Mathematics High School

Name the Property of Equality that justifies the statement: If m<A + M<B = M<C. Then, M<A = M<C - M<B
Transitive Property
Symmetric Property
Reflexive Property
Subtraction Property

Answers

Answer 1
The subtracton property of equality allows you to subtract the same amount from both sides of an equation without changing the truth of the equation.
Answer 2

Answer:

subtraction property

Step-by-step explanation:

Related Questions

draw a number line from 0 to 2 write 3\8 1 and 3\4 and 1.25 on the number line,

Answers

To solve this exercise you must apply the proccedure shown below:
 1- You have the following numbers given in the problem above:
 3/81, 3/4 and 1.25
 2- Therefore, you have that 3/81 in decimal form, is: 
 3/81=0.03
 3- 3/4 in decimal form is:
 3/4=0.75
 3- Keeping this on mind,  you can draw the number line from 0 to 2 and write the numbers given above, as you can see in the figure attached.
The graph of the number line from 0 to 2 is shown in Figure 1. We start this graph by setting the number zero to the left of the number 2, that is, the numbers increases from left to right. Next, we have the following points to be marked in the number line:

 [tex]\frac{3}{8} \\ \\ 1 \\ \\ \frac{3}{4} \\ \\ 1.25[/tex]

But we can rewrite these numbers as decimals:

[tex]\frac{3}{8}=0.375 \\ \\ 1 \\ \\ \frac{3}{4}=0.75 \\ \\ 1.25[/tex]

So Figure 2 shows each point marked on the number line. The way we choose is to set each point on the number line analyzing in which position it must lay. For instance, [tex]\frac{3}{8}[/tex] is less than [tex]\frac{3}{4}[/tex] but greater than zero. So its position is as indicated in Figure 2.

Point A is located at (0, 4) and point B is located at (−2, −3). Find the x value for the point that is 1/4 the distance from point A to point B.

−1

−0.75

−0.5

−0.25,

Answers

- First thing, find the distance between A and B:
 
AB =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex] =
      =[tex] \sqrt{(0-(-2))^{2} + (4-(-3))^{2} } [/tex] =
      = [tex] \sqrt{4+49} [/tex] =
      = √53

- Hence, we know that the distance between point A and the point C to be found is: 
AC = √53 / 4

- The only other thing we know about point C is that it lays on the line that connects A and B. Let's use the point-slope formula to find the equation of this line:

y - y₂ = [tex] \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] (x - x₂)
y - (-3) = (7/2)(x - (-2))
y + 3 = (7/2)(x + 2)
y = (7/2)x + 7 - 3
y = (7/2)x + 4

This is the equation that ties the coordinates of every point laying on it, therefore it is vaid for A, B and, above all, C which will be:
C (x , (7/2)x + 4)

- Now let's find the distnce between A and C:
AC =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]=
      =[tex] \sqrt{(x-0)^{2} + ((7/2)x+4-4)^{2} } [/tex] =
      =[tex]\sqrt{x^{2} + (49/4)x^{2} }[/tex] =
      =[tex] \sqrt{(53/4) x^{2} } [/tex] =
      =+/-(√53/2)x 
- Lastly, we know this distance must be equal to √53 / 4, therefore you need to set and solve the equation:
+/-(√53/2)x = √53 / 4
(1/2)x = +/-(1/4)
x = +/-(1/2)

Since point C is towards point B, we have to take the negative answer: 
x = -(1/2)

- Therefore the correct answer is C: -0.5

Find the zeros of the function. f(x)=9x^2-12x-5

Answers

x=5/3, -1/3

You can use the quadratic formula or you can do any method that your teacher teaches you (box, etc.)
Answer: 5/3 and - 1/3

Explanation:

1) Set the given function equal to 0: 9x^2 - 12x - 5 = 0

2) make 9x^2 = (3x)^2 and 12x = 4(3x)

=> (3x)^2 - 4(3x) - 5 = 0

3) Factor the polynomial:

(3x - )(3x + ) first stept of factoring.

Now find two numbers that sum - 4 and their product of - 5, those are -5 and + 1: =>

(3x - 5) (3x + 1) = 0

4) Set the two factors equal to 0:

3x - 5 = 0 => 3x = 5 => x = 5/3  ↔ one root

3x + 1 = 0 => 3x = - 1 => x = - 1/3 ↔ the other root.

75 less than twice a number

Answers

I think the number is 75 because 75 x 2 = 150 - 75 = 75.

What is the best first step in solving the equation 3 +3 square root 6x = 5? A.)Subtract 3 from both sides.
B.)Find the cube of 3 square root 6x .
C.)Cube both sides of the equation.
D.) Subtract 5 from both sides.

Answers

Final answer:

The best initial step in solving the equation 3 + 3√(6x) = 5 is to subtract 3 from both sides, simplifying the equation to 3√(6x) = 2, which lays a clear path towards isolating and solving for x.So,option A.)Subtract 3 from both sides. is correct.

Explanation:

The best first step in solving the equation 3 + 3√(6x) = 5 is to simplify the equation by isolating the square root term. This can be done by following option A: Subtract 3 from both sides of the equation. This action makes the equation easier to manage step-by-step as you move toward isolating x, which is the ultimate goal of solving for x. The resulting equation after subtracting 3 from both sides is 3√(6x) = 2. This simplified equation can then be further manipulated to solve for x, primarily by squaring both sides to eliminate the square root, and then solving the resulting simple algebraic equation.

Please help!


Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are spades? Are these events independent?


A. 1/17: no, they are dependent events

B. 1/16: yes, they are independent events

C. 25/52: yes, they are independent events

D. 3/52: no, they are dependent events

Answers

Answer: 
Choice A
1/17; no, they are dependent events

============================================

Explanation:

There are 13 spades and 52 cards total. So 13/52 = 1/4 is the probability of drawing one spade

If we do not replace the card we pull out, then the probability of another spade is 12/51 since there are 12 spades left out of 51 total. 

Multiply the fractions 1/4 and 12/51 to get
(1/4)*(12/51) = (1*12)/(4*51) = 12/204 = 1/17

The two events are not independent because the second event (pulling out a second spade) depends entirely on what happens in the first event (pulling out a first spade). The fact that the probability is altered indicates we have dependent events.

Please answer this and thank you

If DE=4x+10, EF=2-1, and DF=9x-15, find DF.

Answers

I hope that 2-1 means 21.

DE + EF = DF
4x + 10 + 21 = 9x - 15
4x + 31 = 9x - 15
31 = 9x - 4x - 15
31 = 5x - 15
46 = 5x
x = 9 1/5 = 9.2

You want 9x - 15
9*9.2 - 15
82.8 - 15
67.8 <<<<< answer. 
If I have given the wrong meaning to 2-1 (which could mean 1) leave another note and I will correct my work. 

Which ordered pair is the best estimate for the solution of the system of equations?

y=−34x−2y=x+6




(−4.25,1.5)

(−4.75,1.75)

(−4.5,1.5)

(−4.5,1.75)

Answers

Final answer:

The best estimate for the solution of the system of equations is (-4.5, 1.5).

Explanation:

The system of equations given is:

y = -34x - 2

y = x + 6

To find the best estimate for the solution, we can substitute the x-coordinate from each ordered pair into the second equation and solve for y.

Let's check each option:

For (-4.25, 1.5):

1.5 = -4.25 + 6

1.5 = 1.75 (not equal)

This is not a solution for the system.

For (-4.75, 1.75):

1.75 = -4.75 + 6

1.75 = 1.25 (not equal)

This is not a solution for the system.

For (-4.5, 1.5):

1.5 = -4.5 + 6

1.5 = 1.5 (equal)

This is a solution for the system.

For (-4.5, 1.75):

1.75 = -4.5 + 6

1.75 = 1.5 (not equal)

This is not a solution for the system.

Therefore, the best estimate for the solution of the system of equations is (-4.5, 1.5).

How do you decide which variable to isolate in order to use the substitution method to solve a system of linear equations?

Answers

Find a variable with no coefficient.If there is more than one variable with no coefficient,it dose not matter which one you isolate.Isolate the variable and then use substitution to solve the system of equations.

The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;

to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.

       A system of linear equations can be solved by three major methods which are;

- Elimination method

- Substitution method

- Graph method

     Now, in this question we want to know how substitution method is done.

Let us say we have two simultaneous equations which are;

2x + 3y = 8   ----(eq 1)

x + 5y = 11     ----(eq 2)

      Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.

In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;

x = 11 - 5y

    In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.

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what is y−4=−2(x+7) written in standard form?

Answers

y=2x+18

Hope that helps!
The standard form of a linear equation is [tex]ax+by=c[/tex], where a, b, and c are numbers.

You are given [tex]y-4=-2(x+7)[/tex]. We need to start by expanding and simplifying.

 [tex]y-4=-2x-14\\y=-2x-14+4\\2x+y=-10[/tex]

Some teachers, including mine when I took Algebra 1, require that you find integers (whole numbers) for a, b, and c, and that a be positive. Here, we are fine.

10 points!
Which graph represents the solution to the system of inequalities?
2x – y ≥ 3
x + 2y < 4

Answers

Graph C is the answer. 

2x – y ≥ 3x + 2y < 4
=y is less than or equal to 2x-3
y is less than -x/2+2



Answer:

graph c is the correct answer hope this helps you get an A.

Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and DF = x - 2 . What is the value of x?

Answers

x=8.

Following the similarity statement, we know that AC is to DF as BC is to EF.  The ratio would be:

24/(x-2) = 20/5

Cross multiply:
24*5 = 20(x-2)

Use the distributive property:
120 = 20x - 40

Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x

Divide both sides by 20:
160/20 = 20x/20
8 = x

Suppose an investment of $2,300 doubles in value every decade. The function gives the value of the investment after x decades. f(x)=2300*2^x How much is the investment worth after 2 decades?
(1 point)$2,355,200
$92,000
$46,000
$9,200

Answers

Final answer:

The investment is worth $9,200 after 2 decades.

Explanation:

To find the value of the investment after 2 decades, we can substitute x = 2 into the function f(x) = 2300 * 2^x.

So, f(2) = 2300 * 2^2 = 2300 * 4 = 9200.

Therefore, the investment is worth $9,200 after 2 decades.

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Shannon collects charms for her charm bracelet. her charm bracelet had 4 charms when she bought it. each year on her vacation she buys 2 more charms to add to her bracelet. assume that shannon continues to buy the same number of charms each year. write an equation that can be used to find how many charms shannon will have on her bracelet after 5 years.

Answers

I think it should be y=4+2*5
2x + 4 = the number of charms that Shannon has

x = the number of years that Shannon has had the bracelet 

Replace x with 5 to find the total number of charms after 5 years

2*5 + 4 = 14 charms after 5 years. 

Rico is making 4 batches of salsa.EAxh batch needs 2/3 cup of corn.He only had a 1/3 cup measure.How many times must rico measure 1/3 cup of corn to have enough for all of the salsa

Answers

He would need to measure the  1/3 cup of corn 2 times

Solve the equation 2cos^2x = sin2x , giving your answer in terms of π. 0

Answers

2cos^2x = sin2x 2cos^2x = 2sin x cos x (2sin x cos x) / (2cos^2x) = 1 sin x / cos x = 1 tan x = 1 x = π/4

Given is [tex] 2*cos^{2} (x)=sin(2x) [/tex]

We can use following formulas to solve this problem :-

1. [tex] \frac{sin\;\theta}{cos\;\theta} = tan\;\theta [/tex]

2. sin(2∅) = 2·sin(∅)·cos(∅)


Solving the given equation :-

[tex] 2*cos^{2} (x)=sin(2x) \\\\2*cos^{2} (x)=2*sin(x)*cos(x) \\\\2*cos^{2} (x)-2*sin(x)*cos(x)=0 \\\\2*cos^{2}(x)*(1-\frac{sin(x)}{cos(x)}) =0 \\\\2*cos^{2}(x)*(1-tan(x)) =0 \\\\cos^{2}(x) = 0 \;or\; (1-tan(x)) =0 \\\\cos(x) = 0 \;or\; tan(x) =1 \\\\x = cos^{-1}(0) \;or\; x=tan^{-1}(1) \\\\x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex]

Hence, final answer is [tex] x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex].

Suppose that a system has 5000 grasshoppers. how many hawks would be expected?

Answers

Probably 2500 or less because they dont need that much hawks.

Please help me on this....

Answers

8x + 4y = 16
x + 7y = 15
multiply second equation by (-8)
-8x - 56y = -120
so now
 8x + 4y = 16
-8x - 56y = -120
-----------------add
-52y = -104
y = 2


7(2) = 15 - x
14 = 15 - x
x = 1

answer is C. 
(1, 2)

Please explain it and tell me how u got the answer
Thx

Answers

The y-intercept of a function is that function's value when x=0.
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.

If you want them to differ by zero (be the same), you have to move them to the same point.

Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.

Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.

Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.

Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.

___
The appropriate choice is the 1st one.
&nbsp; f(x) - 3 and
&nbsp; g(x) + 1

Will mark brainliest ⭐️⭐️⭐️⭐️⭐️

Answers

is a hope this helped

Answer:

answer is d

Step-by-step explanation:

A $50,000 investment earns 18% annually. If B represents the balance and t represents the number of years, determine an expression that gives the account balance, B, after t years. Also, determine an equivalent expression that displays the effective monthly interest rate.

Answers

Using the compound interest formula;
FV=P(1+r/100)^t

FV is the future value
P is the principle 
r is the rate
t is the time

the formula that gives the account balance after t years will be:

FV=50000(1+18/100)^t
FV=50000(1.18)^t

The formula for effective monthly interest rate will be:
monthly interest rate=(annual rate)/(number of months)
annual rate=18%
number of months in a year=12 months
rate=18/12=1.5%

Answer:

usa test prep its B

Step-by-step explanation:

How to find x in this math problem?

Answers

In a triangle, the three interior angles always add to 180°  ⇒
The third interior angle of the triangle = 180 - (30+20) = 130°

Vertical angles are equal ⇒  x = 130°

The answer is 130°

If the state sales tax is 6% and a city adds an additional 1 1/4% tax,
What will the tax be on a purchase of $146.00? (Round the answer to the nearest cent.)

A. $10.59
B. $8.76
C. $10.80
D. $18.25

Answers

Your answer is A. 10.59 is the tax. 

The explicit rule for a sequence is an=14-9n
What is the recursive rule for the sequence?

Answers

you have to add it then divide it 

The explicit rule for the sequence is [tex] a_{n}=14-9n [/tex]

Let us put n=1, we get

[tex] a_{1}=14-(9 \times 1)=5 [/tex]

Now let n=2,

[tex] a_{2}=14-(9 \times 2)=-4 [/tex]

Let n=3,

[tex] a_{3}=14-(9 \times 3)=-13 [/tex]

Similarly, in this manner we obtain a sequence as

5, -4, -13, -22,.....

Since we can clearly observe that the first term is '5' and common difference is '-9'.

So, we get recursive rule for the sequence as:

[tex] a_{n}=a_{n-1}-9 [/tex] , where [tex] a_{1}=5 [/tex].

what is the missing number in the synthetic division problem below?
(everything in picture)

Answers

The answer is C, 10.

When performing synthetic division, we bring down the first number in the box.  We then multiply this number by the number outside the box, and place that result under the second number in the box.  We add these two numbers and bring that sum down.

We then continue this process by multiplying this second number by the number outside the box, and place the result under the third number in the box.  We then add the two numbers in the third column and bring the sum down.  The missing number is under this column; that means it is found by adding 2+8, so it is 10.

In the given problem , missing number in the synthetic division is equal to [tex]10[/tex].

What is synthetic division?

" Synthetic division is defined as simplified way of dividing a polynomial by another polynomial of first degree by writing its coefficient and changing usual subtraction into addition."

According to the question,

As shown in the given synthetic division,

[tex]4 + 20 = 24\\\\-2 + 6 = 4[/tex]

Therefore,

Missing number in the given synthetic division [tex]= 2+ 8[/tex]

                                                                                [tex]=10[/tex]

Hence, Option (C) is the correct answer.

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What context clue in the paragraph best helps in understanding the meaning of the word native?

Question 2 options:

"much in America"


"lived in Nantes, France"


"first in France"


"born in Louisiana"

Answers

What was the Answer?


The length of a rectangular garden is 7 feet longer than its width. if the garden's perimeter is 182 feet, what is the area of the garden in square feet?

Answers

182 - 14=168
168/2
=84
84+7=91
91x84 = 7644 square feet
7644 square feet :))))))))

A roped off area of width x is created around a 4-foot by 6-foot rectangular museum of display of Native American artifacts. The combined area of the display and the roped-off is 120 square feet. Find the width.

Answers

Let
x----------> width a roped off area

we know that
(4+2x)*(6+2x)=120
then
4*6+4*2x+2x*6+2x*2x=120 ---> 24+8x+12x+4x²=120 -------> 4x²+20x+24=120
4x²+20x-96=0

using a graph tool---------> to calculate the quadratic equation
see the attached figure

the solution is 
x=3 ft

the answer is
the width a roped off area is 3 ft

The width of the roped off area around the museum display is 4 feet.

To find the width of the roped off area around the museum display of Native American artifacts, we need to solve for x in the area equation. The area of just the display is 4 feet by 6 feet, which is 24 square feet. Since we know the combined area of the display and the roped-off area is 120 square feet, the equation is:

Area of display + Area of roped-off region = Total Area

(4)(6) + ((4 + 2x)(6 + 2x) - (4)(6)) = 120

24 + (24 + 4x + 12x + 4x2) - 24 = 120

Simplifying, we get:

4x² + 16x - 96 = 0

Divide by 4:

x² + 4x - 24 = 0

Factor the quadratic equation:

(x + 6)(x - 4) = 0

Setting each factor equal to zero gives us two potential solutions:

x + 6 = 0
or
x - 4 = 0

Therefore, x can be -6 or 4. Since a width can't be negative, the only logical solution is:

x = 4 feet

The width of the roped-off area is 4 feet.

Which fraction is NOT equivalent to 8 1/2 ? A) 2 3 B) 24 36 C) 4 6 D) 6 10




What is 5 x 2/3?

A) 3 1/3


B) 3 2/5


C) 5 2/3


D) 10/15

Answers

None of the fractions are equivalent on the first one. 

The answer for the second question is A. 3 1/3.  5/1 x 2/3 =10/3 10/3=3 1/3

In the triangle below, 4/5 represents which ratio?

Answers

Answer:
sin (C)

Explanation:
In a right-angled triangle, special trig functions can be applied. These functions are as follows:
sin (theta) = [tex] \frac{opposite}{hypotenuse} [/tex]

cos (theta) = [tex] \frac{adjacent}{hypotenuse} [/tex]

tan (theta) = [tex] \frac{opposite}{adjacent} [/tex]

Now, let's check the triangle we have:
We have two options:
First option:
5 is the hypotenuse of the triangle
4 is the side adjacent to angle B
Therefore, we can apply the cos function:
cos (B) = [tex] \frac{4}{5} [/tex]

Second option:
5 is the hypotenuse of the triangle
4 is the side opposite to angle C
Therefore, we can apply the sin function:
sin (C) = [tex] \frac{4}{5} [/tex]

Among the two options, the second one is the one found in the choices. Therefore, it will be the correct one.

Hope this helps :)

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