Explain how to write an equation when given the slope and 1 point.

Answer:

463×10³

463×1000

=0.463

Using a system of equations, we have that:

a) It is not possible to solve for any of the variables using only Equation #1 and Equation #2, as there are only 2 equations for 3 variables.

b) It is possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3, as there are 3 equations for 3 variables. The solutions are: x = 12, y = 1, z = -29.

c) These solutions do not hold for equation 4, meaning that equation 4 is inconsistent for the system.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

To solve a system, the number of equations has to be at least the same as the number of variables, hence in item a, it is not possible to solve for any of the variables using only Equation #1 and Equation #2, as there are only 2 equations for 3 variables.

In item b, we can solve. From the second equation, we have that:

x = 5y + 7.

From the first equation, we have that:

z = 8 - 3x - y

z = 8 - 3(5y + 7) - y

z = 8 - 15y - 21 - y

z = -13 - 16y

From the third equation, we can replace and solve for y.

3z + 2x - 2y = 15.

3(-13 - 16y) + 2(5y + 7) - 2y = 15

-39 - 48y + 10y + 14 - 2y = 15.

-40y - 25 = 15

40y = 40.

y = 1.

Then the solutions for x and z are:

Replacing the solutions in equation 4, we have that:

4x + 5y - 2z = -3.

4(12) + 5(1) - 2(-29) = -3, which is false.

These solutions do not hold for equation 4, meaning that equation 4 is inconsistent for the system.

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B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

(a) We can use the formula for exponential growth, which is P(t) = P0e^(kt), where P0 is the initial population, k is the growth rate constant, and e is the base of the natural logarithm. Since the population is proportional to its size, we can write:

P(t) = P0e^(kt)

We know that P(0) = 880 and P(5) = 4400, so we can use these values to find k:

4400 = 880e^(5k)

e^(5k) = 5

5k = ln(5)

k = ln(5)/5

Substituting this value of k into the formula, we get:

P(t) = 880e^(t*ln(5)/5)

(b) To find the population after 7 hours, we can simply plug in t = 7 into the formula we found in part (a):

P(7) = 880e^(7*ln(5)/5) ≈ 11036.29

So there will be approximately 11036 bacteria after 7 hours.

(c) To find how long it takes for the population to reach 2570, we can set P(t) = 2570 and solve for t:

2570 = 880e^(tln(5)/5)

e^(tln(5)/5) = 2570/880

tln(5)/5 = ln(2570/880)

t = 5ln(2570/880)/ln(5)

Using a calculator, we get:

t ≈ 2.51 hours (rounded to 2 decimal places)

So it will take approximately 2.51 hours for the population to reach 2570 bacteria.

Step-by-step explanation:

Answer:

4x=x+18x=

We move all terms to the left:

4x-(x+18x)=0

We add all the numbers together, and all the variables

4x-(+19x)=0

We get rid of parentheses

4x-19x=0

We add all the numbers together, and all the variables

-15x=0

x=0/-15

x=0

Step-by-step explanation:

Answer:

for the number 13

Step-by-step explanation:

\(x = \sqrt{9 { }^ {2} + 6 { }^{2} }\)

by Pythagoras theorem

x= √81+36

x= √117

punch square root of 117 with a calculator, I don't have one now

Answer:

m = 9/5

Step-by-step explanation:

Line m pass-through the points (-5, -29) and (10, -2)

Slope = rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 27 and the x increase by 15, so the slope is

m = 27/15 = 9/5

So, the slope of line m is 9/5

The slope of line m is 27/15.

The slope of a line can be found using the formula: slope = Δy / Δx, where Δy is the change in y-coordinates and Δx is the change in x-coordinates between any two points on the line.

In this case, the coordinates of the two points are (-5, -29) and (10, -2). The change in y-coordinate is -2 - (-29) = 27 and the change in x-coordinate is 10 - (-5) = 15.

Therefore, the slope of line m is 27 / 15.

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Answer:

A

Step-by-step explanation:

Answer:

C. 35 sq. units

Step-by-step explanation:

in order to find the area of a triangle you have to use the formula

1/2 b h

b as in base

h as in height

so if we use the measurements on the triangle and we plug that in we will get

1/2 x 14 (the base) x 5 (the height)

therefore giving us 35 sq. units.

hope this helps!

Answer:

+ 7 and - 2

Step-by-step explanation:

Given

x² + 5x - 14

Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (+ 5)

The factors are + 7 and - 2 , since

7 × - 2 = - 14 and 7 - 2 = + 5 , then

x² + 5x - 14 = (x + 7)(x - 2) ← in factored form

Answer::

Explanation:

Let the number of lasagna cupcakes made = x

Let the number of Gorgonzola onion tarts made = y

0. It takes ,10 minutes, to assemble each pan of lasagna cupcakes.

1. It takes ,15 minutes, to roll out the Gorgonzola onion tarts and fill each pan.

2. She has a maximum of ,2 hours (120 minutes), to assemble the appetizers.

These translate to the inequality:

0. Each pan of lasagna cupcakes takes 20 minutes to bake.

1. Each pan of Gorgonzola tarts takes 6 minutes to bake.

2. She has 60 minutes to bake the appetizers.

These translate to the inequality:

Since she must bake either lasagna cupcakes or Gorgonzola tarts, we have that:

So the system of inequalities is:

The graph that bests represents this scenario is:

Answer:

(0,-1) and (-1,-2)

Step-by-step explanation:

The value of x from the given equation is -4.

The given equation is x + 3 = -x - 5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solved as follows:

x+3=-x-5

x + x = -5-3 (Transpose variable to LHS of an equation and constant to RHS of an equation)

2x = -8

⇒ x = -4

Therefore, the value of x from the given equation is -4.

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\(f(x)=x+7\\g(x)=x-4\\f(x)*g(x)=(x+7)(x-4)\\f(x)*g(x)=x^2+3x-28\)

So it's x^2+3x-28

The simplification form of the provided expression is 2x²y⁴ option first is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

\(= \rm \sqrt[3]{8x^6y^{12}}\)

\(\rm =\sqrt[3]{8}\sqrt[3]{x^6}\sqrt[3]{y^{12}}\)

\(\rm \rm = \rm 2\sqrt[3]{x^6}\sqrt[3]{y^{12}}\)

\(\rm =2x^2\sqrt[3]{y^{12}}\)

\(\rm =2x^2y^4\)

Thus, the simplification form of the provided expression is 2x²y⁴ option first is correct.

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Answer:

pandas

Step-by-step explanation:

Answer:

the first option

Step-by-step explanation:

3/3 is equal to one so when you multiply 5/6 by one it stays the same but in this case it equals 15/18

Answer:

18/95

Step-by-step explanation:

There are a total of 20 names, 9 of which are girl names.

The probability that the first name is a girl name is 9/20.

Since there's one less girl name in the hat, there are now a total of 19 names, 8 of which are girl names.  So the probability that the second name is a girl name is 8/19.

The total probability is (9/20) (8/19) = 18/95.

Answer: slope for line b is 2

Step-by-step explanation:

If a line is parallel to another, that means they have the same slope, different y-intercept.

Since it's given that a is parallel to b, that means the slope is the same, thus the slope of b is 2.

Answer:

Now that the values of m (slope) and b (y-intercept) are known, substitute them into y=mx+b . to find the equation of the line.

y=5/4x+9/4

Step-by-step explanation:

Use y=mx+b to calculate the equation of the line, where m represents the slope and b represents the y-intercept.

To calculate the equation of the line, use the y=mx+b format.

Slope is equal to the change in y over the change in x , or rise over run.

m=(change in y)/(change in x)

The change in x

is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).

m=(y2−y1)/(x2−x1)

Substitute in the values of x and y into the equation to find the slope.

m=1−(6)/−1−(3)

Finding the slope m.

m=5/4

Find the value of b

using the formula for the equation of a line.

b=9/4

The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.

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Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:

Multiply all items by each other to get all of the combinations.

Step-by-step explanation:

Multiply all items by each other to get all of the combinations. This works because multiplying them together calculates all possible combinations in a data set.

The point that preserves the function is option  A(-3,-8).

What do you mean by function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given question,

We have four option for the answer.

Note: if f is a function then each number of the domain has an unique image.

Since (regarding the table) the image of 9 is 6 then the answer D is wrong

The same apply on answers B and C .

Therefore, the right answer is A(-3,-8).

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a) The estimated population for each town is given as follows:

b) The current population of Harmony Corners is of: 7,214.

The expression are found applying the proportions in this problem, given from the percent change in the table.

The multiplier for each expression is given as follows:

Supposing that the population of Harmony Corners was of 6,742 on the Census, we have that:

z = 6742.

Hence the current population is of:

1.07 x 6742 = 7,214.

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

From the question, we have the following parameters that can be used in our computation:

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Given that the derivative of the inverse trigonometric function tan^-1(x/a) with respect to x is 1/(a^2+x^2), we need to find the integral of tan^-1(x/8).Solution: Let y = tan^-1(x/8). option (1) is correct.

(1)Differentiating both sides of equation (1) with respect to x, we get, dy/dx = 1/(1+(x/8)^2) × 1/8

(2) => dy/dx = 1/(64/8^2+x^2) = 1/(64+x^2)

(3) [since x/8 = tan(y) => x = 8tan(y) and (x/8)^2 = tan^2(y) = sec^2(y)-1 = 1/cos^2(y) -1 => (x/8)^2+1 = 1/cos^2(y) => 1+(x/8)^2 = sec^2(y)]

Therefore, from equations (2) and (3), we get the required integral as follows :

Integral of dy/dx = Integral of 1/(64+x^2) with respect to x.=> y = tan^-1(x/8) = Integral of 1/(64+x^2)

with respect to x + C (C = constant of integration). Integrating 1/(64+x^2) with respect to x, we get: S 1/(64+x^2)dx = (1/8) tan^-1(x/8) + C.

∴ The integral of tan^-1(x/8) is (1/8) tan^-1(x/8) + C, where C is the constant of integration. Hence, option (1) is correct.

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a) The probability that the murder was committed with a knife: 0.55

b) The probability that the cook did it, given that the murder was committed with a knife: 0.275

To determine the probability that the murder was committed with a knife, we first need to find the total number of weapons.

The butler has four poison tipped pens, two crowbars and four knives and the cook has three rolling pins and seven knives.

So, the total knives: 4 + 7 = 11

crowbars: 2

poison tipped pens: 4

and rolling pins: 3

So, the total number of weapons: 11 + 2 + 4+ 3 = 20

The probability that the murder was committed with a knife:

p = 11/20

p = 0.55

Now we need to find the probability that the cook did it, given that the murder was committed with a knife.

P = 0.55 × 0.5

P = 0.275

The required probability is 0.275

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Answer: 8

Step-by-step explanation:

8x14=112

Answer:

8 minutes

Step-by-step explanation:

Reason: If 14 miles = 112 minutes. I divided 112 by 14, and got 8, meaning the minutes for one mile.