which of the following is a solution of x^2+4x+6

Answer:

Step-by-step explanation:

r = 5s + 7

r + s = 25

5s + 7 + s = 25

6s + 7 = 25

6s = 25 - 7

6s = 18

s = 18/6

s = 3 <=== sam has 3 video games

r = 5s + 7

r = 5(3) + 7

r = 15 + 7

r = 22 <=== robert has 22 video games

Answer:

Construct MO, where O is the midpoint of CG. (As shown in the attached figure)

(1) LM = MG //given, CM is the median to the hypotenuse      

(2) CO = OG // construction    

(3) MO is a mid-segment   //(1), (2) , Definition of a mid-segment

(4) MO // LC //triangle mid-segment theorem    

(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)

(6) m∠LCO=90°  //given, ΔLCG is a right triangle

(7) m∠MOG=90° //(5), (6), definition of congruent angles

(8) m∠MOC=180° – 90° = 90° // linear pair

(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles

(10) MO=MO //common side, reflexive property of equality  

(11) ΔMCO ≅ ΔMGO  //(2), (9), (10) Side-Angle-Side postulate

(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)      

(13) MG= ½LG // Given, CM is the median to the hypotenuse    

(15) MC = ½LG //(12) , (13), substitution  

Answer:

A

Step-by-step explanation:

neither a relation nor a function

Answer:

NOTE: This is the answer for the equation (y=3x^2-9x+20)                              Both a Relation and a Function

Step-by-step explanation:

Because a Relation can be represented as a verbal descriptions, graphs, mapping diagrams, equations, list ordered pairs, and tables. Which in this case is an equation so its a RELATION.

A function is a type of relation in which every x-value in the domain is paired with exactly one y-value. Which in this case every x-value is paired with one Y-value.

Let me know if this helps. :)

The equation in terms of u as independent variable is w = (-7/6)u

A variable upon which another variable depends is called an Independent variable , On changing the value of the independent variable , the dependent variable changes .

The equation given is

4u +8w = -3u+2w

8w -2w = -3u - 4u

6w = -7u

w = (-7/6) u

Therefore the equation in terms of u as independent variable is w = (-7/6)u.

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Answer:

the equation rearranged with [tex]\( u \)[/tex] as the independent variable is:

[tex]\[ u = -\frac{6}{7}w \][/tex]

Step-by-step explanation:

To rearrange the equation so that [tex]\( u \)[/tex] is the independent variable, we need to isolate [tex]\( u \)[/tex] on one side of the equation.

Starting with the given equation:

[tex]\[ 4u + 8w = -3u + 2w \][/tex]

First, add [tex]\( 3u \)[/tex] to both sides to get all the [tex]\( u \)[/tex] terms on one side:

[tex]\[ 4u + 3u + 8w = -3u + 3u + 2w \][/tex]

[tex]\[ 7u + 8w = 2w \][/tex]

Next, subtract [tex]\( 8w \)[/tex] from both sides to get all the [tex]\( w \)[/tex] terms on the other side:

[tex]\[ 7u + 8w - 8w = 2w - 8w \][/tex]

[tex]\[ 7u = -6w \][/tex]

Finally, divide both sides by [tex]\( 7 \)[/tex] to solve for [tex]\( u \)[/tex]:

[tex]\[ \frac{7u}{7} = \frac{-6w}{7} \] \[ u = -\frac{6}{7}w \][/tex]

So, the equation rearranged with [tex]\( u \)[/tex] as the independent variable is:

[tex]\[ u = -\frac{6}{7}w \][/tex]

This is the final answer, with [tex]\( u \)[/tex] isolated on one side of the equation.

Answer:

It takes approximately 1.5 seconds to reach the people 500 metres away

Step-by-step explanation:

Since ; distance=rate×time​

time= distance/ rate

Distance= 500 metres ,rate= 339.5 m/s

Time= 500/339.5

Time= 1.5 seconds

Answer: 14 butterflies per hour

Step-by-step explanation: "Per hour" means in 1 hour so we can rewrite the given statement using fractions.

42 butterflies over 3 hours = ___ butterflies per hour.

I have attached my work in the image provided.

To find out what goes in the blank, notice that we have a 1 in the denominator of our second fraction. So we want to find a fraction that is equivalent to 42/3 that has a 1 in the denominator.

If we divide the numerator and denominator of 42/3 by 3, we get the equivalent fraction 14/1 or 14 butterflies over 1 hour. So now we have 14 butterflies over 1 hour = ___ butterflies per hour.

Now we can easily see that a 14 must go in the blank which means that the unit rate for 42 butterflies in 3 hours is 14 butterflies per hour.

Answer:

The factors of  [tex]2(x+y)^2-9(x+y)-5[/tex] is ((x+y)-5)(2x+2y+1)

Step-by-step explanation:

Given polynomial

=>[tex]2(x+y)^2-9(x+y)-5[/tex]

To Find:

The factors of the polynomial =?

Solution:

Lets assume  k = (x+y)

Then [tex]2(x+y)^2-9(x+y)-5[/tex] can be written as [tex]2k^2-9k-5[/tex]

Now by using quadratic formula

k =[tex]\frac{-b\pm\sqrt{(b^2-4ac}}{2a}[/tex]

where

a= 2

b= -9

c= -5

Substituting the values, we get

k =[tex]\frac{-b\pm\sqrt{(b^2-4ac)}}{2a}[/tex]

k =[tex]\frac{-(-9) \pm \sqrt{((-9)^2-4(2)(-5)}}{2(2))}[/tex]

k =[tex]\frac{-(-9) \pm \sqrt{(81+40)}}{4}[/tex]

k =[tex]\frac{-(-9) \pm \sqrt{(121)}}{4}[/tex]

k =[tex]\frac{-(-9) \pm 11}}{4}[/tex]

k= [tex]\frac{ 9 \pm 11}{4}[/tex]

k =  [tex]\frac{20}{4}[/tex]                         k =  [tex]\frac{-2}{4}[/tex]    

[tex]k_1 =5[/tex]                                      [tex]k_2 = -\frac{1}{2}[/tex]

[tex]2k^2-9k-5= 2(k-5)(k+\frac{1}{2})[/tex]

Solving the RHS we get

[tex]\frac{2}{2}(k-5)(2k+1)[/tex]

[tex](k-5)(2k+1)[/tex]

Substituting k = x+y

[tex]((x+y)-5)(2(x+y+1)[/tex]

[tex]((x+y)-5)(2x+2y+1)[/tex]

Answer:

distance between points=13 units

Step-by-step explanation:

distance between points=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

put [tex](x_1,x_2)[/tex]=(8,7) and [tex](y_1,y_2)[/tex]=(3,-5)

distance between points=[tex]\sqrt{(3-8)^2+(-5-7)^2}[/tex]

distance between points=[tex]\sqrt{(-5)^2+(-12)^2}[/tex]

distance between points=[tex]\sqrt{25+144}[/tex]

distance between points=[tex]\sqrt{169}[/tex]

distance between points=13 units answer

Answer:

force = 21 kg m/s^2 = 21 N

Step-by-step explanation:

If an object has mass (m)  3 kg, and its acceleration (a) is 7 m/s^2, its force is given by Newton's second law of motion: Force = M * a

Force = 3 kg * 7 m/s^2= 21 kg * m/s^2

This combinations of units (kg * m/s^2) is defined as Newtons in physics and abbreviated "N".

So we can say that the force on this object is of magnitude 21 N

Answer:

You would graph a point at the origin with a slope of 1

Step-by-step explanation:

Y=x means whatever the y value is, the x is the same.

Answer:

1

Step-by-step explanation:

The equation for graphing is y=mx+b and if it’s y=x then it means y=1x because when x is left alone it equals to 1

Answer:

4 students would be eligible for the scholarships

Step-by-step explanation:

Final answer:

In a high school with 400 graduating students, only 4 students would be eligible for scholarships that are offered to students in the top 1% of their class by GPA.

Explanation:

To determine how many students from a high school with 400 graduating students would be eligible for scholarships offered to those in the top 1% of their class, we simply need to calculate 1% of 400. Mathematically, this is represented as:

400 students * 1% = 400 students * 0.01 = 4 students

Therefore, in a high school graduating class of 400 students, only 4 students would be eligible for these scholarships based on being in the top 1% of their class according to GPA.

Answer:

2

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

26

Step-by-step explanation:

The length of GF if, G is the centroid of the triangle ABC is 26.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.

Given:

G is the centroid of the triangle ABC,

The  line segment BD can be written as,

40 is 2x as long as 9x+2

The equation can be written as for the above statement.

40 = 2(9x + 2)

40 = 18x + 4

36 = 8x

x = 2

Put the value of x = 2 in 19X + 14, and divide that answer by 2, because GF is 2x smaller than AG

19x + 14

19 (2) + 14

52

Thus, the length of GF = 52 / 2 = 26.

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The question deals with setting up and solving an equation to find the cost of a clock, when the total cost for a chess set and clock is given. The cost of a clock is found to be $15.

The subject of this question is Mathematics, specifically dealing with setting up and solving an equation. The total cost of the chess set and clock for each member is $125/5 = $25. Jenna knows that the chess set costs $10. So, the cost of a clock would be $25 - $10 = $15. Therefore, the cost of a clock is $15.

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Answer:

Undefined

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-3)/(2-2)

m=-7/0

undefined

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\text{The first coordinates of the points (abscissa) are the same.}\\\text{Conclusion: This is a vertical line.}\\\text{The vertical line has the equation x = a (here x = 2). It has no slope.}\\\\\boxed{\text{Answer: unde}\text{fined}}[/tex]

[tex]\bold{METHOD\ 2:}\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Substitute the coordinates of the given points}\ (2,\ 3)\ \text{and}\ (2,\ -4).\\\\m=\dfrac{-4-3}{2-2}=\dfrac{-7}{0}\\\\\text{The denominator must be different from 0.}\\\text{The expression}\ \dfrac{-7}{0}\ \text{ has no numerical sense.}\\\\\boxed{\text{Conclusion and naswer: unde}\text{fined}}[/tex]

Answer:

x intercept- (-4,0)  y intercept- (0, 9)

Step-by-step explanation:

Subsitute 0 for x to get y = 9.  That is your y intercept.  Subsitute 0 for y and get -4 for your x intercept

Answer:

$22.50

Step-by-step explanation:

25% of $30 is 22.5

Answer:

$22.50

Step-by-step explanation:

25% of 30 is 22.5

Answer:

6x+8

Step-by-step explanation:

To answer this question we just simply use the distributive property to get rid of the parenthesis.

1.5*3x=4.5x

1.5*4=6

So the first parenthesis cancelled out would be : 4.5x+6

Now, onto the second:

0.25*6x=1.5x

0.25*8=2  

So the second one is : 1.5x+2

Not that we have distributed both things, we add these.

4.5x+6+1.5x+2 we combine like terms

4.5x+1.5x=6x

6+2=8

So, the answer is 6x+8

Answer:

6x+8

Step-by-step explanation:

Took the question

Answer:X=2.5

Step-by-step explanation:

Divide both sides by 3

3 over 3 cancels out and 7.5 over 3 equals 2.5

Answer:

x= 2.5

Step-by-step explanation:

divide both sides by 3

Answer:

i

Step-by-step explanation:

Equation 1:

Answer:

x = 1.22

Step-by-step explanation:

[tex]\frac{5x-1}{8} -\frac{5-7x}{2} = \frac{3(6-x)}{6}[/tex]

[tex]\frac{2(5x-1) - 8(5-7x)}{16} = \frac{3(6-x)}{6}[/tex]

[tex]\frac{(10x-2) - (40-56x)}{16} = \frac{3(6-x)}{6}[/tex]

[tex]\frac{(10x-2-40+56x)}{16} = \frac{3(6-x)}{6}[/tex]

[tex]\frac{(66x-42)}{16} = \frac{3(6-x)}{6}[/tex]

[tex]\frac{(66x-42)}{16} = \frac{(18-3x)}{6}[/tex]

[tex](66x-42) \times 6 = (18-3x) \times 16[/tex]

[tex](396x-252) = (288-48x)[/tex]

[tex](396x +48x) = (288+252)[/tex]

[tex]444x = (540)[/tex]

[tex]x = \frac{540}{444}[/tex]

x = 1.22

Equation 2:

Answer:

x = -13.97

Step-by-step explanation:

[tex]\frac{x}{3} - \frac{7(x-2)}{9} = 4- \frac{2x-5}{6}[/tex]

[tex]\frac{9x-3(7(x-2))}{27} = 4- \frac{2x-5}{6}[/tex]

[tex]\frac{9x-3(7x-14))}{27} = 4- \frac{2x-5}{6}[/tex]

[tex]\frac{9x-(21x-42))}{27} = 4- \frac{2x-5}{6}[/tex]

[tex]\frac{9x-(21x-42)}{27} = \frac{24 - (2x-5)}{6}[/tex]

[tex]\frac{-12x+42}{27} = \frac{-2x+29}{6}[/tex]

[tex](-12x+42) \times 6 = (-2x+29) \times 27[/tex]

[tex](-72x+252) = (-34x+783) [/tex]

[tex](252-783) = (-34x +72x) [/tex]

[tex](-531) = (38x) [/tex]

[tex]x =\frac {-531}{38}[/tex]

x = -13.97

Question:

Correctly complete this sequence: 131, 517, ?, 123

Answer:

The completed sequence: 131, 517, 192, 123

Step-by-step explanation:

Given sequence is 131, 517, ?, 123

Step 1: Now, write the given numbers without any commas as below,

                131517?123

Step 2: Then, split it into two digit numbers as 13, 15, 17, _ _, 23

Step 3: Fill the sequence with the missing two digit odd numbers. So, we can write as below

              13, 15, 17, 19, 21, 23

Step 4: Again, rewrite and form the sequence without any commas.

                    131517192123

Step 5: Place the class after every three digits.

                    131, 517, 192, 123

Step 6: At last, found that the missing number is 192.

This is a simple addition sequence. The next number in the sequence would be 903, resulting from the addition of 386 to the previous term 517. So, the completed sequence is 131, 517, 903, 123.

The sequence in question appears to be a simple addition sequence between consecutive terms. If you subtract the first number from the second number, you get 386 (517-131 = 386). Assuming this addition pattern continues, you can find the next number in the sequence by adding 386 to 517. So, the next number in the sequence would be 903 (517 + 386).

This means the completed sequence should read: 131, 517, 903, 123. Always remember to check the difference between your terms when working with sequences like this one.

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Answer:

width = (x-1)

Step-by-step explanation:

The volume of the prisms is defined in the problem as

Volume = x^3 + 9x^2 + 6x − 16

Volume  = width*height* length

And we know that,

length = (x+2)

height = (x+8)

We can find the roots of the equation, which happen to be

x = -8

x = -2

x = 1

(See image below)

This means that the volume can be represented as

Volume = x^3 + 9x^2 + 6x − 16 = (x+8)(x+2)*(x-1)

Therefore,

The width = (x-1)

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

The graph of a proportional relationship is a straight line graph which must pass through the origin.

The only straight line graphs which pass through the origin are B and D

Answer

14x+8y=6

Step-by-step explanation:

9x+5x=14, 7y+y=8y , 15-9=6

Answer:

?

Step-by-step explanation:

?

Answer:

[tex]V=63,829.92\ cm^3[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=69.08\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]69.08=2(3.14)r[/tex]

solve for r

[tex]69.08=6.28r[/tex]

[tex]r=69.08/6.28[/tex]

[tex]r=11\ cm[/tex]

step 2

Find the volume of the cylinder

we know that

The volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]h=168\ cm[/tex]

[tex]r=11\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]V=(3.14)(11)^{2}(168)[/tex]

[tex]V=63,829.92\ cm^3[/tex]

Answer:

[tex]\displaystyle x = 8[/tex]

Step-by-step explanation:

Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.

I am joyous to assist you anytime.

Answer:

Cougar population was 790 at the beginning

830-790=40

Area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter

Solution:

Given that an engineer is going to install a new water pipe. The diameter of this circular pipe is, d = 20 cm

We have to find the area 'A' of the circular cross-section of the pipe.

Given, diameter of the circular section is:

diameter = 20 cm

Let us find the radius

[tex]radius = \frac{diameter}{2}\\\\r = \frac{20}{2} = 10[/tex]

Thus radius = r = 10 cm

The area 'A' of the circular cross-section of the pipe measn we can use the area of circle formula

The area of circle is given as:

[tex]area = \pi r^2[/tex]

Where "r' is the radius of circle

We have to find area in terms of pi

[tex]area = \pi (10)^2\\\\area = \pi \times 10 \times 10\\\\area = 100 \pi[/tex]

Thus area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter