Exercises
Write an algebraic expression for each verbal expression.
Four times a number?

Option C is the next step to construct a congruent angle.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given Data

R makes the same angle with PQ and QR.

Option C is the next step to construct a congruent angle.

Steps to construct congruent triangle:

1) Each of the three sides is equal (SSS: side, side, side)

2) A comparable side and two angles are the same (ASA: angle, side, angle)

3) Both the angle between the two sides and the two sides' dimensions are equal (SAS: side, angle, side)

4) The hypotenuse, the corresponding side, and a right angle are all equal (RHS, right angle, hypotenuse, side).

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so the answer is x=2

Answer:

x=2

Step-by-step explanation:

2(x-4)+7=3

First, multiply the 2 to x-4.

2x-8+7=3

Simplify.

2x-1=3

Add x on both sides.

2x=4

Divide 2 on both sides.

x=2

Answer:

I think your answer is correct

Step-by-step explanation:

You did that right. You moved the point from zero to negative one, then you raised it to negative two. Good job.

The linear equation that models the water left in the bathtub is g = 32 - 4t.

The first step is to determine the rate of drainage of the bathtub. The rate of drainage is the ratio of the change in water to the change in time.

Rate of drainage = change in water levels in the bathtub / change in time

(20 - 36) / (7 - 3)

-16 / 4 = -4

The second step is to determine the amount of water in the bathtub before it started draining

Initial amount of water in the bathtub = 20 + (4 x 3) = 32 gallons

The form of the linear equation that can be used to determine the amount of water left in the tank is:

Water in the bathtub = initial amount of water - (rate of drainage x number of minutes)

g = 32 - 4t

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Answer:

56.4 degrees

Step-by-step explanation:

You can make a right-angle triangle from the isosceles triangle, with height 2.5cm and hypotenuse 3cm.

You have the opposite side to the angle and the hypotenuse, so you use sin x = Opposite/Hypotenuse

sin x = 2.5/3

x = [tex]sin^{-1}[/tex] (2.5/3)

x = 56.44269024

Therefore the base angle of the triangle is 56.4 degrees (3sf)

Answer:

Step-by-step explanation:The walker family uses 45 pounds of crisped rice cereal per year. 1.55 pounds  they save by buying the 18-oz. box for $3.50 rather than the 12-oz. box for $2.75  by using unitary method.

What is called pound?

A pound is a unit of weight used mainly in Britain, America, and other countries where English is spoken. One pound is equal to around 0.454 kilograms. A pound of something is a quantity of it that weighs one pound.

For this, we get the unit price per ounce of each.

3.50/ 18 = 0.1944 unit

2.75 / 12 = 0.229 unit

The walker family uses 45 pounds of crisped rice cereal per year 45 ×0.1944=8.74845 ×0.229= 10.305.

Thus ,they save 10.305 - 8.75 = 1.55

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The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800.  The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.

Let variable x = number of associates, assigned to the case

Let variable y = number of partners assigned to the case.

The system of equations to describe this are:

800 x + 1800 y = 17600

y = x + 2

Plugging equation 2 in equation 1, we get,

800 x + 1800(x+ 2) = 17600

2600 x + 3600 = 17,600

Collect like terms

2400 x = 14,000

Divide both side by 2400x

x = 14,000 / 2400

x = 5.8

x = 6 (Approximately)

So,

y = x + 2

y = 5.8 +3

y = 7.8

y = 8 (Approximately)

Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.

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Answer:

Hamid's original weight was 80 kgs

Answer: The answer is 279

Step-by-step explanation:

12 x 24=288

288-9=279

12(24)-9=279

Using mathematical operations, (D) 6⅔ of water should be mixed with 10 lemon juice.

So, liters of water when mixed with 10 lemon juice:

Solve, the expression as follows:

Therefore, using mathematical operations, (D) 6⅔ of water should be mixed with 10 lemon juice.

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The correct question is given below;
Four liters of water are mixed with 6 juiced lemons to make lemonade. how many liters of water should be mixed with 10 juicer lemons to obtain the same result? (pls kinda show work)

A) 4 2/3

B) 5 1/3

C) 6 1/3

D) 6 2/3

E) 8 1/3

Answer:

4

Step-by-step explanation:

[tex]\frac{(-6) - (-3)}{s - 5} = -3\\-3(s-5)=-3\\s-5=-1\\\\s=4[/tex]

The shortest total distance for the route from Anglemouth to Doncatry is 15 units.

On the table, we can see that there is a dash in the section of:

"Anglemouth to Doncatry"

So there is not a direct route, so we need to try another way.

If we go from Anglemouth to Covenham, we have a distance of 10 units.

If now we go from Covenham to Doncatry, we have a distance of 5 units.

Adding these two distances we get:

Total distance = 10 + 5 = 15 units.

This is also the shortest total distance between the two towns.

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The interquartile range of the number of jumps of the 10 students during the competition is 38.

The interquartile range is the difference between the third quartile and the first quartile. The interquartile range is used to determine the variation of a data set.

Th first step is to determine the median of the first half of the dataset. The median of the first half is the first quartile.

First half of the data set: 30, 36, 38, 45, 57

Median = first quartile =  38

The next step is to determine the median of the second half of the dataset. The median of the second half is the third quartile.

Second half of the data set: 60, 77, 86, 88, 88

Median : third quartile =  86

Interquartile range = third quartile - first quartile

86 - 38 = 48

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Answer:

b, c

Step-by-step explanation:

a) 32=18 - not true

b) 32=18+14 - true

c) 18+32=50 - true

d) 32=-18/16 - not true

If  x and y vary directly, than the relationship between y and x will be →

y = (16/9)x

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

Given is x and y vary directly and y = 32 when x = 18.

Since x and y vary directly, this means that -

y/x = K [constant]

Now, we have -

x = 18

y = 32

Substituting values -

32/18 = K

K = 32/18 = 16/9

y/x = 16/9

y = (16/9)x

Therefore, if  x and y vary directly, than the relationship between y and x will be → y = (16/9)x

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The expression to represent the equation is given by  y = x + 3 .

An algebraic expression is one that was created in mathematics utilizing integer variables, constant, and algebraic procedures (accumulation, deletion, multiplication, separation, and exponentiation by a rational exponent).

The required expressions are :

y₁ = x + 3

y₂ = 3x²

y₃ = 3ˣ

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Morgan will score 150.7 points in 11 season

The first step is to calculate the number of point that Morgan will score in one season

41= 3

x= 1

cross multiply both sides

3x= 41

x= 41/3

x= 13.7

The number of points he will score in 11 game season can be calculated as follows

= 13.7 × 11

= 150.7

Hence Morgan will score 150.7 points in 11 game season

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Answer:

first one (2*2*2*3*3)

Step-by-step explanation:

2*2*2*3*3=72

Answer:

the farmer can sell 55 cartons

Step-by-step explanation:

1 carton = 12 eggs

660 decided by 12 = 55

The maximum profit which this company can expect to earn is $11,650.

The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.

In order to determine the maximum profit which this company can expect to earn, we would differentiate the given function as follows:

f(x) = y = -10x² + 700x - 600

y' = -20x + 700

-20x + 700 = 0

20x = 700

x = 700/20

x = 35.

Substituting the parameter into the formula, we have;

f(x) = -10x² + 700x - 600

f(35) = -10(35)² + 700(35) - 600

f(35) = -12250 + 24,500 - 600

f(35) = $11,650.

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The equation that models the balance y after x months is;

y = 1,700 - 130x

What is Equation of line?

The equation of line with slope m and y intercept at point b is given as;

y = mx + b

Given that;

Zachary purchased a computer for $1,700 on a payment plan.

Seven months after he purchased the computer, his balance was $790.

Eight months after he purchased the computer, his balance was $660.

Now, Let months is represented by x and models the balance is represented by y.

So, We get;

For 0 months, balance is $1,700.

For 7 months, Balance is $790

For 8 months, balance is $660.

So, Slope = (1,700 - 790) / 7

               = 910/7

               = 130

And, Slope = (1,700 - 660) / 8

                = 1,040/8

                = 130

So, The equation with slope 130 and starting balance $1,700 will be;

y = 1,700 - 130x

Thus, The equation that models the balance y after x months is;

y = 1,700 - 130x

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Answer:

2.4

Step-by-step explanation:

tan(theta) is defined as: [tex]tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex]

in the given diagram we only have the opposite and hypotenuse, but we can use the Pythagorean Theorem to solve for the other two missing sides.

Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse.

Plugging in known values we get the following:

[tex]a^2+12^2=13^2[/tex]

in this case the missing side, or the adjacent side is simply "a"

from here we simplify the bases with exponents

[tex]a^2+144=169[/tex]

now subtract 144 from both sides

[tex]a^2=25[/tex]

take the square root of both sides

[tex]a=5[/tex]

So now we know the adjacent side so we can plug it into the tan equation

[tex]tan(z)=\frac{12}{5}\\\\tan(z)=2.4[/tex]

The probability that the amount dispensed per box will have to be increased is 0.0062.

Consider the provided information.

Sample of 16 boxes is selected at random.

If the mean for 1 hour is 1 pound and the standard deviation is 0.1

1 Pound = 16 ounces , then 0.1 Pound = 16/10 = 1.6 ounces

Thus: μ = 16 ounces and σ = 1.6 ounces.

Compute the test probability

z= x−μ/σ/[tex]\sqrt{n}[/tex]

z= 15-16/ 1.6/4

z= -1/ 0.4

z= -2.5

By using the table.

Probability p value = P(Z<-2.50) = 0.0062

Thus, the probability that the amount dispensed per box will have to be increased is 0.0062.

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It should be no mystery that amounts deposited get added to bank balance, and amounts withdrawn by any means get subtracted. Regarding the balance in the bank, a debit card withdrawal is equivalent to a cheque withdrawal.

Regarding the balance in the bank, a debit card withdrawal is equivalent to a cheque withdrawal. The debit card withdrawal differs from a check in the check register in that there is no check number (and frequently no transaction number) connected to it.

initial transaction

$100 is deposited to open the account. The starting balance is that sum.

two-way transaction

You must calculate the tax on the purchases for this issue. Normally, the store would take care of that for you, and you would write a check to cover the debt. The sum owed in this case is...

Rounding up from $43.82 to 45.5728 is 45.57.

Instead of calculating the tax individually and then adding it to the original amount, it is more convenient to use a multiplier to determine the amount with tax. You should be aware that the purchase price multiplied by 100% plus 4% equals 104%, or 1.04 times the price.

As a withdrawal, this $45.57 is deducted from the prior transaction's $100 total, resulting in a new balance of $54.43.

third action

This is a straightforward withdrawal, therefore $46.43 is obtained by deducting the sum from the prior balance.

As previously said, there is no transaction number connected to this. It can occasionally be helpful to keep track of which debit card is being used if you have several debit cards that are taking money out of the account. The final four digits of the card number are used to identify transactions on my bank statement.

Fourth action

You must calculate the payroll deposit amount for this problem. That would typically be handled for you by your employer, along with any deductions for taxes, insurance, union dues, or employee purchases. The sum deposited in this case is...

Hourly rate times 40 equals $9.75, which equals $390.

The previous value is increased by this deposit, making the new balance $436.43.

In most cases, the coupon is applied to transactions including coupons before the tax is calculated. The fact that the purchase amounts are combined should be obvious. (You can calculate the total when there are numerous items at the same price using repeated addition or multiplication; most people find multiplication to be simpler.)

The purchase from the bike shop is arguably the most difficult. The total of the values in brackets is...

$180.00 + 14.95 + 8.95 = 203.90

Then, the 15% discount is applied.

Rounding up to 30.59 from 0.15 x $203.90 = 30.585

Taking this out of the previous amount* yields (before taxes)...

$203.90 -30.59 = $173.31

The amount subject to tax can then be calculated using the same multiplier described above:

Round to $180.24 using the formula: amount with tax = $173.31 x 1.04 = $180.24

* Talk about the 15% discount

As with additional tax, you can calculate the discount using a multiplier:

100% - 15% = 85% . . . 0.85 times as much

The result of applying this multiplier to the number 203.90 is 173.315, which is typically rounded up to 173.32. But this figure results from a discount that is rounded to the nearest half cent (30.585). The discounted amount, 173.315, is rounded down to 173.31 if the discount is rounded up. The intricacy of applying a multiplier to discounts is there.

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Answer:

Step-by-step explanation:

x=0.83

After solving percent equation ,the number of red pins from the set of red and yellow pins that Pam ordered is 910 red pins out of 1000 pins.

Eventually, we'll run into a problem that requires us to calculate a percentage of something. The percent equation is the formula we'll employ and it goes like this: part = percent x whole.

The symbol for percent (%) denotes a percentage of one hundred.

You'll need to convert between a percent and a decimal to express these numbers, so let's take a moment to go over that. When you see a percentage, it means 40 out of 100, or 40/100, and that is our fraction. When you divide 40 by 100, you get the decimal 0.40. Remember that 0.40 is the same as 40/100, which means 40%, when converting a decimal to a percent.

Pam ordered a set of red and yellow pins. She received 1,000 pins, and 91% of them were red, so the amount of red pins is

red pins = 91/100  ×  1000

red pins = 910

Thus, the number of red pins from the set of red and yellow pins that Pam ordered is 910 red pins out of 1000 pins

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The equation h>= 11/2 feet represents the required height of an individual to ride the roller coaster.

Your height = 5 1/3 feet tall

Required height in feet to ride a roller coaster = at least 5 1/2 feet

When the numerator exceeds or is equal to the denominator, the fraction is said to be improper. 5/2 and 8/5, for instance, are improper fractions.

Let h represent the height

h>= 5 1/2

Converting into an improper fraction

h>= 11/2 feet

Your height in improper fraction = 16/3 feet

Comparing the required height and your height we find that

Required height>Your height

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