Explain why the equation 5(2x+1)-2=6x+5 has only one solution. Then find the solution.

To write the given expression (4f-3+2g)-(-4g+2) in standard form, change the signs of the terms subtracted and combine like terms to simplify to 4f + 6g - 5.

To write the expression in standard form, you need to simplify the expression by combining like terms and handling the subtraction of negative numbers properly. Given the expression (4f-3+2g)-(-4g+2), you first remove the parenthesis while changing the signs of the terms inside the parenthesis being subtracted.

The expression -(-4g+2) will become +4g-2 once we apply the rule that subtracting a negative is the same as adding a positive, similarly to the example 2-(-6)=2+6=8.

Now the expression is simplified to 4f - 3 + 2g + 4g - 2. We combine like terms to get 4f + 6g - 5.

The standard form of the given expression is 4f + 6g - 5.

The expression (4f-3+2g)-(-4g+2) can be simplified using the distributive property and combining like terms.

First, distribute the negative sign to the terms inside the parentheses: (-1) * (-4g) = 4g and (-1) * 2 = -2.

The expression becomes (4f-3+2g) + (4g-2).

Next, combine like terms: 4g + 2g = 6g, and -3 - 2 = -5.

The final expression in standard form is 4f + 6g - 5.

x = 83°

Solution:

The reference image to the answer is given below.

Sum of the adjacent angles in a straight line = 180°

⇒ ∠1 + ∠2 + ∠3 = 180°      (Refer image)

⇒ 56° + ∠2 + 41° = 180°

⇒ 56° + 41° + ∠2 = 180°

⇒ 97° + ∠2 = 180°

⇒ ∠2 = 180° – 97°

⇒ ∠2 = 83°

In the given image ∠5 and ∠2 are vertically opposite angles.

Vertical angle theorem:

Vertically opposite angles are equal.

⇒ ∠5 = ∠2

⇒ x = ∠2

⇒ x = 83°

Hence the measure of angle x is 83°.

Answer:

42 and 72

Step-by-step explanation:

Answer:

Reflect the parent function over the x-axis, and translate it 8 units to the left.

Step-by-step explanation:

The given function is

[tex]y = - \sqrt{x + 8} [/tex]

The parent function is

[tex]y = \sqrt{x} [/tex]

Since there is a negative multiply the transformed function, there is a reflection in the x-axis.

Since 8 is adding, within the square root, there is a horizontal translation of 8 units to the left.

Therefore to graph the given function, reflect the parent function over the x-axis, and translate it 8 units to the left.

Take the reflection of the graph about the x-axis and then translate the graph of the function by 8 units in the left direction and this can be determined by using the rules of transformation.

Given :

Function  --  [tex]\rm y = - \sqrt{x+8}[/tex]

The following steps can be used in order to determine the correct statement:

Step 1 - The parent function is given below:

[tex]\rm y = \sqrt{x}[/tex]

Step 2 - Now, draw the graph of the parent function.

Step 3 - Take the reflection of the graph about the x-axis. So, the function becomes:

[tex]y =- \sqrt{x}[/tex]

Step 4 - Now, translate the graph of the function obtained in the above step by 8 units in the left direction. So, the function becomes:

[tex]y = -\sqrt{x+8}[/tex]

Therefore, the correct option is D).

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Answer:

14

Step-by-step explanation:

The revenue earned is represented by t(x)=5x. Since the equation asks for the profit after four seasons you fill in 4 for x and get 20. r(x)=(1.5)x is how much it costs to pay their employees each season so you fill in 4 for x. Now you take revenue earned and subtract it by the cost to pay employees and you get the profit.

5x - 1.5x = Profit

5(4) - 1.5(4) = Profit

20 - 6 = Profit

14 = Profit

Answer:

15

Step-by-step explanation:

Answer:

8.75h

Step-by-step explanation:

8.75 hours will be taken by the submarine to make the descent.

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

Given that a submarine’s descent can be represented as y = -240x, where y is the elevation and x is time in hours.

We need to find the the time it will take this submarine to make the descent to the seafloor 2,100 feet below the surface

Since the submarine to make the descent to the seafloor 2,100 feet below the surface

So y = - 2100

So y = - 240x gives

- 2100 = - 240x

Divide both sides by -240

x=8.75

Hence, 8.75 hours will be taken by the submarine to make the descent

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Answer:30=4x

Step-by-step explanation:

Answer:

[tex]f(w) = 15 - \frac{w}{8345}[/tex]

Step-by-step explanation:

Water begins draining from a tank when the tank has 15 gallons of water in it.

Now, if we define f(w) as a function that represents the number of gallons of water remains in the tank after w pounds of water that have drained from the tank since the tank started draining, then the function can be represented as

[tex]f(w) = 15 - \frac{w}{8345}[/tex]

Since, w pounds of water is equivalent to [tex]\frac{w}{8345}[/tex] gallons of water. (Answer)

(Recall that water weighs 8.345 pounds per gallon.)

The function f should be defined is [tex]f(w) = 15 - \frac{w}{8345}[/tex]

A tank has 15 gallons of water in it when water begins draining from the tank. (Recall that water weighs 8.345 pounds per gallon.)

Since we have to defined the function so it is f(w) that shows the number of gallons of water remains in the tank after w pounds of water.

So, the function should be [tex]f(w) = 15 - \frac{w}{8345}[/tex]

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The coordinates of C’ is (-5,3), the correct option is A.

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.

If you study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

Thus, if you're reflecting a point (x,y) along x axis, then its x

abscissa will stay same but y

ordinates will negate. Thus (x,y) turns to (x, -y)

Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)

Given;

On a coordinate plane, trapezoid A B C D has points (2, 1), (3, 5), (5, 3) and (3, 1).

Now,When a point is reflected across the y-axis, the rule is:

(x,y)→ (-x,y)

C (5.3)= C' (-5,3)

Therefore, the reflection on C will be C (5.3) C' (-5,3).

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Answer:

He have 47 ducks and 7 cows.

Step-by-step explanation:

Given:

Farmer Jones raises ducks and cows.

He looks out his window and sees 54 animals with a total of 122 feet.

Now, to find the each type of animal he have.

Let the number of ducks be [tex]x.[/tex]

And the number of cows be [tex]y.[/tex]

So, total number of animals are:

[tex]x+y=54[/tex]

[tex]x=54-y[/tex]  ....( 1 )

As, the feet of cows are 4 and ducks are 2.

Now, the total number of feet are:

[tex]2(x)+4(y)=122[/tex]

[tex]2x+4y=122[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]2(54-y)+4y=122[/tex]

[tex]108-2y+4y=122[/tex]

[tex]108+2y=122[/tex]

Subtracting both sides by 108 we get:

[tex]2y=14[/tex]

Dividing both sides by 2 we get:

[tex]y=7.[/tex]

The number of cows = 7.

Now, to get the number of ducks we substitute the value of [tex]y[/tex] in equation (1):

[tex]x=54-y\\x=54-7\\x=47.[/tex]

The number of ducks = 47.

Therefore, he have 47 ducks and 7 cows.

Answer:

Minimum value is 0

Maximum value is undefined.

Step-by-step explanation:

The given function is [tex]f(x)=7x^2[/tex]

This function is a parabola that has its vertex at the origin.

The coefficient of the quadratic term is 7, which is greater than zero.

This means that, the graph will open up.

The graph will therefore have a minimum value of y=0

The graph  of this function does not have a maximum value.

Answer:

The age of Noelle's dad is 54 years and that of Noelle is 20 years.

Step-by-step explanation:

Let the age of Noelle's dad is x years and that of Noelle is (74 - x) years.

{Since, the sum of their ages is 74}

Now, given that the age of Noelle's dad is 6 less than 3 times Noelle's age.

So, 3(74 - x) - 6 = x

⇒ 4x = 222 - 6 = 216

⇒ x = 54

So, the age of Noelle's dad is 54 years and that of Noelle is (74 - 54) = 20 years. (Answer)

Answer:

The y-intercept

Answer:

b

Step-by-step explanation:

I am thinking it would be "b" because y=mx+b so not the multiple choice but whichever one says b

Answer: I guessed on the second one

Step-by-step explanation:

The problem falls under mathematics, more specifically algebra, using a system of two equations to solve for the timing of the cardio and weighted workouts. The equations can be formed from the provided data and can be solved using substitution or the elimination method.

This problem is a system of equations questions in mathematics, specifically in the subset of algebra. To be able to solve this, you need to create two equations from the data provided on the table and then solve for both cardio and weighted workout timings. For instance, if I did 2 cardio workouts and 3 weighted workouts in week 1 for a total of 150 minutes and 3 cardio workouts and 1 weighted workout in week 2 for a total of 160 minutes, you can construct these two equations:

2*cardio + 3*weighted = 150 (Equation for week 1)

3*cardio + weighted = 160 (Equation for week 2)

Next, you solve this system of equations either by substitution or elimination- whatever you're more comfortable with. The results will give you the duration of each cardio and weighted workout.

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Answer:

The product of a non-zero rational number and an irrational number will always be an irrational number.

Step-by-step explanation:

Here's a proof by contradiction for this claim.

Consider an irrational number [tex]x[/tex]. Assume by contradiction that this claim isn't true. In other words, assume that there exist a non-zero rational number [tex]y[/tex] such that [tex]x \cdot y[/tex] is a rational number.

By the definition of rational numbers, a number is a rational number if and only if it can be written as the quotient of two integers.

Divide [tex]y[/tex] from both sides of the equation:

[tex]\displaystyle \frac{x\cdot y}{y} = \left.\frac{c}{d}\right/y[/tex].

The left-hand side of this equation is now equal to [tex]x[/tex].

Since [tex]\displaystyle y = \frac{a}{b}[/tex]  by assumption, the [tex]y[/tex] on the right-hand side of this equation can be replaced with [tex]\displaystyle \frac{a}{b}[/tex]. Hence, the right-hand side of this equation would become

[tex]\displaystyle \frac{x\cdot y}{y} = \left.\frac{c}{d}\right/\frac{a}{b} = \frac{c}{d}\cdot \left(\frac{b}{a}\right) = \frac{b \cdot c}{a \cdot d}[/tex].

Combine the two sides of the equation to obtain:

[tex]x = \displaystyle \frac{b \cdot c}{a \cdot d}[/tex].

Since [tex]b[/tex] and [tex]c[/tex] are both integers, their product [tex]b \cdot c[/tex] would also be an integer. Similarly, since [tex]a[/tex] and [tex]d[/tex] are both integers, their product [tex]a \cdot d[/tex] would also be an integer.

In other words, [tex]x[/tex] can now be represented as the quotient of two integers. By the definition of rational numbers,

Hence, the original assumption that this claim isn't true, is not true. That verifies the claim that the product of a non-zero rational number and an irrational number would be an irrational number.

Answer:

Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.

Step-by-step explanation:

Quotient is the required answer if 584 is divided by 17

584 will be the dividend and 17 is the divisor.

To calculate 584/17, 17 will go in 58 3times with 7 as remainder. This remainder 7 will combine with 4 to make 74, 17 will also go in 74 4times with remainder of 6.

The final answer by combining the number of times 17 goes in 584 which is 34 with final remainder of 6. This means that;

584/17 = 34 remainder 6 i.e 34R6

This shows that Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.

Mean = 3.25

Solution:

Step 1 : Given data:

4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2

Step 2:

Sum of the numbers

          = 4.5 + 3 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2

          = 52

Sum of the numbers = 52

Number of terms = 16

Step 3:

[tex]$\text{Mean}=\frac{\text{Sum of the numbers}}{\text{Number of terms}}[/tex]

         [tex]$=\frac{52}{16}[/tex]

         = 3.25

Mean = 3.25

Mean of the distribution is 3.25.

Answer: Mean= 3.25 with a POSITIVE skew

Step-by-step explanation:

edmentum

A) The airplane slowed down. It states that the plane lands and come to a complete stop over a 53 second period.

B) It decelerates. The speed doesn't increase. It slows down.

C) The answer should be positive. Although the deceleration is slowing down the plane, it's not going at a negative speed.

D) The answer is 11.5m/s. I divided the velocity by the amount of seconds it takes to make a complete stop.

The following information should be considered;

A) The airplane falled down. It states that the plane lands and come to a complete stop over a 53 second period.

B) It decelerates. The speed doesn't increase. It slows down.

C) The answer should be positive. The deceleration is slowing down the plane, it's not going at a negative speed.

D) The answer is 11.5m/s. I divided the velocity by the amount of seconds it takes to make a complete stop.

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Answer:

y=5m-3

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

2 x 2 = 4/5

2 x -7 = -14 / 5

Answer:

B) 4/5x-14/5

Step-by-step explanation:

2/5(2x-7)

2/5*2x= 4/5x

2/5*7=14/5

Final answer:

Using an algebraic approach, we found out that if Barbara is 142 cm tall, which is 2 cm less than three times her birth height, then her height at birth was 48 cm.

Explanation:

The question asks us to determine Barbara's height at birth given that she is currently 142 cm tall and that this height is 2 cm less than three times her height at birth. To find her height at birth, we can construct and solve a simple algebraic equation based on this information.

Let h represent Barbara's height at birth. The problem states that:

142 cm = 3h - 2 cm

Adding 2 cm to both sides of the equation, we get:

144 cm = 3h

Dividing both sides of the equation by 3 so we can solve for h, gives us:

h = 144 cm / 3

h = 48 cm

Therefore, Barbara's height at birth was 48 cm.

Answer:

its 90cm^2

Step-by-step explanation:

hope d answer will help u

Answer:

A)

Step-by-step explanation:

The theme is a message that the story was trying to portray. In the story, it seems that the character realizes that his home life and family matter more to him than he thought which is why he moved back to his hometown and became happy from that. He moved away thinking that life would be better without his family and soon regrets it.

Answer:

Step-by-step explanation:

D=rt

180miles = 45mph* times

180miles/45mph =time

Time = 4hours

Answer:

B

Step-by-step explanation:

2/1 frptrhgqhgr4tjtfix jxcfh8u5t8ofszYI7wyt439tfy7efgy5g

Final answer:

Bees can see 4 out of the 6 pure spectral colors, which simplifies to the fraction 2/3 after removing the 2 colors they cannot see, orange and red.

Explanation:

The question involves calculating a fraction, which is a basic mathematical concept. We are told there are 6 pure spectral colors: red, orange, yellow, green, blue, and violet. Bees cannot see orange or red, so we must find out what fraction of the 6 pure spectral colors bees can see. We subtract the 2 colors bees can't see (orange and red) from the total of 6, leaving us with 4 colors they can see which are yellow, green, blue, and violet.

To express this as a fraction, we take the number of colors bees can see (4) and place it over the total number of pure spectral colors (6). Therefore, the fraction of pure spectral colors that bees can see is 4/6. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Thus, the simplified fraction is 2/3.

Answer:

Step-by-step explanation:

(x-3)*(x+3)

we begin by expanding and then simplifying

= (x²+3x-3x-9)

= x² - 9

Answer:

x² - 9

Step-by-step explanation:

hello :

(x - 3 ) (x + 3) = x²+3x-3x-9

(x - 3 ) (x + 3) = x² - 9

Answer:

[tex]d3=13.125[/tex] [tex]miles[/tex]

Step-by-step explanation:

Given data:

[tex]total[/tex] [tex]distance = 21[/tex] [tex]miles[/tex]

[tex]s1=8[/tex] [tex]miles/hr[/tex]

[tex]s2=8[/tex] [tex]miles/hr[/tex]

[tex]s3=10[/tex] [tex]miles/hr[/tex]

First we have to find out the how much time it takes when Supria and Elle meet.

As we know,

[tex]Displacement=rate*time[/tex]

[tex]d1=s1*t[/tex]

[tex]d2=s2*t[/tex]

[tex]d1+d2=21[/tex]

[tex]8t+8t=21[/tex]

[tex]16t=21[/tex]

[tex]t=21/16[/tex]

Now we can find that how much the third friend had traveled during this time period

[tex]d3=s3*t[/tex]

[tex]d3=10*21/16[/tex]

[tex]d3=13.125[/tex] [tex]miles[/tex]

Answer:

here is the answer, out of all my experience i'm not too good on these word problems. You should check number two but if you agree than yay.

Step-by-step explanation:

x+6 is x+6. It's an expression. Not sure what you need help with.

Answer:

You set the problem =0, so (x+6)=0.

Then, you do the inverse to get x alone. 6-6(cancels out) and 0-6 is -6.Now your equation should look like x=-6 and you’re done.

Step-by-step explanation: