the late fee for library books is $2.00 plus 15 cents each day for a book that is late. If Maria's fee for a late book was $3.20,write and solve a linear equation to find many days late the is

[tex](i)\\\\2A = \begin{pmatrix}3x \times 2 & 1 \times 2 & 5 \times 2\\0\times 2 & 2x \times 2 & -3 \times 2\end{pmatrix} = \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix}\\\\\\(ii)\\\\2A + B = C\\\\\implies \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix} + \begin{pmatrix}y & 0 & -4\\1 & -3y & 2\end{pmatrix} = \begin{pmatrix}31& 2 & 6\\1 & 17& -4\end{pmatrix}[/tex]

[tex]\implies \begin{pmatrix}6x+y & 2+0 & 10-4\\0+1 & 4x-3y & -6+2\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\\\implies \begin{pmatrix}6x+y & 2 & 6\\1 & 4x-3y & -4\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\text{System of equations},\\\\6x +y =31,~~ 4x -3y = 17\\\\\\(iii)\\\\6x +y-31 =0 \\\\4x-3y -17=0\\\\\text{Solving by cross multiplication method}\\\\\\\dfrac x{1(-17) - (-31)(-3)} = \dfrac y{4(-31) - 6(-17)} = \dfrac 1{6(-3) - 4(1)}[/tex]

[tex]\implies \dfrac{x}{-17 -93} = \dfrac{y}{-124 +102} = \dfrac 1{-18-4}\\\\\\\implies -\dfrac{x}{110} = -\dfrac{y}{22} = -\dfrac 1{22}\\\\ \implies \dfrac{x}{110} = \dfrac{y}{22} = \dfrac 1{22}\\\ \\\text{Hence,}\\\\\\x=\dfrac{110}{22}=5,~~~~ y= \dfrac{22}{22} =1[/tex]

Answer:

  (i)

  [tex]2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right][/tex]

  (ii) 6x+y=31; 4x-3y=17

  (iii) (x, y) = (5, 1)

Step-by-step explanation:

The matrix 2A is written by multiplying each element of A by 2.

  [tex]2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right][/tex]

__

Variables are seen in elements (1, 1) and (2, 2) of the matrices A and B, so the simultaneous equations can be chosen from those elements of the equation 2A+B=C.

__

A graphing calculator shows the solution to be (x, y) = (5, 1).

Answer:

B. is correct answer I think so

Step-by-step explanation:

i need help please

plz mark me as brilliant

The answer is 2 workers coz there can't be 2.08333... workers

Using implicit differentiation, it is found that the area of the square is increasing at a rate of:

The area of a square of side length l is given by:

[tex]A = l^2[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]\frac{dA}{dt} = 2l\frac{dl}{dt}[/tex]

Then:

[tex]\frac{dA}{dt} = 2l\frac{dl}{dt} = 2(3)(0.8) = 4.8[/tex]

Hence, option A is correct.

To learn more about implicit differentiation, you can take a look at https://brainly.com/question/25608353

Answer:

a driver costs $19, while a putter costs $12

Step-by-step explanation:

driver = d

putter = p

1d + 2p = 43

3d + 1p = 69

d + 2p = 43. eq 1

3d + p = 69. eq 2

make d the subject of the equation

d = 43 - 2p. eq 3

substitute the value of d in eq 3 in eq 2

3(43 - 2p) + p = 69

129 - 6p + p = 69

collect like terms

129 - 69 = 6p - p

60 = 5p

p = 12

substitute the value of p in eq 3

d = 43 - 2(12)

d = 43 - 24

d = 19

Answer: a. [tex]f(x)=3^{x}[/tex]

Step-by-step explanation:

You can plug in the x and y values to get [tex]f(x)=3^{x}[/tex]

Answer:16

Step-by-step explanation:

144^0.5 = 12

400^0.5 = 20

a^2=b^2+c^2

20^2 = 12^2 +x^2

x^2 = 400-144= 256

x =16

Answer:

16

Step-by-step explanation:

Answer:

i need points sorry

Step-by-step explanation:

Answer:

x = 90 degrees

y = 50 degrees

Step-by-step explanation:

The angle where x lies is a right angle, and right angles = 90 degrees. A triangle adds up to 180 degrees, so you add 90 and 40 together and then subtract that from 180 degrees.

Answer:

x ≈ 35.6

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos16° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{37}[/tex] ( multiply both sides by 37 )

37 × cos16° = x , then

x ≈ 35.6 ( to the nearest tenth )

Answer:

x = -4

Step-by-step explanation:

Simplifying

2[x + 4] = 2[-8 + -1x] + -2x

Reorder the terms:

2[4 + x] = 2[-8 + -1x] + -2x

[4 * 2 + x * 2] = 2[-8 + -1x] + -2x

[8 + 2x] = 2[-8 + -1x] + -2x

8 + 2x = [-8 * 2 + -1x * 2] + -2x

8 + 2x = [-16 + -2x] + -2x

Combine like terms: -2x + -2x = -4x

8 + 2x = -16 + -4x

Solving

8 + 2x = -16 + -4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4x' to each side of the equation.

8 + 2x + 4x = -16 + -4x + 4x

Combine like terms: 2x + 4x = 6x

8 + 6x = -16 + -4x + 4x

Combine like terms: -4x + 4x = 0

8 + 6x = -16 + 0

8 + 6x = -16

Add '-8' to each side of the equation.

8 + -8 + 6x = -16 + -8

Combine like terms: 8 + -8 = 0

0 + 6x = -16 + -8

6x = -16 + -8

Combine like terms: -16 + -8 = -24

6x = -24

Divide each side by '6'.

x = -4

Simplifying

x = -4

2( x + 4) = 2 (-8 -x) -2x

Use the distributive property to multiply 2 by x + 4.

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

Use the distributive property to multiply 2 by -8 -x.

2x + 8 = -16 -2x - 2x

Combine -2x and 2x to get -4x.

2x + 8 = -16 - 4x

Add 4x to both sides.

2x + 8 + 4x = -16

Combine 2x and 4x to get 6x.

6x + 8 = -16

Subtract 8 from both sides.

6x = -16 - 8

Subtract 8 from -16 to get -24.

6x = -24

Divide both sides from 6.

x = [tex]\frac{-24}{6}[/tex]

Divide by -24 by 6 to get -4.

x = -4.

Answer:

1.6 hrs remaining, or 3.12 km/h

Step-by-step explanation:

Answer:

210

Step-by-step explanation:

so first i found out how many shirts each prints in a minute

the first machine produced 15/min

the second produced 20/min

now I added the 2 together and got 35

7,350/35 is 210

Answer:

49

Step-by-step explanation:

make an equation:

5/7x=35

x=35*7/5

x=7*7

x=49

x is the total amount

The interval which is horizontal and has a slope of zero shows no distance was covered while time kept increasing, therefore, the interval that shows Kendra stopping to tie her shoes and stretch is: C.

Recall:

Given the graph showing Kendra's morning run, where time running is plotted on the horizontal axis (x-axis) while distance run is plotted on the vertical axis (y-axis).

Learn more about horizontal graphs on:

https://brainly.com/question/13483111

Answer: 65.11%

Step-by-step explanation:

Answer:

67-63x

Step-by-step explanation:

Two units down, line of symmetry at x=0, decreasing from negative infinity to 0, increasing from 0 to infinity

z²-2i=0

Answer:

Solution given:

z⁴=-4

doing square root on both side

[tex]\sqrt{z⁴}=\sqrt{2²*-1}[/tex]

we know i²=-1

substituting i² we get

z²=[tex]\sqrt{2²*i²}[/tex]

z²=2i

z²-2i=0 is a required answer. where

z² and 2 is real number.

Answer:

  z = {-1 -i, -1 +i, 1 -i, 1 +i}

Step-by-step explanation:

Using Euler's formula, we can write the equation as ...

  z^4 = 4e^(i(π +2πn)) . . . . . . where n is any integer

Then the 4th root is ...

  z = (√2)e^(i(π +2πn)/4 = (√2)e^(i(π/4 +nπ/2)) . . . . . for n = 0–3

  z = √2(cos(π/4+nπ/2) +i·sin(π/4 +nπ/2)) . . . . . for n = 0–3

  z = ±1 ±i

  z = {1 +i, -1 +i, -1 -i, 1 -i}

_____

Additional comment

Values of n are only needed in the range 0–3, because the answers repeat for values other than those.

Answer:

Step-by-step explanation:

For a given function f(x), we define the domain as the set of the possible inputs of the function and the range as the set of the outputs of the function.

We will see that both domain and range are the set of all real numbers.

D = (-∞, ∞)

R = (-∞, ∞)

Here we have the function:

The first thing we need to do is find the domain.

We start by assuming that the domain is the set of all real numbers and then we try to find some given values of x that cause some undefined operation, and then we remove these values of x from the domain.

Where this would be something like a zero in the denominator or something like that. We also could have specific restrictions to the domain that are applied in some specific cases (for example if x represents a length we should remove the negative values from the domain).

Here we can see that we do not have any indetermination, thus the domain is the set of all real numbers.

Now to study the range we need to see the general function, we can see that as x tends to negative infinity y will also tend to negative infinity, while when x tends to infinity y will also tend to infinity.

Then the range will also be the set of all real numbers.

Answer:

(1,1)

Step-by-step explanation:

Same thing as before!

First, we can get rid of d(x) simply by looking at it because we can tell it's linear (it's a straight line). If we look at the table, we can see a(x) is also linear because it has a steady rate of growth. b(x) and c(x) both represent exponential growth. The curved shape of b(x) shows us this is exponential growth, and the exponent in c(x) tells us it's also exponential.

Answer:

First number is -2.5

Second number 5

Step-by-step explanation:

Four times the first number minus three times the second number is 2.

To represent this statement, 4x -3y =2

Two times the first number increased by three times the second is 10.

To represent thsi statement, 2x+ 3y = 10

4x - 3y = 2

2x + 3y =10

4x - 2x = 2x

2x = -5

x= -2.5

The first number is -2.5

By using Substitution

2x + 3y = 10

2(-2.5) + 3y = 10

-5 + 3y = 10

3y = 10 +5

3y =15

y = 5

The second number is 5

....To check my answer

-5 + 15 = 10

Answer:

undefined

Step-by-step explanation:

Slope = y - y / x - x

9 - (-1) / -7 - (-7)

= 9 + 1 / -7 + 7

= 10 / 0, undefined.

Cannot divide by zero.

Answer: 25 students per teacher and 12 students per tutor. They need 2.4 tutors for the school

Answer:

3. x=14° y=7

4. x=29° y=3

Step-by-step explanation:

3. this is a 45 - 45- 90 triangle

so the side is a-a-a√2 ( two sides are the same)

4y-3=10+2y+1 -- collect like terms

4y-2y=10+1+3

2y=14

y=7

find the angle of the inside triangle

180-59-90 =

31°

we know the big triangle was a 45-45-90 angle

so x+31=45

x=45-31

x=14°

4. this is a square, all sides are same

5y+3y=24

8y=24

y=3

angle is 90°

x+x+9y+5=90

we know y=3 --substitute

x+x+9(3)+5=90

2x+27+5=90

2x=90-27-5

2x=58

x=58/2

x=29

Answer:

boom bam bam boom bam ba

Answer:

Y intercept = (0,-6)

X intercept = (9,0)

Step-by-step explanation:

To find the y-intercept of an equation, let x = 0 and then solve for y

6(0) - 9y = 54 (6 times 0 gives us 0)

0 - 9y = 54 (subtract 9y from 0 gives you -9)

-9y = 54 (divide both sides by -9, the left side cancels out and the right side gives you -6)

y = -6 and x = 0

To find the x-intercept of the equation just let y = 0 and then solve for x

6x - 9(0) = 54 (9 times 0 gives us 0)

6x - 0 = 54 (subtract 0 from 6x gives us 6x)

6x = 54 (divide both sides by 6, left side cancels, right side gives 9)

x = 9 and y = 0