Write an equation of the line that passes through (–5, 1) and (7, 1)

Answer:

g(x)=x

4

+3x

3

−x

2

−3x

Step-by-step explanation:

The rewritten expression using a common factor is:

4x + 16 = 4*(x + 16)

Here we want to rewrite the expression:

4x + 16

Ussing a common factor, so let's factorize the terms.

The first one is simple:

4x = 4*x

The second one is also simple, we can write:

16 = 4*4

Then the common factor is 4, and we can rewrite the expression as:

4x + 16 = 4*(x + 16)

Learn more about common factors at:

https://brainly.com/question/219464

#SPJ1

Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Learn more about bar chart here

https://brainly.com/question/24741444

#SPJ4

Answer:

39.

Step-by-step explanation:

(15 ÷5) + 9 + (14 - 5 ) x 3

= 3 + 9 + 9 x 3

= 3 + 9 + 27

= 39.

Answer:

the same

Step-by-step explanation:

because the binomial and trinomial is the same

Answer:

x = 4

Step-by-step explanation:

Step 1: Write equation

-72 = 3(-4x - 8)

Step 2: Solve for x

Distribute 3: -72 = -12x - 24

Add 24 to both sides: -48 = -12x

Divide both sides by -12: x = 4

Step 3: Check

Plug in x to verify if it's a solution.

-72 = 3(-4(4) - 8)

-72 = 3(-16 - 8)

-72 = 3(-24)

-72 = -72

Answer:

c

Step-by-step explanation:

Read

Answer:

correct answer is b rotation

Answer:

7

Step-by-step explanation:

Could also be 6 + 1, just whatever adds to 7

Hello There! :)

15+7=7+15

The Commutative Property states:

a+b=b+a

Hope it helps

\(GraceRosalia\)

Answer:

7,670 ft

To find the diffrence you would do the equation -7 + 7,677 = 7,670 ft.

Hope this helps!!

Time intervals = 14/7 = 2

Final Amount = 40(1/2)² = 10

Answer:

They are the same

Step-by-step explanation:

20g = 0.02kg

i. The capacitance of the capacitor is approximately 53.1 nF. ii. The magnitude of charge on each plate is approximately 6.372 μC. iii. The new capacitance with acrylic between the plates is approximately 318.6 nF. iv. The flux density for the capacitor is approximately 1.2712 μC/m².

i. To determine the value of capacitance for the parallel plate capacitor, we can use the formula:

C = ε₀ * (A / d),

where C is the capacitance, ε₀ is the permittivity of vacuum (8.85 x 10^(-12) F/m), A is the cross-sectional area of the plates, and d is the separation between the plates.

Plugging in the given values:

A = 6 x 10^3 m²,

d = 5 mm = 5 x 10^(-3) m,

C = (8.85 x 10^(-12) F/m) * (6 x 10^3 m²) / (5 x 10^(-3) m)

  = 53.1 x 10^(-9) F

  = 53.1 nF.

Therefore, the capacitance of the capacitor is approximately 53.1 nF.

ii. The magnitude of charge on each plate can be determined using the formula:

Q = C * V,

where Q is the charge, C is the capacitance, and V is the voltage.

Plugging in the given values:

C = 53.1 x 10^(-9) F,

V = 120 V,

Q = (53.1 x 10^(-9) F) * (120 V)

  = 6.372 x 10^(-6) C.

Therefore, the magnitude of charge on each plate is approximately 6.372 μC.

iii. If acrylic is placed between the plates, the relative permittivity (εᵣ) of the medium affects the capacitance. The formula for the capacitance with a dielectric material is:

C' = εᵣ * C,

where C' is the new capacitance with the dielectric, εᵣ is the relative permittivity of the dielectric material, and C is the initial capacitance without the dielectric.

Plugging in the given values:

εᵣ (acrylic) = 6,

C (without dielectric) = 53.1 x 10^(-9) F,

C' = 6 * (53.1 x 10^(-9) F)

   = 318.6 x 10^(-9) F

   = 318.6 nF.

Therefore, the new capacitance with acrylic between the plates is approximately 318.6 nF.

iv. The flux density (D) for the capacitor can be calculated using the formula:

D = ε₀ * εᵣ * E,

where D is the flux density, ε₀ is the permittivity of vacuum (8.85 x 10^(-12) F/m), εᵣ is the relative permittivity of the dielectric material, and E is the electric field strength.

In the case of a parallel plate capacitor, the electric field strength is given by:

E = V / d,

where V is the voltage applied to the capacitor and d is the separation between the plates.

Plugging in the given values:

ε₀ = 8.85 x 10^(-12) F/m,

εᵣ (acrylic) = 6,

V = 120 V,

d = 5 x 10^(-3) m,

E = (120 V) / (5 x 10^(-3) m)

  = 24,000 V/m.

D = (8.85 x 10^(-12) F/m) * (6) * (24,000 V/m)

  = 1.2712 x 10^(-6) C/m².

Therefore, the flux density for the capacitor is approximately 1.2712 μC/m².

Learn more about flux density here:

https://brainly.com/question/28499883

#SPJ11

Answer:

9 students played basketball

Step-by-step explanation:

Number of students that played tag:

36*5/12=

180/12 = 15 students that played tag

Number of students that played kickball:

36*1/3=

36/3 = 12 students that played kickball

Number of students that played basketball:

First, find the total number of students that DIDN'T play basketball:

15 students played basketball and 12 played kickball, so:

15 + 12 = 27 students didn't play basketball

36 - 27 = 9 students played basketball

Answer:

9 students played basketball

Step-by-step explanation:

36 students in the class

5/12 played tag (of the 36)

1/3 played kickball

Find a common denominator and add the fractions

5/12 + 1/3 = 5/12 + 4/12 = 9/12

9/12 simplifies to 3/4

3/4 played kickball and tag, the rest played basketball

Subtract kickball and tag students from 1, to find the fraction of basketball players

1 - 3/4 = 1/4 of the students played basketball

The total is 36 students, 1/4 played basketball

1/4 of 36 = 36/4 = 9

9 students played basketball

Let me know if you have any questions!

The domain of the function is `R` and the y-intercept is `(0, -3)`

Given, `y = log4(2x + 1) - 3`.

To determine the domain of the function,

we should look for all values of `x` that would make the given function undefined.

There are no real values of `x` that would make the function undefined.

Therefore, the domain of the function is all real numbers or `R`.

To determine the y-intercept, substitute `x = 0` in the given function.`

y = log4(2(0) + 1) - 3 = log4(1) - 3 = 0 - 3 = -3`

Therefore, the y-intercept of the function is `(0, -3)`.

Hence, the domain of the function is `R` and the y-intercept is `(0, -3)`.

To know more about y-intercept visit:

https://brainly.com/question/14180189

#SPJ11

Step-by-step explanation:

Slope = 3/4

Point = (4,-2)

Using the point Slope form ,

=> x - 4 = 3/4 ( y -(-2))

=> x -4 = 3/4 ( y -2)

=> 4x -16 = 3y -6

=> 4x -3y -16+6=0

=> 4x -3y -10 = 0

Answer:

221 miles

Step-by-step explanation:

The car travels 253 miles in 8 hours, it means the car can travel in 221 miles in 7 hours.

Just imagine it

Answer:

Angles 7 and 8

Angles 4 and 3

Are consecutive interior angles.

Step-by-step explanation:

If Lucinda used a random selection method, made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

what are perpendicular lines?

Perpendicular lines are two lines that intersect at a 90-degree angle, forming four right angles at the point of intersection. In other words, if you were to draw a perpendicular line from one of the lines to the other at their point of intersection, it would form a right angle with each of the original lines.

Without having access to more information about how Lucinda selected the sample of students, it's difficult to determine whether or not the sample is truly random.

However, there are a few things that we can consider when trying to determine whether or not the sample is random. For example:

Did Lucinda use a random selection method to choose the students? If she simply surveyed her friends or classmates, for example, the sample would not be random.

Did Lucinda make any effort to ensure that the sample is representative of the larger population of students? For example, did she make sure to include students from a variety of grades, genders, and ethnic backgrounds.

Therefore, if Lucinda used a random selection method, and made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

To learn more about perpendicular lines here is the given link -

https://brainly.com/question/18271653

#SPJ1

Answer:

300 - 5t means that Ann pays $300 - 5 times the number of guests she brings to the gym.

when t = 5, it equals $275

when t = 10, it equals $250

when t = 15, it equals $225

when t = 20, it equals $200

Step-by-step explanation:

The values of λ :

λ = (9 + 27)/24 = 2 or λ = (9 - 27)/24 = -3/4

For the system (1-λ)x - 3y = 0 and -4x(2-λ)y = 0 to have only the trivial solution, the determinant of the coefficient matrix must be nonzero. The coefficient matrix is:

| 1 - λ -3 |

| -4 2 - λ|

The determinant of this matrix is:

(1-λ)(2-λ)(-3)(-4) = 12λ^2 - 9λ - 8

For the system to have only the trivial solution, this determinant must be nonzero. In other words:

12λ^2 - 9λ - 8 ≠ 0

To find the values of λ that satisfy this inequality, we can use the quadratic formula:

λ = [9 ± √(\(9^2\) + 4(12)(8))]/(2(12))

λ = [9 ± √(729)]/24

λ = (9 ± 27)/24

Therefore, the values of λ for which the system (1-λ)x - 3y = 0 and -4x(2-λ)y = 0 has only the trivial solution are:

λ = (9 + 27)/24 = 2 or λ = (9 - 27)/24 = -3/4

Learn more about trivial solution

brainly.com/question/31315629

#SPJ11

The number of scores above 18 in a sample of 1000 cases with a mean of 14 and a standard deviation of 2.5 is 2 or higher. This can be found using standard normal distribution and z-scores.

To find the number of scores above 18, we need to calculate the z-score that corresponds to 18 and then use a standard normal distribution table to find the proportion of scores that are above that z-score. The z-score can be calculated as (18-14)/2.5 = 2.

Next, we can look up the proportion of scores that correspond to a z-score of 2 or higher in a standard normal distribution table. This proportion represents the number of scores in the sample that are above 18, assuming a normal distribution.

Learn more about Standard Deviation:

https://brainly.com/question/475676

#SPJ4

Answer:

Step-by-step explanation:

One

23 + 52 = 75    This can be done using columns

2  3

5  2      No carries Add.

7   5

Two

72 - 33 = 39

7    2

3    3     You have to borrow a ten from the 7 to make this work

3   9

Three

82 + sqrt(100)

sqrt(100) = 10

82 + 10 = 92

First of all check the attached image showing two triangle. Option (c) is correct.

∆FGH ~ ∆ JKL

i.e, Angle FGH = angle JKL = 63°

and angle GHF = angle KLJ = 29°

also, angle GFH = angle KJL = 88°

so, the ∆FGH ~ ∆ JKL by AA property of similarity !!

• not other options because if we take corresponding angle they are not equal

For eg. for ∆ HFG ~ ∆ JKL

the angle HFG must be equal to angle JKL to be similar !!

but they are not equal so, they are not similar

and such ,all other options except 3rd is wrong

To know more about triangle click here

https://brainly.com/question/6976377

#SPJ4

The pharmacy should send two pills marked  for the patient to take.

To answer this question, we can use the formula below;

Dosage = (Amount of Drug x Patient's Weight) / Time

Since we don't have any information about the patient's weight or the time, we can't calculate the dosage.

However, we can calculate the number of pills required.

So, let's proceed with the calculation.

Each pill contains 2.5 mg of the pain reliever.

We need to administer a low dose, so let's assume the dose required is 5 mg.

To administer this dose, we need to give two pills, i.e., 2 x 2.5 = 5mg.

However, the question asks us to round the answer to the nearest tenth of a pill.

Since we can't divide a pill into parts, we need to round the answer up or down to the nearest whole pill.

In this case, since we need two pills, the answer is 2 pills.

For similar question on administer.

https://brainly.com/question/13152057

#SPJ11

The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

More can be learned about supplementary angles at brainly.com/question/2046046

#SPJ1

Answer:

Step-by-step explanation:

1) Number of nickels = x

Number of quarter = y

x + y = 7   ----------------------(I)

x = 7 - y ------------------------(II)

0.05x + 0.25y = 0.55 -----------(III)

Substitute s = 7 - y in equation (III)

0.05*(7 - y)  + 0.25y = 0.55

0.05*7 - 0.05*y + 0.25y = 0.55

0.35 - 0.05y + 0.25y  = 0.55            {Combine like terms}

0.35  + 0.20y  = 0.55          {Subtract 0.35 from both sides}

  0.2y = 0.55 - 0.35

   0.2y = 0.2       {Divide both sides by 0.2}

        y = 0.2/0.2

y = 1

Substitute y =1 in equation (II)

x = 7 - 1

x = 6

Number of nickels = 6

Number of quarter = 1

2) Number of children tickets = x

Number of adult tickets = y

x + y = 40  -----------------(I)

     x = 40 - y  -----------------(II)

2x + 5y = 170 -----------------(III)

Substitute x = 40 - y in equation (III)

2*(40-y) + 5y = 170

2*40 - 2*y + 5y = 170

80 - 2y + 5y   = 170             {Combine like terms}

80 + 3y = 170                {Subtract 80 from both sides}

       3y = 170 - 80

       3y = 90       {Divide both sides by 3}

         y = 90/3

y = 30

Substitute y = 30 in equation (II)

x  = 40 - 30

x = 10

Number of children tickets = 10

Number of adult tickets =30

3y + 2x = 44 is the equation of the line through (10, 8) and (4, 12).

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

Given, two coordinates of a line \(\left(10,8\right) and \left(4,12\right)\)

The slope of the line formula is:

\(m = \frac{y₂ - y₁}{ x₂ - x₁}\)

Let's substitute our numbers.

\(m = -\frac{8 -12}{4-10}\)  =  -4/6

The GCF of these two numbers is 2

So, our slope  =  -2/3

The general equation of a line is y = mx +c

Therefore the equation of the line is y = -2/3x + c

Since, this line passes through ( 10, 8 )

Hence, it must satisfy these coordinates

8 = -2/3 * 10 + c

44/3 = c

Thus the equation of the line is y = -2/3x +44/3

the equation of the line is 3y + 2x = 44.

Therefore, The equation of the line that passes through (10, 8) and (4, 12) is 3y + 2x = 44.

Learn more about Line here:

https://brainly.com/question/30003330

#SPJ1

Answer:

20,100 I think

Step-by-step explanation:

Answer:

20/10

Step-by-step explanation:

goes up 20

goes to the right 10

Answer:

Calculate the skid speed by multiplying the drag factor times the braking efficiency times the skid distance times 30 and taking the square root of the result. For example, if the car skidded 120.5 feet on a road with a drag factor of 0.5 and left four skid marks, the car was going about 42.51 mph.

Step-by-step explanation:

Answer:

Solution given:

65mph

divide the speed value by 2.237

65/2.237=29.05m/s

So

speed =29.05 m/s

now we have

.speed =~30 d (0.5)

29.05/30=0.5d

d=0.96855/0.5

d=1.93

So

the length of the skid marks to be is 2 m.