factor this linear expression :7x- 3

After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

To know more about radius visit:

https://brainly.com/question/28946570

#SPJ1

Answer:

7

Step-by-step explanation:

:)

Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

\( \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 \)

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

Step-by-step explanation:

Let the coordinates of point b be (x,y).

Given the coordinates of a (-7,5) and c(5,-1)

Now according to question

ab = 5bc

using distance formula

\(\sqrt{(x+7)^2+(y-5)^2} =5\sqrt{(5-x)^2+(-1-y)^2}\)

Solving we can get

\(x=-\frac{-11+\sqrt{-4y^2-10y+25}}{2},\:x=\frac{\sqrt{-4y^2-10y+25}+11}{2}\)'

However, we do need either x or y coordinate of point b to find the other.

Check the picture below.

\(\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=x\\ h=6x-20\\ A=50 \end{cases}\implies 50=\cfrac{1}{2}(x)(6x-20) \\\\\\ 50=\cfrac{6x^2-20x}{2}\implies \boxed{50=3x^2-10x}\)

Answer:

2/9y(3y−4/7)

Use the distributive property to multiply  

9

2

​

y by 3y−

7

4

​

.

9

2

​

y×3y+

9

2

​

y(−

7

4

​

)

Multiply y and y to get y

2

.

9

2

​

y

2

×3+

9

2

​

y(−

7

4

​

)

Express  

9

2

​

×3 as a single fraction.

9

2×3

​

y

2

+

9

2

​

y(−

7

4

​

)

Multiply 2 and 3 to get 6.

9

6

​

y

2

+

9

2

​

y(−

7

4

​

)

Reduce the fraction  

9

6

​

 to lowest terms by extracting and canceling out 3.

3

2

​

y

2

+

9

2

​

y(−

7

4

​

)

Multiply  

9

2

​

 times −

7

4

​

 by multiplying numerator times numerator and denominator times denominator.

3

2

​

y

2

+

9×7

2(−4)

​

y

Do the multiplications in the fraction  

9×7

2(−4)

​

.

3

2

​

y

2

+

63

−8

​

y

Fraction  

63

−8

​

 can be rewritten as −

63

8

​

 by extracting the negative sign.

3

2

​

y

2

−

63

8

​

y

Step-by-step explanation:

The Amount from contributions = R * n

The future value refers to the value of an asset or investment at a specified time in the future, based on a specific interest rate or rate of return.

Without knowing the specific values of R, interest rate, and number of years, we cannot calculate the amounts from contributions and interest. However, we can provide the general formula for calculating the future value of an ordinary annuity:

FV = R * [(1 + i)ⁿ - 1] / i

where FV is the future value of the annuity, R is the periodic payment, i is the interest rate per period, and n is the number of periods.

To calculate the amount from contributions, we can multiply the periodic payment R by the number of periods n.

Amount from contributions = R * n

To calculate the amount from interest, we can subtract the amount from contributions from the future value of the annuity.

Amount from interest = FV - R * n

Once the specific values for R, interest rate, and number of years are provided, we can use these formulas to calculate the amounts from contributions and interest.

To know more about future value, visit:

https://brainly.com/question/30741148

#SPJ1

The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space is a set of all possible outcomes of an experiment or random event. It is the collection of all possible results or outcomes that can occur when a particular event is performed.

In the given question,

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a fair 12-sided die. The sample space would include all possible values that the die can land on when rolled.

Since a 12-sided die has 12 equally likely outcomes, the sample space would consist of the numbers 1 through 12. However, only one of the options presented in the question includes all 12 numbers in the sample space, which is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Option S = {1, 2, 3, 4, 5, 6} represents the sample space of a regular 6-sided die, while options S = {1} and S = {12} only include one possible outcome, which is not applicable for a 12-sided die.

To know more about sets and sample space, visit:

https://brainly.com/question/30464166

#SPJ1

Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)

We can also complete the square (which is faster):

\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)

Answer:

Parallel lines are lines in the same plane

that never intersect and are always the same distance apart

Answer:

2:1 or 16:8

Step-by-step explanation:

Answer:

2:1

Apple: orange

Step-by-step explanation:

Divide the number of apples by the number of oranges

Both prices of stock A and B will be the same after 5.45 hrs.

Linear Equation:

The equation which is used to solve for an unknown value is known as Linear Equation here we use a variable to represent the unknown value or number. Here the variables can be x, y, z, or a, b, c, etc.

Here we have  

The price of Stock A at 9 AM was $13.55.

The price has been increasing at the rate of $0.07 each hour.

At noon the price of Stock B was $14.30.

It begins to decrease at the rate of $0.15 each hour.

Let after x hours the stock prices are will be the same

After x hours the prices of  both stocks can be calculated as given below

For stock A  

The rate of increase per hour = $0.07

For x hours increased price = 13.55 + 0.07x    

For stock B

The rate of increase per hour = $ 0.15

Stock B started at noon i.e at 12

(Which means Stock started late for 4 hrs  by Stock A)    

Then the rate of decrease for (x-4)hrs = 14.30 - 0.15(x-4)    

As we assumed the price after x hours is the same

=> 13.55 + 0.07x = 14.30 - 0.15(x-3)    

=> 0.07x = 14.30 - 13.55 - 0.15x + 0.45

=> 0.07x = - 0.15x + 1.2  

=> 0.22x = 1.2  

=> x = 1.2/0.22 =  5.45

Both prices of stock A and B will be the same after 5.45 hrs.  

Learn more about Linear Equations at

https://brainly.com/question/11897796

#SPJ1

-77 + (-46 )

- 77 - 46 (+ × - = - )

-123

Answer:

-123

Step-by-step explanation:

This is the answer because:

1) First, multiply the negative sign with the positive sign.

Negative x Positive = Negative

Equation: -77 - 46

2) Now, multiply the negative sign with the negative sign.

Negative x Negative =  Positive

Equation: 77 + 46 = 123

3) Finally, add the greater number's sign (-77) in front of the number.

-123

Hope this helps! :D

In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.

The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."

When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.

Read more on sequences here https://brainly.com/question/6561461

#SPJ1

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

Learn more about standard deviation here :

https://brainly.com/question/12402189

#SPJ9

The distribution of Michigan tuitions is option D. We do not have enough information to say whether the distribution is approximately normal

The standard deviation is a measure of how spread out a dataset is. A small standard deviation means that the data points are closely clustered around the mean, while a large standard deviation indicates that the data points are more widely dispersed.

Furthermore, the minimum and maximum values for tuition charges are quite far apart, with a range of

=> 30,823 - 1,873 = 28,950.

This indicates that there are some colleges and universities in Michigan that charge much higher tuition rates than others.

Based on these observations, it is difficult to say whether the distribution of Michigan tuitions is approximately normal. The fact that the minimum is far from the mean suggests that the data is skewed to the right, which is not characteristic of a normal distribution.

Therefore, the answer is D: we do not have enough information to say whether the distribution is approximately normal. However, we can say that the high standard deviation and wide range of values suggest that there is a significant amount of variability in tuition charges among different institutions in Michigan.

To know more about standard deviation here.

https://brainly.com/question/16555520

#SPJ4

Answer:

£3182.7

Step-by-step explanation:

£3000=100%

? =3%

3×3000/100

=£90

£(3000+90)=£3090(1st year)

£3090=100%

? =3%

3×3090/100=£3182.7

Answer:

The answer is A) 379.9

Step-by-step explanation:

3.14(11^2)

3.14*11^2

3.14*(11*11)

379.94 if rounded to the nearest tenth it would be 379.9

Answer:

• mean = 61

• mode = 50

• median = 57.5

Step-by-step explanation:

• The mean is calculated by adding all the values together, and dividing the result by the number of values.

∴ mean =  \(\frac{60 + 50 + 50 + 70 + 40 + 80 + 65 + 55 + 50 + 90}{10}\)

⇒ mean = \(\frac{610}{10}\)

⇒ mean = 61

• The mode of a set of values is the value that is the most common (has highest frequency) among them.

50 is the most common value.

∴ mode = 50

• The median is the middle-value of a set of ordered values.

∴ We have to first rearrange the set:

⇒  40, 50, 50, 50, 55, 60, 65, 70, 80, 90

Now we need to find the middlemost value:

Since we have 10 values, which is an even number, we have to use the formula:

median = \(\frac{(n/2)^{th} \space\ term \space\ + \space\ [(n/2) + 1]^{th} \space\ term }{2}\)

where n is the number of values.

∴ median =  \(\frac{(10/2)^{th} \space\ term \space\ + \space\ [(10/2) + 1]^{th} \space\ term }{2}\)

⇒ median =  \(\frac{5^{th} \space\ term \space\ + \space\ 6^{th} \space\ term }{2}\)

The 5th and 6th terms in our ordered series are 55 and 60 respectively.

∴ median = \(\frac{55 + 60}{2}\)

⇒ median = 57.5

Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

--------------------------------------------------

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

----------------------------------------------------

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

-------------------------------------------------

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

--------------------------------------------------

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Answer:

44°

13 inches

Step-by-step explanation:

__________

Answer:

3x² - 4x - 5

Step-by-step explanation:

Definitions:

Long Division Method of dividing polynomials:

Given:

Rearrange the dividend in descending order of the exponents:

6x³ - 17x² + 2x  + 15

Now use the method of long division to divide (6x³ - 17x² + 2x  + 15) by (2x - 3):

\(\large \begin{array}{r}3x^2-4x-5\phantom{)}\\2x-3{\overline{\smash{\big)}\,6x^3-17x^2+2x+15\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-9x^2)\phantom{-b)))))))).)}}\\-8x^2+2x+15\phantom{)}\\-~\phantom{()}\underline{(-8x^2+12x)\phantom{)))..}}\\-10x+15\phantom{)}\\-~\phantom{()}\underline{(-10x+15)\phantom{}}\\0\phantom{)}\\\end{array}\)

Therefore, the quotient is:

\(\boxed{\boxed{3x^2-4x-5}}\)

Given details in question are as follows :

Alonzo found three pieces of cable in his tool drawer.

Their lengths (in meters) are 16, 13.13, 9.7

The addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum.

The Sum of all the numbers in this question is 16+13.13+9.7

=38.83

Alonzo found three pieces of cable in his tool drawer, the total length of the three pieces is 38.83

Learn more about Addition: brainly.com/question/24247076

#SPJ1

The information that is in question is as follows:

Three cables were located by Alonzo in his tool chest.

16, 13.13, and 9.7 meters are their lengths.

What does a math addition mean?

By combining objects, we can count them as a single huge group by adding them. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

16+13.13+9.7 is the total of all the numbers in this question.

=38.83

Alonzo discovered three cables totaling 38.83 inches in length in his tool drawer.

Answer:

2 cans are cokes.

Step-by-step explanation:

16/1 (total cans) * 1/8 (the amount that are coke) = 16/18 = 2

Answer:

linear

Step-by-step explanation: