Co...
1.2 m
2.5 m
3.5 m
The front of a house needs to be painted black. The garage door is 1.5 m high and 2 m wide.
A) How many square meters of black paint will be needed to paint the house not including the
garage door?
Show your work

∠LMN is an obtuse angle.

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

Explanation

Let's go through the answer choices to see which are true, and which are false.

Answer:

Just give me the questions and ill do it

Step-by-step explanation:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given roots

This means that the roots are:

STEP 2: Write the form of getting a quadratic equation using the roots

STEP 3: Get the equation

Since we know the roots, we write them in a factor form as seen above to have:

We multiply the two factors to get the quadratic equation

Hence, the answer is:

Option A. The slope of the line is zero

How is the slope calculated?

First point = \((x_1,y_1)=(-3, -1)\)

Second point = \((x_2,y_2)= (3,-1)\)

Slope of the line = m

                       \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m =\frac{-1+1}{3+3} \\\\m = \frac{0}{3} \\\\m= 0\)

Thus the slope of the line is zero.

What is a zero slope?

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The equation that represents the line passing through P and parallel to line m would be; B  y+2 = 2(x-3)

An equation is an expression that shows the relationship between two or more numbers and variables.

We have been given the line passing through P and parallel to line m.

We can conclude that the point lies on the line is (3, -2)

The slope of the given line is m = 2.

Thus the equation will be;

y-y₁ = m(x-x₁)

y+2 = 2(x-3)

The equation that represents the line passing through P and parallel to line m would be; B -> y+2 = 2(x-3)

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Based on the two linear equations represented by the tables, the solution to the system of equations include the following: C. (-3, -2).

In order to determine the solution to the system of equations, we would have to find the slope from each of the table and then write the required equation based on the data points contained in the table by using the point-slope form.

Mathematically, the point-slope form of a line is given by this equation:

y - y₁ = m(x - x₁)

Where:

Substituting the given parameters into the point-slope formula, the equation for table A is given by;

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (-1 + 4)/(-2 + 5)(x - (-5))

y + 4 = 3/3(x + 5)

y + 4 = x + 5

y = x + 5 - 4

y = x + 1

For table B, the equation is given by;

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (-2 + 4)/(-3 + 6)(x - (-6))

y + 4 = 2/3(x + 6)

y + 4 = 2x/3 + 4

y = 2x/3 + 4 - 4

y = 2x/3

Equating the two equations, we have;

2x/3 = x + 1

2x/3 - x = 1

-x/3 = 1

x = -3

When point x = -3, the value of point y is given by;

y = 2x/3

y = 2(-3)/3

y = -6/3

y = -2

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Answer:

32.5 is greater than 30.8

Answer: greater than

Step-by-step explanation:

32.5 is greater than 30.8

32.5-30.8=1.7

The difference is positive, which means 32.5 is greater than 30.8

EXTRA: 32.5 is 1.7 more than 30.8

Hope this helps!! :)

Please let me know it you have any question

Answer:

18

Step-by-step explanation:

\(\frac{6}{1/3} =\frac{6*3}{1} \\=18\)

The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

The equation of a line in point-slope form is expressed as;

y - y0 = m(x -x0)

where

m is the slope

(x0, y0) is the point on the line

Given the following parameters

Point (0,8)

Slope from the equation = 3/5

Substitute

y - 8 = 3/5(x - 0)
5(y -8) =3x

5y - 40 = 3x

5y - 3x = 40

Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

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The sum of the scores is equal to 160.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of scores (data set), we have;

∑x = 20 + 60 + 30 + 50

∑x = 160.

Mean = [F(x)]/n = 160/4 = 40.

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Answer:

the square root is 6.48

Answer:

≈6.48

Step-by-step explanation:

\(\sqrt{42}=\\6.4807407...\)

If you multiply it by itself, it will equal 42. (Or you can just use a calculator)

Answer:

b. $16.25

...............

The amount of interest he would pay for a  loan of $10,000 with a 2% interest rate and for 18 months is $300

Amount of money taken as a loan = $10000

The rate of interest = 2%

The time period of interest is 18 months = 1.5 year

Interst = prt/100

= 10000x 2 x 1.5/100

= 300

Therefore, the amount of interest he would pay for a  loan of $10,000 with a 2% interest rate and for 18 months is $300

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Answer:

Option 4.

Step-by-step explanation:

The information is that the points G and H are the midpoints of ED and EF.

For example G will be  (5 + (-2))/ 2 , (4 - 0) / 2 which is  (1.5, 2).

If we calculate H it is (6.5, -3).

The answer is option 4.

Answer:

The required answer is 0.0075 ml .

Step-by-step explanation:

Given that , It takes 200 L of maple sap to make 5 L of maple syrup. And we need to find how much sap it requires to make 300 ml of syrup . Hence on using Unitary method ,

⇒ 200 L of maple sap is used to make 5L of syrup .

⇒ 1L of maple sap is used to make 5L/200 L of syrup .

⇒ 1000 ml of maple sap is used to make 5L/200 L of syrup .

⇒1ml of maple sap is used to make 5L/( 200 * 1000) L of syrup .

⇒300ml of maple sap is used to make 5L * 300/200 L * 1000 of syrup .= 0.0075 ml .

The probability that exactly six out of ten carry a smartphone when travelling is; P(6) = 0.146

The missing part of the question is;

The probability distribution of x is the binomial distribution with n = 10 and p = 0.75.

Calculate P(6)

Where;

p is probability of success

q is probability of failure

n is number of experiments

In this question;

n = 10

p = 75% = 0.75

q = 1 - p

q = 1 - 0.75

q = 0.25

Since six passengers are randomly selected, then applying the formula earlier quoted, we have;

P(6) = ¹⁰C₆ × 0.75⁶ × 0.25⁽¹⁰ ⁻ ⁶⁾

P(6) = 0.146

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From the data given, we estimate the population mean and population standard deviation. Then, we use this estimate to find a 95% confidence interval for the population variance and the population standard deviation.

Sample:

Salaries in millions of dollars: 2.2, 1.5, 0.5, 1.3, 2.4, 1.5, 2.7, 0.3, 2.0, 0.3

Question a:

The mean is the sum of all values divided by the number of values. So

\(\overline{x} = \frac{2.2 + 1.5 + 0.5 + 1.3 + 2.4 + 1.5 + 2.7 + 0.3 + 2.0 + 0.3}{10} = 1.42\)

The sample mean salary is of 1.42 million.

Question b:

The standard deviation is the square root of the difference squared between each value and the mean, divided by one less than the number of values.

So

\(s = \sqrt{\frac{(2.2-1.42)^2 + (1.5-1.42)^2 + (0.5-1.42)^2 + (1.3-1.42)^2 + (2.4-1.42)^2 + (1.5-1.42)^2 + (2.7-1.42)^2 + ...}{9}} = 0.8772\)

Thus, the estimate for the population standard deviation is of 0.8772 million.

Question c:

The sample size is \(n = 10\)

The significance level is \(\alpha = 1 - 0.05 = 0.95\)

The estimate, which is the sample standard deviation, is of \(s = 0.8772\).

Now, we have to find the critical values for the Pearson distribution. They are:

\(\chi^2_{\frac{\alpha}{2},n-1} = \chi^2_{0.025,9} = 19.0228\)

\(\chi^2_{1-\frac{\alpha}{2},n-1} = \chi^2_{0.975,9} = 2.7004\)

The confidence interval for the population variance is:

\(\frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2},n-1}} < \sigma^2 < \frac{(n-1)s^2}{\chi^2_{1-\frac{\alpha}{2},n-1}}\)

\(\frac{9*0.8772^2}{19.0228} < \sigma^2 < \frac{9*0.8772^2}{2.7004}\)

\(0.3641 < \sigma^2 < 2.5646\)

Thus, the 95% confidence interval for the population variance is (0.3641, 2.5646)

Question d:

Standard deviation is the square root of variance, so:

\(\sqrt{0.3641} = 0.6034\)

\(\sqrt{2.5646} = 1.6014\)

The 95% confidence interval for the population standard deviation is (0.6034, 1.6014).

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Answer:

Each of the bold numbers is a statistic.

Step-by-step explanation:

In statistical analysis, observations may either be from a sample or from a population. Samples are smaller subsets a population and hence, if chosen randomly forms a good representative of the population data.

Hence, numerical characteristics of observation which forms a population are called PARAMETER. While numerical characteristics of a given sample are called STATISTIC.

From the scenario given above, 128,000 people were interviewed, this represents a sample from the population and not the entire population. Hence, all numerical characteristic or attribute derived from the sample of 128,000 interviewees will be a statistic.

Yes, I agree with Benito's approach to finding the quotient of 45 ÷ 9.

We have,

When we divide 45 by 9, we are essentially asking, "How many times does 9 go into 45?"

This can also be rephrased as "What is the result of multiplying 9 by some number to get 45?"

Now,

To find the quotient of 45 ÷ 9, we can recall the related multiplication fact that 9 times 5 is equal to 45.

Then, we can use the Commutative Property of Multiplication, which states that the order of multiplication can be changed without changing the result, to recall the other related multiplication fact that 5 times 9 is equal to 45.

Therefore,

The quotient of 45 ÷ 9 is 5, which we can obtain by recalling either the multiplication fact 9 times 5 equals 45 or 5 times 9 equals 45.

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The true statement is; II. Option D

From the information given, we have that;

I. The set of all second-degree polynomials with the standard operations is a vector space

II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space

III. The set of second quadrant vectors with the standard operations is a vector space

Note that;

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THe value of the expression using BODMAS rule is 26

The abbreviation BODMAS, which stands for "Brackets, Order of powers or roots, Division, and Multiplication," is followed by the BODMAS rule. A stands for addition and S for subtraction. According to the BODMAS rule, multi-step mathematical statements must be solved in the BODMAS order from left to right.

The order of operations, or BODMAS, is a method for carrying out operations in an arithmetic statement. Math is all about logic, and there are several established laws that help us with our calculations. BODMAS is one of the established rules for consolidating multiple operator expressions.

An expression or equation in mathematics has two parts:

A character known as an operator joins two integers to form an expression or equation. The four most often used operators in mathematics are addition (+), subtraction (-), multiplication (*), and division (*/*). Finding the solution to mathematical statements or equations with just one operator is usually rather easy.

The expression is 14 + 2 + 3(4) - (6-1-3) = 14 + 2 + 12 - 2 = 26

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Standard form looks like this: Ax + By = C.

y - (-1) = 3(x - 4)

y + 1 = 3x - 12

y = 3x - 12 - 1

y = 3x + 13

Move 13 to left side and y to right side.

-13 = 3x - y

Done!

The function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

To determine the intervals on which the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.

Let's find the derivative of the function f(x) = x + 10√(9 - x) with respect to x.

f'(x) = 1 + 10 * (1/2) * (9 - x)^(-1/2) * (-1)

= 1 - 5√(9 - x) / √(9 - x)

= 1 - 5 / √(9 - x).

To analyze the sign of the derivative, we need to find the critical points where the derivative is equal to zero or undefined.

Setting f'(x) = 0:

1 - 5 / √(9 - x) = 0

5 / √(9 - x) = 1

(√(9 - x))^2 = 5^2

9 - x = 25

x = 9 - 25

x = -16.

The critical point is x = -16.

We can see that the derivative f'(x) is defined for all x values except x = 9, where the function is not differentiable due to the square root term.

Now, let's analyze the sign of the derivative f'(x) in the intervals (-∞, -16), (-16, 9), and (9, ∞).

For x < -16:

Plugging in a test value, let's say x = -17, into the derivative:

f'(-17) = 1 - 5 / √(9 - (-17))

= 1 - 5 / √(9 + 17)

= 1 - 5 / √26

≈ 1 - 0.97

≈ 0.03.

Since f'(-17) is positive, the function is increasing in the interval (-∞, -16).

For -16 < x < 9:

Plugging in a test value, let's say x = 0, into the derivative:

f'(0) = 1 - 5 / √(9 - 0)

= 1 - 5 / √9

= 1 - 5 / 3

≈ 1 - 1.67

≈ -0.67.

Since f'(0) is negative, the function is decreasing in the interval (-16, 9).

For x > 9:

Plugging in a test value, let's say x = 10, into the derivative:

f'(10) = 1 - 5 / √(9 - 10)

= 1 - 5 / √(-1)

= 1 - 5i,

where i is the imaginary unit.

Since the derivative is not a real number for x > 9, we cannot determine the sign.

Combining the information, we conclude that the function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

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From the given expression in our example we have say

y = d-6d-3dd−6d−3d,

the equivalent expression would be  y = -14-3dd

We can see two different terms

the "d" terms and the "dd" terms

Let us collect like terms

we have

y= d-6d-6d-3d-3dd

y = d-12d-3d-3dd

y= d-15d-3dd

y = -14-3dd

Hence the equivalent expression is y = -14-3dd

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Answer:

-8d

guessed and it was right :P

Answer:

8429

Step-by-step explanation:

I HOPE THIS IS THE ANSWER CAPS

Answer:

8429

Step-by-step explanation:

hope this helps! :D

Answer:

3

Step-by-step explanation:

Plug in 6 for the y value. Solve for x.

Answer:

x=3 (3,6)

Step-by-step explanation:

Y = 15 - 3x

Y = 6

6= 15-3x

-15 from each side

-9 = -3x

devide each side

ny -3

x=3

(check)

15-3(3) = 6