Fully factorise this expression

the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.

what is expression  ?

An expression is a mathematical phrase that contains numbers, variables, and/or mathematical operations. It does not have an equal sign, so it cannot be solved.

In the given question,

The correct answer is C.

To simplify the given polynomial expression using the distributive property, we need to distribute the first term (2a³) to each term in the second parentheses, and then add it to the third term.

So, we have:

(2a³) (2a²+ 66²) + (6a²b + 12ab² - 76³)

= 4a⁵ + 132a³ + 6a²b + 12ab² - 76³

Now, we can simplify further by combining like terms:

= 4a³ (a²+ 33) + 6ab (a + 2b) - 76³

Therefore, the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.

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x = 14.8 (OR) x = 74/5.

Step-by-step explanation:

If you add 5 times a number to 6 you will get 80.

We don't know what number is multiplied with five and that number should added with 6. So,

Let, the unknown number be named as x.

The eqⁿ will be

[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} → Eqⁿ(1) [/tex]

Shift 6 to the right side.

[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} = { \red{ \sf{80 - 6}}}[/tex]

[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} = { \red{ \sf{74}}}[/tex]

Divide both the sides by 5. then,

[tex]{ \red{ \sf { \cancel{\frac{5}{5}}}}} { \green{ \sf{x}}} = {{ \frac{ \cancel{74} {}^{ \green{ \sf{{ 14.8}}}} }{ \cancel5}}} [/tex]

[tex]{ \red{ \boxed{ \purple{ \sf{x = 14.8}}}}} \: { \tt{(or)}} \: { \red{ \boxed{ \purple{ \sf{x = \frac{74}{5}}}}}} [/tex]

___________________________________

[tex]{ \red{ \sf{ \underline{verification}}}} [/tex]

Let us substitute the value of x in Eqⁿ(1) then,

[tex]{ \red{ \sf{5}}}{ \green{ \sf{(14.8)}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} [/tex]

[tex]{ \red{ \sf{74}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} [/tex]

[tex]{ \red{ \sf{80}}} = { \red{ \sf{80}}} [/tex]

Hence, our answer is correct

Answer:

Step-by-step explanation:

This seems complicated, huh.  

So think about the question.  They want to know the distance from a line, to a point.  first decide if the point could possibly be on the line and there is zero distance.   The given point is at  (-1, 7)    our coordinates of the point are at  -1 in the X direction and at 7 in the Y direction.  If we were to plug in those two number into the given line equation,   y = 3x  would it be a true statement?  no.    7 = 3(-1)  is not true.   so our given point is not on the line.  Next,  find the right angle to the line and point.  make your own line equation that does have our given point in it.  and is at a right angle to the given line.    recall that using a reciprocal can give you a right angle to your line.  y = (- 1/3)X .  Now we just need the given point to plug into our made up line equation and be true.    7 = (-1/3)(-1) + b    .  we need to make this equation true by moving a number into "b" that makes it true.

b = 6[tex]\frac{2}{3}[/tex]  or [tex]\frac{20}{3}[/tex]

7 = (-1/3)(-1) + [tex]\frac{20}{3}[/tex]

now, when does our made up line, y =(-1/3)x + [tex]\frac{20}{3}[/tex], intersect with the given line, y=3x,  that is,  set the two equal

3x = (-1/3)x + [tex]\frac{20}{3}[/tex]

3[tex]\frac{1}{3}[/tex] X = [tex]\frac{20}{3}[/tex]

[tex]\frac{10}{3}[/tex]X = [tex]\frac{20}{3}[/tex]

X=[tex]\frac{20}{3}[/tex] * [tex]\frac{3}{10}[/tex]

X = [tex]\frac{20}{10}[/tex]

X=2

our two equations intersect at 2,  how handy  :)

now we have our two points that are at a right angle from each other and we just need the distance from them

(given) A(-1,7)   and (found) B(2,6)

Distance = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]

then our given points are A(x1,y1)  and B(x2,y2)

Distance = [tex]\sqrt{(2-(-1))^{2}+(6-7)^{2} }[/tex]

Distance =[tex]\sqrt{3^{2}+(-1)^{2} }[/tex]

Distance = [tex]\sqrt{9+1}[/tex]

Distance = [tex]\sqrt{10}[/tex]

Distance = 3.1622

Distance =3.2 (rounded to nearest 10th)

Yes, that was kinda a lot  :/

Answer:

Step-by-step explanation:

Since the two angles of both triangles are congruent, it makes the remaining angles congruent too:

Then we have:

So both C and F are 30°.

∠1≅∠3 line 2 and 3 have the same reason.

∠1 and ∠3 are vertical angles, so they are formed by intersecting lines. Therefore ang1 and ∠2 are a linear pair, and ∠2 and ∠3 are a linear pair. By the Linear Pair Theorem, ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary. So by the Congruent Supplements Theorem, ∠1 ≅ ∠3.

Statements  - Reason

1. ∠1 and ∠3 are vertical angles  -  Given.

2. a and b are intersecting lines  -  definition of vertical angles

ang1 and ∠2 are a linear pair

3. ∠2 and ∠3 are a linear pair  -  definition of a line

4. ∠ 1 and 2 are supplementary ang2 and ang3 are supplementary - definition of linear pair.

5. ∠1 ≅ ∠3  -  ≅ Supplements theorem

Hence the answer is ∠1≅∠3 line 2 and 3 have the same reason.

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Step-by-step explanation:

[tex]3g = d[/tex]

[tex] \frac{3g}{3} = \frac{d}{3} \\ [/tex]

[tex]g = \frac{d}{3} \\ [/tex]

[tex]{ \purple{ \bold{g = \frac{d}{3}}}} [/tex]

Step-by-step explanation:

The given formula is [tex]{ \orange{ \sf{3g = d}}}[/tex]

In order to get formula for g, let us divide 3 on both the sides.

[tex]{ \orange{ \sf{ \frac{ \cancel3}{ \cancel3}g}}} = { \orange{ \sf{ \frac{d}{3}}}} [/tex]

Therefore, [tex]{ \boxed{ { \tt{g = \frac{d}{3}}}}} [/tex]

Using distributive law and the greatest common factor , the expression (32 + 16) can be factored as 16(2 + 1)

The GCF(greatest common factor) is defined as the largest number that is a factor of two or more numbers.

In a simpler term, the greatest number among all the common factors of two or more numbers is called the greatest common factor or GCF.

Using distributive law and the greatest common factor we can factor an expression.

Therefore, let's factor the expression (32 + 16).

The greatest common factor of 32 and 16 is 16.

Therefore, the expression can be express as follows:

(32 + 16) = 16(2 + 1)

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The choice that best represents David monthly interest rate is 0.625%. The correct option is C.

From the information, David opens a savings account with a 7.5% annual interest rate.

It should be noted that there are 12 months in a year.

Therefore, the monthly interest rate will be:

= Annual interest rate / Number if months in a year

= 7.5% / 12

= 0.625%

The interest is 0.625%.

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Complete question

David opens a savings account with a 7.5% annual interest rate. Which choice best represents his monthly interest rate?

A. 7.5%

B. 12%

C. 0.625%

D. 5%

After the conversion, 133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.

In the given question we have to find how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons.

As given that pool empties at a rate of 12 quarts every 2 minutes.

In 12 quarts = empties in 2 minutes

As we know that 1 gallon = 4 quarts

So 1 quarts = 1/4 gallon

In 12 quarts = 12/4 gallon

12 quarts = 3 gallon

So 3 gallon = empties in 2 minutes

So 1 gallon = empties in 2/3 minutes

12,000 gallon = empties in 2/3 ×12,000 minutes

Simplifying

12,000 gallon = empties in 2×4,000 minutes

12,000 gallon = empties in 8,000 minutes

Now converting minutes in hours.

As we know that 1 minute = 1/60 hours

So 8000 minute = 8000/60 hours

8000 minutes = 133 hours 33 minutes

133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.

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Answer:40

Step-by-step explanation:

so 14 less means that 14 was subtracted. So we need to add that to our main number, 66. When we do that we get 80. Then since 80 is twice the number we are looking for, we divide by 2 (twice is 2 times), and we get 40. Hope this helps

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

replace y with 1/4

x=2(1/4)

x=2/4

x=1/2

Hopes this helps please mark brainliest

From the given table

Part a

The equation of the function is y = ( - 0.7/277)x + 16

Part b

The slope of the line =  - 0.7/277 and the y intercept of the line = 16

From the table

Choose two points

(242, 14.8) and (519, 14.1)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (14.1 - 14.8) / (519 - 242)

= -0.7 / 277

The slope of the line = - 0.7/277

From the table at x = 0, the value of y = 16

Therefore the y intercept is 16

The slope intercept form is

y = mx + b

Substitute the values in the equation

y = ( - 0.7/277)x + 16

Part b

The slope of the line =  - 0.7/277

The y intercept of the line = 16

Hence, from the given table

Part a

The equation of the function is y = ( - 0.7/277)x + 16

Part b

The slope of the line = - 0.7/277 and the y intercept of the line = 16

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According to the two tailed test, the difference between the first and second country is 40.

Two tailed test:

Two tailed test also means the two-sample t-test is used to determine if two population means are equal.

Given,

Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. a random sample of 1800 women from the first country yielded 392 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 352 women with iron-deficiency anemia.

Here we need to find the the proportion of women with anemia in the first country differs from the proportion of women with anemia in the second country.

While we looking into the given question,

For the first country,

Number of samples = 1800

Number of women with iron-deficiency anemia = 392

And for the second country,

Number of samples = 1700

Number of women with iron-deficiency anemia = 352

So, there difference between them is calculated as,

=> 392 - 352

=> 40

And as per the two tailed test both countries doesn't have the same proportion and the sample values is also differs this situation.

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Answer:

145°

Step-by-step explanation:

Answer: y equals 145 degrees

Answer: The answer is 28.

Step-by-step explanation: 8a-y is our problem and we are given two variables, a and y. It is revealed that a=3 and y= -4. So our problem would now look like this: 8*3-(-4). Now see the two minuses (-) next to each other? We have to convert that into a plus (+) sign because two negatives make a positive. So our equation now looks like this: 8*3+4. Now, 8 times 3 (8*3) is equal to 24. Now our equation looks like this: 24+4. Add them together and the sum is 28.
Hope this helps!

Answer: The correct answer is B.

Step-by-step explanation:

In a line with a slope of 0 the x can change but the y cannot in a (x, y).

The burj khalifa is 7.56 football fields tall .

We have the height of the  Burj Khalifa as = 2722 feet

And the given height of  one football field is = 360 feet

Now using the Unitary method we can calculate the number football fields that would be equal to the height of the burj khalifa .

So ,

360 feet is equal to football fields = 1

1 feet is equal to football fields = 1/360 fields

therefore

2722 feet will be equal to fields = (1/360) x 2722

                                                     =  7.56 fields

So the Burj Khalifa is equal to  7.56 football fields.

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Using the normal distribution, it is found that:

a) The 10th percentile for incubation times is of: 18.72 days.

b) The incubation times that make up the middle 95​% are of: Between 18.04 and 21.96 days.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the incubation times are presented as follows:

[tex]\mu = 20, \sigma = 1[/tex]

The 10th percentile for the distribution is X when Z = -1.28, which is the value of Z with a p-value of 0.1, hence:

-1.28 = (X - 20)/1

X - 20 = -1.28

X = -1.28 + 20

Z = 18.72 days.

Considering the symmetry of the normal distribution, the bounds of the middle 95% of values are given as follows:

Hence the lower bound is:

-1.96 = (X - 20)/1

X - 20 = -1.96

X = -1.96 + 20

Z = 18.04 days.

The upper bound is:

1.96 = (X - 20)/1

X - 20 = 1.96

X = 1.96 + 20

Z = 21.96 days.

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Answer:

Step-by-step explanation:

365 day a year

24 hour per day

60 second in a minute

1440 minutes in a day

86400 second in a day!

According to the Symmetric Property of Equality, if AB = CD then CD = AB.

According to the question,

We have the following information:

CD = AB then AB = ?

Now, in order to fill the given blank, we have to use the symmetric property of equality. According to the symmetric property of equality, there is no difference in the final result of an expression if we change the sides of the expression.

For example, if 2 = a then we can also say that a = 2.

So, when CD=AB then we can clearly state that AB = CD.

Hence, according to the Symmetric Property of Equality, if AB = CD then CD = AB.

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By finding the slopes of the two segments we can see that the segments are not parallel nor perpendicular.

The slope for a segment whose endpoints are:

(x₁, y₁) and (x₂, y₂) is:

slope = (y₂ - y₁)/(x₂ - x₁)

Two segments are:

Segment AB has endpoints (-1, -1) and (1, 5), so the slope is:

s = (5 + 1)/(1 + 1) = 3

For segment CD the endpoints are (1, 2) and (5, 4), so the slope is:

s' = (4 - 2)/(5 - 1) = 2/4 = 1/2

So the slopes are different and their product is obviously not -1, then the lines are neither parallel nor perpendicular.

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The statement that best describes the rate of change of the linear function is given as follows:

For each increase of 1ºF in temperature, the average weight of the strawberries decays by 7/3 grams.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

The coefficients are listed as follows:

The input and the output variables for this problem are given as follows:

The function is defined as follows:

y = -7x/3 + 72.75.

Hence the slope is:

m = -7/3.

And the interpretation, considering the input and output variables, is that for each increase of 1ºF in temperature, which is the input variable, the average weight of the strawberries, which is the output variable, decays by 7/3 grams.

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There are 20 players are not in 5th grades.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Total players in the class = 80

And, 75% of the players in the basketball program are 5th graders.

Now.

Number of players in the basketball program are 5th graders = 75% of 80

= 75/100 x 80

= 60

Thus, Number of players are not in 5th graders = 80 - 60

                                                                          = 20

Therefore, There are 20 players are not in 5th grades.

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The standard deviation of the number of residents in the sample who were born in Colorado is 7.82

Standard deviation:

The measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists is know as standard deviation.

Given,

According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. if a sample of 250 Colorado residents is selected at random.

Here we need to find the standard deviation of the number of residents in the sample who were born in Colorado.

Here we know that following details,

Number of sample = 250

Estimated proportion for residents born in Colorado = 42.7% which is equal to = 0.427.

Let us consider X be the random variable of interest (number of residents in the sample), on this case we now that:  

X ~ (n = 250, p = 0.427)

Now, according to the probability mass function for the Binomial distribution is given as:  

E(X) = n x p = 250 x 0.427 = 106. 75.

Now, the standard deviation for the random variable is given by:

SD = √106.75 (1 - 0.427)

SD = √106.75(0.563)

SD = 7.82

Therefore, the standard deviation is 7.82.

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Answer:13234

Step-by-step explanation:

13234 is

Answer:

y= 50x + 200

Step-by-step explanation:

Answer:Let the age of son be x.

Thus, age of father is 4x.

After 5 years, their ages will be x+5 and 4x+5 years respectively.

As per the question, we have

4x+5=3(x+5)

⇒4x+5=3x+15

⇒x=10

Age of father will be 4x=4×10=40 years.

Thus when son is 10 years old, father is 40 years.

Step-by-step explanation:

After 3 years father's age will be five times that of his son. Father age will be 40 years and son age will be 8 years .

Given,

Present age of father = 37 years.

Present age of son = 5 years.

Now,

Let the number of years be x after which the fathers age will be 5 times the age of his son.

So,

Ages after 3 years  ,

Age of father = 40 years

Age of son = 8 years.

Thus age of father is 5 times the age of son.

Therefore after 3 years father's age will be five times that of his son.

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The correct statement is,

''The smallest number that both denominator numbers will include into.''

What is Least common multiple?

The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.

Given that;

The statement is,

The smallest number that both denominator numbers will __ into.

Now,

We know that;

The LCM of two or more numbers is divided by the numbers or its include all the numbers.

Thus, The correct statement is,

''The smallest number that both denominator numbers will include into.''

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Answer:

35

Step-by-step explanation:

y = 25 and x = 5

When two variable quantities have a constant ratio their relationship is called a direct variation. The formula for direct variation is y = kx, where k is called the constant of variation.  If we know k we can find y given x or we can find x given y.

If we solve the equation y = kx for k, we get k = y/x.  If we replace the variables x and y with the actual values from the problem we have:

k = 25/5, which is 5.  

Now we can substitute this value for k into the equation y = kx to find y when x is 7:

y = (5) (7)

y = 35