The point (7, 8) is the solution of which of the following systems of equations?

1. 8x - y = 48
9x + 10y = 142

2. 9x - y = 55
8x + 10y = 140

3. x-6y=-41
8x + 9y = 127

4. x-7y=-49
10x + 9y = 142

Answer:

39

Step-by-step explanation:

1. (2(4)-5)(2(4)+5)

2.(3)(13)

3.39

Answer:

Step-by-step explanation:

This is a difference of squares question. You should 64 = 25 = 39 Let's see if that happens.

Difference of squares

(2x - y) ( 2x + y) = 4x^2 - y^2

4(4)^2 - (5)^2

64 - 25 = 39

Now do the question exactly as it is written.

(2*4 - -5)(2*4 + -5)

(8 +5)(8 - 5)

3 * 13

39

They really do give the same answer.

(a) The n-th partial sum of the infinite series,

[tex]\displaystyle\sum_{n=0}^\infty\frac5{4^n}[/tex]

is

[tex]S_n = \displaystyle\sum_{k=0}^n\frac5{4^k} = 5\left(1+\frac14+\frac1{4^2}+\cdots+\frac1{4^n}\right)[/tex]

Multiplying both sides by 1/4 gives

[tex]\dfrac14S_n = \displaystyle\sum_{k=0}^n\frac5{4^k} = 5\left(\frac14+\frac1{4^2}+\frac1{4^3}+\cdots+\frac1{4^{n+1}}\right)[/tex]

Subtract this from [tex]S_n[/tex] and solve for [tex]S_n[/tex] :

[tex]S_n-\dfrac14S_n = 5\left(1-\dfrac1{4^{n+1}}\right)[/tex]

[tex]\dfrac34 S_n = 5\left(1-\dfrac1{4^{n+1}}\right)[/tex]

[tex]S_n = \dfrac{20}3\left(1-\dfrac1{4^{n+1}}\right)[/tex]

(your solution is also correct)

(b) The infinite sum is equal to the limit of the n-th partial sum:

[tex]\displaystyle\sum_{n=0}^\infty \frac5{4^n} = \lim_{n\to\infty} \boxed{\sum_{k=0}^n \frac5{4^k}}[/tex]

and the sum indeed converges to 20/3.

Answer:

B 3360

Step-by-step explanation:

Area of Rectangle = Length X Width

120 X 28

= 3360 cm

Answered by Gauthmath

Given:

The given expression is:

[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]

It can be written as:

[tex]=(3.5+2.3)\times 10^{-2}[/tex]

[tex]=5.8\times 10^{-2}[/tex]

Therefore, the simplified form of the given expression is [tex]5.8\times 10^{-2}[/tex].

Answer:  (4, -2)  which is choice A

Explanation:

The rule I used is [tex](x,y) \to (-x,-y)[/tex]

Simply swap the sign of each x and y coordinate to go from (-4, 2) to (4, -2)

This rule only works for 180 degree rotations. It doesn't matter if you go clockwise or counterclockwise.

Answer:

Step-by-step explanation:

Answer:

230

Step-by-step explanation:

50: 2

9.2: x

therefore x = 50*9.2 /2 = 230

i think

9514 1404 393

Answer:

   5/9 m/min

Step-by-step explanation:

The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:

  2/5 × 2 m = 4/5 m

Then the surface area of the water is ...

  A = LW = (18 m)(4/5 m) = 14.4 m²

The rate of change of height multiplied by the area gives the rate of change of volume:

  8 m³/min = (14.4 m²)(h')

  h' = (8 m³/min)/(14.4 m²) = 5/9 m/min

Step-by-step explanation:

Count the number of times you have to move the decimal point to the right until it is to the right of the 1st nonzero number.

a) You have to move the decimal point 11 times until it gets to the right of the 1st nonzero number, which is 7. You then rewrite this number as

[tex]7.2×10^{-11}[/tex]

The exponent of 10 is a negative number because you moved the decimal point to the right.

b) Similarly, you have to move the point 9 times to the right so the answer is

[tex]9.5×10^{-9}[/tex]

Answer:

1640

Step-by-step explanation:

Take the total amount and divide by the amount for one

Make sure to write 6 cent in dollar form (.06)

98.41 / .06

1640.1666

Round down since we need to buy whole bottles

1640

Step-by-step explanation:

you're going to have to set up two expressions since it's an absolute value problem

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the function is not given. So, I will make an assumption.

A quadratic function is represented as:

[tex]f(x) = ax^2 + bx + c[/tex]

If [tex]a > 0[/tex], then the function has a minimum x value

E.g. [tex]f(x) = 4x^2 - 5x + 8[/tex] ------ [tex]4 > 0[/tex]

Else, then the function has a maximum x value

E.g. [tex]f(x)= -4x^2 -5x + 8[/tex] ---- [tex]-4 < 0[/tex]

The maximum or minimum x value is calculated using:

[tex]x = -\frac{b}{2a}[/tex]

For instance, the maximum of [tex]f(x)= -4x^2 -5x + 8[/tex] is:

[tex]x = -\frac{-5}{2*-4}[/tex]

[tex]x = -\frac{5}{8}[/tex]

So, the maximum of the function is:

[tex]f(x)= -4x^2 -5x + 8[/tex]

[tex]f(-\frac{5}{8}) = -4 * (-\frac{5}{8})^2 - 5 *(-\frac{5}{8}) +8[/tex]

[tex]f(-\frac{5}{8}) = 9.5625[/tex]

Answer:

she will be using more orange juice

Answer:

she will be using more orange juice

Answer:

60

Step-by-step explanation:

x = 180 - [ 57 + ( 180 - 117 ) ]

= 180 - [ 57 + 63 ]

= 180 - 120

x = 60

Answer:

81 pi cm^2

or approximately 254.34 cm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi (9)^2

A = 81 pi

Using 3.14 as an approximation for pi

A = 81 (3.14)

A =254.34 cm^2

Answer:

81pi cm^2

Step-by-step explanation:

formula : pi*r^2

pi*9^2

pi*81

Answer:

Area of ΔPQR is 28 units²

Step-by-step explanation:

-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)

-rearrange the equation in the point-slope form y=mx+b  to find the y coordinate of the point P( 0, b)

x-2y+2 = 0, subtract x and 2 from both sides

-2y = -x-2, divide by -2 both sides

y= (1/2)x +1 so b=1 and P (0, 1)

-Q  is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)

-rearrange the equation in the point-slope form y=mx+b  to find the y coordinate of the point Q( 0, b)

3x +y -15 =0, subtract 3x and add 15 to both sides

y= -3x +15 so b=15 and Q(0,15)

-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15

(1/2)x +1 =  -3x +15, add 3x and subtract1

(1/2) x+3x = 15-1, combine like terms

(7/2)x = 14 , multiply both sides by 2

7x = 28, divide both sides by 7

x= 4

y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)

- the area of ΔPQR is (base *height)/2

base= 15-1= 14

height = 4

A= (14*4)/2 = 14*2 = 28

Answer:

12

Step-by-step explanation:

arrange the numbers in ascending order and cross out from either side till you have a middle line

FINAL ANSWER:

12

Step-by-step explanation:

Median is the middle number in the data set.

so first of ... we need to arrange the group of numbers from lower to greater.

16, 12, 10, 15, 7, 9, 16 ⇒ 7, 9, 10, 12, 15, 16, 16

Now that we have arranged the numbers from least to greatest all we need to do is to find the middle number of the data set (data set? they are the group of numbers)

Ok, so what you want to do here is to just count the numbers until you get to the middle number of the data set...

7, 9, 10, 12, 15, 16, 16

the median in the given data set is 12.

I hope this helps you!!! Let me know if my answer is incorrect or not...

HAVE A GREAT DAY AND GOD BLESS YOU ;)!!!

Answer:

The image shows the graph of y = 2 tan x.

Answer:

The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.

Step-by-step explanation:

We are given these following probabilities:

[tex]P(X = 0) = 0.6591[/tex]

[tex]P(X = 1) = 0.2872[/tex]

[tex]P(X = 2) = 0.0503[/tex]

[tex]P(X = 3) = 0.0044[/tex]

[tex]P(X = 4) = 0.0015[/tex]

Determine whether a probability distribution is given.

We have to see if the sum of the probabilities of all possible outcomes is 1. So

[tex]0.6591 + 0.2872 + 0.0503 + 0.0044 + 0.0015 = 1.0025[/tex]

The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.

Answer:

Range { 2,3,4,5}

Step-by-step explanation:

The range is the output values

Range { 2,3,4,5}

[tex] \sf Q) \: {3}^{3} + {4}^{2} = {?}[/tex]

[tex] \sf \to \: {3}^{3} + {4}^{2} [/tex]

[tex] \sf \to \: 27 + 16= 43 [/tex]

Thus, the value is 43.

Answer:

39

Step-by-step explanation:

5 + 15 + 12 + 7 = 39

Answer:

39

Step-by-step explanation:

5 + 15 = 20, 12 + 7 = 19, 20 + 19 = 39.

Answer:

6x^2-23x+20

Step-by-step explanation:

i think the expanded form of that equation is equal to it.

(3x-4)(2x-5)

3x(2x-5)-4(2x-5)

6x^2-15x-8x+20

6x^2-23x+20

I hope this helps and sorry if it's wrong

you have to read the bottom link for the answer key

Michael = 210 / 3.5 = 60 miles per hour

Jordan = 330/ 6 =55 miles per hour

Jordan drove 5 miles per hour slower than michael

Answer:

y = 7x - 140

The slope is 7

The y-intersept is -140

= (7, -140)

Step-by-step explanation:

y + 14 = 7(x - 18)

y + 14 = 7x - 126

y =7x - 126 - 14

y = 7x - 140

Answer:

2/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 10 even numbers from 1 to 20

2 4 6 8 10 12 14 16 18 20

There 20 possible choices.

P(Even) = 10 /20 = 1/2

Answer:

[tex]S.E = 0.108[/tex]

Step-by-step explanation:

From the question we are told that:

Mean age [tex]\=x=5.5[/tex]

standard deviation [tex]\sigma= 0.7 years.[/tex]

Sample size [tex]n=43[/tex]

Generally the equation for Standard error is mathematically given by

[tex]S.E= \sigma \bar x[/tex]

[tex]S.E= \frac{\sigma}{\sqrt n}[/tex]

[tex]S.E= \frac{0.7}{\sqrt 43}[/tex]

[tex]S.E = 0.108[/tex]