What is the simplified form of the expression the quantity x squared plus 10x plus 21 end quantity divided by 4 times the quantity x plus 3 end quantity?

the quantity x minus 7 end quantity divided by 4 the quantity x plus 7 end quantity divided by 4 the quantity x plus 7 end quantity divided by quantity x plus 3 end quantity the quantity x minus 7 end quantity divided by quantity x plus 3 end quantity

Answer:

[tex]\textsf{A)} \quad -1\dfrac{3}{20}y+4[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(11-9 \dfrac{3}{5}y\right)+\left(8 \dfrac{9}{20}y-7 \right)[/tex]

Remove the parentheses:

[tex]11-9 \dfrac{3}{5}y+8 \dfrac{9}{20}y-7[/tex]

Collect like terms:

[tex]8 \dfrac{9}{20}y-9 \dfrac{3}{5}y+11-7[/tex]

Subtract the numbers 11 - 7:

[tex]8 \dfrac{9}{20}y-9 \dfrac{3}{5}y+4[/tex]

Factor out y:

[tex]\left(8 \dfrac{9}{20}-9 \dfrac{3}{5}\right)y+4[/tex]

Partition the mixed numbers into fractions and whole numbers, and then subtract them separately.

Subtract the whole numbers:

[tex]\implies 8-9=-1[/tex]

Subtract the fractions by changing both fractions into equivalent fractions so both fractions have the same denominator:

[tex]\implies \dfrac{9}{20}-\dfrac{3}{5}[/tex]

[tex]\implies \dfrac{9}{20}-\dfrac{3 \cdot 4}{5 \cdot 4}[/tex]

[tex]\implies \dfrac{9}{20}-\dfrac{12}{20}[/tex]

[tex]\implies -\dfrac{3}{20}[/tex]

Put the two answers from the whole numbers and fractions back together:

[tex]\implies -1-\dfrac{3}{20}=- \left(1+\dfrac{3}{20}\right)=-1\dfrac{3}{20}[/tex]

Therefore:

[tex]\left(8 \dfrac{9}{20}-9 \dfrac{3}{5}\right)y+4=\left(-1\dfrac{3}{20}\right)y+4=-1\dfrac{3}{20}y+4[/tex]

The rules of logarithms, which are derived from the exponent rules, are what make up the attributes of log. The solution is 36.

The rules of logarithms, which are derived from the exponent rules, are what make up the attributes of log.

These logarithm features are used to simplify logarithmic expressions and solve logarithmic problems.

solution to log4(y – 9) + log43 = log481.

log4 (y − 9) + log4 3 = log4 81

We know that log a(b) + loga ( c) = loga ( b*c)

log4 (y − 9) * 3 = log4 81

We know have log a( BC ) = loga ( d)

This means BC = d

(y − 9) * 3  = 81

Divide each side by 3

y - 9 = 81/3

y - 9 = 27

Add 9 to each side

y-9+9 = 27+9

y = 36

To learn more about logarithmic properties refer

https://brainly.com/question/17263033

#SPJ1

Answer:

y = 36

Step-by-step explanation:

STEP 1:

The given equation is 

log4(y – 9) + log4(3) = log4(81)

STEP 2:

log4(y – 9)(3) = log4(81)

STEP 3:

log4(3y - 27) = log4(81)

STEP 4:

3y - 27 = 81

     +27.   +27

STEP 5:

3y = 108

__   ____

 3.      3

STEP 6:

y = 36

For instance, if the multiplication error is 8 x 7 = 56, then the matching division error  56/8 = 7, demonstrating that the result of the division is the other component that was used in the multiplication.

Finding the product of two or more corresponding integers is done mathematically through the action of multiplication. It is frequently represented by the letters "x" or "*." In order to discover the result of multiplication, a multiplicand, also known as the multiplicand, is multiplied by a multiplier, also known as the multiplier. The result of the two integers, for instance, is 56 if the multiplicand and multiplier are both 8. A multiplication process always yields a greater number as the outcome than either of the initial factors. Multiply is also used to describe the process of adding a number to itself a certain number of times, as in "7 multiplied by 3 equals 21."

How to solve?

 For instance, if the multiplication error is 8 x 7 = 56, then the matching division error  56/8 = 7, demonstrating that the result of the division is the other component that was used in the multiplication.

This connection is true for every multiplication and division problem as long as the numbers are utilised consistently in both operations.

To learn more about multiplication, visit:

https://brainly.com/question/24327297

#SPJ4

Answer:

.63

Step-by-step explanation:

.37 = 0.37

probability = 1 – 0.37

= 0.63 or .63

Answer: We use the SSS

Step-by-step explanation:

SSS method or Side Side Side method is when we test to see if the triangles are the same or not. We know this by checking if the sides of the triangles change at the same rate or not!

Let test the YW is 4 and the WY is 8, we see the side multiply by 2

The VX is 5 and the XZ is 10, wee see the sided multiply by 2

So we use the SSS to show that both triangles are equal

The greatest amount that a person can receive is 19$. Option D

A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.

Total amount = $30

Total number of people = 8

According to the problem, each person gets at least 1$ and also exact amount.Let's consider only one person gets more than 5$ because, we have to find the greatest value.

4 people get more than 1$,that includes the person who gets the maximum amount.

Let the person who gets maximum amount =x

x + 2+2+2+1+1+1+1

Maximum amount = 30- (2+2+2+1+1+1+1+1)= 11$

Hence, the maximum amount will be 19$.

Learn more about word problem at: https://brainly.com/question/13818690

#SPJ1

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

The polynomial with the given roots 5, (3 + 2i), and (1 - 3i) is 45 - 35i = 0

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The roots of a given polynomial are:

5, 3 + 2i, and 1 - 3i

Now,

We can write it as,

5 (3 + 2i) (1 - 3i) = 0

(15 + 10i) (1 - 3i) = 0

15 - 45i + 10i - 30i² = 0

[ i = √-1, i² = -1 ]

15 - 45i + 10i + 30 = 0

Combining the like terms.

45 - 35i = 0

Thus,

The polynomial with the given roots 5, (3 + 2i), and (1 - 3i) is 45 - 35i = 0

Learn more about polynomials here:

https://brainly.com/question/2284746

#SPJ1

Answer:

the first company would be cheaper because it has a lower total cost.

Step-by-step explanation:

To determine which company is more cost-effective, you will need to compare the total costs for each company based on the amount of sugar being transported.

If the first company is used, the total cost for transporting x tons of sugar will be 3204 + 75.25x dollars.

If the second company is used, the total cost for transporting x tons of sugar will be 275.50x dollars.

To determine which company is cheaper for a given amount of sugar, you can compare these two equations by setting them equal to each other and solving for x.

For example, if you want to transport 100 tons of sugar, you can set the two equations equal to each other and solve for x:

3204 + 75.25x = 275.50x

Solving for x, we get: x = 3204 / (75.25 - 275.50) = 107.8 tons

This means that if you want to transport 100 tons of sugar, the first company would be cheaper, because it costs less than the second company for any amount of sugar greater than 107.8 tons.

If you want to transport a different amount of sugar, you can repeat this process to determine which company is cheaper.

The value of the expression 24 + x ÷ 12 as required to be evaluated when the variable, x = -180 as required in the task content is; 9.

It follows from the task content that given expression is required to be evaluated for its value when the variable, x = -180.

Since the given expression is; 24 + x ÷ 12.

It follows that when the variable, x is given as; x = -180; we have that;

24 + ( -180 ) ÷ 12

Following from PEMDAS guidelines in which case;

Therefore, we have that;

24 + ( -180 / 12 )

= 24 + ( -15 )

= 24 - 15

= 9.

Upon evaluation, by means of the PEMDAS guidelines in which case; Parentheses, Exponents, Multiplication, Division , Addition and Subtraction are solved in order; the value of the expression is; 9.

Therefore, the required value of the expression; 24 + x ÷ 12; as required to be evaluated according to the given parameter; x = -180 is; 9.

Read more on expression evaluation;

https://brainly.com/question/23561228

#SPJ1

You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The relationship between the two variables in a bivariate data set is graphically represented by a scatter plot. Consider them to be the graphic depiction of two data sets that have been combined by allocating each axis in the plot to a distinct variable.

Due to the presence of two variables, this type of data is known as bivariate data. Only 1 variable may be displayed on a line plot. You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The standard deviation of each variable and the covariance between them must first be determined in order to calculate the Pearson correlation. Covariance is subtracted from the product of the standard deviations of the two variables to get the correlation coefficient.

To learn more about scatter plot refer to:

https://brainly.com/question/6592115

#SPJ4

Step-by-step explanation:

Using log properties

[tex] log_{7}(rz {}^{12} ) [/tex]

[tex] log_{7}(r) + log_{7}(z {}^{12} ) [/tex]

Then

[tex] log_{7}(r) + 12 log_{7}(z) [/tex]

Plug in the knowns

[tex] - 7.87 + 12( - 12.59)[/tex]

[tex] - 158.95[/tex]

The bound on the probability of such an event is 0.75 or 75 %.

Given :

In a study on eating habits, a particular participant averages 750 cm^3 of food per meal.

it is extraordinarily rare for this participant to eat more than 1000 cm^3 of food at once.

Number of favorable outcomes = 750

Number of possible outcomes = 1000

Probability :

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening.

P = Number of favorable outcomes / Number of possible outcomes

= 750 / 1000

= 75 / 100

= 3 / 4

= 0.75

Learn more about the probability here:

https://brainly.com/question/11234923

#SPJ4

Full question:

In a study on eating habits, a particular participant averages 750 cm^3 of food per meal.

it is extraordinarily rare for this participant to eat more than 1000cm3 offood at once. find a bound on the probability of such an event.

Answer:

here

Step-by-step explanation:

1. How tall was the tree when Vlad moved into the house?

292-26*4.5=175 cm

2. How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

175+26*x=357

357-175=182=26*x

x=7  


hope this helped

The weight of the baby at the end of the 8 months was 18.125lbs.

The weight of baby at birth = 7.25 lb

At the end of 8 months, the baby weighed 2.5 times its birth weight.

We need to find the weight of the baby at the end of 8 months.

[tex]\frac{2}{5}[/tex] = [tex]\frac{4+1}{2}[/tex] = [tex]\frac{5}{2}[/tex]

The weight of the baby at the end of 8 months is 5/2 times of its initial weight.

Total weight = 7.25 x [tex]\frac{5}{2}[/tex]

Total weight = 18.125

Therefore, the weight of baby at the end of 8 month is 18.125 lbs.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The number of cubic feet of concrete that would be needed is 586491840 cubic feet

From the question, we have the following parameters that can be used in our computation:

These parameters can be represented using the following notations

The number of cubic feet of concrete that would be needed is the volume of the dam

So, the number of cubic feet of concrete that would be needed can be calculated using the following volume equation

The number of cubic feet of concrete that would be needed = Length x Width x Height

Substitute the known values in the above equation, so, we have the following representation

The number of cubic feet of concrete that would be needed = 1224 * 660 * 726

Evaluate

The number of cubic feet of concrete that would be needed = 586491840

Hence, the cubic feet is 586491840

Read more about volume at

https://brainly.com/question/463363

#SPJ1

Answer:

y = -x - 4

Step-by-step explanation:

y = mx + b is slope intercept form,

where m is the slope, and b is the y-intercept.

As we can see from the picture, the line has a negative slope of 1 (we can also just say -1). We know this is the slope because it has a rise of -1 and a run of -1. (I hope that made sense lol :/)

[Side note, we use x instead of 1.]

The y-intercept is -4 since we can see the line passes through the y-axis at -4.

Therefore, the equation can be written as y = -x - 4

The measure of angle A and angle B is equal to 70° as per the given relation of both the angles.

As given in the question,

Given measure of angle A is equal to ( 8x + 6 )°

Given measure of angle B is equal to ( 4x + 38 )°

Given condition :

Measure of both the angles are equal to each other

Measure of ∠A = Measure of ∠B

⇒ ( 8x + 6 )° =  ( 4x + 38 )°

Now simplify the above equation to get the value of x

⇒(8x - 4x)° = (38 -6)°

⇒4x°= 32°

⇒x = 32°/4

⇒x = 8°

Measure of ∠A = 8(8) + 6

                         = 70°

Measure of ∠B = 4(8) +38°

                          = 70°

Therefore, the measure of both the angles A and B is equal to 70°.

The complete question is:

The measure of ∠A = (8x + 6)° , measure of ∠B = ( 4x+ 38)° and  both are equal to each other. Find the measure of each angle?

Learn more about angle here

brainly.com/question/28451077

#SPJ4

The value of [tex]\sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2[/tex] is [tex]\pi x^2 \sqrt{x}-17 x^3[/tex]

[tex]$$\begin{aligned}& \sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2 \\& =x^2 \sqrt{x}(\pi-17 \sqrt{x})\end{aligned}$$[/tex]

Apply the distributive law: [tex]$\quad a(b-c)=a b-a c$[/tex]

[tex]$$\begin{aligned}& a=\sqrt{x} x^2, b=\pi, c=\sqrt{x} \cdot 17 \\& =\sqrt{x} x^2 \pi-\sqrt{x} x^2 \sqrt{x} \cdot 17 \\& =\pi x^2 \sqrt{x}-17 x^2 \sqrt{x} \sqrt{x} \\& 17 x^2 \sqrt{x} \sqrt{x}=17 x^3 \\& =\pi x^2 \sqrt{x}-17 x^3\end{aligned}$$[/tex]

What is distributive law?

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

To learn more about distributive law visit:

#SPJ1

The probability that none are broken as calculated from the data given is 0.96.

No of eggs = 12

percentage of broken eggs = 4%

=4/100 * 12 = 0.48 eggs

therefore , probability of getting broken egg

= no of favorable outcome/ no of outcomes

=0.48/12

=0.04

hence probability of not getting any broken egg

= 1 - P(broken)

= 1- 0.04

= 0.96

There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.

When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.

To learn more about probability

brainly.com/question/29521533

#SPJ4

Answer:

  A:) T(t) = 305(230/305)^(t/10) +70

  B:) T(20) ≈ 243.4 °F

Step-by-step explanation:

You have a pie removed from a 375° oven to a room temperature of 70° that has cooled to 300° after 10 minutes. You want to know its temperature after 20 minutes.

Newton's law of cooling tells you the rate of change of an object's temperature is proportional to the difference between the object's temperature and that of its surroundings. The differential equation describing this has an exponential function as its solution. That exponential function can be written as ...

  temperature = (initial temperature difference)·(cooling factor)^(time/(cooling time)) + (final temperature)

Here, the initial temperature difference between the pie and room temperature is ...

  initial temperature difference = 375° -70° = 305°

The final temperature is the room temperature:

  final temperature = 70°

The cooling factor is the multiplier applied to the temperature difference in the time period "cooling time". Here, the pie is at 300°, a temperature difference of 300° -70° = 230° after a cooling time of 10 minutes. The cooling factor is ...

  cooling factor = 230/305

These values let us write the equation as ...

  T(t) = 305(230/305)^(t/10) +70

The temperature after 20 minutes is found using this equation:

  T(20) = 305(230/305)^(20/10) +70 = 305(46/61)^2 +70 = 243 27/61

  T(20) ≈ 243.4 . . . . degrees F

__

Additional comment

The cooling factor can be expressed as a value that lets the exponent be t. Often, it is written as (e^k), where ...

  k = 1/10·ln(230/305) ≈ -0.0282232

Then the equation is ...

  T(t) = 305·e^(-0.0282232t) +70

It could also be written as ...

  T(t) = 305(0.972171^t) +70

where 0.972171 = (46/61)^(1/10).

Answer: (x+5)(2x+10)

Step-by-step explanation: Hope you find it helpful, I am in the rush so can't give you a full explanation on paper yet!

The profit, y, can be written in terms of x, the number of computers sold.  as ​y = 150x

The table that completes the question is added at the end of this solution as an attachment

From the question, we have the following parameters that can be used in our computation:

Amount of items sold = x

Profit made by the company = y

The equation of a proportional relationship is represented as

k = Y/X * h

Where

(X, Y) is the coordinate of any ordered pair from the function or table

Using the above as a guide, we have the following:

(X, Y) = (3, 450)

Substitute the known values in the above equation, so, we have the following representation

y = 450/3 * x

Evaluate the quotients in the equation

y = 150 * x

Evaluate the products in the equation

y = 150x

Hence, the equation of the proportional relationship is y = 150x

Read more about proportional relationships at

https://brainly.com/question/14425347

#SPJ1

Answer:

Step-by-step explanation:

it is an isosceles right triangle, we divide it in two parts and we have two  right triangles, with the Pythagorean theorem we find the hypotenuse and add it to the other side to get the perimeter (SEE FIGURE)

BC and AC = √(8²+6²)

BC and AC = √(64+36)

BC and AC = √100

BC and AC = 10 units

now we add the sides and find the perimeter

16 + 10 + 10 =

36 units

The correct option is a) online by $0.04.

The better deal is online, by $0.04 will save per diaper.

How do I solve for x in a equation?

Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.

Cost of 56 diapers at Babies-R-Us = $28

Cost of 1 diaper at Babies-R-Us = [tex]\frac{28}{56}[/tex]

                                                    =  0.5

Cost of 112 diapers online = $52

Cost of 1 diaper online = [tex]\frac{52}{112}[/tex]

                                      = 0.46

So, the cost of diapers online is cheaper than that at Babies-R-Us.

Difference between 1 diaper in both case = $0.5- $0.46= $0.04

Online deal is better than and you will save by $0.04 per diaper.

To know more about solve for x in a equation:

https://brainly.com/question/18067015

#SPJ1

The possible values of x in the figure are given as follows:

x > 3/2.

The possible values of x are obtained verifying if the given dimensions form a triangle, and the condition is that the sum of the lengths of the two smaller sides has to be greater than the length of the greatest side.

For the triangle given in the image, the dimensions are given as follows:

Hence, applying the condition, the inequality to obtain the values of x is given as follows:

2x + 4x - 3 > 4x.

Then, solving the inequality, the possible values of x in the triangle are given as follows:

2x + 4x - 3 > 4x

2x > 3

x > 3/2.

More can be learned about set of measurements and triangles at brainly.com/question/24432457

#SPJ1

Answer:

Step-by-step explanation:

P+N+2Q=?

P= Pennies

N= Nickels

Q= Quarters

Answer:

(1,3)

Step-by-step explanation:

Substitute in 3x for y in the equation x + y = 4

x + 3x = 4

4x = 4  Divide both sides by 4

x = 1

Substitute 1 for x in either of the 2 original equations

x + y = 4

1 + y = 4  Subtract 1 from both sides

y = 3

(1,3)