The foot of an extenion ladder i 15 feet from the wall. The ladder i 7 feet le than three time longer than the height that it reache on the wall. What i the length of the ladder?

Table (D) represents a linear function which the graph has been attached below.

A linear function is defined as an equation in which the highest exponent of the variable is always one. In mathematics, independent and dependent variables are values that vary in relation to one another.

The table is given in the question, as an option (D)

x:  −2  −1   0    1    2

y:    3    1  −1  −3  −5

According to the above table, we plot the graph through the points then we can see that the graph of a function looks linear.

Thus, this table represents a linear function.

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Answer: 1

Step-by-step explanation:

Anything to the power of 0 is 1

The value of x  when y = 10 and Z = 16, in the given joint variation is: 1120.

If X varies jointly with Y and Z, then we can use the formula X = k * Y * Z, where k is the constant of proportionality.

Using the given information, we can find k by plugging in the values of Y, Z, and X and solving for k:

14 = k * 2 * 4

k = 14 / (2 * 4)

k = 7/2

Now that we know the value of k, we can use it to find the value of X when Y = 10 and Z = 16:

X = k * Y * Z

X = (7/2) * 10 * 16

X = 70 * 16

X = 1120

So the value of X when Y = 10 and Z = 16 is 1120.

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Period of deferral in the deferred annuity = 3 periods or 3 quarters.

Given: Quarterly payment of 300 for 9 years that will start 1 year from now.

To find the Period of deferral in the deferred annuity.

A deferment period is an agreed-upon time during which a borrower does not have to pay the lender interest or principal on a loan.

Solution: Formula for Period of deferral

K = nt - 1

K- Period of deferral

n- number of times compounded

t- time of start

K= nt - 1

K= 4(1) - 1

K= 3

Period of deferral = 3 periods / 3 quarters.

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There are 6 possible outcomes for this experiment.

The total number of outcomes possible for an experiment of drawing two balls one after the other without replacing the first ball, depends on the number of possible outcomes for the first draw, multiplied by the number of possible outcomes for the second draw, given that the first ball was not replaced.

The total number of ways to choose one ball out of three is 3, and the number of ways to choose the second ball out of two remaining balls is 2. Therefore, the total number of outcomes possible for this experiment is 3 x 2 = 6.

The possible outcomes are:

(Red, Purple), (Red, Blue), (Purple, Red), (Purple, Blue), (Blue, Red) and (Blue, Purple)

It's important to notice that this method is called the Multiplication Rule for counting the total number of outcomes of two or more independent events.

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Answer:

Shown Below

Step-by-step explanation:

The difference between the two polynomials 3x^2-4x-5 and 2x^2-7x-3 is the result of subtracting the second polynomial from the first one.

3x^2 - 4x - 5 (first polynomial)

(subtraction operator)

2x^2 - 7x - 3 (second polynomial)

= x^2 - 3x - 2 (difference)

So the difference between 3x^2-4x-5 and 2x^2-7x-3 is x^2 - 3x - 2

This is a polynomial with a degree of 2 (quadratic) and the coefficient of x^2 is 1, x is -3 and the constant is -2.

By simplifying  45y/30y (7x+49)  this  we get 3 / 2(7x + 49).

45y/30y (7x+49)

45y / 30y(7x +49) : 3 / 2(7x + 49)

45y / 30y(7x + 49)

45y / 30(7x + 49)

Factor the number :45 = 15 . 3

=15.3 / 30(7x + 49)

Factor the Number : 30 = 15 . 2

15.3 / 15.2(7x + 49)

Cancel the common factor : 15

= 3 / 2(7x + 49).

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The graph that represents the situation is given in the attached image.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A gymnast joined a yoga studio to improve his flexibility and balance.

He pays a monthly fee and a fee per class he attends.

The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.

The graph of the linear equation is given in the attached image.

And the graph that is equivalent to the graph is also given in the attached image.

Therefore, the equivalent graph is given in the attached image.

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Answer: The front row has 4 fixed seats (s1, s2, s3, s4) and 5 open seats. The back row has 6 fixed seats (s5, s6, s7, s8, s9, s10) and 3 open seats. The remaining students (s11, s12, s13, s14, s15) can be placed in the open seats in the front row or the open seats in the back row in any combination.

The open seats in the front row can be filled by the remaining 5 students in 5! ways.

The open seats in the back row can be filled by the remaining 5 students in 5! ways.

So the total number of ways the students can be seated is (5!)^2 = 54321 * 54321 = 14400

Step-by-step explanation:

Answer:

hypotenuse = 14.8

Step-by-step explanation:

Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]

[tex]3.2^2 + 14.4^2 = c^2\\10.24 + 207.36 = c^2\\\sqrt{217.6} = c\\c = 14.751...\\c = 14.8[/tex]

The area of the base of the parcel box is given by the expression A=2x²+8x+6. The dimensions (length and width) are determined from this expression as (2x+2) and (x+3).

In general, the volume of a rectangular box is calculated by the product of the height, width, and length of the box. From the given hint, we can write the volume of the parcel box as a product of the height and the area of the base. This is written as,

[tex]\begin{aligned}V&=A\times h\\6x^2+24x+18&=A\times 3\\A&=\frac{1}{3}(6x^2+24x+18)\\A&=2x^2+8x+6\end{aligned}[/tex]

The above equation gives the area of the base

Now solving the above quadratic equation to find dimensions, we get,

[tex]\begin{aligned}A&=2x^2+8x+6\\&=2x^2+6x+2x+6\\&=2x(x+3)+2(x+3)\\&=(2x+2)(x+3)\end{aligned}[/tex]

The dimensions are (2x+2) and (x+3).

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For the graph with points (-2, 2) and (2,0), the slope, linear equation and y-intercept is m = -1/2, y = -1/2x + 1 and y = 1 respectively.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first graph shows the points (-2, 2) and (2,0).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[0 - 2]/[2 - (-2)]

(-2)/(2 + 2)

-2/4

-1/2

So, the slope point is obtained as m = -1/2.

The equation becomes - y = -1/2x + b

To find the value of b substitute the values of x and y in the equation -

2 = -1/2(-2) + b

2 = 1 + b

b = 2 - 1

b = 1

So, the value for b is 1.

Now, the equation becomes -

y = -1/2x + 1

To find the y-intercept substitute the value of x = 0 in the equation -

y = -1/2(0) + 1

y = 0 + 1

y = 1

Therefore, the slope is 1, equation is y = -1/2x + 1 and y-intercept is y = 1.

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Answer: I believe your x-intercept is (-7,0) and your y-intercept is (0,2)

Step-by-step explanation: I hope this helps! (It's kind of sad how this is the only bit of math I'm good at)

Volume of the cone with height 18 meters and radius 'r' is given by :

a. Equation to represents the volume of the cone is 6πr²( cubic meters).

b. Three possible examples:

r    (meters )         :       2        4        6

V (cubic meters ) :     24π     96π    216π

Height 'h' of the cone is 18meters.

Radius of the cone is 'r' meters.

a. Equation to represents volume of a cone as function 'r'

Volume 'V' of the cone is = ( 1 / 3 )π ×r² × h

Substitute value h = 18 meters we get,

V = ( 1 / 3 )π ×r² × 18

⇒ V = 6πr² cubic meters

b. Three possible examples for different values of 'r'

When r = 2

V = 6π × ( 2)²

⇒ V = 24π cubic meters

When r = 4

V = 6π × ( 4)²

⇒ V = 96π cubic meters

When r = 6

V = 6π × ( 6)²

⇒ V = 216π cubic meters

Therefore, the required volume of the cone with radius 'r' and height 18meters is:

a. Equation to represents volume is 6πr².

b. Table completion:

r    (meters )         :       2        4        6

V (cubic meters ) :     24π     96π    216π

The above question is incomplete , the complete question is:

There are many possible cones with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.

a. Write an equation that represents the volume V as a function of the radius r.

b. Complete this table for the function, giving three possible examples.

r :  2     _    _

V: ?     ?      ?

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Answer: b) ? · 2 5= 4

d) 4 ÷ 2 5= ?

e) ? ÷ 2 5= 4

The equations that represent the situation are b) ? · 2 5= 4 , d) 4 ÷ 2 5= ?, e) ? ÷ 2 5= 4

The question is asking for an unknown quantity and it is asking to find it by using the 4 and 25, so the equations that represent the situation are the ones that have 4 and 25 in them and have the unknown quantity on one side of the equation and the known quantity 4 on the other side.

a) 4 · 2 5= ? is not a valid equation as it is asking to multiply 4 and 25, which is known and doesn't have any unknown quantity.

c) 2 5÷ 4 = ? is also not a valid equation as it is asking to divide 25 by 4 and doesn't have any unknown quantity.

Step-by-step explanation:

Answer:

A quadratic equation of the form ax^2 + bx + c = 0 has solutions (or roots) that are either real or complex. The solutions of the equation vanish (or become equal to zero) when the equation is equal to zero.

For the equation x^2 (2p-4)x-(3q5)=0 to have a solution that vanishes, the discriminant (b^2 - 4ac) must be equal to zero.

Therefore, the roots of the quadratic equation x^2 (2p-4)x-(3q5)=0 vanish when p = 4 and q = 0

You may not cross a single broken white or yellow line, when doing so would interfere with traffic unless it is safe to do so and without interfering with traffic.  

The yellow line on the road serves as a barrier between opposing lanes of traffic as a traffic safety measure. It is intended to alert drivers to the fact that they are moving in the opposite directions and should keep a safe distance while driving.

The yellow line is typically placed in the centre of the road to indicate the separation of traffic. On highways and interstates, the yellow line is frequently used to mark the separation between two lanes of traffic moving in the same direction.

Drivers should always follow the yellow line and never cross it because doing so can be risky and result in accidents. The yellow line can also be used to show when passing other vehicles is dangerous.

On the driver's side, it is prohibited to pass other cars when a yellow line is interrupted by a solid line. Overall, the yellow line is an important safety measure for drivers to be aware of and obey when on the road.

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Step-by-step explanation:

The f O U r M U la is 72inc hes

Designs have the same fractions o black and white is 16/2

Given,

Four student, each with 2 distinct colors, and no two subsequent flag may share the same color. Hence, the first stripe may be colored in any of 4 different ways.

The second student can be colored in 4 different ways after it is not the same color as the first.

The third flag should not be the same color as the second; it can be colored in 4 different ways.

The fourth flag should not be the same color as the third, allowing for a total of 4 different color combinations. total = 4 * 2  * 2 = 16

designs have the same fractions o black and white is 16/2

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Answer:

c, 64 percent

Step-by-step explanation:

3+3+10+9=25

25-9(yellow)=16

25/16=64

Answer: D: 64%

Step-by-step explanation: 3 + 3 + 9 + 10 = 25, 3 + 3 + 10 = 16 (Alternative: 25 - 9) 16 / 25 = 64. So the answer is 64%

The measure of the angle m∠ABD is 100°.

What is the measure of angle?

In mathematics, an angle is defined as the amount of rotation between two lines or planes that share a common point. The measure of an angle is typically given in degrees or radians. A full rotation is equal to 360 degrees or 2π radians, and the size of an angle can range from 0 degrees (no rotation) to 360 degrees (a full rotation).

In the given figure, m∠ABC = 130° and m∠DBC = 30° is given.

And we have to find the m∠ABD

so

m∠ABC = m∠ABD + m∠DBC

130° = m∠ABD +  30°

m∠ABD =  130° -  30°

m∠ABD = 100°

Hence, the measure of the angle m∠ABD is 100°.

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After applying the sales tax, the expression for the total price of the phone is 1.03p.

What is sales tax?

The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a standard sales tax is imposed, collected by the shop, and paid to the government.

The amount for phone is represented as - p dollars and cents

The sales tax percentage is - 3% = 0.03

The sales tax applied on the phone is - 0.03p

The total price of the phone is denoted by the expression -

Total Price = Price of phone + Sales Tax

Total Price = p + 0.03p

Total Price = 1.03p

Therefore, the total price is obtained as 1.03p.

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Answer: 8/12

Step-by-step explanation:

First you multiply 1/6 with 1/2 that would give us 1/12

Then you add 1/12 with 7/12

Our answer would be 8/12

Answer:

2/3 or in Decimal its 0.6

Step-by-step explanation:

1/6x+7/12 when x= 1/2.

1/6(1/2)+7/12

Answer: A function that increases by a factor of 10 over every unit interval in x and starts at f(0)=1 could be represented by the function rule f(x) = 10^x.

This function starts at f(0) = 10^0 = 1 and for every increase of 1 in the input x, the output f(x) increases by a factor of 10. For example:

f(1) = 10^1 = 10

f(2) = 10^2 = 100

f(3) = 10^3 = 1000

and so on.

Another possible function rule could be f(x) = 10x +1 it starts at f(0) = 1 and for every increase of 1 in the input x, the output f(x) increases by a factor of 10. for example:

f(1) = 101 +1 = 11

f(2) = 102 +1 = 21

f(3) = 103 +1 = 31

and so on.

Both functions have similar behavior and answer the given conditions.

Step-by-step explanation:

There is a 0.81 Probability that the breakdown entails a gas leak. Given that there is a gas leak, there is a 0.63 percent chance that there is evidence of electrical failure. Given that there is evidence of an electrical failure, the likelihood of a gas leak is 0.77.

A)

Total number of  units

= 55 + 32 + 17 + 3

= 107

Hence the Probability that  failure involves a gas leak

= ( 55 + 32 ) / 107

= 0.8131

B) Probability that there is  a evidence of electrical failure given that there is a gas leak

P ( A / B ) = P( A∩B ) = 55/107 = 0.5140

P ( B ) = ( 55 + 32 ) / 107 = 0.8131

Hence P ( A / B ) = 0.5140 / 0.8131 = 0.6322

A = failure due to electrical

B = failure due to gas leak

C)  Probability of a gas leak given that there is evidence of electrical failure

P ( B / A ) =  P ( B ∩ A ) = 0.5140

P( A ) = ( 55 + 17 ) / 107  = 0.6729

Hence P ( B / A ) = 0.5140 / 0.6729 = 0.7639

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If a player who is off the field of play to receive medical treatment trips a player who is on the field of play , then (c) the referee cautions the player and the play is restarted with a indirect free kick.

On the field of play of football , the medical treatment of any player is not permitted under any circumstances.

When the player is bleeding, the player is required to leave the field immediately.

When the play has been restarted, only time the injured player is allowed to return to field of play is after game has started again.

It is exclusive responsibility of match referee to decide whether or not an injured player may return to the game.

The given question is incomplete , the complete question is

A player who is off the field of play to receive medical treatment trips a player who is on the field of play. what decision does the referee make?

(a) A. The referee shows a red card and sends off the player. Play is restarted with an indirect free kick.

(b) The referee shows a yellow card and cautions the player. Play is restarted with an indirect free kick.

(c) The referee cautions the player and Play is restarted with an direct free kick.

(d) The referee cautions the player and restarts with a dropped ball.

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Answer:

  (a)  A(x) = (12 -2x)√(3x -9)

Step-by-step explanation:

You want a formula for the area (a(x)) of an isosceles triangle with congruent sides of length x and perimeter 12. You also want its maximum value, and a graph and the maximum value of z = 2a(3x+3)+1.

Heron's formula for the area of a triangle with side lengths a, b, c is ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

Given a perimeter of 12, and two sides x, this becomes ...

  A(x) = √(6(6 -x)(6 -x)(6 -(12-2x))) = √(6(6 -x)²(2x -6))

  A(x) = 2(6 -x)√(3(x -3)) . . . . . . factor out perfect squares

  A(x) = (12 -2x)√(3x -9) . . . . . . domain: 3 ≤ x ≤ 6

The domain is such that the radical and the area are non-negative.

The derivative of the area function is ...

  [tex]A'(x)=-2\sqrt{3x-9}+\dfrac{3(6-x)}{\sqrt{3x-9}}=\dfrac{-2(3x-9)+3(6-x)}{\sqrt{3x-9}}\\\\A'(x)=\dfrac{-9x+36}{\sqrt{3x-9}}[/tex]

The derivative is zero at the maximum, so ...

  -9x +36 = 0   ⇒   x = 4 . . . . . . . an equilateral triangle

The maximum area is ...

  A(4) = (12 -2·4)√(3·4 -9) = 4√3

The maximum area is 4√3.

Since the maximum of A(x) is 4√3 at x=4, the maximum of 2A(3x+3) +1 will be ...

  2(4√3) +1 = 8√3 +1 . . . . . . . where 3x+3 = 4  ⇒  x = 1/3

The maximum of 2A(3x+3)+1 is 8√3 +1 at x = 1/3.

The function ...

  z = 2A(3x+3) +1 = 2A(3(x+1)) +1

Compare this to ...

  z = p·A(q(x -r)) +s

which is vertically expanded by p, horizontally compressed by q, then translated right r and up s.

We see that the parent function A(x) is vertically expanded by a factor of 2, compressed horizontally by a factor of 3, then translated left 1 and up 1.

Applying these transformations to the original A(x) domain and range, we find the domain is ...

  1/3[3, 6] -1 = [0, 1] . . . . . domain of z

And the range is ...

  2[0, 4√3] +1 = [1, 8√3 +1] . . . . . range of z

Therefore , the solution of the given problem of denominator comes out to be 36.55 is the correct option.

Common denominators are used to describe fractions with the same denominators. Take a look at the following instances: 1/2 + 1/2 = 1 and 3/4 + 1/4 = 1 The fractions' denominators are both common, making it simple to calculate the variable result in both situations.

Here,

Given :

=>29 + 151/20

=> 580 + 151/20

=> 731/20

=> 36.55

As a zero denominator would result in an infinite fraction, a finite fraction can never have a denominator of 0.

Therefore , the solution of the given problem of denominator comes out to be 36.55 is the correct option.

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Answer:

11.6%

Step-by-step explanation:

First, we have to find how much it increases

48 - 43 = $5

We know it increases by $5

Then we take

5 divided by 43, then times 100 = 11.6%

So, it increases 11.6%