Decide whether each equation is true for all, one, or no values of x.

Decide Whether Each Equation Is True For All, One, Or No Values Of X.

Answers

Answer 1

Answer:

For the first equation, it is "True for one value of x."

For the second equation, it is "True for no value of x."

For the third equation, it is "True for all values of x."

Step-by-step explanation:

Just solve the equation and check the numbers:

If both numbers are the same, it is "true for all values of x"

If there is a variable and a number, it is "true for one value of x"

If there are two numbers and they are different, it is "true for no values of x"

Hope this helps!

Please give brainliest

Answer 2

We need to check whether the given equations are true for all values of [tex]x[/tex] , one value of [tex]x[/tex] , or no values of [tex]x[/tex] .

The equations are ,

[tex]3x +9 = -4.5x +20[/tex]

solve this equation for x ,

[tex]\longrightarrow 3x +9=-4.5x+20\\[/tex]

[tex]\longrightarrow 3x+4.5x =20-9\\[/tex]

[tex]\longrightarrow 7.5x =11\\[/tex]

[tex]\longrightarrow \underline{\underline{x =\dfrac{11}{7.5}}}[/tex]

Hence the equation is true for one value of x .

[tex] 9(x+3)=9x+12[/tex]

solve out for x ,

[tex]\longrightarrow 9x +27=9x-12\\ [/tex]

[tex]\longrightarrow 9x -9x =-27-12\\ [/tex]

[tex]\longrightarrow 0 = -39[/tex]

This can never to true , so the equation is true for no values of x .

[tex]4(2x+3)=12+8x[/tex]

solve out for x ,

[tex]\longrightarrow 8x+12=12+8x \\[/tex]

[tex]\longrightarrow 12-12=8x-8x\\[/tex]

[tex]\longrightarrow 0=0 [/tex]

Hence this equation is true for all values of x .

And we are done!


Related Questions

1.2
Which of the following expressions represents "the product of a number and eight"?

8x
X+8
X/8
8-x

Answers

The expression that represents the statement "the product of a number and eight" is 8x.

Expression:

Expression means the mathematical statement that consists of  minimum of two numbers/variables and at least one math operation(addition, subtraction, multiplication and division) in it.

Given,

The given statement is "the product of a number and eight".

Now, we have to find the suitable expression for this statement.

In order to find the suitable expression, we have to divide the given statement and then we have to identify the keyword in it.

By using those keywords, we have to solve it.

In the given statement we have identify the following:

product

number

eight

Here the product refers the multiplication

number is any unknown number that is x.

eight refers the number 8.

When we combine these keywords we can get the expression 8x.

Therefore, the resulting expression is 8x.

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Joanna saves $55 each month from her part-time job. She saves 1/5 of her earnings. Write and solve an equation determine Joanna’s earnings

Answers

If 1/5 of Joanna's monthly savings is $55 the equation of her savings is

x/5 = 55

The solution to the equation is $275

How to determine the equation of Joanna's savings

information from the question include

Joanna saves $55 each month from her part-time job

She saves 1/5 of her earnings

let x represent the Joanna's earnings

The equation of Joanna savings is represented in the form

1/5 of x = 55

This equation deals with multiplication and the term 'of' as used in math represents multiplication

Hence 1/5 of x = 1 / 5 * x = x/5

x/5 = 55

multiplying both sides by 5

x = 275

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Are these parallel or perpendicular or neither? 3x+2y=10 and 2x+3y=-3

Answers

Answer:

These lines are neither parallel nor perpendicular.  

Step-by-step explanation:

Parallel lines are lines that never intersect and perpendicular intersect at a ninety degree angle.

Using desmos, you can find your solution.

I hope this helps

-No one

Delta Airlines' flights from Denver to Dallas are on time 80 % of the time. Suppose 7 flights are randomly selected, and the number on-time flights is recorded.

Round answers to 3 significant figures.


The probability that exactly 4 flights are on time is =



The probability that at most 3 flights are on time is =



The probability that at least 6 flights are on time is =

Answers

1) Probability that exactly 4 flights are selected is; P(X = 4) = 0.11469

2) The probability that at most 3 flights are on time is; P(X ≤ 3) = 0.99533

3) The probability that at least 6 flights are on time is; P(X ≥ 6) = 0.57672

How to solve Binomial Probability Distribution?

The formula for binomial probability distribution is;

P(r) = nCr * p^(r) * (1 − p)^(n − r)

Where;

n = Number of events

r = Number of successful events in the trials

p = Probability of success in the single trial of the events

We are given;

p = 80% = 0.8

n = 7

1) Probability that exactly 4 flights are selected is;

P(X = 4) = ⁷C₄ * 0.8⁴ * (1 − 0.8)^(7 − 4)

P(X = 4) = ⁷C₄ * 0.8⁴ * 0.2³

P(X = 4) = 0.11469

2) The probability that at most 3 flights are on time is;

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Solving using online binomial calculator gives;

P(X ≤ 3) = 0.99533

3) The probability that at least 6 flights are on time is;

P(X ≥ 6) = P(X = 6) + P(X = 7)

P(X ≥ 6) = 0.57672

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i took a sample of the grade point averages for students in my class. for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89. the standard error for the sample was:

Answers

The standard error for the sample was 0.13 when "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89."

What is standard error?

The standard deviation of a statistic's sampling distribution, or an estimate of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean. By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.

Here,

The standard error=standard deviation/√number of samples

=0.65/√25

=0.65/5

=0.13

When "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89," the standard error for the sample was 0.13.

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Find the slope of the line(4,9) and (4,13)

Answers

Answer:

the slope of the line is undefined

The table represents points on a line. What is the slope
X 1 4 7 10
Y 8 6 4 2

Answers

Answer:

slope = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 8) and (x₂, y₂ ) = (10, 2) ← 2 ordered pairs from the table

m = [tex]\frac{2-8}{10-1}[/tex] = [tex]\frac{-6}{9}[/tex] = - [tex]\frac{2}{3}[/tex]

what is 398+8967 i need help with this

Answers

9365 as



8967
+398
9365
9,365



ANDWERRRRrrrrrrrrr

First, complete the story below so that it can be represented by the equation 5000-50x=4800-30x

Pool A started with 5000 liters of water, and 50 liters per minute are being (Drained out or Pumped back in)
Pool B started with 4800 liters of water, and 30 liters per minute are being (Drained out or Pumped back in)

The amount of water after x minutes is more in which pool? Pool A or Pool B?

Answers

Amount of water after x minutes is more in pool B.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given,

Pool A started with 5000 liters of water, and 50 liters per minute are being.

Pool B started with 4800 liters of water, and 30 liters per minute are being.

5000-50x=4800-30x

Add 30x on both sides

5000-50x+30x=4800-30x+30x

5000-20x=4800

5000-4800=20x

200=20x

Divide both sides by 20

20=x

Now substitute x in pool A equation

5000-50x

5000-50(20)=5000-1000

Pool A =4000

Now substitute x in pool B equation

4800-30x

4800-30(20)

4800-600

Pool B =4200

4200>4000

Pool B> Pool A

Hence amount of water after x minutes is more in pool B.

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3. Tina needs to build a fence. The fence
is 30 feet long and 20 feet wide. She
realizes she needs more so she increases
the length and width by x feet. Create an
expression that represents the perimeter
for the fence.

Answers

Solution:
2(30+x)+2(20+x)
Explanation:
Perimeter for a rectangle is “2 times length + 2 times width” (2l+2w)
The perimeter before she added x more was 2(30) + 2(20) now that she added it you have to change it to 2(30+x)+2(20+x).

The garden club at Central Middle School is planting a flower bed. A scale drawing of the flower bed is shown. The scale is 1 in. : 2 ft.

Answers

Answer:

16 and 12

Step-by-step explanation:

A.1 IN=2FT

8IN =2(8)FT

= 16

B.1 IN=2FT

6IN=2(6)FT

=12 FT

if ratings on a measure of creativity contain nothing but random error, what would the reliability of that measure be?

Answers

50 would be the reliability of that measure  by standard error.

What is the standard deviation?

The population mean and sample mean are likely to deviate from one another, and the standard error of the mean, or simply standard error, shows how likely this is. If a study were to be repeated using fresh samples drawn from a single population, it would be possible to calculate how much the sample mean would change.

A measure that has no random error and no true score (i.e., is only random error) has zero reliability. A measure that has random error.

50 would be the reliability of that measure .

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What are the domain and range of the function?
f(x) = -4√x

Answers

The domain is x [tex]\geq[/tex] 0. interval notation:  [0,[tex]\infty[/tex])

the range is f(x)≤0, interval notation:  (-[tex]\infty[/tex],0 ]

What are the domain and range of a function?

The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.

A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)

Find domain:

Set the term under the square root [tex]\geq[/tex]0

So, the domain is x [tex]\geq[/tex] 0. interval notation:  [0,[tex]\infty[/tex])

Find range:

The range of a radical function of the form -c√(ax+b) +k is f(x)≤k

So, the range is f(x)≤0

interval notation:  (-[tex]\infty[/tex],0 ]

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working out the following additions
√8 + √18

Answers

The answer to the following is:
7.07106781187

[tex]\fbox{7.07...}[/tex]

First, we need the square of both numbers (8 and 18)

square of 8:

[tex]\sqrt{8}[/tex]

[tex]=2.828[/tex]

square of 18:

[tex]\sqrt{18}[/tex]

[tex]=4.242[/tex]

Now, let's add both numbers:

[tex]2.828+4.242[/tex]

[tex]=7.07[/tex]

the length length of a species of plants is normally distributed with expected value 60 cm. it is known from past experience that seventy five percent of theses flowers have length between 50 and 70 cm. what can we say about the standard deviation of the length of this plant?

Answers

The standard deviation of the length of this plant be 25.

m = 60(mean)

Let the standard deviation be s,

As, the probability for 50<x<70 be 0.75

Z = (x−m)/s

for x=50,

Z=0

for x=70,

Z=(70−50)/s=20/s

Now, the probability for 50<x<70 be,

P(50<x<70) = 0.75

In the standard form 0<z<(20/s)

using Z-table, the area from 0 to 20/s,

= 0.75

s = 25

Hence, the standard deviation of the length of this plant be 25.

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Solve the following exponential equation
[tex]3 {}^{2x } - 9 = 0[/tex]

Answers

3*2x-3*2=0
2x-2=0
2x=2|:2
x=1

Answer:

x = 1

Step-by-step explanation:

Given exponential equation:

[tex]3^{2x}-9=0[/tex]

Add 9 to both sides of the equation:

[tex]\implies 3^{2x}-9+9=0+9[/tex]

[tex]\implies 3^{2x}=9[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies \left(3^2\right)^{x}=9[/tex]

[tex]\implies9^{x}=9[/tex]

[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]

[tex]\implies9^{x}=9^1[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x=1[/tex]

Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.

T=
U=
V=
W=

Answers

The coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

 T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)

When a point P(x, y) is rotated 270° counterclockwise around the origin, we flip x and y and reverse the sign of x.

Thus,

The rule to rotate a point P(x, y)  after a rotation 270° counterclockwise around the origin is:

P(x, y) → P'(y, -x)

From the Graph,

In our case, we have the points

T = (4, -8)

U = (6, -8)

V = (9, -3)

W = (7, -3)

Thus, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

P(x, y)          →        P'(y, -x)

T (4, -8)       →       T'(-8, -4)

U  (6, -8)      →       U'(-8, -6)

V  (9, -3)      →        V'(-3, -9)

W  (7, -3)     →        W'(-3, -7)

Therefore, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

 T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)

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50 points look at picture (if u troll i will get u banned)

Answers

The measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

According to the question,

We have the following information:

We have a figure where angle MCJ is 130°.

Now, we can extend the two given lines as imaginary lines. After extending the lines, we will find that these lines are parallel and the lines are being cut by another line.

We know that in this case the alternate interior opposite angles are equal and the sum of consecutive alternate interior angles is 180°.

Now, ∠MCJ and ∠CMB are alternate interior opposite angles and thus they are equal.

Hence, the measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

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If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).

Answers

Answer:

(f+g)(x) = x - 7

Step-by-step explanation:

(f+g)(x) tells you to add the functions together. It means

f(x) + g(x)

= -3x - 5 + 4x - 2

combine like terms.

= 4x-3x - 5 - 2

= x - 5 - 2

simplify.

= x - 7

(f+g)(x) means

f(x) + g(x)

= x - 7

help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

there is probably a way to do this w/o calculus,  but I cheated and used that.

A = Length * Width

A = x * ( 650 -2x)

A = 650x -2[tex]x^{2}[/tex]

d/dx ( A = 650x -2[tex]x^{2}[/tex])

0=650 -4x

4x = 650

x = 135 m

A= 650*135 -2*[tex]135^{2}[/tex]

A = 51,300  [tex]m^{2}[/tex]

the age of children in kindergarten on the first day of school is uniformly distributed between 4.74 and 5.85 years old. a first time kindergarten child is selected at random. round answers to 4 decimal places if possible. the mean of this distribution is the standard deviation is the probability that the the child will be older than 5 years old? the probability that the child will be between 4.84 and 5.34 years old is if such a child is at the 9th percentile, how old is that child? years old.

Answers

a) The mean distribution is 5.295.

b) The standard deviation is 0.1026

c) The probability that the child will be older than 5 years old is 0.7657

d) The probability that the child's age is between 4.84 and 5.34 is  0.4504

e) At the 9th percentile, the age of the child is 5.739 years old.

Given interval distribution is

4.74 - 5.85.

a) Firstly, we will find the mean distribution,

Mean distribution = Sum of intervals / Number of intervals

= 4.74+5.85 / 2

= 5.295.

Hence, the mean distribution is 5.295.

b) Now, we will find the standard deviation,

We use the formula:

SD = [tex]\sqrt{\frac{(b-a)^{2} }{12} }[/tex]

b = 5.85

a = 4.74

SD = [tex]\sqrt{\frac{(5.85-4.74)^{2} }{12} }[/tex]

SD = [tex]\sqrt{\frac{(1.11)^{2} }{12} }[/tex]

SD = 0.1026

Hence, the standard deviation is 0.1026

c) The probability that the child will be older than 5 years will be

p(older than 5) = 5.85 - 5 / 5.85 - 4.74

= 0.85 / 1.11

= 0.7657

Hence, the probability that the child will be older than 5 years old is 0.7657

d) The probability that the child will be between 4.84 and 5.34 years old will be

p(between 4.84 and 5.34) = 5.34 - 4.84 / 5.85 - 4.74

= 0.5 / 1.11

= 0.4504

Hence, the probability that the child's age is between 4.84 and 5.34 is  0.4504

e) If the child is at the 9th percentile, the age will be

At the 9th percentile = 4.74 + 9/100 ×(5.85 - 4.74)

= 4.74 +(0.9)(1.11)

= 4.74 + 0.999

= 5.739

Hence, at the 9th percentile, the age of the child is 5.739 years old.

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Solve.

−46=21+3m

Enter your answer as a mixed number in simplest form in the box.

m =

Answers

Answer:

-22 1/3

Step-by-step explanation:

We should start by subtracting both sides of the equality by 21.

After doing this, we get that -67=3m.

Furthermore, we can divide both sides by 3 and get -67/3=m.

However, this is an improper fraction, not a mixed number.

If we divide -67 by 3, we get -22 1/3.

Therefore, m= -22 1/3

What are the first 5 terms

Answers

The first five terms of the given sequence are a₁ = 50, a₂ = 25, a₃ = 12.5, a₄ = 6.25 and a₅ = 3.125.

What is a geometric sequence?

In a geometric sequence the ratio of any two consecutive terms are equal. This ratio is known as the common ratio of the sequence.

Given that,

a₁ = 50 and aₙ = aₙ₋₁ ÷ 2

The first five terms are a₁, a₂, a₃, a₄  and a₅.

All the terms can be written using  aₙ = aₙ₋₁ ÷ 2 as follows,

a₂ = a₁ ÷ 2

⇒ a₂ = 50 ÷ 2

⇒ a₂ = 25

a₃ = a₂ ÷ 2

⇒ a₃ = 25 ÷ 2

⇒ a₃ = 12.5

a₄ = a₃ ÷ 2

⇒ a₄ = 12.5 ÷ 2

⇒ a₄ = 6.25

a₅ = a₄ ÷ 2

⇒ a₅ = 6.25 ÷ 2

⇒ a₅ = 3.125

Hence, the first five terms are 50, 25, 12.5, 6.25 and 3.125 respectively.

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A line passes through the points (–5, –4) and (0, 4). What is its equation in slope-intercept form?

Answers

Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-4) and (0,4) is y=8/5x + 4.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.

Equation in slope-intercept form in this case

Being (x₁, y₁)= (-5, -4) and (x₂, y₂)= (0,4), the slope m can be calculated as:

m= (4 - (-4))÷ (0 - (-5))

m= (4 + 4)÷ (0 +5)

m= 8÷ 5

m= 8/5

Considering point 2 and the slope m, you obtain:

4= 8/5×0 + b

4= 0 +b

4= b

Finally, the equation of the line is y=8/5x + 4.

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Dario bakes a lasagna containing $\frac 23$ pound of parmesan cheese, $1\frac 34$ pounds of ricotta cheese, and $1\frac 13$ pounds of mozzarella cheese.

Dario cuts the lasagna into several equal slices, each containing exactly $\frac 14$ pound of cheese. How many slices are there?

Answers

Dario cuts the lasagna into 15 equal slices.

Given,

Quantity of Parmesan cheese = 2/3 pounds

Quantity of Ricotta cheese = 1 3/4 = 7/4 pounds

Quantity of Mozzarella cheese = 1 1/3 = 4/3 pounds

The quantity of cheese in each pieces when the lasagna is cut = 1/4 pounds

We have to find the number of slices of cheese.

Here,

Total quantity of cheese;

2/3 + 7/4 + 4/3 = 2 + 7/4 = 15/4 pounds

Number of slices = total cheese / quantity of cheese in pieces

= (15/4) / (1/4) = 15 slices

That is,

Dario cuts the lasagna into 15 equal slices.

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what is the scale factor of a figure with a shape with a side lengths of 12 and is dilated to a shape with 4

Answers

The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.

What is a scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that a figure with side length of 12 units is being dilated in a figure with side length of 4.

In this case, the scale factor = 4/12 = 1/3

Hence, The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.

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your sister earns $30 per day selling clothes at the market, but in order to sell at the market, she has to pay $60 to get a license. You earn $20 per day helping rake your neighbors' lawns. How many days will it take for your sister to earn as much as you?

Answers

It will take 6 days for the sister to earn as much as the brother.

What is an equation?

Two or more expressions with an equal sign are defined as an equation.

Given that, the sister earns $30 per day and pays a $60 license fee and the brother earns$20 per day.

The income of the sister in x days is:

30x - 60

The income of the brother in x days is:

20x

The income of the sister and the brother is equal when:

30x - 60 = 20x

30x - 20x = 60

10x = 60

x = 6

Hence, It will take 6 days for the sister to earn as much as the brother.

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Work out (3 x 10^199) + (2 × 10^201).
Give your answer in standard form.

Answers

The standard form of  (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

The expression given is (3x10^199)+(2*10^201) we need to write it in the standard form

Take 10^199 from the equation

=10^199((3x1)+(2x10^2))

=10^199(3+(2x100))

=10^199(3+200)

=10^199(203)

=203x10^199

2.03 x 10^201

1. there are 201 zeros after 2 and 199 zeros after 3

2. difference  between  201 and 199 is 2

3. on adding both of them the 3 will come 2 spaces to the right of 2

The value of (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

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Find the area of a regular hexagon
with a side length of 5 cm. Round to
the nearest tenth.
5 cm
[? ]cm²

Answers

Answer: 64.95

Step-by-step explanation: The formula is (3√3 s2)/2 so using that we can find the answer which is, 64.95

of the 20 students in Kendra's class 5 have black hair eight have blonde hair 5 have brown hair 2 have red hair.kendra used ​

Answers

The probability of selecting a blonde is 0.40

What is probability?

Probability is the likelihood that something will occur.

In this case, from the twenty students, it should be noted that the number of blondes are 8.

Black hair = 5

Blonde hair = 8

Brown hair = 5

Red hair = 2

Therefore, the probability of choosing a blonde will be:

= Number of blonde / Total students

= 8/20

= 0.40

The probability is 0.40

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Complete question

Of the 20 students in Kendra's class 5 have black hair eight have blonde hair 5 have brown hair 2 have red hair.kendra used the spinner to blonde hair. What's the experimental probability that the student will have blonde hair?

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