Which of the following terms are equivalent to the slope in a proportional relationship? Select all that apply.
a.) Constant Rate of Change
b.) origin
c.) Change in y / Change in x
d.) rise/run
e.) inverse

The perimeter of the triangle is 18 feet.

Polygon which has three sides and three vertices is called as triangle.

Sum of all the angles of the triangle is 180°.

Given the sides of the triangle are 4 feet , 6 feet and 8 feet.

And the perimeter of the triangle

= sum of all three side of the triangle.

The perimeter of the triangle = 4 + 6 + 8

perimeter of the triangle = 18 feet

Therefore, the perimeter of the triangle is 18 feet.

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Answer:

C

Step-by-step explanation:

Answer:

To find the ratio m/k, we need to combine the proportions m/n and n/k. One way to do this is to multiply the fractions to get the product m/k. This can be done by multiplying the numerators to get m, then multiplying the denominators to get k.

For example, if we let m=1, n=2, and k=5, then we have the following:

m/n = 1/2

n/k = 2/5

If we multiply the numerators and denominators to get the product m/k, we get:

(1 * 2) / (2 * 5) = 2/10 = 1/5

Therefore, the ratio m/k is 1/5.

Another way to find the ratio m/k is to use the fact that proportions are equivalent to equations. We can set up an equation using the given proportions, then solve for m/k.

For example, using the same values as before, we have:

m/n = 1/2

n/k = 2/5

We can set up an equation by setting the two proportions equal to each other:

m/n = (1/2) = n/k = (2/5)

Then we can cross-multiply to solve for m/k:

m/n * n/k = (1/2) * (2/5)

(m * 2) / (n * 5) = 1/5

m/k = (2/5) = 1/5

Therefore, in this case, the ratio m/k is also 1/5.

In general, to find the ratio m/k given the proportions m/n and n/k, we can either multiply the fractions or set up and solve an equation using the given proportions.

The inequality that represents the possible depths d  reached by the vehicle is d < -725.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Depth record = less than -715 feet.

This means,

The depth must be -716 or less.

The vehicle breaks the depth record by more than 10 feet.

This means,

-715 - 10 = -725

The depth record must be less than -725

Thus,

The possible depths d reached by the vehicle is d < -725.

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The variance in the sample data is 220

We are given the following data of 5 salespeople (expressed in thousands of dollars); 40, 60, 65, 70, 80

Suppose that the considered data set is

Then, its standard deviation is the positive square root of the variance of this data set. Variance of data set is the sum of squared differences of the data values from its mean to the total count of data values.

Thus, we get:

[tex]\sigma = \sqrt{\dfrac{1}{n} \sum_{i=1}^{n} (x_i-\overline{x})^2[/tex]

In the formula above, x represents the mean of the data points, x is the value of an individual data point, and N is the total number of data points.

x = (40+60+65+70+80)/5

x=63

So, the mean of the sample data is 63

Variance =

[tex]\sigma^2 = \dfrac{\sum_{\forall x_i} (x_i - \overline{x})^2}{n}[/tex]

Therefore, the variance is 220

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Answer:

x < 2 11/15

Step-by-step explanation:

Hope this helps!

Answer:

the solution of the system is x = 18/5 and y = 27/5.

Step-by-step explanation:

To solve a system of equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the x-variable:

(-3x - 4y) + (x + y) = -54 + 15

-2x - 3y = -39

Dividing both sides by -3, we get:

(2/3)x + (1/3)y = 13/3

This equation tells us that x is equal to 2/3 times the value of y. Substituting this expression for x in one of the original equations, we can solve for y:

-3(2/3)y - 4y = -54

This simplifies to:

(-6/3)y - 4y = -54

Combining like terms, we get:

(-10/3)y = -54

Dividing both sides by -10/3, we get:

y = 27/5

Substituting this value for y in the expression for x, we get:

x = (2/3)(27/5) = 18/5

Therefore, the solution of the system is x = 18/5 and y = 27/5.

Answer: x=6, y=9

(6,9)

Step-by-step explanation:

Multiply x+y=15 by 3 to eliminate x

3(x+y)=15(-3)

3x+3y=45

-3x-4y=-54

-1y=-9

y=9

sub in 9 to y to get x

x+9=15

x=6

Answer:

Step-by-step explanation:

Given that,

m∠L = 40°, m∠M = 90°

Since ΔLMN ≅ ΔPQR

(17x - y)° = 40°

(2x + 4y)° = 50°

Since, the sum of three angles of a triangle is 180 degrees.  

Then, m∠R = 1800 – 400 – 900 = 500

Remove degree from both side

17x – y = 40

2x + 4y = 50

Solving these two equations then,

x = 3, y = 11

The value of x and y would be x = 3 and y = 11.

What are congruent triangles?

Congruent triangles are triangles that have the same size and shape. In other words, congruent triangles are identical in all respects.

Given Data:

ΔLMN ≅ ΔPQR, m∠L = 40°, m∠M = 90°, m∠P = (17x - y)°, m∠R = (2x + 4y)°

as m∠L = m∠P

   17x - y = 40 ----------(I)

we know that,

m∠L + m∠M + m∠N = 180

  40 +  90 + m∠N = 180

m∠N = 50

As m∠N = m∠R

   2x + 4y = 50 -------(II)

Solving (I) and (II), we get

x=3, y=11

Hence, the value of x and y would be x = 3 and y = 11.

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Answer: C; 5.32

Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!

Answer: 16-x

Step-by-step explanation:

Collect like terms.

-x + (6 + 10)

Simplify.

16 - x

From my calculations using  the Cymath calculator, 16 - x would be the answer, Hope I could help.

Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

Answer:

m = -4

Step-by-step explanation:

7m + 29 = 2m + 9

-2m          -2m

--------------------------

5m + 29 = 9

      -29     -29

-----------------------

5m = -20

÷5     ÷5

--------------------

m = -4

I hope this helps!

Part A:

We can set up a system of equations to represent the number of rocks in each person's collection. Let "S" be the number of rocks in Samuel's collection and "L" be the number of rocks in Lewis's collection. We can represent the situation as follows:

Equation 1: S = 18 + 4t

Equation 2: L = 30 + 3t

Here, "t" represents the number of weeks that have passed.

Part B:

To find out how many weeks it will take for Samuel and Lewis to have the same number of rocks in their collections, we need to set Equation 1 equal to Equation 2 and solve for "t". This gives us the following:

S = L

18 + 4t = 30 + 3t

1t = 12

t = 12 weeks

It will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.

Part C:

To find out how many rocks Samuel and Lewis will have when the amount of rocks in their collection is equal, we can substitute the value of "t" that we found in Part B into either Equation 1 or Equation 2. For example, substituting "t = 12" into Equation 1 gives us the following:

S = 18 + 4(12)

S = 18 + 48

S = 66 rocks

Therefore, when the amount of rocks in their collection is equal, Samuel and Lewis will have 66 rocks each.

a) 16 or 2/5 ratio of blue marbles not chosen

b) 86 total no. of marbles was there before the game

c) 24 blue marbles were picked

Explanation:

a) total no of blue marbles = 40

ratio of chosen blue marbles = 3/5

blue marbles picked = 40 × 3/5 = 24

blue marbles not picked = 40-24 = 16

b) total no of blue marbles + total no of red marbles = 40+ 46

total no. of marbles was there before the game = 86

c) explained in a)

What is a Ratio?

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division.

A survey of 20 respondents revealed that 13 of them preferred cake to ice cream and 7 preferred ice cream to cake. This data set can be represented as the ratio 13:7, where 13 is the antecedent and 7 is the consequent.

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Answer:

26.7%

Step-by-step explanation:

Percentages are values in terms of values divided by 100.

Eg.

[tex] \frac{34}{100} = 34percent [/tex]

To solve this question, we have to make sure the denominator is 100.

4 : 15

[tex] = \frac{4}{15} \\ = \frac{4 \\ \times 10}{15 \times 10} \\ = \frac{40 \div 1.5}{150 \div 1.5} \\ = \frac{26.667}{100} [/tex]

Therefore the percentage is 26.7%. (3 Significant Figures)

Answer:

8.857142857

Step-by-step explanation:

Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.

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[tex]P(x)=100_{e}({4}/{ln4} )x[/tex]

what is bacteria?

Microbes known as bacteria have simpler cell structures than many other types of creatures. One DNA loop serves as their command centre and houses all of their genetic data. Instead of a nucleus, some bacteria contain an additional ring of genetic material called a plasmid. Genes that offer the bacterium a competitive edge over other bacteria are frequently found on the plasmid.

There are a few options for doing this. A set of equations may be used.

Use the equation P = a*bx, where x is the number of hours and P represents the population of bacteria.

A and B are two unknowns.

We will enter form points to solve (x, P)

A point equals (2, 200). (after 2 hours, the population is 200)

Consequently, a formula is 200 = [tex]a*b^{2}[/tex]

Second, there is (6, 800).

A second equation is thus 800 = [tex]a*b^{6}[/tex]

We'll repeat the equations in writing:

800 = [tex]a*b^{6}[/tex]

200 = [tex]a*b^{2}[/tex]

These two equations can be divided.

When we divide the equations, we obtain 800/200 = 4 on the left.

When we split on the right side,the equations, we get [tex]a*b6 / (a*b2) = b4[/tex]

Therefore, [tex]4 = b^{4}[/tex]

Solve for b:

b = [tex]\sqrt[4]{4}[/tex]

Next, solve for a, by plugging in b into the second equation

[tex]200 = a * (\sqrt[4]{4})^{2} = a * \sqrt{4} = a * 2[/tex]

Therefore, dividing both sides by 2, gives us that a = 100

Lastly, write out the equation with the known values of a and b.

[tex]P(x)=100_{e}({4}/{ln4} )x[/tex]

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Answer:

[tex]\frac{33\sqrt{31}}{200}[/tex]

Step-by-step explanation:

[tex]\cos x=\frac{11}{20} \implies \sin x=\sqrt{1-(11/20)^2}=\frac{3\sqrt{31}}{20} \\ \\ \sin 2x=2\sin x \cos x =2 \cdot \frac{3\sqrt{31}}{20} \cdot \frac{11}{20} =\frac{33\sqrt{31}}{200}[/tex]

The simplification of the given expression is (a² + a + 1)/a².

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is a+1/2a + 3/a².

It can be evaluated as follows,

a+1/2a + 3/a²

Take the LCM of a and a² as a².

= (a(a + 1)+ 3)/a²

= (a² + a + 1)/a²

Hence, the given expression can be simplified to obtain (a² + a + 1)/a².

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Answer:

Step-by-step explanation:

45 out of 100

Algebraic representation:

[tex]\frac{4}{5}[/tex]

 is that algebra?

If not it   is  [tex]2 < 2x < 6[/tex]

so 2 is smaller  Then then 2x with is most likely a decimal I could be a decimal are you working on decimals?

I can't give a great answer as i might mix thing up Also what grade are you in?

Answer: The temperature was -21.75 after 5.5 hours passed.

Step-by-step explanation:

-2.5 starting degrees,

-3.5*5.5 = -19.25

-19.25 + the original -2.5 = -21.75

The relation between curl vector and rotations is v = wdj

A vector field is a vector field's curl. The tendency of particles at point P to spin about the axis that faces the direction of the curl at P is measured by the curl of a vector field at P. If and only if its curl is zero, a vector field with a simply linked domain is considered conservative.

Let v represent the particle's velocity as a vector.

vector v=ui+vj+wk

curl v =

curl v  = [tex]\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\u&v&w\end{array}\right][/tex]

= (dw/dy - dv/dz )i - (dw/dx - du/dz)j +  (dv/dx - du/dy )k

Now by comparing with rotational matrix ,

We know that w = rotational matrix

[tex]w_{x}[/tex] = 1/2 (dw/dy - dv/dz )

[tex]w_{y}[/tex] = 1/2 (dw/dx - du/dz)

[tex]w_{z}[/tex] = 1/2  (dv/dx - du/dy )

w = [tex]w_{x} i +w_{y} j + w_{z} k[/tex]

w =  1/2[ (dw/dy - dv/dz )i + (dw/dx - du/dz)j + (dv/dx - du/dy )k]

w = 1/2 curl v , rotation = 1/2 curl v

let B be a rigid rotating about z axis

w = w.k

tangential speed =wk *di

v = wdj

curl of v=  [tex]\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\0&w_{x} &0\end{array}\right][/tex]

v = wdj ,

The relation between curl vector and rotations is v = wdj

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Answer:

0.15

Step-by-step explanation:

10/x=67.50

10=x*67.5

10/67.5 = x

x=0.14814814814

Answer:

C - Reflect over the x-axis

Step-by-step explanation:

This is a reflection over the x-axis.

To remember the difference between reflectinon over the x-axis and reflectino over the y-axis, memorize this.

If you reflect over the x-axis, the x value of the reflected point stays the same.  (only the y is multiplied by -1)

If you reflect over the y-axis, the y value of the reflected point stays the same. (only the x is multiplied by -1)

Roation about the origin involves multiplying both x and y by -1.  (x and y change)

Answer:

180 - (54 + 35) = 91

The answer is 'D'