Explain how a number line is used to determine the sum of -3 + 7

Answer:

2,3 and 4

Step-by-step explanation:

The image of the coordinates after a dilation of (9, −7) by a scale factor of 4 centered at the origin include the following: (36, -28).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage (9, -7) by using a scale factor of 4 centered at the origin as follows:

Coordinate A (9, -7) → Coordinate A' (9 × 4, -7 × 4) = Coordinate A' (36, -28).

In conclusion, the coordinates of the image after a dilation are  (36, -28).

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Answer:

j = -4/(k - h)

Step-by-step explanation:

h - 4/j = k

use inverse operation

h - 4/j = k

-h         -h

-4/j = k - h

*j      *j

-4 = j( k - h )

/( k - h )  /( k - h )

-4/( k - h ) = j

The slope of the least squares regression line represents the change in the response variable (in this case, the ride duration in seconds) for each unit increase in the predictor variable (the length of the roller coaster track in feet).

In the given context, the slope of the least squares regression line indicates the average change in the duration of the roller coaster ride in seconds for each additional foot of track length. If the slope is positive, it means that as the length of the roller coaster track increases by one foot, the ride duration is expected to be longer by the value of the slope.

Conversely, if the slope is negative, it means that as the track length increases by one foot, the ride duration is expected to be shorter by the absolute value of the slope.

To predict the length of the new roller coaster ride, we can use the equation of the least squares regression line and substitute the given track length. By multiplying the track length by the slope of the regression line and rounding the result to the nearest second, we can estimate the expected ride duration for the new roller coaster.

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Answer:0.18%

Step-by-step explanation: It is simply but how you know that it is a percentage and you then have to add it as a decimal.

Answer:

then the height would be 2 because 3*2=6

Step-by-step explanation:

Answer:

4 cm

Step-by-step explanation:

area of triangle is: area = (base*height)/2.

since the area is 6 m^2, and base is 3 cm,

6 m^2  = (3 m*height)/2

12m^2 = 3 m*height

height = 4 m

Answer:

Step-by-step explanation:multiple types of numbers have been shown in so 467x it will be 873

Answer:

Step-by-step explanation:

Inverse variation functions have the form y = k / x, where k is a constant.

When k > 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k > 0, the hyperbola opens upwards and the two branches of the hyperbola move away from the x-axis as x increases. This means that as x increases, the value of y decreases. When x approaches 0 from the right, y approaches positive infinity, and when x approaches 0 from the left, y approaches negative infinity.

On the other hand, when k < 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k < 0, the hyperbola opens downwards and the two branches of the hyperbola move toward the x-axis as x increases. This means that as x increases, the value of y increases. When x approaches 0 from the right or left, y approaches negative infinity.

In both cases, the inverse variation function is undefined for x = 0, as division by zero is undefined.

Answer:

what?

Step-by-step explanation:

Answer:

what you mean

I do not understand what this means

The required length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So we have:

\($c^2 = a^2 + b^2$\)

where c is the length of the hypotenuse, a and b are the lengths of the legs.

We are given that the length of the hypotenuse is 3 cm and the length of one leg is 2 cm. Let's substitute these values into the equation above:

\($3^2 = 2^2 + b^2$\)

\($9 = 4 + b^2$\)

\($b^2 = 5$\)

\($b = \sqrt{5}$\)

So the length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm (rounded to one decimal place).

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We can fill in the boxes to make each equation complete as follows:

1. x³x⁹ = x¹²

2. x⁷/x³ = x⁴

3. 1/x⁻⁵ = x⁵

4. (7b³c⁵)³ = 343b⁹c¹⁵

To solve the exponents as provided above, the rules have to be factored in. One of the rules is that when multiplying exponents of the same base, we simply add their powers together. So, we have the powers of 3 and 9 for the first expression and they add up to 12.

1. x³x⁹ = x³ ⁺ ⁹ = x¹²

For the second expression, the rule of exponents says that when dividing, we will subtract the powers. This gives us x⁴ for the second expression.

2. x⁷/x³ = x⁷ ⁻ ³ = x⁴

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Answer:

19   23  

Step-by-step explanation:

19 and  23  are the only primes in her range

Answer:

8

Step-by-step explanation:

\(P = \{3,6,9\}\\\\\text{Number of elements,}~ n = 3\\\\\text{Number of subset} = 2^n = 2^3 = 8\)

The equation of a line that has a slope of 1/6 and it passes through the point (-6, 6) is y = x/6 + 7.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

From the information provided above, we have the following slope and data points on the line:

Points = (-6, 6).

Slope, m = 1/6

At data point (-6, 6), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 1/6(x + 6)

y - 6 = x/6 + 1

y = x/6 + 1 + 6

y = x/6 + 7

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Factorial notation is used to represent the product of a series of descending positive integers, and is denoted by an exclamation mark.

For example, 5! represents 5 x 4 x 3 x 2 x 1, which equals 120. If the study involves counting the number of ways a certain group of items can be arranged, factorial notation may be used to express the total number of possible arrangements. However, without knowing the specifics of Dr. Elder's study, it is impossible to provide the correct factorial notation. Therefore, I would recommend providing more details about the study in order to receive a more accurate answer.

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Answer:

0

Step-by-step explanation:

because they are heading in the same direction

The perimeter and the area of each composite figure are, respectively:

Case 10: Perimeter: p = 16 + 8√2, Area: A = 24

Case 12: Perimeter: p = 28, Area: A = 32

Case 14: Perimeter: p = 6√2 + 64 + 3π , Area: A = 13 + 9π

In this question we find three composite figures, whose perimeter and area must be found. The perimeter is the sum of all side lengths, while the area is the sum of the areas of simple figures. The length of each line is found by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

The perimeter of the semicircle is given by following formula:

s = π · r

And the area formulas needed are:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Semicircle

A = 0.5π · r²

Where:

Now we proceed to determine the perimeter and the area of each figure:

Case 10

Perimeter: p = 2 · 8 + 4 · √(2² + 2²) = 16 + 8√2

Area: A = 4 · 0.5 · 2² + 4² = 8 + 16 = 24

Case 12

Perimeter: p = 2 · 4 + 4 · 2 + 4 · 2 + 2 · 2 = 8 + 8 + 8 + 4 = 28

Area: A = 4 · 6 + 2 · 2² = 24 + 8 = 32

Case 14

Perimeter: p = 2√(3² + 3²) + 2 · 2 + 2 · 2 + 2 · 2 + π · 3 = 6√2 + 64 + 3π

Area: A = 2 · 0.5 · 3² + 2² + π · 3² = 9 + 4 + 9π = 13 + 9π

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The error occurred in line (3) because the factorization was not performed correctly.

A product is the result obtained from multiplying two or more numbers or expressions together.

From line (2) to line (3), there was a mistake

In line (2), the factorization is correct:

-3y³ + 9y² + 30y = 3y(y² - 3y - 10)

However, in line (3), the factorization is incorrect. The expression should be factored using the sum and product method:

y² - 5y - 10 = (y - 5)(y + 2)

Therefore, the correct factorization is:

-3y³ + 9y² + 30y = 3y(y² - 3y - 10)

= -3y(y² - 5y - 10)

= -3y(y - 5)(y + 2)

The error occurred in line (3) because the factorization was not performed correctly. Instead of using the sum and product method to factor y² - 5y - 10, the expression was factored as y² - 3y + 2y - 10, which is incorrect.

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Answer:

30/5=6

Step-by-step explanation:

There’s 30 fish put into five bowls, and there’s six fish in each

The concept which is the main idea of estimating a population​ proportion is

C. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.

The concept stated in option C is not a main idea of estimating a population proportion.

Estimating a population proportion involves inferential statistics, which is concerned with making inferences or drawing conclusions about a population based on information from a sample. In this context, descriptive statistics refers to methods that summarize and describe the characteristics of a sample or population, such as measures of central tendency and variability.

The main ideas of estimating a population proportion include:

A. The sample proportion is the best point estimate of the population proportion: When estimating a population proportion, the sample proportion (the proportion observed in the sample) is commonly used as the point estimate for the population proportion. This is because it provides an unbiased estimate of the unknown population proportion.

B. Knowing the sample size necessary to estimate a population proportion is important: The sample size plays a crucial role in estimating a population proportion. A larger sample size generally leads to a more precise estimate with a smaller margin of error. Determining an appropriate sample size is essential to ensure the desired level of confidence and accuracy in the estimate.

D. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion: Constructing a confidence interval is a common method to estimate the true value of a population proportion. By using the sample proportion along with the standard error and a chosen level of confidence, a range of values is calculated within which the true population proportion is likely to fall.

In contrast, option C refers to using a sample statistic to estimate the population proportion by utilizing descriptive statistics. However, estimating a population proportion typically involves inferential statistics rather than descriptive statistics.

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Answer:

C; The triangles may be congruent

Step-by-step explanation:

Here, we have two sides of the each of the triangles equal already

By congruency, we might have SSS or SAS

if SSS, this mean that all the sides are equal

Since we do not know the measure of the third side, we cannot say that they are not congruent or they are congruent

Also, we do not know the measure of the angles of the triangles

If we have an angle that is equal in the two triangles, then we can have congruency through SAS

But since we do not know how these measures, we use the word ‘may’

2x + y ≤ 7 is the solution

All the three brothers get,

⇒  10,000

⇒ 6,000

⇒ 4,000

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

Share R20 000 among three brothers in the ratio 5 : 3 : 2.

Hence, We can formulate;

All the three brothers get, 5x, 3x and 2x

So, We get;

⇒ 5x + 3x + 2x = 20000

⇒ 10x = 20,000

⇒ x = 2000

Thus, All the three brothers get,

⇒ 5x = 5 × 2000 = 10,000

⇒ 3x = 3 × 2000 = 6,000

⇒ 2x = 2 × 2000 = 4,000

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Answer: the slope of a perpendicular line is the opposite slope of the other line

for example if one lines slope is -2, the perpendicular slope is 1/2

Using the exterior angle theorem which involves the use of two interior angles in the polygon, the value of angle ACD in the triangle is 150 degrees

An exterior angle of a polygon is an angle that is formed outside of the polygon by extending one of its sides. It is the supplementary angle of an interior angle.

Exterior angle theorem states that the sum of two interior angles is equal to one exterior angle.

Using that theorem in this problem;

∠ACD = 33 + 117

∠ACD = 150°

The value of angle ACD in the triangle is equal to 150 degrees

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Answer:x − x^{2} − 1.

Step-by-step explanation:

.

ANSWERS

A. AB ≅ FG

B. ∡C≅ ∡H

EXPLANATION

A. To use SAS theorem, we have to know if one more side is congruent to the corresponding side of the other triangle. SAS is side-angle-side. The angle must be included between the two sides. Therefore the missing side is AB congruent to FG:

B. To use ASA Theorem we have to know one more angle. Since ASA is angle-side-angle, the side must be between two angles. Therefore, the missing angle is angle C congruent to angle H:

Step-by-step explanation:

The speed of the boat is absolute value of the velocity vector. To find the speed of the boat, take the magnitude of the velocity vector which is

\( \sqrt{ {a}^{2} + {b}^{2} } = {c}^{} \)

Where a and b is the vector

a is -4, b is 3

so

\( \sqrt{16 + 9} = \sqrt{25} = 5\)

So the speed of the boat is 5 meters per hour.

To find the direction of the vector, we need to find the angle it is traveling in.

Using trigonometry, we can do this.

\( \tan( \alpha ) = - \frac{3}{4} \)

\(arc \tan( - \frac{3}{4} ) = \alpha \)

\( \alpha = - 36.87\)

The boat is traveling at angle 36.87 degree clockwise.

P : Principal amount deposited : $600

r : interest rate : 5 % = 0.05 ( decimal form)

n : number of compounding periods in a year : 4 (4 times in a year)

t : years

Apply compound interest formula:

A= P (1+r/n)^nt

Replace by the values given:

A = 600 (1+0.05/4)^(4.3)

A = 600 ( 1.0125) ^12

A =$ 696.45