What is the equation of the line that passes through the point (-4, 5) and has an
undefined slope?

Answer:

11/48

Step-by-step explanation:

x-2/5=2/3-3x-2/6

collect like terms

x-2/5 + 3x = 2/3 - 2/6

taking LCM on both sides

[(x-2) + 5(3x)]/5 = [2(2) -2]/6

(16x - 2)/5 = 2/6

cross multiply

6(16x - 2) = 5(2)

96x - 12 = 10

96x = 22

therefore; X = 22/96

= 11/48

CHECK:

(11/48 - 2)/5 = 2/3 - 3(11/48) - 2/6

(-85/48)/5 = 2/3 - 11/16 - 2/6

-85/48 × ⅕ = -17/48

-17/48 = -17/48

Answer:

[tex]x=\frac{11}{60}[/tex]

Step-by-step explanation:

Given the equation

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2}{6}[/tex]

Lets solve for x.

Simplify the right side of the equation.

Cancel the common factor of 2 and 6 .

Factor 2 out of 2 .

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2(1)}{2(3)}[/tex]

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{1}{3}[/tex]

Combine the numerators over the common denominator.

[tex]x-\frac{2}{5}=-3x-\frac{2-1}{3}[/tex]

[tex]x-\frac{2}{5}=-3x-\frac{1}{3}[/tex]

Move all terms containing x to the left side of the equation.

Add [tex]3x[/tex] to both sides of the equation.

[tex]x-\frac{2}{5}+3x=\frac{1}{3}[/tex]

Add [tex]x[/tex] and [tex]3x[/tex].

[tex]4x-\frac{2}{5}=\frac{1}{3}[/tex]

Move all terms not containing x to the right side of the equation.

Add [tex]\frac{2}{5}[/tex] to both sides of the equation.

[tex]4x=\frac{1}{3}+\frac{2}{5}[/tex]

To write [tex]\frac{1}{3}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{5}{5}[/tex] .

[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}[/tex]

To write [tex]\frac{2}{5}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex]

[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}*\frac{3}{3}[/tex]

Simplify.

Write each expression with a common denominator of 15 , by multiplying each by an appropriate factor of 1 .

[tex]4x=\frac{11}{15}[/tex]

Divide each term in [tex]4x=\frac{11}{15}[/tex] by 4 and simplify.

[tex]x=\frac{11}{60}[/tex]

The average speed of Erin on the return part is 12 miles/hour

Given, Erin leaves home at 11am. She cycles at a speed of 16 miles per hour for 90 minutes. She stops for half an hour. Erin then cycles home and arrives at 3pm.

We have to find the average speed on the return part of her cycle.

Now, using distance formula, we get

Distance = Speed × Time

Distance = 16 miles per hour × 90 × 1/60 hours

Distance = 24 miles

As, average speed = Total distance/Total time

Average speed = 24 miles / 2 hours

Average speed = 12 miles per hour

Hence, the average speed of Erin on the return part is 12 miles/hour

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The 8 cm² area on a map  represent the actual area = 3200000000 cm² .

Scale factor of a map

S = 1/20000

The scale factor for area is found by squaring the scale factor for length. Thus the scale factor for area is S^2

When applied to the area we consider  S^2 as a scale factor.

The area on the map = 8 cm²

So The actual area = 8 × (20000)^2 = 8× 20000×20000

=3200000000 cm²  = 320000 m² =32 hectare.

So the 8 cm² area on a map  represent the actual area = 3200000000 cm² .

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The resulting ordered pair is (15, 37.50) when the value of x as 15.

Ordered pair

Ordered pair refers a set of numbers that tells us where to find a point on a coordinate grid. In the grid, the first number represents the value on the x-axis and the second number represents the value on the y-axis.

Given,

A student used the equation below to create a table.

y = 2.50x

The student used 15 as one of the values for the x.

Here we need to find the resulting ordered pair.

Through the given question we have identified that the given function is,

y = 2.50x.

Here x represents the number of students.

Now, we have to calculate the y value for 15 number of students,

So, here we have to apply the value x as 15, then we get,

y = 2.50 (15)

Now, we have to perform the multiplication on it,

y = 37.50

Therefore, the resulting ordered pair is (15, 37.50)

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The statements are characterized as converse, inverse, and contrapositive statements as follows:

Converse statements:

Inverse statements:

Contrapositive statements:

So, the given sentences are:

Therefore, the statements are characterized as converse, inverse, and contrapositive statements as follows:

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Answer:

1,2,4

Step-by-step explanation:

edem

The probability of getting at least 1 red marbles is 3/7.

What is probability?

Probability of getting at least one red = 1 − Probability of getting red marbles

Total number of marbles = 7

Probability of getting red marbles = 4/7

Probability of getting at least one red = 1 - Probability of getting red marbles

= (7-4)/7

= 3/7

Hence, The probability of getting at least 1 red marbles is 3/7.

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Answer: 2

Step-by-step explanation:

if you plug in -6 into x, we get

36 - 36 + 2

the 36s will cancel each other out, leaving us with only 2 as our final answer.

Answer: -70

Step-by-step explanation:

-[tex]6^{2}[/tex] + 6(-6)+2

= -36 - 36 + 2

= - 70

The total flying time for the round trip if there was no wind would be 2 hours 24 minutes. The result is obtained by using the elimination method.

The elimination method is a method for solving system of linear equations where we eliminate one variable so that we can get an equation in one variable. In doing that, we can either add or subtract the equations.

Given the case that an airplane takes 1 hour 30 minutes to fly 600 km against the wind. It takes only 1 hour in the return trip.

What would be the total flying time for the round trip if there was no wind?

Let's say:

When the airplane leaves,

v - w = 600 km / 1.5 hour

v - w = 400 kph ... (equation 1)

When the airplane returns,

v + w = 600 km / 1 hour

v + w = 600 kph ... (equation 2)

We eliminate the equation 2 and 1 to get the speed of the airplane.

v - w = 400 kph

v + w = 600 kph +

2v = 1000 kph

v = 1000 ÷ 2

v = 500 kph

For the round trip, the airplane would fly 600 × 2 = 1200 km.

The total flying time if there was no wind would be

t = s/v

t = 1200/500

t = 2.4 hour

t = 2 hours 24 minutes

Hence, the  total flying time for the round trip if there was no wind is 2 hours 24 minutes.

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Perimeter of the polygon with given vertices is 22.43

Given:

Point 1 : (-2,4) ,

Point 2 : (3,4),

Point 3 :(3,-4)  

Perimeter of a polygon  = Sum of all the sides length of polygon  

1. Length of Point 1 and point 2 = √[(x₂-x₁)²+(y₂-y₁)² ]                

= √[(3+2)²+(4-4)² ]                  

= 5  

2.Length of Point 1 and point 3 = √[(x₂-x₁)²+(y₂-y₁)² ]

           =  √[(3+2)²+(-4-4)² ]                    

= 9.43  

3. Length of Point 2 and point 3  =√[(x₂-x₁)²+(y₂-y₁)² ]            

= √[ (3-3)²+(-4-4)² ]                      

= 8

So, Perimeter of the polygon = 5+9.43+8

Perimeter of the polygon  = 22.43

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This is the required final answer  Emily spends $300y/x  and Andy spends $432y/x for wire.

The answer provided below has been developed in a clear step-by-step manner.

1 foot =12 inches

1 yard=36 inches

Emily needs (25×12)=300 inches wire

and Andy needs (12×36)=432inches wire

As the cost for x inches wire is $y

cost for a 1-inch wire is $x/y

So, the cost for 300 inches of wire is $300y/x

cost for 432 inches of wire is $432y/x

so, Emily spends $300y/x

and Andy spends $432y/x for wire.

More than 20 different currencies go by the name dollar. The Australian dollar, Brunei dollar, Canadian dollar, Hong Kong dollar, Hogan dollar, Jamaican dollar, Liberian dollar, Namibian dollar, New Taiwan dollar, New Zealand dollar, Singapore dollar, United States dollar, Trinidad and Tobago dollar, and a number of others are among them. Like many nations that use the peso as their currency, the majority of those currencies are denoted by the dollar sign $.

The word "dollar" is a translation of the German word "thaler," which means "person or thing from the valley" in English. America's monetary unit is called after the "thaler," the name given to the first silver mine-produced coins, which were initially coined in Joachimsthal, Bohemia, in 1519.

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The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .

In the question ,

it is given that ,

the the exponential function is y = 660(0.902)ˣ

we need to determine that , the equation represents a growth or decay .

0.902 is the variable that will determine a growth or decay .

Since, 0.902 is less than 1 , so it represents a decay function .

To find the rate we subtract 0.902 from 1

= 1 - 0.902

= 0.098

= 9.8% decrease rate

Therefore , The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .

The given question is incomplete , the complete question is

Identify if it's Growth or Decay , and determine the percentage rate of increase or decrease , the function is y = 660(0.902)ˣ ?

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The person has about 20 yellow beads.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the person received 45 beads out of which 45% are yellow.

Therefore, the number of yellow beads is,

45% of 45

= (45×45)/100

= 2025/100

= 20.25

≈ 20

Hence, the person has about 20 yellow beads.

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you can refer to the explanation I wrote for you on paper since it is much easier... look at the pic uploaded

The value of x on the frequency density axis is 200.

What is frequency?

The frequency of a repeated event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively.

What is density?

The mass of a substance per unit of volume is its density. Density is most frequently represented by the symbol, however, the Latin letter D may also be used.

Here, we have

x is about half of the number of beehives producing 16 to 18 kg of honey, for the middle blue bar.

x = half of 400

x = 200

Hence, The value of x on the frequency density axis is 200.

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Trip of 700 km required 70 liter  gasoline

For go 200 km Distance total gasoline required = 20 liter

For go 1 km Distance total gasoline required = 20÷200

                                                                          =  0.1 liter

Total trip distance =700 km

Total gasoline required for  going 700 km = Total distance×Gasoline required for 1 km

 Total gasoline required for  going 700 km  = 700×0.01                                                          

                                                                         = 70 liters

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70 liters of gasoline will be used on a trip of 700 kilometers.

Given that,

200 kilometer is covered by 20 liters of gasoline.

For go 1 km Distance total gasoline required = 20÷200

                                                                          =  0.1 liter

Now,

Let x be the liters of gasoline required for a 700-km trip.

            ⇒ 20/200 = x/700

            ⇒ (200) (x) = (20) (700)

            ⇒ 200x = 14,000

            ⇒ 200x/200 = 14,000/200

              or,  x = 70

Therefore, the answer is :

70 liters of gasoline will be needed for a 700 kilometer of trip.

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A six sided dice is tossed twice. The probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9 .

A dice has six faces or sides and it is throws twice . When a dice is toss first time,

Total possible outcomes on toss = 6 ={ 1,2,3,4,5,6}

In our first toss we want to get 1 or 2

So, favourable outcomes of getting 1 or 2 = 2

Probability of getting 1 or 2 on first toss= favourable cases /total outcomes = 2/6 = 1/3

For second toss, we want to get a1 or a2 again.

Total possible outcomes = 6

Probability of getting a1 or a2 on second toss= 2/6= 1/3

Now, Multiply these probsbilites togethers and chance of getting 1 or 2 on first and second which is 1/3× 1/3 = 1/9

Hence , probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9.

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Answer:

  about 21.3 cm²

Step-by-step explanation:

Given a triangle with three sides 6 cm, 8 cm, and 12 cm, and smallest angle 26.4°, you want the area.

  A = 1/2ab·sin(C)

  A = 1/2(12 cm)(8 cm)·sin(26.4°) ≈ 21.34 . . . . square units

The semiperimeter is ...

  s = (6 +8 +12)/2 = 13

The area is ...

  A = √(s(s -a)(s -b)(s -c))

  A = √(13·(13 -12)(13 -8)(13 -6)) = √(13·1·5·7) = √455

  A ≈ 21.33 . . . . square centimeters

The area of the triangle is about 21.3 cm².

__

Additional comment

The problem with over specifying the dimensions of a geometry problem is that it is often difficult to make them consistent. Here, the area values agree to three significant figures. That is about all we can expect, given the angle precision is 3 significant figures.

Your answer depends on the set of dimensions you choose to use. It will be different yet if you use the Law of Sines to find angle A or B for the Sine Formula, especially if you round the angle value to tenths.

The attachment shows the solution using side lengths only.

Answer:

x=−286

Step-by-step explanation:

22=(x)/(-13) just follow the order

The correct answer is False because, If the sample size is large enough (n greater than or equal to 30) the sampling distribution is approximately normal regardless of the shape of the population.

The sample fraction, often called the "p-hat", is the ratio of the number of sample successes to the size of the sample. The standard deviation of (p) decreases as the sample size n increases. This is because n is included in the denominator of the standard deviation formula. That is, (p has) has fewer variables for larger samples. The P-hat (must be a lowercase p with a caret (^) circumflex) indicates the percentage of the sample (this is the x-bar, the average of the samples).

A p-hat (proportion) sampling distribution is a collection of equal-sized repeated sample proportions drawn from the same population to represent it. According to the central limit theorem, the sampling distribution of p-hat is approximately normally distributed for large sample sizes.

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The parabola has a positive leading coefficient, which means that it opens upwards.

We want to find the leading coefficient and see how the parabola opens.

A general quadratic equation is written as:

y = A*X^2 +b*X+ c

Where a is the leading coefficient.

If a is positive, then the parabola opens upwards, and if a is negative, the parabola opens downwards.

In this case, the equation is:

y = x^2 - 5x - 7

The leading coefficient is a = 1, it is positive, so the parabola opens upwards.

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Answer:y=8x-5

Step-by-step explanation:

you put the problem into slope intercept form y minus y one equals the slope the parentheses x minus x one then use the distributor property so then it’s y=

After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x)+5.

What does a graphing translation mean?

The rules for transforming a function f(x) into g(x):

g(x) = a·f(b(x-c)) + d

Hence, After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x) + 5.

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Answer:

132 rs

Step-by-step explanation:

Cost of one orange = 48 : 12 = 4 rs

cost of 30 orange = 4 * 30 = 120 rs

10 : 100 = x : 120

x = (120 * 10)/100

x = 12 rs

final price = 120 + 12 = 132 rs

The point at which this cable would pass through the road shown is at the y-intercept of (0, -17/2).

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the road shown in the graph above, the points on the line include the following:

Points (x, y) = (0, -2)

Points (x, y) = (-3, 0)

Substituting the given points into the formula, we have;

Slope, m = (0 + 2)/(-3 - 0)

Slope, m = 2/-3

Slope, m = -2/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-2/3 × m₂ = -1

-2m₂ = -3

m₂ = 3/2

At point (7, 2), a linear equation for the line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - 2 = 3/2(x - 7)

y - 2 = 3x/2 - 21/2

y = 3x/2 - 21/2 + 2

y = 3x/2 - 17/2

At the y-intercept of (0, -17/2), the cable pass through the road.

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Answer:

1. 51°

2. 55°

3. 5x + 10

Step-by-step explanation:

1. We know ∠B + 39° = 90°, so ∠B = 90 - 39 = 51

2. We can use an algebraic equation to solve this problem.

    2x + 70 = 180

    2x + 70 (-70) = 180 (-70)

    2x (/2) = 110 (/2)

    x = 55

3. ∠ABD = (3x + 10) + (2x) = 5x + 10

Answer:

8 bagels

Step-by-step explanation:

This is a remainder division problem. We need to divide 719 by 9 and find the remainder.

First off, 9 is bigger than 7, so we need to move to the next digit. How many times does 9 go into 71? 9 times 7 is 63! That's the closest smaller number we can get, so I will write a 7 in the long division problem above the 1. I will subtract 63 from 71 to get 8.

      7

9 | 719

   -63

       8

Now, the 9 can be brought down, making our 8 into an 89. How many times does 9 go into 89? 9 times 9 is 81! That's the closest we can get! I will write a 9 by the 7 above the 9 in 719, and write 81 below the 89. Subtracting these leaves us with a remainder of 8.

      79

9 | 719

  -63 ↓

      89

      -81

         8

This means that the bagels were sent in 9 equal shipments of 79 bagels each, and the baker was left with 8 bagels!

Answer:

C: 9

Step-by-step explanation:

3^4/3^2

3*3*3*3/3*3 cancel out 2 threes from the bottom and top.

3*3=9

Measure of angle M is 76°, angle N is 76° and side LN is 18 in.

According to figure,

LM = 18 in

∠NLM = 28°

In triangle LMN

LN = LM

     = 18 in

Therefore, ∠LMN = ∠LNM = x     (LN = LM)

∠LMN + ∠NLM + ∠LNM = 180°

x + 28 + x = 180

   2x + 28 = 180

           2x = 180 - 28

           2x = 152

             x = 152/2

             x = 76

Hence, ∠M = ∠N = 76°.

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