Use Order of Operations
to solve.
4 to the third power -(24 ÷6) +8

Answer:

the next 3 terms are 64, 128, and 256

Answer:

-327

Step-by-step explanation:

20+22-369=-327

Answer:

5 + 3d - 1.5 = 0.5

3d + 3.5 = 0.5

3d = -3

d = -1

Answer:

Step-by-step explanation

5+1.5(2d)1.5(-1)=0.5

5+3d-0.5=0.5

5+3d=1

3d=-4

D=1.33

Answer:

≠

Step-by-step explanation:

it would be unequal to

Answer:

A:False

Step-by-step explanation:

Answer:

The area of the rectangular plot is 396 square unit.

Step-by-step explanation:

let [7p +4q ]= length of the rectangular plot. And

[ 3p+8p ] = width of the rectangular plot

given that p=2 and q=1

substitute them in the expression for the length

length=7(2)+4(1)

length=14+4

length=18units

again subject the values for p and q into the expression for the width

width=3(2)+8(2)

width=6+16

width=22units

but mathematically,

Area of a rectangular plot

= Length×width

A=L×W

given L=18units and W=22units

A=18units × 22units

A=396 square unit.

Answer:

See explanation

Step-by-step explanation:

To subtract mentally 81 from 304, complete following steps:

Step 1: Write number 304 as

[tex]304=300+4\\ \\304=200+100+3+1\\ \\304=200+20+80+3+1[/tex]

Step 2: Write number 81 as

[tex]81=80+1[/tex]

Step 3: Now subtract 80 and 1 from number 304:

[tex]304-81=(200+20+80+1+3)-(80+1)\\ \\304-81=200+20+3\\ \\304-81=223[/tex]

Final answer:

To mentally subtract 304-81, round 81 to 100, subtract from 304 to get 204, then add back the difference (19) for a result of 223.

Explanation:

To calculate 304-81 mentally, we can round 81 up to 100 to make the numbers easier to work with. We know that 304 - 100 = 204.

Since we've subtracted too much by rounding up, we need to add back the difference between 81 and 100, which is 19.

So the full calculation would be 304 - 81 = 304 - 100 + 19 = 204 + 19 = 223.

The coherent sequence of equations aligning with this reasoning would be:

Answer:

The measures of the labeled angles are 58°.

Step-by-step explanation:

Since the two angles are opposite angles, they have to be equal, meaning:

[tex]2x = 87 - x[/tex]

Solve by adding x to both sides and dividing by 3.

[tex]3x = 87 \\ x = 29[/tex]

If x = 29°, then 2x= 58°.

Since opposite angels are equal, the other angle is also 58°.

This can be checked:

[tex]87 - 29 = 58[/tex]

The integer that makes the division sentence x / (-2) = -3 true is 6.

Here's how we can solve for x:

Multiply both sides of the equation by -2 to isolate x:

x = -3 * (-2)

Simplify the right side:

x = 6

Therefore, dividing any number by -2 and then multiplying by -2 again should result in the original number. In this case, dividing 6 by -2 and then multiplying by -2 again gives us 6:

(6 / -2) * -2 = -3 * -2 = 6

Remember, when dividing by negative numbers, the result is flipped compared to dividing by positive numbers. This is why we need to multiply by -2 again to get back to the original number.

The integer that satisfies the division sentence x ÷ (−2) = −3 is 6, following the rule that multiplying two negative numbers yields a positive result.

To find the integer that makes the division sentence true, we look at the equation given: x ÷ (−2) = −3. To solve for x, we multiply both sides by −2, because division by a number is the inverse operation of multiplying by that number. So, we have x = −3 * (−2).

According to the rules of multiplication, when two negative numbers are multiplied together, the answer has a positive sign. Therefore, we get x = 6 as our solution. Since we know that dividing a positive number by a negative number yields a negative result, our calculated integer 6 is a valid answer because 6 ÷ (−2) indeed equals −3.

Following the rules of operations with negatives, such as in the examples 5 − (+3) that becomes 5 − 3 = 2, and 2 − (−6) that turns into 2 + 6 = 8, we can consistently apply the rule for division which mirrors the multiplication rules for signs to solve for our missing integer.

Final answer:

In this problem, we are given the percentage (25%) and the amount (40), and we need to find the base. To find the base, we can set up an equation and solve for x. The base in this problem is 160.

Explanation:

In this problem, we are given the percentage (25%) and the amount (40), and we need to find the base. The base represents the whole quantity or number that the percentage is taken from.

Let x be the base. We can set up the equation: 25% of x is equal to 40, or 0.25x = 40.

To find the base, we divide both sides of the equation by 0.25: x = 40 / 0.25.

Simplifying, we get x = 160. Therefore, the base is 160.

To summarize, the percent is 25%, the amount is 40, and the base is 160.

Answer:

$7.90 tip the total is $47.40

Step-by-step explanation:

Final answer:

To find the total cost of a $39.50 family dinner after adding a 20% tip, first calculate the amount of the tip by multiplying the cost of the dinner by the tip percentage. Then, add the tip to the cost of the dinner to get the total amount.

Explanation:

To find the total cost of a $39.50 family dinner after adding a 20% tip, you first need to calculate the amount of the tip. Tip is calculated by multiplying the cost of the dinner by the tip percentage. In this case, the tip would be 20% of $39.50, which is

$39.50 × 0.20 = $7.90

Next, you add the tip to the cost of the dinner to get the total amount:

$39.50 + $7.90 = $47.40

So, the total cost of the family dinner after adding a 20% tip is $47.40.

Answer:D. 2(3x-5)^2

Step-by-step explanation:

18x^2-60x+50=2(9x^2-30x+25)

Answer:

D. 2(3x - 5)²

Step-by-step explanation:

18x² - 60x + 50

The expression can be factorize as follows;

18x² - 60x + 50

divide through by 2

2(9x² - 30x + 25)

The bracket equation can be factorized further

Find the square value that can be multiplied to get 9x² and 25

The values are 3x and 5

2( (3x- 5)(3x - 5) )

2(3x - 5)²

Answer:

x =7

Step-by-step explanation:

  f (x)   =   g (x)

3x + 4 = 5x - 10

4 + 10  = 5x - 3x

    14    = 2x

   14/2  =  x

     7 = x

Answer:

5.7

Step-by-step explanation:

The roads are two lines and they intersect at  90° .

Intersecting lines cross each other at some arbitrary angle .

Two geometric objects are perpendicular if they intersect at a right angle. A line is said to be perpendicular to another line if the two lines intersect at a right angle.

According to the question

Roads have 2 lanes and have crossing lane .

Now,

Those roads  are two lines and they intersect at a right angle by making 90° at there point of intersection .

So,

They are perpendicular lines .

Hence, the roads are two lines and they intersect at  90° .

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Answer:

v = +5 m/s

Step-by-step explanation:

v = d/t

d = 10

t = 2

v = 10/2

v = +5 m/s

Answer:

58°

Step-by-step explanation:

65°+57°=122°

180°-122°=58°

Answer: 6 inches

Step-by-step explanation:

formula for area of a rectangle is length times width

LW=A

substitute

7(W)=42

divide 7 on both sides

42/7 = 6

Answer: 6

Answer:

From the table shown the years in which there was a budget deficit are

2002,2003,2005,2006,2008,2010

Step-by-step explanation:

Budget deficit is said to be when expenditure exceed or is greater than the budgeted revenue.

For 2002:

Revenue = $5 trillion and expenditure = $7 trillion

To check for budget deficit = Revenue - expenditure ( $5 trillion - $7 trillion)

=  -$2 trillion ( there was a budget deficit of $2 trillion)

For 2003:

Revenue = $8 trillion and expenditure = $10 trillion

to check for budget deficit = Revenue - expenditure ($8 trillion - $10 trillion)

= -$2 trillion (there was a budget deficit of $2 trillion)

For 2005:

Revenue = $15 trillion and expenditure = $18 trillion

to check for budget deficit = Revenue - expenditure ($15 trillion - $18 trillion)

= -$3 trillion (there was a budget deficit of $2 trillion)

For 2006:

Revenue = $8 trillion and expenditure = $10 trillion

to check for budget deficit = Revenue - expenditure ( $8 trillion - $10 trillion)

= -$2 trillion (there was a budget deficit of $2 trillion)

For 2008:

Revenue = $2 trillion and expenditure = $4 trillion

to check for budget deficit = Revenue - expenditure ( $2 trillion - $4 trillion)

= - $2 trillion ( there was a budget deficit of $2 trillion)

For 2010:

Revenue = $5 trillion and expenditure = $9 trillion

to check for budget deficit = Revenue - expenditure ( $5 trillion - $9 trillion)

= -$4 trillion (there was a budget deficit of $4 trillion)

From the table shown the years in which there was a budget deficit are

2002,2003,2005,2006,2008,2010

Budget deficit is said to be when expenditure exceed or is greater than the budgeted revenue.

For 2002:

Revenue = $5 trillion and expenditure = $7 trillion

To check for budget deficit = Revenue - expenditure ( $5 trillion - $7 trillion)

=  -$2 trillion ( there was a budget deficit of $2 trillion)

For 2003:

Revenue = $8 trillion and expenditure = $10 trillion

to check for budget deficit = Revenue - expenditure ($8 trillion - $10 trillion)

= -$2 trillion (there was a budget deficit of $2 trillion)

For 2005:

Revenue = $15 trillion and expenditure = $18 trillion

to check for budget deficit = Revenue - expenditure ($15 trillion - $18 trillion)

= -$3 trillion (there was a budget deficit of $2 trillion)

For 2006:

Revenue = $8 trillion and expenditure = $10 trillion

to check for budget deficit = Revenue - expenditure ( $8 trillion - $10 trillion)

= -$2 trillion (there was a budget deficit of $2 trillion)

For 2008:

Revenue = $2 trillion and expenditure = $4 trillion

to check for budget deficit = Revenue - expenditure ( $2 trillion - $4 trillion)

= - $2 trillion ( there was a budget deficit of $2 trillion)

For 2010:

Revenue = $5 trillion and expenditure = $9 trillion

to check for budget deficit = Revenue - expenditure ( $5 trillion - $9 trillion)

= -$4 trillion (there was a budget deficit of $4 trillion)

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Answer:

Step-by-step explanation:

f(x)=(x²+20x+100) -3  because : 97 = 100 -  3

f(x) = (x+10)² -3 ....vertex form

Marcy is correct if Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%.

As we know,

The ratio of two integers is stated as a fraction of a hundred parts. It is a metric for comparing two sets of data

= (70% + 100%)/2

= 170%/2

= 85%

Thus, Marcy is correct if Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%.

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Final answer:

To raise her score to 85%, Marcy needs to get an average of 1.83 on the final exam. Since it is not possible to score more than 100%, her claim of needing a 100% is not correct.

Explanation:

To determine whether Marcy can raise her score to 85% by getting a 100% on the final exam, we need to calculate the average needed on the final exam.

To find the average Marcy needs, we can use the formula: Final Average = (Current Average * Weight) + (Final Exam Score * (1 - Weight)), where the weight represents the percentage of the final exam in the overall grade.

Let's assume the weight of the final exam is 30%. Plugging in the values, we get:

85% = (70% * 0.7) + (Final Exam Score * 0.3)

Solving for the Final Exam Score:

85% - (70% * 0.7) = Final Exam Score * 0.3

0.55 = Final Exam Score * 0.3

Final Exam Score = 0.55 / 0.3

Final Exam Score = 1.83

Since it is not possible to score more than 100% on the final exam, Marcy's claim of needing to get a 100% on the final to raise her score to 85% is not correct.

Answer:

1000+80+4+0.9

Step-by-step explanation:

Keep in mind that expanded form means to expand the number by adding the individual places values to form a mathematical expression. In other words, numbers are expanded to show the value of each of its digits.

For the thousands place:

1,084.9 ---> 1,000.0

Hundreds place:

Because the value is 0, you needn't to include it in the expression.

Tens place:

1,084.9 ---> 80.0

Ones place:

1,084.9 ---> 4

Tenths place:

1,084.9 ---> 0.9

The value of the equation is A = 1,000 + 80 + 9 + 0.40 = 1,084.90

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as A

Now , the value of A is

A = 1,084.90   be equation (1)

On simplifying the equation , we get

1 x 1000 = 1000

0 x 100 = 0

8 x 10 = 80

4 x 1 = 4

0.90 x 1 = 0.90

Substituting the values in the equation , we get

A = 1,000 + 80 + 9 + 0.40

On further simplification , we get

A = 1,084.90

Hence , the equation is solved

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Answer:

[tex]\large\boxed{12^{-2}=\dfrac{1}{144}}[/tex]

Step-by-step explanation:

[tex]12^2\cdot12^{-4}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=12^{2+(-4)}=12^{-2}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{12^2}=\dfrac{1}{12\cdot12}=\dfrac{1}{144}[/tex]

Answer:

Step-by-step explanation:

This is the same to have 12^2/12^4

This is equal to have 1/12^2

1/144=0,0069

Answer:

_

1/3, or 0.3 is there difference

Answer:

Step-by-step explanation:To convert part-to-part ratios to fractions:

Use the total number as the denominator: 6 + 8 = 14.

Use each of the ratio terms as the numerator in a fraction: ...

Reduce each fraction to lowest terms: ...

The part-to-part ratio 6 : 8 converts into the fractions:

To convert a rational expression to a fraction, create a common denominator, multiply by the inverse when dividing fractions, and simplify by canceling out common factors after prime factorization.

Converting a rational expression to a fraction involves creating a common denominator for the terms involved. When dividing fractions, the process is to change the division to multiplication by the inverse of the second fraction and then multiplying the numerators and denominators as above. A conversion factor in a measurement context is simply a fraction equal to one, with the original unit in the denominator to cancel it out and the new unit in the numerator.

When simplifying fractions it's useful to remember that multiplying or dividing both numerator and denominator by the same number does not change the value of the fraction; this is often referred to as multiplying by a fraction that equals one (1/2, 2/2, 3/3, etc.). Simplifying a fraction may involve finding these 'fractions equal to one' to cancel out the same factors in both the numerator and denominator.

Answer:

answer is D

Step-by-step explanation:

5(-2) + y = 1      5(1) + y = 1   5(6) + y = 1  

-10 + y = 1          5 + y = 1      30 + y = 1

y - 10 = 1            y + 5 = 1       y + 30 = 1

y = 11                 y = -4            y= -29

The corresponding range function 5x + y=1 which has the domain (-2, 1, 6) will be option (D) {11,-4,-29}

A function is a correspondence or rule that assigns to each element in one set, called the domain D, exactly one element from a second set, called the range R.

The Steps are as follow:

Function = 5x + y = 1

domain  = (-2 , 1, 6)

Corresponding range = ?

let x = -2

∴ 5x + y =1

∴ 5(-2) + y =1

∴  -10 + y =1

∴ y = 11

x = 1

∴ 5x + y = 1

∴ 5(1) + y = 1

∴ 5 + y = 1

∴ y = -4

x = 6

∴ 5x + y =1

∴ 5(6) + y = 1

∴ 30 + y =1

∴ y = -29

So the corresponding range function 5x + y=1 which has the domain (-2, 1, 6) will be option (D) {11,-4,-29}

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Answer:

PS = 37

Step-by-step explanation:

The opposite sides of a rectangle are congruent, thus

perimeter = 2(3x + 1) + 2(4x - 3) = 136 ← distribute and simplify left side

6x + 2 + 8x - 6 = 136

14x - 4 = 136 ( add 4 to both sides )

14x = 140 ( divide both sides by 14 )

x = 10

Hence

PS = 4x - 3 = (4 × 10) - 3 = 40 - 3 = 37

Answer:whats the heck is this

Step-by-step explanation:473658857