factorise 49 a^2 + 4b^2 +9c^2 -28ab + 12bc- 42 ac

A lock with 60 digits and a combination involving turning right to the first number, left to the second number, and right to the third number can have 212,400 possible combinations.

A lock with 60 digits and a combination involving turning right to the first number, left to the second number, and right to the third number can have 60 x 59 x 60 possible combinations.

Here's the explanation:

By multiplying these options together, you get the total number of possible combinations: 60 x 59 x 60 = 212,400.

Final answer:

The total number of possible combinations for a lock with a 60-digit combination, turning right, left, and right is 60 × 60 × 60, leading to 216,000 unique combinations.

Explanation:

To calculate the number of possible combinations for a lock with a 60-digit sequence where you turn right to the first number, left to the second number, and right to the third number, you need to apply the basic principle of counting. Each of the three steps in the combination can be any of the 60 digits, with the choice of one step not affecting the choices for the other steps. Therefore, each step has 60 options, and the total number of possible combinations is the product of these options.

The calculation for the total number of combinations is: 60 × 60 × 60, which simplifies to 60^3. When you calculate that, you get 216,000 possible combinations for the lock.

Answer:

4 muffins are of $2.90

1 muffin is of  2.90/4 =0.725

1 dozen(12 muffens) 0.725x12=

Step-by-step explanation:

Answer:

8.70

Step-by-step explanation:

3 * 4 = 12.

12 = 1 dozen

So you have to multiply 2.90 * 3

The answer is 8.70

=======================

That's one way to do the problem. Here's another.

4 muffins = $2.90

12 muffins = x                Cross multiply.

4x = 12*2.90

4x = 34.80                     Divide by 4

4x/4 = 34.80/4              Do the division

x = $8.70

Answer:

The point-slope equation for a line that goes through the point (4, 1/3) with a slope of 3/4 is:

Choice B: [tex]\displaystyle y - \frac{1}{3} = \frac{3}{4}(x - 4)[/tex].

Step-by-step explanation:

This question gives

Consider the point-slope form of the equation of a line in a cartesian plane:

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

where

For this line:

The point-slope equation of this line will be:

[tex]\displaystyle y - \frac{1}{3} = \frac{3}{4}(x - 4)[/tex].

Answer:

B.

Step-by-step explanation:

Got Correct On MyPath.

Answer:

1. x = -a/6

2. x = 3/a

x = -6/a

Step-by-step explanation:

1. 4 = (6/a)x+5

subtract 5 from both sides

-1 = (6/a)x

divide by 6/a on both sides

x = -a/6

To make that last part simpler, you could think of it as first multiplying by a and then dividing by 6.

2. 7+2ax = 13

subtract 7

2ax = 6

divide by 2

ax = 3

divide by a

x = 3/a

3. -ax-20 = -14

add 20

-ax = 6

divide by -a

x = 6/-a = -6/a

To solve for x in an equation linked with equilibrium concentration and solubility, identify known values, select the right conversion equations, utilize the ICE table method, and substitute the known values into the solubility product expression. Rearrange the equation to solve for x.

In this question, we are looking to solve equations linked with equilibrium concentration and solubility. First, we will identify known values from the problem and list them out. This includes figuring out the terms we need to substitute into the solubility product expression and identifying our unknown, x. Afterwards, we need to select the right conversion equations and substitute the known values.

The chemical reaction gives us an ICE (Initial, Change, Equilibrium) table, which is a simplified method used to solve equilibrium problems. Sometimes it might be necessary to consider momenta in the x and y directions to solve for the unknown. When we have the equilibrium concentrations, we substitute these terms into the solubility product expression and solve for x.

Always remember that the goal is to rearrange the equation so that x is on one side by itself, making it easier to solve for. This kind of problem requires a clear understanding of solubility, equilibrium, and algebraic conventions.

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We can solve this problem by using the known value (115) to solve for the angle parallel to the equation.

To find the solve for the angle to the exact right of 115, subtract 115 from 180. This works because 115 and the unknown angle form to make a straight line, which is 180 degrees.

180-115=65

Now, since it is parallel, we know that 5x+5=65 degrees.

Solve the equation.

Subtract 5 on both sides.

5x=60

Divide both sides by 5 to isolate x.

5x=13

The value of x is 13.

Hope this helps!

Answer:

the solution of linear equation 4b + 6 = 2 - 6 + 4 is b = -2

Step-by-step explanation:

We need to solve the linear equation

4b + 6 = 2 - 6 +4

Adding constants

4b + 6 = 0

Adding -6 on both sides

4b + 6 -6 = 0 -6

4b = -6

Dividing with 4 on both sides

4b/4 = -6/4

b = -2

So, the solution of linear equation 4b + 6 = 2 - 6 + 4 is b = -2

Answer:

0

Step-by-step explanation:

Answer:

Part 1) The x-component of the vertex is 2 and the y-component of the vertex is -18

Part 2) The discriminant is 144

Step-by-step explanation:

we have

[tex]f(x)=2x^{2}-8x-10[/tex]

step 1

Find the discriminant

The discriminant of a quadratic equation is equal to

[tex]D=b^{2}-4ac[/tex]

in this problem we have

[tex]f(x)=2x^{2}-8x-10[/tex]

so

[tex]a=2\\b=-8\\c=-10[/tex]

substitute

[tex]D=(-8)^{2}-4(2)(-10)[/tex]

[tex]D=64+80=144[/tex]

The discriminant is greater than zero, therefore the quadratic equation has two real solutions

step 2

Find the vertex

Convert the quadratic equation into vertex form

[tex]f(x)+10=2x^{2}-8x[/tex]

[tex]f(x)+10=2(x^{2}-4x)[/tex]

[tex]f(x)+10+8=2(x^{2}-4x+4)[/tex]

[tex]f(x)+18=2(x-2)^{2}[/tex]

[tex]f(x)=2(x-2)^{2}-18[/tex] -----> equation in vertex form

The vertex is the point (2,-18)

therefore

The x-component of the vertex is 2

The y-component of the vertex is -18

Answer:

Consider the quadratic function f(x) = 2x2 – 8x – 10.

The x-component of the vertex is

✔ 2

The y-component of the vertex is

✔ –18

The discriminant is b2 – 4ac = (–8)2 – (4)(2)(–10) =

✔ 144

Answer:

I have put my answer in the form (x,y,z)

One solution (3,2,4)

Another solution (-5,-4,-6)

Step-by-step explanation:

I'm going to try to do this by a bunch of substitution.

I'm going to solve first equation for x, second for y, and third for z.

Commutative property x+xy+y=11

Distributive property x(1+y)+y=11

Subtraction property  x(1+y)=11-y

Division property x=(11-y)/(1+y)

I'm going to do the other 2 equations in a similar way:

So the second equation solving for y:    y=(14-z)/(1+z)

The third equation solving for z:  z=(19-x)/(1+x)

I'm going to plug my new first equation into my third equation giving me:

z=(19-[(11-y)/(1+y)])/(1+[(11-y)/(1+y)]

Now I'm going to clean this up by multiplying by compound fraction by (1+y)/(1+y).

z=(19(1+y)-(11-y)]/[1(1+y)+(11-y)]

z=[19+19y-11+y]/[1+y+11-y]

z=[8+20y]/[12]

Simplify

z=(2+5y)/3

Now I'm going to sub this into my non-rewrite of equation 2:

y+(2+5y)/3+y(2+5y)/3=14

Multiply both sides by 3 to clear fractions

3y+(2+5y)+y(2+5y)=42

3y+2+5y+2y+5y^2=42

5y^2+10y+2=42

Subtract 42 on both sides

5y^2+10y-40=0

Divide both sides by 5

y^2+2y-8=0

Factor

(y+4)(y-2)=0

So y=-4 or y=2

If y=-4  then x=(11-(-4))/(1+(-4))=15/-3=-5 and z=(2+5*-4)/3=-18/3=-6

So one solution is (-5,-4,-6)

If y=2 then x=(11-2)/(1+2)=9/3=3 and z=(2+5*2)/3=12/3=4

So another solution is (3,2,4)

Answer:

C. [tex]x=0,\ y=1,\ z=0[/tex]

Step-by-step explanation:

Consider the system of three equations:

[tex]\left\{\begin{array}{l}4x+3y+6z=3\\5x+5y+6z=5\\6x+3y+6z=3\end{array}\right.[/tex]

Multiply the first equation by 5, the second equation by 4 and subtract them:

[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\6x+3y+6z=3\end{array}\right.[/tex]

Multiply the first equation by 3, the second equation by 2 and subtract them:

[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\3y+6z=3\end{array}\right.[/tex]

Multiply the second equation by 3, the third equation by 5 and add the second and the third equations:

[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\48z=0\end{array}\right.[/tex]

Fro mthe third equation

[tex]z=0[/tex]

Substitute it into the second equation:

[tex]-5y+6\cdot 0=-5\\ \\-5y=-5\\ \\y=1[/tex]

Substitute y=1 and z=0 into the first equation:

[tex]4x+3\cdot 1+6\cdot 0=3\\ \\4x+3=3\\ \\4x=0\\ \\x=0[/tex]

The solution is

[tex]x=0,\ y=1,\ z=0[/tex]

Answer:

ageed its C

Step-by-step explanation:

Answer:

The figures are not similar

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Verify

BC/JI=AB/FJ=ED/GH

substitute the given values

5.1/3.6=2.8/2.1=3.7/2.7

1.417=1.333=1.370 ------> is not true

therefore

The figures are not similar

Answer:

Option C is correct.

Step-by-step explanation:

We need to find the greatest common factor of the polynomial

10x^5+15x^4-25x^3

The greatest common factor is the number that is divisible by all 3 terms of the polynomial.

so, the common factor is 5x^3 for above polynomial

Taking out the common factor

5x^3(2x^2+3x-5)

Now the term in the bracket has no other common factor

So, the greatest common factor of 10x^5+15x^4-25x^3 is 5x^3

So, Option C is correct.

Answer:

Third option.

Step-by-step explanation:

The greatest common factor (GCF) for a polynomial is defined as the largest monomial that divides each term.

Given the polynomial [tex]10x^5+15x^4-25x^3[/tex], the GCF of the coefficients can be found by descompose each one of them into their prime factors:

[tex]10=2*5\\15=2*5\\25=5*5[/tex]

You can observe that the GCF of the coefficients is:

[tex]GFC_{(coefficients)}=5[/tex]

Now you need to find the GCF of the variables. You can notice that each term has at least one x³, then:

 [tex]GFC_{(variables)}=x^3[/tex]

Threfore, the GCF of the polynomial is:

[tex]GCF=5x^3[/tex]

Answer:

85

Step-by-step explanation:

I assume by 2x3 you mean 2x^3 and 3y2 means 3y^2. If so then just plug in the values:

2x^3 + 3y^2 - 17 = ?

2(3)^3 + 3(4)^2 - 17 = ?

2(27) + 3(16) - 7 = ?

54 + 48 - 17

102 - 17 = ?

85 = ?

Answer:

The decimal point move to the left

Step-by-step explanation:

Let

x ----> a number

we know that

[tex]0.01=\frac{1}{100}[/tex]

When you multiply a number by 0.01 is equal to divide the number by 100

so

[tex]x*(0.01)=\frac{x}{100}[/tex]

therefore

The decimal point move to the left

The figure that is shaded 6/8 is the square.

If you split the square on more time along like a box pizza, you will get 8 slices and 6 of them shaded.

Answer:

The volume of the sphere is [tex]V=18\pi\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]V=27\pi\ ft^{3}[/tex]

substitute

[tex]27\pi=\pi r^{2}h[/tex]

simplify

[tex]27=r^{2}h[/tex]

Remember that

A sphere and a cylinder have the same radius and height

so

The height of cylinder is equal to the diameter of sphere

h=2r

substitute

[tex]27=r^{2}(2r)[/tex]

[tex]13.5=r^{3}[/tex] -----> equation A

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

substitute equation A in the formula of the volume of sphere

[tex]V=\frac{4}{3}\pi (13.5)[/tex]

[tex]V=18\pi\ ft^{3}[/tex]

Answer:

It's (A.) guys

Step-by-step explanation:

[tex]y=2x\\y=x^2-15\\\\x^2-15=2x\\x^2-2x-15=0\\x^2-5x+3x-15=0\\x(x-5)+3(x-5)=0\\(x+3)(x-5)=0\\x=-3 \vee x=5\\\\y=2\cdot(-3) \vee y=2\cdot5\\y=-6 \vee y=10\\\\(x,y)\in\{(-3,-6),(5,10)\}[/tex]

Answer:

A,D,E

Step-by-step explanation:

If it just lists out the numbers then it is discrete.  So the following are not discrete since it isn't just a list:  B and C.

The following are lists:  A,D,E

Answer:

5.69034 × 1011

Step-by-step explanation:

Decimal  

1234000000

Scientific Notation  

1.234 x 10^9

×10^  

9

1st Number  

1.234

×10^  

9

Operation  

2nd Number  

5.678

×10^  

11

Answer: $343.96

Step-by-step explanation:

x-0.75x=85.99

0.25x=85.99

Answer:

343.96

Step-by-step explanation:

The discount it 75%.  That means we pay 25%

25% of the original price is 85.99

Let x be the original price

x*25% = 85.99

.25x = 85.99

Divide each side by .25

.25x/.25 = 85.99/.25

x =343.96

The original price is 343.96

Answer:

Expressions are not equivalent

Step-by-step explanation:

Given expressions are:

[tex]4(3w+4)\ and\ 16w+12[/tex]

Putting w=1 in both expressions

[tex]4(3w+4)\\=4[3(1)+4]\\=4(3+4)\\=4(7)\\=28\\\\16w+12\\=16(1)+12\\=16+12\\=28[/tex]

Both expression have value 28 on w=1

Putting w=3 in both expressions

[tex]4(3w+4)\\=4[3(3)+4]\\=4(9+4)\\=4(13)\\=52\\\\16w+12\\=16(3)+12\\=48+12\\=60[/tex]

Both expression have different values at w=3

Hence, in order for the expressions to be equivalent they both should produce same value on w=3 too.

So, it can be concluded that both expressions are not equivalent ..

Answer:They are both not equivalent

Step-by-step explanation:

You’re welcome

Answer:

Week: $173.25

Month: $693

Year: $8,316

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

First, there is no x in your equation. I think you meant y = mx + b.

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

Answer:

case 1) [tex]2.144*10^{12}[/tex]

case 2) [tex]2.144*10^{8}[/tex]

Step-by-step explanation:

case 1) If we have

[tex]6.7*10^{6}[/tex] and [tex]3.2*10^{5}[/tex]

step 1

Calculate the product of the coefficients and powers separately

[tex]6.7*3.2=21.44[/tex]

[tex]10^{6}*10^{5}[/tex] -----> Apply the product of powers rule to add the exponents

[tex]10^{6}*10^{5}=10^{6+5}=10^{11}[/tex]

step 2

we have

[tex]21.44*10^{11}[/tex]

The product is not in scientific notation because the coefficient is greater than 10

step 3

Change the coefficient by moving the decimal one place to the left and increasing the exponent by one

[tex]2.144*10^{12}[/tex]

case 2) If we have

[tex]6.7*10^{6}[/tex] and [tex]3.2*10^{1}[/tex]

step 1

Calculate the product of the coefficients and powers separately

[tex]6.7*3.2=21.44[/tex]

[tex]10^{6}*10^{1}[/tex] -----> Apply the product of powers rule to add the exponents

[tex]10^{6}*10^{1}=10^{6+1}=10^{7}[/tex]

step 2

we have

[tex]21.44*10^{7}[/tex]

The product is not in scientific notation because the coefficient is greater than 10

step 3

Change the coefficient by moving the decimal one place to the left and increasing the exponent by one

[tex]2.144*10^{8}[/tex]

Answer:

Calculate the product of the coefficients and powers separately. Apply the product of powers rule to add the exponents. The product is not in scientific notation because the coefficient is greater than 10. Change the coefficient by moving the decimal one place to the left and increasing the exponent by one.

Step-by-step explanation:

(sample response from edgenuity)

Answer:

x = [tex]\frac{1}{a-b}[/tex]

Step-by-step explanation:

Given

ax = bx + 1

Collect the terms in x on the left side by subtracting bx from both sides

ax - bx = 1 ← factor out x from each term on the left side

x(a - b) = 1 ← divide both sides by (a - b)

x = [tex]\frac{1}{a-b}[/tex]

Answer:

=√18

Step-by-step explanation:

The absolute value of a complex number is its distance from zero on graph. The formula for absolute value of a complex number is:

|a+bi|= √(a^2+b^2 )

where a is the real part of the complex number and b is the imaginary part of the complex number.

So for the given number,

a= -4

b=-√2

Putting in the formula:

|-4-√2 i|= √((-4)^2+(-√2)^2 )

= √(16+2)

=√18  ..

ANSWER

[tex]3 \sqrt{2} \: units[/tex]

EXPLANATION

The absolute value of the complex number

[tex] |a +b i| = \sqrt{ {a}^{2} + {b}^{2} } [/tex]

This is also known as the modulus of the complex number.

This implies that:

[tex]| - 4 - \sqrt{2} i| = \sqrt{ {( - 4)}^{2} + {( - \sqrt{2} )}^{2} } [/tex]

[tex]| - 4 - \sqrt{2} i| = \sqrt{ 16 +2 } [/tex]

We simplify further to get;

[tex]| - 4 - \sqrt{2} i| = \sqrt{ 18 } = 3 \sqrt{2} \: units[/tex]

Answer:

Third option: [tex]35,669 ft^3[/tex]

Step-by-step explanation:

You need to use the formula for calculate the volume of a cylinder:

[tex]V_c=\pi r^2h[/tex]

Where r is the radius (In this case is 8 feet) and h is the height (In this case is 172 feet).

The formula for calculate the volume of a half sphere is:

[tex]V_s= \frac{2}{3} \pi  r^3[/tex]

Where r is the radius (In this case is 8 feet)

You need to add the volume of the cylinder and the volume of the half-sphere. Then the volume of grain that could completely fill this silo, rounded to the nearest whole number is (Remeber to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex]):

[tex]V=(\frac{22}{7}) (8ft)^2(172ft)+ (\frac{2}{3})(\frac{22}{7})(8ft)^3=35,669 ft^3[/tex]

Answer:

The correct answer is third option 35,669 feet³

Step-by-step explanation:

It is given that, Grain silo formed by cylinder with radius 8 feet and height 172 feet and a half sphere on the top

We have to find the volume of cylinder + volume of semi sphere

To find the volume of cylinder

Here r = 8 feet and f cylinder = πr²h

 = (22/7) * 8² * 172

 = 34596.57 ≈ 34597 feet³

To find the volume of hemisphere

here r = 8 feet

Volume of hemisphere = (2/3)πr³

 = (2/3) * (22/7) * 8³

 = 1072.76 ≈ 1073 feet³

To find the total volume

Total volume = volume of cylinder + volume of hemisphere

 = 34597 + 1073

 = 35,669 feet³

The correct answer is third option 35,669 feet³

[tex]\dfrac{_nP_3}{_nC_2}=6\\\\\dfrac{\dfrac{n!}{(n-3)!}}{\dfrac{n!}{2!(n-2)!}}=6\\\\\dfrac{n!}{(n-3)!}\cdot \dfrac{2(n-2)!}{n!}=6\\\\2(n-2)=6\\\\2n-4=6\\\\2n=10\\\\n=5[/tex]

The value of n is 5

The formula to calculate permulation and combination are:

[tex]_nP_r = \frac{n!}{(n-r)!}\\\\\\_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Putting in values we get:

[tex]_nP_3 = \frac{n!}{(n-3)!}\\\\\\_nC_2 = \frac{n!}{2!(n-2)!}[/tex]

Now we know that

[tex]\frac{_nP_3}{_nC_2} = 6[/tex]

So, putting in values we get:

[tex]\frac{\frac{n!}{(n-3)!}}{\frac{n!}{2!(n-2)!}} =6\\\\ \frac{n!}{(n-3)!} \times \frac{(n-2)! \times 2!}{ n!} = 6\\\\ \frac{1}{(n-3)!} \times (n-2)! \times 2! = 6\\\\ 2(n-2) = 6\\\\ n = 5[/tex]

Thus the value of n is 5.

Answer:

D

Step-by-step explanation:

For the segment addition postulate, two segments added together have to equal the third segment. In other words, if we added them together, the sum should be the first letter of the first line and the second letter of the second line.

BC + CD = BD

The value of the given expression [tex]\log_{7} e[/tex] will be 0.51, i.e. option C.

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

We have,

 [tex]\log_{7} e[/tex]

So,

Using the log rule,

On solving we get,

[tex]\log_{7} e =0.51[/tex]

So,

This the value of the given expression.

Hence, we can say that the value of the given expression [tex]\log_{7} e[/tex] will be 0.51, i.e. option C.

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Final answer:

The given expression Log₇^eA can be simplified and evaluated to approximately 0.43 when rounded to two decimal places.

Explanation:

Logarithms:

The expression Log₇^eA can be rewritten as Log₇(e). Applying the change of base formula to convert it to a common logarithm form, Log₇(e) = ln(e) / ln(7). Since ln(e) = 1, the result is approximately 0.43, rounded to two decimal places.