Alex came home after school one day and found that his mother had left a plate of cookies. Alex ate 1/4 of the cookies. When his sister Bernice came home, she ate 1/3 of the remaining cookies, and when Carla came home, she ate 1/2 of the cookies on the plate. When their mother came home, there were 5 cookies on the plate. How many did each child eat?

Answer:

Ax + By = C is standard form.

Step-by-step explanation:

It is standard form because slope intercept is y = mx + b and point slope is y-y₁=m(x-x₁)

Hope this helps

Answer:

Standard form.

Step-by-step explanation:

y=mx + b is the slope-intercept form.

Answer:

[tex]x=-\frac{21}{8}[/tex]

Step-by-step explanation:

[tex]-4(2x+4)=5 \\ \\ 2x+4=-\frac{5}{4} \\ \\ 2x=-\frac{21}{4} \\ \\ x=-\frac{21}{8}[/tex]

The system of equation is 45x+75y=1455.

The number of small boxes is 14 and large boxes is 11.

In the given question,

The paper will be shipped in small boxes and large boxes.

Each small box of paper weights 45 pounds.

Each large box of paper weights 75 pounds.

There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds.

We have to write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped.

We also have to define the variables that we use to write the system.

Let x be the number of small boxes.

Let y be the number of large boxes.

There were 3 more small boxes shipped than large boxes.

So x = y+3

Weight of x number of small boxes = 45x

Weight of y number of small boxes = 75y

Total weight of boxes = 1455

So; 45x+75y=1455

Now putting the value of x to this system of equation

45(y+3)+75y=1455

45y+135+75y=1455

120y+135=1455

Subtract 135 on both side, we get

120y=1320

Divide by 120 on both side, we get;

y=11

Now putting the value of y in x=y+3

x = 14

Hence, the number of small boxes is 14 and large boxes is 11.

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All the possible lengths for the third side lie between 13 to 35 feet.

What is a triangle Inequality Theorem?

In Euclidean geometry, the theorem is that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

The Triangle Inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

So, a difference of two sides <x< sum of two sides, will give you the possible length of a triangle.

Therefore, 24 − 11 < x < 24 + 11

13 < x < 35 is the possible length of the third side of a triangle.

13 < x < 35 satisfies the triangle inequality theorem.

Hence, all the possible lengths for the third side lie between 13 to 35 feet.

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Solve x(4.4)(1.4) given that x = 5

Plug x into equation

5(4.4)(1.4)

Distribute 5 into 4.4

22(1.4)

Distribute 22 into 1.4

30.8

Hope this helps :)

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- Jeron

The slope of the ramp is the ratio of the y and x coordinates thus it will be 24 feet.

A slope is a tangent or angle at a point or a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

The situation is making a right-angle triangle as shown below.

The slope of the wheelchair = 2 feet / x

2/x = 1/12

x = 2 x 12 = 24 feet

Hence "The ramp will be 24 feet long since the slope is determined by the ratio of the y and x variables".

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Answer:

y=x-1

Is the line equation.

Step-by-step explanation:

As we know that general equation of line is given by

y=mx + c

M is the slope and C is is Y intercept

Know m = 1 and point (x,y) as (5,4)

So plug in the values and solve for c

4=1*(5)+c

c=-1

So, equation of the line is

y=x-1

Answer:

Step-by-step explanation:

I'm sorry, but I'm not sure what you're asking. It's not clear to me what you mean by "point (3'6)" or "(3-5)." Could you please provide more information or clarify your question

The linear regression equation for the data is given as follows:

y = 0.55x + 0.3.

The prediction of Adam's shoe size when he is 14-years-old is given by the following option:

A. 8.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

From the table, the points are given as follows:

(6,3), (8, 4.5), (10,5), (12, 7.5).

Inserting these points into a calculator, the regression equation predicting the shoe size at an age of x is given as follows:

y = 0.55x + 0.3.

Then the estimate for the shoe size at an age of 14 is found when x = 14, hence:

y = 0.55(14) + 0.3 = 8.

Meaning that option A is correct.

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Answer:

81

Step-by-step explanation:

81 * 1 = 81

If the 81x1 is = 81 * 1 then it should be 81.

If its not I will redo my answer.

Answer:

81 x 1 is 81

81

x 1

81

There are no local extrema since there isn't any x value that causes the first derivative to be equal to 0.

z = 5x + 3 y

Discover the function's first derivative.

By applying the Sum Rule, the derivative of 5 x + 3 y with respect to x is d d x [ 5 x ] + d /d x [ 3 y ].

d/d x [ 5 x] + d /d x [ 3 y]

Analyze d /d x [ 5 x ].

Tap to take other actions...

5 + d /d x [ 3 y]

Because 5 is independent of x, its derivative is 5 d d x [ x ] since 5 is constant with respect to x.

5 d/ d x [ x ] + d /d x [ 3 y]

The Power Rule, which asserts that d d x [ x n ] is n x n 1 where n = 1. 5 1 + d d x [ 3 y ] is a method of differentiation, says that you should differentiate.

Subtract 1 from 5 and multiply the result by 5 + d /d x [ 3 y ]

The Constant Rule can be used to differentiate.

Because 3 y is constant in relation to x, its derivative in relation to x is 0 (5 + 0).

Subtract 5 from 0 to get 5.

Since 5 is constant in relation to x, its derivative in relation to x is 0 (f " (x ) = 0).

By setting the derivative to 0, you can solve the problem and discover the function's local maximum and lowest values.

5 = 0

There are no local extrema since there isn't any x value that causes the first derivative to be equal to 0.

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The measure of the length EF of the triangle is; 21

We are given the the triangle BCD and we are told that;

E is the midpoint of BD.

F is the midpoint of CD

Now, since we have those midpoints, it means that by the concept of similar triangles, that;

DF/DC = EF/BC

Since F is the midpoint of DC, then it means that;

2DF = DC

We are given;

EF = 43 - 4x, and BC = 32 - 2x

Thus, we now have;

DF/(2DF) = (43 - 4x)/(32 - 2x)

1/2 = (43 - 4x)/(32 - 2x)

Cross multiply to get;

32 - 2x = 43 - 4x

4x - 2x = 43 - 32

2x = 11

x = 11/2

x = 5.5

Thus;

EF = 43 - 4(5.5)

EF = 43 - 22

EF = 21

Thus, we conclude that the side length EF is 21.

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Answer: 42

Step-by-step explanation: ik additive inverse

The product of the polynomials (4 + 2x³)(4 − 2x³) is 16 - 4x⁶

From the question, we have the following parameters that can be used in our computation:

Polynomial products: (4 + 2x3 )(4 − 2x3 )

Rewrite the above product properly

So, we have the following representation

Polynomial products = (4 + 2x³)(4 − 2x³)

Using the difference of two squares identity

We have the following representation

Polynomial products = (4)² - (2x³)²

Evaluate the exponents

Polynomial products = 16 - 4x⁶

Hence, the product is 16 - 4x⁶

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The new coordinates are X'(8, 7), Y'(5, -2), Z'(7, 0).

The coordinates of the triangle are given as

X(-7, 8), Y(2, 5), Z(0,7).

The rotation is given as r(90,0) XYZ

This means that

We have (x, y) ⇒ (y, -x)

Substitute X(-7, 8), Y(2, 5), Z(0,7) in (x, y) ⇒ (y, -x)

So, we have

X'(8, 7), Y'(5, -2), Z'(7, 0).

Hence, the coordinates of the image are X'(8, 7), Y'(5, -2), Z'(7, 0).

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There are 3,125 different places to sit if they don't mind sharing s desk sometimes and there are 120 different places to sit, if they all sit on separate tables.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that there are five different tables in the class and five students

Each table can be occupied by only one student

There are 200 days of studying years.

As a small prank on their teacher students would like to sit in a new way every day, so there are no two days during their studying year such that all students are occupying the same tables.

5×4×3×2×1 = 120

There are 120 different places to sit, if they all sit on separate tables.

5×5×5×5×5 = 3,125

There are 3,125 different places to sit if they don't mind sharing s desk sometimes.

Hence, there are 120 different places to sit, if they all sit on separate tables and there are 3,125 different places to sit if they don't mind sharing s desk sometimes.

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Using the AAS rule.

ST ≅ UT (given)

∠SRT≅∠UVT (given)

∠RTS ≅ ∠UVT (opposite angles)

∠RST ≅ ∠VUT (AAS rule)

Proved.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

AAS rule:

When two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

From the figure we have,

ST ≅ UT (given)

∠SRT≅∠UVT (given)

∠RTS ≅ ∠UVT (opposite angles)

∠RST ≅ ∠VUT (AAS rule)

Thus,

∠RST is congurent to ∠VUT using the AAS rule.

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Answer:

17

Step-by-step explanation:

You need to use the formula for Arithmetic Sequences.

[tex]a_{n}=a_{1}+(n-1)d[/tex]

You need to plug in the value for [tex]a_{1}[/tex] which is just the first value in your sequence. As well as [tex]n[/tex] which is the term your looking for, in this case it's 48. Lastly [tex]d[/tex] which is the amount that the pattern is increasing or decreasing by. If the sequence is increasing then the [tex]d[/tex] is positive but if the sequence is decreasing then the [tex]d\\[/tex] is negative.

The quadratic equation (x + 1)² / 46.667 - (y - 5)² / 56 = 1 represents the hyperbola in standard form.

In this question we find the equation of a hyperbola in general form, that is, a quadratic equation of the form A · x² + B · y² + C · x + D · y + E = 0, and we need to obtain the standard form of the hyperbola:

(x - h)² / a² - (y - k)² / b² = 1

Where:

We can switch from general form into standard form by completing the square, an application of algebra properties:

6 · x² - 5 · y² + 12 · x + 50 · y - 149 = 0

(6 · x² + 12 ·  x) - (5 · y² - 50 · y) = 149

6 · (x² + 2 · x) - 5 · (y² - 10 · y) = 149

6 · (x² + 2 · x + 1) - 5 · (y² - 10 · y + 25) = 149 + 6 + 125

6 · (x + 1)² - 5 · (y - 5)² = 280

(x + 1)² / 46.667 - (y - 5)² / 56 = 1

The equation of the hyperbola in standard form is (x + 1)² / 46.667 - (y - 5)² / 56 = 1.

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Domain - the set of possible x-coordinates of a function.

Range - the set of possible y-coordinates of a function.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is a function as it passes the vertical line test.

The parameters of the absolute value function g(x) = -|2x| + 5 are given as follows:

The standard definition of the absolute value function is given as follows:

f(x) = a|bx + c| + d.

The meaning of each parameter is given as follows:

In this problem, the function is defined as follows:

g(x) = −|2x| + 5.

Compared with the standard absolute value function, the values of these parameters are given as follows:

a = -1, b = 2, c = 0, d = 5.

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Answer:

to solve a system of linear equations by elimination, we need to eliminate one of the variables, for example, we could add the two equations together to eliminate the variable y. However, we need to make sure that the coefficients of the two equations are the same before we can add them together. We can do this by multiplying the first equation by -1.5 and the second equation by 1.5. This gives us the following system of equations:

-2.25x - 13.5y = -31.5

2.25x - 4.5y = 13.5

We can now add these two equations together to eliminate the variable y, which gives us the following equation:

0 = -18

This equation is not possible, so the system of equations does not have a solution.

Answer:

Math  can help you get your answer it has a linear equation by option

Step-by-step explanation:

If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.

Proportion refers to the two ratios equated to each other.

Proportion shows how much quantity or value is contained in another.

We depict proportions using fractional values, such as fractions, decimals, and percentages.

The number of coconuts produced by Group 1 trees = 150

The percentage by which Group 1 trees produce more than Group 2 = 25%

Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)

Let Group 2's production = 100% = 150/125 x 100

= 120 coconuts

Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.

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Answer:

D) 4, H) 14

Step-by-step explanation:

D) both angles form a linear pair so 101-5x + 2x+70 = 180

Simplify

171-3x = 180

-3x = 9

x = -3

H) 11x-23 = 41 + 90 because they are opposite angles

Simplify

11x = 154

x = 14

when me I would say the 1st one but who knows lol

By ASA, the two triangles are congruent.  They share 2 angles and the line in between them.

To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:

x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)

x^2 = 100 + 36 - 120

x^2 = 16

x = sqrt(16) = 4

Therefore, the length of the side x is 4.

To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:

a/sin(A) = b/sin(B) = c/sin(C)

In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:

10/sin(0) = 12/sin(C)

sin(C) = 0

Therefore, the measure of the angle C is 0 degrees.

this is original answer

To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:

x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)

x^2 = 100 + 36 - 120

x^2 = 16

x = sqrt(16) = 4

Therefore, the length of the side x is 4.

To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:

a/sin(A) = b/sin(B) = c/sin(C)

In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:

10/sin(0) = 12/sin(C)

sin(C) = 0

Therefore, the measure of the angle C is 0 degrees.

The graph of the function C = 49 + 20m is a discrete function and is represented by vertical lines for whole numbered values of 'm'.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, That no. of months is a whole month and hence it is discrete as it can not take decimal values.

The graph of the equation C = 49 + 20m would have vertical lines at each whole value of 'm'.

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