Use the pythagorean theorem to find the distance between from A(5, -3) to B (6,0)

A. 1.43
B.2.18
C. 3.16
D.11.40

Please explain

Answer:

[tex]64=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2=2^6[/tex]

Step-by-step explanation:

Gabrielle and John each

wrote the prime factorization of 64.

64 can be break into 32 times 2

32 can be break into 16 times 2

16 can be break into 8 and 2

8 can be break into 4 times 2

4 can be break into 2 times 2

So 64 is equal to 2 times 2 times 2 times 2 times 2 times 2

[tex]64=2^6[/tex]

The question involves analyzing the prime factorization of the number 64, which should be 2¶. The correctness of Gabrielle and John's factorizations can be checked by ensuring the base is 2 and the power is 6. Any deviation from this would indicate a mistake in their factorization.

The question concerns the prime factorization of the number 64. A prime factorization is the expression of a number as a product of prime numbers. For the number 64, which is a power of 2, the prime factorization should be 2¶ since 64 is 2 multiplied by itself 6 times (2 x 2 x 2 x 2 x 2 x 2).

If Gabrielle and John wrote their prime factorizations of 64 differently, at least one of them has made an error. To verify if their prime factorizations are correct, they should end up with the same base number, which is 2 in this case, raised to the same power, which should be 6 for the number 64. Any other combination of numbers in the factorization would be incorrect, since 64 is not divisible by any other prime numbers.

When analyzing their work, one should check if they thoroughly factored the number down to only prime numbers and did not mistakenly include a composite number or an incorrect exponent in the factorization. To correct errors, divide the number progressively by the prime number 2 until the quotient is 1. Each division step represents an exponent in the prime factorization of 64.

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Answer:

x^7

Step-by-step explanation:

(x^5)(x^2)=x^(5+2)=x^7

Answer:

The value in box of circle B is 3 and the value in box which belongs in both circle B and S is 6 and value which belongs in circle S is 1 and the value of box outside both the circle is 2.

Step-by-step explanation:

In given Venn diagram

ε = class of 12 pupils

pupils who have brother B = 9

pupils who have sister S = 7

pupils who have neither brother nor sister = 2

Hence the Venn diagram is drawn in the attachment for your reference.

n(E) =12

n(neither B nor S) = 2

So, n(B or S)= n(E) - n(neither B nor S)= 12-2=10

n(B) = 9

n(S) = 7

Now, addition theorem,

n(B or S) = n(B) + n(S) - n(B and S)

[tex]10=9+7-n(B\ and \ S)\\n(B\ and \ S) = 6[/tex]

So the value in box which is in both circle B and S is 6.

So the Box which contains only brothers = n(B) - n(B and S)  = 9 - 6 = 3

Value in box of circle B is 3.

So the Box which contains only Sisters = n(S) - n(B and S)  = 7 - 6 = 1

Value in box of circle S is 1.

There are 12 pupils in a class so, the number of pupils having both brother and sisters are 6 and the pupils had either brother or sister are 10.

Given :

Given that there are pupils in a class that is, n(E) = 12

Pupils who have brother, n(B) = 9

Pupils who have sister, n(S) = 7

Pupils who have neither brother nor sister, n(neither B nor S) = 2

So,  n(B or S) = n(E) - n(neither B nor S)

                      = 12 - 2 = 10

n(B or S) = 10

Now, through the addition theorem:

n(B or S) = n(B) + n(S) - n(B and S)

10 = 9 + 7 - n(B and S)

n(B and S) = 6

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Mr. Jackson invested $800 at 6% per year and $ 2400  at 4 % per year

Mr. Jackson invested a sum of money at 6% per year, and 3 times as much at 4% per year.

Let the sum invested be ‘a’ and ‘3a’ at 6% per year and 4 % per year respectively

Also, his annual return totaled $144

We can form following equation on the basis of question:-

[tex]\begin{array}{l}{\text { Then, } \frac{a \times 6 \times 1}{100}+\frac{3 a \times 4 \times 1}{100}=\$ 144} \\\\ {\frac{6 a}{100}+\frac{12 a}{100}=144} \\\\ {\frac{6 a+12 a}{100}=144} \\\\ {\frac{18 a}{100}=144} \\\\ {18 a=14400} \\\\ {a=14400 \div 18}\end{array}[/tex]

a = $800

The amount of money invested at 6% = a = 800

The amount of money invested at 4 % = 3a = 3(800) = 2400

So, the amount of money invested at 6% is $800 and the amount of money invested at 4% is $ 2400

To determine the amounts Mr. Jackson invested, the problem was solved by setting up a simple equation and solving for x, which represents the amount at 6% interest. Mr. Jackson invested $800 at 6% and $2400 at 4% to receive a total annual return of $144.

The question involves solving a system of linear equations to find how much Mr. Jackson invested at two different interest rates if his total annual return is $144. To solve the problem, let's define the amount invested at 6% per year as x and the amount invested at 4% as 3x, since the latter is three times as much.

The interest from the investment at 6% would be 0.06x, and the interest from the investment at 4% would be 0.04 × 3x. Since these add up to $144, we can write the equation:

0.06x + 0.04 × 3x = 144

Solving this equation:

Since x represents the amount at 6%, Mr. Jackson invested $800 at 6% and $2400 at 4% because the investment at 4% is three times as much.

The perimeter of given rectangle can be given by: [tex]14x-6[/tex]

Step-by-step explanation:

Let

L be the width of the rectangle and

W be the width of the rectangle

Here,

L = 6x-2

W=x-1

The perimeter of rectangle is given by:

[tex]P=2(L+W)[/tex]

Putting the values of L and W

[tex]P=2[(6x-2)+(x-1)]\\=2(6x-2+x-1)\\=2(7x-3)\\=14x-6[/tex]

The perimeter of given rectangle can be given by: [tex]14x-6[/tex]

Keywords: Rectangle, Perimeter

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Answer:

grab a ruler and put the 0 on the inches side up to the R and she what it's at when it hits S and do it again at T

Answer:

C

Step-by-step explanation:

THe markup is the difference between the Selling Price and Cost.

As a percentage, we would get the markup in terms of cost.

First,

Selling Price = 4.50

Cost = 3.00

So,

Markup = SP - Cost = 4.50 - 3.00 = 1.50

As a percentage, we would divide the markup by cost and then multiply the answer by 100. That's:

1.50/3 = 0.5 * 100 = 50%

THe markup is 50%

C is the correct answer.

Answer:

C

Step-by-step explanation:

The markup is the difference between the Selling Price and Cost.

As a percentage, we would get the markup in terms of cost.

First,

Selling Price = 4.50

Cost = 3.00

So,

Markup = SP - Cost = 4.50 - 3.00 = 1.50

As a percentage, we would divide the markup by cost and then multiply the answer by 100. That's:

1.50/3 = 0.5 * 100 = 50%

The markup is 50%

C is the correct answer.

Answer: 5:37

Step-by-step explanation:

The answer is d/5:37pm

Step-by-step explanation:

2:07+2:30=4:37

Cheyenne is 1 he ahead

4:37+1:00=5:37

Answer:

A= 24 ounces and B= 36 ounces.

Step-by-step explanation:

Given: Solution A contain 30% salt= 0.30 salt.

           Solution B contain 55% salt= 0.55 salt.

           New mixture should be of 60 ounces with 45% salt.

Let x be the amount of mixture for solution A. Let y be the amount of mixture of solution B.

Scientist need to to obtain 60 ounce of mixture from solution A and B.

∴ [tex]x+y= 60\ ounces[/tex]

y= [tex]60-x[/tex]         equation 1

Now, solving to get final solution.

∴ [tex]0.3x+0.55y=0.45\times 60\ ounces[/tex]

Substituting the value of y from equation 1

⇒ [tex]0.3x+ 0.55\times (60-x)= 27[/tex]

⇒ [tex]0.3x+33-0.55x= 27[/tex]

⇒ [tex]-0.25x= -6[/tex]

∴ x= 24 ounces

Next, finding y

y= 60-x

∴ y= [tex]60-24= 36\ ounces.[/tex]

y= 36 ounces.

Now, we can say scientist would require 24 ounces of solution A and 36 ounces of solution B to obtain mixture of 60 ounces with 45% salt.

Answer:

No

Step-by-step explanation:

-3/0 is actually undefined because dividing by zero is undefined but 0/-3=0 because 0 divided by anything is 0.

Answer:

6.3

Explanation:

To get from 4.5 to 5.4, you need to add 0.9. If you add 0.9 two more times, you get 7.2. Therefore, the middle term should be 6.3. I don't know if you made a typo and forgot the decimal when writing the options cause it says "63", but I believe the answer is 6.3.

Answer:

Nathan's estimate would be greater than the actual product.

Step-by-step explanation:

Let a, b, c, d be natural numbers such that a<c and b<d

Multiplying a positive number on both sides doesn't affect the inequality

⇒a×b < c×b and c×b < c×d

⇒a×b < c×d

Here 67<70 and 36<40

∴67×36<70×40

Hence, Nathan's estimate would be greater than the actual product.          

Answer:

the answer is A 6.1

Step-by-step explanation:

Answer:

6, 7, 8, 9

Step-by-step explanation:

There ya go. The numbers of possible amounts of mangos he could buy without exceeding his budget.

The possible values of mangos if, The cost of peaches is $2, The cost of the mangos is $1.25, and the Total money is $20, are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

A formula known as an equation uses the equals sign to denote the equality of two expressions. In other terms, it is a mathematical statement stating that "this is equivalent to that."

Given:

The cost of peaches =$2,

The cost of the mangos = $1.25,

Total money = $20,

Write the equation, if Henry buys 10 peaches,

10 × 2 + 1.25x = 20

Here, x is the number of mangos,

1.25x =  20 - 20

x = 0

Write the equation when Henry buys 4 peaches,

4 × 2 + 1.25x = 20

8 + 1.25x = 20

x = 20 - 8 / 1.25

x = 9.6 or 9 mangos

Thus, Henry can buy a maximum of 9 mangos if he buys at least 4 peaches.

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Answer:

0.5

Step-by-step explanation:

0.5 x 4 = 2, 2 + 7 = 9

Answer:n=1/2

Step-by-step explanation:

4n+7=9

   -7   -7

4n=2

divide by 4 on both sides

n=1/2

The edge of cube is: 2.5 cm

Step-by-step explanation:

Let V be the volume of cube

V = 15.625 cm^3

Let x be the side of the cube then

[tex]V = x^3\\15.625 = x^3[/tex]

Taking cube root on both sides

[tex]\sqrt[3]{x^3} = \sqrt[3]{15.625} \\x = 2.5\ cm[/tex]

The edge of cube is: 2.5 cm

Keywords: Volume, Cube

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Answer:

c 12/15

Step-by-step explanation:

Because you have to multiply 3 to the denominator and what ever you do to the denominator u have to do to the numerator so If u did 3 time 5 it would be 15 but if u do 5 time 2 it would be 10 not 12 because the unit rate fraction is 2/3 so u multiply 3 to each denominator and numerator since 2/3 is the unit rate fraction

Answer:

n > 3

Step-by-step explanation:

n - 5 > -2

Add 5 to both sides

n > 3

-5 is neither greater or equal to -2.

-2 is greater than -5.

Or, if you meant if 5 is greater than or equal to -2, then 5 is greater than -2.

Edit: Oh, wait nevermind I didn't see the N there

How do I delete my answer?

Answer:

The width is 5 inches and the height is 18 inches.

Step-by-step explanation:

The area of a triangle can be calculated as:

A = w*h/2

where w is the width of the base, and h is the height.

then we have that:

w*h/2 = 45 in^2

and the height is 2 less than 4 times the width.

h = 4*w - 2in

then we have a system with 2 equations:

w*h/2 = 45 in^2

h = 4*w - 2in

We can replace the second one in the first one and solve it for w.

w*(4*2 - 2in)/2 = 45 in^2

2w^2 - w = 45in^2

2w^2 - w - 45in = 0

then we have to solve the quadratic equation:

the solutions are:

w = (1 +- √(1^2 - 4*2*(-45))/(2*2) = (1 + - √361)/4

where we have two solutions for w, one for each sign of the square root.

we obviously need to take the positive solution (because we can not have a negative length)

w = (1 + √361)/4 = 5in

now, we can replace it in the equation "h = 4*w - 2in" to get the height.

h = 4*5in - 2in = 18in

The width and height of the triangle can be calculated using the given information and the equations for the area of a triangle and the relationship between the width and height.

The subject of this question is algebraic problem solving, specifically involving the concept of an area of a triangle. First, we need to remember that the area of a triangle is calculated using the formula A = 1/2 * base * height. We know that the area equals 45 square inches, so we can write an equation: 45 = 1/2 * width * height. Additionally, the question states that height is two less than four times the width, which is another equation: height = 4 * width - 2.

Now, we can substitute the height (which is 4 * width - 2) into our formula for the area. This gives us the equation: 45 = 1/2 * width * (4 * width - 2), which will allow us to solve for the width of the triangle. After solving for the width, we can use the equation height = 4 * width - 2 to find the height of the triangle.

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Answer:

106°

Step-by-step explanation:

For the equilateral ΔBCD all angles are 60° (180/3 = 60).

m∠ADB is 67° Since the triangle is isosceles the base angles are =.

m∠ ABD will be 180 - (67+67) = 46°.

m∠DBC = 60° so  m∠ABC = 46 + 60 = 106°

Answer:

For the equilateral ΔBCD all angles are 60° (180/3 = 60).

m∠ADB is 67° Since the triangle is isosceles the base angles are =.

m∠ ABD will be 180 - (67+67) = 46°.

m∠DBC = 60° so  m∠ABC = 46 + 60 = 106°

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Step-by-step explanation:

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the statement we have two points through which the line passes:

[tex](x_ {1}, y_ {1}): (2,2)\\(x_ {2}, y_ {2}): (12, -3)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y- {1}} {x_ {2} -x_ {1}} = \frac {-3-2} {12-2} = \frac {-5} {10 } = - \frac {1} {2}[/tex]

Thus, the equation is of the form:

[tex]y = - \frac {1} {2} x + b[/tex]

We substitute one of the points and find "b":

[tex]2 = - \frac {1} {2} (2) + b\\2 = -1 + b\\2 + 1 = b\\b = 3[/tex]

Finally, the equation is of the form:

[tex]y = - \frac {1} {2} x + 3[/tex]

We write the equation of the standard form[tex]ax + by = c[/tex]

[tex]y-3 = -\frac {1} {2} x\\2y-6 = -x\\x + 2y = 6[/tex]

ANswer:

[tex]x + 2y = 6[/tex]

Answer:

undefined

Step-by-step explanation:

csc(x) = 1/sin(x)

csc0 = 1/sin0

sin0 = 0

1/0 = undefined

The value remains under the radical is 8 ⇒ last answer

Step-by-step explanation:

Let us revise how to write the exponent as a radical

Example:

Now let us solve your problem

∵ [tex]1250^{\frac{3}{4}}=\sqrt[4]{1250^{3}}[/tex]

- Factorize 1250 to its prime factors

∵ 1250 = 2 × 5 × 5 × 5 × 5

∴ [tex]1250=2*5^{4}[/tex]

∴ [tex]\sqrt[4]{(2*5^{4})^{3}}=\sqrt[4]{2^{3}*5^{12}}[/tex]

∵ 2³ can not go out the radical because 3 < 4 and not divisible by it

- [tex]5^{12}[/tex] can go out the radical because 12 can divided by 4

∵ 12 ÷ 4 = 3

∴ [tex]5^{12}[/tex] can go out the radical as 5³

∴ [tex]\sqrt[4]{1250}=5^{3}\sqrt[4]{2^{3}}[/tex]

∴ [tex]\sqrt[4]{1250}=125\sqrt[4]{8}[/tex]

∴ The value remains under the radical = 8

The value remains under the radical is 8

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Answer:

8

Explanation:

Egde 2020

Hope this helps :)

Answer with Step-by-step explanation:

We are given that

M is the mid point of AB

[tex]\angle A=\angle B[/tex]

We have to match the reasons with statements given in proof.

Proof:

1.Statement:[tex]\angel A=\angle B[/tex], M is the midpoint of AB

Reason: Given

2.Statement:[tex]AM=MB[/tex]

Reason: Definition of midpoint

3.Statement:[tex]AC=BC[/tex]

Reason:Opposite sides of equal angle are equal.

4.Statement:[tex]\triangle AMC\cong \triangle BMC[/tex]

Reason:SAS Postulate

Answer:

Proof is below.

Step-by-step explanation:

Given: < A = < B , M is the midpoint of AB

Definition of midpoint: AM = MB

Sides opposite = <'s are equal: AC = BC

Triangle AMC congruent to triangle BMC: SAS

Hence, proved.

She would have used 1200 messages in all by the month of August.

Step-by-step explanation:

Messages allowed per month = 150

There will be 8 months starting from January to August, therefore,

Time period = 8 months

Messages in 8 months = Messages per month * Time period

[tex]Messages\ in\ 8\ months=150*8\\Messages\ in\ 8\ months=1200[/tex]

She would have used 1200 messages in all by the month of August.

Keywords: Multiplication

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To evaluate the given expression 5x−6y+20z4yz, for x = 5, y = 3, and z = 1/4, we substitute the given values and apply the order of operations to solve the problem.

The question requires us to evaluate the mathematical expression given as 5x−6y+20z4yz with provided values of x = 5, y = 3, and z = 1/4. Let us substitute the values into the expression as follows:

First, replace each 'x', 'y', 'z' in the expression with the given values:

= 5×5 - 6×3 + 20×(1/4) / (4×3×(1/4))

= 25 - 18 + 20 / (3)

= 7 + 20/3

Finally, you can calculate the exact numerical result depending on whether you are allowed to leave it as an improper fraction or if you need to convert it to a mixed number or decimal form.

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Let the number be x. "Three times a number increased by 10" is mathematically translated as

3x + 10

"is equal" is mathematically translated as twenty less than six times the number" is mathematically translated as

6x - 20

The whole sentence "Three times a number increased by ten is equal to twenty less than six times the number" is translated as

3x + 10 = 6x - 20

We now solve the above linear equation to find the number x

3x - 6x = - 20 - 10

- 3x = - 30

x = 10

Check answer

Three times a number increased by ten : 3 × 10 + 10 = 40

Twenty less than six times the number : 6 × 10 - 20 = 40

Final answer:

The simple linear equation given can be solved by defining the unknown number as 'x', setting up the equation, and solving for 'x'. After isolating x on one side, the result is that x equals 10.

Explanation:

The question is a classic example of a simple linear equation in one variable. We can define a variable, let's call it x, to represent the number in question. The problem statement translates to the equation:

3x + 10 = 6x - 20

Now, let's solve for x by isolating it on one side of the equation:

Subtract 3x from both sides:

10 = 3x - 20

Add 20 to both sides to get:

30 = 3x

Finally, divide both sides by 3 to find x:

x = 10

Therefore, the number we are looking for is 10.

Answer:

Total number of people in the line for the dunking machine is 8.

Step-by-step explanation:

Here, let us assume the number of people in the line for hoop shoot = 12

So, the number of people in the line for cakewalk

=  One- Third of the number of people in line for Hoop Shoot

= [tex]\frac{1}{3}  \times 12 = 4[/tex]

Also, the number of people in the line for dunking machine

=  2 x ( The number of people in line for Cakewalk)

=  2  x  4  = 8

Hence, the total number of people in line for the dunking machine is 8.

Final answer:

To find the number of people in line for the dunking machine when given the number in line for the hoop shoot, we calculate the cake walk line as one-third of the hoop shoot line, then double that for the dunking machine line, resulting in 8 people.

Explanation:

Given that the line for the dunking machine was twice as long as the cake walk line and that the cake walk line was one-third the length of the hoop shoot line, we can derive the relationship between the numbers of people in line for each activity.

First, since there were 12 people in line for the hoop shoot, and given that the cake walk line was one-third of this, the cake walk had 12 / 3 = 4 people in line.

Next, since the dunking machine line was twice as long as the cake walk line, it had 4 × 2 = 8 people in line.

Answer:

Option C.

Option E.

Step-by-step explanation:

Let be "f" the price of a loaf of French bread, "w" the price of the grain bread and "c" the price of the cinnamon raisin bread.

We know that Melissa paid twice as much for the whole grain bread as for the French bread. This can be represented with this equation:

[tex]w=2f[/tex]       [Equation 1]

Since she paid $2.50 more for the cinnamon raisin bread than for the whole grain bread, we can write this equation:

[tex]c=w+2.50[/tex]       [Equation 2]

The total amount of money she spent was $11.25, then:

[tex]f+w+c=11.25[/tex]     [Equation 3]

Now you must substitute the Equation 1 into the Equation 2:

[tex]c=2f+2.50[/tex]      [Equation 4]

Substituting the [Equation 1] and the [Equation 4] into the [Equation 3], you get:

[tex]f+2f+(2f+2.50)=11.25[/tex]

If you simplify the equation, you get:

[tex]5f=8.75[/tex]

The correct equations that describe this situation are: A. f + f + (f + 2.50) = 11.25 and D. 2f + 2.50 = 11.25.

The correct equations that describe this situation are:

To solve this problem, let's assign variables to represent the prices. Let f be the price of a loaf of French bread. According to the information given, the whole grain bread costs twice as much as the French bread, so its price is 2f. The cinnamon raisin bread costs $2.50 more than the whole grain bread, so its price is (2f + 2.50). The total cost of the 3 loaves is $11.25, so we can set up the equations:

Simplifying these equations gives us the correct choices A and D.