If x²y - 3x = y³ – 3, then at the point (-1,2), dy/dx=

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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Answer:

Y-int = -45, X-int =-11.25

Step-by-step explanation:

Please read this before moving on :)

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+b, where m is slope and b is the y-intercept.

We know that equation of a line is y=mx+b. To find the value of the x-intercept of the line we simply need to put the value of the y as 0.

Using the Slope Equation : Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

2 points; (0,-40), (-10,0)

0-(-40)/(-10)-0 = 40/-10 = -4

Y=MX+B

Y=MX+(-45)

Y=MX-45

Y-int = -45

Y=MX+B

0=(-4)x+-45

45=-4x

X-int =-11.25

The x-intercept and y-intercept of the graph is (5,0) and (0,4)

How to find the intercept ?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

1. To find the x-intercept we put y=0

The equation becomes

4x + 5(0) = 20

4x = 20

 x =  [tex]\frac{20}{4}[/tex]

 x = 5

∴ The x-intercept is (5,0)

2. To find the y-intercept we put x=0

The equation becomes

4(0) + 5y = 20

5y = 20

 y =  [tex]\frac{20}{5}[/tex]

 y =  4

∴ The y-intercept is (0,4)

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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 scientist will take 23 seconds to get back to the sea level.

Let us calculate the distance covered by the scientist at the given speeds and at the specified times.

She travels down for 41 seconds at speed of 4.9 feet per second.

Distance travelled = 41 × 4.9 = 200.9 feet

Elevation = -200.9 feet

She then goes up for 49 seconds at speed of 3.2 feet per second.

Distance travelled = 49 × 3.2 = 156.8 feet

Elevation = -222.9 + 156.8 = -44.1

So she is at a depth of 44.1 feet below the sea level.

Time taken = 44.1 / 3.6 = 12.25 seconds

Therefore it will take her about 12.25 seconds to go back to the sea level.

The average surface level of one or more of the Earth's coastal bodies of water is known as mean sea level (MSL), which can be used to calculate heights like elevation.

There are several terminologies that describe the ebb and flow of the relationship between sea level and dry land.

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The point on a line that is at an equal distance from either end.

Hence, the equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].

What is midpoint ?

The point on a line that is at an equal distance from either end.

Here, the coordinates of [tex]A(1,-1),P(3,7),Q(\frac{-1}{2},\frac{7}{2})[/tex]

The general formula of the midpoint is

[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+t_2}{2})[/tex]

The equation of [tex]AP[/tex] is

[tex]AP=(\frac{1+3}{2},\frac{7-1}{2})\\AP=(\frac{4}{2},\frac{6}{2})\\AP=(2,3)\\[/tex]

The equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is

where [tex]AP(2,3),Q(\frac{-1}{2},\frac{7}{2})[/tex].

[tex](AP,Q)=(\frac{2+\frac{-1}{2}}{2},\frac{3+\frac{7}{2}}{2})\\(AP,Q)=(\frac{\frac{4-1}{2}}{2},\frac{\frac{6+7}{2}}{2})\\(AP,Q)=(\frac{\frac{3}{2}}{2},\frac{\frac{13}{2}}{2})\\\\(AP,Q)=(\frac{3}{4},\frac{13}{4})\\[/tex]

Hence, the equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].

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Using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.

Distance Formula: d = √[(x₂ - x₁)² - (y₂ - y₁)²]

Now, calculate the distance using the distance formula as follows:

(A) The distance between A and B is:

(B) The distance between C and D is:

(C) The distance between E and F is:

(D) The distance between G and H is 2.

(E) The distance between J and K is:

(F) The distance between L and M is:

Hence, the distance using the distance formula is:

Therefore, using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.

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The number of minutes after Cayaln puts the trays in the oven will he first remove the scones, muffins, and cookie at the same time is 300 minutes

Find the least common multiple of 25, 12 and 10 minutes

The least common multiple of of 25, 12 and 10 minutes is 300 minutes.

Therefore, the number of minutes Cayal removes the scones, muffins, and cookie at the same time is 300 minutes

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you are about to roll 2 fair six-sided dice, hoping to get a double. (a double is when both dice show the same value on top). Each double will occur once with the probability of 1/36

The sample space for the event of  rolling 2 fair six-sided  dice is  :

S={ (1, 1),(1, 2),(1,3),(1,4),(1,5),(1,6),(2,1)........., (6,5),(6,6) } , So in total for the outcome, we get a total of 36 pairs, with the probability of getting an event as 1/36, now the situation given to us is the vent of getting a double.So the event space for getting a double while  rolling 2  dice  is E = { (1, 1),(2, 2),(3,3),(4,4),(5,5),(6,6) } , the outcome will be 6 pairs, so the probability for each double pair to  come out when we roll the  2 dice is:  1/36  and the probability of getting the least double from  the 6 pairs of double is: 1/6

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Answer:

26

Step-by-step explanation:

4⅓×6

=13/3 × 6

=26

smash as brainliest

Answer:

Step-by-step explanation:

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

Answer:

3/4

Step-by-step explanation:

Get into y=mx+b

Subtract 3x

4y=3x+36

Divide by 4

y=3/4x+9

Parallel= 3/4

Perpendicular= -4/3

Answer:

The answer is III: 4.5

Step-by-step explanation:

It's not the first option since there has to be more than one person living in those houses. It's not the second since 3 is greater than 0, and median is in order from least to greatest. It's three since it's reasonable and is in order from least to greatest.

Answer: x= 9

Step-by-step explanation:

I just checked that its right!

Answer:

The correct answer would be 9

Step-by-step explanation:

The time it takes for a rocket following the path h(x)= -4x² + 16x to hit the ground is 4 seconds.

How to find the time for a rocket to hit the ground?

The given path equation is a function of x which is a time variable here. When the rocket hits ground, height of the rocket gets zero.

Hence equating the equation of height to zero and solving for x will give the time required for the rocket to hit the ground.

According to the given question:

We are given equation for height as

h(x) = -4x² + 16x

where x is the time in seconds

When object hits the ground the height becomes 0

So, we can set h(x) = 0 and then we can solve for x

-4x² + 16x = 0

Dividing by -4x from both sides

x - 4 = 0

x = 4 sec

So, the time it takes for a rocket  to hit the ground is 4 seconds.

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Answer:

  23346

Step-by-step explanation:

You want to know the number of hits on Grace's website 7 weeks from now if she gets 38,800 now and the number decreases 7% per week.

The growth factor per week is ...

  growth factor = 1 + growth rate

The growth rate of hits is -7% per week, so this is ...

  growth factor = 1 -7% = 0.93

The exponential function describing the number of hits can be written ...

  hits = (initial value)(growth factor)^weeks

  hits = 38,800(0.93^weeks)

Then in 7 weeks, the number of hits is expected to be ...

  hits = 38,800(0.93^7) ≈ 23,346

Grace can expect to get about 23,346 hits in 7 weeks.

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Answer:

Q1 = 6.45f/s

Q2 = 0.633 times

Q3 = 0.107 miles

Step-by-step explanation:

Q1: Since

4.4 miles = 1 hour

and

1 mile = 5,280 feet

1 hour = 3600 seconds

Then 4.4 miles

= 5,280 feet × 4.4

= 23,232 feet / 3600 seconds

= 6.453f/s

= 6.45f/s

Q2: Wing beat per minute

= 38 ÷ 60

= 0.633 times

Q3: Miles per minute

Since 6.4 miles = 1 hour,

6.4 miles = 1 × 60

6.4 miles = 60 minutes

x miles = 1 minute

= 6.4/60

= 0.107 miles

Answer:

31-6/1-1

=25/0

=undefined

The monthly payment for the first condition is $1750.11 and the total number of payments is 156.

What is the monthly payment?

Monthly payment is defined as the amount paid every month depending on the terms of the mortgage loan. This includes the principal, which is the actual balance on the loan, and the interest on the loan.

The formula for monthly payments on the mortgage is given:

                                [tex]MP = \frac{P(\frac{r}{n}) }{1- (1+\frac{r}{n})^{-nt} }[/tex]

where, MP = monthly payment

            P = principal amount

             r = rate of interest

             n = number of payments per year

              t = number of years

Given, a couple buys a house for $290000 and makes a down payment of 15%

Down payment = 0.15*290000 = $ 43500

First condition,

Present value of loan (P) = $290000 - $43500 = $246500

rate of interest (r) = 3.4% = 0.034

number of payments per year (n) = 12

number of years (t) = 15 years

Then, the monthly payment is calculated by:

             [tex]MP = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*15} } = 1750.11[/tex]

Therefore, monthly payment = $1750.11

Second condition,

monthly payment (MP) = $1950

Present value of loan (P) = $290000 - $43500 = $246500

rate of interest (r) = 3.4% = 0.034

number of payments per year (n) = 12

time in years (t) = x years

Then,

or,  [tex]1950 = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*x} }[/tex]

or, [tex]x = 13.06 = 13[/tex]

So, the total number of payments =  13*12 = 156

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The probability of a family owning a cat given that the family owns a dog is 0.164

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

Here

probability of a family owning a dog is 0.91,

P(dog) = 0.91

probability of a family owning a cat and a dog is 0.15,

P(dog ∩ cat) = 0.15

according to conditional probability

the probability of occurring of B after event A takes place is

P(A|B)=P(A∩B)/P(A)

so, the probability of a family owning a cat given that the family owns a dog is

        P(dog | cat) =P(dog∩cat)/P(dog)

                            = 0.15/0.91

                            =0.164

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The equation could be used to determine cc is 5.25x + 133 = 579.25 and cost of labor per hour is $85.

Given:

The technician at the store worked on the computer for 5.25 hours and charged her $133 for parts.

Total charged = 579.25

Let x be the charge per hour.

so the equation = 5.25x + 133 = 579.25.

Technician charge  = 579.25 - 133 = 446.25

5.25 hours = 446.25

divide by 5.25 on both sides

5.25 hours / 5.25 = 446.25/5.25

1 hour = $85

Therefore The equation could be used to determine cc is 5.25x + 133 = 579.25 and cost of labor per hour is $85.

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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 25 Kg weight will stretch the spring 120.84 cm .

In the question ,

it is given that

the distance(D) that spring  stretches by hanging objects vary directly to the weight(W) of the object .

which means

D ∝ W

to remove the proportionality sign , we write the constant k

So, D = k × W  ,

where k is the constant of proportionality

given that 6 Kg weight stretches the spring 29 cm

So,

29 = k * 6

k = 29/6

to find the stretch for 25 Kg weight

D = (29/6)*25

D = 120.84 cm

Therefore ,The 25 Kg weight will stretch the spring 120.84 cm .

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The probability that the sample mean is less than 200 pounds is 33% or 0.33

Given that,

The average annual meat consumption in the United States was 218.4 pounds, with a standard deviation of 42 pounds, and was normally distributed. A random sample of 30 individuals was chosen.

Mean  (μ) = 218.4

Standard deviation (σ) =42        

Probability = P(X< 200) = P[(X-μ ) / σ < (200-218.4) /42 ]

= P(z <-0.44 )

Using z table                                            

=0.3300

Probability=0.3300                                                        

Therefore, 33% or 0.33 of the time, the sample mean will weigh less than 200 pounds.

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Dad's car's gas tank holds 14.8 gallons of the gas.

A mixed fraction is one generated by integrating a whole number as well as a fraction.

Changed the mixed fraction in decimal.

Total gas purchased = 37/2 = 18.5 gallons of gas.

Let x be the gallons of gas tank contains.

Then,

(1/2)x + (3/4)x = 18.5

Multiply both sides by 4,

2x + 3x = 74

5x = 74

x = 14.8 gallons

Thus, Dad's car's gas tank holds  14.8 gallons of the gas.

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Prior to cellular radio, mobile radio and telephone services required

a. high-power transmitter/receiver.

A radio transmitter, also known as a transmitter, is an electronic device that generates radio waves using an antenna in electronics and telecommunications. The transmitter generates alternating current with a radio frequency that is applied to the antenna. The antenna emits radio waves when it is excited by this alternating current.

Typically, the term transmitter refers to equipment that generates radio waves for communication or radiolocation, such as radar and navigational transmitters. Even though they frequently use similar circuits, radio wave generators for heating or industrial purposes, such as microwave ovens or diathermy equipment, are not typically referred to as transmitters.

Transmitters are required components of all radio-communication devices, including radio and television broadcasting stations, cell phones, walkie-talkies, wireless computer networks, and Bluetooth-enabled devices.

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The sum of three consecutive even numbers is 558, The first number is 184.

The Sum of three consecutive even numbers is 558

We have to find the first number

Let the three consecutive even numbers be:

First number = x

Second number = x + 2

Third number = x + 4

Since their sum is 558

Therefore,

x + x + 2 + x + 4 = 558

3x + 6 = 558

3x = 558 - 6

3x = 552

Divide both sides by 3

Then the first number is 184.

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There are 6188 ways are there to choose two dozen croissants with at least two of each kind.

A combination is the combination of two or more distinct things. Although it is not necessary to combine things in pairs, the term "combining" comes from the Latin word for "joining together two by two."Combination repetition is permitted.

There are six different varieties of croissants (n = 6), and we must select two dozen croissants (r = 12) with at least two of each type.

In combination, The order does not matter and repetition is allowed.

thus, according to combination,

[tex]C( n+ r - 1,r) = \frac{(n + r - 1 )!}{r! (n-1)!} \\\\C( 6+ 12 - 1,12) = \frac{(6 + 12 - 1 )!}{12! (6-1)!} \\\\ = \frac{17!}{12!5!} \\= 6188[/tex]

thus, there are 6188 ways possible to choose two dozen croissants with at least two of each kind.

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