The length of a rectangle is the sum of the width and 1. the area of the rectangle is 30 units. what is the width,in units, of the rectangle

Answer:

2x^2 -x -10 is the answer as a product

3x-3 as a sum

Step-by-step explanation:

Assuming (2x-5)(x+2)=0

Let's distribute.

(2x^2+4x)(-5x-10)=0

Then combine like terms

2x^2 -x -10 is the answer as a product

3x-3 as a sum

Answer:

Domain = { -2 , 0 , 2 , 4 }

Range = { 3 }

Step-by-step explanation:

Domain is the x-values that the Function have and Range is the y-values that the Function have corresponding to these x-values

Since the x-values for the Function attached are -2 , 0 , 2 , 4

and the y-values for the Function is 3

Then the Domain = { -2 , 0 , 2 , 4 }

and the Range = { 3 }

Glad to Help

The dimension of the box will be (40 inch × 40 inch × 10 inch).

How to determine the maximum and minimum values of an expression using differentiation?
Any given expression can have both minimum and maximum outcomes for any number in a real world scenario, which can be determined using differentiation; first order differentiation when equated to zero reveals the value that will solute to produce the maximum or minimum and then the upon differentiating the obtained expression again and then substituting the variable in acceptable positions, if the outcome is a positive number then the obtained number in first differentiation suggests a minimum value of the given expression.

Given, the volume of the box described = 4000 inch³
Let the dimension of the base of the box be = 'a' inch × 'a' inch = a² inch²
Therefore, height of the box = (4000 inch³)/(a² inch²) = (4000/a²) inch
Total surface area of the described box = S = a² + [4a×(4000/a²)]
= [a² + 16000/a] inch
For the limiting values of S, dS/da = 0 ⇒ d[a² + 16000/a]/da = 0
⇒ 2a - [16000/a²] = 0 ⇒ 2a = 16000/a² ⇒ a³ = 8000 ⇒ a = ∛8000 = 20
Therefore, the value of a is 20 inch.
Thus, height of the box = 4000/a² = 4000/400 = 10 inch
For S to have the minimum limited value, d²S/da² > 0 for a = 20 inch, which is satisfied by the available value of S.
∴ The minimal surface area = a² + 16000/a = 400 + (16000/400)
= 440 inch²
We are aware that the least amount of material will be needed to build the box when its overall surface area is the smallest.
Thus, to minimize the amount of material in consideration, the dimension of the box will be (40 inch × 40 inch × 10 inch).

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The new mirror must have at least 81 cm² of the area.

The area of the square is defined as the product of the length and width.

As per the given question, we have

Dominic requires a new bicycle mirror. His old mirror was a square with a 9-cm side length.

He wants the replacement mirror to have an area that is as near to his previous bike mirror as feasible.

We have to determine the area of the previous bike mirror.

The area of the previous bike mirror = (side length)²

The area of the previous bike mirror = (9)² = 9 x 9

The area of the previous bike mirror = 81 cm²

So the new mirror must have greater than 81 cm² of area.

Thus, the new mirror must have at least 81 cm² of the area.

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Answer:

5 cm

Step-by-step explanation:

hope this helps

Answer: -64

Step-by-step explanation:

(8−2 • 35)−2

8-70-2

8-72

-64

Answer:

(8 - 2 • 35) - 2 = -64

Step-by-step explanation:

Given problem,

→ (8 - 2 • 35) - 2

Let's solve the problem,

→ (8 - 2 • 35) - 2

→ (8 - (2 × 35)) - 2

→ (8 - 70) - 2

→ -62 - 2

→ -64

Hence, the answer is -64.

The probability that Sara will pick a blue marker is 3/20.

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math's to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given,

the box contains red markers = 5

blue marker = 3

purple marker = 9

pink markers = 3

Total number of markers = 20

The probability that she picks blue marker = 3/20

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Answer:

The range of the data set is 16.

Step-by-step explanation:

The range of a box plot is the difference between the maximum and minimum value. To find the range of the given box plot, we can simply subtract the value located at the lower whisker from the value located at the upper whisker.

18 - 2 = 16

Hope this helps :)

Using the concepts of statistics, we got that 2004 is the sample size needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence.

The number of observations used to calculate estimates for the certain population is known as the sample size. The sample size was actually determined by drawing from the population. Sampling is a practice of choosing a portion of a population from which to draw conclusions about the characteristics of a entire population. A subset of the population is chosen for analysis based on the number of entities in it.

We have  Margin of error(E)=0.02,

Significance level([tex]\alpha[/tex])=0.01

Proportion(p)=0.13

Therefore, q is defined by =1-p

                =>  q =1-0.13

                =>q=0.87

So, the Z-score is 2.582

Now, we know that sample size(S) is given by

                =>S =[ [ [Z²×p×(1-p)] / e²] / [1+(Z²×p×(1-p)/e²)] ]

               =>S=[ [ ( 2.582)²×0.13×0.87/(0.02)²] / [1 + [(2.582)²×0.13×0.87] / (0.02)²]

               =>S= ([0.754/0.0004] / [1+(0.754/0.0004)])×1000

               =>S=([885.01] / [1+1885.01]) × 1000

                =>S=(0.200351)×1000

                =>S=2003.51=2004 (approx)

Hence, a federal report indicated that 13% of children under age 6 live in poverty in Massachusetts, an increase over previous years in that case size of  sample which is needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence is 2004.

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Answer:

sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1

Answer:

[tex]\textsf{Quotient}: \quad 2i^3+4i^2-5i+6[/tex]

[tex]\textsf{Simplified Quotient}: \quad 2-7i[/tex]

Step-by-step explanation:

Long division method

Given rational expression:

[tex]\dfrac{2i^4-6i^3-25i^2 +31i-30}{i -5}[/tex]

Solve using long division:

[tex]\large \begin{array}{r}2i^3+4i^2-5i+6\phantom{)}\\i-5{\overline{\smash{\big)}\,2i^4-6i^3-25i^2 +31i-30\phantom{)}}}\\{-~\phantom{(}\underline{(2i^4-10i^3)\phantom{-b00000000000.)}}\\4i^3-25i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(4i^3-20i^2)\phantom{))))))))))))}}\\-5i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(-5i^2+25i)\phantom{........}}\\6i-30\phantom{)}\\-~\phantom{()}\underline{(6i-30)\phantom{}}\\0\phantom{)}\end{array}[/tex]

Therefore, the quotient is:

[tex]2i^3+4i^2-5i+6[/tex]

Imaginary number rule

[tex]i^2=-1[/tex]

Simplify the quotient:

[tex]\implies 2i^3+4i^2-5i+6[/tex]

[tex]\implies 2i^3+4(-1)-5i+6[/tex]

[tex]\implies 2i^3-4-5i+6[/tex]

[tex]\implies 2i^3-5i-4+6[/tex]

[tex]\implies i(2i^2-5)+2[/tex]

[tex]\implies i(2(-1)-5)+2[/tex]

[tex]\implies-7i+2[/tex]

[tex]\implies 2-7i[/tex]

Answer:

£250

Step-by-step explanation:

Divide $405 by $1.62 which is 250.

Multiply that by £1 which is £250.

Answer:

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

the label are marked by numbers

The actual area represented by 3.5-inches-by-10-inches on map is 995.5 miles.

As the measure of 3/4 inch is provided, working out the calculation for 1 inch.

3/4 inch = 4 miles

1 inch = (4×4)/3

1 inch = 16/3

1 inch = 5.33 miles

Now, the actual area of the region = 3.5 × 10

The actual area of the region = 35 inches²

Converting the area in square miles

The actual area of the region = 35 × (5.33)²

Taking square on Right Hand Side of the equation

The actual area of the region = 35 × 28.4

Performing multiplication on Right Hand Side of the equation

The actual area of the region = 995.5 square miles

Thus, the actual area of the region is 995.5 square miles.

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The amount that Omar will pay when he bought 3.5k of onions are 8.90 per kilo is $31.15.

From the information given, Omah wants to know the total amount that he will pay for the onions. It's important to know the cost for each kilogram of onion and then multiply it but the number of kilograms that are bought.

In this case, Omar bought 3.5k of onions are 8.90 per kilo.

The amount that Omar will pay for the onions will be:

= Number of kilograms × Cost per kg

= 3.5 × 8.90

= $31.15

In conclusion, the amount is $31.15.

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Answer:

Divide by Three Trick

This is a fun trick. If the sum of the digits in a number can be divided by three, then the number can as well.

Examples:

1) The number 12. The digits 1+2=3 and 12 ÷ 3 = 4.

2) The number 15. The digits 1+5 = 6, which is divisible by 3. It turns out that 15 ÷ 3 = 5

Step-by-step explanation:

There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.

a. Find the percentage of marbles that are not blue.

100% - 40% = 60%

b. Find the number of marbles that are not blue​.

60% = 0.6

0.6 * 185 = 111 marbles

Total amount that Mikaela spent on the paddleboard is 578.5065.

According to given data,

original price = 899$ and 40% off.

state tax rate is 7.25%.

Solution:-

Applying formula,

⇒ 899 × (7.25% + 1) × (1 - 40%)

⇒ 899 × 1.0725 × 0.6

⇒ 578.5065.

Total amount that Mikaela spent on the paddleboard is 578.5065.

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Answer:

1 piece = 1 slice then the answer is 4/3 = $1.33 (still … 3 slices will be $3.99 rounded to 4). A pizza costs £5.50 and fries cost £1.00, John orders 3 pizzas and 5 fries but the …

Answer:

Neither of them are solutions unless you had a typo in the question.

Step-by-step explanation:

1) plug in the known values into both of the equations

First Coordinate:

y-x[tex]\leq[/tex]-5
(1)-(0)[tex]\leq[/tex]-5
1[tex]\leq[/tex]-5 which is not true.
In this case, we do not need to plug in (0,1) into both of the equations because the coordinate cannot be a solution unless the coordinate works in BOTH of the equations.

Second Coordinate:

1)  y-x[tex]\leq[/tex]-5
(-6)-(-1)[tex]\leq[/tex]-5

(-6)+1[tex]\leq[/tex]-5 -->    It becomes a +1 because two negatives make a positive

-5 [tex]\leq[/tex]-5 - -> which means this is true because -5 is less than or equal to -5

2) y-2x>-5
(-6)-2(-1)>-5

-6(2)>-5
-12>-5 NOT TRUE

ANSWER: Neither of them are solutions unless you had a typo in the question.

Answer:

length = 13 cm , width = 14 cm

Step-by-step explanation:

let the length be n , then the width is n + 1

the perimeter (P) of a rectangle is calculated as

P = 2(l + w) ← l is the length and w the width

given P = 54 , then

2(n + n + 1) = 54 ( divide both sides by 2 )

2n + 1 = 27 ( subtract 1 from both sides )

2n = 26 ( divide both sides by 2 )

n = 13

n + 1 = 13 + 1 = 14

so, length = 13 cm and width = 14 cm

The linear function with f values f(0) = -3 and f(7) = 11 is f(x) = 2x - 3

linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain it in the same linear function condition.

if f(0) = -3, it means at x = 0, f(x) = -3

and if f(7) = 11, it means at x = 7, f(x) = 11

So the Linear equation that will yield these results is f(x) = 2x - 3

In conclusion, the Linear function is f(x) = 2x - 3

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The number of terms in the expression 5x - 2 is 2

The number of terms in an expression or equation refers to the values separated by a mathematical operator. A mathematical operator could be

The terms can be like terms or unlike terms

The two terms given is separated by the subtraction operator and are both unlike terms

The first term 5x consist of

The second term is just a constant which is 2

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The final answer of the given quadratic equation is 2x - 3y + 7= 0.

What is the quadratic equation?

Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.

We have,

                 2x = 3y - 7

Converting the given equation in the form of ax + by + c = 0, we get

                 2x - 3y + 7= 0

Hence, the final answer of the quadratic equation is 2x - 3y + 7= 0.

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14 people can go to the amusement park. Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.

Inequality: 33p + $12.50 ≤ $465

14 people can go to the amusement park

Inequality:

$465= Amount of money they have

$12.50= Parking Cost

$33= Cost of tickets per person

Because they only have $465, they can't spend more than that amount.

Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (aka x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:

33p+ $12.50 ≤ $465

$465- $12.50 = $452.5 (452.5 is how much is left for tickets after subtracting the parking cost)

$33 x1 4 = $462 (14 tickets can be bought for the price of $33)

$462 - $452.5 = $9.5 (9.5 isn't enough for another person)

So, the solution to the inequality is 14 people can go to the amusement park.

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Answer: 45.5p is less than or equal to 465

Probability that the professional other than Tokyo, Kyoto or Osaka is 6803/13839.

Total number of professional train pushers who are diagnosed with carpal tunnel is 13839

Number such professional from Tokyo = 2551

Number such professional from Osaka = 3049

Number such professional from Kyoto = 1436

So, number such professional from other than these three cities = 13839 - (2551+3049+1436) = 6803

Hence the probability that the professional other than Tokyo, Kyoto or Osaka is = 6803/13839

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The vertex is at (8, -2).The point (10, -22) is also on the parabola.

Step-by-step explanation:

Here is the graph of the function:

The vertex is at (8, -2).

To plot another point on the parabola, we can choose any x-value and plug it into the equation to solve for y.

For example, if we choose x = 10, then we have:

f(x)   = -5(x - 8)² - 2

f(10) = -5(10 - 8)² - 2

f(10) = -5(2)² - 2

f(10) = -5(4) - 2

f(10) = -20 - 2

f(10) = -22

So, the point (10, -22) is also on the parabola.

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