What is an equation of a line that passes through the points (8 , -3) (8 , 4)

~ Simplifying

-2(7x + -5) = -14x + 10

~ Reorder the terms:

-2(-5 + 7x) = -14x + 10

(-5 * -2 + 7x * -2) = -14x + 10

(10 + -14x) = -14x + 10

~ Reorder the terms:

10 + -14x = 10 + -14x

~ Add '-10' to each side of the equation.

10 + -10 + -14x = 10 + -10 + -14x

~ Combine like terms: 10 + -10 = 0

0 + -14x = 10 + -10 + -14x

-14x = 10 + -10 + -14x

~ Combine like terms: 10 + -10 = 0

-14x = 0 + -14x

-14x = -14x

~ Add '14x' to each side of the equation.

-14x + 14x = -14x + 14x

~ Combine like terms: -14x + 14x = 0

0 = -14x + 14x

~ Combine like terms: -14x + 14x = 0

0 = 0

~ Solving

0 = 0

~ This equation is an identity, all real numbers are solutions.

Answer:

The mileages for which company A charge less than company B when , y [tex]>[/tex] 50 .

Step-by-step explanation:

Given as :

The two truck companies have following prices

Company A

The initial fee = i = $110

And unlimited mileage

Company B

The initial fee = I = $65

Additional charge = $0.90 per mile driven

Let it driven x mile

Let The mileages for which company A charge less than company B = y

Now, According to question

Charges of company A = charges of company B

i.e i = I + 0.90 × x

Or, $110 = $65 + 0.90 × x

Or, $110 - $65 = 0.90 × x

Or, $45 = 0.90 × x

∴    x = [tex]\dfrac{45}{0.90}[/tex]

i.e  x = 50

i.e  Company B driven x = 50 miles

So, The mileages for which company A charge less than company B = y

And y [tex]>[/tex] x

i.e y [tex]>[/tex] 50

Hence, The mileages for which company A charge less than company B when , y [tex]>[/tex] 50 . Answer

Answer:

16.72

Step-by-step explanation:

To find the answer divide 83.61 by 100 then multiply it by 20

20% of 83.61 is = 16.72

Answer:

  h(x) ≤ 5

Step-by-step explanation:

The function is continuous and has a maximum value of 5. Its range is ...

  h(x) ≤ 5

Answer:

b

Step-by-step explanation:

edge 2020

Answer:

Full charge will be done in 360 minutes.

Step-by-step explanation:

A tablet takes 120 mins to charge.

So, in one minute the tablet is charged by [tex]\frac{1}{120} = 0.00833[/tex] parts.

Again, the fully charged tablet gives 180 mins of game time.

So, the tablet discharges fully in 180 mins gaming.

Then, in 1 minute of game playing the tablet is discharged by [tex]\frac{1}{180} = 0.00556[/tex] parts. (Appx.)

If charging and discharging by playing games both continue from the zero charge in the tablet, then in one minute it will be charged by (0.00833 - 0.00556) = 0.00277 parts. (Appx.)

Then full charge will be done in [tex]\frac{1}{0.00277} = 360[/tex] minutes. (Answer)

Answer:

$1039.55

Step-by-step explanation:

The total cost of the 2-year service of premium cable will be $344.6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a company offers premium cable for 39.95 per month plus a one-time setup fee. The total cost for setup and months of service was 264.70.

The total cost will be calculated by forming an equation as below,

C = 39.9m + 264.70

For 2 years the total cost will be,

C = (39.9 x 2) + 264.70

C = 79.9 + 264.70

C = $344.6

Therefore, the total cost of the 2-year service of premium cable will be $344.6.

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Answer:

Below.

Step-by-step explanation:

I'll do number 20, 21, 22 for you.

20.  It is ±1, ±2, ±4, ±8.

21.   Reflected over the x-axis and down 4.

22. Common ratio = 25/5 = 5.

23.  Imaginary roots occur in pairs so there is also a root -5i.

The answer is c.

19. Option (a).

This is a translation of 4 to the left ( due to the (x + 4).

Answer:

The expression that comes after solving the two linear equation is independent of variables So , The system of equations has no solutions

Step-by-step explanation:

Given two linear equations as :

2 y - 4 x = 6               .......1

y - 2 x = 7      

Or, y = 2 x + 7            .......2

Now, Solving these two equations

Put the value of y from eq 2 into eq1

So, 2 y - 4 x = 6

∴ 2 × (2 x + 7) - 4 x = 6

Or, 4 x + 14 - 4 x = 6

or, (4 x - 4 x) = 6 - 14

i.e 0 = - 8

∵ The expression that comes after solving the two linear equation is independent of variables So , The system of equations has no solutions Answer

Answer:

4x^2+20x+24

Step-by-step explanation:

(4x+8)(x+3)=4x^2+8x+12x+24=4x^2+20x+24

Answer:

Step-by-step explanation:

9.5+0.5c=t

Answer:

8.5C + 9.5

Step-by-step explanation:

Im pretty sure u meant to put 8.5

The number of pennies in bank is 42

Solution:

Given that ratio of pennies to quarters in a piggy bank is 14 : 3

Let 14x be the number of pennies in piggy bank

Let 3x be the number of quarters in piggy bank

To find: number of pennies

Given that there are 51 quarters

number of pennies in piggy bank + number of quarters in piggy bank = 51

14x + 3x = 51

17x = 51

x = 3

number of pennies = 14x = 14(3) = 42

Thus the number of pennies in bank is 42

To find the number of pennies in the piggy bank, set up a proportion using the given ratio and the number of quarters. Cross-multiply and solve for x to find the number of pennies. There are 238 pennies in the piggy bank.

To find the number of pennies in the piggy bank, we need to use the given ratio and information. The ratio of pennies to quarters is 14:3. This means that for every 14 pennies, there are 3 quarters. We are given that there are 51 quarters in the bank. We can set up a proportion to find the number of pennies:

So, there are (14 * 51) / 3 = 238 pennies in the piggy bank.

Answer:

[tex]\displaystyle y - 3 = -1\frac{1}{5}x\:OR\:y + 3 = -1\frac{1}{5}x - 5[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \frac{3 + 3}{-5 ± 0} = -\frac{6}{5} = -\frac{1}{5}[/tex]

Then plug these coordinates into the Point-Slope Formula Remember, in this formula, all the negative symbols give the OPPOSITE terms of what they really, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS. It does not matter which ordered pair you choose:

[tex]\displaystyle y - y_1 = m[x - x_1] \\ \\ y - 3 = -1\frac{1}{5}x\:OR\:y + 3 = -1\frac{1}{5}x - 5[/tex]

I am joyous to assist you anytime.

Answer:

Therefore the area of parallelogram  is 32 cm².

Step-by-step explanation:

Given:

[] ABCD is a Parallelogram .........Given

AB = 4 cm = Base

BC = 10 cm

CE  = Height of Parallelogram  

To Find:

area of parallelogram  = ?

Solution:

In Right angle triangle BEC  by Pythagoras theorem we have

[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]

Substituting the values we get

[tex]10^{2}=6^{2} +CE^{2} \\\\CE^{2}=100-36=64\\ \\\therefore CE = 8\ cm\\[/tex]

Which is the Height of Parallelogram

Now, area of parallelogram  given by

[tex]\textrm{Area of Parallelogram} = Base\times Height[/tex]

Substituting the values we get

[tex]\textrm{Area of Parallelogram} = 4\times 8=32[/tex]

[tex]\textrm{Area of Parallelogram} = 32\ cm^{2}[/tex]

Therefore the area of parallelogram  is 32 cm².

The number 0.66666666666 rounded to the nearest whole number is 1, and rounded to the nearest tenth is 0.7, following standard rounding rules.

The number 0.66666666666, when rounded, will depend on what decimal place you are rounding to. For example:

These rounding rules apply consistently across various operations including multiplication and division, similar to those in addition and subtraction. Let's consider a few examples where these rules are used:

These examples demonstrate the standard rules of rounding numbers with precision.

Final answer:

To round 0.66666666666 to the nearest tenth, it rounds up to 0.7 because the digit after the tenths place is greater than 5.

Explanation:

When rounding the number 0.66666666666, we must first decide the decimal place to which we want to round.

If we round to the nearest tenth, the number would round up to 0.7 because the digit following the tenth's place is a 6, which is greater than 5.

These same rules apply for other numbers: for example, 0.028675 rounds up to 0.0287 as the dropped digit, a 7, is greater than 5.

It's important to consider the digit immediately following the place value you're rounding to, as it will determine whether you round up or down.

Answer:

1. (x, y) → (x + 3, y - 2)

Vertices of the image

a) (-2, - 3)

b) (-2, 3)

c) (2, 2)

2. (x, y) → (x - 3, y + 5)

Vertices of the image

a) (-3, 2)

b) (0, 2)

c) (0, 4)

d) (2, 4)

3. (x, y) → (x + 4, y)

Vertices of the image

a) (-1, -2)

b) (1, -2)

c) (3, -2)

4. (x, y) → (x + 6, y + 1)

Vertices of the image

a) (1, -1)

b) (1, -2)

c) (2, -2)

d) (2, -4)

e) (3, -1)

f) (3, -3)

g) (4, -3)

h) (1, -4)

5. (x, y) → (x, y - 4)

Vertices of the image

a) (0, -2)

b) (0, -3)

c) (2, -2)

d) (2, -4)

6. (x, y) → (x - 1, y + 4)

Vertices of the image

a) (-5, 3)

b) (-5, -1)

c) (-3, 0)

d) (-3, -1)

Explanation:

To identify each IMAGE you should perform the following steps:

1. (x, y) → (x + 3, y - 2)

The rule means that every point of the preimage is translated three units to the right and 2 units down.

Vertices of the preimage      Vertices of the image

a) (-5,2)                                   (-5 + 3, -1 - 2) = (-2, - 3)

b) (-5, 5)                                  (-5 + 3, 5 - 2) = (-2, 3)

c) (-1, 4)                                   (-1 + 3, 4 - 2) = (2, 2)

2. (x,y) → (x - 3, y + 5)

The rule means that every point of the preimage is translated three units to the left and five units down.

Vertices of the preimage      Vertices of the image

a) (0, -3)                                   (0 - 3, -3 + 5) = (-3, 2)

b) (3, -3)                                   (3 - 3, -3  + 5) = (0, 2)

c) (3, -1)                                    (3 - 3, -1 + 5) = (0, 4)

d) (5, -1)                                    (5 - 3, -1 + 5) = (2, 4)

3. (x, y) → (x + 4, y)

The rule represents a translation 4 units to the right.

Vertices of the preimage   Vertices of the image

a) (-5, -2)                               (-5 + 4, -2) = (-1, -2)

b) (-3, -5)                               (-3 + 4, -2) = (1, -2)

c) (-1, -2)                                (-1 + 4, -2) = (3, -2)

4. (x, y) → (x + 6, y + 1)

Vertices of the preimage      Vertices of the image

a) (-5, -2)                                  (-5 + 6, -2 + 1) = (1, -1)

b) (-5, -3)                                  (-5 + 6, -3 + 1) = (1, -2)

c) (-4, -3)                                   (-4 + 6, -3 + 1) = (2, -2)

d) (-4, -5)                                  (-4 + 6, -5 + 1) = (2, -4)

e) (-3, -2)                                  (-3 + 6, -2 + 1) = (3, -1)

f) (-3, -4)                                   (-3 + 6, -4 + 1) = (3, -3)

g) (-2, -4)                                  (-2 + 6, -4 + 1) = (4, -3)

h) (-2, -5)                                  (-2 + 3, -5 + 1) = (1, -4)

5. (x, y) → (x, y - 4)

This is a translation four units down

Vertices of the preimage      Vertices of the image

a) (0, 2)                                    (0, 2 - 4) = (0, -2)

b) (0,1)                                      (0, 1 - 4) = (0, -3)

c) (2, 2)                                     (2, 2 - 4) = (2, -2)

d) (2,0)                                     (2, 0 - 4) = (2, -4)

6. (x, y) → (x - 1, y + 4)

This is a translation one unit to the left and four units up.

Vertices of the pre-image     Vertices of the image

a) (-4, -1)                                   (-4 - 1, -1 + 4) = (-5, 3)

b) (-4 - 5)                                  (-4 - 1, -5 + 4) = (-5, -1)

c) (-2, -4)                                  (- 2 - 1, -4 + 4) = (-3, 0)

d) (-2, -5)                                 (-2 - 1, -5 + 4) = (-3, -1)

Sid will pay $76.26 in total including ta and tip.

Step-by-step explanation:

Given,

Cost of Sid's bill = $62.00

Tax rate = 8%

Tip = 15%

Tax amount = 15% of bill

[tex]Tax\ amount=\frac{8}{100}*62.00\\Tax\ amount=0.08*62.00\\Tax\ amount=\$4.96[/tex]

As the tip will be on Pre-tax amount, therefore,

Tip amount = 15% of bill

[tex]Tip\ amount=\frac{15}{100}*62.00\\Tip\ amount=0.15*62.00\\Tip\ amount=\$9.30[/tex]

Total amount = Bill + Tax amount + Tip amount

Total amount = 62.00 + 4.96 + 9.30 = $76.26

Sid will pay $76.26 in total including ta and tip.

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Answer:

76.26

Step-by-step explanation:

Answer:

Step-by-step explanation:

3+3+4+5+6+6+7+7+7+8+8=64

64÷11=5.81818181818

simplify to......5.82

Answer: 5.81818181818

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

So to find the mean of the data set shown here, let's begin by adding the numbers.

So we have [tex]\frac{3 +3+4+5+6+6+7+7+7+8+8}{11}[/tex] and notice that I put an 11 on the bottom since there are 11 numbers.

Adding the numbers, we get 64. This will be divide by how many numbers are in the set or 11.

[tex]\frac{64}{11} = 5.81818181818[/tex]

Therefore, the mean of the data set is 5.81818181818.

Answer:

the seventh graders

Step-by-step explanation:

Answer:

The Seventh Graders

Step-by-step explanation

Answer:

See the attached figure.

Step by step solution:

Part (1):

When ΔABC is an isosceles triangle with AB = AC

The summing of the three of the triangle = 180°

∴ m∠ABC + m∠BAC + m∠ACB = 180°

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

Part (2):

When ΔABC is an isosceles triangle with AB = AC

So, m∠ABC = m∠ACB = x

if m∠BAC = 70

∵ m∠ABC  + m∠ACB + m∠BAC= 180°

∴ x + x + 70 = 180 ⇒ x = 55°

∴ m∠ABC = 55°

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

Part (3):

When m∠QRP = 30°, and ΔPQR is an isosceles triangle with PQ = QR

So, m∠QPR = m∠QRP = 30°

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

Part (4):

When m∠BAC = 45° and points D and E are the midpoints of AB and BC in ΔABC

∵ Points D and E are the midpoints of AB and BC in ΔABC

∴ DE // AC

∴ m∠BDE = m∠BAC ⇒ the corresponding angles are congruent

∴ m∠BDE = 45°

Answer:

No. The differences between two elements should be same. For example 4-7-10-13 is a arithmetic sequence.

Step-by-step explanation:

Answer: 2/5

Step-by-step explanation:

14:7=2

35:7=5

14/35= 2/5

Answer:

The lowest form of [tex]\frac{14}{35}[/tex] is [tex]\frac{2}{5}[/tex].

Step-by-step explanation:

The given rational number is [tex]\frac{14}{35}[/tex].

At first, we will find the HCF of 14 and 35 and then divide the numerator and denominator by the HCF of 14 and 35 to evaluate the lowest form of [tex]\frac{14}{35}[/tex].

The prime factorisation of 14 and 35 is,

14 = 2 × 7

35 = 5 × 7

Since, prime factor '7' is common in the prime factorisation of 14 and 35, so the HCF of 14 and 35 is 7.

[tex]\frac{14}{35}=\frac{\frac{14}{7} }{\frac{35}{7}}=\frac{2}{5}[/tex]

So, the lowest form of [tex]\frac{14}{35}[/tex] is [tex]\frac{2}{5}[/tex].

Answer:

$486

Step-by-step explanation:

First you find the area of the window. The area of a square is equal to h×w, so we take 9×9 which equals 81. Since it costs $6 per square foot, we now take 81×6, which gives us an answer of $486.

The glass to replace the window will cost $486 to Linda.

The Area of a figure is the space inside its 2D perimeter.

To determine the area of a square we just square the length of its side.

Area of a square = (side)²

We are said that the window is in the shape of a square, with 9 feet as its side's length.

∴ Area of the window = 9² square feet = 81 square feet.

Cost of 1 square foot of glass = $6/square foot

∴ Cost of the glass for window = Area of the window * rate of glass

= $81*6 = $486.

∴ The glass to replace the window will cost $486 to Linda.

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The equation of the line perpendicular to line AB, which is a vertical line with an undefined slope, and passing through the point (2, 4) is y = 4.

Determine the equation of the perpendicular line:

Find the slope of line AB:

Since both points A and B have the same x-coordinate (-6), the line AB is a vertical line.

Vertical lines have an undefined slope.

Determine the slope of the perpendicular line:

The slope of a line perpendicular to a vertical line is 0. This means the perpendicular line will be a horizontal line.

Use the point-slope form to find the equation of the perpendicular line:

The point-slope form of a linear equation is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

We know the slope (m = 0) and we have a point on the line (2, 4).

Plugging these values into the point-slope form, we get: y - 4 = 0(x - 2)

Simplify the equation:

Since the slope is 0, the term 0(x - 2) becomes 0.

Therefore, the equation simplifies to: y - 4 = 0

Add 4 to both sides to isolate y:

y = 4

Therefore, the equation of the line perpendicular to line AB and passing through the point (2, 4) is y = 4.

Complete question:

Line AB passes through points A(-6,7) and B(-6,-3) as shown on the coordinate grid . below. Determine the equation of a line that is perpendicular to line AB and passes through the point (2,4).

Answer:

y = (7/2)x - 2

Step-by-step explanation:

Use slope-intercept formula for linear equations y = mx + b

x and y show what points are on the line. We know (4, 12). x= 4 and y = 12

b is the y-intercept, which b = -2.

m is the slope.

To write the equation, you need the slope and y-intercept. Find the slope by putting x, y and b into the formula.

y = mx + b

12 = 4m - 2

14 = 4m

14/4 = m

m = 7/2

Put "m" into the formula with "b"

y = (7/2)x - 2

Answer:

3.125

Step-by-step explanation:

Answer:

88 feet

Step-by-step explanation:

perimeter (P)=2πr

P= 2*22/7*14

P=88 feet

Answer:

2. B, 25.12 feet.

3. B, 88 feet.

P=2πr, r = radius or 1/2 diameter, replace [tex]\pi[/tex] with given value for each question and then simplify.

Answer:

k=f(x)+2x+2

Step-by-step explanation:

f(x)=-2x-2+k

-2x-2=f(x)-k

f(x)-(-2x-2)=k

f(x)+2x+2=k

Answer:

0.5 miles per hour

Step-by-step explanation:

Ben is 19 years old now

Solution:

Let the age of Ishaan be "x"

Given that ben is 12 years older than Ishaan

Therefore, age of ben = x + 12

Therefore, before three years,

Age of Ishaan before three years = x - 3

Age of Ben before three years = x + 12 - 3 = x + 9

From question,Three  years  ago, ben  was  4  times  as  old  as  ishaan

Age of Ben before three years = 4(Age of Ishaan before three years)

x + 9 = 4(x - 3)

x + 9 = 4x - 12

4x - x = 9 + 12

3x = 21

x = 7

Therefore age of ben now = x + 12 = 7 + 12 = 19

Thus Ben is 19 years old now