How do you solve for a²+b²=289 when b+a=23

Answer:

8.9 x 10^3

:D

Step-by-step explanation:

Answer:

D. -17/2

Step-by-step explanation:

1/2 - 4 (1/2 + 1)^2

First we evaluate what is inside the parentheses

1/2 - 4  (3/2) ^2

Now we square what is inside the parentheses

1/2 - 4(9/4)

Now multiply

1/2 -9

Get a common denominator  9 = 9 *2/2 = 18/2

1/2 - 18/2

-17/2

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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[tex]\dfrac{1}{2}-4\left(\dfrac{1}{2}+1\right)^2=\dfrac{1}{2}-4\left(1\dfrac{1}{2}\right)^2=\dfrac{1}{2}-4\left(\dfrac{1\cdot2+1}{2}\right)^2\\\\=\dfrac{1}{2}-4\left(\dfrac{3}{2}\right)^2=\dfrac{1}{2}-4\cdot\dfrac{3^2}{2^2}=\dfrac{1}{2}-4\cdot\dfrac{9}{4}=\dfrac{1}{2}-1\cdot\dfrac{9}{1}\\\\=\dfrac{1}{2}-9=\boxed{-8\dfrac{1}{2}=-\dfrac{8\cdot2+1}{2}=\boxed{-\dfrac{17}{2}}}\to\boxed{D.}[/tex]

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\-------------------------\\\\\text{We have}\ 5x+3y=8\qquad\text{subtract 5x from both sides}\\\\3y=-5x+8\qquad\text{divide both sides by 3}\\\\y=-\dfrac{5}{3}x+\dfrac{8}{3}\to m_1=-\dfrac{5}{3}\\\\\text{Therefore}\ m_2=-\dfrac{1}{-\frac{5}{3}}=\dfrac{3}{5}\\\\Answer:\ \boxed{b.\ \dfrac{3}{5}}[/tex]

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[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\\text{We have}\ 3x-5y=10\qquad\text{subtract 3x from both sides}\\\\-5y=-3x+10\qquad\text{divide both sides by (-5)}\\\\y=\dfrac{3}{5}x-2\to m_1=\dfrac{3}{5}\\\\\text{Therefore we have}\ m_2=\dfrac{3}{5}.\\\\Answer:\ \boxed{D.\ y=\dfrac{3}{5}x}[/tex]

Answer:

Answer Left Panel: 3/5 or B

Answer Right Panel: D

Step-by-step explanation:

Left Panel

Right Panel

The slope of a line parallel to another line is the same as the given line.

Answer: 42 inch 16:9 television

Step-by-step explanation:

The dimensions of 42 inch 16:9 television are:

Width of the television = 36.6 inches

Height of the television = 20.6 inches

Screen Area of the television = 36.6 x 20.6 = 753.96 sq inches

The dimensions of 32 inch 4:3 television are:

Width of the television = 25.6 nches

Height of the television = 19.2 inches

Screen Area of the television = 25.6 x 19.2 = 491.52 sq inches

Thus 42 inches 16:9 television has 262.44 square inches more screen area.

Hope it helps.

Thanks you :)

[tex]\text{Look at the picture.}[/tex]

[tex]x, y - some\ units\ of\ leng th[/tex]

[tex]\text{Use the Pythagorean theorem:}[/tex]

[tex](16x)^2+(9x)^2=42^2\\\\256x^2+81x^2=1764\\\\337x^2=1764\qquad\text{divide both sides by 337}\\\\x^2=\dfrac{1764}{337}\to x=\sqrt{\dfrac{1764}{337}}[/tex]

[tex]\text{The area:}\\\\A_1=16\sqrt{\dfrac{1764}{337}}\cdot9\sqrt{\dfrac{1764}{337}}=(16)(9)\left(\sqrt{\dfrac{1764}{337}}\right)^2\\\\=144\cdot\dfrac{1764}{337}\approx754\ in^2[/tex]

[tex](4x)^2+(3x)^2=32^2\\\\16x^2+9x^2=1024\\\\25x^2=1024\qquad\text{divide both sides by 25}\\\\x^2=40.96\to x=\sqrt{40.96}\to x=6.4\ in\\\\\text{The area:}\\\\A_2=4(6.4)\cdot3(6.4)=25.6\cdot19.2=491.52\ in^2[/tex]

[tex]754 > 491.52[/tex]

Answer:

distance = 427.5 miles

Step-by-step explanation:

We can determine the distance by multiplying the miles per gallon by the number of gallons.

distance = mpg * gallons

distance = 28.5 mpg * 15 gallons

distance = 427.5 miles

Answer:

427.5 miles of gas

Step-by-step explanation:

This problem will require using multiplication to determine the distance in total.

We can multiply amount of gas car can hold times the miles per gallon to find the total distance.

Create an equation.

amount of gas car can hold * miles per gallon = distance

Solve by inputting numbers.

15 * 28.5 = 427.5

Answer:

F(-1/2)= 5 1/3

Step-by-step explanation:

-1/2 X -2/3 = 1/3 because the two negatives cancle out. 1/3 + 5=

5 and 1/3.

Answer:

5 1/3

Step-by-step explanation:

For this case, we must indicate which of the given functions is not defined for[tex]x = 0[/tex]

By definition, we know that:

[tex]f (x) = \sqrt {x}[/tex] has a domain from 0 to infinity.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. For it to be defined, the term within the root must be positive.

Thus, we observe that:

[tex]y = \sqrt {x-2}[/tex] is not defined, the term inside the root is negative when [tex]x = 0[/tex].

While [tex]y = \sqrt {x + 2}[/tex] if it is defined for [tex]x = 0.[/tex]

[tex]f(x)=\sqrt[3]{x}[/tex], your domain is given by all real numbers.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. In the same way, its domain will be given by the real numbers, independently of the sign of the term inside the root.

So, we have:

[tex]y = \sqrt [3] {x-2}[/tex] with x = 0: [tex]y = \sqrt [3] {- 2}[/tex] is defined.

[tex]y = \sqrt [3] {x + 2}[/tex]with x = 0: [tex]y = \sqrt [3] {2}[/tex]in the same way is defined.

Answer:

[tex]y = \sqrt {x-2}[/tex]

Option b

The function that are undefined for (x=0) is  [tex]y = \sqrt[3]{x-2}[/tex] and [tex]y = \sqrt{x-2}[/tex] and this can be determined by putting (x=0) in all the given expressions.

Given :

Function 1 - [tex]y = \sqrt[3]{x-2}[/tex]

Function 2 - [tex]y = \sqrt{x-2}[/tex]

Function 3 - [tex]y = \sqrt[3]{x+2}[/tex]

Function 4 - [tex]y = \sqrt{x+2}[/tex]

Evaluate each function at (x = 0) to determine which function is undefined for (x = 0).

Function 1 - [tex]y = \sqrt[3]{x-2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt[3]{-2}[/tex]

Therefore, it can be concluded that the above function is not defined for (x=0).

Function 2 - [tex]y = \sqrt{x-2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt{-2}[/tex]

Therefore, it can be concluded that the above function is not defined for (x=0).

Function 3 - [tex]y = \sqrt[3]{x+2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt[3]{2}[/tex]

Therefore, it can be concluded that the above function is defined for (x=0).

Function 4 - [tex]y = \sqrt{x+2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt{2}[/tex]

Therefore, it can be concluded that the above function is defined for (x=0).

For more information, refer to the link given below:

https://brainly.com/question/2263981

Given

Step 1: They multiplied 3 on both sides of the equation to get rid of the denominator (you can do this because the denominators were the same number, which was 3)

Step 2: They distributed 6 into (x + 2)

Step 3: They added 1 on both sides

Step 4: They subtracted 6x on both sides to get "x" on one side of the equation

Step 5: They divided -4 on both sides to get "x" by itself

6 cupcakes is 1/4 of 24 ( 24 / 6 = 4).

This means you would need 1/4 the amount of flour.

Divide the amount needed for 24 cups by 4:

15.25 / 4 = 3.8125

Round answer as needed.

Answer:

3.8125 (108g) of flour are required

Step-by-step explanation:

We can use ratio's to solve this problem

432 g                 x  g

------------     =   -----------

24 cupcakes    6 cupcakes

Using cross products

432*6 = 24x

Divide each side by 24

432*6/24 = 24x/24

108 =x

108 grams

If we needed to use 15.25  units? instead

15.25                 x  

------------     =   -----------

24 cupcakes    6 cupcakes

15.25 * 6 = 24x

Dividing by 24 on each side

15.25 *6/24 = 24x/24

3.8125 =x

Answer:

$300

Step-by-step explanation:

Let Dave's saving be D and Sam's savings be S

[tex]\frac{D}{S}=\frac{5}{4}\\4D=5S\\\frac{4}{5}D=S[/tex]

So we subtract 40 from each of them and then the ratio becomes 13 is to 10. Hence we can write:

[tex]\frac{D-40}{S-40}=\frac{13}{10}\\10(D-40)=13(S-40)\\10D-400=13S-520\\-400+520=13S-10D\\120=13S-10D[/tex]

Plugging in [tex]\frac{4}{5}D[/tex] into S (as we found earlier), we can solve for D (our answer):

[tex]120=13S-10D\\120=13(\frac{4}{5}D)-10D\\120=\frac{52}{5}D-10D\\120=\frac{2}{5}D\\D=\frac{120}{\frac{2}{5}}=120*\frac{5}{2}=300[/tex]

So, Dave's savings at first, D, is $300.

Answer:

9%

Step-by-step explanation:

1/11 students

1 divided by 11

=0.09090909090909

to convert the decimal to a percentage, multiply 100 to .09

9%

Answer:

1.0

Step-by-step explanation:

The answer is 1.0 It is not a tenth but 99 is closer to 100. witch is 1.0 Do you try looking it up. This is a site i used. It is great. It is called calculator soup.

Answer:

3216.99

Step-by-step explanation:

A = 4 [tex]\pi[/tex] [tex]r^{2}[/tex]

d = 2r

A =[tex]\pi[/tex] [tex]d^{2}[/tex]

= [tex]\pi[/tex] * 32^2 = 3216.99  

Answer:

The range could be written in inequality form will be [tex]-2500\leq x\leq -100[/tex].

Step-by-step explanation:

Slitsnails live in the deep water. It is given that they live between a depth of 100 ft to 2500 ft.

Let [tex]x[/tex] represents the depth of water from the water surface.

As we go down the water, the depth will be negative.

So, the depth could vary from 100 ft to 2500 ft.

The minimum depth should be 100 ft and the maximum depth is 2500 ft.

Thus, the range could be written in inequality form as,

[tex]-2500\leq x\leq -100[/tex]

In a graph, the inequality can be shown as,

For more details, refer the link:

https://brainly.com/question/15137133?referrer=searchResults

The inequality representing the range of elevations for Slitsnails is x ≥ 100 and x ≤ 2500. The graph of the inequality shows the range on a number line.

The range of elevations for Slitsnails is from 100ft to 2500ft. To write an inequality, we'll use the variable x to represent the elevation. The inequality can be written as:

x ≥ 100 and x ≤ 2500

To graph this inequality, we'll plot the values on a number line. We'll start at 100 and draw a closed circle to represent that the value is included in the range. Then, we'll draw an arrow to the right to show that the values continue up to 2500, but do not include 2500. The graph will look like:

https://brainly.com/question/11815755

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Final answer:

By applying the given formula d = sqrt(3h/2), we find that Addison can see 2.82 miles farther to the horizon than Kaylib, based on their eye-level heights above sea level.

Explanation:

The question asks how much farther Addison can see to the horizon compared to Kaylib based on their different eye-level heights above sea level, using the formula d = sqrt(3h/2). To solve this, we need to first calculate the distance each person can see to the horizon and then find the difference between the two distances.

Let's calculate the distance for Kaylib:
h = 48 ft, so d = sqrt(3 * 48 / 2) = sqrt(72) = 8.49 miles.

Now let's calculate the distance for Addison:
h = 85¹⁄₃ ft, which we convert to a decimal: 85.333 ft, so d = sqrt(3 * 85.333 / 2) = sqrt(128) = 11.31 miles.

The difference between Addison's horizon and Kaylib's is 11.31 miles - 8.49 miles = 2.82 miles.

Addison can see 2.82 miles farther to the horizon than Kaylib.

Answer: B

Step-by-step explanation:

Answer:

nooooooooooooooooooo

Step-by-step explanation:

if you divide -2 by 6, you get -0.3333333333... and since their negative -2/6 is a bigger number because -0.397 goes more left on the x axis.

Its geometric as you are multiplying by -3 each time

Answer:

Step-by-step explanation:

If we pay attention to the sequence, we would observe that [tex]f(n)[/tex] is increasing by a reason of [tex]-3[/tex], because

[tex]12(-3)=-36\\-36(-3)=108\\108(-3)=-324\\-324(-3)=972[/tex]

So, basically, each term is being multiplied by [tex]-3[/tex], that's what makes the sequence, which is a geometric sequence, because it's being built by a factor, that is, a number which multiplies each term.

When you have to deduct if you have a arithmetic sequence or a geometric sequence, you need to observe if such sequence is increasing or decreasing faster. Like this case, you can see that the numbers are increasing rapidly, that means it's built based on a factor, not a difference, because when we use a difference to form a sequence, that will grow slower and it would be an arithmetic sequence.

Therefore, the given sequence is geometric, which reason is -3.

Answer:

a progression is a summation of quantities based upon a sequence.

Step-by-step explanation:

example of a progression

1,4,7,10,13,16,.........

a1=1

a2=4

a3=7

difference =d=a2-aq=4-1=3

similarly

d=a3-a2=7-4=3

we can clearly see that there is a difference of 3 between two consecutive terms of a progression

on the other hand successive terms of a progression can be obtained by adding a unique value in backward term to get successive term.

hence a progression is   a summation of quantities based upon a sequence

Answer:

A summation of quantities based upon a sequence, and an arrangement of quantities whose positions are based upon the natural numbers

Step-by-step explanation:

It cannot be "Any list of numbers" because a progression only contains natural numbers, meaning no decimals or fractions. It is also not a new discovery in mathematics.  

Answer:

The slope of the line is 3/4

Step-by-step explanation:

There is a difference of 3 in the y coordinate and 4 for the x coordinate from each exact point.

Answer:

[tex]a_n=A(n)=3n+3.[/tex]

Step-by-step explanation:

You are given recursive formula [tex]A(n)=A(n-1)+3,[/tex] where [tex]A(1)=6.[/tex]

Find some terms of the sequence:

[tex]a_1=A(1)=6,\\ \\a_2=A(2)=A(1)+3=6+3=9,\\ \\a_3=A(3)=A(2)+3=9+3=12,\\ \\a_4=A(4)=A(3)+3=12+3=15,...[/tex]

You van see that these terms form the arithmetic sequence with first term [tex]a_1=6[/tex] and difference [tex]d=3.[/tex]

An explicit formula for n-th term of arithmetic sequence is

[tex]a_n=a_1+(n-1)d.[/tex]

In your case,

[tex]a_n=6+(n-1)\cdot 3,\\ \\a_n=6+3n-3,\\ \\a_n=3n+3.[/tex]

Answer:

-16x^9z^12

Step-by-step explanation:

you . multiply the exponents with the three in this type of equation.

Answer: choice B) 70 degrees

Minor arc AB is equal in measure to the central angle BPA, which cuts off the arc in question.

Answer:

-35%  

Step-by-step explanation:

To solve this equation, the first thing we have to do is to convert percentages to decimals because we are doing mathematical operations with a fraction.

To convert a percentage to a decimal, we just divide by 100. So, 60% equals 0.60, and 25% equals 0.25.

Next, we subtract these values from 1/2.

So, we have the following steps:

1. Calculate 1/2 - 0.60 (which is the decimal equivalent of 60%). This gives us -0.10.

2. Then subtract 0.25 (which is the decimal equivalent of 25%) from the result. So, -0.10 - 0.25 equals -0.35.

Therefore, 1/2 - 60% - 25% equals -0.35.

Answer:

how much did the stuff cost to rent per hour

Answer:

Step-by-step explanation:

9y + 6 = 9 + 2y + 2y

9y + 6 = 9 + (2y + 2y)

9y + 6 = 9 + 4y      subtract 6 from both sides

9y = 3 + 4y     subtract 4y from both sides

Answer:

5y = 3

Step-by-step explanation:

9y + 6 = 9 + 2y + 2y

9y + 6 = 9 + (2y + 2y)

9y + 6 = 9 + 4y      subtract 6 from both sides

9y = 3 + 4y     subtract 4y from both sides

5y = 3

Answer:

The perimeter is 22.

Step-by-step explanation:

If you turn this shape into a rectangle, the perimeter doesn't change.

The width is given, it is 7.5. The height is BC+DE = 3.5

Then the perimeter is twice the width plus twice the height:

7.5*2 + 3.5*2 = 15+7 = 22

Answer: The length is 10ft, the width is 7ft.

Step-by-step explanation:

Let L be the length

Let w be the width

The equation for the perimeter is:

2L+2w=34

We also know that L=2w-4

So we can insert L=2w-4 into 2L+2w=34

2(2w-4)+2w=34

4w-8+2w=34

6w=42

w=7

If the width is 7, we can insert it into 2L+2w=34 to find out the length

2L+14=34

2L=20

L=10

The width is 7 ft, the length is 10 ft.

The length and width of the rectangle are 10 feet and 7 feet respectively. This is determined by setting up and solving equations based on the given information about the relationship between the length and width and the perimeter of the rectangle.

Given that the length (L) of the rectangle is 4 less than twice the width (W), we can represent this as:

L = 2W - 4

. We also know that the perimeter (P) of the rectangle is 34 feet. The formula for the perimeter of a rectangle is

P = 2L + 2W

. Substituting L in the perimeter equation gives

P = 2(2W - 4) + 2W = 34

. Simplifying the equation leads to

4W - 8 + 2W = 34

, and then

6W = 42

when you add 8 to both sides. Solving for W gives

W = 7 feet

. Substituting W = 7 into the length equation gives

L = 2(7) - 4 = 10 feet

. Therefore, the width and length of the rectangle are 7 feet and 10 feet respectively.

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Subtract the cost of the pencils from the total cost. This will be he amount she spent on erasers. Then divide that amount by the cost of each eraser to get the total.

4.25 - 1.75 = 2.50 spent on erasers

2.50 / 0.25 = 10

She bought 10 erasers.