9) through: (-5, 4) and (1, -2)
A) y + 5 = 3(x+4)
B) y+4=3(x+5)
C) y - 4 = -(x + 5)
D) y - 4 = 3(x+5)

Answer:

They are all true

Step-by-step explanation:

1. 3² +4² = 5²

3x3 + 4x4 = 5x5

  9   +  16  =  25

25 = 25

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

2. 6² + 8² = 10²

36 + 64 = 100

100 = 100

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

3. 9² + 12² = 15²

81 + 144 = 225

225 = 225

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

4. 5² +12² =13²

25 + 144 = 169

169 =169

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

Answer:

m = 3/4

Step-by-step explanation:

The new coordinates of triangle RST after the rotation are R'(8, 8), S'(3, 8), and T'(8, -2).

A rotation involves rotating the figure through a certain angle around the center of rotation, which is usually denoted by the letter 'O'. The angle of rotation can be measured in degrees or radians.

In a two-dimensional space, the direction of the rotation can be either clockwise or counterclockwise. A clockwise rotation is in the direction opposite to the hands of a clock, while a counterclockwise rotation is in the same direction as the hands of a clock.

The image produced by a rotation is a transformed figure that is congruent to the original figure. This means that the two figures have the same shape and size, but may be positioned differently in space.

To graph the image of triangle RST after a rotation of 270° counterclockwise around the origin, we need to find the new coordinates of each vertex using the rotation formula:

x' = x cosθ - y sinθ

y' = x sinθ + y cosθ

where (x, y) are the original coordinates of a vertex, (x', y') are the new coordinates after rotation, and θ is the angle of rotation (270° counterclockwise in this case).

Using this formula, we get:

R' = (8 cos270° - (-8) sin270°, 8 sin270° + (-8) cos270°) = (8, 8)

S' = (8 cos270° - (-3) sin270°, 8 sin270° + (-3) cos270°) = (3, 8)

T' = (2 cos270° - (-8) sin270°, 2 sin270° + (-8) cos270°) = (8, -2)

Therefore, the new coordinates of triangle RST after the rotation are R'(8, 8), S'(3, 8), and T'(8, -2). The graph of the rotated triangle would look like:

       T'(8, -2)

          /\

        /     \

      /         \

 S'(3, 8)   R'(8, 8)

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Answer:

30 minutes

Step-by-step explanation:

talking to her relatives during the month.

Answer:

Lerato sees that Vodolite has a new price plan for prepaid

phones only, available until 30 April 2022. The rates applicable

to this price plan are set out in TABLE 1 out below. She likes

the plan and decides to sign up.

TABLE 1

Use TABLE 1 above to answer the questions.

USAGE COST

Local call (any network any time) 90 cents per minute (bill per

second)

SMS 80 cents per SMS all day

MMS (300 KB or less) R1,20 per MMS

International SMS R1,95 per SMS all day

1.1.1 During the month of February, Lerato sends one SMS per day to

relatives. Calculate how much this activity costs her in rands.

(3)

1.1.2 Lerato spends 2 hours 30 minutes talking to her relatives during the

month. Calculate how much this costs her.

(4)

1.1.3 Lerato’s mothers monthly cellphone bill was R312. Her mother was

only able to pay 75% of the monthly bill. Determine how much was paid

towards the cellphone bill.

(2)

1.2 Lerato is planning to go on holiday in a minibus. She estimates that

the petrol cost will be R800 to get to the destination.

The average median and mode price is $18. Option C is correct.

Given that certain item is available at 7 stores, three stores sell them for $20, two stores sell them for $15, one store sells them for $13, and one sells them for $16.

The mean is the average of the given numbers and is calculated by dividing the sum of the given numbers by the total number of numbers.

Firstly, we will find the median of the given items by arranging the given numbers in ascending order, we get

13,15,15,16,20,20,20

To find the median use the formula (n+1)/2, where n is the number of values in your dataset.

(7+1)/2=8/2=4

In the ascending order numbers 4th term is 16.

So, median is 16

Mode is the highest repeating term in the set or numbers.

So, here mode is 20

Now, we will calculate the average of median and mode, we get

Average=(median +mode)/2

Average=(16+20)/2

Average=18

Hence, the average (arithmetic mean) of the median price and the mode price where certain item is available at 7 stores, three stores sell it for $20, two stores sell it for $15, one store sells it for $13, and one sells it for $16 is $18.

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a) The function F represents the difference between the demand and supply functions. The implicit function P = f(l) exists if the demand function is invertible with respect to price.  b) An exogenous increase in income will increase the price of the good (assuming it is normal).

a) The function F represents the market equilibrium condition, where F(P,I) = D(P,I) - S(P) = 0. It shows the difference between the demand function D(P,I) and the supply function S(P). The equilibrium occurs when the quantity demanded equals the quantity supplied.

The implicit function P = f(l) exists when the demand function is invertible with respect to price. This means that for each level of income, there is a unique price that equates demand and supply. The necessary and sufficient condition for the existence of the implicit function is that the partial derivative ∂D/∂P is non-zero and continuous.

b) An exogenous increase in income will affect the price of the good. Assuming the good is normal, meaning that as income increases, the demand for the good also increases, the price will rise. This can be illustrated on a graph by plotting the demand and supply curves. When income increases, the demand curve shifts outward, causing an increase in price.

To determine the effect quantitatively, we can use the implicit function theorem to calculate the comparative-static derivative dP/dl. This derivative represents the change in price with respect to a change in income. By evaluating this derivative at the given point, we can determine the direction and magnitude of the price change in response to the increase in income.

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Thus, the values corresponding to the function and constraints will be:

Objective Function:\(C=3.33X+2.00Y\)

Constraints:\(407X+271Y\geq 4700\\407X+271Y\leq 9400\)

We begin by defining the variables. Let call:

X = of servings of dried apricots

Y= of servings of dried dates

For apricots, there are 3 servings in one pound. This means that the cost per serving is $9.99/3 = $3.33. The cost for X:

\(3.33X\)

For dates, there are 4 servings per pound. This means that the cost per serving is $7.99/4=$2.00. The cost for Y:

\(2.00Y\)

The total cost would be:  

\(C=3.33X+2.00Y\)

Product must contain at least 4700mg of potassium

\(407X+271Y\geq 4700\\407X+271Y\leq 9400\)

So now with the equations set it is possible to see that the desired values are between 9400 and 4700. Then using the critical points X=0, Y=0 for the two given equations. This will inform the points of interest for X and Y if this analysis is needed for the exercise.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

\( 2.58 \times {10}^{8} \)

Step-by-step explanation:

\(9.3. {10}^{7} - 3.4. {10}^{6} \\ = (27 \times 10 - 12) \times {10}^{6}\\ = (270 - 12) \times {10}^{6} \\ = 258 \times {10}^{6} \\ = 2.58 \times {10}^{6 + 2} \\ = 2.58 \times {10}^{8} \)

Answer: i don't know

Step-by-step explanation:

what is this

also i need points! sry

To determine whether there are differences between more than two population variances, utilise anova is True

What is Anova?

A statistical technique called analysis of variance, or ANOVA, divides observed variance data into various components for use in further testing. When there are three or more data groups, a one-way ANOVA is used to find out how the dependent and independent variables are related.

Concept:

One-way ANOVAs are typically used when there are three or more categorical independent groups, although they can also be employed when there are only two groups (but an independent-samples t-test is more commonly used for two groups)

A statistical procedure called Analysis of Variance (ANOVA) is used to examine variations between the means (or averages) of several groups. It is used in a variety of situations to discover whether there are any differences between the means of various groups.

To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilised. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.

The absence of a difference in means is always the null hypothesis in an ANOVA. The alternative or research hypothesis, which is typically expressed in words rather than mathematical symbols, asserts that the means are not all equal. The research hypothesis involves any difference in means, such as when all four means are different from one another, one mean differs from the other three, two means differ, and so on. All scenarios other than the equality of all means described in the null hypothesis are covered by the alternative hypothesis, as it was previously illustrated.

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A statistical procedure called Analysis of Variance (ANOVA) is used to examine variations between the means (or averages) of several groups. It is used in a variety of situations to discover whether there are any differences between the means of various groups.

To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilised. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.

Answer:

85 units²

Step-by-step explanation:

Add up your given areas to find the missing area using the Pythagorean Theorem:

a²+b²=c²

35+50=c²

85=c²

Therefore, the area of the blue square is 85 units²

Answer:

85 units²

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

It is ok for the inputs to have the same outputs, but not ok for the outputs to have the same inputs.

Answer:

37.7 inches

Step-by-step explanation:

She wants to paint the line along the circumference of the plate.

The plate is circular; the circumference of a circle is given as:

C = πD

where D = diameter

The diameter of the plate is 12 inches, therefore:

C = π * 12 = 37.7 inches

The line will be 37.7 inches long.

The amount of money invested at an annual interest rate of 9.25% can be calculated using the formula for simple interest. After 5 years, a total of $5,781.25 was collected in interest. By rearranging the formula, we can determine that the principal amount invested was $25,000.

To calculate the principal amount, we can rearrange the formula for simple interest: Interest = (Principal × Rate × Time). In this case, the interest collected after 5 years is given as $5,781.25, and the interest rate is 9.25% per annum. Plugging in these values, we get: $5,781.25 = (Principal × 0.0925 × 5). Simplifying the equation further, we have: $5,781.25 = 0.4625 × Principal. To find the Principal, we divide both sides of the equation by 0.4625, resulting in: Principal = $5,781.25 ÷ 0.4625. Solving this equation, we find that the principal amount invested was $25,000. Therefore, $25,000 was initially invested at an annual interest rate of 9.25%.

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To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:∫CF.v dlWhere v = (x²+2yz)i + y²j and dl = dx i + dy j + dz kTherefore,∫CF.(x²+2yz) dx + y² dy … (1)Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴

The above line integral is the required value. So, we need to evaluate this integral. To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:

∫CF.v dl

Where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

Therefore,

∫CF.(x²+2yz) dx + y² dy … (1)

Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴ The above line integral is the required value. So, we need to evaluate this integral.The integral is a line integral of a vector field, with the curve path of integration is given by C as follows: C: (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1)In other words, we need to evaluate the integral of the dot product of the vector field v with the differential of the curve:

∫CF.v dl...

where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

We must split the curve C into three distinct segments before we can start evaluating the integral. The segments will be from (0,0,0) to (1,0,0), from (1,0,0) to (1,1,0), and from (1,1,0) to (1,1,1).Let's start with the first segment, from (0,0,0) to (1,0,0). We can set x = t, y = 0, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = dt, dy = 0, dz = 0. We have:∫(0,0,0)to(1,0,0)

vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(t²+0)dt + 0 + 0= [t³/3]0to1= 1/3

Now, let's evaluate the second segment, from (1,0,0) to (1,1,0). We can set x = 1, y = t, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = dt, dz = 0. We have:

∫(1,0,0)to(1,1,0)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+0)dx + t²dy + 0dz= 1∫0to1(t²)dt= [t³/3]0to1= 1/3

Finally, let's evaluate the third segment, from (1,1,0) to (1,1,1). We can set x = 1, y = 1, z = t, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = 0, dz = dt. We have:

∫(1,1,0)to(1,1,1)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+2(1)(t))dx + 1²dy + 0dz= ∫0to1(1+2t)dt + 1(0to1)+ 0= [t²+t]0to1+ 1= 3/2

Therefore, the line integral is the sum of the integrals along the three segments:

∫CF.v dl= 1/3+ 1/3+ 3/2= 2

Thus, the value of the line integral of the given function v = x²+2yzi + y²j from (0,0,0) the point (1,1,1) by the route (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1) is equal to 2.

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Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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Given:

We will find the zeros of the function:

Factor the given function:

So, there are four zeros

So, the answer will be:

If ū and ū have the same length, then the projection of u onto ū and the projection of ū onto ū will always have the same length. This is because the projection of a vector onto another vector is simply the vector that is parallel to the first vector and has the same length as the first vector.

If the two vectors have the same length, then the projection of one vector onto the other will also have the same length. If ū and ū do not have the same length, then it is possible for the projection of u onto ū and the projection of ū onto ū to have the same length.

This is because the projection of a vector onto another vector is not necessarily the same length as the first vector. If the two vectors are not parallel, then the projection of one vector onto the other will be shorter than the first vector. However, if the two vectors are perpendicular, then the projection of one vector onto the other will be the same length as the first vector.

The projection of a vector onto another vector is a vector that is parallel to the first vector and has the same length as the first vector. The projection of u onto ū can be calculated using the following formula:

proj_ū(u) = (u ⋅ ū) / ||ū||^2 * ū

where u ⋅ ū is the dot product of u and ū, and ||ū|| is the magnitude of ū. The projection of ū onto u can be calculated using the following formula:

proj_u(ū) = (ū ⋅ u) / ||u||^2 * u

where ū ⋅ u is the dot product of ū and u, and ||u|| is the magnitude of u. If ū and ū have the same length, then ||ū|| = ||u||. This means that the two formulas for the projection are the same, and the projection of u onto ū will have the same length as the projection of ū onto u.

If ū and ū do not have the same length, then ||ū|| ≠ ||u||. This means that the two formulas for the projection are not the same, and the projection of u onto ū may or may not have the same length as the projection of ū onto u. If the two vectors are not parallel, then the projection of one vector onto the other will be shorter than the first vector. However, if the two vectors are perpendicular, then the projection of one vector onto the other will be the same length as the first vector.

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The area of the bedroom in the terms of p and q is (6p7q)² square units.

What is the area of square?

The amount of square units required to fill a square is referred to as the area of a square. In general, the region contained within a flat object's or 2D figure's boundary is referred to as the area. The unit of measurement is square, with square metres serving as the default.

We are given that a bedroom is in the shape of a square with the length as 6p7q.

We know that area of a square is the square of the side.

So, from this we get

⇒ Area = (6p7q)² square units

Hence, the area of the bedroom in the terms of p and q is (6p7q)² square units.

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Answer:

Has an undefined slope

Step-by-step explanation:

The slope formula is y2-y1 / x2-x1.

When the x values are the same, like they are in a vertical line, you get 0 in the denominator. You can't divide by 0, so the slope is undefined

The standard error of the mean is $128.125

Given:

a random sample is made of 256 middle managers concerning their annual incomes. the sample mean is computed to be $35,420. if the population standard deviation is $2,050.

n = 256

σ = 2050

standard error = standard deviation / sqrt of n

= 2050/\(\sqrt{256}\)

= 2050 / \(\sqrt{16*16}\)

= 2050 / \(\sqrt{16^2}\)

= 2050/16

= 1025/8

= 128.125

Therefore The standard error of the mean is $128.125.

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Answer:

91 pizzas

Step-by-step explanation:

Answer:

150

Step-by-step explanation: dont give away 50 points

Answer:

16 my guy.

Step-by-step explanation:

Answer:

4*4=16

4+4+4+4=16

Answer:

linear means a line (that eliminates c and d)

as "X" increases the "Y" value "DECREASES" so the answer is "B"

Step-by-step explanation:

Answer:

B. Linear decreasing

Step-by-step explanation:

The graph appears to have a negative slope, and it is a straight line. This means the graph will be linear. An exponential growth/decay would have a curved line, so those are automatically out. Since the farther the points go the more downwards the line is, this means it is decreasing.

hope this helped. :)

Answer: Multiply $2.00 by however many scoops there are and multiply $0.20 by however many toppings they choose. After that, add them together.

Step-by-step explanation:

If there are 2 scoops do $2.00 times 2

If there are 2 toppings do $0.20 times 2

Answer:

what

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given quadratic function:

\(y=3x^2 - 9, \qquad x \leq 0\)

The domain of the given function is restricted to values of x less than or equal to zero. Therefore:

As 3x² ≥ 0, then range of the given function is restricted to values of y greater than or equal to -9.

\(\hrulefill\)

To find the inverse of the given function, first interchange the x and y variables:

\(x = 3y^2 - 9\)

Now, solve the equation for y:

\(\begin{aligned}x& = 3y^2 - 9\\\\x+9&=3y^2\\\\\dfrac{x+9}{3}&=y^2\\y&=\pm \sqrt{\dfrac{x+9}{3}}\end{aligned}\)

The range of the inverse function is the domain of the original function.

As the domain of the original function is restricted to x ≤ 0, then the range of the inverse function is restricted to y ≤ 0.

Therefore, the inverse function is the negative square root:

\(f^{-1}(x)=-\sqrt{\dfrac{x+9}{3}}\)

The  domain of the inverse function is the range of the original function.

As the range of the original function is restricted to y ≥ -9, then the domain of the inverse function is restricted to x ≥ -9.

\(\boxed{f^{-1}(x)=-\sqrt{\dfrac{x+9}{3}}\qquad x \geq -9}\)

So the correct statement is:

When subtracting a positive rational number from a negative rational number, the difference will be negative.

This is because subtracting a positive number is equivalent to adding its additive inverse, and the additive inverse of a positive number is negative.

In rational arithmetic, a negative rational number is represented as a fraction with a negative numerator and a positive denominator. Similarly, a positive rational number has a positive numerator and a positive denominator. When subtracting a positive rational number from a negative rational number, we are essentially combining these two numbers.

The subtraction process involves finding a common denominator for the two rational numbers and then subtracting their numerators while keeping the denominator the same. Since the negative rational number has a negative numerator, subtracting a positive rational number from it will result in a negative difference.

For example, if we subtract 2/3 from -5/4, the common denominator is 12. The calculation would be (-5/4) - (2/3) = -15/12 - 8/12 = -23/12, which is a negative rational number.

Therefore, when subtracting a positive rational number from a negative rational number, the difference will be a negative rational number.

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Yes, it makes sense to do a 60x60 square and count each 3x3 square on it. By doing so, you will be able to count the total number of 3x3 squares present in the 60x60 square.

To calculate the total number of 3x3 squares present in the 60x60 square, you can use the formula:

Total number of 3x3 squares = (60-2) x (60-2) = 58 x 58 = 3364

Here, we are subtracting 2 from both sides because each 3x3 square will have a 1x1 square on each side, which is why we are subtracting 2 from the total length and width of the square.

Hence, it is a valid and efficient method to count the total number of 3x3 squares present in a 60x60 square by counting each 3x3 square present in it.

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Answer:the answer is 22/9 or in mixed form would be 2 4/9 but in decimal it’s 2.4 but the 4 is repeated