A commercial laundry charges $5.25 per load. You have $31.50. Write and solve an inequality to find the greatest number of loads of laundry you can do. A. 5.25w ≤ 31.5; w ≤ 26.25 B. w ≤ 31.5 − 5.25; w ≤ 26.25 C. 5.25w ≤ 31.5; w ≤ 6 D. 5.25 + w ≤ 31.5; w ≤ 6

Lilliana's hair was 48 inches long and she cut off 2/3 of it. After calculating 2/3 of 48, which is 32 inches, we subtract this from the original length. Lilliana's hair was 16 inches long after her haircut.

The student's question concerns the length of Lilliana's hair after she has asked her hairdresser to cut 2/3 of it off. If we know that Lilliana's hair was originally 48 inches long, we need to calculate 2/3 of this length and then subtract it from the original length to find the new length of her hair after the haircut.

Calculate 2/3 of 48 inches: (2/3) times 48 = 32 inches.

Subtract the amount cut from the original length: 48 inches - 32 inches = 16 inches.

Therefore, after Lilliana's haircut, her hair was 16 inches long.

The answer for the first one is (x)°+(3x)°+(5x)°=180° and the answer for the second one is x=20. If you need me to explain how they got the answer, i'm here.

Answer:

Fill the blanks

1) (x)°+(3x)°+(5x)°=180°

2) x°=20°

Step-by-step explanation:

Consider the provided information.

Given: Triangle PQR with m∠P=(x)°, m∠Q=(3x)°, and m∠R=(5x)°.

We need to prove that x = 20

Consider the provided figure.

By the triangle sum theorem the sum of the angles in a triangle is equal to 180. Therefore using the give and triangle sum theorem,

m∠P+m∠Q+m∠R=180°

Now use substitution property.

(x)°+(3x)°+(5x)°=180°

Simplify the equation gets

9x°=180°

Finally, using the division property of equality.

9x°/9=180°/9

x°=20°

Hence proved

d - 2 < -1 is how this inequality would be displayed.

However, we can solve for the value of d by treating this like a standard algebraic equation.

d - 2 < -1

Add 2 to both sides.

d < 1

The value of d is less than 1.

Let me know if you have any other questions.

Answer:

Given phrase,

a number d minus 2 is less than -1

∵ '-' is the sign of minus,

⇒ d minus 2 = d - 2

Also, '<' is the sign of less than,

⇒ d minus 2 is less than -1 = d - 2 < - 1

Hence, the required inequality would be,

[tex]d-2 < -1[/tex]

Now, by further solving,

Add 2 on the both sides of inequality ( additive property of inequality )

[tex]d < -1 + 2\implies d < 1[/tex]

⇒ d ∈ ( -∞, 1 )

8*10^6+5*10^9 should be

5,008,000,000

Answer:

The error student make is he multiply the terms instead of addition.

Step-by-step explanation:

Given : A student found the product of 8 × 10 to the 6 power + 5 × 10 to the 9th power to be 4 × 10 to 15 power.

To find : What is the error ?

Solution :

8 × 10 to the 6 power - [tex]8\times 10^6[/tex]

5 × 10 to the 9th power - [tex]5\times 10^9[/tex]

4 × 10 to 15 power -  [tex]4\times 10^{15}[/tex]

According to student, [tex]8\times 10^6+5\times 10^9=4\times 10^{15}[/tex]

We solve the expression,

[tex]=8\times 10^6+5\times 10^9[/tex]

[tex]=8\times 10^6+5000\times 10^6[/tex]

[tex]=10^6(8+5000)[/tex]

[tex]=5008\times 10^6[/tex]

The error student make is he multiply the terms instead of addition.

g(x) = -3x² - 2x + 3

g(-2) = -3(-2)² - 2(-2) + 3

g(-2) = -12 + 4 + 3 = -5

Answer:

D. 26.75 pounds/minute

Step-by-step explanation:

For calculate unit rate that reflects the speed of the processor we can use the following equation:

[tex]Speed = \frac{Total Pounds}{RequiredTime}[/tex]

Taking into account that the answers are in pounds per hour and pounds per minute, we re going to calculate the speeds in booth units.

1. Speed in Pounds per hours: Replacing Total Pounds by 4,815 and Required time by 3 hours, we get:

[tex]Speed = \frac{4,815Pounds}{3 Hours}=1,605 Pounds/hour[/tex]

2. Speed in Pounds per minute: Every hour have 60 minutes, the 3 hours have 180 minutes, so replacing Total Pounds by 4,815 and Required time by 180 minutes, we get:

[tex]Speed = \frac{4,815Pounds}{180 Hours}=26.75 Pounds/hour[/tex]

So, chosen the rate that appear in the answers, we can say that the correct answer is D. 26.75 pounds/hours.

4 (1/5 ) = 21/5

21 / 5 divided by 2 / 3 equals

21 / 5 * 3 / 2 equals 63 / 10 equals

6 (3 / 10)

B would be the answer because if you were to search up a picture of alternate interior angles, it would be the same as <CAD and <ACB

Answer:

(B) ∠CAD≅∠ACB

Step-by-step explanation:

Given in the question quadrilateral ABCD is a rectangle and a table of two-column proof with missing statement for proves that the diagonals of the rectangle bisect each other.

If we want to prove that the diagonals bisects to each other, then for this  first we will prove that ΔADE≅ΔCBE. But given in the two-column proof  

∠ADB≅∠CBE , side BC= side AD .  ∠CAD ≅ACD must be  necessary for to prove that ΔADE≅ΔCBE (ASA postulate). Hence statement  ∠CAD ≅ACD can be used to fill in the blank space.

The correct answer is A) g≥5

This is because when you look at an absolute value function, the constant at the end is the y value of the vertex. Since it is an absolute value equation, we know that the values can only go up. Therefore, it must be greater than or equal to the constant at the end (5)

The plane travels at 60 mph and the wind is blowing at 20 mph.  

By setting up and solving a system of equations, we find that the speed of the plane in still air is 63 mph and the speed of the wind is 21 mph.

To answer this question, you first need to set up equations to represent the speed of the plane and the speed of the wind. You can denote the speed of the plane in still air as 'p' and the speed of the wind as 'w'. The plane's speed with the wind (going to Phoenix) is represented by p+w and against the wind (coming back) is p-w.

For the trip to Phoenix, you know that distance = speed * time. That gives us the equation 1176 = 14(p+w). After simplification, we obtain the equation, p+w = 84.

For the return flight, our equation is 1176 = 28(p-w). On simplification, we find the equation p-w = 42.

Now you have a system of equations that you can solve: p+w = 84p-w = 42. Solving these equations together, you find that the speed of the plane (p) in still air is 63 mph, and the speed of the wind (w) is 21 mph.

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Answer: B) The lengths of both transverse axes are the same.

Step-by-step explanation: Given Hyperbola equations :

[tex]\frac{x^2}{3^2}-\frac{y^2}{4^2}=1[/tex] and

[tex]\frac{y^2}{3^2}-\frac{x^2}{4^2}=1[/tex]

First one : [tex]\frac{x^2}{3^2}-\frac{y^2}{4^2}=1[/tex] is a Horizontal Hyperbola.

a = 3 and 2a = 6.

Length of transverse axis = 6.

And second one :  [tex]\frac{y^2}{3^2}-\frac{x^2}{4^2}=1[/tex] is a Vertical Hyperbola.

b=3 and 2b = 6

Length of transverse axis = 6.

The lengths of both transverse axes are the same.

Therefore, correct option is B option :

Answer:

B

Step-by-step explanation:

the answer is that it is false

(x/7)-12=-2

Add 12 to both sides.

x/7=10

Multiply both sides by 7.

x=70

Final answer: 70

hope this helps :)

we are given

the quotient of y and 6

we always start from left to right order of operation

we know that

quotient means division

so, we can write as

the quotient of y and 6 is

[tex]\frac{y}{6}[/tex]...............Answer

Let 1 piece = X

The 2nd piece would be X + 2 feet

Add:

x +x+2 = 26 feet

2x +2 = 26 feet

Subtract 2 from each side:

2x = 24

Divide both sides by 2:

x = 24 / 2

X = 12

One piece is 12 feet the other piece is 14 feet.

Answer: The statement is [tex]\frac{AD}{DB} +1=\frac{CE}{EB}+1[/tex] and the reason is add 1 both sides.

Explanation:

The given equation is [tex]\frac{AD}{DB} =\frac{CE}{EB}[/tex].

We know that according to the addition property the equation x=y and x+c=y+c are equivalent equations, where c is a constant.

So we can add 1 both sides in the given equation.

[tex]\frac{AD}{DB} +1=\frac{CE}{EB}+1[/tex]

Now we can take LCM and we get,

[tex]\frac{AD+DB}{DB} =\frac{CE+EB}{EB}[/tex]

The above step is the third step of the given proof. By follow the given steps we can prove that DE is parallel to AC.

Therefore, the missing step is addition of 1 on both the sides of the given equation.

To prove that DE is parallel to AC, we need to show that the lines DE and AC have the same slope. By rearranging the given equations to isolate the currents I₁, I₂, and I₃, and then setting these expressions equal to each other, we can determine the relationship between the currents and thereby the slopes of DE and AC.

To prove that DE is parallel to AC, we need to show that the lines DE and AC have the same slope. The given equations 1₁ - 12 - 13 = 0, I₁ R₁ + I₂ R₂ = V₁, and I₂ R₂ − I₃ (R₃ + R₄) = V₂ can be rearranged to isolate the currents I₁, I₂, and I₃ in terms of voltage and resistance. By setting these expressions equal to each other, we can determine the relationship between the currents and thereby the slopes of DE and AC.

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Answer:

28 questions

Step-by-step explanation:

In the first 10 mins she answered 2/5 of 40 which is 16. The remaining amount is 24 questions and half of that is 12. So she answered 12 questions in 15 mins. Finally you add them to get 28 questions in 25 minutes.

the prime factors for 150 are:

2 x 3 x 5 x 5

In exponential form:

2^1 x 3^1 x 5^2

Hope this helps

Answer:

Step-by-step explanation:the prime factors for 150 are:

2 x 3 x 5 x 5

option A  IS correct option.

27,515 is the actual answer.

Estimated, it is about 27,500

Hope I helped!

a + b + c = 180

b = 2a

c = 3a

a + 2a + 3a = 180

6a = 180

a = 30

b = 2(30)

b = 60

c = 3(30)

c = 90

Answer:

a = 30

b = 60

c = 90

Answer:

For this expression, you will have to use the distribution property to get your answer.

First, distribute the 4 to the x and -1

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

[tex]4(-1)=-4[/tex]

[tex]4x-4-3(x+2)[/tex]

Now do the same with the -3, x and 2

[tex]-3(x)=-3x[/tex]

[tex]-3(2)=-6[/tex]

[tex]4x-4-3x-6[/tex]

Now combine like terms to get your final answer

[tex]4x-3x=x[/tex]

[tex]-4-6=-10[/tex]

Thus, your solution is: x - 10

Step one: 4(x-1)-3(x+2)=0        (set equal to zero)

Step two: 4x-4-3x-6=0            (multiply numbers on the outside to inside of "( )")

Step three: x-10=0                   (combine like terms)

Step four: 0+10=10, x=10         (inverse operation)

Answer: x=10

i think that you would just take 23/4=$5.75

so take 6 times 5.75 and you should get $34.5

To answer this question, we first need to determine the unit cost (cost per t-shirt).

Step 1: Find the unit cost
Alicia bought 4 T-shirts for a total of $23.00. To calculate the cost per T-shirt (the unit rate), we need to divide the total cost by the number of T-shirts.

So, $23.00 (total cost) divided by 4 (number of T-shirts) equals $5.75. Thus, the unit cost of one T-shirt is $5.75.

Step 2: Calculate the cost for 6 T-shirts
Now that we know the unit cost, we can find out how much 6 T-shirts will cost. To do this, we multiply the unit cost by the number of T-shirts.

So, $5.75 (cost per T-shirt) times 6 (number of T-shirts) equals $34.50.

Therefore, it would cost $34.50 for 6 T-shirts, given the unit rate.

f(x)=40

x=8

so if x=2 it would be 40/8 which is 5

C

since the quantities vary directly then

x = kf(x) ( where k is the constant of variation )

to find k use the given condition , f(x) = 40 when x = 2

k = [tex]\frac{x}{f(x)}[/tex] = [tex]\frac{8}{40}[/tex] = [tex]\frac{1}{5}[/tex]

thus x = [tex]\frac{1}{5}[/tex]f(x)

when x = 2

f(x) = [tex]\frac{x}{k}[/tex] = [tex]\frac{2}{\frac{1}{5} }[/tex] = 10

A) is 164 because 6 times 6 is 36. 500 - 36 is 164

Here is the solution...

1) [tex]\sqrt[3]{135} \\[/tex]

Solution

We can rewrite [tex]\sqrt[3]{135} = \sqrt[3]{27} *\sqrt[3]{5}[/tex]

Here, [tex]\sqrt[3]{27} = 3[/tex]

Now substitute the value, we get

[tex]\sqrt[3]{135} = 3 \sqrt[3]{5}[/tex]

The answer is [tex]3\sqrt[3]{5}[/tex]

2) [tex]-5\sqrt[3]{40}

Solution

[tex]-5\sqrt[3]{40} = -5\sqrt[3]{8} *\sqrt[3]{5}[/tex]

Here [tex]\sqrt[3]{8} = \sqrt[3]{2^{3} } = 2\\[/tex]

Therefore, we get [tex]-5*2\sqrt[3]{5} = -10 \sqrt[3]{5}[/tex]

The answer is-10 \sqrt[3]{5}[/tex]

2) [tex]2\sqrt[3]{5} * 4\sqrt[3]{8}[/tex]

Solution

[tex]\sqrt[3]{8} = 2[/tex]

Now plug in the above in the given expression, we get

[tex]2\sqrt[3]{5} * 4*2 = 16\sqrt[3]{5}[/tex]                         {2*4*2 = 16]

The answer is [tex]16\sqrt[3]{5}[/tex]

The measure of angle ∣4 is 250 degrees. The measure of angle ∣A is 67 degrees.

To find the measure of angle ∣4, we can use the fact that angles around a point add up to 360 degrees.

We know that ∣1 is 45 degrees and ∣3 is 65 degrees.

To find ∣4, we can subtract the sum of angles ∣1 and ∣3 from 360 degrees.

Therefore, ∣4 = 360 - (∣1 + ∣3) = 360 - (45 + 65) = 360 - 110 = 250 degrees.

To find the measure of angle ∣A, we can use the fact that the sum of the angles in a triangle is 180 degrees.

We know that ∣B is 90 degrees because it is a right angle.

Therefore, ∣A + ∣B + ∣C = 180 degrees.

Substituting the given values, we get (3x - 8) + 90 + (x - 2) = 180. Simplifying the equation, we get 4x + 80 = 180.

Solving for x, we get x = 25.

Substituting x back into the equation for ∣A, we get ∣A = (3(25) - 8) = 67 degrees.