
[tex]x\text{ =}\frac{5000}{250}=20[/tex]So that, we can conclude that the correct answer is:
20%.
Solve using the problem solving strategy for word problems. The difference of three times a number and ten is 20. Find the number.
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Let the number be x
According to the statement,
[tex]3x-10=20[/tex]Solving it,
[tex]\begin{gathered} 3x-10=20 \\ 3x=20+10 \\ 3x=30 \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]Hence, the number is 10.
Your grandmother is in the hospital and is put on a liquid diet. After examining her chart, a mistake is found stating that her weight is 500 kg. What is the equivalent weight in pounds? (1kg = 2.205lbs)
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Answer:
1102.5 lbs
Explanation:
Let the equivalent weight in pounds be x.
We can go ahead and determine the value of x by setting up proportions as seen below;
[tex]\frac{1\operatorname{kg}}{2.205\text{ lbs}}=\frac{500\operatorname{kg}}{x\text{ lbs}}[/tex]If we cross multiply, we'll have;
[tex]\begin{gathered} x=500\times2.205 \\ x=1102.5 \end{gathered}[/tex]A bond is initially bought for 250. It doubles in value every decade.
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We have a bond that doubles it value every decade.
Initially, at decade=0, its value is 250.
Then, if it doubles, we will have:
[tex]\begin{gathered} V(1)=2\cdot V(0)=2\cdot250=500 \\ V(2)=2\cdot V(1)=2\cdot500=1000 \\ V(3)=2\cdot V(2)=2\cdot1000=2000 \end{gathered}[/tex]We can generalize this formula as:
[tex]\begin{gathered} V(1)=2\cdot V(0) \\ V(2)=2\cdot V(1)=2\cdot(2\cdot V(0))=2^2\cdot V(0) \\ V(3)=2\cdot V(2)=2\cdot(2^2\cdot V(0))=2^3\cdot V(0) \\ V(d)=2^d\cdot V(0)=2^d\cdot250=250\cdot2^d \end{gathered}[/tex]We can find the amount of decades that it takes for the bond to reach a value of $10,000 using the equation for V(d):
[tex]\begin{gathered} V(d)=10000 \\ 250\cdot2^d=10000 \\ 2^d=\frac{10000}{250} \\ 2^d=40 \\ d=\log _2(40)\approx5.32\approx6 \end{gathered}[/tex]It will take 6 decades for the bond to have a value that is more than $10,000.
Answer:
1)
Decades since bond is bought | Dollar value of bond
0 | 250
1 | 500
2 | 1000
3 | 2000
d | 250*2^d
2) It will take 6 decades for the bond to have a value that is more than $10,000.
3) V(d)=250*2^d
Solve for X:X+ 11=3
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We have the initial equation:
X + 11 = 3
To solve for X, we subtract 11 from both sides of the equation as:
X + 11 - 11 = 3 - 11
X = -8
Answer: X = -8
Practice Exam question and answer choices are in the image.
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Answer:
x = 10°
Step-by-step explanation:
We know that a right angle = 90°
Therefore, we know:
5x+4x = 90°
Simplify:
9x = 90°
Divide:
x = 10°
Emma has half of her investments in stock paying an 11% dividend and the other half in stock paying 14% interest if her total annual is 460 how much does she have invested?
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Given that half of her investments in a 11% dividend and the other half in a stock paying 14% interest.
Let the total investment be 2x dollars. So, x is invested in 11% dividend and x in a stock paying 14% interest.
Interest on both the investment is given below:
[tex]\begin{gathered} 0.11x+0.14x=460 \\ 0.25x=460 \\ \frac{0.25x}{0.25}=\frac{460}{0.25} \\ x=1840 \end{gathered}[/tex]So, the total investment is 2x = 2(1840) = $3680.
Find a formula for the exponential function that satisfies h(3) = 18 and h(6) = 6.174h(x) =
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ANSWER
[tex]h(x)=52.48\cdot(0.7)^x^{}[/tex]EXPLANATION
We have to find the exponential function h(x) such that:
[tex]\begin{gathered} h(3)=18 \\ h(6)=6.174 \end{gathered}[/tex]The general form of an exponential function is:
[tex]h(x)=a\cdot b^x^{}[/tex]where a = coefficient; b = base
We have to find the values of a and b.
First, substitute x = 3 and h(x) = 18 into the general function:
[tex]18=a\cdot b^3[/tex]Next, repeat the procedure for x = 6 and h(x) = 6.174:
[tex]6.174=a\cdot b^6[/tex]Next, divide the two equations:
[tex]\begin{gathered} \Rightarrow\frac{6.174}{18}=\frac{a\cdot b^6}{a\cdot b^3} \\ \Rightarrow0.343=b^{6-3} \\ \Rightarrow b^3=0.343 \end{gathered}[/tex]Find the cube root of both sides:
[tex]\begin{gathered} b=\sqrt[3]{0.343} \\ b=0.7 \end{gathered}[/tex]Now, substitute the value of b into the first equation to find a:
[tex]\begin{gathered} 18=a\cdot(0.7)^3 \\ 18=a\cdot0.343 \\ \Rightarrow a=\frac{18}{0.343} \\ a\approx52.48 \end{gathered}[/tex]Therefore, the formula for the exponential function h(x) is:
[tex]h(x)=52.48\cdot(0.7)^x[/tex]