In the accompanying diagram, parallel lines AB and CD are intersected by GH at E and F
respectively. If m

Step-by-step explanation:

1. if to rewrite the given equation, then

y= -3(x+5)²+1;

2. the vertex of the parabola is (-5;1) and it is the highest point. Then

3. domain: x is any value, x∈(-∞;+∞);

range: y not greater than 1, y∈(-∞;1].

For the parabola f(x) = -3x² - 30x - 74, the domain is all real numbers (-∞, ∞), and the range is also all real numbers (-∞, ∞).

To determine the domain and range of the given parabola f(x) = -3x² - 30x - 74, we need to understand the behavior of parabolas.

The domain of a function represents all the possible x-values for which the function is defined. In this case, there are no restrictions on the x-values for the given quadratic function. Therefore, the domain is all real numbers, expressed as (-∞, ∞).

The range of a function represents all the possible y-values that the function can produce. For a parabola, if the coefficient of the squared term (in this case, -3) is negative, the parabola opens downward. Since the coefficient is negative, the parabola will have a maximum value. In this example, there is no minimum or maximum specified; thus, the range will also be all real numbers.

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Answer:

dd

Step-by-step explanation:d

Answer:

Step-by-step explanation:

a0 - x-y=3

The percent of decrease is 4%.

One year, the population of a city was 215,000. Several years later it was 206,400.

To find out the percent decrease:

A fraction with denominator equals 100 to a percentage: 4%

Based on the given conditions, formulate: [tex]\frac{215000-206400}{215000}[/tex]

Calculate the sum or difference: [tex]\frac{8600}{215000}[/tex]

Cross out the common factor: [tex]\frac{1}{25}[/tex]

Multiply a number to both the numerator and the denominator: [tex]\frac{1}{25}* \frac{4}{4}[/tex]

Write as a single fraction: [tex]\frac{4}{25*4}[/tex]

Calculate the product or quotient: [tex]\frac{4}{100}[/tex]

Rewrite a fraction with denominator equals 100 to a percentage: 4%

Hence the answer is the percent of decrease is 4%.

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The set of side measurements that could be used to form a triangle are 8, 14, 20.

The concept that will be used is the concept of triangle inequality theorem.

To know if the given 3 side lengths are a triangle, then the use of the  triangle inequality theorem comes into play.

This rule tells us that when we sum 2 sides of a triangle  the value must be greater than the third side.

Then this rule can be applied as

The first option; 8, 14, 20

a+b>c  = 8+14>20

a+c>b  =  8+20>14

b+c>a   = 20+14>8

Therefore, first option is correct.

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Answer:10

Step-by-step explanation:

1.20 + (4.75 × x) = 48.701.20 + 4.75x = 48.70Collect like terms 4.75x = 48.70 - 1.204.75x = 47.50Divide both side by 4.754.75x/4.75 = 47.50/4.75.x = 10

The lines which are skewed in the rectangular prisms shown are Line QT (↔QT) and Line WX(↔WX).

What is skew in geometry?

This refers to two lines that do not cut across (intersect)  each other and are not parallel to each other. the pair of lines must also be opposite edges of the shape. The lines are not also lying or acting in the same plane. i.e non-coplanar.

How to identify skew lines?

a) Locate lines that do not intersect each other.

b)Find out if these pairs of lines are also not parallel to each other.

c) Examine if these non-intersecting and non-parallel lines are non-coplanar.

If yes then the chosen pair of lines are skew lines.

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The calculation of the required financial ratios for Sunland Company is as follows:

The return on assets is 6%.

The Asset Turnover is 2.06 times.

The profit margin is 2.9%.

Financial ratios express the numerical relationships of two or more financial statement elements.

Financial ratios are used to make comparisons of the financial performance or position of companies from one year to another (trend analysis) and between companies or the industry average.

Net sales $11,257.9

Net earnings $327.9

Total assets, ending = $5,560.0

Total assets, beginning = $5,370.0

Average assets = (Beginning total assets + Ending total assets) ÷ 2

= $5,465 ($5,560 + $5,370)/2

Return on assets = Net earnings/Average total assets x 100

= 6% ($327.9/$5,465 x 100)

Asset Turnover = Net Sales/Average total assets

= 2.06x ($11,257.9/$5,465)

Profit margin = Net earnings/Net Sales x 100

= 2.9% ($327.9/$11,257.9 x 100)

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Answer:

13

Step-by-step explanation:

if b = 5, then 3(5) - 2 = 15 - 2 = 13

Answer:

5/16

Step-by-step explanation:

This is a geometric sequence

aₙ=a₁*rⁿ⁻¹

a₆=10*.5⁶⁻¹

a₆=10*.5⁵

a₆=10*(1/2)⁻⁵

a₆=10*1/32

a₆=10/32=5/16

Answer:

Step-by-step explanation:

Instead you do 45 divided by 8

And you will get 5.625

The price of each bag of apples is $3.5 and price of  each bag of potatoes is $2.

Given:

a person can buy two bags of apples and two bags of potatoes for $11 at a farmers market the same person by two bags of apples and three bags of potatoes for $13.

Let x be the apples and y be the potatoes.

2x + 2y = 11

2x + 3y = 13

on solving:

2x + 2y - 2x - 3y = 11 - 13

2y - 3y = -2

-y = -2

y = 2

2x + 2y = 11

2x + 2*2 = 11

2x + 4 = 11

2x = 7

x = 7/2

x = 3.5

Therefore The price of each bag of apples is $3.5 and price of  each bag of potatoes is $2.

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Answer:

Apples cost $3.50, potatoes cost $2.

Step-by-step explanation:

If you only add one bag of potatoes and the price jumps two dollars, then the potatoes cost two dollars each. We can substitute this into the equation, which can be solved to find apple price.

Answer:

Rational x Irrational = Irrational

Step-by-step explanation:

6 is a rational number.  It can be written as an integer over and integer [tex]\frac{6}{1}[/tex]

[tex]\pi[/tex] is irrational.  This is a number that never repeats or terminates, so it can not be written as an integer over and integer.

Answer:  Choice B

Rational x Irrational = Irrational

==============================================

Reason:

6 = a rational number

3pi = an irrational number

18pi = an irrational number

Anything involving pi is irrational. The value 6 is rational because 6 = 6/1.

pi is irrational since we cannot write it as a ratio of two integers. We can get approximations like 22/7, but we can't nail down the exact value of pi with a fraction.

The error in the volume of the cube is gotten as; ±120 in³

In this type of situation, there could be maximum error, relative error and percentage error.

The maximum error is gotten by differentiating the volume equation.

The relative error is gotten by dividing the change in volume by the volume likewise change in length.

The percentage error is just converting the relative error to percentage. Thus;

Thus;

Volume of a cube is given by the formula;

V = x³

dV/dx = 3x²

dV = 3x²(dx)

We are given dx = 1/10

Thus;

dV = ±(3 * 20² × (1/10))

dV = ±120 in³

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Answer:

1 and 3

Step-by-step explanation:

discriminant = 16 - 4 * 1 * 3 = 16 - 12 = 4

x1 = (4 + √4)/2 = (4+2)/2 = 6/2 = 3

x2 = (4 - √4)/2 = (4-2)/2 = 2/2 = 1

Answer:

The y-intercept is when $x=0$ so $y=32\frac{ft}{s}*0-\frac{1}{2}*9.8*0^2=0$, so the ball starts on the ground. The maximum height is when $v=0$, so $0=32\frac{ft}{s}-9.8t$ and solving for $t$ we get $t=\frac{32}{9.8}=3.265s$, and plugging this back in for $y$ we get $y=32\frac{ft}{s}*3.265s-\frac{1}{2}*9.8*3.265^2=156.205 ft$. So the ball will be at its maximum height of 156.205 ft at 3.265 seconds.

Step-by-step explanation:

The $y$-intercept is $-1$.  The maximum height of the baseball is when $y=0$; that is when $x=\ln(4)$.  Here is a sketch of the path.

From the $y$-intercept, we see that the baseball starts at height $y=-1$.  It reaches a maximum height at $x=\ln(4)$; that is, $y=0$.  From there, it falls and reaches the ground at $x=2\ln(4)$; that is, $y=-1$ again.

Answer:

540 cm₂

Step-by-step explanation:

       [tex]\sf \boxed{Area = (b_1+b_2+b_3)*l + bh}\\\\[/tex]

[tex]\sf \text{where $b_1$, $b_2$ and $b_3$ are the sides of the triangle l is the length of the rectangle}\\\\ \text{and b is the base of the triangle and h is the altitude of the triangle}[/tex]

    b₁ = 12 cm ; b₂ = 5 cm ; b₃ = 13 cm

   l = 16 cm  ;  b = 12 cm and h = 5 cm

Area  = (12 + 5 + 13)*16 + (12*5)

          = 30*16 + 60

          = 480 + 60

          = 540 cm²

Answer:

y=3x+1

y=-17

Step-by-step explanation:

y=3x+1

7=3(2)+1

7=6+1

7=7

y=3(-6)+1

y=-18+1

y=-17

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Using the table, the average daily balance of the credit card for the August 1 through August 31 billing period is $705.

The average daily balance refers to the computed total balance divided by the number of days in the billing cycle.

The computed total balance is the sum of closing balance multiplied by the number of days covered in the billing cycle before the next credit card transaction or activity.

Day   Activity     Adjustment     Closing Balance  No. of days     Total

1           --                     --                      950                     7            $6,650

8       Payment           −600                350                     8              2,800

16      Purchase         +300                650                     8              5,200

24     Purchase         +250                900                     8              7,200

Total                                                                             31           $21,850

Average daily balance = $705 ($21,850/31)

Thus, the average daily balance on the credit card is $705.

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The time taken by Ashley and Laura to meet each other is 3 hrs

The speed of an object tells us how slow or fast an object moves. The formula for speed is given below

The speed of an object is directly proportional to Distance and Inversely proportional to Time. Hence,

Here we have,

Ashley and Laura are 60 miles apart, traveling toward each other

This means the distance between Ashley and Laura is 60 miles

Speed of Laura = 12 mph

Speed of Ashley = 8 mph

Let us assume that Both Ashley and Laura meet after t hours

Then

The distance traveled by Laura in t hours = 12 mph × t hrs = 12t m

The distance traveled by Ashley in t hours = 8 mph × t hrs = 8t m

As we know the distance between Laura and Ashley is 60 miles

=>  12t m + 8t m = 60 miles

=>  20t miles = 60 miles

=> t = 60/20

=> t = 3hrs

Therefore,

The time taken by Ashley and Laura to meet each other is 3 hrs

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The side x of the right triangle is 235.72 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be found using trigonometric ratios or Pythagoras theorem depending on the sides and angles given.

Hence, let find the value of x in the combine right triangles.

Therefore,

tan 28 = opposite / adjacent

tan 28 = 105 / l

cross multiply

l = 105 / tan 28

l = 105 / 0.53170943166

l = 197.479781832

l = 197.50

tan 70 = 105 / a

a = 105 / tan 70

a = 38.2168804325

a = 38.22

Therefore,

x = 197.50 + 38.22

x = 235.72 units

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The formula for y in terms of x is a cubic equation:

y = 0.25*x³

We know that y is directly proportional to x³, then we can write the equation:

y = k*x³

Where k is the constant of proportionality.

In this case, we know that when x = 10, the value of y is 250, then we can replace these values in the above equation to find the value of x:

250 = k*10³

250 = k*1,000

Dividing both sides by 1,000 we get:

250/1,000 = k

0.25 = k

Then the equation is:

y = 0.25*10³

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The sample space in regard to the vacations is 24

Choice of 3 destinations: Cozumel (C), Jamaica (J), or Grand Caymans (G) =

3C1

A choice of 2 types of rooms: balcony (B) or inside view =  2C1

And a choice of 4 types of excursions: water sports (W), horseback riding (H), parasailing (P), or zip-lining (Z) = 4C1

Choosing only one of each, the sample space in regard to the vacations

Sample space = choice of destination x choice of room x choice of water sports

= 3C1 x 2C1 X 4C1

= 3 x 2 x 4 = 24

Therefore,  the sample space in regard to the vacations is 24

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The area of the hula hoop is equal to 450π square inches.

A hula hoop is a toy with the form of a circle, whose area (A), in square inches, has to be found. The area of a circle is described by the following formula:

A = 2π · R²

Where R is the radius of the hula hoop, in inches.

If we know that R = 15 inches, then the area covered by the hula hoop is:

A = 2π · (15 in)²

A = 450π in²

The area is equal to 450π square inches.

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Angle BCD is the same as angle FGH which is 122

Step-by-step explanation:

congruent means that they have the same angles.

so, the angle BCD = 122

The equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.

The standard equation of a circle is given by:

(x – h)² + (y – k)² = r²

Where (h, k) is the center of the circle and r is the radius.

We are given:

The circle has a center at (–4, 0) and passes through the point (–2, 1).

Substitute (h, k) with (–4, 0) in the above equation, we will get;

(x – (-4))² + (y – 0)² = r²

(x + 4)² + y² =  r²

Substitute (x, y) with (–2, 1) in the above equation to get the value of r:

(-2 + 4)² + 1² =  r²

(2)² + 1² =  r²

r² = 5

Put the value r² = 5 in (x + 4)² + y² =  r², we will get;

(x + 4)² + y² =  5

So, the equation of the circle is (x + 4)² + y² =  5.

Thus, the equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.

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Suban need to leave $10000 investment in the bank at 5% per year simple interest for 10 years so that it grows to $15000

According to question,

Principal (P) = 10,000

Rate of interest (I) = 5%

Interest = Amount - Principal

= 15000 - 10000

= 5000

We need to find the number of years

T = ?

Interest = P * R * T / 100

5000 = 10000 * 5 * T / 100

T = 10 years

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Answer:

38.88in²

Step-by-step explanation:

Area of shaded region = Area of square - Area of semi circle

First lets find the area of the square and semi circle

Area of square = s²

Where s = side length

Here we have a given side length of 8in

So s = 8

This means area = 8² = 64in²

Area of semicircle = (πr²)/2

Where r = radius

Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in

To convert from diameter to radius we simply divide by 2

So radius = 8 / 2 = 4

Now we have Area = (πr²)/2

==> plug in r = 4 and π = 3.14

Area = (3.14(4)²))/2

==> simplify exponent

Area = (3.14(16))/2

==> multiply 3.14 and 16

Area = 50.24/2

==> simplify division

Area = 25.12in²

Area of shaded region

We now subtract the two areas

Area of shaded region = Area of square - Area of semi circle

Area of square = 64in² and Area of semicircle = 25.12in²

Area of shaded region = 64in² - 25.12in² = 38.88in²

Answer:

130 in standard form
100+30 in expanded form

Step-by-step explanation:

standard from is writing the sentence in a number fro example
three hundred seventy two is writen as 372 in standard for
expanded form is 300+70+2

Answer:

130 in standard form

In expanded form is100+30=1300

Step-by-step explanation:

For further example 4236

In standard form is 4236

In expanded form is 4000+200+30+6=4236