What is the result of adding these two equations?
2x + 3y = -5
5x - y = -12

Answer:

-2

Step-by-step explanation:

The original equation

 3x-6y=144

6y= 3x-144

y=1/2x -24

The slope of the line perpendicular =is "m"

(1/2) × m= -1

m= -2



Answer:

A

Step-by-step explanation:

In this question, we are concerned with selecting which of the options best represents the difference of two squares.

Let’s have an exposition below as follows;

Consider two numbers, which are perfect squares and can be expressed as a square of their square roots;

a^2 and b^2

where a and b represents the square roots of the numbers respectively.

Inserting a difference between the two, we have;

a^2 - b^2

Now by applying the difference of two squares, these numbers will become;

a^2 - b^2 = (a + b)(a-b)

So our answer out of the options will be that option that could be expressed as above.

The correct answer to this is option A

Kindly note that;

x^2 -9 can be expressed as x^2 - 3^2 and consequently, this can be written as;

(x-3)(x + 3)

Answer:

Yes please upload the pic

Step-by-step explanation:

:)

A time-series is a graphical representation of a particular variable that varies over time. In the above question, we are given a time series showing the sale of a particular product over the past 12 months. To construct a time-series plot, we first plot the months on the x-axis and sales on the y-axis.Months Sales1 1052 1353 1204 1055 906 1207 1458 1409 10010 8011 10012 110

From the time-series plot, we can see that there is a pattern present in the data. The pattern is not completely regular, but we can observe that the sales of the product have a tendency to increase from the months of May to August and from November to January.

The sales tend to decline during the other months of the year. The pattern that we can observe from the time-series plot is the seasonal pattern.

The seasonal pattern is observed when the series has regular fluctuations that occur at regular intervals, such as days, weeks, months, or quarters.

Here, we can observe that the sales of the product have regular fluctuations that occur at intervals of 4 months.

We can observe that the sales tend to increase during the summer and winter months and decline during the other months.

The seasonal pattern can help in forecasting future sales of the product and can be used by businesses to optimize their production and sales strategies.

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Total distance represented by the simplified expression for which the car was tested equals option c. x² + 2x - 4 .

Total distance drive on flat road = x miles

Total distance drive on downhill =  (x²+ 3) miles

Total distance drive on uphill =  ( x - 7 ) miles

Simplified expression which is equivalent to total distance drive by a car

= Distance drive on ( flat road + downhill + uphill )

= ( x +  x²+ 3 + x - 7 ) miles

= ( x² + 2x - 4 ) miles

Therefore, the simplified expression equivalent to the total distance drive by a tested car is equal to option c.  ( x² + 2x - 4 ) miles.

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The above question is incomplete , the complete question is:

A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road,    (x²+ 3) miles downhill, and (x - 7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested?

a.3x² _ 4

b. 3x² + 10

c. x² + 2x - 4

d. x² + 2x + 10

Answer:

Step-by-step explanation:

Given function:

The vertex is (2, 3)

We know the vertex form:

Substitute coordinates to get:

Compare with given to find out:

Answer:

A

Step-by-step explanation:

a memo of investigation mathematical literacy 2023 grade 12 from mpumalanga province

At a significance level of 0.01, we can confidently state that the student's claim is true.

The hypothesis in this question can be stated as follows:

Null Hypothesis: H0: μ1 = μ2 (There is no difference between the mean of four-year college enrollment and two-year college enrollment.)

Alternative Hypothesis: H1: μ1 > μ2 (Mean enrollment of four-year colleges is greater than the mean enrollment of two-year colleges in the United States.)

The significance level (α) is given as 0.01, which represents the probability of rejecting the null hypothesis when it is actually true.

To calculate the test statistic, we can use the formula:

z = ((X1 - X2) - (μ1 - μ2)) / √((σ1² / n1) + (σ2²  / n2))

Substituting the given values:

z = ((6193 - 4305) - (0)) / √((598²  / 35) + (572²  / 35))

z = 10.33

Since this is a right-tailed test, we need to compare the test statistic with the critical value. At a significance level of 0.01, the critical value is 2.33.

The calculated test statistic (10.33) is greater than the critical value (2.33). Therefore, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the mean enrollment at four-year colleges is higher than at two-year colleges in the United States.

In conclusion, at a significance level of 0.01, we can confidently state that the student's claim is true. The mean enrollment at four-year colleges is higher than at two-year colleges in the United States.

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Therefore, the sign of f'(x) is determined by the sign of x, which means that f(x) is decreasing for x > 0 and increasing for x < 0. Thus, we can conclude that f(x) is a decreasing function in its domain.

The function f(x) = 2 + √(9-x²) is a decreasing function in its domain.

A function is said to be decreasing if as x increases, y decreases. To prove that f(x) is a decreasing function in its domain, we need to show that its derivative is negative.

The derivative of f(x) can be found using the chain rule. Let u = 9 - x², then f(x) = 2 + √u. The derivative of f(x) with respect to x is given by:

f'(x) = (d/dx)(2 + √u)

= (d/dx)(2 + u^(1/2))

= (d/dx)(2 + (9-x²)^(1/2))

= (d/dx)(2 + (9-x²)^(-1/2)(-2x))

= -x/(√(9-x²))

Since x is in the domain of f(x), we know that 9-x² ≥ 0, which means that the denominator of f'(x) is always positive. Therefore, the sign of f'(x) is determined by the sign of x, which means that f(x) is decreasing for x > 0 and increasing for x < 0. Thus, we can conclude that f(x) is a decreasing function in its domain.

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The population of the bird for the next five weeks based on the information is 80.

The information is incomplete. Therefore, an overview will be given. Let's assume that the population of the birds was 100 and the birds reduce by 5 every week.

Therefore, the number of birds by the fifth week will be:

= a + (n - 1)d

where,

a = 100

n = 5

d = -5

= a + (n - 1)d

= 100 + (5 - 1) -5

= 100 - (4 × 5)

= 100 - 20

= 80

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The minimum number of $5-notes she has 32/3

Now, According to the question:

Siti opened her money box to find 50 pieces of $5-notes and $2-notes.

If the total value of all the notes is more than $132.

To find the minimum number of $5-notes she has

Based on the given condition:

= 2 × (50 - x) + 5x = 132

Apply Multiplicative Distributive law:

100 - 2x + 5x = 132

Rearrange the unknown terms on left sides of the equation:
-2x + 5x = 132 - 100

Combine like terms:

3x = 132 - 100

Calculate the sum or difference:

3x = 32

Divide the both sides of the equation by the coefficient of the variable:

x = 32 ÷ 3

Rewrite as fraction :

x = 32/3

Hence,  the minimum number of $5-notes she has 32/3

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Answer:

52?

Step-by-step explanation:

Answer:

The first one and the third one are true and the rest are false

Step-by-step explanation:

Answer:

first and therd are right

Step-by-step explanation:

Answer:

A. similar, AA

Step-by-step explanation:

Angles F and H are given as congruent in the figure.

From the figure, we see that angles EGF and JGH are congruent since they are vertical angles.

We have two angles of one trianfgle congruent to two angles of the other triangle.

The triangles are similar by AA Similarity.

Answer: A. similar, AA

The image of A as a composition of transformations is (r(45°, A) (-120°. 3))(A)​

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

WE are given that AB is rotated 120° clockwise about B.

AB is rotated 120° clockwise about B. Then AB  is rotated 45° counterclockwise about A.

It is rotated 120° clockwise and clockwise is negative and the other is rotated 45° counterclockwise and counterclockwise is positive.

Therefore,

The image of A as a composition of transformations is (r(45°, A) (-120°. 3))(A)​

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We can start by creating a table to organize the information:

                  Likes Chocolate (c) Does Not Like Chocolate (~c) Total

Likes Sprinkles (s) 0.25                                                           0.40

Does Not Like Sprinkles (~s)            0.60

Total 0.70                                               0.30                       1.00        

We are given that 40% of friends like sprinkles, so we can fill in that cell of the table. We are also given that 25% of friends who like chocolate also like sprinkles, so we can fill in the cell for likes chocolate and likes sprinkles as 0.25.

To find the proportion of friends who like sprinkles and chocolate, we need to divide the number of friends who like both by the total number of friends who like sprinkles:

proportion = likes chocolate and sprinkles / likes sprinkles

proportion = 0.25 / 0.40

proportion = 0.625

So, approximately 62.5% of friends who like sprinkles also like chocolate.

Answer:

it should be

Step-by-step explanation:

no.c half - open

An angle bisector is a line that divides an angle into two equal parts

From the figure attached, we will observe that Line RU bisects Angle TRP into two parts (TRU & PRU)

Hence, the corect answer is a. (RU)

Answer:

Option C(66.0)

Step-by-step explanation:

C = 2πr

C=Circumference

π=3.14(pi)

r=radius

C=2x3.14x10.5

3.14x10.5=32.97

32.97x2=65.94

65.94 rounded to nearest tenth is 65.9, so basically 66.0.

The gametes that can be produced by individual bgbg are B, and G, and the gametes that the offspring can produce are BB, BG, BG, BG, BG, BG, BG, and GG.

a. bgbg

The individual bgbg can produce gametes that are either B or G, as they carry one allele of each. Therefore, the gametes that can be produced by this individual are:

B, G

b. bbgg x bbgg

The individuals bbgg x bbgg are heterozygous for two different traits (B and G). In this cross, each parent can contribute either a B or a G allele to the offspring.

There are four possible combinations of gametes for each parent, for a total of 16 possible offspring combinations:

   BB x BB = B offspring: BB, BG, BG, BB

   BB x BG = B offspring: BB, BG, BG, BG

   BB x GG = B offspring: BG, BG, BG, BG

   BG x BG = B offspring: BG, BG, BG, BG

   BG x GG = G offspring: BG, BG, BG, GG

   GG x GG = G offspring: GG, GG, GG, GG

So, the gametes that can be produced by the offspring are:

BB, BG, BG, BG, BG, BG, BG, and GG

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perimeter

= 2 (l+b) inches

= 2(10+5) inches

= 2(15) inches

= 30 inches

Answer:she will have $25 left .

Step-by-step explanation:

0.25(60)  = 15

$40 - $15 = $ 25

Step-by-step explanation:

answer is last one.

if you solve all simultaneously, you'll find the last one has a different x and y value than the other 3

Topic: simultaneous eqn

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a) two representatives be picked in 5850 ways so that one is a mathematics major and the other is a computer science major. b) one representative be picked in 343 ways who is either a mathematics major or a computer science major.

Product Rule: If one event occurs in m ways and a second event occurs in n ways, the number of ways the two events occur in the sequence is m×n ways.

Sum Rule: If an event occurs either in m ways or in n ways (non-overlapping), the number of ways the event can occur is m+n ways.

according to the question,

Mathematics majors =18 and Computer science majors = 325

A. We need to use the product rule because the first event is picking up a Mathematics major and the second event is picking up a computer science major.

= 18 x 325

= 5850

B. Here sum rule is applicable because the event is picking up a mathematics major or a computer science major.

= 18 + 325

= 343

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(complete question)

there are 18 mathematics majors and 325 computer science majors at a college. a) in how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? b) in how many ways can one representative be picked who is either a mathematics major or a computer science major.

Responder:

1/15

Explicación paso a paso:

Dado que :

Número bolas verdes = 3

Número de bolas rojas = 5

Número de bolas azules = 2

Dibujo sin reemplazo; probabilidad de que el primero sea azul, el segundo sea verde

Probabilidad = resultado requerido / Total de resultados posibles

Resultados posibles totales = 3 + 5 + 2 = 10

P (1er azul) = número de azules / 10

P (1er azul) = 2/10 = 1/5

Sin reemplazo :

Total restante = 10 - 1 = 9

P (segundo verde) = número de verdes / 9 = 3/9

Probabilidad del primer azul y del segundo verde:

1/5 * 3/9 = 3/45 = 1/15

The probability that the first is blue and the second is green is 1/15

Probability is the likelihood or chance that an event will occur.

If a box contains 3 green balls, 5 red balls and 2 blue balls, the total number of balls is 10balls

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Answer:

20

Step-by-step explanation:

if you divide 50 from 2.5 you get 20

then take 20x2.5 and you get 50.

The standard deviation of the number of free throws that Billups will make is approximately 0.754.

This problem is an example of a binomial distribution, where there are a fixed number of trials (in this case, 6 free throws) and each trial can have only one of two outcomes (making or missing the free throw).

The probability of making a free throw is p = 0.894, based on Billups' career free-throw percentage. The probability of missing a free throw is therefore q = 1 - p = 0.106.

The mean of the binomial distribution is given by:

μ = np = 6 x 0.894 = 5.364

where n is the number of trials.

The variance of the binomial distribution is given by:

σ^2 = npq = 6 x 0.894 x 0.106 = 0.569

Therefore, the standard deviation of the number of free throws that Billups will make is:

σ = √(npq) = √(0.569) ≈ 0.754

So the standard deviation of the number of free throws that Billups will make is approximately 0.754.

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The statement "the product of two nonzero elements of R must be nonzero" is true for some rings but not true for all rings.

In general, for a ring to satisfy this property, it must be an integral domain. An integral domain is a commutative ring with unity in which the product of any two nonzero elements is nonzero. In other words, there are no zero divisors in an integral domain. However, there exist rings that are not integral domains. For example, consider the ring of integers modulo 6, denoted as Z/6Z. In this ring, the elements 2 and 3 are nonzero, but their product is 2 * 3 = 6 ≡ 0 (mod 6), which is zero in Z/6Z.

Therefore, the statement is false because there are rings where the product of two nonzero elements can be zero.

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Answer:

Z' = (6, 3 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

Z (3, 6 ) → Z' (6, 3 )