translate each phrase into a mathematical expression
q1the quotient of four less than y and twice x


q2the product of a and the sum of a thirteen

both 2 questions answer plz

Answer:

118.13

Step-by-step explanation:

6 3/4= 6.75

3 1/2 = 3.5

Answer:

Step-by-step explanation:

Given the inequality

3x —7y <—21

Make y subject of formulae to know the slope and intercept on y axis

—7y < —3x — 21

Divide through by -7, note the inequalities sign will change since we are dividing with a negative

Then,

y > 3x/7 + 3

Then, the intercept is 3 and the slope is 3/7 when compared to equation of a line y = mx + c

We know that

y is greater than 3x/7 + 3, so the upper part should be shaded since y is greater than 3x/7 + 3

Then, option B and C are wrong since the below is shaded

Let find the intercept on the x axis to know the answer between A and B

I.e. when y = 0

3x —7y <—21

3x < —21

x < -7, then, line should pass through the negative of x and not positive x

So, the first option (A) is correct

The expression 15x - 6 is already in its simplest form and cannot be simplified further without additional information or context.

The student is asking for an expression that is equal to 15x - 6. In mathematics, we often look for ways to simplify or manipulate expressions to find equivalents. However, the given expression 15x - 6 is already in its simplest form and cannot be simplified further without additional context or constraints. Sometimes in algebra, we expand, factor, or use algebraic rules to rewrite expressions, but without more information, 15x - 6 stands as it is. It's important to ensure that we understand the context in which an expression is used, as this could influence how it may be manipulated or simplified.

This problem is a system of linear equations. The first equation represents the total number of files (pictures and songs) downloaded: p + s = 16. The second equation represents the total size of the downloads in terms of pictures and songs: 650p + 2200s = 18150.

This problem is an example of a system of linear equations. In this scenario, we have two types of files - pictures, represented by 'p', and songs, represented by 's'. The cost in megabytes for each is also provided. We can take these details and construct two equations:

Equation 1: The total numbers of pictures and songs downloaded: p + s = 16.
Equation 2: The total size of the downloads: 650p + 2200s = 18150.

You can solve these equations by substitution or elimination method to find the actual numbers of pictures and songs that were downloaded.

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Answer:[tex]4.5\times10^6[/tex] light bulbs

Step-by-step explanation:

Given : The number of bulbs produced by company in 1 week=[tex]4.56\times10^3[/tex] lights

Then the number of  bulbs produced by company in [tex]9.36\times10^2[/tex] weeks is given by :-

[tex]4.56\times10^3\times9.36\times10^2\\\\=4.56\times9.36\times10^{3+2}\\\\=42.6816\times10^5\approx45\times10^5....\text{[To the nearest 5s]}\\\\=4.5\times10^6[/tex]light bulbs

Hence, the number of  bulbs produced by company in [tex]9.36\times10^2[/tex] weeks=[tex]4.5\times10^6[/tex] light bulbs

Answer: 9

Step-by-step explanation:

An outlier is an observation point in any data plot that appears farthest from the other data observations.

In the given data plot, the plot shows the number of cakes sold each day in aunt Alice’s cake shop last month.

Here, we have one observation point that appearing farthest from all the other observation points i.e. point at 9.

Therefore the number of cakes sold is an outlier = 9

The slope of a line parallel to the line with the equation 3x - 4y = 8 is 3/4, which is option C.

To find the slope of a line parallel to the given line, first, we need to write the equation of the given line in slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept. Starting with the equation 3x - 4y = 8, we rearrange it to solve for y:

3x - 4y = 8
-4y = -3x + 8
y = (3/4)x - 2

The slope of the original line is therefore 3/4. Lines that are parallel to each other have the same slope. Therefore, the slope of a line parallel to the given line is also 3/4, which is option C.

Answer:

51/100

Step-by-step explanation:

The question mixes physical and geometric concepts without a clear relationship or sufficient details to calculate the length of KN in the trapezoid KLMN, making it difficult to provide a step-by-step solution.

The question appears to involve various mathematical and physical concepts, most notably relating to trapezoid geometry and principles of force and motion. However, the specific information provided does not directly lead to a clear method for finding the value of KN in a trapezoid given the other conditions mentioned. It mixes principles from physics, particularly force equations, with geometric properties of trapezoids without presenting a typical geometry problem's clear setup or goal.

Normally, to solve for the length of a side in a trapezoid like KN, one would use properties of trapezoids (e.g., parallel sides, angle properties, or potentially the Pythagorean theorem if right angles are involved). However, the information given mixes unrelated physical equations (such as the force equation F = ma and friction models) with geometric figures without presenting a coherent relation between them.

Without additional specific geometric information or a clearer connection between these physical principles and the geometry of trapezoid KLMN, providing a step-by-step solution for finding KN is not feasible. It is advisable to request more specific details or clarification on how these concepts are supposed to interact within the context of the problem.

No, Diego cannot fit 65 smaller cubes into the large box. There will be 5 cubes that cannot be put in.

Volume in math is the amount of three-dimensional space occupied by an object, substance, or closed surface. Volume can be measured by multiplying the length, width, and height of an object or by counting the number of unit cubes it contains.

Given that, Diego has a large box that is 4 feet high, 3 feet wide, and 5 feet long, we need to determine whether he can fit 65 smaller boxes that each have a volume of 1 cubic foot in the large box,

For determining the same, we will find both volume and compare,

Volume of the large box = 4 x 3 x 5 = 60 ft³

Volume of a cube = 1 ft³

Total number of cubes = 1 x 65 = 65 ft³

Since, both the volumes are equal,

Therefore,

He cannot fit 65 smaller cubes into the large box, as he will be left with 5 boxes out of the box.

Hence, Diego can not put 65 boxes in the larger one.

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Answer: D

i think it is D

Step-by-step explanation:

Answer:

Image IV

Step-by-step explanation:

We are given that

Heart 1 is translated 3 units down to heart 2.

We have to find the image which shows this transformation.

The translation rule when a figure is shift 3 units down is given by

[tex](x,y)\rightarrow (x,y-3)[/tex]

The coordinates of a point lie on heart are (-2.5,3)

After translation 3 units, the coordinates of corresponding point which lie on the heart

[tex](-2.5,3)\rightarrow (-2.5,0)[/tex]

Therefore,the heart shift from II quadrant to III quadrant.

Image I is not true because the heart 1 shift to heart 2 in  quadrant III not in IV quadrant.

In image II ,the corresponding point of the point (-2.5,3) is (-2.5,-3).

Image II is not true because the corresponding  point is (-2.5 ,0) not (-2.5,-3).

Image III is not true because heart 2 should be in quadrant III not in quadrant I after translation 3 units down of heart 1.

Image IV is true because the corresponding point of the point (-2,5,3) is (-2.5,0) and heart 2 lies in quadrant III.

First, find the volume. For a square polyhedron, the formula for the volume is the following:

Volume=length×width×height

Hope this helps.

First, find the volume of the pool. For a rectangular prism, the formula for the volume is the following:

Volume=length×width×height

divide the total volume by 5 to find how long it will take for the pool to fill.

Havce a nice day

It will take 15 days to manufacture 28000 bottles.

We have a factory makes 12 bottles every 2 minutes and makes bottles for 8 hours each work day.

We have to determine the number of days it will take to make 28000 bottles.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to question, we have -

Number of bottles manufactured in 2 minutes = 12.

In 8 hours = 8 x 60 = 480 minutes = 2 x 240 minutes.

Number of bottles manufactured in 1 day = 8 x 240 = 1920 bottles.

Number of days needed to make 28000 bottles = 14.58 = 15 days.

Hence, it will take 15 days to manufacture 28000 bottles.

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