The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 64 m find its length and width in meters

Answer:

x=y , x-3y=4. x = y x = y , x − 3y = 4 x - 3 y = 4. Replace all occurrences of x x with y y in each equation. Tap for more steps... −2y = 4 - 2 y = 4. x = y x = y. Divide each term in −2y = 4 - 2 y = 4 by −2 - 2 and simplify. Tap for more steps... y = −2 y = - 2.

Step-by-step explanation:

Just smart

Answer:

C) 29

Step-by-step explanation:

1st equation - 2nd equation,

x+y - (x-3y) = 40-(-4)

x+y-x+3y = 40+4

4y = 44

y = 44÷4

y = 11

substituting y into the first equation,

x + 11 = 40

x = 40-11 = 29

answer is C

hope it helps. :)

Step-by-step explanation:

that means that

$37.45 = 107%

as the price was 100% base price + 7% tax.

1% = 107%/107

100% = 1% × 100 = 107% × 100 / 107

so, the basic price (the "original cost") is

37.45 × 100/107 = $35.00

Answer:

Step-by-step explanation:

I

Answer:

a.  x = 1.75,  x = 4.25

b.  y = -7

c.  Maximum point at (3, 5).

d.  Domain:  (-∞, ∞)

e.  Range:  (-∞, 5]

f.  See attachment.

Step-by-step explanation:

Given function:

[tex]\text{f}(x)=-4|x-3|+5[/tex]

As per the question, use a graphing calculator to graph the given function.

The x-intercept(s) are the points at which the curve crosses the x-axis.

The y-intercept is the point at which the curve crosses the y-axis.

From inspection of the graph:

The domain of a function is the set of all possible input values (x-values).

The domain of the given function is unrestricted.

The range of a function is the set of all possible output values (y-values).

As the function has a maximum point at y = 5, the range is restricted.

Graph label the axes using a scale of 1 (see attachment).

Substitute x = 5 into the function to find the value of y at that point:

[tex]\begin{aligned}\implies \text{f}(5)&=-4|5-3|+5\\&=-4|2|+5\\&=-4(2)+5\\&=-8+5\\&=-3\end{aligned}[/tex]

Answer: first graph

Step-by-step explanation:

In  linear equation, option A,B,C are equal expect D .

What in mathematics is a linear equation?

The given equation is  3x -4y =21.

A.  (11, 3)

3(11) - 4(3) = 21

21 = 21 > equal

B.  (7, 0)

3(7) - 4(0) = 21

21 = 21 > equal

C.  (−1, −6)

3(-1) - 4(-6) = 21

21 = 21 > Equal

D.  (−3, 3)

3x – 4y = 21

3(-3) - 4(3) = 21

-21 = 21 > not equal

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12 ounces of water.

Total mass of the solution: 30 ounces.

Total mass of salt (solute): (30*0.07)= 2.1 ounces.

Total mass of water (solvent): (30*0.93) 27.9 ounces.

2. Find an equation that relates amount of water and percentage of salt.

Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:

[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.

Side note: The number "0.05" is 5% converted into a decimal.

[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]

42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.

12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.

Answer:

-4 is not a solution to the following equation.

Step-by-step explanation:

It you replace x with -4 on both sides of the equation you get -2=-12 and they are not equal to each other. Therefore, -4 is not a solution to the equation.

If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.

What is a value function?

The value function represents the optimal payoff of the system over the interval [t, t1] when started at the time- t state variable x(t)=x.

What is a variable?

A quantity that could take on any of a number of different values. : a sign that denotes a variable. : anything has a range. : a variable that might alter in a scientific experiment.

Here, we have

x = -4 and y = 3

then by putting the value of a function in a given equation, we get

1/2*(-4) + 3*(-4)*(3)²

= -110

Hence, If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.

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Step-by-step explanation:

T2= -6

T5=750

ar=-6

ar4=750

both a's cancel each other

we have;

r=-6

r4=750

r4-1(The law of indices) =750

r3=750

r=3√750

r=9.1

Using the t-distribution, it is found that:

a)

b)

The bounds of the confidence interval are given according to the rule presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are listed as follows:

The margin of error of the interval is:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

Then the interval can be interpreted as the sample mean plus/minus the margin of error.

For the confidence interval in this problem, using a calculator, the parameters are given as follows:

[tex]\mu = 1280.1111, s = 33.5799, n = 9[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 9 - 1 = 8 df, is t = 1.86.

Then the margin of error of the interval is:

M = 1.86 x 33.5799/sqrt(9) = 21.

Then the bounds of the interval are:

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The value of x in the rhombus is 24 units.

According to the question,

We have the following information:

LM = 2x - 9 and KN = x + 15 in rhombus KLMN.

Now, we know that in a rhombus opposite sides are equal. In this case, LM and KN are opposite sides.

So, we have the following expression:

2x-9 = x+15

Adding 9 to both sides of the equation:

2x = x+15+9

2x = x+24

Subtracting x from both sides of the equation:

2x-x = 24

x = 24

Hence, the value of x for the given rhombus is 24 units.

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Answer:

40%

Step-by-step explanation:

Answer:

d = 15

Step-by-step explanation:

(-5, 4), (4, -8)

(x₁, y₁)   (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4 - (-5))² + (-8 - 4)²

d = √(4 + 5)² + (-12)²

d = √(9)² + (-12)²

d = √81 + 144

d = √225

d = 15

I hope this helps!

Answer:

33.8ohms

Step-by-step explanation:

10A : 13ohm

26A : 33.8ohm

Answer:

D: 3x9/5

Step-by-step explanation:

the formula for dividing fractions is skip flip multiply where we keep the first term the same and then flip the second to multiply

Hopes this helps please mark brainliest

The 14th term of the geometric sequence will be -1220703125.

What is geometric sequence?

The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

[tex]1*(-5)^{13}[/tex]The terms are given, 1,-5,25

a = 1

r = -5/1 = -5

The 14th term will be= [tex]ar^{13}[/tex]

= [tex]1*(-5)^{13}[/tex]

= -1220703125

Hence, the 14th term of the geometric sequence will be -1220703125.

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The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.

Given,

In the question:

To see the figure:

To select the values that makes the inequality  s ≤ 4 true.

Number table are given in figure.

To see the figure and analysis.

Now, According to the question;

To make the inequality s ≤ 4 true.

The selected value must be less than 4 {Properties of Inequality}

The values are sorted from small to large:

So, The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.

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Answer:

kind423

Step-by-step explanation:

Answer: 2(1.9)+1.30x<10

Step-by-step explanation:

Orange= $1.30/lb

Pear= $1.90/lb

$1.30/lb = $y/2lb

y=1.30*2

y=$2.6 for 2lb of orange

So

She spent

2(1.30)+1.90x< $10

2.6+1.90x<10

1.90x<10-2.6

1.90x<7.4

x<7.4/1.90

x<3.89

According to 2(1.30)+1.90x< $10

2.6+1.90*3.89<10

9.991<10

The number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Enrique who has a pay-per-use plan on his cell phone. It costs $0.10 per minute talk, $0.20 per text message, and $0.25 per picture message. His total bill last month was $30.95. The total number of text and picture messages sent was 87. The cost for the use of minutes was $1.60 less than the cost of the text messages

Assume that [x], [y] and [z] represents the number of minute talk's, text message's and picture message's respectively. Then -

0.1x + 0.2y + 0.25z = 30.95         ..[1]

y + z = 87           ..[2]

0.1x = 0.2y - 1.6     ...[3]

We can write Eq[1] as -

0.2y - 1.6 + 0.2y + 0.25z = 30.95  

z = 87 - y

0.2y - 1.6 + 0.2y + 0.25(87 - y) = 30.95  

Solving, we get y = 72.

So z = 87 - 72 = 15

and

0.1x = 0.2 x 72 - 1.6

0.1x = 14.4 - 1.6

x = 128

Therefore, the number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.

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On average, Jaya drinks 0.46 ounces glasses of water does she drink in one hour.

Average:

Average refers the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

On average, Jaya drinks of a 6-ounce glass of water in 13 hours.

Here we need to find the number of glasses of water does she drink in one hour.

Let x be the number of glasses of water does she drink in one hour.

We know that, Jaya drinks of a 6-ounce glass of water in 13 hours.

So, in order to find the average we have to divide the number of glasses by the time taken.

So, it can be written as,

=> 6/13

=> 0.46

Therefore, for one hour Jaya drinks 0.46 ounces of water.

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The possible cards can be made 6719448100.

What is permutation & combination?

Subsets of a set can be created in two separate ways combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.

We have,

Letters must only be consonants = 26 - 5.

So, the total number of consonants are 21.  

There are 21 choices for the first letter, 21 choices for the second letter,  21 choices for the thirds letter,  21 choices for the fourth letter. For each of these letters, therefore 21 × 21 × 21 × 21 = 194481 possible pairs of letters.

There are 10 possibilities for the first digit & 10 possibilities for the second. therefore there are 10 x 10 = 100 different numbers.

Combining these results, it follows that there are 67194481 x 100 =  6719448100 different cards.

Hence, The possible cards can be made 6719448100.

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Answer:

Line v:  y = x + 5

Step-by-step explanation:

Given two lines are perpendicular and the equation of one line, we use the following formula to find the slope of the other line where m1 is the slope of the line we're given and m2 is the slope of the line we want to find:

[tex]m_{2}=-\frac{1}{m_{1} }\\m_{2}=1[/tex]

The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept.  

Therefore we plug in our slope and the point (-3, 2) to find the y-intercept of line v:

[tex]2=1(-3)+b\\2=-3+b\\5=b[/tex]

The distance (in ft) that the car will travel in the first 10 seconds is 16.8 feet.

Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, you can calculate the average speed of an object.

The speed formula is speed = distance/time.

We have been given certain vehicles that can accelerate from a standing start to a speed of v(t) = −0.24t² + 12t feet per second after t seconds (for 0 ≤ t < 30).

Then the distance that it will travel from its starting point in the first t seconds is;

[tex]\int\limits^{30}_b {v(t) } \, dx \\\\\\\int\limits^{30}_b {-0.24t^2 + 12t } \, dt \\\\\\\int\limits^{30}_b {-0.48t + 12} \, dt \\\\-0.48(30) + 12\\\\14.4 + 12 = 26.4[/tex]

At zero it will be 12 feet.

b. the distance (in ft) that the car will travel in the first 10 seconds.

-0.48(10) + 12 = 16.8 feet.

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Using the stem-and-leaf plot, the mean of the data is 3.85.

It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.

To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values and divide by the number of values that was represented on the stem-and-leaf plot.

Given the stem-and-leaf plot above, using the key, the data points represented are:

2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5

Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12

Mean = 46.2/12

Mean = 3.85 feet

The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.

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The Answer is:

3.85 ft.
* *

-

The Z distribution also referred to as the standard normal distribution is the distribution that we would have to use here.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.

By transforming the values of any normal distribution into z-scores, it is possible to standardize it. Z-scores indicate the number of standard deviations from the mean that each value falls within.

This is the z distribution given that the value of n is more than 30.

We have to make use of z when n which is the number of samples  is greater than 30.

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Answer: 1/6

Step-by-step explanation:

To subtract fractions, you must have a common denominator. To do this, the common multiple of 3 and 2 is 6. So 2/3 is multiplied by 2/2 and 1/2 is multiplied by 3/3. The multiplication is valid since we multiplied by one, it didn't alter the value but rather it put it into an alternate, equivalent form.

The total middle school enrollment is 889 for the given city.

According to the question,

We have the following information:

Three middle schools in a city had enrollments of 296,315 and 278.

Now, the total middle school enrollment can be easily found by adding the enrollments in three middle schools of the city.

So, we have the following expression:

Total middle school enrollment = 296+315+278

(We already know that the digits are first added from the right hand side and then we move to the left hand side.)

Total middle school enrollment = 889

Hence, the total middle school enrollment is 889 for the given city.

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Answer:

D. The denominator means three out of five are shaded

Answer:

Step-by-step explanation: First since the cookies are 36.44 dollars and the total spent is 102.44, use 102.44-36.44= 66 dollars

66/11=6 cupcake boxes

6 cupcake boxes + 1 cookie box = 7 boxes in total