Lucas wants to write 3 ÷ 2 as a mixed number. He performs the division below. 3 ÷ 2 = 1 R1 Explain how to write the quotient as a mixed number. Drag the words to complete the explanation. Words may be used once or not at all. quotientdivisordividendremainder Use the whole number part of the as the whole number part of the mixed number. Write the in the numerator of the fraction and write the in the denominator of the fraction.

Answer:

117

Step-by-step explanation:

9^2 + 6^2 = 81 + 36

= 117

Answer: 117

Step-by-step explanation: To find the sum of 9² and 6²​, first you’ll have to find the whole number value of both integers (9² and 6²​). Next, in order to do this, multiply 9 x 9 and 6 x 6. (9 x 9 = 81; 6 x 6 = 36). Lastly, add your two sums, being 81 and 36 to give you a final answer or sum of 117.

Answer:

the third one

Step-by-step explanation:

8x + 40 ≥ 0

8x ≥ -40

x ≥ -5

Answer:

4). [tex]y<\frac{1}{2}x-4[/tex] (look at my explanation for how to graph)

5.) [tex]y<\frac{?}{?}x+?[/tex] (look at my explanation for how to get the correct numbers)

6.) [tex]x\geq 2[/tex] (look at my explanation for how to graph)

Step-by-step explanation:

Question 4:

    Solving for y:

First it's better if you solve for y then graph, it's easier that way.

[tex]x-2y>8\\-2y>-x+8\\y<\frac{1}{2}x-4[/tex]

As you might notice the greater than sign flipped, that doesn't always happen. It only happens when you are dividing by a negative number.

    Graphing the inequality:

When you start graphing you should always start by plotting the y-intercept. Which in this case it's [tex](0,-4)[/tex]. Then starting from that point you would go up 1 unit then right 2 units then plot the new point because the slope is [tex]\frac{1}{2}[/tex]. The 1 would be the up and down as for the 2 it will be the right and left. This goes up 1 and right 2 because it's positive. So you keep going creating new points as you go then when you reached the end of the graph you would go back to [tex](0,-4)[/tex] and do the opposite so you will do down 1 then left 2. When you run out of room you will have to draw a line, but be careful the line has to be dotted because the solid lines are used for the greater/less than or equal to signs. Then make sure to add arrows at each side of the dotted line to indicate that this line is infinite.

Question 5:

I'm very sorry but I can't see the picture since it's a bit blurry. So I'll try to explain how to write the inequality the best I can. So first we need to know the y-intercept it should be the point directly on the y-axis. Then find the slope by seeing how it gets to the next perfect point. I can tell you that the slope will be positive. Also for the sign it's dotted that means the sign is [tex]<[/tex]. So the inequality should look something like this [tex]y<\frac{?}{?}x+?[/tex]. Make sure you have the signs correct too don't change the ones I already put in.

Question 6:

For this one the inequality will look like this [tex]x\geq 2[/tex]. Then for the graph you will plot [tex](2,0)[/tex]. Then make a solid line that goes vertically since the only x-value is 3 the y-value will be changing without the x. Then for the shading you will shade the right side of the line.

Answer:

No, the student did not check the solution to the derived equation in the original equation.

No, a possible solution is a = –2, but it does not check in the original equation because it makes two of the denominators equal to zero.

No, a = –2 is an extraneous solution, and there is no solution to the original rational equation.

Step-by-step explanation:

just did on edge good luck!

The student is wrong in his answer to the equation

3/a + 2 − 6a/2a − 4 = 1/a − 2 is - 2, the correct answer is 2/3.

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, 3/a + 2 − 6a/2a − 4 = 1/a − 2.

3/a + 2 - 3 - 4 = 1/a - 2.

3/a - 1/a = 3.

2/a = 3.

a/2 = 1/3.

a = 2/3.

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Answer:

5/42=0.11904762

Step-by-step explanation:

convert to fraction

31/5 divided by 1302/25

do the reciprocal

31/5 x 25/1302

reduce the numbers with the greatest common facter 5

31 x 5/1302

reduce the numbers with the greatest common factor 31

5/42

turn into decimal

5/42=0.11904762

Answer:

This sequence is arithmetic, and the next term is 25

Step-by-step explanation:

The common difference of the sequence is 6, so the next term is 19+6=25.

The difference between the consecutive terms is constant => sequence is arithmetic.

7-1=6

13-7=6

19-13=6

Answer:

Step-by-step explanation:

a=1

c.d. d=13-7=6

[tex]a_{n} =a_{1}+(n-1)d\\a_{n}=1+(n-1)6\\a_{n}=1+6n-6\\a_{n}=6n-5[/tex]

Answer:

x = -6

Step-by-step explanation:

let's call the number x.

"five less than"

[expression] - 5

"the quotient of a number and 3"

x/3

x/3 - 5

"is -7"

x/3 - 5 = -7

add 5 to both sides of the equation

x/3 - 5 + 5 = -7 + 5

x/3 = -2

multiply both sides of the equation by 3

x/3 * 3 = -2 * 3

x = -6

Answer:

X = number,

so the expression becomes X/5 - 14

Step-by-step explanation:

x

5

<

4

Explanation:

"Quotient" is the answer to a division.

Let's call the number

x

.

The quotient of a number (

x

) and

5

means

x

5

The quotient we have must be less than 4 , which is written

<

4

So,

x

5

<

4

Answer:

X = 27 bags

Step-by-step explanation:

Given the following data;

Ratio of mulch to fertilizer = 1:6

Quantity of mulch = 4.5 bags

Let the quantity of fertilizer = x

Therefore,

1 mulch = 6 fertilizer

4.5 mulch = x fertilizer

Cross multiplying, we have

x = 6 * 4.5

x = 27

Therefore, if she uses 4.5 bags of mulch, then she should use 27 bags of fertilizer.

The correct answer is (b) a bacteria culture triples in size every day describes a exponential function.

A relation is a function if it has only One y-value for each x-value.

The growth of a population, bacteria culture, or puppy can be modeled by an exponential function if the growth rate is proportional to the current size.

In other words, if the growth rate is constant, then the growth can be modeled by an exponential function.

Out of the three situations given, option (ii) is the only one that has a constant growth rate, since the bacteria culture triples in size every day. This means that the growth rate is constant at 200% per day.

Option (i) has a growth rate that is not constant but increases every year, so it is not best modeled by an exponential function.

Option (iii) also has a growth rate that is not constant, since the puppy grows by a fixed amount of 2 pounds every month regardless of its current weight.

Therefore, the correct answer is (b) a bacteria culture triples in size every day describes a exponential function.

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Answer:

Step-by-step explanation:

15x+5y=8-3x

18x+5y=8⇒eqn 1

15x+5y=20y

15x-15y=0⇒eqn 2

eqn 1 * 3

 54x + 15y=24⇒eqn 3

eqn 3 + eqn 2

69x=24

x=24/69=0.3478

eqn  1⇒

    5y=8-18(24/69)

     y=1.7391/5

     y=0.3478

The solution to the system of equations is (10/3, -2).

Two or more expressions with an equal sign are defined as an equation.

The given equations are 15x + 5y = 20 and y = 8-3x.

15x + 15y = 20

Substitute y = 8-3x into the above equation:

15x + 15(8-3x) = 20

15x + 120 - 45x = 20

45x - 15x = 120 - 20

30x = 100

x = 10/3

Substitute x = 10/3 in y = 8 - 3x:

y = 8 - 3 (10/3)

y = 8 - 10

y = -2

Hence, the solution to the system of equations is (10/3, -2).

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Answer:

The length of the legs is 8.64cm and 14.64cm respectively

Step-by-step explanation:

I've added an attachment to aid my explanation.

At different intervals, I'll be making reference to it.

Given

[tex]AB = 17[/tex]

[tex]PAMC = 32[/tex]

[tex]PBMC = 25[/tex]

From the attachment, we have:

[tex]y + z = AB[/tex]

Since, M is the Midpoint

[tex]y = z = \½AB[/tex]

Substitute 17 for AB

[tex]y = z = \½ * 17[/tex]

[tex]y = z = 8.5[/tex]

Also, from the attachment

[tex]v + x + z = PAMC[/tex]

[tex]v + x + y = 32[/tex]

Substitute 8.5 for y

[tex]v + x + 8.5 = 32[/tex]

[tex]v + x = 32 - 8.5[/tex]

[tex]v + x = 23.5[/tex] --------- (1)

Also, from the attachment

[tex]v + w + z = 25[/tex]

Substitute 8.5 for z

[tex]v + w + 8.5 = 25[/tex]

[tex]v + w = 25 - 8.5[/tex]

[tex]v + w = 17.5[/tex] ----------- (2)

Subtract (2) from (1)

[tex]v - v + x - w = 23.5 - 17.5[/tex]

[tex]x - w = 6[/tex]

Make x the subject

[tex]x = 6 + w[/tex]

Apply Pythagoras Theorem:

We have that:

[tex]AB^2 = AC^2 + BC^2[/tex]

The above can be replaced with

[tex]17^2 = x^2 + w^2[/tex] (see attachment)

[tex]289 = x^2 + w^2[/tex]

Substitute 6 + w for x

[tex]289 = (6 + w)^2 + w^2[/tex]

[tex]289 = 36 + 12w + w^2 + w^2[/tex]

[tex]289 - 36 = 12w + 2w^2[/tex]

[tex]253 = 12w + 2w^2[/tex]

Reorder

[tex]2w^2 + 12w - 253 = 0[/tex]

Solve using quadratic equation:

[tex]w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

Where

[tex]a = 2[/tex]

[tex]b = 12[/tex]

[tex]c = -253[/tex]

[tex]w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}[/tex]

[tex]w = \frac{-12 \± \sqrt{144 + 2024}}{4}[/tex]

[tex]w = \frac{-12 \± \sqrt{2168}}{4}[/tex]

[tex]w = \frac{-12 \± 46.56}{4}[/tex]

Split:

[tex]w = \frac{-12 + 46.56}{4}[/tex] or [tex]w = \frac{-12 - 46.56}{4}[/tex]

[tex]w = \frac{34.56}{4}[/tex] or [tex]w = \frac{-58.56}{4}[/tex]

[tex]w = 8.64[/tex] or [tex]w = -14.64[/tex]

But length can't be negative

So:

[tex]w = 8.64[/tex]

Recall that: [tex]x = 6 + w[/tex]

[tex]x = 6 + 8.64[/tex]

[tex]x = 14.64[/tex]

Hence, the length of the legs is 8.64cm and 14.64cm respectively

Answer:

Step-by-step explanation:

[tex]a_n=a_1+d(n-1)\\\\a_{20}=a_1+d(20-1)\\\\36=a_1+4\cdot19\\\\36=a_1+76\\\\a_1=36-76\\\\a_1=-40[/tex]

Answer:

420 miles

Step-by-step explanation:

1 inch is equal to 105 miles. The amount of inches between the two towns is 4, and 4 inches is 4 times the amount of inches in the scale. If the amount of inches is multiplied by 4, then the amount of miles should be multiplied by 4 too:

105 * 4 = 420

The actual distance is 420 miles.

Hope this helps :)

Answer:

9

Step-by-step explanation:

Answer:-20

Step-by-step explanation:

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

= -22-(-2)/(-4-(-4)

= -20/0

Answer:

definition of perpendicular bisector

Step-by-step explanation:

You need to show the entire problem including the given.

I assume the given info states that

Segment MP is the perpendicular bisector of segment NO.

If that's the case, then the reason for lengths NP and OP being equal is

"definition of perpendicular bisector"

Answer:

y = 8x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 8 and c = 2 , thus

y = 8x + 2 ← equation of line

Answer:

The ratio of boys and girls =3:5

Let

Number of boys=3x

Number of girls =5x

[tex]{:}\longrightarrow[/tex][tex]\sf 5x=130 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {130}{5}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=26 [/tex]

The number of boys=3x

=3×26=78

[tex]\therefore[/tex]Number of boys is 78.

Answer:b,c,e

Step-by-step explanation:

I got it on edg 2020

Answer:

B C D

Step-by-step explanation:

Answer:A rubric is a grading tool that describes the criteria, or "what counts," for the assignment.  It also describes each of the criteria according to gradations of quality, with descriptions of strong, middling, and problematic student work.  The criteria are listed in the column on the left.  The numbers in the top row indicate quality, with 3 being the best.   The number 0 is something everyone wants to avoid.  Students may use the rubric as a check list to determine if the writing meets the criteria of the assignment.

Point Value

2 points

1 points

.5 points

0 points

Topic Sentence

Interesting, original topic sentence, reflecting thought and insight; focused on one interesting main idea.

Clearly stated topic sentence presents one main idea.

Acceptable topic sentence presents one idea.

Missing, invalid, or inappropriate topic sentence;  main idea is missing.

Supporting Details

Interesting, concrete and descriptive examples and details with explanations that relate to the topic.  

Examples and details relate to the topic and some explanation is included.

Sufficient number of examples and details that relate to the topic.

Insufficient, vague, or undeveloped examples.

Organization and Transitions

Thoughtful, logical progression of supporting examples; Mature transitions between ideas.

Details are arranged in a logical progression; appropriate transitions.

Acceptable arrangement of examples; transitions may be weak.

No discernible pattern of organization; Unrelated details; no transitions.

Style

Appropriate tone, distinctive voice; pleasing variety in sentence structure; Vivid diction, precise word choices.

Appropriate tone; Clear sentences with varied structures; Effective diction.

Acceptable tone; some variety in sentence structures; Adequate diction and word choices.

Inconsistent or Inappropriate tone; Awkward, unclear, or incomplete sentences; Bland diction, poor word choice.

Mechanics

Consistent standard English usage, spelling, and punctuation. No errors.

Some errors, but none major, in usage, spelling, or punctuation. (1-2)

A few errors in usage, spelling, or punctuation (3-4)

Distracting errors in usage, spelling, or punctuation

Topic Sentences                                      ______

Supporting Details and Organization    ______

Organization/Transitions                        ______

Style                                                          ______

Mechanics                                                ______

           Total Points  ______ = grade of ______

*Your instructor will average the scores of both paragraphs to generate your final grade for Assignment #1.

Grade Equivalent:

A =  8 - 10 points

B =  6 -7  points

C =  4 - 5 points

D =  2 - 3 points

F =  0 - 1

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

try all of them

Answer:

Is there any answer choices?

Step-by-step explanation:

Answer:

half

Step-by-step explanation:

if one out of every two people is a man then half

Answer:

The above one

The formula should be the same. most likely

Answer:

x=−2

Step-by-step explanation:

Answer:

the answer is y=-1/6x-1

Answer:

You put a 1 in the Green Box

Step-by-step explanation:

The full equation is y=1/6x-1

Answer: your formula is y=-1x+11

Step-by-step explanation: this is because the line decreases which means the slope is negative. 11 is the y-intercept.

Answer:

10 inches

Step-by-step explanation:

11 inches - 1 hour =10

Answer:

.9

Step-by-step explanation:

Answer:

.9

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

Answer:

Its C because think about it

Step-by-step explanation: