One number is equal to two times a second number. Two times the first number plus two times the second number is 24. If you let x stand for the first number and y for the second, what are the two numbers? A. x = –24, y = –12 B. x = 12, y = 6 C. x = 8, y = 4 D. x = 24, y = 12

Answer:

Circumcenter =(-1,0)

Orthocenter =(2,-3)

Step-by-step explanation:  

Given : Points A = (2,3), B = (-4,-3), C = (2,-3)  

Formula used :  

→Mid point of two points- [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

→Slope of two points - [tex]\frac{y_2-y_1}{x_2-x_1})[/tex]

→Perpendicular of a line = [tex]\frac{-1}{slope of line})[/tex]

Circumcenter- The point where the perpendicular bisectors of a triangle meets.

Orthocenter-The intersecting point for all the altitudes of the triangle.

To find out the circumcenter we have to solve any two bisector equations.

We solve for line AB and AC

So, mid point of AB =[tex](\frac{2-4}{2},\frac{3-3}{2})=(-1,0)[/tex]

Slope of AB =[tex]\frac{-3-3}{-4-2}=1[/tex]

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = -1  

Equation of AB with slope -1 and the coordinates (-1,0) is,  

(y – 0) = -1(x – (-1))  

y+x=-1………………(1)  

Similarly, for AC  

Mid point of AC = [tex](\frac{2+2}{2},\frac{3-3}{2})=(2,0)[/tex]

Slope of AC = [tex]\frac{-3-3}{2-2}=\frac{-6}{0}[/tex]  

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = 0  

Equation of AC with slope 0 and the coordinates (2,0) is,  

(y – 0) = 0(x – 2)  

y=0 ………………(2)  

By solving equation (1) and (2),  

put y=0 in equation (1)

y+x=-1

0+x=-1

⇒x=-1  

So the circumcenter(P)= (-1,0)

To find the orthocenter we solve the intersections of altitudes.

We solve for line AB and BC

So, mid point of AB =[tex](\frac{2-4}{2},\frac{3-3}{2})=(-1,0)[/tex]

Slope of AB =[tex]\frac{-3-3}{-4-2}=1[/tex]

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of CF = -1  

Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF  

(y – 0) = -1(x – (-1))  

y+x=-1………………(3)  

Similarly, mid point of BC =[tex](\frac{-4+2}{2},\frac{-3-3}{2})=(-1,-3)[/tex]

Slope of AB =[tex]\frac{-3+3}{-4-2}=0[/tex]

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of AD = 0

Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD

(y-(-3)) = 0(x – (-1))  

y+3=0

y=-3………………(4)  

Solve equation (3) and (4),

Put y=-3 in equation (3)

y+x=-1

-3+x=-1

x=2

Therefore, orthocenter(O)= (2,-3)

To find the coordinates of the Circumcenter of Triangle ABC, we find the equations of the perpendicular bisectors of two sides and solve them simultaneously. To find the coordinates of the Orthocenter, we find the equations of the altitudes and solve them simultaneously.

The Circumcenter of a triangle is the point of concurrency of the perpendicular bisectors of the triangle's sides. The Orthocenter of a triangle is the point of concurrency of the triangle's altitudes. To find the coordinates of the Circumcenter, we can find the equations of the perpendicular bisectors of two sides of the triangle and solve them simultaneously. To find the coordinates of the Orthocenter, we can find the equations of the altitudes and solve them simultaneously.

For Triangle ABC with vertices A(2,3), B(-4,-3), and C(2,-3):

Circumcenter coordinates:

Orthocenter coordinates:

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Answer:

Since the exponent of the scientific notation is positive  4, move the decimal point  4  places to the right.  

56800

Step-by-step explanation:

5.68(104)

=5.68*104

=5.68*(10*10*10*10)

=56800

Answer:

The standard form of [tex]5.68\times 10^{4}[/tex] is [tex]56800[/tex]

Step-by-step explanation:

We need to write [tex]5.68\times 10^{4}[/tex] in standard form

Re-write [tex]5.68\times 10^{4}[/tex] as,

[tex]5.68\times 10000[/tex]

⇒[tex]56800[/tex]

Therefore, standard form of [tex]5.68\times 10^{4}[/tex] is [tex]56800[/tex]

Answer:

See below

Step-by-step explanation:

13x + 5 + 17x - 4.5 + x

NOTE: You can only add/subtract LIKE terms . Here we have  variable terms in x  (13x , 17x and x) and 2 constants ( 5 and 4.5).

Sarah's next line is

18x + 17x - 4.5 + x

This is incorrect . It looks like she  added 13x + 5 and got 18x!! Which is of course wrong because they are NOT LIKE terms. 5 is a constant and 13x is a variable term in x.

The third line is correct:-

35x - 4.5 + x.

She has added the 2 variables 17x and 18x.

Fourth line  is  30.5x + x. She's at it again - Trying to subtract 4.5 from 35x .

Last line 31.5x

She has added  the 2 terms in x correctly, but the final answer is wrong of course due to the earlier errors.

Answer:

The reference angle for the angle with measure -pi/4 is the angle pi/4

Step-by-step explanation:

The angle -pi/4 is in clockwise and the angle pi/4 is in counterclockwise

The reference angle for the angle with measure -pi/4 is pi/4.

The reference angle for the angle with measure -π/4 is π/4.

A reference angle is the positive acute angle between the terminal side of the given angle and the x-axis in standard position.

In this case, the given angle is in the third quadrant, and its reference angle is the positive acute angle formed by the terminal side of the angle and the negative x-axis. Since the third quadrant is 180 degrees away from the positive x-axis, the reference angle is π/4.

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Answer:

Step-by-step explanation:

7-9x=56

Answer:

Hey!

Your answer is £2121.80 in the account!

Step-by-step explanation:

So to do this, you have to first find out how much would be left after 1 year...

=     3 / 100 x 2000 = £60 *we now add this on to the £2000*

=     2000 + 60 = £2060 *this is what is in the account after 1 YEAR*

Then, find out the amount for the second year!

=     3 / 100 x 2060 = £61.80 *we now add this on to the £2060*

=     2060 + 61.80 = £2121.80 *this is what is in the account after 2 YEARS*

SO AFTER 2 YEARS, THERE IS AN AMOUNT OF £2121.80 IN THE BANK ACCOUNT!

HOPE THIS HELPS!!

Answer:

trrtrtrtrtrtrtrtrt

Step-by-step explanation:

Answer:

Jose: 2/3 = 8/12

Jenna: 7/12

Jose has finished more of the race.

Answer:

distribute

Step-by-step explanation:

so multiply -1 with 5 and -3

this turns it to 2x(-5+3x)=4x+2

then you multiply 2x to -5 and 3x

so on...

Answer:

well it's not D

Step-by-step explanation:

Answer:

1 / 4 US cups = 4 US tablespoons

Step-by-step explanation:

trust me its right

Answer:

x = 1/3

Step-by-step explanation:

3x + 5 = 6

3x = 6 -5

3x = 1

x = 1/3

Proof:

3 * 1/3 + 5 = 6

3/3 + 5 = 6

1 + 5 = 6

6 = 6

Hello.

X= −5/14 y

Step 1: Add -15x to both sides.

x−5y+ −15x= 15x+ −15x

−14x−5y=0

Step 2: Add 5y to both sides.

−14x −5y+5y= 0+5y

−14x=5y

Step 3: Divide both sides by -14.

−14x/−14= 5y/−14

x= −5/14 y

Have a nice day

Answer:

x = 27976.22021

Step-by-step explanation:

10x + .0085x = 280000

Combine like terms

10.0085x = 280000

Divide by 10.0085 on each side

10.0085x /10.0085= 280000/10.0085

x = 27976.22021

(5q2 − r2s)(25q^4+5q^2r^2s+1r^4s^2)

To factor the expression, identify the difference of squares in the first part and the sum of cubes in the second part. Apply the relevant factoring formulas to obtain the fully factored form.

To factor the expression[tex](q^2 - r^2s) (q^4 + q^2r^2s + r^4s^2),[/tex] we must first recognize that the second part is a sum of cubes. The formula for factoring a sum of cubes is [tex]a^3 + b^3 = (a + b)(a^2 - ab +b^2)[/tex]. The first part, [tex]q^2 - r^2s,[/tex] can be recognized as the difference of squares, which factors as (q - rs)(q + rs). Therefore, after applying these patterns the factored form of the expression is:

[tex](q - rs)(q + rs)(q^2 + qrs + r^2s^2)[/tex]

Answer:

The answer is 2x^2 - xy^2 - 6y^4

Step-by-step explanation:

2xx + 2x(-2y^2) + 3y^2x + 3y^2(-2y^2)

2xx - 2 · 2xy^2 + 3xy^2 - 3 · 2y^2y^2

= 2x^2 - xy^2 - 6y^4

[tex]\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-5\\ n=10\\ a_{10}=13 \end{cases} \\\\\\ a_{10}=a_1+(10-1)d\implies 13=-5+(10-1)d \\\\\\ 13=-5+9d\implies 18=9d\implies \cfrac{18}{9}=d\implies 2=d[/tex]

Answer:

Common difference = 2

Step-by-step explanation:

[tex]n^{th}[/tex] term of an arithmetic progression is given by a + (n-1)d, where a is the first term and d is the common difference.

Here first term is given as -5

           a = -5

Tenth term is 13

           n = 10

          [tex]n^{th}[/tex] term = 13

We have

       -5 + (10-1)d = 13

         9 d = 13 + 5

            9 d = 18

               d = 2

Common difference = 2

Answer:

3/2 or 1.5

Step-by-step explanation:To find the perimeter you need to multiply the four sides why the same number like: 3/8in(4)wich equal 3/2in or in decimal point 1.5 hope it helps. :)

Answer:

The box of cereal contained 20 ounces

Step-by-step explanation:

Answer:

12:00pm in Montana USA.

Step-by-step explanation:

Time zone in South Carolina, USA follows GMT-5hrs.

Time zone in Montana, USA follows GMT-7hrs.

So the difference between two time zones are 2 hours.

It means South Carolina USA is 2 hours ahead of Montana USA. Or Montana's time lags South Carolina's time by 2 hours.

So if it is 2:00pm in South Carolina USA, then it would be 12:00pm in Montana USA.

Answer:

5feet per year

Step-by-step explanation:

We need to find the distance it grew in that 7 1/2 years:

63 - 25 1/2 = 37 1/2

Now to find the average yearly growth we can divide this by 7 1/2:

37.5 ÷ 7.5 = 5

So the yearly rate of growth of the tree is 5f/y

Lyla needs 5 seed packets to grow a total of 40 flowers, assuming the relationship between flowers and seed packets is directly proportional.

Lyla grew 16 flowers with 2 seed packets. To find out how many seed packets Lyla needs to grow a total of 40 flowers, assuming the relationship is directly proportional, we set up a proportion. We have the ratio of flowers to seed packets, which is 16 flowers for 2 seed packets. We need to find how many seed packets would be needed for 40 flowers.

First, write the proportion:

\(\frac{16 \text{ flowers}}{2 \text{ seed packets}} = \frac{40 \text{ flowers}}{x \text{ seed packets}}\)

Solve for \(x\):

\(\frac{16}{2} = \frac{40}{x}\)

\(8 = \frac{40}{x}\)

Multiply both sides by \(x\) and divide both sides by 8 to find the value of \(x\):

\(x \cdot 8 = 40\)

\(x = \frac{40}{8}\)

\(x = 5\)

Therefore, Lyla needs 5 seed packets to grow 40 flowers.

Answer:

A and D. SSS theorem

B. ASA or AAS theorems

C. SAS theorem

E. AAS theorem

Step-by-step explanation:

SSS theorem states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

SAS theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

AAS theorem states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

ASA theorem states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Thus:

A. If each pair of corresponding sides is congruent, then two triangles are congruent by SSS theorem.

B. If two pairs of corresponding angles are congruent and a pair of corresponding sides are congruent, then two triangles are congruent by ASA or AAS theorems.

C. If two pairs of corresponding sides and the angles included between them are congruent, then two triangles are congruent by SAS theorem.

D. If  three sides of one triangle are congruent to three sides of a second triangle, then two triangles are congruent by SSS theorem.

E. If two angles and a non-included sides of each triangle are congruent, then two triangles are congruent by AAS theorem.

The theorems signified are:

a) SSS

b) ASA and AAS

c) SAS

d) SSS

e) AAS.

a) SSS (Side-Side-Side): All three sides of one triangle are congruent to the corresponding sides of the other triangle.

b)Here, two theorems can be used:

ASA (Angle-Side-Angle): Two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle.

AAS (Angle-Angle-Side): Two angles and a non-included side of one triangle are congruent to the corresponding parts of the other triangle.

c) SAS (Side-Angle-Side): Two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle.

d) SSS (Side-Side-Side): All three sides of one triangle are congruent to the corresponding sides of the other triangle.

e) AAS (Angle-Angle-Side): Two angles and a non-included side of one triangle are congruent to the corresponding parts of the other triangle.

Thus, the theorems signified are:

a) SSS

b) ASA and AAS

c) SAS

d) SSS

e) AAS

Correct question:

Identify the congruency rule in each

Two triangles are congruent if:

a) each pair of corresponding sides is congruent

b) two pairs of corresponding angles are congruent and a pair of corresponding sides

are congruent

c) two pairs of corresponding sides and the angles included between them are

congruent

d) If three sides of one triangle are congruent to three sides of a second triangle,

e) If two angles and a non-included sides of each triangle are congruent

A fraction will be bigger than another if for the same denominator the numerator is bigger therefore fraction 7/8 will be bigger than 13/15.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.

As per the given fractions 7/8 and 13/15

Multiply 15 numerators and denominators to 7/8

(7/8) × 15/15 = (7 × 15/8)/15

⇒ 13.125/15

Since 13.125 > 13

Since A fraction will be bigger than another if for the same denominator the numerator is bigger.

So 7/8 > 13/15.

Hence " A fraction will be bigger than another if for the same denominator the numerator is bigger therefore fraction 7/8 will be bigger than 13/15".

For more about fractions,

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It is given that, Altitude above sea level =Positive Values

                                          =Positive Integer{1,2,3,4,5,6,7,8,.......}

Altitude below sea Level=Negative values

                                     =Negative Integer{-1,-2,-3,-4,-5,-6,.......}

Now, The situation given is

 A hiker in Death Valley stopping at an altitude of 0 feet

Zero(0)= The Point 0, means neither Positive nor Negative, that is additive Identity with respect to Addition of Integers.That is when two integers having Opposite sign, means additive Inverse of each other, are added together it yields Zero.

For example

-2 + 2=0

2 and -2 are Additive Inverse of each other.

Answer:

4(x +3)(x +4)

Step-by-step explanation:

First of all, recognize that each coefficient is a multiple of 4.

Factoring that out makes it easier to see that you need factors of 12 that add to give 7. Those are not hard to find as being 3 and 4. These numbers go into the binomial factors to give ...

... 4x^2 +28x +48 = 4(x^2 +7x +12) = 4(x +3)(x +4)

Answer:

[tex]4x^2 + 28x +48 = 4(x+4)(x+3)[/tex]

Step-by-step explanation:

We are given the following information in the equation:

[tex]4x^2 + 28x +48[/tex]

We have to factorize the given expression.

We will use the technique of splitting the middle term to factorize.

Factorization can be done in the following manner:

[tex]4x^2 + 28x +48\\\Rightarrow 4(x^2 + 7x + 12)\\\Rightarrow 4(x^2 + 4x + 3x + 12)\\\Rightarrow 4[x(x+4)+3(x+4)]\\\Rightarrow 4(x+3)(x+4)[/tex]

Hence, the given expression can be factorized as:

[tex]4x^2 + 28x +48 = 4(x+4)(x+3)[/tex]

Answer:

Out of every 5 rectangles 2 shall be purple.

3 scarves have 3 times 5 rectangles.

Thus they shall be 3 times 2 that are purple.

Final answer:

To find 3/4 of 12, you multiply 12 by the fraction 3/4. Multiplying 0.75 (the decimal equivalent of 3/4) by 12 results in 9. Hence, 3/4 of 12 is 9.

Explanation:

To solve the problem: "What is 3/4 of 12," you would multiply. This type of problem is asking for a part of a whole, where 'of' typically signifies multiplication in mathematics. We can think about this conceptually: if half of 12 is 6, then three-quarters would be half of 12 plus half of 6. In mathematical terms, you would calculate 3/4 × 12 to find the answer.

To break it down:

Convert 3/4 to a decimal if needed, which is 0.75.

Multiply 0.75 by 12.

The result is 9, so 3/4 of 12 equals 9.

This is because when you are finding a portion of a number, you are determining how many times that portion fits into the whole. So, you're effectively scaling the number 12 by the fraction 3/4, which is accomplished through multiplication.

Answer:1/6

Step-by-step explanation: because there are 6 side to a cube and you can only have a outcome of 1 so therefore, the answer is 1/6

Final answer:

Juan's experience of rolling the number 2 on a six-sided die 4 times deals with the concept of independent events in probability. The probability of getting a 2 on any single roll is 1/6 and to roll a 2 four times consecutively, you multiply the probabilities, resulting in a much smaller overall probability.

Explanation:

The question involves understanding the probability of rolling a certain number on a six-sided die, which is a concept in mathematics. When Juan rolls the six-sided number cube 4 times and gets the result of 2 each time, we are analyzing a sequence of independent events in probability. Since each roll of the die is independent, the outcome of one roll does not affect the outcome of the next roll and the probability of rolling a 2 on each individual roll remains constant at 1/6.

Event X, described as rolling an even number, has a probability of 3/6 or 1/2, since the even numbers on a die are 2, 4, and 6. However, the probability of rolling multiple 2's in sequence would be the product of probabilities for each roll. That is, the probability of rolling a 2 four times in a row would be (1/6) * (1/6) * (1/6) * (1/6), which is a much smaller probability. This reflects the notion that rolling the same number consecutively multiple times is less likely than rolling it once.