A shelf can be packed from end to end with 30 large books or 45 small books.
Kevin already packed the shelf with 3 large books and 23 small books.
At most, how many more large books can Kevin pack the shelf with?
Ans:

The coefficient are as follows:

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

1. 12s + 4t

Variables: s, t

Coefficient: 12, 4

2. 46rs + 10x

Variables: r, s, x

Coefficient: 46, 10

3. 12q + 14x

Variables: q, x

Coefficient: 12, 14

4. 10x + 10y

Variables: x, y

Coefficient: 10, 10

5. 17rs + 32x

Variables: r, s, x

Coefficient: 17, 32

6. 5x + 7y - 12z

Variables: x, y, z

Coefficient: 5, 7, -12

7. 36ab + 70m

Variables: a, b, m

Coefficient: 36, 70

8. 3r + 19a + 10m

Variables: r, a, m

Coefficient: 3, 19, 10

9. 7k + 16m

Variables: k, m

Coefficient: 7, 16

10. 8r + 5s

Variables: r, s

Coefficient: 8, 5

11. 9h + 120m

Variables: h, m

Coefficient: 9, 120

12. 12k + m

Variables: k, m

Coefficient: 12, 1

13. 7g + 15h + w

Variables: g, h, w

Coefficient: 7, 15 , 1

14. 4c - 8d + 12f

Variables: c, d, f

Coefficient: 4, -8, 12

15. 6t + 17r - 35j

Variables: t, r, j

Coefficient: 6, 17, -35

Learn more about algebra here:

https://brainly.com/question/953809

#SPJ1

Answer:

Step-by-step explanation:

Solution

Interesting question.

The formula for the sum of the interior angles is

(n - 2)*180 = x

In this case, x = 1260

(n - 2)*180 = 1260                            Divide both sides by 180

(n -2 )* 180/180 = 1260/180

( n - 2) = 7                                         Remove the brackets

n - 2 = 7                                            Add 2 to both sides

n - 2 + 2 = 7 +2                                 The 2s on the left cancel

n = 9

Answer: Nonagon

The polygon with an interior angle sum of 1260° is the nonagon as per the concept of interior angles.

To find the sum of the interior angles of a polygon, we can use the formula:

Sum of interior angles = (n - 2) × 180°

where "n" is the number of sides of the polygon.

To achieve an interior angle sum of 1260°, we would need to consider a polygon with fewer sides.

For example, a nonagon (9 sides) would have an interior angle sum of 1260°:

Sum of interior angles = (9 - 2) × 180°

Sum of interior angles = 7 × 180°

Sum of interior angles = 1260°

So, a nonagon (a polygon with nine sides) has an interior angle sum of 1260°.

To learn more about the interior angles;

brainly.com/question/10638383

#SPJ3

The 3-D figure and combination of shapes that Scarlett can use is A. Equilateral triangle prism with two equilateral triangles and three rectangles

This refers to the solid figure or shape that has defined dimensions of length, width, and height.

Therefore, based on the fact that a 3-D figure is made up of six equal squares, option A is the best answer because it contains a total of six squares.

Read more about 3-D figures here:

https://brainly.com/question/12925490

#SPJ1

3x + 6 = 48 (alternate angles are equal)

- 6

3x. = 42

÷3

x = 14 degrees

180-48 - 2y + 5y-9 =180

123 + 3y = 180

-123

3y = 57

÷3

y = 19 degrees

Explanation:

To find the last angle on the top straight line, do:

180 - (the 2 given angles).

So, 180 - (3x + 16, which is 48 due to alternate angles being equal). Then, minus the 2y.

(180 - 48 - 2y) & simplify => 132 - 2y

This gives you the equation for the missing angle on our top straight line.

Thus, co-interior angles add to 180. So, we add the new equation (132 - 2y) to 5y - 9.

Simplify

=> 123 + 3y (because - 2+5 =3)

and put it equal to 180. Solve for y

Hope this helps!

Answer:

y-2=2(x-5), y=2x-8, y+16=2(x+4)

Step-by-step explanation

Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

The parameters for this problem are given as follows:

A = 144, r = 0.06, n = (68 - 24) x 12 = 528.

Then:

r/12 = 0.06/12 = 0.005.

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}[/tex]

[tex]P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}[/tex]

P = $26,731.23.

More can be learned about the monthly payment formula at https://brainly.com/question/26476748

#SPJ1

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

This question is incomplete, the complete question is;

Which equation is correct for ∆FON?

Answers:

A.) cos F= 9/18

B.) sin F 9/18

C.) sin F=18/9

D.) cos F=18/9

From the diagram, we have a right angle triangle.

Note that; sinθ = Opposite / Hypotenuse

Therefore, for angle F

sin F = Opposite / Hypotenuse

sin F = 9/18

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

Learn more about trigonometric ratio here: https://brainly.com/question/28016662

#SPJ1

The value of line AL is 21. 51cm

Let's start by finding line AB using

Sin α = opposite/ hypotenuse

Sin 90 = x/ 24

1 = x/24

Then, cross multiply

We have line AB = 24cm

Now, let's find line AC

Sin angle B = line AC/24

Let's find angle B

We know that angle A + angle B + angle C = 180

But angle B = 2 Angle A

x + 2x + 90 = 180

3x + 90 = 180

3x = 180-90

x = 30°

Then Angle B = 2 × x = 2 × 30 = 60°

Sin 60 = x/ 24

0. 8660 = x/24

Cross multiply

x = 24 × 0. 8660

x = 20. 78cm

From the diagram, we have the angle of A  in the given triangle to be divide into two by the bisector, angle A = 15°

To find line AL, let's use

Cos α = adjacent/ line AL

Cos 15 = 20. 78/ line AL

Line AL = 20. 78/ cos 15

Line AL = 20. 78 / 0. 9659

Line AL = 21. 51 cm

Thus, the value of line AL is 21. 51cm

Learn more about trigonometric ratio here:

https://brainly.com/question/11967894

#SPJ1

Answer: D

Step-by-step explanation:

Answer: Choice D

Open hole at -3 with shading to the left.

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

Explanation:

The inequality [tex]-3 > \text{x}[/tex] is the same as [tex]\text{x} < -3[/tex]

When swapping both sides, the inequality sign flips as well.

Since we're looking for numbers smaller than -3, this includes things like -4, -5, -6, -7, and so on. Therefore we shade to the left of -3 on the number line.

We have an open hole at -3 to indicate it's not included as part of the solution set. We would include it if there as an "or equal to" as part of the inequality sign.

Based on the calculations, the slope of line YZ in simplest form is equal to 2.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since points X, Y, and Z are collinear, we can deduce that the line passes through line Z at 6 units form the origin and 3 units for Y from the origin.

Substituting the parameters into the formula, we have;

[tex]Slope, m = \frac{6\;-\;0}{3\;-\;0}[/tex]

Slope, m = 6/3

Slope, m = 2.

Read more on slope here: https://brainly.com/question/17601248

#SPJ1

Round

8724 to the nearest whole number is 8720

The slope of the line will be – 1/5. Then the correct option is B.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

Take two point from the graph.

(0, 2) and (1, –3)

Then the slope will be

m = (2 – (–3)) / (0 – 1)

m = 5 / (–1)

m = – 1/5

Then the correct option is B.

More about the equation of line link is given below.

https://brainly.com/question/21511618

#SPJ1

Answer:

1,483

Step-by-step explanation:

The equation that models this set of data is y=17.2x^2-226.3x+2184.5. Since x=0 represents 6:00 a.m, x=5 represents 11:00 a.m. Substitute 5 for x in the model, and solve for y.

Based on the number of registered users who log into the social media app during weekdays and weekends, the following are true:

The given model for the users in the week is:

y = 17.2x² - 226.3x + 2,184.5

x is 5 because 11 am is 5 hours after 6 am:
= 17.2(5)² - 226.3(5) + 2,184.5

= 1,483 users

The company should post when there are the most people online and on weekdays that's 14 hours after 6 am which is:
=14 + 6

= 20:00

= 8 pm

On weekends this is 6 hours after 6 am:

= 6 + 6

= 12 pm

Missing information from question:

Model for calculating weekday users y = 17.2x² - 226.3x + 2,184.5.

Find out more on social media marketing at https://brainly.com/question/4241587.

#SPJ1

The number that completes the System of Linear Inequalities represented by the Graph y >= 2x – 2 and x + 4y > =  is -12. Hence, x + 4y [tex]\geq[/tex] -12

A collection of linear inequalities in the same variables is referred to as a system of linear inequalities. Any ordered pair that fulfills all of the inequalities is the solution.

Recall that:

y = mx + c

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

Given that

The orange line intersects y-axis at (0,-2), therefore the y-intercept is -2.

The orange line intersect the points that are (1,0)  and (0, -2).

The slope of the line can be obtained as follows:

m = (-2-0)/(0-1)

= -2/-1

= 2

The slope of the line is m = 2.

Therefore, the orange line is y [tex]\geq[/tex] 2x -2

The blue line intersects y-axis at (0,-3), therefore the y-intercept is -3.

The blue line intersect the points that are (-4, -2) and  (0, -3)

The slope of the line can be obtained as follows.

m = (-3-(-2))/(0-(-4))

= (-3 + 2)/4

= - (1/4)

The slope of the line is:
m = -(1/4)

The inequalities is x + 4y [tex]\geq[/tex] b passes through the point (0, -3)

(0) + 4 (-3) = b

-12 =b

Thus, -12 in is the number that completes the system. Hence, x + 4y [tex]\geq[/tex] -12

Learn more about system of inequalities at;
https://brainly.com/question/9774970
#SPJ1

Answer:

-x + 7 / x + 1

Step-by-step explanation:

6 -(x - 1)/ x + 1

Apply distributive law: -(x - 1) = -x + 1

= 6 - x + 1 / x +1

Group like terms:

= -x + 7/ x + 1

Answer:  its 5x+7/x+1

Step-by-step explanation:

Answer:

25 hours.

Step-by-step explanation:

Let the hours worked be x

2/5x = 10

2x = 50

x = 25

She has to work 25 hours to spend 10 hours doing paperwork.

The value of this car is decreasing at a rate of 6% per year.

The function V(t) = 38000 (0.94)^t represents the value (in dollars) of a car "t" years after its purchase

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,

V(t) = 38000 (0.94)^t
Cleary, above function is an exponential function
while putting certain values in equation we have certain outcomes.
for,
V(1) = 35720;    V(2) =33576.8;      V(3) = 31562.192

Now, the rate of change is given by = [V(2)-V(1)/ V(1)] x 100
= [(33576.8-35720)/35720]*100
= 6%

now V(2) x 6% = V(3)
33576.8 x 6% = 31562.192 = V(3)

Thus, The required rate of decreasing care price is 6%.

Learn more about rate of change here:
https://brainly.com/question/13103052

#SPJ1

Answer:

[tex] {x}^{2} - 16 = 0 \: is \: the \: equation[/tex]

Step-by-step explanation:

[tex]x = - 4 \\ or \: x = 4[/tex]

[tex](x + 4) = 0 \: or \: (x - 4) = 0 \\ (x + 4)(x - 4) = 0 \\ open \: the \: bracket[/tex]

[tex]x(x - 4) + 4(x - 4) = 0[/tex]

[tex] {x}^{2} - 4x + 4x - 16 = 0 \\ {x}^{2} - 16 = 0[/tex]

Answer:

4x

Step-by-step explanation:

[tex]\frac{500x^{4} }{(5x)^{3} }[/tex] = [tex]\frac{500x^{4} }{125x^{3} }[/tex] = [tex]4x[/tex]

Answer:

199.5 ft^3

Step-by-step explanation:

to find your answer you simply multiply all the measurements together

19 * 1.5 * 7 is your equation

19 * 1.5 * 7 = 199.5

it is 199.5 ft^3

Answer:

3/500

Step-by-step explanation:

.6%   = .006   =    6/1000  = 3/500

Explanation:

The first step is to add up all the values given:

11.01 + 10.50 + 5.70 + 14.67 + 9.50 + 12.54 + 8.90 + 13.56 + 11.23 + 6.80 + 3.00 + 10.55 = 117.96

Then we divide this sum over n = 12 since this is the sample size given (i.e. the number of customers)

117.96/n = 117.96/12 = 9.83

Answer:

( x-7) ( x-5)

Step-by-step explanation:

x^2 -12x + 35

To factor this problem, we want to know that two numbers multiply to 35 and add to -12

-7 * -5 = 35

-7 + -5 = -12

( x-7) ( x-5)

Answer:

The answer is (x-7)( x-5)

Step-by-step explanation:

We need to find two numbers that add up to −12 and those same two numbers should have a product of 35

Here the common factors are -7 and -5 because when added they give -12 and when multiplied they give 35.

Therefore we write the answer as (x-7)(x-5)

Answer:

x = 41* & y = 90.

Step-by-step explanation:

Since we know that the figure is a right triangle, we can solve for y easily, as 90+y = 180

y = 90

to solve for x, we have 49+90+x, since the angle that makes up the left side is perpendicular to the triangle,

so 139+x = 180

x = 180-139

x = 41

The formula of P(x) = -0.7 (x-2)²(x+4)

A root of a polynomial is defined as the point or value at which the overall value of the polynomial = 0

It is given that

for a polynomial of degree 3

root x=2, multiplicity 2:  (x-2)²

root x= - 4, multiplicity 1:  (x+4)                  ³ ²

P(x) = a(x-2)²(x+4)

here a is constant

y-intercept =  -11.2

P(0) = -11.2

a(0-2)²(0+4) = -11.2

a * 4 * 4  = -11.2

16a = -11.2

a = -11.2/(16)

a= -11.2/16

P(x) = -(11.2/16)(x-2)²(x+4)

P(x) = -0.7 (x-2)²(x+4)

Therefore the formula of P(x) = -0.7 (x-2)²(x+4)

To know more about Roots of Polynomial

https://brainly.com/question/1514617

#SPJ1

Here are the awnsers

1. D ⅔

2.C 60%

The value of x in the equation 1/2x = -1/2x when 4 is subtracted from both sides is 0(not defined)

Subtraction of fraction

Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction

1/2x = -1/2x

1/2x - 4 = -1/2x - 4

(x-8) / 2 = (-x-8) / 2

(x - 8) / 2 = (-x-8) / 2

2(x - 8) = 2(-x - 8)

2x - 16 = -2x - 16

2x + 2x = -16 + 16

4x = 0

Learn more about fraction:

https://brainly.com/question/11562149

#SPJ1

Answer:c

is the answer

Step-by-step explanation: