write the equation for the line through (4,3) with a slope of -1/2 in slope intercept form

The rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

The distance covered in a unit of time is known as speed.

Given that, the airplane travels 7680 km in 8 hours flying against the wind, and 12420 km in 9 hours.

Therefore, the rate of the airplane against the wind is:

7680/8

= 960 km / hr

The rate of the airplane with the wind is:

12420/9

=1380 km / hr

Let the rate of the airplane in still air be a and the rate of the wind be w.

The net rate while flying against the air is:

a - w = 960       (1)

The net rate while flying with the wind is:

a + w = 1380      (2)

Add equations (1) and (2):

2a = 2340

a = 1170 km/hr

Substitute a = 1170 into equation (1):

1170 - w = 960

1170 - 960 = w

210 = w

Hence, the rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

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Answer:

[tex]-4i\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

[tex] - 4 \sqrt{3i} [/tex]

Answer:

here is the answer have a good day

Answer:

1. 40/5=8

8 x 3p=24p

8(3p+5)=24p+40

2. 48/8=6

    64/8=8

8(6q-8)=48q-64

The sum of all angles in a triangle sum up to 180.

∠1 = x+37

∠2=x+67

∠3=90° (right triangle)

∠1+∠2+∠3 = 180°

(x+37)+(x+67)+90=180

2x+104+90=180

2x+194=180

2x=-14

x=-7

An angle can't be negative, but when plugged in it works!!

∠1 = -7+37=30

∠2=-7+67=60

30+60+90=180

Hope it helps!

Answer:

D

Step-by-step explanation:

there are no restrictions on the domain and

- ∞ < x < ∞

That is the domain is all real numbers

Answer:

y= 38 + 0.20x

The equation will be y=38+0.20x where x is the number of texts and y is in dollars.

An equation is a relationship between the variables and constants representing how they are related to each other. It includes equal to "=" sign.

It is known that the fixed payment is of $38 and each text costs $0.20.

Assume Colette sends x texts in a month and y be the total cost.

Determine the monthly cost equation.

Total cost= Fixed cost+ x(cost of each text)

y=38+0.20x

So, the total monthly cost will be represented by the equation, y=38+0.20x.

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The solution of the inequality 2b + 5 ≤ 30 is b ≤ 12.5

Inequalities refers to some type of equations where the relationship between the left hand side and the right hand side of an equation is expressed in terms of symbols other than equal to

The symbols include

In the problem given the symbol used is less than or equal to and the equation is solved by

2b + 5 ≤ 30

2b + 5 - 5 ≤ 30 - 5

2b ≤ 25

dividing through by 2

2b / 2 ≤ 30 / 2

b ≤ 12.5

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Answer: What??

Step-by-step explanation:

There is a 0.990025 probability that this area won't experience a major earthquake in the next two years.

In the field of mathematics called probability theory, random occurrences are studied. The outcome of a random event can take any number of distinct shapes, but it cannot be anticipated before it occurs. The outcome is believed to have been decided by chance.

Given,

In a region where large earthquakes of magnitude 7 or higher have occurred about once every 200 years,

First, the likelihood of an earthquake with a magnitude of 7 or higher is 1/200 = 0.005.

The likelihood of there not being an earthquake is then requested, and it is 1-0.005 = 0.995.

The likelihood that there won't be an earthquake in two years is then

0.995 x 0.995, or.0990025.

The probability that we will not have a big earthquake in this region in the next two years is 0.990025.

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The number -58 is a real number and it cannot be represented as a complex number

From the question, we have the following expression that can be used in our computation:

Expression = -58

The given expression above is a number

And also, it is a negative number

Negative numbers of this form are real numbers

This means that the such numbers cannot be represented as a complex number

Hence, the number -58 does not have a complex equivalent

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The interval of the cost of the car is [5600, ∞).

Here we have to find the cost of the car.

Let x be the cost of the car.

So from the question, we have that the cost of the repair is 25% or more of the car's value.

So we have to find the interval notation of the cost of the car.

x ×25% ≥ 1400

x × 25/100 ≥ 1400

x ≥ 1400× 100/25

x≥ 5600

So we get that the cost of the car is greater than $5600.

Therefore the cost of the car in an interval is [5600, ∞)

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There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

In mathematics, the greatest common divisor of two or more nonzero integers is the largest positive integer that divides each integer

. The greatest common divisor (GCF) of a set of numbers is the greatest factor of division of all numbers.

GCF by listing factor method :-

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

other two methods are attached below .

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Answer:

L=66 degrees

KL=3.5

LM=8.7

The price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.

Let the price of 1 kilogram of jelly bean cost be x

and the price of 1 kilograms of gummy worms be y

Dean bought 2 kilograms of jelly beans and 3 kilograms of gummy worms

for $38

2x + 3y = 38......equation 1

Sue bought 3 kilograms of jelly beans and 3 kilograms of gummy worms

for $45

3x + 3y = 45........equation 2

Subtracting equation 2 from equation 1

2x + 3y - (3x + 3y) = 38 - 45

2x - 3x + 3y - 3y = -7

-x = -7

x = 7

2(7) + 3y = 38

14 + 3y = 38

3y = 24

y = 8

Therefore, the price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.

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The homogeneity of variance is an assumption for the one-way between-subjects anova means each population from which the samples are drawn has the same level of variation.

Both t tests and F tests (also known as analyses of variance, or ANOVAs) are based on the premise that the population variances (i.e., the distribution, or "spread," of scores around the mean) of two or more samples are identical. The independent samples t-test and ANOVA employ the t and F statistics, which, provided that group sizes are equal, are often resistant to breaches of the assumption. A ratio of less than 1.5 between the largest and smallest group can be used to identify equal group sizes.

The independent samples t-test and ANOVA make the assumption of homogeneity of variance, which states that all comparison groups have the same variance. The homogeneity of variance is an assumption for the one-way between-subjects anova means each population from which the samples are drawn has the same level of variation.

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By using the vertex and the given point, we will see that the graphed quadratic equation is:

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

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)^2 + k

Here the vertex is (2, 4), replacing that we get:

y = a*(x - 2)^2 + 4

Now we also can see that the line passes through the point (0, -8), replacing these values we get:

-8 = a*(0 - 2)^2 - 4

-8 = 4a - 4

-8 + 4 = 4a

-4 = 4a

-4/4 = a

-1 = a

The quadratic equation is:

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

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The circumcenter is where three perpendicular bisectors intersect and the incenter is where the three angle bisectors intersect.

The circumscribed circle or circumcircle of a polygon in geometry is a circle that passes through each of the polygon's vertices. This circle's circumcenter and circumradius are its centre and radius, respectively.

Construct angle bisectors of each angle of the triangle and their intersection point gives the incenter.

To find Circumcenter:

Construct perpendicular bisectors of all sides of the triangle and their intersection point gives the circumcenter.

Circumcenter Theorem: It states that the vertices of a triangle are equidistant from the circumcenter.

Incenter Theorem: It states that the incenter is equidistant from the sides of the triangle.

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For the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

As given in the question,

Geometric mean GM = 30

Let us assume the first number is x

and second number i.e. 9 times of the first number is 9x

By the formula GM = [tex]\sqrt{x.y}[/tex]

Now putting the value

30 = [tex]\sqrt{x.9x}[/tex]

30 = [tex]\sqrt{9x^{2} }[/tex]

30 = 3x (∴ square root of 9 is 3 and sq root of x² is x)

10 = x  (by dividing both the side by 3)

Therefore, for the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

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Answer:

Paco, Tim, Jenny, Maria

Step-by-step explanation:

The total amount of water Karla drank before and after the tennis practice is 5 cups and 9 fluid ounces.

The correct answer option is option C.

Convert fluid ounces to cups:

1 fluid ounces = 0.125 cups

15 fluid ounces = 1.875 cups

Total volume of water Kayla drank = Volume of water Karla drank before tennis practice + Volume of water Karla drank after tennis practice

= 1.875 cups + 4 cups

= 5.875 cups

Approximately,

5 cups and 9 fluid ounces

Therefore, the total volume of water Karla drank is approximately 5 cups and 9 fluid ounce

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The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

Let the length (cm) be l , width (cm) be w , area be A ([tex]cm^{2}[/tex]) and time (s) be t .

Given : dl / dt = 6 cm/s and dw / dt = 8 cm/s

Area of rectangle = l * w

Differentiating wrt. t ,

dA / dt = ( l ) ( dw / dt ) + ( dl / dt ) ( w )

Therefore , dA / dt = 8l + 6w

Hence , when l = 12 cm and w = 10 cm

dA / dt = ( 8 * 12 ) + ( 6 * 10 )

dA / dt = 156 [tex]cm^{2}[/tex]/s .

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

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The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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Answer:

y=1/4x+3

Step-by-step explanation:

To write an equation, let's infer we need to write it in slope-intercept form. We need the y-intercept. We can plug 1/4 and (-4,2) into y=mx+b, to solve for b. We have:

2=1/4*-4+b

2=-1+b

3=b

Since we have the slope, 1/4, we can create our equation:

y=1/4x+3

Solve for b in (y=mx+b):

b=y-mx

b=2-(1/4)(-4)

b=2+1

b=3

So the equation is y= (1/4)x + 3

The ordered pair of the values of f(x) and g(x) of (4, 3) and (4, 3) indicates that the input value that produces the same output value for f(x) and g(x) functions is x = 3

The input values of a function are the values that serve as the argument of the function. They are also known as the independent variable. The operations of a function are performed on the input values such that each input produces only one output, which is known as the dependent variable. The set of the input values is known as the domain of the function.

The output value of a function are the values of the function that gives the image of the input values, and they are known as the dependent variable. The set of the output values is the range of the function.

The points on the graph are;

Therefore, from the graph, at the point x = 3, f(x) = g(x) = 4

The input value that produces the same output value for the two functions on the graph is the x-value of 3

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The processing fee was = $36.96

acc to our question-

let the price of headphones be= x

Hence,The processing fee was = $36.96

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Answer:

70%

Explan your answer :

200-130=70 and 70% of 100 = 30% so

Answer: 65

Step-by-step explanation:

0.65

×

100

=

0.65×100=

65

%

65%

What does 3x-19 equal? You can find x without it being an equation

The solution is, the value of x is 6.33.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

(3x-19) = 0,

here, we have to make the given expression simple, as we have to find the value of x.

so, we get, by isolating the variable & numbers,

adding 19 on both sides we get,

3x = 19

dividing both sides by 3, we get,

or, x = 19/3

or, x = 6.33

Hence, The solution is, the value of x is 6.33.

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Answer:

Last option: 31

Step-by-step explanation:

No. of catalogs that can be arranged

= (longest side of shelf ÷ longest side of catalog) × (shortest side of shelf ÷ shortest side of catalog)

= (56 ÷ 5) × (5 ÷ 4)

= 31

With the help of factorisation we can conclude our answer.

acc to our question-

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