A 42-inch string is to be cut so that one piece is 7 inches longer than the other. what is the length of the shorter piece? the shorter piece has a length of __ inches.

Answer:

X = 4

Step-by-step explanation:

The value in Mexican pesos of an item that costs 15 Chinese yuan is 0.474 x.

x yuan to y dollars = f(x)

f(x) = 0.15 x

y dollars to x yuan =

y= 0.15 x

x =  [tex]\frac{y}{0.15}[/tex]

y dollars to x pesos =g(y)

g(y) =14.07 y

x pesos to y dollars

x = 14.07 y

y = [tex]\frac{x}{14.07}[/tex]

Substituting the result of second into first,

pesos → dollars → yuan

Lets call this function, h(x) = converts x pesos into y yuan.

h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15

= 0.474 x

To learn more about function, refer

https://brainly.com/question/20811155

#SPJ4

Real and complex zeros of a polynomial function can be find as:

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. For example, 2x+5 is a polynomial that has exponent equal to 1.

Given:

We have to find all real and complex zeros of a polynomial function.

first convert the polynomial to factored form. Once all factors are found, set each individual factor equal to zero to solve for the real zeros

So, according to fundamental theorem of Algebra

It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.

A complex zero is a complex number that is a zero of a polynomial. For example, i (the square root of negative one) is a complex zero of the polynomial x² + 1, since i² + 1 = 0.

Learn more about Polynomial function here:

https://brainly.com/question/22256909

#SPJ1

Answer:

x = -7

Step-by-step explanation:

to solve this first subtract 5 to both sides

5 - x - 5 = 12 - 5

- x = 7

now multiply -1 to both sides

-x(-1) = 7(-1)

x = -7

that is your answeer

After solving the given inequality the answer is x∈(-∞, 1].

To solve the inequality:

Given: 2(4)x⁺³≤8

Then,

[tex]\begin{aligned}&2 \cdot 4 x^3 \leq 8\\&8 x^3 \leq 8\\&8 x^3+(-8) \leq 8+(-8)\\&8 x^3-8 \leq 8-8\\&8 x^3-8 \leq 0\\&2^3 \cdot x^3-2^3 \leq 0\\&2^3\left(\frac{2^3 \cdot x^3}{2^3}-\frac{2^3}{2^3}\right) \leq 0\\&8\left(x^3-1\right) \leq 0\\&x^3-1 \leq 0\\&x^3-1^3 \leq 0\end{aligned}[/tex]

Then,

[tex]\begin{aligned}&(x-1)\left(x^2+x+1\right) \leq 0\\&\left\{\begin{array}{l}x-1=0 \\x^2+x+1=0\end{array}\right.\\&\left\{\begin{array}{l}(x-1)+1=1 \\x_1=\frac{-1+\sqrt{1-4}}{2} \\x_2=\frac{-1-\sqrt{1-4}}{2}\end{array}\right.\\&\left\{\begin{array}{l}x-1+1=1 \\x_1=\frac{-1+\sqrt{-3}}{2} \\x_2=\frac{-1-\sqrt{-3}}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=\frac{-1+\sqrt{3} \cdot \sqrt{-1}}{2} \\x_2=\frac{-1-\sqrt{3} \cdot \sqrt{-1}}{2}\end{array}\right.\end{aligned}[/tex]

So,

[tex]\begin{aligned}&\left\{\begin{array}{l}x=1 \\x_1=\frac{-1+\sqrt{3} \cdot i}{2} \\x_2=\frac{-1-\sqrt{3} \cdot i}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=-\frac{1}{2}+\frac{\sqrt{3}}{2} i \\x_2=-\frac{1+\sqrt{3} \cdot i}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=-\frac{1}{2}+\frac{\sqrt{3}}{2} i \\x_2=-\frac{1}{2}-\frac{\sqrt{3}}{2} i\end{array}\right.\\&\left\{\begin{array}{l}x \leq 1 \\x \geq 1\end{array}\right.\end{aligned}[/tex]

So, finally, it gives:

[tex]2 \cdot 4 x^3 \leq 8\\2 \cdot 4 \cdot 0^3 \leq 8\\\begin{aligned}&x \leq 1 \\&x \in(-\infty, 1]\end{aligned}[/tex]

Therefore, after solving the given inequality the answer is x∈(-∞, 1].

Know more about inequality here:

https://brainly.com/question/24372553

#SPJ4

Answer:

61

Step-by-step explanation:

The volume of the triangular prism that is 16 ft long is calculated as: 288 ft³

A triangular prism has two triangular bases. The volume of the triangular prism can be found by using the formula below:

Volume of triangular prism = 0.5 * b * h * L, where:

Given the parameters below:

Length of the the base of the triangular face (b) = 4 ft

Height of the triangular face (h) = 9 ft

the length is triangular prism (L) = 16 ft

Volume of the triangular prism = 0.5 * 4 * 9 * 16

Volume of the triangular prism = 288 ft³

Learn more about the triangular prism on:

https://brainly.com/question/1284982

#SPJ1

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{(~~ 4- 0~~)^2 + (~~ -1- 3~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 4 )^2 + ( -4)^2}\implies \boxed{BC=\sqrt{32}}[/tex]

[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) ~\hfill CE=\sqrt{(~~ 2- 4~~)^2 + (~~ -3- (-1) ~~)^2} \\\\\\ ~\hfill CE=\sqrt{( -2)^2 + ( -2)^2}\implies \boxed{CE=\sqrt{8}} \\\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad F(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ -2- 2~~)^2 + (~~ 1- (-3)~~)^2} \\\\\\ ~\hfill EF=\sqrt{( -4)^2 + ( 4)^2}\implies \boxed{EF=\sqrt{32}}[/tex]

[tex]F(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill FB=\sqrt{(~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill FB=\sqrt{( 2)^2 + ( 2)^2}\implies \boxed{FB=\sqrt{8}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter} }{\sqrt{32}+\sqrt{8}+\sqrt{32}+\sqrt{8} ~~ \approx ~~ \text{\LARGE 16.97}}[/tex]

The value of x is 14 and the measure of angle J s 103

The given angles are external angles of parallel lines and a transversal

So, we have:

6x - 7 + 7x + 5 = 180

Evaluate the like terms

13x = 182

Divide both sides by 13

x = 14

Substitute x = 14 in J = 7x + 5

J = 7 x 14 + 5

Evaluate

J = 103

Hence, the value of x is 14 and the measure of angle J s 103

Read more about angles at:

https://brainly.com/question/25716982

#SPJ1

The values of x and angle J are 14 and 103 degrees respectively.

It is important to note that angles on a transversal line are supplementary, that is, they sum up to 180 degrees

Given the angles as;

Equate the angles

6x - 7 + 7x + 5 = 180

collect like terms

6x + 7x = 180 +2

13x = 182

Make 'x' the subject

13x/ 13 = 182/ 13

x = 14

But angle J = 7x + 5 = 7(14) + 5 = 98 + 5 = 103

Thus, the values of x and angle J are 14 and 103 degrees respectively.

Learn more about supplementary here:

https://brainly.com/question/12919120

#SPJ1

According to the linear equation , the number of visits Valeria must make to earn a free movie ticket is 14.

According to the statement

We have to find that the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

She receives 80 rewards points just for signing up.She earns 7.5 points for each visit to the movie theater.She needs 185 points for a free movie ticket.

then

The linear equation becomes:

The equation that can be used to represent the explanation given in the question is : 185 = 80 + 7.5x

Then

Combine similar terms

185 = 80 + 7.5x

185 -80 = 7.5x

105 = 7.5x

x = 105 /7.5

x = 14.

So, According to the linear equation , the number of visits Valeria must make to earn a free movie ticket is 14.

Learn more about linear equation here

https://brainly.com/question/4074386

#SPJ9

Answer:The probability would be 5 out of 12.

The value of  f(0) = 2 and f(-2) = -2 given the equation that we have in this image.

The function that we have here is given as

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

We have to find the value of f(-2)

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

= - 4 - 2 / -1(-3)

= -6 / 3

= -2

Hence  f(-2) = -2

Next we have to find f(0)

2(0) - 2 / (0 + 1) (0 - 1)

= -2 / 1 * -1

= -2 / -1

= 2

Hence we can say that the value of  f(0) = 2 and f(-2) = -2 given the equation that we have in this image.

Read more on functions here:

https://brainly.com/question/17043948

#SPJ1

The large square covers more

(See attachment below)

Explanation- The large square has the highest dimension and by extension, it has the highest area.

This means that, less large squares will be needed to cover more areas compared to other sizes of the squares

Area of the square =(side)².

square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle and a special kind of parallelogram.

By observation,

9 small squares are equivalent to one large square, implying that the 5 large squares are giving us 45 small squares.

4 small squares can fit into one medium square, implying that the 10 medium squares are giving us 40 small squares.

There are only 10 small squares.

Hence, the large square covers more of the plane

To learn more about Area of square

visit - https://brainly.ph/question/3596201

#SPJ9

Answer:

Step-by-step explanation:

Answer:

y = 8.40x

y = the total amount that he earned and x = the number of hours that he worked.

Step-by-step explanation:

The probability that a girl is chosen is 1/10 and the probability that a left-handed girl is chosen is 11/20.

Probability may be defined as the possibility of occurrence of an event. Probability of an event can be 0 or 1 but it can never be negative. If probability is 0 then the event will not occur and if probability is 1 then the event will definitely occur. Probability is given by the formula.

Probability = Favorable outcomes/Total number of outcomes.

Here, total number of outcomes = 20.

Now in the first case we need to find probability of picking a girl so favorable outcome is 2.

Probability of picking a girl = 2/20

Probability of picking a girl = 1/10

In the second case we need to find probability of picking a left-handed girl, so the favorable outcomes are 2 + 9 = 11 as total number of girls are 2 and total number of left-handed people are 9.

Probability of picking left-handed girl = 9 + 2/20

Probability of picking left-handed girl = 11/20

Thus, probability that a girl is chosen is 1/10 and the probability that a left-handed girl is chosen is 11/20.

Learn more about Probability at:

brainly.com/question/13604758

#SPJ9

The function y=0.0015(10)ˣ showcases exponential growth.

So,

Given function: y=0.0015(10)ˣ

If we put x = 1 as follows:

Then, if we put x = 2 as follows:

Hence, we see that 0.15 > 0.15.

Therefore, the function y=0.0015(10)ˣ showcases exponential growth.

Know more about exponential function here:

https://brainly.com/question/2456547

#SPJ4

The extraneous solution for the equation √3 x + 3 - 1 = x is x = - 1 ± √ 3.

We are given an equation:

√3 x + 3 - 1 = x

√3 x + 2 = x

Subtract 2 from both the sides, we get that:

√3 x = x - 2

Raise both sides to the power 2, we get that:

3 x² = x² + 4 - 4 x

2 x² = 4 - 4 x

x² = 2 - 2 x

x² + 2 x - 2 = 0

x = - 1 ± √ 3

Therefore, we get that, the extraneous solution for the equation √3 x + 3 - 1 = x is x = - 1 ± √ 3.

Learn more about equation here:

https://brainly.com/question/1214333

#SPJ4

Answer:

d=-2/3f+7

Step-by-step explanation:

Answer:

Step-by-step explanation:

rgvm

Answer:the answer is A haha

Step-by-step explanation:

i just did this kahn academy lesson-

Answer:

2/5+9+7+4+11 or 2/11

Step-by-step explanation:

2 is the smallest then we just add everything on the bottom together

Or just 2/11 since 2 is the smallest and 11 is the biggest

If you have a question ask

The product of 3.82 x 0.63 is 2.4066.

One of the four fundamental mathematical operations, along with addition, subtraction, and division .In mathematics refers to the continual addition of sets of identical size Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication is called as multiplication.

Given that,

The product of      

 3.82

x 0.63

 1146

2292 x

000 x  x

 2.4066

Therefore, the product of 3.82 x 0.63 is 2.4066.

To learn more about multiplication visit:

https://brainly.com/question/5992872

#SPJ9

The given quotient ( ∛8 x⁶ y¹² ) / ( √4 x⁴ y⁸ ) is x² y⁴.

This question can be easily solved by using the concept of roots. The two root terms mentioned in the question are ∛8 ( cubic root of 8 ) and  √4 (square root of 4 ). This question can be solved in 4 easy steps

Determining the power of the root and find the LCM of those numbers..

In this case, the powers of root for ∛8 and √4 are 3 and 2, respectively. Take LCM of 3 and 2.

LCM = 3 x 2 = 6

=> We get the LCM of 3 and 2 as 6.

Writing the given numbers as fractional powers.

∛8 = 8¹ˡ³  => The power of 8 = 1/3

√4 = 4¹ˡ²  => The power of 4 = 1/2

Step 3 : Multiply and divide the powers of the base number ( in this case 8 and 4 ) with a number such that you get the denominator as the LCM's ( in this case 6 )

1/3  can be multiplied and divided by 2 to get the denominator as 6

=> 1 * 2 / 3 * 2 = 2/6

1/2  can be multiplied and divided by 3 to get the denominator as 6

=> 1 * 3 / 2 * 3 = 3/6

Step 4 : Divide the two terms

6√8² x 6√4³ = 6√( 4 x 2 x 4 x 2 / 4 x 4 ) = 6√1 = 1

Also,  x⁶ y¹² / x⁴ y⁸ = x² y⁴

Therefore, using the concept of roots and fractions, we get The quotient ( ∛8 x⁶ y¹² ) / ( √4 x⁴ y⁸ ) as x² y⁴.

Learn more about Roots here:

https://brainly.com/question/16932620?referrer=searchResults

#SPJ9

The answer to the question is 1350.68

so we are given $500 is deposited at the start of the first year and the interest rate is 2 percent

so the interest =2/100×500 =$10

total amount =$510

we are given that $200 is deposited at the start of the next year, now total amount =$710

interest rate is 2 percent

so the interest =2/100×710 =$14.2

total amount =$724.2

we are given that  $600 is deposited at the start of the following year now total amount =1324.2

interest rate is 2 percent

so the interest =2/100×1324.2 =$14.2

total amount =$1350.68

Hence the answer is $1350.68

Learn more about percentage here:https://brainly.com/question/24877689

#SPJ9

Using the properties of logarithm the value of the expression is   [tex]log_{2}4 - log_{2}16 = -2[/tex]

We have been given two logarithm terms that is the first term is  [tex]log_{2}4[/tex] and second term is [tex]log_{2}16[/tex].

The propertied of logarithm that we are going to use are

          [tex]log a^{m} = m * log a[/tex]     and   [tex]log_{a} a = 1[/tex]

First we will find the value of the two terms and operate the above mentioned properties of logarithm to obtained the values of the logarithm.

Thus,

                [tex]log_{2}4 = log_{2}2^{2} \\ = 2* log_{2}2\\ = 2*1\\ = 2[/tex]         

Similarly,            

                 [tex]log_{2}16 = log_{2}2^{4} \\ = 4* log_{2}2\\ = 4*1\\ = 4[/tex]                          

Now subtracting both the terms by substituting its respective values which we have calculated above, we get

[tex]log_{2}4 - log_{2}16 = 2 - 4 = -2[/tex]

Thus the value of the expression is [tex]log_{2}4 - log_{2}16 = -2[/tex]

Learn more about logarithm here : https://brainly.com/question/10208274

#SPJ4

Rick paddles in still water at a rate of 6.5 mph. The rate of the current is 1.5 mph.

The rate at which an object moves from one point to another is also called speed. It can be measured by dividing the distance over time.

rate = distance/time

Let x = rate at which Rick paddles

c = rate of the current

If Rick paddles a kayak 20 miles upstream in 4 hours, and going upstream means the current is against your direction, then the equation for the travel is:

x - c = 20 miles/4 hours

x - c = 5     (equation 1)

If the return trip downstream takes him 2.5 hours, and downstream means that the current is going the same direction as you are, then the equation for the downstream travel is:

x + c = 20 miles/2.5 hours

x + c = 8     (equation 2)

Using elimination method, solve the two equations.

x + c = 8

x - c = 5

2x     = 13

x = 6.5

rate at which Rick paddles = 6.5 mph

Substitute x in equation 1 and solve for c.

x - c = 5     (equation 1)

6.5 - c = 5

c = 6.5 - 5

c = 1.5

rate of the current = 1.5 mph

Learn more about rate here: https://brainly.com/question/841956

#SPJ4

Inverse of the given function F(x) = 3 x³- 4 is F⁻¹(x) = ∛[ ( y + 4 ) / 3 ]

Given is a function of x, F(x) = 3 x³- 4

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = 3 x³- 4 becomes y =  3 x³- 4

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = 3 x³- 4, we get

x =  3 y³- 4

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x =  3 y³- 4

=> x + 4 = 3 y³

=> 3 y³ = x + 4

=> y³ = ( x + 4 ) / 3

=> y = ∛( x + 4 ) / 3

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = ∛( x + 4 ) / 3 becomes F⁻¹(x) = ∛( x + 4 ) / 3

Therefore, we get the inverse of the given function F(x) = 3 x³- 4 as F⁻¹(x) = ∛( x + 4 ) / 3

Learn more about Inverse of a Function here:

https://brainly.com/question/2541698?referrer=searchResults

#SPJ9

Answer:

The answer to your question is going to be c

Answer:

81 times.

Step-by-step explanation:

A dice has 6 sides.

The dice is fair, so each side has a 1/6 chance of being rolled.

The are 3 numbers greater than 3 - 4, 5 and 6.

Each of those numbers have a 1/6 chance of being rolled.

Together, their chance of being rolled is:

1/6 + 1/6 + 1/6 = 3/6 = 1/2

The dice is rolled 162 times.

162 x 1/2 = 81

Gordon should roll a number greater than 3 81 times.