The width of a rectangle is 3 yards less than its length. The perimeter is 130 yards. Find the length and width of the rectangle.

Answer:

6

Step-by-step explanation:

set x=0 and solve

(0+4)(0+2)=y

y=6

The corrrect statements about angle are:

Please refer to the attached picture below for visualization of the angles.

Based on the attached picture, we can consider the relationship of each angle, such as:

Alternate interior angles and congruent:

Angle 4 and angle 5

Angle 3 and angle 6

Alternate exterior angles and congruent:

Angle 1 and angle 8

Angle 2 and angle 7

Consecutive interior angles and supplementary:

Angle 3 and angle 5

Angle 4 and angle 6

Corresponding angles and congruent:

Angle 1 and angle 5

Angle 2 and angle 6

Angle 3 and angle 7

Angle 4 and angle 8

Vertical angles and congruent:

Angle 1 and angle 4

Angle 2 and angle 3

Angle 5 and angle 8

Angle 6 and angle 7

Supplementary angles:

Angle 1 and angle 2

Angle 3 and angle 4

Angle 5 and angle 6

Angle 7 and angle 8

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Answer:

The granite countertop will cost $ 608.

Step-by-step explanation:

Given that a counter in Spencer's kitchen is 4 feet wide and 8 feet long, and Spencer wants to replace the counter with a granite countertop, which would cost $ 19.00 per square foot, to determine how much would the granite countertop cost the following calculation must be performed:

(4 x 8) x 19 = X

32 x 19 = X

608 = X

Therefore, the granite countertop will cost $ 608.

Answer:5.7

Step-by-step explanation:

There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.

To choose a president, a vice-president, and a secretary from a committee of 20 members,

We will use the formula for combinations,

which is: C(n, k) = n! / (k! (n - k)!)

where n is the total number of members and k is the number of members being chosen.

So, for n = 20 and k = 1, we have:

C(20, 1) = 20! / (1! (20 - 1)!) = 20

This gives us 20 choices for the president.

For the vice president,

We need to choose 1 member from the remaining 19 members.

So, for n = 19 and k = 1,

we have:

C(19, 1) = 19! / (1! (19 - 1)!) = 19

This gives us 19 choices for the vice president.

Finally, for the secretary,

We need to choose 1 member from the remaining 18 members.

So, for n = 18 and k = 1,

we have:

C(18, 1) = 18! / (1! (18 - 1)!) = 18

This gives us 18 choices for the secretary.

Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:

So, the required number of ways will be 20 * 19 * 18 = 6840

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The Brewster's angle for an air-glass (n=1.58) surface is approximately 56.309 degrees.

Brewster's angle is the angle of incidence at which light with a specific polarization, known as p-polarization, is perfectly transmitted through a transparent dielectric surface, with no reflection.

The formula for Brewster's angle is:

θB = arctan(n)

Where θB is Brewster's angle and n is the refractive index of the second medium (in this case, glass).

Substituting n=1.58, we get:

θB = arctan(1.58)

Using a calculator, we find:

θB ≈ 56.309°

Therefore, the Brewster's angle for an air-glass (n=1.58) surface is approximately 56.309 degrees.

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Answer:

x = -9

Step-by-step explanation:

-4x = -1/2(10x + 18)

Distribute

-4x= - 5x -9

Add 5x to each side

-4x+5x = -5x+5x -9

x = -9

Answer:

\(360 = 2\pi \\\\90 = \frac{2\pi }{4} =\frac{\pi }{2} \\\\180 = \pi \\\\270 = \frac{6\pi }{4} = \frac{3\pi }{2}\)

Answer:

  True

Step-by-step explanation:

The ASA postulate applies. Angles at either end of the common segment are marked congruent. Thus the triangle are congruent.

The probability that a randomly selected cup will be overfilled is approximately 0.2514 or 25.14%.

It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. A probability of 0.5 (or 50%) means that the event is equally likely to occur or not to occur.

We need to find the probability that the amount of Dr. Pepper dispensed will be greater than 32.0 oz, which can be written as:

P(X > 32.0)

where X is the amount of Dr. Pepper dispensed by the machine.

We can standardize this value by subtracting the mean and dividing by the standard deviation:

P(Z > (32.0 - 31.0) / 1.50)

Simplifying this expression gives:

P(Z > 0.67)

Using a standard normal table or calculator, we can find that the probability of a standard normal random variable being greater than 0.67 is approximately 0.2514.

Therefore, the probability that a randomly selected cup will be overfilled is approximately 0.2514 or 25.14%.

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you're absolutely correct, it's a polynomial, well, it has only one term, recall that each term is separated by either "-" or "+", so we only have one term here, that makes it a monomial.  Now, about the degree, for the degree of a polynomial, we look at each term, and add its variable's exponents, let's do that in this one.

\(-\cfrac{x^3y^5}{3}\implies -\cfrac{1}{3}x^3 y^5\impliedby degree~of~^{3+5},~na mely~\text{\LARGE 8}\)

The price elasticity of demand measured using midpoint method, for a price change between $10 and $2 can be determined as follows:Price elasticity of demand (mid-point method) = [ΔQ / {(Q1 + Q2)/2}] ÷ [ΔP / {(P1 + P2)/2}]Given that P1 = $10, P2 = $2, Q1 = Q2, and the price has decreased from $10 to $2.

Therefore, the midpoint price (P) = (P1 + P2) / 2 = ($10 + $2) / 2 = $6The midpoint quantity (Q) = (Q1 + Q2) / 2 = Q1 / 2 + Q2 / 2 = Q / 2 + Q / 2 = Q.ΔP = $2 − $10 = −$8ΔQ = Q − Q = 0Hence, the absolute value of the price elasticity of demand using the midpoint method for a change in price from $10 to $2 is :Price elasticity of demand (mid-point method) = [ΔQ / {(Q1 + Q2)/2}] ÷ [ΔP / {(P1 + P2)/2}]E = [0 / {Q / 2}] ÷ [−8 / $6]E = 0 ÷ −1.3333E = 0

So, the correct answer is option B: 1.

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The values of a, b and c in the given quadratic equation; 5x² = 4x + 7 are; 5, -4 and -7 respectively.

It follows from the task content that the values of a, b and c be determined in the quadratic equation; 5x² = 4x + 7.

Recall, the standard form of a quadratic equation takes the form; ax² + bx + c = 0.

Therefore, for the given equation; 5x² = 4x + 7; we have that;

5x² - 4x - 7 = 0.

Ultimately, the value of a is 5, b is -4 and c is -7.

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Answer:

f(5) = 3(5+2) - 8

f(5) = 15+6 -8

f(5) = 21 - 8

f(5) = 13

The factors of the expression  w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)

(w - 4) will be the height

(w + 10) will be the length

Given,

The length of the enclosure for the pancake tortoise will be greater than the height, that is: l > h

The volume of enclosure = w³ + 6w² - 40w

Where w is the width.

Now, factorize the expression:

w³ + 6w² - 40w = 0

10 - 4 = 6

10 × (-4) = -40

Therefore, the factors of the expression  w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)

Here, we know that length is greater than height.

So, (w - 4) will be the height and (w + 10) will be the length.

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If Caroline has 6.8 L of lemonade to serve 20 people. Caroline can pour 340 milliliters of lemonade into each glass.

To find out how many milliliters of lemonade Caroline can pour into each glass, we need to convert the volume of lemonade from liters to milliliters and then divide it equally among the 20 guests.

1 liter is equal to 1000 milliliters. So, Caroline has 6.8 L * 1000 mL/L = 6800 mL of lemonade.

To divide it equally among 20 guests, we divide the total volume of lemonade by the number of guests:

6800 mL / 20 = 340 mL.

Therefore, Caroline can pour 340 milliliters of lemonade into each glass.

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Answer:

12

Step-by-step explanation:

She spent $8 on a sketchpad and $17 in total.

Amount of money she spent on drawing pencils = \(17-8=9\)

A drawing pencil cost $0.75 and she spent $9.

Thus, she bought \(9\div0.75=12\) drawing pencils.

Answer:

12

Step-by-step explanation:

First I subtracted 8 from 17 and I got 9. Then I divided 9 by .75 and got 12. Then to check I substituted 12 into the equation which is 12(.75) + 8 and I get 17.

Hopefully this helps you :)

pls give me brainlest ;)

Answer:

\(\frac{22}{\sqrt{11} } = \frac{22\sqrt{11} }{11} = 2\sqrt{11}\)

Answer: P≈15.5 units.

Step-by-step explanation:

The perimeter of a triangle is equal to the sum of all its sides:

                                          P = a + b + c,

where P is the perimeter and a, b, c are the sides of the triangle.

The segment length formula makes it possible to calculate the distance between two arbitrary points in the plane, provided that the coordinates of these points are known:

                               \(\boxed {d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} }\)

1) (1,6)   (3,1)  ⇒   x₁=1    x₂=3     y₁=6      y₂=1

\(a=\sqrt{(1-3)^2+(6-1)^2} \\\\a=\sqrt{(-2)^2+5^2} \\\\a=\sqrt{4+25} \\\\a=\sqrt{29} \approx5.4\ units\\\)

2) (1,6)   (6,1)  ⇒  x₁=1    x₂=6   y₁=6   y₂=1

\(b=\sqrt{(1-6)^2+(6-1)^2} \\\\b=\sqrt{(-5)^2+5^2} \\\\b=\sqrt{25+25} \\\\b=\sqrt{50} \approx7.1\ units\\\)

3) (3,1)   (6,1)   ⇒   x₁=3   x₂=6   y₁=1   y₂=1

\(c=\sqrt{(3-6)^2+(1-1)^2} \\\\c=\sqrt{(-3)^2+0^2} \\\\a=\sqrt{9+0} \\\\a=\sqrt{9} =3\ units\\\)

4) P=a+b+c

P≈5.4+7.1+3

P≈15.5 units.

The probability that the first card is a heart and the second card is a 10 is 1/52.

The probability of drawing a heart as the first card is 13/52 (since there are 13 hearts in a deck of 52 cards).

Assuming the heart is not put back into the deck, there are now 51 cards left, of which four are 10s (the 10 of hearts,

diamonds, clubs, and spades).

Therefore, the probability of drawing a 10 as the second card given that the first card was a heart is 4/51.

The probability of both events happening (drawing a heart first and a 10 second) is the product of the two probabilities:

13/52 x 4/51 = 1/52

So, the probability that the first card is a heart and the second card is a 10 is 1/52.

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Answer: es

Step-by-step explanation: I know Spanish

The value of x in the given right angle triangle is: x = 2√10

Pythagoras Theorem is defined as the way in which we can can find the missing length of a right angled triangle.

The triangle possesses three sides, which are the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Thus:

The hypotenuse of the smaller triangle is:

h = √(8²- 5²)

h = √(64 - 25)

h = √49

h = 7

Thus:

x = √(7² - 3²)

x = √40

x = 2√10

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Answer:

8

Step-by-step explanation:

The first step is to simplify the fraction inside the parentheses,

using a^b / a^c = a^(b-c)

6^7  3^3             6^(7-6)   3^(3-4)   = 6^1  3^-1   =  6/3  =2

-----------------  =                                                    

6^6    3^4          

Now we take care of the outside parentheses

3^2 = 2*2*2 = 8                                                            

The coordinates of B in the segment is (2, 7)

The given parameters are

A = (-4, 3)

M = (-1, 5)

The midpoint of the segment AB is calculated as

M = 1/2(x1 + x2, y1 + y2)

So, we have

(-1, 5) = 1/2 * (-4 + x, 3 + y)

Multiply both sides of the equation by 2

So, we have

(-2, 10) = (-4 + x, 3 + y)

By comparison, we have the following

-4 + x = -2

3 + y = 10

Evaluate the like terms

x = 2

y = 7

This means that

B = (2, 7)

Hence, the coordinates of B in the segment is (2, 7)

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The integer that can be  inserted on the blank line in the list is: -2

The number line is given as:

-15, -3, ____, -1.5, 2, 3, 5

Now, a number line is defined as a line on which numbers are marked at intervals, used to illustrate simple numerical operations.

In this case, we see that the interval of the number line is from -15 to 5.

Thus, the range of values for the blank space will fall in between those two numbers.

Now, since we have positive 2 on the number line, then we must likely also have the negative one to balance it as the blank number.

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1) The line integral value is : ∫F dr = 6

2) The line integral value is : ∫F dr = 6

3) The line integral value is : ∫F dr = 6

Here we are given:

\(F.dr = (3x + 2y)dx + (2x -2z)dy + (3x -2y)dz,\)

where\(\vec{F}\) is a conservative field

So,

f(x, y , z) = \(\int\limits (3x + 2y)dx + (2x -2z)dy + (3x -2y)dz,\)

f(x , y , z) = (3zx +2yx) + (2xy - 2zy) + (3xz - 2yz) + c(x , y , z)

\(f(x, y, z) = (6xz + 4xy - 4yz) + c(x, y, z)\)

Now substitute the values of x , y ,z ,

1)

Line segment from (0, 0 , 0) to (1,1 ,1)

∫F dr = f(1,1,1) - f(0,0,0)

= |6 + 4 - 4 |- |0 + 0 - 0|

∫F dr = 6

2)

Line segment from (0,0,0) to (0,0,1) to (1,1,1)

First we take (0,0,0) to (0,0,1)

\(\int _c \vec{F}.\vec{dr}=f(0,0,1)-f(0,0,0) =[6(0)(1)+4(0)(0)-4(0)(1)]-[6(0)(0)+4(0)(0)-4(0)(0)] =[0+0-0]-[0+0-0]\)

∫F dr = 0

\(\Rightarrow \int _{c}\vec{F}.\vec{dr}=0+6 [F.dr = 6\)

3)

Line segment from (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1)

First we take (0,0,0) to (1,0,0)

\(\int _c \vec{F}.\vec{dr}=f(1,0,0)-f(0,0,0) =[6(1)(0)+4(1)(0)-4(0)(0)]-[6(0)(0)+4(0)(0)-4(0)(0)] =[0+0-0]-[0+0-0]\int _{c}\vec{F}.\vec{dr}=0\)

Next we take (1,0,0) to (1,1,0)

\(\int _c \vec{F}.\vec{dr}=f(1,1,0)-f(1,0,0) = [6(1)(0) + 4(1)(1) − 4(1)(0)] - [6(1)(0) + 4(1)(0) — 4(0)(0)] = [0+4-0] - [0+0-0]\int _{c}\vec{F}.\vec{dr}=4\)

Lastly we take (1,1,0) to (1,1,1)

\(F.dr = f(1,1,1) ƒ(1,1,0) = [6(1)(1) +4(1)(1) − 4(1)(1)] - [6(1)(0) + 4(1)(1) — 4(1)(0)] =[6+4-4]-[0+4-0]\int _{c}\vec{F}.\vec{dr}=2\)

Adding the three results we get

\(\Rightarrow \int _{c}\vec{F}.\vec{dr}=0+4+2\\\\\int\limits F.dr = 6\)

Therefore we see that the Line integral for the three cases comes out to be same between the initial and final points since it is independent of the path taken.

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