The area of a rectangle is 27ft squared, and the length of the rectangle is 3ft less than twice the width. Find the dimensions of the rectangle.

Answer:

this threw me off ,i got the same question:(

Step-by-step explanation:

Answer:

both are a minimum

Step-by-step explanation:

Given a quadratic function in vertex form

y = a(x - h)² + k

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here

f(x) = (x + 4)² + 2 ← with a = 1 > 0 ⇒ minimum vertex

g(x) = (x - 2)² - 2 ← with a = 1 > 0 ⇒ minimum vertex

Equidistant

When a point is equal between two objects, this is know as a equidistant. In geometry, an equidistant is a locus between two points in a perpendicular bisector.

______

Best Regards,

Wolfyy :)

Final answer:

A point is equidistant from two objects if it lies at the same distance from each object. This concept is framed within the realm of geometry, where theorems and corollaries help describe the spatial relationships between points and lines. Equidistance is a fundamental concept for understanding geometrical constructions and relationships.

Explanation:

A point is equidistant from two objects if it is the same distance from the objects. This can be understood through theorems and corollaries in geometry. For instance, a theorem states that if two lines are perpendicular to a third line, then points that are equidistant from the third line will also be equidistant from each other.

A corollary stemming from this theorem would be that two points that are equidistant from the ends of a straight line will determine a perpendicular bisector of that line. This signifies the point of intersection of both equidistant points with the line, which is also the midpoint of the straight line.

When it comes to determining if a point (x, y) is equidistant from two given lines represented by equations, we can use algebra to evaluate the relationships and find the solution that satisfies the distance criteria for the point in question.

In geometry, a point in space is considered the fundamental unit, which has no dimensions but can have a position that is described relative to other points. For example, to say that a point is equidistant from two other points or objects means that a rigid scale, if used, would measure the same distance from the point in question to each of the two objects.

Answer:

The margin of error is 1.85 cm to 1.95 cm.

Step-by-step explanation:

Given:

Will measured the diameter of a penny as 1.9 cm using the ruler.

We need to find the margin error.

Now, as we know that the margin of error is a statistic expressing the amount of random sampling error in a survey's results.

It is an amount (usually small) that is allowed for in case of miscalculation or change of circumstances.

Now, we have the margin of error to be:

1.85 cm to 1.95 cm.

As, the value of change to the left and right of 19 is same and is small it is 0.05.

So, 1.9-0.05 = 1.85 cm

and 1.9+0.05 = 1.95 cm .

Hence, the margin of error is: ± 0.05.

Therefore, the margin of error is 1.85 cm to 1.95 cm.

To prove that 3(x+1)(x+7)-(2x+5)² is never positive, we can expand and simplify the expression to -x²+4x-4, which is always negative.

To prove that 3(x+1)(x+7)-(2x+5)² is never positive, we can use algebraic manipulation and properties of quadratic equations. Let's expand and simplify the expression:

3(x+1)(x+7)-(2x+5)² = 3(x²+8x+7)-(4x²+20x+25) = 3x²+24x+21-4x²-20x-25 = -x²+4x-4

Since the leading coefficient of the quadratic term is negative (-1), the graph of this equation will be a downward-opening parabola. Therefore, the quadratic expression is never positive.

The expression [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x.

Step 1

To prove that [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x, we can simplify the expression and analyze its sign.

Expanding the expression:

[tex]\[3(x+1)(x+7)-(2x+5)^2 = 3(x^2 + 8x + 7) - (4x^2 + 20x + 25)\][/tex]

[tex]\[= 3x^2 + 24x + 21 - 4x^2 - 20x - 25\][/tex]

[tex]\[= -x^2 + 4x - 4\][/tex]

Step 2

Now, we have a quadratic expression [tex]\( -x^2 + 4x - 4\)[/tex]. The coefficient of [tex]\(x^2\)[/tex] is negative, indicating a downward-opening parabola. Therefore, the maximum value of the expression occurs at the vertex, which lies at [tex]\(x = \frac{-b}{2a} = \frac{-4}{2(-1)} = 2\)[/tex].

Substituting x = 2 into the expression, we get:

[tex]\[ -2^2 + 4(2) - 4 = -4 + 8 - 4 = 0 \][/tex]

Since the maximum value is 0, the expression is always non-positive.

The expression [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x, as proven by its maximum value of 0.

Answer:

it's 18 if your talking about multiplication

It's 42 if your talking about the powers

Step-by-step explanation:

Multiplication-(6•0)+(6•1)+(6•2)= 18

The powers-(6^0)+(6^1)+(6^2)=42

Answer:

the answer is 43

Step-by-step explanation:

Answer:

Express s in terms of v and t

s= v/t, multiplying both sides of the equation by t

Express t in terms of v and s

t= s/v ( from s=vt)

Step-by-step explanation:

Final answer:

To express s in terms of v and t, the formula is rearranged to s = vt. To express t in terms of v and s, the formula becomes t = s/v after rearranging.

Explanation:

To express s in terms of v and t using the formula v = s/t, we can rearrange the equation by multiplying both sides by t to get s = vt. Similarly, to express t in terms of v and s, we rearrange the formula to solve for t by dividing both sides by v, which gives us t = s/v.

To further clarify these transformations:

The set of equations x = t and y = 3t could be parametric equations ⇒ 3rd answer

Step-by-step explanation:

Lets explain the meaning of parametric equations

A parametric equation is where the x and y coordinates are both written in terms of another letter

Examples:

Let us find the set of the parametric equations from the answer

Fist answer:

∵ y = x and y = 3x

∴ It is a set of linear equations

Second answer:

∵ y = x + 1 and y = 3x²

∴ It is a set of linear and quadratic equations

Third answer:

∵ x = t and y = 3t

∵ x and y are represented in terms of t

∴ It is a set of parametric equations

Fourth answer:

∵ x = 3y and y = x + 1

∴ It is a set of linear equations

The set of equations x = t and y = 3t could be parametric equations

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Answer:

The area of the given figure is [tex]66.5\ cm^2[/tex].

Step-by-step explanation:

To find out the area we should have to redraw the figure having nomenclature ABCDE and join BD. Thus we have a rectangle ABDE and a triangle BCD.

The new figure is in the attachment.

Given,

Length of AE = 7 cm

Length of DE = 8 cm

Length of CF = 11 cm

Solution,

Area of rectangle ABDE = [tex]length\times breadth=length\ of AE\timeslength\ of DE[/tex]

Area of ABDE = [tex]7\times8=56\ cm^2[/tex]

Now for triangle BCD,

Length of BD = length of AE = 7 cm

Length of GF = Length of DE = 8 cm

∴ Length of CG = Length of CF-Length of GF = [tex]11-8=3\ cm[/tex]

Area of triangle BCD = [tex]\frac{1}{2}\times base\times height}=\frac{1}{2}\times length\ of\ BD\times length\ of\ GF[/tex]

Area of BCD =  [tex]\frac{1}{2}\times7\times3=\frac{21}{2}=10.5\ cm^2[/tex]

Area of ABCDE = Area of ABDE + Area of BCD = [tex]56+10.5=66.5\ cm^2[/tex]

Thus the area of the given figure is [tex]66.5\ cm^2[/tex].

Answer: c) 1 unit

Step-by-step explanation: Because if u take the scale factor and multiply it by 3

Answer:

C:  1 unit

Step-by-step explanation:

(3 units) times scale factor (1/3) comes out to (1/3)(3 units), or 1 unit.

The correct answer is C:  1 unit.

Answer:

slope = - 2, y- intercept = - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 6x + 3y = - 3 into this form by subtracting 6x from both sides

3y = - 6x - 3 ( divide all terms by 3 )

y = - 2x - 1 ← in slope- intercept form

with slope m = - 2 and y- intercept c = - 1

Answer:

b = 8 your welcome

Answer:

2x + 2(x - 5) = 78

x + x - 5 = 39

2x = 44

x = 22

Rate of the slower cyclist = 17 mph

Rate of the faster cyclist = 22 mph

Answer:

3 months

Explanation:

Amount saved in Gina’s saving account= 250

Amount Gina puts  in her account each month= 4% of 3100

=[tex]\frac{4}{100} \times 3100[/tex]

= 4 × 31

= 124

Hence total amount  added in each month =124

Therefore money credited x months

= 250 + 124 x

Amount saved in Rodger’s account = 350

Amount Rodger puts in his account each month = 3% of 2900

=[tex]\frac{3}{100} \times 290[/tex]

=87

Hence total amount added in each month = 87

Therefore money credited x months

=350 + 87 x

Now to calculate the nearest month when Gina have more in her account than Rodger does

=Amount of money credited in x months in Gina’s account ≥  Amount of money credited in x months in Rodger’s account

=250+124 x ≥ 350+87 x

=37 x≥100

= x≥2.78

=3

Answer:

x=2, y=0. (2, 0).

Step-by-step explanation:

x-y=2

2.5x+y=5

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

x=y+2

2.5(y+2)+y=5

2.5y+5+y=5

3.5y=5-5

3.5y=0

y=0/3.5

y=0

x=0+2=2

Answer:   (x-7)/(x-5)

The (x+1) terms divide and cancel out due to the rule that x/x = 1, when x is nonzero. In that rule, we can replace 'x' with any algebraic expression we want.

Answer:

30

Step-by-step explanation:

Simplify from left to right

6-3+15-1+8+11-6

=3+15-1+8+11-6

=18-1+8+11-6

=17+8+11-6

=25+11-6

=36-6

=30

Answer:

When Sum of square of two Sides is equal to square of third side of triangle.

Step-by-step explanation:

Given:

Three side length of triangle are given we need find the which value to substitute for a, b, c in Pythagoras theorem.

First we will find the squares of all length, then we will check which two square of side are equal to square of third side as per Pythagoras theorem.

Hence the two side would according be a and b and third side will become c.

For example if length of triangle  is given as 6 cm, 8 cm and 10 cm.

We will first take square of all

[tex]6^2=36\\8^2=64\\10^2=100[/tex]

Now we can see that

[tex]36+64=100\\6^2+8^2=10^2[/tex]

Now by Pythagoras theorem.

[tex]a^2+b^2=c^2[/tex]

Hence we can say a = 6 cm, b = 8 cm, c= 10 cm  

The Pythagorean Theorem is specifically applicable to right-angled triangles and states that:

[tex]\[a^2 + b^2 = c^2\][/tex]

Theorem, follow these steps:

1. Identify the longest side: The hypotenuse  c is always the longest side in a right-angled triangle.

2. Assign the longest side to c : Among the three given side lengths, the one with the greatest value should be assigned to c .

Example

Suppose you are given three side lengths: 5, 12, and 13. To determine which lengths correspond to  a ,  b , and c :

1. Identify the longest side: Among 5, 12, and 13, the longest side is 13.

2. Assign the longest side to c : So, c = 13 .

3. Assign the remaining sides to  a  and  b: Thus,  a and  b can be 5 and 12, respectively (or vice versa).

Verify using the Pythagorean Theorem:

[tex]a^2 + b^2 = c^2[/tex]

[tex]5^2 + 12^2 = 13^2[/tex]

25 + 144 = 169

169 = 169

Since the equation holds true, the side lengths 5, 12, and 13 do indeed form a right-angled triangle, with 13 being the hypotenuse.

General Case

When given any three side lengths x ,  y , and z :

1. Determine the longest side and assign it to c .

2. The remaining two sides are a  and b

3. Check if [tex]\( a^2 + b^2 = c^2 \)[/tex] to verify if the triangle is a right-angled triangle.

By following this process, you can correctly identify the sides to substitute into the Pythagorean Theorem.

Answer: -39

Step-by-step explanation:

9 x -4 -3 = -39

Answer:

A

Step-by-step explanation:

United states is too broad and too many different conditions for the land. You do not base weather on the date either.

Historically, in this area, it has snowed 10% of the time on days with similar meteorological conditions as today best describes the most likely way the probability was determined. Thus option A is correct.

The mathematical discipline known as probability specializes with determining the possibility of an event occurring. Composite reliabilities vary from 0 to 1, with 1 representing certainty and 0 representing hesitation.

Probability, which expresses the probability of a risk, is calculated by dividing the total possible combinations by the frequency of favorable events. Mornings with weather levels comparable to today's, precipitation has fallen 10% of the time. The Weather Forecast estimates there remains a 10% chance of snowfall around his region today.

Therefore, option A is the correct option.

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Answer:

20 cups

Step-by-step explanation:

16 ounces = 1 pound

8 ounces = 1 cup

16 ounces = 2 cups

1 pound = 2 cups

10 pounds = 20 cups

Answer:

20 cups

Step-by-step explanation:

Think

1 pound is 16 oz

So each cup has 8 oz

This you have to convert the 10 pound into ounces

Which then equals 160 ounces

Now divide 160 ounces by 8 and you get..

You get 20

So, 10 pounds of apples fit into 20 cups

Answer:

x = ±√y

Step-by-step explanation:

y = x²

±√y=√x²

±√y = x

Final answer:

To find the milliliters of acid in the solution, multiply the total volume of the solution by the acid percentage.

Explanation:

To find the milliliters of acid in the solution, we first need to calculate the volume of acid. We know that 13.2% of the solution is acid, so we can calculate the volume of acid by multiplying the total volume of the solution by the acid percentage:

Volume of acid = 357 mL * 0.132 = 47.124 mL

Rounding to the nearest tenth, we get:

Volume of acid = 47.1 mL

For this case we must multiply the following expression:

[tex](6a ^ 3-5) (4a ^ 3-11a) =[/tex]

We apply distributive property considering that:

[tex]+ * + = +\\+ * - = -\\- * - = +[/tex]

So:

[tex]6a ^ 3 * 4a ^ 3-6a ^ 3 * 11a-5 * 4a ^ 3 + 5 * 11a =[/tex]

To multiply powers of the same base, we place the same base and add the exponents.

[tex]24a^ {3 + 3} -66a^ {3 + 1} -20a ^ 3 + 55a =\\24a ^ 6-66a ^ 4-20a ^ 3 + 55a[/tex]

Answer:

[tex]24a ^ 6-66a ^ 4-20a ^ 3 + 55a[/tex]

Answer:

4

Step-by-step explanation:

36 / 9 = 4

4 x 9 = 36

Answer:

2/3=16/24

5/8=15/24

Step-by-step explanation:

2/3= 16/24

5/8= 15/24

because if you multiply across 2/3 by 8/8 equal 16/24

and if you multiply across 5/8 by 3/3 equal 15/24

The equivalent fraction for 2/3 and 5/8 are 16/24 and 15/24 respectively.

Given the following fractions

2/3

5/8

We are to rewrite the fractions as a denominator of 24.

For 2/3:

We will multiply both the numerator and denominator by 8 to have:

2/3 * 8/8  = 16/24

Similarly:

For 5/8:

We will multiply both the numerator and denominator by 3 to have:

5/8 * 3/3  = 15/24

Hence the equivalent fraction for 2/3 and 5/8 are 16/24 and 15/24 respectively.

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Answer:

36 cm

Step-by-step explanation:

We know that the perimeter is 2 l + 2 w.

In this case, the equation is 36 + 2 w = 108

2 w = 72

w = 36

Answer:

k = -5

Step-by-step explanation:

2(7k + 1) - 5(3k + 3) = 1 - 2k + 6 + 5k

At first, we will break the parenthesis by multiplying by the adjacent number. As we know, (+) x (-) = (-) and (-) x (-) = (+) [Algebraic operation]

or, (2*7k) + (2*1) - (5*3k) - (5*3) = (1 + 6) + 5k - 2k

or, 14k + 2 - 15k - 15 = 7 + 3k

Interchanging the values, we can get,

or, 14k - 15k - 3k = 7 + 15 - 2

or, 14k - 18k = 22 - 2

or, -4k = 20

or, k = 20/(-4)

or, k = -5

Therefore, the answer is -5

Answer:

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Step-by-step explanation:

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