a line with slope 2 intersects a line with slope 6 at the point (40, 30). what is the distance between the x-intercepts of these two line

Answer:

3/2

Step-by-step explanation:

To multiply fraction×fraction, you multiply top×top and bottom×bottom.

2/3 × 3/2

= 6/6

= 1

The 3/2 is called the reciprocal. Take the number in the problem and flip it over to find the reciprocal.

The equation from the given graph is y=-2/3 x²+5.

From the given graph the vertex is (h, k)=(0, 5).

A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

Here, point on the given line from the graph is (3, -1)

Put (x, y)=(3, -1) and (h, k)=(0, 5) in y = a(x - h)² + k, we get

-1=a(3-0)²+5

⇒ 9a=-6

⇒ a=-2/3

Now, y=-2/3(x-0)²+5

y=-2/3 x²+5

Hence, the equation from the given graph is y=-2/3 x²+5.

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The figure that is a dilation of figure E is the figure F

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The graph represents the given parameter

From the figure, we have the original shape to be figure E

The center point of figure E is the origin

This means that a line drawn from the origin that passes through point E must pass through the same point on the shape

From the figure, the line passes through the same point on figure E and F

Hence, figure F is a dilation of figure

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Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.

Cost of both the plans will be equal for 6 movies.

A linear function is defined as a function that has either one or two variables without exponents.

Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.

According to question,

A = 19 + 0.50x and

B = 13 + 1.5x

For costs being equal, we have,

A = B

19 + 0.50x = 13 + 1.5x

x = 6

Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x

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Answer:

  x = 3

Step-by-step explanation:

You want the equation of the line through points (3, -3) and (3, -6).

The two points have the same x-value, indicating the line through them is a vertical line. That will have an equation of the form x = c.

The x-value of the given points is 3, so the equation is ...

  x = 3

__

Additional comment

We note that the answer box is pre-filled with "y =". There is no "y =" equation that will go through these points. The slope is undefined, so the slope-intercept form of the equation cannot be used.

There is 2.1 miles distance between the last water stop and the end of the race.

Total miles Julio will run = 13.1 miles

Distance at which water stops are location = 2.75

Total number of water stops in full race of 13.1 miles = 13.1 / 2.75

=4.764

so , there are 4 stops in the runs for drinking water every 2.75 miles

Distance from starting point of race and last water stops = 4 × 2.75 = 11 miles

Distance between the last water stop and the end of the race = 13.1 - 11

= 2.1 miles

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1/36 is the probability that you score 4 points both times.It is the likelihood of scoring four points twice.

1/6 * 1/6 =1/36

The probability of an event occurring is measured by its probability. It determines the probability of an event. The probability calculation is P(E) = Number of Favourable Outcomes/Total Outcomes.A game is a formalized form of play that is frequently done for amusement or fun but can also serve as a teaching game tool.

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The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

The area of a circle, A, is calculated using the formula A = pi * r2, where r is the circle's radius. Since we already know that a semicircle is half of a circle, we can easily divide that equation by two to determine the area of a semicircle. As a result, A = pi * r2/2 is the formula for calculating the area of a semicircle.

With the aid of the following formula, we can determine a semicircle's perimeter: The semicircle's perimeter is equal to r + 2r units, where r is the radius of the semicircle.

Diameter of the semi-circle = 84cm

Now,

the circumference of the semi-circle  =  πr + 2r

Substituting the value of r in the given formula:

the circumference of the semi-circle  =  πr + 2r

                                                              = πr + 2r

                                                               = 48π + 42

The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

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The bearing of the helicopter from B to A is 75.96 degrees

Information from the question

A helicopter leaves A and flies 40 miles due east

the helicopter flies

10 miles due south

Work out the bearing of B from A = ?

The bearing from B to A is worked using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = 40 miles

adjacent = 10 miles

The bearing is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

tan x = 40 / 10

tan x = 4

x = arc tan 4

x = 75.96 degrees

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The cross-sectional area is (h × w ) + ((1 ÷ 2) × 0.9 × w²) and the dimensions of the window which minimize the perimeter is (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A.

height of rectangle = h

height of the triangle = t

T = 0.9

width of the rectangle = w

The formula of Cross-sectional area is,

A = h × w + (1 ÷ 2)T × w

A = (h × w ) + ((1 ÷ 2) × 0.9 × w²)

Perimeter,

P = w + (2 × h) + 2√(T² + (w ÷ 2)²)

P = w + (2 × h) + 2√((0.9)² + (1 ÷ 2)²)

P = 2h + 2√((0.9)² + (1 ÷ 2)² + 1) × w

Therefore, [tex]C_{0}[/tex] = 0.9 ÷ 2, [tex]C_{1}[/tex] = 2, [tex]C_{2}[/tex] = 2√((0.9)² + (1 ÷ 2)² + 1)

minP=[tex]c_1[/tex]h+[tex]c_2[/tex]w

A = (h × w) + [tex]c_{0}[/tex]w²

substituting h = (A - [tex]c_{0}[/tex]w²) ÷ hw in P,

P = [tex]c_1[/tex]w + ([tex]c_1[/tex](A - [tex]c_{0}[/tex]w²) ÷ w)

Differentiating both sides,

(dP ÷ dw) = -2[tex]c_{0}[/tex][tex]c_{1}[/tex] + [tex]c_{2}[/tex] - ([tex]c_{2}[/tex](A - [tex]c_{0}[/tex]w²) ÷ w²) = 0

[tex]w_{0}[/tex] = (√[tex]c_{1}[/tex]A ÷ (√[tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex])) = 0.962445√A

and consequently,

[tex]h_{0}[/tex] = (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A

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The time in hours for the Tran family's sprinkler will be 30 hours.

The time in hours for the Campbell family's sprinkler will be 35 hours.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The water output rate for the Tran family's sprinkler was 35 L per hour.

The water output rate for the Campbell family's sprinkler was 25 L per hour.

And, The families used sprinklers for a combined total of 65 hours, which is resulting in a total water output of 1925 L.

Now,

Let time in hours for the Tran family's sprinkler = t

And, The time in hours for the Campbell family's sprinkler = 65 - t

So, We can formulate by the given condition,

⇒ 35t + 25 (65 - t) = 1925

Solve for t as;

⇒ 35t + 25 (65 - t) = 1925

⇒ 35t + 1625 - 25t = 1925

⇒ 10t + 1625 = 1925

⇒ 10t = 1925 - 1625

⇒ 10t = 300

⇒ t = 30

Thus, The time in hours for the Tran family's sprinkler = t

                                                                                   = 30 hours

And, The time in hours for the Campbell family's sprinkler = 65 - t

                                                                                          = 65 - 30

                                                                                          = 35 hours.

Therefore, we get;

The time in hours for the Tran family's sprinkler will be 30 hours.

The time in hours for the Campbell family's sprinkler will be 35 hours.

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Answer:

2.5 × 10^-1

step-by-step explanation:

To get to standard form, you must move the decimal to the right one place so the number before it is not a 0. Because you move the decimal, you must add the second part of the equation so that the value does not change.

Answer:

02.5 but the 0 at the beginning isn't significant so 2.5

Step-by-step explanation:

because to find the standard form you move the decimal point so that there is only one non-zero digit in front of the decimal point.

The probability of each event will be

a. 0.122

b. 0.1

c. 0.64

d. 0.63

Probability of a $2 winner is 1 in 10

Probability of a $5 winner is 1 in 50

Probability of a $10 winner is 1 in 500

The formula to find probability is

1. no. of favorable outcomes / total no. of favorable outcomes

                                                  OR

2. P(A) = n(A)/n(S)

where

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space

Now we will use formula to find probability of different events happening

a. To find the probability of getting either a $2, or $5, or $10 winner we

will find probability of $2 , $5 and $10 and add them together.

1/10 + 1/50 + 1/500 = 0.122

b. The probability of getting a $2 winner will be

1/10 = 0.1

c. The probability of getting no $5 winner is (49/50)^50 = 0.36

So the probability of getting $5 winner will be 1 - 0.37 = 0.64

d. The probability of getting no $10 winner is (499/500)^500 = 0.37

And we can take probability of total no. of outcomes as 1.

So the probability of getting $10 winner will be 1 - 0.37 = 0.63

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Answer:

Step-by-step explanation:

the degree of the function ,  also means how many zeros , or roots,  There will be.

Answer:6 is the correct answer

Step-by-step explanation:

Because 16 + 20 equals 36 and the sq root of 36 is 6. So you chose the correct answer.

Answer:

6

Step-by-step explanation:

[tex]\sqrt{16+20}[/tex]

[tex]\sqrt{36}[/tex]

6

The interior angles of the second triangle will be 50°, 55°, and 75° respectively.

What are similar triangles?

If the corresponding angles and sides of two triangles are congruent, then the two triangles are said to be similar.

In other words, similar triangles have the same shape but may differ in size.

Given, a triangle has interior angles of 50°, 55°, and 75° with side lengths of 3.1 m, 3.2 m, and 4.0 m.

And, a second triangle has side lengths of 10.3 m, 10.5 m, and 12.0 m.

The corresponding sides of both triangles are 3.1 m, 3.2 m, and 4.0 m with  10.3 m, 10.5 m, and 12.0 m respectively.

Then, the angles of both triangles are also corresponding to each other.

So we get, the interior angles of the second triangle will be 50°, 55°, and 75° respectively.

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Time taken by pipe 1 to fill the pool is 6 and by pipe 2 is 12.

Here we have to find the time taken by each pipe to fill the pool.

Formula to find the work:

w = r × t

where

w =  is the work done

r = is the rate of work done

t =  is the time taken to do the work

For pipe 1 working alone to fill 1 pool, the work done is 1

w1 = r1 t1

1 = r1 × t1

t1 = 1/r1

For pipe 2 working alone to fill 1 pool, the work done is 1;

w2 = r2 t2

1 = r2 × t2

t2 = 1/r2

From the question, it would take 9 hours if each pipe took turns filling half the pool. That is;

t1/2 + t2/2 = 9

t1 + t2 = 18

However, if both pipes worked together, it would take 4 hours for each pipe. That is;

w1 + w2 = w

r1t1 + r2t2 = 1

4r1 + 4r2 = 1

r1 + r2 = 1/4

As we know from the above:

r1 = 1/t1 and r2 = 1/t2

So;

1/t1 + 1/t2 = 1/4

(t2 + t1)/ t1 t2 = 1/4

t1 + t2 = 18

So

t1 t2 = 72

The only factors of 72 that satisfy the conditions

t1 + t2 = 18

t1 . t2 = 72

are 6 and 12.

Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours.

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A retailer raised a shirt's original price by a certain percentage before lowering it by the same percentage. The price was increased and decreased by 40% as the final cost was 84% of the initial cost.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Here,

Let's say the shirt originally cost Rs 100, and we're adding t% to the price.

The new price of the shirt is therefore 100 + (t/100 * 100) = Rs. 100+t after the initial t% increase.

The price is then reduced by t%.

Cost of a new shirt: (100 + t) - (t/100)

[100+t] = (100+t)

[1-(t/100] = [(100+t)/100]

therefore, the final price is equal to 84% of Rs 100, or Rs 84.

10000 - t^2 = 84.

t^2 = 1600

 t = 40

The price was thus raised and lowered by 40%.

The original price of a shirt was increased by a specific percentage before being decreased by the same percentage by the retailer. As the final price was 84% of the initial price, the price was both increased and decreased by 40%.

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Given the slope of the line and the pair of points, the missing y - value can be found to be - 17

The slope formula is:

y = Slope(x) + y - intercept

Using the point (4, 8), the y - intercept can be found by the formula:
8 = 5/2 (4) + y - intercept

y - intercept = 8 - 10

y - intercept = -2

The missing y value is therefore:

y = Slope(x) + y - intercept

= -6 (5/2) - 2

= -15 - 2

= - 17

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In regards to the question above, the solution for the equation is x=-2(1+2x)/x^2-4.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. Equations come in two varieties: identities and conditional equations.

How to solve this:

2/x^2-4 -1/x+2=3/x-2

collecting like terms

2/x^2-4 -1/x+2 -3/x-2=0

Divides through by:

x^2-42 -1(x-2) -3(x+2)/x^2-4=0

Remove bracket: 2-x+2-3x-6/x^2-4

Lastly, collecting like terms:

2+2-6-x-3x/x^2-4-2-4x/x^2-4

=-2(1+2x)/x^2-4

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Part (a)

Each year is independent of any other. This allows us to simply multiply the probability values for each increase. Recall that P(A and B) = P(A)*P(B) if and only if events A & B are independent.

(0.65)*(0.65)*(0.65) = (0.65)^3 = 0.274625

=========================================

Part (b)

We calculated the probability of an increase for each of the 3 years back in part (a). Let's calculate we have a decrease 3 times in a row.

0.65 is the probability of increase for any given year, which makes 1-0.65 = 0.35 the probability of decrease for any given year.

Therefore (0.35)^3 = 0.042875 represents the probability of 3 decreases in a row.

Add this result to what we got in part (a)

0.274625+0.042875 = 0.3175

This is done because we could have 3 increases OR 3 decreases (pick one). Think of it like this P(A or B) = P(A) + P(B) where A & B are mutually exclusive events.

=========================================

Part (c)

In the previous part we calculated 0.042875 as the probability of 3 decreases in a row.

1-0.042875 = 0.957125 is the probability of at least one increase. Note how the events "no increases" and "at least one increase" are complementary events. They are opposite. One or the other must happen, which allows us to subtract from 1.

You can think of it like this

P(no increases) + P(at least one increase) = 1

P(at least one increase) = 1 - P(no increases)

Side note: none of the final answers have been rounded.

The rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2

Given data,

A partially filled inverted cone contains water. The inverted cone has a 16 mm radius. The inverted cone is 18 mm in height. if the water's volume is growing at a pace of 548 cubic millimeters per hour.

The rate in mm per hour at which the height of the water is changing when the height of the water is 2 mm;

r/h = 16/18

    = 8/9

r = 8h/9

The volume of the cone is;

v = [tex]\frac{1}{3}\pi r^2h[/tex]

v = [tex]\frac{1}{3}\pi (8h/9)^2h[/tex]

v =  [tex]\frac{64}{243}\pi h^3[/tex]

Now, differentiating concerning x;

[tex]\frac{dv}{dt}[/tex]= [tex]\frac{d}{dt}[/tex]        [tex]\frac{64}{243}\pi h^3[/tex]

[tex]\frac{dv}{dt}[/tex]=  64π/243*[tex]\frac{d}{dt}[/tex] h³

[tex]\frac{dv}{dt}[/tex]= [tex]\frac{64}{81}\pi h^2\frac{dh}{dt}[/tex]

We have;

[tex]\frac{dv}{dt}[/tex]= 548 and h = 2mm

[tex]\frac{dh}{dt} = \frac{548*81}{256\pi }[/tex]

[tex]\frac{dh}{dt}[/tex] = 55.19

           [tex]\frac{dh}{dt}[/tex] = 55.2mm per hour.

Hence, the rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2

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The unit rate of change , d with respect to t is =  1.6  .

In the question,

it is given that ,  the relationship between d and t is proportional

also given that "  increase of 5 units in t corresponds to increase of 8 units in d ".

which is represented as 5t = 8d

Divide both sides of the equation  5t = 8d by "5" ,

t = 8/5d

t = 1.6d

next we plot the graph of t = 1.6d

we see that the above equation is a proportional linear equation

and A proportional linear equation is represented as

t = md , Where m represents the unit rate .

So , after comparing , we get

m = 1.6

Therefore , The unit rate of change of d with respect to t is 1.6  .

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Y=5p+3

Y equals the total amount of tape rolls

P is for the number of packages there are.

Hope this helped!

:)

Answer:

Y=5p+4

Y equals the total amount of tape rolls

P is for the amount of packages there are

Step-by-step explanation:

Given that the delivery person works an 8-hour shift, he needs 4 gallons of gasoline in his tank.

A function is defined as the expression that relates a independent variable with a dependent variable. To evaluate a function is to substitute the value of the independent variable and then calculate the function value.

Given that the delivery person works an 8-hour shift, substitute x = 8 to the function of y.

y = f(x) = x² + 3x

y = 8² + 3(8)

y = 88

To determine the amount of gasoline needed, substitute the value of y to the function of g of y.

g = y / 22

g = 88 / 22

g = 4

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Answer:

3×10^7

Step-by-step explanation:

Write 30 000 000 in standard form.

=3×10,000,000

=3×10^7

Step-by-step explanation:

this is

3.0 × 10⁷

as 30 000 000 has 7 zeroes (7 sequential and continuously increasing powers of 10 starting with 10¹).

and the first non-zero digit is 3.

Answer:

f = 3cm g = 16cm

Step-by-step explanation:

Area of ABCE = 60cm²

Area of ABCD = 48cm²

60 - 48 = 12

Area of ADE = 12cm²

A to D = 3cm

f = 3cm

g = 16cm

When the sample size is smaller than 30, the following requirements must be met for the sampling distribution of the sample mean to be considered normal:

If these conditions are satisfied then the sampling distribution of the sample mean to be normal when sample size is less than 30.

A statistic's sampling distribution is a form of probability distribution produced by selecting several random samples of a predetermined size from the same population. You may better comprehend the variations in a sample statistic by using these distributions.

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Answer for No.2
Answer: 1/4

Step-by-step explanation:

Hits = 12

Misses = 60-12 = 48

Ratio of hits to misses = 12/48 = ¼

So the answer is 1/4.