Is each statement true for parallelogram DEFG? Drag each statement into the correct box.
DF=EG
EF=DG
∠DEG ≅ ∠FGE

Answer:

(X+6)(x-8)

Step-by-step explanation:

Answer:

(x-8)(x+6)

Step-by-step explanation:

Factor the trinomial using the AC method.

x * x = x^2

-8 + 6 = -2

-8 * 6 = -48

Answer:

42

Step-by-step explanation:

(adjacent straight angles sum up to 180)

3x+54=180

x=42

Answer:

The value of this investment at the end of the 5 years is of $662.5.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Dina invests $600 for 5 years at a rate of 2% per year compound interest.

This means that [tex]P = 600, t = 5, r = 0.02, n = 1[/tex]. Thus

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(t) = 600(1 + \frac{0.02}{1})^{t}[/tex]

[tex]A(t) = 600(1.02)^t[/tex]

Calculate the value of this investment at the end of the 5 years.

This is A(5). So

[tex]A(5) = 600(1.02)^5 = 662.5[/tex]

The value of this investment at the end of the 5 years is of $662.5.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graphing calculator does a nice job of graphing these equations.

__

The very steep slope suggests the graph will need somewhat different vertical and horizontal scales in order to show anything useful.

Answer:

1.333333333333

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

d part it is. this is the answer

9514 1404 393

Answer:

Step-by-step explanation:

Descarte's rule of signs tells you there is 1 positive real root. The rational root theorem tells you any real roots are factors of ±14, so will be ±1, ±2, ±7, or ±14.

We note that the sum of all coefficients is negative, so +1 is not a root.

We note that the sum of coefficients of odd-degree terms is 1-19 = -18, and the sum of coefficients of even-dgree terms is -4-14 = -18. These are the same value, indicating that -1 is a root. The corresponding factor is (x +1).

The result of dividing the factor (x+1) from the polynomial using synthetic division is shown in the first attachment. The coefficients found mean the quotient is ...

  Q(x) = x^2 -5x -14

Factoring this using any method you like gives ...

  Q(x) = (x +2)(x -7)

This means the full set of zeros is {-2, -1, +7} and the factorization is ...

  P(x) = (x +2)(x +1)(x -7)

_____

Additional comment

My personal favorite method of finding the zeros is to let a graphing calculator show them to me. That result is shown in the second attachment.

Answer:

A study that compares two groups of people: those with the disease or condition under study (cases) and a very similar group of people who do not have the disease or condition (controls). Researchers study the medical and lifestyle histories of the people in each group to learn what factors may be associated with the disease or condition. For example, one group may have been exposed to a particular substance that the other was not. Also called retrospective study.

Step-by-step explanation:

Answer:

A case-control study is designed to help determine if an exposure is associated with an outcome (i.e., disease or condition of interest).

Step-by-step explanation:

Answer:

quadratic formula is ur answer for letter B

Answer: [tex]6x^3 +30x^2 +4x+20[/tex]

Step-by-step explanation:

[tex](6x^2 +4)(x+5)\\\\ =6x^3 +30x^2 +4x+20[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

a) Let p and d represent the prices of a bag of popcorn and a drink, respectively.

Mohamed's purchase is ...

  2p +3d = 18.25

Miguel's purchase is ...

  4p +2d = 27.50

__

b) We can subtract half the second equation from the first to get an equation for the cost of a drink.

  (2p +3d) -1/2(4p +2d) = (18.25) -1/2(27.50)

  2d = 4.50 . . . . . . simplify

  d = 2.25 . . . . . . divide by 2

  4p +2(2.25) = 27.50 . . . . substitute for d in the second equation

  4p = 23.00 . . . . . . . . . subtract 4.50

  p = 5.75 . . . . . . . . . divide by 4

The cost of a bag of popcorn is $5.75; the cost of a drink is $2.25.

Answer:

v = 15 mph

Step-by-step explanation:

Given that,

A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.

Total distance, d = 3 + 7 = 10 miles

Total time, t = 15 + 25 = 40 minutes = 0.6667 hours

Average speed,

[tex]v=\dfrac{d}{t}[/tex]

Put all the value,

[tex]v=\dfrac{10}{0.6667}\\\\= $$14.99\ mph[/tex]

or

v = 15 mph

So, the required average speed is equal to 15 mph.

Answer:

9.05 horse power

Step-by-step explanation:

Given:

Force = 270 Newton

Speed = 25 m/s

Power = Force * velocity

Power = 270 Newton * 25 m/s

Power = 6750 watt

Recall:

1 horse power = 746 watts

Hence, required horsepower is :

6750 watt / 746 watt

9.048 hp

9.05 horse power

Answer:

[tex]\$32[/tex]

Step-by-step explanation:

Let the cost of the game be [tex]x[/tex]. Since one-fourth of the cost of the game is equal to 8 dollars, we have the following equation:

[tex]\frac{1}{4}x=8[/tex]

Multiply both sides by 4 to isolate and solve for [tex]x[/tex]:

[tex]x=8\cdot 4=\boxed{\$32}[/tex]

Answer:

7 square root 9^4

Step-by-step explanation:

Answer:

The probability mass function is:

[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]

Step-by-step explanation:

The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability mass of the hypergeometric probability distribution is given by:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this question:

22 + 25 = 47 jurors, so [tex]N = 47[/tex]

22 are women, which means that [tex]k = 22[/tex]

Jury of 12, which means that [tex]n = 12[/tex].

Thus

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]

Which is the probability mass function.

Answer:

a. 0.302 dB/s

b. 2.34 dB/s

c. 1.24 dB/s

Step-by-step explanation:

a) Find the rate of change of the sound pressure P with respect to time if W=7.2 and dW/dt = 0.5 at some given time t.

Since P = 10log(W/W₀), its rate of change with respect to time is

dP/dt = dP/dW × dW/dt

dP/dW = d[10logW - 10logW₀]/dt

dP/dW = d[10lnW/2.303 - 10logW₀]/dt

= 10/2.303W - 0

= 10/(2.303W)

dP/dt = dP/dW × dW/dt

dP/dt = 10/(2.303W) × dW/dt

Since dW/dt = 0.5 when W = 7.2, then

dP/dt = 10/(2.303 × 7.2) × 0.5

dP/dt = 10/16.5816 × 0.5

dP/dt = 0.603 × 0.5

dP/dt = 0.302 dB/s

b) If the variable sound power W is given by W = t² + t + 1, find the rate of change of the sound pressure P, at time t = 3s.

Since P = 10log(W/W₀), its rate of change with respect to time is

dP/dt = dP/dW × dW/dt

dP/dW = d[10logW - 10logW₀]/dt

dP/dW = d[10lnW/2.303 - 10logW₀]/dt

= 10/2.303W - 0

= 10/(2.303W)

and dW/dt = d(t² + t + 1)/dt = 2t + 1

So, dP/dt = dP/dW × dW/dt

dP/dt = 10/(2.303W) × (2t + 1)

dP/dt = 10(2t + 1)/(2.303W)

dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]

we then substitute t = 3 into the equation

dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]

dP/dt = 10(2(3) + 1)/[2.303((3)² + 3 + 1)]

dP/dt = 10(6 + 1)/[2.303(9 + 3 + 1)]

dP/dt = 10(7)/[2.303(13)]

dP/dt = 70/29.939

dP/dt = 2.34 dB/s

c) If W = cos 0.2t, find the rate of change of the sound pressure P, at time t = 15 (calculators in radians)

Since dP/dt = dP/dW × dW/dt and dP/dW = 10/(2.303W) and W = cos(0.2t), dW/dt = -0.2sin(0.2t)

So, dP/dt = dP/dW × dW/dt

dP/dt = 10/(2.303W) × -0.2sin(0.2t)

dP/dt = -20sin(0.2t)/(2.303W)

dP/dt = -20sin(0.2t)/(2.303cos(0.2t))

dP/dt = -20tan(0.2t)/2.303

when t = 15, we have

dP/dt = -20tan(0.2 × 15)/2.303

dP/dt = -20tan3/2.303

dP/dt = -20 × -0.1425/2.303

dP/dt = 2.8509/2.303

dP/dt = 1.238

dP/dt ≅ 1.24 dB/s

Second-degree price discrimination occurs when a company charges a different price for different quantities consumed, such as quantity discounts on bulk purchases.

mark me brainliestt :))

Answer: a+b+c=0 and 3a+5b+c=0

Step-by-step explanation:

If you find a solution to these equations, you will find an equation of your line. Please notice that (a,b,c) defines the same line as (ka,kb,kc) and for any non-zero k, and a=b=c=0 defines no line equation at all. Now you can take a=1 and solve for b and c, or take b=1 and solve for a and c, or take c=1 and solve for a and b, at least one of these will work.

Work Shown:

cos(angle) = adjacent/hypotenuse

cos(64) = x/28

x/28 = cos(64)

x = 28*cos(64)

x = 12.2743921100941

x = 12.27

Check the picture below.

so if we simply subtract the strip area with the pond and the area of the pond only, what's leftover is the area of the strip alone, so

[tex]\stackrel{\textit{area of the grass \underline{with} pond}}{(15+2x)(18+2x)}-\stackrel{\textit{area of the pond}}{(15)(18)}=\stackrel{\textit{their difference}}{232} \\\\\\ 270+30x+16x+4x^2-270=232\implies 46x+4x^2=232 \\\\\\ 23x+2x^2=116\implies 2x^2+23x-116=0[/tex]

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+23}x\stackrel{\stackrel{c}{\downarrow }}{-116}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-23\pm \sqrt{23^2-4(2)(-116)}}{2(2)}\implies x = \cfrac{-23\pm \sqrt{1457}}{4}[/tex]

now, the negative root will simply yield a negative value, which is not applicable here, so we'll only use the positive root, since it's the only feasible one for the phenomena

[tex]x = \cfrac{-23+ \sqrt{1457}}{4}\implies x \approx 3.792667341996157\implies \stackrel{\textit{rounded up}}{x = 3.8}[/tex]

Answer:

3 feet

Step-by-step explanation:

Let x be the width of the grass strip.

So the length of the grass strip=18+2x

Area of the grass strip =2(18+2x)(x)+2(15)(x)=2(18x+2x^2)+2(15x)=(36x+4x^2)+30x=4x^2+66x^2

But the available grass seed is enough for 234 ft squared

4x^2+66x=234

4x^2+66x-234=0

x={-66+-[(66)^2–4(4)(-234)]^1/2}/2(4)

x={-66+-[4356+3744]^1/2}/8={-66+-[8100]^1/2}/8

x={-66+-(90)}/8

Two values of x: x=(-66+90)/8=24/8=3 and the other value of x=(-66–90)/8=-19.5. Adopt the positive value of x=3 feet (answer)

So the width of the strip is 3 feet.

Check for the area of grass strip around the fish pond : Area=2(18+6)(3)+2(15)(3)=2(24)(3)+90=144+90=234 square feet

Other area check =4x^2+66x=4(3)^2+66(3)=36+198=234 square feet

Therefore the strip is 3 feet wide

Answer:

10π in.

Step-by-step explanation:

circumference of a circle = 2πr

=2*π*5

=10π in.

Answer:

x+4=72

x=72-4

x=68

Step-by-step explanation:

let x be one number and 4 be anothe number then sum of the two number be x and 4

Answer:

Option B, The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times

Step-by-step explanation:

The distribution of apple candies can be represented as normal curve and hence the sample proportion for this is true and can be drawn.

The rest other cases do not represent a normal distribution and hence it will not be easy to plot curve for these samples.

hence, option B is correct

Answer:

46

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Answer:

Table A

Step-by-step explanation:

y  = 3x^2 +2x -8

The quadratic is in the form

y = a x^2 +bx+c

a = 3  b = 2 c = -8

Since a > 0 it opens up

The y intercept is c so the y intercept is -8

Answer:

7 boxes

Step-by-step explanation:

We can use ratios to solve

12 bars            42 bars

----------    = ---------------

2 boxes      x boxes

Using cross products

12x = 2 *42

12x = 84

Divide by 12

12x/12 = 84/12

x = 7

Step-by-step explanation:

everything can be found in the picture

Answer:

For example, 6(1001) + 3(110) = 6006 + 330 = 6336 is a palindrome. Since 11 is a factor of both 1001 and 110, we conclude that all four digit palindromes are divisible by 11.