Mathematics High School

Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality 7.2b + 6.5 > 4.8b – 8.1. Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1. Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1. Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6. Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b. Which student’s first step was incorrect, and why? Amelia’s, because the variable term must be isolated on the left side Luis’s, because he flipped the inequality sign when he subtracted Shauna’s, because she did not apply the subtraction property of equality properly Clarence’s, because the terms he added together were not like terms

Answers

Answer 1
Luis’s, because he flipped the inequality sign when he subtracted 
Answer 2

Answer: Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

Related Questions

Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school. Anna draws a map with a number line connecting her house to Ben’s house. On the number line, the school is at 0 and her house is at the point +2.5. On the map, Ben’s house is at the point

Answers

Answer:

Ben's house is at point -2

Step-by-step explanation:

Given that Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school

When Anna draws a map with a number line connecting her house to Ben’s house, with school marked as 0 then to the east would be +2.5

Since Ben lives 2 miles to the west, Ben would be marked as negative -2.

(West denotes negative in number line)

So answer is Ben's house is at point -2

Ben's house is at the point -2 on the map of number line.

What is Number line?

A number line is pictorially represented as a horizontal straight line where numbers are placed at equal distance. Usually integers are placed in the number line with negative numbers placed to the left of 0 and positive numbers placed to the right of 0.

Number lines are used in performing basic operations in mathematics such as addition, multiplication, subtraction and division.

Here, it is given that Anna lives 2.5 miles to the east of her school and Ben lives 2 miles to the west of the same school.

So school is a common point here with respect to which both of their distance to house are marked.

On the number line school is at 0.

Anna's and Ben's house lies two opposite sides from the school.

So if one of their houses is at the positive side, the house of other one's will be at the negative side.

Given that, Anna's house is at positive side at the point +2.5.

Then clearly Ben's house will be at the negative side and the point will be -2 since it is 2 miles away from the school.

Hence, Ben's house will be at the negative side of the number line at point -2.

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Solve by completing the square
X^2+12x-13=0

Answers

I order to do this question, you need to put the 13 on the right side. So now you have x^2+12x+0=13. Now, take half of 12, and square it. Add this to both sides to get x^2+12x+36=49. Now factor the left side by putting the half of 12 into this blank to get, (x+_)^2=49. Final Answer is,
(x+6)^2=49.

Final answer:

To solve the quadratic equation x^2 + 12x - 13 = 0 by completing the square, follow these steps. The solutions to the equation are x = 1 or x = -13.

Explanation:

To solve the quadratic equation x^2 + 12x - 13 = 0 by completing the square, follow these steps:

Move the constant term to the other side of the equation:x^2 + 12x = 13Take half of the coefficient of the x-term and square it:(12/2)^2 = 36Add this value to both sides of the equation:x^2 + 12x + 36 = 13 + 36Factor the left side of the equation, which should be a perfect square:(x + 6)^2 = 49Take the square root of both sides and solve for x:x + 6 = ±√49x + 6 = ±7x = -6 ± 7Therefore, the solutions to the equation are x = 1 or x = -13.

help in math ...........................................

Answers

Your answer would be B.

The triangles would be congruent, because the lines GH and FI are congruent and the angle H and I are the same, and since the line HI is shared by the two, it would then be SAS.
Any of the last three choices is valid.

Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. x = 2.5 when y = 100.

Answers

2.5x40=100 100/40=2.5

Answer:

constant of variation(k) is, 250.

[tex]y = \frac{250}{x}[/tex]

Step-by-step explanation:

The inverse variation says that:

[tex]y \propto \frac{1}{x}[/tex]

then, the equation is in the form of :

[tex]y = \frac{k}{x}[/tex]        ....[1] where, k is the constant of variation

As per the statement:

Suppose that y varies inversely with x.

then,

by definition of inverse variation we have;

[tex]y = \frac{k}{x}[/tex]

When x = 2.5 and y = 100 then

Substitute these in [1] we have;

[tex]100 = \frac{k}{2.5}[/tex]

Multiply 2.5 both sides we have;

[tex]250 = k[/tex]

or

k = 250

⇒[tex]y = \frac{250}{x}[/tex]

Therefore, the constant of variation is, 250 and the equation we get [tex]y = \frac{250}{x}[/tex]

Type an equation of the horizontal line that passes through the point (-2,5)

Answers

It is specified that the equation is a horizontal line, we do not need to consider the slope (since the slope would be 0). The equation would essentially become f(x)=5 

You can see, from the attached graph, that it would also pass through (-2, 5) 

Hope I helped :) 

The equation of the horizontal line that passes through the point ( -2 , 5 ) is

y = 5

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , let the point be A ( x₁ , y₁ )

The value of A ( x₁ , y₁ ) = A ( -2 , 5 )

Now , the slope of the line m is given by

Since , the line is a horizontal line , the slope of the line m = 0

Slope m = 0

Now , the equation of line is given by the equation

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = 0 ( x + 2 )

y - 5 = 0

Adding 5 on both sides of the equation, we get

y = 5

Therefore, the value of A is y = 5

Hence ,

The equation of the horizontal line that passes through the point ( -2 , 5 ) is y = 5

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Five more than three times a number q is written as

Answers

5+(3q)= is the answer

Answer:

Step-by-step explanation:

5+(3q) I think

Question 14 a certain drug is made from only two ingredients: compound a and compound
b. there are 3 milliliters of compound a used for every 4 milliliters of compound
b. if a chemist wants to make 497 milliliters of the drug, how many milliliters of compound b are needed?

Answers

A drug is made from a compound A and a compound B:
A : B = 3 : 4
A = 3 k
B = 4 k
3 k + 4 k = 7 k
7 k = 497 ml
k = 497 ml : 7 = 71 ml
B = 4 * 71 ml
B = 284 ml.
Answer: 284 ml of compound B are needed.

Express the complex number -3i in trigonometric form.

Answers

Use the formula z=a+bi=|z|(cosθ+isinθ), with |z|=√(a²+b²), and tanθ=b/a

in this case, a=0, b=-3 so |z|=√0²+(-3)²)=3
tanθ=[tex] \frac{-3}{0} [/tex], notice the denominator is 0, undefined, so the value of θ=π/2
Substitute the values of θ=π/2 and |z|=3. into the formula, you'll get 3(cos([tex] \frac{ \pi }{2} [/tex])+isin([tex] \frac{ \pi }{2} [/tex]))

what percent is 608 million of 845 million

Answers

Hello,

To find the percentage, simply divide the smaller number to the larger number. In this situation, we divide 608 million by 845 million, which will get you:
0.719526627219. At this point, move the decimal place 2 places to the right to get the percent form of the decimal. Let's also round this decimal up.

After you move the decimal place, it's now 71.9526627219, and if we round it to the nearest 10th, it would be 71.95%.

In conclusion, the percent is 71.95%.

Hope this helps!

May

Which angle in triangle XYZ has the largest measure?

Answers

Answer:

A. [tex]\angle x[/tex]

Step-by-step explanation:

We have been given measure of three sides of a triangle. We are asked to determine, which angle has the largest measure.

We know that the side of triangle corresponds to its opposite angle. The angle opposite to smallest side will have smallest measure and angle opposite to largest side will have largest measure.

We can see that the measure of largest side of our given triangle is 9 and it is opposite to angle x, therefore, [tex]\angle x[/tex] has the largest measure and option A is the correct choice.

HEEEEEEEEEEEEEEEEEEEEEEELPLLLLPLPLPLPLPLPLPLPLPLPLPLPLPL

Natalie recorded her exercise for a week. She ran 16 miles, swam 3 miles, biked 22 miles, and rollerbladed 7 miles. What part of her total distance during the week did she run?

Answers

Total distance = 16 + 3 + 22 + 7 = 48 miles

Distance she covered by running = 16 miles

Required answer = 16/48 = 1/3 = 0.33........ it's non-terminating

Hope This Helps You!
16 + 3 + 22 + 7 = 48
16/48 = 0.33
33/100 was how much distance she ran vs over-all distance

hope this helps

In which number is the digit 8 ten times larger than it is in the number 18? A) 108 B) 387 C) 801 D) 1,840 E) 8,205

Answers

B. is the correct answer as 387 contains 80 and 8 * 10 = 80. I hope this helps!!
umm D I'm pretty shure

Miranda wants to buy as many collectible dolls as possible, for $2.50 each. If she has $45.00 to spend, how many dolls can she buy?


Which equation BEST represents this situation?
A) 45x = 2.5
B) 2.5x = 45
C) x + 2.5 = 45
D) x + 45 = 2.5

Answers

Answer choice B is the best one
B. 2.5x = 45 because your wanting to buy as many dollars possible with 45 dollars and to do that  you would multiply 2.5 by x. For the fun of it I will solve. 45 divided by 2.5 is 18    x = 18


Hope I helped


Brainliest if happy :D

Tommy is twice as old as his younger sister.The sum of the siblings' ages is 21. Which equation can be used to determine the age of Tommy's younger sister? A. x-2=21 B. x+2x=21 C. 2x=21 or D. x/2=21

Answers

2x+x=21(tommy+his sister is 21)It could be B
C. 2x=21 because he Is 21 and that can solve

Help me please i will award

Answers

The number of weeds will increase to infinity, or without bound. This is because it constantly goes up.

Hope this helps!

In space, the intersection of a line and a plane is
A) not possible.
B) a point or a line.
C) a line or a plane.
D) a point or a plane.

Answers

i believe the answer is A) Not possible not sure

Expand the logarithm. log₅ 5x⁻⁵

PLS HELP!

Answers

Recall that logab=loga + logb

log₅5x⁻⁵=log₅5+log₅x⁻⁵=1-5log₅x. 

Someone help with number 11 please!! Thank you

Answers

36 degrees (it's an acute angle)
The sum of the measures of the interior angles of an n-sided polygon is 180(n - 2).

A pentagon has 5 sides, so for a pentagon, the sum of the measures of the interior angles is

180(n - 2) =

= 180 (5 - 2)

= 180 * 3

= 540

Since this pentagon is regular, all interior angles are congruent.
Each one measures 540/5 = 108, or 108 degrees.

The upper 108-degree angle together with the 2 angles marked x form a straight angle.

x + x + 108 = 180

2x + 108 = 180

2x = 72

x = 36

what fractions is 0.75 equal to

Answers

0.75 = 3/4. 

If you want any others, comment below or PM me!!

Glad I Could Help, And Good Luck!

Which are the possible side lengths of a triangle?

A.3 cm, 5 cm, 9 cm
B.4 cm, 8 cm, 10 cm
C.6 cm, 9 cm, 17 cm
D.8 cm, 10 cm, 18 cm

Answers

Final answer:

The possible side lengths of a triangle, according to the Triangle Inequality Theorem, must adhere to the principle that the sum of any two sides must be greater than the third side. Option B, with side lengths of 4 cm, 8 cm, and 10 cm, fulfills this requirement and forms a valid triangle.

Explanation:

The question asks which set of side lengths can form a triangle. In order to determine the possible side lengths of a triangle, we must use the Triangle Inequality Theorem. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Now, let's evaluate the options provided:

A. 3 cm, 5 cm, 9 cm: Here, 3 + 5 is not greater than 9, so these sides do not satisfy the theorem.

B. 4 cm, 8 cm, 10 cm: In this case, 4 + 8 is greater than 10, 8 + 10 is greater than 4, and 4 + 10 is greater than 8, satisfying the inequality.

C. 6 cm, 9 cm, 17 cm: For these measurements, 6 + 9 is less than 17, failing to meet the criteria.

D. 8 cm, 10 cm, 18 cm: Here too, 8 + 10 is less than 18, thus not compliant.

Hence, the correct answer is B. 4 cm, 8 cm, 10 cm, as these are the only side lengths that satisfy the Triangle Inequality Theorem and can form a triangle.

In the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK? Point G cannot be a centroid because JG does not equal GE. Point G cannot be a centroid because JG is shorter than GE. Point G can be a centroid because GE and JG are in the ratio 2:1. Point G can be a centroid because JG + GE = JE.

Answers

Point G cannot be a centroid because JG is shorter than GE. Without the diagram, this problem is rather difficult. But given what a centroid is for a triangle, let's see what statements make or do not make sense. Assumptions made for this problem. G is a point within the interior of the triangle HJK. E is a point somewhere on the perimeter of triangle HJK and that a line passing from that point to a vertex of triangle HJK will have point G somewhere on it. Point G cannot be a centroid because JG does not equal GE. * If G was a centroid, then JG would not be equal to GE because if that were the case, you could construct a circle that's both tangent to all sides of the triangle while simultaneously passing through a vertex of the triangle. That's impossible, so this can't be the correct choice. Point G cannot be a centroid because JG is shorter than GE. * This statement would be true. So this is a good possibility as the correct answer assuming the above assumptions are correct. Point G can be a centroid because GE and JG are in the ratio 2:1. * There's no fixed relationship between the lengths of the radius of a circle who's center is at the centroid and the distance from that center to a vertex of the triangle. And in fact, it's highly likely that such a ratio will not even be constant within the same triangle because it will only be constant of the triangle is an equilateral triangle. So this statement is nonsense and therefore a bad choice. Point G can be a centroid because JG + GE = JE. * Assuming that the assumption about point E above is correct, then this relationship would hold true for ANY point E on the side of the triangle that's opposite to vertex J. And only 1 of the infinite possible points is correct for the line JE to pass through the centroid. So this is also an incorrect choice. Since of the 4 available choices, all but one are complete and total nonsense when speaking about a centroid in a triangle, that one has to be the correct answer. So "Point G cannot be a centroid because JG is shorter than GE."

in short terms it's b lol

Solve the following equation. Then place the correct number in the box provided. 2x - 1 ≤ x + 5

Answers

Answer:

The solution for the inequality is [tex]x \leq 6[/tex].

Step-by-step explanation:

Consider the provided inequality.  

[tex]2x - 1 \leq x + 5[/tex]

Subtract x from both the sides.

[tex]2x -x- 1 \leq x-x + 5[/tex]

[tex]x- 1 \leq 5[/tex]

Add 1 to both the sides.

[tex]x- 1+1 \leq 5+1[/tex]

[tex]x \leq 6[/tex]

Hence the solution for the inequality is [tex]x \leq 6[/tex].

An unfair coin with p(h) = 0.6 is flipped 3 times and the result of each toss is noted. what is the probability that there are at least two heads?

Answers

Total possible outcomes: (2)³=8 (heads or tails possibility on each toss) 

Draw out a Tree diagram to illustrate the given example, labelling the probability on each branch. 

Adding all the possible situations with P(t)≥2, we get 0.352 as the probability. 

Hope I helped :) 

HELP PLEASE!!

Graph the system of linear equations.
-1/2y=1/2x+5 and y=2x+2

The solution to the system is ( _ , _ )

Answers

the correct answer is -4, -6

find the center and radius for the circle, given the equation: x2+16x+y2-6y=-24

Answers

Hello,

[tex]x^2+16x+y^2-6y=-24\\\\ x^2+2*8*x+64+y^2-2*3*y+9-64-9=-24\\\\ (x+8)^2+(y-3)^2=49\\\\ [/tex]
Center=(-8,3), radius=7

Multiply (2x2 + 3x − 6)(x − 1).

Answers

2x^3+x^2-9x+6

Distribute

2x^3+x^2-9x+6

Distribute

the greatest wind speed ever recorded on earth's surface is 231 miles per hour. what is the speed in kilometers per hour

Answers

if it is 231 mph it would be 372 km/h

To convert 231 miles per hour to kilometers per hour, multiply by the conversion factor of 1.60934, resulting in approximately 371.76 km/h.

The greatest wind speed ever recorded on Earth's surface is 231 miles per hour (mph). To convert this speed into kilometers per hour (km/h), we use the conversion factor that 1 mile is approximately 1.60934 kilometers. Therefore, the speed in kilometers per hour is given by multiplying the speed in miles per hour by this conversion factor.

Here is the calculation:
231 mph  x 1.60934 = 371.75774 km/h.

Approximately, the wind speed would be 371.76 km/h after converting from miles per hour.

At day camp, hiking began at 8:30 a.m. and lasted 2 hours and 42 minutes. What time did hiking end? A. 9:02 a.m. B. 10:12 a.m. C. 11:12 a.m. D. 12:02 p.m.
Plz help ppl

Answers

The correct answer is B. 10:12

A piggy bank contains $2.40 in nickels and dimes. If there are 33 coins in all, how many nickels are there?

Answers

Final answer:

To find the number of nickels in the piggy bank, you can set up a system of equations based on the total number of coins and the total value of all the coins. By solving this system, you can determine the number of nickels.

Explanation:

To find the number of nickels in the piggy bank, we need to set up a system of equations. Let's use n to represent the number of nickels and d to represent the number of dimes.

The total value of the nickels can be calculated by multiplying the number of nickels (n) by the value of each nickel, which is $0.05. So, the value of the nickels is 0.05n.

The total value of the dimes can be calculated by multiplying the number of dimes (d) by the value of each dime, which is $0.10. So, the value of the dimes is 0.10d.

We can set up two equations based on the given information:

Equation 1: n + d = 33 (total number of coins)

Equation 2: 0.05n + 0.10d = 2.40 (total value of all coins)

Now we can solve this system of equations to find the number of nickels (n).

Multiplying Equation 1 by 0.05 gives us: 0.05n + 0.05d = 1.65

Subtracting Equation 2 from this gives us: 0.05d - 0.10d = 1.65 - 2.40

Simplifying, we get: -0.05d = -0.75

Dividing both sides by -0.05, we find: d = 15

Substituting this value back into Equation 1, we get: n + 15 = 33

Subtracting 15 from both sides, we find: n = 18

Therefore, there are 18 nickels in the piggy bank.

Final answer:

To find the number of nickels in the piggy bank, set up a system of equations and solve. There are 18 nickels in the piggy bank.

Explanation:

To find the number of nickels in the piggy bank, you need to set up a system of equations based on the information given. Let's assume that the number of nickels is represented by 'n' and the number of dimes is represented by 'd'. From the problem, we know that there are 33 coins in total, so we can write the equation 'n + d = 33'. We also know that the value of the nickels, in cents, is 5n and the value of the dimes, in cents, is 10d. Since the total value of the coins is $2.40, we can write the equation '5n + 10d = 240'. Now we can solve this system of equations to find the number of nickels.

To solve the system of equations, we can use the substitution method. Rearrange the first equation to get 'n = 33 - d', and substitute this expression for 'n' in the second equation: '5(33 - d) + 10d = 240'. Simplify the equation to get '165 - 5d + 10d = 240'. Combine like terms to get '5d = 75'. Divide both sides by 5 to get 'd = 15'. Substitute this value of 'd' back into the first equation to find 'n': 'n + 15 = 33', 'n = 18'.

Therefore, there are in the piggy bank.

The number of State Parks in California is 36 more than one third the number of State Parks in Florida. There are 85 State Parks in California. Which of the following equations would you use to find the number of State Parks in Florida? Note: f represents the number of state parks in Florida. 3(f − 36) = 85 1 over 3f + 36 = 85 Quantity f minus 36 all over 3 equals 85 Quantity f plus 36 all over 3 equals 85 Question 3(Mu

Answers

c = 1/3f + 36
c = 85

1/3f + 36 = 85 <===
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