Which theorem can be used to prove ABC ~ EDC ? ​

Answer:

Step-by-step explanation:

I answer for what I understand, the question is not clear.

2 divided by what times what equals 7

2 : x = 7

x = -2/-7

x = 2/7

-------------

check

2 : 2/7 = 7

2 * 7/2 = 7

7 = 7

the answer is good

After divide, the solution of the expression is, 285

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

190 divided by 2/3.

Now, We can simplify as;

⇒ 190 ÷ 2/3

⇒ 190 × 3/2

⇒ 95 × 3

⇒ 285

Thus, The solution of the expression is, 285

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The half life of the radioactive substance is 10.22 years.

Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).

It is given that

y = ae⁻ᵇˣ

here a is the initial amount , y is the amount remaining after x years

a = 90mg at x =0

Value of y = 12.6 mg at x = 29 years

On substitution of value

12.6 = 90 e⁻²⁹ᵇ

0.14 = e⁻²⁹ᵇ

b = 0.0678

The equation is

[tex]\rm y = 90 e^{-0.0678 * x}\\[/tex]

Half life is when the concentration is reduced to half

On 1st half life , the concentration = 90/2 = 45 mg

[tex]\rm 45 = 90 e^{-0.0678 * x}\\[/tex]

x = 10.22 years

Therefore the half life of the radioactive substance is 10.22 years.

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Answer:

5th or 6th grade

Step-by-step explanation:

The reason why we learn geography in 5th grade is to prepare us for 6th grade geography. The reason why we learn geography in 6th grade is because Geography helps us understand basic physical systems that affect everyday life. In other words, geography is a nice skill to have when you're learning about the water cycle or rock formations, or the moving of the tectonic plates (and other natural disasters). It's also a very important skill to have when you want to start traveling.

The average rate of change for this function for the interval from x = 2

to x = 4 is 20

The function is given as:

x   y

0  18

2   32

3    50

4   72

The average rate of change at the interval from x = 2 to x = 4 is calculated using:

m = (f(4) - f(2))/(4 - 2)

Using the table values, we have:

m = (72 - 32)/(4 - 2)

Evaluate

m = 20

Hence, the average rate of change is 20

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Answer:

m3+5

Step-by-step explanation:

m is miles

take the number of miles  multiply by3

take that answer add 5

The equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

A statement that relate two expressions with an equal sign is called an Equation.

It is given that

A cab company charges a $5 boarding

Charges for every mile is $3 per mile

Let x be the mile travelled

The cab's total charge is represented by y

then y = 3x + 5

Therefore the equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

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185.4m  (rounded to 1dp)

Circumference of a circle is the diameter times by pi. 59×pi=185.4

Answer:

59 meters

or approximately 185.26 ( using 3.14 for pi)

or 185.3539666 meters using the pi button

Step-by-step explanation:

The circumference is given by

C = pi *d where d is the diameter

C = pi * 59 m

C = 59 pi meters

We can approximate pi by 3.14

C =185.26 meters

or by using the pi button the calculator

185.3539666 meter

Answer:

22/7

Step-by-step explanation:

22/7 is not very close to pi, but it is sometimes used as an estimation for pi

Answer:

22/7 is estimation

Answer:

21 grandchildren

Explanation:

2/7ths + 5/7th = all

5/7ths = 15   <- divide both sides by 3 to get 1/7th

1/7th = 3 (multiply both sides by 7 to get "1")

  7/7ths    = 21

so, eva has 21 grandchildren

Answer:

21

Step-by-step explanation:

If 2/7th of Eva's grandchildren live in one location, we know that 5/7th (the remaining portion of Eva's grandchildren) must live in the other location

Wales + Australia = all of the kids (100% = 1/1  (which is equal to 7/7) )

Wales + Australia = 7/7ths

{x is the total number of kids}

Australia = 5/7ths

15 = [tex]\frac{5}{7}x[/tex]   {multiply both sides by 7 to get rid of fraction}

105 = 5x   {divide both sides to find 1x}

21 = x

check:

2/7th of 21 = 6

5/7th of 21 = 15  {which we know}

6 + 15 = 21

21 = 21

(TRUE)

So, Eva has 21 grandchildren

hope this helps!!

When faced with an unknown variable in a maths problem, it is advised to find the subject formula and then use it to solve the equation to find the answer.

This refers to the type of variable in a given equation that has to be solved for because its properties or value is not known.

Hence, we can see that when faced with an unknown variable in a given math problem, it is better to find the subject formula, then input the value of this into an equation, to find the value of the variable.

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Answer:

Sum of all the angles of a triangle = 180° ( angle sum property).

Angle D + Angle E + Angle F = 180°

8x - 1 + 5x + 90° = 180°

8x + 5x + 89 = 180

13x = 180 - 89

13x = 91

x = 7.

Angle D = 8x - 1

= 8(7)-1

= 56 - 1

= 55

Angle E = 90° ( given)

Angle F = 5x

= 5 * 7

= 35

Answer:

m∠E: 90°

m∠D: 55°

m∠F: 35°

Step-by-step explanation:

Since the interior angles of a right triangle sum up to 180°, the sum of angles D, E, F will equal 180°. We can then form an equation from that information.

[tex]90+(8x-1)+5x=180\\13x-1=90\\13x=91\\x=7[/tex]

From this, we can plug in the variable.

[tex]mE=90\\mD=55\\mF=35[/tex]

a) 2/8 = 1/4

b) There are 3 females who can speak French and 2 males who can speak French, so the probability is 3/5

Answer:

133 sodas

87 hot dogs

I've completed the work in the photo, just trying to reach the letter count lol

Answer:

All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are  ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex] by using rational zeroes theorem.

Step-by-step explanation:

Rational zeroes theorem gives the possible roots of polynomial f(x) by taking ratio of p and q where p is a factor of constant term and q is a factor of the leading coefficient.

The polynomial f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex]

Find all factors (p) of the constant term.

Here we are looking for the factors of 4, which are:

±1 , ±2 and ±4

Now find all factors (q) of the coefficient of the leading term

we are looking for the factors of 3, which are:

±1 and ±3

List all possible combinations of ± [tex]\frac{p}{q}[/tex]  as the possible zeros of the polynomial.

Thus, we have ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex] as the possible zeros of the polynomial

Simplify the list to remove and repeated elements.

All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are  ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex]

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It is wider and shifted 3 units to the left , Option A is the right answer.

Function is a mathematical statement that shows relation between two variables.

The parent function given is

f(x) = |x|

The transformed function is given by

f(x) = 0.1|x -3|

The function is shifted towards the left

and as the scale factor is 0.1 therefore , It is wider

Therefore Option A is the right answer.

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Answer:

The answer for this is B.

Step-by-step explanation:

Figured it out the hard way on EDGE. 2022

(╯‵□′)╯︵┻━┻

Answer: [A] addition property of equality

Step-by-step explanation:

    Mitch used the addition property of equality because he added 43 to both sides of the equation.

         75r - 43 = 332

         43 + (75r - 43) = (332) + 43

         75r = 375

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Answer:

1/7

Step-by-step explanation:

Alternative Form: 0.142857, 7^-1

Answer:

Step-by-step explanation:

Givens

r = 14 miles / hour

Problem

Convert to feet per second.

Solution

Later on, you will learn how to solve these kinds of conversion problems using a method called Unit Analysis. Since you likely have not been taught this method, will just use proportions.

1 mile = 5280 feet

14 miles = x                          Cross multiply

x = 14 * 5280                       Simplify

x = 73920 feet

1 hour = 3600 seconds

Answer

r = 73920 feet / 3600 seconds

r = 20.533 feet  / secpmd

D

Step-by-step explanation:

The points dx are at -1, 1, 2 and 3 so it must be D

Answer:

To find the range,

first see the value of each points -

first = (3,5)

second = (2,0)

third = ( 1,3)

fourth, ( -1, 2)

let's take X Axix to find the range

so the range is ( -1, 1 , 2 ,3)

Option D is correct

The fraction of the total number of marbles is left in the bag after removing and giving part to her friend is 3/8

let

Remaining marbles = x - 1/2x

= (2x-x) / 2

= x/2

= 1/2x

Number of marbles given to her friend = 1/4 of 1/2x

= 1/4 × 1/2x

= 1/8x

Number of marbles left in the bag = Remaining marbles - Number of marbles given to her friend

= 1/2x - 1/8x

= (4x-x) / 8

= 3x/8

= 3/8x

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Answer:

sorry

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{1}{r^4^2}[/tex]  (option B)

Step-by-step explanation:

[tex]\left(a^b\right)^c=a^{bc},[/tex]

So, we need to first multiple -7 × 6 (= -42)

our new value is [tex]r^{-42\\}[/tex]

[tex]\:a^{-b}=\frac{1}{a^b}[/tex]

So, we simplify [tex]r^{-42\\}[/tex] to [tex]\frac{1}{r^4^2}[/tex]

Using the sine and cosine ratios, the true statement is: D. sin(J) = cos(L).

Sine ratio: sin ∅ = opp/hyp.

Cosine ratio: cos ∅ = adj/hyp.

In the image given, find sin(J) using the sine ratio:

∅ = J

Opposite = KL = √(219² - 178²) = 127.6 [Pythagorean theorem]

Hypotenuse = LJ = 219

Sin(J) = 127.6/219

Find cos(L) using the cosine ratio:

∅ = L

Adj = KL = 127.6

Hypotenuse = LJ = 219

Cos(L) = 127.6/219

Therefore, the true statement is: D. sin(J) = cos(L).

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Yes, by using the factor theorem and synthetic division method, x + 3 is a factor of -x³ + 4x - 15.

According to the factor theorem, a given polynomial of f(x) has a factor if and only if f=0.

From the given information:

Using the synthetic division method:

[tex]\mathbf{= \dfrac{-x^3+4x - 5}{x+3} }[/tex]

[tex]\mathbf{\implies \dfrac{-(x+3) (x^2-3x + 5)}{x+3} }[/tex]

Cancel out the common factors, we have:

[tex]\mathbf{\implies - (x^2-3x + 5)}[/tex]

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Answer:

(3, 0) and (−1, −8)

Equation's:

2x − (x² − 9) = 6

2x - x²  + 9 = 6

-x² + 2x + 9 - 6 = 0

-x² + 2x + 3 = 0

x² - 2x - 3 = 0

x² - 3x + x - 3 = 0

x(x - 3) + 1(x - 3) = 0

(x + 1)(x - 3) = 0

x = -1, x = 3

If x = -1, then y = (-1)² - 9 = -8

If x = 3, then y = (3)² - 9 = 0

(x, y) = (-1, -8), (3, 0)

The 2 colors can be chosen in 6 different ways.

Here we need to identify the selections and the numbers of options for each.

Here the selections are:

And the numbers of options for each are:

The total number of combinations is:

C = 3*2 = 6

The 2 colors can be chosen in 6 different ways.

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Answer:

x = [tex]\frac{172-2y}{6}[/tex]

Step-by-step explanation:

6x + 2y + 8 = 180 ( subtract 8 from both sides )

6x + 2y = 172 ( subtract 2y from both sides )

6x = 172 - 2y ( divide both sides by 6 )

x = [tex]\frac{172-2y}{6}[/tex]

Answer:

[tex] \frac{1}{4} (3a + 2b)[/tex]

The expression from the given condition is 1/4(3a+4b).

We have given that,

The product of a quarter of 3 more than a number a and 2 times a number b.

The quarter means divided into four equal or corresponding parts.

Therefore we get the expression from the given condition is

1/4(3a+4b).

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Answer:

x is approximately 20.89

Step-by-step explanation:

cos(40°) = 16/x

x cos(40°) = 16

x = 16 / cos(40°) = 16/.766 = 20.89

The approximate value of x in the diagram is,

⇒ x = 20.77

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, We can formulate by the given figure;

⇒ sin 50° = 16 / x

⇒ 0.77 = 16 / x

⇒ x = 16 / 0.77

⇒ x = 20.77

Thus, The approximate value of x in the diagram is,

⇒ x = 20.77

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Solution: Below! ^^

Detailed explanation:

Hii! I'm sorry, I can't graph the line for you, but I'll try to give you the best possible explanation.

First, note that the question provides us with the info that the y intercept is -8. This is a very valuable piece of information!

This means that the line crosses the y axis (since it's the y intercept) at the point (0,-8). Plot it on the co-ordinate plane.

Next, this question also provides us with the fact that the slope of the line is 1/4. This is yet another valuable piece of information!

What this tells us is: from that point (0,-8), you need to go up 1 unit, then over 4, and so forth, until you obtain a line.

_________

Hope I helped, best wishes & happy studies!

Please reach out to me if any queries arise.

_________

Answer:

Image attached below

Step-by-step explanation:

The line should cross y axis as -8 and should have a point of (0,-8)

The line should have a gradient / slope of 1/4