3. 64 chairs were arranged in equal rows. 56 students came to sit in the chairs. If the same number of students sat in each row, how many chairs could have been in each row? Explain your thinking​

Answer:

  3, 8, 14, 30, 58

Step-by-step explanation:

As with all formulas, put the numbers in place of the corresponding variables, and do the arithmetic.

  [tex]a_1=3\qquad\text{given}\\\\a_2=8\qquad\text{given}\\\\a_3=2a_1+a_2=2(3)+8=14\\\\a_4=2a_2+a_3=2(8)+14=30\\\\a_5=2a_3+a_4=2(14)+30=58[/tex]

The first 5 terms of the sequence are 3, 8, 14, 30, 58.

Your median is 5 because that is the number that is mentioned the most.

A median is a number that i said the most.

And in the pic your median is 7.

Hope this helps you :0

Answer:

The maximum rate of change of the given function is equal to 3√2.

The direction at which the vector points is given by the unit vector [tex]\displaystyle \frac{\sqrt{2}}{2} \hat{\i} + \frac{\sqrt{2}}{2} \hat{\j}[/tex].

General Formulas and Concepts:
Pre-Calculus

Vectors

Calculus

Differentiation

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Multivariable Calculus

Partial Derivatives

Gradient:
[tex]\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}[/tex]

Gradient Property [Addition/Subtraction]:
[tex]\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle f(x, y) = x^2y^2 + xy - 10[/tex]

[tex]\displaystyle \text{Point} \ (1, 1)[/tex]

Step 2: Find Maximum Rate of Change

∴ the maximum rate of change of the given function f(x, y) is equal to 3√2.

Step 3: Find Direction

∴ we have found the direction of the gradient.

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Topic: Multivariable Calculus

Unit: Directional Derivatives

Answer:

6

Step-by-step explanation:

Negative ×negative always gives gives a positive

Answer:

see below

Step-by-step explanation:

cscx=4

sinx=1/4

cosx=-√(1-sin^2x)=-√(1-(1/16))=-√(15/16)=-√15/4

note: cos<0,sin>0 in quadrant II

sin(x/2)= [tex]\sqrt{\frac{1+cos(x)}{2} } =\sqrt\frac{1+\sqrt{\frac{15}{4} } }{2} =\sqrt{\frac{4+\sqrt{15} }{8} }[/tex]

cos(x/2)= [tex]\sqrt{\frac{1-cos(x)}{2} } =\sqrt{\frac{1-\sqrt{\frac{15}{4} } }{2} } =\sqrt{\frac{4-\sqrt{15} }{8} }[/tex]

tan(x/2)= [tex]\frac{sin(x)}{1-cos(x)} =\frac{\frac{1}{4} }{(1-\frac{\sqrt{15} }{4} )} =\frac{\frac{1}{4} }{\frac{4-\sqrt{15} }{4} } =\frac{1}{4-\sqrt{15} }[/tex]

Calculator check:

[tex]sinx=\frac{1}{4}[/tex]

[tex]x\neq 165.52[/tex]˚ in quadrant II

[tex]\frac{x}{2} \neq 82.76[/tex] ˚

sin(x/2)≈sin(82.76)≈0.9920..

exact value=√(4+√15)/8≈0.9920..

..

cos(x/2)≈cos(82.76)≈0.1260..

exact value=√(4-√15)/8≈0.1260..

..

tan(x/2)=tan(82.76)≈7.872..

exact value=1/(4-√15)≈7.872..

Answer:

157.78

Step-by-step explanation:

Area of a trapezoid = ( sum of base lengths / 2 ) × height

the base lengths of the trapezoid shown are 8.7m and 16.3 + 7.2 = 23.5m

the height is 9.8m

so area = (( 8.7 + 23.5 ) / 2) × 9.8

==> add 8.7 and 23.5

area = (32.2 / 2) × 9.8

==> divide 32.2 by 2

area = 16.1 × 9.8

==> multiply 16.1 and 9.8

area = 157.78

Answer:

-2

Step-by-step explanation:

The slope is rise over run. If we look at the points we can see the rise is -2 and the run is 1. -2/1 = -2, so my answer is correct.

Answer:

Hi I’m the friend

Step-by-step explanation:

by the way I also need brainliest, so you get to choose who to mark as brainliest

Answer:

m<MLO = 120°

Step-by-step explanation:

Equilateral Triangles have all 60° angles.

m<MLN = m<OLN = 60°

60°+60°=120°

Answer:

add all of them together (x and y’s) the divide the sum by the amt of numbers

Step-by-step explanation:

Answer:

1. 0

2. -2.5

3. 5

4.  -2.5

5.  -4

Step-by-step explanation:

Did this by adding the scores together and then dividing by the number of scores added

Answer:

The  answer is b

Step-by-step explanation:

Answer: B

I had to help my brother with this

Answer:

Step-by-step explanation:

The following inequality can be solved by separating the term x from one side.

4x+15≥x+6

First, subtract by 15 from both sides.

4x+15-15≥x+6-15

Solve.

4x≥x-9

Then, you subtract by x from both sides.

4x-x≥x-9-x

Solve.

3x≥-9

Divide by 3 from both sides.

3x/3≥-9/3

Solve.

Divide the numbers from left to right.

-9/3=-3

[tex]\Longrightarrow: \boxed{\sf{x\geq -3}}[/tex]

I hope this helps, let me know if you have any questions.

Answer:

x ≥ -3

Step-by-step explanation:

To determine the solution to the inequality, we need to isolate the variable and its coefficient on one side of the equation. Furthermore, isolate the variable by dividing the coefficient by both sides of the equation. The inequality obtained after doing these steps is the solution to the inequality.

Given inequality:

As said above, let's isolate "x" and it's coefficient on one side of the equation. This can be done by subtracting "x + 15" to both sides of the equation.

As said above, let's further isolate "x" by dividing the coefficient of "x" to both sides of the equation.

Therefore, the solution is x ≥ -3.

The resulting equation after the first step in the solution is:

2v + 4 = 8.

An equation is a mathematical statement that asserts the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.

we have the Equation v + 4 + v  =8

Now, simplifying we get

2v + 4= 8

2v = 4

v =2

To obtain this equation, we combined the like terms "v" on the left side of the equation, which gives us 2v. The rest of the equation remains unchanged.

Therefore, the correct answer is : 2v + 4 = 8.

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Answer:

here

Step-by-step explanation:

if you need more explanation comment on this

[tex]\text{nth term of an arithmetic sequence,}\\\\a_n = a_1 + (n-1)d\\\\a_4 = a_1 +3d=107~~~......(i)\\ \\a_8=a_1+7d = 191~~~......(ii)\\\\\\\text{(ii) -(i):}\\\\~~~~~~a_1+7d-a_1-3d = 191 -107\\\\\implies 4d = 84\\\\\implies d = \dfrac{84}4\\\\\implies d= 21\\\\\text{Substitute d= 21 in eq~(i):}\\ \\~~~~~ a_1 +3(21) = 107\\\\\implies a_1 + 63 = 107\\\\\implies a_1 = 107-63\\\\\implies a_1 =44[/tex]

Answer:

r = h + m

Step-by-step explanation:

h = r - m

Switch sides.

r - m = h

Add m to both sides.

r - m + m = h + m

Simplify the left side. -m + m = 0

r = h + m

a) The first five terms in the sequence is 100, 95, 90, 85 and 80

b) The nth term of the sequence will be 100 + (n - 1)(5) = 5n + 95

Sequences are set of values arranged in a particular order. Given the recursive formula for a sequence expressed as;

an=an-1-5

If the first term a1 = 100, then;

a2 = a1 - 5
a2 = 100 - 5
a2 = 95

For the third term

a3= a2 - 5
a3= 95 - 5
a3 = 90

The other two terms will be 85 and 80

a) The first five terms in the sequence is 100, 95, 90, 85 and 80

b) The nth term of the sequence will be 100 + (n - 1)(5) = 5n + 95

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Using the slope intercept formula, the equation for the line in slope intercept form is y = -x - 4

The slope intercept equation can be describe as follows:

y = mx + b

where

Therefore,

(-4, 0)(1, -5)

m = -5 - 0 / 1 + 4 = -5 / 5 = -1

Therefore, let's find b using (1, -5)

-5 = -1(1) + b

-5  = -1 + b

b = -5 + 1

b = -4

Therefore, the equation is y = -x - 4

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Answer:

$573.50 per week

Step-by-step explanation:

wages =  40 hr/wk * 7.25 $/hr   $290 per week

tips   90 tables * ( 21*.15) = 283.50

total    290 + 283.5 = 573.50  

Answer:

That is a linear function

Step-by-step explanation:

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.

If you try to graph that function on a graphing calculator, you will get a straight line.

Therefore, it is a linear function.

mark brainliest please!

Answer:

I think it's a linear one(function)

y=6x÷19

Answer: 10/8 = 1 1/4

Step-by-step explanation:

2x5 =10

4x2 =8

10/8= 1 2/8 = 1 1/4

Answer:

24:37

Simplify the ratio by dividing by the GCF, in this case, two.

[tex]\frac{48 / 2}{74 / 2} = \frac{24}{37}~also~known~as~24:37[/tex]

Answer: The slope is -1

Step-by-step explanation:  

When you are given a line on a graph all you need to do is pick two points on the line and calculate the change over both the x and y-axis.

Pick both points to be at a position on the line that is easy to read. IE the intersection between two grid lines.  For this problem lets go with the first point at (0,1) and the second point at (1,0).

Now we want to calculate the change in rise (the y-component) and divide by the change in the run (the x-component).  Point 1 has a y-component of 1 and point 2 has a y-component of 0.

1 - 0 = 1 = rise

Point 1 has an x-component of 0 and point 2 has an x-component of 1.

0 - 1 = -1 = run

rise/run = 1/-1

Slope = -1

Step-by-step explanation:

a.) 9

When you divide with a fraction you do the reciprocal of the fraction (basically flipping numerator and denominator) then multiplying (since the opposite of division is multiplication.

So if you flip

[tex]\frac{1}{9} [/tex]

It would be:

[tex] \frac{9}{1} [/tex]

9/1 is the same as 9 so:

1 times 9 = 9

b.) 15

Same thing like we did above, just do the reciprocal the multiply.

[tex] \frac{1}{5} [/tex]

Becomes

[tex] \frac{5}{1} [/tex]

5/1 is the same as 5.

3 times 5 = 15

Answer:

Below!

Step-by-step explanation:

Let the irrational number be known as "x".

[tex]\implies -\sqrt{41} \times x = 1[/tex]

Divide both sides by -√41.

[tex]\implies \dfrac{(-\sqrt{41} \times x)}{-\sqrt{41} } = \dfrac{1}{\sqrt{-41} }[/tex]

[tex]\implies x = \dfrac{1}{-\sqrt{41} }[/tex]

Take the "-" to the numerator:

[tex]\implies x = \dfrac{-1}{\sqrt{41} }[/tex]

Use parenthesis to isolate the "-"

[tex]\implies x = -\huge\text{(}\dfrac{1}{\sqrt{41} } \huge\text{)}[/tex]

Note: 1 can also be written as √1. (√1 = √1 × √1 = 1)

[tex]\implies {x = -\huge\text{(}\dfrac{\sqrt{1}}{\sqrt{41} }\huge\text{)}}[/tex]

Combine the roots in the equation:

[tex]\implies {x = -\huge\text{(}\sqrt{\dfrac{1}{41} }} \huge\text{)}}[/tex]

Remove the parenthesis:

[tex]\implies {x = -\sqrt{\dfrac{1}{41} }}[/tex]

Thus, Option C is correct.

Answer:

The digit 5 is equal to is 5,000 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

The thousandth digit!

Step-by-step explanation:

Answer:

um..is this finished question ????

Answer:

First,you need to find the components of each force.

Answer:

15 ft

Step-by-step explanation:

I'm not sure but I think u add them together to get ur answer

hope it helps

Answer: 21

Step-by-step explanation: