Which pair of expressions are equivalent?
6t+5+ 2t and 11t+5
P+3+ 2p and 5t+3
3n+7+n and 4n+ 7
2X+2+7x and 9x+7

Answer:

Answer: 3

Step-by-step explanation:

Use BODMAS

Step 1: Open bracket (1 2/5 +3.5÷1 1/4 )

Convert mixed fractions into improper fractions

7/5 + 3.5 ÷ 5/4

Divide 3.5 by 5/4

7/5 + 2.8 = 4.2

Step 2: Carry out all divisions

Convert mixed fraction into improper fractions

4.2 ÷2 2/5 +3.4÷2 1 /8 −0.35

4.2 ÷ 12/5 + 3.4 ÷ 17/8 - 0.35

1.75 + 1.6 - 0.35

Step 3: Solve

1.75 + 1.6 - 0.35

3.35 - 0.35

Answer = 3

Answer:

125i

Step-by-step explanation:

The simplification of the complex number (5i)³ is; -125i

We are given the complex number; (5i)³

Expanding the given complex number gives;

(5i)³ = 5³ * i³

⇒ 125i * i²

From complex number multiplication, we know that i² = -1. Thus;

125i * i² = -125i

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Check the picture below.

make sure your calculator is in Degree mode.

Deborah spends 240 hours per month on consulting work. This was calculated by understanding 48 hours is 1/5 of her time, and multiplying it by 5 to find the total hours.

The subject of this question is mathematics, and it involves the concept of fractions to solve a real-world problem. Deborah spends 1/5, or 20% of her time, writing grant proposals. If she spends 48 hours per month on this task, 48 hours represents 1/5 of her total consulting time.

To find the total consulting time, we need to do these steps: divide 48 by 1 to get 48 (since 48 hours is the 1/5), then multiply 48 by 5 (the denominator of the fraction, which represents the whole).

So, 48 (hours) divided by 1 equals 48, and 48 multiplied by 5 equals 240. Therefore, Deborah spends 240 hours per month on consulting work.

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Answer:

Negative Twelve Times a Number Plus Two

Step-by-step explanation:

Answer:

h = V / ar

Step-by-step explanation:

V = arh

arh = V   (divide both sides by "ar" )

h = V / ar

Answer:

4.24

Step-by-step explanation:

Answer:

That is written in standard form. Hope this helps.

The original price was 142 dollar.

Suppose the value of which a thing is expressed in percentage is "a' the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts.

We are given that store is having a 20% off sale. If the reduced

price of an item is $126.40,

We need to find the original price.

Therefore, we can write as ;

0.80x = 113.60

Now divide both sides by .80

x=142

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To find the original price of the item that was reduced by 20% to $126.40, divide the sale price by 0.80, which yields an original price of $158.00.

To determine the original price of an item that has been marked 20% off, we need to work backward from the sale price. The sale price represents 80% of the original price because 100% - 20% = 80%.

The question is provided with the reduced price which is $126.40. To find the original price, we divide the reduced price by 0.80.

Therefore, the original price of the item was $158.00.

Answer:

{y|10 < y}; ○ y > 10

Step-by-step explanation:

Whenever you have a Rational-Radical function, the answer will ALWAYS result in greater than.

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Answer:

[tex]4\frac{1}{6}\ cups[/tex]

Step-by-step explanation:

we know that

The recipe calls for 1 2/3 of sugar

To make 2 1/2 times the recipe

Multiply 2 1/2 by 1 2/3

Convert mixed numbers to an improper fraction

[tex]1\frac{2}{3}=\frac{1*3+2}{3}=\frac{5}{3}\ cups[/tex]

[tex]2\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}[/tex]

so

[tex]\frac{5}{2}(\frac{5}{3})=\frac{25}{6}\ cups[/tex]

Convert to mixed number

[tex]\frac{25}{6}=\frac{24}{6}+\frac{1}{6}=4\frac{1}{6}\ cups[/tex]

Final answer:

To find out how much sugar is needed for the new recipe that is 2 1/2 times as much, follow the three-step process.

Explanation:

To find the amount of sugar needed:

Calculate 1 2/3 cups of sugar is equal to 5/3 cups of sugar.

Multiply 5/3 by 2 1/2, which equals 25/6.

Convert 25/6 to a mixed number, which is 4 1/6 cups of sugar needed for the new recipe.

16.2

filler filler filler

Answer:

Two thirds of the Senate must approve it

The minimum number of Senate members needed to approve a treaty is two-thirds of the Senate.

The minimum number of members of the Senate that must approve a treaty for it to go into effect is two-thirds (⅔) of the Senate. The Constitution of the United States, Article II, Section 2, Clause 2 states that the President has the power to make treaties, but they require the advice and consent of the Senate.

For example, if the Senate has 100 members, then 67 votes would be needed to approve a treaty for it to go into effect. However, it is important to note that the Senate may require a supermajority vote, which would mean a higher percentage of approval than two-thirds, depending on their rules and procedures.

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By setting up the question as an algebraic equation, 1/2 * x = 21, and solving for x, it's determined that half of 42 is equal to 21.

The question we're looking to solve is: "1/2 of what number is 7 times 3?" First, let's understand that 7 times 3 equals 21. The question asks which number, when halved, gives us 21. This can easily be set up as an algebraic equation: 1/2 * x = 21, where x represents the number we're trying to find.

To solve for x, we first multiply both sides of the equation by 2 to get rid of the fraction (1/2). This leaves us with: x = 21 * 2. Therefore, x = 42. The number, when cut in half, that results in 21, is 42.

Answer:

x = 180

Step-by-step explanation:

First, you need to know

1. Double-angle formula:

cos(2x) = [tex]cos^{2}x - sin^{2}x[/tex]

2. Pythagorean identity:

[tex]cos^{2}x + sin^{2}x = 1[/tex]

Back to your problem, replacing the variable by the above:

[tex]5cosx-sin\frac{x}{2}+7 = 0[/tex]

[tex]5(cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0[/tex] By Double-angle formula

[tex]5(1 - 2sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0[/tex] By Pythagorean identity

Given [tex]y = \frac{x}{2}[/tex]

[tex]5(1-2sin^{2}y) - 2siny + 7 = 0[/tex]

[tex]10sin^{2}y+2siny-12=0[/tex]

[tex]5sin^{2}y+siny-6=0[/tex]

[tex](5siny + 6)(siny - 1)=0[/tex], we know -1 < sinx < 1, for every x ∈ R

[tex]siny = 1, y =90 [/tex]

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

[tex]x = 180[/tex]

Answer:

r = -29/20 or r = -1.45

Step-by-step explanation:

I believe you are saying that the equation is -2 1/4 = r - 4/5. If so, then I would solve it in this way:

-2 1/4 = r - 4/5

-9/4 = r - 4/5

-9/4 (20) = r (20) - 4/5 (20)

-45 = 20r - 16

20r = -29

r = -29/20

r = -1.45

Check:

-2 1/4 = r - 4/5

-9/4 = r - 4/5

-2.25 = r - 0.8

-2.25 = -1.45 - 0.8

-2.25 = -2.25

-9/4 = -9/4

The calculated value of variable r is r = -1.45.

An equation is a mathematical statement that shows the equality between two expressions. It typically consists of variables, constants, and mathematical operations (e.g., addition, subtraction, multiplication, division) with an equal sign (=) in between.

To solve for r in the equation -21/4 = r - 4/5

Step 1: Add 4/5 to both sides of the equation to isolate r:

r = -2.25 + 4/5

Convert -2.25 to a fraction with a common denominator of 5:

r = (-11.25/5) + (4/5)

Add the fractions:

r = (-11.25 + 4)/5

Simplify:

r = -7.25/5

r = -1.45

So, r = -1.45.

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Answer:

75 and 79

Step-by-step explanation:

An integer is any whole number. So you can  use practically any combination of numbers as long as one is greater than 77 and one is lower than 77.

So an example would be, 79 and 75

Answer:

Step-by-step explanation:

16 feet

Answer:

Option C.

Step-by-step explanation:

Let x be the distance from holes center in feet and y be the depth from level ground in feet.

The given table represents a quadratic functions.

x :    -2             0           2

y :    -6            -8          -6

The depth from level ground in feet is same at x=-2 and x=2 it means the hole is symmetric about the line x=0.

The value of a quadratic function is on its extreme at line of symmetry.

In the given function the line of symmetry is x=0. So, the depth of the hole is defined on x=0.

From the table it is clear that at x=0 the depth from level ground is 8 feet.

Therefore, the correct option is C.

Answer:

see explanation

Step-by-step explanation:

27 = 3 × 9 ← is one way

27 = 3³ ← is another way

The two (2) ways you can represent the number 27 using the number 3 are shown below.

In this exercise, you're required to represent the number 27 by using the number 3. This simply means that you will represent the number 27 in terms of 3.

First way;

Since 3 is a factor of 27, we would multiply it to get 27.

[tex]27 = 3 * 3 * 3[/tex]

Second way;

From the above, we can see that the product of 3 is equal to 27.

[tex]27 = 3^{3}[/tex]

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Answer:

the answer is C

Step-by-step explanation:

You can solve this by changing everything to fractional powers. 4th root of x^3 can be written as x^3/4. Since you are dividing you will subtract their powers, so 3/4 - 1/12 will give you the power raised by x. You can rewrite to 9/12 - 1/12 to get 8/12 which will end up as x^2/3

I tried to answer the last time you asked but you closed the question haha, I hope you understand!

Answer:

She lost $15 on her 50 dollar credit card.

Explanation:

Since Kendra looses 5$ each month, we have to look at how many months the card was left unused. The card was left unused for 3 months. Multiply the $5 by 3 months to get $15. Her card is now at $35

The amount of money Kendra lost in her gift card is required.

Kendra lost $15.

Initial value of the gift card = $50

Money lost per month = $5

Let M be the number of months after the gift card was bought.

The money lost after M months passed would be

[tex]5M[/tex]

Kendra forgot about the gift card for 3 months

So, [tex]M=3[/tex]

[tex]5\times3=15[/tex]

Kendra lost $15.

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Answer:

5,500,000 = (5 x 100000000) + (0 x 10000000) + (5 x 1000000) + (0 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1)

Step-by-step explanation:

The expanded form of 5,500,000 is  (5 x 1000000) + (5 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1).

The expanded form of the number is the splitting of numbers based on the place value, such as ones, tens, hundreds, thousands, ten thousands,and so on. The number that is represented by the sum of each digit multiplied by its place value is called the expanded form of the number.

Now the given number is,

5,500,000

Now each digit place value is given as,

5 =  (5 x 1000000)  

5 =  (5 x 100000)

0 =  (0 x 10000)

0 =  (0 x 1000)  

0 =  (0 x 100)

0 =  (0 x 10)

0 =  (0 x 1)

Adding this together, we get

5,500,000 = (5 x 1000000) + (5 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1).

Hence, The expanded form of 5,500,000 is  (5 x 1000000) + (5 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1).

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x = -6 is the solution to the equation 6x + 7 = 13 + 7x

To solve the equation 6x + 7 = 13 + 7x, you can follow these steps:

Group the x terms on one side and the constant terms on the other side:

6x - 7x = 13 - 7

Combine like terms:

-x = 6

Multiply both sides of the equation by -1 to isolate x:

-1*(-x) = -1*6

This simplifies to:

x = -6

Therefore, the solution to the equation 6x + 7 = 13 + 7x is x = -6.

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Answer:3.3

Step-by-step explanation:

You want to look at the 3.2 because the 2 in the hundredths place so you will round it up because 6 is higher than 5 so it will be 3.3

Rounded to the nearest hundredth is 3.26

Answer:

False

Step-by-step explanation:

The absolute value always returns a positive value, however the expression inside can be positive or negative, that is

Given

| z - 7 | - 2 = 2 ( add 2 to both sides )

| z - 7 | = 4, then

z - 7 = 4 OR - (z - 7) = 4

z = 4 + 7 = 11 OR

- z + 7 = 4

- z = 4 - 7 = - 3 ( multiply both sides by - 1 )

z = 3

As a check

z = 11

| 11 - 7 | - 2 = | 4 | - 2 = 4 - 2 = 2 ←  True

z = 3

| 3 - 7 | - 2 = | - 4 | - 2 = 4 - 2 = 2 ← True

Hence z = 11 or z = 3 are the solutions

Answer:

4.32       46

Step-by-step explanation:

ok im lazy and just googled it here

Answer:

Rafael gets $4,32 In tips. The old lady gets $41.68 in change.

Step-by-step explanation:

Step 1: To calculate the tip we must take into account that it is 8% of the total amount of the bill.

$54 * 8%/100% = $4,32

Rafael gets $4,32 In tips.

Step 2: Now we must calculate the change the old lady receives. For this, we must subtract from the $100 that she gives the part corresponding to the payment for food and the part corresponding to the tip.

$100 - $54 - $4,32 = $41,68

The old lady gets $41.68 in change.

Have a nice day!

Answer:

[tex]x = 19[/tex]

Step-by-step explanation:

If two lines are perpendicular, they create 4 90° angles. Meaning, in this case, that m<DBC = 90 and m<DBA = 90.

We're given that m<DBE = 2x - 1 and that m<CBE = 5x - 42.

The sum of angles DBE and CBE = m<DBC = 90°

We can add the two angles and set it equal to 90 to find x

[tex]2x - 1 + 5x - 42 = 90\\7x - 43 = 90\\7x = 133\\x = \frac{133}{7} =19[/tex]

Answer:

-18

Step-by-step explanation:

Follow PEMDAS. So first you do 2x2=4 then 4-7x= -3-15= -18

Good evening ,

_______

Answer:

x’=5

x’’=(-3)/2

____________________

Step-by-step explanation:

Δ=(-7)²-4×(2)×(-15)=49+120=169

√Δ=√169=13

then

x’=(7+13)/4=20/4=5

x’’=(7-13)/4=(-6)/4=(-3)/2.

:)

Answer:

68

Step-by-step explanation:

4^3-(24÷6)+8

4³-(4)+8= 68

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Answer:

68

Step-by-step explanation:

[tex] {4}^{3} - (24 \div 6) + 8 = 64 - 4 + 8 = 60 + 8 = 68[/tex]

According to the Order of Operations [GEMS\BOMDAS\PEMDAS etc.], in this case, you deal with the grouping symbols first before anything else, then comes the exponents, and finally comes Subtraction & Addition from right to left [or left to right, if you know what you are doing correctly]. Doing all of these will give sixty-eight.

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Answer:

D. 16.8

Step-by-step explanation:

It is right trust me!!!

Answer:

Additional amount of clearance between the truck and overpass is 16.8 inches.

Step-by-step explanation:

A law states that a a freight truck must have the clearance of at least 3 feet to travel under the a overpass.

Sign on an overpass states that the overpass is 18 feet above the road's surface.

Height of the truck is 13.6 feet.

As per rule height of overpass from the road must be height of the truck + clearance.

Additional amount of clearance between the truck and the overpass

= Distance between the road and the overpass - (height of the truck + clearance)

= 18 - (13.6 + 3)

= 18 - 16.6

= 1.4 feet

Since 1.4 feet = 12 inches

1.4 feet = 12×1.4 = 16.8 inches

Therefore, additional amount of clearance between the truck and overpass is 16.8 inches.