URGENT
Translate into an equation. (Use x to represent the smaller number. Translate the second sentence to write your equation.)

The sum of two numbers is fourteen. The total of three times the smaller and twice the larger is thirty-one.

The commission amount the salesperson earn is $29.7.

The percentage formula is dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Selling price = $495

Commission = 6%

Now,

The amount of commission.

= 6% of 495

= 6/100 x 495

= 29.7

Thus,

The commission the salesperson earn is $29.7.

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The discriminant of a quadratic equation in standard form, [tex]ax^2 + bx + c = 0[/tex] , is given by the expression: [tex]b^2 - 4ac[/tex]

The expression gives the discriminant: [tex]b^2 - 4ac[/tex]

This expression is used to determine the nature of the roots of the quadratic equation. Specifically, if the discriminant is positive, then the equation has two real and distinct roots. If the discriminant is zero, then the equation has one real root with a multiplicity of 2. If the discriminant is negative, then the equation has two complex conjugate roots.

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is a variable and a, b, and c are constants. The coefficient "a" cannot be zero, since otherwise, the equation would become a linear equation.

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A statement which best describes the reflection include the following: C. a reflection over the line x = 3.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

Based on the graph of triangle ABC and triangle ΔA’B’C’, we can logically deduce the following coordinates after a reflection over the line x = 3:

A = (-2, 2)   → A' = (8,2)

B = (0, 4)    → B' = (6, 4)

C = (2,2)     → C' = (4, 2)

Therefore, the two triangles are identical (similar) because they are reflections of each other. Also, the distance between the point C and point C' is 2 units, therefore, with a line that is parallel to the y-axis and lies at point x = 3, as shown in the image attached below.

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Complete Question:

ΔA’B’C’ is a reflection of ΔABC. Which best describes the reflection?

A coordinate plane showing triangles A B C and A prime B prime C prime. The coordinates of the first figure are A negative 2 comma 2, B zero comma 4, and C 2 comma 2. The coordinates of the second figure are A prime 8 comma 2, B prime 6 comma 4, and C prime 4 comma 2.

a.)A reflection over the line x = 2

b.)A reflection over the line y = 3

c.)A reflection over the line x = 3

d.)A reflection over the y-axis

Answer:

The correct answer is:

You can map ABC to A'B'C' by translating it 6 units left and reflecting it across the x-axis, which is a series of rigid motions.

Explanation:

In ABC, the coordinates are:

A(1, -3)

B(5, 3)

C(4, -1).

In A'B'C', the coordinates are:

A'(-5, 3)

B'(-1, -3)

C'(-2, 1)

Each point is mapped to its image:

A(1, -3)→A'(-5, 3)

B(5, 3)→B'(-1, -3)

C(4, -1)→C'(-2, 1

Comparing the x-coordinates in the pre-image and image, we notice that the image has an x-coordinate that is 6 less than that of the pre-image:

1-6 = -5

5-6 = -1

4-6 = -2

This means that the figure must be translated 6 units left; that is the only way to have this change on the pre-image to form the image.

Comparing the y-coordinates of the pre-image with those of the image, we notice that they are negated:

-(-3) = 3

-(3) = -3

-(-1) = 1

This means the pre-image was reflected across the x-axis; this is the only way to negate the y-coordinate and not change the x-coordinate.

These are rigid motions because they do not change the shape or size, they simply move it and change its orientation.

Step-by-step explanation:

Hope this will help u

Answer:

To solve the system of equations graphically, you can plot the two lines on a coordinate plane and find the point where they intersect, which represents the solution to the system.

First, let's start by rewriting the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

For the first equation:

3x + y = 15

y = -3x + 15

For the second equation:

3x - 4y = 0

y = (3/4)x

Next, we can plot these two lines on a coordinate plane by using any two points on each line and connecting them with a straight line.

Once the lines are plotted, we can find the point where they intersect, which represents the solution to the system. In this case, the solution is (2, 9), meaning that at x = 2 and y = 9, both equations are satisfied.

So, the solution to the system of equations is (2, 9), which means that the two lines intersect at the point (2, 9).

If the equation describes the situation is 2x + 40 = 62, then the variable x represents the option (D) number of push ups Noah does

The given statements are

Diego does twice as many push ups as Noah

Therefore, if Noah does x push ups Diego does 2x push ups

Number of jumping jacks that Diego does = 40

Total number of exercises that he does = 62

The linear equation that represents the situation is

2x + 40 = 62

From the given equation

2x = 62 - 40

2x = 22

x = 22/2

x = 11

Here we can see that x is the number of push ups Noah does and 2x is the number of push ups Diego does

Therefore, the variable x is the number of push ups Diego does

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Answer:

(-x+2)(2x+1) — first option

Step-by-step explanation:

The rectangles represent an x, red means negative and yellow is positive.

The squares represent a unit (the number 1).

The diagram attached below demonstrates how this works.

Basically the top row of this tile equation is (-x + 2)

And the column is (2x+1).

Expanding this makes -2x²+3x+2

Answer:

Shape of the graph is exponentially decreasing

The horizontal asymptote is y = 0

The y intercept is at x = 0 and is at y = 3/2

Graph attached

Step-by-step explanation:

Not sure what exactly the question is asking for.

Here is what I figured out

Shape of the graph is exponentially decreasing

The horizontal asymptote is y = 0

The y intercept is at x = 0 and is at y = 3/2

We can also rewrite this equation as:

[tex]g(x) = \dfrac{3}{2} \cdot \dfrac{2}{3} \cdot \left(\dfrac{2}{3}\right)^{x-1}\\\\\\= \left(\dfrac{2}{3}\right)^{x-1}[/tex]

Answer: Given the equation V = Sp.v, to solve for v, we need to divide both sides of the equation by Sp.

V / Sp = v

So v = V / Sp

Here, V is the volume of the item being sold, Sp is the price per unit, and v is the number of units being sold. By dividing V by Sp, we can find the number of units being sold (v) at a given price per unit.

Step-by-step explanation:

Lindsey made 35 free throws, 143 two-point field goals, and 107 three-point field goals during the 2006 regular season.

Two or more expressions with an Equal sign is called as Equation.

Let's denote the number of two-point field goals Lindsey made by x, and the number of three-point field goals she made by y.

x + y + (x+y-71)/2 + (x+y-71)/2 - 21 = 862 (total points equation)

x = 2y - 71 (two-point field goals equation)

Simplifying the first equation and substituting the second equation, we get:

3x + 3y = 1964

Substituting x = 2y - 71 into this equation, we get:

3(2y-71) + 3y = 1964

Solving for y, we get:

y = 107

Substituting this value into the equation x = 2y - 71, we get:

x = 143

Now, (x + y - 71)/2 - 21 = (143 + 107 - 71)/2 - 21 = 35

Therefore, Lindsey made 35 free throws, 143 two-point field goals, and 107 three-point field goals during the 2006 regular season.

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The t-test yields the probability (p value) that the null hypothesis is option (B) incorrect

The p-value in a t-test represents the probability of obtaining the observed test statistic (or one more extreme) assuming that the null hypothesis is true. The null hypothesis is typically a statement of "no effect" or "no difference" between two groups being compared in the test.

Therefore, a low p-value (generally less than 0.05) indicates that the observed data is unlikely to have occurred by chance under the null hypothesis and suggests that the null hypothesis is likely to be false.

In other words, a low p-value provides evidence against the null hypothesis and in favor of the alternative hypothesis (which typically represents the hypothesis that the researchers are interested in testing).

Thus, the p-value does not directly tell us whether the null hypothesis is correct or incorrect, but rather whether the evidence supports rejecting it or not.

Therefore, the correct option is (B) incorrect

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Answer: Let's call the length of the main supporting arm AP = x.

We can use the Pythagorean theorem to find the length of the cable dropping from point A to the ground:

c^2 = x^2 + (46 - 96 + 215)^2

c^2 = x^2 + (175 - 50)^2

c^2 = x^2 + 125^2

c^2 = x^2 + 15625

Since the angle between the main supporting arm and the horizontal is 55°, we can use the trigonometric relationship between the length of the opposite side (the cable) and the length of the adjacent side (the main supporting arm) to find x:

tan 55° = c / x

x / c = tan 55°

x / 215 = tan 55°

x = 215 * tan 55°

The value of x can be calculated using a scientific calculator or by using a table of tangent values. To the nearest centimetre, x = 204 cm.

Step-by-step explanation:

Answer:

Area = 91 square inches

Step-by-step explanation:

Let

L = length of the rectangle in inches

W = width of rectangle in inches

We are given:
The length of a rectangle is one inch less than twice the width

In math terms this is equivalent to:
L = 2W - 1

he perimeter of the rectangle is 40 in.
The perimeter of the rectangle = 2(L+ W)

So in math terms;
2(L + W) = 40

L + W = 40/2

L + W = 20

Since L = 2W - 1 we can substitute for L in terms of W in the above equation:
L + W = 2W - 1 + W = 3W - 1

Equating it to 20 gives
3W - 1 = 20

Add 1 both sides:
3W = 21

W = 7

Which gives

L = 2W - 1 = 2(7) - 1 = 14 - 1 = 13

So L = 13

The area of the rectangle = L x W

= 13 x 7

= 91 square inches

Step-by-step explanation:

please review the attachment

Only one decimal place in the product of 8x0. 5 because the final zeros in the product do not change the value of the number.

One decimal place to the left of the decimal point is the ones place. One decimal place to the right of the decimal place is the tenths place.

This is a result of the rules of significant figures. These are the digits of the numbers that matter. For operations involving multiplication, the product should have the same significant numbers with the least significant numbers of the given data. In this case, that would be 0.5. Since 0.5 has one significant figure, then the product should be reported with one significant number. That should be 4.0.

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Answer:

  8√2 feet

Step-by-step explanation:

You want the length of the diagonal of a square that is 8 ft on a side.

The diagonal of a square is the hypotenuse of the isosceles right triangle with leg lengths equal to the sides of the square. The ratios of side lengths in such a triangle is ...

  1 : 1 : √2

Then the lengths of the sides of that triangle are ...

  8 ft : 8 ft : 8√2 ft . . . . . multiply ratio values by 8 ft

The diagonal length is 8√2 feet.

__

Additional comment

If you use the Pythagorean theorem to find the diagonal length, you will determine it is ...

  d = √(8² +8²) = 8√(1+1) = 8√2 . . . . feet

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Answer:

False.

Step-by-step explanation:

Longitude and latitude are geographical coordinates used to determine the location of a place on the earth's surface. They are not easily calculated by observing the direction that fish are swimming. Latitude is determined by observing the position of the sun relative to the earth's equator and longitude is determined by observing the position of the sun relative to the Prime Meridian. To accurately calculate latitude and longitude, one would need to use specialized instruments, such as a sextant, or rely on GPS technology. Observing the direction that fish are swimming would not provide enough information to accurately determine latitude and longitude.

False

the longitude and latitude can be easily calculated and determined with using a map not by observing the direction that the fish are swimming.

Answer:

just use the properties of the figure for rxample in number 3 they are equal as the oppositevangle are equal

The measures regarding the angles of the triangle are given as follows:

The angle measures are defined as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the value of x is obtained as follows:

5x - 14 + x - 5 + 2x - 9 = 180

8x = 208

x = 208/8

x = 26.

Then the measures are given as follows:

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No. The statement given by Yuki that 43 is a 2 digit odd number that is composite is not correct.

A composite number is a positive integer greater than 1 that has more than two positive divisors. In other words, a composite number is a number that can be divided by more than just 1 and itself. For example, 4 is a composite number because it can be divided by 1, 2, and 4.

On the other hand, a prime number is a positive integer greater than 1 that has exactly two positive divisors, 1 and itself. For example, 5 is a prime number because it can be divided only by 1 and 5.

Now, let's consider the number 43. 43 is a two-digit odd number, which means it has two digits and is not divisible by 2. However, 43 is a prime number, which means it has exactly two positive divisors, 1 and 43. Therefore, 43 is not a composite number.

To further verify this, we can check the divisors of 43. The divisors of 43 are 1 and 43, because 43 is not divisible by any other positive integer. Therefore, we can conclude that 43 is a prime number and not a composite number.

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The value of 5% of 260 is 13 as it is 5 times of 1% of 260 and the value of 1% of 260 is 2.6.

Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

so, according to the question

Let 1% of 2600 = X

1/100 * 260 = X

X = 2.6

5% is 5 times of 1% so we can just multiply the value we got after 1% of 260

i.e., 2.6

so 5% of 260 is 5 * 2.6

            = 13.0

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Understand the strengths and weaknesses of the tools, eliminate the outliers, critically analyze the correlations, and look at the context are all methods that help to consider any limitations of the data.

When preparing for a question-and-answer session after a presentation, it is important to consider any limitations of the data used. To do this, it is important to understand the strengths and weaknesses of the tools used to collect and analyze the data. Eliminating outliers from the data can help to ensure accuracy, as outliers can skew the results. It is also important to critically analyze any correlations that may be present in the data, as these could be indicative of a limitation in the data. Additionally, looking at the wider context of the data can help to identify any potential limitations, as certain factors may not have been taken into account when collecting the data. All of these methods can help to ensure accuracy and validity of the data used in the presentation.

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The Statement which is true is (c) the smaller the standard deviation, the more concentrated the data will be.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.

The smallest possible value for the standard deviation is 0, and that happens only in contrived situations where every single number in the data set is exactly the same

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Answer:

y = 2x + 10

Step-by-step explanation:

y = 2x + 10  

y is the total number of loaves of bread.

x is the number of days.

If the baker baked for ten days, he would have 30 loaves of bread

y = 2x + 10

y = 2(10) + 10

y = 20 + 10

y = 30

If he baked for 50 days, he would have baked 110 loaves

y = 2x + 10

y = 2(50) + 10

y = 100 + 10

y = 110

And so on and so on...

Answer:

Step-by-step explanation:

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions. Option c is correct.

An equation will have infinite solutions if both sides of the equal sign are the exact same thing, for instance . (You can test this with any value of x and find that they all work!)

So to find the equations that have infinite solutions, we need to see which have the same exact sides.

(Choice A)

-6x+35 = -6x-35 have the different thing on each side: , so this has no solution.

(Choice B)

6x+35  = -6x-35 does not have the same thing on each side, so it doesn’t have infinite solutions (it has 1).

(Choice C)

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

(Choice D)

6x+35=-6x+35 And finally,  has the different thing on each side: , so it has one solution.

Hence , -6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

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The exponential function for the given table will be y=0.01(2)ˣ where x=positive integer.

What exactly are exponential functions?

An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.

Growth that is exponential

The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.

Now,

as given in the table initial value = 0.01

and it is increasing into multiples of 2ˣ where x=positive integer

Then for the value of y for any value of x will be

y=0.01(2)ˣ where x=positive integer

Hence,

           The exponential function for the given table will be y=0.01(2)ˣ.

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The most reasonable answer for left pocket money to Jesse after spending it on Monday, Tuesday and Wednesday is 1/8.

Let's assume that the amount of pocket money Jesse has is "x".

On Monday, he spends 1/2 of his pocket money, so he has 1/2 of his pocket money left:

Amount left after Monday = x - (1/2)x = (1/2)x

On Tuesday, he spends 2/3 of what is left, which is 2/3 of (1/2)x:

Amount left after Tuesday = (1/2)x - (2/3)(1/2)x = (1/6)x

On Wednesday, he spends 1/4 of what remains, which is 1/4 of (1/6)x:

Amount left after Wednesday = (1/6)x - (1/4)(1/6)x = (1/8)x

Therefore, the fraction of the pocket money he has left is:

Amount left / Original amount = (1/8)x / x = 1/8

So, the most reasonable answer is 1/8.

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____The given question is incorrect, the correct question is given below:

Jesse spends 1/2 of his pocket money on Monday. On Tuesday, he spends 2/3 of what is left. On Wednesday, he spends 1/4 of what remains. What fraction of the pocket money does he have left? Choose the most reasonable answer.

There are a few general reasons why Marcus's results might differ from Zara and Arun's:

In terms of Solubility: Different solutes have different solubilities, which means they will dissolve to different extents in water. It's possible that the solutes Marcus is using have lower solubilities than the solutes used by Zara and Arun, which could lead to differences in the amount of solute that dissolves.

   Amount of solute added: Even if all three individuals add the same amount of solute to their test tubes, the amount of solute that actually dissolves may differ due to differences in solubility. If Marcus is using solutes with lower solubilities, he may be adding the same amount of solute as Zara and Arun, but a smaller proportion of it is dissolving.

  Spatula size: Marcus has the same number of spatulas for all three solutes, but it's possible that the size of his spatulas differs from those used by Zara and Arun. If Marcus's spatulas are smaller, he may be adding less solute to his test tubes, which could explain the differences in his results.

 Lastly, in terms of Experimental error: Finally, it's possible that there is some experimental error that is affecting Marcus's results. For example, he may not be measuring the amount of solute accurately, or he may be adding it to the test tube in a way that doesn't allow it to dissolve as well.

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Answer:

B

Step-by-step explanation:

3+3 = 6 which is not more than 6 hours

3 x $25 = $75

3 x $15 = $45

$75 + $45 = $120