Helene invested a total of 1,200 $

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:

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

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:

i

Step-by-step explanation:

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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" Rachel must pay a $20 membership fee to join the gym " can be interpreted from the y-intercept of the function ⇒ D

Step-by-step explanation:

The form of the linear function is f(x) = mx + b, where

∵ f(x) = 37 x + 20 models the total cost for Rachel to be a member

   at a gym for x months

∵ f(x) = m x + b

∴ m = 37 and b = 20

∵ m represents the rate of change

- That means she must to pay 37 per month for x months

∴ Rachel must pay $37 per month to use the gym

∵ b represents the initial amount

- That means she pays a fixed amount one time

∴ Rachel must pay a $20 membership fee to join the gym

" Rachel must pay a $20 membership fee to join the gym " can be interpreted from the y-intercept of the function

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Answer:

y = 3x

Step-by-step explanation:

Given

9x - y = - 6x + 4y ( subtract 4y from both sides )

9x - 5y = - 6x ( subtract 9x from both sides )

- 5y = - 15x ( divide both sides by - 5 )

y = 3x

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:

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:

72.3%

Step-by-step explanation:

To determine which decimal is bigger between 0.33 and 0.34, we compare the digits after the decimal point. Since the hundredths place in 0.34 is 4 and in 0.33 is 3, 0.34 is the larger decimal.

The question is asking to compare two decimals to determine which is larger. To compare 0.33 and 0.34, you look at the digits from left to right. Both numbers have a 0 before the decimal point, so you compare the digits after the decimal point. First, you compare the tenths place, the digit immediately after the decimal point. In both numbers, this digit is 3, so they are equal up to this point. Next, you look at the hundredths place, the next digit to the right. In 0.33, the digit is 3, while in 0.34, the digit is 4. Because 4 is greater than 3, 0.34 is the larger decimal.

Final answer:

0.34 is larger than 0.33 because the digit in the hundredths place is greater for 0.34.

Explanation:

When comparing two decimals, 0.33 and 0.34, we can determine which is larger by examining the digits from left to right. Here, both numbers have 0 before the decimal point and a '3' in the tenths place, but they differ in the hundredths place. Since 4 is greater than 3, the decimal 0.34 is larger than 0.33. To compare 0.33 and 0.34, we can look at the digits to the right of the decimal point. In this case, 0.34 has a larger digit than 0.33, so it is bigger.

In the equation y=2/7x, y is directly proportional to x.

To determine if the equation y = (2/7)x represents a proportional relationship, you can check if it fits the criteria for proportionality. In a proportional relationship, the ratio between y and x should remain constant. This means that if you double x, y should also double, and so on.

In the equation y = (2/7)x, the coefficient 2/7 is a constant, and it is the same for all values of x.

Therefore, this equation represents a proportional relationship.

In this case, if you double the value of x, the value of y will also double, and if you triple x, y will also become three times its original value, and so on. This is a key characteristic of a proportional relationship.

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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:

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:

Cougar population was 790 at the beginning

830-790=40

Answer:

y-5=-3(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-3)

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:

Discrete random variable

Step-by-step explanation:

We are given the following in the question:

x is the number of number of oranges purchased in a grocery store.

Thus, it have the following properties.

Thus, it is a discrete random variable

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. :)

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:

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:

-3.5 degrees per hour

[tex] - 3.5t[/tex]

Step-by-step explanation:

The total change is temperature is -12.25 degrees.

The total time is 3.5 hours.

This means that temperature changes by -3.5 degrees per hour (-12.25 degrees ÷ 3.5 hours).

As an expression of hours, simple multiply the coefficient by a variable. I'm assuming the letter t for time (where t is the number of hours):

[tex] - 3.5t[/tex]

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

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:A should be the best answer to this problem

Step-by-step explanation:

Answer:

The ratio of boys to girls is 7:6

Step-by-step explanation:

1/2 of 14 is 7. So the boys would be equal to 7. 1/2 of 12 is 6.

So the girls would be equal to 6. If you put that in a ratio it would be 7(boys):6(girls) = 7:6

Therefore your answer is A: The ratio of boys to girls is 7:6

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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:

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