During a class trip to an apple orchard, a group of
students picked 2436 apples. They packed them into
6 boxes to take to the local food bank. If each box
held the same number of apples, how many apples
were in each box?
2) 46
3) 460
4) 406
5) 14,616

The equations, y=5x, b = 1/2 a, m=5n are direct variations.

A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately. Similar to the last example, if one quantity declines, the other amount also declines. The link between direct variation and the graph will be linear, resulting in a straight line.

We know that any equation, which can be expressed in the form of y=kx, can be called a direct variation.

y = 5x is in the form of y = kx, where k =5, hence this is a direct variation

y = 2x + 1 is not in the form of y = kx, hence this is not a direct variation

xy = 3 is not in the form of y = kx, hence this is not a direct variation

b = 1/2 a is in the form of y = kx, where k =1/2, hence this is a direct variation

y = 2/x is not in the form of y = kx, hence this is not a direct variation

m = 5n is in the form of y = kx, where k =5, hence this is a direct variation

Thus, y=5x, b = 1/2 a, m=5n are direct variation

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Answer:

Undefined

Step-by-step explanation:

Knowledge Needed

Slope if is the constant change of the y-value when the x-value increases by 1 on a line.

Slope Formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Question

Plug in your points.

[tex]\frac{-19--3}{-8--8}[/tex]

[tex]\frac{-16}{0}[/tex]

Any number divided by 0 is undefined.

The slope is undefined. This means the line is completely vertical.

The function operation h(8) - f(-7) of the functions f(x) = -4x+1, and h(x) = 19-3x is -34.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, solve for the output value of h(8) by replacing x with 8 and simplify.

h(x) = 19 - 3x

h(8) = 19 - 3(8)

h(8) = 19 - 24

h(8) = -5

Next, solve for the output value of f(-7) by replacing x with -7 and simplify.

f(x) = -4x + 1

f( -7 ) = -4( -7 ) + 1

f( -7 ) = 28 + 1

f( -7 ) = 29

Now, replace the function designators with the actual output values.

h(8) - f(-7) =  -5 - ( 29 )

h(8) - f(-7) =  -5 - 29

h(8) - f(-7) =  -34

Therefore, the output of the function operation h(8) - f(-7) is -34.

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Buy the land !all angles will be greater than 30 °

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.

A branch of mathematics called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided shape can be decomposed into a group of triangles, trigonometry can be found throughout all of geometry.

cos x = 500²+800²-900²/-2(800)(900)

x = [tex]cos^{-1}[/tex](+1200000/+1440000)

=336°

Buy the land !all angles will be greater than 30 °

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Answer: It's in the picture

Step-by-step explanation:

Answer:

b.) y=3x+2

Step-by-step explanation: The linear equation is y= mx + b

m is the slope and b is the y-intercept

Answer b is the linear equation!

The dimensions of the rectangle in terms of x  are (x-6) and (x+3).

What in mathematics is a quadratic equation?

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given that:

A = x^(2) - 3x - 18

By solving this equation we can get the values of length and breath of rectangle

A = x^(2) - 6x + 3x - 18

A = x(x-6)+3(x-6)

A = (x-6)(x+3)

Hence the area of rectangle is equal to L * W

Hence, the dimensions of the rectangle are (x-6) and (x+3).

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Answer:

$27

Step-by-step explanation:

We find 50% of $18 and add it to $18.

50% of $18 = 5/100 × $18 = 0.5 × $18 = $9

Today, it is worth $9 more.

$18 + $9 = $27

Answer: 6

Step-by-step explanation:

40x0.15

6 are teens

By evaluating the function in x = -4, we will get:

f(-4) = 12

Here we have the following function:

f(x) = -4 + 4*|x|

So we have an absolute value function.

We want to find f(-4), so we want to evaluate the function in x = -4, to do that, just replace the variable by that number.

We will get:

f(-4) = -4 + 4*|-4|

Remember that the absolute value of a negative number gives the opposite:

|-4| = 4

Then:

f(-4) = -4 + 4*|-4|

f(-4) = -4 + 4*4

f(-4) = -4 + 16 = 12

f(-4) = 12

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Answer:

47.21

Step-by-step explanation:

a=47.4

b=0.19

a – b

47.4 – 0.19

=47.21

The amount of sugar that both companies would charge the same is 20 tons.

The cost when the two companies would charge the same is $9010.

The linear equation that represents the total charge of the companies : cost to rent truck + (ton of sugar x cost per ton)

The linear equation that represents the total charge of the first company : $5500 + ($175 x s)

$5500 + $175s

The linear equation that represents the total charge of the second company : $4995 + ($200.75 x s)

$4995 + $200.75s

When the two companies charge the same, the two linear functions above would be equal.

$4995 + $200.75s  = $5500 + $175s

In order to determine the value of s, take the following steps:

200.75s - 175.50s = $5500 - $4995

25.25s = 505

s = 505 / 27.25

s = 20

In order to determine when the cost of the two companies would be the same, substitute for s in either of the above linear functions.

$5500 + $175.50(20)

$5,500 + 3510 = $9010

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0.05×0.04=0.002 is the product represented by the model

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

Given:

5 column (hundred grid) = 5/100 = 0.05

4 row (hundred grid) = 4/100 = 0.04

We need to find Area equation

Computation:

Area equation = 0.05 x 0.04

0.05 x 0.04 = 0.002

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Answer:

1

Step-by-step explanation:

3(-0.5)+2(7+0.8)

13+1.1

-1.5+2(7+0.8)

13+1.1

-1.5+15.6

14.1

14.1

14.1

divide

1

hope that helps :)

Answer:

Sin(angle) = Opposite /  hypotenuse

Sin(x) = 5/14

X = arcsin(5/14)

x = 20.9

X = 21 degrees.

the answer is da da b!

Step-by-step explanation:

Answer:

g(3) = - 6

Step-by-step explanation:

g(3) = 9 - 5(3)

g(3) = 9 - 15

g(3) = - 6

For the provided points (-7,-8) and (-5,-6) on the line, the slope is 1.

The slope of a line is a measure of its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

Here,

Slope=(y2-y1)/(x2-x1)

=(-6-(-8))/(-5-(-7))

=2/2

=1

The slope of the line for given point (-7,-8) and (-5,-6) will be 1.

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Measure of angle I greater than angle K and J. Therefore, option D is the correct answer.

Given that, in triangle IJK, JK=18, KI=11, and IJ=14.

If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.

Here, JK is the longest side and KI is the shortest side

So, opposite to side JK, angle I is the biggest and opposite to the side KI angle J is the smallest

Here, the measure of IJ is greater than the side KI, then the angle K opposite to side IJ is greater than the angle J

Thus, m∠I>m∠K>m∠J

Measure of angle I greater than angle K and J. Therefore, option D is the correct answer.

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We can infer from the data set provided that more women than men are interested in basketball.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

From table given in question

Number of males that like basketball = 21

Number of females that like basketball = 29

Percentage of males that like basketball =  (21/50)*100 = 42%

Percentage of females that like basketball =  (29/50)*100 = 58%

So, from above data we can conclude that females like basketball more than that of males.

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Step-by-step explanation:

-12 < -3x - 15 <= 36 | add 15 everywhere

3 < -3x <= 51 | divide by 3 everywhere

1 < -x <= 17 | multiply by -1 everywhere

-1 > x >= -17

or

-17 <= x < -1

remember that with every multiplication or division of a negative number the orientation of the inequality signs flip.

the same happens, of course, when we exchange the upper and lower limits from left to right and right to left, so that the smaller number is on the left, and the larger number on the right (yes, -1 is larger than -17).

Answer:

£ 76

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

Multiply 42 by 1/3 which is 14.

Then subtract 42-14 because your subtracting the discount from the original price which gives you 28.

Answer: 180cm^2

Step-by-step explanation:

The equation is  a^2 + b^2 = c^2

a^2 = area of square 3 = 80cm^2

b^2 = area of square 2 = 100cm^2

c^2 = a^2 + b^2 = 80 + 100 = 180cm^2

So answer is 180cm^2

Answer:

x < 5

Step-by-step explanation:

the dot is empty so we don’t consider 5

The coloured arrow continues to the left so we use this symbol : < (minor)

x<5

The inequality for the number line show is x<5.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We can see that the inequality starts from 5 moves towards 2.

As, the starting of number line have open dot which shows we cannot include 5.

So, the inequality will have sign '<'.

Now, the inequality of the number line is

x < 5.

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29$ 16% of 25 is 4, so add it, and theres the answer

Step-by-step explanation:

Pirya needs 1 1/2 cups of raspberries for 3/4 of a cake, so she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.

A fraction is a numerical representation of a portion of a total. It consists of two integers, a numerator and a denominator, separated by a line or slash. The numerator reflects the number of equal portions of the whole that are being considered, while the denominator represents the total number of equal parts in the whole. For instance, the fraction "1/2" denotes one of two identical pieces, or half, of the whole. Mathematicians frequently utilize fractions to represent quantities, ratios, and proportions. They are also used in everyday life to signify amounts, such as one-half of a pizza or one-third of a cups of sugar.

How to solve?

she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.

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Answer:

Step-by-step explanation:

From the ratio gotten, the total cost of the pepper will be $129.90.

How to solve a ratio

Since the students planted 8 tomato plants and 16 pepper plants in a school garden. The ratio will be:

= 8/16 = 1:2

This year, the students planted 15 tomato plants, the number of pepper will be:

= 15 × 2 = 30

Since pepper plants cost $4.33 each, the total cost will be:

= 30 × $4.33

= $129.90

Answer: C. Infinitely many solutions

Step-by-step explanation: If the answer is <0, then there is no solution; if it is >1, then there is more than one solution; if = 0, then there are Infinitely many solutions

-14(z-5) = -14z +70 can be write as

-14z + 70 = -14z + 70

-14z = -14z

 z= 0

Because the answer is 0 so there Infinitely many solutions

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Answer:

C. Infinite many solutions.

Step-by-step explanation:

Simplify the left side of the equation. Note the parenthesis. Distribute -14 to all terms within the parenthesis:

-14(z -  5) = -14z + 70

-14z + 70 = -14z + 70

C. Infinitely many solutions is your answer, as no matter what number you plug in for the variable z, the equation would still be true.

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The equation of the line passing through the given points and having slope -2/7 is obtained as y = -2/7m - 2.

A straight line can be written in the slope-intercept form as, y = mx + c.

In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.

The given point and the slope for line are as (14,-6) and -2/7 respectively.

The general form of slope-intercept equation is as below,

y = mx + c

Substitute the value of x = 14, y = -6 and m = -2/7 to get,

-6 = -2/7 × 14 + c

⇒ c = -6 + 4 = -2

Thus, the equation can be written as follows,

y = mx + c

Substitute m = -2/7 and c = -2 to obtain,

y = -2/7x + (-2)

⇒ y = -2/7m - 2

Hence, the equation of the line is given as y = -2/7m - 2.

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Answer:

D. 6, 8, 10

Step-by-step explanation:

Apply the Pythagorean theorem equation to all set of number, and see which one works.

A.

3² + 11² ≠ 20²

9 + 121 ≠ 400

131 ≠ 400

B.

5² + 9² ≠ 17²

25 + 81 ≠ 289

106 ≠ 289

C.

6² + 7² ≠ 8²

36 + 49 ≠ 64

85 ≠ 64

D.

6² + 8² = 10²

36 + 64 = 100

100 = 100

On solving the provided the question, we got that - f(x) = 7/3[x - (2)] [x - (-1)] (x +3) is the equation which is formed.

An equation can be defined in a variety of ways. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions.

Gives zeroes are -

-3, -1 and 2

and it passes through (0, -14)

Constructing a function from a product of factors containing the zeros, with an unknown coefficient

f(x) = a [x - (2)] [x - (-1)] (x +3)

with a ≠ 0.

f(x) = a(x -2)(x + 1)((x +3)

Use f(0) = -14 to find a.

-14 = a(-2)(1)(3) = -6a

a = 7/3

Now,

f(x) = 7/3[x - (2)] [x - (-1)] (x +3)

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