Factor the following polynomial completely.

Answer: R=8

Step-by-step explanation:

-7 is added to 1 making it R= 1+7 resulting in R=8

Answer:

[tex]\huge \boxed{R=8}[/tex]

Step-by-step explanation:

[tex]R-7=1[/tex]

Adding 7 to both sides of the equation.

[tex]R-7+7=1+7[/tex]

[tex]R=8[/tex]

always true

Step-by-step explanation:

Assuming that you mean by true that it has solutions

we have

[tex]3x^2-9x-2=0[/tex]

to know if it has real solutions we need to know if

[tex]b^2-4ac[/tex]

is greater, equal or less than zero

if it's greater it's always

if it's equal it's sometimes

if it's less it's never

so

b=-9

a=3

c=-2

[tex](-9)^2-4(3)(-2)\\\\=81+24\\\\=105[/tex]

so it's always

The equation  (3x² +2) = 9x + 4 is sometimes true.

An equation is an mathematical expression stating that left hand side and the right hand side are equal.

The equation (3x² +2) = 9x + 4 is only true for the roots of the formed equation

3x² + 2 = 9x + 4

3x² = 9x + 2

3x² - 9x -2 = 0

∴ x = (3 + [tex]\sqrt{105}[/tex])/2 OR (3 - [tex]\sqrt{105}[/tex])/2

Only for these values of x the equation 3x² + 2 = 9x + 4 are true except these two values it is never true.

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Answer:

-81

Step-by-step explanation:

[tex]\frac{x^2}{3}[/tex] is the same as [tex]\frac{1}{3}x^2[/tex]

Dividing by 3 is the same as multiplying by the fraction 1/3

Answer:

5(p + 6)(q - 4)

Step-by-step explanation:

Factors are a set of numbers, alphabets or both that when multiplied would give a certain expression.

The expression with three factors is:  5(p + 6)(q - 4)

So that;

5(p + 6)(q - 4) = (5p + 30)(q - 4)

Then,

(5p + 30)(q - 4) = 5pq - 20p + 30q - 120

Therefore, the factorization of 5pq - 20p + 30q - 120 gives the factors; 5(p + 6)(q - 4).

Answer:

5 (p+6) (q−4)

'

Answer:

Step-by-step explanation:

From the plot line you have (1x3) + (2x 1 1/4) + (3x 1 1/2) = 10

The total weight of all the cantaloupes that weigh no more than 2 pounds should be 10.

Since Josh weighed cantaloupes he picked from his garden.

So here the total weight should be like

[tex]= (1\times 3) + (2\times 1\ 1\div 4) + (3\times 1\ 1\div 2)[/tex]

= 10

hence, The total weight of all the cantaloupes that weigh no more than 2 pounds should be 10.

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Answer: A globe shows all the countries with landmass and water bodies but a map shows only a specific country with its size shape and features  .

Step-by-step explanation:

Answer:

1177.58 cm³

Step-by-step explanation:

The volume of a sphere is given by V = (4/3)πr³. In this case, if the width (diameter) of the cup is 16.51cm, then the radius is 8.255 cm. So the volume of the cup, if it were a sphere, would be:

V = (4/3) * 3.14 * (8.255)³ ≈ 2355.1557 cm³

But since this is a hemisphere (i.e., half a sphere), we cut that value in half to get the volume of the cup:

2355.1557 / 2 ≈ 1177.58 cm³

Answer:

Step-by-step explanation:

To solve first take logarithm to both sides

That's

But

So we have

[tex]x = log_{10}(1200) [/tex]

Write 1200 as a number with the factor 100

That's

1200 = 100 × 12

So we have

Using the rules of logarithms

That's

Rewrite the expression

That's

x = 3.079

So we have the final answer as

Hope this helps you

Answer:

f(4) is 1/2

f(x)= 4 when x is 8

Answer:

Step-by-step explanation:

A:  The distance is the sum of |-1.6| and 0.3:  |-1.6| + 0.3

B.  This distance is 1.6 + 0.3 = 0.9

Answer:

Quantity of milk = 60 x 2/3 litres = 40 litres.

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

Then, milk : water = 40 /20 + x

Now, 40 /20 + x = 1/2

20 + x = 80

x = 60.

Quantity of water to be added = 60 litres.

Answer:

The intensity of the earthquake in Chile was about 16 times the intensity of the earthquake in Haiti.

Step-by-step explanation:

Given:

magnitude of earthquake in Chile =  8.2

magnitude of earthquake in Haiti = 7.0

To find:

Compare the intensities of the two earthquakes

Solution:

The magnitude R of earthquake is measured by R = log I

R is basically the magnitude on Richter scale

I is the intensity of shock wave

For Chile:

given magnitude R of earthquake in Chile =  8.2

R = log I

8.2 = log I

We know that:

[tex]y = log a_{x}[/tex]  is equivalent to: [tex]x = a^{y}[/tex]  

[tex]R = log I[/tex]

8.2 = log I becomes:

[tex]I = 10^{8.2}[/tex]

So the intensity of the earthquake in Chile:

[tex]I_{Chile} = 10^{8.2}[/tex]

For Haiti:

R = log I

7.0 = log I

We know that:

[tex]y = log a_{x}[/tex]  is equivalent to: [tex]x = a^{y}[/tex]  

[tex]R = log I[/tex]

7.0 = log I becomes:

[tex]I = 10^{7.0}[/tex]

So the intensity of the earthquake in Haiti:

[tex]I_{Haiti} = 10^{7}[/tex]

Compare the two intensities :

[tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]

[tex]= \frac{10^{8.2} }{10^{7} }[/tex]

= [tex]10^{8.2-7.0}[/tex]

= [tex]10^{1.2}[/tex]

= 15.848932

Round to the nearest whole number:

16

Hence former earthquake was 16 times as intense as the latter earthquake.

Another way to compare intensities:

Find the ratio of the intensities i.e. [tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]

[tex]log I_{Chile}[/tex] - [tex]log I_{Haiti}[/tex] = 8.2 - 7.0

[tex]log(\frac{I_{Chile} }{I_{Haiti} } })[/tex] = 1.2

Convert this logarithmic equation to an exponential equation

[tex]log(\frac{I_{Chile} }{I_{Haiti} } })[/tex] = 1.2

[tex]10^{1.2}[/tex] = [tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]

Hence

[tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]  = 16

Answer:

The intensity of the 2014 earthquake was about 16 times the intensity of the 2010 earthquake

Step-by-step explanation:

Answer: B.Construct a circle of any arbitrary radius.

Step-by-step explanation:

had to complete the question first.

A.Connect every arc along the circle.

B.Construct a circle of any arbitrary radius.

C.Set the compass width to greater than half the diameter of the circle.

D. Set the compass width to the radius of the circle.

Explanation:

when constructing an inscribed square and an inscribed equilateral triangle, the most important step and which turns out to be same for both procedures is the constructio of of a circle of an arbitrary radius. Because it’s is within this circle both the triangle and square would be drawn. Just their method of construction are different.

Answer:

Solution : (15, - 11)

Step-by-step explanation:

We want to solve this problem using a matrix, so it would be wise to apply Gaussian elimination. Doing so we can start by writing out the matrix of the coefficients, and the solutions ( - 5 and - 2 ) --- ( 1 )

[tex]\begin{bmatrix}-4&-5&|&-5\\ -6&-8&|&-2\end{bmatrix}[/tex]

Now let's begin by canceling the leading coefficient in each row, reaching row echelon form, as we desire --- ( 2 )

Row Echelon Form :

[tex]\begin{pmatrix}1\:&\:\cdots \:&\:b\:\\ 0\:&\ddots \:&\:\vdots \\ 0\:&\:0\:&\:1\end{pmatrix}[/tex]

Step # 1 : Swap the first and second matrix rows,

[tex]\begin{pmatrix}-6&-8&-2\\ -4&-5&-5\end{pmatrix}[/tex]

Step # 2 : Cancel leading coefficient in row 2 through [tex]R_2\:\leftarrow \:R_2-\frac{2}{3}\cdot \:R_1[/tex],

[tex]\begin{pmatrix}-6&-8&-2\\ 0&\frac{1}{3}&-\frac{11}{3}\end{pmatrix}[/tex]

Now we can continue canceling the leading coefficient in each row, and finally reach the following matrix.

[tex]\begin{bmatrix}1&0&|&15\\ 0&1&|&-11\end{bmatrix}[/tex]

As you can see our solution is x = 15, y = - 11 or (15, - 11).

Answer:

Two expressions for the perimeter would be

22x+23 and 2x+3x+17x+7+16

Step-by-step explanation:

you want to add the variables of the same kind in this case

2x        

3x         7

17x       16

_________

22x  +     23

Answer:

w/2

Step-by-step explanation:

Calculating half of something is the same as dividing it by 2. In this case, the "something" is w so the answer is w/2.

Answer:

idk

Step-by-step explanation:

Answer:

Side 3 or side 4

Step-by-step explanation:

The ground has 6 sides

Each side is:

It is assumed that total distance is one cycle of 270 m.

Since no diagram attached, the start point X is the beginning of side 1.

Then the distance covered is:

As

the scouts reached the side 3 or side 4 of the ground depending on direction of movement (clockwise vs anti-clockwise)

Answer:

Below

Step-by-step explanation:

● y -(-3) = (1/4) (x-9)

Replace 1/4 by 0.25 to make it easier

● y + 3 = 0.25(x-9)

● y + 3 = 0.25x - 2.25

Add 3 to both sides

● y +3-3 = 0.25x -2.25-3

● y = 0.25x -5.25

To the coordinates of a point from this line replace x by a value.

The easiest one is 0.

● y = 0.25×0 -5.25

● y = 5.25

5.25 is 21/4

So the coordinates are (0, 21/4)

The coordinate of a point on the line whose equation in point-slope form is y − (−3) = 1/4 (x − 9) is (9, -3)

The equation of a line in point-slope form is expressed as;

[tex](y-y_0)=m(x-x_0)[/tex] where:

m is the slope

[tex](x_0, y_0)[/tex] is the point on the line.

Given the equation in the point-slope form expressed as

[tex]y - (-3) = 1/4 (x - 9)[/tex]

Comparing the general equation with the given equation:

[tex]y_0 = -3\\x_0 = 9[/tex]

Hence the coordinate of a point on the line whose equation in point-slope form is y − (−3) = 1/4 (x − 9) is (9, -3)

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Answer:

Step-by-step explanation:

[tex]8(x + 5) = \\ 8(x) + 8(5) \\ = 8x + 40[/tex]

[tex] - 2(3m + 9) \\ = - 2(3m) - 2(9) \\ = - 6m - 18[/tex]

Answer:

[See Below]

Step-by-step explanation:

If you replace the x with -1 and evaluate the function you get -5.

Answer:

3x³ - 14x² - 7x + d = (x + 1)(ax² + bx + c)

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

  (x + 1)(ax² + bx + c)  

= ax³ + bx² + cx + ax² + bx + c

= ax³ + (a + b)x² + (b + c)x + c

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

ax³ + (a + b)x² + (b + c)x + c = 3x³ - 14x² - 7x + d

=> a = 3

    a + b = -14

    b + c = -7

    c = d

=> a = 3, b = -17, c = 10, d = 10

Answer:

Idek

Step-by-step explanation:

Ya I just need points

Answer:

13.5

Step-by-step explanation:

Use fractions to help. 12/16 = x/18.

12/16 simplifies to 3/4, so now divide 18 by 4 and multiply by 3.

18 / 4 = 4.5

4.5 x 3 = 13.5

Complete question is;

A student scores 56 on a geography test and 267 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 22.

If the data for both tests are normally distributed, on which test did the student score better?

Answer:

The geography test is the one in which the student scored better.

Step-by-step explanation:

To solve this question, we will make use if the z-score formula to find the w test in which the student scored better. The z-score formula is;

z = (x - μ)/σ

Now, for geography, we are given;

Test score; x = 56

Mean; μ = 80

Standard deviation; σ = 20

Thus, the z-score here will be;

z = (56 - 80)/20

z = -1.2

Similarly, for Mathematics, we are given;

Test score; x = 267

Mean; μ = 300

Standard deviation; σ = 22

Thus, the z-score here will be;

z = (267 - 300)/22

z = -1.5

Since the z-score for geography is lesser than that of Mathematics, thus, we can conclude that the geography test is the one in which the student scored better.

Answer:

417 $

b h h h h h h h h h h h h

Answer:

The approximate error rate the manager should expect for a worker who receives 6 hours of training is 0.07 error rate

Step-by-step explanation:

The given relation between the number of hours of training a worker receives, x and the worker's error rate y can be presented follows;

y = 0.1 - 0.005·r

Therefore, the approximate error rate the manager should expect for a worker who receives 6 hours of training can be given as follows;

When x = 6 hours, we have

y  = 0.1 - 0.005 × 6 = 0.07

The approximate error rate the manager should expect for a worker who receives 6 hours of training is 0.07.

Which is an error rate o 7%

Answer:

f(x) is neither

Step-by-step explanation:

The given function is neither even nor odd. The correct option is B.

When the value of the function is negative after putting the value of the variable negative in the function then the function is odd and if the value of the function is positive after putting the negative value of the variable then the function is even.

Given that Eileen is trying to test if the function f(x) = x² + 2x + 5 is even, odd or neither. She produces the following work: f(– x) = (–x)² + 2(–x) + 5 = x² – 2x + 5.

The function will be solved as below:-

f(x)     = x² + 2x + 5

f(– x) = (–x)² + 2(–x) + 5

f(-x)   = x² – 2x + 5.

Here the resultant function is not giving any clear information the given function is neither even nor odd. The correct option is B.

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Answer:

Step-by-step explanation:Cuando un número se escribe en notación científica, el exponente te dice si el término es un número muy grande o muy pequeño. Un exponente positivo indica un número grande y un exponente negativo indica un número muy pequeño que está entre 0 y 1.

Answer:

Below

Step-by-step explanation:

● 1.3×10^6 - 6.8 × 10^5

● 13 × 10^5 - 6.8 × 10^5

● 10^5 (13 -6.8)

● 6.2 × 10^5