The perimeter of a rectangle is to be no greater than 70 centimeters
and the width must be 5 centimeters. Find the maximum length of the
rectangle.

Answer: Using the pythaorean theoream we have to det

By cross multiplying the given equation, we have

By multiplying the right hand side, we get

Then, by subtracting 6x to both sides, we have

or equivalently,

Since the left hand side is a conjugate binomial, it can be expressed as

Then, we have the equation

Therefore, the values of x that make the equation true are x= 4 and x= -4

The value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k. Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Given Data

X 5 6 7 8

Y 1 2/3 2 2 1/3 2 2/3

Yes, the table shows proportional relationship.

Value of Y when X will be 10 is

x = 10

= 3[tex]\frac{1}{3}[/tex]

the value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].

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The shape of the distribution for the given dot plot is as follows:

The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.

A dot plot shows the number of times that each measure appears in the data-set.

In the context of this problem, we have that from the given dot plot, the measures are as follows:

62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.

The mean is the sum of all observations divided by the number of observations, hence, applying it's formula, it is given by:

74.55.

The median is the middle value of the data-set, the value of which 50% of the measures are greater and 50% are less. The data-set in this problem has 20 elements, hence the median is the mean of the 10th and the 11th elements, which are 72 and 75, respectively, hence:

Median = (72 + 75)/2 = 73.5.

The median is less than the median, hence the distribution is skewed to the right, which means that the third option is correct.

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Answer:

The data is not symmetrically distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.

Step-by-step explanation:

its not skewed right and this is the next one that makes sense

Given that tanθ = 3.2603 where π < θ < 3π/2

From the calculation the value of θ = 72.95, hence the correct the error by adding 180

because it dint dnt fall in the range of

And to correct the error add 180 to their answer,

Hence the value of θ = 180 + 72.95 = 252.95 degree

EXPLANATION

Let's see the facts:

Length = 4*longer leg

Shorter leg of the base= 1/2 longer leg

We know that Volume = 5832 = 1/2* length* longer leg* shorter leg

Let's call x to the longer leg, the variables are:

length= 4*longer leg= 4x --> x is the longer leg

Shorter leg= 1/2longer leg= 1/2x --> x is the longer leg

Substituting terms, the equation would be:

Multiplying like terms:

Simplifying:

Switching sides:

Isolating x:

Solving the cubic root:

So, x is the value of the longer leg.

Now, we need to find the length, we know that length=4*longer leg

So, the length of the carton is 4*18= 72

The answer is 72

Answer:

greater

Step-by-step explanation:

if it wasn't bidmas then the product would be 5.104 which is greater than 2.324

Mean=54.1 Median=55 Mode=1 Midrange=53 are the correct values of mean, median, mode and midrange.

(a) Mean= sum of data/ number of data

=(55+64+45+77+88+51+41+54+35+67+18)/11

=595/11

=54.09 or 54.1

(b) Median is the middle value, which in this case is 51.

(c)  Mode is the count of the number stating how many time it has been repeated in the data.

For instance in the given data :-

55 64 45 77 88 51 41 54 35 67 18

mode of 55 is 1, since it appears only one time.

No numbers in the given data repeats, i.e. all the values are unique. Thus the mode of the given data is 1.

(d) Mid-range is (highest value in the data + lowest value in the data)/2

in this case, the highest value is 88 and the lowest value is 18. Substituting these values in the formula:

(88+18)/2

=106/2

=53

What is mean median mode and midrange?

Mean is the sum of data divided by number of data, Median is the middle value of the data when arranged in ascending or descending order, Mode is the count of the number stating how many time it has been repeated in the data and Mid-range is highest value in the data plus lowest value in the data whole divided by 2.

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The input value x when the output value f( x ) = 4 in the function f( x ) = 5x - 7 is 11/5.

A function is simply a relationship that maps one input to one output, each x-value can only have one y-value.

Given the data in the question;

To determine the input value x when the output value f( x ) = 4, replace f( x ) by 4 in the function and solve for x.

f( x ) = 5x - 7

4 = 5x - 7

Collect like terms

4 + 7 = 5x

5x = 11

Divide both sides by 5

5x/5 = 11/5

x = 11/5

Therefore, the input value x is 11/5, this forms an ordered pair of ( 11/5, 4 ).

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Answer:

[tex] - \frac{1}{3} \geqslant - \frac{4}{5} x[/tex]

[tex] \frac{1}{3} \leqslant \frac{4}{5} x[/tex]

[tex]5 \leqslant 12x[/tex]

[tex]12x \geqslant 5[/tex]

[tex]x \geqslant \frac{5}{12} [/tex]

Answer:

Steps to find the equation of a line from two points:

Find the slope using the slope formula. ...

Use the slope and one of the points to solve for the y-intercept (b). ...

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

Step-by-step explanation:

Answer:

[tex]y=-2x+30[/tex]

where y is the weight of the cat (in pounds) and x is the number of months.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

The y-intercept is the y-value when x is zero, so the initial value.

If the cat initially weighs 30 pounds, the y-intercept is 30.

The slope is the rate of change.

If the cat lost 2 pounds per month, then the rate of change is -2.

Therefore, the equation the models the given word problem is:

[tex]\boxed{\begin{minipage}{7 cm}\phantom{ww}\\$y=-2x+30$\\\\where:\\ \phantom{ww}$\bullet$ $y$ is the weight of the cat (in pounds). \\ \phantom{ww}$\bullet$ $x$ is the number of months.\\\end{minipage}}[/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x² + y² = 16[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The distance between the centre and the point through which the circle is passing is equal to the radius of the circle.

so, let's use distance formula here :

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

[tex]\qquad \tt \rightarrow \: \sqrt{(0 - 0) {}^{2} + (4 - 0) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{0 + (4) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{ {4}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: 4 \: \: units[/tex]

Now, let's write the equation of circle in standard form :

[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {4}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 16 [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Either. They are both correct

Step-by-step explanation:

So 7+4(1-8p): 7+4-32p => 11-32p => -32p+11.

Answer:

11-32p

Step-by-step explanation:

The answer is 11-32p because your only distributing the 4 to the 1 and 8p.

Answer:

  3(n +5)

Step-by-step explanation:

You want the math expression that means "three times the sum of a number and five."

A sum is represented using a plus sign. "A number" is represented using a variable. "x" is a variable commonly used for an unknown value. "n" can also be used to represent "a number."

The sum of a number and 5 will be ...

  n + 5

We want an expression that is 3 times that sum, so we multiply it by 3:

  3(n +5) . . . . . . 3 times the sum of a number and 5

__

Additional comment

Note that the expression above is not the same as 3n+5, which would represent "the sum of 3 times a number and 5".

Let's classify the angles.

The angles are alternate interior angles.

The

Answer:

Step-by-step explanation:

Let David will need m months to save to able to afford his birthday party.

Then 43m>=250 that is m>=5.814 .

But since months are whole numbers

So We take m>=6.

He will need at least 6 months to save to able to afford his birthday party.

The answer is 6 months .

When solving an inequality, treat it like an equal sign while solving.

y - 4 ≤ -13
y - 4 + 4 ≤ -13 + 4
y ≤ -9

a) the two angles are supplementary, then:

(3x - 45) + (2x + 25) = 180

(3x + 2x) + (-45 + 25) = 180

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 200/5

x = 40

Then, the measure of the angles are:

3x - 45 = 3*40 - 45 = 75°

2x + 25 = 2*40 + 25 = 105°

b) the two angles are complementary, then:

(2y) + (6y - 30) = 90

(2y + 6y) - 30 = 90

8y = 90 + 30

8y = 120

y = 120/8

y = 15

Then, the measure of the angles are:

2y = 2*15 = 30°

6y - 30 = 6*15 - 30 = 60°

c) the two angles are vertical angles, then they are congruent, that is,

2z + 7 = 5z - 23

7 + 23 = 5z - 2z

30 = 3z

30/3 = z

10 = z

Then, the measure of the angles are:

2z + 7 = 2*10 + 7 = 27°

5z - 23 = 5*10 - 23 = 27°

d) the two angles are alternative exterior angles, then they are congruent, that is,

4x - 5 = 3x + 15

4x - 3x = 15 + 5

x = 20

Then, the measure of the angles are:

4x - 5 = 4*20 - 5 = 75°

3x + 15 = 3*20 + 15 = 75°

First, we will start by converting 607,200 feet to miles

1 mile= 5280 foot

607, 200 feet can be changed to mile by dividing it by 5280

That is;

607,200 feet to mile = 607, 200 / 5280 = 115 miles

Hence; speed

= distance over t/

= 115 /1

=115 miles per hour

By using division, when the restaurant needs at least 736 knives and there are currently 155 knives, if each set on sale contains 12 knives then he minimum number of sets of knives Kaj should buy is 49 sets

The total number of knife that restaurant needs = 736 knives

Number of knives that restaurant has = 155 knives

The number of knife that he want to buy = 736-155

= 581

Number of knives on one set = 12

To find the number of set he wants to buy, we have to use division

Number of sets he wants to buy = 581/12

= 48.41

≈49 sets

Hence, by using division, when the restaurant needs at least 736 knives and there are currently 155 knives, if each set on sale contains 12 knives then he minimum number of sets of knives Kaj should buy is 49 sets

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The sum of the values is referred to as the operands, arguments, or inputs, while the result is referred to as the value, output, or result. Operations may require less than two inputs or more (including the case of zero input and infinitely many inputs). The answer will be 0.9+0.06+0.004= 0.964

Not all possible values of the domain may be covered by an operation's definition. For instance, it is impossible to square the roots of negative integers or divide by zero in real numbers. An operation's domain of definition, also known as the active domain, is the set of values for which the operation is specified. The set that the values created are contained in is known as the codomain, while the set that the operation really produced is known as the codomain of definition, active codomain, image, or range. For instance, only non-negative numbers are produced by the squaring operation when applied to the real numbers; the set of real numbers is the codomain, but the non-negative numbers are the range.

A scalar can be multiplied by a vector to create another vector (a process known as scalar multiplication), and two vectors can be combined to make a scalar quantity in an inner product operation. An operation may or may not have specific characteristics, such as being idempotent, associative, commutative, or anticommutative.

The sum of the values is referred to as the operands, arguments, or inputs, while the result is referred to as the value, output, or result. Operations may require less than two inputs or more (including the case of zero input and infinitely many inputs).

9x1/10+6x1/100+4x1/1000

0.9+0.06+0.004= 0.964

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Step-by-step explanation:

Your slope and your x and y intercept.

x + 2y =7

Divide through by 2, we have:

x/2 + 2y/2 = 7/2

x/2 + y = 7/2

y = 7/2 - x/2

In the form y = mx + c gives.

Where m is the slope.

.: The slope = -1

The total amount that must be repaid will be $26,015.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

A = P + (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

For $21,500, Norman buys a brand-new vehicle. The loan amount (plus simple interest) must be repaid in full within five years, and the simple interest rate is 4.2%.

The total amount that must be repaid will be given as,

A = $21,500 + ($21,500 x 4.2 x 5)/100

A = $21,500 + $4,515

A = $26,015

The total amount that must be repaid will be $26,015.

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The quadratic equation with roots 4 and -2 and leading coefficient 4 is;

⇒ 4x² - 8x - 32

What is Quadratic equation?

A quadratic equation is an algebraic equation of the second degree of x.

Given that;

Roots of a quadratic equation = 4 and -2

Leading coefficient = 4

Now, The quadratic equation whose roots 4 and -2 with leading coefficient is calculated as;

⇒ 4 ( x - 4) (x + 2)

Solve as;

= 4 (x - 4) (x + 2)

= 4 (x² + 2x - 4x - 8)

= 4 (x² - 2x - 8)

= 4x² - 8x - 32

Thus, The quadratic equation with roots 4 and -2 and leading coefficient 4 is;

⇒ 4x² - 8x - 32

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This is a problem with a non-linear equation. The data is the temperature of water and the time. But we have to fit a line anyway.

We can the Least Squares Method, the best line fit is:

Now, we apply the formula above:

Answer:

see explanation

Step-by-step explanation:

(a)

the 2 angles are same- side interior angles and are supplementary.

(c)

since they are supplementary , they sum to 180° , that is

6x + 14 + 10x - 10 = 180

16x + 4 = 180 ( subtract 4 from both sides )

16x = 176 ( divide both sides by 16 )

x = 11

(d)

then

6x + 14 = 6(11) + 14 = 66 + 14 = 80

10x - 10 = 10(11) - 10 = 110 - 10 = 100

note 80 + 100 = 180 ( supplementary angles )

The location of the image of point S is the midpoint of the line segment RS. A representation of the geometric system and the rigid transformation is shown in the image attached below.

Herein we know the center of dilation and the location of point S, which must be dilated by a rigid transformation, that is, a transformation applied on the point such that its Euclidean distance is conserved. The operation is defined by the following equation:

RS' = k · RS

S'(x) - R(x) = k · S(x) - k · R(x)

Where k is the scale factor.

If we know that R(x) = 0, S(x) = 6 and k = 1 / 2, then the location of the point S' is:

S'(x) - 0 = (1 / 2) · 6 - 0

S'(x) = 3

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Answer:

|2x - 3| ≥ 1

Step-by-step explanation:

Since the absolute value function is always ≥ 0 we can conclude that                
|2x - 3| ≥ 0 so we can eliminate choices 2 and 4

That leaves two possibilities:
|2x - 3| ≥ 1  and |2x - 3| ≤  1

There are two ways to go about solving this

Pick a point in the given graph on each side of the segment marked in red and see which of the two inequalities both points satisfy

Two points which are on both segments are x = 0 and x = 1

Plug x = 0 into |2x - 3|
|2x - 3| at x = 0
=> | 2 ·0 - 3|  
=> |0 - 3|
=> |-3|
= 3  

Since 3 ≥ 1,  point x = 0 satisfies |2x - 3| ≥ 1

But it does not satisfies |2x - 3| ≤  1 since 3 is not less than or equal to 1

So the correct inequality is |2x - 3| ≥ 1

To write the sentence:

Number k is 4/5 of the number t in algebraic language, we can proceed as follows:

We need to express that k is equal to the four-fifths of t.

Then, the answer is k = (4/5)*t.