Are the expressions -0.5(3x + 5) and -1.5x + 2.5 equivalent? Explain why or why not

Step-by-step explanation:

We have,

[tex](x^{\dfrac{1}{8}})(x^{\dfrac{3}{8}})=12[/tex]

To find, the possible value of x = ?

∴ [tex](x^{\dfrac{1}{8}})(x^{\dfrac{3}{8}})=12[/tex]

⇒ [tex]x^{\dfrac{1}{8}+\dfrac{3}{8}}=12[/tex]

Using the exponential identity,

[tex]a^{m} a^{n} =a^{m+n}[/tex]

⇒ [tex]x^{\dfrac{1+3}{8}}=12[/tex]

⇒ [tex]x^{\dfrac{4}{8}}=12[/tex]

⇒ [tex]x^{\dfrac{1}{2}}=12[/tex]

Squaring both sides, we get

[tex](x^{\dfrac{1}{2}})^2=(12)^2[/tex]

⇒ [tex]x^{{\dfrac{1}{2}}\times2}=144[/tex]

⇒ x = 144

∴ The possible value of x = 144

Thus, the required 'option C) 144' is correct.

Answer:

144

Step-by-step explanation:

Answer: It’s A

Step-by-step explanation:

If you reflect over the y axis your point changes

To find the sum, add the numbers together. To find the difference, subtract the smaller numbers from the larger numbers.

To find the sum of 147, 167, 204, and 107, simply add the numbers together:

147 + 167 + 204 + 107 = 625

To find the difference, subtract the smaller numbers from the larger numbers:

204 - 147 = 57

167 - 107 = 60

Therefore, the sum is 625 and the differences are 57 and 60.

Answer: $30

Step-by-step explanation:

The lamp was selling for $30 which is 25% less than what Cindy bought.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Cindy bought a new lamp for $40.00.

She later saw the lamp on sale for 25% less than what she had originally paid.

∴ The discounted price of the lamp is 75% of the price for which Cindy bought which is,

= (75/100)×40.

= $30.00

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Answer:

The question is incomplete. The complete question is shown below

1. What is the probability that Earl will have to do both chores?

Ans. (0.8 * 0.8 = 0.64)

2. What is the probability that Earl will have to take out the garbage but will not need to wash the dishes

Ans.( 0.8 * 0.2 = 0.16)

Step-by-step explanation:

1. The probability that Earl will have to do the chores is 0.8

Therefore the probability that Earl will have to do both chores is 0.8 * 0.8 = 0.64

2.The probability that Earl will have to take out the garbage but not need to wash the dishes

0.8 * 0.2 = 0.16

Answer:

5/9

Step-by-step explanation:

Answer: Terri brought 10 more centimeters of rope than Gracie.

Step-by-step explanation:

Answer:

-3 and positive 3

Step-by-step explanation:

Answer:

7 and 1

Step-by-step explanation:

To evaluate f(- 5) substitute x = - 5 into f(x)

f(- 5) = - (- 5) + 2 = 5 + 2 = 7

Similarly for f(1)

f(1) = - 1 + 2 = 1

Answer:

9x+6

Step-by-step explanation:

3 x 2= 6x 3 x 1= 3

6x + 3 + 3x + 3

6x + 3x = 9x

3 + 3 =6

Slope-intercept form:  y = mx + b

[m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]

For lines to be perpendicular, their slopes have to be negative reciprocals of each other. [basically changing the sign (+/-) and flipping the fraction/or switching the numerator and the denominator]

For example:

m = 2 or [tex]\frac{2}{1}[/tex]

Perpendicular line's slope = [tex]-\frac{1}{2}[/tex]

m = [tex]-\frac{1}{4}[/tex]

Perpendicular line's slope = [tex]\frac{4}{1}[/tex] or 4

Since you know the slope of the line is:

y = -3/4x + 5

m = [tex]-\frac{3}{4}[/tex]      

The perpendicular line's slope is [tex]\frac{4}{3}[/tex], so plug it into the equation

y = mx + b

[tex]y=\frac{4}{3} x+b[/tex]        To find b, plug in the point (-3, -3) into the equation

[tex]-3=\frac{4}{3} (-3)+b[/tex]

-3 = -4 + b   Add 4 on both sides to get "b" by itself

1 = b

The y-intercept is 1

Answer:

V=512^2/3* 19683^1/3*256^1/4    = 6912

Step-by-step explanation:

V= [tex](512^{\frac{2}{3} } ) \times (19683^{\frac{1}{3} } )\times (256^{\frac{1}{4} } )\\[/tex]

As

[tex]2^{9} = 512\\2^{8} = 256\\19683^{\frac{1}{3} } = 27\\[/tex]

putting values in equation

V= [tex]2^{9(^{\frac{2}{3} } )} \times 27 \times 2^{8^({\frac{1}{4}) } } \\[/tex]  let it be equation 1

As

[tex]2^9^{\frac{2}{3} } = 2^6 according\,to\,exponential\,rule\\2^8^\frac{1}{4} = 2^2 according\,to\,exponential\,rule\\\\[/tex]

putting values in equation 1

[tex]V= 2^6\times 27\times 2^2[/tex]

According to exponential rule [tex]2^6 \times 2^2 = 2^8[/tex]

V=[tex]2^8 \times 27\\[/tex]

[tex]V=256\times 27\\V=6912[/tex]

So

V= 6912

Keywords: Algebra

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Answer:

8x and 5x are like terms and the constant is 2 because it is by itself.

Step-by-step explanation:

Hope my answer has helped you and if not I am sorry.

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

By definition, if two lines are parallel then their slopes are equal. A line parallel to[tex]y = -3x + 1[/tex], will have the same slope -3. Thus, the equation will be of the form:

[tex]y = -3x + b[/tex]

We substitute the given point and find "b":

[tex]2=-3(4)+b\\2=-12+b\\2+12=b\\b=14[/tex]

Finally, the equation is:

[tex]y = -3x + 14[/tex]

Answer:

[tex]y = -3x + 14[/tex]

Answer:

63 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (a + b)

where a and b are the parallel bases and h the perpendicular height

Here a = 7, b = 14 and h = 6, thus

A = [tex]\frac{1}{2}[/tex] × 6 × (7 + 14) = 3 × 21 = 63 ft²

Answer:

144

Step-by-step explanation:

Step 1:  Convert 4 yards into feet

1 yard = 3 feet

4 * 3 = 12 feet

Step 2:  Convert 12 feet into inches

1 foot = 12 inches

12 * 12 = 144 inches

Answer:  Bobby can cut 144 1-inch strips.

Answer:

144

Step-by-step explanation:

All you would need to know is that there is 36 inches in one yard and then you would just multiply the 36 by four to make the four yards total

Answer:

(-7,8.5)

Step-by-step explanation:

On a reflection off the y-axis, the x value gets negated. So 7 would become -7.

Answer:11/15

Step-by-step explanation:

Most common denominator is 15 multiply 2/5 by 3 and 1/3 by 5 and that’s what you get

Answer:

x < 9  

Step-by-step explanation:

Writing this entirely with symbols, we get:

-5(x - 1) > -40

We must solve for x.  

Carrying out the multiplication, we get:

-5x + 5 > -40, or

-5x > -45

Dividing both sides by -5 isolates x:

x < 9  

Note that when working with an inequality such as this one, dividing both sides by a negative number requires changing the direction of the inequality symbol.

Answer:

[tex]x(x-4)[/tex]

Step-by-step explanation:

Factor [tex]x[/tex] out of [tex]x^2[/tex]

[tex]x[/tex]·[tex]x[/tex] [tex]-4x[/tex]

Factor [tex]x[/tex] out of [tex]-4x[/tex]

[tex]x[/tex]·[tex]x[/tex]+[tex]x[/tex]·[tex]-4\\[/tex]

Factor [tex]x[/tex] out of [tex]x[/tex]·[tex]x[/tex]+[tex]x[/tex]·[tex]-4\\[/tex]

[tex]x(x-4)[/tex]

If you have any questions feel free to ask in the comments - Mark

Also when you have the chance please mark me brainliest.

Answer:3

Step-by-step explanation:

3 ^x= 27

X=3

m=rise/run. so it is also going to the right so it is going to be positive do the rise is one and the run is two. That way m=1/2.

Answer:

7 gallons of gas

Step-by-step explanation:

because the car can drive 53 miles on 1 gallon and your trying to find the amount of gallons needed for 371 miles you would divide 371 by 53 and you get 7.

Final answer:

To find out how many gallons of gas are used to drive 371 miles in a hybrid car with a fuel economy of 53 miles per gallon, divide 371 by 53, resulting in 7 gallons of gas needed.

Explanation:

To determine how many gallons of gas a hybrid car will use to drive a total of 371 city miles when the car can drive 53 miles on 1 gallon of gas, you can set up a simple division problem. The formula to calculate gallons used is:

Total miles driven ÷ Miles per gallon = Gallons of gas used

In this case, we divide 371 miles by 53 miles per gallon to find the total gallons of gas used:

371 miles ÷ 53 miles/gallon = 7 gallons

So, the hybrid car will use 7 gallons of gas to drive 371 city miles.

Answer:

x>26

Step-by-step explanation:

Subtract 47 from 21.

Now that you have 26, that is the least amount needed because in the question it says "at least". (The inequality sign is suppose to be greater than or equal to)

Answer:
The answer is x>26

Step-by-step explanation:

to graph this inequality you would have to put an open circle on 26 and go right.

Answer:

The points are plotted in the graph attached.

Step-by-step explanation:

The points are plotted in the graph attached.

Answer: 36 degrees

Step-by-step explanation:

The angle a is 63 degrees because 177 and a are supplementary and equal 180 degrees. Because there are 180 degrees in a triangle, 63+ 81 is 144. 36 and 144 is 180, therefore b is equal to 36.

Hope this helped!

An exterior angle of a triangle equals the sum of its opposite interiors.

The measure of b is 36 degrees

To calculate angle b, we use the following equation

[tex]b + 81 = 117[/tex] ------- because b and 81 are opposite interior angles to 117

Solving further, we have:

[tex]b = 117 - 81[/tex]

Evaluate like terms

[tex]b = 36^o[/tex]

Hence, the measure of b is 36 degrees

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Answer:

301.44 feet.

Step-by-step explanation:

Given: Distance between the girl and the center of the carousel is 8 feet.

            Girl stands in a carousel and rotates around the ride 6 times.

We know the radius if carousel is 8 feet.

Now, finding the circumference of carousel to find the area covered in one rotation of carousel.

Circumference= [tex]2\pi r[/tex]

⇒ Circumference= [tex]2\pi \times 8[/tex]

∴ Circumference= [tex]16\pi[/tex]

As given, carousel rotated 6 times.

Length covered in 6 rotation of carousel= [tex]6\times 16\pi[/tex]

⇒ Length covered in 6 rotation of carousel= [tex]96\pi[/tex]

Taking, π = 3.14

⇒ Length covered in 6 rotation of carousel= [tex]96\times 3.14[/tex]

∴Length covered in 6 rotation of carousel= [tex]301.44\ feet[/tex]

Hence, 301.44 feet travelled by little girl in a Carousel.

The little girl traveled approximately 301.62 feet.

To find the distance the little girl traveled on the carousel, we need to calculate the circumference of the circle and then multiply by the number of rotations.

The formula for the circumference of a circle is:

C = 2 × π × r

where r is the radius. Here, the radius r is 8 feet.

C = 2 × π × 8

C = 16π

So, the circumference is approximately 50.27 feet (since π ≈ 3.14).

Since the girl rotates around the carousel 6 times:

Total Distance = Number of Rotations × Circumference

Total Distance = 6 × 50.27

Total Distance ≈ 301.62 feet

Therefore, the little girl traveled approximately 301.62 feet.

Answer:

x = 1 y = 3

Step-by-step explanation:

6x - 3 + 3 = 4x - 1 + 3

6x - 4x = 4x - 4x + 2

2x = 2 ÷ 2

x = 1

y = 6x - 3

y = 6 (1) - 3

y = 6 - 3

y = 3

Area of the rectangle is 18 units.

Step-by-step explanation:

Area of the rectangle = length[tex]\times[/tex]width