Select the expressions that are equivalent to 7(-7u - 4) - 5.
(-7u - 4)7 - 5
7(-8u+ u 4) - 5
-33u - 49
-7u - 33

Answer:

50.27

Step-by-step explanation:

The probability that a break will occur in the first 50 meters of the tightrope is about 15.625%.

Probability:

The term probability refers the possibility occurring the particular event.

Given,

A 320 meter long tightrope is suspended between two poles.

Here we assume that the line has an equal chance of breaking anywhere along its length.

Now, we need to determine the probability that the break will occur within 20 meters of a pole.

From the given question,

The line has an equal chance of breaking anywhere along its length.

The first 50 meters form ,

=> [ 50 / 320 ] x 100

=> [ 5 / 32 ] x 100

=> [ 0.15625] x 100

=> 15.625 %.

Therefore, the probability that a break will occur in the first 50

meters of the tightrope is about 15.625%.

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Answer:

a = 4(d - g)

Step-by-step explanation:

d - g = [tex]\frac{1}{4}[/tex] a ( multiply both sides by 4 to clear the fraction )

4(d - g) = a

The formula for finding the sum of a geometric series is:

S n = a₁ (1-rⁿ )/(1-r)

The four quantities in the formula are S n, a₁, r, n

An infinite geometric series is the outcome of an unlimited geometric sequence. An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series.

The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.

The formula for finding the sum of a geometric series is:

S n = a₁ (1-rⁿ )/(1-r)

The four quantities in the formula are S n, a₁, r, n

The description is as follows:

n be the number of terms

a₁ be the first term

r be the common ratio

[tex]S_n[/tex] be the sum of a geometric series

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Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

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The marble will roll 180cm distance in fifth second.

Distance travelled by an object in rectilinear motion is always in arithmetic Progression. Arithmetic Progression is collection of number in increasing or decreasing order with a common difference.

The marble rolls 20cm, 60cm, 100cm, 140cm in 1st, 2nd, 3rd, 4rth second respectively

As the ball travels in rectilinear motion on floor, so the distance covered by it in successive seconds will be in Arithmetic Progression

so, 5th term of the AP 20,60,100,140..... will be the distance travelled by it 5th second

Since A=20 and common difference(d)=40

then, 5th term= A + (5-1)d

or, 20+ (4×40) = 180cm

Final answer, the marble will roll 180cm in 5th second.

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Answer:15

Step-by-step explanation: if your at -9,-5 you would be on the 3rd quadrant, and in order to get to 6,-5 (4th quadrant) you would just move to the right. you would only move right because the y-axis stays the same but the x-axis changes.

Answer: 15

Step-by-step explanation:

the equation to find the length of a line using the points given:

[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

therefore you should understand which is y2, x2,y1 and x1

so you should always check which y value is bigger (the y value is the number in the right side of the point) so if the y value is bigger (y2) then eventually the value next to it which is x will always become x2 if the y value is big (y2)

so the other two values of the other point should become x1 and y1 since you already figured out the lager y value.

so now as for this question y2= -5, y1= -5, x2= 6 and x1= -9

now substitute these values to the equation I mentioned before ( you should make sure to remember the equation for sure as it is required when doing these types of questions)

[tex]\sqrt{[6-(-9)]^{2} +[-5-(-5)]^2} \\\sqrt{(6+9)^2 + (-5+5)^2[/tex]

[tex]\sqrt{15^2+0^2} \\\sqrt{225} \\15[/tex](therefore 15 is the answer you have been looking for!)

I hope you understood and don't forget the equation which is the main help!

The equation which correctly gives P in terms of E, O and M as required is; P = 6E - 4M - O.

It follows from the task content that the expression which represents P in terms of E, O and M be determined.

On this note, since the initial formula is;

E = (O + 4M + P)/6

Multiply both sides by 6;

6E = O + 4M + P

Subtract O and 4M from both sides;

P = 6E - 4M - O.

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The number of ways of picking a panel of judges comprising of 2 men and 2 women is 280 ways

Given data

number on men = 5

number of women = 8

The number of ways of picking a panel of 2 men and 2 women

= 5 combination 2 * 8 combination 2

= 5 C 2 * 8 C 2

= 5! / ( 2! ( 5 - 2 )! * 8! / ( 2! ( 8 - 2 )!

= 5! / ( 2! 3! ) *  8! / ( 2! 6! )

= 5 * 4 * 3! / ( 2! * 3! ) * 8 * 7 * 6! / ( 2! * 6! )

= 20 / 2 * 56 / 2

= 10 * 28

= 280 ways

The number of ways of picking a panel of judges comprising of 2 men and 2 women is 280 ways

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Answer:

x < 1

Step-by-step explanation:

By elimination, the solution of the system of equations, 5x - y = 4 and 2x - y = 1, is (1 , 1).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Subtracting the two equations will eliminate the variable y.

5x - y = 4     (equation 1)

2x - y = 1     (equation 2)

3x      = 3

x = 1

Substitute the value of x to any of the two equations and solve for y.

5x - y = 4     (equation 1)

5(1) - y = 4

-y = 4 - 5

-y = -1

y = 1

Hence, the solution of the system of equations is (1 , 1).

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Answer:

Step-by-step explanation:

[tex]A(-5)=4(-5)^{2} -3(-5)+2\\A(-5)=100+15+2\\A(-5)=117[/tex]

Beth knows the perimeter, P, and width, w, of a

rectangular window in her living room. Which

formula can she use to find the length, 1, of the

window?

First we know about How to Find the perimeter?

Rectangles have four sides, congruent opposite sides, and four right angles and we find the perimeter of a rectangle with the equation P=2l+2w. Explore this formula, rectangles, and examples of finding rectangle perimeters.

so ,

The formula for the perimeter of a rectangle is given below: Perimeter = length + length + width + width P = l + l + w + w Or, P = 2 ( l + w) Hence, the formula for the perimeter of a rectangle, P = 2 × (length + width) = 2 × (sum of adjacent sides) .

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Answer:Omg JUST use slope intercept form like I said: Pick a point in this case I have picked, but you can any: (15, 560) (20, 480). Remember

Y2 - Y1 /X2-X1 = M (Your slope). In this case 480-560/20-15 = -80/5 = -16

Now you have your slope. Y - Y2=M(x - x1). In this case Y - 560 = -16(x-15)

Distrubute: Y - 560 = -16x +240. Add 560 on both side. Y= -16x +800

And yes it water decreases as time increases.

Step-by-step explanation:

Answer: 2000.18 unit^3

Step-by-step explanation:

radius = 14 / 2 = 7

V of cylinder = π x r^2 x h

= 3.14 x 7^2 x 13

= 3.14 x 49 x 13

= 2000.18 unit^3

Answer:

22 yards

Step-by-step explanation:

Let x equal the number of yards of ribbon at $.07 per yard:

$18.46 + 0.07x = $20.00

Solve for x

Subtract $18.46 from both sides

0.07x = $1.54

Divide both sides by .07

x = 22

The subtraction equation to addition equation is as follows;

By converting the subtraction equation to addition equation, we have to change the sign from subtraction to addition but the equation overall remain the same.

Therefore,

a - 9 = 6

add 9 to both sides

a - 9 + 9 = 6 + 9

a  = 6 + 9

p - 20  = -30

add 20 to both sides

p = -30 + 20

z - (-12) = 15

open the bracket by multiplying the signs

Therefore,

z + 12 = 15

x - (-7) = -20

open the bracket by multiplying the signs

x + 7 = -20

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Answer:

Step-by-step explanation:

y = mx + b is the equationof the line where m is the slope and b is the y intercept

slope between t points = (8 - 0)/ (3 -1 )

= 8/2

=  4

y = 4x + b

substitute (1,0) in the equation to get b

0 = 4(1) + b

b = -4

equation will be y = 4x -4

23 lies between the two perfect squares 16 and 25 which are the squares of 4 and 5 respectively.

The value of √23 lies between 4 and 5.

What in mathematics is a perfect square?

Informally: A square number, perfect square, or simply "a square" is the result of multiplying an integer (a "whole" number), positive, negative, or zero, times itself. Therefore, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.

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The function C that represents how much more it costs to rent a luxury car than an economy car is; C = 8.45 + 0.45M

We are given the function that represents the charge E(in dollars) to rent an economy car as;

E = 12.95 + 0.60M

The function that represents the charge L (in dollars) to rent a luxury car is given by; L = 21.40 + 1.05M

Now, we are told that the function C represents how much more it costs to rent a luxury car than an economy car. This is expressed as;

C = L - E

Thus;

C = 21.40 + 1.05M - (12.95 + 0.60M)

C = 21.40 + 1.05M - 12.95 - 0.60M

C = 8.45 + 0.45M

Thus, the function C that represents how much more it costs to rent a luxury car than an economy car is; C = 8.45 + 0.45M

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The value for the given line DF are-

For the given values in question,

DE = 6x + 1 and EF = 7x - 4.

As, E is the midpoint of DF.

Thus,

DE = EF

Pu the values.

6x + 1 = 7x - 4

On solving.

x = 5

Put the values in the lines.

DE = 6x + 1

DE = 6×5 + 1

DE = 31 units.

EF = 7x - 4

EF = 7×5 - 4

EF = 31 units.

DF = DE + EF

DF = 31+ 31

DF = 62 units.

Thus, the values for the line segment are obtained.

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Total cost function is C=42000+21t

Revenue function is R=45t

Profit function is P=24t-42000

The breakeven number of hours is 1,750

What is the total variable cost per hour of operating the truck?

The total variable cost per hour of operating shingle delivery truck is the sum of the hourly fuel and maintenance cost and the hourly rate of the operator

total variable cost per hour=$9.50+$11.50

total variable cost per hour=$21.00

The liner equation  formula for total cost is as shown below:

y=a+bx

y=total cost=C

a=fixed cost=cost of truck=42000

b=total variable cost per hour=21

x=number of hours the truck is operated=t

C=42000+21t

The total revenue is the customer charge per hour multiplied by number of hours

R=45t

P=R-C

P=45t-(42000+21t)

P=24t-42000

The breakeven number of hours is achieved at the point where the total cost is the same as revenue

45t=42000+21t

45t-21t=42000

24t=42000

t=42000/24

t=1,750 hours

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Answer:

The smallest number that Aleena could be thinking of is 2.75.

The arithmetic mean an of the given terms a_{n-1}=7, a_{n+1}=1  is

a (n) = -3.

a_{n-1}=7, a_{n+1}=1  

a(n) =(1-7)/2

a (n) = -3

The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.

The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).

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The coordinate of intersection with the x-axis is: (-3, 0).

The coordinate of intersection with the y-axis is: (0, 6).

The area of the triangle is 9 unit²

A linear equation is defined as an equation in which the highest power of the variable is always one.

The linear equation is given as:

y = 2x+6

Intersection with the y-axis

Substitute, x = 0

⇒ y = 2x + 6

⇒ y = 2(0) + 6

⇒ y = 6

As a result,: y = 2x+6 intersects with the y-axis at (0, 6)

Intersection with the x-axis

Substitute, y = 0

⇒ y = 2x + 6

⇒ 0 = 2x + 6

⇒ 2x =  - 6

⇒ x = - 3

As a result,: y = 2x + 6 intersects with the x-axis at: (-3, 0)

The area of the right-angled triangle

The area is calculated as:

Area of triangle = 1/2×Base×Height

Area of triangle = 1/2×3×6

Area of triangle = 9 unit²

The coordinate of intersection with the x-axis is: (-3, 0).

The coordinate of intersection with the y-axis is: (0, 6).

The area of the triangle is 9 unit²

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The equation of line tangent is y-35x+30=0.

What is tangent of a line?

A tangent line to a circle is a line that touches the circle exactly one time in Euclidean plane geometry and never enters the interior of the circle. Tangent lines to circles are the focus of various theorems and are crucial to numerous geometric structures and mathematical arguments.

Given equation y=2x+33x-2

                       =>y=35x-2

General slope intercept form is y=mx+b

Comparing and we get m = 35

The equation of tangent is y-5=35 (x-1)

=> y-5=35x-35

=> y=35x-35+5

=>y-35x+30=0

Therefore, the equation of line tangent is y-35x+30=0.

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The value of x is 27/4

Given that [tex]\frac{x}{3}-2=\frac{1}{4}[/tex]

So, we will start by

Finding common denominator and combining them

[tex]\frac{x}{3}-2=\frac{1}{4} \\\frac{x}{3}+\frac{3(-2)}{3}=\frac{1}{4}[/tex]

[tex]\frac{x+3(-2)}{3}=\frac{1}{4}[/tex]

[tex]\frac{x-6}{3}=\frac{1}{4}[/tex]

then cross multiplying them

[tex]4(x-6)=1(3)\\4x - 24 = 3[/tex]

Add 24 to both sides

4x-24=3

4x - 24 + 24 = 3 + 24

Simplify Add the numbers

4x=27

Divide both sides by the same factor

4x=27

[tex]\frac{4x}{4}}=\frac{27}{4}}[/tex]

Simplify and Cancel terms that are in both the numerator and denominator

[tex]x=\frac{27}{4}[/tex]

So, the value of x for the given is x = 27/4.

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The value of x for the equation [tex]\frac{x}{3}-2 =\frac{1}{4}[/tex] is 27/4

Given that [tex]\frac{x}{3}-2 =\frac{1}{4}[/tex]

So, we will start by

Finding common denominator and combining them

[tex]\frac{x}{3}-2 =\frac{1}{4}\\\frac{x-6}{3} =\frac{1}{4}\\[/tex]

[tex]4({x-6}) =3({1})\\\\4x - 24 = 3\\[/tex]

Divide both sides by the same factor

[tex]4x - 24 + 24 = 3 +24\\x = \frac{27}{4}\\\\Simplify \ Add \ the \ numbers\\4x=27\\x=\frac{27}{4}[/tex]

So, the value of x for the given is x = 27/4.

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Statement in step 8 is the proof that <ABD and <EBC are complementary angles.

An angle in mathematics refers to an arc that joins two points. For angles to be formed there should be two points, the starting point and the ending point. In some cases the starting point coincides with the ending point, in this case the angle formed is 360 degrees which is equivalent to a circle. We can hence say that angle in a circle is 360 degrees

When angles are formed by two points in the same straight line or say two colinear points the angle formed here is 180 degree. Hence we say angles in a straight line is 180 degrees.  In a case where a line intersects the straight line, the intersecting line bisects the the angle in a straight line. The sum of the two angles formed is 180 degrees. Such angles are said to be supplementary angles.

Assuming the bisector of the straight line in a perpendicular bisector, here the angle 180 is divided into two equal parts then each angle is 90 degrees.

When angle 90 degrees is bisected two different angles are formed. The sum of these two angles are known as complementary angles.

Hence angle <ABD and <EBC are complementary angles formed from bisecting angle <DBC which is 90 degrees or a right angle triangle

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Answer:

how are you doing where you can do it for 5 Pts

Step-by-step explanation:

A ratio shows us the number of times a number contains another number. If the ratio between their radii of two circles is 2, then the ratio of their circumference will also be equal to 2.

A ratio shows us the number of times a number contains another number.

Given that the ratio of the radius of two circles is 2. Therefore, we can write the ratio as,

Now, a conjecture that can be made regarding the ratio of the circumference of the circle is that the ratio of the circumference of circle A and circle B will also be 2.

Further, let's check the ratio of the circumference of the circle.

The ratio of the circumferences can be written as,

Circumference of the circle A/Circumference of the circle B = 2πk / 4πk

Circumference of the circle A/Circumference of the circle B = 1/2

Hence, If the ratio between their radii of two circles is 2, then the ratio of their circumference will also be equal to 2.

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