What is an equation of the line that passes through the points (-6,-5) and(-4,-6)?pleasee I’ll give u BRAINLEST

The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Temperature change for water due to sheer drop is approximately 0.7 °C when Multnomah Falls in the Columbia River has a sheer drop of 543 ft.

Given that,

Multnomah Falls in the Columbia River Gorge has a sheer drop of 543 feet.

We have to find estimate the water temperature change in °F caused by this drop using the steady flow energy equation.

We know that,

Sheer drop is z₁ - z₂ = 543 feet

We required to calculate temperature change that is ∆T caused by this drop using steady flow energy equation says SFEE.

Assuming

Adiabatic flow i.e. Q =0

No work done, i.e. W=0

Neglecting kinetic energies.

Steady flow energy equation is a mathematical expression that states that for a steady flow the net energy at the inlet of control volume is equal to the net energy at the exit of of the control volume.

SFEE is given as,

h₁ + \(\frac{(v_1)^2}{2}\) + gz₁ + Q = h₂ + \(\frac{(v_2)^2}{2}\) + gz₂ + Q -------> equation(1)

Where, h₁ and h₂ enthalpies at inlet and exit of control volume,

v₁ and v₂ are velocities at inlet and exit of control volume (kinetic energies),

z₁ and z₂ are elevation at inlet and exit of control volume (potential energies),  

Q is energy flow into the control volume and

W is work done by control volume.

Neglecting change in kinetic energies ; Q=0; W=0

Then equation (1) will be,

h₁ - h₂ = g(z₂ - z₁)

Cp(ΔT) =  g(z₂ - z₁)

ΔT = \(\frac{g(z_2-z_1)}{Cp}\)

Here,

Value of g is 32.2 feet per second square and value of Cp for water is 25100 feet

Substituting all values we get,

ΔT = \(\frac{32.2(543)}{25000}\)

ΔT = 0.69°C

ΔT = 0.7°C (approximately)

Therefore, Temperature change for water due to sheer drop is approximately 0.7 °C.

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Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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The measure of the final unknown interior angle in the polygon is 172°.

Given the other interior angles of the polygon to be:

162°, 110°, 115°, 138°, 105° and 98°

If we are to find the final interior angle, it means the polygons have 7 interior angles.

Hence, it is a heptagon.

Sum of the interior angle of a heptagon equals 900 degrees.

Let, the final interior angle be x:

Hene:

162° + 110° + 115° + 138° + 105° + 98° + x = 900°

Solve for x:

728 + x = 900

728 - 728 + x = 900 - 728

x = 900 - 728

x = 172°

Therefore, the missing interior angle is 172°.

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Answer:

300 divided by 50=6 meters per second

Hope This Helps!!!

Step-by-step explanation:

Solution,

speed = distance traveled ÷ time taken

= 300÷50s

= 6/1

Therefore, speed is 6/1 [6 by 1]

Answer:

d=4

Step-by-step explanation:

Answer:150000 grams

Step-by-step explanation:

The density of water is 1g/cm^3, The mass of water needed to fill the  tank is 150000 grams

Step-by-step explanation:

13-9=6x

4-6x

This is the coefficient

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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Answer:

[1, ∞)

Step-by-step explanation:

1) Solve for x

-4x + 21 \(\leq\) 3x + 14

21 \(\leq\) 7x + 14

7 \(\leq\) 7x

1 \(\leq\) x

2) 1 is the lowest possible value of x and since it's a smaller or equal to inequality, you use a square bracket. If it was 1 < x, it would be a round bracket. Since there isn't a boundary for the highest value of x, you write an infinity. When you have an infinity, it's always a round bracket.

Answer:

x ≥ 1

 [1, ∞)

Step-by-step explanation:

Note: 3 < 7 and 8 > 2 this is obvious

2,3,7,8 are on the RIGHT SIDE of the number zero "0"

now look at this sequence :

-3 > -7 and -8 < -2

the numbers are the same but thy are on the opposite side of the ZERO.

now notice that the <> signs flipped from the fist to the second set...

when you do these problems, "Multiplying or dividing by a negative number"

effectively moves you from one side of the zero to the other....

the "thing" you have to do is REMEBER AFTER EACH STEP...

IF YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER (not add or subtract)  

YOU HAVE TO FLIP THE SIGN...

-4x+21 ≤ 3x +14

-4x ≤ 3x - 7          |||| subtracted 21 NO sign flip

-7x ≤ -7                ||| subtracted 3X NO sign flip

x ≥ 1                     ||| Divided by "-1" SIGN MUST FLIP !!!

Answer:

last one h babysat for 6 hours

The answer to this  system of inequalities 20x + 5y ≥ -10 , 12x - 3y ≥ -6 is: x ≥ -1/2 and y ≥ 0.

We can start by dividing each term by the greatest common factor (GCF) to simplify both inequalities. The GCF in this instance is 5.

The system is now:

4x + y ≥ -2

12x - 3y ≥ -6

We can multiply the first inequality by three and add it to the second inequality to get rid of y:

(3) (4x + y ≥ -2) => 12x + 3y ≥ -6

12x - 3y ≥ -6

The result of adding the two inequality is:

24x ≥ -12

When we multiply both sides by 24, we get:

x ≥ -1/2

In order to solve for y, we can now enter this value of x into either of the initial inequalities.

20x + 5y ≥ -10

If we replace x with -1/2

20(-1/2) + 5y ≥ -10

If we simplify

-10 + 5y ≥ -10

10 is added to both sides

5y ≥ 0

When we multiply both sides by 5

y ≥ 0

So, the inequality system is:

x ≥ -1/2 and y ≥ 0.

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Answer:

x ≤ -1 or x ≤ -5

Step-by-step explanation:

if the quest is x^2 + 6x ≤ -5

then x ≤ -1 or x ≤ -5

Answer:

6 problems per hour

Step-by-step explanation:

Total problems = 24

she completed the first 12 problems in 1 hour

The last 12 in 3 hours.

Total time = 1 hour + 3 hours

= 4 hours

unit rate for all 24 problems = total number of problems / total time taken

= 24 problems / 4 hours

= 6 problems per hour

Answer:

The profit function P(x) is defined as the difference between the revenue function R(x) and the cost function C(x): P(x) = R(x) - C(x). Substituting the given functions for R(x) and C(x), we get:

P(x) = (-31.72x^2 + 2030x) - (-126.96x + 26391) = -31.72x^2 + 2156.96x - 26391

To find the maximum profit, we need to find the vertex of this quadratic function. The x-coordinate of the vertex is given by the formula x = -b/(2a), where a = -31.72 and b = 2156.96. Substituting these values into the formula, we get:

x = -2156.96/(2 * (-31.72)) ≈ 34

Substituting this value of x into the profit function, we find that the maximum profit is:

P(34) = -31.72(34)^2 + 2156.96(34) - 26391 ≈ $4,665

The selling price of the dog food is given by the revenue function divided by x: R(x)/x = (-31.72x^2 + 2030x)/x = -31.72x + 2030. Substituting x = 34 into this equation, we find that the selling price of the dog food should be set to:

-31.72(34) + 2030 ≈ $92

So, the maximum profit of $4,665 can be made when the selling price of the dog food is set to $92 per bag.

Answer:

---------------------------

Multiply the two numbers first:

Round the number to the first digit:

Write 80000000 as the product of a single digit and a power of 10:

Domain: (-∞, ∞)

Range: (-∞, ∞)

Domain and range help us describe the values a graph covers.

Defining Domain and Range

Remember that the x-values are along the horizontal axis, and the y-values are on the vertical axis.

The function given to us extends infinitely to the left and right as shown by the arrows. Additionally, the graph extends up and down infinitely; thus the range is also infinite.

Interval Notation

Interval notation should be written as (minimum value, maximum value). If the minimum and maximum values are included within the range or domain, then the parentheses should be replaced with brackets. This looks like [included minimum, included maximum]. Since a function cannot actually include infinity, an infinity symbol should never have brackets.

Eventually, this linear function will reach every single x and y-value in existence. So, both axes have a minimum of -∞ and a maximum of ∞. Thus, both the domain and range are (-∞, ∞).

Hint for future problems: all linear functions will have a domain and range of (-∞, ∞).

Answer:

a) s = -16\(t^{2}\) + 192t + 96

b) Height of the football after 2 seconds is 448 feet.

ii. The football would not hit the ground after 2 seconds.

Step-by-step explanation:

Given:

s = -16\(t^{2}\) + \(V_{o}\)t + \(s_{o}\)

where: s is the height of the football above the ground, t is the time, \(V_{o}\) is the initial velocity and \(s_{o}\) is the initial height.

The height of the building = \(V_{o}\) = 192 feet and the initial speed of the ball = \(s_{o}\) = 96 feet per second, then;

s = -16\(t^{2}\) + 192t + 96

a) The polynomial is given as:

s = -16\(t^{2}\) + 192t + 96

b) The height of the football when t = 2 seconds is;

s = -16(2) + 192(2) + 96

 = -32 + 384 + 96

 = -32 + 480

s = 448

The height of the football when t = 2 seconds is 448 feet.

ii. The football would not hit the ground after 2 seconds.

Answer:

6n + 3 - 3 = 9 - 3

6n = 6

n = 1

Step-by-step explanation:

Answer:

step one: subtract 3 on both sides 6n=6

then divide 6 on both sides n=1

Answer:

f(-2) = -7

Step-by-step explanation:

f(x) = 3/2x - 4                         f(-2)

f(-2) = 3/2(-2) - 4

f(-2) = -3 - 4

f(-2) = -7

The answer is:

Work/explanation:

We should evaluate \(\sf{f(x)=3/2x-4}\) for x = -2.

So I plug in -2:

\(\sf{f(-2)=\dfrac{3}{2}\times(-2)-4}\)

\(\sf{f(2)=\dfrac{3}{2}\times\bigg(-\dfrac{2}{1}\bigg)-4}\)

\(\sf{f(-2)=\dfrac{3}{1} \times-\bigg(\dfrac{1}{1}\bigg)-4}\)

\(\sf{f(-2)=-3-4}\)

\(\sf{f(-2)=-7}\)

The amount Jerry paid in interest is $1,040.

Given to us,

Jerry's principal amount = $ 22,000,

quarterly payment for each quarter = $ 640

Total time for which Jerry paid each quarter = 9 years

As We know that in a year there are 4 quarters,

so, \(\rm 1\ year = 4\ quarters\),

\(\rm 9\ year = 9\times 4\ quarters\),

9 years = 36 quarters,

The total amount paid by Jerry for nine years in each quarter =

quarterly payment for each quarter x no. of quarters for which amount paid

\(\rm Total\ amount\ paid\ by\ Jerry\ for\ nine\ years\ in\ each\ quarter = \$640\times 36 quarters = \$23,040\)

Thus, the total amount paid by Jerry for nine years in each quarter is $23,040.

Therefore,

\(\rm Amount\ Jerry\ pay\ in\ interest = Amount\ Jerry\ paid- Principal\ amount\),

\(\rm Amount\ Jerry\ pay\ in\ interest = \$23,040-\$22,000 = \$1040\)

Hence, the amount Jerry paid in interest is $1,040.

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Answer:

example: find lcm of 48 and 32

48: 48, 96, 144, 192

32: 32,64,96,128,160,192

Step-by-step explanation:

list multiples and then find the smallest number that is both their multiple. That is Lcm

Step-by-step explanation:

the lowest common multiple of 2 numbers.

I recommend prime factorization.

starting with 2 you divide each number by lowest possible prime factor as many times as possible without remainder.

then you go to the next higher prime number and keep dividing without remainder.

and the next and the next until you reach 1 as the remaining number.

and then you combine (multiply) the longest streaks per prime number.

the result : the LCM

example :

98 and 36

98

2 49 (no more 2 division, 3 does not work, 5 does not work, but 7)

7 7

7 1

36

2 18

2 9

3 3

3 1

so, the longest streaks per prime number are

2×2 = 4

3×3 = 9

7×7 = 49

and the LCM = 4×9×49 = 1764

Answer:

Hey there!

We have tan 9= 21/BW

tan 9 (BW)=21

BW= 21/tan 9

BW= 132. 59

Hope this helps  :)

Answer:

A- 132.59

Step-by-step explanation:

since we have to find the adjacent and already have the opposite we'll use tanθ = opp/adj

tan(9)= 21/WB

WB = 21/tan(9)   (make WB the subject)

WB = 132.5887818   or   132.59

The dimension for the enclosure that is most economical to construct will be length=11.13 feet and width=27.85 feet.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

A=l*b

=310

b=310/l

total cost=(8b+4l+16l)

=8b+20l

=8*310/l+20l

t=2480/l+20l

t'=20-2480/l²

t'=0

20l²=2480

l²=124

l=11.13 feet

b=310/11.13

b=27.85 feet

The enclosure's length and width, which add up to 11.13 feet and 27.85 feet respectively, will be the most cost-effective dimensions to build.

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Answer:

x=3

so we substitute 3 in the equation

f(3)= (3)2+(3)3+5

f(3)=6+9+5

f(3)=20

Answer: \(f(3)=\Large\boxed{23}\)

Step-by-step explanation:

Given function expression

\(f(x)=x^2+3x+5\)

Requirements of the question

\(\text{Find the value of }f(3)\)

Substitute values into the expression

\(f(3)=(3)^2+3(3)+5\)

Simplify the exponent

\(f(3)=9+3(3)+5\)

Simplify by multiplication

\(f(3)=9+9+5\)

Simplify by addition

\(f(3)=18+5\)

\(f(3)=\Large\boxed{23}\)

Hope this helps!! :)

Please let me know if you have any questions