Which of the following equations has exactly one solution?
A. 4x – 4 + 2x = 6x - 4
B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
D. 3x + 5 = 2x - 6

Answers

Answer 1
A. 4X+2X-6X = -4+4
A. 0X = 0 Every number

B. 8X+10 = 8X+ 10
B. 8X -8X = 10-10
B. 0X = 0. Every number

C. 4x -8 = 4X -16
C. 4x-4x = -16+ 8
C. 0x = -8 >>no solution

D. 3X + 5 = 2x -6
D. 3x-2X = -6-5
D. x = -11 one solution

Answer D
Answer 2

The equation with exactly one solution is  3x + 5 = 2x - 6. Option D is correct.

To determine which equation has exactly one solution, we need to solve each equation and see if we end up with a unique value for 'x'.

4x – 4 + 2x = 6x - 4

Combine the x terms on the left side: 6x - 4 = 6x - 4

This equation is an identity and holds true for all values of x. It doesn't have a unique solution.

B. 2(4x + 5) = 8x + 10

Distribute the 2 on the left side: 8x + 10 = 8x + 10

Similar to the previous equation, this equation is also an identity and holds true for all values of x.

It doesn't have a unique solution.

4x - 8 = 4(x - 4)

Distribute the 4 on the right side: 4x - 8 = 4x - 16

Subtract 4x from both sides: -8 = -16

This equation is contradictory and has no solution.

3x + 5 = 2x - 6

Subtract 2x from both sides: x + 5 = -6

Subtract 5 from both sides: x = -11

This equation has a unique solution, x = -11.

So, the equation with exactly one solution is  3x + 5 = 2x - 6. Option D is correct.

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Related Questions

HELPPP! Pleaze I will give 30 points!


Triangle XYZ has vertices at X(-2, 3), Y(3, 0), and Z(2, 1). What are the coordinates of the image of Triangle XYZ after the translation (x, y) --> (x + 3, y + 1)?

Answers

Answer:

u need my help OK bet

Step-by-step explanation:

so heres tge answer

Answer:

is it x(1,4) y(6,1) z(5,2)

give brainliest

Take the number you are given, double the difference between your number and 5, add four, divide by 2. If the first number is 12, what will be the value of the third number.

A) -3
B) -2
C) 2
D) 3
E) 7

Answers

Answer:

3

Step-by-step explanation:

Here's the rundown of values:

12=9

9=6

6=3

3rd value=3

*The values are created through going through the numerical process.

Write an equation in point-slope form of the line that passes through the given point and has the given slope.
(16,-4);m=-3/4

Answers

12 square + 16 squared = c squared
144 + 256= c squared
400= c squared
C = 20

Find the length of the segment indicated. Round your answer to the nearest 10th of necessary.

Answers

Answer:

Step-by-step explanation:

Just using pythagorean theorem,

13.2²+16.9²=c²

174.24+285.61=c²

c²=√459.85

c= 21.4441134114

c = 21.4 (nearest tenth)

Olympia ate lunch at a restaurant. The amount of her check was $6.89. She left $8.00 on the table, which included the amount she owed plus a tip for the waiter. Which equation shows t, the amount of her tip, in dollars?
6.89 + t = 8.00
6.89 - t = 8.00
6.89t = 8.00
6.89 = 8.00 Divided by t

Answers

Answer:

not sure if the answer is obvious but I'd say $6.89 + t = $8.00

Step-by-step explanation:

so to make it more understandable you have to first go over the question and ask your self is the tip included in the totally amount owed or is it apart

after you figure out that its apart all you have to do is plug in the numbers you could verify this by checking every equation like this

$6.89 + t = $8.00 (t) in this case is the tip which would be $1.11 all you do to arrive at that answer is subtract the amout owed from the amount given like this $8.00 - $6.89 = $1.11 which will be your tip

now continue checking your answer next is , $6.89 - t = $8.00

which would be $6.89- $1.11 = $5.78 not quite right because now she is short on the pay , on to the next its $6.89t= $8.00 which would be $6.89 x $1.11= $7.65 rounded to neartest tenth which would included the amount but not all the tip given meaning tip would be short 0.35 cents and finally $6.89= $8.00 divided by t , now this takes the amount give which is $8.00 and divides by t which is $1.11 doing this $6.89 = $8.00/$1.11 which it is trying to imply that $6.89 is equal to $7.21 which would be incorrect making the only reasonable equation $6.89 + t = $8.00 reaveling that the tip given was $1.11

hopefully that help maybe i can get brainlist?!

Answer:

6.89 + t = 8.00

Step-by-step explanation:

it's A

Edge 2021


PLEASE HELP IM TRYING TO FINISH THIS BY NEXT MONDAY AND IVE BEEN STUCK ON THIS

Answers

Answer:

Step-by-step explanation:

Choice A is the only one that is applicable.

Answer:

A. F(x) has 1 relative minimum and maximum.

Step-by-step explanation:

[tex]{ \bf{F(x) = 2 {x}^{3} - 2 {x}^{2} + 1 }}[/tex]

As x and F(x) tend to positive and negative infinity:

[tex]{ \sf{x→ \infin : f(x) = \infin}} \\ { \sf{x→ {}^{ - } \infin : f(x) → {}^{ - } \infin}}[/tex]

❎So, B and C are excluded.

Roots of the polynomial:

[tex]{ \sf{f(x) = 2 {x}^{3} - 2 {x}^{2} + 1}} \\ { \sf{f(x) = - 0.6 \: \: and \: \: 0.8}}[/tex]

, D is also excluded.

✔, A

None of the multiple choice add up to 102 degrees any help? ​

Answers

Answer:

26

Step-by-step explanation:

Let x = the third angle in the triangle

x = 102 because they are vertical angles

The sum of the angles in the triangle are 180

b+2b+102 =180

3b+102 =180

3b = 180-102

3b = 78

Divide by 3

3b/3 = 78/3

b = 26

Answer:

Its is 26 aka E

Step-by-step explanation:

So we know that a triangle has 180 degrees in total. So we know one side is 102 degrees. 180-102=78. we can do 78 divide by 3 since there is 3b's in total. 78/3=26. Therefore, it is 26 which is E. I hope this helped ^^.

Adrian, Ben and Charlie share some sweets in the ratio 6:3:8
Charlie got 22 more sweets than Adrian.Work out the total amount of sweets.

Answers

Answer:

187 sweets

Step-by-step explanation:

8 units - 6 units = 2 units

2 units = 22 sweets

1 unit = 22 sweets ÷ 2

= 11 sweets

Total amount of sweets = 11 sweets × (6 units + 3 units + 8 units) = 11 sweets × 17 = 187 sweets

What is the equation of the graph

Answers

Answer:

y=6^x-2

Step-by-step explanation:

Start with the parent function, a^x. The graph looks like it has been translated b units down, so our function is a^x+b. Now at x=0, y=-2. So b=-2. Next at x=1, y=3. 3=a^(1)-2, a=6. y=6^x-2 is the equation

The 12th term of the arithmetic sequence is 10.5. The 18th term of this sequence is 13.5. Find the common difference and the first term.

Answers

1st way:

let the n'th term be called x, and the value of the term y,

then there is a function y=a*x + b

that will give us all term we want.

this formula is also used for straight lines.

we just need a and b. we already got two data points. we can just plug the known x/y pairs into the formula

10.5 = a*12 + b

13.5 = a*18 + b

now lets manipulate these lines.

multiply the first line by 3 and the second line by 2

31.5 = a*36 + 3b

27 = a*36 + 2b

subtract the second line from the first line

4.5 = b

yey, we now know b, let's plus b into either line from above, I'll go with the first one, looks easier.

10.5 = a*12 + 4.5

6 = a*12

0.5 = a

now y=a*x + b can be filled with a and b

y = 0.5 * x + 4.5

for x=1 (the first term) it's f(1)=5

each step is 0.5, hence the common difference.

2and way:

(13.5-10.5)/(18-12)

= 3 / 6

= 0.5

we got the comment difference by looking at the full difference over 6 steps and divined by these 6 steps.

from step 12 to step one it's 11 steps down

10.5 - 0.5*11

= 10.5 - 5.5

= 5

okay I admit... 2and way to do it might be faster and more intuitive... :D

SEE QUESTION IN IMAGE

Answers

Answer:

46.

Total number in favour:

128 + 96 = 224

Probability:

P(favour, A) = 128/224 = 4/747.

Total number in against:

32 + 48 = 80

Probability:

P(against, not B) = 32/80 = 2/5

Given: LMN = PQR Find: m

Answers

Answer:

I don't understand the question?

Which represents the solution(s) of the system of equations, y = x2 – 2x – 15 and y = 8x – 40? Determine the solution set algebraically.

Answers

Answer:

Therefore, the value of x is 5.

Step-by-step explanation:

We can match each equation to find the solutions.

[tex]8x-40=x^{2}-2x-15[/tex]

[tex]0=x^{2}-2x-8x-15+40[/tex]

[tex]x^{2}-10x+25=0[/tex]

Now, we need solve this quadratic equation.

[tex](x-5)^{2}=0[/tex]

Therefore, the value of x is 5.

I hope it helps you!

 

50 apples cost 25$ how much would 75$ apples cost?

Answers

Answer:

100

Step-by-step explanation:

Hey there!

First, to find the cost of one apple, 50 ÷ 25, which equals 2.

At this point, i am not very sure if you meant to say 75 apples, or $75 apples, so I am just going to give both solutions.

If you meant 75 apples: 75 x 2 = $150

If you meant $75 apples: $75 ÷ 2 = 37.5

Since it isn't realistic to buy 37 apples and one half, round it to 37 apples.

Hope this helps!

Have a great day!

What is the initial value of the sequence?
1
2
3
8

Answers

Answer:

2

Step-by-step explanation:

The initial value is the y value of the first term shown ( when x=1)

y = 2 when x=1

The initial value is 2

Answer:

What is the initial value of the sequence?

1 2 <<<CORRECT 3 8

Step-by-step explanation:

Edge 2021

The cardinality of the set of positive integer is infinity. (True or False)

Answers

Answer:

It is false, because infinity is not a cardinality. The set  N  of positive integers is infinite and its cardinality is, if you wish,  ℵ0 , the smallest infinite cardinal number, at least in an axiomatic set theory. A set  S  is infinite if and only if there exists a bijection between  S  and a proper subset of  S , i.e. a subset of  S  different from  S . Now the successor function  s:N→N∗  is such a bijection; this follows from Peano’s axioms for arithmetic.

Answer: false

please click thanks and mark brainliest if you like :)

if an angle is 10 degree less than its complement, find the angle.

Answers

Let one be x

Other one is x-10

ATQ

[tex]\\ \sf \longmapsto x+x-10=90[/tex]

[tex]\\ \sf \longmapsto 2x-10=90[/tex]

[tex]\\ \sf \longmapsto 2x=90+10[/tex]

[tex]\\ \sf \longmapsto 2x=100[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{100}{2}[/tex]

[tex]\\ \sf \longmapsto x=50[/tex]

[tex]\\ \sf \longmapsto x-10=50-10=40[/tex]

At the laundromat, Carol used to pay $1.50 per load, but the company has increased the price per load by 20%. Estimate the amount Carol will pay to was 6 loads of laundry.

Answers

Answer:

$10.80 (about $11)

Brainliest, please!

Step-by-step explanation:

20% = 0.2

+20% = x 1.2

1.5 x 1.2 = 1.8

1.8 x 6 = 10.8

A survey was taken of children between the ages of 3 and 7. Let A be the event that the person has 2 siblings, and let B be the event that the person does not have a pet.
Which statement is true about whether A and B are independent events?

A and B are independent events because P(A∣B) = P(A) = 0.18.
A and B are independent events because P(A∣B) = P(A) = 0.4.
A and B are not independent events because P(A∣B) = 0.4 and P(A) = 0.18.
A and B are not independent events because P(A∣B) = 0.18 and P(A) = 0.4.

Answers

Answer: A and B are not independent events because P(A∣B) = 0.18 and P(A) = 0.4.

Step-by-step explanation:

They are not independent events because if they were P(A∣B) and P(A) would be equal.

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

y= -2x+11


y=-3x+21

Answers

Answer:

x=10

y=-9

Step-by-step explanation:

eqn 2-1

-1x+10=0

x=10

in eqn 1

y=-2 ×10+11

-20+11

-9

please help have a lot of math to do

Answers

Answer:

The surface area of the rectangular prism is 814[tex]in^{2}[/tex]

Step-by-step explanation:

In order to find the surface area for a rectangular prism you have to solve using the following formula

A=2(wl+hl+hw)

Hope this helps!

The surface area is 814inches squared

Please help pleaseeee

Answers

Answer:

False

Step-by-step explanation:

When you compare the dots to the numbers, you can see that the 5s and 8s don't match.

The dot plot has 6 5s, but the data has 5.

The dot plot has 2 8s, but the data has 1.

I hope this helps!

pls ❤ and give brainliest pls

Organize the data set:

8,7,5,5,4,2,3,3,4,6,5,4,5,5

2,3,3,4,4,4,5,5,5,5,5,6,7,8

False

shop sells shirts. In
January they reduce the
price of all their £50 shirts
by 50%. In February they
decide to increase the price
of all their shirts by 50%. In
March they decide to
reduce the price of their
shirts by 50% again. What is
the cost of a shirt in March?

Answers

50% off £50 = £25
The shirts cost £25 in January
50% more of £25 = £12.5
The shirts cost £37.5 in February
50% off of £37.5 = £18.75
A shirt in March cost £18.75

Please Help Me With This Geometry Problem

Answers

Answer:

Remember that the area of a square of sidelength L is:

A = L^2

And the area of a circle of diameter D is:

A = pi*(D/2)^2

If we inscribe a square in a circle, we will get four segments, like the ones shaded in the image below:

Notice that the diameter of the circle will be equal to the diagonal of the square.

And the diagonal of a square of side length L is:

d = √(2)*L

knowing that the side length of our square is 6 inches, the diameter of the circle will be:

D = √2*6in

Now, the total area of the four shaded parts will be equal to the difference between the area of the circle and the area of the square.

The area of the circle is:

A = pi*(√2*6in/2)^2 = (pi/2)*36in^2

The area of the square is:

A' = (6in)^2 = 36in^2

The difference is:

A - A' =  (pi/2)*36in^2 - 36in^2 = (pi/2 - 1)*36in^2

And there are 4 of these segments, then the area of every single one is one-fourth of that:

a = (1/4)*(pi/2 - 1)*36in^2 = (pi/2 - 1)*9 in^2

The area of each segment is:

a =  (pi/2 - 1)*9 in^2

if we replace pi by 3.14, the exact area will be:

a = (3.14/2 - 1)*9in^2 = 5.13 in^2

Which equation represents an exponential function with an initial value of 500?

f(x) = 100(5)x
f(x) = 100(x)5
f(x) = 500(2)x
f(x) = 500(x)2

Answers

Answer:

y = 500 * (2)^x is an exponential function

Step-by-step explanation:

An exponential function is of the form

y = a b^x  where a is the initial value and b is the growth/decay factor

y = 500 * (2)^x is an exponential function

The correct equation that represents an exponential function with an initial value of 500 is:

f(x) = 500(2)x

What is a logarithmic function?

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

We are given that the initial value of the exponential function is 500. The initial value refers to the value of the function when x is equal to zero. Therefore, the value of f(0) is 500.

Out of the four given options, only option (c) represents an exponential function with an initial value of 500, since f(0) is equal to 500 when x is equal to zero:

f(x) = 500(2)^x

Option (a) represents an exponential function with an initial value of 100 and a base of 5.

Option (b) represents a power function, not an exponential function.

Option (d) represents an exponential function with an initial value of 0 and a base of x^2, which can take any value including negative values, thus it doesn't satisfy the conditions of a valid exponential function.

Learn more about logarithmic functions here:

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Answers

Answer:

C

Step-by-step explanation:

cot =cos/sin =a/b

cos=a/b*sin

(sin-cos)/(sin+cos) =(sin-sin*a/b)(sin+sin*a/b)

=(1-a/b)/(a+a/b)

=(b-a)/(a+b)

What would -4|5+-3| be

Answers

Answer:

-8

Step-by-step explanation:


Find the FACTORS of
36

Answers

Answer:

factors of 36 are 1,2,3,4,6,9,12,18,and 36

Find the sum of a 22-term arithmetic sequence, where the first term is 7 and the last term is 240.

Answers

Answer:

The sum of the arithmetic series is 2717.

Step-by-step explanation:

The sum of an arithmetic sequence is given by:

[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]

Where k is the number of terms, a is the initial term, and x_k is the last term.

There are 22 terms, the first term is 7, and the last term is 240. Hence, the sum is:

[tex]\displaystyle \begin{aligned} S &= \frac{(22)}{2}\left((7) + (240)} \\ \\ &= 11(247) \\ \\ &= 2717\end{aligned}[/tex]

In conclusion, the sum of the arithmetic series is 2717.

find the missing segment in the image below​

Answers

Answer:

3

Step-by-step explanation:

Intercept theorem

DE // CB ⇒ [tex]\frac{AD}{AC} = \frac{AE}{AB}[/tex]

⇒ [tex]\frac{6}{6+?} =\frac{4}{4+2}[/tex]

⇒ ? = 3

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