Determine the number of solutions for the system of equations

Y=16x-19
Y=3x^2+4x-7

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

Below.

Step-by-step explanation:

So let's do some math.

5+10+14+20(Number of people in the class.)

=49.

40 percent of 49= to 19.6 a student cant be half of a student.

So?

Round up to 20.

Forty percent of the students were able to type at 45-59 wpms.

Forty percent of the students were able to type at 15-29 speed interval

percentage, a relative value indicating hundredth parts of any quantity.

The total number of students are 5+10+14+20

Number of students =49

Now let us find 20% of 49

Convert 20% to decimal

20/100=0.2

Now multiply 0.2 with 49

0.2×49

9.8

Which is nearly 10

Hence, Forty percent of the students were able to type at 15-29 speed interval

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Answer:

18/5

Step-by-step explanation:

The standard form of the "quarter car model" couple equations, with x = u.(a) To put the third order scalar ODE into standard form, we need to introduce a new variable. Let x = z, then we have:

d³ x / dt³ + 2x = 3 d² u / dt² + 4u

(b) To put the "quarter car model" couple equations into standard form, we need to eliminate the variables z1 and z2. Using the first equation to solve for z1, we get:

z¹ = (m¹z² + k¹z² - c¹*z²) / (m¹ + k¹)

Substituting this expression into the second equation and simplifying, we obtain:

(m¹k² + m²k¹ + k¹k²) × z²

= k²u × (m¹ + m²) + c²um¹ - (c¹m¹ + c¹m² + c²× m¹)× z²

Dividing both sides by (m¹k² + m²k¹ + k¹× k²), we get:

z²= (k²u(m¹ + m²) + c²um¹) / (m¹k² + m²k¹ + k¹k² + c¹m¹ + c¹m² + c²₉m¹)

Substituting this expression for z2 into the first equation, we obtain:

  m¹ × [(k²u(m¹ + m²) + c²um¹) / (m¹k² + m²k¹ + k¹k² + c¹m¹ + c¹m² + c²m1)]

= k¹× [(m²k²u + c²m²u) / (m¹k² + m²k¹ + k¹k² + c¹m¹ + c¹m² + c²m¹)]

This is the standard form of the "quarter car model" couple equations, with x = u.

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Answer:

1 out of 179

Step-by-step explanation:

Answer:

$80

Step-by-step explanation:

Answer:

It’s 32

Step-by-step explanation:

Explanation:

The equation y = 2 is horizontal. Anything parallel to this will also be horizontal. The answer is of the form y = k, where k is some real number. We replace k with 1 since we need the answer to go through (4,1). All points on the answer line have a y coordinate of 1.

The equation y = 1 is the same as y = 0x+1, which shows we have a slope of 0.

By using the figure below, the value of line segment PT is equal to 54 units.

In Mathematics, the midpoint of a line segment with two endpoints can be calculated by adding each point on a line segment together and then divide by two (2).

Since T is the midpoint of PQ, we have the following:

Line segment PT = Line segment TQ

7x + 5 = 9x - 9

9x - 7x = 9 + 5

2x = 14

x = 14/2

x = 7.

Now, we can determine the value of PT:

PT = 7x + 5

PT = 7(7) + 5

PT = 54 units.

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Complete Question:

Use the figure to the right to find the value of PT. T is the midpoint of PQ PT=7x+9 and TQ=9x-5

Answer:

The opposite of 1/2 is -2/1, which can also be written as -2.

Answer: A

Step-by-step explanation:

Domain: 8, 9, 10, 11.Range: -7, 7 This relation does not represent a function because the same x-value (8, 10, 11) is associated with more than one y-value (-7, 7).

Domain: 8, 9, 10, 11

Range: -7, 7

A function is a relation between a set of inputs and a set of outputs such that each input is associated with exactly one output. This particular relation fails to meet this condition because the domain value 8 is associated with two different range values (-7 and 7). In other words, the same input (8) is associated with two different outputs, which means the relation does not represent a function. The domain of the relation is 8, 9, 10, 11 and the range is -7 and 7. Therefore, this relation does not represent a function because it violates the condition that each input must have one and only one associated output.

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Answer:

x = -10

Step-by-step explanation:

9x-1=10x+9

9x-1+1=10x+9+1

9x=10x+10

9x-10x=10x-10x+10

-x=10

-x/-1=10/-1

x= -10

hope it's helpful ❤❤❤❤❤❤

THANK YOU.

#

Answer:

slope means the monthly salary is $425

Step-by-step explanation:

4050 - 3200 / 6 - 4     =   850 / 2  which is same as 425 / 1

4475 - 4050 / 7 - 6     =   425 / 1

4900 - 4475 / 8 - 7     =  425 / 1

Answer:

.74

Step-by-step explanation:

9.60 - .72= 8.88

8.88 / 12 =.74

hope this helps

The x value for the third quartile for this distribution is 106.8

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

where μ is the mean, x = raw score and σ is the standard deviation.

Given μ = 100, σ = 10.

The third quartile correspond with a z score of 0.675, hence:

0.675 = (x - 100) / 10

x = 106.8

The x value for the third quartile for this distribution is 106.8

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A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

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Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side

The range of a statistical set is the difference between the greatest and least number in the dataset

While the mean is the average of the data set

To obtain the mean, we will use the formula

The total number of data

The area of the shaded which is obtained using the composite figure formed the shaded region and the area under the curve of the specified function is; (2·π - 3·√3)/2 square units

A composite figure is one that is composed of two or more simpler figures.

The area can be considered of comprising of a composite figure of the area under the curve of the function and the area of the shaded region

The function representing the curve under the shaded region can be presented as follows;

y = 3·cos(x) + 1

The interval specified under the curve can be expressed as follows;

0 ≤ x ≤ π/3

Therefore, the area under the curve can be found as follows;

\(\int\limits^\frac{\pi}{3} _3 {3\cdot cos(x) + 1} \, dx = [3\cdot sin(x) + x]^{\frac{\pi}{3} }_0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3} - 0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3}\)

sin(π/3) = (√3)/2

Therefore; 3·sin(π/3) + π/3 = 3·(√3)/2 + π/3 = (2·π + 9·√3)/6

The area of the rectangle = (4 - 0) × (π/3 - 0) = 4·π/3

The area of the shaded region = Area of the rectangle - Area under the curve of the specified function

Therefore, area of the shaded region = 4·π/3 - (2·π + 9·√3)/6 = (2·π - 3·√3)/2

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Answer:

\(5 { \times 54}^{2} \)

The additional wire, in feet, that the factory needs in order to wrap the deliveries would be = 37.6 feet

That is option B.

The total length of wire needed in the factory to wrap up all the deliveries for the house project = 175 ft.

The lengths of wires available = 2 × 12 yrd = 24 yrd.

But 1 yard = 3 foot

24 yards = X

Make X the subject of formula;

X = 24×3 = 72 ft

The second wire available = 65.4 ft

To calculate the remaining wire first add all the available wire. That is;

= 72+65.4 = 137.4ft

Subtract fro the total wire;

= 175-137.4 = 37.4 feet.

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\(13-4x = 13 -4(-8) = 13 +32 = 45\)

=> 13 - 4x

=> 13 - 4(-8) ..(when x = (-8))..

=> 13 - (-32) ..( (-) , (-) = + )..

=> 13 + 32

=> 45

☆- PhysicsMaths - ☆

The value of m is 32, the measure of the angle ∠ MLE is 16° and the measure of ∠ ELB is 74°.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Given:

The measure of ∠ MLE = 1 / 2 m, ∠ ELB = 2 (m + 5)

Calculate the value of m as shown below,

∠ MLE + ∠ ELB  = 90  (As given on figure)

1 / 2 m + 2 (m + 5) = 90

1 / 2 m + 2 m + 10 = 90

m + 4 m + 20 = 180

5 m = 180 - 20

m = 160 / 5

m = 32

Hence, ∠ MLE = 32 / 2 = 16°, and ∠ ELB = 2 (32 + 5) = 74°

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The complete question is attached below.

Answer:

It is 390.5 (volume, not surface area)

Step-by-step explanation:

Answer:

The probability that the weight of a randomly selected pilot is between 120 lbs. and 161 lbs. is 0.52.

Step-by-step explanation:

Let X = weight of pilots.

It is provided that X follows a normal distribution with mean, μ = 130 lbs. and standard deviation, σ = 27.3 lbs.

Compute the probability that the weight of a randomly selected pilot is between 120 lbs. and 161 lbs. as follows:

\(P(120<X<161)=P(\frac{120-130}{27.3}<\frac{X-\mu}{\sigma}<\frac{161-130}{27.3})\\\\=P(-0.37<Z<1.14)\\\\=P(Z<1.14)-P(Z<-0.37)\\\\=0.87286-0.35569\\\\=0.51717\\\\\approx 0.52\)

Thus, the probability that the weight of a randomly selected pilot is between 120 lbs. and 161 lbs. is 0.52.

Answer:

Can't help you on an ASIT

Step-by-step explanation:

Answer:

option 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x + 10 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{6}\)

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - \(\frac{1}{6}\) and (a, b ) = (5, - 8 ) , then

y - (- 8) = - \(\frac{1}{6}\) (x - 5 ) , that is

y + 8 = - \(\frac{1}{6}\) (x - 5) ← equation of perpendicular line