Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?

The solutions of the inequality are given by:

x > -3

Here we have the following inequality:

-(4x - 5) + 16x > -31

To solve this, we need to isolate the variable x in one of the sides of the inequality, so let's do that.

-(4x - 5) + 16x > -31

-4x + 5 + 16x > -31

(-4 + 16)*x + 5 > -31

12x + 5 > -31

12x > -31 - 5

12x> -36

x > -36/12

x > -3

So all the values of x that are larger than -3 are solutions of the inequality.

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The distance between point (12,6) and the line y = x - 14 is given as follows:

5.6 feet.

The standard equation of a line is given by the rule presented as follows:

ax + by + c = 0.

The coordinates of the point which we want to find the distance from the line are given as follows:

(x0,y0).

The equation that obtains the shortest distance of the point (x0, y0) to the line ax + by + c = 0 is presented as follows:

[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]

The line for this problem is given by the rule presented as follows:

y = x - 14.

In standard notation, it is defined by the rule presented as follows:

x - y - 14 = 0.

Hence the coefficients are presented as follows:

a = 1, b = -1, c = -14.

The point has the coordinates given as follows:

(12,6).

Hence:

x0 = 12, y0 = 6.

Thus the distance from the point to the line is obtained as follows:

[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]

D = |1(12) -1(6) - 14|/sqrt(1²+(-1)).

D = 8/sqrt(2)

D = 5.6 feet.

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The rate of the boat in still water is 45.5 km/hr and  the rate of the current is 100.5 km/hr.

A motorboat travels 74 km in 2 hours going upstream.

Rate = Distance/time

Rate = 74 /2

Rate = 36 km/hr

It travels 110 km going downstream

Rate = Distance/time = 110/2

Rate  = 55 km/hr

Equations:

Upstream: b-c = 36 km/hr

Downstrm: b+c = 55 km/hr

Add and solve for b

2b = 36 km/hr + 55 km/hr

2b = 91 km/hr

Divide both side by 2b

b = 91 km/hr /2

b = 45.5 km/hr (speed of the boat)

Solve for c

b+c = 55

45.5+ c = 55

c = 55 + 45.5

c = 100.5 km/hr (speed of the current)

Therefore  45.5 km/hr  and  100.5 km/hr are the speed.

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Answer: 2%

Step-by-step explanation:

First, we know that the experimental value is 13.3, and the true value 13.6. After plugging in, we get |13.3 - 13.6| = -0.3 which is just 0.3 as it is the absolute value. Then, we divide it by 13.6 which brings us the equation 0.3/1.36 which rounds to 0.022. Continuing, we multiply it by 100 which gets our answer of 2.2. The nearest percent is 2, so our answer is 2 percent.

Answer:

Step-by-step explanation:

Take the square root of both sides

[tex]\sqrt{x^2}[/tex]=[tex]\sqrt{25}[/tex]

x=±5

The relation among unit rate, slope and constant rate of change of a proportional linear relationship is y = kx.

What is unit rate?

The rate of change is the ratio between the x and y (or input and output) values in a relationship. Another term for the rate of change for proportional relationships is the constant of proportionality. If the rate of change is yx, then so is the constant of proportionality.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.

The slope is defined as y = mx +b

b =1, m=k

y =k x.

Here, k is constant rate of change.

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Jon's semi-final jump compared with Anthony's was 3 inches lower. This was based on the heights given.

Given that Jon jumped 1 inches below the qualifying height, but his friend Anthony

made it to 2 inches above the qualifying height.

In this case, the difference in the jump will be gotten by subtracting the values. This will be illustrated as:

= Anthony's jump - Jon's jump

= 2 - (-1)

= 2 + 1

= 3

Therefore, Jon was 3 inches lower.

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The  amount of money that she yas to pay at the end of 3 yesrs to clear her debt  is:  $16,140.

First step is to find the interest

Interest = ( Principal × Interest rate × time)

Interest = $12,000 × 11.5% × 3

Interest = $4,140

Now let find the amount she use to clear the debt

Amount = Principal + Interest

Amount = $12,000 + $4,140

Amount = $16,140

Therefore she will use $16,140 to clear the debt.

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Answer: It could be (3, -3) (3,3) or (-3,-3)

Step-by-step explanation:

they are all 3 away.

Answer:

0.075%

Step-by-step explanation:

Answer:

1.57500 US$

Step-by-step explanation:

You equation looked like this:

$1.50; + 5% so guugle thought something else it should be:

$1.50 + 5% without the " ; "

The ammount of 5% = 0.075

Since your adding the 5% or 0.075 it would be =

1.50 + 0.075 = 1.57500

y'all get it now?

B.

The age of a person's systolic pressure is 130 mm Hg is 45.98 years.

P = 0.004[tex]y^{2}[/tex] - 0.01y + 122

substitute p = 130 mm

130 = 4/1000 [tex]y^{2}[/tex] - 1/100 y + 122

8 = 4[tex]y^{2}[/tex] - 10y / 1000

8000 = 4[tex]y^{2}[/tex] - 10 y

[tex]2y^{2} -5y -4000=0[/tex]

y = 45.98 years

Therefore the age of a person's systolic pressure is 130 mm Hg is 45.98 years.

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Answer:

The three numbers are -4, 0, and 1.

The sum of three numbers is -3: -4 + 0 + 1 = -3

If the second number is subtracted from the sum of the first and third numbers, the result is -3: (-4 + 1) - 0 = -3

If the third number is subtracted from the sum of the first and second numbers, the result is -5: (-4 + 0) - 1 = -5

Step-by-step explanation:

x --> first number

y --> second number

z --> third number

x + y + z = -3

(x + z) - y = -3

(x + y) - z = -5

x = -3 - y - z

(-3 - y - z + z) - y = -3

-3 - y - y = -3

-2y = 0

y = 0

(-3 - y - z + y) - z = -5

-3 - z - z = -5

-3 - 2z = -5

-2z = -2

z = 1

x = -3 - 0 - 1

x = -4

Answer:

1st = 2 sin (x)

2nd = cos^2 (x)

3rd = sin^2 (x)

Answer:

36

48

60

Reason:

Since it is multiples of twelve, we can find out and multiply

12*3= 36

12*4= 48

12*5= 60

I hope this helps!

Answer: 36, 48, and 60.

Step-by-step explanation:

36, 48, and 60 are the only numbers that can be divided by 12 into a whole number.

36/12 = 3

48/12 = 4

60/12 = 5

As per the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.

As given in the question,

Let us consider the cost of each pound of walnuts is equal to $x.

And cost of each pound of chocolate chips is equal to $y.

Now as per the given condition system of equation is given by,

4x + 8y = 25  __(1)

2x + 3y = 11   __-(2)

Multiply (2) by 2 and subtract it from (1) we get,

4x + 8y = 25

4x + 6y = 22

0x + 2y = 3

⇒y = $(3/2)

Substitute value of y in (1) to get the value of x,

4x + 8(3/2) = 25

⇒4x = 25-12

⇒x = $(13/4)

Therefore, for the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.

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Mazda was traveling faster than Ford Explorer by 0.57 miles per hour.

We know that the relation between distance, speed, and time is given by:

distance = speed * time

speed = distance / time

We are given;

A Mazda traveled 326 miles in 7 hours.

A Ford Explorer traveled 230 miles in 5 hours.

Let us find the rate or speed one by one:

For Mazda;

Distance = 326 miles

Time = 7 hours

Rate = distance / time = 326 / 7 mile per hour = 46.57 mile per hour

For Ford Explorer;

Distance = 230 miles

Time = 5 hours

Rate = distance / time = 230 / 5 mile per hour = 46 mile per hour

We can analyze that Mazda was traveling faster than Ford Explorer.

Thus, Mazda was traveling faster than Ford Explorer by 0.57 miles per hour.

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Answer:

Step-by-step explanation:

Slope: 6/3 = -2

since the line is going from left to right, it is a negative slope

Answer:

-7/3 or 2.3333333333333

Step-by-step explanation:

X= -1 – -4 = 3

Y= -4 – 3 = -7

y = -2.3333333333333x – 6.3333333333333

or

y = -7/3 x - 19/3

So when y= -6.33 that will mean x= -2.71

Answer:

feeling good

Step-by-step explanation:

I am just happy

If a decimal number, x = 0.3 then 10x is 10 multiplying 0.3 the result is 3

A decimal is a number that is divided into two parts: a whole and a fraction.

Between integers and fractions, decimal numbers reflect the numerical value of whole

0.3 is x which is a decimal

10 multiplies 0.3 the result is 3

The process involve converting a fraction to a whole number as the result of multiplication changed the number system from decimal to a whole number

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The binomial distribution is a parametric probability distribution with two parameters, X and B. For a large number of trials, n, binomial probability tends to follow a continuous normal probability distribution.

The binomial distribution is a type of probability distribution that models the likelihood of one of two outcomes given a set of parameters. It sums up the number of trials when each trial has the same chance of achieving a single outcome.

Therefore,

The following is the definition of the Binomial distribution's probability mass function:

P (X = x) = (n x)p x(1p)n x, where x = 0, 1, 2, 3,..., n

Given,

Probability of defective, p = 0.03

Number of bulbs, n = 144

(i) The required probability is P(X = 5).

P(X = 5) = (1445) 0.035(1 − 0.03)144 − 5

= 144151 × (144 − 5) 1 × 0.035(1 − 0.03)144 − 5 ≈ 0.169

Within a carton of 144 bulbs, there is a 0.169 percent chance that 5 of them will be defective.

(ii) The required probability is P(X>2).

P(X>2) = 1 − P(X≤2)

= 1 − P(X = 0) − P(X = 1) − P(X = 2)

= 1 − 144101 × (144 − 0)10.030

Then simplifying,

(1 − 0.03)144 − 0 − 14411 × (144 − 1) 10.031 (1 − 0.03)144 − 1 − 14412 × (144 − 2)10.032 (1 − 0.03)144 − 2

= 1 − 0.01245 − 0.0554 − 0.1226

= 0.810

There is a 0.810 percent chance that there will be more than two faulty bulbs in a carton of 144 bulbs.

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The equation to represent this scenario is y = 43*(3)ˣ  , the correct option is (a) .

In the question ,

it is given that ,

Number of pennies that Kyle starts the fundraiser =  43 pennies

goal is to triple the number of pennies each day .

let  "x" to represent the number of days .

let the total number of pennies be "y" .

this situation is represented by an exponential increase ,

that can be represented as

y = 3ˣ * 43

y = 43*3ˣ

Therefore , The equation to represent this scenario is y = y = 43*3ˣ  .

The given question is incomplete , the complete question is

Kyle starts a fundraiser with 43 pennies. He recruits all of the players on his baseball team to participate. His goal is to triple the number of pennies each day. Assume Kyle meets his daily goal. Use x to represent the number of days and y to represent the total number of pennies .

Select the Equation that represents the this scenario ?

(a) y = 43(3)ˣ

(b) y = 3(43)ˣ

(c) y = [(43)(3)]ˣ

(d) y = 43(x)³

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Answer:

Step-by-step explanation:

x=7/11

Answer: They have to climb 11,535 ft.

Step-by-step explanation:

To solve this equation, we need to do this equation:

29,035 ft - 17,500 ft.

29,035 ft - 17,500 ft = 11,535 ft.

Answer:

4/3 or 1.333333

Step-by-step explanation:

Using Laws of exponents, the solution to the expression √(3p⁹q⁷r⁶)/(16x⁶y¹²) is;  (p⁴q³r³/(x³y⁶))√(3pq/16)

The different laws of exponents are;

1) Product With the Same Bases; a^m × a^n = a^(m+n)

where;

m and n are real numbers.

2) Quotient with Same Bases;

a^m/a^n = a^(m-n)

where;

a is a non-zero term and m and n are integers.

3) Power Raised to a Power; (a^m)^n = a^(mn)

where;

a is a non-zero term and m and n are integers.

4) Product to a Power; a^n * b^n = (ab)^(n)

where;

a is a non-zero term and n is the integer.

5) Quotient to a Power; It states that the fraction of two different bases with the same power is represented as; a^n/b^n = (a/b)^n

where;

a and b are non-zero terms and n is an integer.

6) Zero Power; When the power of any integer is zero, then it means that its' value is equal to 1, such that;

a⁰ = 1

where;

a is any non-zero term.

7) Negative Exponent Rule; a^(-m) = 1/(a^m)

We are given the expression as;

√(3p⁹q⁷r⁶)/(16x⁶y¹²)

Applying the laws of exponents, we will have;

√(3p⁹q⁷r⁶)/(16x⁶y¹²) = (p⁴q³r³/(x³y⁶))√(3pq/16)

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Answer:

[tex]1+\sqrt{1190}[/tex] and [tex]\sqrt{1190}-11[/tex]

Step-by-step explanation:

Let the length in meters be [tex]l[/tex]. Then, the width is [tex]l-12[/tex].

[tex]l(l-12)=1189 \\ \\ l^2-12l=1189 \\ \\ l^2-2l-1189=0 \\ \\ l=\frac{2 +\sqrt{(-2)^2-4(1)(-1189)}}{2(1)} \text{ } (l>0) \\ \\ l=1+\sqrt{1190} \\ \\ \implies l-12=\sqrt{1190}-11[/tex]

Considering the uniform distribution, we have that:

a) The density curve is given by the image at the end of the answer.

b) The percentage of time in which an enemy will appear between 0.5 minutes and 2 minutes after the timer starts is of 60%.

c) The 20th percentile for the distribution is of 0.75 minutes.

The uniform probability distribution is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

In this problem, the bounds are given as follows:

a = 0.25, b = 2.75.

The height of the density curve is of:

f(x) = 1/(b - a).

Hence:

f(x) = 1/(2.75 - 0.25) = 0.4.

As shown by the image given at the end of the answer.

The probability that a measure is between two values is given by:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Hence, for item b:

P(0.5 < X < 2) = (2 - 0.5)/(2.75 - 0.25) = 0.6 = 60%.

The 20th percentile is the value of X for which:

X = a + 0.2(b - a).

Hence:

X = 0.25 + 0.2(2.75 - 0.25) = 0.75 minutes.

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Answer:

a) Consecutive interior angles.

b) Alternate exterior angles.

c) Corresponding angles.

d) Alternate interior angles.

e) Corresponding angles.

f) None.

g) Alternate exterior angles.

h) Consecutive interior angles.

i) None.

j) Corresponding angles.

k) Corresponding angles.

l) Alternate exterior angles.

m) Alternate interior angles.

n) Consecutive interior angles.

Step-by-step explanation:

Transversal

A line that crosses two other lines in the same plane at two distinct points.

Corresponding angles

A pair of angles that are in the same position relative to both lines crossed by the transversal.

Alternate interior angles

A pair of angles on the inner side of the two lines that the transversal crosses, but on opposite sides of the transversal.

Alternate exterior angles

A pair of  angles on the outer side of the two lines that the transversal crosses, but on opposite sides of the transversal.

Consecutive interior angles

A pair of angles on the inner side of the two lines that the transversal crosses, and are on the same side of the transversal.

a) Lines p and q are crossed by transversal line s.

Therefore, ∠4 and ∠7 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.

b) Lines r and s are crossed by transversal line p.

Therefore, ∠2 and ∠11 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal p.

c) Lines p and q are crossed by transversal line s.

Therefore, ∠12 and ∠16 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.

d) Lines r and s are crossed by transversal line q.

Therefore, ∠8 and ∠13 are alternate interior angles as they are on the inner side of lines r and s, but on opposite sides of the transversal q.

e) Lines p and q are crossed by transversal line s.

Therefore, ∠11 and ∠15 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.

f) ∠7 and ∠10 have no relationship.

g) Lines p and q are crossed by transversal line r.

Therefore, ∠1 and ∠14 are alternate exterior angles as they are on the outer side of lines p and q, but on opposite sides of the transversal r.

h) Lines p and q are crossed by transversal line s.

Therefore, ∠12 and ∠15 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.

i) ∠6 and ∠7 have no relationship

j) Lines r and s are crossed by transversal line p.

Therefore, ∠1 and ∠3 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal p.

k) Lines r and s are crossed by transversal line q.

Therefore, ∠14 and ∠16 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal q.

l) Lines r and s are crossed by transversal line q.

Therefore, ∠6 and ∠15 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal q.

m) Lines p and q are crossed by transversal line r

Therefore, ∠5 and ∠10 are alternate interior angles as they are on the inner side of lines p and q, but on opposite sides of the transversal r.

n) Lines r and s are crossed by transversal line q.

Therefore, ∠8 and ∠14 are consecutive interior angles as they are on the inner side of lines r and s, and are on the same side of the transversal q.