Which is the slope of the line that passes through the points (−3,1)
(
-
3
,
1
)
and (4,−2)
(
4
,
-
2
)
?

Answer:

[tex]x+2y=-11[/tex]

Step-by-step explanation:

Slope intercept form of a line is given by:

[tex]y=mx+b[/tex]

Where

m is the slope and b is the y-intercept

Given slope is  [tex]-\frac{1}{2}[/tex]

We can write:

[tex]y=-\frac{1}{2}x+b[/tex]

Now to find b, we replace x with -3 and y with -4, given, so we have:

[tex]y=-\frac{1}{2}x+b\\-4=-\frac{1}{2}(-3)+b\\-4=\frac{3}{2}+b\\b=-5.5[/tex]

So, the equation is:

[tex]y=-\frac{1}{2}x-\frac{11}{2}[/tex]

Now,

The standard form is given by:

[tex]Ax+By=C[/tex]

So, we take x and y to left side and the constant to right side. Rearranging, we get:

[tex]y=-\frac{1}{2}x-\frac{11}{2}\\2y=-x-11\\x+2y=-11[/tex]

The first answer choice is right.

Final answer:

The equation of line b that passes through the point (-3, -4) and has a slope of -1/2 in standard form is x + 2y = -11.

Explanation:

To find the equation of line b that passes through the point (-3, -4) and has a slope of -1/2, we will start with the slope-intercept form of a line equation y = mx + b, where m is the slope and b is the y-intercept. While we know the slope (-1/2), we do not yet have the y-intercept. We can use the given point to solve for b. Plugging the point into the equation gives -4 = (-1/2)(-3) + b, which simplifies to -4 = 3/2 + b. Solving for b yields b = -11/2.

Now we have the slope-intercept form of the line: y = (-1/2)x - 11/2. To convert this to standard form, which is Ax + By = C, we multiply through by 2 to clear the fractions, which gives us 2y = -x - 11. Rearranging this, we add x to both sides to get x + 2y = -11. Therefore the correct equation in standard form is x + 2y = -11.

Answer: [tex]k=\frac{M^t(v-P)}{P}[/tex]

Step-by-step explanation:

Given the following equation provided in the exercise:

[tex]P=\frac{v}{1+kM^{-t}}[/tex]

You can follow these steps in order to solve for "k":

1. You must multiply both sides of the equation by [tex]1+kM^{-t}[/tex]:

[tex](P)(1+kM^{-t})=(\frac{v}{1+kM^{-t}})(1+kM^{-t})\\\\P+PkM^{-t}=v[/tex]

2. The next step is to subtract "P" from both sides of the equation:

[tex]P+PkM^{-t}-(P)=v-(P)\\\\PkM^{-t}=v-P[/tex]

3. Now apply the Negative Exponent Rule, which states that:

[tex]a^{-n}=\frac{1}{a^n}[/tex]

Then:

[tex]\frac{Pk}{M^{t}}=v-P[/tex]

4. Multiply both sides of the equation by [tex]M^t[/tex]:

[tex](M^t)(\frac{Pk}{M^{t}})=(M^t)(v-P)\\\\Pk=M^t(v-P)[/tex]

5. And finally, you must divide both sides of the equation by "P":

[tex]\frac{Pk}P=\frac{M^t(v-P)}{P}\\\\k=\frac{M^t(v-P)}{P}[/tex]

Answer:

5

Step-by-step explanation:

The population density of Hawaii is 109.09 with an area of [tex]1.1 \times 10^4[/tex]square miles and a population of [tex]1.2 \times 10^6[/tex] people.

Given that:

The area of Hawaii is 1.1 × 10^4 square miles

The population  of Hawaii is  1.2 × 10^6 square miles

The population density of Hawaii can be calculated as:

[tex]Population \ density = \dfrac{Number \ of \ people} {land\ area}[/tex]

Substitute the values in the given formula:

[tex]Population \ density = \dfrac{ 1.2 \times 10^6} {1.1 \times 10^4}[/tex]

This can be further solved as:

[tex]Population \ density = \dfrac{ 1.2 \times 10^{(6 -4)}} {1.1}[/tex]

The laws of exponent are used here,

Where,  [tex]\dfrac{x^m}{x^n} = x^{(m-n)[/tex]

This can be solved as:

Population  density = [tex]1.0909 \times10^2[/tex]

                                   = [tex]1.0909 \times 100[/tex]

                                    = 109.09

The population density of Hawaii is 109.09.

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The complete question is :

Hawaii has an area of [tex]1.1 \times 10^4[/tex] square miles and a population of [tex]1.2 \times 10^6[/tex] people. Which keystrokes on a calculator will give the population density of Hawaii?

Final answer:

To find the population density of Hawaii, divide the population by the area. The key strokes on a calculator would be 1.2 divided by 1.1 equals 1.09. The population density of Hawaii is approximately 1.09 people per square mile.

Explanation:

To calculate the population density of Hawaii, you will need to divide the population by the area. The formula for population density is: Population Density = Population / Area. Using the provided information, the key strokes on a calculator to find the population density of Hawaii would be: 1.2 / 1.1 = 1.09. Therefore, the population density of Hawaii is approximately 1.09 people per square mile.

Answer:

-1.777...

Step-by-step explanation:

Using the LCM of 18 for the denominator, these values are:

-1 7/9 -1 1/2

-32/18 -27/18 0

--------------|-------------------|-------------------------------------|-----------

So, the easy values to identify are: -31/18, -30/18, -29/18, and -28/18

All of these numbers have repeating decimals (because 9 is a factor of the denominator).

Now, you may realize that -1 3/4 is within the range specified.

-1 7/9 -1 1/2

-32/18 -27/18 0

--------------|-------------------|-------------------------------------|-----------

|

-1 3/4

-1.75

This is because -1.75 is between -1.5 and -1.7777.... Note that it is not repeating.

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Answer:

67.5

Step-by-step explanation:

Okay so I spent way to long overthinking this problem but in the end, I just used common sense to figure this one out. *it still may be wrong though...

A way to check if this is correct is dividing 67.5 by 5 and it equals to 13.5 which should make that answer correct?

Answer:

67.5

Step-by-step explanation:

Okay so I spent way to long overthinking this problem but in the end, I just used common sense to figure this one out. *it still may be wrong though...

A way to check if this is correct is dividing 67.5 by 5 and it equals to 13.5 which should make that answer correct?

Answer:

Jackie is incorrect.

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] [tex]\left {x2} \atop {x2}} \right.[/tex] = [tex]\frac{6}{8}[/tex]

[tex]\frac{3}{4}[/tex] is equivalent to [tex]\frac{6}{8}[/tex] not [tex]\frac{7}{8}[/tex]

Jackie is mistaken when she claims that the fraction 7/8 is equal to 3/4. We compare the numerator (the top number) and denominator (the bottom number) of two fractions to see if they are equal.

In this instance, 3/4 has a denominator of 3 and a numerator of 4, whereas 7/8 has a numerator of 7 and a denominator of 8, respectively. The fractions cannot be equal since the numerators and denominators vary.

Two fractions must have the same numerator to denominator ratio in order for them to be equal. In this situation, 7/8 is a bigger fraction than 3/4. Jackie's assertion that 7/8 is comparable to 3/4 is therefore false.

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Answer:

2x+8>12

Step-by-step explanation:

Answer: 2 1/6

Step-by-step explanation:

Because the denominators are different, and there are whole numbers involved, then first make the fractions improper.

4 1/2 -> 9/2

6 2/3 -> 20/3

Next, make the denominators the same by multiplying each fraction by the denominator of the other.

9/2 * 3 = 27/6

20/3 * 2 = 40/6

Then you can subtract the numerators because the denominators are the same:

40/6-27/6= 13/6

Then you can convert to a mixed fraction if need be.

Answer:

$7 per cupcake

Step-by-step explanation:

A unit rate is the cost of one item. So we would do $168 divided by twenty-four. That would be equivalent to seven.

Answer:

$remaining=86-6m

Step-by-step explanation:

$remaining = 80 - (m + 2m) - (3m-6)

$remaining = 80 - 3m - 3m +6

$remaining = 86 - 6m

80 -> total amount she brings into the store

m -> money spent on milk

2m -> money spent on fruit (two x m)

3m-6 -> bread (six dollars less than three times the milk value)

Simplify and the result is 86-6m

Answer:

5n

Step-by-step explanation:

Answer:

total cost of the candy bars = 5 x n

Step-by-step explanation:

Answer:

68°, 82°, and 30°

Step-by-step explanation:

x+x+14+x-38=180

combine like terms

3x-24=180

put variables on one side

3x=204

divide

x=68

substitute

x=68

x+14=82

x-38=30

By using the triangle angle sum theorem, we find that the measures of the angles of the triangle in question are 68 degrees, 82 degrees, and 30 degrees.

This question involves using the fact that the sum of internal angles in any triangle totals 180 degrees. In this triangle, the three angles are given as x, x+14, and x-38. To find the measures of these angles, we set up the below equation:

x + (x+14) + (x−38) = 180

The step above incorporates the triangle angle sum theorem. Now we simplify and solve for 'x':

3x - 24 = 180
3x = 204
x = 68

So the measure of the angles in the triangle are 68 degrees, 82 degrees, and 30 degrees.

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Answer: Rational "yes"

Step-by-step explanation: The square root of 25 is indeed a rational number. Rational numbers are numbers. The square root of 25 is a perfect square which means that it has a number that can be multiplied by itself which gives us 25.

In this case, the number is 5 so yes, it's rational.

Answer:

I think 28. Sorry if its wrong

Step-by-step explanation

The kite is a quadrilateral with 4 sides and angles. The length of line segment CD from the given kite is 28 units

The kite is a quadrilateral with 4 sides and angles.

From the given diagram,

AB = 3x + 1

BC = 22

Since AB = BC, hence;

3x + 1 = 22

3x = 22 - 1

3x = 21

x = 7

Since AD = CD = 4x, hence;

CD = 4x

CD = 4(7)

CD = 28 units

Hence the length of line segment CD from the given kite is 28 units

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Answer:

least common multiple

Step-by-step explanation:

Find the lcm of the given numbers, do you know how to do that?

Alright, so you're looking for the GCF.

Greatest Common Factor

I don't wanna go into detail of what that is (if you don't already know what it is, please watch a video on what it is and how to find it.)

Our numbers are 18, 36, 54

What is the gcf of these numbers? They all are both divisble by 18 and that's the largest 18 can go, so 18 is the GCF.

18 is the answer.

The equation of the line is [tex]5x+y-38=0[/tex]

Step-by-step explanation:

The slope is [tex]m=-5[/tex]

Also, the line passes through the points [tex](7,3)[/tex]

To find a line with slope [tex]m=-5[/tex] that passes through the points [tex](7,3)[/tex], let us use the equation of a line with slope that passes through the point is given by [tex](y-y_{1} )=m(x-x_{1} )[/tex] where m is the slope and [tex](x_{1} ,y_{1} )[/tex] are the points [tex](7,3)[/tex].

Thus, substituting the values in the equation of a line, we get,

[tex](y-3)=-5(x-7)[/tex]

Multiplying the term [tex](x-7)[/tex] by -5, we get,

[tex]y-3=-5 x+35[/tex]

Adding both sides by 5x,

[tex]5x+y-3=35[/tex]

Subtracting 35 from both sides of the equation,

[tex]5x+y-38=0[/tex]

Thus, the equation of the line is [tex]5x+y-38=0[/tex]

Answer:

4 and 8

Step-by-step explanation:

corresponding angles are two angles that have the same angle degree and are on the same side of the graph if you were to take the bottom part and move it up to the top part

Answer:2m/s

Step-by-step explanation:

Velocity=distance÷time

Velocity=8÷4

Velocity=2m/s

the answer for this question is:

1/17

Answer:

True

Step-by-step explanation:

Sorry if it's wrong lol

Answer:

Step-by-step explanation:

a + c = 24......a = 24 - c

5.5a + 2c = 83

5.5(24 - c) + 2c = 83

132 - 5.5c + 2c = 83

-5.5c + 2c = 83 - 132

-3.5c = - 49

c = -49 / -3.5

c = 14 <==== 14 child tickets

a + c = 24

a + 14 = 24

a = 24 - 14

a = 10 ........and 10 adult tickets

Answer:

4x – 12 ≤ 16 + 8x; x>-7

Step-by-step explanation:

i dont remember how i did it

Answer:

x≥-7

Hope this helps

From other source on the internet this question is:

Which absolute value expression represents the distance between 3 and - 2 on a number line?

Answer:

Both are equivalent.

Explanation:

The distance between two numbers in a number line is the absolute value of the difference between the two numbers.

Thus, the distance between a number x and a number y is |x - y|, which is also equivalent to |y - x|.

In this case the distance between 3 and - 2 can be represented by either of the expressions:

Note that when you simplify them you get the same value:

Answer:

The distance between 3 and  

9

2

on a number line is |3 −  

9

2

|. The distance between two numbers is equal to the absolute value of their difference.

|3 −  

9

2

| = |−

3

2

| =  

3

2

Step-by-step explanation:

so the answer is A

[tex]\text{Hey there!}[/tex]

[tex]\text{What is }\dfrac{2}{20}+\dfrac{10}{75}[/tex]

[tex]\text{For the LCD (Lowest Common Denominator) it should be equal to 300}[/tex]

[tex]\dfrac{2\times15}{20\times15}+\dfrac{10\times4}{75\times4}[/tex]

[tex]\bf{2\times15=30}\\\bf{20\times15=300}\\\\\bf{10\times4=40}\\\bf{75\times4=300}[/tex]

[tex]\text{Your new equation}\rightarrow\dfrac{30}{300}+\dfrac{40}{300}[/tex]

[tex]\text{With the denominators being alike we can leave the same}[/tex]

[tex]\text{New equation}\rightarrow\dfrac{30+40}{300}[/tex]

[tex]\text{30 + 40 = 70}[/tex]

[tex]\text{New equation}\rightarrow\dfrac{70}{100}[/tex]

[tex]\text{Since both of the terms have 10 in their like terms, let's divide both sides by it}[/tex]

[tex]\dfrac{70\div10}{300\div10}[/tex]

[tex]\bf{70\div10=7}[/tex] [tex]\leftarrow\text{Your numerator}[/tex]

[tex]\bf{300\div10=30}[/tex] [tex]\leftarrow\text{Your denominator}[/tex]

[tex]\boxed{\bf{Thus,\ your\ answer\ should\ be:\dfrac{7}{30}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer: Answer is 38ft.

Step-by-step explanation: The figure that measures 10ft by 9ft is a rectangle which means two sides measure 10ft each (length) and two sides measure 9ft each (width). A perimeter simply measures all sides of the entire shape, that is;

10ft + 9ft + 10ft + 9ft = 38ft.

Answer: 5

Step-by-step explanation:

[tex]log_{2}[/tex] 32

32 can be written in index form as 2x2x2x2x2 , which could be written as [tex]2^{5}[/tex].

[tex]log_{2}[/tex] 32 the becomes

[tex]log_{2}[/tex] [tex]2^{5}[/tex]

Which could be written as

5 [tex]log_{2}[/tex] 2

From law of logarithms;  [tex]log_{2}[/tex] 2 = 1

Therefore : 5 [tex]log_{2}[/tex] 2 = 5 x 1 = 5

Answer:

5

Step-by-step explanation:

We gonna multiply the 36 inches long, 8 inches wide and 10 inches tall and divide it by no of bag (576)

Answer:

[tex]\int k(x + 18)dx = \int kx + 18k dx[/tex] = [tex]k\frac{x^{2} }{2}[/tex] + [tex]18kx[/tex] + C where C is the constant of integration.

Step-by-step explanation:

i)it is given that the rate of change of W with respect to x is proportional to          

     x + 18. Therefore [tex]\frac{dW}{dx}[/tex] = k(x + 18) where k is a constant.

ii) Therefore [tex]\int k(x + 18)dx = \int kx + 18k dx[/tex] = [tex]k\frac{x^{2} }{2}[/tex] + [tex]18kx[/tex] + C where C is the constant of integration.

iii) the complete solution can only be found if we know the constant of proportion and also the constant of integration.