2 Look at the open number line in
Problem 1. How would you change the
numbers to show 9 + 5?

Step-by-step explanation:

6 2/7is rational

-19is rational but next I dont know

Answer:

[tex]|x - 85| = 12[/tex]

[tex]x = 73 \ (smaller\ number )[/tex]

[tex]x = 97 \ (larger \ number )[/tex]

Step-by-step explanation:

From the question we are told that

  The  grade is  [tex]k = 85\%[/tex]

   The  variation is  [tex]v = 12 \%[/tex]

Generally the absolute value equation is mathematically represented as

        [tex]|x - 85| = 12[/tex]

=>  [tex]x -85 = \pm 12[/tex]

So

    [tex]x = 85 + 12[/tex]

    [tex]x = 97 \ (larger \ number )[/tex]

And

     [tex]x = -12 + 85[/tex]

=>  [tex]x = 73 \ (smaller\ number )[/tex]

Answer:

32 cm²

Step-by-step explanation:

SA = 2(lw + lh + hw)

      = 2(2x2 + 2x3 + 3x2)

      = 2(4 + 6 + 6)

      = 2(16)

      = 32 cm²

Answer:

X= -12 +6√10

X= 6.973

Step-by-step explanation:

Volume of the box= (36-2x)(24-2x)x

Volume of the box

=( 864 -96x -4x²)x

But 864 -96x -4x²

=216 - 24x-x²

Solving for x quadratically

X= (24+12√10)/-2

X= -12 -6√10

X= -30.97

Or

X= (24-12√10)/-2

X= -12 +6√10

X= 6.973

X will definitely be a positive number

So X= -12 +6√10

X= 6.973

Increasing or decreasing the side length of the square that gives the

maximum volume, gives a volume that is less than the maximum.

Reasons:

The given dimensions of the box = 24 in. by 36 in.

Let x represent the dimensions of the square removed from the corners, we have;

Width of box = 24 - 2·x

Length of box = 36 - 2·x

Height of the box = x

Volume of a box = Width × Length × Height

Therefore;

Volume of the box, V = (24 - 2·x)·(36 - 2·x)·x = 4·x³ - 120·x² + 864·x

At the maximum or minimum point of the volume, we have;

Which gives;

12·x² - 240·x + 864 = 0

x² - 20·x + 72 = 0

Which gives;

[tex]\displaystyle x = \dfrac{20\pm \sqrt{(-20)^{2}-4\times 1\times 72}}{2\times 1} = \mathbf{10 \pm 2\cdot \sqrt{7}}[/tex]

At x = 10 + 2·√7, we have;

[tex]\displaystyle 10 + 2 \cdot \sqrt{7} > \frac{24}{2}[/tex]

2 × (10 + 2·√7) in. > 24 in. which is the width of the cardboard

Therefore, (10 + 2·√7) is too long to be cut from the cardboard

At x = 10 - 2·√7, we have;

V = 4·(10 - 2·√7)³ - 120·(10 - 2·√7)² + 864·(10 - 2·√7) ≈ 1,828.3

Therefore;

The maximum volume corresponds with a cut out square of side length x = 10 - 2·√7 inches  ≈ 4.71 inches

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Answer:

Step-by-step explanation:

perp. -2/3 slope

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

y - 4 = -2/3x - 2

y = -2/3x + 2

Answer:

Straight angle

<----------------------------->

You can determine if an angle is a straight angle only if it is 180 degrees. You can also draw it by drawing a straight line and drawing an arrow facing outward at each end.

Answer:

1 1/14 lbs

Step-by-step explanation:

We can use ratios to solve

2/3 crate        1 crate

----------------- = -----------------

5/7 lb                 x lbs

Using cross products

2/3x = 5/7 *1

Multiply each side by 3/2

3/2 * 2/3 x = 3/2 * 5/7

x = 15/14

x = 1 1/14

Answer:

[tex]\huge\boxed{\sf 1 \ crate = \frac{15}{14} \ lbs}[/tex]

Step-by-step explanation:

[tex]\sf \frac{2}{3}\ of \ a\ crate = \frac{5}{7} \ of \ a\ pound \\\\We \ need \ to \ find\ the \ weight \ of \ one \ crate\\\\So, Multiplying \ both \ sides \ by \ the\ reciprocal \ of \ \frac{2}{3} \ i.e. \frac{3}{2} \\\\1 \ crate = \frac{5}{7} * \frac{3}{2} \ lbs\\\\1 \ crate = \frac{5*3}{7*2} \ lbs\\\\1 \ crate = \frac{15}{14} \ lbs[/tex]

Answer:

.75

Step-by-step explanation:

there is only 1 number

0.75

The decimal forms of rational numbers either end or repeat a pattern. To convert fractions to decimals you just divide the top by the bottom — divide the numerator by the denominator — and if the division doesn't come out evenly, you can stop after a certain number of decimal places and round off.

Answer:

The answer is (1,-1)

Step-by-step explanation:

The best approach for this problem is to plug in the coordinates into the given inequality.

[tex]7x-3y\geq 10\\[/tex]

(3,4) ------> [tex]7(3)-3(4)=9[/tex]

9 is less than 10 so, we can rule this one out.

(1,0) -------> [tex]7(1)-3(0)=7[/tex]

7 is less than 10 so, we can rule this one out.

(1,2) -------> [tex]7(1)-3(2)=1[/tex]

1 is less than 10 so, we can rule this one out.

(1,-1) -------> [tex]7(1)-3(-1)=10[/tex]

10 is equal to 10, so this is the answer.

Hope this helps!

As mentioned by Mark there are an unlimited number of pairs that satisfy your equation. So let us see how you can characterize these solutions

if 7x - 3y > 10 then

7x > 10 +3y

Now we can substitute any value for y and get the appropriate value for x. For example I can choose y to be 6

then by substitution

7  must be > 10+ 3*6

or 7x must be > 28

or x must be > 4

So all pairs such that x is > 4 and y = 6 are solutions.

I can create an infinite number of pairs choosing any number for y. Likewise I could have chosen x and solved the problem for y. In the above example I chose 6 for y to make the division easy. I could have chosen any number(real or integer) for y and solved the equation for x  to derive appropriate  pairs

Answer:

Length of QR = 7

Step-by-step explanation:

20 - 13 = 7

Answer:

3. 2x+18=4x+26

Step-by-step explanation:

2(x+9)=4(x+7)+2

2x+18=4x+28+2

2x+18=4x+30

The step that made an error in solving this linear equation is step 3.

Hope this helps ;) ❤❤❤

===============================================

Explanation:

2/3 is the probability of passing a test, so 1/3 is the probability of failing

Note how 2/3 and 1/3 add to 3/3 = 1 to represent 100%

The probability of failing 3 tests in a row is (1/3)^3 = (1/3)*(1/3)*(1/3) = 1/27 assuming each test event is independent from one another.

-------

Side note: the probability of passing at least one test is 1-1/27 = 26/27 and the probability of passing all three tests in a row is (2/3)^3 = 8/27

Answer:

Step-by-step explanation:

Find the required diagram to the question in the attachment.

From the diagram it can be seen that the distance of the lines projecting from the centre of the circle to the line segment is equal i,e they are both 8. This means that the length of both chords given will be equal. For the known chord length, it can be seen that the line perpendicular to the chord cuts them at the centre. and since both sides of the chord are parallel, the other sides too will be 10 making the total length to be 10+10 = 20.

Since the length of the known chord is equal to the length of the unknown chord x, hence, the value of x will also be 20

Answer:

D. x=20

Step-by-step explanation:

correct on EDGE2021

3 tests at 75% each = 3 x 75 = 225 total points

First two tests = 79 + 84 = 163

Third test needs to be at least: 225 - 163  = 62%

So any score less than 62 would get you into trouble.

Answer:

[tex]-57-39i[/tex]

Step-by-step explanation:

So we have the expression:

[tex](7+2i)(-9-3i)[/tex]

FOIL:

[tex]=7(-9)+7(-3i)+2i(-9)+2i(-3i)[/tex]

Simplify:

[tex]=-63-21i-18i-6i^2[/tex]

Recall that i² is just -1. Thus:

[tex]=-63-21i-18i-6(-1)[/tex]

Simplify:

[tex]=-63-21i-18i+6[/tex]

Combine like terms:

[tex]=(-63+6)+(-21i-18i)[/tex]

Add:

[tex]=-57-39i[/tex]

And we're done!

Answer: 6/7

Step-by-step explanation:

Answer: i - j - k

Step-by-step explanation:

Taking the cross product between two vectors will give you a third vector that is orthogonal(perpendicular) to both vectors.

<1,1,0> x <1,0,1>

[tex]det(\left[\begin{array}{ccc}i&j&k\\1&1&0\\1&0&1\end{array}\right] )[/tex]

the determinate of the matrix: <1,-(1),-1>

or: i - j - k

Answer:         n = 3                                              n = 4                

               Upper Sum ≈ 3.41                      Upper Sum ≈ 3.25

               Lower Sum ≈ 2.15                      Lower Sum ≈ 2.25

Step-by-step explanation:

You are trying to find the area under the curve.  Area = height x width.

Height is the y-value at the given coordinate --> f(x)

Width is the distance between the x-values --> dx

n = 3

First, let's figure out dx:  the distance from -1 to +1 is 2 units. We need to divide that into 3 sections because n = 3 --> dx = 2/3

So the points we will evaluate is when x = {-1, -1/3, 1/3, 1}

For the upper sum, we find the max y-value for each interval

For the lower sum, we find the min y-value for each interval

Next, let's find the height for each of the x-values:

f(x) = 1 + x²

f(-1) = 1 + (-1)²   = 2

f(-1/3) = 1 + (-1/3)² = 1 + 1/9 --> 10/9

f(1/3) =  1 + (1/3)² = 1 + 1/9 --> 10/9

f(1) = 1 + (1)²   = 2

Interval         Max                      Min

{-1, -1/3}          f(-1) = 2                   f(-1/3) = 10/9

{-1/3, 1/3}        f(-1/3) = 10/9           f(0) = 1   (vertex lies in this interval)

{1/3, 1}             f(1) = 2                   f(1/3) = 10/9

Now, let's find the Area: A = f(x) dx:

[tex]\text{Upper Sum:}\quad A=\dfrac{2}{3}\bigg(2+\dfrac{10}{9}+2\bigg)\\\\.\qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{46}{9}\bigg)\\\\.\qquad \qquad \qquad =\dfrac{92}{27}\\\\.\qquad \qquad \qquad =\large\boxed{3.41}[/tex]

[tex]\text{Lower Sum:}\qquad A=\dfrac{2}{3}\bigg(\dfrac{10}{9}+1+\dfrac{10}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{29}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{58}{27}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.15}[/tex]

*****************************************************************************************

n = 4

First, let's figure out dx:  the distance from -1 to +1 is 2 units. We need to divide that into 4 sections because n = 4 --> dx = 2/4 = 1/2 (simplified)

So the points we will evaluate is when x = {-1, -1/2, 0, 1/2, 1}

For the upper sum, we find the max y-value for each interval

For the lower sum, we find the min y-value for each interval

Next, let's find the height for each of the x-values:

f(x) = 1 + x²

f(-1) = 1 + (-1)²   = 2

f(-1/2) = 1 + (-1/2)² = 1 + 1/4 --> 5/4

f(0) = 1 + (0)² = 1

f(1/2) =  1 + (1/2)² = 1 + 1/4 --> 5/4

f(1) = 1 + (1)²   = 2

Interval         Max                      Min

{-1, -1/2}          f(-1) = 2                   f(-1/2) = 5/4

{-1/2, 0}          f(-1/2) = 5/4            f(0) = 1  

{0, 1/2}           f(1/2) = 5/4             f(0) = 1

{1/2, 1}            f(1) = 2                   f(1/3) = 5/4

Now, let's find the Area: A = f(x) dx:

[tex]\text{Upper Sum:}\qquad A=\dfrac{1}{2}\bigg(2+\dfrac{5}{4}+\dfrac{5}{4}+2\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{26}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{13}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{3.25}[/tex]

[tex]\text{Lower Sum:}\qquad A=\dfrac{1}{2}\bigg(\dfrac{5}{4}+1+1+\dfrac{5}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{18}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{9}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.25}[/tex]

Answer:

The two marks on the right and left side of the triangle means that it's an isosles triangle which means that the base angles are equal and any triangle in the world the sum of its angles is 180° and you have an angle with 100° so you should subtract 100 from 180 that gives 80° and dived 80 by 2 that gives you 40°

Answer: The amount he earns from lifeguarding = $252 ($18×14). The total amount he needs to make a week is $270.

$270-$252=$18, he needs to earn $18 more from clearing tables.

$18÷9=2, so the minimum number of whole hours clearing tables is 2

Step-by-step explanation:

16=-2x-1

17=-2x

x=-17/2

x=-8.5

(this one isn't in the correct order but it's one of the answers ¯\_(ツ)_/¯

16 = -2x - 1

-8=x-1

-7=x

x=-7

Answer:

The answer is  -8.4

Answer/Step-by-step explanation:

A. [tex] -7x^2y^2(8x^2y - 5xy + 11xy^2 - 31) [/tex]

[tex] -7x^2y^2(8x^2y) - (-7x^2y^2)(5xy) + (-7x^2y^2)(11xy^2) - (-7x^2y^2)(31) [/tex] (distributive property)

[tex] -56x^4y^3 + 35x^3y^3 - 77x^3y^4 + 217x^2y^2 [/tex] (note: - × - = + and - × + = -)

B. [tex] (\frac{4}{5}t^3 - 5t)(\frac{1}{4}t^2 - 3t) [/tex]

[tex] (\frac{4}{5}t^3)(\frac{1}{4}t^2 - 3t) - 5t(\frac{1}{4}t^2 - 3t) [/tex] (distributive property)

[tex] \frac{4*1}{5*4}t^3*t^2 - \frac{4*3}{5}t^3*t - \frac{5*1}{4}t*t^2 + 15t^2 [/tex]

[tex] \frac{1}{5}t^5 - \frac{12}{5}t^3 - \frac{5}{4}t^3 + 15t^2 [/tex]

Combine like terms

[tex] \frac{1}{5}t^5 - \frac{73}{20}t^3 + 15t^2 [/tex] (note: -12/5 - 5/4 = -73/20)

C. (4x² - 7x + 5)(2x - 5)

4x²(2x - 5) - 7x(2x - 5) + 5(2x - 5) (distributive property)

8x³ - 20x² - 14x² + 35x + 10x - 25

Combine like terms

8x³ - 34x² + 45x - 25

D. (3m² - 5m + 2)²

= (3m² - 5m + 2)(3m² - 5m + 2)

= 3m²(3m² - 5m + 2) - 5m(3m² - 5m + 2) + 2(3m² - 5m + 2) (distributive property)

= 9m⁴ - 15m³ + 6m² - 15m³ + 25m² - 10m + 6m² - 10m + 4

Combine like terms

= 9m⁴ - 15m³ - 15m³ + 6m² + 25m² + 6m² - 10m - 10m + 4

= 9m⁴ - 30m³ + 37m² - 20m + 4

Answer:

.8L

Explanation:

Logic

The liters of water left are 0.8 liters.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The quantity of water in a water bottle is 1 liter.

The amount of water Tom drank is 200 milliliters.

Let x be the amount of water left in the bottle.

The liter has to be converted into milliliters.

1 liters = 1000 milliliters

The equation formed is,

1000 - 200 = x

x = 1000 - 200

x = 800 milliliters.

The water left in the water bottle is 800 milliliters.

1000 milliliters = 1 liters

800 milliliters = 0.8 liters

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Answer:

10000

Step-by-step explanation:

First, highlight parts of the question. Since it says round to the nearest ten, draw a number line to start. Start by drawing a number line from 9990 to 10000. Whenever a number has the digit from 5 till any number less than 10, you round up. If the number you are trying to round to any digit is less than 5, then you can round down. Since the part of the number that is important for the question is 5.2, we round above. You get 10000 from this.

Answer: $500

Step-by-step explanation:

The vertical axis of the graph represents the value of the copy machine and the horizontal axis represents the years.

Using the line, one can see that in the first year, the value of the machine went from $7,000 to $6,500.

The loss in value is therefore;

= 7,000 - 6,500

= $500

The needed graph is attached.