Mathematics College

PLEASEEEEE HEEEEEELPPPPPPPPPPPPPPP

Suppose ABCD is a rhombus such that the angle bisector of ∠ABD meets AD at point K. Prove that m∠AKB = 3m∠ABK.

Answers

Answer 1

1. Let m∠ABK=x°. Since line BK bisects ∠ABD, then

m∠ABK=m∠KBD=x°.

Also m∠ABD=m∠ABK+m∠KBD=2x°.

2. The diagonal BD of rhombus ABCD bisects ∠ABC, then

m∠ABD=m∠DBC=2x°.

This gives you that

m∠ABC=4x°.

3. Angles A and B are supplementary, so

m∠A+m∠B=180°,

m∠A=180°-4x°.

4. Consider triangle ABK. The sum of the measures of interior angles in triangle is always 180°, thus

m∠A+m∠ABK+m∠AKB=180°,

m∠AKB=180°-x°-(180°-4x°),

m∠AKB=3x°=3m∠ABK.

Answer 2

Answer:

Given information: ABCD is a rhombus, angle bisector of ∠ABD meets AD at point K.

[tex]\angle ABK\cong \angle DBK[/tex]         (Definition of angle bisector)

[tex]m\angle ABK=m\angle DBK[/tex]          (Definition of concurrency)

Let as assume the measure of angle ABK is x.

[tex]m\angle ABK=x[/tex]

[tex]m\angle ABD=m\angle ABK+m\angle DBK[/tex]

[tex]m\angle ABD=x+x[/tex]

[tex]m\angle ABD=2x[/tex]

All sides of a rhombus are same.

Since AB=AD, therefore ABD is an isosceles triangle and two angles of an isosceles triangle are congruent.

[tex]m\angle ADB=m\angle ABD[/tex]

[tex]m\angle ADB=2x[/tex]

According to exterior angle theorem, sum of two interior angles of a triangle is equal to third exterior angle.

Using exterior angle theorem, we get

[tex]m\angle AKB=m\angle ADB+m\angle DBK[/tex]

[tex]m\angle AKB=2x+x[/tex]

[tex]m\angle AKB=3x[/tex]

[tex]m\angle AKB=3(m\angle ABK)[/tex]

Hence proved.

PLEASEEEEE HEEEEEELPPPPPPPPPPPPPPPSuppose ABCD Is A Rhombus Such That The Angle Bisector Of ABD Meets

Related Questions

Which is greater 320 fl oz of 18 pt

Answers

16 ounces = 1 pint
320/16 = 20 pints

320 fl oz is greater than 18 pt

496 rounded to the nearest 10 is 500 true or false

Answers

True, It would round up to 500.
True if it was 495 then it would be 490 but because its 496 that's closer to 500

pete's dog weighed 30 pounds . then lost 16% of its weight , how much weight did the dog loose

Answers

The dog would now way 25.2 pounds, having lost 4.8 pounds.
the dog had lost 4.8

In microeconomics, price helps determine both quantity supplied and quantity demanded. Which other factors also help determine each? Quantity supplied is determined by production costs, and quantity demanded is determined by desire for the product. Quantity supplied is determined by production costs, and quantity demanded is determined by producer behavior. Quantity supplied is determined by consumer behavior, and quantity demanded is determined by aggregate demand. Quantity supplied is determined by producer behavior, and quantity demanded is determined by desire for the product

Answers

Answer :- First option is correct.

Microeconomics is the study of psychology of individuals at small scale.

In microeconomics, price of goods helps to determine the quantity supplied and the quantity demanded.

Quantity demanded is determined by

1. Desire of any good 2. Willingness to buy that good 3.Ability to buy a good

Other than that quantity supplied is determined by

1.Production cost [supply can increase with decrease in cost of production]

2. Productivity [supply can increase with increase in number of workers or hard working workers]

3.Technology[supply can increase with increase in the use of new technology related to production]

4.Govt regulation [it can either restrict or advertise the goods that can either increase or decrease the supply of that good respectively.]

5.Taxes and subsidies [implication of taxes can decrease the supply but by implication of subsidies supply can increase]etc.

So, Ist option is correct that the quantity supplied is determined by production cost and quantity demanded is determined by desire for the product.


At a certain time of day the angle of elevation of the sun is 30 a tree has a shadow that is 25 feet long find the tree to the nearest foot

Answers

If we draw out this scenario, we can see that it is a 30-60-90 right triangle, and the tree shadow is the leg opposite of the 60 degree angle. The problem asks for the length of the tree, which is the leg opposite of the 30 degree angle. In a 30-60-90 triangle, the leg opposite of the 30 degree angle has length “x”, and the leg opposite of the 60 degree angle has length “x times sqrt 3” (or “x rad 3”). We know the leg opposite of the 60 degree angle is 25 feet, so we can setup the equation “x rad 3 = 25”. We divide sqrt of 3 on both sides and end up with “x = 25/sqrt 3”. The problem asked for the leg opposite of the 30 degree angle, which we set as “x”. The problem asks for the length to the nearest foot. When put into a calculator, “25/sqrt 3” ends up being about 14 feet, which is our final answer.

The width of a rectangle is 7 inches. Its length is 10 inches. What is the ratio of its width to its length?\

Answers

the ratio would be exactly 

1.42857143 : 1

Carlisle is testing different types of planting soil to determine which type is most effective in growing blueberry bushes. He purchases 2 different brands of planting soil from a local store. Carlisle applies Brand A to an area of the yard that receives full sunlight and Brand B to another area of the yard that is in partial shade. He waters both areas daily. At the end of the study, Carlisle concludes Brand A is more effective in growing blueberry bushes. Why is his conclusion not valid?

Answers

This conclusion is not valid because BOTH SOIL BRANDS WERE NOT SUBJECTED TO THE SAME CONDITIONS. 
Carlisle applied brand A to the part of the yard that received full sunlight while brand B was applied to the area of the yard which received partial sunlight. This implies that the soils were subjected to different conditions and this ought not to be so, since sunlight is a very important factor, which the soils need.
His conclusion is not valid because his dependent variables weren't the same. When testing out an independent variable, which is the soil in this case, all the other factors of the experiment has to remain the same in order to provide a correct conclusion. Since Carlisle was testing out two different types of soils, he had to set all the other conditions of the plants exactly the same, including the amount of lights that the plants receive. Brand B received full sunlight whereas brand A received less. This could definitely have impaired the results of this experiment, therefore, making it invalid.

Help with this math question please had to post picture side ways for it to fit thanks

Answers

Hello,
Please, see the attached files.
Thanks.

how would you graph y=| x-2|-4

Answers

To graph ty function simply make a table of values, where you choose any value for x and substitute that value in the function.

Then take the absolute value of the expression in the square bracket.

It is always positive, the absolute value of -6 is 6 etc.

Then graph the resulting points.

Another way to do it is simply draw the graph of y = |x| then move it 2 spaces to the right and 4 spaces down, I believe.

5.1 times 10 to the fourth power

Answers

The answer is 6,765,201. I apologize if I got this wrong.
5.1*10=51
so, 51*51*51*51=6765201

Distance between New York and San Francisco is 2539.79 MI a train travels at an average speed of 90 miles per hour what equation shows the relationship between distance traveled (Dl speed (s) and time taken (t)

Answers

D = s*t . . . . . . . distance is the product of speed and time

_____
If you want to know the time it takes to get from New York to San Francisco, you can substitute the given values and solve for t.
  2539.79 = 90t
  2539.79/90 = t ≈ 28.2199 . . . . hours

Lee associates borrowed $60,000. The company plans to set up a sinking fund that will pay back the loan at the end of 12 years. Assuming a rate of 8% compounded semiannually, the amount to be paid into the fund each period is?

Answers

If your choices are the following:
A. $1,350
B. $1,536
C. $1,653
D. $5,163
E. None of these

Then the answer is B. $1,536.

Solution:
$60,000 x .0256
=1,536

Select three rations that are equivalent to 7: 6.

Answers

14:12
21:18
28:24
............

Buying something in order to increase social status is known as _____ consumption.

1 Conspicuous
2 Emotional
3 Research
4 Wise

Answers

1) conspicuous consumption

1) Conspicous Consumption

-4x-2y=-12 and 4x+8y=-24 using addition/eliminatin method

Answers

Use the elimination method:

-4x - 2y = -12
+4x + 8y = -12
--------------------
 0  + 6y = -24

6y = -24
6y/6 = -24/6
y = -4

Plug in -4 for y in one of the equations
-4x - 2y = -12
-4x - 2(-4) = -12
-4x + 8 = -12
-4x + 8 (-8) = -12 (-8)
-4x = -20
-4x/-4 = -20/-4
x = 5

x = 5, y = -4

hope this helps
elimination method is best because one equation has 4x and the other has -4x. Add the two equations together.

 -4x - 2y = -12
+4x + 8y = -24
----------------------
   0 + 6y = - 36

divide by 6 both sides 
y = -6 

use this to find x in either equation.
4x + 8(-6) = -24
4x  - 48 = -24
4x = -24 + 48
4x = 24
x = 6

Compare and contrast y=square root of x and f(x)=square root of x

Answers

 For this case we have the following functions:
 y = square root of x
 f (x) = square root of x
 Rewriting the functions we have:
 [tex]y = x ^ {(1/2)} f (x) = x ^ {(1/2)}[/tex]
 We observed that:
 The functions are exactly the same.
 The difference is that when writing f (x) we know that the function depends on x.
 When writing the letter y, we have two variables:
 y: dependent variable.
 x: independent variable.

Answer:

Step-by-step explanation:

Given are two functions

[tex]y=\sqrt{x} :\\f(x) =\sqrt{x}[/tex]

We have to compare and contrast these two functions.

On comparing we have both are the same.

FIrst one is written as y = form while second function is written as function of x

Sometimes we use y and sometimes we use f(x) in practice.

In both the cases, x is the independent variable and normally marked on x axis and y or f(x) the dependent variable marked on vertical y axis.

Can you please explain this

Answers

1st triangle is isoceles triangle as one as two angles are equal due to the equal sides......
2nd triangle is equilateral triangle as all sides are same
The two triangles are not congruent because we do not know if the third sides of both triangles are congruent. We can see that the first and second sides are congruent to their corresponding sides in the 2nd triangle. However, if we do not know that the third side in the first triangle is congruent to its corresponding side in the second triangle, then we cannot conclude that the two sides are congruent.

Imagine a world in which only decimal,not fractions,are used.how would your life be different

Answers

This answer depends a bit on your age, the types of activities you partake in and the kind of work you do/are planning to do but here goes:

I am thinking of some uses of fractions where decimals are not typically used. One might be cooking. Often the ingredients (1/2 cup of four and so on) are measured using fractions. If you were in a world with decimals you might need to make (1/3) the servings of a recipe that calls for 1/4 of a cup of some ingredient and instead of 1/12 have to deal with a long repeating decimal that probably would need to be approximated so would not be precise.

While on the subject of food ordering pizza (1/2 with pepperoni, 1/4 mushrooms and 1/4 plain) would be doable after you got used to it but probably not as comfortable. Dividing up slices of pizza among friends (one slice is usually 1/8 of a pie) might be awkward though eventually doable.

Estimation - the biggest issue is exactitude versus estimation. When we use a fraction like 1/3 that is an exact value, but when we use .333 or .3333333 no matter how many 3s we use we are only estimating because the 3s go on forever and we can't write them forever. Yes, we can use .3 (with a bar over the 3, but now try to multiply that with .456565656 with a bar over the 56. This becomes practically impossible unless we estimate ... so the biggest issue would be that you would lose precision in many calculations and measurements and have to deal with answers that are good enough (but not exact).

Now say you work on some major car company or you design bridges or you are a scientist developing medicine that cures diseases, would not you want the ability to measure and compute precisely? If I split the pizza up wrong it is not a big deal. If I use a little more flour or a little less than I should in the recipe it might not make much of a difference in the end but if I am doing something that impacts the health, safety or well being of another human being, I would not want to live in a world where I have to estimate and can't count on having the exact, precise value.

how do you graph y=2sin(2x)

Answers

Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.
on the a axis, you set the x value at 0, π/4, π/2, 3π/4, π
2sin0=0, 2sin(π/2)=2, 2sinπ=0, 2sin(3π/2)=-2, 2sin(2π)=0
so the y values are 0, 2, 0, -2, 0 respectively
locate the points and connect
extend the pattern left and right if there is no limit for x. It should look like a wave

What is the arc length of a circle (in meters) with a radius of 2 meters that has an arc angle of 90°? A 2π B π C 2 D 4π

Answers

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad de grees\\ ------\\ r=2\\ \theta =90 \end{cases}\implies s=\cfrac{(90)\pi (2)}{180}\implies s=\pi [/tex]

when using fraction strips how do you know that two fractions are equivalent

Answers

The same strip area is covered by equivalent fractions. That's what makes them equivalent.
She is correct. The first person that answered

If the correlation between height and weight of a large group of people is 0.75​, find the coefficient of determination​ (as a​ percent) and explain what it means. assume that height is the predictor and weight is the​ response, and assume that the association between height and weight is linear.

Answers

Independent variable is the predictor variable which is the height and dependent variable is the response variable which is weight in this scenario.

The square of correlation coefficient gives the coefficient of determination. It is denoted by R² (R squared).

We are given:
R = 0.75

So,
R²  = 0.75²

R² = 0.5625

R²  = 56.25 %
The coefficient of determination tells how much of the trend of dependent data can be explained by the independent data using the linear regression model. So in the given case, Height can explain 56.25% of the trend in the weight.

Answer:

Step-by-step explanation:

Given that  the correlation between height and weight of a large group of people is 0.75

Coefficient of determination = [tex]R^2 =0.75^2 =0.5625=56.25%[/tex]

Coefficient of determination gives us the strength of association between two variables and how much the variability of the response variable i.e. weight is due to the variability of the predictor variable i.e. height

When there is a linear association correlation coefficient square gives us the reason for the variability and percentage due to the variability in predictor variable

Find the missing dimension of each triangle described Height: 7 in., area: 21 in2

Answers

To find the missing dimension of a triangle given the height and area, we can use the formula for the area of a triangle: Area = 1/2 * base * height. We're given the height as 7 inches and the area as 21 square inches. Plugging these values into the formula, we can solve for the base using algebraic manipulation.

To find the missing dimension of a triangle given the height and area, we can use the formula for the area of a triangle: Area = 1/2 * base * height. We're given the height as 7 inches and the area as 21 square inches. Plugging these values into the formula, we get: 21 = 1/2 * base * 7. Solving for the base, we can multiply both sides of the equation by 2 and divide by 7 to get the base: base = (21 * 2) / 7 = 6 inches.

Learn more about Finding missing dimension of a triangle here:

https://brainly.com/question/32030154

#SPJ2

Final answer:

By using the area formula for a triangle, A = (b × h) / 2, with the provided height of 7 inches and area of 21 square inches, the base is calculated to be 6 inches.

Explanation:

To find the missing dimension of a triangle, given the height and area, we can use the formula for the area of a triangle A = (b × h) / 2, where A is the area, b is the base, and h is the height. Given that the height h is 7 inches and the area A is 21 square inches, we can rearrange the formula to solve for the base b:
Area = (base × height) / 2 → 21 = (b × 7) / 2 → b = (21 × 2) / 7 → b = 6

The missing dimension, the base of the triangle, is 6 inches, provided height of 7 inches and area of 21 square inches.

How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3?

Answers

infinitely many solutions. Since your slope and Y axis values are the same on both sides no matter what you fill in for x your answer will be true.

translated 2 units left and 9 units down

Answers

Move 2 times to the left and go down 9 times i think....

The translation of the given expression is "[tex]\bold{y=(x+2)^2-9}[/tex]"

Translation of equation:

Given:

"translated 2 units left and 9 units down".

we assume the equation is "y" so, the translation of the above-given expression is equal to "[tex]\bold{y=(x+2)^2-9}[/tex]".

Please find the attached diagram for the translated expression.

Find out more information about the translation here:

brainly.com/question/24649944

Please help with 34 ASAP!!

Answers

90-54w you have to use the distributive property meaning multiply the 18 by every number in the pretenses to get your equation 

What number lies between 7x8/10=

Answers

the number that lies between that is 7
the number that  between 7x8/10 is:

7x8=56
56/10= 5.6

therefore the answer is 5.6


hope this helps

-Rachael
(yahtzee05)


A town has two fire engines, a and b, that operate independently. the probability that engine a is available when needed is 0.96. the probability that engine b is available when needed is also 0.96. 12. what is the probability that neither fire engine is available when needed?

Answers

P(both unavailable) = P(A unavailable)*P(B unavailable) = 0.04^2 = 0.0016

3 over 5 is 30% of what number?

Answers

3/5 = 0.3 * x
3/5 is 30% of x - This is how they match up from the word problem to a number sentence

So to solve it...
3/5 = 0.3x
x = 3/5 ÷ 0.3 = 2

Which of the following is the same as 5(2 − 1)?

a 5 − 2 − 1

b 5 × 2 × 1

c 10 − 1

d 10 − 5

e one of the above

Answers

I believe it would be D
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