4x + 2(x – 3) = 4x + 2x – 11 Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points) Part B: Name one property you used to solve this equation. (4 points)

Answers

Answer 1

A.

4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 4x + 2x - 11
6x - 6 = 6x - 11
-6 = -11

since -6 is not equal to -11, so there's no solution

B. Distributive property

Answer 2

Final answer:

The given equation has no solution, as simplifying both sides leads to the false statement -6 = -11. The number of solutions is zero, and the Distributive Property was used to solve the equation.

Explanation:

To solve the equation 4x + 2(x – 3) = 4x + 2x – 11, follow these steps:

Expand the left side of the equation: 4x + 2x - 6.

Combine like terms: 6x - 6.

Since the left and right side both have 4x, we can cancel out 4x from both sides, leaving 2x - 6 = 2x - 11.

Subtract 2x from both sides to get -6 = -11, which is a contradiction.

There is no solution to this equation because we arrived at a false statement. Therefore, the number of solutions is zero.

Part B: The property I used to solve this equation is the Distributive Property when expanding 2(x - 3).

Related Questions

Line EF has an equation of a line y = −2x + 7. Which of the following could be an equation for a line that is perpendicular to line EF?

y = 2x − 3
y = 1 over 2x − 3
y = −2x − 3
y = −1 over 2x − 3

Answers

1.

When a line is given in the form y=mx+n,

m is the slope of this line.

For example, the slope of the line y=-2x+7 is -2.

2.

If lines y=mx+n and y=kx+t are perpendicular, then the multiplication of their slopes is -1, that is

m*k = -1, so k=-1/m

3.

any line perpendicular to y=-2x+7 has slope = -1/(-2)=1/2

4.

Among the choices, y=(1/2)x-3 is a line perpendicular to the given line.

Answer:

b. y=(1/2)x-3

Answer:

[tex]y=\frac{1}{2} x-3[/tex]

Step-by-step explanation:

Step 1

Find the slope of the line EF

we have

[tex]y=-2x+7[/tex]

The slope of the line EF is equal to

[tex]m=-2[/tex]

Step 2

Find the slope of the line perpendicular to the line EF

we know that

If two lines are perpendicular, then the product of its slopes is equal to minus one

[tex]m1*m2=-1[/tex]

we have

[tex]m1=-2[/tex] -----> slope of the line EF

Find the value of m2

substitute

[tex](-2)*m2=-1[/tex]

[tex]m2=1/2[/tex]

therefore

the equation [tex]y=\frac{1}{2} x-3[/tex] could be an equation for a line that is perpendicular to line EF

A triangle has one leg measuring 10 inches and the hypotenuse measuring 20 inches. the other leg measures 10\sqrt[]{3} 10 3 inches. what type of triangle is represented here?

Answers

From the description given for the triangle above, I think the type of triangle that is represented would be a right triangle. This type of triangle contains a right angle and two acute angles. In order to say or prove that it is a right triangle, it should be able to satisfy the Pythagorean Theorem which relates the sides of the triangle. It is expressed as follows:

c^2 = a^2 + b^2

where c is the hypotenuse or the longest side and a, b are the two shorter sides.

To prove that the triangle is indeed a right triangle, we use the equation above.

c^2 = a^2 + b^2
c^2 = 20^2 = 10^2 + (10sqrt(3))^2
400 = 100 + (100(3))
400 = 400

A bag contains 20 candies: 3 cherry, 4 orange, 7 lemon, and 6 grape. if two candies are selected simultaneously, what is the probability that they are both the same flavor?

Answers

the answer is shown below

I NEED THIS QUICK

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?
9x + 4y = 36
6x + 2.5y = 24

Answers

After multiplying by the given coefficients and adding, the new equation obtained is:
8y - 7.5y = 0

after doing the calculations the answer is:
y = 0
x = 4

Because the two equations formed were independent, they had one solution

Answer:

its C

Step-by-step explanation:

For Jane's Uber business, she charges $5 initial fee and $0.10 a mile. Joe's Uber business charges $4 initial fee and $0.20 per mile.
1. Write a function for jane's Uber buisiness
2. write a function for joe's Uber business

Answers

Jane : y = 0.10x + 5...or f(x) = 0.10x + 5
Joe : y = 0.20x + 4...or f(x) = 0.20x + 4

The linear equations to calculate the earning by Jane and Joe's Uber business per ride, given the initial fee and charge per mile:

Jane: y = 5 + 0.1x

Joe: y = 4 + 0.2x

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

For Jane's Uber business, she charges $5 initial fee and $0.10 a mile.

Let Jane's earning from a ride be $y.

Let the number of miles she drove in that ride be x miles.

Linear equation to calculate the earning from a ride given the number of miles rode: y = 5 + 0.1x

For Joe's Uber business, he charges $4 initial fee and $0.20 a mile.

Let Joe's earning from a ride be $y.

Let the number of miles he drove in that ride be x miles.

Linear equation to calculate the earning from a ride given the number of miles rode: y = 4 + 0.2x

Learn more about linear equation here

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Write the equation in logarithmic form.

25 = 32

A. log32 = 5 • 2

B. log232 = 5

C. log32 = 5

D. log532 = 2

Answers

The equation in logarithmic form is B.log₂32 = 2.

To convert the equation 2⁵ = 32 into logarithmic form, you need to identify the base, the exponent, and the result. The given equation can be interpreted as 2 raised to the power of 5 equals 32.

The general form of a logarithmic equation is: log_base (result) = exponent

In this specific case, we have:

base = 2
result = 32
exponent = 5

Putting it into the logarithmic form, we get: log₂32 = 5

So, the correct option is: B.log₂32 = 2

Simplify 10x - 3x + (-5x).
-2x
2x
18x
-18x

Answers

This answer is 2x. Hope it helps!

+(-5x) = -5x so

its 10x - 3x - 5x

= 10x - 8x = 2x Answer

A perfect circle figure has four lines of symmetry. True or false?

Answers

True, because the lines can be drawn from all directions of the circle, therefore that must be at least 4 lines of symmetry

How many three-letter "words" can be made from 5 letters "fghij" if repetition of letters (a) is allowed?

Answers

From the given, there are 5 letters to choose from. For the first letter of the three-letter word, we can choose from all 5 of them.

Also, for the second letter of the word, we can also have 5 choices because it is stated that repetition is allowed. Similarly, there are also 5 choices for the last letter of the word. By fundamental principle of counting, we multiply the numbers identified in the sentences above,

n = 5 x 5 x 5 = 125

Thus, 125 words can be formed from the given letters.

Write the sum using summation notation, assuming the suggested pattern continues.

-1 + 2 + 5 + 8 + ... + 44

A) summation of negative three times n from n equals zero to fifteen
B) summation of the quantity negative one plus three n from n equals zero to fifteen
C)summation of negative three times n from n equals zero to infinity
D) summation of the quantity negative one plus three n from n equals zero to infinity

Answers

The answer is C. Summation of negative three times n from n equals zero to infinity

HELP ASAP 30 POINTS

Evaluate f(3) for the piecewise function: f(x) = Which value represents f(3)?
–11
8
12.5
16

Answers

Answer:

-11

Step-by-step explanation:

If y = 4x + 3 were changed to y = -4x + 3, how would the graph of the new function compare with the original?

Answers

4x+3 times -1 reflects the graph about the x axis

-4x-3 adding 6 moves the graph upwards by 6 units

-4x-3+6

-4x+3

Answer:

The graph of y=-4x+3 will be as a reflexion in a mirror of y=4x+3

Step-by-step explanation:

y=4x+3 y=-4x+3

. .

Triangle END is translated using the rule (x, y) → (x − 4, y − 1) to create triangle E'N'D'. If a line segment is drawn from point E to point E' and from point N to point N', which statement would best describe the line segments drawn? (1 point

Answers

Here are the choices for this problem:
They are parallel and congruent.
They are perpendicular to each other.
They share the same midpoints.
They create diameters of concentric circles.

The transformation that is done is a translation. Which means that the coordinates will be translated or moved in the coordinate plane without changing the size and the orientation of the image. If is a line was drawn from E to E' and another line was drawn from N to N', the two lines would be parallel and congruent since the translation done to E is the same to that of N.

The answer is
They are parallel and congruent.

This answer is right!!!!! They are parallel and congruent.

Solve |x| + 7 < 4.
........................

Answers

hello :
|x| + 7 < 4.
|x| < 4.-7
|x| < -3
no reals solutions because for all reals x : |x| ≥ 0

A group of hikers are 675 ft from the base of Guadalupe Peak, which is 8,749 ft tall. What is the angle of elevation when they look at the top of the Peak? Round to the nearest hundredth.

Answers

tan x = 8749/675
x= arctan (8749/675) arctan = tan^-1
x=85.59 degrees

What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms?

Answers

9 - 3 = 6, 15-9 = 6 the difference is 6, So d = 6

First term: a1 = 3

Sn = n*(a1 + an)/2

Sn = n*(a1 + a1 + (n-1)*d)/2

Sn = n*(2*a1 + (n-1)*d)/2

substitute 26 for n
S26 = 26*(2*a1 + (26-1)*d)/2

substitute 3 for a1

S26 = 26*(2*3 + (26-1)*d)/2

substitute 6 for d

S26 = 26*(2*3 + (26-1)*6)/2

S26 = 2,028

Sum of an arithmetic series is:

S = n*(a_1+a_n)/2, that easy.

n is the number of terms, 26 in your case. a_n is a_26. We need to find the series!

a_n = a_1 + (n-1)*d, the difference, d, is 6.

So a_n = 3 + (n-1)*6 = 6*n-3 (check it works: 3, 9, 15, ...)

Now a_26 = 6*26-3 = 153, so finally:

S = 26*(3+153)/2 = 26*78 = 2028

2028 is the answer

A rectangle has an area of k2 + 19k + 60 square inches. If the value of k and the dimensions of the rectangle are all natural numbers, which statement about the rectangle could be true?

Answers

the width of the rectangle is k+4 inches

The tip of a 15-inch wiper blade wipes a path that is 36 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
2.4 radians
1.2 radians
2.8 radians
0.4 radians

Answers

The length of the arc is a fraction of the circumference of the circle depending on the length of the radius and the intercepted angle. This can be calculated through the equation,

L = (2πr) x (θ /360)

where L is the length of arc, r is the radius, and θ is the intercepted angle in terms of degrees.

Substituting the known values to the equation,

36 = (2π)(15) x (θ / 360)

We translate the equation to find the value of θ,

θ = (36)(360) / 2π(15)

The value of θ is equal to 137.51°.

This can be coverted to radians through the equation below,

θ (in radians) = 137.51° x (2π rad / 360°) = 2.4 rad

What is the graph of the function f(x) = the quantity of x squared plus 3 x plus 5, all over x plus 2

Answers

Answer:

Your answer is in the picture below

The graph approaches x=−2 asymptotically, has no x-intercepts, and the y-intercept of the graph is the point (0, 5).

Attached graph.

The graph of the function f(x) = (x² + 3x + 5 )/(x+ 2) is a parabola that is shifted to the left by 2 units.

The parabola is similar to the graph of the function y = x², but it is narrower because the denominator of the fraction is x + 2.

The graph also has a hole at the point (-2, 5), which is the point where the denominator of the fraction is 0.

Attached graph.

Here are the steps on how to sketch the graph of the function:

Sketch the graph of the function y = x².

Shift the graph to the left by 2 units.

Add a hole at the point (-2, 5).

The attached figure shows the graph of the function f(x) = (x² + 3x + 5 )/(x+ 2):

The graph of the function has the following features,

The domain of the function is all real numbers except for -2.

The range of the function is all real numbers except for 5.

The function has a minimum point at (-4, 1).

The function has a hole at the point (-2, 5).

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Student identification codes at a high school are 4-digit randomly generated codes beginning with 1 letter and ending with 3 numbers. there are 26,000 possible codes. what is the probability that you will be assigned the code a123?

Answers

[tex]\dfrac{1}{26,000}\approx3.8\%[/tex]

solve for x in the diagram (right triangle smallest side 9,bottom side 12,longest x)

Answers

The hypotenuse (x) is 15, use the Pythagorean Theorem.

Erica purchased adult and youth tickets for a movie. She bought x adult tickets for $7 each and y youth tickets for $5. Write an expression that can be used to show the total cost, C, of all tickets.

Answers

7x plus 5y equals C(cost)

Answer:

7x + 5y = C

Step-by-step explanation:

X is the number of people buying an adult ticket

Y is the number of people buying a youth ticket

Using this we can find C, cost

A scale model of a human heart is 198 inches long. The scale is 34 to 1. How many inches long is the actual heart? Round your answer to the nearest whole number.

Answers

would be 198 / 34 = 5.82 = 6 inches to nearest whole number.

George plays basketball in a week-long camp. On Day 2, he scored 8 points. On day 4, he scored 12 points. Explain how to measure his average rate of change

Answers

you got the avg of two days((8+12)\2=10)so you can guess that its around 70 in a week.
avg rate of change is x+2=y

What is the simplified expression for ?

Answers

The simplified expression is 16

determine the valie of x for which v || w if m2 =100 and. m7 =4x+10

Answers

I believe that x=22.5

Determine the slope of a line that makes an angle of 5pi/4 radians with the x-axis.

Answers

check the picture.

π radians is the angle 180 degrees, so π/4 radians is 180°/4=45°.

to construct the angle [tex]5 \frac{ \pi}{4} [/tex] we can proceed as shown in the figure, that is, we open an angle equal to 5 half right angles.

We see that the line making the angle 5pi/4 is the same line making the angle pi/4 radians, that is 45 degrees.

A line making the angle 45 degrees with the x axis, has slope equal to 1.

Remark, we have considered a line passing through the origin, as it represents all other lines making 5pi/4 radians.

Answer: slopi=1

What is the length of the side opposite the 30° angle? HELP

Answers

the answer is B
√3 times as long as the side opposite the 30 degree so the side opposite the 30 degree angle is 5/√3 inches long.

How much money should be deposited today in an account that earns 6% compounded monthly so that it will accumulate to $9000 in three years?

Answers

The formula is
A=p (1+r/k)^kt
A future value 9000
P present value?
R interest rate 0.06
K compounded monthly 12
T time 3years
We need to solve for p
P=A÷(1+r/k)^kt
P=9,000÷(1+0.06÷12)^(12×3)
P=7,520.80

The area of a rectangle is 33 m2 , and the length of the rectangle is 5 m less than double the width. find the dimensions of the rectangle.

Answers

By definition, a rectangle is a quadrilateral (4-sided polygon) containing two sets of equal and parallel sides called the length and the width. For determining the area of a rectangle, you simply have to multiply length times width. In this problem, let L be the length and W be the width. Then, we formulate the two independent formulas: formula for area, and formula relating L and W

A = LW = 33
L = 2W-5

Substituting the second equation to the first,

A = 33 = (2W - 5)W
33 = 2W² - 5W
2W² - 5W -33 = 0
W = 5.5 and -3

Since the equation is quadratic, there are two possible roots: 5.5 and -3. However, we can only use the positive value. Thus, W=5.5 m. Consequently,

L = 2(5.5)-5
L = 6 m

Therefore, the dimensions of the rectangle is 6 m by 5.5 m.

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