Given: `Delta`ABC
Prove: The sum of the interior angle measures of `Delta`ABC is 180°.
What is the missing step in this proof?

Call that number x.

Then rewrite as equation:

4x+6=7x

solve for x

6=3x

2=x

So the number is 2.

Check that 2 is the number by following the original wording, mentally.

Hey there!!

Let's take the number as 'x'

4 times the number is 4x

This is increased by 6

We will have to add 6.

... 4x + 6

7 times a number is 7x

... 7x

Both these values are equal.

Hence,

... 4x + 6 = 7x

... 6 = 3x

... x = 2

Hence, the number is 2.

The binomial coefficient

[tex] \displaystyle \binom{4}{2} = \dfrac{4!}{2!(4-2)!} = \dfrac{4\cdot 3}{2} = 2\cdot 3 = 6 [/tex]

Tells you that there are 6 ways of choosing a subset of two letters from the four given letters.

For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)

So, there is a total of 12 combinations of the letters w, x, y, z, taking two at a time.

There are 6 ways of choosing a subset of two letters from the four given letters.

The arrangement of the different things or numbers in a number of ways is called the combination.

For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)

So, there is a total of 6 combinations of the letters w, x, y, z, taking two at a time.

The combination will be calculated as:-

[tex]^4C_2=\dfrac{4!}{2!(4-2)!}[/tex]

[tex]^4C_2=\dfrac{4\times 3}{2}[/tex]

[tex]^4C_2=6[/tex]

Therefore there are 6 ways of choosing a subset of two letters from the four given letters.

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Answer:

The minimum value of C is -9

Step-by-step explanation:

we have

[tex]C=-2x+y[/tex]

[tex]x\geq -5[/tex]

[tex]x\leq 4[/tex]

[tex]y\geq -1[/tex]

[tex]y\leq 3[/tex]

using a graphing tool

The solution is the shaded rectangle

see the attached figure

The vertices of the rectangle are the points

[tex](-5,3),(4,3),(4,-1),(-5,-1)[/tex]

To find the the minimum value of C, substitute the value of x and the value of y of each vertex and calculate the value of C, then compare the results

For [tex](-5,3)[/tex]

[tex]C=-2(-5)+3=13[/tex]

For [tex](4,3)[/tex]

[tex]C=-2(4)+3=-5[/tex]

For [tex](4,-1)[/tex]

[tex]C=-2(4)-1=-9[/tex]

For [tex](-5,-1)[/tex]

[tex]C=-2(-5)-1=9[/tex]

therefore

The minimum value of C is -9

To calculate the median: you want to organize all the numbers in it's data so it should look like this:  2, 5, 5, 8, 10, 12, 18, 20.

Now that it is organized look for the middle number so 9 is our median. I got this by adding 8 + 10 which equals 18 then dividing it by 2. So anytime you have 2 middle numbers add them then divide it by 2 it will always be your median.

To determine the mode: look for the number the occurs the most. I only see two 5's so the answer is 5 for our mode.

To determine the mean: Add all the numbers together then divide it by how many numbers there are so there are 8 numbers divide it by 8 after we add them.

2+5+5+8+10+12+18+20= 80 divide it by 8 and it equals 10. So 10 is the mean.

Answer:

Intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

Step-by-step explanation:

Required vector is consists of the two components

vx= 2+4=6 units  and vy= 1 unit and vx ⊥ vy

We will use Pythagorian theorem to find intensity of the vector v

v∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 units

The angle ∡α between vector and east direction we wil find with tanα

tanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

Good luck!!!

Answer:

The vector that describes their hike from their starting position to their final destination is  < 6, 1 >

The answer would be the bottom left. You can't fold it in half and have it match up with the other side.

Answer: .0000356

Step-by-step explanation:

3.56 x 10⁻⁵

the exponent of 5 tells you to move the decimal 5 places

the negative sign tells you to move the decimal to the left.

Equation Given: 3.56 x 10^-5  

Simple Explanatio: Lets start with this 10^-5 since the exponents is a negative you must subtract the exponent from the base and after you do so this is what your left with -5 and now since we have done the work lets rewrite the answer as 3.56 x 10^-5 the equation may not be changed but that's how i was told to do it and now solve. The decimal in 3.56 will be moved to the left five times because this equation has an negative exponent not a positive so you should end up with the simple answer of 0.0000356

Hopefully this helps  ^0^

Remember to isolate the variable. Subtract 9 from both sides

10 (-9) ≥ 9 (-9) + v

10 - 9 ≥ v

Simplify. Combine like terms

1 ≥ v

1 ≥ v is your answer

hope this helps

Answer:

D

Step-by-step explanation:

hello!!! the correct answer for this problem is D

Answer:

D. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5

and translated up 5 units.

Step-by-step explanation:

Answer:

5.23 years, the time at which the coin has increased in value to $150.

Step-by-step explanation:

Use the exponential function f(t) = 4*2^t.

Substitute $150 for f(t):  $150 = 4*2^t.

Simplify this by dividing both sides by 4:  $150/4 = 2^t, or $37.50 = 2^t.

Next, solve for the value of t.  To do this, take the common log of both sides, obtaining:

log 37.50 = t*log 2.  Thus, t = [log 37.50] / [log 2].  Evaluate this using a calculator:

t = 1.57403 / 0.30103 = 5.23 time units.  For example, this could be 5.23 years.

Answer:

It will take about 17.7 years, or almost 18 years, for the coin to be worth $150.

Because the initial year was 2016, the coin is predicted to be worth $150 in 2034.

Step-by-step explanation:

Answer:

for anyone in the future that needs this the answer is The rule (x,y) ----> (x+2, y-4) represents a translation 2 units RIGHT and 4 units DOWN

Step-by-step explanation:

A translation is a transformation that moves every point in a figure in the same direction by the same amount. The rule (x, y)→(x+2, y−4) represents a translation of 2 units right and 4 units downwards

A translation is a transformation that moves every point in a figure in the same direction by the same amount. It is also a sort of transformation in which each point in a figure is moved the same distance in the same direction resulting in the same figure again.

For any graph, if the value of x is increased it moves in the right direction while it moves in the left direction if the value is decreased.

Similarly, For any graph, if the value of y is increased it moves upwards while it moves in downwards if the value is decreased.

Now, as per the given rule of transformation, (x, y)→(x+2, y−4), the graph will translate 2 units right and 4 units downwards.

Hence, The rule (x, y)→(x+2, y−4) represents a translation 2 units right and 4 units downwards.

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The complete statement is:

There were 59 bacteria after 5 hours

The initial population of the bacteria is given as:

[tex]a =100[/tex]

The proportion left after each hour is given as:

[tex]b = 90\%[/tex]

An exponential function is represented as:

[tex]f(x) = ab^x[/tex]

Substitute values for (a) and (b)

[tex]f(x) = 100 \times (90\%)^x[/tex]

Express percentage as decimal

[tex]f(x) = 100 \times (0.9)^x[/tex]

After 5 hours, the value of x is 5

i.e. x = 5

So, we have:

[tex]f(x) = 100 \times (0.9)^5[/tex]

Evaluate the exponent

[tex]f(x) = 100 \times 0.59049[/tex]

Multiply

[tex]f(x) = 59.049[/tex]

Approximate

[tex]f(x) = 59[/tex]

Hence, there were 59 bacteria after 5 hours

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Answer:

x = 5/2

Step-by-step explanation:

Isolate x by adding 2x to both sides, obtaining:  5 - 2x + 2x = 2x.  Then 5 = 2x, and dividing both sides by 2 results in x = 5/2.

Substitute x = 2 into each of the expressions

left: 6* 8  - 2(2) = 48 - 4 = 44

right: 6(5 +2) = 6(7) = 42

44 > 42

Answer

>

1. Culture A.

Since the number of cells increases by 200 each day and every day thereafter, then after seven days the number of cells will increase by

[tex]200\cdot 7=1,400.[/tex]

2. Culture B.

The initial number of cells was 1,000. Since the number of cells increases 8% each day and every day thereafter, then after seven days the number of cells will be

[tex]1,000\cdot (1.08)^7\approx 1,713.[/tex]

The number of cells that have grown by the end of the seventh day is

1,713-1,000=713.

Answer: option A -- Culture A: 1400 cells Culture B: 713 cells

Answer:

A is correct: Culture A: 1400 cells

                    Culture B: 713 cells

Step-by-step explanation:

Correct on Edge 2020 Quiz

When dealing with a quadratic equation, you usually assign the following name to the coefficients of the variables:

[tex] ax^2+bx+c=0 [/tex]

So, [tex] a [/tex] is the coefficient of [tex] x^2 [/tex], [tex] b [/tex] is the coefficient of [tex] x [/tex] and [tex] c [/tex] is the constant term.

In your case, the coefficient of [tex] x^2 [/tex] is -3, so [tex] a=-3 [/tex]

The coefficient of [tex] x [/tex] is -2, so [tex] b = -2 [/tex]

The constant term is 6, so [tex] c = 6 [/tex]

Answer,

Explanation,

All you need to do is simplify,

15 - (-3) -4 = ?

15 - (-3) = 18

18 - 4 = 14

Hope this helps :-)

Answer:its correct got a 100

Step-by-step explanation:

The given figure is a rectangle.

Given angles are- m∠BDC = 47°, m∠CAB = 52°, and m∠BEC = 99°

The sum of the angles m∠BDC = 47°, m∠CAB = 52° is the measure of  m∠BEC  which is 99°

This is sufficient to prove. Measure of angle A and D are 90 degrees each as they are right angles triangles. So, inner angle A is 90-52 = 38 degrees. Inner angle D will be    90-47  =43 degrees.

Measure of triangle AED = 180 degrees

Let inner E = x

then, 38+43+x=180

x=99 degrees

Outer E and inner are vertical angles and so, they are same.

Moreover, triangles AED and BEC are same so E is 99 degrees

Simplify: 12 + 10i +14i = 12 +24i

answer

B) 12 +24i

24i+12 thats pretty basic though

"An on-line electronics store must sell at least $5000 worth of computers and printers per day"

The bold faced words tell us greater than or equal to 5000

"The store can ship a maximum of 20 items per day"

The bold faced words tell us less than or equal to 20

We can automatically eliminate A and B since they don't have EQUAL sign in them. From C and D, we choose D because it correctly attaches the price of printers and computers to the respective variables (printers is p & computers is q). Choice C does this wrong!

ANSWER: D

[tex]x-intercept(\frac{26}{3},0)

y -intercept (0,\frac{13}{2} )[/tex]

y is a lil messed up in term of looks but meh

have a good day breh

Domain=all real numbers

Range is x≤4

Hope this helps :)

Answer:

The value of f(2)≈1.57

The time it takes an object to fall 2 feet is 1.57 seconds.

Step-by-step explanation:

Consider the provided function.

[tex]f(d) = 1.11\sqrt{d}[/tex]

It takes for an object to fall a distance, d, in feet,

We need to determine f(2).

Substitute the value d = 2 in the above function.

[tex]f(2) = 1.11\sqrt{2}[/tex]

[tex]f(2)\approx 1.57[/tex]

The value of f(2)≈1.57

The time it takes an object to fall 2 feet is 1.57 seconds.

We know that

when we start exercise our hear beats starts increasing gradually

because blood flowing rate becomes higher

and it keeps increasing upto a certain limit

because for normal human beings maximum heart rate is 135 beats per minute

and it remains constant there for few minutes

and as we slow down slowly

It will start decreasing  gradually and then becomes normal

we can see the graph

so,

The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes..........Answer

Answer:The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes. Positive

Step-by-step explanation:

Answer:

12.68%

Step-by-step explanation:

To calculate effective annual interest rate we need to use the following formula:

[tex]i=(1+\frac{r}{m})^m-1[/tex]

Where, 'i' is the effective annual interest rate

'r' is the annual rate of interest

'm' is the frequency of compounding.

When there is continuous compounding the effective annual rate uses the following formula:

[tex]i=e^r-1[/tex]

In our case we would are assume that there is continuous compounding since no information regarding the frequency of compounding is given:  

Plugging r=12%=0.12, we get:

[tex]i=e^{0.12}-1[/tex]

[tex]i=1.1274-1=0.1274[/tex]

[tex]i=0.1274[/tex]

[tex]i=12.74\%[/tex]

Therefore, the effective annual interest rate is 12.74%.

Answer:

13.2

Step-by-step explanation:

direct linear variation is a straight line in which the y intercept is 0

a- wrong because it is quadratic, not linear.

b- correct, linear with a y intercept of 0

c- wrong because its exponential

d- wrong, its linear but the y intercept is 3, not 0